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d5efd131
MF		 1.file "sinh.s"
2
3
4// Copyright (c) 2000 - 2005, Intel Corporation
5// All rights reserved.
6//
d5efd131
MF		 7//
8// Redistribution and use in source and binary forms, with or without
9// modification, are permitted provided that the following conditions are
10// met:
11//
12// * Redistributions of source code must retain the above copyright
13// notice, this list of conditions and the following disclaimer.
14//
15// * Redistributions in binary form must reproduce the above copyright
16// notice, this list of conditions and the following disclaimer in the
17// documentation and/or other materials provided with the distribution.
18//
19// * The name of Intel Corporation may not be used to endorse or promote
20// products derived from this software without specific prior written
21// permission.
22
23// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
24// "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
25// LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
26// A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL INTEL OR ITS
27// CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
28// EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
29// PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
30// PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY
31// OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY OR TORT (INCLUDING
32// NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
33// SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
34//
35// Intel Corporation is the author of this code, and requests that all
36// problem reports or change requests be submitted to it directly at
37// http://www.intel.com/software/products/opensource/libraries/num.htm.
38//
39// History
40//==============================================================
41// 02/02/00 Initial version
42// 04/04/00 Unwind support added
43// 08/15/00 Bundle added after call to __libm_error_support to properly
44// set [the previously overwritten] GR_Parameter_RESULT.
45// 10/12/00 Update to set denormal operand and underflow flags
46// 01/22/01 Fixed to set inexact flag for small args.
47// 05/02/01 Reworked to improve speed of all paths
48// 05/20/02 Cleaned up namespace and sf0 syntax
49// 11/20/02 Improved speed with new algorithm
50// 03/31/05 Reformatted delimiters between data tables
51
52// API
53//==============================================================
54// double sinh(double)
55
56// Overview of operation
57//==============================================================
58// Case 1: 0 < |x| < 2^-60
59// Result = x, computed by x+sgn(x)*x^2) to handle flags and rounding
60//
61// Case 2: 2^-60 < |x| < 0.25
62// Evaluate sinh(x) by a 13th order polynomial
63// Care is take for the order of multiplication; and A1 is not exactly 1/3!,
64// A2 is not exactly 1/5!, etc.
65// sinh(x) = x + (A1*x^3 + A2*x^5 + A3*x^7 + A4*x^9 + A5*x^11 + A6*x^13)
66//
67// Case 3: 0.25 < |x| < 710.47586
68// Algorithm is based on the identity sinh(x) = ( exp(x) - exp(-x) ) / 2.
69// The algorithm for exp is described as below. There are a number of
70// economies from evaluating both exp(x) and exp(-x). Although we
71// are evaluating both quantities, only where the quantities diverge do we
72// duplicate the computations. The basic algorithm for exp(x) is described
73// below.
74//
75// Take the input x. w is "how many log2/128 in x?"
