summary refs log tree commit diff
path: root/sysdeps/ia64/fpu/e_coshf.S
blob: 51a87b840e085832340cdcc532b469bbd1e90884 (plain) (blame)
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
582
583
584
585
586
587
588
589
590
591
592
593
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
611
612
613
614
615
616
617
618
619
620
621
622
623
624
625
626
627
628
629
630
631
632
633
634
635
636
637
638
639
640
641
642
643
644
645
646
647
648
649
650
651
652
653
654
655
656
657
658
659
660
661
662
663
664
665
666
667
668
669
670
671
672
673
674
675
676
677
678
679
680
681
682
683
684
685
686
687
688
689
690
691
692
693
694
695
696
697
698
699
700
701
702
703
704
705
706
707
708
709
710
711
712
.file "coshf.s"


// Copyright (c) 2000 - 2005, Intel Corporation
// All rights reserved.
//
// Contributed 2000 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
//*********************************************************************
// 02/02/00 Initial version
// 02/16/00 The error tag for coshf overflow changed to 65 (from 64).
// 04/04/00 Unwind support added
// 08/15/00 Bundle added after call to __libm_error_support to properly
//          set [the previously overwritten] GR_Parameter_RESULT.
// 05/07/01 Reworked to improve speed of all paths
// 05/20/02 Cleaned up namespace and sf0 syntax
// 11/15/02 Improved algorithm based on expf
// 03/31/05 Reformatted delimiters between data tables
//
// API
//*********************************************************************
// float coshf(float)
//
// Overview of operation
//*********************************************************************
// Case 1:  0 < |x| < 0.25
//  Evaluate cosh(x) by a 8th order polynomial
//  Care is take for the order of multiplication; and A2 is not exactly 1/4!,
//  A3 is not exactly 1/6!, etc.
//  cosh(x) = 1 + (A1*x^2 + A2*x^4 + A3*x^6 + A4*x^8)
//
// Case 2:  0.25 < |x| < 89.41598
//  Algorithm is based on the identity cosh(x) = ( exp(x) + exp(-x) ) / 2.
//  The algorithm for exp is described as below.  There are a number of
//  economies from evaluating both exp(x) and exp(-x).  Although we
//  are evaluating both quantities, only where the quantities diverge do we
//  duplicate the computations.  The basic algorithm for exp(x) is described
//  below.
//
// Take the input x. w is "how many log2/128 in x?"
//  w = x * 64/log2
//  NJ = int(w)
//  x = NJ*log2/64 + R

//  NJ = 64*n + j
//  x = n*log2 + (log2/64)*j + R
//
//  So, exp(x) = 2^n * 2^(j/64)* exp(R)
//
//  T =  2^n * 2^(j/64)
//       Construct 2^n
//       Get 2^(j/64) table
//           actually all the entries of 2^(j/64) table are stored in DP and
//           with exponent bits set to 0 -> multiplication on 2^n can be
//           performed by doing logical "or" operation with bits presenting 2^n

//  exp(R) = 1 + (exp(R) - 1)
//  P = exp(R) - 1 approximated by Taylor series of 3rd degree
//      P = A3*R^3 + A2*R^2 + R, A3 = 1/6, A2 = 1/2
//

//  The final result is reconstructed as follows
//  exp(x) = T + T*P

// Special values
//*********************************************************************
// coshf(+0)    = 1.0
// coshf(-0)    = 1.0

// coshf(+qnan) = +qnan
// coshf(-qnan) = -qnan
// coshf(+snan) = +qnan
// coshf(-snan) = -qnan

// coshf(-inf)  = +inf
// coshf(+inf)  = +inf

// Overflow and Underflow
//*********************************************************************
// coshf(x) = largest single normal when
//     x = 89.41598 = 0x42b2d4fc
//
// There is no underflow.

