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// This implementation uses the main path for |x| in [2^{-5},2^65).
36// For |x| in [2^{-64},2^{-5}), a secondary path is used.
37// For the biased exponent of X within 3FFH-64 and 3FF+64, we use one branch.
38// We use the following definition of B and X` so that the formula
39// atan(X) = Tau + atan( (X`-B) / (One + BX) ) is correct
40//
41// X = (-1)^s * 2^k * 1. x1 x2 ... x52
42//
43// Define X`  = 0 if k >= 5; and X`  = |X| otherwise
44// Define One = 0 if k >= 5; and One = 1 otherwise
45// Define B  = 0 if k <= -6; B =  2^k * 1.x1 x2 x3 x4 1  if -5 <= k <= 4
46// Define B  =  2^5 * 1.0 0 ... 0   if  k >= 5
47//
48// Tau is 0 if k <= -6;
49// Tau is atan( B )  if -5 <= k <= 4
50// Tau is pi/2 if k >= 5
51//
52// Special cases:
53//  atan(NaN) = quiet NaN
54//  atan(+/-INF) = +/-Pi/2
55//  atan(+/-0) = +/-0
56//
57/******************************************************************************/
58
59#include <private/bionic_asm.h>
60# -- Begin  static_func
61        .text
62        .align __bionic_asm_align
63        .type static_func, @function
64static_func:
65..B1.1:
66        call      ..L2
67..L2:
68        popl      %eax
69        lea       _GLOBAL_OFFSET_TABLE_+[. - ..L2](%eax), %eax
70        lea       static_const_table@GOTOFF(%eax), %eax
71        ret
72        .size   static_func,.-static_func
73# -- End  static_func
74
75# -- Begin  atan
76ENTRY(atan)
77# parameter 1: 8 + %ebp
78..B2.1:
79..B2.2:
80        pushl     %ebp
81        movl      %esp, %ebp
82        subl      $104, %esp
83        movl      %ebx, 48(%esp)
84        call      static_func
85        movl      %eax, %ebx
86        movsd     112(%esp), %xmm0
87        movsd     2640(%ebx), %xmm3
88        movsd     2624(%ebx), %xmm5
89        movsd     2656(%ebx), %xmm4
90        movsd     %xmm0, 8(%esp)
91        pextrw    $3, %xmm0, %edx
92        andpd     %xmm0, %xmm3
93        pshufd    $68, %xmm0, %xmm1
94        orpd      %xmm4, %xmm3
95        movl      %edx, %eax
96        andl      $32767, %edx
97        subl      $16288, %edx
98        cmpl      $159, %edx
99        ja        .L_2TAG_PACKET_0.0.2
100        mulsd     %xmm3, %xmm1
101        subsd     %xmm3, %xmm0
102        addsd     %xmm5, %xmm1
103        divsd     %xmm1, %xmm0
104        addl      $1, %edx
105        movsd     2672(%ebx), %xmm2
106        movsd     2688(%ebx), %xmm4
107        andl      $32768, %eax
108        xorpd     %xmm7, %xmm7
109        pinsrw    $3, %eax, %xmm7
110        addl      %edx, %edx
111        movsd     (%ebx,%edx,8), %xmm6
112        movsd     8(%ebx,%edx,8), %xmm5
113        xorpd     %xmm7, %xmm5
114        xorpd     %xmm7, %xmm6
115        movsd     2680(%ebx), %xmm7
116        pshufd    $68, %xmm0, %xmm1
117        mulsd     %xmm0, %xmm0
118        pshufd    $68, %xmm1, %xmm3
119        addsd     %xmm6, %xmm1
120        mulsd     %xmm0, %xmm2
121        addsd     %xmm0, %xmm4
122        subsd     %xmm1, %xmm6
123        mulsd     %xmm0, %xmm4
124        addsd     %xmm7, %xmm2
125        mulsd     %xmm3, %xmm0
126        addsd     %xmm3, %xmm6
127        mulsd     %xmm2, %xmm0
128        addsd     2696(%ebx), %xmm4
