flint-sys 0.9.0

/*
    Copyright (C) 2007, 2008 David Harvey (zn_poly)
    Copyright (C) 2013 William Hart

    This file is part of FLINT.

    FLINT is free software: you can redistribute it and/or modify it under
    the terms of the GNU Lesser General Public License (LGPL) as published
    by the Free Software Foundation; either version 3 of the License, or
    (at your option) any later version.  See <https://www.gnu.org/licenses/>.
*/

#include "mpn_extras.h"
#include "nmod_vec.h"
#include "nmod_poly.h"

/*
   Multiplication/squaring using Kronecker substitution at 2^b, -2^b,
   2^(-b) and -2^(-b).
*/
void
_nmod_poly_mul_KS4(nn_ptr res, nn_srcptr op1, slong n1,
                  nn_srcptr op2, slong n2, nmod_t mod)
{
   int sqr, v3m_neg;
   ulong bits, b, w, a1, a2, a3;
   slong n1o, n1e, n2o, n2e, n3o, n3e, n3, k1, k2, k3;
   nn_ptr v1_buf0, v2_buf0, v1_buf1, v2_buf1, v1_buf2, v2_buf2, v1_buf3, v2_buf3, v1_buf4, v2_buf4;
   nn_ptr v1on, v1en, v1pn, v1mn, v2on, v2en, v2pn, v2mn, v3on, v3en, v3pn, v3mn;
   nn_ptr v1or, v1er, v1pr, v1mr, v2or, v2er, v2pr, v2mr, v3or, v3er, v3pr, v3mr;
   nn_ptr z, zn, zr;
   TMP_INIT;

   if (n2 == 1)
   {
      /* code below needs n2 > 1, so fall back on scalar multiplication */
      _nmod_vec_scalar_mul_nmod(res, op1, n1, op2[0], mod);
      return;
   }

   TMP_START;

   sqr = (op1 == op2 && n1 == n2);

   /* bits in each output coefficient */
   bits = 2 * (FLINT_BITS - mod.norm) + FLINT_CLOG2(n2);

   /*
      we're evaluating at x = B, -B, 1/B, -1/B,
      where B = 2^b, and b = ceil(bits / 4)
   */
   b = (bits + 3) / 4;

   /* number of ulongs required to store each base-B^2 digit */
   w = (2*b - 1)/FLINT_BITS + 1;

   /*
      Write f1(x) = f1e(x^2) + x * f1o(x^2)
            f2(x) = f2e(x^2) + x * f2o(x^2)
             h(x) =  he(x^2) + x *  ho(x^2)
      "e" = even, "o" = odd
   */

   n1o = n1 / 2;
   n1e = n1 - n1o;

   n2o = n2 / 2;
   n2e = n2 - n2o;

   n3 = n1 + n2 - 1;   /* length of h */
   n3o = n3 / 2;
   n3e = n3 - n3o;

   /*
      Put k1 = number of limbs needed to store f1(B) and |f1(-B)|.
      In f1(B), the leading coefficient starts at bit position b * (n1 - 1)
      and has length 2b, and the coefficients overlap so we need an extra bit
      for the carry: this gives (n1 + 1) * b + 1 bits. Ditto for f2.
   */
   k1 = ((n1 + 1) * b)/FLINT_BITS + 1;
   k2 = ((n2 + 1) * b)/FLINT_BITS + 1;
   k3 = k1 + k2;

   /* allocate space */
   v1_buf0 = TMP_ALLOC(sizeof(ulong) * 5 * k3); /* k1 limbs */
   v2_buf0 = v1_buf0 + k1;         /* k2 limbs */
   v1_buf1 = v2_buf0 + k2;         /* k1 limbs */
   v2_buf1 = v1_buf1 + k1;         /* k2 limbs */
   v1_buf2 = v2_buf1 + k2;         /* k1 limbs */
   v2_buf2 = v1_buf2 + k1;         /* k2 limbs */
   v1_buf3 = v2_buf2 + k2;         /* k1 limbs */
   v2_buf3 = v1_buf3 + k1;         /* k2 limbs */
   v1_buf4 = v2_buf3 + k2;         /* k1 limbs */
   v2_buf4 = v1_buf4 + k1;         /* k2 limbs */

