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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//    x=2^k * mx, mx in [1,2)
36//
37//    Get B~1/mx based on the output of rcpss instruction (B0)
38//    B = int((B0*2^7+0.5))/2^7
39//
40//    Reduced argument: r=B*mx-1.0 (computed accurately in high and low parts)
41//
42//    Result:  k*log(2) - log(B) + p(r) if |x-1| >= small value (2^-6)  and
43//             p(r) is a degree 7 polynomial
44//             -log(B) read from data table (high, low parts)
45//             Result is formed from high and low parts
46//
47// Special cases:
48//  log(NaN) = quiet NaN, and raise invalid exception
49//  log(+INF) = that INF
50//  log(0) = -INF with divide-by-zero exception raised
51//  log(1) = +0
52//  log(x) = NaN with invalid exception raised if x < -0, including -INF
53//
54/******************************************************************************/
55
56#include <private/bionic_asm.h>
57# -- Begin  log
58ENTRY(log)
59# parameter 1: %xmm0
60..B1.1:
61..___tag_value_log.1:
62        subq      $24, %rsp
63..___tag_value_log.3:
64        movsd     %xmm0, (%rsp)
65..B1.2:
66        movq      $0x3ff0000000000000, %rax
67        movd      %rax, %xmm2
68        movq      $0x77f0000000000000, %rdx
69        movd      %rdx, %xmm3
70        movl      $32768, %ecx
71        movd      %rcx, %xmm4
72        movq      $0xffffe00000000000, %r8
73        movd      %r8, %xmm5
74        movq      %xmm0, %xmm1
75        pextrw    $3, %xmm0, %eax
76        orpd      %xmm2, %xmm0
77        movl      $16352, %ecx
78        psrlq     $27, %xmm0
79        lea       L_tbl(%rip), %r11
80        psrld     $2, %xmm0
81        rcpps     %xmm0, %xmm0
82        psllq     $12, %xmm1
83        pshufd    $228, %xmm5, %xmm6
84        psrlq     $12, %xmm1
85        subl      $16, %eax
86        cmpl      $32736, %eax
87        jae       .L_2TAG_PACKET_0.0.2
88.L_2TAG_PACKET_1.0.2:
89        paddd     %xmm4, %xmm0
90        orpd      %xmm3, %xmm1
91        movd      %xmm0, %edx
92        psllq     $29, %xmm0
93        andpd     %xmm1, %xmm5
94        andpd     %xmm6, %xmm0
95        subsd     %xmm5, %xmm1
96        mulpd     %xmm0, %xmm5
97        andl      $32752, %eax
98        subl      %ecx, %eax
99        cvtsi2sd  %eax, %xmm7
100        mulsd     %xmm0, %xmm1
101        movq      log2(%rip), %xmm6
102        movapd    coeff(%rip), %xmm3
103        subsd     %xmm2, %xmm5
104        andl      $16711680, %edx
105        shrl      $12, %edx
106        movapd    (%r11,%rdx), %xmm0
107        movapd    16+coeff(%rip), %xmm4
108        addsd     %xmm5, %xmm1
109        movapd    32+coeff(%rip), %xmm2
110        mulsd     %xmm7, %xmm6
111        movddup   %xmm1, %xmm5
112        mulsd     8+log2(%rip), %xmm7
113        mulsd     %xmm1, %xmm3
114        addsd     %xmm6, %xmm0
115        mulpd     %xmm5, %xmm4
116        mulpd     %xmm5, %xmm5
117        movddup   %xmm0, %xmm6
118        addsd     %xmm1, %xmm0
119        addpd     %xmm2, %xmm4
120        mulpd     %xmm5, %xmm3
121        subsd     %xmm0, %xmm6
122        mulsd     %xmm1, %xmm4
123        pshufd    $238, %xmm0, %xmm2
124        addsd     %xmm6, %xmm1
125        mulsd     %xmm5, %xmm5
126        addsd     %xmm2, %xmm7
127        addpd     %xmm3, %xmm4
128        addsd     %xmm7, %xmm1
129        mulpd     %xmm5, %xmm4
130        addsd     %xmm4, %xmm1
131        pshufd    $238, %xmm4, %xmm5
132        addsd     %xmm5, %xmm1
133        addsd     %xmm1, %xmm0
134        jmp       ..B1.5
135.L_2TAG_PACKET_0.0.2:
136        movq      (%rsp), %xmm0
