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
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
|
/*
Copyright (c) 2014, Intel Corporation
All rights reserved.
Redistribution and use in source and binary forms, with or without
modification, are permitted provided that the following conditions are met:
* Redistributions of source code must retain the above copyright notice,
* this list of conditions and the following disclaimer.
* Redistributions in binary form must reproduce the above copyright notice,
* this list of conditions and the following disclaimer in the documentation
* and/or other materials provided with the distribution.
* Neither the name of Intel Corporation nor the names of its contributors
* may be used to endorse or promote products derived from this software
* without specific prior written permission.
THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND
ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR
ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
(INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON
ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
(INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
*/
/******************************************************************************/
// ALGORITHM DESCRIPTION
// ---------------------
//
// X87 version:
// Use 80-bit FPU precision fmul, fsqrt to compute square and sqrt.
//
// SSE version:
// Swap x, y if |x|<|y|
// For x=2^k*x, get y=y*2^(-k)
// Get S ~ sqrt(x^2+y^2) (leading 1 + leading 25 mantissa bits)
//
// Get D = ( RN(x^2+y^2) - S^2 ) + ( x^2 - RN(x^2) ) +
// + ( y^2 - ((RN(x^2+y^2)-RN(x^2)) )
//
// Result is 2^k*(S + Se), where Se = S*e
// S*e is approximated as (D/2S)*( 1 - (D/2S)^2*1.0/S )
//
// Return 2^k*(S+Se)
//
// For |y/x|<2^(-64), return x
//
// For cases where maximum biased exponent is either greater than 7fdh or
// below 32, take a special path to check for special cases (0, NaN, Inf),
// possible overflow, and more accurate computation for denormal results
//
// Special cases:
// hypot(x,y), hypot(y,x), and hypot(x,-y) are equivalent
// hypot(x,+-0) is equivalent to fabs(x)
// hypot(x,y) = y if (x==NaN or x==INF) and y==INF
// hypot(x,y) = x if (x==NaN or x==INF) and y!=INF (even if y==NaN!)
// hypot(x,y) = y if (x!=NaN and x!=INF) and (y==NaN or y==INF)
//
/******************************************************************************/
#include <private/bionic_asm.h>
# -- Begin hypot
ENTRY(hypot)
# parameter 1: %xmm0
# parameter 2: %xmm1
..B1.1:
..___tag_value_hypot.1:
..___tag_value_hypot.3:
..B1.2:
subq $64, %rsp
movapd static_const_table(%rip), %xmm3
movsd %xmm0, 48(%rsp)
movsd %xmm1, 56(%rsp)
andpd %xmm3, %xmm0
andpd %xmm3, %xmm1
pextrw $3, %xmm0, %eax
pextrw $3, %xmm1, %edx
cmpl $24528, %eax
ja .L_2TAG_PACKET_0.0.1
cmpl $24528, %edx
ja .L_2TAG_PACKET_0.0.1
.L_2TAG_PACKET_1.0.1:
fldl 48(%rsp)
fldl 56(%rsp)
fxch %st(1)
fmul %st(0), %st
fxch %st(1)
nop
fmul %st(0), %st
faddp %st, %st(1)
fsqrt
jmp .L_2TAG_PACKET_2.0.1
.L_2TAG_PACKET_0.0.1:
cmpl $32752, %eax
movl %eax, %ecx
jae .L_2TAG_PACKET_3.0.1
subl %edx, %ecx
cmpl $32752, %edx
jae .L_2TAG_PACKET_3.0.1
addl $928, %ecx
addl %edx, %eax
cmpl $1856, %ecx
ja .L_2TAG_PACKET_4.0.1
cmpl $49056, %eax
jb .L_2TAG_PACKET_1.0.1
fldl 48(%rsp)
fldl 56(%rsp)
fxch %st(1)
fmul %st(0), %st
fxch %st(1)
nop
fmul %st(0), %st
faddp %st, %st(1)
fsqrt
.L_2TAG_PACKET_5.0.1:
fstl (%rsp)
fstpt 16(%rsp)
xorl %eax, %eax
movw 24(%rsp), %ax
cmpl $17407, %eax
jae .L_2TAG_PACKET_6.0.1
fldl (%rsp)
jmp .L_2TAG_PACKET_7.0.1
.L_2TAG_PACKET_4.0.1:
movsd %xmm0, 32(%rsp)
movsd %xmm1, 40(%rsp)
fldl 32(%rsp)
faddl 40(%rsp)
jmp .L_2TAG_PACKET_5.0.1
.L_2TAG_PACKET_6.0.1:
fldl (%rsp)
jmp .L_2TAG_PACKET_7.0.1
.L_2TAG_PACKET_3.0.1:
shufpd $0, %xmm1, %xmm0
movdqa %xmm0, %xmm2
movdqa 16+static_const_table(%rip), %xmm3
movsd %xmm0, 32(%rsp)
movsd %xmm1, 40(%rsp)
cmppd $3, %xmm0, %xmm2
cmppd $0, %xmm0, %xmm3
movmskpd %xmm2, %edx
movmskpd %xmm3, %rax
testl %edx, %edx
je .L_2TAG_PACKET_8.0.1
fldl 32(%rsp)
fmull 40(%rsp)
testq $1, %rax
jne .L_2TAG_PACKET_9.0.1
testq $2, %rax
jne .L_2TAG_PACKET_10.0.1
jmp .L_2TAG_PACKET_2.0.1
.L_2TAG_PACKET_8.0.1:
fldl 32(%rsp)
faddl 40(%rsp)
jmp .L_2TAG_PACKET_2.0.1
.L_2TAG_PACKET_9.0.1:
fstpl 40(%rsp)
fldl 32(%rsp)
jmp .L_2TAG_PACKET_7.0.1
.L_2TAG_PACKET_10.0.1:
fstpl 32(%rsp)
fldl 40(%rsp)
jmp .L_2TAG_PACKET_7.0.1
.L_2TAG_PACKET_2.0.1:
.L_2TAG_PACKET_7.0.1:
fstpl 16(%rsp)
movq 16(%rsp), %xmm0
addq $64, %rsp
ret
..B1.3:
..___tag_value_hypot.4:
END(hypot)
# -- End hypot
.section .rodata, "a"
.align 16
.align 16
static_const_table:
.long 4294967295
.long 2147483647
.long 4294967295
.long 2147483647
.long 0
.long 2146435072
.long 0
.long 2146435072
.type static_const_table,@object
.size static_const_table,32
.data
.section .note.GNU-stack, "",@progbits
// -- Begin DWARF2 SEGMENT .eh_frame
.section .eh_frame,"a",@progbits
.eh_frame_seg:
.align 1
.4byte 0x00000014
.8byte 0x00527a0100000000
.8byte 0x08070c1b01107801
.4byte 0x00000190
.4byte 0x00000014
.4byte 0x0000001c
.4byte ..___tag_value_hypot.1-.
.4byte ..___tag_value_hypot.4-..___tag_value_hypot.1
.2byte 0x0400
.4byte ..___tag_value_hypot.3-..___tag_value_hypot.1
.2byte 0x100e
# End
|
