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//  cosh(x)=(exp(x)+exp(-x))/2
36//
37//  Let |x|=xH+xL (upper 26 bits, lower 27 bits)
38//  log2(e) rounded to 26 bits (high part) plus a double precision low part is
39//          L2EH+L2EL (upper 26, lower 53 bits)
40//
41//  Let xH*L2EH=k+f+r`, where (k+f)*2^7=int(xH*L2EH*2^7),
42//                              f=0.b1 b2 ... b7, k integer
43//  2^f is approximated as Tp[f]+Dp[f], and 2^{-f} as Tn[f]+Dn[f]
44//  Tp stores higher 53 bits, Dp stores (2^f-Tp[f]) rounded to double precision
45//
46//  e^|x|=2^{k+f}*2^r, r=r`+xL*L2EH+|x|*L2EL, |r|<2^{-8}+2^{-14},
47//                       for |x| in [1/8,3*2^8)
48//  e^{-|x|}=2^{-k-f}*2^{-r}
49//
50//  e^|x| is approximated as 2^k*Tp+2^k*Tp*c1*r(1+c2*r+..+c5*r^4)+2^k*Dp=
51//                           =2^k*Tp+2^k*Tp*P15+2^k*Dp
52//  e^{-|x|} approximated as 2^{-k}*Tn-2^{-k}*Tn*c1*r(1-c2*r+..+c5*r^4)
53//
54//  For |x| in [1/8, 3*2^7), cosh(x) is formed as
55//   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
56//
57//  For |x| in [3*2^7, 3*2^8), (e^|x|)/2 is returned, and
58//  the result is checked for overflow.
59//
60//  For |x|<1/8, a Taylor polynomial expansion is used (degree 10)
61//  (error bound for polynomial expansion is below 0.501 ulp)
62//
63// Special cases:
64//  cosh(NaN) = quiet NaN, and raise invalid exception
65//  cosh(INF) = that INF
66//  cosh(0)=1
67//  for finite argument, only cosh(0)=1 is exact
68//  For IEEE double
69//  cosh(x) overflows
70//  for x > 710.47586007394386342639336362481117248535156250 = MAXLOG+log(2)
71//
72/******************************************************************************/
73
74#include <private/bionic_asm.h>
75# -- Begin  static_func
76        .text
77        .align __bionic_asm_align
78        .type static_func, @function
79static_func:
80..B1.1:
81        call      ..L2
82..L2:
83        popl      %eax
84        lea       _GLOBAL_OFFSET_TABLE_+[. - ..L2](%eax), %eax
85        lea       static_const_table@GOTOFF(%eax), %eax
86        ret
87        .size   static_func,.-static_func
88# -- End  static_func
89
90# -- Begin  cosh
91ENTRY(cosh)
92# parameter 1: 8 + %ebp
93..B2.1:
94..B2.2:
95        pushl     %ebp
96        movl      %esp, %ebp
97        subl      $104, %esp
98        movl      %ebx, 40(%esp)
99        call      static_func
100        movl      %eax, %ebx
101        movsd     112(%esp), %xmm0
102        movsd     4240(%ebx), %xmm3
103        xorpd     %xmm4, %xmm4
104        movsd     4192(%ebx), %xmm1
105        movsd     4200(%ebx), %xmm2
106        movl      $32768, %eax
107        pinsrw    $3, %eax, %xmm4
108        movsd     4096(%ebx), %xmm6
109        pextrw    $3, %xmm0, %ecx
110        andpd     %xmm0, %xmm3
111        andnpd    %xmm0, %xmm4
112        pshufd    $68, %xmm4, %xmm5
113        andl      $32767, %ecx
114        subl      $16320, %ecx
115        cmpl      $200, %ecx
116        jae       .L_2TAG_PACKET_0.0.2
117        subsd     %xmm3, %xmm4
118        mulsd     %xmm1, %xmm3
119        mulsd     %xmm5, %xmm2
120        cvtsd2si  %xmm3, %eax
121        movapd    %xmm3, %xmm7
122        addsd     %xmm6, %xmm3
123        mulsd     %xmm4, %xmm1
124        xorpd     %xmm5, %xmm5
125        subsd     %xmm6, %xmm3
126        movapd    4112(%ebx), %xmm4
127        addsd     %xmm1, %xmm2
128        movapd    4128(%ebx), %xmm6
129        subsd     %xmm3, %xmm7
130        movl      $32704, %edx
131        pinsrw    $3, %edx, %xmm5
132        movapd    4144(%ebx), %xmm1
133        addsd     %xmm7, %xmm2
134        movl      $127, %edx
135        andl      %eax, %edx
136        addl      %edx, %edx
137        shrl      $3, %eax
138        andl      $65520, %eax
139        addl      $16352, %eax
140        xorpd     %xmm0, %xmm0
