| blob | f60907b72b8401afa865079c11a53ed071c378f8 |
1 .file "sinh.s"
4 // Copyright (c) 2000 - 2005, Intel Corporation
5 // All rights reserved.
6 //
7 // Contributed 2000 by the Intel Numerics Group, Intel Corporation
8 //
9 // Redistribution and use in source and binary forms, with or without
10 // modification, are permitted provided that the following conditions are
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12 //
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14 // notice, this list of conditions and the following disclaimer.
15 //
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19 //
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21 // products derived from this software without specific prior written
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24 // THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
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34 // SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
35 //
36 // Intel Corporation is the author of this code, and requests that all
37 // problem reports or change requests be submitted to it directly at
38 // http://www.intel.com/software/products/opensource/libraries/num.htm.
39 //
40 // History
41 //==============================================================
42 // 02/02/00 Initial version
43 // 04/04/00 Unwind support added
44 // 08/15/00 Bundle added after call to __libm_error_support to properly
45 // set [the previously overwritten] GR_Parameter_RESULT.
46 // 10/12/00 Update to set denormal operand and underflow flags
47 // 01/22/01 Fixed to set inexact flag for small args.
48 // 05/02/01 Reworked to improve speed of all paths
49 // 05/20/02 Cleaned up namespace and sf0 syntax
50 // 11/20/02 Improved speed with new algorithm
51 // 03/31/05 Reformatted delimiters between data tables
53 // API
54 //==============================================================
55 // double sinh(double)
57 // Overview of operation
58 //==============================================================
59 // Case 1: 0 < |x| < 2^-60
60 // Result = x, computed by x+sgn(x)*x^2) to handle flags and rounding
61 //
62 // Case 2: 2^-60 < |x| < 0.25
63 // Evaluate sinh(x) by a 13th order polynomial
64 // Care is take for the order of multiplication; and A1 is not exactly 1/3!,
65 // A2 is not exactly 1/5!, etc.
66 // sinh(x) = x + (A1*x^3 + A2*x^5 + A3*x^7 + A4*x^9 + A5*x^11 + A6*x^13)
67 //
68 // Case 3: 0.25 < |x| < 710.47586
69 // Algorithm is based on the identity sinh(x) = ( exp(x) - exp(-x) ) / 2.
70 // The algorithm for exp is described as below. There are a number of
71 // economies from evaluating both exp(x) and exp(-x). Although we
72 // are evaluating both quantities, only where the quantities diverge do we
73 // duplicate the computations. The basic algorithm for exp(x) is described
74 // below.
75 //
76 // Take the input x. w is "how many log2/128 in x?"
77 // w = x * 128/log2
78 // n = int(w)
79 // x = n log2/128 + r + delta
81 // n = 128M + index_1 + 2^4 index_2
82 // x = M log2 + (log2/128) index_1 + (log2/8) index_2 + r + delta
84 // exp(x) = 2^M 2^(index_1/128) 2^(index_2/8) exp(r) exp(delta)
85 // Construct 2^M
86 // Get 2^(index_1/128) from table_1;
87 // Get 2^(index_2/8) from table_2;
88 // Calculate exp(r) by 5th order polynomial
89 // r = x - n (log2/128)_high
90 // delta = - n (log2/128)_low
91 // Calculate exp(delta) as 1 + delta
94 // Special values
95 //==============================================================
96 // sinh(+0) = +0
97 // sinh(-0) = -0
99 // sinh(+qnan) = +qnan
100 // sinh(-qnan) = -qnan
