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1 .file "tgammaf.s"
2
3
4 // Copyright (c) 2001 - 2005, Intel Corporation
5 // All rights reserved.
6 //
7 // Contributed 2001 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.
23
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,
29 // EXEMPLARY,OR CONSEQUENTIAL DAMAGES (INCLUDING,BUT NOT LIMITED TO,
30 // PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,DATA,OR
31 // PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY
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.
39 //
40 //*********************************************************************
41 //
42 // History:
43 // 11/30/01 Initial version
44 // 05/20/02 Cleaned up namespace and sf0 syntax
45 // 02/10/03 Reordered header: .section, .global, .proc, .align
46 // 04/04/03 Changed error codes for overflow and negative integers
47 // 04/10/03 Changed code for overflow near zero handling
48 // 12/16/03 Fixed parameter passing to/from error handling routine
49 // 03/31/05 Reformatted delimiters between data tables
50 //
51 //*********************************************************************
52 //
53 //*********************************************************************
54 //
55 // Function: tgammaf(x) computes the principle value of the GAMMA
56 // function of x.
57 //
58 //*********************************************************************
59 //
60 // Resources Used:
61 //
62 // Floating-Point Registers: f8-f15
63 // f33-f75
64 //
65 // General Purpose Registers:
66 // r8-r11
67 // r14-r29
68 // r32-r36
69 // r37-r40 (Used to pass arguments to error handling routine)
70 //
71 // Predicate Registers: p6-p15
72 //
73 //*********************************************************************
74 //
75 // IEEE Special Conditions:
76 //
77 // tgammaf(+inf) = +inf
78 // tgammaf(-inf) = QNaN
79 // tgammaf(+/-0) = +/-inf
80 // tgammaf(x<0, x - integer) = QNaN
81 // tgammaf(SNaN) = QNaN
82 // tgammaf(QNaN) = QNaN
83 //
84 //*********************************************************************
85 //
86 // Overview
87 //
88 // The method consists of three cases.
89 //
90 // If 2 <= x < OVERFLOW_BOUNDARY use case tgamma_regular;
91 // else if 0 < x < 2 use case tgamma_from_0_to_2;
92 // else if -(i+1) < x < -i, i = 0...43 use case tgamma_negatives;
93 //
94 // Case 2 <= x < OVERFLOW_BOUNDARY
95 // -------------------------------
96 // Here we use algorithm based on the recursive formula
97 // GAMMA(x+1) = x*GAMMA(x). For that we subdivide interval
98 // [2; OVERFLOW_BOUNDARY] into intervals [8*n; 8*(n+1)] and
99 // approximate GAMMA(x) by polynomial of 22th degree on each
100 // [8*n; 8*n+1], recursive formula is used to expand GAMMA(x)
101 // to [8*n; 8*n+1]. In other words we need to find n, i and r
102 // such that x = 8 * n + i + r where n and i are integer numbers
103 // and r is fractional part of x. So GAMMA(x) = GAMMA(8*n+i+r) =
104 // = (x-1)*(x-2)*...*(x-i)*GAMMA(x-i) =
105 // = (x-1)*(x-2)*...*(x-i)*GAMMA(8*n+r) ~
106 // ~ (x-1)*(x-2)*...*(x-i)*P12n(r).
107 //
108 // Step 1: Reduction
109 // -----------------
110 // N = [x] with truncate
111 // r = x - N, note 0 <= r < 1
112 //
113 // n = N & ~0xF - index of table that contains coefficient of
114 // polynomial approximation
115 // i = N & 0xF - is used in recursive formula
116 //
117 //
118 // Step 2: Approximation
119 // ---------------------
120 // We use factorized minimax approximation polynomials
121 // P12n(r) = A12*(r^2+C01(n)*r+C00(n))*
122 // *(r^2+C11(n)*r+C10(n))*...*(r^2+C51(n)*r+C50(n))
123 //
124 // Step 3: Recursion
125 // -----------------
126 // In case when i > 0 we need to multiply P12n(r) by product
127 // R(i,x)=(x-1)*(x-2)*...*(x-i). To reduce number of fp-instructions
128 // we can calculate R as follow:
129 // R(i,x) = ((x-1)*(x-2))*((x-3)*(x-4))*...*((x-(i-1))*(x-i)) if i is
130 // even or R = ((x-1)*(x-2))*((x-3)*(x-4))*...*((x-(i-2))*(x-(i-1)))*
131 // *(i-1) if i is odd. In both cases we need to calculate
132 // R2(i,x) = (x^2-3*x+2)*(x^2-7*x+12)*...*(x^2+x+2*j*(2*j-1)) =
133 // = ((x^2-x)+2*(1-x))*((x^2-x)+6*(2-x))*...*((x^2-x)+2*(2*j-1)*(j-x)) =
134 // = (RA+2*RB)*(RA+6*(1-RB))*...*(RA+2*(2*j-1)*(j-1+RB))
135 // where j = 1..[i/2], RA = x^2-x, RB = 1-x.
