s_tan.S revision 5d4f0e6a26b66f1dab8d20a65af4469c6dd7370d 
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// Polynomials coefficients and other constants.
36//
37// Note that in this algorithm, there is a different polynomial for
38// each breakpoint, so there are 32 sets of polynomial coefficients
39// as well as 32 instances of the other constants.
40//
41// The polynomial coefficients and constants are offset from the start
42// of the main block as follows:
43//
44//   0:  c8 | c0
45//  16:  c9 | c1
46//  32: c10 | c2
47//  48: c11 | c3
48//  64: c12 | c4
49//  80: c13 | c5
50//  96: c14 | c6
51// 112: c15 | c7
52// 128: T_hi
53// 136: T_lo
54// 144: Sigma
55// 152: T_hl
56// 160: Tau
57// 168: Mask
58// 176: (end of block)
59//
60// The total table size is therefore 5632 bytes.
61//
62// Note that c0 and c1 are always zero. We could try storing
63// other constants here, and just loading the low part of the
64// SIMD register in these cases, after ensuring the high part
65// is zero.
66//
67// The higher terms of the polynomial are computed in the *low*
68// part of the SIMD register. This is so we can overlap the
69// multiplication by r^8 and the unpacking of the other part.
70//
71// The constants are:
72// T_hi + T_lo = accurate constant term in power series
73// Sigma + T_hl = accurate coefficient of r in power series (Sigma=1 bit)
74// Tau = multiplier for the reciprocal, always -1 or 0
75//
76// The basic reconstruction formula using these constants is:
77//
78// High = tau * recip_hi + t_hi
79// Med = (sgn * r + t_hl * r)_hi
80// Low = (sgn * r + t_hl * r)_lo +
81//       tau * recip_lo + T_lo + (T_hl + sigma) * c + pol
82//
83// where pol = c0 + c1 * r + c2 * r^2 + ... + c15 * r^15
84//
85// (c0 = c1 = 0, but using them keeps SIMD regularity)
86//
87// We then do a compensated sum High + Med, add the low parts together
88// and then do the final sum.
89//
90// Here recip_hi + recip_lo is an accurate reciprocal of the remainder
91// modulo pi/2
92//
93// Special cases:
94//  tan(NaN) = quiet NaN, and raise invalid exception
95//  tan(INF) = NaN and raise invalid exception
96//  tan(+/-0) = +/-0
97//
98/******************************************************************************/
99
100#include <private/bionic_asm.h>
101# -- Begin  static_func
102        .text
103        .align __bionic_asm_align
104        .type static_func, @function
105static_func:
106..B1.1:
107        call      ..L2
108..L2:
109        popl      %eax
110        lea       _GLOBAL_OFFSET_TABLE_+[. - ..L2](%eax), %eax
111        lea       static_const_table@GOTOFF(%eax), %eax
112        ret
113        .size   static_func,.-static_func
114# -- End  static_func
115
116# -- Begin  tan
117ENTRY(tan)
118# parameter 1: 8 + %ebp
119..B2.1:
120..B2.2:
121        pushl     %ebp
122        movl      %esp, %ebp
123        subl      $120, %esp
124        movl      %ebx, 56(%esp)
125        call      static_func
126        movl      %eax, %ebx
127        movsd     128(%esp), %xmm0
128        pextrw    $3, %xmm0, %eax
129        andl      $32767, %eax
130        subl      $14368, %eax
131        cmpl      $2216, %eax
132        ja        .L_2TAG_PACKET_0.0.2
133        movapd    5840(%ebx), %xmm5
134        movapd    5856(%ebx), %xmm6