76// w = x * 128/log2
77// n = int(w)
78// x = n log2/128 + r + delta
79
80// n = 128M + index_1 + 2^4 index_2
81// x = M log2 + (log2/128) index_1 + (log2/8) index_2 + r + delta
82
83// exp(x) = 2^M 2^(index_1/128) 2^(index_2/8) exp(r) exp(delta)
84// Construct 2^M
85// Get 2^(index_1/128) from table_1;
86// Get 2^(index_2/8) from table_2;
87// Calculate exp(r) by 5th order polynomial
88// r = x - n (log2/128)_high
89// delta = - n (log2/128)_low
90// Calculate exp(delta) as 1 + delta
91
92
93// Special values
94//==============================================================
95// sinh(+0) = +0
96// sinh(-0) = -0
97
98// sinh(+qnan) = +qnan
99// sinh(-qnan) = -qnan
100// sinh(+snan) = +qnan
101// sinh(-snan) = -qnan
102
103// sinh(-inf) = -inf
104// sinh(+inf) = +inf
105
106// Overflow and Underflow
107//=======================
108// sinh(x) = largest double normal when
109// |x| = 710.47586 = 0x408633ce8fb9f87d
110//
111// Underflow is handled as described in case 1 above
112
113// Registers used
114//==============================================================
115// Floating Point registers used:
116// f8, input, output
117// f6 -> f15, f32 -> f61
118
119// General registers used:
120// r14 -> r40
121
122// Predicate registers used:
123// p6 -> p15
124
125// Assembly macros
126//==============================================================
127
128rRshf = r14
129rN_neg = r14
130rAD_TB1 = r15
131rAD_TB2 = r16
132rAD_P = r17
133rN = r18
134rIndex_1 = r19
135rIndex_2_16 = r20
136rM = r21
137rBiased_M = r21
138rSig_inv_ln2 = r22
139rIndex_1_neg = r22
140rExp_bias = r23
141rExp_bias_minus_1 = r23
142rExp_mask = r24
143rTmp = r24
144rGt_ln = r24
145rIndex_2_16_neg = r24
146rM_neg = r25
147rBiased_M_neg = r25
148rRshf_2to56 = r26
149rAD_T1_neg = r26
150rExp_2tom56 = r28
151rAD_T2_neg = r28
152rAD_T1 = r29
153rAD_T2 = r30
154rSignexp_x = r31
155rExp_x = r31
156
157GR_SAVE_B0 = r33
158GR_SAVE_PFS = r34
159GR_SAVE_GP = r35
160
161GR_Parameter_X = r37
162GR_Parameter_Y = r38
163GR_Parameter_RESULT = r39
164GR_Parameter_TAG = r40
165
166
167FR_X = f10
168FR_Y = f1
169FR_RESULT = f8
170
171fRSHF_2TO56 = f6
172fINV_LN2_2TO63 = f7
173fW_2TO56_RSH = f9
174f2TOM56 = f11
175fP5 = f12
176fP4 = f13
177fP3 = f14
178fP2 = f15
179
180fLn2_by_128_hi = f33
181fLn2_by_128_lo = f34
182
183fRSHF = f35
184fNfloat = f36
185fNormX = f37
186fR = f38
187fF = f39
188
189fRsq = f40
190f2M = f41
191fS1 = f42
192fT1 = f42
193fS2 = f43
194fT2 = f43
195fS = f43
196fWre_urm_f8 = f44
197fAbsX = f44
198
199fMIN_DBL_OFLOW_ARG = f45
200fMAX_DBL_NORM_ARG = f46
201fXsq = f47
202fX4 = f48
203fGt_pln = f49
204fTmp = f49
205
206fP54 = f50
207fP5432 = f50
208fP32 = f51
209fP = f52
210fP54_neg = f53
211fP5432_neg = f53
212fP32_neg = f54
213fP_neg = f55
214fF_neg = f56
215
216f2M_neg = f57
217fS1_neg = f58
218fT1_neg = f58
219fS2_neg = f59
220fT2_neg = f59
221fS_neg = f59
222fExp = f60
223fExp_neg = f61
224
225fA6 = f50
226fA65 = f50
227fA6543 = f50
228fA654321 = f50
229fA5 = f51
230fA4 = f52
231fA43 = f52
232fA3 = f53
233fA2 = f54
234fA21 = f54
235fA1 = f55
236fX3 = f56
237
238// Data tables
239//==============================================================
240
241RODATA
242.align 16
243
244// ************* DO NOT CHANGE ORDER OF THESE TABLES ********************
245
246// double-extended 1/ln(2)
247// 3fff b8aa 3b29 5c17 f0bb be87fed0691d3e88
248// 3fff b8aa 3b29 5c17 f0bc
249// For speed the significand will be loaded directly with a movl and setf.sig
250// and the exponent will be bias+63 instead of bias+0. Thus subsequent
251// computations need to scale appropriately.
252// The constant 128/ln(2) is needed for the computation of w. This is also
253// obtained by scaling the computations.
