1/*
2Copyright (c) 2014, Intel Corporation
3All rights reserved.
4
5Redistribution and use in source and binary forms, with or without
6modification, are permitted provided that the following conditions are met:
7
8    * Redistributions of source code must retain the above copyright notice,
9    * this list of conditions and the following disclaimer.
10
11    * Redistributions in binary form must reproduce the above copyright notice,
12    * this list of conditions and the following disclaimer in the documentation
13    * and/or other materials provided with the distribution.
14
15    * Neither the name of Intel Corporation nor the names of its contributors
16    * may be used to endorse or promote products derived from this software
17    * without specific prior written permission.
18
19THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND
20ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
21WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
22DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR
23ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
24(INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
25LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON
26ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
27(INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
28SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
29*/
30
31/******************************************************************************/
32//                     ALGORITHM DESCRIPTION
33//                     ---------------------
34//
35//  To compute acos(s), separate schemes are used when s is in different
36//  intervals.
37//
38//  |s| in [2^{-4}, sqrt(3)/2):
39//       Let t=2^k*1.b1 b2..b6 1, where s=2^k*1.b1 b2 .. b52
40//       acos(s)=pi/2-asin(t)-asin(r), where r=s*sqrt(1-t^2)-t*sqrt(1-s^2)
41//       asin(r)-r evaluated as 7-degree polynomial (c3*r^3+c5*r^5+c7*r^7)
42//       For the first degree term, r is evaluated as
43//                R=(s^2-t^2)/(sqrt(1-t^2)*s+sqrt(1-s^2)*t)
44//       (sqrt(1-t^2) read from table)
45//  The main source of error is still R (may still be affected by up to 3 ulps
46//  of rounding error). The table size must be sufficiently large, to minimize
47//  this effect.
48//
49//  |s| in [sqrt(3)/2, 255/256):
50//       Let t=2^k*1.b1 b2..b6 1, where sqrt(1-s^2)=2^k*1.b1 b2 .. b52 (rounded)
51//       acos(|s|)=asin(t)-asin(r), r=s*t-sqrt(1-s^2)*sqrt(1-t^2)
52//   acos(-|s|)=pi-acos(|s|)
53//       (The -PI constant, or 0, is added to the result. The sign is set at
54//        the end)
55//       asin(r) evaluated as a polynomial (same as above)
56//       The first degree term is evaluated as
57//                        r=(s^2+t^2-1)/(s*t+sqrt(1-s^2)*sqrt(1-t^2))
58//
59//  |s|<2^{-4}: acos(s)=pi/2-asin(s)
60//              evaluate asin(s) as 13-degree polynomial
61//
62//  |s| in [255/256,1): acos(|s|)=2*asin(q), where q=sqrt((1-|s|)/2)
63//  asin(q) is evaluated as 13-degree polynomial
64//      q^2=(1-|s|)/2 is obtained in advance
65//         2*q*eps ~ ((1-|s|)/2-q^2)/q used for first term
66//   acos(-|s|)=pi-acos(|s|)
67//       (The -PI constant, or 0, is added to the result. The sign is set at
68//        the end)
69//
70// Special cases:
71//  acos(NaN) = quiet NaN, and raise invalid exception
72//  acos(INF) = QNaN and raise invalid exception
73//  acos(x) = QNaN and raise invalid exception, for |x|>1.0
74//  acos(1) = +0
75//
76/******************************************************************************/
77
78#include <private/bionic_asm.h>
79# -- Begin  static_func
80        .text
81        .align __bionic_asm_align
82        .type static_func, @function
83static_func:
84..B1.1:
85        call      ..L2
