| blob | f995c597f44f3b781a3fcf253bd91d3e726a8a30 |
1 .file "asin.s"
4 // Copyright (c) 2000 - 2003 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
11 // met:
12 //
13 // * Redistributions of source code must retain the above copyright
14 // notice, this list of conditions and the following disclaimer.
15 //
16 // * Redistributions in binary form must reproduce the above copyright
17 // notice, this list of conditions and the following disclaimer in the
18 // documentation and/or other materials provided with the distribution.
19 //
20 // * The name of Intel Corporation may not be used to endorse or promote
21 // products derived from this software without specific prior written
22 // permission.
24 // THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
25 // "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
26 // LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
27 // A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL INTEL OR ITS
28 // CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
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32 // OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY OR TORT (INCLUDING
33 // NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
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.
40 // History
41 //==============================================================
42 // 02/02/00 Initial version
43 // 08/17/00 New and much faster algorithm.
44 // 08/31/00 Avoided bank conflicts on loads, shortened |x|=1 path,
45 // fixed mfb split issue stalls.
46 // 12/19/00 Fixed small arg cases to force inexact, or inexact and underflow.
47 // 08/02/02 New and much faster algorithm II
48 // 02/06/03 Reordered header: .section, .global, .proc, .align
50 // Description
51 //=========================================
52 // The asin function computes the principal value of the arc sine of x.
53 // asin(0) returns 0, asin(1) returns pi/2, asin(-1) returns -pi/2.
54 // A doman error occurs for arguments not in the range [-1,+1].
55 //
56 // The asin function returns the arc sine in the range [-pi/2, +pi/2] radians.
57 //
58 // There are 8 paths:
59 // 1. x = +/-0.0
60 // Return asin(x) = +/-0.0
61 //
62 // 2. 0.0 < |x| < 0.625
63 // Return asin(x) = x + x^3 *PolA(x^2)
64 // where PolA(x^2) = A3 + A5*x^2 + A7*x^4 +...+ A35*x^32
65 //
66 // 3. 0.625 <=|x| < 1.0
67 // Return asin(x) = sign(x) * ( Pi/2 - sqrt(R) * PolB(R))
68 // Where R = 1 - |x|,
69 // PolB(R) = B0 + B1*R + B2*R^2 +...+B12*R^12
70 //
71 // sqrt(R) is approximated using the following sequence:
72 // y0 = (1 + eps)/sqrt(R) - initial approximation by frsqrta,
73 // |eps| < 2^(-8)
74 // Then 3 iterations are used to refine the result:
75 // H0 = 0.5*y0
76 // S0 = R*y0
77 //
78 // d0 = 0.5 - H0*S0
79 // H1 = H0 + d0*H0
80 // S1 = S0 + d0*S0
81 //
82 // d1 = 0.5 - H1*S1
83 // H2 = H1 + d0*H1
84 // S2 = S1 + d0*S1
85 //
86 // d2 = 0.5 - H2*S2
87 // S3 = S3 + d2*S3
88 //
89 // S3 approximates sqrt(R) with enough accuracy for this algorithm
90 //
91 // So, the result should be reconstracted as follows:
92 // asin(x) = sign(x) * (Pi/2 - S3*PolB(R))
93 //
94 // But for optimization perposes the reconstruction step is slightly
95 // changed:
96 // asin(x) = sign(x)*(Pi/2 - PolB(R)*S2) + sign(x)*d2*S2*PolB(R)
97 //
98 // 4. |x| = 1.0
99 // Return asin(x) = sign(x)*Pi/2
100 //
101 // 5. 1.0 < |x| <= +INF
102 // A doman error occurs for arguments not in the range [-1,+1]
103 //
104 // 6. x = [S,Q]NaN
105 // Return asin(x) = QNaN
106 //
107 // 7. x is denormal
108 // Return asin(x) = x + x^3,
109 //
110 // 8. x is unnormal
111 // Normalize input in f8 and return to the very beginning of the function
112 //
113 // Registers used
114 //==============================================================
115 // Floating Point registers used:
116 // f8, input, output
117 // f6, f7, f9 -> f15, f32 -> f63
119 // General registers used:
120 // r3, r21 -> r31, r32 -> r38
122 // Predicate registers used:
123 // p0, p6 -> p14
125 //
126 // Assembly macros
127 //=========================================
128 // integer registers used
129 // scratch
130 rTblAddr = r3
132 rPiBy2Ptr = r21
133 rTmpPtr3 = r22
134 rDenoBound = r23
135 rOne = r24
136 rAbsXBits = r25
137 rHalf = r26
138 r0625 = r27
139 rSign = r28
140 rXBits = r29
141 rTmpPtr2 = r30
142 rTmpPtr1 = r31
144 // stacked
145 GR_SAVE_PFS = r32
146 GR_SAVE_B0 = r33
147 GR_SAVE_GP = r34
148 GR_Parameter_X = r35
149 GR_Parameter_Y = r36
150 GR_Parameter_RESULT = r37
151 GR_Parameter_TAG = r38
153 // floating point registers used
154 FR_X = f10
155 FR_Y = f1
156 FR_RESULT = f8
159 // scratch
160 fXSqr = f6
161 fXCube = f7
162 fXQuadr = f9
163 f1pX = f10
164 f1mX = f11
165 f1pXRcp = f12
166 f1mXRcp = f13
167 fH = f14
168 fS = f15
169 // stacked
170 fA3 = f32
171 fB1 = f32
172 fA5 = f33
173 fB2 = f33
174 fA7 = f34
175 fPiBy2 = f34
176 fA9 = f35
177 fA11 = f36
178 fB10 = f35
179 fB11 = f36
180 fA13 = f37
181 fA15 = f38
182 fB4 = f37
183 fB5 = f38
184 fA17 = f39
185 fA19 = f40
186 fB6 = f39
187 fB7 = f40
188 fA21 = f41
189 fA23 = f42
190 fB3 = f41
191 fB8 = f42
192 fA25 = f43
193 fA27 = f44
194 fB9 = f43
195 fB12 = f44
196 fA29 = f45
197 fA31 = f46
198 fA33 = f47
199 fA35 = f48
200 fBaseP = f49
201 fB0 = f50
202 fSignedS = f51
203 fD = f52
204 fHalf = f53
205 fR = f54
206 fCloseTo1Pol = f55
207 fSignX = f56
208 fDenoBound = f57
209 fNormX = f58
