| blob | 30d11a6f88059dd007b161db783567ecaf9a942b |
1 .file "tancotf.s"
4 // Copyright (c) 2000 - 2005, Intel Corporation
5 // All rights reserved.
6 //
7 //
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18 //
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23 // THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
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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 // 12/27/00 Improved speed
44 // 02/21/01 Updated to call tanl
45 // 05/30/02 Improved speed, added cotf.
46 // 11/25/02 Added explicit completer on fnorm
47 // 02/10/03 Reordered header: .section, .global, .proc, .align
48 // 04/17/03 Eliminated redundant stop bits
49 // 03/31/05 Reformatted delimiters between data tables
50 //
51 // APIs
52 //==============================================================
53 // float tanf(float)
54 // float cotf(float)
55 //
56 // Algorithm Description for tanf
57 //==============================================================
58 // The tanf function computes the principle value of the tangent of x,
59 // where x is radian argument.
60 //
61 // There are 5 paths:
62 // 1. x = +/-0.0
63 // Return tanf(x) = +/-0.0
64 //
65 // 2. x = [S,Q]NaN
66 // Return tanf(x) = QNaN
67 //
68 // 3. x = +/-Inf
69 // Return tanf(x) = QNaN
70 //
71 // 4. x = r + (Pi/2)*N, N = RoundInt(x*(2/Pi)), N is even, |r|<Pi/4
72 // Return tanf(x) = P19(r) = A1*r + A3*r^3 + A5*r^5 + ... + A19*r^19 =
73 // = r*(A1 + A3*t + A5*t^2 + ... + A19*t^9) = r*P9(t), where t = r^2
74 //
75 // 5. x = r + (Pi/2)*N, N = RoundInt(x*(2/Pi)), N is odd, |r|<Pi/4
76 // Return tanf(x) = -1/r + P11(r) = -1/r + B1*r + B3*r^3 + ... + B11*r^11 =
77 // = -1/r + r*(B1 + B3*t + B5*t^2 + ... + B11*t^5) = -1/r + r*P11(t),
78 // where t = r^2
79 //
80 // Algorithm Description for cotf
81 //==============================================================
82 // The cotf function computes the principle value of the cotangent of x,
83 // where x is radian argument.
84 //
85 // There are 5 paths:
86 // 1. x = +/-0.0
87 // Return cotf(x) = +/-Inf and error handling is called
88 //
89 // 2. x = [S,Q]NaN
90 // Return cotf(x) = QNaN
91 //
92 // 3. x = +/-Inf
93 // Return cotf(x) = QNaN
94 //
95 // 4. x = r + (Pi/2)*N, N = RoundInt(x*(2/Pi)), N is odd, |r|<Pi/4
96 // Return cotf(x) = P19(-r) = A1*(-r) + A3*(-r^3) + ... + A19*(-r^19) =
97 // = -r*(A1 + A3*t + A5*t^2 + ... + A19*t^9) = -r*P9(t), where t = r^2
98 //
99 // 5. x = r + (Pi/2)*N, N = RoundInt(x*(2/Pi)), N is even, |r|<Pi/4
100 // Return cotf(x) = 1/r + P11(-r) = 1/r + B1*(-r) + ... + B11*(-r^11) =
101 // = 1/r - r*(B1 + B3*t + B5*t^2 + ... + B11*t^5) = 1/r - r*P11(t),
102 // where t = r^2
103 //
104 // We set p10 and clear p11 if computing tanf, vice versa for cotf.