254//
255// Two shifting constants are loaded directly with movl and setf.d.
256// 1. fRSHF_2TO56 = 1.1000..00 * 2^(63-7)
257// This constant is added to x*1/ln2 to shift the integer part of
258// x*128/ln2 into the rightmost bits of the significand.
259// The result of this fma is fW_2TO56_RSH.
260// 2. fRSHF = 1.1000..00 * 2^(63)
261// This constant is subtracted from fW_2TO56_RSH * 2^(-56) to give
262// the integer part of w, n, as a floating-point number.
263// The result of this fms is fNfloat.
264
265
266LOCAL_OBJECT_START(exp_table_1)
267data8 0x408633ce8fb9f87e // smallest dbl overflow arg
268data8 0x408633ce8fb9f87d // largest dbl arg to give normal dbl result
269data8 0xb17217f7d1cf79ab , 0x00003ff7 // ln2/128 hi
270data8 0xc9e3b39803f2f6af , 0x00003fb7 // ln2/128 lo
271//
272// Table 1 is 2^(index_1/128) where
273// index_1 goes from 0 to 15
274//
275data8 0x8000000000000000 , 0x00003FFF
276data8 0x80B1ED4FD999AB6C , 0x00003FFF
277data8 0x8164D1F3BC030773 , 0x00003FFF
278data8 0x8218AF4373FC25EC , 0x00003FFF
279data8 0x82CD8698AC2BA1D7 , 0x00003FFF
280data8 0x8383594EEFB6EE37 , 0x00003FFF
281data8 0x843A28C3ACDE4046 , 0x00003FFF
282data8 0x84F1F656379C1A29 , 0x00003FFF
283data8 0x85AAC367CC487B15 , 0x00003FFF
284data8 0x8664915B923FBA04 , 0x00003FFF
285data8 0x871F61969E8D1010 , 0x00003FFF
286data8 0x87DB357FF698D792 , 0x00003FFF
287data8 0x88980E8092DA8527 , 0x00003FFF
288data8 0x8955EE03618E5FDD , 0x00003FFF
289data8 0x8A14D575496EFD9A , 0x00003FFF
290data8 0x8AD4C6452C728924 , 0x00003FFF
291LOCAL_OBJECT_END(exp_table_1)
292
293// Table 2 is 2^(index_1/8) where
294// index_2 goes from 0 to 7
295LOCAL_OBJECT_START(exp_table_2)
296data8 0x8000000000000000 , 0x00003FFF
297data8 0x8B95C1E3EA8BD6E7 , 0x00003FFF
298data8 0x9837F0518DB8A96F , 0x00003FFF
299data8 0xA5FED6A9B15138EA , 0x00003FFF
300data8 0xB504F333F9DE6484 , 0x00003FFF
301data8 0xC5672A115506DADD , 0x00003FFF
302data8 0xD744FCCAD69D6AF4 , 0x00003FFF
303data8 0xEAC0C6E7DD24392F , 0x00003FFF
304LOCAL_OBJECT_END(exp_table_2)
305
306
307LOCAL_OBJECT_START(exp_p_table)
308data8 0x3f8111116da21757 //P5
309data8 0x3fa55555d787761c //P4
310data8 0x3fc5555555555414 //P3
311data8 0x3fdffffffffffd6a //P2
312LOCAL_OBJECT_END(exp_p_table)
313
314LOCAL_OBJECT_START(sinh_p_table)
315data8 0xB08AF9AE78C1239F, 0x00003FDE // A6
316data8 0xB8EF1D28926D8891, 0x00003FEC // A4
317data8 0x8888888888888412, 0x00003FF8 // A2
318data8 0xD732377688025BE9, 0x00003FE5 // A5
319data8 0xD00D00D00D4D39F2, 0x00003FF2 // A3
