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
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
|
/* Function sinhf vectorized with SSE4.
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/. */
/*
* ALGORITHM DESCRIPTION:
*
* Compute sinh(x) as (exp(x)-exp(-x))/2,
* where exp is calculated as
* exp(M*ln2 + ln2*(j/2^k) + r) = 2^M * 2^(j/2^k) * exp(r)
*
* Special cases:
*
* sinh(NaN) = quiet NaN, and raise invalid exception
* sinh(INF) = that INF
* sinh(x) = x for subnormals
* sinh(x) overflows for big x and returns MAXLOG+log(2)
*
*/
/* Offsets for data table __svml_ssinh_data_internal
*/
#define _sInvLn2 0
#define _sLn2hi 16
#define _sLn2lo 32
#define _sSign 48
#define _sShifter 64
#define _iDomainRange 80
#define _sPC1 96
#define _sPC2 112
#define _sPC3 128
#define _sPC4 144
#define _sPC5 160
#define _sPC6 176
#define _iHalf 192
#include <sysdep.h>
.text
.section .text.sse4,"ax",@progbits
ENTRY(_ZGVbN4v_sinhf_sse4)
subq $72, %rsp
cfi_def_cfa_offset(80)
/*
* Implementation
* Abs argument
*/
movups _sSign+__svml_ssinh_data_internal(%rip), %xmm14
andps %xmm0, %xmm14
movaps %xmm14, %xmm10
/*
* Load argument
* dM = x/log(2) + RShifter
*/
movups _sInvLn2+__svml_ssinh_data_internal(%rip), %xmm7
pxor %xmm0, %xmm10
mulps %xmm10, %xmm7
/*
* Check for overflow\underflow
* MORE faster than GE?
*/
movaps %xmm10, %xmm1
movups _sShifter+__svml_ssinh_data_internal(%rip), %xmm2
/* sR = sX - sN*Log2_hi */
movups _sLn2hi+__svml_ssinh_data_internal(%rip), %xmm3
addps %xmm2, %xmm7
/*
* R
* sN = sM - RShifter
*/
movaps %xmm7, %xmm4
/*
* G1,G2 2^N,2^(-N)
* iM now is an EXP(2^N)
*/
pslld $23, %xmm7
/* sR = (sX - sN*Log2_hi) - sN*Log2_lo */
movups _sLn2lo+__svml_ssinh_data_internal(%rip), %xmm5
subps %xmm2, %xmm4
mulps %xmm4, %xmm3
mulps %xmm4, %xmm5
subps %xmm3, %xmm10
/*
* sinh(r) = r*((a1=1)+r^2*(a3+r^2*(a5+{v1 r^2*a7})))) = r + r*(r^2*(a3+r^2*(a5+r^2*a7))) ....
* sSinh_r = (a3+r^2*a5)
*/
movups _sPC5+__svml_ssinh_data_internal(%rip), %xmm8
subps %xmm5, %xmm10
/* sR2 = sR^2 */
movaps %xmm10, %xmm12
mulps %xmm10, %xmm12
/*
* sinh(X) = sG2 + sG1*sinh(dR) + sG2*sR2*(a2+sR2*(a4+a6*sR2)
* sOut = (a4 +a6*sR2)
*/
movups _sPC6+__svml_ssinh_data_internal(%rip), %xmm9
mulps %xmm12, %xmm8
mulps %xmm12, %xmm9
addps _sPC3+__svml_ssinh_data_internal(%rip), %xmm8
addps _sPC4+__svml_ssinh_data_internal(%rip), %xmm9
/* sSinh_r = r^2*(a3+r^2*a5) */
mulps %xmm12, %xmm8
/* sOut = a2+sR2*(a4+a6*sR2) */
mulps %xmm12, %xmm9
/* sSinh_r = r + r*(r^2*(a3+r^2*a5)) */
mulps %xmm10, %xmm8
addps _sPC2+__svml_ssinh_data_internal(%rip), %xmm9
addps %xmm8, %xmm10
/* sOut = sR2*(a2+sR2*(a4+a6*sR2) */
mulps %xmm9, %xmm12
movdqu _iHalf+__svml_ssinh_data_internal(%rip), %xmm6
movdqa %xmm6, %xmm13
psubd %xmm7, %xmm6
paddd %xmm7, %xmm13
/* sG1 = 2^(N-1)+2^(-N-1) */
movdqa %xmm13, %xmm11
/* sG2 = 2^(N-1)-2^(-N-1) */
subps %xmm6, %xmm13
addps %xmm6, %xmm11
/* sOut = sG2*sR2*(a2+sR2*(a4+a6*sR2) */
mulps %xmm13, %xmm12
/* sOut = sG1*sinh(dR)+sG2*sR2*(a2+sR2*(a4+a6*sR2) */
mulps %xmm10, %xmm11
pcmpgtd _iDomainRange+__svml_ssinh_data_internal(%rip), %xmm1
addps %xmm11, %xmm12
movmskps %xmm1, %edx
/* sOut = sG2 + sG1*sinh(dR) + sG2*sR2*(a2+sR2*(a4+a6*sR2) */
addps %xmm12, %xmm13
/* Ret H */
orps %xmm13, %xmm14
testl %edx, %edx
/* Go to special inputs processing branch */
jne L(SPECIAL_VALUES_BRANCH)