105 //
106 //
107 // Registers used
108 //==============================================================
109 // Floating Point registers used:
110 // f8, input
111 // f32 -> f80
112 //
113 // General registers used:
114 // r14 -> r23, r32 -> r39
115 //
116 // Predicate registers used:
117 // p6 -> p13
118 //
119 // Assembly macros
120 //==============================================================
121 // integer registers
122 rExp = r14
123 rSignMask = r15
124 rRshf = r16
125 rScFctrExp = r17
126 rIntN = r18
127 rSigRcpPiby2 = r19
128 rScRshf = r20
129 rCoeffA = r21
130 rCoeffB = r22
131 rExpCut = r23
133 GR_SAVE_B0 = r33
134 GR_SAVE_PFS = r34
135 GR_SAVE_GP = r35
136 GR_Parameter_X = r36
137 GR_Parameter_Y = r37
138 GR_Parameter_RESULT = r38
139 GR_Parameter_Tag = r39
141 //==============================================================
142 // floating point registers
143 fScRcpPiby2 = f32
144 fScRshf = f33
145 fNormArg = f34
146 fScFctr = f35
147 fRshf = f36
148 fShiftedN = f37
149 fN = f38
150 fR = f39
151 fA01 = f40
152 fA03 = f41
153 fA05 = f42
154 fA07 = f43
155 fA09 = f44
156 fA11 = f45
157 fA13 = f46
158 fA15 = f47
159 fA17 = f48
160 fA19 = f49
161 fB01 = f50
162 fB03 = f51
163 fB05 = f52
164 fB07 = f53
165 fB09 = f54
166 fB11 = f55
167 fA03_01 = f56
168 fA07_05 = f57
169 fA11_09 = f58
170 fA15_13 = f59
171 fA19_17 = f60
172 fA11_05 = f61
173 fA19_13 = f62
174 fA19_05 = f63
175 fRbyA03_01 = f64
176 fB03_01 = f65
177 fB07_05 = f66
178 fB11_09 = f67
179 fB11_05 = f68
180 fRbyB03_01 = f69
181 fRbyB11_01 = f70
182 fRp2 = f71
183 fRp4 = f72
184 fRp8 = f73
185 fRp5 = f74
186 fY0 = f75
187 fY1 = f76
188 fD = f77
189 fDp2 = f78
190 fInvR = f79
191 fPiby2 = f80
192 //==============================================================
195 RODATA
196 .align 16
198 LOCAL_OBJECT_START(coeff_A)
199 data8 0x3FF0000000000000 // A1 = 1.00000000000000000000e+00
200 data8 0x3FD5555556BCE758 // A3 = 3.33333334641442641606e-01
201 data8 0x3FC111105C2DAE48 // A5 = 1.33333249100689099175e-01
202 data8 0x3FABA1F876341060 // A7 = 5.39701122561673229739e-02
203 data8 0x3F965FB86D12A38D // A9 = 2.18495194027670719750e-02
204 data8 0x3F8265F62415F9D6 // A11 = 8.98353860497717439465e-03
205 data8 0x3F69E3AE64CCF58D // A13 = 3.16032468108912746342e-03
206 data8 0x3F63920D09D0E6F6 // A15 = 2.38897844840557235331e-03
207 LOCAL_OBJECT_END(coeff_A)
209 LOCAL_OBJECT_START(coeff_B)
210 data8 0xC90FDAA22168C235, 0x3FFF // pi/2
211 data8 0x3FD55555555358DB // B1 = 3.33333333326107426583e-01
212 data8 0x3F96C16C252F643F // B3 = 2.22222230621336129239e-02
213 data8 0x3F61566243AB3C60 // B5 = 2.11638633968606896785e-03
214 data8 0x3F2BC1169BD4438B // B7 = 2.11748132564551094391e-04
215 data8 0x3EF611B4CEA056A1 // B9 = 2.10467959860990200942e-05