136 //
137 // Step 4: Reconstruction
138 // ----------------------
139 // Reconstruction is just simple multiplication i.e.
140 // GAMMA(x) = P12n(r)*R(i,x)
141 //
142 // Case 0 < x < 2
143 // --------------
144 // To calculate GAMMA(x) on this interval we do following
145 // if 1.0 <= x < 1.25 than GAMMA(x) = P7(x-1)
146 // if 1.25 <= x < 1.5 than GAMMA(x) = P7(x-x_min) where
147 // x_min is point of local minimum on [1; 2] interval.
148 // if 1.5 <= x < 1.75 than GAMMA(x) = P7(x-1.5)
149 // if 1.75 <= x < 2.0 than GAMMA(x) = P7(x-1.5)
150 // and
151 // if 0 < x < 1 than GAMMA(x) = GAMMA(x+1)/x
152 //
153 // Case -(i+1) < x < -i, i = 0...43
154 // ----------------------------------
155 // Here we use the fact that GAMMA(-x) = PI/(x*GAMMA(x)*sin(PI*x)) and
156 // so we need to calculate GAMMA(x), sin(PI*x)/PI. Calculation of
157 // GAMMA(x) is described above.
158 //
159 // Step 1: Reduction
160 // -----------------
161 // Note that period of sin(PI*x) is 2 and range reduction for
162 // sin(PI*x) is like to range reduction for GAMMA(x)
163 // i.e rs = x - round(x) and |rs| <= 0.5.
164 //
165 // Step 2: Approximation
166 // ---------------------
167 // To approximate sin(PI*x)/PI = sin(PI*(2*n+rs))/PI =
168 // = (-1)^n*sin(PI*rs)/PI Taylor series is used.
169 // sin(PI*rs)/PI ~ S17(rs).
170 //
171 // Step 3: Division
172 // ----------------
173 // To calculate 1/x and 1/(GAMMA(x)*S12(rs)) we use frcpa
174 // instruction with following Newton-Raphson interations.
175 //
176 //
177 //*********************************************************************
178
179 GR_ad_Data = r8
180 GR_TAG = r8
181 GR_SignExp = r9
182 GR_Sig = r10
183 GR_ArgNz = r10
184 GR_RqDeg = r11
185
186 GR_NanBound = r14
187 GR_ExpOf025 = r15
188 GR_ExpOf05 = r16
189 GR_ad_Co = r17
190 GR_ad_Ce = r18
191 GR_TblOffs = r19
192 GR_Arg = r20
193 GR_Exp2Ind = r21
194 GR_TblOffsMask = r21
195 GR_Offs = r22
196 GR_OvfNzBound = r23
197 GR_ZeroResBound = r24
198 GR_ad_SinO = r25
199 GR_ad_SinE = r26
200 GR_Correction = r27
201 GR_Tbl12Offs = r28
202 GR_NzBound = r28
203 GR_ExpOf1 = r29
204 GR_fpsr = r29
205
206 GR_SAVE_B0 = r33
207 GR_SAVE_PFS = r34
208 GR_SAVE_GP = r35
209 GR_SAVE_SP = r36
210
211 GR_Parameter_X = r37
212 GR_Parameter_Y = r38
213 GR_Parameter_RESULT = r39
214 GR_Parameter_TAG = r40
215
216
217 FR_X = f10
218 FR_Y = f1
219 FR_RESULT = f8
220
221 FR_iXt = f11
222 FR_Xt = f12
223 FR_r = f13
224 FR_r2 = f14
225 FR_r4 = f15
226
227 FR_C01 = f33
228 FR_A7 = f33
229 FR_C11 = f34
230 FR_A6 = f34
231 FR_C21 = f35