137        movq      (%rsp), %xmm1
138        addl      $16, %eax
139        cmpl      $32768, %eax
140        jae       .L_2TAG_PACKET_2.0.2
141        cmpl      $16, %eax
142        jb        .L_2TAG_PACKET_3.0.2
143.L_2TAG_PACKET_4.0.2:
144        addsd     %xmm0, %xmm0
145        jmp       ..B1.5
146.L_2TAG_PACKET_5.0.2:
147        ja        .L_2TAG_PACKET_4.0.2
148        cmpl      $0, %edx
149        ja        .L_2TAG_PACKET_4.0.2
150        jmp       .L_2TAG_PACKET_6.0.2
151.L_2TAG_PACKET_3.0.2:
152        xorpd     %xmm1, %xmm1
153        addsd     %xmm0, %xmm1
154        movd      %xmm1, %edx
155        psrlq     $32, %xmm1
156        movd      %xmm1, %ecx
157        orl       %ecx, %edx
158        cmpl      $0, %edx
159        je        .L_2TAG_PACKET_7.0.2
160        xorpd     %xmm1, %xmm1
161        movl      $18416, %eax
162        pinsrw    $3, %eax, %xmm1
163        mulsd     %xmm1, %xmm0
164        movq      %xmm0, %xmm1
165        pextrw    $3, %xmm0, %eax
166        orpd      %xmm2, %xmm0
167        psrlq     $27, %xmm0
168        movl      $18416, %ecx
169        psrld     $2, %xmm0
170        rcpps     %xmm0, %xmm0
171        psllq     $12, %xmm1
172        pshufd    $228, %xmm5, %xmm6
173        psrlq     $12, %xmm1
174        jmp       .L_2TAG_PACKET_1.0.2
175.L_2TAG_PACKET_2.0.2:
176        movd      %xmm1, %edx
177        psrlq     $32, %xmm1
178        movd      %xmm1, %ecx
179        addl      %ecx, %ecx
180        cmpl      $-2097152, %ecx
181        jae       .L_2TAG_PACKET_5.0.2
182        orl       %ecx, %edx
183        cmpl      $0, %edx
184        je        .L_2TAG_PACKET_7.0.2
185.L_2TAG_PACKET_6.0.2:
186        xorpd     %xmm1, %xmm1
187        xorpd     %xmm0, %xmm0
188        movl      $32752, %eax
189        pinsrw    $3, %eax, %xmm1
190        mulsd     %xmm1, %xmm0
191        movl      $3, 16(%rsp)
192        jmp       .L_2TAG_PACKET_8.0.2
193.L_2TAG_PACKET_7.0.2:
194        xorpd     %xmm1, %xmm1
195        xorpd     %xmm0, %xmm0
196        movl      $49136, %eax
197        pinsrw    $3, %eax, %xmm0
198        divsd     %xmm1, %xmm0
199        movl      $2, 16(%rsp)
200.L_2TAG_PACKET_8.0.2:
201        movq      %xmm0, 8(%rsp)
202..B1.3:
203        movq      8(%rsp), %xmm0
204.L_2TAG_PACKET_9.0.2:
205..B1.5:
206        addq      $24, %rsp
207..___tag_value_log.4:
208        ret
209..___tag_value_log.5:
210END(log)
211# -- End  log
212	.section .rodata, "a"
213	.align 16
214	.align 16
215L_tbl:
216	.long	4277811200
217	.long	1072049730
218	.long	2479318832
219	.long	1026487127
220	.long	2854492160
221	.long	1072033410
222	.long	215631550
223	.long	1025638968
224	.long	1547061248
225	.long	1072017216
226	.long	2886781435
227	.long	1026423395
228	.long	649825280
229	.long	1072001146
230	.long	4281533405
231	.long	1024038923
232	.long	646346752
233	.long	1071985198
234	.long	1562735921
235	.long	1023790276
236	.long	2203734016
237	.long	1071969370
238	.long	1838397691
239	.long	3173936209
240	.long	1872169984
241	.long	1071953661
242	.long	3981202460
243	.long	1022325013
244	.long	669557760
245	.long	1071938069
246	.long	4182597802
247	.long	3173174122
248	.long	4076413952
249	.long	1071922591
250	.long	1209029111
251	.long	3170736207
252	.long	556125184
253	.long	1071907228
254	.long	821086028
255	.long	3173437049
256	.long	204914688
257	.long	1071891976
258	.long	2097025986
259	.long	3171071798
260	.long	387545088
261	.long	1071876834
262	.long	3142936996
263	.long	3173092218
264	.long	2912783360
265	.long	1071861800
266	.long	2502420140
267	.long	1024505919