216 data8 0x3EC600F9E32194BF // B11 = 2.62305891234274186608e-06
217 data8 0xBF42BA7BCC177616 // A17 =-5.71546981685324877205e-04
218 data8 0x3F4F2614BC6D3BB8 // A19 = 9.50584530849832782542e-04
219 LOCAL_OBJECT_END(coeff_B)
222 .section .text
224 LOCAL_LIBM_ENTRY(cotf)
226 { .mlx
227 getf.exp rExp = f8 // ***** Get 2^17 * s + E
228 movl rSigRcpPiby2= 0xA2F9836E4E44152A // significand of 2/Pi
229 }
230 { .mlx
231 addl rCoeffA = @ltoff(coeff_A), gp
232 movl rScRshf = 0x47e8000000000000 // 1.5*2^(63+63+1)
233 }
234 ;;
236 { .mfi
237 alloc r32 = ar.pfs, 0, 4, 4, 0
238 fclass.m p9, p0 = f8, 0xc3 // Test for x=nan
239 cmp.eq p11, p10 = r0, r0 // if p11=1 we compute cotf
240 }
241 { .mib
242 ld8 rCoeffA = [rCoeffA]
243 mov rExpCut = 0x10009 // cutoff for exponent
244 br.cond.sptk Common_Path
245 }
246 ;;
248 LOCAL_LIBM_END(cotf)
251 GLOBAL_IEEE754_ENTRY(tanf)
253 { .mlx
254 getf.exp rExp = f8 // ***** Get 2^17 * s + E
255 movl rSigRcpPiby2= 0xA2F9836E4E44152A // significand of 2/Pi
256 }
257 { .mlx
258 addl rCoeffA = @ltoff(coeff_A), gp
259 movl rScRshf = 0x47e8000000000000 // 1.5*2^(63+63+1)
260 }
261 ;;
263 { .mfi
264 alloc r32 = ar.pfs, 0, 4, 4, 0
265 fclass.m p9, p0 = f8, 0xc3 // Test for x=nan
266 cmp.eq p10, p11 = r0, r0 // if p10=1 we compute tandf
267 }
268 { .mib
269 ld8 rCoeffA = [rCoeffA]
270 mov rExpCut = 0x10009 // cutoff for exponent
271 nop.b 0
272 }
273 ;;
275 // Below is common path for both tandf and cotdf
276 Common_Path:
277 { .mfi
278 setf.sig fScRcpPiby2 = rSigRcpPiby2 // 2^(63+1)*(2/Pi)
279 fclass.m p8, p0 = f8, 0x23 // Test for x=inf
280 mov rSignMask = 0x1ffff // mask for sign bit
281 }
282 { .mlx
283 setf.d fScRshf = rScRshf // 1.5*2^(63+63+1)
284 movl rRshf = 0x43e8000000000000 // 1.5 2^63 for right shift
285 }
286 ;;
288 { .mfi
289 and rSignMask = rSignMask, rExp // clear sign bit
290 (p10) fclass.m.unc p7, p0 = f8, 0x07 // Test for x=0 (for tanf)
291 mov rScFctrExp = 0xffff-64 // exp of scaling factor
292 }
293 { .mfb
294 adds rCoeffB = coeff_B - coeff_A, rCoeffA
295 (p9) fma.s.s0 f8 = f8, f1, f8 // Set qnan if x=nan
296 (p9) br.ret.spnt b0 // Exit for x=nan
297 }
298 ;;
300 { .mfi
301 cmp.ge p6, p0 = rSignMask, rExpCut // p6 = (E => 0x10009)
302 (p8) frcpa.s0 f8, p0 = f0, f0 // Set qnan indef if x=inf
303 mov GR_Parameter_Tag = 227 // (cotf)
304 }
305 { .mbb
306 ldfe fPiby2 = [rCoeffB], 16
307 (p8) br.ret.spnt b0 // Exit for x=inf
308 (p6) br.cond.spnt Huge_Argument // Branch if |x|>=2^10
309 }
310 ;;
312 { .mfi
313 nop.m 0
314 (p11) fclass.m.unc p6, p0 = f8, 0x07 // Test for x=0 (for cotf)
315 nop.i 0
316 }
317 { .mfb
318 nop.m 0
319 fnorm.s0 fNormArg = f8
320 (p7) br.ret.spnt b0 // Exit for x=0 (for tanf)
321 }
322 ;;
324 { .mmf
325 ldfpd fA01, fA03 = [rCoeffA], 16
326 ldfpd fB01, fB03 = [rCoeffB], 16