232 FR_A5 = f35
233 FR_C31 = f36
234 FR_A4 = f36
235 FR_C41 = f37
236 FR_A3 = f37
237 FR_C51 = f38
238 FR_A2 = f38
239
240 FR_C00 = f39
241 FR_A1 = f39
242 FR_C10 = f40
243 FR_A0 = f40
244 FR_C20 = f41
245 FR_C30 = f42
246 FR_C40 = f43
247 FR_C50 = f44
248 FR_An = f45
249 FR_OvfBound = f46
250 FR_InvAn = f47
251
252 FR_Multplr = f48
253 FR_NormX = f49
254 FR_X2mX = f50
255 FR_1mX = f51
256 FR_Rq0 = f51
257 FR_Rq1 = f52
258 FR_Rq2 = f53
259 FR_Rq3 = f54
260
261 FR_Rcp0 = f55
262 FR_Rcp1 = f56
263 FR_Rcp2 = f57
264
265 FR_InvNormX1 = f58
266 FR_InvNormX2 = f59
267
268 FR_rs = f60
269 FR_rs2 = f61
270
271 FR_LocalMin = f62
272 FR_10 = f63
273
274 FR_05 = f64
275
276 FR_S32 = f65
277 FR_S31 = f66
278 FR_S01 = f67
279 FR_S11 = f68
280 FR_S21 = f69
281 FR_S00 = f70
282 FR_S10 = f71
283 FR_S20 = f72
284
285 FR_GAMMA = f73
286 FR_2 = f74
287 FR_6 = f75
288
289
290
291
292 // Data tables
293 //==============================================================
294 RODATA
295 .align 16
296 LOCAL_OBJECT_START(tgammaf_data)
297 data8 0x3FDD8B618D5AF8FE // local minimum (0.461632144968362356785)
298 data8 0x4024000000000000 // 10.0
299 data8 0x3E90FC992FF39E13 // S32
300 data8 0xBEC144B2760626E2 // S31
301 //
302 //[2; 8)
303 data8 0x4009EFD1BA0CB3B4 // C01
304 data8 0x3FFFB35378FF4822 // C11
305 data8 0xC01032270413B896 // C41
306 data8 0xC01F171A4C0D6827 // C51
307 data8 0x40148F8E197396AC // C20
308 data8 0x401C601959F1249C // C30
309 data8 0x3EE21AD881741977 // An
310 data8 0x4041852200000000 // overflow boundary (35.04010009765625)
311 data8 0x3FD9CE68F695B198 // C21
312 data8 0xBFF8C30AC900DA03 // C31
313 data8 0x400E17D2F0535C02 // C00
314 data8 0x4010689240F7FAC8 // C10
315 data8 0x402563147DDCCF8D // C40
316 data8 0x4033406D0480A21C // C50
317 //
318 //[8; 16)
319 data8 0x4006222BAE0B793B // C01
320 data8 0x4002452733473EDA // C11
321 data8 0xC0010EF3326FDDB3 // C41
322 data8 0xC01492B817F99C0F // C51
323 data8 0x40099C905A249B75 // C20
324 data8 0x4012B972AE0E533D // C30
325 data8 0x3FE6F6DB91D0D4CC // An
326 data8 0x4041852200000000 // overflow boundary
327 data8 0x3FF545828F7B73C5 // C21
328 data8 0xBFBBD210578764DF // C31
329 data8 0x4000542098F53CFC // C00
330 data8 0x40032C1309AD6C81 // C10
331 data8 0x401D7331E19BD2E1 // C40
332 data8 0x402A06807295EF57 // C50
333 //
334 //[16; 24)
335 data8 0x4000131002867596 // C01
336 data8 0x3FFAA362D5D1B6F2 // C11
337 data8 0xBFFCB6985697DB6D // C41
338 data8 0xC0115BEE3BFC3B3B // C51
339 data8 0x3FFE62FF83456F73 // C20
340 data8 0x4007E33478A114C4 // C30
