Crate maryada 

A no_std binary64 real interval arithmetic library conforming to IEEE 1788.1.

The rectangular complex interval extension is outside the scope of the standard.

maryada provides Interval and DecoratedInterval for outward-rounded real interval arithmetic, ComplexBox for rectangular complex intervals when the complex feature is enabled, and text and binary interchange operations. Most arithmetic functions are generic over IntervalDatum, so the same free-function API works with bare and decorated intervals.

The inherent methods offer the same operations in a chaining-friendly form:

use maryada::Interval;

let x = Interval::new(1.0, 2.0);
let y = x.sqr();

assert_eq!(y.bounds(), (1.0, 4.0));

Operations return enclosing intervals. Decorated operations additionally propagate the weakest input or operation decoration. APIs that report IEEE exception conditions accept a SignalSink; pass &mut () to ignore them.

Modules

prelude

Common interval types for glob imports.

Structs

DecoratedInterval

A binary64 interval paired with an IEEE 1788 decoration.

Interval

A closed binary64 interval, or the distinguished empty interval.

InvalidDecoration

Error returned when a byte or string is not a valid Decoration.

ParseIntervalError

Error returned by core::str::FromStr for an invalid interval literal.

SignalFlags

An accumulating bit set of raised Signal values.

Enums

Decoration

The definedness and continuity information attached to an interval result.

Signal

An IEEE 1788 exception condition reported by an interval operation.

TextError

Error returned when formatting an interval into a caller-provided buffer.

Constants

DECORATED_INTERVAL_ENCODED_LEN

Encoded length of a decorated interval: two endpoints and one decoration.

INTERVAL_ENCODED_LEN

Encoded length of a bare interval: two binary64 endpoints.

Traits

IntervalDatum

Common sealed representation surface used by all generic operations.

SignalSink

Receives exception conditions raised by interval operations.

Functions

abs

Encloses the absolute value of every value in x.

acos

Encloses the inverse cosine over the part of x in [-1, 1].

acosh

Encloses inverse hyperbolic cosine over the part of x at least one.

add

Encloses all pairwise sums of values from x and y.

asin

Encloses the inverse sine over the part of x in [-1, 1].

asinh

Encloses the inverse hyperbolic sine of every value in x.

atan

Encloses the inverse tangent of every value in x.

atan2

Encloses the two-argument angle atan2(y, x).

atanh

Encloses inverse hyperbolic tangent over the part of x in (-1, 1).

cancel_minus

Computes the cancellative subtraction operation x ⊖ y.

cancel_plus

Computes the cancellative addition operation x ⊕ y.

ceil

Encloses the ceiling of every value in x.

convex_hull

Returns the smallest interval containing both x and y.

cos

Encloses the cosine of every value in x.

cosh

Encloses the hyperbolic cosine of every value in x.

decorated_interval_from_be_bytes

Decodes a big-endian decorated interval.

decorated_interval_from_le_bytes

Decodes a little-endian decorated interval.

decorated_interval_to_be_bytes

Encodes a decorated interval using big-endian endpoint bytes.

decorated_interval_to_le_bytes

Encodes a decorated interval using little-endian endpoint bytes.

decoration_part

Returns the decoration component of a decorated interval.

disjoint

Returns whether x and y have no common members.

div

Encloses all defined quotients x / y.

empty

Returns the empty interval.

entire

Returns the interval containing every real number.

equal

Returns whether x and y denote the same set.

exp

Encloses e^x over the input interval.

exp2

Encloses 2^x over the input interval.

exp10

Encloses 10^x over the input interval.

floor

Encloses the floor of every value in x.

fma

Encloses the fused expression x * y + z with one final rounding step.

hypot

Encloses sqrt(x² + y²) for values drawn from both intervals.

inf

Returns the lower endpoint, or NaN for NaI.

interior

Returns whether x is contained in the topological interior of y.

intersection

Returns the set intersection of x and y.

interval_from_be_bytes

Decodes a big-endian bare interval.

interval_from_le_bytes

Decodes a little-endian bare interval.

interval_part

Extracts the bare interval, signaling and returning empty for NaI.

interval_to_be_bytes

Encodes a bare interval using big-endian IEEE 754 endpoint bytes.

interval_to_le_bytes

Encodes a bare interval using little-endian IEEE 754 endpoint bytes.

interval_to_text

IEEE intervalToText.

is_empty

Returns whether x is the empty interval; NaI is not empty.

is_entire

Returns whether x contains every real number.

is_nai

Returns whether a decorated interval is Not an Interval.

log

Encloses the natural logarithm over the positive part of x.

log2

Encloses the base-two logarithm over the positive part of x.

log10

Encloses the base-ten logarithm over the positive part of x.

mag

Returns the magnitude, the greatest absolute value in x.

max

Encloses the pointwise maximum of values from x and y.

mid

Returns a representative midpoint, or NaN for an empty interval or NaI.

mid_rad

Returns a midpoint and an upward-rounded radius enclosing x.

mig

Returns the mignitude, the least absolute value in x.

min

Encloses the pointwise minimum of values from x and y.

mul

Encloses all pairwise products of values from x and y.

neg

Computes the additive inverse of every value in x.

new

Constructs an interval datum with endpoints inf and sup.

new_dec

Attaches the strongest valid decoration to a bare interval.

pow

Encloses the real-valued power function for bases in x and exponents in y.

pown

Raises every value in x to the integer power p.

rad

Returns the radius rounded upward.

recip

Encloses the reciprocals of the nonzero values in x.

round_ties_to_away

Encloses rounding to nearest integer with ties away from zero.

round_ties_to_even

Encloses rounding to nearest integer with ties to even.

set_dec

Attaches decoration, weakening it when required by the interval.

sign

Maps negative values to -1, zero to 0, and positive values to 1.

sin

Encloses the sine of every value in x.

singleton

Constructs the singleton interval containing value.

sinh

Encloses the hyperbolic sine of every value in x.

sqr

Encloses the squares of all values in x.

sqrt

Encloses the real square roots of the nonnegative part of x.

sub

Encloses all pairwise differences x - y.

subset

Returns whether every member of x is also a member of y.

sup

Returns the upper endpoint, or NaN for NaI.

tan

Encloses the defined tangent values over x.

tanh

Encloses the hyperbolic tangent of every value in x.

trunc

Encloses truncation toward zero for every value in x.

wid

Returns the interval width rounded upward.

zero

Returns the singleton interval containing zero.