aboutsummaryrefslogtreecommitdiff
path: root/sysdeps/ia64/fpu/s_tanhf.S
blob: e4e91cfe6397e401661b6f6e593a8b432b88b7a2 (plain)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
580
581
.file "tanhf.s"


// Copyright (c) 2001 - 2005, Intel Corporation
// All rights reserved.
//
// Contributed 2001 by the Intel Numerics Group, Intel Corporation
//
// Redistribution and use in source and binary forms, with or without
// modification, are permitted provided that the following conditions are
// met:
//
// * Redistributions of source code must retain the above copyright
// notice, this list of conditions and the following disclaimer.
//
// * Redistributions in binary form must reproduce the above copyright
// notice, this list of conditions and the following disclaimer in the
// documentation and/or other materials provided with the distribution.
//
// * The name of Intel Corporation may not be used to endorse or promote
// products derived from this software without specific prior written
// permission.

// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS 
// "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT 
// LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
// A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL INTEL OR ITS 
// CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
// EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, 
// PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR 
// PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY 
// OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY OR TORT (INCLUDING
// NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS 
// SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. 
// 
// Intel Corporation is the author of this code, and requests that all
// problem reports or change requests be submitted to it directly at 
// http://www.intel.com/software/products/opensource/libraries/num.htm.
//
// History
//==============================================================
// 05/30/01 Initial version
// 05/20/02 Cleaned up namespace and sf0 syntax
// 02/10/03 Reordered header: .section, .global, .proc, .align
// 03/31/05 Reformatted delimiters between data tables
//
// API
//==============================================================
// float tanhf(float)
//
// Overview of operation
//==============================================================
// Background
//
//
// There are 9 paths:
// 1. x = +/-0.0
//    Return tanhf(x) = +/-0.0
//
// 2. 0.0 < |x| < 0.3125
//    Return tanhf(x) = x + x^3*Pol3(x^2),
//    where Pol3(x^2) = C3*x^6 + C2*x^4 + C1*x^2 + C0
//
// 3. 0.3125 <= |x| < 8.0
//    Return tanhf(x) = sign(x)*PolD(x)*PolC(|x|) + sign(x)*PolA(|x|),
//    where sign(x)*PolD(x) = sign(x)*(|x|^7 + D2*x^6 + D1*|x|^5 + D0*x^4),
//          PolC(|x|) = B0*x^4 + C3*|x|^3 + C2*|x|^2 + C1*|x| + C0,
//          PolA(|x|) = A3|x|^3 + A2*x^2 + A1*|x| + A0
//
//    Actually range 0.3125<=|x|< 8.0 is split to 5 subranges.
//    For each subrange there is particular set of coefficients.
//    Below is the list of subranges:
//    3.1 0.3125 <= |x| < 0.5
//    3.2 0.5 <= |x| < 1.0
//    3.3 1.0 <= |x| < 2.0
//    3.4 2.0 <= |x| < 4.0
//    3.5 4.0 <= |x| < 8.0
//
// 4. 8.0 <= |x| < 9.125
//    Return tanhf(x) = sign(x)*(A3|x|^3 + A2*x^2 + A1*|x| + A0)
//
// 5. 9.125 <= |x| < +INF
//    Return tanhf(x) = sign(x)*(1.0d - 2^(-52))
//
// 6. |x| = INF
//    Return tanhf(x) = sign(x) * 1.0
//
// 7. x = [S,Q]NaN 
//    Return tanhf(x) = QNaN
//
// 8. x is positive denormal
//    Return tanhf(x) = x - x^2
//
// 9. x is negative denormal
//    Return tanhf(x) = x + x^2
//
// Registers used
//==============================================================
// Floating Point registers used: 
// f8, input
// f32 -> f59

// General registers used:  
// r32 -> r46, r2, r3

// Predicate registers used:
// p0, p6 -> p15

// p6           to filter out case when x = [Q,S]NaN or +/-0
// p7           to filter out case when x = denormal
// p8           set if |x| >= 0.3125, used also to process denormal input
// p9           to filter out case when |x| = inf
// p10          to filter out case when |x| < 0.3125
// p11          to filter out case when 0.3125 <= |x| < 9.125
// p12          to filter out case when |x| >= 9.125
// p13          to filter out case when 8.0 <= |x| < 9.125
// p14          set to 1 for positive x
// p15          set to 1 for negative x