101 // sinh(+snan) = +qnan
102 // sinh(-snan) = -qnan
104 // sinh(-inf) = -inf
105 // sinh(+inf) = +inf
107 // Overflow and Underflow
108 //=======================
109 // sinh(x) = largest double normal when
110 // |x| = 710.47586 = 0x408633ce8fb9f87d
111 //
112 // Underflow is handled as described in case 1 above
114 // Registers used
115 //==============================================================
116 // Floating Point registers used:
117 // f8, input, output
118 // f6 -> f15, f32 -> f61
120 // General registers used:
121 // r14 -> r40
123 // Predicate registers used:
124 // p6 -> p15
126 // Assembly macros
127 //==============================================================
129 rRshf = r14
130 rN_neg = r14
131 rAD_TB1 = r15
132 rAD_TB2 = r16
133 rAD_P = r17
134 rN = r18
135 rIndex_1 = r19
136 rIndex_2_16 = r20
137 rM = r21
138 rBiased_M = r21
139 rSig_inv_ln2 = r22
140 rIndex_1_neg = r22
141 rExp_bias = r23
142 rExp_bias_minus_1 = r23
143 rExp_mask = r24
144 rTmp = r24
145 rGt_ln = r24
146 rIndex_2_16_neg = r24
147 rM_neg = r25
148 rBiased_M_neg = r25
149 rRshf_2to56 = r26
150 rAD_T1_neg = r26
151 rExp_2tom56 = r28
152 rAD_T2_neg = r28
153 rAD_T1 = r29
154 rAD_T2 = r30
155 rSignexp_x = r31
156 rExp_x = r31
158 GR_SAVE_B0 = r33
159 GR_SAVE_PFS = r34
160 GR_SAVE_GP = r35
162 GR_Parameter_X = r37
163 GR_Parameter_Y = r38
164 GR_Parameter_RESULT = r39
165 GR_Parameter_TAG = r40
168 FR_X = f10
169 FR_Y = f1
170 FR_RESULT = f8
172 fRSHF_2TO56 = f6
173 fINV_LN2_2TO63 = f7
174 fW_2TO56_RSH = f9
175 f2TOM56 = f11
176 fP5 = f12
177 fP4 = f13
178 fP3 = f14
179 fP2 = f15
181 fLn2_by_128_hi = f33
182 fLn2_by_128_lo = f34
184 fRSHF = f35
185 fNfloat = f36
186 fNormX = f37
187 fR = f38
188 fF = f39
190 fRsq = f40
191 f2M = f41
192 fS1 = f42
193 fT1 = f42
194 fS2 = f43
195 fT2 = f43
196 fS = f43
197 fWre_urm_f8 = f44
198 fAbsX = f44
200 fMIN_DBL_OFLOW_ARG = f45
201 fMAX_DBL_NORM_ARG = f46
202 fXsq = f47
203 fX4 = f48
204 fGt_pln = f49
205 fTmp = f49
207 fP54 = f50
208 fP5432 = f50
209 fP32 = f51
210 fP = f52
211 fP54_neg = f53
212 fP5432_neg = f53
213 fP32_neg = f54
214 fP_neg = f55
215 fF_neg = f56
217 f2M_neg = f57
218 fS1_neg = f58
219 fT1_neg = f58
220 fS2_neg = f59
221 fT2_neg = f59
222 fS_neg = f59
223 fExp = f60
224 fExp_neg = f61
226 fA6 = f50
227 fA65 = f50
228 fA6543 = f50
229 fA654321 = f50
230 fA5 = f51
231 fA4 = f52
232 fA43 = f52
233 fA3 = f53
234 fA2 = f54
235 fA21 = f54
236 fA1 = f55
237 fX3 = f56
239 // Data tables
240 //==============================================================
242 RODATA
243 .align 16
245 // ************* DO NOT CHANGE ORDER OF THESE TABLES ********************
247 // double-extended 1/ln(2)
248 // 3fff b8aa 3b29 5c17 f0bb be87fed0691d3e88
249 // 3fff b8aa 3b29 5c17 f0bc
250 // For speed the significand will be loaded directly with a movl and setf.sig
251 // and the exponent will be bias+63 instead of bias+0. Thus subsequent
252 // computations need to scale appropriately.
253 // The constant 128/ln(2) is needed for the computation of w. This is also
254 // obtained by scaling the computations.
255 //
256 // Two shifting constants are loaded directly with movl and setf.d.
257 // 1. fRSHF_2TO56 = 1.1000..00 * 2^(63-7)
258 // This constant is added to x*1/ln2 to shift the integer part of
259 // x*128/ln2 into the rightmost bits of the significand.
260 // The result of this fma is fW_2TO56_RSH.
261 // 2. fRSHF = 1.1000..00 * 2^(63)
262 // This constant is subtracted from fW_2TO56_RSH * 2^(-56) to give
263 // the integer part of w, n, as a floating-point number.
264 // The result of this fms is fNfloat.
