1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
|
/* Euclidean distance function. Double/Binary64 version.
Copyright (C) 2021-2023 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/>. */
/* 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 <errno.h>
#include <math.h>
#include <math_private.h>
#include <math-underflow.h>
#include <math-narrow-eval.h>
#include <math-use-builtins.h>
#include <math-svid-compat.h>
#include <libm-alias-finite.h>
#include <libm-alias-double.h>
#include "math_config.h"
#define SCALE 0x1p-600
#define LARGE_VAL 0x1p+511
#define TINY_VAL 0x1p-459
#define EPS 0x1p-54
static inline double
handle_errno (double r)
{
if (isinf (r))
__set_errno (ERANGE);
return r;
}
/* 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
__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 handle_errno (math_narrow_eval (ax + ay));
return handle_errno (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);
}
strong_alias (__hypot, __ieee754_hypot)
libm_alias_finite (__ieee754_hypot, __hypot)
#if LIBM_SVID_COMPAT
versioned_symbol (libm, __hypot, hypot, GLIBC_2_35);
libm_alias_double_other (__hypot, hypot)
#else
libm_alias_double (__hypot, hypot)
#endif
|