268	.long	1144260608
269	.long	1071846874
270	.long	3315658140
271	.long	3173469843
272	.long	1471209472
273	.long	1071832053
274	.long	129621009
275	.long	3172443877
276	.long	1829683200
277	.long	1071817336
278	.long	3885467693
279	.long	1025535275
280	.long	288676864
281	.long	1071802722
282	.long	86139472
283	.long	3171639793
284	.long	3636378624
285	.long	1071788208
286	.long	1850238587
287	.long	1024654342
288	.long	1606817792
289	.long	1071773795
290	.long	3388899795
291	.long	3173675586
292	.long	1236164608
293	.long	1071759480
294	.long	3983599207
295	.long	1020046558
296	.long	1089616896
297	.long	1071745262
298	.long	4171974224
299	.long	1024773198
300	.long	4143093760
301	.long	1071731139
302	.long	2727587401
303	.long	3173965207
304	.long	600267776
305	.long	1071717112
306	.long	3147685042
307	.long	3173353031
308	.long	2249313280
309	.long	1071703177
310	.long	125835074
311	.long	1025255832
312	.long	3805303808
313	.long	1071689334
314	.long	2289991207
315	.long	1025460331
316	.long	87278592
317	.long	1071675583
318	.long	1106114045
319	.long	1025933602
320	.long	3195405312
321	.long	1071661920
322	.long	3885316576
323	.long	3171206239
324	.long	3853649920
325	.long	1071648346
326	.long	2977069852
327	.long	3171236771
328	.long	2944026624
329	.long	1071625048
330	.long	1008093493
331	.long	1023444474
332	.long	3993180160
333	.long	1071598247
334	.long	1862355595
335	.long	1024642533
336	.long	1454641152
337	.long	1071571617
338	.long	1514603089
339	.long	1026500596
340	.long	3286085632
341	.long	1071545154
342	.long	1400028424
343	.long	3173279056
344	.long	438773760
345	.long	1071518858
346	.long	120727864
347	.long	3172148914
348	.long	1212979200
349	.long	1071492725
350	.long	1625055594
351	.long	3172901933
352	.long	1189017600
353	.long	1071466754
354	.long	3920062376
355	.long	1025727407
356	.long	403064832
357	.long	1071440943
358	.long	1053271728
359	.long	3171391427
360	.long	3343210496
361	.long	1071415289
362	.long	3243395502
363	.long	3173627613
364	.long	1765777408
365	.long	1071389792
366	.long	2145968512
367	.long	1026354304
368	.long	461430784
369	.long	1071364449
370	.long	4094322285
371	.long	1026021467
372	.long	71706624
373	.long	1071339258
374	.long	763632021
375	.long	1024496933
376	.long	1380503552
377	.long	1071314217
378	.long	1383547992
379	.long	3173088453
380	.long	1015732224
381	.long	1071289325
382	.long	3198646877
383	.long	1025390322
384	.long	35977216
385	.long	1071264580
386	.long	2141026805
387	.long	1025754693
388	.long	3927306240
389	.long	1071239979
390	.long	282116272
391	.long	3173394334
392	.long	1125341184
393	.long	1071215523
394	.long	2768427504
395	.long	3172279059
396	.long	1666971648
397	.long	1071191208
398	.long	786837629
399	.long	3172427445
400	.long	2827694080
401	.long	1071167033
402	.long	3857122416
403	.long	3173014241
404	.long	2003683328
405	.long	1071142997
406	.long	859010954
407	.long	1026545007
408	.long	1004017664
409	.long	1071119098
410	.long	3356644970
411	.long	3173458064
412	.long	1753020416
413	.long	1071095334
414	.long	788338552
415	.long	1026157693
416	.long	1992718336
417	.long	1071071704
418	.long	1239179443
419	.long	1026394889
420	.long	3870234624
421	.long	1071048206
422	.long	2082614663
423	.long	1024926053
424	.long	1050437632
425	.long	1071024840
426	.long	660007840
427	.long	1025548499
428	.long	188395520
429	.long	1071001603
430	.long	3878792704
431	.long	3173889571
432	.long	3747176448
433	.long	1070978493
434	.long	144991708
435	.long	3171552042
436	.long	1405669376
437	.long	1070955511
438	.long	3999088879
439	.long	1025486317