341 data8 0x41E9B2B73795ED57 // An
342 data8 0x4041852200000000 // overflow boundary
343 data8 0x3FEEB1F345BC2769 // C21
344 data8 0xBFC3BBE6E7F3316F // C31
345 data8 0x3FF14E07DA5E9983 // C00
346 data8 0x3FF53B76BF81E2C0 // C10
347 data8 0x4014051E0269A3DC // C40
348 data8 0x40229D4227468EDB // C50
349 //
350 //[24; 32)
351 data8 0x3FFAF7BD498384DE // C01
352 data8 0x3FF62AD8B4D1C3D2 // C11
353 data8 0xBFFABCADCD004C32 // C41
354 data8 0xC00FADE97C097EC9 // C51
355 data8 0x3FF6DA9ED737707E // C20
356 data8 0x4002A29E9E0C782C // C30
357 data8 0x44329D5B5167C6C3 // An
358 data8 0x4041852200000000 // overflow boundary
359 data8 0x3FE8943CBBB4B727 // C21
360 data8 0xBFCB39D466E11756 // C31
361 data8 0x3FE879AF3243D8C1 // C00
362 data8 0x3FEEC7DEBB14CE1E // C10
363 data8 0x401017B79BA80BCB // C40
364 data8 0x401E941DC3C4DE80 // C50
365 //
366 //[32; 40)
367 data8 0x3FF7ECB3A0E8FE5C // C01
368 data8 0x3FF3815A8516316B // C11
369 data8 0xBFF9ABD8FCC000C3 // C41
370 data8 0xC00DD89969A4195B // C51
371 data8 0x3FF2E43139CBF563 // C20
372 data8 0x3FFF96DC3474A606 // C30
373 data8 0x46AFF4CA9B0DDDF0 // An
374 data8 0x4041852200000000 // overflow boundary
375 data8 0x3FE4CE76DA1B5783 // C21
376 data8 0xBFD0524DB460BC4E // C31
377 data8 0x3FE35852DF14E200 // C00
378 data8 0x3FE8C7610359F642 // C10
379 data8 0x400BCF750EC16173 // C40
380 data8 0x401AC14E02EA701C // C50
381 //
382 //[40; 48)
383 data8 0x3FF5DCE4D8193097 // C01
384 data8 0x3FF1B0D8C4974FFA // C11
385 data8 0xBFF8FB450194CAEA // C41
386 data8 0xC00C9658E030A6C4 // C51
387 data8 0x3FF068851118AB46 // C20
388 data8 0x3FFBF7C7BB46BF7D // C30
389 data8 0x3FF0000000000000 // An
390 data8 0x4041852200000000 // overflow boundary
391 data8 0x3FE231DEB11D847A // C21
392 data8 0xBFD251ECAFD7E935 // C31
393 data8 0x3FE0368AE288F6BF // C00
394 data8 0x3FE513AE4215A70C // C10
395 data8 0x4008F960F7141B8B // C40
396 data8 0x40183BA08134397B // C50
397 //
398 //[1.0; 1.25)
399 data8 0xBFD9909648921868 // A7
400 data8 0x3FE96FFEEEA8520F // A6
401 data8 0xBFED0800D93449B8 // A3
402 data8 0x3FEFA648D144911C // A2
403 data8 0xBFEE3720F7720B4D // A5
404 data8 0x3FEF4857A010CA3B // A4
405 data8 0xBFE2788CCD545AA4 // A1
406 data8 0x3FEFFFFFFFE9209E // A0
407 //
408 //[1.25; 1.5)
409 data8 0xBFB421236426936C // A7
410 data8 0x3FAF237514F36691 // A6
411 data8 0xBFC0BADE710A10B9 // A3
412 data8 0x3FDB6C5465BBEF1F // A2
413 data8 0xBFB7E7F83A546EBE // A5
414 data8 0x3FC496A01A545163 // A4
415 data8 0xBDEE86A39D8452EB // A1
416 data8 0x3FEC56DC82A39AA2 // A0
417 //