// Assembly macros
//==============================================================
rDataPtr           = r2
rDataPtr1          = r3

rBias              = r33
rCoeffAddr3        = r34
rNearSaturation    = r35
rCoeffAddr1        = r36
rCoeffAddr2        = r37
rOffset2           = r38
rBias2             = r39
rMask              = r40
rArg               = r41
rBound             = r42
rSignBit           = r43
rAbsArg            = r44
rDataPtr2          = r45
rSaturation        = r46

//==============================================================
fA0                = f32
fA1                = f33
fA2                = f34
fA3                = f35
fC0                = f36
fC1                = f37
fC2                = f38
fC3                = f39
fD0                = f40
fD1                = f41
fD2                = f42
fB0                = f43
fArgSqr            = f44
fAbsArg            = f45
fSignumX           = f46
fArg4              = f47
fArg4Sgn           = f48
fArg3              = f49
fArg3Sgn           = f50
fArg7Sgn           = f51
fArg6Sgn           = f52
fPolC              = f53
fPolCTmp           = f54
fPolA              = f55
fPolATmp           = f56
fPolD              = f57
fPolDTmp           = f58
fArgSqrSgn         = f59

// Data tables
//==============================================================

RODATA

.align 16

LOCAL_OBJECT_START(tanhf_data)
// Polynomial coefficients for the tanh(x), 0.3125 <= |x| < 0.5
data8 0x3F9BEEDFDD177D7B // C0
data8 0x3F970D10C7F32458 // C1
data8 0x3F766D6B051F3A38 // C2
data8 0xBF732F2001B23402 // C3
data8 0xBF854BE1CE1ED499 // D0
data8 0x4013C944F3999A16 // D1
data8 0xC01106C6975222C0 // D2
data8 0x3F783D5ACCF9EBE8 // B0
// Polynomial coefficients for the tanh(x), 0.5 <= |x| < 1.0
data8 0xBF5D631440786869 // C0
data8 0xBF575D79A0D52069 // C1
data8 0xBF7E2237B7EFC705 // C2
data8 0x3F6A7ACBC273041F // C3
data8 0xC040E32EA52D91EB // D0
data8 0x403D19463E5DB4D7 // D1
data8 0xC02216F61F759F39 // D2
data8 0xBF55B4EA0B844BE7 // B0
// Polynomial coefficients for the tanh(x), 1.0 <= |x| < 2.0
data8 0x3F8637DBE5B3E690 // C0
data8 0xBF7F7FEC158C07F5 // C1
data8 0x3F711C586706838A // C2
data8 0xBF50EF7EF605554E // C3
data8 0xC054D45448354E25 // D0
data8 0x404ADFEEA282E730 // D1
data8 0xC028AEE456D59549 // D2
data8 0x3F25232D1BED59A8 // B0
// Polynomial coefficients for the tanh(x), 2.0 <= |x| < 4.0
data8 0xBF52602285F2D06C // C0
data8 0x3F2E57C298FFE1E0 // C1
data8 0xBF15ED575DB3C811 // C2
data8 0x3EE428878A08525C // C3
data8 0xC0895A26849039C1 // D0
data8 0x406E3C60BBFBB575 // D1
data8 0xC03A06F62867C75A // D2
data8 0xBEB114C70F1C723E // B0
// Polynomial coefficients for the tanh(x), 4.0 <= |x| < 8.0
data8 0x3EF4B22BD17039A3 // C0
data8 0xBEB704ADC040C57F // C1
data8 0x3E937A98288AFE1A // C2
data8 0xBE4F33B2C9FFE7E7 // C3
data8 0xC0BE48CFADE2431E // D0
data8 0x4090E74249760FDD // D1
data8 0xC04B6F537FCF2F1E // D2
data8 0x3E0DCD879C91ADEA // B0
// Polynomial coefficients for the tanh(x), -0.3125 < x < 0.3125 
data8 0xBFD555551E8245B7 // A0
data8 0x3FC110E63F52E689 // A1
data8 0xBFAB8CD6A5B7BAFA // A2
data8 0x3F945D467FCEB553 // A3
// Polynomial coefficients for the tanh(x), 0.3125 <= |x| < 0.5
data8 0xBE3DCC92FCAECBB6 // A0
data8 0x3FF0000043B7D267 // A1
data8 0xBED18BF28ACFC4B1 // A2
data8 0xBFD554A56F82837E // A3
// Polynomial coefficients for the tanh(x), 0.5 <= |x| < 1.0
data8 0x3EFD6054758539F9 // A0
data8 0x3FEFFBFC77198EBE // A1
data8 0x3F700327CA98D237 // A2
data8 0xBFD68955F5BB2FA1 // A3
// Polynomial coefficients for the tanh(x), 1.0 <= |x| < 2.0
data8 0xBF71A53F229DF01B // A0
data8 0x3FF0AECFD730DE50 // A1
data8 0xBFC882F88E5DF3BA // A2
data8 0x3FC6EDF212CA2A8D // A3
// Polynomial coefficients for the tanh(x), 2.0 <= |x| < 4.0
data8 0xBFAF0B712E9EDA47 // A0
data8 0x3FF1C208080BEA64 // A1
data8 0x3FC3D29B20C8946E // A2
data8 0xBFF04514ED900A6A // A3
// Polynomial coefficients for the tanh(x), 4.0 <= |x| < 8.0
data8 0xBFB1DEA49A831CBC // A0
data8 0x3FFA729FC7085674 // A1
data8 0xBFF2F44D923A8FA4 // A2
data8 0x3FE092FC5712227E // A3
// Polynomial coefficients for the tanh(x), 8.0 <= |x| <= 9.125 
data8 0x3FEFFF5769EE3041 // A0
data8 0x3EFBBF148D850891 // A1
data8 0xBEC86BCEF0F5C2FE // A2
data8 0x3E7CBA4F3A885A5C // A3
//
data8 0x3FEFFFFFFFFFFFFF // 1.0 - epsilon
LOCAL_OBJECT_END(tanhf_data)