141        cmpl      $184, %ecx
142        jae       .L_2TAG_PACKET_1.0.2
143        pshufd    $68, %xmm5, %xmm5
144        pinsrw    $3, %eax, %xmm0
145        pshufd    $68, %xmm0, %xmm0
146        psubw     %xmm0, %xmm5
147        mulpd     (%ebx,%edx,8), %xmm0
148        mulpd     2048(%ebx,%edx,8), %xmm5
149        pshufd    $68, %xmm2, %xmm3
150        movapd    4160(%ebx), %xmm7
151        pshufd    $68, %xmm2, %xmm2
152        mulpd     %xmm3, %xmm3
153        mulpd     %xmm2, %xmm4
154        mulpd     %xmm2, %xmm6
155        mulpd     4176(%ebx), %xmm2
156        mulpd     %xmm3, %xmm1
157        mulpd     %xmm3, %xmm7
158        mulpd     %xmm3, %xmm4
159        mulpd     %xmm3, %xmm1
160        addpd     %xmm7, %xmm6
161        movapd    %xmm0, %xmm7
162        addpd     %xmm1, %xmm4
163        shufpd    $0, %xmm5, %xmm7
164        addpd     %xmm5, %xmm0
165        mulpd     %xmm7, %xmm2
166        addpd     %xmm6, %xmm4
167        subsd     %xmm0, %xmm7
168        mulpd     %xmm2, %xmm4
169        pshufd    $238, %xmm0, %xmm6
170        addsd     %xmm5, %xmm7
171        addpd     %xmm2, %xmm4
172        addsd     %xmm6, %xmm7
173        pshufd    $238, %xmm4, %xmm2
174        addsd     %xmm7, %xmm2
175        addsd     %xmm4, %xmm2
176        addsd     %xmm2, %xmm0
177        jmp       .L_2TAG_PACKET_2.0.2
178.L_2TAG_PACKET_0.0.2:
179        addl      $16320, %ecx
180        cmpl      $16320, %ecx
181        ja        .L_2TAG_PACKET_3.0.2
182        cmpl      $15952, %ecx
183        jae       .L_2TAG_PACKET_4.0.2
184        addsd     %xmm2, %xmm6
185        movsd     4248(%ebx), %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      $64, %edx
223        cmpl      $32752, %eax
224        je        .L_2TAG_PACKET_5.0.2
225        jmp       .L_2TAG_PACKET_2.0.2
226.L_2TAG_PACKET_4.0.2:
227        movapd    4208(%ebx), %xmm1
228        mulpd     %xmm5, %xmm5
229        movapd    4224(%ebx), %xmm2
230        xorpd     %xmm3, %xmm3
231        movapd    %xmm5, %xmm0
232        mulpd     %xmm5, %xmm1
233        movsd     4248(%ebx), %xmm6
234        mulpd     %xmm5, %xmm5
235        movl      $16352, %eax
236        pinsrw    $3, %eax, %xmm3
237        addpd     %xmm2, %xmm1
238        mulpd     %xmm5, %xmm1
239        pshufd    $238, %xmm1, %xmm2
240        mulsd     %xmm1, %xmm5
241        mulsd     %xmm3, %xmm0
242        addsd     %xmm5, %xmm2
243        addsd     %xmm2, %xmm0
244        addsd     %xmm6, %xmm0
245        jmp       .L_2TAG_PACKET_2.0.2
246.L_2TAG_PACKET_3.0.2:
247        cmpl      $32752, %ecx
248        jae       .L_2TAG_PACKET_6.0.2
249        xorpd     %xmm0, %xmm0
250        movl      $32736, %eax
251        pinsrw    $3, %eax, %xmm0
252        mulsd     %xmm0, %xmm0
253        movl      $64, %edx
254.L_2TAG_PACKET_5.0.2:
255        movsd     %xmm0, (%esp)
256        movsd     112(%esp), %xmm0
257        fldl      (%esp)
258        jmp       .L_2TAG_PACKET_7.0.2
259.L_2TAG_PACKET_6.0.2:
260        mulsd     %xmm0, %xmm0
261        jmp       .L_2TAG_PACKET_2.0.2
262.L_2TAG_PACKET_2.0.2:
263        movsd     %xmm0, 24(%esp)
264        fldl      24(%esp)
265.L_2TAG_PACKET_7.0.2:
266        movl      40(%esp), %ebx
267        movl      %ebp, %esp
268        popl      %ebp
269        ret
270..B2.3:
271END(cosh)
272# -- End  cosh
273
274# Start file scope ASM
275ALIAS_SYMBOL(coshl, cosh);
276# End file scope ASM
277	.section .rodata, "a"
278	.align 16
279	.align 16
280static_const_table:
281	.long	0
282	.long	1072693248
283	.long	0
284	.long	0
285	.long	2851812149
286	.long	1072698941
287	.long	2595802551
288	.long	1016815913
289	.long	1048019041
290	.long	1072704666
291	.long	1398474845
292	.long	3161559171
293	.long	3899555717
294	.long	1072710421
