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/******************************************************************************/
33//                     ALGORITHM DESCRIPTION
34//                     ---------------------
35//
36//  sinh(x)=(exp(x)-exp(-x))/2
37//
38//  Let |x|=xH+xL (upper 26 bits, lower 27 bits)
39//  log2(e) rounded to 26 bits (high part) plus a double precision low part is
40//          L2EH+L2EL (upper 26, lower 53 bits)
41//
42//  Let xH*L2EH=k+f+r`, where (k+f)*2^7=int(xH*L2EH*2^7),
43//                              f=0.b1 b2 ... b7, k integer
44//  2^f is approximated as Tp[f]+Dp[f], and 2^{-f} as Tn[f]+Dn[f]
45//  Tp stores the high 53 bits, Dp stores (2^f-Tp[f]) rounded to double precision
46//
47//  e^|x|=2^{k+f}*2^r, r=r`+xL*L2EH+|x|*L2EL, |r|<2^{-8}+2^{-14},
48//                       for |x| in [23/64,3*2^7)
49//  e^{-|x|}=2^{-k-f}*2^{-r}
50//
51//  e^|x| is approximated as 2^k*Tp+2^k*Tp*c1*r(1+c2*r+..+c5*r^4)+2^k*Dp=
52//                           =2^k*Tp+2^k*Tp*P15+2^k*Dp
53//  e^{-|x|} approximated as 2^{-k}*Tn-2^{-k}*Tn*c1*r(1-c2*r+..+c5*r^4)+2^{-k}*Dn
54//
55//  For |x| in [1/8, 3*2^7), sinh(x) is formed as
56//      RN(2^k*Tp-2^{-k}*Tn)+2^k*Tp*P15-2^{-k}*Tn*P`15-2^{-k}*TnL-2^{-k}*Dn+2^k*Dp
57//
58//  For x in (3*2^7, 3*2^8), sign(x)*(e^|x|)/2 is returned, and
59//  the result is checked for overflow.
60//
61//  For |x|<23/64, a Taylor polynomial expansion is used (degree 13)
62//  To reduce rounding errors, the p3*x^3 term is computed as
63//     (p3*xh^3)_high+[(p3*xl*(3*x*xh+xl^2))+(p3*xh^3)_low],
64//  where x=xh+xl, (xh are the leading 17 bits of x), and
65//     (p3*xh^3)_high=RN(x+p3*xh^3)-x
66//  (error bound for polynomial expansion is below 0.51 ulp)
67//
68// Special cases:
69//  sinh(NaN) = quiet NaN, and raise invalid exception
70//  sinh(+/-INF) = +/-INF
71//  sinh(x) = x for subnormals
72//  for finite argument, only sinh(0)=0 is exact
73//  For IEEE double
74//    sinh(x) overflows  for x >
75//    710.47586007394386342639336362481117248535156250 = MAXLOG+log(2)
76//
77/******************************************************************************/
78
79#include <private/bionic_asm.h>
80# -- Begin  static_func
81        .text
82        .align __bionic_asm_align
83        .type static_func, @function
84static_func:
85..B1.1:
86        call      ..L2
87..L2:
88        popl      %eax
89        lea       _GLOBAL_OFFSET_TABLE_+[. - ..L2](%eax), %eax
90        lea       static_const_table@GOTOFF(%eax), %eax
91        ret
92        .size   static_func,.-static_func
93# -- End  static_func
94
95# -- Begin  sinh
96ENTRY(sinh)
97# parameter 1: 8 + %ebp
98..B2.1:
99..B2.2:
100        pushl     %ebp
101        movl      %esp, %ebp
102        subl      $104, %esp
103        movl      %ebx, 40(%esp)
104        call      static_func
105        movl      %eax, %ebx
106        movsd     112(%esp), %xmm0
107        movsd     4272(%ebx), %xmm3
108        xorpd     %xmm4, %xmm4
109        movsd     4192(%ebx), %xmm1
110        movsd     4200(%ebx), %xmm2
111        movl      $32768, %eax
