mirror of
https://sourceware.org/git/glibc.git
synced 2024-11-14 01:00:07 +00:00
116 lines
3.5 KiB
C
116 lines
3.5 KiB
C
/* Compute full X * Y for double type.
|
|
Copyright (C) 2013-2023 Free Software Foundation, Inc.
|
|
This file is part of the GNU C Library.
|
|
|
|
The GNU C Library is free software; you can redistribute it and/or
|
|
modify it under the terms of the GNU Lesser General Public
|
|
License as published by the Free Software Foundation; either
|
|
version 2.1 of the License, or (at your option) any later version.
|
|
|
|
The GNU C Library is distributed in the hope that it will be useful,
|
|
but WITHOUT ANY WARRANTY; without even the implied warranty of
|
|
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
|
|
Lesser General Public License for more details.
|
|
|
|
You should have received a copy of the GNU Lesser General Public
|
|
License along with the GNU C Library; if not, see
|
|
<https://www.gnu.org/licenses/>. */
|
|
|
|
#ifndef _MUL_SPLIT_H
|
|
#define _MUL_SPLIT_H
|
|
|
|
#include <float.h>
|
|
|
|
/* Calculate X * Y exactly and store the result in *HI + *LO. It is
|
|
given that the values are small enough that no overflow occurs and
|
|
large enough (or zero) that no underflow occurs. */
|
|
|
|
static void
|
|
mul_split (double *hi, double *lo, double x, double y)
|
|
{
|
|
#ifdef __FP_FAST_FMA
|
|
/* Fast built-in fused multiply-add. */
|
|
*hi = x * y;
|
|
*lo = __builtin_fma (x, y, -*hi);
|
|
#else
|
|
/* Apply Dekker's algorithm. */
|
|
*hi = x * y;
|
|
# define C ((1 << (DBL_MANT_DIG + 1) / 2) + 1)
|
|
double x1 = x * C;
|
|
double y1 = y * C;
|
|
# undef C
|
|
x1 = (x - x1) + x1;
|
|
y1 = (y - y1) + y1;
|
|
double x2 = x - x1;
|
|
double y2 = y - y1;
|
|
*lo = (((x1 * y1 - *hi) + x1 * y2) + x2 * y1) + x2 * y2;
|
|
#endif
|
|
}
|
|
|
|
/* Add a + b exactly, such that *hi + *lo = a + b.
|
|
Assumes |a| >= |b| and rounding to nearest. */
|
|
static inline void
|
|
fast_two_sum (double *hi, double *lo, double a, double b)
|
|
{
|
|
double e;
|
|
|
|
*hi = a + b;
|
|
e = *hi - a; /* exact */
|
|
*lo = b - e; /* exact */
|
|
/* Now *hi + *lo = a + b exactly. */
|
|
}
|
|
|
|
/* Multiplication of two floating-point expansions: *hi + *lo is an
|
|
approximation of (h1+l1)*(h2+l2), assuming |l1| <= 1/2*ulp(h1)
|
|
and |l2| <= 1/2*ulp(h2) and rounding to nearest. */
|
|
static inline void
|
|
mul_expansion (double *hi, double *lo, double h1, double l1,
|
|
double h2, double l2)
|
|
{
|
|
double r, e;
|
|
|
|
mul_split (hi, lo, h1, h2);
|
|
r = h1 * l2 + h2 * l1;
|
|
/* Now add r to (hi,lo) using fast two-sum, where we know |r| < |hi|. */
|
|
fast_two_sum (hi, &e, *hi, r);
|
|
*lo -= e;
|
|
}
|
|
|
|
/* Calculate X / Y and store the approximate result in *HI + *LO. It is
|
|
assumed that Y is not zero, that no overflow nor underflow occurs, and
|
|
rounding is to nearest. */
|
|
static inline void
|
|
div_split (double *hi, double *lo, double x, double y)
|
|
{
|
|
double a, b;
|
|
|
|
*hi = x / y;
|
|
mul_split (&a, &b, *hi, y);
|
|
/* a + b = hi*y, which should be near x. */
|
|
a = x - a; /* huge cancellation */
|
|
a = a - b;
|
|
/* Now x ~ hi*y + a thus x/y ~ hi + a/y. */
|
|
*lo = a / y;
|
|
}
|
|
|
|
/* Division of two floating-point expansions: *hi + *lo is an
|
|
approximation of (h1+l1)/(h2+l2), assuming |l1| <= 1/2*ulp(h1)
|
|
and |l2| <= 1/2*ulp(h2), h2+l2 is not zero, and rounding to nearest. */
|
|
static inline void
|
|
div_expansion (double *hi, double *lo, double h1, double l1,
|
|
double h2, double l2)
|
|
{
|
|
double r, e;
|
|
|
|
div_split (hi, lo, h1, h2);
|
|
/* (h1+l1)/(h2+l2) ~ h1/h2 + (l1*h2 - l2*h1)/h2^2 */
|
|
r = (l1 * h2 - l2 * h1) / (h2 * h2);
|
|
/* Now add r to (hi,lo) using fast two-sum, where we know |r| < |hi|. */
|
|
fast_two_sum (hi, &e, *hi, r);
|
|
*lo += e;
|
|
/* Renormalize since |lo| might be larger than 0.5 ulp(hi). */
|
|
fast_two_sum (hi, lo, *hi, *lo);
|
|
}
|
|
|
|
#endif /* _MUL_SPLIT_H */
|