210 fX8 = f59
211 fRSqr = f60
212 fRQuadr = f61
213 fR8 = f62
214 fX16 = f63
215 // Data tables
216 //==============================================================
217 RODATA
218 .align 16
219 LOCAL_OBJECT_START(asin_base_range_table)
220 // Ai: Polynomial coefficients for the asin(x), |x| < .625000
221 // Bi: Polynomial coefficients for the asin(x), |x| > .625000
222 data8 0xBFDAAB56C01AE468 //A29
223 data8 0x3FE1C470B76A5B2B //A31
224 data8 0xBFDC5FF82A0C4205 //A33
225 data8 0x3FC71FD88BFE93F0 //A35
226 data8 0xB504F333F9DE6487, 0x00003FFF //B0
227 data8 0xAAAAAAAAAAAAFC18, 0x00003FFC //A3
228 data8 0x3F9F1C71BC4A7823 //A9
229 data8 0x3F96E8BBAAB216B2 //A11
230 data8 0x3F91C4CA1F9F8A98 //A13
231 data8 0x3F8C9DDCEDEBE7A6 //A15
232 data8 0x3F877784442B1516 //A17
233 data8 0x3F859C0491802BA2 //A19
234 data8 0x9999999998C88B8F, 0x00003FFB //A5
235 data8 0x3F6BD7A9A660BF5E //A21
236 data8 0x3F9FC1659340419D //A23
237 data8 0xB6DB6DB798149BDF, 0x00003FFA //A7
238 data8 0xBFB3EF18964D3ED3 //A25
239 data8 0x3FCD285315542CF2 //A27
240 data8 0xF15BEEEFF7D2966A, 0x00003FFB //B1
241 data8 0x3EF0DDA376D10FB3 //B10
242 data8 0xBEB83CAFE05EBAC9 //B11
243 data8 0x3F65FFB67B513644 //B4
244 data8 0x3F5032FBB86A4501 //B5
245 data8 0x3F392162276C7CBA //B6
246 data8 0x3F2435949FD98BDF //B7
247 data8 0xD93923D7FA08341C, 0x00003FF9 //B2
248 data8 0x3F802995B6D90BDB //B3
249 data8 0x3F10DF86B341A63F //B8
250 data8 0xC90FDAA22168C235, 0x00003FFF // Pi/2
251 data8 0x3EFA3EBD6B0ECB9D //B9
252 data8 0x3EDE18BA080E9098 //B12
253 LOCAL_OBJECT_END(asin_base_range_table)
256 .section .text
257 GLOBAL_LIBM_ENTRY(asin)
258 asin_unnormal_back:
259 { .mfi
260 getf.d rXBits = f8 // grab bits of input value
261 // set p12 = 1 if x is a NaN, denormal, or zero
262 fclass.m p12, p0 = f8, 0xcf
263 adds rSign = 1, r0
264 }
265 { .mfi
266 addl rTblAddr = @ltoff(asin_base_range_table),gp
267 // 1 - x = 1 - |x| for positive x
268 fms.s1 f1mX = f1, f1, f8
269 addl rHalf = 0xFFFE, r0 // exponent of 1/2
270 }
271 ;;
272 { .mfi
273 addl r0625 = 0x3FE4, r0 // high 16 bits of 0.625
274 // set p8 = 1 if x < 0
275 fcmp.lt.s1 p8, p9 = f8, f0
276 shl rSign = rSign, 63 // sign bit
277 }
278 { .mfi
279 // point to the beginning of the table
280 ld8 rTblAddr = [rTblAddr]
281 // 1 + x = 1 - |x| for negative x
282 fma.s1 f1pX = f1, f1, f8
283 adds rOne = 0x3FF, r0
284 }
285 ;;
286 { .mfi
287 andcm rAbsXBits = rXBits, rSign // bits of |x|
288 fmerge.s fSignX = f8, f1 // signum(x)
289 shl r0625 = r0625, 48 // bits of DP representation of 0.625
290 }
291 { .mfb
292 setf.exp fHalf = rHalf // load A2 to FP reg
293 fma.s1 fXSqr = f8, f8, f0 // x^2
294 // branch on special path if x is a NaN, denormal, or zero
