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
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
|
/* Function atan2f vectorized with SSE4.
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/. */
/*
* ALGORITHM DESCRIPTION:
* For 0.0 <= x <= 7.0/16.0: atan(x) = atan(0.0) + atan(s), where s=(x-0.0)/(1.0+0.0*x)
* For 7.0/16.0 <= x <= 11.0/16.0: atan(x) = atan(0.5) + atan(s), where s=(x-0.5)/(1.0+0.5*x)
* For 11.0/16.0 <= x <= 19.0/16.0: atan(x) = atan(1.0) + atan(s), where s=(x-1.0)/(1.0+1.0*x)
* For 19.0/16.0 <= x <= 39.0/16.0: atan(x) = atan(1.5) + atan(s), where s=(x-1.5)/(1.0+1.5*x)
* For 39.0/16.0 <= x <= inf : atan(x) = atan(inf) + atan(s), where s=-1.0/x
* Where atan(s) ~= s+s^3*Poly11(s^2) on interval |s|<7.0/0.16.
*
*
*/
/* Offsets for data table __svml_satan2_data_internal
*/
#define sZERO 0
#define sSIGN_MASK 16
#define sABS_MASK 32
#define sPIO2 48
#define sPI 64
#define sPC8 80
#define sPC7 96
#define sPC6 112
#define sPC5 128
#define sPC4 144
#define sPC3 160
#define sPC2 176
#define sPC1 192
#define sPC0 208
#define iCHK_WORK_SUB 224
#define iCHK_WORK_CMP 240
#include <sysdep.h>
.section .text.sse4, "ax", @progbits
ENTRY(_ZGVbN4vv_atan2f_sse4)
subq $88, %rsp
cfi_def_cfa_offset(96)
movaps %xmm0, %xmm12
/*
* #define NO_VECTOR_ZERO_ATAN2_ARGS
* Declarations
* Variables
* Constants
* The end of declarations
* Implementation
* Arguments signs
*/
movups sABS_MASK+__svml_satan2_data_internal(%rip), %xmm10
movaps %xmm1, %xmm13
movaps %xmm10, %xmm11
andps %xmm12, %xmm10
andps %xmm13, %xmm11
movaps %xmm10, %xmm7
cmpltps %xmm11, %xmm7
/*
* 1) If y<x then a= y, b=x, PIO2=0
* 2) If y>x then a=-x, b=y, PIO2=Pi/2
*/
movups sSIGN_MASK+__svml_satan2_data_internal(%rip), %xmm6
movaps %xmm7, %xmm0
orps %xmm11, %xmm6
movaps %xmm10, %xmm4
andnps %xmm6, %xmm0
movaps %xmm7, %xmm6
movaps %xmm11, %xmm5
andps %xmm7, %xmm4
andnps %xmm10, %xmm6
andps %xmm7, %xmm5
orps %xmm4, %xmm0
orps %xmm5, %xmm6
/* Division a/b. */
divps %xmm6, %xmm0
/* Testing on working interval. */
movdqu iCHK_WORK_SUB+__svml_satan2_data_internal(%rip), %xmm14
movaps %xmm11, %xmm15
movaps %xmm10, %xmm3
psubd %xmm14, %xmm15
psubd %xmm14, %xmm3
movdqa %xmm15, %xmm1
movdqu iCHK_WORK_CMP+__svml_satan2_data_internal(%rip), %xmm2
movdqa %xmm3, %xmm14
pcmpgtd %xmm2, %xmm1
pcmpeqd %xmm2, %xmm15
pcmpgtd %xmm2, %xmm14
pcmpeqd %xmm2, %xmm3
por %xmm15, %xmm1
por %xmm3, %xmm14
por %xmm14, %xmm1
/* Polynomial. */
movaps %xmm0, %xmm14
mulps %xmm0, %xmm14
movaps %xmm13, %xmm4
movmskps %xmm1, %ecx
movaps %xmm14, %xmm15
movaps %xmm11, %xmm9
mulps %xmm14, %xmm15
pxor %xmm13, %xmm9
movups sPC8+__svml_satan2_data_internal(%rip), %xmm2
movaps %xmm10, %xmm8
mulps %xmm15, %xmm2
pxor %xmm12, %xmm8
movups sPC7+__svml_satan2_data_internal(%rip), %xmm3
xorl %edx, %edx
mulps %xmm15, %xmm3
addps sPC6+__svml_satan2_data_internal(%rip), %xmm2
mulps %xmm15, %xmm2
addps sPC5+__svml_satan2_data_internal(%rip), %xmm3