   /*
      arrange overlapping buffers to minimise memory use
      "p" = plus, "m" = minus
      "n" = normal order, "r" = reciprocal order
   */
   v1en = v1_buf0;
   v1on = v1_buf1;
   v1pn = v1_buf2;
   v1mn = v1_buf0;
   v2en = v2_buf0;
   v2on = v2_buf1;
   v2pn = v2_buf2;
   v2mn = v2_buf0;
   v3pn = v1_buf1;
   v3mn = v1_buf2;
   v3en = v1_buf0;
   v3on = v1_buf1;

   v1er = v1_buf2;
   v1or = v1_buf3;
   v1pr = v1_buf4;
   v1mr = v1_buf2;
   v2er = v2_buf2;
   v2or = v2_buf3;
   v2pr = v2_buf4;
   v2mr = v2_buf2;
   v3pr = v1_buf3;
   v3mr = v1_buf4;
   v3er = v1_buf2;
   v3or = v1_buf3;

   z = TMP_ALLOC(sizeof(ulong) * 2*w*(n3e + 1));
   zn = z;
   zr = z + w*(n3e + 1);

   /* -------------------------------------------------------------------------
          "normal" evaluation points
   */

   if (!sqr)
   {
      /* multiplication version */

      /*
         evaluate f1e(B^2) and B * f1o(B^2)
         We need max(2 * b*n1e, 2 * b*n1o + b) bits for this packing step,
         which is safe since (n1 + 1) * b + 1 >= max(2 * b*n1e, 2 * b*n1o + b).
         Ditto for f2 below.
      */
      _nmod_poly_KS2_pack(v1en, op1, n1e, 2, 2 * b, 0, k1);
      _nmod_poly_KS2_pack(v1on, op1 + 1, n1o, 2, 2 * b, b, k1);

      /*
         compute  f1(B)  =  f1e(B^2) + B * f1o(B^2)
            and |f1(-B)| = |f1e(B^2) - B * f1o(B^2)|
      */
      mpn_add_n (v1pn, v1en, v1on, k1);
      v3m_neg = flint_mpn_signed_sub_n(v1mn, v1en, v1on, k1);

      /* evaluate f2e(B^2) and B * f2o(B^2) */
      _nmod_poly_KS2_pack(v2en, op2, n2e, 2, 2 * b, 0, k2);
      _nmod_poly_KS2_pack(v2on, op2 + 1, n2o, 2, 2 * b, b, k2);

      /*
         compute  f2(B)  =  f2e(B^2) + B * f2o(B^2)
            and |f2(-B)| = |f2e(B^2) - B * f2o(B^2)|
      */
      mpn_add_n(v2pn, v2en, v2on, k2);
      v3m_neg ^= flint_mpn_signed_sub_n(v2mn, v2en, v2on, k2);

      /*
         compute  h(B)  =  f1(B)   *  f2(B)
            and |h(-B)| = |f1(-B)| * |f2(-B)|
         hn_neg is set if h(-B) is negative
      */
      flint_mpn_mul(v3pn, v1pn, k1, v2pn, k2);
      flint_mpn_mul(v3mn, v1mn, k1, v2mn, k2);
   }
   else
   {
      /* squaring version */

      /* evaluate f1e(B^2) and B * f1o(B^2) */
      _nmod_poly_KS2_pack(v1en, op1, n1e, 2, 2 * b, 0, k1);
      _nmod_poly_KS2_pack(v1on, op1 + 1, n1o, 2, 2 * b, b, k1);

      /*
         compute  f1(B)  =  f1e(B^2) + B * f1o(B^2)
            and |f1(-B)| = |f1e(B^2) - B * f1o(B^2)|
      */
      mpn_add_n (v1pn, v1en, v1on, k1);
      flint_mpn_signed_sub_n(v1mn, v1en, v1on, k1);

      /*
         compute h(B) =  f1(B)^2
            and h(-B) = |f1(-B)|^2
         hn_neg is cleared since h(-B) is never negative
      */
      flint_mpn_sqr(v3pn, v1pn, k1);
      flint_mpn_sqr(v3mn, v1mn, k1);
      v3m_neg = 0;
   }

