decimal 2.1.0

/* ------------------------------------------------------------------ */
/* Decimal Number arithmetic module                                   */
/* ------------------------------------------------------------------ */
/* Copyright (c) IBM Corporation, 2000, 2009.  All rights reserved.   */
/*                                                                    */
/* This software is made available under the terms of the             */
/* ICU License -- ICU 1.8.1 and later.                                */
/*                                                                    */
/* The description and User's Guide ("The decNumber C Library") for   */
/* this software is called decNumber.pdf.  This document is           */
/* available, together with arithmetic and format specifications,     */
/* testcases, and Web links, on the General Decimal Arithmetic page.  */
/*                                                                    */
/* Please send comments, suggestions, and corrections to the author:  */
/*   mfc@uk.ibm.com                                                   */
/*   Mike Cowlishaw, IBM Fellow                                       */
/*   IBM UK, PO Box 31, Birmingham Road, Warwick CV34 5JL, UK         */
/* ------------------------------------------------------------------ */
/* This module comprises the routines for arbitrary-precision General */
/* Decimal Arithmetic as defined in the specification which may be    */
/* found on the General Decimal Arithmetic pages.  It implements both */
/* the full ('extended') arithmetic and the simpler ('subset')        */
/* arithmetic.                                                        */
/*                                                                    */
/* Usage notes:                                                       */
/*                                                                    */
/* 1. This code is ANSI C89 except:                                   */
/*                                                                    */
/*    a) C99 line comments (double forward slash) are used.  (Most C  */
/*       compilers accept these.  If yours does not, a simple script  */
/*       can be used to convert them to ANSI C comments.)             */
/*                                                                    */
/*    b) Types from C99 stdint.h are used.  If you do not have this   */
/*       header file, see the User's Guide section of the decNumber   */
/*       documentation; this lists the necessary definitions.         */
/*                                                                    */
/*    c) If DECDPUN>4 or DECUSE64=1, the C99 64-bit int64_t and       */
/*       uint64_t types may be used.  To avoid these, set DECUSE64=0  */
/*       and DECDPUN<=4 (see documentation).                          */
/*                                                                    */
/*    The code also conforms to C99 restrictions; in particular,      */
/*    strict aliasing rules are observed.                             */
/*                                                                    */
/* 2. The decNumber format which this library uses is optimized for   */
/*    efficient processing of relatively short numbers; in particular */
/*    it allows the use of fixed sized structures and minimizes copy  */
/*    and move operations.  It does, however, support arbitrary       */
/*    precision (up to 999,999,999 digits) and arbitrary exponent     */
/*    range (Emax in the range 0 through 999,999,999 and Emin in the  */
/*    range -999,999,999 through 0).  Mathematical functions (for     */
/*    example decNumberExp) as identified below are restricted more   */
/*    tightly: digits, emax, and -emin in the context must be <=      */
/*    DEC_MAX_MATH (999999), and their operand(s) must be within      */
/*    these bounds.                                                   */
/*                                                                    */
/* 3. Logical functions are further restricted; their operands must   */
/*    be finite, positive, have an exponent of zero, and all digits   */
/*    must be either 0 or 1.  The result will only contain digits     */
/*    which are 0 or 1 (and will have exponent=0 and a sign of 0).    */
/*                                                                    */
/* 4. Operands to operator functions are never modified unless they   */
/*    are also specified to be the result number (which is always     */
/*    permitted).  Other than that case, operands must not overlap.   */
/*                                                                    */
/* 5. Error handling: the type of the error is ORed into the status   */
/*    flags in the current context (decContext structure).  The       */
/*    SIGFPE signal is then raised if the corresponding trap-enabler  */
/*    flag in the decContext is set (is 1).                           */
/*                                                                    */
/*    It is the responsibility of the caller to clear the status      */
/*    flags as required.                                              */
/*                                                                    */
/*    The result of any routine which returns a number will always    */
/*    be a valid number (which may be a special value, such as an     */
/*    Infinity or NaN).                                               */
/*                                                                    */
/* 6. The decNumber format is not an exchangeable concrete            */
/*    representation as it comprises fields which may be machine-     */
/*    dependent (packed or unpacked, or special length, for example). */
/*    Canonical conversions to and from strings are provided; other   */
/*    conversions are available in separate modules.                  */
/*                                                                    */
/* 7. Normally, input operands are assumed to be valid.  Set DECCHECK */
/*    to 1 for extended operand checking (including NULL operands).   */
/*    Results are undefined if a badly-formed structure (or a NULL    */
/*    pointer to a structure) is provided, though with DECCHECK       */
/*    enabled the operator routines are protected against exceptions. */
/*    (Except if the result pointer is NULL, which is unrecoverable.) */
/*                                                                    */
/*    However, the routines will never cause exceptions if they are   */
/*    given well-formed operands, even if the value of the operands   */
/*    is inappropriate for the operation and DECCHECK is not set.     */
/*    (Except for SIGFPE, as and where documented.)                   */
/*                                                                    */
/* 8. Subset arithmetic is available only if DECSUBSET is set to 1.   */
/* ------------------------------------------------------------------ */
/* Implementation notes for maintenance of this module:               */
/*                                                                    */
/* 1. Storage leak protection:  Routines which use malloc are not     */
/*    permitted to use return for fastpath or error exits (i.e.,      */
/*    they follow strict structured programming conventions).         */
/*    Instead they have a do{}while(0); construct surrounding the     */
/*    code which is protected -- break may be used to exit this.      */
/*    Other routines can safely use the return statement inline.      */
/*                                                                    */
/*    Storage leak accounting can be enabled using DECALLOC.          */
/*                                                                    */
/* 2. All loops use the for(;;) construct.  Any do construct does     */
/*    not loop; it is for allocation protection as just described.    */
/*                                                                    */
/* 3. Setting status in the context must always be the very last      */
/*    action in a routine, as non-0 status may raise a trap and hence */
/*    the call to set status may not return (if the handler uses long */
/*    jump).  Therefore all cleanup must be done first.  In general,  */
/*    to achieve this status is accumulated and is only applied just  */
/*    before return by calling decContextSetStatus (via decStatus).   */
/*                                                                    */
/*    Routines which allocate storage cannot, in general, use the     */
/*    'top level' routines which could cause a non-returning          */
/*    transfer of control.  The decXxxxOp routines are safe (do not   */
/*    call decStatus even if traps are set in the context) and should */
/*    be used instead (they are also a little faster).                */
/*                                                                    */
/* 4. Exponent checking is minimized by allowing the exponent to      */
/*    grow outside its limits during calculations, provided that      */
/*    the decFinalize function is called later.  Multiplication and   */
/*    division, and intermediate calculations in exponentiation,      */
/*    require more careful checks because of the risk of 31-bit       */
/*    overflow (the most negative valid exponent is -1999999997, for  */
/*    a 999999999-digit number with adjusted exponent of -999999999). */
/*                                                                    */
/* 5. Rounding is deferred until finalization of results, with any    */
/*    'off to the right' data being represented as a single digit     */
/*    residue (in the range -1 through 9).  This avoids any double-   */
/*    rounding when more than one shortening takes place (for         */
/*    example, when a result is subnormal).                           */
/*                                                                    */
/* 6. The digits count is allowed to rise to a multiple of DECDPUN    */
/*    during many operations, so whole Units are handled and exact    */
/*    accounting of digits is not needed.  The correct digits value   */
/*    is found by decGetDigits, which accounts for leading zeros.     */
/*    This must be called before any rounding if the number of digits */
/*    is not known exactly.                                           */
/*                                                                    */
/* 7. The multiply-by-reciprocal 'trick' is used for partitioning     */
/*    numbers up to four digits, using appropriate constants.  This   */
/*    is not useful for longer numbers because overflow of 32 bits    */
/*    would lead to 4 multiplies, which is almost as expensive as     */
/*    a divide (unless a floating-point or 64-bit multiply is         */
/*    assumed to be available).                                       */
/*                                                                    */
/* 8. Unusual abbreviations that may be used in the commentary:       */
/*      lhs -- left hand side (operand, of an operation)              */
/*      lsd -- least significant digit (of coefficient)               */
/*      lsu -- least significant Unit (of coefficient)                */
/*      msd -- most significant digit (of coefficient)                */
/*      msi -- most significant item (in an array)                    */
/*      msu -- most significant Unit (of coefficient)                 */
/*      rhs -- right hand side (operand, of an operation)             */
/*      +ve -- positive                                               */
/*      -ve -- negative                                               */
/*      **  -- raise to the power                                     */
/* ------------------------------------------------------------------ */

#include <stdlib.h>                // for malloc, free, etc.

#include <stdio.h>                 // for printf [if needed]

#include <string.h>                // for strcpy

#include <ctype.h>                 // for lower

#include "decNumber.h"             // base number library

#include "decNumberLocal.h"        // decNumber local types, etc.


/* Constants */
// Public lookup table used by the D2U macro
const uByte d2utable[DECMAXD2U+1]=D2UTABLE;

#define DECVERB     1              // set to 1 for verbose DECCHECK

#define powers      DECPOWERS      // old internal name


// Local constants
#define DIVIDE      0x80           // Divide operators

#define REMAINDER   0x40           // ..

#define DIVIDEINT   0x20           // ..

#define REMNEAR     0x10           // ..

#define COMPARE     0x01           // Compare operators

#define COMPMAX     0x02           // ..

#define COMPMIN     0x03           // ..

#define COMPTOTAL   0x04           // ..

#define COMPNAN     0x05           // .. [NaN processing]

#define COMPSIG     0x06           // .. [signaling COMPARE]

#define COMPMAXMAG  0x07           // ..

#define COMPMINMAG  0x08           // ..


#define DEC_sNaN     0x40000000    // local status: sNaN signal

#define BADINT  (Int)0x80000000    // most-negative Int; error indicator

// Next two indicate an integer >= 10**6, and its parity (bottom bit)
#define BIGEVEN (Int)0x80000002

#define BIGODD  (Int)0x80000003


static Unit uarrone[1]={1};   // Unit array of 1, used for incrementing

/* Granularity-dependent code */
#if DECDPUN<=4
  #define eInt  Int           // extended integer

  #define ueInt uInt          // unsigned extended integer

  // Constant multipliers for divide-by-power-of five using reciprocal
  // multiply, after removing powers of 2 by shifting, and final shift
  // of 17 [we only need up to **4]
  static const uInt multies[]={131073, 26215, 5243, 1049, 210};
  // QUOT10 -- macro to return the quotient of unit u divided by 10**n
  #define QUOT10(u, n) ((((uInt)(u)>>(n))*multies[n])>>17)

#else
  // For DECDPUN>4 non-ANSI-89 64-bit types are needed.
  #if !DECUSE64
    #error decNumber.c: DECUSE64 must be 1 when DECDPUN>4
  #endif
  #define eInt  Long          // extended integer

  #define ueInt uLong         // unsigned extended integer

#endif

/* Local routines */
static decNumber * decAddOp(decNumber *, const decNumber *, const decNumber *,
                              decContext *, uByte, uInt *);
static Flag        decBiStr(const char *, const char *, const char *);
static uInt        decCheckMath(const decNumber *, decContext *, uInt *);
static void        decApplyRound(decNumber *, decContext *, Int, uInt *);
static Int         decCompare(const decNumber *lhs, const decNumber *rhs, Flag);
static decNumber * decCompareOp(decNumber *, const decNumber *,
                              const decNumber *, decContext *,
                              Flag, uInt *);
static void        decCopyFit(decNumber *, const decNumber *, decContext *,
                              Int *, uInt *);
static decNumber * decDecap(decNumber *, Int);
static decNumber * decDivideOp(decNumber *, const decNumber *,
                              const decNumber *, decContext *, Flag, uInt *);
static decNumber * decExpOp(decNumber *, const decNumber *,
                              decContext *, uInt *);
static void        decFinalize(decNumber *, decContext *, Int *, uInt *);
static Int         decGetDigits(Unit *, Int);
static Int         decGetInt(const decNumber *);
static decNumber * decLnOp(decNumber *, const decNumber *,
                              decContext *, uInt *);
static decNumber * decMultiplyOp(decNumber *, const decNumber *,
                              const decNumber *, decContext *,
                              uInt *);
static decNumber * decNaNs(decNumber *, const decNumber *,
                              const decNumber *, decContext *, uInt *);
static decNumber * decQuantizeOp(decNumber *, const decNumber *,
                              const decNumber *, decContext *, Flag,
                              uInt *);
static void        decReverse(Unit *, Unit *);
static void        decSetCoeff(decNumber *, decContext *, const Unit *,
                              Int, Int *, uInt *);
static void        decSetMaxValue(decNumber *, decContext *);
static void        decSetOverflow(decNumber *, decContext *, uInt *);
static void        decSetSubnormal(decNumber *, decContext *, Int *, uInt *);
static Int         decShiftToLeast(Unit *, Int, Int);
static Int         decShiftToMost(Unit *, Int, Int);
static void        decStatus(decNumber *, uInt, decContext *);
static void        decToString(const decNumber *, char[], Flag);
static decNumber * decTrim(decNumber *, decContext *, Flag, Flag, Int *);
static Int         decUnitAddSub(const Unit *, Int, const Unit *, Int, Int,
                              Unit *, Int);
static Int         decUnitCompare(const Unit *, Int, const Unit *, Int, Int);

#if !DECSUBSET
/* decFinish == decFinalize when no subset arithmetic needed */
#define decFinish(a,b,c,d) decFinalize(a,b,c,d)

#else
static void        decFinish(decNumber *, decContext *, Int *, uInt *);
static decNumber * decRoundOperand(const decNumber *, decContext *, uInt *);
#endif

/* Local macros */
// masked special-values bits
#define SPECIALARG  (rhs->bits & DECSPECIAL)

#define SPECIALARGS ((lhs->bits | rhs->bits) & DECSPECIAL)


/* Diagnostic macros, etc. */
#if DECALLOC
// Handle malloc/free accounting.  If enabled, our accountable routines
// are used; otherwise the code just goes straight to the system malloc
// and free routines.
#define malloc(a) decMalloc(a)

#define free(a) decFree(a)

#define DECFENCE 0x5a              // corruption detector

// 'Our' malloc and free:
static void *decMalloc(size_t);
static void  decFree(void *);
uInt decAllocBytes=0;              // count of bytes allocated
// Note that DECALLOC code only checks for storage buffer overflow.
// To check for memory leaks, the decAllocBytes variable must be
// checked to be 0 at appropriate times (e.g., after the test
// harness completes a set of tests).  This checking may be unreliable
// if the testing is done in a multi-thread environment.
#endif

#if DECCHECK
// Optional checking routines.  Enabling these means that decNumber
// and decContext operands to operator routines are checked for
// correctness.  This roughly doubles the execution time of the
// fastest routines (and adds 600+ bytes), so should not normally be
// used in 'production'.
// decCheckInexact is used to check that inexact results have a full
// complement of digits (where appropriate -- this is not the case
// for Quantize, for example)
#define DECUNRESU ((decNumber *)(void *)0xffffffff)

#define DECUNUSED ((const decNumber *)(void *)0xffffffff)

#define DECUNCONT ((decContext *)(void *)(0xffffffff))

static Flag decCheckOperands(decNumber *, const decNumber *,
                             const decNumber *, decContext *);
static Flag decCheckNumber(const decNumber *);
static void decCheckInexact(const decNumber *, decContext *);
#endif

#if DECTRACE || DECCHECK
// Optional trace/debugging routines (may or may not be used)
void decNumberShow(const decNumber *);  // displays the components of a number
static void decDumpAr(char, const Unit *, Int);
#endif

/* ================================================================== */
/* Conversions                                                        */
/* ================================================================== */

/* ------------------------------------------------------------------ */
/* from-int32 -- conversion from Int or uInt                          */
/*                                                                    */
/*  dn is the decNumber to receive the integer                        */
/*  in or uin is the integer to be converted                          */
/*  returns dn                                                        */
/*                                                                    */
/* No error is possible.                                              */
/* ------------------------------------------------------------------ */
decNumber * decNumberFromInt32(decNumber *dn, Int in) {
  uInt unsig;
  if (in>=0) unsig=in;
   else {                               // negative (possibly BADINT)
    if (in==BADINT) unsig=(uInt)1073741824*2; // special case
     else unsig=-in;                    // invert
    }
  // in is now positive
  decNumberFromUInt32(dn, unsig);
  if (in<0) dn->bits=DECNEG;            // sign needed
  return dn;
  } // decNumberFromInt32

decNumber * decNumberFromUInt32(decNumber *dn, uInt uin) {
  Unit *up;                             // work pointer
  decNumberZero(dn);                    // clean
  if (uin==0) return dn;                // [or decGetDigits bad call]
  for (up=dn->lsu; uin>0; up++) {
    *up=(Unit)(uin%(DECDPUNMAX+1));
    uin=uin/(DECDPUNMAX+1);
    }
  dn->digits=decGetDigits(dn->lsu, up-dn->lsu);
  return dn;
  } // decNumberFromUInt32

/* ------------------------------------------------------------------ */
/* to-int32 -- conversion to Int or uInt                              */
/*                                                                    */
/*  dn is the decNumber to convert                                    */
/*  set is the context for reporting errors                           */
/*  returns the converted decNumber, or 0 if Invalid is set           */
/*                                                                    */
/* Invalid is set if the decNumber does not have exponent==0 or if    */
/* it is a NaN, Infinite, or out-of-range.                            */
/* ------------------------------------------------------------------ */
Int decNumberToInt32(const decNumber *dn, decContext *set) {
  #if DECCHECK
  if (decCheckOperands(DECUNRESU, DECUNUSED, dn, set)) return 0;
  #endif

  // special or too many digits, or bad exponent
  if (dn->bits&DECSPECIAL || dn->digits>10 || dn->exponent!=0) ; // bad
   else { // is a finite integer with 10 or fewer digits
    Int d;                         // work
    const Unit *up;                // ..
    uInt hi=0, lo;                 // ..
    up=dn->lsu;                    // -> lsu
    lo=*up;                        // get 1 to 9 digits
    #if DECDPUN>1                  // split to higher

      hi=lo/10;
      lo=lo%10;
    #endif
    up++;
    // collect remaining Units, if any, into hi
    for (d=DECDPUN; d<dn->digits; up++, d+=DECDPUN) hi+=*up*powers[d-1];
    // now low has the lsd, hi the remainder
    if (hi>214748364 || (hi==214748364 && lo>7)) { // out of range?
      // most-negative is a reprieve
      if (dn->bits&DECNEG && hi==214748364 && lo==8) return 0x80000000;
      // bad -- drop through
      }
     else { // in-range always
      Int i=X10(hi)+lo;
      if (dn->bits&DECNEG) return -i;
      return i;
      }
    } // integer
  decContextSetStatus(set, DEC_Invalid_operation); // [may not return]
  return 0;
  } // decNumberToInt32

uInt decNumberToUInt32(const decNumber *dn, decContext *set) {
  #if DECCHECK
  if (decCheckOperands(DECUNRESU, DECUNUSED, dn, set)) return 0;
  #endif
  // special or too many digits, or bad exponent, or negative (<0)
  if (dn->bits&DECSPECIAL || dn->digits>10 || dn->exponent!=0
    || (dn->bits&DECNEG && !ISZERO(dn)));                   // bad
   else { // is a finite integer with 10 or fewer digits
    Int d;                         // work
    const Unit *up;                // ..
    uInt hi=0, lo;                 // ..
    up=dn->lsu;                    // -> lsu
    lo=*up;                        // get 1 to 9 digits
    #if DECDPUN>1                  // split to higher

      hi=lo/10;
      lo=lo%10;
    #endif
    up++;
    // collect remaining Units, if any, into hi
    for (d=DECDPUN; d<dn->digits; up++, d+=DECDPUN) hi+=*up*powers[d-1];

    // now low has the lsd, hi the remainder
    if (hi>429496729 || (hi==429496729 && lo>5)) ; // no reprieve possible
     else return X10(hi)+lo;
    } // integer
  decContextSetStatus(set, DEC_Invalid_operation); // [may not return]
  return 0;
  } // decNumberToUInt32

/* ------------------------------------------------------------------ */
/* to-scientific-string -- conversion to numeric string               */
/* to-engineering-string -- conversion to numeric string              */
/*                                                                    */
/*   decNumberToString(dn, string);                                   */
/*   decNumberToEngString(dn, string);                                */
/*                                                                    */
/*  dn is the decNumber to convert                                    */
/*  string is the string where the result will be laid out            */
/*                                                                    */
/*  string must be at least dn->digits+14 characters long             */
/*                                                                    */
/*  No error is possible, and no status can be set.                   */
/* ------------------------------------------------------------------ */
char * decNumberToString(const decNumber *dn, char *string){
  decToString(dn, string, 0);
  return string;
  } // DecNumberToString

char * decNumberToEngString(const decNumber *dn, char *string){
  decToString(dn, string, 1);
  return string;
  } // DecNumberToEngString

/* ------------------------------------------------------------------ */
/* to-number -- conversion from numeric string                        */
/*                                                                    */
/* decNumberFromString -- convert string to decNumber                 */
/*   dn        -- the number structure to fill                        */
/*   chars[]   -- the string to convert ('\0' terminated)             */
/*   set       -- the context used for processing any error,          */
/*                determining the maximum precision available         */
/*                (set.digits), determining the maximum and minimum   */
/*                exponent (set.emax and set.emin), determining if    */
/*                extended values are allowed, and checking the       */
/*                rounding mode if overflow occurs or rounding is     */
/*                needed.                                             */
/*                                                                    */
/* The length of the coefficient and the size of the exponent are     */
/* checked by this routine, so the correct error (Underflow or        */
/* Overflow) can be reported or rounding applied, as necessary.       */
/*                                                                    */
/* If bad syntax is detected, the result will be a quiet NaN.         */
/* ------------------------------------------------------------------ */
decNumber * decNumberFromString(decNumber *dn, const char chars[],
                                decContext *set) {
  Int   exponent=0;                // working exponent [assume 0]
  uByte bits=0;                    // working flags [assume +ve]
  Unit  *res;                      // where result will be built
  Unit  resbuff[SD2U(DECBUFFER+9)];// local buffer in case need temporary
                                   // [+9 allows for ln() constants]
  Unit  *allocres=NULL;            // -> allocated result, iff allocated
  Int   d=0;                       // count of digits found in decimal part
  const char *dotchar=NULL;        // where dot was found
  const char *cfirst=chars;        // -> first character of decimal part
  const char *last=NULL;           // -> last digit of decimal part
  const char *c;                   // work
  Unit  *up;                       // ..
  #if DECDPUN>1
  Int   cut, out;                  // ..
  #endif
  Int   residue;                   // rounding residue
  uInt  status=0;                  // error code

  #if DECCHECK
  if (decCheckOperands(DECUNRESU, DECUNUSED, DECUNUSED, set))
    return decNumberZero(dn);
  #endif

  do {                             // status & malloc protection
    for (c=chars;; c++) {          // -> input character
      if (*c>='0' && *c<='9') {    // test for Arabic digit
        last=c;
        d++;                       // count of real digits
        continue;                  // still in decimal part
        }
      if (*c=='.' && dotchar==NULL) { // first '.'
        dotchar=c;                 // record offset into decimal part
        if (c==cfirst) cfirst++;   // first digit must follow
        continue;}
      if (c==chars) {              // first in string...
        if (*c=='-') {             // valid - sign
          cfirst++;
          bits=DECNEG;
          continue;}
        if (*c=='+') {             // valid + sign
          cfirst++;
          continue;}
        }
      // *c is not a digit, or a valid +, -, or '.'
      break;
      } // c

    if (last==NULL) {              // no digits yet
      status=DEC_Conversion_syntax;// assume the worst
      if (*c=='\0') break;         // and no more to come...
      #if DECSUBSET
      // if subset then infinities and NaNs are not allowed
      if (!set->extended) break;   // hopeless
      #endif
      // Infinities and NaNs are possible, here
      if (dotchar!=NULL) break;    // .. unless had a dot
      decNumberZero(dn);           // be optimistic
      if (decBiStr(c, "infinity", "INFINITY")
       || decBiStr(c, "inf", "INF")) {
        dn->bits=bits | DECINF;
        status=0;                  // is OK
        break; // all done
        }
      // a NaN expected
      // 2003.09.10 NaNs are now permitted to have a sign
      dn->bits=bits | DECNAN;      // assume simple NaN
      if (*c=='s' || *c=='S') {    // looks like an sNaN
        c++;
        dn->bits=bits | DECSNAN;
        }
      if (*c!='n' && *c!='N') break;    // check caseless "NaN"
      c++;
      if (*c!='a' && *c!='A') break;    // ..
      c++;
      if (*c!='n' && *c!='N') break;    // ..
      c++;
      // now either nothing, or nnnn payload, expected
      // -> start of integer and skip leading 0s [including plain 0]
      for (cfirst=c; *cfirst=='0';) cfirst++;
      if (*cfirst=='\0') {         // "NaN" or "sNaN", maybe with all 0s
        status=0;                  // it's good
        break;                     // ..
        }
      // something other than 0s; setup last and d as usual [no dots]
      for (c=cfirst;; c++, d++) {
        if (*c<'0' || *c>'9') break; // test for Arabic digit
        last=c;
        }
      if (*c!='\0') break;         // not all digits
      if (d>set->digits-1) {
        // [NB: payload in a decNumber can be full length unless
        // clamped, in which case can only be digits-1]
        if (set->clamp) break;
        if (d>set->digits) break;
        } // too many digits?
      // good; drop through to convert the integer to coefficient
      status=0;                    // syntax is OK
      bits=dn->bits;               // for copy-back
      } // last==NULL

     else if (*c!='\0') {          // more to process...
      // had some digits; exponent is only valid sequence now
      Flag nege;                   // 1=negative exponent
      const char *firstexp;        // -> first significant exponent digit
      status=DEC_Conversion_syntax;// assume the worst
      if (*c!='e' && *c!='E') break;
      /* Found 'e' or 'E' -- now process explicit exponent */
      // 1998.07.11: sign no longer required
      nege=0;
      c++;                         // to (possible) sign
      if (*c=='-') {nege=1; c++;}
       else if (*c=='+') c++;
      if (*c=='\0') break;

      for (; *c=='0' && *(c+1)!='\0';) c++;  // strip insignificant zeros
      firstexp=c;                            // save exponent digit place
      for (; ;c++) {
        if (*c<'0' || *c>'9') break;         // not a digit
        exponent=X10(exponent)+(Int)*c-(Int)'0';
        } // c
      // if not now on a '\0', *c must not be a digit
      if (*c!='\0') break;

      // (this next test must be after the syntax checks)
      // if it was too long the exponent may have wrapped, so check
      // carefully and set it to a certain overflow if wrap possible
      if (c>=firstexp+9+1) {
        if (c>firstexp+9+1 || *firstexp>'1') exponent=DECNUMMAXE*2;
        // [up to 1999999999 is OK, for example 1E-1000000998]
        }
      if (nege) exponent=-exponent;     // was negative
      status=0;                         // is OK
      } // stuff after digits

    // Here when whole string has been inspected; syntax is good
    // cfirst->first digit (never dot), last->last digit (ditto)

    // strip leading zeros/dot [leave final 0 if all 0's]
    if (*cfirst=='0') {                 // [cfirst has stepped over .]
      for (c=cfirst; c<last; c++, cfirst++) {
        if (*c=='.') continue;          // ignore dots
        if (*c!='0') break;             // non-zero found
        d--;                            // 0 stripped
        } // c
      #if DECSUBSET
      // make a rapid exit for easy zeros if !extended
      if (*cfirst=='0' && !set->extended) {
        decNumberZero(dn);              // clean result
        break;                          // [could be return]
        }
      #endif
      } // at least one leading 0

    // Handle decimal point...
    if (dotchar!=NULL && dotchar<last)  // non-trailing '.' found?
      exponent-=(last-dotchar);         // adjust exponent
    // [we can now ignore the .]

    // OK, the digits string is good.  Assemble in the decNumber, or in
    // a temporary units array if rounding is needed
    if (d<=set->digits) res=dn->lsu;    // fits into supplied decNumber
     else {                             // rounding needed
      Int needbytes=D2U(d)*sizeof(Unit);// bytes needed
      res=resbuff;                      // assume use local buffer
      if (needbytes>(Int)sizeof(resbuff)) { // too big for local
        allocres=(Unit *)malloc(needbytes);
        if (allocres==NULL) {status|=DEC_Insufficient_storage; break;}
        res=allocres;
        }
      }
    // res now -> number lsu, buffer, or allocated storage for Unit array

    // Place the coefficient into the selected Unit array
    // [this is often 70% of the cost of this function when DECDPUN>1]
    #if DECDPUN>1
    out=0;                         // accumulator
    up=res+D2U(d)-1;               // -> msu
    cut=d-(up-res)*DECDPUN;        // digits in top unit
    for (c=cfirst;; c++) {         // along the digits
      if (*c=='.') continue;       // ignore '.' [don't decrement cut]
      out=X10(out)+(Int)*c-(Int)'0';
      if (c==last) break;          // done [never get to trailing '.']
      cut--;
      if (cut>0) continue;         // more for this unit
      *up=(Unit)out;               // write unit
      up--;                        // prepare for unit below..
      cut=DECDPUN;                 // ..
      out=0;                       // ..
      } // c
    *up=(Unit)out;                 // write lsu

    #else
    // DECDPUN==1
    up=res;                        // -> lsu
    for (c=last; c>=cfirst; c--) { // over each character, from least
      if (*c=='.') continue;       // ignore . [don't step up]
      *up=(Unit)((Int)*c-(Int)'0');
      up++;
      } // c
    #endif

    dn->bits=bits;
    dn->exponent=exponent;
    dn->digits=d;

    // if not in number (too long) shorten into the number
    if (d>set->digits) {
      residue=0;
      decSetCoeff(dn, set, res, d, &residue, &status);
      // always check for overflow or subnormal and round as needed
      decFinalize(dn, set, &residue, &status);
      }
     else { // no rounding, but may still have overflow or subnormal
      // [these tests are just for performance; finalize repeats them]
      if ((dn->exponent-1<set->emin-dn->digits)
       || (dn->exponent-1>set->emax-set->digits)) {
        residue=0;
        decFinalize(dn, set, &residue, &status);
        }
      }
    // decNumberShow(dn);
    } while(0);                         // [for break]

  if (allocres!=NULL) free(allocres);   // drop any storage used
  if (status!=0) decStatus(dn, status, set);
  return dn;
  } /* decNumberFromString */

/* ================================================================== */
/* Operators                                                          */
/* ================================================================== */

/* ------------------------------------------------------------------ */
/* decNumberAbs -- absolute value operator                            */
/*                                                                    */
/*   This computes C = abs(A)                                         */
/*                                                                    */
/*   res is C, the result.  C may be A                                */
/*   rhs is A                                                         */
/*   set is the context                                               */
/*                                                                    */
/* See also decNumberCopyAbs for a quiet bitwise version of this.     */
/* C must have space for set->digits digits.                          */
/* ------------------------------------------------------------------ */
/* This has the same effect as decNumberPlus unless A is negative,    */
/* in which case it has the same effect as decNumberMinus.            */
/* ------------------------------------------------------------------ */
decNumber * decNumberAbs(decNumber *res, const decNumber *rhs,
                         decContext *set) {
  decNumber dzero;                      // for 0
  uInt status=0;                        // accumulator

  #if DECCHECK
  if (decCheckOperands(res, DECUNUSED, rhs, set)) return res;
  #endif

  decNumberZero(&dzero);                // set 0
  dzero.exponent=rhs->exponent;         // [no coefficient expansion]
  decAddOp(res, &dzero, rhs, set, (uByte)(rhs->bits & DECNEG), &status);
  if (status!=0) decStatus(res, status, set);
  #if DECCHECK
  decCheckInexact(res, set);
  #endif
  return res;
  } // decNumberAbs

/* ------------------------------------------------------------------ */
/* decNumberAdd -- add two Numbers                                    */
/*                                                                    */
/*   This computes C = A + B                                          */
/*                                                                    */
/*   res is C, the result.  C may be A and/or B (e.g., X=X+X)         */
/*   lhs is A                                                         */
/*   rhs is B                                                         */
/*   set is the context                                               */
/*                                                                    */
/* C must have space for set->digits digits.                          */
/* ------------------------------------------------------------------ */
/* This just calls the routine shared with Subtract                   */
decNumber * decNumberAdd(decNumber *res, const decNumber *lhs,
                         const decNumber *rhs, decContext *set) {
  uInt status=0;                        // accumulator
  decAddOp(res, lhs, rhs, set, 0, &status);
  if (status!=0) decStatus(res, status, set);
  #if DECCHECK
  decCheckInexact(res, set);
  #endif
  return res;
  } // decNumberAdd

/* ------------------------------------------------------------------ */
/* decNumberAnd -- AND two Numbers, digitwise                         */
/*                                                                    */
/*   This computes C = A & B                                          */
/*                                                                    */
/*   res is C, the result.  C may be A and/or B (e.g., X=X&X)         */
/*   lhs is A                                                         */
/*   rhs is B                                                         */
/*   set is the context (used for result length and error report)     */
/*                                                                    */
/* C must have space for set->digits digits.                          */
/*                                                                    */
/* Logical function restrictions apply (see above); a NaN is          */
/* returned with Invalid_operation if a restriction is violated.      */
/* ------------------------------------------------------------------ */
decNumber * decNumberAnd(decNumber *res, const decNumber *lhs,
                         const decNumber *rhs, decContext *set) {
  const Unit *ua, *ub;                  // -> operands
  const Unit *msua, *msub;              // -> operand msus
  Unit *uc,  *msuc;                     // -> result and its msu
  Int   msudigs;                        // digits in res msu
  #if DECCHECK
  if (decCheckOperands(res, lhs, rhs, set)) return res;
  #endif

  if (lhs->exponent!=0 || decNumberIsSpecial(lhs) || decNumberIsNegative(lhs)
   || rhs->exponent!=0 || decNumberIsSpecial(rhs) || decNumberIsNegative(rhs)) {
    decStatus(res, DEC_Invalid_operation, set);
    return res;
    }

  // operands are valid
  ua=lhs->lsu;                          // bottom-up
  ub=rhs->lsu;                          // ..
  uc=res->lsu;                          // ..
  msua=ua+D2U(lhs->digits)-1;           // -> msu of lhs
  msub=ub+D2U(rhs->digits)-1;           // -> msu of rhs
  msuc=uc+D2U(set->digits)-1;           // -> msu of result
  msudigs=MSUDIGITS(set->digits);       // [faster than remainder]
  for (; uc<=msuc; ua++, ub++, uc++) {  // Unit loop
    Unit a, b;                          // extract units
    if (ua>msua) a=0;
     else a=*ua;
    if (ub>msub) b=0;
     else b=*ub;
    *uc=0;                              // can now write back
    if (a|b) {                          // maybe 1 bits to examine
      Int i, j;
      *uc=0;                            // can now write back
      // This loop could be unrolled and/or use BIN2BCD tables
      for (i=0; i<DECDPUN; i++) {
        if (a&b&1) *uc=*uc+(Unit)powers[i];  // effect AND
        j=a%10;
        a=a/10;
        j|=b%10;
        b=b/10;
        if (j>1) {
          decStatus(res, DEC_Invalid_operation, set);
          return res;
          }
        if (uc==msuc && i==msudigs-1) break; // just did final digit
        } // each digit
      } // both OK
    } // each unit
  // [here uc-1 is the msu of the result]
  res->digits=decGetDigits(res->lsu, uc-res->lsu);
  res->exponent=0;                      // integer
  res->bits=0;                          // sign=0
  return res;  // [no status to set]
  } // decNumberAnd

/* ------------------------------------------------------------------ */
/* decNumberCompare -- compare two Numbers                            */
/*                                                                    */
/*   This computes C = A ? B                                          */
/*                                                                    */
/*   res is C, the result.  C may be A and/or B (e.g., X=X?X)         */
/*   lhs is A                                                         */
/*   rhs is B                                                         */
/*   set is the context                                               */
/*                                                                    */
/* C must have space for one digit (or NaN).                          */
/* ------------------------------------------------------------------ */
decNumber * decNumberCompare(decNumber *res, const decNumber *lhs,
                             const decNumber *rhs, decContext *set) {
  uInt status=0;                        // accumulator
  decCompareOp(res, lhs, rhs, set, COMPARE, &status);
  if (status!=0) decStatus(res, status, set);
  return res;
  } // decNumberCompare

/* ------------------------------------------------------------------ */
/* decNumberCompareSignal -- compare, signalling on all NaNs          */
/*                                                                    */
/*   This computes C = A ? B                                          */
/*                                                                    */
/*   res is C, the result.  C may be A and/or B (e.g., X=X?X)         */
/*   lhs is A                                                         */
/*   rhs is B                                                         */
/*   set is the context                                               */
/*                                                                    */
/* C must have space for one digit (or NaN).                          */
/* ------------------------------------------------------------------ */
decNumber * decNumberCompareSignal(decNumber *res, const decNumber *lhs,
                                   const decNumber *rhs, decContext *set) {
  uInt status=0;                        // accumulator
  decCompareOp(res, lhs, rhs, set, COMPSIG, &status);
  if (status!=0) decStatus(res, status, set);
  return res;
  } // decNumberCompareSignal

/* ------------------------------------------------------------------ */
/* decNumberCompareTotal -- compare two Numbers, using total ordering */
/*                                                                    */
/*   This computes C = A ? B, under total ordering                    */
/*                                                                    */
/*   res is C, the result.  C may be A and/or B (e.g., X=X?X)         */
/*   lhs is A                                                         */
/*   rhs is B                                                         */
/*   set is the context                                               */
/*                                                                    */
/* C must have space for one digit; the result will always be one of  */
/* -1, 0, or 1.                                                       */
/* ------------------------------------------------------------------ */
decNumber * decNumberCompareTotal(decNumber *res, const decNumber *lhs,
                                  const decNumber *rhs, decContext *set) {
  uInt status=0;                        // accumulator
  decCompareOp(res, lhs, rhs, set, COMPTOTAL, &status);
  if (status!=0) decStatus(res, status, set);
  return res;
  } // decNumberCompareTotal

/* ------------------------------------------------------------------ */
/* decNumberCompareTotalMag -- compare, total ordering of magnitudes  */
/*                                                                    */
/*   This computes C = |A| ? |B|, under total ordering                */
/*                                                                    */
/*   res is C, the result.  C may be A and/or B (e.g., X=X?X)         */
/*   lhs is A                                                         */
/*   rhs is B                                                         */
/*   set is the context                                               */
/*                                                                    */
/* C must have space for one digit; the result will always be one of  */
/* -1, 0, or 1.                                                       */
/* ------------------------------------------------------------------ */
decNumber * decNumberCompareTotalMag(decNumber *res, const decNumber *lhs,
                                     const decNumber *rhs, decContext *set) {
  uInt status=0;                   // accumulator
  uInt needbytes;                  // for space calculations
  decNumber bufa[D2N(DECBUFFER+1)];// +1 in case DECBUFFER=0
  decNumber *allocbufa=NULL;       // -> allocated bufa, iff allocated
  decNumber bufb[D2N(DECBUFFER+1)];
  decNumber *allocbufb=NULL;       // -> allocated bufb, iff allocated
  decNumber *a, *b;                // temporary pointers

  #if DECCHECK
  if (decCheckOperands(res, lhs, rhs, set)) return res;
  #endif

  do {                                  // protect allocated storage
    // if either is negative, take a copy and absolute
    if (decNumberIsNegative(lhs)) {     // lhs<0
      a=bufa;
      needbytes=sizeof(decNumber)+(D2U(lhs->digits)-1)*sizeof(Unit);
      if (needbytes>sizeof(bufa)) {     // need malloc space
        allocbufa=(decNumber *)malloc(needbytes);
        if (allocbufa==NULL) {          // hopeless -- abandon
          status|=DEC_Insufficient_storage;
          break;}
        a=allocbufa;                    // use the allocated space
        }
      decNumberCopy(a, lhs);            // copy content
      a->bits&=~DECNEG;                 // .. and clear the sign
      lhs=a;                            // use copy from here on
      }
    if (decNumberIsNegative(rhs)) {     // rhs<0
      b=bufb;
      needbytes=sizeof(decNumber)+(D2U(rhs->digits)-1)*sizeof(Unit);
      if (needbytes>sizeof(bufb)) {     // need malloc space
        allocbufb=(decNumber *)malloc(needbytes);
        if (allocbufb==NULL) {          // hopeless -- abandon
          status|=DEC_Insufficient_storage;
          break;}
        b=allocbufb;                    // use the allocated space
        }
      decNumberCopy(b, rhs);            // copy content
      b->bits&=~DECNEG;                 // .. and clear the sign
      rhs=b;                            // use copy from here on
      }
    decCompareOp(res, lhs, rhs, set, COMPTOTAL, &status);
    } while(0);                         // end protected

  if (allocbufa!=NULL) free(allocbufa); // drop any storage used
  if (allocbufb!=NULL) free(allocbufb); // ..
  if (status!=0) decStatus(res, status, set);
  return res;
  } // decNumberCompareTotalMag

/* ------------------------------------------------------------------ */
/* decNumberDivide -- divide one number by another                    */
/*                                                                    */
/*   This computes C = A / B                                          */
/*                                                                    */
/*   res is C, the result.  C may be A and/or B (e.g., X=X/X)         */
/*   lhs is A                                                         */
/*   rhs is B                                                         */
/*   set is the context                                               */
/*                                                                    */
/* C must have space for set->digits digits.                          */
/* ------------------------------------------------------------------ */
decNumber * decNumberDivide(decNumber *res, const decNumber *lhs,
                            const decNumber *rhs, decContext *set) {
  uInt status=0;                        // accumulator
  decDivideOp(res, lhs, rhs, set, DIVIDE, &status);
  if (status!=0) decStatus(res, status, set);
  #if DECCHECK
  decCheckInexact(res, set);
  #endif
  return res;
  } // decNumberDivide