267 LOCAL_OBJECT_START(exp_table_1)
268 data8 0x408633ce8fb9f87e // smallest dbl overflow arg
269 data8 0x408633ce8fb9f87d // largest dbl arg to give normal dbl result
270 data8 0xb17217f7d1cf79ab , 0x00003ff7 // ln2/128 hi
271 data8 0xc9e3b39803f2f6af , 0x00003fb7 // ln2/128 lo
272 //
273 // Table 1 is 2^(index_1/128) where
274 // index_1 goes from 0 to 15
275 //
276 data8 0x8000000000000000 , 0x00003FFF
277 data8 0x80B1ED4FD999AB6C , 0x00003FFF
278 data8 0x8164D1F3BC030773 , 0x00003FFF
279 data8 0x8218AF4373FC25EC , 0x00003FFF
280 data8 0x82CD8698AC2BA1D7 , 0x00003FFF
281 data8 0x8383594EEFB6EE37 , 0x00003FFF
282 data8 0x843A28C3ACDE4046 , 0x00003FFF
283 data8 0x84F1F656379C1A29 , 0x00003FFF
284 data8 0x85AAC367CC487B15 , 0x00003FFF
285 data8 0x8664915B923FBA04 , 0x00003FFF
286 data8 0x871F61969E8D1010 , 0x00003FFF
287 data8 0x87DB357FF698D792 , 0x00003FFF
288 data8 0x88980E8092DA8527 , 0x00003FFF
289 data8 0x8955EE03618E5FDD , 0x00003FFF
290 data8 0x8A14D575496EFD9A , 0x00003FFF
291 data8 0x8AD4C6452C728924 , 0x00003FFF
292 LOCAL_OBJECT_END(exp_table_1)
294 // Table 2 is 2^(index_1/8) where
295 // index_2 goes from 0 to 7
296 LOCAL_OBJECT_START(exp_table_2)
297 data8 0x8000000000000000 , 0x00003FFF
298 data8 0x8B95C1E3EA8BD6E7 , 0x00003FFF
299 data8 0x9837F0518DB8A96F , 0x00003FFF
300 data8 0xA5FED6A9B15138EA , 0x00003FFF
301 data8 0xB504F333F9DE6484 , 0x00003FFF
302 data8 0xC5672A115506DADD , 0x00003FFF
303 data8 0xD744FCCAD69D6AF4 , 0x00003FFF
304 data8 0xEAC0C6E7DD24392F , 0x00003FFF
305 LOCAL_OBJECT_END(exp_table_2)
308 LOCAL_OBJECT_START(exp_p_table)
309 data8 0x3f8111116da21757 //P5
310 data8 0x3fa55555d787761c //P4
311 data8 0x3fc5555555555414 //P3
312 data8 0x3fdffffffffffd6a //P2
313 LOCAL_OBJECT_END(exp_p_table)
315 LOCAL_OBJECT_START(sinh_p_table)
316 data8 0xB08AF9AE78C1239F, 0x00003FDE // A6
317 data8 0xB8EF1D28926D8891, 0x00003FEC // A4
318 data8 0x8888888888888412, 0x00003FF8 // A2
319 data8 0xD732377688025BE9, 0x00003FE5 // A5
320 data8 0xD00D00D00D4D39F2, 0x00003FF2 // A3
321 data8 0xAAAAAAAAAAAAAAAB, 0x00003FFC // A1
322 LOCAL_OBJECT_END(sinh_p_table)
325 .section .text
326 GLOBAL_IEEE754_ENTRY(sinh)
328 { .mlx
329 getf.exp rSignexp_x = f8 // Must recompute if x unorm
330 movl rSig_inv_ln2 = 0xb8aa3b295c17f0bc // significand of 1/ln2
331 }
332 { .mlx
333 addl rAD_TB1 = @ltoff(exp_table_1), gp
334 movl rRshf_2to56 = 0x4768000000000000 // 1.10000 2^(63+56)
335 }
336 ;;
338 { .mfi
339 ld8 rAD_TB1 = [rAD_TB1]
340 fclass.m p6,p0 = f8,0x0b // Test for x=unorm
341 mov rExp_mask = 0x1ffff
342 }
343 { .mfi
344 mov rExp_bias = 0xffff
345 fnorm.s1 fNormX = f8
346 mov rExp_2tom56 = 0xffff-56
347 }
348 ;;
350 // Form two constants we need
351 // 1/ln2 * 2^63 to compute w = x * 1/ln2 * 128