135        unpcklpd  %xmm0, %xmm0
136        movapd    5712(%ebx), %xmm4
137        andpd     %xmm0, %xmm4
138        movapd    5632(%ebx), %xmm1
139        mulpd     %xmm0, %xmm1
140        orpd      %xmm4, %xmm5
141        addpd     %xmm5, %xmm1
142        movapd    %xmm1, %xmm7
143        unpckhpd  %xmm7, %xmm7
144        cvttsd2si %xmm7, %edx
145        cvttpd2dq %xmm1, %xmm1
146        cvtdq2pd  %xmm1, %xmm1
147        mulpd     %xmm6, %xmm1
148        movapd    5664(%ebx), %xmm3
149        movsd     5728(%ebx), %xmm5
150        addl      $469248, %edx
151        movapd    5680(%ebx), %xmm4
152        mulpd     %xmm1, %xmm3
153        andl      $31, %edx
154        mulsd     %xmm1, %xmm5
155        movl      %edx, %ecx
156        mulpd     %xmm1, %xmm4
157        shll      $1, %ecx
158        subpd     %xmm3, %xmm0
159        mulpd     5696(%ebx), %xmm1
160        addl      %ecx, %edx
161        shll      $2, %ecx
162        addl      %ecx, %edx
163        addsd     %xmm0, %xmm5
164        movapd    %xmm0, %xmm2
165        subpd     %xmm4, %xmm0
166        movsd     5744(%ebx), %xmm6
167        shll      $4, %edx
168        lea       (%ebx), %eax
169        andpd     5776(%ebx), %xmm5
170        movapd    %xmm0, %xmm3
171        addl      %edx, %eax
172        subpd     %xmm0, %xmm2
173        unpckhpd  %xmm0, %xmm0
174        divsd     %xmm5, %xmm6
175        subpd     %xmm4, %xmm2
176        movapd    16(%eax), %xmm7
177        subsd     %xmm5, %xmm3
178        mulpd     %xmm0, %xmm7
179        subpd     %xmm1, %xmm2
180        movapd    48(%eax), %xmm1
181        mulpd     %xmm0, %xmm1
182        movapd    96(%eax), %xmm4
183        mulpd     %xmm0, %xmm4
184        addsd     %xmm3, %xmm2
185        movapd    %xmm0, %xmm3
186        mulpd     %xmm0, %xmm0
187        addpd     (%eax), %xmm7
188        addpd     32(%eax), %xmm1
189        mulpd     %xmm0, %xmm1
190        addpd     80(%eax), %xmm4
191        addpd     %xmm1, %xmm7
192        movapd    112(%eax), %xmm1
193        mulpd     %xmm0, %xmm1
194        mulpd     %xmm0, %xmm0
195        addpd     %xmm1, %xmm4
196        movapd    64(%eax), %xmm1
197        mulpd     %xmm0, %xmm1
198        addpd     %xmm1, %xmm7
199        movapd    %xmm3, %xmm1
200        mulpd     %xmm0, %xmm3
201        mulsd     %xmm0, %xmm0
202        mulpd     144(%eax), %xmm1
203        mulpd     %xmm3, %xmm4
204        movapd    %xmm1, %xmm3
205        addpd     %xmm4, %xmm7
206        movapd    %xmm1, %xmm4
207        mulsd     %xmm7, %xmm0
208        unpckhpd  %xmm7, %xmm7
209        addsd     %xmm7, %xmm0
210        unpckhpd  %xmm1, %xmm1
211        addsd     %xmm1, %xmm3
212        subsd     %xmm3, %xmm4
213        addsd     %xmm4, %xmm1
214        movapd    %xmm2, %xmm4
215        movsd     144(%eax), %xmm7
216        unpckhpd  %xmm2, %xmm2
217        addsd     152(%eax), %xmm7
218        mulsd     %xmm2, %xmm7
219        addsd     136(%eax), %xmm7
220        addsd     %xmm1, %xmm7
221        addsd     %xmm7, %xmm0
222        movsd     5744(%ebx), %xmm7
223        mulsd     %xmm6, %xmm4
224        movsd     168(%eax), %xmm2
225        andpd     %xmm6, %xmm2
226        mulsd     %xmm2, %xmm5
227        mulsd     160(%eax), %xmm6
228        subsd     %xmm5, %xmm7