86..L2:
87        popl      %eax
88        lea       _GLOBAL_OFFSET_TABLE_+[. - ..L2](%eax), %eax
89        lea       static_const_table@GOTOFF(%eax), %eax
90        ret
91        .size   static_func,.-static_func
92# -- End  static_func
93
94# -- Begin  acos
95ENTRY(acos)
96# parameter 1: 8 + %ebp
97..B2.1:
98..B2.2:
99        pushl     %ebp
100        movl      %esp, %ebp
101        subl      $104, %esp
102        movl      %ebx, 48(%esp)
103        call      static_func
104        movl      %eax, %ebx
105        movsd     112(%esp), %xmm0
106        movsd     6048(%ebx), %xmm4
107        movsd     6080(%ebx), %xmm3
108        xorpd     %xmm5, %xmm5
109        movsd     6064(%ebx), %xmm2
110        movapd    %xmm0, %xmm1
111        movsd     %xmm0, 8(%esp)
112        psrlq     $44, %xmm0
113        movd      %xmm0, %edx
114        movapd    %xmm1, %xmm7
115        movl      $8192, %ecx
116        pinsrw    $2, %ecx, %xmm5
117        movapd    %xmm1, %xmm0
118        movl      $524287, %eax
119        andl      %edx, %eax
120        subl      $260864, %eax
121        cmpl      $955, %eax
122        jae       .L_2TAG_PACKET_0.0.2
123        mulsd     %xmm1, %xmm1
124        andl      $65535, %edx
125        subsd     %xmm1, %xmm3
126        sqrtsd    %xmm3, %xmm3
127        andpd     %xmm7, %xmm2
128        andl      $-4, %edx
129        subl      $64256, %edx
130        movsd     3840(%ebx,%edx,2), %xmm1
131        orpd      %xmm5, %xmm2
132        movapd    (%ebx,%edx,4), %xmm4
133        movapd    %xmm7, %xmm6
134        addsd     %xmm2, %xmm7
135        subsd     %xmm2, %xmm0
136        mulsd     %xmm0, %xmm7
137        mulsd     %xmm1, %xmm6
138        mulsd     %xmm2, %xmm3
139        movapd    %xmm6, %xmm1
140        addsd     %xmm3, %xmm6
141        divsd     %xmm6, %xmm7
142        movsd     5976(%ebx), %xmm0
143        movsd     5960(%ebx), %xmm5
144        subsd     %xmm3, %xmm1
145        psrlq     $63, %xmm2
146        movapd    %xmm1, %xmm3
147        psllq     $63, %xmm2
148        mulsd     %xmm1, %xmm1
149        pshufd    $68, %xmm2, %xmm2
150        movsd     5968(%ebx), %xmm6
151        mulsd     %xmm1, %xmm3
152        mulsd     %xmm1, %xmm0
153        xorpd     %xmm2, %xmm4
154        mulsd     %xmm3, %xmm5
155        subpd     5888(%ebx), %xmm4
156        mulsd     %xmm1, %xmm3
157        addsd     %xmm6, %xmm0
158        mulsd     %xmm3, %xmm0
159        subsd     %xmm4, %xmm5
160        pshufd    $238, %xmm4, %xmm4
161        addsd     %xmm5, %xmm0
162        subsd     %xmm7, %xmm0
163        subsd     %xmm4, %xmm0
164        movsd     %xmm0, (%esp)
165        fldl      (%esp)
166        jmp       .L_2TAG_PACKET_1.0.2
167.L_2TAG_PACKET_0.0.2:
168        subl      $955, %eax
169        cmpl      $65, %eax
170        jae       .L_2TAG_PACKET_2.0.2
171        psrlq     $38, %xmm7
172        psllq     $38, %xmm7
173        pmovmskb  %xmm0, %eax
174        andnpd    %xmm0, %xmm4
175        subsd     %xmm7, %xmm1
176        movapd    %xmm7, %xmm6
177        mulsd     %xmm7, %xmm7
178        addsd     %xmm6, %xmm0
179        orpd      %xmm4, %xmm5
180        subsd     %xmm7, %xmm3
181        mulsd     %xmm1, %xmm0
182        movapd    %xmm3, %xmm4
183        subsd     %xmm0, %xmm3
184        sqrtsd    %xmm3, %xmm3
185        andl      $128, %eax
186        shrl      $7, %eax
187        negl      %eax
188        movapd    %xmm3, %xmm7
189        andpd     %xmm3, %xmm2
190        psllq     $2, %xmm3
191        pextrw    $3, %xmm3, %edx
192        orpd      %xmm5, %xmm2
193        movd      %eax, %xmm3
194        pshufd    $0, %xmm3, %xmm3
195        subl      $65216, %edx
196        addl      %edx, %edx
197        mulsd     3840(%ebx,%edx,4), %xmm7