352 // 1.1000..000 * 2^(63+63-7) to right shift int(w) into the significand
354 { .mfi
355 setf.sig fINV_LN2_2TO63 = rSig_inv_ln2 // form 1/ln2 * 2^63
356 fclass.m p8,p0 = f8,0x07 // Test for x=0
357 nop.i 999
358 }
359 { .mlx
360 setf.d fRSHF_2TO56 = rRshf_2to56 // Form const 1.100 * 2^(63+56)
361 movl rRshf = 0x43e8000000000000 // 1.10000 2^63 for right shift
362 }
363 ;;
365 { .mfi
366 ldfpd fMIN_DBL_OFLOW_ARG, fMAX_DBL_NORM_ARG = [rAD_TB1],16
367 fclass.m p10,p0 = f8,0x1e3 // Test for x=inf, nan, NaT
368 nop.i 0
369 }
370 { .mfb
371 setf.exp f2TOM56 = rExp_2tom56 // form 2^-56 for scaling Nfloat
372 nop.f 0
373 (p6) br.cond.spnt SINH_UNORM // Branch if x=unorm
374 }
375 ;;
377 SINH_COMMON:
378 { .mfi
379 ldfe fLn2_by_128_hi = [rAD_TB1],16
380 nop.f 0
381 nop.i 0
382 }
383 { .mfb
384 setf.d fRSHF = rRshf // Form right shift const 1.100 * 2^63
385 nop.f 0
386 (p8) br.ret.spnt b0 // Exit for x=0, result=x
387 }
388 ;;
390 { .mfi
391 ldfe fLn2_by_128_lo = [rAD_TB1],16
392 nop.f 0
393 nop.i 0
394 }
395 { .mfb
396 and rExp_x = rExp_mask, rSignexp_x // Biased exponent of x
397 (p10) fma.d.s0 f8 = f8,f1,f0 // Result if x=inf, nan, NaT
398 (p10) br.ret.spnt b0 // quick exit for x=inf, nan, NaT
399 }
400 ;;
402 // After that last load rAD_TB1 points to the beginning of table 1
403 { .mfi
404 nop.m 0
405 fcmp.eq.s0 p6,p0 = f8, f0 // Dummy to set D
406 sub rExp_x = rExp_x, rExp_bias // True exponent of x
407 }
408 ;;
410 { .mfi
411 nop.m 0
412 fmerge.s fAbsX = f0, fNormX // Form |x|
413 nop.i 0
414 }
415 { .mfb
416 cmp.gt p7, p0 = -2, rExp_x // Test |x| < 2^(-2)
417 fma.s1 fXsq = fNormX, fNormX, f0 // x*x for small path
418 (p7) br.cond.spnt SINH_SMALL // Branch if 0 < |x| < 2^-2
419 }
420 ;;
422 // W = X * Inv_log2_by_128
423 // By adding 1.10...0*2^63 we shift and get round_int(W) in significand.
424 // We actually add 1.10...0*2^56 to X * Inv_log2 to do the same thing.
426 { .mfi
427 add rAD_P = 0x180, rAD_TB1
428 fma.s1 fW_2TO56_RSH = fNormX, fINV_LN2_2TO63, fRSHF_2TO56
429 add rAD_TB2 = 0x100, rAD_TB1
430 }
431 ;;
433 // Divide arguments into the following categories:
434 // Certain Safe - 0.25 <= |x| <= MAX_DBL_NORM_ARG
435 // Possible Overflow p14 - MAX_DBL_NORM_ARG < |x| < MIN_DBL_OFLOW_ARG
436 // Certain Overflow p15 - MIN_DBL_OFLOW_ARG <= |x| < +inf
437 //
438 // If the input is really a double arg, then there will never be
439 // "Possible Overflow" arguments.
440 //
442 { .mfi
443 ldfpd fP5, fP4 = [rAD_P] ,16
444 fcmp.ge.s1 p15,p14 = fAbsX,fMIN_DBL_OFLOW_ARG
445 nop.i 0
446 }
447 ;;
449 // Nfloat = round_int(W)
450 // The signficand of fW_2TO56_RSH contains the rounded integer part of W,
451 // as a twos complement number in the lower bits (that is, it may be negative).