// Registers used
//*********************************************************************
// Floating Point registers used:
// f8 input, output
// f6,f7, f9 -> f15,  f32 -> f45

// General registers used:
// r2, r3, r16 -> r38

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

// Assembly macros
//*********************************************************************
// integer registers used
// scratch
rNJ                   = r2
rNJ_neg               = r3

rJ_neg                = r16
rN_neg                = r17
rSignexp_x            = r18
rExp_x                = r18
rExp_mask             = r19
rExp_bias             = r20
rAd1                  = r21
rAd2                  = r22
rJ                    = r23
rN                    = r24
rTblAddr              = r25
rA3                   = r26
rExpHalf              = r27
rLn2Div64             = r28
rGt_ln                = r29
r17ones_m1            = r29
rRightShifter         = r30
rJ_mask               = r30
r64DivLn2             = r31
rN_mask               = r31
// stacked
GR_SAVE_PFS           = r32
GR_SAVE_B0            = r33
GR_SAVE_GP            = r34
GR_Parameter_X        = r35
GR_Parameter_Y        = r36
GR_Parameter_RESULT   = r37
GR_Parameter_TAG      = r38

// floating point registers used
FR_X                  = f10
FR_Y                  = f1
FR_RESULT             = f8
// scratch
fRightShifter         = f6
f64DivLn2             = f7
fNormX                = f9
fNint                 = f10
fN                    = f11
fR                    = f12
fLn2Div64             = f13
fA2                   = f14
fA3                   = f15
// stacked
fP                    = f32
fT                    = f33
fMIN_SGL_OFLOW_ARG    = f34
fMAX_SGL_NORM_ARG     = f35
fRSqr                 = f36
fA1                   = f37
fA21                  = f37
fA4                   = f38
fA43                  = f38
fA4321                = f38
fX4                   = f39
fTmp                  = f39
fGt_pln               = f39
fWre_urm_f8           = f40
fXsq                  = f40
fP_neg                = f41
fT_neg                = f42
fExp                  = f43
fExp_neg              = f44
fAbsX                 = f45


RODATA
.align 16

LOCAL_OBJECT_START(_coshf_table)
data4 0x42b2d4fd         // Smallest single arg to overflow single result
data4 0x42b2d4fc         // Largest single arg to give normal single result
data4 0x00000000         // pad
data4 0x00000000         // pad
//
// 2^(j/64) table, j goes from 0 to 63
data8 0x0000000000000000 // 2^(0/64)
data8 0x00002C9A3E778061 // 2^(1/64)
data8 0x000059B0D3158574 // 2^(2/64)
data8 0x0000874518759BC8 // 2^(3/64)
data8 0x0000B5586CF9890F // 2^(4/64)
data8 0x0000E3EC32D3D1A2 // 2^(5/64)
data8 0x00011301D0125B51 // 2^(6/64)
data8 0x0001429AAEA92DE0 // 2^(7/64)
data8 0x000172B83C7D517B // 2^(8/64)
data8 0x0001A35BEB6FCB75 // 2^(9/64)
data8 0x0001D4873168B9AA // 2^(10/64)
data8 0x0002063B88628CD6 // 2^(11/64)
data8 0x0002387A6E756238 // 2^(12/64)
data8 0x00026B4565E27CDD // 2^(13/64)
data8 0x00029E9DF51FDEE1 // 2^(14/64)
data8 0x0002D285A6E4030B // 2^(15/64)
data8 0x000306FE0A31B715 // 2^(16/64)
data8 0x00033C08B26416FF // 2^(17/64)
data8 0x000371A7373AA9CB // 2^(18/64)
data8 0x0003A7DB34E59FF7 // 2^(19/64)
data8 0x0003DEA64C123422 // 2^(20/64)
data8 0x0004160A21F72E2A // 2^(21/64)
data8 0x00044E086061892D // 2^(22/64)
data8 0x000486A2B5C13CD0 // 2^(23/64)
data8 0x0004BFDAD5362A27 // 2^(24/64)
data8 0x0004F9B2769D2CA7 // 2^(25/64)
data8 0x0005342B569D4F82 // 2^(26/64)
data8 0x00056F4736B527DA // 2^(27/64)
data8 0x0005AB07DD485429 // 2^(28/64)
data8 0x0005E76F15AD2148 // 2^(29/64)
data8 0x0006247EB03A5585 // 2^(30/64)
data8 0x0006623882552225 // 2^(31/64)
data8 0x0006A09E667F3BCD // 2^(32/64)
data8 0x0006DFB23C651A2F // 2^(33/64)
data8 0x00071F75E8EC5F74 // 2^(34/64)
data8 0x00075FEB564267C9 // 2^(35/64)
data8 0x0007A11473EB0187 // 2^(36/64)
data8 0x0007E2F336CF4E62 // 2^(37/64)
data8 0x00082589994CCE13 // 2^(38/64)
data8 0x000868D99B4492ED // 2^(39/64)
data8 0x0008ACE5422AA0DB // 2^(40/64)
data8 0x0008F1AE99157736 // 2^(41/64)
data8 0x00093737B0CDC5E5 // 2^(42/64)
data8 0x00097D829FDE4E50 // 2^(43/64)
data8 0x0009C49182A3F090 // 2^(44/64)
data8 0x000A0C667B5DE565 // 2^(45/64)
data8 0x000A5503B23E255D // 2^(46/64)
data8 0x000A9E6B5579FDBF // 2^(47/64)
data8 0x000AE89F995AD3AD // 2^(48/64)
data8 0x000B33A2B84F15FB // 2^(49/64)
data8 0x000B7F76F2FB5E47 // 2^(50/64)
data8 0x000BCC1E904BC1D2 // 2^(51/64)
data8 0x000C199BDD85529C // 2^(52/64)
data8 0x000C67F12E57D14B // 2^(53/64)
data8 0x000CB720DCEF9069 // 2^(54/64)
data8 0x000D072D4A07897C // 2^(55/64)
data8 0x000D5818DCFBA487 // 2^(56/64)
data8 0x000DA9E603DB3285 // 2^(57/64)
data8 0x000DFC97337B9B5F // 2^(58/64)
data8 0x000E502EE78B3FF6 // 2^(59/64)
data8 0x000EA4AFA2A490DA // 2^(60/64)
data8 0x000EFA1BEE615A27 // 2^(61/64)
data8 0x000F50765B6E4540 // 2^(62/64)
data8 0x000FA7C1819E90D8 // 2^(63/64)
LOCAL_OBJECT_END(_coshf_table)