229        subsd     128(%eax), %xmm2
230        subsd     %xmm4, %xmm7
231        mulsd     %xmm6, %xmm7
232        movapd    %xmm3, %xmm4
233        subsd     %xmm2, %xmm3
234        addsd     %xmm3, %xmm2
235        subsd     %xmm2, %xmm4
236        addsd     %xmm4, %xmm0
237        subsd     %xmm7, %xmm0
238        addsd     %xmm3, %xmm0
239        movsd     %xmm0, (%esp)
240        fldl      (%esp)
241        jmp       .L_2TAG_PACKET_1.0.2
242.L_2TAG_PACKET_0.0.2:
243        jg        .L_2TAG_PACKET_2.0.2
244        shrl      $4, %eax
245        cmpl      $268434558, %eax
246        jne       .L_2TAG_PACKET_3.0.2
247        movapd    %xmm0, %xmm3
248        mulsd     5808(%ebx), %xmm3
249.L_2TAG_PACKET_3.0.2:
250        movsd     5792(%ebx), %xmm3
251        mulsd     %xmm0, %xmm3
252        addsd     %xmm0, %xmm3
253        mulsd     5808(%ebx), %xmm3
254        movsd     %xmm3, (%esp)
255        fldl      (%esp)
256        jmp       .L_2TAG_PACKET_1.0.2
257.L_2TAG_PACKET_2.0.2:
258        movq      5712(%ebx), %xmm7
259        andpd     %xmm0, %xmm7
260        xorpd     %xmm0, %xmm7
261        ucomisd   5760(%ebx), %xmm7
262        je        .L_2TAG_PACKET_4.0.2
263        subl      $32, %esp
264        movsd     %xmm0, (%esp)
265        lea       40(%esp), %eax
266        movl      %eax, 8(%esp)
267        movl      $2, %eax
268        movl      %eax, 12(%esp)
269        call      __libm_tancot_huge
270        addl      $32, %esp
271        fldl      8(%esp)
272        jmp       .L_2TAG_PACKET_1.0.2
273.L_2TAG_PACKET_4.0.2:
274        movq      %xmm0, (%esp)
275        fldl      (%esp)
276        fsubl     (%esp)
277.L_2TAG_PACKET_1.0.2:
278        movl      56(%esp), %ebx
279        movl      %ebp, %esp
280        popl      %ebp
281        ret
282..B2.3:
283END(tan)
284# -- End  tan
285
286# Start file scope ASM
287.weak tanl
288.equ tanl, tan
289# End file scope ASM
290	.section .rodata, "a"
291	.align 16
292	.align 16
293static_const_table:
294	.long	0
295	.long	0
296	.long	0
297	.long	0
298	.long	2284589306
299	.long	1066820852
300	.long	0
301	.long	0
302	.long	0
303	.long	0
304	.long	0
305	.long	0
306	.long	1441186365
307	.long	1065494243
308	.long	1431655765
309	.long	1070945621
310	.long	0
311	.long	0
312	.long	0
313	.long	0
314	.long	236289504
315	.long	1064135997
316	.long	286331153
317	.long	1069617425
318	.long	0
319	.long	0
320	.long	0
321	.long	0
322	.long	1160476131
323	.long	1062722102
324	.long	463583772
325	.long	1068212666
326	.long	0
327	.long	0
328	.long	0
329	.long	0
330	.long	0
331	.long	1072693248
332	.long	0
333	.long	0
334	.long	0
335	.long	0
336	.long	0
337	.long	0
338	.long	1313038235
339	.long	1066745731
340	.long	0
341	.long	0
342	.long	1013878342
343	.long	1067152618
344	.long	0
345	.long	0
346	.long	3663426833
347	.long	1065725283
348	.long	3693284251
349	.long	1069118808
350	.long	650852232
351	.long	1065882376
352	.long	1996245381
353	.long	1071000265
354	.long	2008746170
355	.long	1064664197
356	.long	3055842593
357	.long	1068578846
358	.long	1495406348
359	.long	1064652437
360	.long	2269530157
361	.long	1069711235
362	.long	285563696
363	.long	1063576465
364	.long	1046897440
365	.long	1067705865
366	.long	233429731
367	.long	1063453151
368	.long	522045958
369	.long	1068476590
370	.long	2354785698
