third-party-mirror / mingw-w64 / 9b207d4da4806fdaea3bf9f4a5d66dc6056670b6 / . / mingw-w64-crt / math / fmal.c

/** | |

* This file has no copyright assigned and is placed in the Public Domain. | |

* This file is part of the mingw-w64 runtime package. | |

* No warranty is given; refer to the file DISCLAIMER.PD within this package. | |

*/ | |

long double fmal(long double x, long double y, long double z); | |

#if defined(_ARM_) || defined(__arm__) || defined(_ARM64_) || defined(__aarch64__) | |

double fma(double x, double y, double z); | |

/* On ARM `long double` is 64 bits. And ARM has hardware FMA. */ | |

long double fmal(long double x, long double y, long double z){ | |

return fma(x, y, z); | |

} | |

#elif defined(_AMD64_) || defined(__x86_64__) || defined(_X86_) || defined(__i386__) | |

/** | |

* x87-specific software-emulated FMA by LH_Mouse (lh_mouse at 126 dot com). | |

* This file is donated to the mingw-w64 project. | |

* Note: This file requires C99 support to compile. | |

*/ | |

#include <math.h> | |

#include <stdint.h> | |

/* See <https://en.wikipedia.org/wiki/Extended_precision#x86_extended_precision_format>. | |

* Note the higher half of the mantissa has fewer significant bits than the lower | |

* half, which reduces rounding errors in the more significant position but increases | |

* them in the other end. | |

*/ | |

typedef union x87reg_ { | |

struct __attribute__((__packed__)) { | |

uint64_t mlo : 33; | |

uint64_t mhi : 31; | |

uint16_t exp : 15; | |

uint16_t sgn : 1; | |

}; | |

long double f; | |

} x87reg; | |

static inline void break_down(x87reg *restrict lo, x87reg *restrict hi, long double x) { | |

hi->f = x; | |

/* Erase low-order significant bits. `hi->f` now has only 31 significant bits. */ | |

hi->mlo = 0; | |

/* Store the low-order half. It will be normalized by the hardware. */ | |

lo->f = x - hi->f; | |

/* Preserve signness in case of zero. */ | |

lo->sgn = hi->sgn; | |

} | |

long double fmal(long double x, long double y, long double z) { | |

/* | |

POSIX-2013: | |

1. If x or y are NaN, a NaN shall be returned. | |

2. If x multiplied by y is an exact infinity and z is also an infinity | |

but with the opposite sign, a domain error shall occur, and either a NaN | |

(if supported), or an implementation-defined value shall be returned. | |

3. If one of x and y is infinite, the other is zero, and z is not a NaN, | |

a domain error shall occur, and either a NaN (if supported), or an | |

implementation-defined value shall be returned. | |

4. If one of x and y is infinite, the other is zero, and z is a NaN, a NaN | |

shall be returned and a domain error may occur. | |

5. If x* y is not 0*Inf nor Inf*0 and z is a NaN, a NaN shall be returned. | |

*/ | |

/* Check whether the result is finite. */ | |

long double ret = x * y + z; | |

if(!isfinite(ret)) { | |

return ret; /* If this naive check doesn't yield a finite value, the FMA isn't | |

likely to return one either. Forward the value as is. */ | |

} | |

x87reg xlo, xhi, ylo, yhi; | |

break_down(&xlo, &xhi, x); | |

break_down(&ylo, &yhi, y); | |

/* The order of these four statements is essential. Don't move them around. */ | |

ret = z; | |

ret += xhi.f * yhi.f; /* The most significant item comes first. */ | |

ret += xhi.f * ylo.f + xlo.f * yhi.f; /* They are equally significant. */ | |

ret += xlo.f * ylo.f; /* The least significant item comes last. */ | |

return ret; | |

} | |

#else | |

#error Please add FMA implementation for this platform. | |

#endif |