LOCAL_OBJECT_START(cosh_p_table)
data8 0x3efa3001dcf5905b // A4
data8 0x3f56c1437543543e // A3
data8 0x3fa5555572601504 // A2
data8 0x3fdfffffffe2f097 // A1
LOCAL_OBJECT_END(cosh_p_table)


.section .text
GLOBAL_IEEE754_ENTRY(coshf)

{ .mlx
      getf.exp        rSignexp_x = f8  // Must recompute if x unorm
      movl            r64DivLn2 = 0x40571547652B82FE // 64/ln(2)
}
{ .mlx
      addl            rTblAddr = @ltoff(_coshf_table),gp
      movl            rRightShifter = 0x43E8000000000000 // DP Right Shifter
}
;;

{ .mfi
      // point to the beginning of the table
      ld8             rTblAddr = [rTblAddr]
      fclass.m        p6, p0 = f8, 0x0b   // Test for x=unorm
      addl            rA3 = 0x3E2AA, r0   // high bits of 1.0/6.0 rounded to SP
}
{ .mfi
      nop.m           0
      fnorm.s1        fNormX = f8 // normalized x
      addl            rExpHalf = 0xFFFE, r0 // exponent of 1/2
}
;;

{ .mfi
      setf.d          f64DivLn2 = r64DivLn2 // load 64/ln(2) to FP reg
      fclass.m        p15, p0 = f8, 0x1e3   // test for NaT,NaN,Inf
      nop.i           0
}
{ .mlx
      // load Right Shifter to FP reg
      setf.d          fRightShifter = rRightShifter
      movl            rLn2Div64 = 0x3F862E42FEFA39EF // DP ln(2)/64 in GR
}
;;

{ .mfi
      mov             rExp_mask = 0x1ffff
      fcmp.eq.s1      p13, p0 = f0, f8 // test for x = 0.0
      shl             rA3 = rA3, 12    // 0x3E2AA000, approx to 1.0/6.0 in SP
}
{ .mfb
      nop.m           0
      nop.f           0
(p6)  br.cond.spnt    COSH_UNORM            // Branch if x=unorm
}
;;