mulps %xmm15, %xmm3
addps sPC4+__svml_satan2_data_internal(%rip), %xmm2
mulps %xmm15, %xmm2
addps sPC3+__svml_satan2_data_internal(%rip), %xmm3
mulps %xmm15, %xmm3
addps sPC2+__svml_satan2_data_internal(%rip), %xmm2
mulps %xmm2, %xmm15
addps sPC1+__svml_satan2_data_internal(%rip), %xmm3
mulps %xmm3, %xmm14
addps sPC0+__svml_satan2_data_internal(%rip), %xmm15
/* if x<0, sPI = Pi, else sPI =0 */
movups __svml_satan2_data_internal(%rip), %xmm5
xorl %eax, %eax
andnps sPIO2+__svml_satan2_data_internal(%rip), %xmm7
addps %xmm14, %xmm15
cmpleps %xmm5, %xmm4
/* Reconstruction. */
mulps %xmm15, %xmm0
andps sPI+__svml_satan2_data_internal(%rip), %xmm4
addps %xmm7, %xmm0
orps %xmm9, %xmm0
addps %xmm4, %xmm0
orps %xmm8, %xmm0
/* Special branch for fast (vector) processing of zero arguments */
testl %ecx, %ecx
/* Go to auxiliary branch */
jne L(AUX_BRANCH)
# LOE rbx rbp r12 r13 r14 r15 eax edx xmm0 xmm1 xmm4 xmm5 xmm6 xmm7 xmm8 xmm9 xmm10 xmm11 xmm12 xmm13
/* Return from auxiliary branch
* for out of main path inputs
*/
L(AUX_BRANCH_RETURN):
/*
* Special branch for fast (vector) processing of zero arguments
* The end of implementation
*/
testl %edx, %edx
/* Go to special inputs processing branch */
jne L(SPECIAL_VALUES_BRANCH)
# LOE rbx rbp r12 r13 r14 r15 eax edx xmm0 xmm12 xmm13
/* Restore registers
* and exit the function
*/
L(EXIT):
addq $88, %rsp
cfi_def_cfa_offset(8)
ret
cfi_def_cfa_offset(96)
/* Branch to process
* special inputs
*/
L(SPECIAL_VALUES_BRANCH):
movups %xmm12, 32(%rsp)
movups %xmm13, 48(%rsp)
movups %xmm0, 64(%rsp)
# LOE rbx rbp r12 r13 r14 r15 eax edx xmm0
movq %r12, 16(%rsp)
cfi_offset(12, -80)
movl %eax, %r12d
movq %r13, 8(%rsp)
cfi_offset(13, -88)
movl %edx, %r13d
movq %r14, (%rsp)
cfi_offset(14, -96)
# 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 64(%rsp), %xmm0
/* Go to exit */
jmp L(EXIT)
cfi_offset(12, -80)
cfi_offset(13, -88)
cfi_offset(14, -96)
# LOE rbx rbp r12 r13 r14 r15 xmm0
/* Scalar math function call
* to process special input
*/
L(SCALAR_MATH_CALL):
movl %r12d, %r14d
movss 32(%rsp, %r14, 4), %xmm0
movss 48(%rsp, %r14, 4), %xmm1
call atan2f@PLT
# LOE rbx rbp r14 r15 r12d r13d xmm0
movss %xmm0, 64(%rsp, %r14, 4)
/* Process special inputs in loop */
jmp L(SPECIAL_VALUES_LOOP)
cfi_restore(12)
cfi_restore(13)
cfi_restore(14)
# LOE rbx rbp r15 r12d r13d
/* Auxiliary branch
* for out of main path inputs
*/
L(AUX_BRANCH):
/* Check if both X & Y are not NaNs: iXYnotNAN */
movaps %xmm13, %xmm3
movaps %xmm12, %xmm2
cmpordps %xmm13, %xmm3
cmpordps %xmm12, %xmm2
/*
* Path for zero arguments (at least one of both)
* Check if both args are zeros (den. is zero)
*/
cmpeqps %xmm5, %xmm6
/* Check if at least on of Y or Y is zero: iAXAYZERO */
pcmpeqd %xmm5, %xmm11
pcmpeqd %xmm5, %xmm10
andps %xmm2, %xmm3
por %xmm10, %xmm11
/* Check if at least on of Y or Y is zero and not NaN: iAXAYZEROnotNAN */