295 (p12) br.cond.spnt asin_special
296 }
297 ;;
298 { .mfi
299 adds rPiBy2Ptr = 272, rTblAddr
300 nop.f 0
301 shl rOne = rOne, 52 // bits of 1.0
302 }
303 { .mfi
304 adds rTmpPtr1 = 16, rTblAddr
305 nop.f 0
306 // set p6 = 1 if |x| < 0.625
307 cmp.lt p6, p7 = rAbsXBits, r0625
308 }
309 ;;
310 { .mfi
311 ldfpd fA29, fA31 = [rTblAddr] // A29, fA31
312 // 1 - x = 1 - |x| for positive x
313 (p9) fms.s1 fR = f1, f1, f8
314 // point to coefficient of "near 1" polynomial
315 (p7) adds rTmpPtr2 = 176, rTblAddr
316 }
317 { .mfi
318 ldfpd fA33, fA35 = [rTmpPtr1], 16 // A33, fA35
319 // 1 + x = 1 - |x| for negative x
320 (p8) fma.s1 fR = f1, f1, f8
321 (p6) adds rTmpPtr2 = 48, rTblAddr
322 }
323 ;;
324 { .mfi
325 ldfe fB0 = [rTmpPtr1], 16 // B0
326 nop.f 0
327 nop.i 0
328 }
329 { .mib
330 adds rTmpPtr3 = 16, rTmpPtr2
331 // set p10 = 1 if |x| = 1.0
332 cmp.eq p10, p0 = rAbsXBits, rOne
333 // branch on special path for |x| = 1.0
334 (p10) br.cond.spnt asin_abs_1
335 }
336 ;;
337 { .mfi
338 ldfe fA3 = [rTmpPtr2], 48 // A3 or B1
339 nop.f 0
340 adds rTmpPtr1 = 64, rTmpPtr3
341 }
342 { .mib
343 ldfpd fA9, fA11 = [rTmpPtr3], 16 // A9, A11 or B10, B11
344 // set p11 = 1 if |x| > 1.0
345 cmp.gt p11, p0 = rAbsXBits, rOne
346 // branch on special path for |x| > 1.0
347 (p11) br.cond.spnt asin_abs_gt_1
348 }
349 ;;
350 { .mfi
351 ldfpd fA17, fA19 = [rTmpPtr2], 16 // A17, A19 or B6, B7
352 // initial approximation of 1 / sqrt(1 - x)
353 frsqrta.s1 f1mXRcp, p0 = f1mX
354 nop.i 0
355 }
356 { .mfi
357 ldfpd fA13, fA15 = [rTmpPtr3] // A13, A15 or B4, B5
358 fma.s1 fXCube = fXSqr, f8, f0 // x^3
359 nop.i 0
360 }
361 ;;
362 { .mfi
363 ldfe fA5 = [rTmpPtr2], 48 // A5 or B2
364 // initial approximation of 1 / sqrt(1 + x)
365 frsqrta.s1 f1pXRcp, p0 = f1pX
366 nop.i 0
367 }
368 { .mfi
369 ldfpd fA21, fA23 = [rTmpPtr1], 16 // A21, A23 or B3, B8
370 fma.s1 fXQuadr = fXSqr, fXSqr, f0 // x^4
371 nop.i 0
372 }
373 ;;
374 { .mfi
375 ldfe fA7 = [rTmpPtr1] // A7 or Pi/2
376 fma.s1 fRSqr = fR, fR, f0 // R^2
377 nop.i 0
378 }
379 { .mfb
380 ldfpd fA25, fA27 = [rTmpPtr2] // A25, A27 or B9, B12
381 nop.f 0
382 (p6) br.cond.spnt asin_base_range;
383 }
384 ;;
386 { .mfi
387 nop.m 0
388 (p9) fma.s1 fH = fHalf, f1mXRcp, f0 // H0 for x > 0
389 nop.i 0
390 }
391 { .mfi
392 nop.m 0
393 (p9) fma.s1 fS = f1mX, f1mXRcp, f0 // S0 for x > 0
394 nop.i 0
395 }
396 ;;
397 { .mfi
398 nop.m 0
399 (p8) fma.s1 fH = fHalf, f1pXRcp, f0 // H0 for x < 0
400 nop.i 0
401 }
402 { .mfi
403 nop.m 0
404 (p8) fma.s1 fS = f1pX, f1pXRcp, f0 // S0 for x > 0
405 nop.i 0
406 }
407 ;;
408 { .mfi
409 nop.m 0
410 fma.s1 fRQuadr = fRSqr, fRSqr, f0 // R^4
411 nop.i 0
412 }
413 ;;
414 { .mfi
415 nop.m 0