327 fmerge.s f10 = f8, f8 // Save input for error call
328 }
329 ;;
331 { .mmf
332 setf.exp fScFctr = rScFctrExp // get as real
333 setf.d fRshf = rRshf // get right shifter as real
334 (p6) frcpa.s0 f8, p0 = f1, f8 // cotf(+-0) = +-Inf
335 }
336 ;;
338 { .mmb
339 ldfpd fA05, fA07 = [rCoeffA], 16
340 ldfpd fB05, fB07 = [rCoeffB], 16
341 (p6) br.cond.spnt __libm_error_region // call error support if cotf(+-0)
342 }
343 ;;
345 { .mmi
346 ldfpd fA09, fA11 = [rCoeffA], 16
347 ldfpd fB09, fB11 = [rCoeffB], 16
348 nop.i 0
349 }
350 ;;
352 { .mfi
353 nop.m 0
354 fma.s1 fShiftedN = fNormArg,fScRcpPiby2,fScRshf // x*2^70*(2/Pi)+ScRshf
355 nop.i 0
356 }
357 ;;
359 { .mfi
360 nop.m 0
361 fms.s1 fN = fShiftedN, fScFctr, fRshf // N = Y*2^(-70) - Rshf
362 nop.i 0
363 }
364 ;;
366 .pred.rel "mutex", p10, p11
367 { .mfi
368 getf.sig rIntN = fShiftedN // get N as integer
369 (p10) fnma.s1 fR = fN, fPiby2, fNormArg // R = x - (Pi/2)*N (tanf)
370 nop.i 0
371 }
372 { .mfi
373 nop.m 0
374 (p11) fms.s1 fR = fN, fPiby2, fNormArg // R = (Pi/2)*N - x (cotf)
375 nop.i 0
376 }
377 ;;
379 { .mmi
380 ldfpd fA13, fA15 = [rCoeffA], 16
381 ldfpd fA17, fA19 = [rCoeffB], 16
382 nop.i 0
383 }
384 ;;
386 Return_From_Huges:
387 { .mfi
388 nop.m 0
389 fma.s1 fRp2 = fR, fR, f0 // R^2
390 (p11) add rIntN = 0x1, rIntN // N = N + 1 (cotf)
391 }
392 ;;
394 { .mfi
395 nop.m 0
396 frcpa.s1 fY0, p0 = f1, fR // Y0 ~ 1/R
397 tbit.z p8, p9 = rIntN, 0 // p8=1 if N is even
398 }
399 ;;
401 // Below are mixed polynomial calculations (mixed for even and odd N)
402 { .mfi
403 nop.m 0
404 (p9) fma.s1 fB03_01 = fRp2, fB03, fB01 // R^2*B3 + B1
405 nop.i 0
406 }
407 { .mfi
408 nop.m 0
409 fma.s1 fRp4 = fRp2, fRp2, f0 // R^4
410 nop.i 0
411 }
412 ;;
414 { .mfi
415 nop.m 0
416 (p8) fma.s1 fA15_13 = fRp2, fA15, fA13 // R^2*A15 + A13
417 nop.i 0
418 }
419 { .mfi
420 nop.m 0
421 (p8) fma.s1 fA19_17 = fRp2, fA19, fA17 // R^2*A19 + A17
422 nop.i 0
423 }
424 ;;
426 { .mfi
427 nop.m 0
428 (p8) fma.s1 fA07_05 = fRp2, fA07, fA05 // R^2*A7 + A5
429 nop.i 0
430 }
431 { .mfi
432 nop.m 0
433 (p8) fma.s1 fA11_09 = fRp2, fA11, fA09 // R^2*A11 + A9
434 nop.i 0
435 }
436 ;;
438 { .mfi
439 nop.m 0
440 (p9) fma.s1 fB07_05 = fRp2, fB07, fB05 // R^2*B7 + B5
441 nop.i 0
442 }
443 { .mfi
444 nop.m 0
445 (p9) fma.s1 fB11_09 = fRp2, fB11, fB09 // R^2*B11 + B9
446 nop.i 0
447 }
448 ;;
450 { .mfi
451 nop.m 0
452 (p9) fnma.s1 fD = fR, fY0, f1 // D = 1 - R*Y0
453 nop.i 0
454 }
455 { .mfi
456 nop.m 0
457 (p8) fma.s1 fA03_01 = fRp2, fA03, fA01 // R^2*A3 + A1
458 nop.i 0
459 }
460 ;;
462 { .mfi
463 nop.m 0
464 fma.s1 fRp8 = fRp4, fRp4, f0 // R^8
465 nop.i 0
466 }
467 { .mfi
468 nop.m 0
469 fma.s1 fRp5 = fR, fRp4, f0 // R^5
470 nop.i 0
471 }
472 ;;
474 { .mfi
475 nop.m 0
476 (p8) fma.s1 fA11_05 = fRp4, fA11_09, fA07_05 // R^4*(R^2*A11 + A9) + ...