andps %xmm3, %xmm11
/* Exclude from previous callout mask zero (and not NaN) arguments */
movaps %xmm11, %xmm10
pandn %xmm1, %xmm10
/* Set sPIO2 to zero if den. is zero */
movaps %xmm6, %xmm1
andnps %xmm7, %xmm1
andps %xmm5, %xmm6
orps %xmm6, %xmm1
/* Res = sign(Y)*(X<0)?(PIO2+PI):PIO2 */
pcmpgtd %xmm13, %xmm5
orps %xmm9, %xmm1
andps %xmm4, %xmm5
/* Merge results from main and spec path */
movaps %xmm11, %xmm4
addps %xmm5, %xmm1
/* Go to callout */
movmskps %xmm10, %edx
orps %xmm8, %xmm1
andnps %xmm0, %xmm4
andps %xmm11, %xmm1
movaps %xmm4, %xmm0
orps %xmm1, %xmm0
/* Return to main vector processing path */
jmp L(AUX_BRANCH_RETURN)
# LOE rbx rbp r12 r13 r14 r15 eax edx xmm0 xmm12 xmm13
END(_ZGVbN4vv_atan2f_sse4)
.section .rodata, "a"
.align 16
#ifdef __svml_satan2_data_internal_typedef
typedef unsigned int VUINT32;
typedef struct {
__declspec(align(16)) VUINT32 sZERO[4][1];
__declspec(align(16)) VUINT32 sSIGN_MASK[4][1];
__declspec(align(16)) VUINT32 sABS_MASK[4][1];
__declspec(align(16)) VUINT32 sPIO2[4][1];
__declspec(align(16)) VUINT32 sPI[4][1];
__declspec(align(16)) VUINT32 sPC8[4][1];
__declspec(align(16)) VUINT32 sPC7[4][1];
__declspec(align(16)) VUINT32 sPC6[4][1];
__declspec(align(16)) VUINT32 sPC5[4][1];
__declspec(align(16)) VUINT32 sPC4[4][1];
__declspec(align(16)) VUINT32 sPC3[4][1];
__declspec(align(16)) VUINT32 sPC2[4][1];
__declspec(align(16)) VUINT32 sPC1[4][1];
__declspec(align(16)) VUINT32 sPC0[4][1];
__declspec(align(16)) VUINT32 iCHK_WORK_SUB[4][1];
__declspec(align(16)) VUINT32 iCHK_WORK_CMP[4][1];
} __svml_satan2_data_internal;
#endif
__svml_satan2_data_internal:
.long 0x00000000, 0x00000000, 0x00000000, 0x00000000 // sZERO
.align 16
.long 0x80000000, 0x80000000, 0x80000000, 0x80000000 // sSIGN_MASK
.align 16
.long 0x7FFFFFFF, 0x7FFFFFFF, 0x7FFFFFFF, 0x7FFFFFFF // sABS_MASK
.align 16
.long 0x3FC90FDB, 0x3FC90FDB, 0x3FC90FDB, 0x3FC90FDB // sPIO2
.align 16
.long 0x40490FDB, 0x40490FDB, 0x40490FDB, 0x40490FDB // sPI
.align 16
.long 0x3B322CC0, 0x3B322CC0, 0x3B322CC0, 0x3B322CC0 // sA08
.align 16
.long 0xBC7F2631, 0xBC7F2631, 0xBC7F2631, 0xBC7F2631 // sA07
.align 16
.long 0x3D2BC384, 0x3D2BC384, 0x3D2BC384, 0x3D2BC384 // sA06
.align 16
.long 0xBD987629, 0xBD987629, 0xBD987629, 0xBD987629 // sA05
.align 16
.long 0x3DD96474, 0x3DD96474, 0x3DD96474, 0x3DD96474 // sA04
.align 16
.long 0xBE1161F8, 0xBE1161F8, 0xBE1161F8, 0xBE1161F8 // sA03
.align 16
.long 0x3E4CB79F, 0x3E4CB79F, 0x3E4CB79F, 0x3E4CB79F // sA02
.align 16
.long 0xBEAAAA49, 0xBEAAAA49, 0xBEAAAA49, 0xBEAAAA49 // sA01
.align 16
.long 0x3F800000, 0x3F800000, 0x3F800000, 0x3F800000 // sA00
.align 16
.long 0x81000000, 0x81000000, 0x81000000, 0x81000000 // iCHK_WORK_SUB
.align 16
.long 0xFC000000, 0xFC000000, 0xFC000000, 0xFC000000 // iCHK_WORK_CMP
.align 16
.type __svml_satan2_data_internal, @object
.size __svml_satan2_data_internal, .-__svml_satan2_data_internal
|