112        pinsrw    $3, %eax, %xmm4
113        movsd     4096(%ebx), %xmm6
114        pextrw    $3, %xmm0, %ecx
115        andpd     %xmm0, %xmm3
116        andnpd    %xmm0, %xmm4
117        pshufd    $68, %xmm4, %xmm5
118        movl      $32768, %edx
119        andl      %ecx, %edx
120        andl      $32767, %ecx
121        subl      $16343, %ecx
122        cmpl      $177, %ecx
123        jae       .L_2TAG_PACKET_0.0.2
124        subsd     %xmm3, %xmm4
125        mulsd     %xmm1, %xmm3
126        mulsd     %xmm5, %xmm2
127        cvtsd2si  %xmm3, %eax
128        shll      $3, %edx
129        orl       %edx, %eax
130        movapd    %xmm3, %xmm7
131        addsd     %xmm6, %xmm3
132        mulsd     %xmm4, %xmm1
133        xorpd     %xmm5, %xmm5
134        subsd     %xmm6, %xmm3
135        movapd    4112(%ebx), %xmm4
136        addsd     %xmm1, %xmm2
137        movapd    4128(%ebx), %xmm6
138        subsd     %xmm3, %xmm7
139        movl      $32704, %edx
140        pinsrw    $3, %edx, %xmm5
141        movapd    4144(%ebx), %xmm1
142        addsd     %xmm7, %xmm2
143        movl      $127, %edx
144        andl      %eax, %edx
145        addl      %edx, %edx
146        shrl      $3, %eax
147        andl      $65520, %eax
148        addl      $16352, %eax
149        xorpd     %xmm0, %xmm0
150        cmpl      $161, %ecx
151        jae       .L_2TAG_PACKET_1.0.2
152        pshufd    $68, %xmm5, %xmm5
153        pinsrw    $3, %eax, %xmm0
154        pshufd    $68, %xmm0, %xmm0
155        psubw     %xmm0, %xmm5
156        mulpd     (%ebx,%edx,8), %xmm0
157        mulpd     2048(%ebx,%edx,8), %xmm5
158        pshufd    $68, %xmm2, %xmm3
159        movapd    4160(%ebx), %xmm7
160        pshufd    $68, %xmm2, %xmm2
161        mulpd     %xmm3, %xmm3
162        mulpd     %xmm2, %xmm4
163        mulpd     %xmm2, %xmm6
164        mulpd     4176(%ebx), %xmm2
165        mulpd     %xmm3, %xmm1
166        mulpd     %xmm3, %xmm7
167        mulpd     %xmm3, %xmm4
168        mulpd     %xmm3, %xmm1
169        addpd     %xmm7, %xmm6
170        movapd    %xmm0, %xmm7
171        addpd     %xmm1, %xmm4
172        shufpd    $0, %xmm5, %xmm7
173        subpd     %xmm5, %xmm0
174        mulpd     %xmm7, %xmm2
175        addpd     %xmm6, %xmm4
176        subsd     %xmm0, %xmm7
177        mulpd     %xmm2, %xmm4
178        pshufd    $238, %xmm0, %xmm6
179        subsd     %xmm5, %xmm7
180        addpd     %xmm2, %xmm4
181        addsd     %xmm6, %xmm7
182        pshufd    $238, %xmm4, %xmm2
183        addsd     %xmm7, %xmm2
184        addsd     %xmm4, %xmm2
185        addsd     %xmm2, %xmm0
186        jmp       .L_2TAG_PACKET_2.0.2
187.L_2TAG_PACKET_1.0.2:
188        subl      $16352, %eax
189        movl      %eax, %ecx
190        andl      $32752, %eax
191        shrl      $1, %eax
192        andl      $65520, %eax
193        subl      %eax, %ecx
194        addl      $16352, %eax
195        pinsrw    $3, %eax, %xmm0
196        pshufd    $68, %xmm0, %xmm0
197        mulpd     (%ebx,%edx,8), %xmm0
198        pshufd    $68, %xmm2, %xmm3
199        movsd     4160(%ebx), %xmm7
