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
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
|
/* Copyright (C) 1996-2015 Free Software Foundation, Inc.
Contributed by David Mosberger (davidm@cs.arizona.edu).
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
<http://www.gnu.org/licenses/>. */
#include <math.h>
#include <math_private.h>
#include <shlib-compat.h>
#if !defined(_IEEE_FP_INEXACT)
/*
* This version is much faster than generic sqrt implementation, but
* it doesn't handle the inexact flag. It doesn't handle exceptional
* values either, but will defer to the full ieee754_sqrt routine which
* can.
*/
/* Careful with rearranging this without consulting the assembly below. */
const static struct sqrt_data_struct {
unsigned long dn, up, half, almost_three_half;
unsigned long one_and_a_half, two_to_minus_30, one, nan;
const int T2[64];
} sqrt_data __attribute__((used)) = {
0x3fefffffffffffff, /* __dn = nextafter(1,-Inf) */
0x3ff0000000000001, /* __up = nextafter(1,+Inf) */
0x3fe0000000000000, /* half */
0x3ff7ffffffc00000, /* almost_three_half = 1.5-2^-30 */
0x3ff8000000000000, /* one_and_a_half */
0x3e10000000000000, /* two_to_minus_30 */
0x3ff0000000000000, /* one */
0xffffffffffffffff, /* nan */
{ 0x1500, 0x2ef8, 0x4d67, 0x6b02, 0x87be, 0xa395, 0xbe7a, 0xd866,
0xf14a, 0x1091b,0x11fcd,0x13552,0x14999,0x15c98,0x16e34,0x17e5f,
0x18d03,0x19a01,0x1a545,0x1ae8a,0x1b5c4,0x1bb01,0x1bfde,0x1c28d,
0x1c2de,0x1c0db,0x1ba73,0x1b11c,0x1a4b5,0x1953d,0x18266,0x16be0,
0x1683e,0x179d8,0x18a4d,0x19992,0x1a789,0x1b445,0x1bf61,0x1c989,
0x1d16d,0x1d77b,0x1dddf,0x1e2ad,0x1e5bf,0x1e6e8,0x1e654,0x1e3cd,
0x1df2a,0x1d635,0x1cb16,0x1be2c,0x1ae4e,0x19bde,0x1868e,0x16e2e,
0x1527f,0x1334a,0x11051,0xe951, 0xbe01, 0x8e0d, 0x5924, 0x1edd }
};
asm ("\
/* Define offsets into the structure defined in C above. */ \n\
$DN = 0*8 \n\
$UP = 1*8 \n\
$HALF = 2*8 \n\
$ALMOST_THREE_HALF = 3*8 \n\
$NAN = 7*8 \n\
$T2 = 8*8 \n\
\n\
/* Stack variables. */ \n\
$K = 0 \n\
$Y = 8 \n\
\n\
.text \n\
.align 5 \n\
.globl __ieee754_sqrt \n\
.ent __ieee754_sqrt \n\
__ieee754_sqrt: \n\
ldgp $29, 0($27) \n\
subq $sp, 16, $sp \n\
.frame $sp, 16, $26, 0\n"
#ifdef PROF
" lda $28, _mcount \n\
jsr $28, ($28), _mcount\n"
#endif
" .prologue 1 \n\
\n\
.align 4 \n\
stt $f16, $K($sp) # e0 : \n\
mult $f31, $f31, $f31 # .. fm : \n\
lda $4, sqrt_data # e0 : \n\
fblt $f16, $fixup # .. fa : \n\
\n\
ldah $2, 0x5fe8 # e0 : \n\
ldq $3, $K($sp) # .. e1 : \n\
ldt $f12, $HALF($4) # e0 : \n\
ldt $f18, $ALMOST_THREE_HALF($4) # .. e1 : \n\
\n\
sll $3, 52, $5 # e0 : \n\
lda $6, 0x7fd # .. e1 : \n\
fnop # .. fa : \n\
fnop # .. fm : \n\
\n\
subq $5, 1, $5 # e1 : \n\
srl $3, 33, $1 # .. e0 : \n\
cmpule $5, $6, $5 # e0 : \n\
beq $5, $fixup # .. e1 : \n\
\n\