452 // That twos complement number (called N) is put into rN.
454 // Since fW_2TO56_RSH is scaled by 2^56, it must be multiplied by 2^-56
455 // before the shift constant 1.10000 * 2^63 is subtracted to yield fNfloat.
456 // Thus, fNfloat contains the floating point version of N
458 { .mfi
459 ldfpd fP3, fP2 = [rAD_P]
460 (p14) fcmp.gt.unc.s1 p14,p0 = fAbsX,fMAX_DBL_NORM_ARG
461 nop.i 0
462 }
463 { .mfb
464 nop.m 0
465 fms.s1 fNfloat = fW_2TO56_RSH, f2TOM56, fRSHF
466 (p15) br.cond.spnt SINH_CERTAIN_OVERFLOW
467 }
468 ;;
470 { .mfi
471 getf.sig rN = fW_2TO56_RSH
472 nop.f 0
473 mov rExp_bias_minus_1 = 0xfffe
474 }
475 ;;
477 // rIndex_1 has index_1
478 // rIndex_2_16 has index_2 * 16
479 // rBiased_M has M
481 // rM has true M
482 // r = x - Nfloat * ln2_by_128_hi
483 // f = 1 - Nfloat * ln2_by_128_lo
484 { .mfi
485 and rIndex_1 = 0x0f, rN
486 fnma.s1 fR = fNfloat, fLn2_by_128_hi, fNormX
487 shr rM = rN, 0x7
488 }
489 { .mfi
490 and rIndex_2_16 = 0x70, rN
491 fnma.s1 fF = fNfloat, fLn2_by_128_lo, f1
492 sub rN_neg = r0, rN
493 }
494 ;;
496 { .mmi
497 and rIndex_1_neg = 0x0f, rN_neg
498 add rBiased_M = rExp_bias_minus_1, rM
499 shr rM_neg = rN_neg, 0x7
500 }
501 { .mmi
502 and rIndex_2_16_neg = 0x70, rN_neg
503 add rAD_T2 = rAD_TB2, rIndex_2_16
504 shladd rAD_T1 = rIndex_1, 4, rAD_TB1
505 }
506 ;;
508 // rAD_T1 has address of T1
509 // rAD_T2 has address if T2
511 { .mmi
512 setf.exp f2M = rBiased_M
513 ldfe fT2 = [rAD_T2]
514 nop.i 0
515 }
516 { .mmi
517 add rBiased_M_neg = rExp_bias_minus_1, rM_neg
518 add rAD_T2_neg = rAD_TB2, rIndex_2_16_neg
519 shladd rAD_T1_neg = rIndex_1_neg, 4, rAD_TB1
520 }
521 ;;
523 // Create Scale = 2^M
524 // Load T1 and T2
525 { .mmi
526 ldfe fT1 = [rAD_T1]
527 nop.m 0
528 nop.i 0
529 }
530 { .mmf
531 setf.exp f2M_neg = rBiased_M_neg
532 ldfe fT2_neg = [rAD_T2_neg]
533 fma.s1 fF_neg = fNfloat, fLn2_by_128_lo, f1
534 }
535 ;;
537 { .mfi
538 nop.m 0
539 fma.s1 fRsq = fR, fR, f0
540 nop.i 0
541 }
542 { .mfi
543 ldfe fT1_neg = [rAD_T1_neg]
544 fma.s1 fP54 = fR, fP5, fP4
545 nop.i 0
546 }
547 ;;
549 { .mfi
550 nop.m 0
551 fma.s1 fP32 = fR, fP3, fP2
552 nop.i 0
553 }
554 { .mfi
555 nop.m 0
556 fnma.s1 fP54_neg = fR, fP5, fP4
557 nop.i 0
558 }
559 ;;
561 { .mfi
562 nop.m 0
563 fnma.s1 fP32_neg = fR, fP3, fP2
564 nop.i 0
565 }
566 ;;
568 { .mfi
569 nop.m 0
570 fma.s1 fP5432 = fRsq, fP54, fP32
571 nop.i 0
572 }
573 { .mfi
574 nop.m 0
575 fma.s1 fS2 = fF,fT2,f0
576 nop.i 0
577 }
578 ;;
580 { .mfi
581 nop.m 0