# LOE rbx rbp r12 r13 r14 r15 edx xmm0 xmm14
/* Restore registers
* and exit the function
*/
L(EXIT):
movaps %xmm14, %xmm0
addq $72, %rsp
cfi_def_cfa_offset(8)
ret
cfi_def_cfa_offset(80)
/* Branch to process
* special inputs
*/
L(SPECIAL_VALUES_BRANCH):
movups %xmm0, 32(%rsp)
movups %xmm14, 48(%rsp)
# LOE rbx rbp r12 r13 r14 r15 edx
xorl %eax, %eax
movq %r12, 16(%rsp)
cfi_offset(12, -64)
movl %eax, %r12d
movq %r13, 8(%rsp)
cfi_offset(13, -72)
movl %edx, %r13d
movq %r14, (%rsp)
cfi_offset(14, -80)
# LOE rbx rbp r15 r12d r13d
/* Range mask
* bits check
*/
L(RANGEMASK_CHECK):
btl %r12d, %r13d
/* Call scalar math function */
jc L(SCALAR_MATH_CALL)
# LOE rbx rbp r15 r12d r13d
/* Special inputs
* processing loop
*/
L(SPECIAL_VALUES_LOOP):
incl %r12d
cmpl $4, %r12d
/* Check bits in range mask */
jl L(RANGEMASK_CHECK)
# LOE rbx rbp r15 r12d r13d
movq 16(%rsp), %r12
cfi_restore(12)
movq 8(%rsp), %r13
cfi_restore(13)
movq (%rsp), %r14
cfi_restore(14)
movups 48(%rsp), %xmm14
/* Go to exit */
jmp L(EXIT)
cfi_offset(12, -64)
cfi_offset(13, -72)
cfi_offset(14, -80)
# LOE rbx rbp r12 r13 r14 r15 xmm14
/* Scalar math fucntion call
* to process special input
*/
L(SCALAR_MATH_CALL):
movl %r12d, %r14d
movss 32(%rsp,%r14,4), %xmm0
call sinhf@PLT
# LOE rbx rbp r14 r15 r12d r13d xmm0
movss %xmm0, 48(%rsp,%r14,4)
/* Process special inputs in loop */
jmp L(SPECIAL_VALUES_LOOP)
# LOE rbx rbp r15 r12d r13d
END(_ZGVbN4v_sinhf_sse4)
.section .rodata, "a"
.align 16
#ifdef __svml_ssinh_data_internal_typedef
typedef unsigned int VUINT32;
typedef struct
{
__declspec(align(16)) VUINT32 _sInvLn2[4][1];
__declspec(align(16)) VUINT32 _sLn2hi[4][1];
__declspec(align(16)) VUINT32 _sLn2lo[4][1];
__declspec(align(16)) VUINT32 _sSign[4][1];
__declspec(align(16)) VUINT32 _sShifter[4][1];
__declspec(align(16)) VUINT32 _iDomainRange[4][1];
__declspec(align(16)) VUINT32 _sPC1[4][1];
__declspec(align(16)) VUINT32 _sPC2[4][1];
__declspec(align(16)) VUINT32 _sPC3[4][1];
__declspec(align(16)) VUINT32 _sPC4[4][1];
__declspec(align(16)) VUINT32 _sPC5[4][1];
__declspec(align(16)) VUINT32 _sPC6[4][1];
__declspec(align(16)) VUINT32 _iHalf[4][1];
} __svml_ssinh_data_internal;
#endif
__svml_ssinh_data_internal:
.long 0x3FB8AA3B, 0x3FB8AA3B, 0x3FB8AA3B, 0x3FB8AA3B /* _sInvLn2 */ //k=0
.align 16
.long 0x3F317000, 0x3F317000, 0x3F317000, 0x3F317000 /* _sLn2hi */
.align 16
.long 0x3805FDF4, 0x3805FDF4, 0x3805FDF4, 0x3805FDF4 /* _sLn2lo */
.align 16
.long 0x80000000, 0x80000000, 0x80000000, 0x80000000 /* _sSign */
.align 16
.long 0x4b400000, 0x4b400000, 0x4b400000, 0x4b400000 /* _sShifter */
.align 16
.long 0x42AEAC4E, 0x42AEAC4E, 0x42AEAC4E, 0x42AEAC4E /* _iDomainRange */
.align 16
.long 0x3F800000, 0x3F800000, 0x3F800000, 0x3F800000 /* _sPC1=1 */
.align 16
.long 0x3f000000, 0x3f000000, 0x3f000000, 0x3f000000 /* _sPC2 */
.align 16
.long 0x3e2aaa57, 0x3e2aaa57, 0x3e2aaa57, 0x3e2aaa57 /* _sPC3 */
.align 16
.long 0x3d2aaa72, 0x3d2aaa72, 0x3d2aaa72, 0x3d2aaa72 /* _sPC4 */
.align 16
.long 0x3c091461, 0x3c091461, 0x3c091461, 0x3c091461 /* _sPC5 */
.align 16
.long 0x3ab6a8a3, 0x3ab6a8a3, 0x3ab6a8a3, 0x3ab6a8a3 /* _sPC6 */
// Integer constants
.align 16
.long 0x3f000000, 0x3f000000, 0x3f000000, 0x3f000000 /* _iHalf*/
.align 16
.type __svml_ssinh_data_internal,@object
.size __svml_ssinh_data_internal,.-__svml_ssinh_data_internal
|