/* ------------------------------------------------------------------ */
/* decNumberDivideInteger -- divide and return integer quotient       */
/*                                                                    */
/*   This computes C = A # B, where # is the integer divide operator  */
/*                                                                    */
/*   res is C, the result.  C may be A and/or B (e.g., X=X#X)         */
/*   lhs is A                                                         */
/*   rhs is B                                                         */
/*   set is the context                                               */
/*                                                                    */
/* C must have space for set->digits digits.                          */
/* ------------------------------------------------------------------ */
decNumber * decNumberDivideInteger(decNumber *res, const decNumber *lhs,
                                   const decNumber *rhs, decContext *set) {
  uInt status=0;                        // accumulator
  decDivideOp(res, lhs, rhs, set, DIVIDEINT, &status);
  if (status!=0) decStatus(res, status, set);
  return res;
  } // decNumberDivideInteger

/* ------------------------------------------------------------------ */
/* decNumberExp -- exponentiation                                     */
/*                                                                    */
/*   This computes C = exp(A)                                         */
/*                                                                    */
/*   res is C, the result.  C may be A                                */
/*   rhs is A                                                         */
/*   set is the context; note that rounding mode has no effect        */
/*                                                                    */
/* C must have space for set->digits digits.                          */
/*                                                                    */
/* Mathematical function restrictions apply (see above); a NaN is     */
/* returned with Invalid_operation if a restriction is violated.      */
/*                                                                    */
/* Finite results will always be full precision and Inexact, except   */
/* when A is a zero or -Infinity (giving 1 or 0 respectively).        */
/*                                                                    */
/* An Inexact result is rounded using DEC_ROUND_HALF_EVEN; it will    */
/* almost always be correctly rounded, but may be up to 1 ulp in      */
/* error in rare cases.                                               */
/* ------------------------------------------------------------------ */
/* This is a wrapper for decExpOp which can handle the slightly wider */
/* (double) range needed by Ln (which has to be able to calculate     */
/* exp(-a) where a can be the tiniest number (Ntiny).                 */
/* ------------------------------------------------------------------ */
decNumber * decNumberExp(decNumber *res, const decNumber *rhs,
                         decContext *set) {
  uInt status=0;                        // accumulator
  #if DECSUBSET
  decNumber *allocrhs=NULL;        // non-NULL if rounded rhs allocated
  #endif

  #if DECCHECK
  if (decCheckOperands(res, DECUNUSED, rhs, set)) return res;
  #endif

  // Check restrictions; these restrictions ensure that if h=8 (see
  // decExpOp) then the result will either overflow or underflow to 0.
  // Other math functions restrict the input range, too, for inverses.
  // If not violated then carry out the operation.
  if (!decCheckMath(rhs, set, &status)) do { // protect allocation
    #if DECSUBSET
    if (!set->extended) {
      // reduce operand and set lostDigits status, as needed
      if (rhs->digits>set->digits) {
        allocrhs=decRoundOperand(rhs, set, &status);
        if (allocrhs==NULL) break;
        rhs=allocrhs;
        }
      }
    #endif
    decExpOp(res, rhs, set, &status);
    } while(0);                         // end protected

  #if DECSUBSET
  if (allocrhs !=NULL) free(allocrhs);  // drop any storage used
  #endif
  // apply significant status
  if (status!=0) decStatus(res, status, set);
  #if DECCHECK
  decCheckInexact(res, set);
  #endif
  return res;
  } // decNumberExp

/* ------------------------------------------------------------------ */
/* decNumberFMA -- fused multiply add                                 */
/*                                                                    */
/*   This computes D = (A * B) + C with only one rounding             */
/*                                                                    */
/*   res is D, the result.  D may be A or B or C (e.g., X=FMA(X,X,X)) */
/*   lhs is A                                                         */
/*   rhs is B                                                         */
/*   fhs is C [far hand side]                                         */
/*   set is the context                                               */
/*                                                                    */
/* Mathematical function restrictions apply (see above); a NaN is     */
/* returned with Invalid_operation if a restriction is violated.      */
/*                                                                    */
/* C must have space for set->digits digits.                          */
/* ------------------------------------------------------------------ */
decNumber * decNumberFMA(decNumber *res, const decNumber *lhs,
                         const decNumber *rhs, const decNumber *fhs,
                         decContext *set) {
  uInt status=0;                   // accumulator
  decContext dcmul;                // context for the multiplication
  uInt needbytes;                  // for space calculations
  decNumber bufa[D2N(DECBUFFER*2+1)];
  decNumber *allocbufa=NULL;       // -> allocated bufa, iff allocated
  decNumber *acc;                  // accumulator pointer
  decNumber dzero;                 // work

  #if DECCHECK
  if (decCheckOperands(res, lhs, rhs, set)) return res;
  if (decCheckOperands(res, fhs, DECUNUSED, set)) return res;
  #endif

  do {                                  // protect allocated storage
    #if DECSUBSET
    if (!set->extended) {               // [undefined if subset]
      status|=DEC_Invalid_operation;
      break;}
    #endif
    // Check math restrictions [these ensure no overflow or underflow]
    if ((!decNumberIsSpecial(lhs) && decCheckMath(lhs, set, &status))
     || (!decNumberIsSpecial(rhs) && decCheckMath(rhs, set, &status))
     || (!decNumberIsSpecial(fhs) && decCheckMath(fhs, set, &status))) break;
    // set up context for multiply
    dcmul=*set;
    dcmul.digits=lhs->digits+rhs->digits; // just enough
    // [The above may be an over-estimate for subset arithmetic, but that's OK]
    dcmul.emax=DEC_MAX_EMAX;            // effectively unbounded ..
    dcmul.emin=DEC_MIN_EMIN;            // [thanks to Math restrictions]
    // set up decNumber space to receive the result of the multiply
    acc=bufa;                           // may fit
    needbytes=sizeof(decNumber)+(D2U(dcmul.digits)-1)*sizeof(Unit);
    if (needbytes>sizeof(bufa)) {       // need malloc space
      allocbufa=(decNumber *)malloc(needbytes);
      if (allocbufa==NULL) {            // hopeless -- abandon
        status|=DEC_Insufficient_storage;
        break;}
      acc=allocbufa;                    // use the allocated space
      }
    // multiply with extended range and necessary precision
    //printf("emin=%ld\n", dcmul.emin);
    decMultiplyOp(acc, lhs, rhs, &dcmul, &status);
    // Only Invalid operation (from sNaN or Inf * 0) is possible in
    // status; if either is seen than ignore fhs (in case it is
    // another sNaN) and set acc to NaN unless we had an sNaN
    // [decMultiplyOp leaves that to caller]
    // Note sNaN has to go through addOp to shorten payload if
    // necessary
    if ((status&DEC_Invalid_operation)!=0) {
      if (!(status&DEC_sNaN)) {         // but be true invalid
        decNumberZero(res);             // acc not yet set
        res->bits=DECNAN;
        break;
        }
      decNumberZero(&dzero);            // make 0 (any non-NaN would do)
      fhs=&dzero;                       // use that
      }
    #if DECCHECK
     else { // multiply was OK
      if (status!=0) printf("Status=%08lx after FMA multiply\n", (LI)status);
      }
    #endif
    // add the third operand and result -> res, and all is done
    decAddOp(res, acc, fhs, set, 0, &status);
    } while(0);                         // end protected

  if (allocbufa!=NULL) free(allocbufa); // drop any storage used
  if (status!=0) decStatus(res, status, set);
  #if DECCHECK
  decCheckInexact(res, set);
  #endif
  return res;
  } // decNumberFMA

/* ------------------------------------------------------------------ */
/* decNumberInvert -- invert a Number, digitwise                      */
/*                                                                    */
/*   This computes C = ~A                                             */
/*                                                                    */
/*   res is C, the result.  C may be A (e.g., X=~X)                   */
/*   rhs is A                                                         */
/*   set is the context (used for result length and error report)     */
/*                                                                    */
/* C must have space for set->digits digits.                          */
/*                                                                    */
/* Logical function restrictions apply (see above); a NaN is          */
/* returned with Invalid_operation if a restriction is violated.      */
/* ------------------------------------------------------------------ */
decNumber * decNumberInvert(decNumber *res, const decNumber *rhs,
                            decContext *set) {
  const Unit *ua, *msua;                // -> operand and its msu
  Unit  *uc, *msuc;                     // -> result and its msu
  Int   msudigs;                        // digits in res msu
  #if DECCHECK
  if (decCheckOperands(res, DECUNUSED, rhs, set)) return res;
  #endif

  if (rhs->exponent!=0 || decNumberIsSpecial(rhs) || decNumberIsNegative(rhs)) {
    decStatus(res, DEC_Invalid_operation, set);
    return res;
    }
  // operand is valid
  ua=rhs->lsu;                          // bottom-up
  uc=res->lsu;                          // ..
  msua=ua+D2U(rhs->digits)-1;           // -> msu of rhs
  msuc=uc+D2U(set->digits)-1;           // -> msu of result
  msudigs=MSUDIGITS(set->digits);       // [faster than remainder]
  for (; uc<=msuc; ua++, uc++) {        // Unit loop
    Unit a;                             // extract unit
    Int  i, j;                          // work
    if (ua>msua) a=0;
     else a=*ua;
    *uc=0;                              // can now write back
    // always need to examine all bits in rhs
    // This loop could be unrolled and/or use BIN2BCD tables
    for (i=0; i<DECDPUN; i++) {
      if ((~a)&1) *uc=*uc+(Unit)powers[i];   // effect INVERT
      j=a%10;
      a=a/10;
      if (j>1) {
        decStatus(res, DEC_Invalid_operation, set);
        return res;
        }
      if (uc==msuc && i==msudigs-1) break;   // just did final digit
      } // each digit
    } // each unit
  // [here uc-1 is the msu of the result]
  res->digits=decGetDigits(res->lsu, uc-res->lsu);
  res->exponent=0;                      // integer
  res->bits=0;                          // sign=0
  return res;  // [no status to set]
  } // decNumberInvert

/* ------------------------------------------------------------------ */
/* decNumberLn -- natural logarithm                                   */
/*                                                                    */
/*   This computes C = ln(A)                                          */
/*                                                                    */
/*   res is C, the result.  C may be A                                */
/*   rhs is A                                                         */
/*   set is the context; note that rounding mode has no effect        */
/*                                                                    */
/* C must have space for set->digits digits.                          */
/*                                                                    */
/* Notable cases:                                                     */
/*   A<0 -> Invalid                                                   */
/*   A=0 -> -Infinity (Exact)                                         */
/*   A=+Infinity -> +Infinity (Exact)                                 */
/*   A=1 exactly -> 0 (Exact)                                         */
/*                                                                    */
/* Mathematical function restrictions apply (see above); a NaN is     */
/* returned with Invalid_operation if a restriction is violated.      */
/*                                                                    */
/* An Inexact result is rounded using DEC_ROUND_HALF_EVEN; it will    */
/* almost always be correctly rounded, but may be up to 1 ulp in      */
/* error in rare cases.                                               */
/* ------------------------------------------------------------------ */
/* This is a wrapper for decLnOp which can handle the slightly wider  */
/* (+11) range needed by Ln, Log10, etc. (which may have to be able   */
/* to calculate at p+e+2).                                            */
/* ------------------------------------------------------------------ */
decNumber * decNumberLn(decNumber *res, const decNumber *rhs,
                        decContext *set) {
  uInt status=0;                   // accumulator
  #if DECSUBSET
  decNumber *allocrhs=NULL;        // non-NULL if rounded rhs allocated
  #endif

  #if DECCHECK
  if (decCheckOperands(res, DECUNUSED, rhs, set)) return res;
  #endif

  // Check restrictions; this is a math function; if not violated
  // then carry out the operation.
  if (!decCheckMath(rhs, set, &status)) do { // protect allocation
    #if DECSUBSET
    if (!set->extended) {
      // reduce operand and set lostDigits status, as needed
      if (rhs->digits>set->digits) {
        allocrhs=decRoundOperand(rhs, set, &status);
        if (allocrhs==NULL) break;
        rhs=allocrhs;
        }
      // special check in subset for rhs=0
      if (ISZERO(rhs)) {                // +/- zeros -> error
        status|=DEC_Invalid_operation;
        break;}
      } // extended=0
    #endif
    decLnOp(res, rhs, set, &status);
    } while(0);                         // end protected

  #if DECSUBSET
  if (allocrhs !=NULL) free(allocrhs);  // drop any storage used
  #endif
  // apply significant status
  if (status!=0) decStatus(res, status, set);
  #if DECCHECK
  decCheckInexact(res, set);
  #endif
  return res;
  } // decNumberLn

/* ------------------------------------------------------------------ */
/* decNumberLogB - get adjusted exponent, by 754 rules                */
/*                                                                    */
/*   This computes C = adjustedexponent(A)                            */
/*                                                                    */
/*   res is C, the result.  C may be A                                */
/*   rhs is A                                                         */
/*   set is the context, used only for digits and status              */
/*                                                                    */
/* For an unrounded result, digits may need to be 10 (A might have    */
/* 10**9 digits and an exponent of +999999999, or one digit and an    */
/* exponent of -1999999999).                                          */
/*                                                                    */
/* This returns the adjusted exponent of A after (in theory) padding  */
/* with zeros on the right to set->digits digits while keeping the    */
/* same value.  The exponent is not limited by emin/emax.             */
/*                                                                    */
/* Notable cases:                                                     */
/*   A<0 -> Use |A|                                                   */
/*   A=0 -> -Infinity (Division by zero)                              */
/*   A=Infinite -> +Infinity (Exact)                                  */
/*   A=1 exactly -> 0 (Exact)                                         */
/*   NaNs are propagated as usual                                     */
/* ------------------------------------------------------------------ */
decNumber * decNumberLogB(decNumber *res, const decNumber *rhs,
                          decContext *set) {
  uInt status=0;                   // accumulator

  #if DECCHECK
  if (decCheckOperands(res, DECUNUSED, rhs, set)) return res;
  #endif

  // NaNs as usual; Infinities return +Infinity; 0->oops
  if (decNumberIsNaN(rhs)) decNaNs(res, rhs, NULL, set, &status);
   else if (decNumberIsInfinite(rhs)) decNumberCopyAbs(res, rhs);
   else if (decNumberIsZero(rhs)) {
    decNumberZero(res);                 // prepare for Infinity
    res->bits=DECNEG|DECINF;            // -Infinity
    status|=DEC_Division_by_zero;       // as per 754
    }
   else { // finite non-zero
    Int ae=rhs->exponent+rhs->digits-1; // adjusted exponent
    if (set->digits>=10) decNumberFromInt32(res, ae);  // lay it out
     else {
      decNumber buft[D2N(10)];          // temporary number
      decNumber *t=buft;                // ..
      decNumberFromInt32(t, ae);        // lay it out
      decNumberPlus(res, t, set);       // round as necessary
      }
    }

  if (status!=0) decStatus(res, status, set);
  return res;
  } // decNumberLogB

/* ------------------------------------------------------------------ */
/* decNumberLog10 -- logarithm in base 10                             */
/*                                                                    */
/*   This computes C = log10(A)                                       */
/*                                                                    */
/*   res is C, the result.  C may be A                                */
/*   rhs is A                                                         */
/*   set is the context; note that rounding mode has no effect        */
/*                                                                    */
/* C must have space for set->digits digits.                          */
/*                                                                    */
/* Notable cases:                                                     */
/*   A<0 -> Invalid                                                   */
/*   A=0 -> -Infinity (Exact)                                         */
/*   A=+Infinity -> +Infinity (Exact)                                 */
/*   A=10**n (if n is an integer) -> n (Exact)                        */
/*                                                                    */
/* Mathematical function restrictions apply (see above); a NaN is     */
/* returned with Invalid_operation if a restriction is violated.      */
/*                                                                    */
/* An Inexact result is rounded using DEC_ROUND_HALF_EVEN; it will    */
/* almost always be correctly rounded, but may be up to 1 ulp in      */
/* error in rare cases.                                               */
/* ------------------------------------------------------------------ */
/* This calculates ln(A)/ln(10) using appropriate precision.  For     */
/* ln(A) this is the max(p, rhs->digits + t) + 3, where p is the      */
/* requested digits and t is the number of digits in the exponent     */
/* (maximum 6).  For ln(10) it is p + 3; this is often handled by the */
/* fastpath in decLnOp.  The final division is done to the requested  */
/* precision.                                                         */
/* ------------------------------------------------------------------ */
decNumber * decNumberLog10(decNumber *res, const decNumber *rhs,
                          decContext *set) {
  uInt status=0, ignore=0;         // status accumulators
  uInt needbytes;                  // for space calculations
  Int p;                           // working precision
  Int t;                           // digits in exponent of A

  // buffers for a and b working decimals
  // (adjustment calculator, same size)
  decNumber bufa[D2N(DECBUFFER+2)];
  decNumber *allocbufa=NULL;       // -> allocated bufa, iff allocated
  decNumber *a=bufa;               // temporary a
  decNumber bufb[D2N(DECBUFFER+2)];
  decNumber *allocbufb=NULL;       // -> allocated bufb, iff allocated
  decNumber *b=bufb;               // temporary b
  decNumber bufw[D2N(10)];         // working 2-10 digit number
  decNumber *w=bufw;               // ..
  #if DECSUBSET
  decNumber *allocrhs=NULL;        // non-NULL if rounded rhs allocated
  #endif

  decContext aset;                 // working context

  #if DECCHECK
  if (decCheckOperands(res, DECUNUSED, rhs, set)) return res;
  #endif

  // Check restrictions; this is a math function; if not violated
  // then carry out the operation.
  if (!decCheckMath(rhs, set, &status)) do { // protect malloc
    #if DECSUBSET
    if (!set->extended) {
      // reduce operand and set lostDigits status, as needed
      if (rhs->digits>set->digits) {
        allocrhs=decRoundOperand(rhs, set, &status);
        if (allocrhs==NULL) break;
        rhs=allocrhs;
        }
      // special check in subset for rhs=0
      if (ISZERO(rhs)) {                // +/- zeros -> error
        status|=DEC_Invalid_operation;
        break;}
      } // extended=0
    #endif

    decContextDefault(&aset, DEC_INIT_DECIMAL64); // clean context

    // handle exact powers of 10; only check if +ve finite
    if (!(rhs->bits&(DECNEG|DECSPECIAL)) && !ISZERO(rhs)) {
      Int residue=0;               // (no residue)
      uInt copystat=0;             // clean status

      // round to a single digit...
      aset.digits=1;
      decCopyFit(w, rhs, &aset, &residue, &copystat); // copy & shorten
      // if exact and the digit is 1, rhs is a power of 10
      if (!(copystat&DEC_Inexact) && w->lsu[0]==1) {
        // the exponent, conveniently, is the power of 10; making
        // this the result needs a little care as it might not fit,
        // so first convert it into the working number, and then move
        // to res
        decNumberFromInt32(w, w->exponent);
        residue=0;
        decCopyFit(res, w, set, &residue, &status); // copy & round
        decFinish(res, set, &residue, &status);     // cleanup/set flags
        break;
        } // not a power of 10
      } // not a candidate for exact

    // simplify the information-content calculation to use 'total
    // number of digits in a, including exponent' as compared to the
    // requested digits, as increasing this will only rarely cost an
    // iteration in ln(a) anyway
    t=6;                                // it can never be >6

    // allocate space when needed...
    p=(rhs->digits+t>set->digits?rhs->digits+t:set->digits)+3;
    needbytes=sizeof(decNumber)+(D2U(p)-1)*sizeof(Unit);
    if (needbytes>sizeof(bufa)) {       // need malloc space
      allocbufa=(decNumber *)malloc(needbytes);
      if (allocbufa==NULL) {            // hopeless -- abandon
        status|=DEC_Insufficient_storage;
        break;}
      a=allocbufa;                      // use the allocated space
      }
    aset.digits=p;                      // as calculated
    aset.emax=DEC_MAX_MATH;             // usual bounds
    aset.emin=-DEC_MAX_MATH;            // ..
    aset.clamp=0;                       // and no concrete format
    decLnOp(a, rhs, &aset, &status);    // a=ln(rhs)

    // skip the division if the result so far is infinite, NaN, or
    // zero, or there was an error; note NaN from sNaN needs copy
    if (status&DEC_NaNs && !(status&DEC_sNaN)) break;
    if (a->bits&DECSPECIAL || ISZERO(a)) {
      decNumberCopy(res, a);            // [will fit]
      break;}

    // for ln(10) an extra 3 digits of precision are needed
    p=set->digits+3;
    needbytes=sizeof(decNumber)+(D2U(p)-1)*sizeof(Unit);
    if (needbytes>sizeof(bufb)) {       // need malloc space
      allocbufb=(decNumber *)malloc(needbytes);
      if (allocbufb==NULL) {            // hopeless -- abandon
        status|=DEC_Insufficient_storage;
        break;}
      b=allocbufb;                      // use the allocated space
      }
    decNumberZero(w);                   // set up 10...
    #if DECDPUN==1
    w->lsu[1]=1; w->lsu[0]=0;           // ..
    #else
    w->lsu[0]=10;                       // ..
    #endif
    w->digits=2;                        // ..

    aset.digits=p;
    decLnOp(b, w, &aset, &ignore);      // b=ln(10)

    aset.digits=set->digits;            // for final divide
    decDivideOp(res, a, b, &aset, DIVIDE, &status); // into result
    } while(0);                         // [for break]

  if (allocbufa!=NULL) free(allocbufa); // drop any storage used
  if (allocbufb!=NULL) free(allocbufb); // ..
  #if DECSUBSET
  if (allocrhs !=NULL) free(allocrhs);  // ..
  #endif
  // apply significant status
  if (status!=0) decStatus(res, status, set);
  #if DECCHECK
  decCheckInexact(res, set);
  #endif
  return res;
  } // decNumberLog10

/* ------------------------------------------------------------------ */
/* decNumberMax -- compare two Numbers and return the maximum         */
/*                                                                    */
/*   This computes C = A ? B, returning the maximum by 754 rules      */
/*                                                                    */
/*   res is C, the result.  C may be A and/or B (e.g., X=X?X)         */
/*   lhs is A                                                         */
/*   rhs is B                                                         */
/*   set is the context                                               */
/*                                                                    */
/* C must have space for set->digits digits.                          */
/* ------------------------------------------------------------------ */
decNumber * decNumberMax(decNumber *res, const decNumber *lhs,
                         const decNumber *rhs, decContext *set) {
  uInt status=0;                        // accumulator
  decCompareOp(res, lhs, rhs, set, COMPMAX, &status);
  if (status!=0) decStatus(res, status, set);
  #if DECCHECK
  decCheckInexact(res, set);
  #endif
  return res;
  } // decNumberMax

/* ------------------------------------------------------------------ */
/* decNumberMaxMag -- compare and return the maximum by magnitude     */
/*                                                                    */
/*   This computes C = A ? B, returning the maximum by 754 rules      */
/*                                                                    */
/*   res is C, the result.  C may be A and/or B (e.g., X=X?X)         */
/*   lhs is A                                                         */
/*   rhs is B                                                         */
/*   set is the context                                               */
/*                                                                    */
/* C must have space for set->digits digits.                          */
/* ------------------------------------------------------------------ */
decNumber * decNumberMaxMag(decNumber *res, const decNumber *lhs,
                         const decNumber *rhs, decContext *set) {
  uInt status=0;                        // accumulator
  decCompareOp(res, lhs, rhs, set, COMPMAXMAG, &status);
  if (status!=0) decStatus(res, status, set);
  #if DECCHECK
  decCheckInexact(res, set);
  #endif
  return res;
  } // decNumberMaxMag

/* ------------------------------------------------------------------ */
/* decNumberMin -- compare two Numbers and return the minimum         */
/*                                                                    */
/*   This computes C = A ? B, returning the minimum by 754 rules      */
/*                                                                    */
/*   res is C, the result.  C may be A and/or B (e.g., X=X?X)         */
/*   lhs is A                                                         */
/*   rhs is B                                                         */
/*   set is the context                                               */
/*                                                                    */
/* C must have space for set->digits digits.                          */
/* ------------------------------------------------------------------ */
decNumber * decNumberMin(decNumber *res, const decNumber *lhs,
                         const decNumber *rhs, decContext *set) {
  uInt status=0;                        // accumulator
  decCompareOp(res, lhs, rhs, set, COMPMIN, &status);
  if (status!=0) decStatus(res, status, set);
  #if DECCHECK
  decCheckInexact(res, set);
  #endif
  return res;
  } // decNumberMin

/* ------------------------------------------------------------------ */
/* decNumberMinMag -- compare and return the minimum by magnitude     */
/*                                                                    */
/*   This computes C = A ? B, returning the minimum by 754 rules      */
/*                                                                    */
/*   res is C, the result.  C may be A and/or B (e.g., X=X?X)         */
/*   lhs is A                                                         */
/*   rhs is B                                                         */
/*   set is the context                                               */
/*                                                                    */
/* C must have space for set->digits digits.                          */
/* ------------------------------------------------------------------ */
decNumber * decNumberMinMag(decNumber *res, const decNumber *lhs,
                         const decNumber *rhs, decContext *set) {
  uInt status=0;                        // accumulator
  decCompareOp(res, lhs, rhs, set, COMPMINMAG, &status);
  if (status!=0) decStatus(res, status, set);
  #if DECCHECK
  decCheckInexact(res, set);
  #endif
  return res;
  } // decNumberMinMag

/* ------------------------------------------------------------------ */
/* decNumberMinus -- prefix minus operator                            */
/*                                                                    */
/*   This computes C = 0 - A                                          */
/*                                                                    */
/*   res is C, the result.  C may be A                                */
/*   rhs is A                                                         */
/*   set is the context                                               */
/*                                                                    */
/* See also decNumberCopyNegate for a quiet bitwise version of this.  */
/* C must have space for set->digits digits.                          */
/* ------------------------------------------------------------------ */
/* Simply use AddOp for the subtract, which will do the necessary.    */
/* ------------------------------------------------------------------ */
decNumber * decNumberMinus(decNumber *res, const decNumber *rhs,
                           decContext *set) {
  decNumber dzero;
  uInt status=0;                        // accumulator

  #if DECCHECK
  if (decCheckOperands(res, DECUNUSED, rhs, set)) return res;
  #endif

  decNumberZero(&dzero);                // make 0
  dzero.exponent=rhs->exponent;         // [no coefficient expansion]
  decAddOp(res, &dzero, rhs, set, DECNEG, &status);
  if (status!=0) decStatus(res, status, set);
  #if DECCHECK
  decCheckInexact(res, set);
  #endif
  return res;
  } // decNumberMinus

/* ------------------------------------------------------------------ */
/* decNumberNextMinus -- next towards -Infinity                       */
/*                                                                    */
/*   This computes C = A - infinitesimal, rounded towards -Infinity   */
/*                                                                    */
/*   res is C, the result.  C may be A                                */
/*   rhs is A                                                         */
/*   set is the context                                               */
/*                                                                    */
/* This is a generalization of 754 NextDown.                          */
/* ------------------------------------------------------------------ */
decNumber * decNumberNextMinus(decNumber *res, const decNumber *rhs,
                               decContext *set) {
  decNumber dtiny;                           // constant
  decContext workset=*set;                   // work
  uInt status=0;                             // accumulator
  #if DECCHECK
  if (decCheckOperands(res, DECUNUSED, rhs, set)) return res;
  #endif

  // +Infinity is the special case
  if ((rhs->bits&(DECINF|DECNEG))==DECINF) {
    decSetMaxValue(res, set);                // is +ve
    // there is no status to set
    return res;
    }
  decNumberZero(&dtiny);                     // start with 0
  dtiny.lsu[0]=1;                            // make number that is ..
  dtiny.exponent=DEC_MIN_EMIN-1;             // .. smaller than tiniest
  workset.round=DEC_ROUND_FLOOR;
  decAddOp(res, rhs, &dtiny, &workset, DECNEG, &status);
  status&=DEC_Invalid_operation|DEC_sNaN;    // only sNaN Invalid please
  if (status!=0) decStatus(res, status, set);
  return res;
  } // decNumberNextMinus

/* ------------------------------------------------------------------ */
/* decNumberNextPlus -- next towards +Infinity                        */
/*                                                                    */
/*   This computes C = A + infinitesimal, rounded towards +Infinity   */
/*                                                                    */
/*   res is C, the result.  C may be A                                */
/*   rhs is A                                                         */
/*   set is the context                                               */
/*                                                                    */
/* This is a generalization of 754 NextUp.                            */
/* ------------------------------------------------------------------ */
decNumber * decNumberNextPlus(decNumber *res, const decNumber *rhs,
                              decContext *set) {
  decNumber dtiny;                           // constant
  decContext workset=*set;                   // work
  uInt status=0;                             // accumulator
  #if DECCHECK
  if (decCheckOperands(res, DECUNUSED, rhs, set)) return res;
  #endif

  // -Infinity is the special case
  if ((rhs->bits&(DECINF|DECNEG))==(DECINF|DECNEG)) {
    decSetMaxValue(res, set);
    res->bits=DECNEG;                        // negative
    // there is no status to set
    return res;
    }
  decNumberZero(&dtiny);                     // start with 0
  dtiny.lsu[0]=1;                            // make number that is ..
  dtiny.exponent=DEC_MIN_EMIN-1;             // .. smaller than tiniest
  workset.round=DEC_ROUND_CEILING;
  decAddOp(res, rhs, &dtiny, &workset, 0, &status);
  status&=DEC_Invalid_operation|DEC_sNaN;    // only sNaN Invalid please
  if (status!=0) decStatus(res, status, set);
  return res;
  } // decNumberNextPlus

/* ------------------------------------------------------------------ */
/* decNumberNextToward -- next towards rhs                            */
/*                                                                    */
/*   This computes C = A +/- infinitesimal, rounded towards           */
/*   +/-Infinity in the direction of B, as per 754-1985 nextafter     */
/*   modified during revision but dropped from 754-2008.              */
/*                                                                    */
/*   res is C, the result.  C may be A or B.                          */
/*   lhs is A                                                         */
/*   rhs is B                                                         */
/*   set is the context                                               */
/*                                                                    */
/* This is a generalization of 754-1985 NextAfter.                    */
/* ------------------------------------------------------------------ */
decNumber * decNumberNextToward(decNumber *res, const decNumber *lhs,
                                const decNumber *rhs, decContext *set) {
  decNumber dtiny;                           // constant
  decContext workset=*set;                   // work
  Int result;                                // ..
  uInt status=0;                             // accumulator
  #if DECCHECK
  if (decCheckOperands(res, lhs, rhs, set)) return res;
  #endif

  if (decNumberIsNaN(lhs) || decNumberIsNaN(rhs)) {
    decNaNs(res, lhs, rhs, set, &status);
    }
   else { // Is numeric, so no chance of sNaN Invalid, etc.
    result=decCompare(lhs, rhs, 0);     // sign matters
    if (result==BADINT) status|=DEC_Insufficient_storage; // rare
     else { // valid compare
      if (result==0) decNumberCopySign(res, lhs, rhs); // easy
       else { // differ: need NextPlus or NextMinus
        uByte sub;                      // add or subtract
        if (result<0) {                 // lhs<rhs, do nextplus
          // -Infinity is the special case
          if ((lhs->bits&(DECINF|DECNEG))==(DECINF|DECNEG)) {
            decSetMaxValue(res, set);
            res->bits=DECNEG;           // negative
            return res;                 // there is no status to set
            }
          workset.round=DEC_ROUND_CEILING;
          sub=0;                        // add, please
          } // plus
         else {                         // lhs>rhs, do nextminus
          // +Infinity is the special case
          if ((lhs->bits&(DECINF|DECNEG))==DECINF) {
            decSetMaxValue(res, set);
            return res;                 // there is no status to set
            }
          workset.round=DEC_ROUND_FLOOR;
          sub=DECNEG;                   // subtract, please
          } // minus
        decNumberZero(&dtiny);          // start with 0
        dtiny.lsu[0]=1;                 // make number that is ..
        dtiny.exponent=DEC_MIN_EMIN-1;  // .. smaller than tiniest
        decAddOp(res, lhs, &dtiny, &workset, sub, &status); // + or -
        // turn off exceptions if the result is a normal number
        // (including Nmin), otherwise let all status through
        if (decNumberIsNormal(res, set)) status=0;
        } // unequal
      } // compare OK
    } // numeric
  if (status!=0) decStatus(res, status, set);
  return res;
  } // decNumberNextToward

/* ------------------------------------------------------------------ */
/* decNumberOr -- OR two Numbers, digitwise                           */
/*                                                                    */
/*   This computes C = A | B                                          */
/*                                                                    */
/*   res is C, the result.  C may be A and/or B (e.g., X=X|X)         */
/*   lhs is A                                                         */
/*   rhs is B                                                         */
/*   set is the context (used for result length and error report)     */
/*                                                                    */
/* C must have space for set->digits digits.                          */
/*                                                                    */
/* Logical function restrictions apply (see above); a NaN is          */
/* returned with Invalid_operation if a restriction is violated.      */
/* ------------------------------------------------------------------ */
decNumber * decNumberOr(decNumber *res, const decNumber *lhs,
                        const decNumber *rhs, decContext *set) {
  const Unit *ua, *ub;                  // -> operands
  const Unit *msua, *msub;              // -> operand msus
  Unit  *uc, *msuc;                     // -> result and its msu
  Int   msudigs;                        // digits in res msu
  #if DECCHECK
  if (decCheckOperands(res, lhs, rhs, set)) return res;
  #endif

  if (lhs->exponent!=0 || decNumberIsSpecial(lhs) || decNumberIsNegative(lhs)
   || rhs->exponent!=0 || decNumberIsSpecial(rhs) || decNumberIsNegative(rhs)) {
    decStatus(res, DEC_Invalid_operation, set);
    return res;
    }
  // operands are valid
  ua=lhs->lsu;                          // bottom-up
  ub=rhs->lsu;                          // ..
  uc=res->lsu;                          // ..
  msua=ua+D2U(lhs->digits)-1;           // -> msu of lhs
  msub=ub+D2U(rhs->digits)-1;           // -> msu of rhs
  msuc=uc+D2U(set->digits)-1;           // -> msu of result
  msudigs=MSUDIGITS(set->digits);       // [faster than remainder]
  for (; uc<=msuc; ua++, ub++, uc++) {  // Unit loop
    Unit a, b;                          // extract units
    if (ua>msua) a=0;
     else a=*ua;
    if (ub>msub) b=0;
     else b=*ub;
    *uc=0;                              // can now write back
    if (a|b) {                          // maybe 1 bits to examine
      Int i, j;
      // This loop could be unrolled and/or use BIN2BCD tables
      for (i=0; i<DECDPUN; i++) {
        if ((a|b)&1) *uc=*uc+(Unit)powers[i];     // effect OR
        j=a%10;
        a=a/10;
        j|=b%10;
        b=b/10;
        if (j>1) {
          decStatus(res, DEC_Invalid_operation, set);
          return res;
          }
        if (uc==msuc && i==msudigs-1) break;      // just did final digit
        } // each digit
      } // non-zero
    } // each unit
  // [here uc-1 is the msu of the result]
  res->digits=decGetDigits(res->lsu, uc-res->lsu);
  res->exponent=0;                      // integer
  res->bits=0;                          // sign=0
  return res;  // [no status to set]
  } // decNumberOr

/* ------------------------------------------------------------------ */
/* decNumberPlus -- prefix plus operator                              */
/*                                                                    */
/*   This computes C = 0 + A                                          */
/*                                                                    */
/*   res is C, the result.  C may be A                                */
/*   rhs is A                                                         */
/*   set is the context                                               */
/*                                                                    */
/* See also decNumberCopy for a quiet bitwise version of this.        */
/* C must have space for set->digits digits.                          */
/* ------------------------------------------------------------------ */
/* This simply uses AddOp; Add will take fast path after preparing A. */
/* Performance is a concern here, as this routine is often used to    */
/* check operands and apply rounding and overflow/underflow testing.  */
/* ------------------------------------------------------------------ */
decNumber * decNumberPlus(decNumber *res, const decNumber *rhs,
                          decContext *set) {
  decNumber dzero;
  uInt status=0;                        // accumulator
  #if DECCHECK
  if (decCheckOperands(res, DECUNUSED, rhs, set)) return res;
  #endif

  decNumberZero(&dzero);                // make 0
  dzero.exponent=rhs->exponent;         // [no coefficient expansion]
  decAddOp(res, &dzero, rhs, set, 0, &status);
  if (status!=0) decStatus(res, status, set);
  #if DECCHECK
  decCheckInexact(res, set);
  #endif
  return res;
  } // decNumberPlus

/* ------------------------------------------------------------------ */
/* decNumberMultiply -- multiply two Numbers                          */
/*                                                                    */
/*   This computes C = A x B                                          */
/*                                                                    */
/*   res is C, the result.  C may be A and/or B (e.g., X=X+X)         */
/*   lhs is A                                                         */
/*   rhs is B                                                         */
/*   set is the context                                               */
/*                                                                    */
/* C must have space for set->digits digits.                          */
/* ------------------------------------------------------------------ */
decNumber * decNumberMultiply(decNumber *res, const decNumber *lhs,
                              const decNumber *rhs, decContext *set) {
  uInt status=0;                   // accumulator
  decMultiplyOp(res, lhs, rhs, set, &status);
  if (status!=0) decStatus(res, status, set);
  #if DECCHECK
  decCheckInexact(res, set);
  #endif
  return res;
  } // decNumberMultiply

/* ------------------------------------------------------------------ */
/* decNumberPower -- raise a number to a power                        */
/*                                                                    */
/*   This computes C = A ** B                                         */
/*                                                                    */
/*   res is C, the result.  C may be A and/or B (e.g., X=X**X)        */
/*   lhs is A                                                         */
/*   rhs is B                                                         */
/*   set is the context                                               */
/*                                                                    */
/* C must have space for set->digits digits.                          */
/*                                                                    */
/* Mathematical function restrictions apply (see above); a NaN is     */
/* returned with Invalid_operation if a restriction is violated.      */
/*                                                                    */
/* However, if 1999999997<=B<=999999999 and B is an integer then the  */
/* restrictions on A and the context are relaxed to the usual bounds, */
/* for compatibility with the earlier (integer power only) version    */
/* of this function.                                                  */
/*                                                                    */
/* When B is an integer, the result may be exact, even if rounded.    */
/*                                                                    */
/* The final result is rounded according to the context; it will      */
/* almost always be correctly rounded, but may be up to 1 ulp in      */
/* error in rare cases.                                               */
/* ------------------------------------------------------------------ */
decNumber * decNumberPower(decNumber *res, const decNumber *lhs,
                           const decNumber *rhs, decContext *set) {
  #if DECSUBSET
  decNumber *alloclhs=NULL;        // non-NULL if rounded lhs allocated
  decNumber *allocrhs=NULL;        // .., rhs
  #endif
  decNumber *allocdac=NULL;        // -> allocated acc buffer, iff used
  decNumber *allocinv=NULL;        // -> allocated 1/x buffer, iff used
  Int   reqdigits=set->digits;     // requested DIGITS
  Int   n;                         // rhs in binary
  Flag  rhsint=0;                  // 1 if rhs is an integer
  Flag  useint=0;                  // 1 if can use integer calculation
  Flag  isoddint=0;                // 1 if rhs is an integer and odd
  Int   i;                         // work
  #if DECSUBSET
  Int   dropped;                   // ..
  #endif
  uInt  needbytes;                 // buffer size needed
  Flag  seenbit;                   // seen a bit while powering
  Int   residue=0;                 // rounding residue
  uInt  status=0;                  // accumulators
  uByte bits=0;                    // result sign if errors
  decContext aset;                 // working context
  decNumber dnOne;                 // work value 1...
  // local accumulator buffer [a decNumber, with digits+elength+1 digits]
  decNumber dacbuff[D2N(DECBUFFER+9)];
  decNumber *dac=dacbuff;          // -> result accumulator
  // same again for possible 1/lhs calculation
  decNumber invbuff[D2N(DECBUFFER+9)];

  #if DECCHECK
  if (decCheckOperands(res, lhs, rhs, set)) return res;
  #endif

  do {                             // protect allocated storage
    #if DECSUBSET
    if (!set->extended) { // reduce operands and set status, as needed
      if (lhs->digits>reqdigits) {
        alloclhs=decRoundOperand(lhs, set, &status);
        if (alloclhs==NULL) break;
        lhs=alloclhs;
        }
      if (rhs->digits>reqdigits) {
        allocrhs=decRoundOperand(rhs, set, &status);
        if (allocrhs==NULL) break;
        rhs=allocrhs;
        }
      }
    #endif
    // [following code does not require input rounding]

    // handle NaNs and rhs Infinity (lhs infinity is harder)
    if (SPECIALARGS) {
      if (decNumberIsNaN(lhs) || decNumberIsNaN(rhs)) { // NaNs
        decNaNs(res, lhs, rhs, set, &status);
        break;}
      if (decNumberIsInfinite(rhs)) {   // rhs Infinity
        Flag rhsneg=rhs->bits&DECNEG;   // save rhs sign
        if (decNumberIsNegative(lhs)    // lhs<0
         && !decNumberIsZero(lhs))      // ..
          status|=DEC_Invalid_operation;
         else {                         // lhs >=0
          decNumberZero(&dnOne);        // set up 1
          dnOne.lsu[0]=1;
          decNumberCompare(dac, lhs, &dnOne, set); // lhs ? 1
          decNumberZero(res);           // prepare for 0/1/Infinity
          if (decNumberIsNegative(dac)) {    // lhs<1
            if (rhsneg) res->bits|=DECINF;   // +Infinity [else is +0]
            }
           else if (dac->lsu[0]==0) {        // lhs=1
            // 1**Infinity is inexact, so return fully-padded 1.0000
            Int shift=set->digits-1;
            *res->lsu=1;                     // was 0, make int 1
            res->digits=decShiftToMost(res->lsu, 1, shift);
            res->exponent=-shift;            // make 1.0000...
            status|=DEC_Inexact|DEC_Rounded; // deemed inexact
            }
           else {                            // lhs>1
            if (!rhsneg) res->bits|=DECINF;  // +Infinity [else is +0]
            }
          } // lhs>=0
        break;}
      // [lhs infinity drops through]
      } // specials

    // Original rhs may be an integer that fits and is in range
    n=decGetInt(rhs);
    if (n!=BADINT) {                    // it is an integer
      rhsint=1;                         // record the fact for 1**n
      isoddint=(Flag)n&1;               // [works even if big]
      if (n!=BIGEVEN && n!=BIGODD)      // can use integer path?
        useint=1;                       // looks good
      }

    if (decNumberIsNegative(lhs)        // -x ..
      && isoddint) bits=DECNEG;         // .. to an odd power

    // handle LHS infinity
    if (decNumberIsInfinite(lhs)) {     // [NaNs already handled]
      uByte rbits=rhs->bits;            // save
      decNumberZero(res);               // prepare
      if (n==0) *res->lsu=1;            // [-]Inf**0 => 1
       else {
        // -Inf**nonint -> error
        if (!rhsint && decNumberIsNegative(lhs)) {
          status|=DEC_Invalid_operation;     // -Inf**nonint is error
          break;}
        if (!(rbits & DECNEG)) bits|=DECINF; // was not a **-n
        // [otherwise will be 0 or -0]
        res->bits=bits;
        }
      break;}

    // similarly handle LHS zero
    if (decNumberIsZero(lhs)) {
      if (n==0) {                            // 0**0 => Error
        #if DECSUBSET
        if (!set->extended) {                // [unless subset]
          decNumberZero(res);
          *res->lsu=1;                       // return 1
          break;}
        #endif
        status|=DEC_Invalid_operation;
        }
       else {                                // 0**x
        uByte rbits=rhs->bits;               // save
        if (rbits & DECNEG) {                // was a 0**(-n)
          #if DECSUBSET
          if (!set->extended) {              // [bad if subset]
            status|=DEC_Invalid_operation;
            break;}
          #endif
          bits|=DECINF;
          }
        decNumberZero(res);                  // prepare
        // [otherwise will be 0 or -0]
        res->bits=bits;
        }
      break;}

    // here both lhs and rhs are finite; rhs==0 is handled in the
    // integer path.  Next handle the non-integer cases
    if (!useint) {                      // non-integral rhs
      // any -ve lhs is bad, as is either operand or context out of
      // bounds
      if (decNumberIsNegative(lhs)) {
        status|=DEC_Invalid_operation;
        break;}
      if (decCheckMath(lhs, set, &status)
       || decCheckMath(rhs, set, &status)) break; // variable status

      decContextDefault(&aset, DEC_INIT_DECIMAL64); // clean context
      aset.emax=DEC_MAX_MATH;           // usual bounds
      aset.emin=-DEC_MAX_MATH;          // ..
      aset.clamp=0;                     // and no concrete format

      // calculate the result using exp(ln(lhs)*rhs), which can
      // all be done into the accumulator, dac.  The precision needed
      // is enough to contain the full information in the lhs (which
      // is the total digits, including exponent), or the requested
      // precision, if larger, + 4; 6 is used for the exponent
      // maximum length, and this is also used when it is shorter
      // than the requested digits as it greatly reduces the >0.5 ulp
      // cases at little cost (because Ln doubles digits each
      // iteration so a few extra digits rarely causes an extra
      // iteration)
      aset.digits=MAXI(lhs->digits, set->digits)+6+4;
      } // non-integer rhs

     else { // rhs is in-range integer
      if (n==0) {                       // x**0 = 1
        // (0**0 was handled above)
        decNumberZero(res);             // result=1
        *res->lsu=1;                    // ..
        break;}
      // rhs is a non-zero integer
      if (n<0) n=-n;                    // use abs(n)

      aset=*set;                        // clone the context
      aset.round=DEC_ROUND_HALF_EVEN;   // internally use balanced
      // calculate the working DIGITS
      aset.digits=reqdigits+(rhs->digits+rhs->exponent)+2;
      #if DECSUBSET
      if (!set->extended) aset.digits--;     // use classic precision
      #endif
      // it's an error if this is more than can be handled
      if (aset.digits>DECNUMMAXP) {status|=DEC_Invalid_operation; break;}
      } // integer path

    // aset.digits is the count of digits for the accumulator needed
    // if accumulator is too long for local storage, then allocate
    needbytes=sizeof(decNumber)+(D2U(aset.digits)-1)*sizeof(Unit);
    // [needbytes also used below if 1/lhs needed]
    if (needbytes>sizeof(dacbuff)) {
      allocdac=(decNumber *)malloc(needbytes);
      if (allocdac==NULL) {   // hopeless -- abandon
        status|=DEC_Insufficient_storage;
        break;}
      dac=allocdac;           // use the allocated space
      }
    // here, aset is set up and accumulator is ready for use

    if (!useint) {                           // non-integral rhs
      // x ** y; special-case x=1 here as it will otherwise always
      // reduce to integer 1; decLnOp has a fastpath which detects
      // the case of x=1
      decLnOp(dac, lhs, &aset, &status);     // dac=ln(lhs)
      // [no error possible, as lhs 0 already handled]
      if (ISZERO(dac)) {                     // x==1, 1.0, etc.
        // need to return fully-padded 1.0000 etc., but rhsint->1
        *dac->lsu=1;                         // was 0, make int 1
        if (!rhsint) {                       // add padding
          Int shift=set->digits-1;
          dac->digits=decShiftToMost(dac->lsu, 1, shift);
          dac->exponent=-shift;              // make 1.0000...
          status|=DEC_Inexact|DEC_Rounded;   // deemed inexact
          }
        }
       else {
        decMultiplyOp(dac, dac, rhs, &aset, &status);  // dac=dac*rhs
        decExpOp(dac, dac, &aset, &status);            // dac=exp(dac)
        }
      // and drop through for final rounding
      } // non-integer rhs

     else {                             // carry on with integer
      decNumberZero(dac);               // acc=1
      *dac->lsu=1;                      // ..