295	.long	427280750
296	.long	3163595548
297	.long	3541402996
298	.long	1072716208
299	.long	2759177317
300	.long	1015903202
301	.long	702412510
302	.long	1072722027
303	.long	3803266087
304	.long	3163328991
305	.long	410360776
306	.long	1072727877
307	.long	1269990655
308	.long	1013024446
309	.long	3402036099
310	.long	1072733758
311	.long	405889334
312	.long	1016154232
313	.long	1828292879
314	.long	1072739672
315	.long	1255956747
316	.long	1016636974
317	.long	728909815
318	.long	1072745618
319	.long	383930225
320	.long	1016078044
321	.long	852742562
322	.long	1072751596
323	.long	667253586
324	.long	1010842135
325	.long	2952712987
326	.long	1072757606
327	.long	3293494651
328	.long	3161168877
329	.long	3490863953
330	.long	1072763649
331	.long	960797498
332	.long	3163997456
333	.long	3228316108
334	.long	1072769725
335	.long	3010241991
336	.long	3159471380
337	.long	2930322912
338	.long	1072775834
339	.long	2599499422
340	.long	3163762623
341	.long	3366293073
342	.long	1072781976
343	.long	3119426314
344	.long	1015169130
345	.long	1014845819
346	.long	1072788152
347	.long	3117910646
348	.long	3162607681
349	.long	948735466
350	.long	1072794361
351	.long	3516338028
352	.long	3163623459
353	.long	3949972341
354	.long	1072800603
355	.long	2068408548
356	.long	1015962444
357	.long	2214878420
358	.long	1072806880
359	.long	892270087
360	.long	3164164998
361	.long	828946858
362	.long	1072813191
363	.long	10642492
364	.long	1016988014
365	.long	586995997
366	.long	1072819536
367	.long	41662348
368	.long	3163676568
369	.long	2288159958
370	.long	1072825915
371	.long	2169144469
372	.long	1015924597
373	.long	2440944790
374	.long	1072832329
375	.long	2492769774
376	.long	1015196030
377	.long	1853186616
378	.long	1072838778
379	.long	3066496371
380	.long	1016705150
381	.long	1337108031
382	.long	1072845262
383	.long	3203724452
384	.long	1015726421
385	.long	1709341917
386	.long	1072851781
387	.long	2571168217
388	.long	1015201075
389	.long	3790955393
390	.long	1072858335
391	.long	2352942462
392	.long	3164228666
393	.long	4112506593
394	.long	1072864925
395	.long	2947355221
396	.long	1015419624
397	.long	3504003472
398	.long	1072871551
399	.long	3594001060
400	.long	3158379228
401	.long	2799960843
402	.long	1072878213
403	.long	1423655381
404	.long	1016070727
405	.long	2839424854
406	.long	1072884911
407	.long	1171596163
408	.long	1014090255
409	.long	171030293
410	.long	1072891646
411	.long	3526460132
412	.long	1015477354
413	.long	4232894513
414	.long	1072898416
415	.long	2383938684
416	.long	1015717095
417	.long	2992903935
418	.long	1072905224
419	.long	2218154406
420	.long	1016276769
421	.long	1603444721
422	.long	1072912069
423	.long	1548633640
424	.long	3163249902
425	.long	926591435
426	.long	1072918951
427	.long	3208833762
428	.long	3163962090
429	.long	1829099622
430	.long	1072925870
431	.long	1016661181
432	.long	3164509581
433	.long	887463927
434	.long	1072932827
435	.long	3596744163
436	.long	3161842742
437	.long	3272845541
438	.long	1072939821
439	.long	928852419
440	.long	3164536824
441	.long	1276261410
442	.long	1072946854
443	.long	300981948
444	.long	1015732745
445	.long	78413852
446	.long	1072953925
447	.long	4183226867
448	.long	3164065827
449	.long	569847338
450	.long	1072961034
451	.long	472945272
452	.long	3160339305
453	.long	3645941911
454	.long	1072968181
455	.long	3814685081
456	.long	3162621917
457	.long	1617004845
458	.long	1072975368
459	.long	82804944
460	.long	1011391354
461	.long	3978100823
462	.long	1072982593
463	.long	3513027190
464	.long	1016894539
465	.long	3049340112
466	.long	1072989858
467	.long	3062915824
468	.long	1014219171
469	.long	4040676318
470	.long	1072997162
471	.long	4090609238
472	.long	1016712034
473	.long	3577096743
474	.long	1073004506
475	.long	2951496418