129        addsd     %xmm5, %xmm6
130        mulsd     %xmm4, %xmm0
131        addsd     %xmm6, %xmm0
132        addsd     %xmm1, %xmm0
133        movsd     %xmm0, (%esp)
134        fldl      (%esp)
135        jmp       .L_2TAG_PACKET_1.0.2
136.L_2TAG_PACKET_0.0.2:
137        addl      $944, %edx
138        cmpl      $1103, %edx
139        ja        .L_2TAG_PACKET_2.0.2
140        movsd     2672(%ebx), %xmm4
141        movsd     2688(%ebx), %xmm7
142        movsd     8(%esp), %xmm0
143        mulsd     %xmm1, %xmm1
144        movsd     2680(%ebx), %xmm2
145        movsd     2696(%ebx), %xmm5
146        mulsd     %xmm1, %xmm4
147        addsd     %xmm1, %xmm7
148        movapd    %xmm1, %xmm6
149        mulsd     %xmm0, %xmm1
150        addsd     %xmm4, %xmm2
151        mulsd     %xmm6, %xmm7
152        mulsd     %xmm1, %xmm2
153        addsd     %xmm5, %xmm7
154        mulsd     %xmm7, %xmm2
155        addsd     %xmm2, %xmm0
156        movsd     %xmm0, (%esp)
157        fldl      (%esp)
158        jmp       .L_2TAG_PACKET_1.0.2
159.L_2TAG_PACKET_2.0.2:
160        addl      $15344, %edx
161        cmpl      $16368, %edx
162        ja        .L_2TAG_PACKET_3.0.2
163        movsd     8(%esp), %xmm0
164        movsd     8(%esp), %xmm1
165        cmpl      $16, %edx
166        jae       .L_2TAG_PACKET_4.0.2
167        mulsd     %xmm0, %xmm1
168.L_2TAG_PACKET_4.0.2:
169        movsd     %xmm0, (%esp)
170        fldl      (%esp)
171        jmp       .L_2TAG_PACKET_1.0.2
172.L_2TAG_PACKET_3.0.2:
173        cmpl      $17392, %edx
174        jae       .L_2TAG_PACKET_5.0.2
175        xorpd     %xmm1, %xmm1
176        movl      $49136, %ecx
177        pinsrw    $3, %ecx, %xmm1
178        divsd     %xmm0, %xmm1
179        movsd     2672(%ebx), %xmm2
180        movsd     2688(%ebx), %xmm4
181        andl      $32768, %eax
182        xorpd     %xmm7, %xmm7
183        pinsrw    $3, %eax, %xmm7
184        addl      %edx, %edx
185        movsd     2592(%ebx), %xmm6
186        movsd     2600(%ebx), %xmm5
187        xorpd     %xmm7, %xmm5
188        xorpd     %xmm7, %xmm6
189        movsd     2680(%ebx), %xmm7
190        pshufd    $68, %xmm1, %xmm0
191        mulsd     %xmm1, %xmm1
192        pshufd    $68, %xmm0, %xmm3
193        addsd     %xmm6, %xmm0
194        mulsd     %xmm1, %xmm2
195        addsd     %xmm1, %xmm4
196        subsd     %xmm0, %xmm6
197        mulsd     %xmm1, %xmm4
198        addsd     %xmm7, %xmm2
199        mulsd     %xmm3, %xmm1
200        addsd     %xmm3, %xmm6
201        mulsd     %xmm2, %xmm1
202        addsd     2696(%ebx), %xmm4
203        addsd     %xmm5, %xmm6
204        mulsd     %xmm4, %xmm1
205        addsd     %xmm6, %xmm1
206        addsd     %xmm1, %xmm0
207        movsd     %xmm0, (%esp)
208        fldl      (%esp)
209        jmp       .L_2TAG_PACKET_1.0.2
210.L_2TAG_PACKET_5.0.2:
211        movsd     8(%esp), %xmm4
212        movsd     2608(%ebx), %xmm0
213        movsd     2592(%ebx), %xmm2
214        movsd     2600(%ebx), %xmm3
215        movd      %xmm1, %eax
216        psrlq     $32, %xmm1
217        movd      %xmm1, %edx
218        andl      $2147483647, %edx
219        cmpl      $2146435072, %edx
220        jae       .L_2TAG_PACKET_6.0.2