      // if a negative power the constant 1 is needed, and if not subset
      // invert the lhs now rather than inverting the result later
      if (decNumberIsNegative(rhs)) {   // was a **-n [hence digits>0]
        decNumber *inv=invbuff;         // asssume use fixed buffer
        decNumberCopy(&dnOne, dac);     // dnOne=1;  [needed now or later]
        #if DECSUBSET
        if (set->extended) {            // need to calculate 1/lhs
        #endif
          // divide lhs into 1, putting result in dac [dac=1/dac]
          decDivideOp(dac, &dnOne, lhs, &aset, DIVIDE, &status);
          // now locate or allocate space for the inverted lhs
          if (needbytes>sizeof(invbuff)) {
            allocinv=(decNumber *)malloc(needbytes);
            if (allocinv==NULL) {       // hopeless -- abandon
              status|=DEC_Insufficient_storage;
              break;}
            inv=allocinv;               // use the allocated space
            }
          // [inv now points to big-enough buffer or allocated storage]
          decNumberCopy(inv, dac);      // copy the 1/lhs
          decNumberCopy(dac, &dnOne);   // restore acc=1
          lhs=inv;                      // .. and go forward with new lhs
        #if DECSUBSET
          }
        #endif
        }

      // Raise-to-the-power loop...
      seenbit=0;                   // set once a 1-bit is encountered
      for (i=1;;i++){              // for each bit [top bit ignored]
        // abandon if had overflow or terminal underflow
        if (status & (DEC_Overflow|DEC_Underflow)) { // interesting?
          if (status&DEC_Overflow || ISZERO(dac)) break;
          }
        // [the following two lines revealed an optimizer bug in a C++
        // compiler, with symptom: 5**3 -> 25, when n=n+n was used]
        n=n<<1;                    // move next bit to testable position
        if (n<0) {                 // top bit is set
          seenbit=1;               // OK, significant bit seen
          decMultiplyOp(dac, dac, lhs, &aset, &status); // dac=dac*x
          }
        if (i==31) break;          // that was the last bit
        if (!seenbit) continue;    // no need to square 1
        decMultiplyOp(dac, dac, dac, &aset, &status); // dac=dac*dac [square]
        } /*i*/ // 32 bits

      // complete internal overflow or underflow processing
      if (status & (DEC_Overflow|DEC_Underflow)) {
        #if DECSUBSET
        // If subset, and power was negative, reverse the kind of -erflow
        // [1/x not yet done]
        if (!set->extended && decNumberIsNegative(rhs)) {
          if (status & DEC_Overflow)
            status^=DEC_Overflow | DEC_Underflow | DEC_Subnormal;
           else { // trickier -- Underflow may or may not be set
            status&=~(DEC_Underflow | DEC_Subnormal); // [one or both]
            status|=DEC_Overflow;
            }
          }
        #endif
        dac->bits=(dac->bits & ~DECNEG) | bits; // force correct sign
        // round subnormals [to set.digits rather than aset.digits]
        // or set overflow result similarly as required
        decFinalize(dac, set, &residue, &status);
        decNumberCopy(res, dac);   // copy to result (is now OK length)
        break;
        }

      #if DECSUBSET
      if (!set->extended &&                  // subset math
          decNumberIsNegative(rhs)) {        // was a **-n [hence digits>0]
        // so divide result into 1 [dac=1/dac]
        decDivideOp(dac, &dnOne, dac, &aset, DIVIDE, &status);
        }
      #endif
      } // rhs integer path

    // reduce result to the requested length and copy to result
    decCopyFit(res, dac, set, &residue, &status);
    decFinish(res, set, &residue, &status);  // final cleanup
    #if DECSUBSET
    if (!set->extended) decTrim(res, set, 0, 1, &dropped); // trailing zeros
    #endif
    } while(0);                         // end protected

  if (allocdac!=NULL) free(allocdac);   // drop any storage used
  if (allocinv!=NULL) free(allocinv);   // ..
  #if DECSUBSET
  if (alloclhs!=NULL) free(alloclhs);   // ..
  if (allocrhs!=NULL) free(allocrhs);   // ..
  #endif
  if (status!=0) decStatus(res, status, set);
  #if DECCHECK
  decCheckInexact(res, set);
  #endif
  return res;
  } // decNumberPower

/* ------------------------------------------------------------------ */
/* decNumberQuantize -- force exponent to requested value             */
/*                                                                    */
/*   This computes C = op(A, B), where op adjusts the coefficient     */
/*   of C (by rounding or shifting) such that the exponent (-scale)   */
/*   of C has exponent of B.  The numerical value of C will equal A,  */
/*   except for the effects of any rounding that occurred.            */
/*                                                                    */
/*   res is C, the result.  C may be A or B                           */
/*   lhs is A, the number to adjust                                   */
/*   rhs is B, the number with exponent to match                      */
/*   set is the context                                               */
/*                                                                    */
/* C must have space for set->digits digits.                          */
/*                                                                    */
/* Unless there is an error or the result is infinite, the exponent   */
/* after the operation is guaranteed to be equal to that of B.        */
/* ------------------------------------------------------------------ */
decNumber * decNumberQuantize(decNumber *res, const decNumber *lhs,
                              const decNumber *rhs, decContext *set) {
  uInt status=0;                        // accumulator
  decQuantizeOp(res, lhs, rhs, set, 1, &status);
  if (status!=0) decStatus(res, status, set);
  return res;
  } // decNumberQuantize

/* ------------------------------------------------------------------ */
/* decNumberReduce -- remove trailing zeros                           */
/*                                                                    */
/*   This computes C = 0 + A, and normalizes the result               */
/*                                                                    */
/*   res is C, the result.  C may be A                                */
/*   rhs is A                                                         */
/*   set is the context                                               */
/*                                                                    */
/* C must have space for set->digits digits.                          */
/* ------------------------------------------------------------------ */
// Previously known as Normalize
decNumber * decNumberNormalize(decNumber *res, const decNumber *rhs,
                               decContext *set) {
  return decNumberReduce(res, rhs, set);
  } // decNumberNormalize

decNumber * decNumberReduce(decNumber *res, const decNumber *rhs,
                            decContext *set) {
  #if DECSUBSET
  decNumber *allocrhs=NULL;        // non-NULL if rounded rhs allocated
  #endif
  uInt status=0;                   // as usual
  Int  residue=0;                  // as usual
  Int  dropped;                    // work

  #if DECCHECK
  if (decCheckOperands(res, DECUNUSED, rhs, set)) return res;
  #endif

  do {                             // protect allocated storage
    #if DECSUBSET
    if (!set->extended) {
      // reduce operand and set lostDigits status, as needed
      if (rhs->digits>set->digits) {
        allocrhs=decRoundOperand(rhs, set, &status);
        if (allocrhs==NULL) break;
        rhs=allocrhs;
        }
      }
    #endif
    // [following code does not require input rounding]

    // Infinities copy through; NaNs need usual treatment
    if (decNumberIsNaN(rhs)) {
      decNaNs(res, rhs, NULL, set, &status);
      break;
      }

    // reduce result to the requested length and copy to result
    decCopyFit(res, rhs, set, &residue, &status); // copy & round
    decFinish(res, set, &residue, &status);       // cleanup/set flags
    decTrim(res, set, 1, 0, &dropped);            // normalize in place
                                                  // [may clamp]
    } while(0);                              // end protected

  #if DECSUBSET
  if (allocrhs !=NULL) free(allocrhs);       // ..
  #endif
  if (status!=0) decStatus(res, status, set);// then report status
  return res;
  } // decNumberReduce

/* ------------------------------------------------------------------ */
/* decNumberRescale -- force exponent to requested value              */
/*                                                                    */
/*   This computes C = op(A, B), where op adjusts the coefficient     */
/*   of C (by rounding or shifting) such that the exponent (-scale)   */
/*   of C has the value B.  The numerical value of C will equal A,    */
/*   except for the effects of any rounding that occurred.            */
/*                                                                    */
/*   res is C, the result.  C may be A or B                           */
/*   lhs is A, the number to adjust                                   */
/*   rhs is B, the requested exponent                                 */
/*   set is the context                                               */
/*                                                                    */
/* C must have space for set->digits digits.                          */
/*                                                                    */
/* Unless there is an error or the result is infinite, the exponent   */
/* after the operation is guaranteed to be equal to B.                */
/* ------------------------------------------------------------------ */
decNumber * decNumberRescale(decNumber *res, const decNumber *lhs,
                             const decNumber *rhs, decContext *set) {
  uInt status=0;                        // accumulator
  decQuantizeOp(res, lhs, rhs, set, 0, &status);
  if (status!=0) decStatus(res, status, set);
  return res;
  } // decNumberRescale

/* ------------------------------------------------------------------ */
/* decNumberRemainder -- divide and return remainder                  */
/*                                                                    */
/*   This computes C = A % B                                          */
/*                                                                    */
/*   res is C, the result.  C may be A and/or B (e.g., X=X%X)         */
/*   lhs is A                                                         */
/*   rhs is B                                                         */
/*   set is the context                                               */
/*                                                                    */
/* C must have space for set->digits digits.                          */
/* ------------------------------------------------------------------ */
decNumber * decNumberRemainder(decNumber *res, const decNumber *lhs,
                               const decNumber *rhs, decContext *set) {
  uInt status=0;                        // accumulator
  decDivideOp(res, lhs, rhs, set, REMAINDER, &status);
  if (status!=0) decStatus(res, status, set);
  #if DECCHECK
  decCheckInexact(res, set);
  #endif
  return res;
  } // decNumberRemainder

/* ------------------------------------------------------------------ */
/* decNumberRemainderNear -- divide and return remainder from nearest */
/*                                                                    */
/*   This computes C = A % B, where % is the IEEE remainder operator  */
/*                                                                    */
/*   res is C, the result.  C may be A and/or B (e.g., X=X%X)         */
/*   lhs is A                                                         */
/*   rhs is B                                                         */
/*   set is the context                                               */
/*                                                                    */
/* C must have space for set->digits digits.                          */
/* ------------------------------------------------------------------ */
decNumber * decNumberRemainderNear(decNumber *res, const decNumber *lhs,
                                   const decNumber *rhs, decContext *set) {
  uInt status=0;                        // accumulator
  decDivideOp(res, lhs, rhs, set, REMNEAR, &status);
  if (status!=0) decStatus(res, status, set);
  #if DECCHECK
  decCheckInexact(res, set);
  #endif
  return res;
  } // decNumberRemainderNear

/* ------------------------------------------------------------------ */
/* decNumberRotate -- rotate the coefficient of a Number left/right   */
/*                                                                    */
/*   This computes C = A rot B  (in base ten and rotating set->digits */
/*   digits).                                                         */
/*                                                                    */
/*   res is C, the result.  C may be A and/or B (e.g., X=XrotX)       */
/*   lhs is A                                                         */
/*   rhs is B, the number of digits to rotate (-ve to right)          */
/*   set is the context                                               */
/*                                                                    */
/* The digits of the coefficient of A are rotated to the left (if B   */
/* is positive) or to the right (if B is negative) without adjusting  */
/* the exponent or the sign of A.  If lhs->digits is less than        */
/* set->digits the coefficient is padded with zeros on the left       */
/* before the rotate.  Any leading zeros in the result are removed    */
/* as usual.                                                          */
/*                                                                    */
/* B must be an integer (q=0) and in the range -set->digits through   */
/* +set->digits.                                                      */
/* C must have space for set->digits digits.                          */
/* NaNs are propagated as usual.  Infinities are unaffected (but      */
/* B must be valid).  No status is set unless B is invalid or an      */
/* operand is an sNaN.                                                */
/* ------------------------------------------------------------------ */
decNumber * decNumberRotate(decNumber *res, const decNumber *lhs,
                           const decNumber *rhs, decContext *set) {
  uInt status=0;              // accumulator
  Int  rotate;                // rhs as an Int

  #if DECCHECK
  if (decCheckOperands(res, lhs, rhs, set)) return res;
  #endif

  // NaNs propagate as normal
  if (decNumberIsNaN(lhs) || decNumberIsNaN(rhs))
    decNaNs(res, lhs, rhs, set, &status);
   // rhs must be an integer
   else if (decNumberIsInfinite(rhs) || rhs->exponent!=0)
    status=DEC_Invalid_operation;
   else { // both numeric, rhs is an integer
    rotate=decGetInt(rhs);                   // [cannot fail]
    if (rotate==BADINT                       // something bad ..
     || rotate==BIGODD || rotate==BIGEVEN    // .. very big ..
     || abs(rotate)>set->digits)             // .. or out of range
      status=DEC_Invalid_operation;
     else {                                  // rhs is OK
      decNumberCopy(res, lhs);
      // convert -ve rotate to equivalent positive rotation
      if (rotate<0) rotate=set->digits+rotate;
      if (rotate!=0 && rotate!=set->digits   // zero or full rotation
       && !decNumberIsInfinite(res)) {       // lhs was infinite
        // left-rotate to do; 0 < rotate < set->digits
        uInt units, shift;                   // work
        uInt msudigits;                      // digits in result msu
        Unit *msu=res->lsu+D2U(res->digits)-1;    // current msu
        Unit *msumax=res->lsu+D2U(set->digits)-1; // rotation msu
        for (msu++; msu<=msumax; msu++) *msu=0;   // ensure high units=0
        res->digits=set->digits;                  // now full-length
        msudigits=MSUDIGITS(res->digits);         // actual digits in msu

        // rotation here is done in-place, in three steps
        // 1. shift all to least up to one unit to unit-align final
        //    lsd [any digits shifted out are rotated to the left,
        //    abutted to the original msd (which may require split)]
        //
        //    [if there are no whole units left to rotate, the
        //    rotation is now complete]
        //
        // 2. shift to least, from below the split point only, so that
        //    the final msd is in the right place in its Unit [any
        //    digits shifted out will fit exactly in the current msu,
        //    left aligned, no split required]
        //
        // 3. rotate all the units by reversing left part, right
        //    part, and then whole
        //
        // example: rotate right 8 digits (2 units + 2), DECDPUN=3.
        //
        //   start: 00a bcd efg hij klm npq
        //
        //      1a  000 0ab cde fgh|ijk lmn [pq saved]
        //      1b  00p qab cde fgh|ijk lmn
        //
        //      2a  00p qab cde fgh|00i jkl [mn saved]
        //      2b  mnp qab cde fgh|00i jkl
        //
        //      3a  fgh cde qab mnp|00i jkl
        //      3b  fgh cde qab mnp|jkl 00i
        //      3c  00i jkl mnp qab cde fgh

        // Step 1: amount to shift is the partial right-rotate count
        rotate=set->digits-rotate;      // make it right-rotate
        units=rotate/DECDPUN;           // whole units to rotate
        shift=rotate%DECDPUN;           // left-over digits count
        if (shift>0) {                  // not an exact number of units
          uInt save=res->lsu[0]%powers[shift];    // save low digit(s)
          decShiftToLeast(res->lsu, D2U(res->digits), shift);
          if (shift>msudigits) {        // msumax-1 needs >0 digits
            uInt rem=save%powers[shift-msudigits];// split save
            *msumax=(Unit)(save/powers[shift-msudigits]); // and insert
            *(msumax-1)=*(msumax-1)
                       +(Unit)(rem*powers[DECDPUN-(shift-msudigits)]); // ..
            }
           else { // all fits in msumax
            *msumax=*msumax+(Unit)(save*powers[msudigits-shift]); // [maybe *1]
            }
          } // digits shift needed

        // If whole units to rotate...
        if (units>0) {                  // some to do
          // Step 2: the units to touch are the whole ones in rotate,
          //   if any, and the shift is DECDPUN-msudigits (which may be
          //   0, again)
          shift=DECDPUN-msudigits;
          if (shift>0) {                // not an exact number of units
            uInt save=res->lsu[0]%powers[shift];  // save low digit(s)
            decShiftToLeast(res->lsu, units, shift);
            *msumax=*msumax+(Unit)(save*powers[msudigits]);
            } // partial shift needed

          // Step 3: rotate the units array using triple reverse
          // (reversing is easy and fast)
          decReverse(res->lsu+units, msumax);     // left part
          decReverse(res->lsu, res->lsu+units-1); // right part
          decReverse(res->lsu, msumax);           // whole
          } // whole units to rotate
        // the rotation may have left an undetermined number of zeros
        // on the left, so true length needs to be calculated
        res->digits=decGetDigits(res->lsu, msumax-res->lsu+1);
        } // rotate needed
      } // rhs OK
    } // numerics
  if (status!=0) decStatus(res, status, set);
  return res;
  } // decNumberRotate

/* ------------------------------------------------------------------ */
/* decNumberSameQuantum -- test for equal exponents                   */
/*                                                                    */
/*   res is the result number, which will contain either 0 or 1       */
/*   lhs is a number to test                                          */
/*   rhs is the second (usually a pattern)                            */
/*                                                                    */
/* No errors are possible and no context is needed.                   */
/* ------------------------------------------------------------------ */
decNumber * decNumberSameQuantum(decNumber *res, const decNumber *lhs,
                                 const decNumber *rhs) {
  Unit ret=0;                      // return value

  #if DECCHECK
  if (decCheckOperands(res, lhs, rhs, DECUNCONT)) return res;
  #endif

  if (SPECIALARGS) {
    if (decNumberIsNaN(lhs) && decNumberIsNaN(rhs)) ret=1;
     else if (decNumberIsInfinite(lhs) && decNumberIsInfinite(rhs)) ret=1;
     // [anything else with a special gives 0]
    }
   else if (lhs->exponent==rhs->exponent) ret=1;

  decNumberZero(res);              // OK to overwrite an operand now
  *res->lsu=ret;
  return res;
  } // decNumberSameQuantum

/* ------------------------------------------------------------------ */
/* decNumberScaleB -- multiply by a power of 10                       */
/*                                                                    */
/* This computes C = A x 10**B where B is an integer (q=0) with       */
/* maximum magnitude 2*(emax+digits)                                  */
/*                                                                    */
/*   res is C, the result.  C may be A or B                           */
/*   lhs is A, the number to adjust                                   */
/*   rhs is B, the requested power of ten to use                      */
/*   set is the context                                               */
/*                                                                    */
/* C must have space for set->digits digits.                          */
/*                                                                    */
/* The result may underflow or overflow.                              */
/* ------------------------------------------------------------------ */
decNumber * decNumberScaleB(decNumber *res, const decNumber *lhs,
                            const decNumber *rhs, decContext *set) {
  Int  reqexp;                // requested exponent change [B]
  uInt status=0;              // accumulator
  Int  residue;               // work

  #if DECCHECK
  if (decCheckOperands(res, lhs, rhs, set)) return res;
  #endif

  // Handle special values except lhs infinite
  if (decNumberIsNaN(lhs) || decNumberIsNaN(rhs))
    decNaNs(res, lhs, rhs, set, &status);
    // rhs must be an integer
   else if (decNumberIsInfinite(rhs) || rhs->exponent!=0)
    status=DEC_Invalid_operation;
   else {
    // lhs is a number; rhs is a finite with q==0
    reqexp=decGetInt(rhs);                   // [cannot fail]
    // maximum range is larger than getInt can handle, so this is
    // more restrictive than the specification
    if (reqexp==BADINT                       // something bad ..
     || reqexp==BIGODD || reqexp==BIGEVEN    // it was huge
     || (abs(reqexp)+1)/2>(set->digits+set->emax)) // .. or out of range
      status=DEC_Invalid_operation;
     else {                                  // rhs is OK
      decNumberCopy(res, lhs);               // all done if infinite lhs
      if (!decNumberIsInfinite(res)) {       // prepare to scale
        Int exp=res->exponent;               // save for overflow test
        res->exponent+=reqexp;               // adjust the exponent
        if (((exp^reqexp)>=0)                // same sign ...
         && ((exp^res->exponent)<0)) {       // .. but result had different
          // the calculation overflowed, so force right treatment
          if (exp<0) res->exponent=DEC_MIN_EMIN-DEC_MAX_DIGITS;
           else      res->exponent=DEC_MAX_EMAX+1;
          }
        residue=0;
        decFinalize(res, set, &residue, &status); // final check
        } // finite LHS
      } // rhs OK
    } // rhs finite
  if (status!=0) decStatus(res, status, set);
  return res;
  } // decNumberScaleB

/* ------------------------------------------------------------------ */
/* decNumberShift -- shift the coefficient of a Number left or right  */
/*                                                                    */
/*   This computes C = A << B or C = A >> -B  (in base ten).          */
/*                                                                    */
/*   res is C, the result.  C may be A and/or B (e.g., X=X<<X)        */
/*   lhs is A                                                         */
/*   rhs is B, the number of digits to shift (-ve to right)           */
/*   set is the context                                               */
/*                                                                    */
/* The digits of the coefficient of A are shifted to the left (if B   */
/* is positive) or to the right (if B is negative) without adjusting  */
/* the exponent or the sign of A.                                     */
/*                                                                    */
/* B must be an integer (q=0) and in the range -set->digits through   */
/* +set->digits.                                                      */
/* C must have space for set->digits digits.                          */
/* NaNs are propagated as usual.  Infinities are unaffected (but      */
/* B must be valid).  No status is set unless B is invalid or an      */
/* operand is an sNaN.                                                */
/* ------------------------------------------------------------------ */
decNumber * decNumberShift(decNumber *res, const decNumber *lhs,
                           const decNumber *rhs, decContext *set) {
  uInt status=0;              // accumulator
  Int  shift;                 // rhs as an Int

  #if DECCHECK
  if (decCheckOperands(res, lhs, rhs, set)) return res;
  #endif

  // NaNs propagate as normal
  if (decNumberIsNaN(lhs) || decNumberIsNaN(rhs))
    decNaNs(res, lhs, rhs, set, &status);
   // rhs must be an integer
   else if (decNumberIsInfinite(rhs) || rhs->exponent!=0)
    status=DEC_Invalid_operation;
   else { // both numeric, rhs is an integer
    shift=decGetInt(rhs);                    // [cannot fail]
    if (shift==BADINT                        // something bad ..
     || shift==BIGODD || shift==BIGEVEN      // .. very big ..
     || abs(shift)>set->digits)              // .. or out of range
      status=DEC_Invalid_operation;
     else {                                  // rhs is OK
      decNumberCopy(res, lhs);
      if (shift!=0 && !decNumberIsInfinite(res)) { // something to do
        if (shift>0) {                       // to left
          if (shift==set->digits) {          // removing all
            *res->lsu=0;                     // so place 0
            res->digits=1;                   // ..
            }
           else {                            //
            // first remove leading digits if necessary
            if (res->digits+shift>set->digits) {
              decDecap(res, res->digits+shift-set->digits);
              // that updated res->digits; may have gone to 1 (for a
              // single digit or for zero
              }
            if (res->digits>1 || *res->lsu)  // if non-zero..
              res->digits=decShiftToMost(res->lsu, res->digits, shift);
            } // partial left
          } // left
         else { // to right
          if (-shift>=res->digits) {         // discarding all
            *res->lsu=0;                     // so place 0
            res->digits=1;                   // ..
            }
           else {
            decShiftToLeast(res->lsu, D2U(res->digits), -shift);
            res->digits-=(-shift);
            }
          } // to right
        } // non-0 non-Inf shift
      } // rhs OK
    } // numerics
  if (status!=0) decStatus(res, status, set);
  return res;
  } // decNumberShift

/* ------------------------------------------------------------------ */
/* decNumberSquareRoot -- square root operator                        */
/*                                                                    */
/*   This computes C = squareroot(A)                                  */
/*                                                                    */
/*   res is C, the result.  C may be A                                */
/*   rhs is A                                                         */
/*   set is the context; note that rounding mode has no effect        */
/*                                                                    */
/* C must have space for set->digits digits.                          */
/* ------------------------------------------------------------------ */
/* This uses the following varying-precision algorithm in:            */
/*                                                                    */
/*   Properly Rounded Variable Precision Square Root, T. E. Hull and  */
/*   A. Abrham, ACM Transactions on Mathematical Software, Vol 11 #3, */
/*   pp229-237, ACM, September 1985.                                  */
/*                                                                    */
/* The square-root is calculated using Newton's method, after which   */
/* a check is made to ensure the result is correctly rounded.         */
/*                                                                    */
/* % [Reformatted original Numerical Turing source code follows.]     */
/* function sqrt(x : real) : real                                     */
/* % sqrt(x) returns the properly rounded approximation to the square */
/* % root of x, in the precision of the calling environment, or it    */
/* % fails if x < 0.                                                  */
/* % t e hull and a abrham, august, 1984                              */
/* if x <= 0 then                                                     */
/*   if x < 0 then                                                    */
/*     assert false                                                   */
/*   else                                                             */
/*     result 0                                                       */
/*   end if                                                           */
/* end if                                                             */
/* var f := setexp(x, 0)  % fraction part of x   [0.1 <= x < 1]       */
/* var e := getexp(x)     % exponent part of x                        */
/* var approx : real                                                  */
/* if e mod 2 = 0  then                                               */
/*   approx := .259 + .819 * f   % approx to root of f                */
/* else                                                               */
/*   f := f/l0                   % adjustments                        */
/*   e := e + 1                  %   for odd                          */
/*   approx := .0819 + 2.59 * f  %   exponent                         */
/* end if                                                             */
/*                                                                    */
/* var p:= 3                                                          */
/* const maxp := currentprecision + 2                                 */
/* loop                                                               */
/*   p := min(2*p - 2, maxp)     % p = 4,6,10, . . . , maxp           */
/*   precision p                                                      */
/*   approx := .5 * (approx + f/approx)                               */
/*   exit when p = maxp                                               */
/* end loop                                                           */
/*                                                                    */
/* % approx is now within 1 ulp of the properly rounded square root   */
/* % of f; to ensure proper rounding, compare squares of (approx -    */
/* % l/2 ulp) and (approx + l/2 ulp) with f.                          */
/* p := currentprecision                                              */
/* begin                                                              */
/*   precision p + 2                                                  */
/*   const approxsubhalf := approx - setexp(.5, -p)                   */
/*   if mulru(approxsubhalf, approxsubhalf) > f then                  */
/*     approx := approx - setexp(.l, -p + 1)                          */
/*   else                                                             */
/*     const approxaddhalf := approx + setexp(.5, -p)                 */
/*     if mulrd(approxaddhalf, approxaddhalf) < f then                */
/*       approx := approx + setexp(.l, -p + 1)                        */
/*     end if                                                         */
/*   end if                                                           */
/* end                                                                */
/* result setexp(approx, e div 2)  % fix exponent                     */
/* end sqrt                                                           */
/* ------------------------------------------------------------------ */
decNumber * decNumberSquareRoot(decNumber *res, const decNumber *rhs,
                                decContext *set) {
  decContext workset, approxset;   // work contexts
  decNumber dzero;                 // used for constant zero
  Int  maxp;                       // largest working precision
  Int  workp;                      // working precision
  Int  residue=0;                  // rounding residue
  uInt status=0, ignore=0;         // status accumulators
  uInt rstatus;                    // ..
  Int  exp;                        // working exponent
  Int  ideal;                      // ideal (preferred) exponent
  Int  needbytes;                  // work
  Int  dropped;                    // ..

  #if DECSUBSET
  decNumber *allocrhs=NULL;        // non-NULL if rounded rhs allocated
  #endif
  // buffer for f [needs +1 in case DECBUFFER 0]
  decNumber buff[D2N(DECBUFFER+1)];
  // buffer for a [needs +2 to match likely maxp]
  decNumber bufa[D2N(DECBUFFER+2)];
  // buffer for temporary, b [must be same size as a]
  decNumber bufb[D2N(DECBUFFER+2)];
  decNumber *allocbuff=NULL;       // -> allocated buff, iff allocated
  decNumber *allocbufa=NULL;       // -> allocated bufa, iff allocated
  decNumber *allocbufb=NULL;       // -> allocated bufb, iff allocated
  decNumber *f=buff;               // reduced fraction
  decNumber *a=bufa;               // approximation to result
  decNumber *b=bufb;               // intermediate result
  // buffer for temporary variable, up to 3 digits
  decNumber buft[D2N(3)];
  decNumber *t=buft;               // up-to-3-digit constant or work

  #if DECCHECK
  if (decCheckOperands(res, DECUNUSED, rhs, set)) return res;
  #endif

  do {                             // protect allocated storage
    #if DECSUBSET
    if (!set->extended) {
      // reduce operand and set lostDigits status, as needed
      if (rhs->digits>set->digits) {
        allocrhs=decRoundOperand(rhs, set, &status);
        if (allocrhs==NULL) break;
        // [Note: 'f' allocation below could reuse this buffer if
        // used, but as this is rare they are kept separate for clarity.]
        rhs=allocrhs;
        }
      }
    #endif
    // [following code does not require input rounding]

    // handle infinities and NaNs
    if (SPECIALARG) {
      if (decNumberIsInfinite(rhs)) {         // an infinity
        if (decNumberIsNegative(rhs)) status|=DEC_Invalid_operation;
         else decNumberCopy(res, rhs);        // +Infinity
        }
       else decNaNs(res, rhs, NULL, set, &status); // a NaN
      break;
      }

    // calculate the ideal (preferred) exponent [floor(exp/2)]
    // [It would be nicer to write: ideal=rhs->exponent>>1, but this
    // generates a compiler warning.  Generated code is the same.]
    ideal=(rhs->exponent&~1)/2;         // target

    // handle zeros
    if (ISZERO(rhs)) {
      decNumberCopy(res, rhs);          // could be 0 or -0
      res->exponent=ideal;              // use the ideal [safe]
      // use decFinish to clamp any out-of-range exponent, etc.
      decFinish(res, set, &residue, &status);
      break;
      }

    // any other -x is an oops
    if (decNumberIsNegative(rhs)) {
      status|=DEC_Invalid_operation;
      break;
      }

    // space is needed for three working variables
    //   f -- the same precision as the RHS, reduced to 0.01->0.99...
    //   a -- Hull's approximation -- precision, when assigned, is
    //        currentprecision+1 or the input argument precision,
    //        whichever is larger (+2 for use as temporary)
    //   b -- intermediate temporary result (same size as a)
    // if any is too long for local storage, then allocate
    workp=MAXI(set->digits+1, rhs->digits);  // actual rounding precision
    workp=MAXI(workp, 7);                    // at least 7 for low cases
    maxp=workp+2;                            // largest working precision

    needbytes=sizeof(decNumber)+(D2U(rhs->digits)-1)*sizeof(Unit);
    if (needbytes>(Int)sizeof(buff)) {
      allocbuff=(decNumber *)malloc(needbytes);
      if (allocbuff==NULL) {  // hopeless -- abandon
        status|=DEC_Insufficient_storage;
        break;}
      f=allocbuff;            // use the allocated space
      }
    // a and b both need to be able to hold a maxp-length number
    needbytes=sizeof(decNumber)+(D2U(maxp)-1)*sizeof(Unit);
    if (needbytes>(Int)sizeof(bufa)) {            // [same applies to b]
      allocbufa=(decNumber *)malloc(needbytes);
      allocbufb=(decNumber *)malloc(needbytes);
      if (allocbufa==NULL || allocbufb==NULL) {   // hopeless
        status|=DEC_Insufficient_storage;
        break;}
      a=allocbufa;            // use the allocated spaces
      b=allocbufb;            // ..
      }

    // copy rhs -> f, save exponent, and reduce so 0.1 <= f < 1
    decNumberCopy(f, rhs);
    exp=f->exponent+f->digits;               // adjusted to Hull rules
    f->exponent=-(f->digits);                // to range

    // set up working context
    decContextDefault(&workset, DEC_INIT_DECIMAL64);
    workset.emax=DEC_MAX_EMAX;
    workset.emin=DEC_MIN_EMIN;

    // [Until further notice, no error is possible and status bits
    // (Rounded, etc.) should be ignored, not accumulated.]

    // Calculate initial approximation, and allow for odd exponent
    workset.digits=workp;                    // p for initial calculation
    t->bits=0; t->digits=3;
    a->bits=0; a->digits=3;
    if ((exp & 1)==0) {                      // even exponent
      // Set t=0.259, a=0.819
      t->exponent=-3;
      a->exponent=-3;
      #if DECDPUN>=3
        t->lsu[0]=259;
        a->lsu[0]=819;
      #elif DECDPUN==2
        t->lsu[0]=59; t->lsu[1]=2;
        a->lsu[0]=19; a->lsu[1]=8;
      #else
        t->lsu[0]=9; t->lsu[1]=5; t->lsu[2]=2;
        a->lsu[0]=9; a->lsu[1]=1; a->lsu[2]=8;
      #endif
      }
     else {                                  // odd exponent
      // Set t=0.0819, a=2.59
      f->exponent--;                         // f=f/10
      exp++;                                 // e=e+1
      t->exponent=-4;
      a->exponent=-2;
      #if DECDPUN>=3
        t->lsu[0]=819;
        a->lsu[0]=259;
      #elif DECDPUN==2
        t->lsu[0]=19; t->lsu[1]=8;
        a->lsu[0]=59; a->lsu[1]=2;
      #else
        t->lsu[0]=9; t->lsu[1]=1; t->lsu[2]=8;
        a->lsu[0]=9; a->lsu[1]=5; a->lsu[2]=2;
      #endif
      }

    decMultiplyOp(a, a, f, &workset, &ignore);    // a=a*f
    decAddOp(a, a, t, &workset, 0, &ignore);      // ..+t
    // [a is now the initial approximation for sqrt(f), calculated with
    // currentprecision, which is also a's precision.]