320data8 0xAAAAAAAAAAAAAAAB, 0x00003FFC // A1
321LOCAL_OBJECT_END(sinh_p_table)
322
323
324.section .text
325GLOBAL_IEEE754_ENTRY(sinh)
326
327{ .mlx
328 getf.exp rSignexp_x = f8 // Must recompute if x unorm
329 movl rSig_inv_ln2 = 0xb8aa3b295c17f0bc // significand of 1/ln2
330}
331{ .mlx
332 addl rAD_TB1 = @ltoff(exp_table_1), gp
333 movl rRshf_2to56 = 0x4768000000000000 // 1.10000 2^(63+56)
334}
335;;
336
337{ .mfi
338 ld8 rAD_TB1 = [rAD_TB1]
339 fclass.m p6,p0 = f8,0x0b // Test for x=unorm
340 mov rExp_mask = 0x1ffff
341}
342{ .mfi
343 mov rExp_bias = 0xffff
344 fnorm.s1 fNormX = f8
345 mov rExp_2tom56 = 0xffff-56
346}
347;;
348
349// Form two constants we need
350// 1/ln2 * 2^63 to compute w = x * 1/ln2 * 128
351// 1.1000..000 * 2^(63+63-7) to right shift int(w) into the significand
352
353{ .mfi
354 setf.sig fINV_LN2_2TO63 = rSig_inv_ln2 // form 1/ln2 * 2^63
355 fclass.m p8,p0 = f8,0x07 // Test for x=0
356 nop.i 999
357}
358{ .mlx
359 setf.d fRSHF_2TO56 = rRshf_2to56 // Form const 1.100 * 2^(63+56)
360 movl rRshf = 0x43e8000000000000 // 1.10000 2^63 for right shift
361}
362;;
363
364{ .mfi
365 ldfpd fMIN_DBL_OFLOW_ARG, fMAX_DBL_NORM_ARG = [rAD_TB1],16
366 fclass.m p10,p0 = f8,0x1e3 // Test for x=inf, nan, NaT
367 nop.i 0
368}
369{ .mfb
370 setf.exp f2TOM56 = rExp_2tom56 // form 2^-56 for scaling Nfloat
371 nop.f 0
372(p6) br.cond.spnt SINH_UNORM // Branch if x=unorm
373}
374;;
375
376SINH_COMMON:
377{ .mfi
378 ldfe fLn2_by_128_hi = [rAD_TB1],16
379 nop.f 0
380 nop.i 0
381}
382{ .mfb
383 setf.d fRSHF = rRshf // Form right shift const 1.100 * 2^63
384 nop.f 0
385(p8) br.ret.spnt b0 // Exit for x=0, result=x
386}
387;;
388
389{ .mfi
390 ldfe fLn2_by_128_lo = [rAD_TB1],16
391 nop.f 0
392 nop.i 0
393}
394{ .mfb
395 and rExp_x = rExp_mask, rSignexp_x // Biased exponent of x
396(p10) fma.d.s0 f8 = f8,f1,f0 // Result if x=inf, nan, NaT
397(p10) br.ret.spnt b0 // quick exit for x=inf, nan, NaT
398}
399;;
400
401// After that last load rAD_TB1 points to the beginning of table 1
402{ .mfi
403 nop.m 0
404 fcmp.eq.s0 p6,p0 = f8, f0 // Dummy to set D
405 sub rExp_x = rExp_x, rExp_bias // True exponent of x
406}
407;;
408
409{ .mfi
410 nop.m 0
411 fmerge.s fAbsX = f0, fNormX // Form |x|
412 nop.i 0
413}
414{ .mfb
415 cmp.gt p7, p0 = -2, rExp_x // Test |x| < 2^(-2)
416 fma.s1 fXsq = fNormX, fNormX, f0 // x*x for small path
417(p7) br.cond.spnt SINH_SMALL // Branch if 0 < |x| < 2^-2
418}
419;;
420
421// W = X * Inv_log2_by_128
422// By adding 1.10...0*2^63 we shift and get round_int(W) in significand.