418 //[1.5; 1.75)
419 data8 0xBF94730B51795867 // A7
420 data8 0x3FBF4203E3816C7B // A6
421 data8 0xBFE85B427DBD23E4 // A3
422 data8 0x3FEE65557AB26771 // A2
423 data8 0xBFD59D31BE3AB42A // A5
424 data8 0x3FE3C90CC8F09147 // A4
425 data8 0xBFE245971DF735B8 // A1
426 data8 0x3FEFFC613AE7FBC8 // A0
427 //
428 //[1.75; 2.0)
429 data8 0xBF7746A85137617E // A7
430 data8 0x3FA96E37D09735F3 // A6
431 data8 0xBFE3C24AC40AC0BB // A3
432 data8 0x3FEC56A80A977CA5 // A2
433 data8 0xBFC6F0E707560916 // A5
434 data8 0x3FDB262D949175BE // A4
435 data8 0xBFE1C1AEDFB25495 // A1
436 data8 0x3FEFEE1E644B2022 // A0
437 //
438 // sin(pi*x)/pi
439 data8 0xC026FB0D377656CC // S01
440 data8 0x3FFFB15F95A22324 // S11
441 data8 0x406CE58F4A41C6E7 // S10
442 data8 0x404453786302C61E // S20
443 data8 0xC023D59A47DBFCD3 // S21
444 data8 0x405541D7ABECEFCA // S00
445 //
446 // 1/An for [40; 48)
447 data8 0xCAA7576DE621FCD5, 0x3F68
448 LOCAL_OBJECT_END(tgammaf_data)
449
450 //==============================================================
451 // Code
452 //==============================================================
453
454 .section .text
455 GLOBAL_LIBM_ENTRY(tgammaf)
456 { .mfi
457 getf.exp GR_SignExp = f8
458 fma.s1 FR_NormX = f8,f1,f0
459 addl GR_ad_Data = @ltoff(tgammaf_data), gp
460 }
461 { .mfi
462 mov GR_ExpOf05 = 0xFFFE
463 fcvt.fx.trunc.s1 FR_iXt = f8 // [x]
464 mov GR_Offs = 0 // 2 <= x < 8
465 };;
466 { .mfi
467 getf.d GR_Arg = f8
468 fcmp.lt.s1 p14,p15 = f8,f0
469 mov GR_Tbl12Offs = 0
470 }
471 { .mfi
472 setf.exp FR_05 = GR_ExpOf05
473 fma.s1 FR_2 = f1,f1,f1 // 2
474 mov GR_Correction = 0
475 };;
476 { .mfi
477 ld8 GR_ad_Data = [GR_ad_Data]
478 fclass.m p10,p0 = f8,0x1E7 // is x NaTVal, NaN, +/-0 or +/-INF?
479 tbit.z p12,p13 = GR_SignExp,16 // p13 if |x| >= 2
480 }
481 { .mfi
482 mov GR_ExpOf1 = 0xFFFF
483 fcvt.fx.s1 FR_rs = f8 // round(x)
484 and GR_Exp2Ind = 7,GR_SignExp
485 };;
486 .pred.rel "mutex",p14,p15
487 { .mfi
488 (p15) cmp.eq.unc p11,p0 = GR_ExpOf1,GR_SignExp // p11 if 1 <= x < 2
489 (p14) fma.s1 FR_1mX = f1,f1,f8 // 1 - |x|
490 mov GR_Sig = 0 // if |x| < 2
491 }
492 { .mfi
493 (p13) cmp.eq.unc p7,p0 = 2,GR_Exp2Ind
494 (p15) fms.s1 FR_1mX = f1,f1,f8 // 1 - |x|
495 (p13) cmp.eq.unc p8,p0 = 3,GR_Exp2Ind
496 };;
497 .pred.rel "mutex",p7,p8
498 { .mfi
499 (p7) mov GR_Offs = 0x7 // 8 <= |x| < 16
500 nop.f 0
501 (p8) tbit.z.unc p0,p6 = GR_Arg,51
502 }
503 { .mib
504 (p13) cmp.lt.unc p9,p0 = 3,GR_Exp2Ind
505 (p8) mov GR_Offs = 0xE // 16 <= |x| < 32
506 // jump if x is NaTVal, NaN, +/-0 or +/-INF?