COSH_COMMON:
{ .mfi
      setf.exp        fA2 = rExpHalf        // load A2 to FP reg
      nop.f           0
      mov             rExp_bias = 0xffff
}
{ .mfb
      setf.d          fLn2Div64 = rLn2Div64 // load ln(2)/64 to FP reg
(p15) fma.s.s0        f8 = f8, f8, f0       // result if x = NaT,NaN,Inf
(p15) br.ret.spnt     b0                    // exit here if x = NaT,NaN,Inf
}
;;

{ .mfi
      // min overflow and max normal threshold
      ldfps           fMIN_SGL_OFLOW_ARG, fMAX_SGL_NORM_ARG = [rTblAddr], 8
      nop.f           0
      and             rExp_x = rExp_mask, rSignexp_x // Biased exponent of x
}
{ .mfb
      setf.s          fA3 = rA3                  // load A3 to FP reg
(p13) fma.s.s0        f8 = f1, f1, f0            // result if x = 0.0
(p13) br.ret.spnt     b0                         // exit here if x =0.0
}
;;

{ .mfi
      sub             rExp_x = rExp_x, rExp_bias // True exponent of x
      fmerge.s        fAbsX = f0, fNormX         // Form |x|
      nop.i           0
}
;;

{ .mfi
      nop.m           0
      // x*(64/ln(2)) + Right Shifter
      fma.s1          fNint = fNormX, f64DivLn2, fRightShifter
      add             rTblAddr = 8, rTblAddr
}
{ .mfb
      cmp.gt          p7, p0 = -2, rExp_x        // Test |x| < 2^(-2)
      fma.s1          fXsq = fNormX, fNormX, f0  // x*x for small path
(p7)  br.cond.spnt    COSH_SMALL                 // Branch if 0 < |x| < 2^-2
}
;;

{ .mfi
      nop.m           0
      // check for overflow
      fcmp.ge.s1      p12, p13 = fAbsX, fMIN_SGL_OFLOW_ARG
      mov             rJ_mask = 0x3f             // 6-bit mask for J
}
;;

{ .mfb
      nop.m           0
      fms.s1          fN = fNint, f1, fRightShifter // n in FP register
      // branch out if overflow
(p12) br.cond.spnt    COSH_CERTAIN_OVERFLOW
}
;;

{ .mfi
      getf.sig        rNJ = fNint                   // bits of n, j
      // check for possible overflow
      fcmp.gt.s1      p13, p0 = fAbsX, fMAX_SGL_NORM_ARG
      nop.i           0
}
;;

{ .mfi
      addl            rN = 0xFFBF - 63, rNJ      // biased and shifted n-1,j
      fnma.s1         fR = fLn2Div64, fN, fNormX // R = x - N*ln(2)/64
      and             rJ = rJ_mask, rNJ          // bits of j
}
{ .mfi
      sub             rNJ_neg = r0, rNJ          // bits of n, j for -x
      nop.f           0
      andcm           rN_mask = -1, rJ_mask      // 0xff...fc0 to mask N
}
;;

{ .mfi
      shladd          rJ = rJ, 3, rTblAddr // address in the 2^(j/64) table
      nop.f           0
      and             rN = rN_mask, rN     // biased, shifted n-1
}
{ .mfi
      addl            rN_neg = 0xFFBF - 63, rNJ_neg // -x biased, shifted n-1,j
      nop.f           0
      and             rJ_neg = rJ_mask, rNJ_neg     // bits of j for -x
}
;;

{ .mfi
      ld8             rJ = [rJ]                    // Table value
      nop.f           0
      shl             rN = rN, 46 // 2^(n-1) bits in DP format
}
{ .mfi
      shladd          rJ_neg = rJ_neg, 3, rTblAddr // addr in 2^(j/64) table -x
      nop.f           0
      and             rN_neg = rN_mask, rN_neg     // biased, shifted n-1 for -x
}
;;

