1.file "tancotf.s"
2
3
4// Copyright (c) 2000 - 2005, Intel Corporation
5// All rights reserved.
6//
7//
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9// modification, are permitted provided that the following conditions are
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14//
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18//
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20// products derived from this software without specific prior written
21// permission.
22
23// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
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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// 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
122rExp                        = r14
123rSignMask                   = r15
124rRshf                       = r16
125rScFctrExp                  = r17
126rIntN                       = r18
127rSigRcpPiby2                = r19
128rScRshf                     = r20
129rCoeffA                     = r21
130rCoeffB                     = r22
131rExpCut                     = r23
132
133GR_SAVE_B0                  = r33
134GR_SAVE_PFS                 = r34
135GR_SAVE_GP                  = r35
136GR_Parameter_X              = r36
137GR_Parameter_Y              = r37
138GR_Parameter_RESULT         = r38
139GR_Parameter_Tag            = r39
140
141//==============================================================
142// floating point registers
143fScRcpPiby2                 = f32
144fScRshf                     = f33
145fNormArg                    = f34
146fScFctr                     = f35
147fRshf                       = f36
148fShiftedN                   = f37
149fN                          = f38
150fR                          = f39
151fA01                        = f40
152fA03                        = f41
153fA05                        = f42
154fA07                        = f43
155fA09                        = f44
156fA11                        = f45
157fA13                        = f46
158fA15                        = f47
159fA17                        = f48
160fA19                        = f49
161fB01                        = f50
162fB03                        = f51
163fB05                        = f52
164fB07                        = f53
165fB09                        = f54
166fB11                        = f55
167fA03_01                     = f56
168fA07_05                     = f57
169fA11_09                     = f58
170fA15_13                     = f59
171fA19_17                     = f60
172fA11_05                     = f61
173fA19_13                     = f62
174fA19_05                     = f63
175fRbyA03_01                  = f64
176fB03_01                     = f65
177fB07_05                     = f66
178fB11_09                     = f67
179fB11_05                     = f68
180fRbyB03_01                  = f69
181fRbyB11_01                  = f70
182fRp2                        = f71
183fRp4                        = f72
184fRp8                        = f73
185fRp5                        = f74
186fY0                         = f75
187fY1                         = f76
188fD                          = f77
189fDp2                        = f78
190fInvR                       = f79
191fPiby2                      = f80
192//==============================================================
193
194
195RODATA
196.align 16
197
198LOCAL_OBJECT_START(coeff_A)
199data8 0x3FF0000000000000 // A1  = 1.00000000000000000000e+00
200data8 0x3FD5555556BCE758 // A3  = 3.33333334641442641606e-01
201data8 0x3FC111105C2DAE48 // A5  = 1.33333249100689099175e-01
202data8 0x3FABA1F876341060 // A7  = 5.39701122561673229739e-02
203data8 0x3F965FB86D12A38D // A9  = 2.18495194027670719750e-02
204data8 0x3F8265F62415F9D6 // A11 = 8.98353860497717439465e-03
205data8 0x3F69E3AE64CCF58D // A13 = 3.16032468108912746342e-03
206data8 0x3F63920D09D0E6F6 // A15 = 2.38897844840557235331e-03
207LOCAL_OBJECT_END(coeff_A)
208
209LOCAL_OBJECT_START(coeff_B)
210data8 0xC90FDAA22168C235, 0x3FFF // pi/2
211data8 0x3FD55555555358DB // B1  = 3.33333333326107426583e-01
212data8 0x3F96C16C252F643F // B3  = 2.22222230621336129239e-02
213data8 0x3F61566243AB3C60 // B5  = 2.11638633968606896785e-03
214data8 0x3F2BC1169BD4438B // B7  = 2.11748132564551094391e-04
215data8 0x3EF611B4CEA056A1 // B9  = 2.10467959860990200942e-05
216data8 0x3EC600F9E32194BF // B11 = 2.62305891234274186608e-06
217data8 0xBF42BA7BCC177616 // A17 =-5.71546981685324877205e-04
218data8 0x3F4F2614BC6D3BB8 // A19 = 9.50584530849832782542e-04
219LOCAL_OBJECT_END(coeff_B)
220
221
222.section .text
223
224LOCAL_LIBM_ENTRY(cotf)
225
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;;
235
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;;
247
248LOCAL_LIBM_END(cotf)
249
250
251GLOBAL_IEEE754_ENTRY(tanf)
252
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;;
262
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;;
274
275// Below is common path for both tandf and cotdf
276Common_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;;
287
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;;
299
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;;
311
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;;
323
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;;
330
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;;
337
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;;
344
345{ .mmi
346      ldfpd     fA09, fA11  = [rCoeffA], 16
347      ldfpd     fB09, fB11  = [rCoeffB], 16
348      nop.i     0
349}
350;;
351
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;;
358
359{ .mfi
360      nop.m     0
361      fms.s1    fN          = fShiftedN, fScFctr, fRshf // N = Y*2^(-70) - Rshf
362      nop.i     0
363}
364;;
365
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;;
378
379{ .mmi
380      ldfpd     fA13, fA15  = [rCoeffA], 16
381      ldfpd     fA17, fA19  = [rCoeffB], 16
382      nop.i     0
383}
384;;
385
386Return_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;;
393
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;;
400
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;;
413
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;;
425
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;;
437
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;;
449
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;;
461
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;;
473
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;;
485
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;;
497
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;;
509
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;;
522
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;;
535
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;;
550
551GLOBAL_IEEE754_END(tanf)
552libm_alias_float_other (__tan, tan)
553
554
555LOCAL_LIBM_ENTRY(__libm_callout)
556Huge_Argument:
557.prologue
558
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;;
566
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}
573
574.body
575{ .mmb
576      nop.m 999
577      nop.m 999
578(p10) br.cond.sptk.many  call_tanl ;;
579}
580
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}
587
588{ .mfi
589      mov gp        = GR_SAVE_GP
590      fnorm.s.s0 f8 = f8
591      mov b0        = GR_SAVE_B0
592}
593;;
594
595{ .mib
596      nop.m 999
597      mov ar.pfs    = GR_SAVE_PFS
598      br.ret.sptk     b0
599;;
600}
601
602// Here if we should call tanl (p10=1, p11=0)
603call_tanl:
604{ .mmb
605      nop.m 999
606      nop.m 999
607      br.call.sptk.many  b0=__libm_tanl# ;;
608}
609
610{ .mfi
611      mov gp        = GR_SAVE_GP
612      fnorm.s.s0 f8 = f8
613      mov b0        = GR_SAVE_B0
614}
615;;
616
617{ .mib
618      nop.m 999
619      mov ar.pfs    = GR_SAVE_PFS
620      br.ret.sptk     b0
621;;
622}
623
624LOCAL_LIBM_END(__libm_callout)
625
626.type __libm_tanl#,@function
627.global __libm_tanl#
628.type __libm_cotl#,@function
629.global __libm_cotl#
630
631
632LOCAL_LIBM_ENTRY(__libm_error_region)
633.prologue
634
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};;
648
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};;
656
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};;
674
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};;
687
688LOCAL_LIBM_END(__libm_error_region)
689
690.type   __libm_error_support#,@function
691.global __libm_error_support#
692