.section .text
GLOBAL_LIBM_ENTRY(tanhf)

{ .mfi
      alloc          r32 = ar.pfs, 1, 14, 0, 0
      fmerge.s       fAbsArg = f1, f8             // |x|
      addl           rMask = 0x806, r0
}
{ .mfi
      addl           rDataPtr = @ltoff(tanhf_data), gp
      fma.s1         fArgSqr = f8, f8, f0         // x^2
      adds           rSignBit = 0x1, r0
}
;;

{ .mfi
      getf.s         rArg = f8                    // x in GR 
      fclass.m       p7,p0 = f8, 0x0b             // is x denormal ?
      // sign bit and 2 most bits in significand
      shl            rMask = rMask, 20               
}
{ .mfi
      ld8            rDataPtr = [rDataPtr]
      nop.f          0
      adds           rBias2 = 0x1F4, r0
}
;;

{ .mfi
      adds           rNearSaturation = 0x14, r0
      fmerge.s       fSignumX = f8, f1            // signum(x)
      shl            rSignBit = rSignBit, 31      // mask for sign bit
}
{ .mfi
      adds           rBound = 0x3EA, r0
      nop.f          0
      addl           rSaturation = 0x4112, r0
}
;;

{ .mfi
      andcm          rOffset2 = rArg, rMask
      fclass.m       p6,p0 = f8, 0xc7             // is x [S,Q]NaN or +/-0 ?
      shl            rBound = rBound, 20          // 1.0f in GR
}
{ .mfb
      andcm          rAbsArg = rArg, rSignBit     // |x| in GR
      nop.f          0
(p7)  br.cond.spnt   tanhf_denormal               // branch out if x is denormal
}
;;

{ .mfi
      adds           rCoeffAddr2 = 352, rDataPtr
      fclass.m       p9,p0 = f8, 0x23            // is x +/- inf?
      shr            rOffset2 = rOffset2, 21
}
{ .mfi
      cmp.lt         p10, p8 = rAbsArg, rBound   // |x| < 0.3125? 
      nop.f          0
      adds           rCoeffAddr3 = 16, rDataPtr
}
;;

