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/* Euclidean distance function. Double/Binary64 version.
Copyright (C) 2021 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/>. */
/* The implementation uses a correction based on 'An Improved Algorithm for
hypot(a,b)' by Carlos F. Borges [1] usingthe MyHypot3 with the following
changes:
- Handle qNaN and sNaN.
- Tune the 'widely varying operands' to avoid spurious underflow
due the multiplication and fix the return value for upwards
rounding mode.
- Handle required underflow exception for subnormal results.
The expected ULP is ~0.792 or ~0.948 if FMA is used. For FMA, the
correction is not used and the error of sqrt (x^2 + y^2) is below 1 ULP
if x^2 + y^2 is computed with less than 0.707 ULP error. If |x| >= |2y|,
fma (x, x, y^2) has ~0.625 ULP. If |x| < |2y|, fma (|2x|, |y|, (x - y)^2)
has ~0.625 ULP.
[1] https://arxiv.org/pdf/1904.09481.pdf */
#include <math.h>
#include <math_private.h>
#include <math-underflow.h>
#include <math-narrow-eval.h>
#include <math-use-builtins.h>
#include <libm-alias-finite.h>
#include "math_config.h"
#define SCALE 0x1p-600
#define LARGE_VAL 0x1p+511
#define TINY_VAL 0x1p-459
#define EPS 0x1p-54
/* Hypot kernel. The inputs must be adjusted so that ax >= ay >= 0
and squaring ax, ay and (ax - ay) does not overflow or underflow. */
static inline double
kernel (double ax, double ay)
{
double t1, t2;
#ifdef __FP_FAST_FMA
t1 = ay + ay;
t2 = ax - ay;
if (t1 >= ax)
return sqrt (fma (t1, ax, t2 * t2));
else
return sqrt (fma (ax, ax, ay * ay));
#else
double h = sqrt (ax * ax + ay * ay);
if (h <= 2.0 * ay)
{
double delta = h - ay;
t1 = ax * (2.0 * delta - ax);
t2 = (delta - 2.0 * (ax - ay)) * delta;
}
else
{
double delta = h - ax;
t1 = 2.0 * delta * (ax - 2.0 * ay);
t2 = (4.0 * delta - ay) * ay + delta * delta;
}
h -= (t1 + t2) / (2.0 * h);
return h;
#endif
}
double
__ieee754_hypot (double x, double y)
{
if (!isfinite(x) || !isfinite(y))
{
if ((isinf (x) || isinf (y))
&& !issignaling_inline (x) && !issignaling_inline (y))
return INFINITY;
return x + y;
}
x = fabs (x);
y = fabs (y);
double ax = USE_FMAX_BUILTIN ? fmax (x, y) : (x < y ? y : x);
double ay = USE_FMIN_BUILTIN ? fmin (x, y) : (x < y ? x : y);
/* If ax is huge, scale both inputs down. */
if (__glibc_unlikely (ax > LARGE_VAL))
{
if (__glibc_unlikely (ay <= ax * EPS))
return math_narrow_eval (ax + ay);
return math_narrow_eval (kernel (ax * SCALE, ay * SCALE) / SCALE);
}
/* If ay is tiny, scale both inputs up. */
if (__glibc_unlikely (ay < TINY_VAL))
{
if (__glibc_unlikely (ax >= ay / EPS))
return math_narrow_eval (ax + ay);
ax = math_narrow_eval (kernel (ax / SCALE, ay / SCALE) * SCALE);
math_check_force_underflow_nonneg (ax);
return ax;
}
/* Common case: ax is not huge and ay is not tiny. */
if (__glibc_unlikely (ay <= ax * EPS))
return ax + ay;
return kernel (ax, ay);
}
#ifndef __ieee754_hypot
libm_alias_finite (__ieee754_hypot, __hypot)
#endif
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