440	.long	121151488
441	.long	1070932654
442	.long	2170865497
443	.long	1026473584
444	.long	2652319744
445	.long	1070909920
446	.long	453695652
447	.long	3173916809
448	.long	3262236672
449	.long	1070887309
450	.long	157800053
451	.long	3173984206
452	.long	601221120
453	.long	1070864820
454	.long	3968917661
455	.long	1023992886
456	.long	1999843328
457	.long	1070842450
458	.long	3053895004
459	.long	1024998228
460	.long	1992167424
461	.long	1070820199
462	.long	2968614856
463	.long	1024552653
464	.long	3788726272
465	.long	1070798065
466	.long	3542170808
467	.long	3173573242
468	.long	2094829568
469	.long	1070776048
470	.long	1246758132
471	.long	1026202874
472	.long	288675840
473	.long	1070754146
474	.long	3747328950
475	.long	1026331585
476	.long	1829681152
477	.long	1070732357
478	.long	3125197546
479	.long	1024100318
480	.long	1666869248
481	.long	1070710681
482	.long	1363656119
483	.long	1026336493
484	.long	3417110528
485	.long	1070689116
486	.long	4154791553
487	.long	1026267853
488	.long	2183653376
489	.long	1070667662
490	.long	1671819292
491	.long	3173785870
492	.long	1734434816
493	.long	1070646317
494	.long	373091049
495	.long	1025972363
496	.long	1615681536
497	.long	1070625080
498	.long	384650897
499	.long	1022926043
500	.long	1445382144
501	.long	1070603950
502	.long	344320330
503	.long	3172397196
504	.long	1823715328
505	.long	1070569756
506	.long	3389841200
507	.long	1025231852
508	.long	3839688704
509	.long	1070527917
510	.long	1706790417
511	.long	3167363349
512	.long	4293332992
513	.long	1070486286
514	.long	1614935088
515	.long	1019351591
516	.long	2966720512
517	.long	1070444861
518	.long	4145393717
519	.long	3173711658
520	.long	4066729984
521	.long	1070403639
522	.long	1974925028
523	.long	3171437182
524	.long	3337621504
525	.long	1070362619
526	.long	3314953170
527	.long	3169971314
528	.long	943448064
529	.long	1070321799
530	.long	1498682038
531	.long	3173862340
532	.long	1465634816
533	.long	1070281176
534	.long	1319952810
535	.long	3171693965
536	.long	1015734272
537	.long	1070240749
538	.long	1347821929
539	.long	3173544515
540	.long	118001664
541	.long	1070200516
542	.long	1751482746
543	.long	1026134093
544	.long	3707174912
545	.long	1070160474
546	.long	1486946159
547	.long	1023930920
548	.long	3946381312
549	.long	1070120623
550	.long	2867408081
551	.long	3171368276
552	.long	1699848192
553	.long	1070080961
554	.long	2590187139
555	.long	1025379803
556	.long	2235846656
557	.long	1070041485
558	.long	1888568069
559	.long	3172754960
560	.long	2339729408
561	.long	1070002194
562	.long	3852214753
563	.long	3173323149
564	.long	3196850176
565	.long	1069963086
566	.long	742141560
567	.long	1025101707
568	.long	1800683520
569	.long	1069924160
570	.long	3949500444
571	.long	3172102179
572	.long	3835801600
573	.long	1069885413
574	.long	3848895943
575	.long	1025913832
576	.long	2201202688
577	.long	1069846845
578	.long	1425913464
579	.long	1025868665
580	.long	2778279936
581	.long	1069808453
582	.long	2120889677
583	.long	3173831128
584	.long	2954203136
585	.long	1069770236
586	.long	592147081
587	.long	1019621288
588	.long	210141184
589	.long	1069732193
590	.long	3414275233
591	.long	1023647084
592	.long	709476352
593	.long	1069694321
594	.long	2413027164
595	.long	1024462115
596	.long	2116284416
597	.long	1069656619
598	.long	1144559924
599	.long	1026336654
600	.long	2183651328
601	.long	1069619086
602	.long	3459057650
603	.long	1025634168
604	.long	3047047168
605	.long	1069581720
606	.long	1879674924
607	.long	3173508573
608	.long	970711040
609	.long	1069541521
610	.long	1335954173