{ .mfi
      ld8             rJ_neg = [rJ_neg]            // Table value for -x
      nop.f           0
      shl             rN_neg = rN_neg, 46 // 2^(n-1) bits in DP format for -x
}
;;

{ .mfi
      or              rN = rN, rJ // bits of 2^n * 2^(j/64) in DP format
      nop.f           0
      nop.i           0
}
;;

{ .mmf
      setf.d          fT = rN            // 2^(n-1) * 2^(j/64)
      or              rN_neg = rN_neg, rJ_neg // -x bits of 2^n * 2^(j/64) in DP
      fma.s1          fRSqr = fR, fR, f0 // R^2
}
;;

{ .mfi
      setf.d          fT_neg = rN_neg    // 2^(n-1) * 2^(j/64) for -x
      fma.s1          fP = fA3, fR, fA2  // A3*R + A2
      nop.i           0
}
{ .mfi
      nop.m           0
      fnma.s1         fP_neg = fA3, fR, fA2  // A3*R + A2 for -x
      nop.i           0
}
;;

{ .mfi
      nop.m           0
      fma.s1          fP = fP, fRSqr, fR // P = (A3*R + A2)*R^2 + R
      nop.i           0
}
{ .mfi
      nop.m           0
      fms.s1          fP_neg = fP_neg, fRSqr, fR // P = (A3*R + A2)*R^2 + R, -x
      nop.i           0
}
;;

{ .mfi
      nop.m           0
      fmpy.s0         fTmp = fLn2Div64, fLn2Div64       // Force inexact
      nop.i           0
}
;;

{ .mfi
      nop.m           0
      fma.s1          fExp = fP, fT, fT                 // exp(x)/2
      nop.i           0
}
{ .mfb
      nop.m           0
      fma.s1          fExp_neg = fP_neg, fT_neg, fT_neg // exp(-x)/2
      // branch out if possible overflow result
(p13) br.cond.spnt    COSH_POSSIBLE_OVERFLOW
}
;;

{ .mfb
      nop.m           0
      // final result in the absence of overflow
      fma.s.s0        f8 = fExp, f1, fExp_neg  // result = (exp(x)+exp(-x))/2
      // exit here in the absence of overflow
      br.ret.sptk     b0              // Exit main path, 0.25 <= |x| < 89.41598
}
;;

// Here if 0 < |x| < 0.25.  Evaluate 8th order polynomial.
COSH_SMALL:
{ .mmi
      add             rAd1 = 0x200, rTblAddr
      add             rAd2 = 0x210, rTblAddr
      nop.i           0
}
;;

{ .mmi
      ldfpd           fA4, fA3 = [rAd1]
      ldfpd           fA2, fA1 = [rAd2]
      nop.i           0
}
;;

{ .mfi
      nop.m           0
      fma.s1          fX4 = fXsq, fXsq, f0
      nop.i           0
}
;;

{ .mfi
      nop.m           0
      fma.s1          fA43 = fXsq, fA4, fA3
      nop.i           0
}
{ .mfi
      nop.m           0
      fma.s1          fA21 = fXsq, fA2, fA1
      nop.i           0
}
;;

{ .mfi
      nop.m           0
      fma.s1          fA4321 = fX4, fA43, fA21
      nop.i           0
}
;;

// Dummy multiply to generate inexact
{ .mfi
      nop.m           0
      fmpy.s0         fTmp = fA4, fA4
      nop.i           0
}
{ .mfb
      nop.m           0
      fma.s.s0        f8 = fA4321, fXsq, f1
      br.ret.sptk     b0                // Exit if 0 < |x| < 0.25
}
;;

COSH_POSSIBLE_OVERFLOW:

// Here if fMAX_SGL_NORM_ARG < x < fMIN_SGL_OFLOW_ARG
// This cannot happen if input is a single, only if input higher precision.
// Overflow is a possibility, not a certainty.