200        mulsd     %xmm3, %xmm3
201        mulsd     %xmm2, %xmm4
202        mulsd     %xmm2, %xmm6
203        mulsd     4176(%ebx), %xmm2
204        mulsd     %xmm3, %xmm1
205        mulsd     %xmm3, %xmm7
206        mulsd     %xmm3, %xmm4
207        addl      $16368, %ecx
208        pinsrw    $3, %ecx, %xmm5
209        mulsd     %xmm3, %xmm1
210        addsd     %xmm7, %xmm6
211        addsd     %xmm1, %xmm4
212        mulsd     %xmm0, %xmm2
213        addsd     %xmm6, %xmm4
214        mulsd     %xmm2, %xmm4
215        pshufd    $238, %xmm0, %xmm6
216        addsd     %xmm6, %xmm4
217        addsd     %xmm4, %xmm2
218        addsd     %xmm2, %xmm0
219        mulsd     %xmm5, %xmm0
220        pextrw    $3, %xmm0, %eax
221        andl      $32752, %eax
222        movl      $127, %edx
223        cmpl      $32752, %eax
224        je        .L_2TAG_PACKET_3.0.2
225        jmp       .L_2TAG_PACKET_2.0.2
226.L_2TAG_PACKET_0.0.2:
227        addl      $16343, %ecx
228        cmpl      $16343, %ecx
229        ja        .L_2TAG_PACKET_4.0.2
230        cmpl      $15856, %ecx
231        jb        .L_2TAG_PACKET_5.0.2
232        movapd    4208(%ebx), %xmm1
233        pshufd    $68, %xmm0, %xmm6
234        mulpd     %xmm5, %xmm5
235        movapd    4224(%ebx), %xmm2
236        pshufd    $68, %xmm0, %xmm7
237        movapd    4240(%ebx), %xmm3
238        pshufd    $68, %xmm0, %xmm4
239        andpd     4256(%ebx), %xmm6
240        mulpd     %xmm5, %xmm1
241        mulsd     %xmm5, %xmm2
242        subpd     %xmm6, %xmm4
243        mulpd     %xmm5, %xmm7
244        addpd     %xmm3, %xmm1
245        pshufd    $68, %xmm6, %xmm3
246        mulpd     %xmm5, %xmm5
247        mulsd     %xmm7, %xmm2
248        mulpd     %xmm7, %xmm1
249        pshufd    $68, %xmm0, %xmm7
250        mulsd     %xmm6, %xmm6
251        addsd     %xmm7, %xmm7
252        mulsd     %xmm4, %xmm4
253        mulpd     %xmm5, %xmm1
254        addsd     %xmm0, %xmm7
255        mulsd     %xmm3, %xmm6
256        mulsd     %xmm3, %xmm7
257        pshufd    $238, %xmm1, %xmm3
258        mulsd     %xmm5, %xmm1
259        pshufd    $238, %xmm4, %xmm5
260        addsd     %xmm2, %xmm3
261        pshufd    $238, %xmm2, %xmm2
262        addsd     %xmm4, %xmm7
263        movapd    %xmm0, %xmm4
264        mulsd     %xmm2, %xmm6
265        mulsd     %xmm5, %xmm7
266        addsd     %xmm6, %xmm0
267        mulsd     %xmm2, %xmm7
268        subsd     %xmm0, %xmm4
269        addsd     %xmm7, %xmm1
270        addsd     %xmm4, %xmm6
271        addsd     %xmm3, %xmm1
272        addsd     %xmm6, %xmm1
273        addsd     %xmm1, %xmm0
274        jmp       .L_2TAG_PACKET_2.0.2
275.L_2TAG_PACKET_5.0.2:
276        cmpl      $16, %ecx
277        jae       .L_2TAG_PACKET_6.0.2
278        movapd    %xmm0, %xmm1
279        mulsd     %xmm1, %xmm1
280        jmp       .L_2TAG_PACKET_2.0.2
281.L_2TAG_PACKET_6.0.2:
282        xorpd     %xmm2, %xmm2
283        movl      $17392, %ecx
284        pinsrw    $3, %ecx, %xmm2
285        xorpd     %xmm3, %xmm3
286        movl      $15344, %edx