   /*
      Each coefficient of h(B) is up to 4b bits long, so h(B) needs at most
      ((n1 + n2 + 2) * b + 1) bits. (The extra +1 is to accommodate carries
      generated by overlapping coefficients.)  The buffer has at least
      ((n1 + n2 + 2) * b + 2) bits. Therefore we can safely store 2*h(B) etc.
   */

   /*
      compute     2 * he(B^2) = h(B) + h(-B)
      and     B * 2 * ho(B^2) = h(B) - h(-B)
   */
   if (v3m_neg)
   {
      mpn_sub_n(v3en, v3pn, v3mn, k3);
      mpn_add_n (v3on, v3pn, v3mn, k3);
   }
   else
   {
      mpn_add_n (v3en, v3pn, v3mn, k3);
      mpn_sub_n (v3on, v3pn, v3mn, k3);
   }

   /* -------------------------------------------------------------------------
          "reciprocal" evaluation points
   */

   /*
      correction factors to take into account that if a polynomial has even
      length, its even and odd coefficients are swapped when the polynomial
      is reversed
   */
   a1 = (n1 & 1) ? 0 : b;
   a2 = (n2 & 1) ? 0 : b;
   a3 = (n3 & 1) ? 0 : b;

   if (!sqr)
   {
      /* multiplication version */

      /* evaluate B^(n1-1) * f1e(1/B^2) and B^(n1-2) * f1o(1/B^2) */
      _nmod_poly_KS2_pack(v1er, op1 + 2*(n1e - 1), n1e, -2, 2 * b, a1, k1);
      _nmod_poly_KS2_pack(v1or, op1 + 1 + 2*(n1o - 1), n1o, -2, 2 * b, b - a1, k1);

      /*
         compute  B^(n1-1) * f1(1/B) =
                      B^(n1-1) * f1e(1/B^2) + B^(n1-2) * f1o(1/B^2)
            and  |B^(n1-1) * f1(-1/B)| =
                     |B^(n1-1) * f1e(1/B^2) - B^(n1-2) * f1o(1/B^2)|
      */
      mpn_add_n(v1pr, v1er, v1or, k1);
      v3m_neg = flint_mpn_signed_sub_n(v1mr, v1er, v1or, k1);

      /* evaluate B^(n2-1) * f2e(1/B^2) and B^(n2-2) * f2o(1/B^2) */
      _nmod_poly_KS2_pack(v2er, op2 + 2*(n2e - 1), n2e, -2, 2 * b, a2, k2);
      _nmod_poly_KS2_pack(v2or, op2 + 1 + 2*(n2o - 1), n2o, -2, 2 * b, b - a2, k2);

      /*
         compute  B^(n2-1) * f2(1/B) =
                      B^(n2-1) * f2e(1/B^2) + B^(n2-2) * f2o(1/B^2)
            and  |B^(n1-1) * f2(-1/B)| =
                     |B^(n2-1) * f2e(1/B^2) - B^(n2-2) * f2o(1/B^2)|
      */
      mpn_add_n (v2pr, v2er, v2or, k2);
      v3m_neg ^= flint_mpn_signed_sub_n(v2mr, v2er, v2or, k2);

      /*
         compute B^(n3-1) * h(1/B) =
                         (B^(n1-1) * f1(1/B)) * (B^(n2-1) * f2(1/B))
             and |B^(n3-1) * h(-1/B)| =
                         |B^(n1-1) * f1(-1/B)| * |B^(n2-1) * f2(-1/B)|
         hr_neg is set if h(-1/B) is negative
      */
      flint_mpn_mul(v3pr, v1pr, k1, v2pr, k2);
      flint_mpn_mul(v3mr, v1mr, k1, v2mr, k2);
   }
   else
   {
      /* squaring version */

      /* evaluate B^(n1-1) * f1e(1/B^2) and B^(n1-2) * f1o(1/B^2) */
      _nmod_poly_KS2_pack(v1er, op1 + 2*(n1e - 1), n1e, -2, 2 * b, a1, k1);
      _nmod_poly_KS2_pack(v1or, op1 + 1 + 2*(n1o - 1), n1o, -2, 2 * b, b - a1, k1);