423// We actually add 1.10...0*2^56 to X * Inv_log2 to do the same thing.
424
425{ .mfi
426 add rAD_P = 0x180, rAD_TB1
427 fma.s1 fW_2TO56_RSH = fNormX, fINV_LN2_2TO63, fRSHF_2TO56
428 add rAD_TB2 = 0x100, rAD_TB1
429}
430;;
431
432// Divide arguments into the following categories:
433// Certain Safe - 0.25 <= |x| <= MAX_DBL_NORM_ARG
434// Possible Overflow p14 - MAX_DBL_NORM_ARG < |x| < MIN_DBL_OFLOW_ARG
435// Certain Overflow p15 - MIN_DBL_OFLOW_ARG <= |x| < +inf
436//
437// If the input is really a double arg, then there will never be
438// "Possible Overflow" arguments.
439//
440
441{ .mfi
442 ldfpd fP5, fP4 = [rAD_P] ,16
443 fcmp.ge.s1 p15,p14 = fAbsX,fMIN_DBL_OFLOW_ARG
444 nop.i 0
445}
446;;
447
448// Nfloat = round_int(W)
449// The signficand of fW_2TO56_RSH contains the rounded integer part of W,
450// as a twos complement number in the lower bits (that is, it may be negative).
451// That twos complement number (called N) is put into rN.
452
453// Since fW_2TO56_RSH is scaled by 2^56, it must be multiplied by 2^-56
454// before the shift constant 1.10000 * 2^63 is subtracted to yield fNfloat.
455// Thus, fNfloat contains the floating point version of N
456
457{ .mfi
458 ldfpd fP3, fP2 = [rAD_P]
459(p14) fcmp.gt.unc.s1 p14,p0 = fAbsX,fMAX_DBL_NORM_ARG
460 nop.i 0
461}
462{ .mfb
463 nop.m 0
464 fms.s1 fNfloat = fW_2TO56_RSH, f2TOM56, fRSHF
465(p15) br.cond.spnt SINH_CERTAIN_OVERFLOW
466}
467;;
468
469{ .mfi
470 getf.sig rN = fW_2TO56_RSH
471 nop.f 0
472 mov rExp_bias_minus_1 = 0xfffe
473}
474;;
475
476// rIndex_1 has index_1
477// rIndex_2_16 has index_2 * 16
478// rBiased_M has M
479
480// rM has true M
481// r = x - Nfloat * ln2_by_128_hi
482// f = 1 - Nfloat * ln2_by_128_lo
483{ .mfi
484 and rIndex_1 = 0x0f, rN
485 fnma.s1 fR = fNfloat, fLn2_by_128_hi, fNormX
486 shr rM = rN, 0x7
487}
488{ .mfi
489 and rIndex_2_16 = 0x70, rN
490 fnma.s1 fF = fNfloat, fLn2_by_128_lo, f1
491 sub rN_neg = r0, rN
492}
493;;
494
495{ .mmi
496 and rIndex_1_neg = 0x0f, rN_neg
497 add rBiased_M = rExp_bias_minus_1, rM
498 shr rM_neg = rN_neg, 0x7
499}
500{ .mmi
501 and rIndex_2_16_neg = 0x70, rN_neg
502 add rAD_T2 = rAD_TB2, rIndex_2_16