198        mulsd     %xmm2, %xmm6
199        mulsd     %xmm2, %xmm1
200        mulsd     %xmm2, %xmm2
201        subsd     %xmm7, %xmm6
202        andpd     5904(%ebx), %xmm3
203        addsd     %xmm1, %xmm6
204        subsd     %xmm2, %xmm4
205        addsd     %xmm7, %xmm7
206        movsd     5960(%ebx), %xmm5
207        subsd     %xmm0, %xmm4
208        addsd     %xmm6, %xmm7
209        movsd     5976(%ebx), %xmm0
210        divsd     %xmm7, %xmm4
211        movsd     5968(%ebx), %xmm2
212        addpd     (%ebx,%edx,8), %xmm3
213        movapd    %xmm6, %xmm1
214        mulsd     %xmm6, %xmm6
215        mulsd     %xmm6, %xmm0
216        mulsd     %xmm6, %xmm1
217        mulsd     %xmm1, %xmm5
218        mulsd     %xmm6, %xmm1
219        addsd     %xmm2, %xmm0
220        pxor      %xmm6, %xmm6
221        mulsd     %xmm1, %xmm0
222        addsd     %xmm3, %xmm5
223        addsd     %xmm5, %xmm0
224        andl      $32768, %eax
225        pinsrw    $3, %eax, %xmm6
226        movapd    %xmm4, %xmm5
227        pshufd    $238, %xmm3, %xmm3
228        addsd     %xmm3, %xmm4
229        subsd     %xmm4, %xmm3
230        addsd     %xmm3, %xmm5
231        addsd     %xmm5, %xmm0
232        addsd     %xmm4, %xmm0
233        xorpd     %xmm6, %xmm0
234        movsd     %xmm0, (%esp)
235        fldl      (%esp)
236        jmp       .L_2TAG_PACKET_1.0.2
237.L_2TAG_PACKET_2.0.2:
238        addl      $15291, %eax
239        cmpl      $14336, %eax
240        jae       .L_2TAG_PACKET_3.0.2
241        unpcklpd  %xmm0, %xmm0
242        movapd    5984(%ebx), %xmm6
243        unpcklpd  %xmm0, %xmm1
244        movapd    6000(%ebx), %xmm2
245        movapd    6016(%ebx), %xmm4
246        mulpd     %xmm0, %xmm0
247        movapd    5888(%ebx), %xmm5
248        mulpd     %xmm0, %xmm1
249        mulpd     %xmm0, %xmm6
250        mulpd     %xmm0, %xmm0
251        movapd    %xmm1, %xmm3
252        mulsd     %xmm1, %xmm1
253        addpd     %xmm2, %xmm6
254        mulpd     %xmm0, %xmm4
255        mulsd     %xmm3, %xmm1
256        addpd     %xmm4, %xmm6
257        pshufd    $238, %xmm5, %xmm0
258        mulpd     %xmm6, %xmm1
259        pshufd    $238, %xmm5, %xmm6
260        subsd     %xmm7, %xmm0
261        pshufd    $238, %xmm1, %xmm2
262        subsd     %xmm1, %xmm5
263        subsd     %xmm0, %xmm6
264        subsd     %xmm2, %xmm5
265        subsd     %xmm6, %xmm7
266        subsd     %xmm7, %xmm5
267        addsd     %xmm5, %xmm0
268        movsd     %xmm0, (%esp)
269        fldl      (%esp)
270        jmp       .L_2TAG_PACKET_1.0.2
271.L_2TAG_PACKET_3.0.2:
272        subl      $15356, %eax
273        cmpl      $4, %eax
274        jae       .L_2TAG_PACKET_4.0.2
275        xorpd     %xmm6, %xmm6
276        andpd     6048(%ebx), %xmm7
277        movsd     6096(%ebx), %xmm4
278        movapd    5984(%ebx), %xmm1
279        mulsd     %xmm4, %xmm7
280        movapd    6000(%ebx), %xmm2
281        subsd     %xmm7, %xmm4
282        movapd    6016(%ebx), %xmm3
283        pshufd    $68, %xmm4, %xmm7
284        sqrtsd    %xmm4, %xmm4
285        mulpd     %xmm7, %xmm1
286        pshufd    $68, %xmm7, %xmm5
287        pextrw    $3, %xmm0, %eax
288        mulpd     %xmm7, %xmm7
289        addpd     %xmm1, %xmm2
290        movsd     5936(%ebx), %xmm1
291        mulpd     %xmm7, %xmm3
292        cmpsd     $1, %xmm6, %xmm0
293        mulsd     %xmm5, %xmm7
294        addpd     %xmm3, %xmm2
295        pshufd    $68, %xmm0, %xmm0
296        mulsd     %xmm7, %xmm2
297        andpd     5904(%ebx), %xmm0
298        mulpd     %xmm5, %xmm2
299        andpd     %xmm4, %xmm1
300        pshufd    $68, %xmm4, %xmm3
301        subsd     %xmm1, %xmm4
302        addsd     %xmm3, %xmm3
303        mulsd     %xmm1, %xmm1
