89 lines
3.2 KiB
C
89 lines
3.2 KiB
C
/**
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* This file has no copyright assigned and is placed in the Public Domain.
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* This file is part of the mingw-w64 runtime package.
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* No warranty is given; refer to the file DISCLAIMER.PD within this package.
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*/
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long double fmal(long double x, long double y, long double z);
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#if defined(_ARM_) || defined(__arm__) || defined(_ARM64_) || defined(__aarch64__)
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double fma(double x, double y, double z);
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/* On ARM `long double` is 64 bits. And ARM has hardware FMA. */
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long double fmal(long double x, long double y, long double z){
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return fma(x, y, z);
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}
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#elif defined(_AMD64_) || defined(__x86_64__) || defined(_X86_) || defined(__i386__)
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/**
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* x87-specific software-emulated FMA by LH_Mouse (lh_mouse at 126 dot com).
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* This file is donated to the mingw-w64 project.
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* Note: This file requires C99 support to compile.
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*/
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#include <math.h>
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#include <stdint.h>
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/* See <https://en.wikipedia.org/wiki/Extended_precision#x86_extended_precision_format>.
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* Note the higher half of the mantissa has fewer significant bits than the lower
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* half, which reduces rounding errors in the more significant position but increases
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* them in the other end.
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*/
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typedef union x87reg_ {
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struct __attribute__((__packed__)) {
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uint64_t mlo : 33;
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uint64_t mhi : 31;
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uint16_t exp : 15;
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uint16_t sgn : 1;
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};
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long double f;
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} x87reg;
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static inline void break_down(x87reg *restrict lo, x87reg *restrict hi, long double x) {
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hi->f = x;
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/* Erase low-order significant bits. `hi->f` now has only 31 significant bits. */
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hi->mlo = 0;
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/* Store the low-order half. It will be normalized by the hardware. */
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lo->f = x - hi->f;
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/* Preserve signness in case of zero. */
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lo->sgn = hi->sgn;
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}
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long double fmal(long double x, long double y, long double z) {
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/*
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POSIX-2013:
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1. If x or y are NaN, a NaN shall be returned.
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2. If x multiplied by y is an exact infinity and z is also an infinity
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but with the opposite sign, a domain error shall occur, and either a NaN
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(if supported), or an implementation-defined value shall be returned.
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3. If one of x and y is infinite, the other is zero, and z is not a NaN,
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a domain error shall occur, and either a NaN (if supported), or an
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implementation-defined value shall be returned.
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4. If one of x and y is infinite, the other is zero, and z is a NaN, a NaN
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shall be returned and a domain error may occur.
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5. If x* y is not 0*Inf nor Inf*0 and z is a NaN, a NaN shall be returned.
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*/
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/* Check whether the result is finite. */
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long double ret = x * y + z;
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if(!isfinite(ret)) {
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return ret; /* If this naive check doesn't yield a finite value, the FMA isn't
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likely to return one either. Forward the value as is. */
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}
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x87reg xlo, xhi, ylo, yhi;
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break_down(&xlo, &xhi, x);
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break_down(&ylo, &yhi, y);
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/* The order of these four statements is essential. Don't move them around. */
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ret = z;
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ret += xhi.f * yhi.f; /* The most significant item comes first. */
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ret += xhi.f * ylo.f + xlo.f * yhi.f; /* They are equally significant. */
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ret += xlo.f * ylo.f; /* The least significant item comes last. */
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return ret;
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}
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#else
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#error Please add FMA implementation for this platform.
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#endif
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