503 shladd rAD_T1 = rIndex_1, 4, rAD_TB1
504}
505;;
506
507// rAD_T1 has address of T1
508// rAD_T2 has address if T2
509
510{ .mmi
511 setf.exp f2M = rBiased_M
512 ldfe fT2 = [rAD_T2]
513 nop.i 0
514}
515{ .mmi
516 add rBiased_M_neg = rExp_bias_minus_1, rM_neg
517 add rAD_T2_neg = rAD_TB2, rIndex_2_16_neg
518 shladd rAD_T1_neg = rIndex_1_neg, 4, rAD_TB1
519}
520;;
521
522// Create Scale = 2^M
523// Load T1 and T2
524{ .mmi
525 ldfe fT1 = [rAD_T1]
526 nop.m 0
527 nop.i 0
528}
529{ .mmf
530 setf.exp f2M_neg = rBiased_M_neg
531 ldfe fT2_neg = [rAD_T2_neg]
532 fma.s1 fF_neg = fNfloat, fLn2_by_128_lo, f1
533}
534;;
535
536{ .mfi
537 nop.m 0
538 fma.s1 fRsq = fR, fR, f0
539 nop.i 0
540}
541{ .mfi
542 ldfe fT1_neg = [rAD_T1_neg]
543 fma.s1 fP54 = fR, fP5, fP4
544 nop.i 0
545}
546;;
547
548{ .mfi
549 nop.m 0
550 fma.s1 fP32 = fR, fP3, fP2
551 nop.i 0
552}
553{ .mfi
554 nop.m 0
555 fnma.s1 fP54_neg = fR, fP5, fP4
556 nop.i 0
557}
558;;
559
560{ .mfi
561 nop.m 0
562 fnma.s1 fP32_neg = fR, fP3, fP2
563 nop.i 0
564}
565;;
566
567{ .mfi
568 nop.m 0
569 fma.s1 fP5432 = fRsq, fP54, fP32
570 nop.i 0
571}
572{ .mfi
573 nop.m 0
574 fma.s1 fS2 = fF,fT2,f0
575 nop.i 0
576}
577;;
578
579{ .mfi
580 nop.m 0
581 fma.s1 fS1 = f2M,fT1,f0
582 nop.i 0
583}
584{ .mfi
585 nop.m 0
586 fma.s1 fP5432_neg = fRsq, fP54_neg, fP32_neg
587 nop.i 0
588}
589;;
590
591{ .mfi
592 nop.m 0
593 fma.s1 fS1_neg = f2M_neg,fT1_neg,f0
594 nop.i 0
595}
596{ .mfi
597 nop.m 0
598 fma.s1 fS2_neg = fF_neg,fT2_neg,f0
599 nop.i 0
600}
601;;
602
603{ .mfi
604 nop.m 0
605 fma.s1 fP = fRsq, fP5432, fR
606 nop.i 0
607}
608{ .mfi
609 nop.m 0
610 fma.s1 fS = fS1,fS2,f0
611 nop.i 0
612}
613;;
614
615{ .mfi
616 nop.m 0
617 fms.s1 fP_neg = fRsq, fP5432_neg, fR
618 nop.i 0
619}
620{ .mfi
621 nop.m 0
622 fma.s1 fS_neg = fS1_neg,fS2_neg,f0
623 nop.i 0
624}
625;;
626
627{ .mfb
628 nop.m 0
629 fmpy.s0 fTmp = fLn2_by_128_lo, fLn2_by_128_lo // Force inexact
630(p14) br.cond.spnt SINH_POSSIBLE_OVERFLOW
631}
632;;
633
634{ .mfi
635 nop.m 0
636 fma.s1 fExp = fS, fP, fS
637 nop.i 0
638}
639{ .mfi
640 nop.m 0
641 fma.s1 fExp_neg = fS_neg, fP_neg, fS_neg
642 nop.i 0
643}