507 (p10) br.cond.spnt tgammaf_spec_args
508 };;
509 .pred.rel "mutex",p14,p15
510 .pred.rel "mutex",p6,p9
511 { .mfi
512 (p9) mov GR_Offs = 0x1C // 32 <= |x|
513 (p14) fma.s1 FR_X2mX = FR_NormX,FR_NormX,FR_NormX // x^2-|x|
514 (p9) tbit.z.unc p0,p8 = GR_Arg,50
515 }
516 { .mfi
517 ldfpd FR_LocalMin,FR_10 = [GR_ad_Data],16
518 (p15) fms.s1 FR_X2mX = FR_NormX,FR_NormX,FR_NormX // x^2-|x|
519 (p6) add GR_Offs = 0x7,GR_Offs // 24 <= x < 32
520 };;
521 .pred.rel "mutex",p8,p12
522 { .mfi
523 add GR_ad_Ce = 0x50,GR_ad_Data
524 (p15) fcmp.lt.unc.s1 p10,p0 = f8,f1 // p10 if 0 <= x < 1
525 mov GR_OvfNzBound = 2
526 }
527 { .mib
528 ldfpd FR_S32,FR_S31 = [GR_ad_Data],16
529 (p8) add GR_Offs = 0x7,GR_Offs // 40 <= |x|
530 // jump if 1 <= x < 2
531 (p11) br.cond.spnt tgammaf_from_1_to_2
532 };;
533 { .mfi
534 shladd GR_ad_Ce = GR_Offs,4,GR_ad_Ce
535 fcvt.xf FR_Xt = FR_iXt // [x]
536 (p13) cmp.eq.unc p7,p0 = r0,GR_Offs // p7 if 2 <= |x| < 8
537 }
538 { .mfi
539 shladd GR_ad_Co = GR_Offs,4,GR_ad_Data
540 fma.s1 FR_6 = FR_2,FR_2,FR_2
541 mov GR_ExpOf05 = 0x7FC
542 };;
543 { .mfi
544 (p13) getf.sig GR_Sig = FR_iXt // if |x| >= 2
545 frcpa.s1 FR_Rcp0,p0 = f1,FR_NormX
546 (p10) shr GR_Arg = GR_Arg,51
547 }
548 { .mib
549 ldfpd FR_C01,FR_C11 = [GR_ad_Co],16
550 (p7) mov GR_Correction = 2
551 // jump if 0 < x < 1
552 (p10) br.cond.spnt tgammaf_from_0_to_1
553 };;
554 { .mfi
555 ldfpd FR_C21,FR_C31 = [GR_ad_Ce],16
556 fma.s1 FR_Rq2 = f1,f1,FR_1mX // 2 - |x|
557 (p14) sub GR_Correction = r0,GR_Correction
558 }
559 { .mfi
560 ldfpd FR_C41,FR_C51 = [GR_ad_Co],16
561 (p14) fcvt.xf FR_rs = FR_rs
562 (p14) add GR_ad_SinO = 0x3A0,GR_ad_Data
563 };;
564 .pred.rel "mutex",p14,p15
565 { .mfi
566 ldfpd FR_C00,FR_C10 = [GR_ad_Ce],16
567 nop.f 0
568 (p14) sub GR_Sig = GR_Correction,GR_Sig
569 }
570 { .mfi
571 ldfpd FR_C20,FR_C30 = [GR_ad_Co],16
572 fma.s1 FR_Rq1 = FR_1mX,FR_2,FR_X2mX // (x-1)*(x-2)
573 (p15) sub GR_Sig = GR_Sig,GR_Correction
574 };;
575 { .mfi
576 (p14) ldfpd FR_S01,FR_S11 = [GR_ad_SinO],16
577 fma.s1 FR_Rq3 = FR_2,f1,FR_1mX // 3 - |x|
578 and GR_RqDeg = 0x6,GR_Sig
579 }
580 { .mfi
581 ldfpd FR_C40,FR_C50 = [GR_ad_Ce],16
582 (p14) fma.d.s0 FR_X = f0,f0,f8 // set deno flag
583 mov GR_NanBound = 0x30016 // -2^23
584 };;
585 .pred.rel "mutex",p14,p15
586 { .mfi
587 (p14) add GR_ad_SinE = 0x3C0,GR_ad_Data
588 (p15) fms.s1 FR_r = FR_NormX,f1,FR_Xt // r = x - [x]
589 cmp.eq p8,p0 = 2,GR_RqDeg
590 }
591 { .mfi
592 ldfpd FR_An,FR_OvfBound = [GR_ad_Co]
593 (p14) fms.s1 FR_r = FR_Xt,f1,FR_NormX // r = |x - [x]|
594 cmp.eq p9,p0 = 4,GR_RqDeg
595 };;
596 .pred.rel "mutex",p8,p9