371	.long	1069102779
372	.long	1317599141
373	.long	1012432133
374	.long	0
375	.long	1072693248
376	.long	2828230105
377	.long	1065606626
378	.long	0
379	.long	0
380	.long	0
381	.long	0
382	.long	1512545955
383	.long	1068119047
384	.long	0
385	.long	0
386	.long	1127048698
387	.long	1067909459
388	.long	0
389	.long	0
390	.long	2300200450
391	.long	1067254767
392	.long	3593250296
393	.long	1070233561
394	.long	3009365544
395	.long	1066902117
396	.long	1127373050
397	.long	1071173457
398	.long	3046103305
399	.long	1066371299
400	.long	24583402
401	.long	1069723988
402	.long	4082511758
403	.long	1065914199
404	.long	3223889699
405	.long	1070020367
406	.long	548927984
407	.long	1065415756
408	.long	558065897
409	.long	1068949418
410	.long	680073315
411	.long	1064940726
412	.long	388873200
413	.long	1068944270
414	.long	3763679576
415	.long	1070167541
416	.long	1497360404
417	.long	1009710547
418	.long	0
419	.long	1072693248
420	.long	64931152
421	.long	1067729411
422	.long	0
423	.long	0
424	.long	0
425	.long	0
426	.long	2467582782
427	.long	1069256389
428	.long	0
429	.long	0
430	.long	162150096
431	.long	1068946420
432	.long	0
433	.long	0
434	.long	3702794237
435	.long	1068579152
436	.long	3631919291
437	.long	1070936926
438	.long	3456821413
439	.long	1068217218
440	.long	2031366438
441	.long	1071495745
442	.long	1596664020
443	.long	1067799281
444	.long	1509038701
445	.long	1070601643
446	.long	583171477
447	.long	1067510148
448	.long	3785344682
449	.long	1070618476
450	.long	2402036048
451	.long	1067075736
452	.long	3233018412
453	.long	1069913186
454	.long	411280568
455	.long	1066710556
456	.long	1065584192
457	.long	1069747896
458	.long	895247324
459	.long	1070819848
460	.long	500078909
461	.long	3161288781
462	.long	0
463	.long	1072693248
464	.long	729983843
465	.long	1068994194
466	.long	0
467	.long	0
468	.long	0
469	.long	0
470	.long	1458794562
471	.long	1070398550
472	.long	0
473	.long	0
474	.long	2857777489
475	.long	1070137637
476	.long	0
477	.long	0
478	.long	1024359517
479	.long	1069876531
480	.long	2616040238
481	.long	1071582937
482	.long	1609024636
483	.long	1069675088
484	.long	2529240549
485	.long	1071836633
486	.long	1510128600
487	.long	1069440113
488	.long	2251697184
489	.long	1071253687
490	.long	1262761453
491	.long	1069142850
492	.long	1263091857
493	.long	1071190461
494	.long	3043383486
495	.long	1068885191
496	.long	2476932470
497	.long	1070842002
498	.long	3659995028
499	.long	1068669200
500	.long	855891755
501	.long	1070696894
502	.long	2583490354
503	.long	1071284857
504	.long	3062633575
505	.long	1014008623
506	.long	0
507	.long	1072693248
508	.long	2550940471
509	.long	1069938201
510	.long	0
511	.long	0
512	.long	0
513	.long	0
514	.long	3422807297
515	.long	1071640847
516	.long	0
517	.long	0
518	.long	1151658053
519	.long	1071494715
520	.long	0
521	.long	0
522	.long	929607071
523	.long	1071346340
524	.long	1037049034
525	.long	1072037305
526	.long	2786928657
527	.long	1071215282
528	.long	1447406859
529	.long	1072265209
530	.long	3490952107
531	.long	1071090851
532	.long	3205232916
533	.long	1071968658
534	.long	1297344304
535	.long	1070977120
536	.long	1066110976
537	.long	1071946035
538	.long	3803721480
539	.long	1070871082
540	.long	1496754229
541	.long	1071807201
542	.long	2982550683