477 nop.i 0
478 }
479 { .mfi
480 nop.m 0
481 (p8) fma.s1 fA19_13 = fRp4, fA19_17, fA15_13 // R^4*(R^2*A19 + A17) + ..
482 nop.i 0
483 }
484 ;;
486 { .mfi
487 nop.m 0
488 (p9) fma.s1 fB11_05 = fRp4, fB11_09, fB07_05 // R^4*(R^2*B11 + B9) + ...
489 nop.i 0
490 }
491 { .mfi
492 nop.m 0
493 (p9) fma.s1 fRbyB03_01 = fR, fB03_01, f0 // R*(R^2*B3 + B1)
494 nop.i 0
495 }
496 ;;
498 { .mfi
499 nop.m 0
500 (p9) fma.s1 fY1 = fY0, fD, fY0 // Y1 = Y0*D + Y0
501 nop.i 0
502 }
503 { .mfi
504 nop.m 0
505 (p9) fma.s1 fDp2 = fD, fD, f0 // D^2
506 nop.i 0
507 }
508 ;;
510 { .mfi
511 nop.m 0
512 // R^8*(R^6*A19 + R^4*A17 + R^2*A15 + A13) + R^6*A11 + R^4*A9 + R^2*A7 + A5
513 (p8) fma.d.s1 fA19_05 = fRp8, fA19_13, fA11_05
514 nop.i 0
515 }
516 { .mfi
517 nop.m 0
518 (p8) fma.d.s1 fRbyA03_01 = fR, fA03_01, f0 // R*(R^2*A3 + A1)
519 nop.i 0
520 }
521 ;;
523 { .mfi
524 nop.m 0
525 (p9) fma.d.s1 fInvR = fY1, fDp2, fY1 // 1/R = Y1*D^2 + Y1
526 nop.i 0
527 }
528 { .mfi
529 nop.m 0
530 // R^5*(R^6*B11 + R^4*B9 + R^2*B7 + B5) + R^3*B3 + R*B1
531 (p9) fma.d.s1 fRbyB11_01 = fRp5, fB11_05, fRbyB03_01
532 nop.i 0
533 }
534 ;;
536 .pred.rel "mutex", p8, p9
537 { .mfi
538 nop.m 0
539 // Result = R^5*(R^14*A19 + R^12*A17 + R^10*A15 + ...) + R^3*A3 + R*A1
540 (p8) fma.s.s0 f8 = fRp5, fA19_05, fRbyA03_01
541 nop.i 0
542 }
543 { .mfb
544 nop.m 0
545 // Result = -1/R + R^11*B11 + R^9*B9 + R^7*B7 + R^5*B5 + R^3*B3 + R*B1
546 (p9) fnma.s.s0 f8 = f1, fInvR, fRbyB11_01
547 br.ret.sptk b0 // exit for main path
548 }
549 ;;
551 GLOBAL_IEEE754_END(tanf)
552 libm_alias_float_other (__tan, tan)
555 LOCAL_LIBM_ENTRY(__libm_callout)
556 Huge_Argument:
557 .prologue
559 { .mfi
560 nop.m 0
561 fmerge.s f9 = f0,f0
562 .save ar.pfs,GR_SAVE_PFS
563 mov GR_SAVE_PFS=ar.pfs
564 }
565 ;;
567 { .mfi
568 mov GR_SAVE_GP=gp
569 nop.f 0
570 .save b0, GR_SAVE_B0
571 mov GR_SAVE_B0=b0
572 }
574 .body
575 { .mmb
576 nop.m 999
577 nop.m 999
578 (p10) br.cond.sptk.many call_tanl ;;
579 }
581 // Here if we should call cotl (p10=0, p11=1)
582 { .mmb
583 nop.m 999
584 nop.m 999
585 br.call.sptk.many b0=__libm_cotl# ;;
586 }
588 { .mfi