304        subsd     %xmm4, %xmm3
305        subsd     %xmm1, %xmm5
306        mulsd     %xmm3, %xmm4
307        pshufd    $238, %xmm3, %xmm3
308        subsd     %xmm4, %xmm5
309        divsd     %xmm3, %xmm5
310        addpd     %xmm3, %xmm3
311        mulpd     %xmm3, %xmm2
312        pshufd    $238, %xmm2, %xmm4
313        addsd     %xmm0, %xmm2
314        andl      $32768, %eax
315        pinsrw    $3, %eax, %xmm6
316        pshufd    $238, %xmm0, %xmm0
317        addsd     %xmm4, %xmm2
318        addsd     %xmm5, %xmm2
319        addsd     %xmm3, %xmm2
320        addsd     %xmm2, %xmm0
321        xorpd     %xmm6, %xmm0
322        movsd     %xmm0, (%esp)
323        fldl      (%esp)
324        jmp       .L_2TAG_PACKET_1.0.2
325.L_2TAG_PACKET_4.0.2:
326        addl      $261884, %eax
327        cmpl      $261888, %eax
328        jb        .L_2TAG_PACKET_5.0.2
329        movd      %xmm7, %ecx
330        psrlq     $32, %xmm7
331        movd      %xmm7, %edx
332        andl      $2147483647, %edx
333        movl      $1072693248, %eax
334        subl      %edx, %eax
335        orl       %ecx, %eax
336        cmpl      $0, %eax
337        je        .L_2TAG_PACKET_6.0.2
338        movq      8(%esp), %xmm2
339        movd      %xmm2, %edx
340        psrlq     $32, %xmm2
341        movd      %xmm2, %ecx
342        andl      $2147483647, %ecx
343        subl      $1, %edx
344        sbbl      $2146435072, %ecx
345        cmpl      $0, %ecx
346        jge       .L_2TAG_PACKET_7.0.2
347        xorpd     %xmm1, %xmm1
348        xorpd     %xmm0, %xmm0
349        movl      $32752, %edx
350        pinsrw    $3, %edx, %xmm1
351        mulsd     %xmm1, %xmm0
352        movsd     %xmm0, (%esp)
353        fldl      (%esp)
354        jmp       .L_2TAG_PACKET_1.0.2
355.L_2TAG_PACKET_6.0.2:
356        pextrw    $1, %xmm7, %edx
357        shrl      $15, %edx
358        negl      %edx
359        movd      %edx, %xmm7
360        pshufd    $0, %xmm7, %xmm7
361        movsd     5920(%ebx), %xmm2
362        movsd     5928(%ebx), %xmm0
363        andpd     %xmm7, %xmm2
364        andpd     %xmm7, %xmm0
365        addsd     %xmm2, %xmm0
366        movsd     %xmm0, (%esp)
367        fldl      (%esp)
368        jmp       .L_2TAG_PACKET_1.0.2
369.L_2TAG_PACKET_5.0.2:
370        movsd     5888(%ebx), %xmm2
371        movsd     5896(%ebx), %xmm0
372        addsd     %xmm2, %xmm0
373        movsd     %xmm0, (%esp)
374        fldl      (%esp)
375        jmp       .L_2TAG_PACKET_1.0.2
376.L_2TAG_PACKET_7.0.2:
377        xorpd     %xmm6, %xmm6
378        addsd     %xmm6, %xmm0
379        movsd     %xmm0, (%esp)
380        fldl      (%esp)
381.L_2TAG_PACKET_1.0.2:
382        movl      48(%esp), %ebx
383        movl      %ebp, %esp
384        popl      %ebp
385        ret
386..B2.3:
387END(acos)
388# -- End  acos
389
390# Start file scope ASM
391ALIAS_SYMBOL(acosl, acos);
392# End file scope ASM
393	.section .rodata, "a"
394	.align 16
395	.align 16
396static_const_table:
397	.long	3822952792
398	.long	1021639372
399	.long	182792448
400	.long	1068507836
401	.long	2264213271
402	.long	1019558908
403	.long	649052928
404	.long	1068524253
405	.long	1797139609
406	.long	1022295143
407	.long	1243095296
408	.long	1068540671
409	.long	1415938756
410	.long	1021439537
411	.long	2033294592
412	.long	1068557090
413	.long	2356809978
414	.long	1021777916
415	.long	3088063744
416	.long	1068573510
417	.long	2669055318
418	.long	1022124482
419	.long	180888576
420	.long	1068589932
421	.long	3566445325
422	.long	1021358712
423	.long	1970196992
424	.long	1068606354
425	.long	896980323
426	.long	1021319659
427	.long	4229555456
428	.long	1068622777
429	.long	436049712
430	.long	1021319758
431	.long	2732572160