    // the main calculation loop
    decNumberZero(&dzero);                   // make 0
    decNumberZero(t);                        // set t = 0.5
    t->lsu[0]=5;                             // ..
    t->exponent=-1;                          // ..
    workset.digits=3;                        // initial p
    for (; workset.digits<maxp;) {
      // set p to min(2*p - 2, maxp)  [hence 3; or: 4, 6, 10, ... , maxp]
      workset.digits=MINI(workset.digits*2-2, maxp);
      // a = 0.5 * (a + f/a)
      // [calculated at p then rounded to currentprecision]
      decDivideOp(b, f, a, &workset, DIVIDE, &ignore); // b=f/a
      decAddOp(b, b, a, &workset, 0, &ignore);         // b=b+a
      decMultiplyOp(a, b, t, &workset, &ignore);       // a=b*0.5
      } // loop

    // Here, 0.1 <= a < 1 [Hull], and a has maxp digits
    // now reduce to length, etc.; this needs to be done with a
    // having the correct exponent so as to handle subnormals
    // correctly
    approxset=*set;                          // get emin, emax, etc.
    approxset.round=DEC_ROUND_HALF_EVEN;
    a->exponent+=exp/2;                      // set correct exponent
    rstatus=0;                               // clear status
    residue=0;                               // .. and accumulator
    decCopyFit(a, a, &approxset, &residue, &rstatus);  // reduce (if needed)
    decFinish(a, &approxset, &residue, &rstatus);      // clean and finalize

    // Overflow was possible if the input exponent was out-of-range,
    // in which case quit
    if (rstatus&DEC_Overflow) {
      status=rstatus;                        // use the status as-is
      decNumberCopy(res, a);                 // copy to result
      break;
      }

    // Preserve status except Inexact/Rounded
    status|=(rstatus & ~(DEC_Rounded|DEC_Inexact));

    // Carry out the Hull correction
    a->exponent-=exp/2;                      // back to 0.1->1

    // a is now at final precision and within 1 ulp of the properly
    // rounded square root of f; to ensure proper rounding, compare
    // squares of (a - l/2 ulp) and (a + l/2 ulp) with f.
    // Here workset.digits=maxp and t=0.5, and a->digits determines
    // the ulp
    workset.digits--;                             // maxp-1 is OK now
    t->exponent=-a->digits-1;                     // make 0.5 ulp
    decAddOp(b, a, t, &workset, DECNEG, &ignore); // b = a - 0.5 ulp
    workset.round=DEC_ROUND_UP;
    decMultiplyOp(b, b, b, &workset, &ignore);    // b = mulru(b, b)
    decCompareOp(b, f, b, &workset, COMPARE, &ignore); // b ? f, reversed
    if (decNumberIsNegative(b)) {                 // f < b [i.e., b > f]
      // this is the more common adjustment, though both are rare
      t->exponent++;                              // make 1.0 ulp
      t->lsu[0]=1;                                // ..
      decAddOp(a, a, t, &workset, DECNEG, &ignore); // a = a - 1 ulp
      // assign to approx [round to length]
      approxset.emin-=exp/2;                      // adjust to match a
      approxset.emax-=exp/2;
      decAddOp(a, &dzero, a, &approxset, 0, &ignore);
      }
     else {
      decAddOp(b, a, t, &workset, 0, &ignore);    // b = a + 0.5 ulp
      workset.round=DEC_ROUND_DOWN;
      decMultiplyOp(b, b, b, &workset, &ignore);  // b = mulrd(b, b)
      decCompareOp(b, b, f, &workset, COMPARE, &ignore);   // b ? f
      if (decNumberIsNegative(b)) {               // b < f
        t->exponent++;                            // make 1.0 ulp
        t->lsu[0]=1;                              // ..
        decAddOp(a, a, t, &workset, 0, &ignore);  // a = a + 1 ulp
        // assign to approx [round to length]
        approxset.emin-=exp/2;                    // adjust to match a
        approxset.emax-=exp/2;
        decAddOp(a, &dzero, a, &approxset, 0, &ignore);
        }
      }
    // [no errors are possible in the above, and rounding/inexact during
    // estimation are irrelevant, so status was not accumulated]

    // Here, 0.1 <= a < 1  (still), so adjust back
    a->exponent+=exp/2;                      // set correct exponent

    // count droppable zeros [after any subnormal rounding] by
    // trimming a copy
    decNumberCopy(b, a);
    decTrim(b, set, 1, 1, &dropped);         // [drops trailing zeros]

    // Set Inexact and Rounded.  The answer can only be exact if
    // it is short enough so that squaring it could fit in workp
    // digits, so this is the only (relatively rare) condition that
    // a careful check is needed
    if (b->digits*2-1 > workp) {             // cannot fit
      status|=DEC_Inexact|DEC_Rounded;
      }
     else {                                  // could be exact/unrounded
      uInt mstatus=0;                        // local status
      decMultiplyOp(b, b, b, &workset, &mstatus); // try the multiply
      if (mstatus&DEC_Overflow) {            // result just won't fit
        status|=DEC_Inexact|DEC_Rounded;
        }
       else {                                // plausible
        decCompareOp(t, b, rhs, &workset, COMPARE, &mstatus); // b ? rhs
        if (!ISZERO(t)) status|=DEC_Inexact|DEC_Rounded; // not equal
         else {                              // is Exact
          // here, dropped is the count of trailing zeros in 'a'
          // use closest exponent to ideal...
          Int todrop=ideal-a->exponent;      // most that can be dropped
          if (todrop<0) status|=DEC_Rounded; // ideally would add 0s
           else {                            // unrounded
            // there are some to drop, but emax may not allow all
            Int maxexp=set->emax-set->digits+1;
            Int maxdrop=maxexp-a->exponent;
            if (todrop>maxdrop && set->clamp) { // apply clamping
              todrop=maxdrop;
              status|=DEC_Clamped;
              }
            if (dropped<todrop) {            // clamp to those available
              todrop=dropped;
              status|=DEC_Clamped;
              }
            if (todrop>0) {                  // have some to drop
              decShiftToLeast(a->lsu, D2U(a->digits), todrop);
              a->exponent+=todrop;           // maintain numerical value
              a->digits-=todrop;             // new length
              }
            }
          }
        }
      }

    // double-check Underflow, as perhaps the result could not have
    // been subnormal (initial argument too big), or it is now Exact
    if (status&DEC_Underflow) {
      Int ae=rhs->exponent+rhs->digits-1;    // adjusted exponent
      // check if truly subnormal
      #if DECEXTFLAG                         // DEC_Subnormal too

        if (ae>=set->emin*2) status&=~(DEC_Subnormal|DEC_Underflow);
      #else
        if (ae>=set->emin*2) status&=~DEC_Underflow;
      #endif
      // check if truly inexact
      if (!(status&DEC_Inexact)) status&=~DEC_Underflow;
      }

    decNumberCopy(res, a);                   // a is now the result
    } while(0);                              // end protected

  if (allocbuff!=NULL) free(allocbuff);      // drop any storage used
  if (allocbufa!=NULL) free(allocbufa);      // ..
  if (allocbufb!=NULL) free(allocbufb);      // ..
  #if DECSUBSET
  if (allocrhs !=NULL) free(allocrhs);       // ..
  #endif
  if (status!=0) decStatus(res, status, set);// then report status
  #if DECCHECK
  decCheckInexact(res, set);
  #endif
  return res;
  } // decNumberSquareRoot

/* ------------------------------------------------------------------ */
/* decNumberSubtract -- subtract two Numbers                          */
/*                                                                    */
/*   This computes C = A - B                                          */
/*                                                                    */
/*   res is C, the result.  C may be A and/or B (e.g., X=X-X)         */
/*   lhs is A                                                         */
/*   rhs is B                                                         */
/*   set is the context                                               */
/*                                                                    */
/* C must have space for set->digits digits.                          */
/* ------------------------------------------------------------------ */
decNumber * decNumberSubtract(decNumber *res, const decNumber *lhs,
                              const decNumber *rhs, decContext *set) {
  uInt status=0;                        // accumulator

  decAddOp(res, lhs, rhs, set, DECNEG, &status);
  if (status!=0) decStatus(res, status, set);
  #if DECCHECK
  decCheckInexact(res, set);
  #endif
  return res;
  } // decNumberSubtract

/* ------------------------------------------------------------------ */
/* decNumberToIntegralExact -- round-to-integral-value with InExact   */
/* decNumberToIntegralValue -- round-to-integral-value                */
/*                                                                    */
/*   res is the result                                                */
/*   rhs is input number                                              */
/*   set is the context                                               */
/*                                                                    */
/* res must have space for any value of rhs.                          */
/*                                                                    */
/* This implements the IEEE special operators and therefore treats    */
/* special values as valid.  For finite numbers it returns            */
/* rescale(rhs, 0) if rhs->exponent is <0.                            */
/* Otherwise the result is rhs (so no error is possible, except for   */
/* sNaN).                                                             */
/*                                                                    */
/* The context is used for rounding mode and status after sNaN, but   */
/* the digits setting is ignored.  The Exact version will signal      */
/* Inexact if the result differs numerically from rhs; the other      */
/* never signals Inexact.                                             */
/* ------------------------------------------------------------------ */
decNumber * decNumberToIntegralExact(decNumber *res, const decNumber *rhs,
                                     decContext *set) {
  decNumber dn;
  decContext workset;              // working context
  uInt status=0;                   // accumulator

  #if DECCHECK
  if (decCheckOperands(res, DECUNUSED, rhs, set)) return res;
  #endif

  // handle infinities and NaNs
  if (SPECIALARG) {
    if (decNumberIsInfinite(rhs)) decNumberCopy(res, rhs); // an Infinity
     else decNaNs(res, rhs, NULL, set, &status); // a NaN
    }
   else { // finite
    // have a finite number; no error possible (res must be big enough)
    if (rhs->exponent>=0) return decNumberCopy(res, rhs);
    // that was easy, but if negative exponent there is work to do...
    workset=*set;                  // clone rounding, etc.
    workset.digits=rhs->digits;    // no length rounding
    workset.traps=0;               // no traps
    decNumberZero(&dn);            // make a number with exponent 0
    decNumberQuantize(res, rhs, &dn, &workset);
    status|=workset.status;
    }
  if (status!=0) decStatus(res, status, set);
  return res;
  } // decNumberToIntegralExact

decNumber * decNumberToIntegralValue(decNumber *res, const decNumber *rhs,
                                     decContext *set) {
  decContext workset=*set;         // working context
  workset.traps=0;                 // no traps
  decNumberToIntegralExact(res, rhs, &workset);
  // this never affects set, except for sNaNs; NaN will have been set
  // or propagated already, so no need to call decStatus
  set->status|=workset.status&DEC_Invalid_operation;
  return res;
  } // decNumberToIntegralValue

/* ------------------------------------------------------------------ */
/* decNumberXor -- XOR two Numbers, digitwise                         */
/*                                                                    */
/*   This computes C = A ^ B                                          */
/*                                                                    */
/*   res is C, the result.  C may be A and/or B (e.g., X=X^X)         */
/*   lhs is A                                                         */
/*   rhs is B                                                         */
/*   set is the context (used for result length and error report)     */
/*                                                                    */
/* C must have space for set->digits digits.                          */
/*                                                                    */
/* Logical function restrictions apply (see above); a NaN is          */
/* returned with Invalid_operation if a restriction is violated.      */
/* ------------------------------------------------------------------ */
decNumber * decNumberXor(decNumber *res, const decNumber *lhs,
                         const decNumber *rhs, decContext *set) {
  const Unit *ua, *ub;                  // -> operands
  const Unit *msua, *msub;              // -> operand msus
  Unit  *uc, *msuc;                     // -> result and its msu
  Int   msudigs;                        // digits in res msu
  #if DECCHECK
  if (decCheckOperands(res, lhs, rhs, set)) return res;
  #endif

  if (lhs->exponent!=0 || decNumberIsSpecial(lhs) || decNumberIsNegative(lhs)
   || rhs->exponent!=0 || decNumberIsSpecial(rhs) || decNumberIsNegative(rhs)) {
    decStatus(res, DEC_Invalid_operation, set);
    return res;
    }
  // operands are valid
  ua=lhs->lsu;                          // bottom-up
  ub=rhs->lsu;                          // ..
  uc=res->lsu;                          // ..
  msua=ua+D2U(lhs->digits)-1;           // -> msu of lhs
  msub=ub+D2U(rhs->digits)-1;           // -> msu of rhs
  msuc=uc+D2U(set->digits)-1;           // -> msu of result
  msudigs=MSUDIGITS(set->digits);       // [faster than remainder]
  for (; uc<=msuc; ua++, ub++, uc++) {  // Unit loop
    Unit a, b;                          // extract units
    if (ua>msua) a=0;
     else a=*ua;
    if (ub>msub) b=0;
     else b=*ub;
    *uc=0;                              // can now write back
    if (a|b) {                          // maybe 1 bits to examine
      Int i, j;
      // This loop could be unrolled and/or use BIN2BCD tables
      for (i=0; i<DECDPUN; i++) {
        if ((a^b)&1) *uc=*uc+(Unit)powers[i];     // effect XOR
        j=a%10;
        a=a/10;
        j|=b%10;
        b=b/10;
        if (j>1) {
          decStatus(res, DEC_Invalid_operation, set);
          return res;
          }
        if (uc==msuc && i==msudigs-1) break;      // just did final digit
        } // each digit
      } // non-zero
    } // each unit
  // [here uc-1 is the msu of the result]
  res->digits=decGetDigits(res->lsu, uc-res->lsu);
  res->exponent=0;                      // integer
  res->bits=0;                          // sign=0
  return res;  // [no status to set]
  } // decNumberXor


/* ================================================================== */
/* Utility routines                                                   */
/* ================================================================== */

/* ------------------------------------------------------------------ */
/* decNumberClass -- return the decClass of a decNumber               */
/*   dn -- the decNumber to test                                      */
/*   set -- the context to use for Emin                               */
/*   returns the decClass enum                                        */
/* ------------------------------------------------------------------ */
enum decClass decNumberClass(const decNumber *dn, decContext *set) {
  if (decNumberIsSpecial(dn)) {
    if (decNumberIsQNaN(dn)) return DEC_CLASS_QNAN;
    if (decNumberIsSNaN(dn)) return DEC_CLASS_SNAN;
    // must be an infinity
    if (decNumberIsNegative(dn)) return DEC_CLASS_NEG_INF;
    return DEC_CLASS_POS_INF;
    }
  // is finite
  if (decNumberIsNormal(dn, set)) { // most common
    if (decNumberIsNegative(dn)) return DEC_CLASS_NEG_NORMAL;
    return DEC_CLASS_POS_NORMAL;
    }
  // is subnormal or zero
  if (decNumberIsZero(dn)) {    // most common
    if (decNumberIsNegative(dn)) return DEC_CLASS_NEG_ZERO;
    return DEC_CLASS_POS_ZERO;
    }
  if (decNumberIsNegative(dn)) return DEC_CLASS_NEG_SUBNORMAL;
  return DEC_CLASS_POS_SUBNORMAL;
  } // decNumberClass

/* ------------------------------------------------------------------ */
/* decNumberClassToString -- convert decClass to a string             */
/*                                                                    */
/*  eclass is a valid decClass                                        */
/*  returns a constant string describing the class (max 13+1 chars)   */
/* ------------------------------------------------------------------ */
const char *decNumberClassToString(enum decClass eclass) {
  if (eclass==DEC_CLASS_POS_NORMAL)    return DEC_ClassString_PN;
  if (eclass==DEC_CLASS_NEG_NORMAL)    return DEC_ClassString_NN;
  if (eclass==DEC_CLASS_POS_ZERO)      return DEC_ClassString_PZ;
  if (eclass==DEC_CLASS_NEG_ZERO)      return DEC_ClassString_NZ;
  if (eclass==DEC_CLASS_POS_SUBNORMAL) return DEC_ClassString_PS;
  if (eclass==DEC_CLASS_NEG_SUBNORMAL) return DEC_ClassString_NS;
  if (eclass==DEC_CLASS_POS_INF)       return DEC_ClassString_PI;
  if (eclass==DEC_CLASS_NEG_INF)       return DEC_ClassString_NI;
  if (eclass==DEC_CLASS_QNAN)          return DEC_ClassString_QN;
  if (eclass==DEC_CLASS_SNAN)          return DEC_ClassString_SN;
  return DEC_ClassString_UN;           // Unknown
  } // decNumberClassToString

/* ------------------------------------------------------------------ */
/* decNumberCopy -- copy a number                                     */
/*                                                                    */
/*   dest is the target decNumber                                     */
/*   src  is the source decNumber                                     */
/*   returns dest                                                     */
/*                                                                    */
/* (dest==src is allowed and is a no-op)                              */
/* All fields are updated as required.  This is a utility operation,  */
/* so special values are unchanged and no error is possible.          */
/* ------------------------------------------------------------------ */
decNumber * decNumberCopy(decNumber *dest, const decNumber *src) {

  #if DECCHECK
  if (src==NULL) return decNumberZero(dest);
  #endif

  if (dest==src) return dest;                // no copy required

  // Use explicit assignments here as structure assignment could copy
  // more than just the lsu (for small DECDPUN).  This would not affect
  // the value of the results, but could disturb test harness spill
  // checking.
  dest->bits=src->bits;
  dest->exponent=src->exponent;
  dest->digits=src->digits;
  dest->lsu[0]=src->lsu[0];
  if (src->digits>DECDPUN) {                 // more Units to come
    const Unit *smsup, *s;                   // work
    Unit  *d;                                // ..
    // memcpy for the remaining Units would be safe as they cannot
    // overlap.  However, this explicit loop is faster in short cases.
    d=dest->lsu+1;                           // -> first destination
    smsup=src->lsu+D2U(src->digits);         // -> source msu+1
    for (s=src->lsu+1; s<smsup; s++, d++) *d=*s;
    }
  return dest;
  } // decNumberCopy

/* ------------------------------------------------------------------ */
/* decNumberCopyAbs -- quiet absolute value operator                  */
/*                                                                    */
/*   This sets C = abs(A)                                             */
/*                                                                    */
/*   res is C, the result.  C may be A                                */
/*   rhs is A                                                         */
/*                                                                    */
/* C must have space for set->digits digits.                          */
/* No exception or error can occur; this is a quiet bitwise operation.*/
/* See also decNumberAbs for a checking version of this.              */
/* ------------------------------------------------------------------ */
decNumber * decNumberCopyAbs(decNumber *res, const decNumber *rhs) {
  #if DECCHECK
  if (decCheckOperands(res, DECUNUSED, rhs, DECUNCONT)) return res;
  #endif
  decNumberCopy(res, rhs);
  res->bits&=~DECNEG;                   // turn off sign
  return res;
  } // decNumberCopyAbs

/* ------------------------------------------------------------------ */
/* decNumberCopyNegate -- quiet negate value operator                 */
/*                                                                    */
/*   This sets C = negate(A)                                          */
/*                                                                    */
/*   res is C, the result.  C may be A                                */
/*   rhs is A                                                         */
/*                                                                    */
/* C must have space for set->digits digits.                          */
/* No exception or error can occur; this is a quiet bitwise operation.*/
/* See also decNumberMinus for a checking version of this.            */
/* ------------------------------------------------------------------ */
decNumber * decNumberCopyNegate(decNumber *res, const decNumber *rhs) {
  #if DECCHECK
  if (decCheckOperands(res, DECUNUSED, rhs, DECUNCONT)) return res;
  #endif
  decNumberCopy(res, rhs);
  res->bits^=DECNEG;                    // invert the sign
  return res;
  } // decNumberCopyNegate

/* ------------------------------------------------------------------ */
/* decNumberCopySign -- quiet copy and set sign operator              */
/*                                                                    */
/*   This sets C = A with the sign of B                               */
/*                                                                    */
/*   res is C, the result.  C may be A                                */
/*   lhs is A                                                         */
/*   rhs is B                                                         */
/*                                                                    */
/* C must have space for set->digits digits.                          */
/* No exception or error can occur; this is a quiet bitwise operation.*/
/* ------------------------------------------------------------------ */
decNumber * decNumberCopySign(decNumber *res, const decNumber *lhs,
                              const decNumber *rhs) {
  uByte sign;                           // rhs sign
  #if DECCHECK
  if (decCheckOperands(res, DECUNUSED, rhs, DECUNCONT)) return res;
  #endif
  sign=rhs->bits & DECNEG;              // save sign bit
  decNumberCopy(res, lhs);
  res->bits&=~DECNEG;                   // clear the sign
  res->bits|=sign;                      // set from rhs
  return res;
  } // decNumberCopySign

/* ------------------------------------------------------------------ */
/* decNumberGetBCD -- get the coefficient in BCD8                     */
/*   dn is the source decNumber                                       */
/*   bcd is the uInt array that will receive dn->digits BCD bytes,    */
/*     most-significant at offset 0                                   */
/*   returns bcd                                                      */
/*                                                                    */
/* bcd must have at least dn->digits bytes.  No error is possible; if */
/* dn is a NaN or Infinite, digits must be 1 and the coefficient 0.   */
/* ------------------------------------------------------------------ */
uByte * decNumberGetBCD(const decNumber *dn, uByte *bcd) {
  uByte *ub=bcd+dn->digits-1;      // -> lsd
  const Unit *up=dn->lsu;          // Unit pointer, -> lsu

  #if DECDPUN==1                   // trivial simple copy

    for (; ub>=bcd; ub--, up++) *ub=*up;
  #else                            // chopping needed

    uInt u=*up;                    // work
    uInt cut=DECDPUN;              // downcounter through unit
    for (; ub>=bcd; ub--) {
      *ub=(uByte)(u%10);           // [*6554 trick inhibits, here]
      u=u/10;
      cut--;
      if (cut>0) continue;         // more in this unit
      up++;
      u=*up;
      cut=DECDPUN;
      }
  #endif
  return bcd;
  } // decNumberGetBCD

/* ------------------------------------------------------------------ */
/* decNumberSetBCD -- set (replace) the coefficient from BCD8         */
/*   dn is the target decNumber                                       */
/*   bcd is the uInt array that will source n BCD bytes, most-        */
/*     significant at offset 0                                        */
/*   n is the number of digits in the source BCD array (bcd)          */
/*   returns dn                                                       */
/*                                                                    */
/* dn must have space for at least n digits.  No error is possible;   */
/* if dn is a NaN, or Infinite, or is to become a zero, n must be 1   */
/* and bcd[0] zero.                                                   */
/* ------------------------------------------------------------------ */
decNumber * decNumberSetBCD(decNumber *dn, const uByte *bcd, uInt n) {
  Unit *up=dn->lsu+D2U(dn->digits)-1;   // -> msu [target pointer]
  const uByte *ub=bcd;                  // -> source msd

  #if DECDPUN==1                        // trivial simple copy

    for (; ub<bcd+n; ub++, up--) *up=*ub;
  #else                                 // some assembly needed

    // calculate how many digits in msu, and hence first cut
    Int cut=MSUDIGITS(n);               // [faster than remainder]
    for (;up>=dn->lsu; up--) {          // each Unit from msu
      *up=0;                            // will take <=DECDPUN digits
      for (; cut>0; ub++, cut--) *up=X10(*up)+*ub;
      cut=DECDPUN;                      // next Unit has all digits
      }
  #endif
  dn->digits=n;                         // set digit count
  return dn;
  } // decNumberSetBCD

/* ------------------------------------------------------------------ */
/* decNumberIsNormal -- test normality of a decNumber                 */
/*   dn is the decNumber to test                                      */
/*   set is the context to use for Emin                               */
/*   returns 1 if |dn| is finite and >=Nmin, 0 otherwise              */
/* ------------------------------------------------------------------ */
Int decNumberIsNormal(const decNumber *dn, decContext *set) {
  Int ae;                               // adjusted exponent
  #if DECCHECK
  if (decCheckOperands(DECUNRESU, DECUNUSED, dn, set)) return 0;
  #endif

  if (decNumberIsSpecial(dn)) return 0; // not finite
  if (decNumberIsZero(dn)) return 0;    // not non-zero

  ae=dn->exponent+dn->digits-1;         // adjusted exponent
  if (ae<set->emin) return 0;           // is subnormal
  return 1;
  } // decNumberIsNormal

/* ------------------------------------------------------------------ */
/* decNumberIsSubnormal -- test subnormality of a decNumber           */
/*   dn is the decNumber to test                                      */
/*   set is the context to use for Emin                               */
/*   returns 1 if |dn| is finite, non-zero, and <Nmin, 0 otherwise    */
/* ------------------------------------------------------------------ */
Int decNumberIsSubnormal(const decNumber *dn, decContext *set) {
  Int ae;                               // adjusted exponent
  #if DECCHECK
  if (decCheckOperands(DECUNRESU, DECUNUSED, dn, set)) return 0;
  #endif

  if (decNumberIsSpecial(dn)) return 0; // not finite
  if (decNumberIsZero(dn)) return 0;    // not non-zero

  ae=dn->exponent+dn->digits-1;         // adjusted exponent
  if (ae<set->emin) return 1;           // is subnormal
  return 0;
  } // decNumberIsSubnormal

/* ------------------------------------------------------------------ */
/* decNumberTrim -- remove insignificant zeros                        */
/*                                                                    */
/*   dn is the number to trim                                         */
/*   returns dn                                                       */
/*                                                                    */
/* All fields are updated as required.  This is a utility operation,  */
/* so special values are unchanged and no error is possible.  The     */
/* zeros are removed unconditionally.                                 */
/* ------------------------------------------------------------------ */
decNumber * decNumberTrim(decNumber *dn) {
  Int  dropped;                    // work
  decContext set;                  // ..
  #if DECCHECK
  if (decCheckOperands(DECUNRESU, DECUNUSED, dn, DECUNCONT)) return dn;
  #endif
  decContextDefault(&set, DEC_INIT_BASE);    // clamp=0
  return decTrim(dn, &set, 0, 1, &dropped);
  } // decNumberTrim

/* ------------------------------------------------------------------ */
/* decNumberVersion -- return the name and version of this module     */
/*                                                                    */
/* No error is possible.                                              */
/* ------------------------------------------------------------------ */
const char * decNumberVersion(void) {
  return DECVERSION;
  } // decNumberVersion

/* ------------------------------------------------------------------ */
/* decNumberZero -- set a number to 0                                 */
/*                                                                    */
/*   dn is the number to set, with space for one digit                */
/*   returns dn                                                       */
/*                                                                    */
/* No error is possible.                                              */
/* ------------------------------------------------------------------ */
// Memset is not used as it is much slower in some environments.
decNumber * decNumberZero(decNumber *dn) {

  #if DECCHECK
  if (decCheckOperands(dn, DECUNUSED, DECUNUSED, DECUNCONT)) return dn;
  #endif

  dn->bits=0;
  dn->exponent=0;
  dn->digits=1;
  dn->lsu[0]=0;
  return dn;
  } // decNumberZero

/* ================================================================== */
/* Local routines                                                     */
/* ================================================================== */

/* ------------------------------------------------------------------ */
/* decToString -- lay out a number into a string                      */
/*                                                                    */
/*   dn     is the number to lay out                                  */
/*   string is where to lay out the number                            */
/*   eng    is 1 if Engineering, 0 if Scientific                      */
/*                                                                    */
/* string must be at least dn->digits+14 characters long              */
/* No error is possible.                                              */
/*                                                                    */
/* Note that this routine can generate a -0 or 0.000.  These are      */
/* never generated in subset to-number or arithmetic, but can occur   */
/* in non-subset arithmetic (e.g., -1*0 or 1.234-1.234).              */
/* ------------------------------------------------------------------ */
// If DECCHECK is enabled the string "?" is returned if a number is
// invalid.
static void decToString(const decNumber *dn, char *string, Flag eng) {
  Int exp=dn->exponent;       // local copy
  Int e;                      // E-part value
  Int pre;                    // digits before the '.'
  Int cut;                    // for counting digits in a Unit
  char *c=string;             // work [output pointer]
  const Unit *up=dn->lsu+D2U(dn->digits)-1; // -> msu [input pointer]
  uInt u, pow;                // work

  #if DECCHECK
  if (decCheckOperands(DECUNRESU, dn, DECUNUSED, DECUNCONT)) {
    strcpy(string, "?");
    return;}
  #endif

  if (decNumberIsNegative(dn)) {   // Negatives get a minus
    *c='-';
    c++;
    }
  if (dn->bits&DECSPECIAL) {       // Is a special value
    if (decNumberIsInfinite(dn)) {
      strcpy(c,   "Inf");
      strcpy(c+3, "inity");
      return;}
    // a NaN
    if (dn->bits&DECSNAN) {        // signalling NaN
      *c='s';
      c++;
      }
    strcpy(c, "NaN");
    c+=3;                          // step past
    // if not a clean non-zero coefficient, that's all there is in a
    // NaN string
    if (exp!=0 || (*dn->lsu==0 && dn->digits==1)) return;
    // [drop through to add integer]
    }

  // calculate how many digits in msu, and hence first cut
  cut=MSUDIGITS(dn->digits);       // [faster than remainder]
  cut--;                           // power of ten for digit

  if (exp==0) {                    // simple integer [common fastpath]
    for (;up>=dn->lsu; up--) {     // each Unit from msu
      u=*up;                       // contains DECDPUN digits to lay out
      for (; cut>=0; c++, cut--) TODIGIT(u, cut, c, pow);
      cut=DECDPUN-1;               // next Unit has all digits
      }
    *c='\0';                       // terminate the string
    return;}

  /* non-0 exponent -- assume plain form */
  pre=dn->digits+exp;              // digits before '.'
  e=0;                             // no E
  if ((exp>0) || (pre<-5)) {       // need exponential form
    e=exp+dn->digits-1;            // calculate E value
    pre=1;                         // assume one digit before '.'
    if (eng && (e!=0)) {           // engineering: may need to adjust
      Int adj;                     // adjustment
      // The C remainder operator is undefined for negative numbers, so
      // a positive remainder calculation must be used here
      if (e<0) {
        adj=(-e)%3;
        if (adj!=0) adj=3-adj;
        }
       else { // e>0
        adj=e%3;
        }
      e=e-adj;
      // if dealing with zero still produce an exponent which is a
      // multiple of three, as expected, but there will only be the
      // one zero before the E, still.  Otherwise note the padding.
      if (!ISZERO(dn)) pre+=adj;
       else {  // is zero
        if (adj!=0) {              // 0.00Esnn needed
          e=e+3;
          pre=-(2-adj);
          }
        } // zero
      } // eng
    } // need exponent

  /* lay out the digits of the coefficient, adding 0s and . as needed */
  u=*up;
  if (pre>0) {                     // xxx.xxx or xx00 (engineering) form
    Int n=pre;
    for (; pre>0; pre--, c++, cut--) {
      if (cut<0) {                 // need new Unit
        if (up==dn->lsu) break;    // out of input digits (pre>digits)
        up--;
        cut=DECDPUN-1;
        u=*up;
        }
      TODIGIT(u, cut, c, pow);
      }
    if (n<dn->digits) {            // more to come, after '.'
      *c='.'; c++;
      for (;; c++, cut--) {
        if (cut<0) {               // need new Unit
          if (up==dn->lsu) break;  // out of input digits
          up--;
          cut=DECDPUN-1;
          u=*up;
          }
        TODIGIT(u, cut, c, pow);
        }
      }
     else for (; pre>0; pre--, c++) *c='0'; // 0 padding (for engineering) needed
    }
   else {                          // 0.xxx or 0.000xxx form
    *c='0'; c++;
    *c='.'; c++;
    for (; pre<0; pre++, c++) *c='0';   // add any 0's after '.'
    for (; ; c++, cut--) {
      if (cut<0) {                 // need new Unit
        if (up==dn->lsu) break;    // out of input digits
        up--;
        cut=DECDPUN-1;
        u=*up;
        }
      TODIGIT(u, cut, c, pow);
      }
    }

  /* Finally add the E-part, if needed.  It will never be 0, has a
     base maximum and minimum of +999999999 through -999999999, but
     could range down to -1999999998 for anormal numbers */
  if (e!=0) {
    Flag had=0;               // 1=had non-zero
    *c='E'; c++;
    *c='+'; c++;              // assume positive
    u=e;                      // ..
    if (e<0) {
      *(c-1)='-';             // oops, need -
      u=-e;                   // uInt, please
      }
    // lay out the exponent [_itoa or equivalent is not ANSI C]
    for (cut=9; cut>=0; cut--) {
      TODIGIT(u, cut, c, pow);
      if (*c=='0' && !had) continue;    // skip leading zeros
      had=1;                            // had non-0
      c++;                              // step for next
      } // cut
    }
  *c='\0';          // terminate the string (all paths)
  return;
  } // decToString

/* ------------------------------------------------------------------ */
/* decAddOp -- add/subtract operation                                 */
/*                                                                    */
/*   This computes C = A + B                                          */
/*                                                                    */
/*   res is C, the result.  C may be A and/or B (e.g., X=X+X)         */
/*   lhs is A                                                         */
/*   rhs is B                                                         */
/*   set is the context                                               */
/*   negate is DECNEG if rhs should be negated, or 0 otherwise        */
/*   status accumulates status for the caller                         */
/*                                                                    */
/* C must have space for set->digits digits.                          */
/* Inexact in status must be 0 for correct Exact zero sign in result  */
/* ------------------------------------------------------------------ */
/* If possible, the coefficient is calculated directly into C.        */
/* However, if:                                                       */
/*   -- a digits+1 calculation is needed because the numbers are      */
/*      unaligned and span more than set->digits digits               */
/*   -- a carry to digits+1 digits looks possible                     */
/*   -- C is the same as A or B, and the result would destructively   */
/*      overlap the A or B coefficient                                */
/* then the result must be calculated into a temporary buffer.  In    */
/* this case a local (stack) buffer is used if possible, and only if  */
/* too long for that does malloc become the final resort.             */
/*                                                                    */
/* Misalignment is handled as follows:                                */
/*   Apad: (AExp>BExp) Swap operands and proceed as for BExp>AExp.    */
/*   BPad: Apply the padding by a combination of shifting (whole      */
/*         units) and multiplication (part units).                    */
/*                                                                    */
/* Addition, especially x=x+1, is speed-critical.                     */
/* The static buffer is larger than might be expected to allow for    */
/* calls from higher-level funtions (notable exp).                    */
/* ------------------------------------------------------------------ */
static decNumber * decAddOp(decNumber *res, const decNumber *lhs,
                            const decNumber *rhs, decContext *set,
                            uByte negate, uInt *status) {
  #if DECSUBSET
  decNumber *alloclhs=NULL;        // non-NULL if rounded lhs allocated
  decNumber *allocrhs=NULL;        // .., rhs
  #endif
  Int   rhsshift;                  // working shift (in Units)
  Int   maxdigits;                 // longest logical length
  Int   mult;                      // multiplier
  Int   residue;                   // rounding accumulator
  uByte bits;                      // result bits
  Flag  diffsign;                  // non-0 if arguments have different sign
  Unit  *acc;                      // accumulator for result
  Unit  accbuff[SD2U(DECBUFFER*2+20)]; // local buffer [*2+20 reduces many
                                   // allocations when called from
                                   // other operations, notable exp]
  Unit  *allocacc=NULL;            // -> allocated acc buffer, iff allocated
  Int   reqdigits=set->digits;     // local copy; requested DIGITS
  Int   padding;                   // work

  #if DECCHECK
  if (decCheckOperands(res, lhs, rhs, set)) return res;
  #endif

  do {                             // protect allocated storage
    #if DECSUBSET
    if (!set->extended) {
      // reduce operands and set lostDigits status, as needed
      if (lhs->digits>reqdigits) {
        alloclhs=decRoundOperand(lhs, set, status);
        if (alloclhs==NULL) break;
        lhs=alloclhs;
        }
      if (rhs->digits>reqdigits) {
        allocrhs=decRoundOperand(rhs, set, status);
        if (allocrhs==NULL) break;
        rhs=allocrhs;
        }
      }
    #endif
    // [following code does not require input rounding]

    // note whether signs differ [used all paths]
    diffsign=(Flag)((lhs->bits^rhs->bits^negate)&DECNEG);

    // handle infinities and NaNs
    if (SPECIALARGS) {                  // a special bit set
      if (SPECIALARGS & (DECSNAN | DECNAN))  // a NaN
        decNaNs(res, lhs, rhs, set, status);
       else { // one or two infinities
        if (decNumberIsInfinite(lhs)) { // LHS is infinity
          // two infinities with different signs is invalid
          if (decNumberIsInfinite(rhs) && diffsign) {
            *status|=DEC_Invalid_operation;
            break;
            }
          bits=lhs->bits & DECNEG;      // get sign from LHS
          }
         else bits=(rhs->bits^negate) & DECNEG;// RHS must be Infinity
        bits|=DECINF;
        decNumberZero(res);
        res->bits=bits;                 // set +/- infinity
        } // an infinity
      break;
      }

    // Quick exit for add 0s; return the non-0, modified as need be
    if (ISZERO(lhs)) {
      Int adjust;                       // work
      Int lexp=lhs->exponent;           // save in case LHS==RES
      bits=lhs->bits;                   // ..
      residue=0;                        // clear accumulator
      decCopyFit(res, rhs, set, &residue, status); // copy (as needed)
      res->bits^=negate;                // flip if rhs was negated
      #if DECSUBSET
      if (set->extended) {              // exponents on zeros count
      #endif
        // exponent will be the lower of the two
        adjust=lexp-res->exponent;      // adjustment needed [if -ve]
        if (ISZERO(res)) {              // both 0: special IEEE 754 rules
          if (adjust<0) res->exponent=lexp;  // set exponent
          // 0-0 gives +0 unless rounding to -infinity, and -0-0 gives -0
          if (diffsign) {
            if (set->round!=DEC_ROUND_FLOOR) res->bits=0;
             else res->bits=DECNEG;     // preserve 0 sign
            }
          }
         else { // non-0 res
          if (adjust<0) {     // 0-padding needed
            if ((res->digits-adjust)>set->digits) {
              adjust=res->digits-set->digits;     // to fit exactly
              *status|=DEC_Rounded;               // [but exact]
              }
            res->digits=decShiftToMost(res->lsu, res->digits, -adjust);
            res->exponent+=adjust;                // set the exponent.
            }
          } // non-0 res
      #if DECSUBSET
        } // extended
      #endif
      decFinish(res, set, &residue, status);      // clean and finalize
      break;}

    if (ISZERO(rhs)) {                  // [lhs is non-zero]
      Int adjust;                       // work
      Int rexp=rhs->exponent;           // save in case RHS==RES
      bits=rhs->bits;                   // be clean
      residue=0;                        // clear accumulator
      decCopyFit(res, lhs, set, &residue, status); // copy (as needed)
      #if DECSUBSET
      if (set->extended) {              // exponents on zeros count
      #endif
        // exponent will be the lower of the two
        // [0-0 case handled above]
        adjust=rexp-res->exponent;      // adjustment needed [if -ve]
        if (adjust<0) {     // 0-padding needed
          if ((res->digits-adjust)>set->digits) {
            adjust=res->digits-set->digits;     // to fit exactly
            *status|=DEC_Rounded;               // [but exact]
            }
          res->digits=decShiftToMost(res->lsu, res->digits, -adjust);
          res->exponent+=adjust;                // set the exponent.
          }
      #if DECSUBSET
        } // extended
      #endif
      decFinish(res, set, &residue, status);      // clean and finalize
      break;}

    // [NB: both fastpath and mainpath code below assume these cases
    // (notably 0-0) have already been handled]

    // calculate the padding needed to align the operands
    padding=rhs->exponent-lhs->exponent;

    // Fastpath cases where the numbers are aligned and normal, the RHS
    // is all in one unit, no operand rounding is needed, and no carry,
    // lengthening, or borrow is needed
    if (padding==0
        && rhs->digits<=DECDPUN
        && rhs->exponent>=set->emin     // [some normals drop through]
        && rhs->exponent<=set->emax-set->digits+1 // [could clamp]
        && rhs->digits<=reqdigits
        && lhs->digits<=reqdigits) {
      Int partial=*lhs->lsu;
      if (!diffsign) {                  // adding
        partial+=*rhs->lsu;
        if ((partial<=DECDPUNMAX)       // result fits in unit
         && (lhs->digits>=DECDPUN ||    // .. and no digits-count change
             partial<(Int)powers[lhs->digits])) { // ..
          if (res!=lhs) decNumberCopy(res, lhs);  // not in place
          *res->lsu=(Unit)partial;      // [copy could have overwritten RHS]
          break;
          }
        // else drop out for careful add
        }
       else {                           // signs differ
        partial-=*rhs->lsu;
        if (partial>0) { // no borrow needed, and non-0 result
          if (res!=lhs) decNumberCopy(res, lhs);  // not in place
          *res->lsu=(Unit)partial;
          // this could have reduced digits [but result>0]
          res->digits=decGetDigits(res->lsu, D2U(res->digits));
          break;
          }
        // else drop out for careful subtract
        }
      }

    // Now align (pad) the lhs or rhs so they can be added or
    // subtracted, as necessary.  If one number is much larger than
    // the other (that is, if in plain form there is a least one
    // digit between the lowest digit of one and the highest of the
    // other) padding with up to DIGITS-1 trailing zeros may be
    // needed; then apply rounding (as exotic rounding modes may be
    // affected by the residue).
    rhsshift=0;               // rhs shift to left (padding) in Units
    bits=lhs->bits;           // assume sign is that of LHS
    mult=1;                   // likely multiplier

    // [if padding==0 the operands are aligned; no padding is needed]
    if (padding!=0) {
      // some padding needed; always pad the RHS, as any required
      // padding can then be effected by a simple combination of
      // shifts and a multiply
      Flag swapped=0;
      if (padding<0) {                  // LHS needs the padding
        const decNumber *t;
        padding=-padding;               // will be +ve
        bits=(uByte)(rhs->bits^negate); // assumed sign is now that of RHS
        t=lhs; lhs=rhs; rhs=t;
        swapped=1;
        }

      // If, after pad, rhs would be longer than lhs by digits+1 or
      // more then lhs cannot affect the answer, except as a residue,
      // so only need to pad up to a length of DIGITS+1.
      if (rhs->digits+padding > lhs->digits+reqdigits+1) {
        // The RHS is sufficient
        // for residue use the relative sign indication...
        Int shift=reqdigits-rhs->digits;     // left shift needed
        residue=1;                           // residue for rounding
        if (diffsign) residue=-residue;      // signs differ
        // copy, shortening if necessary
        decCopyFit(res, rhs, set, &residue, status);
        // if it was already shorter, then need to pad with zeros
        if (shift>0) {
          res->digits=decShiftToMost(res->lsu, res->digits, shift);
          res->exponent-=shift;              // adjust the exponent.
          }
        // flip the result sign if unswapped and rhs was negated
        if (!swapped) res->bits^=negate;
        decFinish(res, set, &residue, status);    // done
        break;}

      // LHS digits may affect result
      rhsshift=D2U(padding+1)-1;        // this much by Unit shift ..
      mult=powers[padding-(rhsshift*DECDPUN)]; // .. this by multiplication
      } // padding needed

    if (diffsign) mult=-mult;           // signs differ

    // determine the longer operand
    maxdigits=rhs->digits+padding;      // virtual length of RHS
    if (lhs->digits>maxdigits) maxdigits=lhs->digits;

    // Decide on the result buffer to use; if possible place directly
    // into result.
    acc=res->lsu;                       // assume add direct to result
    // If destructive overlap, or the number is too long, or a carry or
    // borrow to DIGITS+1 might be possible, a buffer must be used.
    // [Might be worth more sophisticated tests when maxdigits==reqdigits]
    if ((maxdigits>=reqdigits)          // is, or could be, too large
     || (res==rhs && rhsshift>0)) {     // destructive overlap
      // buffer needed, choose it; units for maxdigits digits will be
      // needed, +1 Unit for carry or borrow
      Int need=D2U(maxdigits)+1;
      acc=accbuff;                      // assume use local buffer
      if (need*sizeof(Unit)>sizeof(accbuff)) {
        // printf("malloc add %ld %ld\n", need, sizeof(accbuff));
        allocacc=(Unit *)malloc(need*sizeof(Unit));
        if (allocacc==NULL) {           // hopeless -- abandon
          *status|=DEC_Insufficient_storage;
          break;}
        acc=allocacc;
        }
      }

    res->bits=(uByte)(bits&DECNEG);     // it's now safe to overwrite..
    res->exponent=lhs->exponent;        // .. operands (even if aliased)

    #if DECTRACE
      decDumpAr('A', lhs->lsu, D2U(lhs->digits));
      decDumpAr('B', rhs->lsu, D2U(rhs->digits));
      printf("  :h: %ld %ld\n", rhsshift, mult);
    #endif

    // add [A+B*m] or subtract [A+B*(-m)]
    res->digits=decUnitAddSub(lhs->lsu, D2U(lhs->digits),
                              rhs->lsu, D2U(rhs->digits),
                              rhsshift, acc, mult)
               *DECDPUN;           // [units -> digits]
    if (res->digits<0) {           // borrowed...
      res->digits=-res->digits;
      res->bits^=DECNEG;           // flip the sign
      }
    #if DECTRACE
      decDumpAr('+', acc, D2U(res->digits));
    #endif

