mpreal_functions.hpp File Reference

#include "detail/math_integer.hpp"
#include "math_results.hpp"
#include "mpreal.hpp"
#include <cstdint>

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Namespaces
namespace	uni20

Functions
mpreal	uni20::ceil (mpreal const &x)
	Round toward positive infinity; exact inputs produce exact integers.
mpreal	uni20::ceil (mpreal const &x, Precision p)
	Round toward positive infinity, then round the result to finite precision p.
template<detail::MathInteger I>
mpreal	uni20::compound (mpreal const &x, I n)
	Compute (1+x)^n without rounding the sum first, for x >= -1.
template<detail::MathInteger I>
mpreal	uni20::compound (mpreal const &x, I n, Precision p)
	Round the compound result from the original input to finite precision p.
mpreal	uni20::copysign (mpreal const &magnitude, mpreal const &sign)
	Transfer the sign while preserving the magnitude's precision and exactness.
mpreal	uni20::copysign (mpreal const &magnitude, mpreal const &sign, Precision p)
	Round the magnitude to p and transfer the sign; sign precision is immaterial.
mpreal	uni20::fdim (mpreal const &a, mpreal const &b)
	Positive difference max(a-b,0), propagating NaNs.
mpreal	uni20::fdim (mpreal const &a, mpreal const &b, Precision p)
	Positive difference with one rounding at p, without input conversion.
mpreal	uni20::floor (mpreal const &x)
	Round toward negative infinity; exact inputs produce exact integers.
mpreal	uni20::floor (mpreal const &x, Precision p)
	Round toward negative infinity, then round the result to finite precision p.
mpreal	uni20::fma (mpreal const &a, mpreal const &b, mpreal const &c)
	Compute a*b+c with one rounding, including mixed exact rational operands.
mpreal	uni20::fma (mpreal const &a, mpreal const &b, mpreal const &c, Precision p)
	Round a*b+c once at p, without converting operands first.
mpreal	uni20::fmax (mpreal const &a, mpreal const &b)
	Maximum with NaN suppression and positive-zero preference.
mpreal	uni20::fmax (mpreal const &a, mpreal const &b, Precision p)
	Select the maximum before rounding it to result precision p.
mpreal	uni20::fmin (mpreal const &a, mpreal const &b)
	Minimum with NaN suppression and negative-zero preference.
mpreal	uni20::fmin (mpreal const &a, mpreal const &b, Precision p)
	Select the minimum before rounding it to result precision p.
mpreal	uni20::fmod (mpreal const &a, mpreal const &b)
	Truncating-quotient remainder; exact operands retain exact rational results.
mpreal	uni20::fmod (mpreal const &a, mpreal const &b, Precision p)
	Truncating-quotient remainder, rounding only the result at p.
frexp_result< mpreal >	uni20::frexp (mpreal const &x)
	Decompose into a binary fraction and signed 64-bit exponent.
frexp_result< mpreal >	uni20::frexp (mpreal const &x, Precision p)
	Decompose and round the fraction at p, normalizing any rounding carry.
std::int64_t	uni20::ilogb (mpreal const &x)
	Base-two exponent of a finite nonzero value.
template<detail::MathInteger I>
mpreal	uni20::ldexp (mpreal const &x, I exponent)
	Multiply by 2^exponent, preserving exact rational state or input precision.
template<detail::MathInteger I>
mpreal	uni20::ldexp (mpreal const &x, I exponent, Precision p)
	Multiply the original value by 2^exponent and round the result at p.
modf_result< mpreal >	uni20::modf (mpreal const &x)
	Signed fractional and integral parts, using truncation toward zero.
modf_result< mpreal >	uni20::modf (mpreal const &x, Precision p)
	Decompose the original value and round each result component at p.
mpreal	uni20::next_down (mpreal const &x)
	Next value toward negative infinity on the input's finite grid.
mpreal	uni20::next_down (mpreal const &x, Precision p)
	Select grid p by rounding x, then move toward negative infinity.
mpreal	uni20::next_up (mpreal const &x)
	Next value toward positive infinity on the input's finite grid.
mpreal	uni20::next_up (mpreal const &x, Precision p)
	Select grid p by rounding x, then move toward positive infinity.
mpreal	uni20::nextafter (mpreal const &x, mpreal const &direction)
	Adjacent value on x's grid toward direction, whose precision may differ.
mpreal	uni20::nextafter (mpreal const &x, mpreal const &direction, Precision p)
	Round x onto grid p, then step toward the unrounded direction.
template<detail::MathInteger I>
mpreal	uni20::pown (mpreal const &x, I exponent)
	Integer power, preserving exact rational results or the input's finite precision.
template<detail::MathInteger I>
mpreal	uni20::pown (mpreal const &x, I exponent, Precision p)
	Integer power with one final rounding at p, without input conversion.
mpreal	uni20::remainder (mpreal const &a, mpreal const &b)
	Nearest-even-quotient remainder; exact operands retain exact rational results.
mpreal	uni20::remainder (mpreal const &a, mpreal const &b, Precision p)
	Nearest-even-quotient remainder, rounding only the result at p.
remquo_result< mpreal >	uni20::remquo (mpreal const &a, mpreal const &b)
	Nearest-even remainder with the signed low three quotient bits.
remquo_result< mpreal >	uni20::remquo (mpreal const &a, mpreal const &b, Precision p)
	Remainder and quotient bits computed before rounding the remainder at p.
template<detail::MathInteger I>
mpreal	uni20::rootn (mpreal const &x, I degree)
	Real integer-order root; negative orders give reciprocal roots.
template<detail::MathInteger I>
mpreal	uni20::rootn (mpreal const &x, I degree, Precision p)
	Integer-order root with one final rounding at p, without input conversion.
mpreal	uni20::round (mpreal const &x)
	Round to nearest integer, with ties away from zero; exact inputs produce exact integers.
mpreal	uni20::round (mpreal const &x, Precision p)
	Round to nearest integer, with ties away from zero, then round the result to finite precision p.
mpreal	uni20::round_even (mpreal const &x)
	Round to nearest integer, with ties to even; exact inputs produce exact integers.
mpreal	uni20::round_even (mpreal const &x, Precision p)
	Round to nearest integer, with ties to even, then round the result to finite precision p.
template<detail::MathInteger I>
mpreal	uni20::scalbn (mpreal const &x, I exponent)
	Binary scaling, identical to ldexp for Uni20's binary scalar formats.
template<detail::MathInteger I>
mpreal	uni20::scalbn (mpreal const &x, I exponent, Precision p)
	Binary scaling with one rounding to finite result precision p.
sincos_result< mpreal >	uni20::sincos (mpreal const &x)
	Evaluate sine and cosine using the paired provider routine.
sincos_result< mpreal >	uni20::sincos (mpreal const &x, Precision p)
	Paired elementary evaluation at p, matching sin(x,p) and cos(x,p).
sinhcosh_result< mpreal >	uni20::sinhcosh (mpreal const &x)
	Evaluate hyperbolic sine and cosine using the paired provider routine.
sinhcosh_result< mpreal >	uni20::sinhcosh (mpreal const &x, Precision p)
	Paired elementary evaluation at p, matching sinh(x,p) and cosh(x,p).
mpreal	uni20::trunc (mpreal const &x)
	Round toward zero; exact inputs produce exact integers.
mpreal	uni20::trunc (mpreal const &x, Precision p)
	Round toward zero, then round the result to finite precision p.