582 fma.s1 fS1 = f2M,fT1,f0
583 nop.i 0
584 }
585 { .mfi
586 nop.m 0
587 fma.s1 fP5432_neg = fRsq, fP54_neg, fP32_neg
588 nop.i 0
589 }
590 ;;
592 { .mfi
593 nop.m 0
594 fma.s1 fS1_neg = f2M_neg,fT1_neg,f0
595 nop.i 0
596 }
597 { .mfi
598 nop.m 0
599 fma.s1 fS2_neg = fF_neg,fT2_neg,f0
600 nop.i 0
601 }
602 ;;
604 { .mfi
605 nop.m 0
606 fma.s1 fP = fRsq, fP5432, fR
607 nop.i 0
608 }
609 { .mfi
610 nop.m 0
611 fma.s1 fS = fS1,fS2,f0
612 nop.i 0
613 }
614 ;;
616 { .mfi
617 nop.m 0
618 fms.s1 fP_neg = fRsq, fP5432_neg, fR
619 nop.i 0
620 }
621 { .mfi
622 nop.m 0
623 fma.s1 fS_neg = fS1_neg,fS2_neg,f0
624 nop.i 0
625 }
626 ;;
628 { .mfb
629 nop.m 0
630 fmpy.s0 fTmp = fLn2_by_128_lo, fLn2_by_128_lo // Force inexact
631 (p14) br.cond.spnt SINH_POSSIBLE_OVERFLOW
632 }
633 ;;
635 { .mfi
636 nop.m 0
637 fma.s1 fExp = fS, fP, fS
638 nop.i 0
639 }
640 { .mfi
641 nop.m 0
642 fma.s1 fExp_neg = fS_neg, fP_neg, fS_neg
643 nop.i 0
644 }
645 ;;
647 { .mfb
648 nop.m 0
649 fms.d.s0 f8 = fExp, f1, fExp_neg
650 br.ret.sptk b0 // Normal path exit
651 }
652 ;;
654 // Here if 0 < |x| < 0.25
655 SINH_SMALL:
656 { .mfi
657 add rAD_T1 = 0x1a0, rAD_TB1
658 fcmp.lt.s1 p7, p8 = fNormX, f0 // Test sign of x
659 cmp.gt p6, p0 = -60, rExp_x // Test |x| < 2^(-60)
660 }
661 { .mfi
662 add rAD_T2 = 0x1d0, rAD_TB1
663 nop.f 0
664 nop.i 0
665 }
666 ;;
668 { .mmb
669 ldfe fA6 = [rAD_T1],16
670 ldfe fA5 = [rAD_T2],16
671 (p6) br.cond.spnt SINH_VERY_SMALL // Branch if |x| < 2^(-60)
672 }
673 ;;
675 { .mmi
676 ldfe fA4 = [rAD_T1],16
677 ldfe fA3 = [rAD_T2],16
678 nop.i 0
679 }
680 ;;
682 { .mmi
683 ldfe fA2 = [rAD_T1]
684 ldfe fA1 = [rAD_T2]
685 nop.i 0
686 }
687 ;;
689 { .mfi
690 nop.m 0
691 fma.s1 fX3 = fNormX, fXsq, f0
692 nop.i 0
693 }
694 { .mfi
695 nop.m 0
696 fma.s1 fX4 = fXsq, fXsq, f0
697 nop.i 0
698 }
699 ;;
701 { .mfi
702 nop.m 0
703 fma.s1 fA65 = fXsq, fA6, fA5
704 nop.i 0
705 }
706 { .mfi
707 nop.m 0
708 fma.s1 fA43 = fXsq, fA4, fA3
709 nop.i 0
710 }
711 ;;
713 { .mfi
714 nop.m 0
715 fma.s1 fA21 = fXsq, fA2, fA1
716 nop.i 0
717 }
718 ;;
720 { .mfi
721 nop.m 0
722 fma.s1 fA6543 = fX4, fA65, fA43
723 nop.i 0
724 }
725 ;;
727 { .mfi
728 nop.m 0
729 fma.s1 fA654321 = fX4, fA6543, fA21
730 nop.i 0
731 }
732 ;;
734 // Dummy multiply to generate inexact
735 { .mfi
736 nop.m 0
737 fmpy.s0 fTmp = fA6, fA6
738 nop.i 0
739 }
740 { .mfb
741 nop.m 0
742 fma.d.s0 f8 = fA654321, fX3, fNormX
743 br.ret.sptk b0 // Exit if 2^-60 < |x| < 0.25
744 }
745 ;;
747 SINH_VERY_SMALL:
748 // Here if 0 < |x| < 2^-60
749 // Compute result by x + sgn(x)*x^2 to get properly rounded result
750 .pred.rel "mutex",p7,p8
751 { .mfi
752 nop.m 0
753 (p7) fnma.d.s0 f8 = fNormX, fNormX, fNormX // If x<0 result ~ x-x^2
754 nop.i 0
755 }
756 { .mfb
757 nop.m 0
758 (p8) fma.d.s0 f8 = fNormX, fNormX, fNormX // If x>0 result ~ x+x^2
759 br.ret.sptk b0 // Exit if |x| < 2^-60
760 }
761 ;;
764 SINH_POSSIBLE_OVERFLOW:
766 // Here if fMAX_DBL_NORM_ARG < |x| < fMIN_DBL_OFLOW_ARG
767 // This cannot happen if input is a double, only if input higher precision.
768 // Overflow is a possibility, not a certainty.
770 // Recompute result using status field 2 with user's rounding mode,
771 // and wre set. If result is larger than largest double, then we have
772 // overflow
774 { .mfi
775 mov rGt_ln = 0x103ff // Exponent for largest dbl + 1 ulp
776 fsetc.s2 0x7F,0x42 // Get user's round mode, set wre
777 nop.i 0
778 }
779 ;;
781 { .mfi
782 setf.exp fGt_pln = rGt_ln // Create largest double + 1 ulp
783 fma.d.s2 fWre_urm_f8 = fS, fP, fS // Result with wre set
784 nop.i 0
785 }
786 ;;
788 { .mfi
789 nop.m 0
790 fsetc.s2 0x7F,0x40 // Turn off wre in sf2
791 nop.i 0
792 }
793 ;;
795 { .mfi
796 nop.m 0
797 fcmp.ge.s1 p6, p0 = fWre_urm_f8, fGt_pln // Test for overflow
798 nop.i 0
799 }
800 ;;
802 { .mfb
803 nop.m 0
804 nop.f 0
805 (p6) br.cond.spnt SINH_CERTAIN_OVERFLOW // Branch if overflow
806 }
807 ;;
809 { .mfb
810 nop.m 0
811 fma.d.s0 f8 = fS, fP, fS
812 br.ret.sptk b0 // Exit if really no overflow
813 }
814 ;;
816 SINH_CERTAIN_OVERFLOW:
817 { .mfi
818 sub rTmp = rExp_mask, r0, 1
819 fcmp.lt.s1 p6, p7 = fNormX, f0 // Test for x < 0
820 nop.i 0
821 }
822 ;;
824 { .mmf
825 alloc r32=ar.pfs,1,4,4,0
826 setf.exp fTmp = rTmp
827 fmerge.s FR_X = f8,f8
828 }
829 ;;
831 { .mfi
832 mov GR_Parameter_TAG = 127
833 (p6) fnma.d.s0 FR_RESULT = fTmp, fTmp, f0 // Set I,O and -INF result
834 nop.i 0
835 }
836 { .mfb
837 nop.m 0
838 (p7) fma.d.s0 FR_RESULT = fTmp, fTmp, f0 // Set I,O and +INF result
839 br.cond.sptk __libm_error_region
840 }
841 ;;
843 // Here if x unorm
844 SINH_UNORM:
845 { .mfb
846 getf.exp rSignexp_x = fNormX // Must recompute if x unorm
847 fcmp.eq.s0 p6, p0 = f8, f0 // Set D flag
848 br.cond.sptk SINH_COMMON
849 }
850 ;;
852 GLOBAL_IEEE754_END(sinh)
855 LOCAL_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 };;
903 LOCAL_LIBM_END(__libm_error_region)
904 .type __libm_error_support#,@function
905 .global __libm_error_support#