287        pinsrw    $3, %edx, %xmm3
288        mulsd     %xmm0, %xmm2
289        addsd     %xmm2, %xmm0
290        mulsd     %xmm3, %xmm0
291        jmp       .L_2TAG_PACKET_2.0.2
292.L_2TAG_PACKET_4.0.2:
293        cmpl      $32752, %ecx
294        jae       .L_2TAG_PACKET_7.0.2
295        xorpd     %xmm0, %xmm0
296        movl      $32736, %eax
297        pinsrw    $3, %eax, %xmm0
298        orl       %edx, %eax
299        pinsrw    $3, %eax, %xmm1
300        mulsd     %xmm1, %xmm0
301        movl      $127, %edx
302.L_2TAG_PACKET_3.0.2:
303        movsd     %xmm0, (%esp)
304        movsd     112(%esp), %xmm0
305        fldl      (%esp)
306        jmp       .L_2TAG_PACKET_8.0.2
307.L_2TAG_PACKET_7.0.2:
308        xorpd     %xmm1, %xmm1
309        movl      $32768, %eax
310        pinsrw    $3, %eax, %xmm1
311        andnpd    %xmm0, %xmm1
312        mulsd     %xmm1, %xmm0
313        jmp       .L_2TAG_PACKET_2.0.2
314.L_2TAG_PACKET_2.0.2:
315        movsd     %xmm0, 24(%esp)
316        fldl      24(%esp)
317.L_2TAG_PACKET_8.0.2:
318        movl      40(%esp), %ebx
319        movl      %ebp, %esp
320        popl      %ebp
321        ret
322..B2.3:
323END(sinh)
324# -- End  sinh
325
326# Start file scope ASM
327ALIAS_SYMBOL(sinhl, sinh);
328# End file scope ASM
329	.section .rodata, "a"
330	.align 16
331	.align 16
332static_const_table:
333	.long	0
334	.long	1072693248
335	.long	0
336	.long	0
337	.long	2851812149
338	.long	1072698941
339	.long	2595802551
340	.long	1016815913
341	.long	1048019041
342	.long	1072704666
343	.long	1398474845
344	.long	3161559171
345	.long	3899555717
346	.long	1072710421
347	.long	427280750
348	.long	3163595548
349	.long	3541402996
350	.long	1072716208
351	.long	2759177317
352	.long	1015903202
353	.long	702412510
354	.long	1072722027
355	.long	3803266087
356	.long	3163328991
357	.long	410360776
358	.long	1072727877
359	.long	1269990655
360	.long	1013024446
361	.long	3402036099
362	.long	1072733758
363	.long	405889334
364	.long	1016154232
365	.long	1828292879
366	.long	1072739672
367	.long	1255956747
368	.long	1016636974
369	.long	728909815
370	.long	1072745618
371	.long	383930225
372	.long	1016078044
373	.long	852742562
374	.long	1072751596
375	.long	667253586
376	.long	1010842135
377	.long	2952712987
378	.long	1072757606
379	.long	3293494651
380	.long	3161168877
381	.long	3490863953
382	.long	1072763649
383	.long	960797498
384	.long	3163997456
385	.long	3228316108
386	.long	1072769725
387	.long	3010241991
388	.long	3159471380
389	.long	2930322912
390	.long	1072775834
391	.long	2599499422
392	.long	3163762623
393	.long	3366293073
394	.long	1072781976
395	.long	3119426314
396	.long	1015169130
397	.long	1014845819
398	.long	1072788152
399	.long	3117910646
400	.long	3162607681
401	.long	948735466
402	.long	1072794361
403	.long	3516338028
404	.long	3163623459
405	.long	3949972341
406	.long	1072800603
407	.long	2068408548
408	.long	1015962444
409	.long	2214878420
410	.long	1072806880
411	.long	892270087
412	.long	3164164998
413	.long	828946858
414	.long	1072813191
415	.long	10642492
416	.long	1016988014
417	.long	586995997