221.L_2TAG_PACKET_7.0.2:
222        andnpd    %xmm4, %xmm0
223        orpd      %xmm0, %xmm2
224        orpd      %xmm3, %xmm0
225        addsd     %xmm2, %xmm0
226        movsd     %xmm0, (%esp)
227        fldl      (%esp)
228        jmp       .L_2TAG_PACKET_1.0.2
229.L_2TAG_PACKET_6.0.2:
230        subl      $2146435072, %edx
231        orl       %edx, %eax
232        cmpl      $0, %eax
233        je        .L_2TAG_PACKET_7.0.2
234        movapd    %xmm4, %xmm0
235        addsd     %xmm0, %xmm0
236        movsd     %xmm0, (%esp)
237        fldl      (%esp)
238.L_2TAG_PACKET_1.0.2:
239        movl      48(%esp), %ebx
240        movl      %ebp, %esp
241        popl      %ebp
242        ret
243..B2.3:
244END(atan)
245# -- End  atan
246
247# Start file scope ASM
248ALIAS_SYMBOL(atanl, atan);
249# End file scope ASM
250	.section .rodata, "a"
251	.align 16
252	.align 16
253static_const_table:
254	.long	0
255	.long	0
256	.long	0
257	.long	0
258	.long	3819695742
259	.long	1067482761
260	.long	2398680355
261	.long	3155462074
262	.long	2998791009
263	.long	1067548225
264	.long	3868465248
265	.long	3157182472
266	.long	3339424991
267	.long	1067613680
268	.long	3296670360
269	.long	1010752543
270	.long	2710002256
271	.long	1067679126
272	.long	3403896007
273	.long	1010910768
274	.long	3275701428
275	.long	1067744562
276	.long	119959933
277	.long	1011482843
278	.long	2908636881
279	.long	1067809988
280	.long	2464489612
281	.long	1011545526
282	.long	3777889398
283	.long	1067875403
284	.long	3262682165
285	.long	1009703919
286	.long	3759667419
287	.long	1067940807
288	.long	1838130851
289	.long	3157373556
290	.long	732369940
291	.long	1068006200
292	.long	1203428313
293	.long	1010055371
294	.long	1166616461
295	.long	1068071580
296	.long	2901274051
297	.long	3158549977
298	.long	2945472892
299	.long	1068136947
300	.long	3726120658
301	.long	1009762715
302	.long	3954480976
303	.long	1068202301
304	.long	1289173457
305	.long	1009429861
306	.long	2081752829
307	.long	1068267642
308	.long	1836909874
309	.long	1006212095
310	.long	3807999788
311	.long	1068332968
312	.long	2172459940
313	.long	3156162078
314	.long	2731789884
315	.long	1068398280
316	.long	3450718392
317	.long	3159216547
318	.long	1044477961
319	.long	1068463577
320	.long	2230553229
321	.long	1011424339
322	.long	1486930287
323	.long	1068530218
324	.long	2861547474
325	.long	1012041376
326	.long	2293016881
327	.long	1068595466
328	.long	136843272
329	.long	1012684797
330	.long	201518157
331	.long	1068660680
332	.long	63231984
333	.long	1012427198
334	.long	4054234584
335	.long	1068725856
336	.long	3927006960
337	.long	1011878955
338	.long	1246477213
339	.long	1068790995
340	.long	1494265652
341	.long	3155219350
342	.long	678186699
343	.long	1068856093
344	.long	1264361424
345	.long	3159256693
346	.long	2690594995
347	.long	1068921148
348	.long	3906996379
349	.long	1009288267
350	.long	3362611517
351	.long	1068986159
352	.long	1650970041
353	.long	3158331771
354	.long	3102162111
355	.long	1069051124
356	.long	365917035
357	.long	3160264153
358	.long	2352611067
359	.long	1069116041
360	.long	4008970190
361	.long	3159478182
362	.long	1594134794
363	.long	1069180908
364	.long	466690178
365	.long	1012526501
366	.long	1345079306