    // If a buffer was used the result must be copied back, possibly
    // shortening.  (If no buffer was used then the result must have
    // fit, so can't need rounding and residue must be 0.)
    residue=0;                     // clear accumulator
    if (acc!=res->lsu) {
      #if DECSUBSET
      if (set->extended) {         // round from first significant digit
      #endif
        // remove leading zeros that were added due to rounding up to
        // integral Units -- before the test for rounding.
        if (res->digits>reqdigits)
          res->digits=decGetDigits(acc, D2U(res->digits));
        decSetCoeff(res, set, acc, res->digits, &residue, status);
      #if DECSUBSET
        }
       else { // subset arithmetic rounds from original significant digit
        // May have an underestimate.  This only occurs when both
        // numbers fit in DECDPUN digits and are padding with a
        // negative multiple (-10, -100...) and the top digit(s) become
        // 0.  (This only matters when using X3.274 rules where the
        // leading zero could be included in the rounding.)
        if (res->digits<maxdigits) {
          *(acc+D2U(res->digits))=0; // ensure leading 0 is there
          res->digits=maxdigits;
          }
         else {
          // remove leading zeros that added due to rounding up to
          // integral Units (but only those in excess of the original
          // maxdigits length, unless extended) before test for rounding.
          if (res->digits>reqdigits) {
            res->digits=decGetDigits(acc, D2U(res->digits));
            if (res->digits<maxdigits) res->digits=maxdigits;
            }
          }
        decSetCoeff(res, set, acc, res->digits, &residue, status);
        // Now apply rounding if needed before removing leading zeros.
        // This is safe because subnormals are not a possibility
        if (residue!=0) {
          decApplyRound(res, set, residue, status);
          residue=0;                 // did what needed to be done
          }
        } // subset
      #endif
      } // used buffer

    // strip leading zeros [these were left on in case of subset subtract]
    res->digits=decGetDigits(res->lsu, D2U(res->digits));

    // apply checks and rounding
    decFinish(res, set, &residue, status);

    // "When the sum of two operands with opposite signs is exactly
    // zero, the sign of that sum shall be '+' in all rounding modes
    // except round toward -Infinity, in which mode that sign shall be
    // '-'."  [Subset zeros also never have '-', set by decFinish.]
    if (ISZERO(res) && diffsign
     #if DECSUBSET
     && set->extended
     #endif
     && (*status&DEC_Inexact)==0) {
      if (set->round==DEC_ROUND_FLOOR) res->bits|=DECNEG;   // sign -
                                  else res->bits&=~DECNEG;  // sign +
      }
    } while(0);                              // end protected

  if (allocacc!=NULL) free(allocacc);        // drop any storage used
  #if DECSUBSET
  if (allocrhs!=NULL) free(allocrhs);        // ..
  if (alloclhs!=NULL) free(alloclhs);        // ..
  #endif
  return res;
  } // decAddOp

/* ------------------------------------------------------------------ */
/* decDivideOp -- division operation                                  */
/*                                                                    */
/*  This routine performs the calculations for all four division      */
/*  operators (divide, divideInteger, remainder, remainderNear).      */
/*                                                                    */
/*  C=A op B                                                          */
/*                                                                    */
/*   res is C, the result.  C may be A and/or B (e.g., X=X/X)         */
/*   lhs is A                                                         */
/*   rhs is B                                                         */
/*   set is the context                                               */
/*   op  is DIVIDE, DIVIDEINT, REMAINDER, or REMNEAR respectively.    */
/*   status is the usual accumulator                                  */
/*                                                                    */
/* C must have space for set->digits digits.                          */
/*                                                                    */
/* ------------------------------------------------------------------ */
/*   The underlying algorithm of this routine is the same as in the   */
/*   1981 S/370 implementation, that is, non-restoring long division  */
/*   with bi-unit (rather than bi-digit) estimation for each unit     */
/*   multiplier.  In this pseudocode overview, complications for the  */
/*   Remainder operators and division residues for exact rounding are */
/*   omitted for clarity.                                             */
/*                                                                    */
/*     Prepare operands and handle special values                     */
/*     Test for x/0 and then 0/x                                      */
/*     Exp =Exp1 - Exp2                                               */
/*     Exp =Exp +len(var1) -len(var2)                                 */
/*     Sign=Sign1 * Sign2                                             */
/*     Pad accumulator (Var1) to double-length with 0's (pad1)        */
/*     Pad Var2 to same length as Var1                                */
/*     msu2pair/plus=1st 2 or 1 units of var2, +1 to allow for round  */
/*     have=0                                                         */
/*     Do until (have=digits+1 OR residue=0)                          */
/*       if exp<0 then if integer divide/residue then leave           */
/*       this_unit=0                                                  */
/*       Do forever                                                   */
/*          compare numbers                                           */
/*          if <0 then leave inner_loop                               */
/*          if =0 then (* quick exit without subtract *) do           */
/*             this_unit=this_unit+1; output this_unit                */
/*             leave outer_loop; end                                  */
/*          Compare lengths of numbers (mantissae):                   */
/*          If same then tops2=msu2pair -- {units 1&2 of var2}        */
/*                  else tops2=msu2plus -- {0, unit 1 of var2}        */
/*          tops1=first_unit_of_Var1*10**DECDPUN +second_unit_of_var1 */
/*          mult=tops1/tops2  -- Good and safe guess at divisor       */
/*          if mult=0 then mult=1                                     */
/*          this_unit=this_unit+mult                                  */
/*          subtract                                                  */
/*          end inner_loop                                            */
/*        if have\=0 | this_unit\=0 then do                           */
/*          output this_unit                                          */
/*          have=have+1; end                                          */
/*        var2=var2/10                                                */
/*        exp=exp-1                                                   */
/*        end outer_loop                                              */
/*     exp=exp+1   -- set the proper exponent                         */
/*     if have=0 then generate answer=0                               */
/*     Return (Result is defined by Var1)                             */
/*                                                                    */
/* ------------------------------------------------------------------ */
/* Two working buffers are needed during the division; one (digits+   */
/* 1) to accumulate the result, and the other (up to 2*digits+1) for  */
/* long subtractions.  These are acc and var1 respectively.           */
/* var1 is a copy of the lhs coefficient, var2 is the rhs coefficient.*/
/* The static buffers may be larger than might be expected to allow   */
/* for calls from higher-level funtions (notable exp).                */
/* ------------------------------------------------------------------ */
static decNumber * decDivideOp(decNumber *res,
                               const decNumber *lhs, const decNumber *rhs,
                               decContext *set, Flag op, uInt *status) {
  #if DECSUBSET
  decNumber *alloclhs=NULL;        // non-NULL if rounded lhs allocated
  decNumber *allocrhs=NULL;        // .., rhs
  #endif
  Unit  accbuff[SD2U(DECBUFFER+DECDPUN+10)]; // local buffer
  Unit  *acc=accbuff;              // -> accumulator array for result
  Unit  *allocacc=NULL;            // -> allocated buffer, iff allocated
  Unit  *accnext;                  // -> where next digit will go
  Int   acclength;                 // length of acc needed [Units]
  Int   accunits;                  // count of units accumulated
  Int   accdigits;                 // count of digits accumulated

  Unit  varbuff[SD2U(DECBUFFER*2+DECDPUN)];  // buffer for var1
  Unit  *var1=varbuff;             // -> var1 array for long subtraction
  Unit  *varalloc=NULL;            // -> allocated buffer, iff used
  Unit  *msu1;                     // -> msu of var1

  const Unit *var2;                // -> var2 array
  const Unit *msu2;                // -> msu of var2
  Int   msu2plus;                  // msu2 plus one [does not vary]
  eInt  msu2pair;                  // msu2 pair plus one [does not vary]

  Int   var1units, var2units;      // actual lengths
  Int   var2ulen;                  // logical length (units)
  Int   var1initpad=0;             // var1 initial padding (digits)
  Int   maxdigits;                 // longest LHS or required acc length
  Int   mult;                      // multiplier for subtraction
  Unit  thisunit;                  // current unit being accumulated
  Int   residue;                   // for rounding
  Int   reqdigits=set->digits;     // requested DIGITS
  Int   exponent;                  // working exponent
  Int   maxexponent=0;             // DIVIDE maximum exponent if unrounded
  uByte bits;                      // working sign
  Unit  *target;                   // work
  const Unit *source;              // ..
  uInt  const *pow;                // ..
  Int   shift, cut;                // ..
  #if DECSUBSET
  Int   dropped;                   // work
  #endif

  #if DECCHECK
  if (decCheckOperands(res, lhs, rhs, set)) return res;
  #endif

  do {                             // protect allocated storage
    #if DECSUBSET
    if (!set->extended) {
      // reduce operands and set lostDigits status, as needed
      if (lhs->digits>reqdigits) {
        alloclhs=decRoundOperand(lhs, set, status);
        if (alloclhs==NULL) break;
        lhs=alloclhs;
        }
      if (rhs->digits>reqdigits) {
        allocrhs=decRoundOperand(rhs, set, status);
        if (allocrhs==NULL) break;
        rhs=allocrhs;
        }
      }
    #endif
    // [following code does not require input rounding]

    bits=(lhs->bits^rhs->bits)&DECNEG;  // assumed sign for divisions

    // handle infinities and NaNs
    if (SPECIALARGS) {                  // a special bit set
      if (SPECIALARGS & (DECSNAN | DECNAN)) { // one or two NaNs
        decNaNs(res, lhs, rhs, set, status);
        break;
        }
      // one or two infinities
      if (decNumberIsInfinite(lhs)) {   // LHS (dividend) is infinite
        if (decNumberIsInfinite(rhs) || // two infinities are invalid ..
            op & (REMAINDER | REMNEAR)) { // as is remainder of infinity
          *status|=DEC_Invalid_operation;
          break;
          }
        // [Note that infinity/0 raises no exceptions]
        decNumberZero(res);
        res->bits=bits|DECINF;          // set +/- infinity
        break;
        }
       else {                           // RHS (divisor) is infinite
        residue=0;
        if (op&(REMAINDER|REMNEAR)) {
          // result is [finished clone of] lhs
          decCopyFit(res, lhs, set, &residue, status);
          }
         else {  // a division
          decNumberZero(res);
          res->bits=bits;               // set +/- zero
          // for DIVIDEINT the exponent is always 0.  For DIVIDE, result
          // is a 0 with infinitely negative exponent, clamped to minimum
          if (op&DIVIDE) {
            res->exponent=set->emin-set->digits+1;
            *status|=DEC_Clamped;
            }
          }
        decFinish(res, set, &residue, status);
        break;
        }
      }

    // handle 0 rhs (x/0)
    if (ISZERO(rhs)) {                  // x/0 is always exceptional
      if (ISZERO(lhs)) {
        decNumberZero(res);             // [after lhs test]
        *status|=DEC_Division_undefined;// 0/0 will become NaN
        }
       else {
        decNumberZero(res);
        if (op&(REMAINDER|REMNEAR)) *status|=DEC_Invalid_operation;
         else {
          *status|=DEC_Division_by_zero; // x/0
          res->bits=bits|DECINF;         // .. is +/- Infinity
          }
        }
      break;}

    // handle 0 lhs (0/x)
    if (ISZERO(lhs)) {                  // 0/x [x!=0]
      #if DECSUBSET
      if (!set->extended) decNumberZero(res);
       else {
      #endif
        if (op&DIVIDE) {
          residue=0;
          exponent=lhs->exponent-rhs->exponent; // ideal exponent
          decNumberCopy(res, lhs);      // [zeros always fit]
          res->bits=bits;               // sign as computed
          res->exponent=exponent;       // exponent, too
          decFinalize(res, set, &residue, status);   // check exponent
          }
         else if (op&DIVIDEINT) {
          decNumberZero(res);           // integer 0
          res->bits=bits;               // sign as computed
          }
         else {                         // a remainder
          exponent=rhs->exponent;       // [save in case overwrite]
          decNumberCopy(res, lhs);      // [zeros always fit]
          if (exponent<res->exponent) res->exponent=exponent; // use lower
          }
      #if DECSUBSET
        }
      #endif
      break;}

    // Precalculate exponent.  This starts off adjusted (and hence fits
    // in 31 bits) and becomes the usual unadjusted exponent as the
    // division proceeds.  The order of evaluation is important, here,
    // to avoid wrap.
    exponent=(lhs->exponent+lhs->digits)-(rhs->exponent+rhs->digits);

    // If the working exponent is -ve, then some quick exits are
    // possible because the quotient is known to be <1
    // [for REMNEAR, it needs to be < -1, as -0.5 could need work]
    if (exponent<0 && !(op==DIVIDE)) {
      if (op&DIVIDEINT) {
        decNumberZero(res);                  // integer part is 0
        #if DECSUBSET
        if (set->extended)
        #endif
          res->bits=bits;                    // set +/- zero
        break;}
      // fastpath remainders so long as the lhs has the smaller
      // (or equal) exponent
      if (lhs->exponent<=rhs->exponent) {
        if (op&REMAINDER || exponent<-1) {
          // It is REMAINDER or safe REMNEAR; result is [finished
          // clone of] lhs  (r = x - 0*y)
          residue=0;
          decCopyFit(res, lhs, set, &residue, status);
          decFinish(res, set, &residue, status);
          break;
          }
        // [unsafe REMNEAR drops through]
        }
      } // fastpaths

    /* Long (slow) division is needed; roll up the sleeves... */

    // The accumulator will hold the quotient of the division.
    // If it needs to be too long for stack storage, then allocate.
    acclength=D2U(reqdigits+DECDPUN);   // in Units
    if (acclength*sizeof(Unit)>sizeof(accbuff)) {
      // printf("malloc dvacc %ld units\n", acclength);
      allocacc=(Unit *)malloc(acclength*sizeof(Unit));
      if (allocacc==NULL) {             // hopeless -- abandon
        *status|=DEC_Insufficient_storage;
        break;}
      acc=allocacc;                     // use the allocated space
      }

    // var1 is the padded LHS ready for subtractions.
    // If it needs to be too long for stack storage, then allocate.
    // The maximum units needed for var1 (long subtraction) is:
    // Enough for
    //     (rhs->digits+reqdigits-1) -- to allow full slide to right
    // or  (lhs->digits)             -- to allow for long lhs
    // whichever is larger
    //   +1                -- for rounding of slide to right
    //   +1                -- for leading 0s
    //   +1                -- for pre-adjust if a remainder or DIVIDEINT
    // [Note: unused units do not participate in decUnitAddSub data]
    maxdigits=rhs->digits+reqdigits-1;
    if (lhs->digits>maxdigits) maxdigits=lhs->digits;
    var1units=D2U(maxdigits)+2;
    // allocate a guard unit above msu1 for REMAINDERNEAR
    if (!(op&DIVIDE)) var1units++;
    if ((var1units+1)*sizeof(Unit)>sizeof(varbuff)) {
      // printf("malloc dvvar %ld units\n", var1units+1);
      varalloc=(Unit *)malloc((var1units+1)*sizeof(Unit));
      if (varalloc==NULL) {             // hopeless -- abandon
        *status|=DEC_Insufficient_storage;
        break;}
      var1=varalloc;                    // use the allocated space
      }

    // Extend the lhs and rhs to full long subtraction length.  The lhs
    // is truly extended into the var1 buffer, with 0 padding, so a
    // subtract in place is always possible.  The rhs (var2) has
    // virtual padding (implemented by decUnitAddSub).
    // One guard unit was allocated above msu1 for rem=rem+rem in
    // REMAINDERNEAR.
    msu1=var1+var1units-1;              // msu of var1
    source=lhs->lsu+D2U(lhs->digits)-1; // msu of input array
    for (target=msu1; source>=lhs->lsu; source--, target--) *target=*source;
    for (; target>=var1; target--) *target=0;

    // rhs (var2) is left-aligned with var1 at the start
    var2ulen=var1units;                 // rhs logical length (units)
    var2units=D2U(rhs->digits);         // rhs actual length (units)
    var2=rhs->lsu;                      // -> rhs array
    msu2=var2+var2units-1;              // -> msu of var2 [never changes]
    // now set up the variables which will be used for estimating the
    // multiplication factor.  If these variables are not exact, add
    // 1 to make sure that the multiplier is never overestimated.
    msu2plus=*msu2;                     // it's value ..
    if (var2units>1) msu2plus++;        // .. +1 if any more
    msu2pair=(eInt)*msu2*(DECDPUNMAX+1);// top two pair ..
    if (var2units>1) {                  // .. [else treat 2nd as 0]
      msu2pair+=*(msu2-1);              // ..
      if (var2units>2) msu2pair++;      // .. +1 if any more
      }

    // The calculation is working in units, which may have leading zeros,
    // but the exponent was calculated on the assumption that they are
    // both left-aligned.  Adjust the exponent to compensate: add the
    // number of leading zeros in var1 msu and subtract those in var2 msu.
    // [This is actually done by counting the digits and negating, as
    // lead1=DECDPUN-digits1, and similarly for lead2.]
    for (pow=&powers[1]; *msu1>=*pow; pow++) exponent--;
    for (pow=&powers[1]; *msu2>=*pow; pow++) exponent++;

    // Now, if doing an integer divide or remainder, ensure that
    // the result will be Unit-aligned.  To do this, shift the var1
    // accumulator towards least if need be.  (It's much easier to
    // do this now than to reassemble the residue afterwards, if
    // doing a remainder.)  Also ensure the exponent is not negative.
    if (!(op&DIVIDE)) {
      Unit *u;                          // work
      // save the initial 'false' padding of var1, in digits
      var1initpad=(var1units-D2U(lhs->digits))*DECDPUN;
      // Determine the shift to do.
      if (exponent<0) cut=-exponent;
       else cut=DECDPUN-exponent%DECDPUN;
      decShiftToLeast(var1, var1units, cut);
      exponent+=cut;                    // maintain numerical value
      var1initpad-=cut;                 // .. and reduce padding
      // clean any most-significant units which were just emptied
      for (u=msu1; cut>=DECDPUN; cut-=DECDPUN, u--) *u=0;
      } // align
     else { // is DIVIDE
      maxexponent=lhs->exponent-rhs->exponent;    // save
      // optimization: if the first iteration will just produce 0,
      // preadjust to skip it [valid for DIVIDE only]
      if (*msu1<*msu2) {
        var2ulen--;                     // shift down
        exponent-=DECDPUN;              // update the exponent
        }
      }

    // ---- start the long-division loops ------------------------------
    accunits=0;                         // no units accumulated yet
    accdigits=0;                        // .. or digits
    accnext=acc+acclength-1;            // -> msu of acc [NB: allows digits+1]
    for (;;) {                          // outer forever loop
      thisunit=0;                       // current unit assumed 0
      // find the next unit
      for (;;) {                        // inner forever loop
        // strip leading zero units [from either pre-adjust or from
        // subtract last time around].  Leave at least one unit.
        for (; *msu1==0 && msu1>var1; msu1--) var1units--;

        if (var1units<var2ulen) break;       // var1 too low for subtract
        if (var1units==var2ulen) {           // unit-by-unit compare needed
          // compare the two numbers, from msu
          const Unit *pv1, *pv2;
          Unit v2;                           // units to compare
          pv2=msu2;                          // -> msu
          for (pv1=msu1; ; pv1--, pv2--) {
            // v1=*pv1 -- always OK
            v2=0;                            // assume in padding
            if (pv2>=var2) v2=*pv2;          // in range
            if (*pv1!=v2) break;             // no longer the same
            if (pv1==var1) break;            // done; leave pv1 as is
            }
          // here when all inspected or a difference seen
          if (*pv1<v2) break;                // var1 too low to subtract
          if (*pv1==v2) {                    // var1 == var2
            // reach here if var1 and var2 are identical; subtraction
            // would increase digit by one, and the residue will be 0 so
            // the calculation is done; leave the loop with residue=0.
            thisunit++;                      // as though subtracted
            *var1=0;                         // set var1 to 0
            var1units=1;                     // ..
            break;  // from inner
            } // var1 == var2
          // *pv1>v2.  Prepare for real subtraction; the lengths are equal
          // Estimate the multiplier (there's always a msu1-1)...
          // Bring in two units of var2 to provide a good estimate.
          mult=(Int)(((eInt)*msu1*(DECDPUNMAX+1)+*(msu1-1))/msu2pair);
          } // lengths the same
         else { // var1units > var2ulen, so subtraction is safe
          // The var2 msu is one unit towards the lsu of the var1 msu,
          // so only one unit for var2 can be used.
          mult=(Int)(((eInt)*msu1*(DECDPUNMAX+1)+*(msu1-1))/msu2plus);
          }
        if (mult==0) mult=1;                 // must always be at least 1
        // subtraction needed; var1 is > var2
        thisunit=(Unit)(thisunit+mult);      // accumulate
        // subtract var1-var2, into var1; only the overlap needs
        // processing, as this is an in-place calculation
        shift=var2ulen-var2units;
        #if DECTRACE
          decDumpAr('1', &var1[shift], var1units-shift);
          decDumpAr('2', var2, var2units);
          printf("m=%ld\n", -mult);
        #endif
        decUnitAddSub(&var1[shift], var1units-shift,
                      var2, var2units, 0,
                      &var1[shift], -mult);
        #if DECTRACE
          decDumpAr('#', &var1[shift], var1units-shift);
        #endif
        // var1 now probably has leading zeros; these are removed at the
        // top of the inner loop.
        } // inner loop

      // The next unit has been calculated in full; unless it's a
      // leading zero, add to acc
      if (accunits!=0 || thisunit!=0) {      // is first or non-zero
        *accnext=thisunit;                   // store in accumulator
        // account exactly for the new digits
        if (accunits==0) {
          accdigits++;                       // at least one
          for (pow=&powers[1]; thisunit>=*pow; pow++) accdigits++;
          }
         else accdigits+=DECDPUN;
        accunits++;                          // update count
        accnext--;                           // ready for next
        if (accdigits>reqdigits) break;      // have enough digits
        }

      // if the residue is zero, the operation is done (unless divide
      // or divideInteger and still not enough digits yet)
      if (*var1==0 && var1units==1) {        // residue is 0
        if (op&(REMAINDER|REMNEAR)) break;
        if ((op&DIVIDE) && (exponent<=maxexponent)) break;
        // [drop through if divideInteger]
        }
      // also done enough if calculating remainder or integer
      // divide and just did the last ('units') unit
      if (exponent==0 && !(op&DIVIDE)) break;

      // to get here, var1 is less than var2, so divide var2 by the per-
      // Unit power of ten and go for the next digit
      var2ulen--;                            // shift down
      exponent-=DECDPUN;                     // update the exponent
      } // outer loop

    // ---- division is complete ---------------------------------------
    // here: acc      has at least reqdigits+1 of good results (or fewer
    //                if early stop), starting at accnext+1 (its lsu)
    //       var1     has any residue at the stopping point
    //       accunits is the number of digits collected in acc
    if (accunits==0) {             // acc is 0
      accunits=1;                  // show have a unit ..
      accdigits=1;                 // ..
      *accnext=0;                  // .. whose value is 0
      }
     else accnext++;               // back to last placed
    // accnext now -> lowest unit of result

    residue=0;                     // assume no residue
    if (op&DIVIDE) {
      // record the presence of any residue, for rounding
      if (*var1!=0 || var1units>1) residue=1;
       else { // no residue
        // Had an exact division; clean up spurious trailing 0s.
        // There will be at most DECDPUN-1, from the final multiply,
        // and then only if the result is non-0 (and even) and the
        // exponent is 'loose'.
        #if DECDPUN>1
        Unit lsu=*accnext;
        if (!(lsu&0x01) && (lsu!=0)) {
          // count the trailing zeros
          Int drop=0;
          for (;; drop++) {    // [will terminate because lsu!=0]
            if (exponent>=maxexponent) break;     // don't chop real 0s
            #if DECDPUN<=4
              if ((lsu-QUOT10(lsu, drop+1)
                  *powers[drop+1])!=0) break;     // found non-0 digit
            #else
              if (lsu%powers[drop+1]!=0) break;   // found non-0 digit
            #endif
            exponent++;
            }
          if (drop>0) {
            accunits=decShiftToLeast(accnext, accunits, drop);
            accdigits=decGetDigits(accnext, accunits);
            accunits=D2U(accdigits);
            // [exponent was adjusted in the loop]
            }
          } // neither odd nor 0
        #endif
        } // exact divide
      } // divide
     else /* op!=DIVIDE */ {
      // check for coefficient overflow
      if (accdigits+exponent>reqdigits) {
        *status|=DEC_Division_impossible;
        break;
        }
      if (op & (REMAINDER|REMNEAR)) {
        // [Here, the exponent will be 0, because var1 was adjusted
        // appropriately.]
        Int postshift;                       // work
        Flag wasodd=0;                       // integer was odd
        Unit *quotlsu;                       // for save
        Int  quotdigits;                     // ..

        bits=lhs->bits;                      // remainder sign is always as lhs

        // Fastpath when residue is truly 0 is worthwhile [and
        // simplifies the code below]
        if (*var1==0 && var1units==1) {      // residue is 0
          Int exp=lhs->exponent;             // save min(exponents)
          if (rhs->exponent<exp) exp=rhs->exponent;
          decNumberZero(res);                // 0 coefficient
          #if DECSUBSET
          if (set->extended)
          #endif
          res->exponent=exp;                 // .. with proper exponent
          res->bits=(uByte)(bits&DECNEG);          // [cleaned]
          decFinish(res, set, &residue, status);   // might clamp
          break;
          }
        // note if the quotient was odd
        if (*accnext & 0x01) wasodd=1;       // acc is odd
        quotlsu=accnext;                     // save in case need to reinspect
        quotdigits=accdigits;                // ..

        // treat the residue, in var1, as the value to return, via acc
        // calculate the unused zero digits.  This is the smaller of:
        //   var1 initial padding (saved above)
        //   var2 residual padding, which happens to be given by:
        postshift=var1initpad+exponent-lhs->exponent+rhs->exponent;
        // [the 'exponent' term accounts for the shifts during divide]
        if (var1initpad<postshift) postshift=var1initpad;

        // shift var1 the requested amount, and adjust its digits
        var1units=decShiftToLeast(var1, var1units, postshift);
        accnext=var1;
        accdigits=decGetDigits(var1, var1units);
        accunits=D2U(accdigits);

        exponent=lhs->exponent;         // exponent is smaller of lhs & rhs
        if (rhs->exponent<exponent) exponent=rhs->exponent;

        // Now correct the result if doing remainderNear; if it
        // (looking just at coefficients) is > rhs/2, or == rhs/2 and
        // the integer was odd then the result should be rem-rhs.
        if (op&REMNEAR) {
          Int compare, tarunits;        // work
          Unit *up;                     // ..
          // calculate remainder*2 into the var1 buffer (which has
          // 'headroom' of an extra unit and hence enough space)
          // [a dedicated 'double' loop would be faster, here]
          tarunits=decUnitAddSub(accnext, accunits, accnext, accunits,
                                 0, accnext, 1);
          // decDumpAr('r', accnext, tarunits);

          // Here, accnext (var1) holds tarunits Units with twice the
          // remainder's coefficient, which must now be compared to the
          // RHS.  The remainder's exponent may be smaller than the RHS's.
          compare=decUnitCompare(accnext, tarunits, rhs->lsu, D2U(rhs->digits),
                                 rhs->exponent-exponent);
          if (compare==BADINT) {             // deep trouble
            *status|=DEC_Insufficient_storage;
            break;}

          // now restore the remainder by dividing by two; the lsu
          // is known to be even.
          for (up=accnext; up<accnext+tarunits; up++) {
            Int half;              // half to add to lower unit
            half=*up & 0x01;
            *up/=2;                // [shift]
            if (!half) continue;
            *(up-1)+=(DECDPUNMAX+1)/2;
            }
          // [accunits still describes the original remainder length]

          if (compare>0 || (compare==0 && wasodd)) { // adjustment needed
            Int exp, expunits, exprem;       // work
            // This is effectively causing round-up of the quotient,
            // so if it was the rare case where it was full and all
            // nines, it would overflow and hence division-impossible
            // should be raised
            Flag allnines=0;                 // 1 if quotient all nines
            if (quotdigits==reqdigits) {     // could be borderline
              for (up=quotlsu; ; up++) {
                if (quotdigits>DECDPUN) {
                  if (*up!=DECDPUNMAX) break;// non-nines
                  }
                 else {                      // this is the last Unit
                  if (*up==powers[quotdigits]-1) allnines=1;
                  break;
                  }
                quotdigits-=DECDPUN;         // checked those digits
                } // up
              } // borderline check
            if (allnines) {
              *status|=DEC_Division_impossible;
              break;}

            // rem-rhs is needed; the sign will invert.  Again, var1
            // can safely be used for the working Units array.
            exp=rhs->exponent-exponent;      // RHS padding needed
            // Calculate units and remainder from exponent.
            expunits=exp/DECDPUN;
            exprem=exp%DECDPUN;
            // subtract [A+B*(-m)]; the result will always be negative
            accunits=-decUnitAddSub(accnext, accunits,
                                    rhs->lsu, D2U(rhs->digits),
                                    expunits, accnext, -(Int)powers[exprem]);
            accdigits=decGetDigits(accnext, accunits); // count digits exactly
            accunits=D2U(accdigits);    // and recalculate the units for copy
            // [exponent is as for original remainder]
            bits^=DECNEG;               // flip the sign
            }
          } // REMNEAR
        } // REMAINDER or REMNEAR
      } // not DIVIDE

    // Set exponent and bits
    res->exponent=exponent;
    res->bits=(uByte)(bits&DECNEG);          // [cleaned]

    // Now the coefficient.
    decSetCoeff(res, set, accnext, accdigits, &residue, status);

    decFinish(res, set, &residue, status);   // final cleanup

    #if DECSUBSET
    // If a divide then strip trailing zeros if subset [after round]
    if (!set->extended && (op==DIVIDE)) decTrim(res, set, 0, 1, &dropped);
    #endif
    } while(0);                              // end protected

  if (varalloc!=NULL) free(varalloc);   // drop any storage used
  if (allocacc!=NULL) free(allocacc);   // ..
  #if DECSUBSET
  if (allocrhs!=NULL) free(allocrhs);   // ..
  if (alloclhs!=NULL) free(alloclhs);   // ..
  #endif
  return res;
  } // decDivideOp

/* ------------------------------------------------------------------ */
/* decMultiplyOp -- multiplication operation                          */
/*                                                                    */
/*  This routine performs the multiplication C=A x B.                 */
/*                                                                    */
/*   res is C, the result.  C may be A and/or B (e.g., X=X*X)         */
/*   lhs is A                                                         */
/*   rhs is B                                                         */
/*   set is the context                                               */
/*   status is the usual accumulator                                  */
/*                                                                    */
/* C must have space for set->digits digits.                          */
/*                                                                    */
/* ------------------------------------------------------------------ */
/* 'Classic' multiplication is used rather than Karatsuba, as the     */
/* latter would give only a minor improvement for the short numbers   */
/* expected to be handled most (and uses much more memory).           */
/*                                                                    */
/* There are two major paths here: the general-purpose ('old code')   */
/* path which handles all DECDPUN values, and a fastpath version      */
/* which is used if 64-bit ints are available, DECDPUN<=4, and more   */
/* than two calls to decUnitAddSub would be made.                     */
/*                                                                    */
/* The fastpath version lumps units together into 8-digit or 9-digit  */
/* chunks, and also uses a lazy carry strategy to minimise expensive  */
/* 64-bit divisions.  The chunks are then broken apart again into     */
/* units for continuing processing.  Despite this overhead, the       */
/* fastpath can speed up some 16-digit operations by 10x (and much    */
/* more for higher-precision calculations).                           */
/*                                                                    */
/* A buffer always has to be used for the accumulator; in the         */
/* fastpath, buffers are also always needed for the chunked copies of */
/* of the operand coefficients.                                       */
/* Static buffers are larger than needed just for multiply, to allow  */
/* for calls from other operations (notably exp).                     */
/* ------------------------------------------------------------------ */
#define FASTMUL (DECUSE64 && DECDPUN<5)

static decNumber * decMultiplyOp(decNumber *res, const decNumber *lhs,
                                 const decNumber *rhs, decContext *set,
                                 uInt *status) {
  Int    accunits;                 // Units of accumulator in use
  Int    exponent;                 // work
  Int    residue=0;                // rounding residue
  uByte  bits;                     // result sign
  Unit  *acc;                      // -> accumulator Unit array
  Int    needbytes;                // size calculator
  void  *allocacc=NULL;            // -> allocated accumulator, iff allocated
  Unit  accbuff[SD2U(DECBUFFER*4+1)]; // buffer (+1 for DECBUFFER==0,
                                   // *4 for calls from other operations)
  const Unit *mer, *mermsup;       // work
  Int   madlength;                 // Units in multiplicand
  Int   shift;                     // Units to shift multiplicand by

  #if FASTMUL
    // if DECDPUN is 1 or 3 work in base 10**9, otherwise
    // (DECDPUN is 2 or 4) then work in base 10**8
    #if DECDPUN & 1                // odd

      #define FASTBASE 1000000000  // base

      #define FASTDIGS          9  // digits in base

      #define FASTLAZY         18  // carry resolution point [1->18]

    #else
      #define FASTBASE  100000000

      #define FASTDIGS          8

      #define FASTLAZY       1844  // carry resolution point [1->1844]

    #endif
    // three buffers are used, two for chunked copies of the operands
    // (base 10**8 or base 10**9) and one base 2**64 accumulator with
    // lazy carry evaluation
    uInt   zlhibuff[(DECBUFFER*2+1)/8+1]; // buffer (+1 for DECBUFFER==0)
    uInt  *zlhi=zlhibuff;                 // -> lhs array
    uInt  *alloclhi=NULL;                 // -> allocated buffer, iff allocated
    uInt   zrhibuff[(DECBUFFER*2+1)/8+1]; // buffer (+1 for DECBUFFER==0)
    uInt  *zrhi=zrhibuff;                 // -> rhs array
    uInt  *allocrhi=NULL;                 // -> allocated buffer, iff allocated
    uLong  zaccbuff[(DECBUFFER*2+1)/4+2]; // buffer (+1 for DECBUFFER==0)
    // [allocacc is shared for both paths, as only one will run]
    uLong *zacc=zaccbuff;          // -> accumulator array for exact result
    #if DECDPUN==1
    Int    zoff;                   // accumulator offset
    #endif
    uInt  *lip, *rip;              // item pointers
    uInt  *lmsi, *rmsi;            // most significant items
    Int    ilhs, irhs, iacc;       // item counts in the arrays
    Int    lazy;                   // lazy carry counter
    uLong  lcarry;                 // uLong carry
    uInt   carry;                  // carry (NB not uLong)
    Int    count;                  // work
    const  Unit *cup;              // ..
    Unit  *up;                     // ..
    uLong *lp;                     // ..
    Int    p;                      // ..
  #endif

  #if DECSUBSET
    decNumber *alloclhs=NULL;      // -> allocated buffer, iff allocated
    decNumber *allocrhs=NULL;      // -> allocated buffer, iff allocated
  #endif

  #if DECCHECK
  if (decCheckOperands(res, lhs, rhs, set)) return res;
  #endif

  // precalculate result sign
  bits=(uByte)((lhs->bits^rhs->bits)&DECNEG);

  // handle infinities and NaNs
  if (SPECIALARGS) {               // a special bit set
    if (SPECIALARGS & (DECSNAN | DECNAN)) { // one or two NaNs
      decNaNs(res, lhs, rhs, set, status);
      return res;}
    // one or two infinities; Infinity * 0 is invalid
    if (((lhs->bits & DECINF)==0 && ISZERO(lhs))
      ||((rhs->bits & DECINF)==0 && ISZERO(rhs))) {
      *status|=DEC_Invalid_operation;
      return res;}
    decNumberZero(res);
    res->bits=bits|DECINF;         // infinity
    return res;}

  // For best speed, as in DMSRCN [the original Rexx numerics
  // module], use the shorter number as the multiplier (rhs) and
  // the longer as the multiplicand (lhs) to minimise the number of
  // adds (partial products)
  if (lhs->digits<rhs->digits) {   // swap...
    const decNumber *hold=lhs;
    lhs=rhs;
    rhs=hold;
    }

  do {                             // protect allocated storage
    #if DECSUBSET
    if (!set->extended) {
      // reduce operands and set lostDigits status, as needed
      if (lhs->digits>set->digits) {
        alloclhs=decRoundOperand(lhs, set, status);
        if (alloclhs==NULL) break;
        lhs=alloclhs;
        }
      if (rhs->digits>set->digits) {
        allocrhs=decRoundOperand(rhs, set, status);
        if (allocrhs==NULL) break;
        rhs=allocrhs;
        }
      }
    #endif
    // [following code does not require input rounding]

    #if FASTMUL                    // fastpath can be used

    // use the fast path if there are enough digits in the shorter
    // operand to make the setup and takedown worthwhile
    #define NEEDTWO (DECDPUN*2)    // within two decUnitAddSub calls

    if (rhs->digits>NEEDTWO) {     // use fastpath...
      // calculate the number of elements in each array
      ilhs=(lhs->digits+FASTDIGS-1)/FASTDIGS; // [ceiling]
      irhs=(rhs->digits+FASTDIGS-1)/FASTDIGS; // ..
      iacc=ilhs+irhs;

      // allocate buffers if required, as usual
      needbytes=ilhs*sizeof(uInt);
      if (needbytes>(Int)sizeof(zlhibuff)) {
        alloclhi=(uInt *)malloc(needbytes);
        zlhi=alloclhi;}
      needbytes=irhs*sizeof(uInt);
      if (needbytes>(Int)sizeof(zrhibuff)) {
        allocrhi=(uInt *)malloc(needbytes);
        zrhi=allocrhi;}

      // Allocating the accumulator space needs a special case when
      // DECDPUN=1 because when converting the accumulator to Units
      // after the multiplication each 8-byte item becomes 9 1-byte
      // units.  Therefore iacc extra bytes are needed at the front
      // (rounded up to a multiple of 8 bytes), and the uLong
      // accumulator starts offset the appropriate number of units
      // to the right to avoid overwrite during the unchunking.
      needbytes=iacc*sizeof(uLong);
      #if DECDPUN==1
      zoff=(iacc+7)/8;        // items to offset by
      needbytes+=zoff*8;
      #endif
      if (needbytes>(Int)sizeof(zaccbuff)) {
        allocacc=(uLong *)malloc(needbytes);
        zacc=(uLong *)allocacc;}
      if (zlhi==NULL||zrhi==NULL||zacc==NULL) {
        *status|=DEC_Insufficient_storage;
        break;}

      acc=(Unit *)zacc;       // -> target Unit array
      #if DECDPUN==1
      zacc+=zoff;             // start uLong accumulator to right
      #endif

      // assemble the chunked copies of the left and right sides
      for (count=lhs->digits, cup=lhs->lsu, lip=zlhi; count>0; lip++)
        for (p=0, *lip=0; p<FASTDIGS && count>0;
             p+=DECDPUN, cup++, count-=DECDPUN)
          *lip+=*cup*powers[p];
      lmsi=lip-1;     // save -> msi
      for (count=rhs->digits, cup=rhs->lsu, rip=zrhi; count>0; rip++)
        for (p=0, *rip=0; p<FASTDIGS && count>0;
             p+=DECDPUN, cup++, count-=DECDPUN)
          *rip+=*cup*powers[p];
      rmsi=rip-1;     // save -> msi

      // zero the accumulator
      for (lp=zacc; lp<zacc+iacc; lp++) *lp=0;

      /* Start the multiplication */
      // Resolving carries can dominate the cost of accumulating the
      // partial products, so this is only done when necessary.
      // Each uLong item in the accumulator can hold values up to
      // 2**64-1, and each partial product can be as large as
      // (10**FASTDIGS-1)**2.  When FASTDIGS=9, this can be added to
      // itself 18.4 times in a uLong without overflowing, so during
      // the main calculation resolution is carried out every 18th
      // add -- every 162 digits.  Similarly, when FASTDIGS=8, the
      // partial products can be added to themselves 1844.6 times in
      // a uLong without overflowing, so intermediate carry
      // resolution occurs only every 14752 digits.  Hence for common
      // short numbers usually only the one final carry resolution
      // occurs.
      // (The count is set via FASTLAZY to simplify experiments to
      // measure the value of this approach: a 35% improvement on a
      // [34x34] multiply.)
      lazy=FASTLAZY;                         // carry delay count
      for (rip=zrhi; rip<=rmsi; rip++) {     // over each item in rhs
        lp=zacc+(rip-zrhi);                  // where to add the lhs
        for (lip=zlhi; lip<=lmsi; lip++, lp++) { // over each item in lhs
          *lp+=(uLong)(*lip)*(*rip);         // [this should in-line]
          } // lip loop
        lazy--;
        if (lazy>0 && rip!=rmsi) continue;
        lazy=FASTLAZY;                       // reset delay count
        // spin up the accumulator resolving overflows
        for (lp=zacc; lp<zacc+iacc; lp++) {
          if (*lp<FASTBASE) continue;        // it fits
          lcarry=*lp/FASTBASE;               // top part [slow divide]
          // lcarry can exceed 2**32-1, so check again; this check
          // and occasional extra divide (slow) is well worth it, as
          // it allows FASTLAZY to be increased to 18 rather than 4
          // in the FASTDIGS=9 case
          if (lcarry<FASTBASE) carry=(uInt)lcarry;  // [usual]
           else { // two-place carry [fairly rare]
            uInt carry2=(uInt)(lcarry/FASTBASE);    // top top part
            *(lp+2)+=carry2;                        // add to item+2
            *lp-=((uLong)FASTBASE*FASTBASE*carry2); // [slow]
            carry=(uInt)(lcarry-((uLong)FASTBASE*carry2)); // [inline]
            }
          *(lp+1)+=carry;                    // add to item above [inline]
          *lp-=((uLong)FASTBASE*carry);      // [inline]
          } // carry resolution
        } // rip loop