{ .mfi
(p8)  sub            rBias = rOffset2, rBias2
      fma.s1         fArg4 = fArgSqr, fArgSqr, f0 // x^4
      shl            rSaturation = rSaturation, 16
}
{ .mfb
(p10) adds           rBias = 0x14, r0
(p6)  fma.s.s0       f8 = f8,f1,f8                // NaN or +/-0
(p6)  br.ret.spnt    b0                           // exit for x = NaN or +/-0
}
;;

{ .mfi
      shladd         rCoeffAddr1 = rBias, 4, rDataPtr
      fma.s1         fArg3Sgn = fArgSqr, f8, f0  // sign(x)*|x|^3
      // is |x| < 9.125? 
      cmp.lt         p11, p12 = rAbsArg, rSaturation  
}
{ .mfi
      shladd         rCoeffAddr3 = rBias, 4, rCoeffAddr3
      fma.s1         fArg3 = fArgSqr, fAbsArg, f0 // |x|^3
      shladd         rCoeffAddr2 = rBias, 3, rCoeffAddr2
}
;;

{ .mfi
(p11) ldfpd          fC0, fC1 = [rCoeffAddr1]
(p9)  fmerge.s       f8 = f8,f1                   // +/- inf
(p12) adds           rDataPtr = 544, rDataPtr 
}
{ .mfb
(p11) ldfpd          fC2, fC3 = [rCoeffAddr3], 16
      nop.f          0
(p9)  br.ret.spnt    b0                           // exit for x = +/- inf
}
;;

{ .mfi
(p11) ldfpd          fA0, fA1 = [rCoeffAddr2], 16
      nop.f          0
(p8)  cmp.eq.unc     p13, p0 = rBias, rNearSaturation
}
{ .mfi
      add            rCoeffAddr1 = 48, rCoeffAddr1
      nop.f          0
      nop.i          0
}
;;

{ .mfi
(p11) ldfpd          fD0, fD1 = [rCoeffAddr3]
      nop.f          0
      nop.i          0
}
{ .mfb
(p11) ldfpd          fD2, fB0 = [rCoeffAddr1]
      // sign(x)*|x|^2
      fma.s1         fArgSqrSgn = fArgSqr, fSignumX, f0
(p10) br.cond.spnt   tanhf_near_zero
}
;;

{ .mfi
(p11) ldfpd          fA2, fA3 = [rCoeffAddr2], 16
      fcmp.lt.s1     p15, p14 = f8,f0
      nop.i          0
}
{ .mfb
(p12) ldfd           fA0 = [rDataPtr]
      fma.s1         fArg4Sgn = fArg4, fSignumX, f0 // sign(x)*|x|^4
(p12) br.cond.spnt   tanhf_saturation
}
;;
{ .mfi
      nop.m          0
      fma.s1         fArg7Sgn = fArg4, fArg3Sgn, f0  // sign(x)*|x|^7
      nop.i          0
}
{ .mfb
      nop.m          0
      fma.s1         fArg6Sgn = fArg3, fArg3Sgn, f0  // sign(x)*|x|^6
(p13) br.cond.spnt   tanhf_close_to_saturation      
}
;;

{ .mfi
      nop.m          0
      fma.s1         fPolC = fC3, fAbsArg, fC2    // C3*|x| + C2
      nop.i          0
}
{ .mfi
      nop.m          0
      fma.s1         fPolCTmp = fC1, fAbsArg, fC0 // C1*|x| + C0
      nop.i          0
};;

{ .mfi
      nop.m          0
      fma.s1         fPolA = fA1, fAbsArg, fA0    // A1*|x| + A0
      nop.i          0
}
;;

{ .mfi
      nop.m          0
      fma.s1         fPolD = fD1, fAbsArg, fD0    // D1*|x| + D0
      nop.i          0
}
{ .mfi
      nop.m          0
      // sign(x)*(|x|^7 + D2*x^6)
      fma.s1         fPolDTmp = fArg6Sgn, fD2, fArg7Sgn
      nop.i          0
};;

{ .mfi
      nop.m          0
      fma.s1         fPolATmp = fA3, fAbsArg, fA2  // A3*|x| + A2 
      nop.i          0
}
{ .mfi
      nop.m          0
      fma.s1         fB0 = fB0, fArg4, f0          // B0*x^4
      nop.i          0
};;