367	.long	1069245723
368	.long	2268273568
369	.long	3160164092
370	.long	2163300970
371	.long	1069310484
372	.long	2750834800
373	.long	3158113482
374	.long	352522716
375	.long	1069375190
376	.long	1750411372
377	.long	1011790845
378	.long	848541647
379	.long	1069439838
380	.long	2164207573
381	.long	1011698350
382	.long	40647312
383	.long	1069504427
384	.long	2949165434
385	.long	3159107267
386	.long	2216766270
387	.long	1069574357
388	.long	2197920765
389	.long	3161055954
390	.long	1090914384
391	.long	1069638757
392	.long	2330454674
393	.long	1013365998
394	.long	387601244
395	.long	1069703022
396	.long	3185681168
397	.long	1013434071
398	.long	3991640484
399	.long	1069767144
400	.long	1313211590
401	.long	3161087959
402	.long	3322489502
403	.long	1069831118
404	.long	3013977995
405	.long	1013053011
406	.long	3121698570
407	.long	1069894936
408	.long	4069015667
409	.long	1013023362
410	.long	4289964660
411	.long	1069958591
412	.long	1736191156
413	.long	3158266731
414	.long	3903312386
415	.long	1070022077
416	.long	1833592413
417	.long	3159731471
418	.long	3818449864
419	.long	1070085387
420	.long	851036429
421	.long	3159730451
422	.long	2097480306
423	.long	1070148515
424	.long	3506390884
425	.long	3160462302
426	.long	1611694502
427	.long	1070211454
428	.long	2785735540
429	.long	3160465144
430	.long	1464694796
431	.long	1070274198
432	.long	4229277299
433	.long	3159907000
434	.long	1299612775
435	.long	1070336741
436	.long	4116653788
437	.long	3160427739
438	.long	1310544789
439	.long	1070399077
440	.long	1064430331
441	.long	1013218202
442	.long	2253168030
443	.long	1070461200
444	.long	1405044609
445	.long	3157623179
446	.long	1159567373
447	.long	1070523105
448	.long	2353445521
449	.long	3159992176
450	.long	1359373750
451	.long	1070605818
452	.long	1748171336
453	.long	3161879263
454	.long	908341706
455	.long	1070667034
456	.long	3372710815
457	.long	3161775245
458	.long	1743027350
459	.long	1070727765
460	.long	687089934
461	.long	3160507171
462	.long	2055355646
463	.long	1070787992
464	.long	2392855242
465	.long	1013682469
466	.long	690426164
467	.long	1070847697
468	.long	1103926666
469	.long	1014052810
470	.long	1483247847
471	.long	1070906862
472	.long	2082645847
473	.long	3161345479
474	.long	392040270
475	.long	1070965472
476	.long	2407720023
477	.long	1014053754
478	.long	2673846014
479	.long	1071023511
480	.long	1293605532
481	.long	3158464385
482	.long	1384215810
483	.long	1071080967
484	.long	2446095872
485	.long	3159216407
486	.long	3101660631
487	.long	1071137826
488	.long	698040758
489	.long	1014855328
490	.long	2094057058
491	.long	1071194078
492	.long	2282048339
493	.long	1014040385
494	.long	1712750594
495	.long	1071249712
496	.long	1204372378
497	.long	3162276464
498	.long	1411515787
499	.long	1071304719
500	.long	949080808
501	.long	1015006403
502	.long	931538085
503	.long	1071359091
504	.long	3027127039
505	.long	1014307233
506	.long	179139065
507	.long	1071412821
508	.long	4285547492
509	.long	3161934731
510	.long	3387721259
511	.long	1071465902
512	.long	373225773
513	.long	1013486625
514	.long	2132236852
515	.long	1071544299
516	.long	3250533429
517	.long	1014031677
518	.long	1942070284
519	.long	1071645596