mult $f16, $f12, $f11 # fm : $f11 = x * 0.5 \n\
subl $2, $1, $2 # .. e0 : \n\
addt $f12, $f12, $f17 # .. fa : $f17 = 1.0 \n\
srl $2, 12, $1 # e0 : \n\
\n\
and $1, 0xfc, $1 # e0 : \n\
addq $1, $4, $1 # e1 : \n\
ldl $1, $T2($1) # e0 : \n\
addt $f12, $f17, $f15 # .. fa : $f15 = 1.5 \n\
\n\
subl $2, $1, $2 # e0 : \n\
ldt $f14, $DN($4) # .. e1 : \n\
sll $2, 32, $2 # e0 : \n\
stq $2, $Y($sp) # e0 : \n\
\n\
ldt $f13, $Y($sp) # e0 : \n\
mult/su $f11, $f13, $f10 # fm 2: $f10 = (x * 0.5) * y \n\
mult $f10, $f13, $f10 # fm 4: $f10 = ((x*0.5)*y)*y \n\
subt $f15, $f10, $f1 # fa 4: $f1 = (1.5-0.5*x*y*y) \n\
\n\
mult $f13, $f1, $f13 # fm 4: yp = y*(1.5-0.5*x*y^2)\n\
mult/su $f11, $f13, $f1 # fm 4: $f11 = x * 0.5 * yp \n\
mult $f1, $f13, $f11 # fm 4: $f11 = (x*0.5*yp)*yp \n\
subt $f18, $f11, $f1 # fa 4: $f1=(1.5-2^-30)-x/2*yp^2\n\
\n\
mult $f13, $f1, $f13 # fm 4: ypp = $f13 = yp*$f1 \n\
subt $f15, $f12, $f1 # .. fa : $f1 = (1.5 - 0.5) \n\
ldt $f15, $UP($4) # .. e0 : \n\
mult/su $f16, $f13, $f10 # fm 4: z = $f10 = x * ypp \n\
\n\
mult $f10, $f13, $f11 # fm 4: $f11 = z*ypp \n\
mult $f10, $f12, $f12 # fm : $f12 = z*0.5 \n\
subt $f1, $f11, $f1 # fa 4: $f1 = 1 - z*ypp \n\
mult $f12, $f1, $f12 # fm 4: $f12 = z/2*(1 - z*ypp)\n\
\n\
addt $f10, $f12, $f0 # fa 4: zp=res= z+z/2*(1-z*ypp)\n\
mult/c $f0, $f14, $f12 # fm 4: zmi = zp * DN \n\
mult/c $f0, $f15, $f11 # fm : zpl = zp * UP \n\
mult/c $f0, $f12, $f1 # fm : $f1 = zp * zmi \n\
\n\
mult/c $f0, $f11, $f15 # fm : $f15 = zp * zpl \n\
subt/su $f1, $f16, $f13 # .. fa : y1 = zp*zmi - x \n\
subt/su $f15, $f16, $f14 # fa 4: y2 = zp*zpl - x \n\
fcmovge $f13, $f12, $f0 # fa 3: res = (y1>=0)?zmi:res \n\
\n\
fcmovlt $f14, $f11, $f0 # fa 4: res = (y2<0)?zpl:res \n\
addq $sp, 16, $sp # .. e0 : \n\
ret # .. e1 : \n\
\n\
.align 4 \n\
$fixup: \n\
addq $sp, 16, $sp \n\
br __full_ieee754_sqrt !samegp \n\
\n\
.end __ieee754_sqrt");
/* Avoid the __sqrt_finite alias that dbl-64/e_sqrt.c would give... */
#undef strong_alias
#define strong_alias(a,b)
/* ... defining our own. */
#if SHLIB_COMPAT (libm, GLIBC_2_15, GLIBC_2_18)
asm (".global __sqrt_finite1; __sqrt_finite1 = __ieee754_sqrt");
#else
asm (".global __sqrt_finite; __sqrt_finite = __ieee754_sqrt");
#endif
static double __full_ieee754_sqrt(double) __attribute_used__;
#define __ieee754_sqrt __full_ieee754_sqrt
#elif SHLIB_COMPAT (libm, GLIBC_2_15, GLIBC_2_18)
# define __sqrt_finite __sqrt_finite1
#endif /* _IEEE_FP_INEXACT */
#include <sysdeps/ieee754/dbl-64/e_sqrt.c>
/* Work around forgotten symbol in alphaev6 build. */
#if SHLIB_COMPAT (libm, GLIBC_2_15, GLIBC_2_18)
# undef __sqrt_finite
# undef __ieee754_sqrt
compat_symbol (libm, __sqrt_finite1, __sqrt_finite, GLIBC_2_15);
versioned_symbol (libm, __ieee754_sqrt, __sqrt_finite, GLIBC_2_18);
#endif
|