644;;
645
646{ .mfb
647 nop.m 0
648 fms.d.s0 f8 = fExp, f1, fExp_neg
649 br.ret.sptk b0 // Normal path exit
650}
651;;
652
653// Here if 0 < |x| < 0.25
654SINH_SMALL:
655{ .mfi
656 add rAD_T1 = 0x1a0, rAD_TB1
657 fcmp.lt.s1 p7, p8 = fNormX, f0 // Test sign of x
658 cmp.gt p6, p0 = -60, rExp_x // Test |x| < 2^(-60)
659}
660{ .mfi
661 add rAD_T2 = 0x1d0, rAD_TB1
662 nop.f 0
663 nop.i 0
664}
665;;
666
667{ .mmb
668 ldfe fA6 = [rAD_T1],16
669 ldfe fA5 = [rAD_T2],16
670(p6) br.cond.spnt SINH_VERY_SMALL // Branch if |x| < 2^(-60)
671}
672;;
673
674{ .mmi
675 ldfe fA4 = [rAD_T1],16
676 ldfe fA3 = [rAD_T2],16
677 nop.i 0
678}
679;;
680
681{ .mmi
682 ldfe fA2 = [rAD_T1]
683 ldfe fA1 = [rAD_T2]
684 nop.i 0
685}
686;;
687
688{ .mfi
689 nop.m 0
690 fma.s1 fX3 = fNormX, fXsq, f0
691 nop.i 0
692}
693{ .mfi
694 nop.m 0
695 fma.s1 fX4 = fXsq, fXsq, f0
696 nop.i 0
697}
698;;
699
700{ .mfi
701 nop.m 0
702 fma.s1 fA65 = fXsq, fA6, fA5
703 nop.i 0
704}
705{ .mfi
706 nop.m 0
707 fma.s1 fA43 = fXsq, fA4, fA3
708 nop.i 0
709}
710;;
711
712{ .mfi
713 nop.m 0
714 fma.s1 fA21 = fXsq, fA2, fA1
715 nop.i 0
716}
717;;
718
719{ .mfi
720 nop.m 0
721 fma.s1 fA6543 = fX4, fA65, fA43
722 nop.i 0
723}
724;;
725
726{ .mfi
727 nop.m 0
728 fma.s1 fA654321 = fX4, fA6543, fA21
729 nop.i 0
730}
731;;
732
733// Dummy multiply to generate inexact
734{ .mfi
735 nop.m 0
736 fmpy.s0 fTmp = fA6, fA6
737 nop.i 0
738}
739{ .mfb
740 nop.m 0
741 fma.d.s0 f8 = fA654321, fX3, fNormX
742 br.ret.sptk b0 // Exit if 2^-60 < |x| < 0.25
743}
744;;
745
746SINH_VERY_SMALL:
747// Here if 0 < |x| < 2^-60
748// Compute result by x + sgn(x)*x^2 to get properly rounded result
749.pred.rel "mutex",p7,p8
750{ .mfi
751 nop.m 0
752(p7) fnma.d.s0 f8 = fNormX, fNormX, fNormX // If x<0 result ~ x-x^2
753 nop.i 0
754}
755{ .mfb
756 nop.m 0
757(p8) fma.d.s0 f8 = fNormX, fNormX, fNormX // If x>0 result ~ x+x^2
758 br.ret.sptk b0 // Exit if |x| < 2^-60
759}
760;;
761
762
763SINH_POSSIBLE_OVERFLOW:
764
765// Here if fMAX_DBL_NORM_ARG < |x| < fMIN_DBL_OFLOW_ARG
766// This cannot happen if input is a double, only if input higher precision.
767// Overflow is a possibility, not a certainty.