416 fma.s1 fB11 = fB11, fR, fB10
417 nop.i 0
418 }
419 { .mfi
420 nop.m 0
421 fma.s1 fB1 = fB1, fR, fB0
422 nop.i 0
423 }
424 ;;
425 { .mfi
426 nop.m 0
427 fma.s1 fB5 = fB5, fR, fB4
428 nop.i 0
429 }
430 { .mfi
431 nop.m 0
432 fma.s1 fB7 = fB7, fR, fB6
433 nop.i 0
434 }
435 ;;
436 { .mfi
437 nop.m 0
438 fma.s1 fB3 = fB3, fR, fB2
439 nop.i 0
440 }
441 ;;
442 { .mfi
443 nop.m 0
444 fnma.s1 fD = fH, fS, fHalf // d0 = 1/2 - H0*S0
445 nop.i 0
446 }
447 ;;
448 { .mfi
449 nop.m 0
450 fma.s1 fR8 = fRQuadr, fRQuadr, f0 // R^4
451 nop.i 0
452 }
453 { .mfi
454 nop.m 0
455 fma.s1 fB9 = fB9, fR, fB8
456 nop.i 0
457 }
458 ;;
459 {.mfi
460 nop.m 0
461 fma.s1 fB12 = fB12, fRSqr, fB11
462 nop.i 0
463 }
464 {.mfi
465 nop.m 0
466 fma.s1 fB7 = fB7, fRSqr, fB5
467 nop.i 0
468 }
469 ;;
470 {.mfi
471 nop.m 0
472 fma.s1 fB3 = fB3, fRSqr, fB1
473 nop.i 0
474 }
475 ;;
476 { .mfi
477 nop.m 0
478 fma.s1 fH = fH, fD, fH // H1 = H0 + H0*d0
479 nop.i 0
480 }
481 { .mfi
482 nop.m 0
483 fma.s1 fS = fS, fD, fS // S1 = S0 + S0*d0
484 nop.i 0
485 }
486 ;;
487 {.mfi
488 nop.m 0
489 fma.s1 fPiBy2 = fPiBy2, fSignX, f0 // signum(x)*Pi/2
490 nop.i 0
491 }
492 ;;
493 { .mfi
494 nop.m 0
495 fma.s1 fB12 = fB12, fRSqr, fB9
496 nop.i 0
497 }
498 { .mfi
499 nop.m 0
500 fma.s1 fB7 = fB7, fRQuadr, fB3
501 nop.i 0
502 }
503 ;;
504 {.mfi
505 nop.m 0
506 fnma.s1 fD = fH, fS, fHalf // d1 = 1/2 - H1*S1
507 nop.i 0
508 }
509 { .mfi
510 nop.m 0
511 fnma.s1 fSignedS = fSignX, fS, f0 // -signum(x)*S1
512 nop.i 0
513 }
514 ;;
515 { .mfi
516 nop.m 0
517 fma.s1 fCloseTo1Pol = fB12, fR8, fB7
518 nop.i 0
519 }
520 ;;
521 { .mfi
522 nop.m 0
523 fma.s1 fH = fH, fD, fH // H2 = H1 + H1*d1
524 nop.i 0
525 }
526 { .mfi
527 nop.m 0
528 fma.s1 fS = fS, fD, fS // S2 = S1 + S1*d1
529 nop.i 0
530 }
531 ;;
532 { .mfi
533 nop.m 0
534 // -signum(x)* S2 = -signum(x)*(S1 + S1*d1)
535 fma.s1 fSignedS = fSignedS, fD, fSignedS
536 nop.i 0
537 }
538 ;;
539 {.mfi
540 nop.m 0
541 fnma.s1 fD = fH, fS, fHalf // d2 = 1/2 - H2*S2
542 nop.i 0
543 }
544 ;;
545 { .mfi
546 nop.m 0
547 // signum(x)*(Pi/2 - PolB*S2)
548 fma.s1 fPiBy2 = fSignedS, fCloseTo1Pol, fPiBy2
549 nop.i 0
550 }
551 { .mfi
552 nop.m 0
553 // -signum(x)*PolB * S2
554 fma.s1 fCloseTo1Pol = fSignedS, fCloseTo1Pol, f0
555 nop.i 0
556 }
557 ;;
558 { .mfb
559 nop.m 0
560 // final result for 0.625 <= |x| < 1
561 fma.d.s0 f8 = fCloseTo1Pol, fD, fPiBy2
562 // exit here for 0.625 <= |x| < 1
563 br.ret.sptk b0
564 }
565 ;;
568 // here if |x| < 0.625
569 .align 32
570 asin_base_range:
571 { .mfi
572 nop.m 0
573 fma.s1 fA33 = fA33, fXSqr, fA31
574 nop.i 0
575 }
576 { .mfi
577 nop.m 0
578 fma.s1 fA15 = fA15, fXSqr, fA13
579 nop.i 0
580 }
581 ;;
582 { .mfi
583 nop.m 0