543	.long	1070773243
544	.long	4014441989
545	.long	1071736222
546	.long	419968236
547	.long	1071717047
548	.long	3451266538
549	.long	3163444811
550	.long	0
551	.long	1072693248
552	.long	2960267235
553	.long	1070745841
554	.long	0
555	.long	0
556	.long	0
557	.long	0
558	.long	724322768
559	.long	1072881308
560	.long	0
561	.long	0
562	.long	643153048
563	.long	1072905816
564	.long	0
565	.long	0
566	.long	4285079458
567	.long	1072928558
568	.long	3912524733
569	.long	1072622983
570	.long	118362272
571	.long	1072952754
572	.long	4107767972
573	.long	1072827408
574	.long	2689502883
575	.long	1072976922
576	.long	946523347
577	.long	1072772766
578	.long	573204189
579	.long	1073001761
580	.long	581531518
581	.long	1072826391
582	.long	1386236526
583	.long	1073026959
584	.long	3718905905
585	.long	1072832823
586	.long	1145558140
587	.long	1073052673
588	.long	513572637
589	.long	1072861969
590	.long	716700048
591	.long	1071997368
592	.long	547126769
593	.long	1015523525
594	.long	0
595	.long	1072693248
596	.long	1097907398
597	.long	1071420120
598	.long	0
599	.long	0
600	.long	0
601	.long	0
602	.long	3349892442
603	.long	1074290212
604	.long	0
605	.long	0
606	.long	3913197405
607	.long	1074501181
608	.long	0
609	.long	0
610	.long	2494034522
611	.long	1074739170
612	.long	1264738763
613	.long	1073084804
614	.long	1520293906
615	.long	1074899632
616	.long	1958936600
617	.long	1073411493
618	.long	2133649635
619	.long	1075052171
620	.long	4270740730
621	.long	1073574708
622	.long	1728930189
623	.long	1075224844
624	.long	1303998552
625	.long	1073799186
626	.long	618611933
627	.long	1075420255
628	.long	1769828046
629	.long	1073938542
630	.long	2200537986
631	.long	1075641421
632	.long	433361110
633	.long	1074105369
634	.long	719595600
635	.long	1072317184
636	.long	294527206
637	.long	3162140088
638	.long	0
639	.long	1073741824
640	.long	3811788216
641	.long	3218400550
642	.long	0
643	.long	0
644	.long	0
645	.long	0
646	.long	1704352102
647	.long	1075943001
648	.long	0
649	.long	0
650	.long	2284589306
651	.long	1076258036
652	.long	0
653	.long	0
654	.long	2211264291
655	.long	1076659010
656	.long	0
657	.long	1073741824
658	.long	1441186365
659	.long	1077028579
660	.long	1431655765
661	.long	1074091349
662	.long	876943673
663	.long	1077353622
664	.long	2863311531
665	.long	1074440874
666	.long	236289504
667	.long	1077767485
668	.long	286331153
669	.long	1074860305
670	.long	2805473311
671	.long	1078115278
672	.long	95443718
673	.long	1075163227
674	.long	1160476131
675	.long	1078450742
676	.long	463583772
677	.long	1075552698
678	.long	0
679	.long	1072693248
680	.long	0
681	.long	0
682	.long	0
683	.long	1073741824
684	.long	0
685	.long	0
686	.long	0
687	.long	0
688	.long	0
689	.long	0
690	.long	1330165971
691	.long	3207850745
692	.long	0
693	.long	0
694	.long	217536623
695	.long	1059109098
696	.long	0
697	.long	0
698	.long	3492120849
699	.long	3205151475
700	.long	602185705
701	.long	3215678092
702	.long	760422958
703	.long	1056312597
704	.long	555127889
705	.long	1067545266
706	.long	3139784124
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1762	.type	static_const_table,@object
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1764	.data
1765	.hidden __libm_tancot_huge
1766	.section .note.GNU-stack, ""
1767# End
1768