      // The multiplication is complete; time to convert back into
      // units.  This can be done in-place in the accumulator and in
      // 32-bit operations, because carries were resolved after the
      // final add.  This needs N-1 divides and multiplies for
      // each item in the accumulator (which will become up to N
      // units, where 2<=N<=9).
      for (lp=zacc, up=acc; lp<zacc+iacc; lp++) {
        uInt item=(uInt)*lp;                 // decapitate to uInt
        for (p=0; p<FASTDIGS-DECDPUN; p+=DECDPUN, up++) {
          uInt part=item/(DECDPUNMAX+1);
          *up=(Unit)(item-(part*(DECDPUNMAX+1)));
          item=part;
          } // p
        *up=(Unit)item; up++;                // [final needs no division]
        } // lp
      accunits=up-acc;                       // count of units
      }
     else { // here to use units directly, without chunking ['old code']
    #endif

      // if accumulator will be too long for local storage, then allocate
      acc=accbuff;                 // -> assume buffer for accumulator
      needbytes=(D2U(lhs->digits)+D2U(rhs->digits))*sizeof(Unit);
      if (needbytes>(Int)sizeof(accbuff)) {
        allocacc=(Unit *)malloc(needbytes);
        if (allocacc==NULL) {*status|=DEC_Insufficient_storage; break;}
        acc=(Unit *)allocacc;                // use the allocated space
        }

      /* Now the main long multiplication loop */
      // Unlike the equivalent in the IBM Java implementation, there
      // is no advantage in calculating from msu to lsu.  So, do it
      // by the book, as it were.
      // Each iteration calculates ACC=ACC+MULTAND*MULT
      accunits=1;                  // accumulator starts at '0'
      *acc=0;                      // .. (lsu=0)
      shift=0;                     // no multiplicand shift at first
      madlength=D2U(lhs->digits);  // this won't change
      mermsup=rhs->lsu+D2U(rhs->digits); // -> msu+1 of multiplier

      for (mer=rhs->lsu; mer<mermsup; mer++) {
        // Here, *mer is the next Unit in the multiplier to use
        // If non-zero [optimization] add it...
        if (*mer!=0) accunits=decUnitAddSub(&acc[shift], accunits-shift,
                                            lhs->lsu, madlength, 0,
                                            &acc[shift], *mer)
                                            + shift;
         else { // extend acc with a 0; it will be used shortly
          *(acc+accunits)=0;       // [this avoids length of <=0 later]
          accunits++;
          }
        // multiply multiplicand by 10**DECDPUN for next Unit to left
        shift++;                   // add this for 'logical length'
        } // n
    #if FASTMUL
      } // unchunked units
    #endif
    // common end-path
    #if DECTRACE
      decDumpAr('*', acc, accunits);         // Show exact result
    #endif

    // acc now contains the exact result of the multiplication,
    // possibly with a leading zero unit; build the decNumber from
    // it, noting if any residue
    res->bits=bits;                          // set sign
    res->digits=decGetDigits(acc, accunits); // count digits exactly

    // There can be a 31-bit wrap in calculating the exponent.
    // This can only happen if both input exponents are negative and
    // both their magnitudes are large.  If there was a wrap, set a
    // safe very negative exponent, from which decFinalize() will
    // raise a hard underflow shortly.
    exponent=lhs->exponent+rhs->exponent;    // calculate exponent
    if (lhs->exponent<0 && rhs->exponent<0 && exponent>0)
      exponent=-2*DECNUMMAXE;                // force underflow
    res->exponent=exponent;                  // OK to overwrite now


    // Set the coefficient.  If any rounding, residue records
    decSetCoeff(res, set, acc, res->digits, &residue, status);
    decFinish(res, set, &residue, status);   // final cleanup
    } while(0);                         // end protected

  if (allocacc!=NULL) free(allocacc);   // drop any storage used
  #if DECSUBSET
  if (allocrhs!=NULL) free(allocrhs);   // ..
  if (alloclhs!=NULL) free(alloclhs);   // ..
  #endif
  #if FASTMUL
  if (allocrhi!=NULL) free(allocrhi);   // ..
  if (alloclhi!=NULL) free(alloclhi);   // ..
  #endif
  return res;
  } // decMultiplyOp

/* ------------------------------------------------------------------ */
/* decExpOp -- effect exponentiation                                  */
/*                                                                    */
/*   This computes C = exp(A)                                         */
/*                                                                    */
/*   res is C, the result.  C may be A                                */
/*   rhs is A                                                         */
/*   set is the context; note that rounding mode has no effect        */
/*                                                                    */
/* C must have space for set->digits digits. status is updated but    */
/* not set.                                                           */
/*                                                                    */
/* Restrictions:                                                      */
/*                                                                    */
/*   digits, emax, and -emin in the context must be less than         */
/*   2*DEC_MAX_MATH (1999998), and the rhs must be within these       */
/*   bounds or a zero.  This is an internal routine, so these         */
/*   restrictions are contractual and not enforced.                   */
/*                                                                    */
/* A finite result is rounded using DEC_ROUND_HALF_EVEN; it will      */
/* almost always be correctly rounded, but may be up to 1 ulp in      */
/* error in rare cases.                                               */
/*                                                                    */
/* Finite results will always be full precision and Inexact, except   */
/* when A is a zero or -Infinity (giving 1 or 0 respectively).        */
/* ------------------------------------------------------------------ */
/* This approach used here is similar to the algorithm described in   */
/*                                                                    */
/*   Variable Precision Exponential Function, T. E. Hull and          */
/*   A. Abrham, ACM Transactions on Mathematical Software, Vol 12 #2, */
/*   pp79-91, ACM, June 1986.                                         */
/*                                                                    */
/* with the main difference being that the iterations in the series   */
/* evaluation are terminated dynamically (which does not require the  */
/* extra variable-precision variables which are expensive in this     */
/* context).                                                          */
/*                                                                    */
/* The error analysis in Hull & Abrham's paper applies except for the */
/* round-off error accumulation during the series evaluation.  This   */
/* code does not precalculate the number of iterations and so cannot  */
/* use Horner's scheme.  Instead, the accumulation is done at double- */
/* precision, which ensures that the additions of the terms are exact */
/* and do not accumulate round-off (and any round-off errors in the   */
/* terms themselves move 'to the right' faster than they can          */
/* accumulate).  This code also extends the calculation by allowing,  */
/* in the spirit of other decNumber operators, the input to be more   */
/* precise than the result (the precision used is based on the more   */
/* precise of the input or requested result).                         */
/*                                                                    */
/* Implementation notes:                                              */
/*                                                                    */
/* 1. This is separated out as decExpOp so it can be called from      */
/*    other Mathematical functions (notably Ln) with a wider range    */
/*    than normal.  In particular, it can handle the slightly wider   */
/*    (double) range needed by Ln (which has to be able to calculate  */
/*    exp(-x) where x can be the tiniest number (Ntiny).              */
/*                                                                    */
/* 2. Normalizing x to be <=0.1 (instead of <=1) reduces loop         */
/*    iterations by appoximately a third with additional (although    */
/*    diminishing) returns as the range is reduced to even smaller    */
/*    fractions.  However, h (the power of 10 used to correct the     */
/*    result at the end, see below) must be kept <=8 as otherwise     */
/*    the final result cannot be computed.  Hence the leverage is a   */
/*    sliding value (8-h), where potentially the range is reduced     */
/*    more for smaller values.                                        */
/*                                                                    */
/*    The leverage that can be applied in this way is severely        */
/*    limited by the cost of the raise-to-the power at the end,       */
/*    which dominates when the number of iterations is small (less    */
/*    than ten) or when rhs is short.  As an example, the adjustment  */
/*    x**10,000,000 needs 31 multiplications, all but one full-width. */
/*                                                                    */
/* 3. The restrictions (especially precision) could be raised with    */
/*    care, but the full decNumber range seems very hard within the   */
/*    32-bit limits.                                                  */
/*                                                                    */
/* 4. The working precisions for the static buffers are twice the     */
/*    obvious size to allow for calls from decNumberPower.            */
/* ------------------------------------------------------------------ */
decNumber * decExpOp(decNumber *res, const decNumber *rhs,
                         decContext *set, uInt *status) {
  uInt ignore=0;                   // working status
  Int h;                           // adjusted exponent for 0.xxxx
  Int p;                           // working precision
  Int residue;                     // rounding residue
  uInt needbytes;                  // for space calculations
  const decNumber *x=rhs;          // (may point to safe copy later)
  decContext aset, tset, dset;     // working contexts
  Int comp;                        // work

  // the argument is often copied to normalize it, so (unusually) it
  // is treated like other buffers, using DECBUFFER, +1 in case
  // DECBUFFER is 0
  decNumber bufr[D2N(DECBUFFER*2+1)];
  decNumber *allocrhs=NULL;        // non-NULL if rhs buffer allocated

  // the working precision will be no more than set->digits+8+1
  // so for on-stack buffers DECBUFFER+9 is used, +1 in case DECBUFFER
  // is 0 (and twice that for the accumulator)

  // buffer for t, term (working precision plus)
  decNumber buft[D2N(DECBUFFER*2+9+1)];
  decNumber *allocbuft=NULL;       // -> allocated buft, iff allocated
  decNumber *t=buft;               // term
  // buffer for a, accumulator (working precision * 2), at least 9
  decNumber bufa[D2N(DECBUFFER*4+18+1)];
  decNumber *allocbufa=NULL;       // -> allocated bufa, iff allocated
  decNumber *a=bufa;               // accumulator
  // decNumber for the divisor term; this needs at most 9 digits
  // and so can be fixed size [16 so can use standard context]
  decNumber bufd[D2N(16)];
  decNumber *d=bufd;               // divisor
  decNumber numone;                // constant 1

  #if DECCHECK
  Int iterations=0;                // for later sanity check
  if (decCheckOperands(res, DECUNUSED, rhs, set)) return res;
  #endif

  do {                                  // protect allocated storage
    if (SPECIALARG) {                   // handle infinities and NaNs
      if (decNumberIsInfinite(rhs)) {   // an infinity
        if (decNumberIsNegative(rhs))   // -Infinity -> +0
          decNumberZero(res);
         else decNumberCopy(res, rhs);  // +Infinity -> self
        }
       else decNaNs(res, rhs, NULL, set, status); // a NaN
      break;}

    if (ISZERO(rhs)) {                  // zeros -> exact 1
      decNumberZero(res);               // make clean 1
      *res->lsu=1;                      // ..
      break;}                           // [no status to set]

    // e**x when 0 < x < 0.66 is < 1+3x/2, hence can fast-path
    // positive and negative tiny cases which will result in inexact
    // 1.  This also allows the later add-accumulate to always be
    // exact (because its length will never be more than twice the
    // working precision).
    // The comparator (tiny) needs just one digit, so use the
    // decNumber d for it (reused as the divisor, etc., below); its
    // exponent is such that if x is positive it will have
    // set->digits-1 zeros between the decimal point and the digit,
    // which is 4, and if x is negative one more zero there as the
    // more precise result will be of the form 0.9999999 rather than
    // 1.0000001.  Hence, tiny will be 0.0000004  if digits=7 and x>0
    // or 0.00000004 if digits=7 and x<0.  If RHS not larger than
    // this then the result will be 1.000000
    decNumberZero(d);                   // clean
    *d->lsu=4;                          // set 4 ..
    d->exponent=-set->digits;           // * 10**(-d)
    if (decNumberIsNegative(rhs)) d->exponent--;  // negative case
    comp=decCompare(d, rhs, 1);         // signless compare
    if (comp==BADINT) {
      *status|=DEC_Insufficient_storage;
      break;}
    if (comp>=0) {                      // rhs < d
      Int shift=set->digits-1;
      decNumberZero(res);               // set 1
      *res->lsu=1;                      // ..
      res->digits=decShiftToMost(res->lsu, 1, shift);
      res->exponent=-shift;                  // make 1.0000...
      *status|=DEC_Inexact | DEC_Rounded;    // .. inexactly
      break;} // tiny

    // set up the context to be used for calculating a, as this is
    // used on both paths below
    decContextDefault(&aset, DEC_INIT_DECIMAL64);
    // accumulator bounds are as requested (could underflow)
    aset.emax=set->emax;                // usual bounds
    aset.emin=set->emin;                // ..
    aset.clamp=0;                       // and no concrete format

    // calculate the adjusted (Hull & Abrham) exponent (where the
    // decimal point is just to the left of the coefficient msd)
    h=rhs->exponent+rhs->digits;
    // if h>8 then 10**h cannot be calculated safely; however, when
    // h=8 then exp(|rhs|) will be at least exp(1E+7) which is at
    // least 6.59E+4342944, so (due to the restriction on Emax/Emin)
    // overflow (or underflow to 0) is guaranteed -- so this case can
    // be handled by simply forcing the appropriate excess
    if (h>8) {                          // overflow/underflow
      // set up here so Power call below will over or underflow to
      // zero; set accumulator to either 2 or 0.02
      // [stack buffer for a is always big enough for this]
      decNumberZero(a);
      *a->lsu=2;                        // not 1 but < exp(1)
      if (decNumberIsNegative(rhs)) a->exponent=-2; // make 0.02
      h=8;                              // clamp so 10**h computable
      p=9;                              // set a working precision
      }
     else {                             // h<=8
      Int maxlever=(rhs->digits>8?1:0);
      // [could/should increase this for precisions >40 or so, too]

      // if h is 8, cannot normalize to a lower upper limit because
      // the final result will not be computable (see notes above),
      // but leverage can be applied whenever h is less than 8.
      // Apply as much as possible, up to a MAXLEVER digits, which
      // sets the tradeoff against the cost of the later a**(10**h).
      // As h is increased, the working precision below also
      // increases to compensate for the "constant digits at the
      // front" effect.
      Int lever=MINI(8-h, maxlever);    // leverage attainable
      Int use=-rhs->digits-lever;       // exponent to use for RHS
      h+=lever;                         // apply leverage selected
      if (h<0) {                        // clamp
        use+=h;                         // [may end up subnormal]
        h=0;
        }
      // Take a copy of RHS if it needs normalization (true whenever x>=1)
      if (rhs->exponent!=use) {
        decNumber *newrhs=bufr;         // assume will fit on stack
        needbytes=sizeof(decNumber)+(D2U(rhs->digits)-1)*sizeof(Unit);
        if (needbytes>sizeof(bufr)) {   // need malloc space
          allocrhs=(decNumber *)malloc(needbytes);
          if (allocrhs==NULL) {         // hopeless -- abandon
            *status|=DEC_Insufficient_storage;
            break;}
          newrhs=allocrhs;              // use the allocated space
          }
        decNumberCopy(newrhs, rhs);     // copy to safe space
        newrhs->exponent=use;           // normalize; now <1
        x=newrhs;                       // ready for use
        // decNumberShow(x);
        }

      // Now use the usual power series to evaluate exp(x).  The
      // series starts as 1 + x + x^2/2 ... so prime ready for the
      // third term by setting the term variable t=x, the accumulator
      // a=1, and the divisor d=2.

      // First determine the working precision.  From Hull & Abrham
      // this is set->digits+h+2.  However, if x is 'over-precise' we
      // need to allow for all its digits to potentially participate
      // (consider an x where all the excess digits are 9s) so in
      // this case use x->digits+h+2
      p=MAXI(x->digits, set->digits)+h+2;    // [h<=8]

      // a and t are variable precision, and depend on p, so space
      // must be allocated for them if necessary

      // the accumulator needs to be able to hold 2p digits so that
      // the additions on the second and subsequent iterations are
      // sufficiently exact.
      needbytes=sizeof(decNumber)+(D2U(p*2)-1)*sizeof(Unit);
      if (needbytes>sizeof(bufa)) {     // need malloc space
        allocbufa=(decNumber *)malloc(needbytes);
        if (allocbufa==NULL) {          // hopeless -- abandon
          *status|=DEC_Insufficient_storage;
          break;}
        a=allocbufa;                    // use the allocated space
        }
      // the term needs to be able to hold p digits (which is
      // guaranteed to be larger than x->digits, so the initial copy
      // is safe); it may also be used for the raise-to-power
      // calculation below, which needs an extra two digits
      needbytes=sizeof(decNumber)+(D2U(p+2)-1)*sizeof(Unit);
      if (needbytes>sizeof(buft)) {     // need malloc space
        allocbuft=(decNumber *)malloc(needbytes);
        if (allocbuft==NULL) {          // hopeless -- abandon
          *status|=DEC_Insufficient_storage;
          break;}
        t=allocbuft;                    // use the allocated space
        }

      decNumberCopy(t, x);              // term=x
      decNumberZero(a); *a->lsu=1;      // accumulator=1
      decNumberZero(d); *d->lsu=2;      // divisor=2
      decNumberZero(&numone); *numone.lsu=1; // constant 1 for increment

      // set up the contexts for calculating a, t, and d
      decContextDefault(&tset, DEC_INIT_DECIMAL64);
      dset=tset;
      // accumulator bounds are set above, set precision now
      aset.digits=p*2;                  // double
      // term bounds avoid any underflow or overflow
      tset.digits=p;
      tset.emin=DEC_MIN_EMIN;           // [emax is plenty]
      // [dset.digits=16, etc., are sufficient]

      // finally ready to roll
      for (;;) {
        #if DECCHECK
        iterations++;
        #endif
        // only the status from the accumulation is interesting
        // [but it should remain unchanged after first add]
        decAddOp(a, a, t, &aset, 0, status);           // a=a+t
        decMultiplyOp(t, t, x, &tset, &ignore);        // t=t*x
        decDivideOp(t, t, d, &tset, DIVIDE, &ignore);  // t=t/d
        // the iteration ends when the term cannot affect the result,
        // if rounded to p digits, which is when its value is smaller
        // than the accumulator by p+1 digits.  There must also be
        // full precision in a.
        if (((a->digits+a->exponent)>=(t->digits+t->exponent+p+1))
            && (a->digits>=p)) break;
        decAddOp(d, d, &numone, &dset, 0, &ignore);    // d=d+1
        } // iterate

      #if DECCHECK
      // just a sanity check; comment out test to show always
      if (iterations>p+3)
        printf("Exp iterations=%ld, status=%08lx, p=%ld, d=%ld\n",
               (LI)iterations, (LI)*status, (LI)p, (LI)x->digits);
      #endif
      } // h<=8

    // apply postconditioning: a=a**(10**h) -- this is calculated
    // at a slightly higher precision than Hull & Abrham suggest
    if (h>0) {
      Int seenbit=0;               // set once a 1-bit is seen
      Int i;                       // counter
      Int n=powers[h];             // always positive
      aset.digits=p+2;             // sufficient precision
      // avoid the overhead and many extra digits of decNumberPower
      // as all that is needed is the short 'multipliers' loop; here
      // accumulate the answer into t
      decNumberZero(t); *t->lsu=1; // acc=1
      for (i=1;;i++){              // for each bit [top bit ignored]
        // abandon if have had overflow or terminal underflow
        if (*status & (DEC_Overflow|DEC_Underflow)) { // interesting?
          if (*status&DEC_Overflow || ISZERO(t)) break;}
        n=n<<1;                    // move next bit to testable position
        if (n<0) {                 // top bit is set
          seenbit=1;               // OK, have a significant bit
          decMultiplyOp(t, t, a, &aset, status); // acc=acc*x
          }
        if (i==31) break;          // that was the last bit
        if (!seenbit) continue;    // no need to square 1
        decMultiplyOp(t, t, t, &aset, status); // acc=acc*acc [square]
        } /*i*/ // 32 bits
      // decNumberShow(t);
      a=t;                         // and carry on using t instead of a
      }

    // Copy and round the result to res
    residue=1;                          // indicate dirt to right ..
    if (ISZERO(a)) residue=0;           // .. unless underflowed to 0
    aset.digits=set->digits;            // [use default rounding]
    decCopyFit(res, a, &aset, &residue, status); // copy & shorten
    decFinish(res, set, &residue, status);       // cleanup/set flags
    } while(0);                         // end protected

  if (allocrhs !=NULL) free(allocrhs);  // drop any storage used
  if (allocbufa!=NULL) free(allocbufa); // ..
  if (allocbuft!=NULL) free(allocbuft); // ..
  // [status is handled by caller]
  return res;
  } // decExpOp

/* ------------------------------------------------------------------ */
/* Initial-estimate natural logarithm table                           */
/*                                                                    */
/*   LNnn -- 90-entry 16-bit table for values from .10 through .99.   */
/*           The result is a 4-digit encode of the coefficient (c=the */
/*           top 14 bits encoding 0-9999) and a 2-digit encode of the */
/*           exponent (e=the bottom 2 bits encoding 0-3)              */
/*                                                                    */
/*           The resulting value is given by:                         */
/*                                                                    */
/*             v = -c * 10**(-e-3)                                    */
/*                                                                    */
/*           where e and c are extracted from entry k = LNnn[x-10]    */
/*           where x is truncated (NB) into the range 10 through 99,  */
/*           and then c = k>>2 and e = k&3.                           */
/* ------------------------------------------------------------------ */
const uShort LNnn[90]={9016,  8652,  8316,  8008,  7724,  7456,  7208,
  6972,  6748,  6540,  6340,  6148,  5968,  5792,  5628,  5464,  5312,
  5164,  5020,  4884,  4748,  4620,  4496,  4376,  4256,  4144,  4032,
 39233, 38181, 37157, 36157, 35181, 34229, 33297, 32389, 31501, 30629,
 29777, 28945, 28129, 27329, 26545, 25777, 25021, 24281, 23553, 22837,
 22137, 21445, 20769, 20101, 19445, 18801, 18165, 17541, 16925, 16321,
 15721, 15133, 14553, 13985, 13421, 12865, 12317, 11777, 11241, 10717,
 10197,  9685,  9177,  8677,  8185,  7697,  7213,  6737,  6269,  5801,
  5341,  4889,  4437, 39930, 35534, 31186, 26886, 22630, 18418, 14254,
 10130,  6046, 20055};

/* ------------------------------------------------------------------ */
/* decLnOp -- effect natural logarithm                                */
/*                                                                    */
/*   This computes C = ln(A)                                          */
/*                                                                    */
/*   res is C, the result.  C may be A                                */
/*   rhs is A                                                         */
/*   set is the context; note that rounding mode has no effect        */
/*                                                                    */
/* C must have space for set->digits digits.                          */
/*                                                                    */
/* Notable cases:                                                     */
/*   A<0 -> Invalid                                                   */
/*   A=0 -> -Infinity (Exact)                                         */
/*   A=+Infinity -> +Infinity (Exact)                                 */
/*   A=1 exactly -> 0 (Exact)                                         */
/*                                                                    */
/* Restrictions (as for Exp):                                         */
/*                                                                    */
/*   digits, emax, and -emin in the context must be less than         */
/*   DEC_MAX_MATH+11 (1000010), and the rhs must be within these      */
/*   bounds or a zero.  This is an internal routine, so these         */
/*   restrictions are contractual and not enforced.                   */
/*                                                                    */
/* A finite result is rounded using DEC_ROUND_HALF_EVEN; it will      */
/* almost always be correctly rounded, but may be up to 1 ulp in      */
/* error in rare cases.                                               */
/* ------------------------------------------------------------------ */
/* The result is calculated using Newton's method, with each          */
/* iteration calculating a' = a + x * exp(-a) - 1.  See, for example, */
/* Epperson 1989.                                                     */
/*                                                                    */
/* The iteration ends when the adjustment x*exp(-a)-1 is tiny enough. */
/* This has to be calculated at the sum of the precision of x and the */
/* working precision.                                                 */
/*                                                                    */
/* Implementation notes:                                              */
/*                                                                    */
/* 1. This is separated out as decLnOp so it can be called from       */
/*    other Mathematical functions (e.g., Log 10) with a wider range  */
/*    than normal.  In particular, it can handle the slightly wider   */
/*    (+9+2) range needed by a power function.                        */
/*                                                                    */
/* 2. The speed of this function is about 10x slower than exp, as     */
/*    it typically needs 4-6 iterations for short numbers, and the    */
/*    extra precision needed adds a squaring effect, twice.           */
/*                                                                    */
/* 3. Fastpaths are included for ln(10) and ln(2), up to length 40,   */
/*    as these are common requests.  ln(10) is used by log10(x).      */
/*                                                                    */
/* 4. An iteration might be saved by widening the LNnn table, and     */
/*    would certainly save at least one if it were made ten times     */
/*    bigger, too (for truncated fractions 0.100 through 0.999).      */
/*    However, for most practical evaluations, at least four or five  */
/*    iterations will be neede -- so this would only speed up by      */
/*    20-25% and that probably does not justify increasing the table  */
/*    size.                                                           */
/*                                                                    */
/* 5. The static buffers are larger than might be expected to allow   */
/*    for calls from decNumberPower.                                  */
/* ------------------------------------------------------------------ */
decNumber * decLnOp(decNumber *res, const decNumber *rhs,
                    decContext *set, uInt *status) {
  uInt ignore=0;                   // working status accumulator
  uInt needbytes;                  // for space calculations
  Int residue;                     // rounding residue
  Int r;                           // rhs=f*10**r [see below]
  Int p;                           // working precision
  Int pp;                          // precision for iteration
  Int t;                           // work

  // buffers for a (accumulator, typically precision+2) and b
  // (adjustment calculator, same size)
  decNumber bufa[D2N(DECBUFFER+12)];
  decNumber *allocbufa=NULL;       // -> allocated bufa, iff allocated
  decNumber *a=bufa;               // accumulator/work
  decNumber bufb[D2N(DECBUFFER*2+2)];
  decNumber *allocbufb=NULL;       // -> allocated bufa, iff allocated
  decNumber *b=bufb;               // adjustment/work

  decNumber  numone;               // constant 1
  decNumber  cmp;                  // work
  decContext aset, bset;           // working contexts

  #if DECCHECK
  Int iterations=0;                // for later sanity check
  if (decCheckOperands(res, DECUNUSED, rhs, set)) return res;
  #endif

  do {                                  // protect allocated storage
    if (SPECIALARG) {                   // handle infinities and NaNs
      if (decNumberIsInfinite(rhs)) {   // an infinity
        if (decNumberIsNegative(rhs))   // -Infinity -> error
          *status|=DEC_Invalid_operation;
         else decNumberCopy(res, rhs);  // +Infinity -> self
        }
       else decNaNs(res, rhs, NULL, set, status); // a NaN
      break;}

    if (ISZERO(rhs)) {                  // +/- zeros -> -Infinity
      decNumberZero(res);               // make clean
      res->bits=DECINF|DECNEG;          // set - infinity
      break;}                           // [no status to set]

    // Non-zero negatives are bad...
    if (decNumberIsNegative(rhs)) {     // -x -> error
      *status|=DEC_Invalid_operation;
      break;}

    // Here, rhs is positive, finite, and in range

    // lookaside fastpath code for ln(2) and ln(10) at common lengths
    if (rhs->exponent==0 && set->digits<=40) {
      #if DECDPUN==1
      if (rhs->lsu[0]==0 && rhs->lsu[1]==1 && rhs->digits==2) { // ln(10)
      #else
      if (rhs->lsu[0]==10 && rhs->digits==2) {                  // ln(10)
      #endif
        aset=*set; aset.round=DEC_ROUND_HALF_EVEN;
        #define LN10 "2.302585092994045684017991454684364207601"

        decNumberFromString(res, LN10, &aset);
        *status|=(DEC_Inexact | DEC_Rounded); // is inexact
        break;}
      if (rhs->lsu[0]==2 && rhs->digits==1) { // ln(2)
        aset=*set; aset.round=DEC_ROUND_HALF_EVEN;
        #define LN2 "0.6931471805599453094172321214581765680755"

        decNumberFromString(res, LN2, &aset);
        *status|=(DEC_Inexact | DEC_Rounded);
        break;}
      } // integer and short

    // Determine the working precision.  This is normally the
    // requested precision + 2, with a minimum of 9.  However, if
    // the rhs is 'over-precise' then allow for all its digits to
    // potentially participate (consider an rhs where all the excess
    // digits are 9s) so in this case use rhs->digits+2.
    p=MAXI(rhs->digits, MAXI(set->digits, 7))+2;

    // Allocate space for the accumulator and the high-precision
    // adjustment calculator, if necessary.  The accumulator must
    // be able to hold p digits, and the adjustment up to
    // rhs->digits+p digits.  They are also made big enough for 16
    // digits so that they can be used for calculating the initial
    // estimate.
    needbytes=sizeof(decNumber)+(D2U(MAXI(p,16))-1)*sizeof(Unit);
    if (needbytes>sizeof(bufa)) {     // need malloc space
      allocbufa=(decNumber *)malloc(needbytes);
      if (allocbufa==NULL) {          // hopeless -- abandon
        *status|=DEC_Insufficient_storage;
        break;}
      a=allocbufa;                    // use the allocated space
      }
    pp=p+rhs->digits;
    needbytes=sizeof(decNumber)+(D2U(MAXI(pp,16))-1)*sizeof(Unit);
    if (needbytes>sizeof(bufb)) {     // need malloc space
      allocbufb=(decNumber *)malloc(needbytes);
      if (allocbufb==NULL) {          // hopeless -- abandon
        *status|=DEC_Insufficient_storage;
        break;}
      b=allocbufb;                    // use the allocated space
      }

    // Prepare an initial estimate in acc. Calculate this by
    // considering the coefficient of x to be a normalized fraction,
    // f, with the decimal point at far left and multiplied by
    // 10**r.  Then, rhs=f*10**r and 0.1<=f<1, and
    //   ln(x) = ln(f) + ln(10)*r
    // Get the initial estimate for ln(f) from a small lookup
    // table (see above) indexed by the first two digits of f,
    // truncated.

    decContextDefault(&aset, DEC_INIT_DECIMAL64); // 16-digit extended
    r=rhs->exponent+rhs->digits;        // 'normalised' exponent
    decNumberFromInt32(a, r);           // a=r
    decNumberFromInt32(b, 2302585);     // b=ln(10) (2.302585)
    b->exponent=-6;                     //  ..
    decMultiplyOp(a, a, b, &aset, &ignore);  // a=a*b
    // now get top two digits of rhs into b by simple truncate and
    // force to integer
    residue=0;                          // (no residue)
    aset.digits=2; aset.round=DEC_ROUND_DOWN;
    decCopyFit(b, rhs, &aset, &residue, &ignore); // copy & shorten
    b->exponent=0;                      // make integer
    t=decGetInt(b);                     // [cannot fail]
    if (t<10) t=X10(t);                 // adjust single-digit b
    t=LNnn[t-10];                       // look up ln(b)
    decNumberFromInt32(b, t>>2);        // b=ln(b) coefficient
    b->exponent=-(t&3)-3;               // set exponent
    b->bits=DECNEG;                     // ln(0.10)->ln(0.99) always -ve
    aset.digits=16; aset.round=DEC_ROUND_HALF_EVEN; // restore
    decAddOp(a, a, b, &aset, 0, &ignore); // acc=a+b
    // the initial estimate is now in a, with up to 4 digits correct.
    // When rhs is at or near Nmax the estimate will be low, so we
    // will approach it from below, avoiding overflow when calling exp.

    decNumberZero(&numone); *numone.lsu=1;   // constant 1 for adjustment

    // accumulator bounds are as requested (could underflow, but
    // cannot overflow)
    aset.emax=set->emax;
    aset.emin=set->emin;
    aset.clamp=0;                       // no concrete format
    // set up a context to be used for the multiply and subtract
    bset=aset;
    bset.emax=DEC_MAX_MATH*2;           // use double bounds for the
    bset.emin=-DEC_MAX_MATH*2;          // adjustment calculation
                                        // [see decExpOp call below]
    // for each iteration double the number of digits to calculate,
    // up to a maximum of p
    pp=9;                               // initial precision
    // [initially 9 as then the sequence starts 7+2, 16+2, and
    // 34+2, which is ideal for standard-sized numbers]
    aset.digits=pp;                     // working context
    bset.digits=pp+rhs->digits;         // wider context
    for (;;) {                          // iterate
      #if DECCHECK
      iterations++;
      if (iterations>24) break;         // consider 9 * 2**24
      #endif
      // calculate the adjustment (exp(-a)*x-1) into b.  This is a
      // catastrophic subtraction but it really is the difference
      // from 1 that is of interest.
      // Use the internal entry point to Exp as it allows the double
      // range for calculating exp(-a) when a is the tiniest subnormal.
      a->bits^=DECNEG;                  // make -a
      decExpOp(b, a, &bset, &ignore);   // b=exp(-a)
      a->bits^=DECNEG;                  // restore sign of a
      // now multiply by rhs and subtract 1, at the wider precision
      decMultiplyOp(b, b, rhs, &bset, &ignore);        // b=b*rhs
      decAddOp(b, b, &numone, &bset, DECNEG, &ignore); // b=b-1

      // the iteration ends when the adjustment cannot affect the
      // result by >=0.5 ulp (at the requested digits), which
      // is when its value is smaller than the accumulator by
      // set->digits+1 digits (or it is zero) -- this is a looser
      // requirement than for Exp because all that happens to the
      // accumulator after this is the final rounding (but note that
      // there must also be full precision in a, or a=0).

      if (decNumberIsZero(b) ||
          (a->digits+a->exponent)>=(b->digits+b->exponent+set->digits+1)) {
        if (a->digits==p) break;
        if (decNumberIsZero(a)) {
          decCompareOp(&cmp, rhs, &numone, &aset, COMPARE, &ignore); // rhs=1 ?
          if (cmp.lsu[0]==0) a->exponent=0;            // yes, exact 0
           else *status|=(DEC_Inexact | DEC_Rounded);  // no, inexact
          break;
          }
        // force padding if adjustment has gone to 0 before full length
        if (decNumberIsZero(b)) b->exponent=a->exponent-p;
        }

      // not done yet ...
      decAddOp(a, a, b, &aset, 0, &ignore);  // a=a+b for next estimate
      if (pp==p) continue;                   // precision is at maximum
      // lengthen the next calculation
      pp=pp*2;                               // double precision
      if (pp>p) pp=p;                        // clamp to maximum
      aset.digits=pp;                        // working context
      bset.digits=pp+rhs->digits;            // wider context
      } // Newton's iteration

    #if DECCHECK
    // just a sanity check; remove the test to show always
    if (iterations>24)
      printf("Ln iterations=%ld, status=%08lx, p=%ld, d=%ld\n",
            (LI)iterations, (LI)*status, (LI)p, (LI)rhs->digits);
    #endif

    // Copy and round the result to res
    residue=1;                          // indicate dirt to right
    if (ISZERO(a)) residue=0;           // .. unless underflowed to 0
    aset.digits=set->digits;            // [use default rounding]
    decCopyFit(res, a, &aset, &residue, status); // copy & shorten
    decFinish(res, set, &residue, status);       // cleanup/set flags
    } while(0);                         // end protected

  if (allocbufa!=NULL) free(allocbufa); // drop any storage used
  if (allocbufb!=NULL) free(allocbufb); // ..
  // [status is handled by caller]
  return res;
  } // decLnOp

/* ------------------------------------------------------------------ */
/* decQuantizeOp  -- force exponent to requested value                */
/*                                                                    */
/*   This computes C = op(A, B), where op adjusts the coefficient     */
/*   of C (by rounding or shifting) such that the exponent (-scale)   */
/*   of C has the value B or matches the exponent of B.               */
/*   The numerical value of C will equal A, except for the effects of */
/*   any rounding that occurred.                                      */
/*                                                                    */
/*   res is C, the result.  C may be A or B                           */
/*   lhs is A, the number to adjust                                   */
/*   rhs is B, the requested exponent                                 */
/*   set is the context                                               */
/*   quant is 1 for quantize or 0 for rescale                         */
/*   status is the status accumulator (this can be called without     */
/*          risk of control loss)                                     */
/*                                                                    */
/* C must have space for set->digits digits.                          */
/*                                                                    */
/* Unless there is an error or the result is infinite, the exponent   */
/* after the operation is guaranteed to be that requested.            */
/* ------------------------------------------------------------------ */
static decNumber * decQuantizeOp(decNumber *res, const decNumber *lhs,
                                 const decNumber *rhs, decContext *set,
                                 Flag quant, uInt *status) {
  #if DECSUBSET
  decNumber *alloclhs=NULL;        // non-NULL if rounded lhs allocated
  decNumber *allocrhs=NULL;        // .., rhs
  #endif
  const decNumber *inrhs=rhs;      // save original rhs
  Int   reqdigits=set->digits;     // requested DIGITS
  Int   reqexp;                    // requested exponent [-scale]
  Int   residue=0;                 // rounding residue
  Int   etiny=set->emin-(reqdigits-1);

  #if DECCHECK
  if (decCheckOperands(res, lhs, rhs, set)) return res;
  #endif

  do {                             // protect allocated storage
    #if DECSUBSET
    if (!set->extended) {
      // reduce operands and set lostDigits status, as needed
      if (lhs->digits>reqdigits) {
        alloclhs=decRoundOperand(lhs, set, status);
        if (alloclhs==NULL) break;
        lhs=alloclhs;
        }
      if (rhs->digits>reqdigits) { // [this only checks lostDigits]
        allocrhs=decRoundOperand(rhs, set, status);
        if (allocrhs==NULL) break;
        rhs=allocrhs;
        }
      }
    #endif
    // [following code does not require input rounding]

    // Handle special values
    if (SPECIALARGS) {
      // NaNs get usual processing
      if (SPECIALARGS & (DECSNAN | DECNAN))
        decNaNs(res, lhs, rhs, set, status);
      // one infinity but not both is bad
      else if ((lhs->bits ^ rhs->bits) & DECINF)
        *status|=DEC_Invalid_operation;
      // both infinity: return lhs
      else decNumberCopy(res, lhs);          // [nop if in place]
      break;
      }

    // set requested exponent
    if (quant) reqexp=inrhs->exponent;  // quantize -- match exponents
     else {                             // rescale -- use value of rhs
      // Original rhs must be an integer that fits and is in range,
      // which could be from -1999999997 to +999999999, thanks to
      // subnormals
      reqexp=decGetInt(inrhs);               // [cannot fail]
      }

    #if DECSUBSET
    if (!set->extended) etiny=set->emin;     // no subnormals
    #endif

    if (reqexp==BADINT                       // bad (rescale only) or ..
     || reqexp==BIGODD || reqexp==BIGEVEN    // very big (ditto) or ..
     || (reqexp<etiny)                       // < lowest
     || (reqexp>set->emax)) {                // > emax
      *status|=DEC_Invalid_operation;
      break;}

    // the RHS has been processed, so it can be overwritten now if necessary
    if (ISZERO(lhs)) {                       // zero coefficient unchanged
      decNumberCopy(res, lhs);               // [nop if in place]
      res->exponent=reqexp;                  // .. just set exponent
      #if DECSUBSET
      if (!set->extended) res->bits=0;       // subset specification; no -0
      #endif
      }
     else {                                  // non-zero lhs
      Int adjust=reqexp-lhs->exponent;       // digit adjustment needed
      // if adjusted coefficient will definitely not fit, give up now
      if ((lhs->digits-adjust)>reqdigits) {
        *status|=DEC_Invalid_operation;
        break;
        }

      if (adjust>0) {                        // increasing exponent
        // this will decrease the length of the coefficient by adjust
        // digits, and must round as it does so
        decContext workset;                  // work
        workset=*set;                        // clone rounding, etc.
        workset.digits=lhs->digits-adjust;   // set requested length
        // [note that the latter can be <1, here]
        decCopyFit(res, lhs, &workset, &residue, status); // fit to result
        decApplyRound(res, &workset, residue, status);    // .. and round
        residue=0;                                        // [used]
        // If just rounded a 999s case, exponent will be off by one;
        // adjust back (after checking space), if so.
        if (res->exponent>reqexp) {
          // re-check needed, e.g., for quantize(0.9999, 0.001) under
          // set->digits==3
          if (res->digits==reqdigits) {      // cannot shift by 1
            *status&=~(DEC_Inexact | DEC_Rounded); // [clean these]
            *status|=DEC_Invalid_operation;
            break;
            }
          res->digits=decShiftToMost(res->lsu, res->digits, 1); // shift
          res->exponent--;                   // (re)adjust the exponent.
          }
        #if DECSUBSET
        if (ISZERO(res) && !set->extended) res->bits=0; // subset; no -0
        #endif
        } // increase
       else /* adjust<=0 */ {                // decreasing or = exponent
        // this will increase the length of the coefficient by -adjust
        // digits, by adding zero or more trailing zeros; this is
        // already checked for fit, above
        decNumberCopy(res, lhs);             // [it will fit]
        // if padding needed (adjust<0), add it now...
        if (adjust<0) {
          res->digits=decShiftToMost(res->lsu, res->digits, -adjust);
          res->exponent+=adjust;             // adjust the exponent
          }
        } // decrease
      } // non-zero

    // Check for overflow [do not use Finalize in this case, as an
    // overflow here is a "don't fit" situation]
    if (res->exponent>set->emax-res->digits+1) {  // too big
      *status|=DEC_Invalid_operation;
      break;
      }
     else {
      decFinalize(res, set, &residue, status);    // set subnormal flags
      *status&=~DEC_Underflow;          // suppress Underflow [as per 754]
      }
    } while(0);                         // end protected

  #if DECSUBSET
  if (allocrhs!=NULL) free(allocrhs);   // drop any storage used
  if (alloclhs!=NULL) free(alloclhs);   // ..
  #endif
  return res;
  } // decQuantizeOp