584 fma.s1 fA29 = fA29, fXSqr, fA27
585 nop.i 0
586 }
587 { .mfi
588 nop.m 0
589 fma.s1 fA25 = fA25, fXSqr, fA23
590 nop.i 0
591 }
592 ;;
593 { .mfi
594 nop.m 0
595 fma.s1 fA21 = fA21, fXSqr, fA19
596 nop.i 0
597 }
598 { .mfi
599 nop.m 0
600 fma.s1 fA9 = fA9, fXSqr, fA7
601 nop.i 0
602 }
603 ;;
604 { .mfi
605 nop.m 0
606 fma.s1 fA5 = fA5, fXSqr, fA3
607 nop.i 0
608 }
609 ;;
610 { .mfi
611 nop.m 0
612 fma.s1 fA35 = fA35, fXQuadr, fA33
613 nop.i 0
614 }
615 { .mfi
616 nop.m 0
617 fma.s1 fA17 = fA17, fXQuadr, fA15
618 nop.i 0
619 }
620 ;;
621 { .mfi
622 nop.m 0
623 fma.s1 fX8 = fXQuadr, fXQuadr, f0 // x^8
624 nop.i 0
625 }
626 { .mfi
627 nop.m 0
628 fma.s1 fA25 = fA25, fXQuadr, fA21
629 nop.i 0
630 }
631 ;;
632 { .mfi
633 nop.m 0
634 fma.s1 fA9 = fA9, fXQuadr, fA5
635 nop.i 0
636 }
637 ;;
638 { .mfi
639 nop.m 0
640 fma.s1 fA35 = fA35, fXQuadr, fA29
641 nop.i 0
642 }
643 { .mfi
644 nop.m 0
645 fma.s1 fA17 = fA17, fXSqr, fA11
646 nop.i 0
647 }
648 ;;
649 { .mfi
650 nop.m 0
651 fma.s1 fX16 = fX8, fX8, f0 // x^16
652 nop.i 0
653 }
654 ;;
655 { .mfi
656 nop.m 0
657 fma.s1 fA35 = fA35, fX8, fA25
658 nop.i 0
659 }
660 { .mfi
661 nop.m 0
662 fma.s1 fA17 = fA17, fX8, fA9
663 nop.i 0
664 }
665 ;;
666 { .mfi
667 nop.m 0
668 fma.s1 fBaseP = fA35, fX16, fA17
669 nop.i 0
670 }
671 ;;
672 { .mfb
673 nop.m 0
674 // final result for |x| < 0.625
675 fma.d.s0 f8 = fBaseP, fXCube, f8
676 // exit here for |x| < 0.625 path
677 br.ret.sptk b0
678 }
679 ;;
681 // here if |x| = 1
682 // asin(x) = sign(x) * Pi/2
683 .align 32
684 asin_abs_1:
685 { .mfi
686 ldfe fPiBy2 = [rPiBy2Ptr] // Pi/2
687 nop.f 0
688 nop.i 0
689 }
690 ;;
691 {.mfb
692 nop.m 0
693 // result for |x| = 1.0
694 fma.d.s0 f8 = fPiBy2, fSignX, f0
695 // exit here for |x| = 1.0
696 br.ret.sptk b0
697 }
698 ;;
700 // here if x is a NaN, denormal, or zero
701 .align 32
702 asin_special:
703 { .mfi
704 nop.m 0
705 // set p12 = 1 if x is a NaN
706 fclass.m p12, p0 = f8, 0xc3
707 nop.i 0
708 }
709 { .mlx
710 nop.m 0
711 // smallest positive DP normalized number
712 movl rDenoBound = 0x0010000000000000
713 }
714 ;;
715 { .mfi
716 nop.m 0
717 // set p13 = 1 if x = 0.0
718 fclass.m p13, p0 = f8, 0x07
719 nop.i 0
720 }
721 { .mfi
722 nop.m 0
723 fnorm.s1 fNormX = f8
724 nop.i 0
725 }
726 ;;
727 { .mfb
728 // load smallest normal to FP reg
729 setf.d fDenoBound = rDenoBound
730 // answer if x is a NaN
731 (p12) fma.d.s0 f8 = f8,f1,f0
732 // exit here if x is a NaN
733 (p12) br.ret.spnt b0
734 }
735 ;;
736 { .mfb
737 nop.m 0
738 nop.f 0
739 // exit here if x = 0.0
740 (p13) br.ret.spnt b0
741 }
742 ;;
743 // if we still here then x is denormal or unnormal
744 { .mfi
745 nop.m 0
746 // absolute value of normalized x