432	.long	1068639202
433	.long	583123209
434	.long	1020797960
435	.long	1842831872
436	.long	1068655628
437	.long	1370449804
438	.long	1021429270
439	.long	1628994560
440	.long	1068672055
441	.long	2411391464
442	.long	1021057980
443	.long	2159763712
444	.long	1068688483
445	.long	1208692749
446	.long	1021943903
447	.long	3503886336
448	.long	1068704912
449	.long	538793309
450	.long	1019744063
451	.long	1435187200
452	.long	1068721343
453	.long	4085087612
454	.long	1020608419
455	.long	317469952
456	.long	1068737775
457	.long	144386942
458	.long	1021440732
459	.long	219617280
460	.long	1068754208
461	.long	2940088361
462	.long	1019981122
463	.long	1210558208
464	.long	1068770642
465	.long	2176850347
466	.long	1018373705
467	.long	3359268352
468	.long	1068787077
469	.long	2395611454
470	.long	1021889042
471	.long	2439803648
472	.long	1068803514
473	.long	1650705253
474	.long	1020227966
475	.long	2816203520
476	.long	1068819952
477	.long	3702166386
478	.long	1019379914
479	.long	262620672
480	.long	1068836392
481	.long	1855649370
482	.long	1020453124
483	.long	3438159616
484	.long	1068852832
485	.long	923063860
486	.long	1019273834
487	.long	3822105856
488	.long	1068869274
489	.long	4289947947
490	.long	1019434249
491	.long	1483729920
492	.long	1068885718
493	.long	787455814
494	.long	1020738379
495	.long	787321088
496	.long	1068902163
497	.long	3321653337
498	.long	1021842569
499	.long	1802253312
500	.long	1068918609
501	.long	2653633526
502	.long	1021821525
503	.long	302985984
504	.long	1068935057
505	.long	161272028
506	.long	1021655149
507	.long	653966080
508	.long	1068951506
509	.long	2566098667
510	.long	1020066219
511	.long	2924727296
512	.long	1068967956
513	.long	3646493722
514	.long	1014292285
515	.long	2889890304
516	.long	1068984408
517	.long	1081009196
518	.long	1022189620
519	.long	619098112
520	.long	1069000862
521	.long	4011643355
522	.long	1021773297
523	.long	477017600
524	.long	1069017317
525	.long	4030305534
526	.long	1021292252
527	.long	2533403904
528	.long	1069033773
529	.long	2645187591
530	.long	1019527099
531	.long	2563102208
532	.long	1069050231
533	.long	3857293792
534	.long	1022311697
535	.long	635982336
536	.long	1069066691
537	.long	3625936637
538	.long	1017511744
539	.long	1116940800
540	.long	1069083152
541	.long	3653872993
542	.long	1022016631
543	.long	4075964160
544	.long	1069099614
545	.long	2468900271
546	.long	1021769532
547	.long	993165568
548	.long	1069116079
549	.long	1358104224
550	.long	1021199776
551	.long	528586752
552	.long	1069132545
553	.long	2200950332
554	.long	1022024872
555	.long	2752395776
556	.long	1069149012
557	.long	3197072454
558	.long	1017751319
559	.long	3439855616
560	.long	1069165481
561	.long	1651081806
562	.long	1020809338
563	.long	2661257728
564	.long	1069181952
565	.long	539032752
566	.long	1021728805
567	.long	486957312
568	.long	1069198425
569	.long	3136045149
570	.long	1016888671
571	.long	1282340352
572	.long	1069214899
573	.long	2593963259
574	.long	1018956103
575	.long	822921728
576	.long	1069231375
577	.long	2146032737
578	.long	1022306465
579	.long	3474216192
580	.long	1069247852
581	.long	3976811625
582	.long	1021350207
583	.long	716902656
584	.long	1069264332
585	.long	718267222
586	.long	1018624727
587	.long	1211594496
588	.long	1069280813
589	.long	1485641389
590	.long	1018447451
591	.long	734070272
592	.long	1069297296
593	.long	354455128
594	.long	1021341291
595	.long	3650110720
596	.long	1069313780
597	.long	682185947
598	.long	1021651853
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1911	.long	0
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1925	.type	static_const_table,@object
1926	.size	static_const_table,6112
1927	.data
1928	.section .note.GNU-stack, ""
1929# End
1930