/* ------------------------------------------------------------------ */
/* decCompareOp -- compare, min, or max two Numbers                   */
/*                                                                    */
/*   This computes C = A ? B and carries out one of four operations:  */
/*     COMPARE    -- returns the signum (as a number) giving the      */
/*                   result of a comparison unless one or both        */
/*                   operands is a NaN (in which case a NaN results)  */
/*     COMPSIG    -- as COMPARE except that a quiet NaN raises        */
/*                   Invalid operation.                               */
/*     COMPMAX    -- returns the larger of the operands, using the    */
/*                   754 maxnum operation                             */
/*     COMPMAXMAG -- ditto, comparing absolute values                 */
/*     COMPMIN    -- the 754 minnum operation                         */
/*     COMPMINMAG -- ditto, comparing absolute values                 */
/*     COMTOTAL   -- returns the signum (as a number) giving the      */
/*                   result of a comparison using 754 total ordering  */
/*                                                                    */
/*   res is C, the result.  C may be A and/or B (e.g., X=X?X)         */
/*   lhs is A                                                         */
/*   rhs is B                                                         */
/*   set is the context                                               */
/*   op  is the operation flag                                        */
/*   status is the usual accumulator                                  */
/*                                                                    */
/* C must have space for one digit for COMPARE or set->digits for     */
/* COMPMAX, COMPMIN, COMPMAXMAG, or COMPMINMAG.                       */
/* ------------------------------------------------------------------ */
/* The emphasis here is on speed for common cases, and avoiding       */
/* coefficient comparison if possible.                                */
/* ------------------------------------------------------------------ */
decNumber * decCompareOp(decNumber *res, const decNumber *lhs,
                         const decNumber *rhs, decContext *set,
                         Flag op, uInt *status) {
  #if DECSUBSET
  decNumber *alloclhs=NULL;        // non-NULL if rounded lhs allocated
  decNumber *allocrhs=NULL;        // .., rhs
  #endif
  Int   result=0;                  // default result value
  uByte merged;                    // work

  #if DECCHECK
  if (decCheckOperands(res, lhs, rhs, set)) return res;
  #endif

  do {                             // protect allocated storage
    #if DECSUBSET
    if (!set->extended) {
      // reduce operands and set lostDigits status, as needed
      if (lhs->digits>set->digits) {
        alloclhs=decRoundOperand(lhs, set, status);
        if (alloclhs==NULL) {result=BADINT; break;}
        lhs=alloclhs;
        }
      if (rhs->digits>set->digits) {
        allocrhs=decRoundOperand(rhs, set, status);
        if (allocrhs==NULL) {result=BADINT; break;}
        rhs=allocrhs;
        }
      }
    #endif
    // [following code does not require input rounding]

    // If total ordering then handle differing signs 'up front'
    if (op==COMPTOTAL) {                // total ordering
      if (decNumberIsNegative(lhs) & !decNumberIsNegative(rhs)) {
        result=-1;
        break;
        }
      if (!decNumberIsNegative(lhs) & decNumberIsNegative(rhs)) {
        result=+1;
        break;
        }
      }

    // handle NaNs specially; let infinities drop through
    // This assumes sNaN (even just one) leads to NaN.
    merged=(lhs->bits | rhs->bits) & (DECSNAN | DECNAN);
    if (merged) {                       // a NaN bit set
      if (op==COMPARE);                 // result will be NaN
       else if (op==COMPSIG)            // treat qNaN as sNaN
        *status|=DEC_Invalid_operation | DEC_sNaN;
       else if (op==COMPTOTAL) {        // total ordering, always finite
        // signs are known to be the same; compute the ordering here
        // as if the signs are both positive, then invert for negatives
        if (!decNumberIsNaN(lhs)) result=-1;
         else if (!decNumberIsNaN(rhs)) result=+1;
         // here if both NaNs
         else if (decNumberIsSNaN(lhs) && decNumberIsQNaN(rhs)) result=-1;
         else if (decNumberIsQNaN(lhs) && decNumberIsSNaN(rhs)) result=+1;
         else { // both NaN or both sNaN
          // now it just depends on the payload
          result=decUnitCompare(lhs->lsu, D2U(lhs->digits),
                                rhs->lsu, D2U(rhs->digits), 0);
          // [Error not possible, as these are 'aligned']
          } // both same NaNs
        if (decNumberIsNegative(lhs)) result=-result;
        break;
        } // total order

       else if (merged & DECSNAN);           // sNaN -> qNaN
       else { // here if MIN or MAX and one or two quiet NaNs
        // min or max -- 754 rules ignore single NaN
        if (!decNumberIsNaN(lhs) || !decNumberIsNaN(rhs)) {
          // just one NaN; force choice to be the non-NaN operand
          op=COMPMAX;
          if (lhs->bits & DECNAN) result=-1; // pick rhs
                             else result=+1; // pick lhs
          break;
          }
        } // max or min
      op=COMPNAN;                            // use special path
      decNaNs(res, lhs, rhs, set, status);   // propagate NaN
      break;
      }
    // have numbers
    if (op==COMPMAXMAG || op==COMPMINMAG) result=decCompare(lhs, rhs, 1);
     else result=decCompare(lhs, rhs, 0);    // sign matters
    } while(0);                              // end protected

  if (result==BADINT) *status|=DEC_Insufficient_storage; // rare
   else {
    if (op==COMPARE || op==COMPSIG ||op==COMPTOTAL) { // returning signum
      if (op==COMPTOTAL && result==0) {
        // operands are numerically equal or same NaN (and same sign,
        // tested first); if identical, leave result 0
        if (lhs->exponent!=rhs->exponent) {
          if (lhs->exponent<rhs->exponent) result=-1;
           else result=+1;
          if (decNumberIsNegative(lhs)) result=-result;
          } // lexp!=rexp
        } // total-order by exponent
      decNumberZero(res);               // [always a valid result]
      if (result!=0) {                  // must be -1 or +1
        *res->lsu=1;
        if (result<0) res->bits=DECNEG;
        }
      }
     else if (op==COMPNAN);             // special, drop through
     else {                             // MAX or MIN, non-NaN result
      Int residue=0;                    // rounding accumulator
      // choose the operand for the result
      const decNumber *choice;
      if (result==0) { // operands are numerically equal
        // choose according to sign then exponent (see 754)
        uByte slhs=(lhs->bits & DECNEG);
        uByte srhs=(rhs->bits & DECNEG);
        #if DECSUBSET
        if (!set->extended) {           // subset: force left-hand
          op=COMPMAX;
          result=+1;
          }
        else
        #endif
        if (slhs!=srhs) {          // signs differ
          if (slhs) result=-1;     // rhs is max
               else result=+1;     // lhs is max
          }
         else if (slhs && srhs) {  // both negative
          if (lhs->exponent<rhs->exponent) result=+1;
                                      else result=-1;
          // [if equal, use lhs, technically identical]
          }
         else {                    // both positive
          if (lhs->exponent>rhs->exponent) result=+1;
                                      else result=-1;
          // [ditto]
          }
        } // numerically equal
      // here result will be non-0; reverse if looking for MIN
      if (op==COMPMIN || op==COMPMINMAG) result=-result;
      choice=(result>0 ? lhs : rhs);    // choose
      // copy chosen to result, rounding if need be
      decCopyFit(res, choice, set, &residue, status);
      decFinish(res, set, &residue, status);
      }
    }
  #if DECSUBSET
  if (allocrhs!=NULL) free(allocrhs);   // free any storage used
  if (alloclhs!=NULL) free(alloclhs);   // ..
  #endif
  return res;
  } // decCompareOp

/* ------------------------------------------------------------------ */
/* decCompare -- compare two decNumbers by numerical value            */
/*                                                                    */
/*  This routine compares A ? B without altering them.                */
/*                                                                    */
/*  Arg1 is A, a decNumber which is not a NaN                         */
/*  Arg2 is B, a decNumber which is not a NaN                         */
/*  Arg3 is 1 for a sign-independent compare, 0 otherwise             */
/*                                                                    */
/*  returns -1, 0, or 1 for A<B, A==B, or A>B, or BADINT if failure   */
/*  (the only possible failure is an allocation error)                */
/* ------------------------------------------------------------------ */
static Int decCompare(const decNumber *lhs, const decNumber *rhs,
                      Flag abs) {
  Int   result;                    // result value
  Int   sigr;                      // rhs signum
  Int   compare;                   // work

  result=1;                                  // assume signum(lhs)
  if (ISZERO(lhs)) result=0;
  if (abs) {
    if (ISZERO(rhs)) return result;          // LHS wins or both 0
    // RHS is non-zero
    if (result==0) return -1;                // LHS is 0; RHS wins
    // [here, both non-zero, result=1]
    }
   else {                                    // signs matter
    if (result && decNumberIsNegative(lhs)) result=-1;
    sigr=1;                                  // compute signum(rhs)
    if (ISZERO(rhs)) sigr=0;
     else if (decNumberIsNegative(rhs)) sigr=-1;
    if (result > sigr) return +1;            // L > R, return 1
    if (result < sigr) return -1;            // L < R, return -1
    if (result==0) return 0;                   // both 0
    }

  // signums are the same; both are non-zero
  if ((lhs->bits | rhs->bits) & DECINF) {    // one or more infinities
    if (decNumberIsInfinite(rhs)) {
      if (decNumberIsInfinite(lhs)) result=0;// both infinite
       else result=-result;                  // only rhs infinite
      }
    return result;
    }
  // must compare the coefficients, allowing for exponents
  if (lhs->exponent>rhs->exponent) {         // LHS exponent larger
    // swap sides, and sign
    const decNumber *temp=lhs;
    lhs=rhs;
    rhs=temp;
    result=-result;
    }
  compare=decUnitCompare(lhs->lsu, D2U(lhs->digits),
                         rhs->lsu, D2U(rhs->digits),
                         rhs->exponent-lhs->exponent);
  if (compare!=BADINT) compare*=result;      // comparison succeeded
  return compare;
  } // decCompare

/* ------------------------------------------------------------------ */
/* decUnitCompare -- compare two >=0 integers in Unit arrays          */
/*                                                                    */
/*  This routine compares A ? B*10**E where A and B are unit arrays   */
/*  A is a plain integer                                              */
/*  B has an exponent of E (which must be non-negative)               */
/*                                                                    */
/*  Arg1 is A first Unit (lsu)                                        */
/*  Arg2 is A length in Units                                         */
/*  Arg3 is B first Unit (lsu)                                        */
/*  Arg4 is B length in Units                                         */
/*  Arg5 is E (0 if the units are aligned)                            */
/*                                                                    */
/*  returns -1, 0, or 1 for A<B, A==B, or A>B, or BADINT if failure   */
/*  (the only possible failure is an allocation error, which can      */
/*  only occur if E!=0)                                               */
/* ------------------------------------------------------------------ */
static Int decUnitCompare(const Unit *a, Int alength,
                          const Unit *b, Int blength, Int exp) {
  Unit  *acc;                      // accumulator for result
  Unit  accbuff[SD2U(DECBUFFER*2+1)]; // local buffer
  Unit  *allocacc=NULL;            // -> allocated acc buffer, iff allocated
  Int   accunits, need;            // units in use or needed for acc
  const Unit *l, *r, *u;           // work
  Int   expunits, exprem, result;  // ..

  if (exp==0) {                    // aligned; fastpath
    if (alength>blength) return 1;
    if (alength<blength) return -1;
    // same number of units in both -- need unit-by-unit compare
    l=a+alength-1;
    r=b+alength-1;
    for (;l>=a; l--, r--) {
      if (*l>*r) return 1;
      if (*l<*r) return -1;
      }
    return 0;                      // all units match
    } // aligned

  // Unaligned.  If one is >1 unit longer than the other, padded
  // approximately, then can return easily
  if (alength>blength+(Int)D2U(exp)) return 1;
  if (alength+1<blength+(Int)D2U(exp)) return -1;

  // Need to do a real subtract.  For this, a result buffer is needed
  // even though only the sign is of interest.  Its length needs
  // to be the larger of alength and padded blength, +2
  need=blength+D2U(exp);                // maximum real length of B
  if (need<alength) need=alength;
  need+=2;
  acc=accbuff;                          // assume use local buffer
  if (need*sizeof(Unit)>sizeof(accbuff)) {
    allocacc=(Unit *)malloc(need*sizeof(Unit));
    if (allocacc==NULL) return BADINT;  // hopeless -- abandon
    acc=allocacc;
    }
  // Calculate units and remainder from exponent.
  expunits=exp/DECDPUN;
  exprem=exp%DECDPUN;
  // subtract [A+B*(-m)]
  accunits=decUnitAddSub(a, alength, b, blength, expunits, acc,
                         -(Int)powers[exprem]);
  // [UnitAddSub result may have leading zeros, even on zero]
  if (accunits<0) result=-1;            // negative result
   else {                               // non-negative result
    // check units of the result before freeing any storage
    for (u=acc; u<acc+accunits-1 && *u==0;) u++;
    result=(*u==0 ? 0 : +1);
    }
  // clean up and return the result
  if (allocacc!=NULL) free(allocacc);   // drop any storage used
  return result;
  } // decUnitCompare

/* ------------------------------------------------------------------ */
/* decUnitAddSub -- add or subtract two >=0 integers in Unit arrays   */
/*                                                                    */
/*  This routine performs the calculation:                            */
/*                                                                    */
/*  C=A+(B*M)                                                         */
/*                                                                    */
/*  Where M is in the range -DECDPUNMAX through +DECDPUNMAX.          */
/*                                                                    */
/*  A may be shorter or longer than B.                                */
/*                                                                    */
/*  Leading zeros are not removed after a calculation.  The result is */
/*  either the same length as the longer of A and B (adding any       */
/*  shift), or one Unit longer than that (if a Unit carry occurred).  */
/*                                                                    */
/*  A and B content are not altered unless C is also A or B.          */
/*  C may be the same array as A or B, but only if no zero padding is */
/*  requested (that is, C may be B only if bshift==0).                */
/*  C is filled from the lsu; only those units necessary to complete  */
/*  the calculation are referenced.                                   */
/*                                                                    */
/*  Arg1 is A first Unit (lsu)                                        */
/*  Arg2 is A length in Units                                         */
/*  Arg3 is B first Unit (lsu)                                        */
/*  Arg4 is B length in Units                                         */
/*  Arg5 is B shift in Units  (>=0; pads with 0 units if positive)    */
/*  Arg6 is C first Unit (lsu)                                        */
/*  Arg7 is M, the multiplier                                         */
/*                                                                    */
/*  returns the count of Units written to C, which will be non-zero   */
/*  and negated if the result is negative.  That is, the sign of the  */
/*  returned Int is the sign of the result (positive for zero) and    */
/*  the absolute value of the Int is the count of Units.              */
/*                                                                    */
/*  It is the caller's responsibility to make sure that C size is     */
/*  safe, allowing space if necessary for a one-Unit carry.           */
/*                                                                    */
/*  This routine is severely performance-critical; *any* change here  */
/*  must be measured (timed) to assure no performance degradation.    */
/*  In particular, trickery here tends to be counter-productive, as   */
/*  increased complexity of code hurts register optimizations on      */
/*  register-poor architectures.  Avoiding divisions is nearly        */
/*  always a Good Idea, however.                                      */
/*                                                                    */
/* Special thanks to Rick McGuire (IBM Cambridge, MA) and Dave Clark  */
/* (IBM Warwick, UK) for some of the ideas used in this routine.      */
/* ------------------------------------------------------------------ */
static Int decUnitAddSub(const Unit *a, Int alength,
                         const Unit *b, Int blength, Int bshift,
                         Unit *c, Int m) {
  const Unit *alsu=a;              // A lsu [need to remember it]
  Unit *clsu=c;                    // C ditto
  Unit *minC;                      // low water mark for C
  Unit *maxC;                      // high water mark for C
  eInt carry=0;                    // carry integer (could be Long)
  Int  add;                        // work
  #if DECDPUN<=4                   // myriadal, millenary, etc.

  Int  est;                        // estimated quotient
  #endif

  #if DECTRACE
  if (alength<1 || blength<1)
    printf("decUnitAddSub: alen blen m %ld %ld [%ld]\n", alength, blength, m);
  #endif

  maxC=c+alength;                  // A is usually the longer
  minC=c+blength;                  // .. and B the shorter
  if (bshift!=0) {                 // B is shifted; low As copy across
    minC+=bshift;
    // if in place [common], skip copy unless there's a gap [rare]
    if (a==c && bshift<=alength) {
      c+=bshift;
      a+=bshift;
      }
     else for (; c<clsu+bshift; a++, c++) {  // copy needed
      if (a<alsu+alength) *c=*a;
       else *c=0;
      }
    }
  if (minC>maxC) { // swap
    Unit *hold=minC;
    minC=maxC;
    maxC=hold;
    }

  // For speed, do the addition as two loops; the first where both A
  // and B contribute, and the second (if necessary) where only one or
  // other of the numbers contribute.
  // Carry handling is the same (i.e., duplicated) in each case.
  for (; c<minC; c++) {
    carry+=*a;
    a++;
    carry+=((eInt)*b)*m;                // [special-casing m=1/-1
    b++;                                // here is not a win]
    // here carry is new Unit of digits; it could be +ve or -ve
    if ((ueInt)carry<=DECDPUNMAX) {     // fastpath 0-DECDPUNMAX
      *c=(Unit)carry;
      carry=0;
      continue;
      }
    #if DECDPUN==4                           // use divide-by-multiply

      if (carry>=0) {
        est=(((ueInt)carry>>11)*53687)>>18;
        *c=(Unit)(carry-est*(DECDPUNMAX+1)); // remainder
        carry=est;                           // likely quotient [89%]
        if (*c<DECDPUNMAX+1) continue;       // estimate was correct
        carry++;
        *c-=DECDPUNMAX+1;
        continue;
        }
      // negative case
      carry=carry+(eInt)(DECDPUNMAX+1)*(DECDPUNMAX+1); // make positive
      est=(((ueInt)carry>>11)*53687)>>18;
      *c=(Unit)(carry-est*(DECDPUNMAX+1));
      carry=est-(DECDPUNMAX+1);              // correctly negative
      if (*c<DECDPUNMAX+1) continue;         // was OK
      carry++;
      *c-=DECDPUNMAX+1;
    #elif DECDPUN==3
      if (carry>=0) {
        est=(((ueInt)carry>>3)*16777)>>21;
        *c=(Unit)(carry-est*(DECDPUNMAX+1)); // remainder
        carry=est;                           // likely quotient [99%]
        if (*c<DECDPUNMAX+1) continue;       // estimate was correct
        carry++;
        *c-=DECDPUNMAX+1;
        continue;
        }
      // negative case
      carry=carry+(eInt)(DECDPUNMAX+1)*(DECDPUNMAX+1); // make positive
      est=(((ueInt)carry>>3)*16777)>>21;
      *c=(Unit)(carry-est*(DECDPUNMAX+1));
      carry=est-(DECDPUNMAX+1);              // correctly negative
      if (*c<DECDPUNMAX+1) continue;         // was OK
      carry++;
      *c-=DECDPUNMAX+1;
    #elif DECDPUN<=2
      // Can use QUOT10 as carry <= 4 digits
      if (carry>=0) {
        est=QUOT10(carry, DECDPUN);
        *c=(Unit)(carry-est*(DECDPUNMAX+1)); // remainder
        carry=est;                           // quotient
        continue;
        }
      // negative case
      carry=carry+(eInt)(DECDPUNMAX+1)*(DECDPUNMAX+1); // make positive
      est=QUOT10(carry, DECDPUN);
      *c=(Unit)(carry-est*(DECDPUNMAX+1));
      carry=est-(DECDPUNMAX+1);              // correctly negative
    #else
      // remainder operator is undefined if negative, so must test
      if ((ueInt)carry<(DECDPUNMAX+1)*2) {   // fastpath carry +1
        *c=(Unit)(carry-(DECDPUNMAX+1));     // [helps additions]
        carry=1;
        continue;
        }
      if (carry>=0) {
        *c=(Unit)(carry%(DECDPUNMAX+1));
        carry=carry/(DECDPUNMAX+1);
        continue;
        }
      // negative case
      carry=carry+(eInt)(DECDPUNMAX+1)*(DECDPUNMAX+1); // make positive
      *c=(Unit)(carry%(DECDPUNMAX+1));
      carry=carry/(DECDPUNMAX+1)-(DECDPUNMAX+1);
    #endif
    } // c

  // now may have one or other to complete
  // [pretest to avoid loop setup/shutdown]
  if (c<maxC) for (; c<maxC; c++) {
    if (a<alsu+alength) {               // still in A
      carry+=*a;
      a++;
      }
     else {                             // inside B
      carry+=((eInt)*b)*m;
      b++;
      }
    // here carry is new Unit of digits; it could be +ve or -ve and
    // magnitude up to DECDPUNMAX squared
    if ((ueInt)carry<=DECDPUNMAX) {     // fastpath 0-DECDPUNMAX
      *c=(Unit)carry;
      carry=0;
      continue;
      }
    // result for this unit is negative or >DECDPUNMAX
    #if DECDPUN==4                           // use divide-by-multiply

      if (carry>=0) {
        est=(((ueInt)carry>>11)*53687)>>18;
        *c=(Unit)(carry-est*(DECDPUNMAX+1)); // remainder
        carry=est;                           // likely quotient [79.7%]
        if (*c<DECDPUNMAX+1) continue;       // estimate was correct
        carry++;
        *c-=DECDPUNMAX+1;
        continue;
        }
      // negative case
      carry=carry+(eInt)(DECDPUNMAX+1)*(DECDPUNMAX+1); // make positive
      est=(((ueInt)carry>>11)*53687)>>18;
      *c=(Unit)(carry-est*(DECDPUNMAX+1));
      carry=est-(DECDPUNMAX+1);              // correctly negative
      if (*c<DECDPUNMAX+1) continue;         // was OK
      carry++;
      *c-=DECDPUNMAX+1;
    #elif DECDPUN==3
      if (carry>=0) {
        est=(((ueInt)carry>>3)*16777)>>21;
        *c=(Unit)(carry-est*(DECDPUNMAX+1)); // remainder
        carry=est;                           // likely quotient [99%]
        if (*c<DECDPUNMAX+1) continue;       // estimate was correct
        carry++;
        *c-=DECDPUNMAX+1;
        continue;
        }
      // negative case
      carry=carry+(eInt)(DECDPUNMAX+1)*(DECDPUNMAX+1); // make positive
      est=(((ueInt)carry>>3)*16777)>>21;
      *c=(Unit)(carry-est*(DECDPUNMAX+1));
      carry=est-(DECDPUNMAX+1);              // correctly negative
      if (*c<DECDPUNMAX+1) continue;         // was OK
      carry++;
      *c-=DECDPUNMAX+1;
    #elif DECDPUN<=2
      if (carry>=0) {
        est=QUOT10(carry, DECDPUN);
        *c=(Unit)(carry-est*(DECDPUNMAX+1)); // remainder
        carry=est;                           // quotient
        continue;
        }
      // negative case
      carry=carry+(eInt)(DECDPUNMAX+1)*(DECDPUNMAX+1); // make positive
      est=QUOT10(carry, DECDPUN);
      *c=(Unit)(carry-est*(DECDPUNMAX+1));
      carry=est-(DECDPUNMAX+1);              // correctly negative
    #else
      if ((ueInt)carry<(DECDPUNMAX+1)*2){    // fastpath carry 1
        *c=(Unit)(carry-(DECDPUNMAX+1));
        carry=1;
        continue;
        }
      // remainder operator is undefined if negative, so must test
      if (carry>=0) {
        *c=(Unit)(carry%(DECDPUNMAX+1));
        carry=carry/(DECDPUNMAX+1);
        continue;
        }
      // negative case
      carry=carry+(eInt)(DECDPUNMAX+1)*(DECDPUNMAX+1); // make positive
      *c=(Unit)(carry%(DECDPUNMAX+1));
      carry=carry/(DECDPUNMAX+1)-(DECDPUNMAX+1);
    #endif
    } // c

  // OK, all A and B processed; might still have carry or borrow
  // return number of Units in the result, negated if a borrow
  if (carry==0) return c-clsu;     // no carry, so no more to do
  if (carry>0) {                   // positive carry
    *c=(Unit)carry;                // place as new unit
    c++;                           // ..
    return c-clsu;
    }
  // -ve carry: it's a borrow; complement needed
  add=1;                           // temporary carry...
  for (c=clsu; c<maxC; c++) {
    add=DECDPUNMAX+add-*c;
    if (add<=DECDPUNMAX) {
      *c=(Unit)add;
      add=0;
      }
     else {
      *c=0;
      add=1;
      }
    }
  // add an extra unit iff it would be non-zero
  #if DECTRACE
    printf("UAS borrow: add %ld, carry %ld\n", add, carry);
  #endif
  if ((add-carry-1)!=0) {
    *c=(Unit)(add-carry-1);
    c++;                      // interesting, include it
    }
  return clsu-c;              // -ve result indicates borrowed
  } // decUnitAddSub

/* ------------------------------------------------------------------ */
/* decTrim -- trim trailing zeros or normalize                        */
/*                                                                    */
/*   dn is the number to trim or normalize                            */
/*   set is the context to use to check for clamp                     */
/*   all is 1 to remove all trailing zeros, 0 for just fraction ones  */
/*   noclamp is 1 to unconditional (unclamped) trim                   */
/*   dropped returns the number of discarded trailing zeros           */
/*   returns dn                                                       */
/*                                                                    */
/* If clamp is set in the context then the number of zeros trimmed    */
/* may be limited if the exponent is high.                            */
/* All fields are updated as required.  This is a utility operation,  */
/* so special values are unchanged and no error is possible.          */
/* ------------------------------------------------------------------ */
static decNumber * decTrim(decNumber *dn, decContext *set, Flag all,
                           Flag noclamp, Int *dropped) {
  Int   d, exp;                    // work
  uInt  cut;                       // ..
  Unit  *up;                       // -> current Unit

  #if DECCHECK
  if (decCheckOperands(dn, DECUNUSED, DECUNUSED, DECUNCONT)) return dn;
  #endif

  *dropped=0;                           // assume no zeros dropped
  if ((dn->bits & DECSPECIAL)           // fast exit if special ..
    || (*dn->lsu & 0x01)) return dn;    // .. or odd
  if (ISZERO(dn)) {                     // .. or 0
    dn->exponent=0;                     // (sign is preserved)
    return dn;
    }

  // have a finite number which is even
  exp=dn->exponent;
  cut=1;                           // digit (1-DECDPUN) in Unit
  up=dn->lsu;                      // -> current Unit
  for (d=0; d<dn->digits-1; d++) { // [don't strip the final digit]
    // slice by powers
    #if DECDPUN<=4
      uInt quot=QUOT10(*up, cut);
      if ((*up-quot*powers[cut])!=0) break;  // found non-0 digit
    #else
      if (*up%powers[cut]!=0) break;         // found non-0 digit
    #endif
    // have a trailing 0
    if (!all) {                    // trimming
      // [if exp>0 then all trailing 0s are significant for trim]
      if (exp<=0) {                // if digit might be significant
        if (exp==0) break;         // then quit
        exp++;                     // next digit might be significant
        }
      }
    cut++;                         // next power
    if (cut>DECDPUN) {             // need new Unit
      up++;
      cut=1;
      }
    } // d
  if (d==0) return dn;             // none to drop

  // may need to limit drop if clamping
  if (set->clamp && !noclamp) {
    Int maxd=set->emax-set->digits+1-dn->exponent;
    if (maxd<=0) return dn;        // nothing possible
    if (d>maxd) d=maxd;
    }

  // effect the drop
  decShiftToLeast(dn->lsu, D2U(dn->digits), d);
  dn->exponent+=d;                 // maintain numerical value
  dn->digits-=d;                   // new length
  *dropped=d;                      // report the count
  return dn;
  } // decTrim

/* ------------------------------------------------------------------ */
/* decReverse -- reverse a Unit array in place                        */
/*                                                                    */
/*   ulo    is the start of the array                                 */
/*   uhi    is the end of the array (highest Unit to include)         */
/*                                                                    */
/* The units ulo through uhi are reversed in place (if the number     */
/* of units is odd, the middle one is untouched).  Note that the      */
/* digit(s) in each unit are unaffected.                              */
/* ------------------------------------------------------------------ */
static void decReverse(Unit *ulo, Unit *uhi) {
  Unit temp;
  for (; ulo<uhi; ulo++, uhi--) {
    temp=*ulo;
    *ulo=*uhi;
    *uhi=temp;
    }
  return;
  } // decReverse

/* ------------------------------------------------------------------ */
/* decShiftToMost -- shift digits in array towards most significant   */
/*                                                                    */
/*   uar    is the array                                              */
/*   digits is the count of digits in use in the array                */
/*   shift  is the number of zeros to pad with (least significant);   */
/*     it must be zero or positive                                    */
/*                                                                    */
/*   returns the new length of the integer in the array, in digits    */
/*                                                                    */
/* No overflow is permitted (that is, the uar array must be known to  */
/* be large enough to hold the result, after shifting).               */
/* ------------------------------------------------------------------ */
static Int decShiftToMost(Unit *uar, Int digits, Int shift) {
  Unit  *target, *source, *first;  // work
  Int   cut;                       // odd 0's to add
  uInt  next;                      // work

  if (shift==0) return digits;     // [fastpath] nothing to do
  if ((digits+shift)<=DECDPUN) {   // [fastpath] single-unit case
    *uar=(Unit)(*uar*powers[shift]);
    return digits+shift;
    }

  next=0;                          // all paths
  source=uar+D2U(digits)-1;        // where msu comes from
  target=source+D2U(shift);        // where upper part of first cut goes
  cut=DECDPUN-MSUDIGITS(shift);    // where to slice
  if (cut==0) {                    // unit-boundary case
    for (; source>=uar; source--, target--) *target=*source;
    }
   else {
    first=uar+D2U(digits+shift)-1; // where msu of source will end up
    for (; source>=uar; source--, target--) {
      // split the source Unit and accumulate remainder for next
      #if DECDPUN<=4
        uInt quot=QUOT10(*source, cut);
        uInt rem=*source-quot*powers[cut];
        next+=quot;
      #else
        uInt rem=*source%powers[cut];
        next+=*source/powers[cut];
      #endif
      if (target<=first) *target=(Unit)next;   // write to target iff valid
      next=rem*powers[DECDPUN-cut];            // save remainder for next Unit
      }
    } // shift-move

  // propagate any partial unit to one below and clear the rest
  for (; target>=uar; target--) {
    *target=(Unit)next;
    next=0;
    }
  return digits+shift;
  } // decShiftToMost

/* ------------------------------------------------------------------ */
/* decShiftToLeast -- shift digits in array towards least significant */
/*                                                                    */
/*   uar   is the array                                               */
/*   units is length of the array, in units                           */
/*   shift is the number of digits to remove from the lsu end; it     */
/*     must be zero or positive and <= than units*DECDPUN.            */
/*                                                                    */
/*   returns the new length of the integer in the array, in units     */
/*                                                                    */
/* Removed digits are discarded (lost).  Units not required to hold   */
/* the final result are unchanged.                                    */
/* ------------------------------------------------------------------ */
static Int decShiftToLeast(Unit *uar, Int units, Int shift) {
  Unit  *target, *up;              // work
  Int   cut, count;                // work
  Int   quot, rem;                 // for division

  if (shift==0) return units;      // [fastpath] nothing to do
  if (shift==units*DECDPUN) {      // [fastpath] little to do
    *uar=0;                        // all digits cleared gives zero
    return 1;                      // leaves just the one
    }

  target=uar;                      // both paths
  cut=MSUDIGITS(shift);
  if (cut==DECDPUN) {              // unit-boundary case; easy
    up=uar+D2U(shift);
    for (; up<uar+units; target++, up++) *target=*up;
    return target-uar;
    }

  // messier
  up=uar+D2U(shift-cut);           // source; correct to whole Units
  count=units*DECDPUN-shift;       // the maximum new length
  #if DECDPUN<=4
    quot=QUOT10(*up, cut);
  #else
    quot=*up/powers[cut];
  #endif
  for (; ; target++) {
    *target=(Unit)quot;
    count-=(DECDPUN-cut);
    if (count<=0) break;
    up++;
    quot=*up;
    #if DECDPUN<=4
      quot=QUOT10(quot, cut);
      rem=*up-quot*powers[cut];
    #else
      rem=quot%powers[cut];
      quot=quot/powers[cut];
    #endif
    *target=(Unit)(*target+rem*powers[DECDPUN-cut]);
    count-=cut;
    if (count<=0) break;
    }
  return target-uar+1;
  } // decShiftToLeast

#if DECSUBSET
/* ------------------------------------------------------------------ */
/* decRoundOperand -- round an operand  [used for subset only]        */
/*                                                                    */
/*   dn is the number to round (dn->digits is > set->digits)          */
/*   set is the relevant context                                      */
/*   status is the status accumulator                                 */
/*                                                                    */
/*   returns an allocated decNumber with the rounded result.          */
/*                                                                    */
/* lostDigits and other status may be set by this.                    */
/*                                                                    */
/* Since the input is an operand, it must not be modified.            */
/* Instead, return an allocated decNumber, rounded as required.       */
/* It is the caller's responsibility to free the allocated storage.   */
/*                                                                    */
/* If no storage is available then the result cannot be used, so NULL */
/* is returned.                                                       */
/* ------------------------------------------------------------------ */
static decNumber *decRoundOperand(const decNumber *dn, decContext *set,
                                  uInt *status) {
  decNumber *res;                       // result structure
  uInt newstatus=0;                     // status from round
  Int  residue=0;                       // rounding accumulator

  // Allocate storage for the returned decNumber, big enough for the
  // length specified by the context
  res=(decNumber *)malloc(sizeof(decNumber)
                          +(D2U(set->digits)-1)*sizeof(Unit));
  if (res==NULL) {
    *status|=DEC_Insufficient_storage;
    return NULL;
    }
  decCopyFit(res, dn, set, &residue, &newstatus);
  decApplyRound(res, set, residue, &newstatus);

  // If that set Inexact then "lost digits" is raised...
  if (newstatus & DEC_Inexact) newstatus|=DEC_Lost_digits;
  *status|=newstatus;
  return res;
  } // decRoundOperand
#endif

/* ------------------------------------------------------------------ */
/* decCopyFit -- copy a number, truncating the coefficient if needed  */
/*                                                                    */
/*   dest is the target decNumber                                     */
/*   src  is the source decNumber                                     */
/*   set is the context [used for length (digits) and rounding mode]  */
/*   residue is the residue accumulator                               */
/*   status contains the current status to be updated                 */
/*                                                                    */
/* (dest==src is allowed and will be a no-op if fits)                 */
/* All fields are updated as required.                                */
/* ------------------------------------------------------------------ */
static void decCopyFit(decNumber *dest, const decNumber *src,
                       decContext *set, Int *residue, uInt *status) {
  dest->bits=src->bits;
  dest->exponent=src->exponent;
  decSetCoeff(dest, set, src->lsu, src->digits, residue, status);
  } // decCopyFit

/* ------------------------------------------------------------------ */
/* decSetCoeff -- set the coefficient of a number                     */
/*                                                                    */
/*   dn    is the number whose coefficient array is to be set.        */
/*         It must have space for set->digits digits                  */
/*   set   is the context [for size]                                  */
/*   lsu   -> lsu of the source coefficient [may be dn->lsu]          */
/*   len   is digits in the source coefficient [may be dn->digits]    */
/*   residue is the residue accumulator.  This has values as in       */
/*         decApplyRound, and will be unchanged unless the            */
/*         target size is less than len.  In this case, the           */
/*         coefficient is truncated and the residue is updated to     */
/*         reflect the previous residue and the dropped digits.       */
/*   status is the status accumulator, as usual                       */
/*                                                                    */
/* The coefficient may already be in the number, or it can be an      */
/* external intermediate array.  If it is in the number, lsu must ==  */
/* dn->lsu and len must == dn->digits.                                */
/*                                                                    */
/* Note that the coefficient length (len) may be < set->digits, and   */
/* in this case this merely copies the coefficient (or is a no-op     */
/* if dn->lsu==lsu).                                                  */
/*                                                                    */
/* Note also that (only internally, from decQuantizeOp and            */
/* decSetSubnormal) the value of set->digits may be less than one,    */
/* indicating a round to left.  This routine handles that case        */
/* correctly; caller ensures space.                                   */
/*                                                                    */
/* dn->digits, dn->lsu (and as required), and dn->exponent are        */
/* updated as necessary.   dn->bits (sign) is unchanged.              */
/*                                                                    */
/* DEC_Rounded status is set if any digits are discarded.             */
/* DEC_Inexact status is set if any non-zero digits are discarded, or */
/*                       incoming residue was non-0 (implies rounded) */
/* ------------------------------------------------------------------ */
// mapping array: maps 0-9 to canonical residues, so that a residue
// can be adjusted in the range [-1, +1] and achieve correct rounding
//                             0  1  2  3  4  5  6  7  8  9
static const uByte resmap[10]={0, 3, 3, 3, 3, 5, 7, 7, 7, 7};
static void decSetCoeff(decNumber *dn, decContext *set, const Unit *lsu,
                        Int len, Int *residue, uInt *status) {
  Int   discard;              // number of digits to discard
  uInt  cut;                  // cut point in Unit
  const Unit *up;             // work
  Unit  *target;              // ..
  Int   count;                // ..
  #if DECDPUN<=4
  uInt  temp;                 // ..
  #endif

  discard=len-set->digits;    // digits to discard
  if (discard<=0) {           // no digits are being discarded
    if (dn->lsu!=lsu) {       // copy needed
      // copy the coefficient array to the result number; no shift needed
      count=len;              // avoids D2U
      up=lsu;
      for (target=dn->lsu; count>0; target++, up++, count-=DECDPUN)
        *target=*up;
      dn->digits=len;         // set the new length
      }
    // dn->exponent and residue are unchanged, record any inexactitude
    if (*residue!=0) *status|=(DEC_Inexact | DEC_Rounded);
    return;
    }

  // some digits must be discarded ...
  dn->exponent+=discard;      // maintain numerical value
  *status|=DEC_Rounded;       // accumulate Rounded status
  if (*residue>1) *residue=1; // previous residue now to right, so reduce

  if (discard>len) {          // everything, +1, is being discarded
    // guard digit is 0
    // residue is all the number [NB could be all 0s]
    if (*residue<=0) {        // not already positive
      count=len;              // avoids D2U
      for (up=lsu; count>0; up++, count-=DECDPUN) if (*up!=0) { // found non-0
        *residue=1;
        break;                // no need to check any others
        }
      }
    if (*residue!=0) *status|=DEC_Inexact; // record inexactitude
    *dn->lsu=0;               // coefficient will now be 0
    dn->digits=1;             // ..
    return;
    } // total discard

  // partial discard [most common case]
  // here, at least the first (most significant) discarded digit exists

  // spin up the number, noting residue during the spin, until get to
  // the Unit with the first discarded digit.  When reach it, extract
  // it and remember its position
  count=0;
  for (up=lsu;; up++) {
    count+=DECDPUN;
    if (count>=discard) break; // full ones all checked
    if (*up!=0) *residue=1;
    } // up

  // here up -> Unit with first discarded digit
  cut=discard-(count-DECDPUN)-1;
  if (cut==DECDPUN-1) {       // unit-boundary case (fast)
    Unit half=(Unit)powers[DECDPUN]>>1;
    // set residue directly
    if (*up>=half) {
      if (*up>half) *residue=7;
      else *residue+=5;       // add sticky bit
      }
     else { // <half
      if (*up!=0) *residue=3; // [else is 0, leave as sticky bit]
      }
    if (set->digits<=0) {     // special for Quantize/Subnormal :-(
      *dn->lsu=0;             // .. result is 0
      dn->digits=1;           // ..
      }
     else {                   // shift to least
      count=set->digits;      // now digits to end up with
      dn->digits=count;       // set the new length
      up++;                   // move to next
      // on unit boundary, so shift-down copy loop is simple
      for (target=dn->lsu; count>0; target++, up++, count-=DECDPUN)
        *target=*up;
      }
    } // unit-boundary case

   else { // discard digit is in low digit(s), and not top digit
    uInt  discard1;                // first discarded digit
    uInt  quot, rem;               // for divisions
    if (cut==0) quot=*up;          // is at bottom of unit
     else /* cut>0 */ {            // it's not at bottom of unit
      #if DECDPUN<=4
        quot=QUOT10(*up, cut);
        rem=*up-quot*powers[cut];
      #else
        rem=*up%powers[cut];
        quot=*up/powers[cut];
      #endif
      if (rem!=0) *residue=1;
      }
    // discard digit is now at bottom of quot
    #if DECDPUN<=4
      temp=(quot*6554)>>16;        // fast /10
      // Vowels algorithm here not a win (9 instructions)
      discard1=quot-X10(temp);
      quot=temp;
    #else
      discard1=quot%10;
      quot=quot/10;
    #endif
    // here, discard1 is the guard digit, and residue is everything
    // else [use mapping array to accumulate residue safely]
    *residue+=resmap[discard1];
    cut++;                         // update cut
    // here: up -> Unit of the array with bottom digit
    //       cut is the division point for each Unit
    //       quot holds the uncut high-order digits for the current unit
    if (set->digits<=0) {          // special for Quantize/Subnormal :-(
      *dn->lsu=0;                  // .. result is 0
      dn->digits=1;                // ..
      }
     else {                        // shift to least needed
      count=set->digits;           // now digits to end up with
      dn->digits=count;            // set the new length
      // shift-copy the coefficient array to the result number
      for (target=dn->lsu; ; target++) {
        *target=(Unit)quot;
        count-=(DECDPUN-cut);
        if (count<=0) break;
        up++;
        quot=*up;
        #if DECDPUN<=4
          quot=QUOT10(quot, cut);
          rem=*up-quot*powers[cut];
        #else
          rem=quot%powers[cut];
          quot=quot/powers[cut];
        #endif
        *target=(Unit)(*target+rem*powers[DECDPUN-cut]);
        count-=cut;
        if (count<=0) break;
        } // shift-copy loop
      } // shift to least
    } // not unit boundary

  if (*residue!=0) *status|=DEC_Inexact; // record inexactitude
  return;
  } // decSetCoeff