747 fmerge.s fNormX = f1, fNormX
748 nop.i 0
749 }
750 ;;
751 { .mfi
752 nop.m 0
753 // set p14 = 1 if normalized x is greater than or
754 // equal to the smallest denormalized value
755 // So, if p14 is set to 1 it means that we deal with
756 // unnormal rather than with "true" denormal
757 fcmp.ge.s1 p14, p0 = fNormX, fDenoBound
758 nop.i 0
759 }
760 ;;
761 { .mfi
762 nop.m 0
763 (p14) fcmp.eq.s0 p6, p0 = f8, f0 // Set D flag if x unnormal
764 nop.i 0
765 }
766 { .mfb
767 nop.m 0
768 // normalize unnormal input
769 (p14) fnorm.s1 f8 = f8
770 // return to the main path
771 (p14) br.cond.sptk asin_unnormal_back
772 }
773 ;;
774 // if we still here it means that input is "true" denormal
775 { .mfb
776 nop.m 0
777 // final result if x is denormal
778 fma.d.s0 f8 = f8, fXSqr, f8
779 // exit here if x is denormal
780 br.ret.sptk b0
781 }
782 ;;
784 // here if |x| > 1.0
785 // error handler should be called
786 .align 32
787 asin_abs_gt_1:
788 { .mfi
789 alloc r32 = ar.pfs, 0, 3, 4, 0 // get some registers
790 fmerge.s FR_X = f8,f8
791 nop.i 0
792 }
793 { .mfb
794 mov GR_Parameter_TAG = 61 // error code
795 frcpa.s0 FR_RESULT, p0 = f0,f0
796 // call error handler routine
797 br.cond.sptk __libm_error_region
798 }
799 ;;
800 GLOBAL_LIBM_END(asin)
804 LOCAL_LIBM_ENTRY(__libm_error_region)
805 .prologue
806 { .mfi
807 add GR_Parameter_Y=-32,sp // Parameter 2 value
808 nop.f 0
809 .save ar.pfs,GR_SAVE_PFS
810 mov GR_SAVE_PFS=ar.pfs // Save ar.pfs
811 }
812 { .mfi
813 .fframe 64
814 add sp=-64,sp // Create new stack
815 nop.f 0
816 mov GR_SAVE_GP=gp // Save gp
817 };;
818 { .mmi
819 stfd [GR_Parameter_Y] = FR_Y,16 // STORE Parameter 2 on stack
820 add GR_Parameter_X = 16,sp // Parameter 1 address
821 .save b0, GR_SAVE_B0
822 mov GR_SAVE_B0=b0 // Save b0
823 };;
824 .body
825 { .mib
826 stfd [GR_Parameter_X] = FR_X // STORE Parameter 1 on stack
827 add GR_Parameter_RESULT = 0,GR_Parameter_Y // Parameter 3 address
828 nop.b 0
829 }
830 { .mib
831 stfd [GR_Parameter_Y] = FR_RESULT // STORE Parameter 3 on stack
832 add GR_Parameter_Y = -16,GR_Parameter_Y
833 br.call.sptk b0=__libm_error_support# // Call error handling function
834 };;
835 { .mmi
836 add GR_Parameter_RESULT = 48,sp
837 nop.m 0
838 nop.i 0
839 };;
840 { .mmi
841 ldfd f8 = [GR_Parameter_RESULT] // Get return result off stack
842 .restore sp
843 add sp = 64,sp // Restore stack pointer
844 mov b0 = GR_SAVE_B0 // Restore return address
845 };;
846 { .mib
847 mov gp = GR_SAVE_GP // Restore gp
848 mov ar.pfs = GR_SAVE_PFS // Restore ar.pfs
849 br.ret.sptk b0 // Return
850 };;
852 LOCAL_LIBM_END(__libm_error_region)
853 .type __libm_error_support#,@function
854 .global __libm_error_support#