611	.long	3173332182
612	.long	2198478848
613	.long	1069467449
614	.long	2951103968
615	.long	3173892200
616	.long	1669611520
617	.long	1069393703
618	.long	531044147
619	.long	1025149248
620	.long	29114368
621	.long	1069320280
622	.long	3327831251
623	.long	1025918673
624	.long	2376949760
625	.long	1069247176
626	.long	737634533
627	.long	3172176000
628	.long	1085390848
629	.long	1069174390
630	.long	3108243400
631	.long	3171828406
632	.long	1566130176
633	.long	1069101918
634	.long	985483226
635	.long	1025708380
636	.long	792780800
637	.long	1069029758
638	.long	4184866295
639	.long	1024426204
640	.long	183156736
641	.long	1068957907
642	.long	2845699378
643	.long	1022107277
644	.long	1301782528
645	.long	1068886362
646	.long	1012735262
647	.long	3173804294
648	.long	1562411008
649	.long	1068815121
650	.long	2197086703
651	.long	3170187813
652	.long	2815549440
653	.long	1068744181
654	.long	2782613207
655	.long	1026345054
656	.long	2756124672
657	.long	1068673540
658	.long	2929486205
659	.long	3173037800
660	.long	3511050240
661	.long	1068603195
662	.long	1443733147
663	.long	3173331549
664	.long	3047047168
665	.long	1068533144
666	.long	1879674924
667	.long	3172459997
668	.long	3221667840
669	.long	1068427825
670	.long	1338588027
671	.long	3171815742
672	.long	3453861888
673	.long	1068288883
674	.long	1205348359
675	.long	3172624626
676	.long	3506110464
677	.long	1068150514
678	.long	893105198
679	.long	1025571866
680	.long	346013696
681	.long	1068012714
682	.long	3495569021
683	.long	3172563349
684	.long	4074029056
685	.long	1067875476
686	.long	3961106338
687	.long	3171065595
688	.long	3559784448
689	.long	1067738798
690	.long	1975385384
691	.long	3173783155
692	.long	797769728
693	.long	1067602675
694	.long	3760305787
695	.long	1026047642
696	.long	2313633792
697	.long	1067467101
698	.long	1559353171
699	.long	1023480256
700	.long	3960766464
701	.long	1067213778
702	.long	1067365107
703	.long	1025865926
704	.long	684261376
705	.long	1066944805
706	.long	844762164
707	.long	3173687482
708	.long	630718464
709	.long	1066676905
710	.long	2458269694
711	.long	1024033081
712	.long	1486061568
713	.long	1066410070
714	.long	115537874
715	.long	3173243995
716	.long	2743664640
717	.long	1065886792
718	.long	3665098304
719	.long	3173471607
720	.long	1971912704
721	.long	1065357333
722	.long	2577214440
723	.long	3171993451
724	.long	1498939392
725	.long	1064306693
726	.long	3409036923
727	.long	1025599151
728	.long	0
729	.long	0
730	.long	0
731	.long	2147483648
732	.type	L_tbl,@object
733	.size	L_tbl,2064
734	.align 16
735log2:
736	.long	4277811200
737	.long	1067855426
738	.long	2479318832
739	.long	1022292823
740	.type	log2,@object
741	.size	log2,16
742	.align 16
743coeff:
744	.long	2454267026
745	.long	1069697316
746	.long	0
747	.long	3218079744
748	.long	1030730101
749	.long	3217380702
750	.long	1431655765
751	.long	1070945621
752	.long	2576980378
753	.long	1070176665
754	.long	0
755	.long	3219128320
756	.type	coeff,@object
757	.size	coeff,48
758	.data
759	.section .note.GNU-stack, ""
760// -- Begin DWARF2 SEGMENT .eh_frame
761	.section .eh_frame,"a",@progbits
762.eh_frame_seg:
763	.align 1
764	.4byte 0x00000014
765	.8byte 0x00527a0100000000
766	.8byte 0x08070c1b01107801
767	.4byte 0x00000190
768	.4byte 0x0000001c
769	.4byte 0x0000001c
770	.4byte ..___tag_value_log.1-.
771	.4byte ..___tag_value_log.5-..___tag_value_log.1
772	.2byte 0x0400
773	.4byte ..___tag_value_log.3-..___tag_value_log.1
774	.2byte 0x200e
775	.byte 0x04
776	.4byte ..___tag_value_log.4-..___tag_value_log.3
777	.2byte 0x080e
778	.byte 0x00
779# End
780