/* ------------------------------------------------------------------ */
/* decApplyRound -- apply pending rounding to a number                */
/*                                                                    */
/*   dn    is the number, with space for set->digits digits           */
/*   set   is the context [for size and rounding mode]                */
/*   residue indicates pending rounding, being any accumulated        */
/*         guard and sticky information.  It may be:                  */
/*         6-9: rounding digit is >5                                  */
/*         5:   rounding digit is exactly half-way                    */
/*         1-4: rounding digit is <5 and >0                           */
/*         0:   the coefficient is exact                              */
/*        -1:   as 1, but the hidden digits are subtractive, that     */
/*              is, of the opposite sign to dn.  In this case the     */
/*              coefficient must be non-0.  This case occurs when     */
/*              subtracting a small number (which can be reduced to   */
/*              a sticky bit); see decAddOp.                          */
/*   status is the status accumulator, as usual                       */
/*                                                                    */
/* This routine applies rounding while keeping the length of the      */
/* coefficient constant.  The exponent and status are unchanged       */
/* except if:                                                         */
/*                                                                    */
/*   -- the coefficient was increased and is all nines (in which      */
/*      case Overflow could occur, and is handled directly here so    */
/*      the caller does not need to re-test for overflow)             */
/*                                                                    */
/*   -- the coefficient was decreased and becomes all nines (in which */
/*      case Underflow could occur, and is also handled directly).    */
/*                                                                    */
/* All fields in dn are updated as required.                          */
/*                                                                    */
/* ------------------------------------------------------------------ */
static void decApplyRound(decNumber *dn, decContext *set, Int residue,
                          uInt *status) {
  Int  bump;                  // 1 if coefficient needs to be incremented
                              // -1 if coefficient needs to be decremented

  if (residue==0) return;     // nothing to apply

  bump=0;                     // assume a smooth ride

  // now decide whether, and how, to round, depending on mode
  switch (set->round) {
    case DEC_ROUND_05UP: {    // round zero or five up (for reround)
      // This is the same as DEC_ROUND_DOWN unless there is a
      // positive residue and the lsd of dn is 0 or 5, in which case
      // it is bumped; when residue is <0, the number is therefore
      // bumped down unless the final digit was 1 or 6 (in which
      // case it is bumped down and then up -- a no-op)
      Int lsd5=*dn->lsu%5;     // get lsd and quintate
      if (residue<0 && lsd5!=1) bump=-1;
       else if (residue>0 && lsd5==0) bump=1;
      // [bump==1 could be applied directly; use common path for clarity]
      break;} // r-05

    case DEC_ROUND_DOWN: {
      // no change, except if negative residue
      if (residue<0) bump=-1;
      break;} // r-d

    case DEC_ROUND_HALF_DOWN: {
      if (residue>5) bump=1;
      break;} // r-h-d

    case DEC_ROUND_HALF_EVEN: {
      if (residue>5) bump=1;            // >0.5 goes up
       else if (residue==5) {           // exactly 0.5000...
        // 0.5 goes up iff [new] lsd is odd
        if (*dn->lsu & 0x01) bump=1;
        }
      break;} // r-h-e

    case DEC_ROUND_HALF_UP: {
      if (residue>=5) bump=1;
      break;} // r-h-u

    case DEC_ROUND_UP: {
      if (residue>0) bump=1;
      break;} // r-u

    case DEC_ROUND_CEILING: {
      // same as _UP for positive numbers, and as _DOWN for negatives
      // [negative residue cannot occur on 0]
      if (decNumberIsNegative(dn)) {
        if (residue<0) bump=-1;
        }
       else {
        if (residue>0) bump=1;
        }
      break;} // r-c

    case DEC_ROUND_FLOOR: {
      // same as _UP for negative numbers, and as _DOWN for positive
      // [negative residue cannot occur on 0]
      if (!decNumberIsNegative(dn)) {
        if (residue<0) bump=-1;
        }
       else {
        if (residue>0) bump=1;
        }
      break;} // r-f

    default: {      // e.g., DEC_ROUND_MAX
      *status|=DEC_Invalid_context;
      #if DECTRACE || (DECCHECK && DECVERB)
      printf("Unknown rounding mode: %d\n", set->round);
      #endif
      break;}
    } // switch

  // now bump the number, up or down, if need be
  if (bump==0) return;                       // no action required

  // Simply use decUnitAddSub unless bumping up and the number is
  // all nines.  In this special case set to 100... explicitly
  // and adjust the exponent by one (as otherwise could overflow
  // the array)
  // Similarly handle all-nines result if bumping down.
  if (bump>0) {
    Unit *up;                                // work
    uInt count=dn->digits;                   // digits to be checked
    for (up=dn->lsu; ; up++) {
      if (count<=DECDPUN) {
        // this is the last Unit (the msu)
        if (*up!=powers[count]-1) break;     // not still 9s
        // here if it, too, is all nines
        *up=(Unit)powers[count-1];           // here 999 -> 100 etc.
        for (up=up-1; up>=dn->lsu; up--) *up=0; // others all to 0
        dn->exponent++;                      // and bump exponent
        // [which, very rarely, could cause Overflow...]
        if ((dn->exponent+dn->digits)>set->emax+1) {
          decSetOverflow(dn, set, status);
          }
        return;                              // done
        }
      // a full unit to check, with more to come
      if (*up!=DECDPUNMAX) break;            // not still 9s
      count-=DECDPUN;
      } // up
    } // bump>0
   else {                                    // -1
    // here checking for a pre-bump of 1000... (leading 1, all
    // other digits zero)
    Unit *up, *sup;                          // work
    uInt count=dn->digits;                   // digits to be checked
    for (up=dn->lsu; ; up++) {
      if (count<=DECDPUN) {
        // this is the last Unit (the msu)
        if (*up!=powers[count-1]) break;     // not 100..
        // here if have the 1000... case
        sup=up;                              // save msu pointer
        *up=(Unit)powers[count]-1;           // here 100 in msu -> 999
        // others all to all-nines, too
        for (up=up-1; up>=dn->lsu; up--) *up=(Unit)powers[DECDPUN]-1;
        dn->exponent--;                      // and bump exponent

        // iff the number was at the subnormal boundary (exponent=etiny)
        // then the exponent is now out of range, so it will in fact get
        // clamped to etiny and the final 9 dropped.
        // printf(">> emin=%d exp=%d sdig=%d\n", set->emin,
        //        dn->exponent, set->digits);
        if (dn->exponent+1==set->emin-set->digits+1) {
          if (count==1 && dn->digits==1) *sup=0;  // here 9 -> 0[.9]
           else {
            *sup=(Unit)powers[count-1]-1;    // here 999.. in msu -> 99..
            dn->digits--;
            }
          dn->exponent++;
          *status|=DEC_Underflow | DEC_Subnormal | DEC_Inexact | DEC_Rounded;
          }
        return;                              // done
        }

      // a full unit to check, with more to come
      if (*up!=0) break;                     // not still 0s
      count-=DECDPUN;
      } // up

    } // bump<0

  // Actual bump needed.  Do it.
  decUnitAddSub(dn->lsu, D2U(dn->digits), uarrone, 1, 0, dn->lsu, bump);
  } // decApplyRound

#if DECSUBSET
/* ------------------------------------------------------------------ */
/* decFinish -- finish processing a number                            */
/*                                                                    */
/*   dn is the number                                                 */
/*   set is the context                                               */
/*   residue is the rounding accumulator (as in decApplyRound)        */
/*   status is the accumulator                                        */
/*                                                                    */
/* This finishes off the current number by:                           */
/*    1. If not extended:                                             */
/*       a. Converting a zero result to clean '0'                     */
/*       b. Reducing positive exponents to 0, if would fit in digits  */
/*    2. Checking for overflow and subnormals (always)                */
/* Note this is just Finalize when no subset arithmetic.              */
/* All fields are updated as required.                                */
/* ------------------------------------------------------------------ */
static void decFinish(decNumber *dn, decContext *set, Int *residue,
                      uInt *status) {
  if (!set->extended) {
    if ISZERO(dn) {                // value is zero
      dn->exponent=0;              // clean exponent ..
      dn->bits=0;                  // .. and sign
      return;                      // no error possible
      }
    if (dn->exponent>=0) {         // non-negative exponent
      // >0; reduce to integer if possible
      if (set->digits >= (dn->exponent+dn->digits)) {
        dn->digits=decShiftToMost(dn->lsu, dn->digits, dn->exponent);
        dn->exponent=0;
        }
      }
    } // !extended

  decFinalize(dn, set, residue, status);
  } // decFinish
#endif

/* ------------------------------------------------------------------ */
/* decFinalize -- final check, clamp, and round of a number           */
/*                                                                    */
/*   dn is the number                                                 */
/*   set is the context                                               */
/*   residue is the rounding accumulator (as in decApplyRound)        */
/*   status is the status accumulator                                 */
/*                                                                    */
/* This finishes off the current number by checking for subnormal     */
/* results, applying any pending rounding, checking for overflow,     */
/* and applying any clamping.                                         */
/* Underflow and overflow conditions are raised as appropriate.       */
/* All fields are updated as required.                                */
/* ------------------------------------------------------------------ */
static void decFinalize(decNumber *dn, decContext *set, Int *residue,
                        uInt *status) {
  Int shift;                            // shift needed if clamping
  Int tinyexp=set->emin-dn->digits+1;   // precalculate subnormal boundary

  // Must be careful, here, when checking the exponent as the
  // adjusted exponent could overflow 31 bits [because it may already
  // be up to twice the expected].

  // First test for subnormal.  This must be done before any final
  // round as the result could be rounded to Nmin or 0.
  if (dn->exponent<=tinyexp) {          // prefilter
    Int comp;
    decNumber nmin;
    // A very nasty case here is dn == Nmin and residue<0
    if (dn->exponent<tinyexp) {
      // Go handle subnormals; this will apply round if needed.
      decSetSubnormal(dn, set, residue, status);
      return;
      }
    // Equals case: only subnormal if dn=Nmin and negative residue
    decNumberZero(&nmin);
    nmin.lsu[0]=1;
    nmin.exponent=set->emin;
    comp=decCompare(dn, &nmin, 1);                // (signless compare)
    if (comp==BADINT) {                           // oops
      *status|=DEC_Insufficient_storage;          // abandon...
      return;
      }
    if (*residue<0 && comp==0) {                  // neg residue and dn==Nmin
      decApplyRound(dn, set, *residue, status);   // might force down
      decSetSubnormal(dn, set, residue, status);
      return;
      }
    }

  // now apply any pending round (this could raise overflow).
  if (*residue!=0) decApplyRound(dn, set, *residue, status);

  // Check for overflow [redundant in the 'rare' case] or clamp
  if (dn->exponent<=set->emax-set->digits+1) return;   // neither needed


  // here when might have an overflow or clamp to do
  if (dn->exponent>set->emax-dn->digits+1) {           // too big
    decSetOverflow(dn, set, status);
    return;
    }
  // here when the result is normal but in clamp range
  if (!set->clamp) return;

  // here when need to apply the IEEE exponent clamp (fold-down)
  shift=dn->exponent-(set->emax-set->digits+1);

  // shift coefficient (if non-zero)
  if (!ISZERO(dn)) {
    dn->digits=decShiftToMost(dn->lsu, dn->digits, shift);
    }
  dn->exponent-=shift;   // adjust the exponent to match
  *status|=DEC_Clamped;  // and record the dirty deed
  return;
  } // decFinalize

/* ------------------------------------------------------------------ */
/* decSetOverflow -- set number to proper overflow value              */
/*                                                                    */
/*   dn is the number (used for sign [only] and result)               */
/*   set is the context [used for the rounding mode, etc.]            */
/*   status contains the current status to be updated                 */
/*                                                                    */
/* This sets the sign of a number and sets its value to either        */
/* Infinity or the maximum finite value, depending on the sign of     */
/* dn and the rounding mode, following IEEE 754 rules.                */
/* ------------------------------------------------------------------ */
static void decSetOverflow(decNumber *dn, decContext *set, uInt *status) {
  Flag needmax=0;                  // result is maximum finite value
  uByte sign=dn->bits&DECNEG;      // clean and save sign bit

  if (ISZERO(dn)) {                // zero does not overflow magnitude
    Int emax=set->emax;                      // limit value
    if (set->clamp) emax-=set->digits-1;     // lower if clamping
    if (dn->exponent>emax) {                 // clamp required
      dn->exponent=emax;
      *status|=DEC_Clamped;
      }
    return;
    }

  decNumberZero(dn);
  switch (set->round) {
    case DEC_ROUND_DOWN: {
      needmax=1;                   // never Infinity
      break;} // r-d
    case DEC_ROUND_05UP: {
      needmax=1;                   // never Infinity
      break;} // r-05
    case DEC_ROUND_CEILING: {
      if (sign) needmax=1;         // Infinity if non-negative
      break;} // r-c
    case DEC_ROUND_FLOOR: {
      if (!sign) needmax=1;        // Infinity if negative
      break;} // r-f
    default: break;                // Infinity in all other cases
    }
  if (needmax) {
    decSetMaxValue(dn, set);
    dn->bits=sign;                 // set sign
    }
   else dn->bits=sign|DECINF;      // Value is +/-Infinity
  *status|=DEC_Overflow | DEC_Inexact | DEC_Rounded;
  } // decSetOverflow

/* ------------------------------------------------------------------ */
/* decSetMaxValue -- set number to +Nmax (maximum normal value)       */
/*                                                                    */
/*   dn is the number to set                                          */
/*   set is the context [used for digits and emax]                    */
/*                                                                    */
/* This sets the number to the maximum positive value.                */
/* ------------------------------------------------------------------ */
static void decSetMaxValue(decNumber *dn, decContext *set) {
  Unit *up;                        // work
  Int count=set->digits;           // nines to add
  dn->digits=count;
  // fill in all nines to set maximum value
  for (up=dn->lsu; ; up++) {
    if (count>DECDPUN) *up=DECDPUNMAX;  // unit full o'nines
     else {                             // this is the msu
      *up=(Unit)(powers[count]-1);
      break;
      }
    count-=DECDPUN;                // filled those digits
    } // up
  dn->bits=0;                      // + sign
  dn->exponent=set->emax-set->digits+1;
  } // decSetMaxValue

/* ------------------------------------------------------------------ */
/* decSetSubnormal -- process value whose exponent is <Emin           */
/*                                                                    */
/*   dn is the number (used as input as well as output; it may have   */
/*         an allowed subnormal value, which may need to be rounded)  */
/*   set is the context [used for the rounding mode]                  */
/*   residue is any pending residue                                   */
/*   status contains the current status to be updated                 */
/*                                                                    */
/* If subset mode, set result to zero and set Underflow flags.        */
/*                                                                    */
/* Value may be zero with a low exponent; this does not set Subnormal */
/* but the exponent will be clamped to Etiny.                         */
/*                                                                    */
/* Otherwise ensure exponent is not out of range, and round as        */
/* necessary.  Underflow is set if the result is Inexact.             */
/* ------------------------------------------------------------------ */
static void decSetSubnormal(decNumber *dn, decContext *set, Int *residue,
                            uInt *status) {
  decContext workset;         // work
  Int        etiny, adjust;   // ..

  #if DECSUBSET
  // simple set to zero and 'hard underflow' for subset
  if (!set->extended) {
    decNumberZero(dn);
    // always full overflow
    *status|=DEC_Underflow | DEC_Subnormal | DEC_Inexact | DEC_Rounded;
    return;
    }
  #endif

  // Full arithmetic -- allow subnormals, rounded to minimum exponent
  // (Etiny) if needed
  etiny=set->emin-(set->digits-1);      // smallest allowed exponent

  if ISZERO(dn) {                       // value is zero
    // residue can never be non-zero here
    #if DECCHECK
      if (*residue!=0) {
        printf("++ Subnormal 0 residue %ld\n", (LI)*residue);
        *status|=DEC_Invalid_operation;
        }
    #endif
    if (dn->exponent<etiny) {           // clamp required
      dn->exponent=etiny;
      *status|=DEC_Clamped;
      }
    return;
    }

  *status|=DEC_Subnormal;               // have a non-zero subnormal
  adjust=etiny-dn->exponent;            // calculate digits to remove
  if (adjust<=0) {                      // not out of range; unrounded
    // residue can never be non-zero here, except in the Nmin-residue
    // case (which is a subnormal result), so can take fast-path here
    // it may already be inexact (from setting the coefficient)
    if (*status&DEC_Inexact) *status|=DEC_Underflow;
    return;
    }

  // adjust>0, so need to rescale the result so exponent becomes Etiny
  // [this code is similar to that in rescale]
  workset=*set;                         // clone rounding, etc.
  workset.digits=dn->digits-adjust;     // set requested length
  workset.emin-=adjust;                 // and adjust emin to match
  // [note that the latter can be <1, here, similar to Rescale case]
  decSetCoeff(dn, &workset, dn->lsu, dn->digits, residue, status);
  decApplyRound(dn, &workset, *residue, status);

  // Use 754 default rule: Underflow is set iff Inexact
  // [independent of whether trapped]
  if (*status&DEC_Inexact) *status|=DEC_Underflow;

  // if rounded up a 999s case, exponent will be off by one; adjust
  // back if so [it will fit, because it was shortened earlier]
  if (dn->exponent>etiny) {
    dn->digits=decShiftToMost(dn->lsu, dn->digits, 1);
    dn->exponent--;                     // (re)adjust the exponent.
    }

  // if rounded to zero, it is by definition clamped...
  if (ISZERO(dn)) *status|=DEC_Clamped;
  } // decSetSubnormal

/* ------------------------------------------------------------------ */
/* decCheckMath - check entry conditions for a math function          */
/*                                                                    */
/*   This checks the context and the operand                          */
/*                                                                    */
/*   rhs is the operand to check                                      */
/*   set is the context to check                                      */
/*   status is unchanged if both are good                             */
/*                                                                    */
/* returns non-zero if status is changed, 0 otherwise                 */
/*                                                                    */
/* Restrictions enforced:                                             */
/*                                                                    */
/*   digits, emax, and -emin in the context must be less than         */
/*   DEC_MAX_MATH (999999), and A must be within these bounds if      */
/*   non-zero.  Invalid_operation is set in the status if a           */
/*   restriction is violated.                                         */
/* ------------------------------------------------------------------ */
static uInt decCheckMath(const decNumber *rhs, decContext *set,
                         uInt *status) {
  uInt save=*status;                         // record
  if (set->digits>DEC_MAX_MATH
   || set->emax>DEC_MAX_MATH
   || -set->emin>DEC_MAX_MATH) *status|=DEC_Invalid_context;
   else if ((rhs->digits>DEC_MAX_MATH
     || rhs->exponent+rhs->digits>DEC_MAX_MATH+1
     || rhs->exponent+rhs->digits<2*(1-DEC_MAX_MATH))
     && !ISZERO(rhs)) *status|=DEC_Invalid_operation;
  return (*status!=save);
  } // decCheckMath

/* ------------------------------------------------------------------ */
/* decGetInt -- get integer from a number                             */
/*                                                                    */
/*   dn is the number [which will not be altered]                     */
/*                                                                    */
/*   returns one of:                                                  */
/*     BADINT if there is a non-zero fraction                         */
/*     the converted integer                                          */
/*     BIGEVEN if the integer is even and magnitude > 2*10**9         */
/*     BIGODD  if the integer is odd  and magnitude > 2*10**9         */
/*                                                                    */
/* This checks and gets a whole number from the input decNumber.      */
/* The sign can be determined from dn by the caller when BIGEVEN or   */
/* BIGODD is returned.                                                */
/* ------------------------------------------------------------------ */
static Int decGetInt(const decNumber *dn) {
  Int  theInt;                          // result accumulator
  const Unit *up;                       // work
  Int  got;                             // digits (real or not) processed
  Int  ilength=dn->digits+dn->exponent; // integral length
  Flag neg=decNumberIsNegative(dn);     // 1 if -ve

  // The number must be an integer that fits in 10 digits
  // Assert, here, that 10 is enough for any rescale Etiny
  #if DEC_MAX_EMAX > 999999999
    #error GetInt may need updating [for Emax]
  #endif
  #if DEC_MIN_EMIN < -999999999
    #error GetInt may need updating [for Emin]
  #endif
  if (ISZERO(dn)) return 0;             // zeros are OK, with any exponent

  up=dn->lsu;                           // ready for lsu
  theInt=0;                             // ready to accumulate
  if (dn->exponent>=0) {                // relatively easy
    // no fractional part [usual]; allow for positive exponent
    got=dn->exponent;
    }
   else { // -ve exponent; some fractional part to check and discard
    Int count=-dn->exponent;            // digits to discard
    // spin up whole units until reach the Unit with the unit digit
    for (; count>=DECDPUN; up++) {
      if (*up!=0) return BADINT;        // non-zero Unit to discard
      count-=DECDPUN;
      }
    if (count==0) got=0;                // [a multiple of DECDPUN]
     else {                             // [not multiple of DECDPUN]
      Int rem;                          // work
      // slice off fraction digits and check for non-zero
      #if DECDPUN<=4
        theInt=QUOT10(*up, count);
        rem=*up-theInt*powers[count];
      #else
        rem=*up%powers[count];          // slice off discards
        theInt=*up/powers[count];
      #endif
      if (rem!=0) return BADINT;        // non-zero fraction
      // it looks good
      got=DECDPUN-count;                // number of digits so far
      up++;                             // ready for next
      }
    }
  // now it's known there's no fractional part

  // tricky code now, to accumulate up to 9.3 digits
  if (got==0) {theInt=*up; got+=DECDPUN; up++;} // ensure lsu is there

  if (ilength<11) {
    Int save=theInt;
    // collect any remaining unit(s)
    for (; got<ilength; up++) {
      theInt+=*up*powers[got];
      got+=DECDPUN;
      }
    if (ilength==10) {                  // need to check for wrap
      if (theInt/(Int)powers[got-DECDPUN]!=(Int)*(up-1)) ilength=11;
         // [that test also disallows the BADINT result case]
       else if (neg && theInt>1999999997) ilength=11;
       else if (!neg && theInt>999999999) ilength=11;
      if (ilength==11) theInt=save;     // restore correct low bit
      }
    }

  if (ilength>10) {                     // too big
    if (theInt&1) return BIGODD;        // bottom bit 1
    return BIGEVEN;                     // bottom bit 0
    }

  if (neg) theInt=-theInt;              // apply sign
  return theInt;
  } // decGetInt

/* ------------------------------------------------------------------ */
/* decDecap -- decapitate the coefficient of a number                 */
/*                                                                    */
/*   dn   is the number to be decapitated                             */
/*   drop is the number of digits to be removed from the left of dn;  */
/*     this must be <= dn->digits (if equal, the coefficient is       */
/*     set to 0)                                                      */
/*                                                                    */
/* Returns dn; dn->digits will be <= the initial digits less drop     */
/* (after removing drop digits there may be leading zero digits       */
/* which will also be removed).  Only dn->lsu and dn->digits change.  */
/* ------------------------------------------------------------------ */
static decNumber *decDecap(decNumber *dn, Int drop) {
  Unit *msu;                            // -> target cut point
  Int cut;                              // work
  if (drop>=dn->digits) {               // losing the whole thing
    #if DECCHECK
    if (drop>dn->digits)
      printf("decDecap called with drop>digits [%ld>%ld]\n",
             (LI)drop, (LI)dn->digits);
    #endif
    dn->lsu[0]=0;
    dn->digits=1;
    return dn;
    }
  msu=dn->lsu+D2U(dn->digits-drop)-1;   // -> likely msu
  cut=MSUDIGITS(dn->digits-drop);       // digits to be in use in msu
  if (cut!=DECDPUN) *msu%=powers[cut];  // clear left digits
  // that may have left leading zero digits, so do a proper count...
  dn->digits=decGetDigits(dn->lsu, msu-dn->lsu+1);
  return dn;
  } // decDecap

/* ------------------------------------------------------------------ */
/* decBiStr -- compare string with pairwise options                   */
/*                                                                    */
/*   targ is the string to compare                                    */
/*   str1 is one of the strings to compare against (length may be 0)  */
/*   str2 is the other; it must be the same length as str1            */
/*                                                                    */
/*   returns 1 if strings compare equal, (that is, it is the same     */
/*   length as str1 and str2, and each character of targ is in either */
/*   str1 or str2 in the corresponding position), or 0 otherwise      */
/*                                                                    */
/* This is used for generic caseless compare, including the awkward   */
/* case of the Turkish dotted and dotless Is.  Use as (for example):  */
/*   if (decBiStr(test, "mike", "MIKE")) ...                          */
/* ------------------------------------------------------------------ */
static Flag decBiStr(const char *targ, const char *str1, const char *str2) {
  for (;;targ++, str1++, str2++) {
    if (*targ!=*str1 && *targ!=*str2) return 0;
    // *targ has a match in one (or both, if terminator)
    if (*targ=='\0') break;
    } // forever
  return 1;
  } // decBiStr

/* ------------------------------------------------------------------ */
/* decNaNs -- handle NaN operand or operands                          */
/*                                                                    */
/*   res     is the result number                                     */
/*   lhs     is the first operand                                     */
/*   rhs     is the second operand, or NULL if none                   */
/*   context is used to limit payload length                          */
/*   status  contains the current status                              */
/*   returns res in case convenient                                   */
/*                                                                    */
/* Called when one or both operands is a NaN, and propagates the      */
/* appropriate result to res.  When an sNaN is found, it is changed   */
/* to a qNaN and Invalid operation is set.                            */
/* ------------------------------------------------------------------ */
static decNumber * decNaNs(decNumber *res, const decNumber *lhs,
                           const decNumber *rhs, decContext *set,
                           uInt *status) {
  // This decision tree ends up with LHS being the source pointer,
  // and status updated if need be
  if (lhs->bits & DECSNAN)
    *status|=DEC_Invalid_operation | DEC_sNaN;
   else if (rhs==NULL);
   else if (rhs->bits & DECSNAN) {
    lhs=rhs;
    *status|=DEC_Invalid_operation | DEC_sNaN;
    }
   else if (lhs->bits & DECNAN);
   else lhs=rhs;

  // propagate the payload
  if (lhs->digits<=set->digits) decNumberCopy(res, lhs); // easy
   else { // too long
    const Unit *ul;
    Unit *ur, *uresp1;
    // copy safe number of units, then decapitate
    res->bits=lhs->bits;                // need sign etc.
    uresp1=res->lsu+D2U(set->digits);
    for (ur=res->lsu, ul=lhs->lsu; ur<uresp1; ur++, ul++) *ur=*ul;
    res->digits=D2U(set->digits)*DECDPUN;
    // maybe still too long
    if (res->digits>set->digits) decDecap(res, res->digits-set->digits);
    }

  res->bits&=~DECSNAN;        // convert any sNaN to NaN, while
  res->bits|=DECNAN;          // .. preserving sign
  res->exponent=0;            // clean exponent
                              // [coefficient was copied/decapitated]
  return res;
  } // decNaNs

/* ------------------------------------------------------------------ */
/* decStatus -- apply non-zero status                                 */
/*                                                                    */
/*   dn     is the number to set if error                             */
/*   status contains the current status (not yet in context)          */
/*   set    is the context                                            */
/*                                                                    */
/* If the status is an error status, the number is set to a NaN,      */
/* unless the error was an overflow, divide-by-zero, or underflow,    */
/* in which case the number will have already been set.               */
/*                                                                    */
/* The context status is then updated with the new status.  Note that */
/* this may raise a signal, so control may never return from this     */
/* routine (hence resources must be recovered before it is called).   */
/* ------------------------------------------------------------------ */
static void decStatus(decNumber *dn, uInt status, decContext *set) {
  if (status & DEC_NaNs) {              // error status -> NaN
    // if cause was an sNaN, clear and propagate [NaN is already set up]
    if (status & DEC_sNaN) status&=~DEC_sNaN;
     else {
      decNumberZero(dn);                // other error: clean throughout
      dn->bits=DECNAN;                  // and make a quiet NaN
      }
    }
  decContextSetStatus(set, status);     // [may not return]
  return;
  } // decStatus

/* ------------------------------------------------------------------ */
/* decGetDigits -- count digits in a Units array                      */
/*                                                                    */
/*   uar is the Unit array holding the number (this is often an       */
/*          accumulator of some sort)                                 */
/*   len is the length of the array in units [>=1]                    */
/*                                                                    */
/*   returns the number of (significant) digits in the array          */
/*                                                                    */
/* All leading zeros are excluded, except the last if the array has   */
/* only zero Units.                                                   */
/* ------------------------------------------------------------------ */
// This may be called twice during some operations.
static Int decGetDigits(Unit *uar, Int len) {
  Unit *up=uar+(len-1);            // -> msu
  Int  digits=(len-1)*DECDPUN+1;   // possible digits excluding msu
  #if DECDPUN>4
  uInt const *pow;                 // work
  #endif
                                   // (at least 1 in final msu)
  #if DECCHECK
  if (len<1) printf("decGetDigits called with len<1 [%ld]\n", (LI)len);
  #endif

  for (; up>=uar; up--) {
    if (*up==0) {                  // unit is all 0s
      if (digits==1) break;        // a zero has one digit
      digits-=DECDPUN;             // adjust for 0 unit
      continue;}
    // found the first (most significant) non-zero Unit
    #if DECDPUN>1                  // not done yet

    if (*up<10) break;             // is 1-9
    digits++;
    #if DECDPUN>2                  // not done yet

    if (*up<100) break;            // is 10-99
    digits++;
    #if DECDPUN>3                  // not done yet

    if (*up<1000) break;           // is 100-999
    digits++;
    #if DECDPUN>4                  // count the rest ...

    for (pow=&powers[4]; *up>=*pow; pow++) digits++;
    #endif
    #endif
    #endif
    #endif
    break;
    } // up
  return digits;
  } // decGetDigits

#if DECTRACE | DECCHECK
/* ------------------------------------------------------------------ */
/* decNumberShow -- display a number [debug aid]                      */
/*   dn is the number to show                                         */
/*                                                                    */
/* Shows: sign, exponent, coefficient (msu first), digits             */
/*    or: sign, special-value                                         */
/* ------------------------------------------------------------------ */
// this is public so other modules can use it
void decNumberShow(const decNumber *dn) {
  const Unit *up;                  // work
  uInt u, d;                       // ..
  Int cut;                         // ..
  char isign='+';                  // main sign
  if (dn==NULL) {
    printf("NULL\n");
    return;}
  if (decNumberIsNegative(dn)) isign='-';
  printf(" >> %c ", isign);
  if (dn->bits&DECSPECIAL) {       // Is a special value
    if (decNumberIsInfinite(dn)) printf("Infinity");
     else {                                  // a NaN
      if (dn->bits&DECSNAN) printf("sNaN");  // signalling NaN
       else printf("NaN");
      }
    // if coefficient and exponent are 0, no more to do
    if (dn->exponent==0 && dn->digits==1 && *dn->lsu==0) {
      printf("\n");
      return;}
    // drop through to report other information
    printf(" ");
    }

  // now carefully display the coefficient
  up=dn->lsu+D2U(dn->digits)-1;         // msu
  printf("%ld", (LI)*up);
  for (up=up-1; up>=dn->lsu; up--) {
    u=*up;
    printf(":");
    for (cut=DECDPUN-1; cut>=0; cut--) {
      d=u/powers[cut];
      u-=d*powers[cut];
      printf("%ld", (LI)d);
      } // cut
    } // up
  if (dn->exponent!=0) {
    char esign='+';
    if (dn->exponent<0) esign='-';
    printf(" E%c%ld", esign, (LI)abs(dn->exponent));
    }
  printf(" [%ld]\n", (LI)dn->digits);
  } // decNumberShow
#endif

#if DECTRACE || DECCHECK
/* ------------------------------------------------------------------ */
/* decDumpAr -- display a unit array [debug/check aid]                */
/*   name is a single-character tag name                              */
/*   ar   is the array to display                                     */
/*   len  is the length of the array in Units                         */
/* ------------------------------------------------------------------ */
static void decDumpAr(char name, const Unit *ar, Int len) {
  Int i;
  const char *spec;
  #if DECDPUN==9
    spec="%09d ";
  #elif DECDPUN==8
    spec="%08d ";
  #elif DECDPUN==7
    spec="%07d ";
  #elif DECDPUN==6
    spec="%06d ";
  #elif DECDPUN==5
    spec="%05d ";
  #elif DECDPUN==4
    spec="%04d ";
  #elif DECDPUN==3
    spec="%03d ";
  #elif DECDPUN==2
    spec="%02d ";
  #else
    spec="%d ";
  #endif
  printf("  :%c: ", name);
  for (i=len-1; i>=0; i--) {
    if (i==len-1) printf("%ld ", (LI)ar[i]);
     else printf(spec, ar[i]);
    }
  printf("\n");
  return;}
#endif

#if DECCHECK
/* ------------------------------------------------------------------ */
/* decCheckOperands -- check operand(s) to a routine                  */
/*   res is the result structure (not checked; it will be set to      */
/*          quiet NaN if error found (and it is not NULL))            */
/*   lhs is the first operand (may be DECUNRESU)                      */
/*   rhs is the second (may be DECUNUSED)                             */
/*   set is the context (may be DECUNCONT)                            */
/*   returns 0 if both operands, and the context are clean, or 1      */
/*     otherwise (in which case the context will show an error,       */
/*     unless NULL).  Note that res is not cleaned; caller should     */
/*     handle this so res=NULL case is safe.                          */
/* The caller is expected to abandon immediately if 1 is returned.    */
/* ------------------------------------------------------------------ */
static Flag decCheckOperands(decNumber *res, const decNumber *lhs,
                             const decNumber *rhs, decContext *set) {
  Flag bad=0;
  if (set==NULL) {                 // oops; hopeless
    #if DECTRACE || DECVERB
    printf("Reference to context is NULL.\n");
    #endif
    bad=1;
    return 1;}
   else if (set!=DECUNCONT
     && (set->digits<1 || set->round>=DEC_ROUND_MAX)) {
    bad=1;
    #if DECTRACE || DECVERB
    printf("Bad context [digits=%ld round=%ld].\n",
           (LI)set->digits, (LI)set->round);
    #endif
    }
   else {
    if (res==NULL) {
      bad=1;
      #if DECTRACE
      // this one not DECVERB as standard tests include NULL
      printf("Reference to result is NULL.\n");
      #endif
      }
    if (!bad && lhs!=DECUNUSED) bad=(decCheckNumber(lhs));
    if (!bad && rhs!=DECUNUSED) bad=(decCheckNumber(rhs));
    }
  if (bad) {
    if (set!=DECUNCONT) decContextSetStatus(set, DEC_Invalid_operation);
    if (res!=DECUNRESU && res!=NULL) {
      decNumberZero(res);
      res->bits=DECNAN;       // qNaN
      }
    }
  return bad;
  } // decCheckOperands

/* ------------------------------------------------------------------ */
/* decCheckNumber -- check a number                                   */
/*   dn is the number to check                                        */
/*   returns 0 if the number is clean, or 1 otherwise                 */
/*                                                                    */
/* The number is considered valid if it could be a result from some   */
/* operation in some valid context.                                   */
/* ------------------------------------------------------------------ */
static Flag decCheckNumber(const decNumber *dn) {
  const Unit *up;             // work
  uInt maxuint;               // ..
  Int ae, d, digits;          // ..
  Int emin, emax;             // ..

  if (dn==NULL) {             // hopeless
    #if DECTRACE
    // this one not DECVERB as standard tests include NULL
    printf("Reference to decNumber is NULL.\n");
    #endif
    return 1;}

  // check special values
  if (dn->bits & DECSPECIAL) {
    if (dn->exponent!=0) {
      #if DECTRACE || DECVERB
      printf("Exponent %ld (not 0) for a special value [%02x].\n",
             (LI)dn->exponent, dn->bits);
      #endif
      return 1;}

    // 2003.09.08: NaNs may now have coefficients, so next tests Inf only
    if (decNumberIsInfinite(dn)) {
      if (dn->digits!=1) {
        #if DECTRACE || DECVERB
        printf("Digits %ld (not 1) for an infinity.\n", (LI)dn->digits);
        #endif
        return 1;}
      if (*dn->lsu!=0) {
        #if DECTRACE || DECVERB
        printf("LSU %ld (not 0) for an infinity.\n", (LI)*dn->lsu);
        #endif
        decDumpAr('I', dn->lsu, D2U(dn->digits));
        return 1;}
      } // Inf
    // 2002.12.26: negative NaNs can now appear through proposed IEEE
    //             concrete formats (decimal64, etc.).
    return 0;
    }

  // check the coefficient
  if (dn->digits<1 || dn->digits>DECNUMMAXP) {
    #if DECTRACE || DECVERB
    printf("Digits %ld in number.\n", (LI)dn->digits);
    #endif
    return 1;}

  d=dn->digits;

  for (up=dn->lsu; d>0; up++) {
    if (d>DECDPUN) maxuint=DECDPUNMAX;
     else {                   // reached the msu
      maxuint=powers[d]-1;
      if (dn->digits>1 && *up<powers[d-1]) {
        #if DECTRACE || DECVERB
        printf("Leading 0 in number.\n");
        decNumberShow(dn);
        #endif
        return 1;}
      }
    if (*up>maxuint) {
      #if DECTRACE || DECVERB
      printf("Bad Unit [%08lx] in %ld-digit number at offset %ld [maxuint %ld].\n",
              (LI)*up, (LI)dn->digits, (LI)(up-dn->lsu), (LI)maxuint);
      #endif
      return 1;}
    d-=DECDPUN;
    }

  // check the exponent.  Note that input operands can have exponents
  // which are out of the set->emin/set->emax and set->digits range
  // (just as they can have more digits than set->digits).
  ae=dn->exponent+dn->digits-1;    // adjusted exponent
  emax=DECNUMMAXE;
  emin=DECNUMMINE;
  digits=DECNUMMAXP;
  if (ae<emin-(digits-1)) {
    #if DECTRACE || DECVERB
    printf("Adjusted exponent underflow [%ld].\n", (LI)ae);
    decNumberShow(dn);
    #endif
    return 1;}
  if (ae>+emax) {
    #if DECTRACE || DECVERB
    printf("Adjusted exponent overflow [%ld].\n", (LI)ae);
    decNumberShow(dn);
    #endif
    return 1;}

  return 0;              // it's OK
  } // decCheckNumber

/* ------------------------------------------------------------------ */
/* decCheckInexact -- check a normal finite inexact result has digits */
/*   dn is the number to check                                        */
/*   set is the context (for status and precision)                    */
/*   sets Invalid operation, etc., if some digits are missing         */
/* [this check is not made for DECSUBSET compilation or when          */
/* subnormal is not set]                                              */
/* ------------------------------------------------------------------ */
static void decCheckInexact(const decNumber *dn, decContext *set) {
  #if !DECSUBSET && DECEXTFLAG
    if ((set->status & (DEC_Inexact|DEC_Subnormal))==DEC_Inexact
     && (set->digits!=dn->digits) && !(dn->bits & DECSPECIAL)) {
      #if DECTRACE || DECVERB
      printf("Insufficient digits [%ld] on normal Inexact result.\n",
             (LI)dn->digits);
      decNumberShow(dn);
      #endif
      decContextSetStatus(set, DEC_Invalid_operation);
      }
  #else
    // next is a noop for quiet compiler
    if (dn!=NULL && dn->digits==0) set->status|=DEC_Invalid_operation;
  #endif
  return;
  } // decCheckInexact
#endif

#if DECALLOC
#undef malloc
#undef free
/* ------------------------------------------------------------------ */
/* decMalloc -- accountable allocation routine                        */
/*   n is the number of bytes to allocate                             */
/*                                                                    */
/* Semantics is the same as the stdlib malloc routine, but bytes      */
/* allocated are accounted for globally, and corruption fences are    */
/* added before and after the 'actual' storage.                       */
/* ------------------------------------------------------------------ */
/* This routine allocates storage with an extra twelve bytes; 8 are   */
/* at the start and hold:                                             */
/*   0-3 the original length requested                                */
/*   4-7 buffer corruption detection fence (DECFENCE, x4)             */
/* The 4 bytes at the end also hold a corruption fence (DECFENCE, x4) */
/* ------------------------------------------------------------------ */
static void *decMalloc(size_t n) {
  uInt  size=n+12;                 // true size
  void  *alloc;                    // -> allocated storage
  uByte *b, *b0;                   // work
  uInt  uiwork;                    // for macros

  alloc=malloc(size);              // -> allocated storage
  if (alloc==NULL) return NULL;    // out of strorage
  b0=(uByte *)alloc;               // as bytes
  decAllocBytes+=n;                // account for storage
  UBFROMUI(alloc, n);              // save n
  // printf(" alloc ++ dAB: %ld (%ld)\n", (LI)decAllocBytes, (LI)n);
  for (b=b0+4; b<b0+8; b++) *b=DECFENCE;
  for (b=b0+n+8; b<b0+n+12; b++) *b=DECFENCE;
  return b0+8;                     // -> play area
  } // decMalloc

/* ------------------------------------------------------------------ */
/* decFree -- accountable free routine                                */
/*   alloc is the storage to free                                     */
/*                                                                    */
/* Semantics is the same as the stdlib malloc routine, except that    */
/* the global storage accounting is updated and the fences are        */
/* checked to ensure that no routine has written 'out of bounds'.     */
/* ------------------------------------------------------------------ */
/* This routine first checks that the fences have not been corrupted. */
/* It then frees the storage using the 'truw' storage address (that   */
/* is, offset by 8).                                                  */
/* ------------------------------------------------------------------ */
static void decFree(void *alloc) {
  uInt  n;                         // original length
  uByte *b, *b0;                   // work
  uInt  uiwork;                    // for macros

  if (alloc==NULL) return;         // allowed; it's a nop
  b0=(uByte *)alloc;               // as bytes
  b0-=8;                           // -> true start of storage
  n=UBTOUI(b0);                    // lift length
  for (b=b0+4; b<b0+8; b++) if (*b!=DECFENCE)
    printf("=== Corrupt byte [%02x] at offset %d from %ld ===\n", *b,
           b-b0-8, (LI)b0);
  for (b=b0+n+8; b<b0+n+12; b++) if (*b!=DECFENCE)
    printf("=== Corrupt byte [%02x] at offset +%d from %ld, n=%ld ===\n", *b,
           b-b0-8, (LI)b0, (LI)n);
  free(b0);                        // drop the storage
  decAllocBytes-=n;                // account for storage
  // printf(" free -- dAB: %d (%d)\n", decAllocBytes, -n);
  } // decFree
#define malloc(a) decMalloc(a)

#define free(a) decFree(a)

#endif