768
769// Recompute result using status field 2 with user's rounding mode,
770// and wre set. If result is larger than largest double, then we have
771// overflow
772
773{ .mfi
774 mov rGt_ln = 0x103ff // Exponent for largest dbl + 1 ulp
775 fsetc.s2 0x7F,0x42 // Get user's round mode, set wre
776 nop.i 0
777}
778;;
779
780{ .mfi
781 setf.exp fGt_pln = rGt_ln // Create largest double + 1 ulp
782 fma.d.s2 fWre_urm_f8 = fS, fP, fS // Result with wre set
783 nop.i 0
784}
785;;
786
787{ .mfi
788 nop.m 0
789 fsetc.s2 0x7F,0x40 // Turn off wre in sf2
790 nop.i 0
791}
792;;
793
794{ .mfi
795 nop.m 0
796 fcmp.ge.s1 p6, p0 = fWre_urm_f8, fGt_pln // Test for overflow
797 nop.i 0
798}
799;;
800
801{ .mfb
802 nop.m 0
803 nop.f 0
804(p6) br.cond.spnt SINH_CERTAIN_OVERFLOW // Branch if overflow
805}
806;;
807
808{ .mfb
809 nop.m 0
810 fma.d.s0 f8 = fS, fP, fS
811 br.ret.sptk b0 // Exit if really no overflow
812}
813;;
814
815SINH_CERTAIN_OVERFLOW:
816{ .mfi
817 sub rTmp = rExp_mask, r0, 1
818 fcmp.lt.s1 p6, p7 = fNormX, f0 // Test for x < 0
819 nop.i 0
820}
821;;
822
823{ .mmf
824 alloc r32=ar.pfs,1,4,4,0
825 setf.exp fTmp = rTmp
826 fmerge.s FR_X = f8,f8
827}
828;;
829
830{ .mfi
831 mov GR_Parameter_TAG = 127
832(p6) fnma.d.s0 FR_RESULT = fTmp, fTmp, f0 // Set I,O and -INF result
833 nop.i 0
834}
835{ .mfb
836 nop.m 0
837(p7) fma.d.s0 FR_RESULT = fTmp, fTmp, f0 // Set I,O and +INF result
838 br.cond.sptk __libm_error_region
839}
840;;
841
842// Here if x unorm
843SINH_UNORM:
844{ .mfb
845 getf.exp rSignexp_x = fNormX // Must recompute if x unorm
846 fcmp.eq.s0 p6, p0 = f8, f0 // Set D flag
847 br.cond.sptk SINH_COMMON
848}
849;;
850
851GLOBAL_IEEE754_END(sinh)
0609ec0a 852libm_alias_double_other (__sinh, sinh)
d5efd131
MF		 853
854
855LOCAL_LIBM_ENTRY(__libm_error_region)
856.prologue
857{ .mfi
858 add GR_Parameter_Y=-32,sp // Parameter 2 value
859 nop.f 0
860.save ar.pfs,GR_SAVE_PFS
861 mov GR_SAVE_PFS=ar.pfs // Save ar.pfs
862}
863{ .mfi
864.fframe 64
865 add sp=-64,sp // Create new stack
866 nop.f 0
867 mov GR_SAVE_GP=gp // Save gp
868};;
869{ .mmi
870 stfd [GR_Parameter_Y] = FR_Y,16 // STORE Parameter 2 on stack
871 add GR_Parameter_X = 16,sp // Parameter 1 address
872.save b0, GR_SAVE_B0
873 mov GR_SAVE_B0=b0 // Save b0
874};;
875.body
876{ .mib
877 stfd [GR_Parameter_X] = FR_X // STORE Parameter 1 on stack
878 add GR_Parameter_RESULT = 0,GR_Parameter_Y // Parameter 3 address
879 nop.b 0
880}
881{ .mib
882 stfd [GR_Parameter_Y] = FR_RESULT // STORE Parameter 3 on stack
883 add GR_Parameter_Y = -16,GR_Parameter_Y
884 br.call.sptk b0=__libm_error_support# // Call error handling function
885};;
886{ .mmi
887 add GR_Parameter_RESULT = 48,sp
888 nop.m 0
889 nop.i 0
890};;
891{ .mmi
892 ldfd f8 = [GR_Parameter_RESULT] // Get return result off stack
893.restore sp
894 add sp = 64,sp // Restore stack pointer
895 mov b0 = GR_SAVE_B0 // Restore return address
896};;
897{ .mib
898 mov gp = GR_SAVE_GP // Restore gp
899 mov ar.pfs = GR_SAVE_PFS // Restore ar.pfs
900 br.ret.sptk b0 // Return
901};;
902
903LOCAL_LIBM_END(__libm_error_region)
904.type __libm_error_support#,@function
905.global __libm_error_support#
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