476	.long	1014842263
477	.long	2583551245
478	.long	1073011890
479	.long	3161094195
480	.long	1016655067
481	.long	1990012071
482	.long	1073019314
483	.long	3529070563
484	.long	3163861769
485	.long	2731501122
486	.long	1073026778
487	.long	1774031855
488	.long	3163518597
489	.long	1453150082
490	.long	1073034283
491	.long	498154669
492	.long	3162536638
493	.long	3395129871
494	.long	1073041828
495	.long	4025345435
496	.long	3163383964
497	.long	917841882
498	.long	1073049415
499	.long	18715565
500	.long	1016707884
501	.long	3566716925
502	.long	1073057042
503	.long	1536826856
504	.long	1015191009
505	.long	3712504873
506	.long	1073064711
507	.long	88491949
508	.long	1016476236
509	.long	2321106615
510	.long	1073072422
511	.long	2171176610
512	.long	1010584347
513	.long	363667784
514	.long	1073080175
515	.long	813753950
516	.long	1016833785
517	.long	3111574537
518	.long	1073087969
519	.long	2606161479
520	.long	3163808322
521	.long	2956612997
522	.long	1073095806
523	.long	2118169751
524	.long	3163784129
525	.long	885834528
526	.long	1073103686
527	.long	1973258547
528	.long	3163310140
529	.long	2186617381
530	.long	1073111608
531	.long	2270764084
532	.long	3164321289
533	.long	3561793907
534	.long	1073119573
535	.long	1157054053
536	.long	1012938926
537	.long	1719614413
538	.long	1073127582
539	.long	330458198
540	.long	3164331316
541	.long	1963711167
542	.long	1073135634
543	.long	1744767757
544	.long	3161622870
545	.long	1013258799
546	.long	1073143730
547	.long	1748797611
548	.long	3161177658
549	.long	4182873220
550	.long	1073151869
551	.long	629542646
552	.long	3163044879
553	.long	3907805044
554	.long	1073160053
555	.long	2257091225
556	.long	3162598983
557	.long	1218806132
558	.long	1073168282
559	.long	1818613052
560	.long	3163597017
561	.long	1447192521
562	.long	1073176555
563	.long	1462857171
564	.long	3163563097
565	.long	1339972927
566	.long	1073184873
567	.long	167908909
568	.long	1016620728
569	.long	1944781191
570	.long	1073193236
571	.long	3993278767
572	.long	3162772855
573	.long	19972402
574	.long	1073201645
575	.long	3507899862
576	.long	1017057868
577	.long	919555682
578	.long	1073210099
579	.long	3121969534
580	.long	1013996802
581	.long	1413356050
582	.long	1073218599
583	.long	1651349291
584	.long	3163716742
585	.long	2571947539
586	.long	1073227145
587	.long	3558159064
588	.long	3164425245
589	.long	1176749997
590	.long	1073235738
591	.long	2738998779
592	.long	3163084420
593	.long	2604962541
594	.long	1073244377
595	.long	2614425274
596	.long	3164587768
597	.long	3649726105
598	.long	1073253063
599	.long	4085036346
600	.long	1016698050
601	.long	1110089947
602	.long	1073261797
603	.long	1451641639
604	.long	1016523249
605	.long	380978316
606	.long	1073270578
607	.long	854188970
608	.long	3161511262
609	.long	2568320822
610	.long	1073279406
611	.long	2732824428
612	.long	1015401491
613	.long	194117574
614	.long	1073288283
615	.long	777528612
616	.long	3164460665
617	.long	2966275557
618	.long	1073297207
619	.long	2176155324
620	.long	3160891335
621	.long	3418903055
622	.long	1073306180
623	.long	2527457337
624	.long	3161869180
625	.long	2682146384
626	.long	1073315202
627	.long	2082178513
628	.long	3164411995
629	.long	1892288442
630	.long	1073324273
631	.long	2446255666
632	.long	3163648957
633	.long	2191782032
634	.long	1073333393
635	.long	2960257726
636	.long	1014791238
637	.long	434316067
638	.long	1073342563
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1336	.long	1062650220
1337	.long	436314137
1338	.long	1056571808
1339	.long	1431655765
1340	.long	1067799893
1341	.long	4160749568
1342	.long	2147483647
1343	.long	0
1344	.long	1072693248
1345	.type	static_const_table,@object
1346	.size	static_const_table,4256
1347	.data
1348	.section .note.GNU-stack, ""
1349# End
1350