{ .mfi
      nop.m          0
      // C3*|x|^3 + C2*x^2 + C1*|x| + C0
      fma.s1         fPolC = fPolC, fArgSqr, fPolCTmp  
      nop.i          0
}
;;

{ .mfi
      nop.m          0
      // PolD = sign(x)*(|x|^7 + D2*x^6 + D1*|x|^5 + D0*x^4)
      fma.d.s1       fPolD = fPolD, fArg4Sgn, fPolDTmp  
      nop.i          0
}
;;

{ .mfi
      nop.m          0
      // PolA = A3|x|^3 + A2*x^2 + A1*|x| + A0 
      fma.d.s1       fPolA = fPolATmp, fArgSqr, fPolA 
      nop.i          0
}
;;                 

{ .mfi
      nop.m          0
      // PolC = B0*x^4 + C3*|x|^3 + C2*|x|^2 + C1*|x| + C0 
      fma.d.s1       fPolC = fPolC, f1, fB0 
      nop.i          0
}
;;     

{ .mfi
      nop.m          0
(p14) fma.s.s0       f8 = fPolC, fPolD, fPolA     // for positive x
      nop.i          0                           
}
{ .mfb
      nop.m          0
(p15) fms.s.s0       f8 = fPolC, fPolD, fPolA     // for negative x
      br.ret.sptk    b0                           // Exit for 0.3125 <=|x|< 8.0
};;


// Here if |x| < 0.3125
tanhf_near_zero:
{ .mfi
      nop.m          0
      fma.s1         fPolC = fC3, fArgSqr, fC2    // C3*x^2 + C2
      nop.i          0
}
{ .mfi
      nop.m          0
      fma.s1         fPolCTmp = fC1, fArgSqr, fC0  // C1*x^2 + C0
      nop.i          0
};;

{ .mfi
      nop.m          0
      fma.s1         fPolC = fPolC, fArg4, fPolCTmp // C3*x^6 + C2*x^4 + C1*x^2 + C0
      nop.i          0
};;

{ .mfb
      nop.m          0
      // x + x^3*(C3*x^6 + C2*x^4 + C1*x^2 + C0)
      fma.s.s0       f8 = fPolC, fArg3Sgn, f8
      br.ret.sptk    b0                           // Exit for |x| < 0.3125
};;

// Here if 9.125 <= |x| < +inf
tanhf_saturation:
{ .mfb
      nop.m          0
      fma.s.s0       f8 = fA0, fSignumX, f0       // sign(x)*(1.0d - 2^(-52))
      // Exit for 9.125 <= |x| < +inf
      br.ret.sptk    b0                           // Exit for 9.125 <=|x|< +inf
}
;;
      
// Here if  8.0 <= |x| < 9.125
tanhf_close_to_saturation:
{ .mfi
      nop.m          0
      fma.s1         fPolATmp = fA1, fAbsArg, fA0 // A1*|x| + A0
      nop.i          0
}
{ .mfi
      nop.m          0
      fma.s1         fPolA = fA3, fAbsArg, fA2    // A3*|x| + A2
      nop.i          0
}    
;;

.pred.rel "mutex", p14, p15
{ .mfi
      nop.m          0
      // for positive x
(p14) fma.s.s0       f8 = fPolA, fArgSqr, fPolATmp
      nop.i          0                           
}
{ .mfb
      nop.m          0
      // for negative x
(p15) fms.s.s0       f8 = fPolA, fArgSqrSgn, fPolATmp
      br.ret.sptk    b0                           // Exit for 8.0 <=|x|< 9.125
};;

// Here if x is single precision denormal
tanhf_denormal:
{ .mfi
      nop.m          0
      fclass.m       p7,p8 = f8, 0x0a             // is x -denormal ?
      nop.i          0
}
;;

{ .mfi
      nop.m          0
(p7)  fma.s.s0       f8 = f8,f8,f8                // -denormal
      nop.i          0
}
{ .mfb
      nop.m          0
(p8)  fnma.s.s0      f8 = f8,f8,f8                // +denormal
      br.ret.sptk    b0                           // Exit for denormal
}
;;

GLOBAL_LIBM_END(tanhf)