418	.long	1072819536
419	.long	41662348
420	.long	3163676568
421	.long	2288159958
422	.long	1072825915
423	.long	2169144469
424	.long	1015924597
425	.long	2440944790
426	.long	1072832329
427	.long	2492769774
428	.long	1015196030
429	.long	1853186616
430	.long	1072838778
431	.long	3066496371
432	.long	1016705150
433	.long	1337108031
434	.long	1072845262
435	.long	3203724452
436	.long	1015726421
437	.long	1709341917
438	.long	1072851781
439	.long	2571168217
440	.long	1015201075
441	.long	3790955393
442	.long	1072858335
443	.long	2352942462
444	.long	3164228666
445	.long	4112506593
446	.long	1072864925
447	.long	2947355221
448	.long	1015419624
449	.long	3504003472
450	.long	1072871551
451	.long	3594001060
452	.long	3158379228
453	.long	2799960843
454	.long	1072878213
455	.long	1423655381
456	.long	1016070727
457	.long	2839424854
458	.long	1072884911
459	.long	1171596163
460	.long	1014090255
461	.long	171030293
462	.long	1072891646
463	.long	3526460132
464	.long	1015477354
465	.long	4232894513
466	.long	1072898416
467	.long	2383938684
468	.long	1015717095
469	.long	2992903935
470	.long	1072905224
471	.long	2218154406
472	.long	1016276769
473	.long	1603444721
474	.long	1072912069
475	.long	1548633640
476	.long	3163249902
477	.long	926591435
478	.long	1072918951
479	.long	3208833762
480	.long	3163962090
481	.long	1829099622
482	.long	1072925870
483	.long	1016661181
484	.long	3164509581
485	.long	887463927
486	.long	1072932827
487	.long	3596744163
488	.long	3161842742
489	.long	3272845541
490	.long	1072939821
491	.long	928852419
492	.long	3164536824
493	.long	1276261410
494	.long	1072946854
495	.long	300981948
496	.long	1015732745
497	.long	78413852
498	.long	1072953925
499	.long	4183226867
500	.long	3164065827
501	.long	569847338
502	.long	1072961034
503	.long	472945272
504	.long	3160339305
505	.long	3645941911
506	.long	1072968181
507	.long	3814685081
508	.long	3162621917
509	.long	1617004845
510	.long	1072975368
511	.long	82804944
512	.long	1011391354
513	.long	3978100823
514	.long	1072982593
515	.long	3513027190
516	.long	1016894539
517	.long	3049340112
518	.long	1072989858
519	.long	3062915824
520	.long	1014219171
521	.long	4040676318
522	.long	1072997162
523	.long	4090609238
524	.long	1016712034
525	.long	3577096743
526	.long	1073004506
527	.long	2951496418
528	.long	1014842263
529	.long	2583551245
530	.long	1073011890
531	.long	3161094195
532	.long	1016655067
533	.long	1990012071
534	.long	1073019314
535	.long	3529070563
536	.long	3163861769
537	.long	2731501122
538	.long	1073026778
539	.long	1774031855
540	.long	3163518597
541	.long	1453150082
542	.long	1073034283
543	.long	498154669
544	.long	3162536638
545	.long	3395129871
546	.long	1073041828
547	.long	4025345435
548	.long	3163383964
549	.long	917841882
550	.long	1073049415
551	.long	18715565
552	.long	1016707884
553	.long	3566716925
554	.long	1073057042
555	.long	1536826856
556	.long	1015191009
557	.long	3712504873
558	.long	1073064711
559	.long	88491949
560	.long	1016476236
561	.long	2321106615
562	.long	1073072422
563	.long	2171176610
564	.long	1010584347
565	.long	363667784