589 mov gp = GR_SAVE_GP
590 fnorm.s.s0 f8 = f8
591 mov b0 = GR_SAVE_B0
592 }
593 ;;
595 { .mib
596 nop.m 999
597 mov ar.pfs = GR_SAVE_PFS
598 br.ret.sptk b0
599 ;;
600 }
602 // Here if we should call tanl (p10=1, p11=0)
603 call_tanl:
604 { .mmb
605 nop.m 999
606 nop.m 999
607 br.call.sptk.many b0=__libm_tanl# ;;
608 }
610 { .mfi
611 mov gp = GR_SAVE_GP
612 fnorm.s.s0 f8 = f8
613 mov b0 = GR_SAVE_B0
614 }
615 ;;
617 { .mib
618 nop.m 999
619 mov ar.pfs = GR_SAVE_PFS
620 br.ret.sptk b0
621 ;;
622 }
624 LOCAL_LIBM_END(__libm_callout)
626 .type __libm_tanl#,@function
627 .global __libm_tanl#
628 .type __libm_cotl#,@function
629 .global __libm_cotl#
632 LOCAL_LIBM_ENTRY(__libm_error_region)
633 .prologue
635 // (1)
636 { .mfi
637 add GR_Parameter_Y=-32,sp // Parameter 2 value
638 nop.f 0
639 .save ar.pfs,GR_SAVE_PFS
640 mov GR_SAVE_PFS=ar.pfs // Save ar.pfs
641 }
642 { .mfi
643 .fframe 64
644 add sp=-64,sp // Create new stack
645 nop.f 0
646 mov GR_SAVE_GP=gp // Save gp
647 };;
649 // (2)
650 { .mmi
651 stfs [GR_Parameter_Y] = f1,16 // STORE Parameter 2 on stack
652 add GR_Parameter_X = 16,sp // Parameter 1 address
653 .save b0, GR_SAVE_B0
654 mov GR_SAVE_B0=b0 // Save b0
655 };;
657 .body
658 // (3)
659 { .mib
660 stfs [GR_Parameter_X] = f10 // STORE Parameter 1 on stack
661 add GR_Parameter_RESULT = 0,GR_Parameter_Y // Parameter 3 address
662 nop.b 0
663 }
664 { .mib
665 stfs [GR_Parameter_Y] = f8 // STORE Parameter 3 on stack
666 add GR_Parameter_Y = -16,GR_Parameter_Y
667 br.call.sptk b0=__libm_error_support# // Call error handling function
668 };;
669 { .mmi
670 nop.m 0
671 nop.m 0
672 add GR_Parameter_RESULT = 48,sp
673 };;
675 // (4)
676 { .mmi
677 ldfs f8 = [GR_Parameter_RESULT] // Get return result off stack
678 .restore sp
679 add sp = 64,sp // Restore stack pointer
680 mov b0 = GR_SAVE_B0 // Restore return address
681 };;
682 { .mib
683 mov gp = GR_SAVE_GP // Restore gp
684 mov ar.pfs = GR_SAVE_PFS // Restore ar.pfs
685 br.ret.sptk b0 // Return
686 };;
688 LOCAL_LIBM_END(__libm_error_region)
690 .type __libm_error_support#,@function
691 .global __libm_error_support#