// Recompute result using status field 2 with user's rounding mode,
// and wre set.  If result is larger than largest single, then we have
// overflow

{ .mfi
      mov             rGt_ln  = 0x1007f // Exponent for largest single + 1 ulp
      fsetc.s2        0x7F,0x42         // Get user's round mode, set wre
      nop.i           0
}
;;

{ .mfi
      setf.exp        fGt_pln = rGt_ln  // Create largest single + 1 ulp
      fma.s.s2        fWre_urm_f8 = fP, fT, fT    // Result with wre set
      nop.i           0
}
;;

{ .mfi
      nop.m           0
      fsetc.s2        0x7F,0x40                   // Turn off wre in sf2
      nop.i           0
}
;;

{ .mfi
      nop.m           0
      fcmp.ge.s1      p6, p0 =  fWre_urm_f8, fGt_pln // Test for overflow
      nop.i           0
}
;;

{ .mfb
      nop.m           0
      nop.f           0
(p6)  br.cond.spnt    COSH_CERTAIN_OVERFLOW // Branch if overflow
}
;;

{ .mfb
      nop.m           0
      fma.s.s0        f8 = fP, fT, fT
      br.ret.sptk     b0                     // Exit if really no overflow
}
;;

// here if overflow
COSH_CERTAIN_OVERFLOW:
{ .mmi
      addl            r17ones_m1 = 0x1FFFE, r0
;;
      setf.exp        fTmp = r17ones_m1
      nop.i           0
}
;;

{ .mfi
      alloc           r32 = ar.pfs, 0, 3, 4, 0 // get some registers
      fmerge.s        FR_X = f8,f8
      nop.i           0
}
{ .mfb
      mov             GR_Parameter_TAG = 65
      fma.s.s0        FR_RESULT = fTmp, fTmp, f0 // Set I,O and +INF result
      br.cond.sptk    __libm_error_region
}
;;

// Here if x unorm
COSH_UNORM:
{ .mfb
      getf.exp        rSignexp_x = fNormX    // Must recompute if x unorm
      fcmp.eq.s0      p6, p0 = f8, f0        // Set D flag
      br.cond.sptk    COSH_COMMON            // Return to main path
}
;;

GLOBAL_IEEE754_END(coshf)
libm_alias_float_other (__cosh, cosh)


LOCAL_LIBM_ENTRY(__libm_error_region)
.prologue
{ .mfi
      add   GR_Parameter_Y=-32,sp             // Parameter 2 value
      nop.f 0
.save   ar.pfs,GR_SAVE_PFS
      mov  GR_SAVE_PFS=ar.pfs                 // Save ar.pfs
}
{ .mfi
.fframe 64
      add sp=-64,sp                           // Create new stack
      nop.f 0
      mov GR_SAVE_GP=gp                       // Save gp
};;
{ .mmi
      stfs [GR_Parameter_Y] = FR_Y,16         // Store Parameter 2 on stack
      add GR_Parameter_X = 16,sp              // Parameter 1 address
.save   b0, GR_SAVE_B0
      mov GR_SAVE_B0=b0                       // Save b0
};;
.body
{ .mfi
      stfs [GR_Parameter_X] = FR_X            // Store Parameter 1 on stack
      nop.f 0
      add   GR_Parameter_RESULT = 0,GR_Parameter_Y // Parameter 3 address
}
{ .mib
      stfs [GR_Parameter_Y] = FR_RESULT       // Store Parameter 3 on stack
      add   GR_Parameter_Y = -16,GR_Parameter_Y
      br.call.sptk b0=__libm_error_support#   // Call error handling function
};;

{ .mmi
      add   GR_Parameter_RESULT = 48,sp
      nop.m 0
      nop.i 0
};;

{ .mmi
      ldfs  f8 = [GR_Parameter_RESULT]       // Get return result off stack
.restore sp
      add   sp = 64,sp                       // Restore stack pointer
      mov   b0 = GR_SAVE_B0                  // Restore return address
};;
{ .mib
      mov   gp = GR_SAVE_GP                  // Restore gp
      mov   ar.pfs = GR_SAVE_PFS             // Restore ar.pfs
      br.ret.sptk     b0                     // Return
};;

LOCAL_LIBM_END(__libm_error_region)


.type   __libm_error_support#,@function
.global __libm_error_support#