      /*
         compute  B^(n1-1) * f1(1/B) =
                      B^(n1-1) * f1e(1/B^2) + B^(n1-2) * f1o(1/B^2)
            and  |B^(n1-1) * f1(-1/B)| =
                     |B^(n1-1) * f1e(1/B^2) - B^(n1-2) * f1o(1/B^2)|
      */
      mpn_add_n(v1pr, v1er, v1or, k1);
      flint_mpn_signed_sub_n(v1mr, v1er, v1or, k1);

      /*
         compute B^(n3-1) * h(1/B)  = (B^(n1-1) * f1(1/B))^2
             and B^(n3-1) * h(-1/B) = |B^(n1-1) * f1(-1/B)|^2
         hr_neg is cleared since h(-1/B) is never negative
      */
      flint_mpn_sqr(v3pr, v1pr, k1);
      flint_mpn_sqr(v3mr, v1mr, k1);
      v3m_neg = 0;
   }

   /*
      compute 2 * B^(n3-1) * he(1/B^2)
                     = B^(n3-1) * h(1/B) + B^(n3-1) * h(-1/B)
         and  2 * B^(n3-2) * ho(1/B^2)
                     = B^(n3-1) * h(1/B) - B^(n3-1) * h(-1/B)
   */
   if (v3m_neg)
   {
      mpn_sub_n(v3er, v3pr, v3mr, k3);
      mpn_add_n(v3or, v3pr, v3mr, k3);
   }
   else
   {
      mpn_add_n (v3er, v3pr, v3mr, k3);
      mpn_sub_n (v3or, v3pr, v3mr, k3);
   }

   /* -------------------------------------------------------------------------
          combine "normal" and "reciprocal" information
   */

   /* decompose he(B^2) and B^(2*(n3e-1)) * he(1/B^2) into base-B^2 digits */
   _nmod_poly_KS2_unpack(zn, v3en, n3e + 1, 2 * b, 1);
   _nmod_poly_KS2_unpack(zr, v3er, n3e + 1, 2 * b, a3 + 1);

   /* combine he(B^2) and he(1/B^2) information to get even coefficients of h */
   _nmod_poly_KS2_recover_reduce(res, 2, zn, zr, n3e, 2 * b, mod);

   /* decompose ho(B^2) and B^(2*(n3o-1)) * ho(1/B^2) into base-B^2 digits */
   _nmod_poly_KS2_unpack(zn, v3on, n3o + 1, 2 * b, b + 1);
   _nmod_poly_KS2_unpack(zr, v3or, n3o + 1, 2 * b, b - a3 + 1);

   /* combine ho(B^2) and ho(1/B^2) information to get odd coefficients of h */
   _nmod_poly_KS2_recover_reduce(res + 1, 2, zn, zr, n3o, 2 * b, mod);

   TMP_END;
}

void
nmod_poly_mul_KS4(nmod_poly_t res,
                 const nmod_poly_t poly1, const nmod_poly_t poly2)
{
    slong len_out;

    if ((poly1->length == 0) || (poly2->length == 0))
    {
        nmod_poly_zero(res);
        return;
    }

    len_out = poly1->length + poly2->length - 1;

    if (res == poly1 || res == poly2)
    {
        nmod_poly_t temp;
        nmod_poly_init2_preinv(temp, poly1->mod.n, poly1->mod.ninv, len_out);
        if (poly1->length >= poly2->length)
            _nmod_poly_mul_KS4(temp->coeffs, poly1->coeffs, poly1->length,
                              poly2->coeffs, poly2->length,
                              poly1->mod);
        else
            _nmod_poly_mul_KS4(temp->coeffs, poly2->coeffs, poly2->length,
                              poly1->coeffs, poly1->length,
                              poly1->mod);
        nmod_poly_swap(res, temp);
        nmod_poly_clear(temp);
    }
    else
    {
        nmod_poly_fit_length(res, len_out);
        if (poly1->length >= poly2->length)
            _nmod_poly_mul_KS4(res->coeffs, poly1->coeffs, poly1->length,
                              poly2->coeffs, poly2->length,
                              poly1->mod);
        else
            _nmod_poly_mul_KS4(res->coeffs, poly2->coeffs, poly2->length,
                              poly1->coeffs, poly1->length,
                              poly1->mod);
    }

    res->length = len_out;
    _nmod_poly_normalise(res);
}