520	.long	1237964179
521	.long	3163239113
522	.long	1532707802
523	.long	1071695380
524	.long	330645583
525	.long	1012495610
526	.long	2294184979
527	.long	1071743834
528	.long	3959472897
529	.long	1015833116
530	.long	3805060714
531	.long	1071790961
532	.long	2671256142
533	.long	1013727772
534	.long	2215037898
535	.long	1071836770
536	.long	2683359117
537	.long	1015831902
538	.long	483661594
539	.long	1071881273
540	.long	836288326
541	.long	3162648643
542	.long	1534679894
543	.long	1071924486
544	.long	373258696
545	.long	3162470096
546	.long	1538714628
547	.long	1071966430
548	.long	3199433068
549	.long	1015325501
550	.long	527642555
551	.long	1072007128
552	.long	3636832592
553	.long	3161843145
554	.long	291339150
555	.long	1072046605
556	.long	890169537
557	.long	3160586117
558	.long	2450210201
559	.long	1072084888
560	.long	1636353294
561	.long	3163193400
562	.long	2411367951
563	.long	1072122007
564	.long	374899873
565	.long	1011331750
566	.long	681549971
567	.long	1072157992
568	.long	506411689
569	.long	1015373954
570	.long	1466745541
571	.long	1072192873
572	.long	2143860931
573	.long	1013364334
574	.long	2845622366
575	.long	1072226682
576	.long	2869178209
577	.long	3162423682
578	.long	2838871438
579	.long	1072275456
580	.long	3742223599
581	.long	1014338577
582	.long	4200275274
583	.long	1072337034
584	.long	1566539915
585	.long	3161839550
586	.long	3034733530
587	.long	1072394897
588	.long	652621408
589	.long	3162261964
590	.long	3207412993
591	.long	1072449290
592	.long	3206124665
593	.long	1014408733
594	.long	624461478
595	.long	1072500450
596	.long	932437485
597	.long	1015204343
598	.long	767665908
599	.long	1072548600
600	.long	1037911952
601	.long	3163527627
602	.long	1110773639
603	.long	1072593952
604	.long	2371517912
605	.long	3160465741
606	.long	1940828530
607	.long	1072636704
608	.long	2731408428
609	.long	3162895795
610	.long	1911329388
611	.long	1072677041
612	.long	1773089615
613	.long	3159569267
614	.long	1764715788
615	.long	1072704191
616	.long	691346949
617	.long	3164069946
618	.long	3332979233
619	.long	1072722195
620	.long	3550733983
621	.long	1014770628
622	.long	1321870254
623	.long	1072739231
624	.long	1415315820
625	.long	1016224052
626	.long	3657429030
627	.long	1072755365
628	.long	3910539033
629	.long	1015966402
630	.long	4197624557
631	.long	1072770661
632	.long	2333399254
633	.long	3164546480
634	.long	1512059493
635	.long	1072785177
636	.long	2701510318
637	.long	1016178092
638	.long	453379037
639	.long	1072798965
640	.long	4046344253
641	.long	3162814364
642	.long	1942345162
643	.long	1072818388
644	.long	621134147
645	.long	1016335195
646	.long	4210176273
647	.long	1072842164
648	.long	2701013387
649	.long	3164326619
650	.long	4185644010
651	.long	1072863795
652	.long	4163699341
653	.long	1016203112
654	.long	679688788
655	.long	1072883543
656	.long	4147276762
657	.long	1014066750
658	.long	29432865
659	.long	1072901630
660	.long	970415797
661	.long	1016902063
662	.long	4070721092
663	.long	1072918247
664	.long	2539004411
665	.long	3163736096
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930	.type	static_const_table,@object
931	.size	static_const_table,2704
932	.data
933	.section .note.GNU-stack, ""
934# End
935