566	.long	1073080175
567	.long	813753950
568	.long	1016833785
569	.long	3111574537
570	.long	1073087969
571	.long	2606161479
572	.long	3163808322
573	.long	2956612997
574	.long	1073095806
575	.long	2118169751
576	.long	3163784129
577	.long	885834528
578	.long	1073103686
579	.long	1973258547
580	.long	3163310140
581	.long	2186617381
582	.long	1073111608
583	.long	2270764084
584	.long	3164321289
585	.long	3561793907
586	.long	1073119573
587	.long	1157054053
588	.long	1012938926
589	.long	1719614413
590	.long	1073127582
591	.long	330458198
592	.long	3164331316
593	.long	1963711167
594	.long	1073135634
595	.long	1744767757
596	.long	3161622870
597	.long	1013258799
598	.long	1073143730
599	.long	1748797611
600	.long	3161177658
601	.long	4182873220
602	.long	1073151869
603	.long	629542646
604	.long	3163044879
605	.long	3907805044
606	.long	1073160053
607	.long	2257091225
608	.long	3162598983
609	.long	1218806132
610	.long	1073168282
611	.long	1818613052
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1313	.long	2952712987
1314	.long	1071709030
1315	.long	3293494651
1316	.long	3160120301
1317	.long	852742562
1318	.long	1071703020
1319	.long	667253586
1320	.long	1009793559
1321	.long	728909815
1322	.long	1071697042
1323	.long	383930225
1324	.long	1015029468
1325	.long	1828292879
1326	.long	1071691096
1327	.long	1255956747
1328	.long	1015588398
1329	.long	3402036099
1330	.long	1071685182
1331	.long	405889334
1332	.long	1015105656
1333	.long	410360776
1334	.long	1071679301
1335	.long	1269990655
1336	.long	1011975870
1337	.long	702412510
1338	.long	1071673451
1339	.long	3803266087
1340	.long	3162280415
1341	.long	3541402996
1342	.long	1071667632
1343	.long	2759177317
1344	.long	1014854626
1345	.long	3899555717
1346	.long	1071661845
1347	.long	427280750
1348	.long	3162546972
1349	.long	1048019041
1350	.long	1071656090
1351	.long	1398474845
1352	.long	3160510595
1353	.long	2851812149
1354	.long	1071650365
1355	.long	2595802551
1356	.long	1015767337
1357	.long	0
1358	.long	1127743488
1359	.long	0
1360	.long	3275227136
1361	.long	3607404736
1362	.long	1044146952
1363	.long	3607404736
1364	.long	3191630600
1365	.long	4277811695
1366	.long	1063661122
1367	.long	4277811695
1368	.long	3211144770
1369	.long	2140175755
1370	.long	1033864261
1371	.long	2140175755
1372	.long	1033864261
1373	.long	4289495988
1374	.long	1054113747
1375	.long	4289495988
1376	.long	1054113747
1377	.long	4277811695
1378	.long	1064709698
1379	.long	4277811695
1380	.long	1064709698
1381	.long	1610612736
1382	.long	1080497479
1383	.long	4166901572
1384	.long	1053077003
1385	.long	329805064
1386	.long	1038488134
1387	.long	2773927730
1388	.long	1053236707
1389	.long	286331153
1390	.long	1065423121
1391	.long	1431655765
1392	.long	1069897045
1393	.long	1744127201
1394	.long	1046144581
1395	.long	436314137
1396	.long	1059717536
1397	.long	0
1398	.long	4294967280
1399	.long	0
1400	.long	4294967280
1401	.long	4160749568
1402	.long	2147483647
1403	.type	static_const_table,@object
1404	.size	static_const_table,4280
1405	.data
1406	.section .note.GNU-stack, ""
1407# End
1408