597 { .mfi
598 (p14) ldfpd FR_S21,FR_S00 = [GR_ad_SinE],16
599 (p8) fma.s1 FR_Rq0 = FR_2,f1,FR_1mX // (3-x)
600 tbit.z p0,p6 = GR_Sig,0
601 }
602 { .mfi
603 (p14) ldfpd FR_S10,FR_S20 = [GR_ad_SinO],16
604 (p9) fma.s1 FR_Rq0 = FR_2,FR_2,FR_1mX // (5-x)
605 cmp.eq p10,p0 = 6,GR_RqDeg
606 };;
607 { .mfi
608 (p14) getf.s GR_Arg = f8
609 (p14) fcmp.eq.unc.s1 p13,p0 = FR_NormX,FR_Xt
610 (p14) mov GR_ZeroResBound = 0xC22C // -43
611 }
612 { .mfi
613 (p14) ldfe FR_InvAn = [GR_ad_SinE]
614 (p10) fma.s1 FR_Rq0 = FR_6,f1,FR_1mX // (7-x)
615 cmp.eq p7,p0 = r0,GR_RqDeg
616 };;
617 { .mfi
618 (p14) cmp.ge.unc p11,p0 = GR_SignExp,GR_NanBound
619 fma.s1 FR_Rq2 = FR_Rq2,FR_6,FR_X2mX // (x-3)*(x-4)
620 (p14) shl GR_ZeroResBound = GR_ZeroResBound,16
621 }
622 { .mfb
623 (p14) mov GR_OvfNzBound = 0x802
624 (p14) fms.s1 FR_rs = FR_rs,f1,FR_NormX // rs = round(x) - x
625 // jump if x < -2^23 i.e. x is negative integer
626 (p11) br.cond.spnt tgammaf_singularity
627 };;
628 { .mfi
629 nop.m 0
630 (p7) fma.s1 FR_Rq1 = f0,f0,f1
631 (p14) shl GR_OvfNzBound = GR_OvfNzBound,20
632 }
633 { .mfb
634 nop.m 0
635 fma.s1 FR_Rq3 = FR_Rq3,FR_10,FR_X2mX // (x-5)*(x-6)
636 // jump if x is negative integer such that -2^23 < x < 0
637 (p13) br.cond.spnt tgammaf_singularity
638 };;
639 { .mfi
640 nop.m 0
641 fma.s1 FR_C01 = FR_C01,f1,FR_r
642 (p14) mov GR_ExpOf05 = 0xFFFE
643 }
644 { .mfi
645 (p14) cmp.eq.unc p7,p0 = GR_Arg,GR_OvfNzBound
646 fma.s1 FR_C11 = FR_C11,f1,FR_r
647 (p14) cmp.ltu.unc p11,p0 = GR_Arg,GR_OvfNzBound
648 };;
649 { .mfi
650 nop.m 0
651 fma.s1 FR_C21 = FR_C21,f1,FR_r
652 (p14) cmp.ltu.unc p9,p0 = GR_ZeroResBound,GR_Arg
653 }
654 { .mfb
655 nop.m 0
656 fma.s1 FR_C31 = FR_C31,f1,FR_r
657 // jump if argument is close to 0 negative
658 (p11) br.cond.spnt tgammaf_overflow
659 };;
660 { .mfi
661 nop.m 0
662 fma.s1 FR_C41 = FR_C41,f1,FR_r
663 nop.i 0
664 }
665 { .mfb
666 nop.m 0
667 fma.s1 FR_C51 = FR_C51,f1,FR_r
668 // jump if x is negative noninteger such that -2^23 < x < -43
669 (p9) br.cond.spnt tgammaf_underflow
670 };;
671 { .mfi
672 nop.m 0
673 (p14) fma.s1 FR_rs2 = FR_rs,FR_rs,f0
674 nop.i 0
675 }
676 { .mfb
677 nop.m 0
678 (p14) fma.s1 FR_S01 = FR_rs,FR_rs,FR_S01
679 // jump if argument is 0x80200000
680 (p7) br.cond.spnt tgammaf_overflow_near0_bound
681 };;
682 { .mfi
683 nop.m 0
684 (p6) fnma.s1 FR_Rq1 = FR_Rq1,FR_Rq0,f0
685 nop.i 0
686 }
687 { .mfi
688 nop.m 0
689 (p10) fma.s1 FR_Rq2 = FR_Rq2,FR_Rq3,f0
690 and GR_Sig = 0x7,GR_Sig
691 };;
692 { .mfi
693 nop.m 0
694 fma.s1 FR_C01 = FR_C01,FR_r,FR_C00
695 nop.i 0
696 }
697 { .mfi
698 nop.m 0
699 fma.s1 FR_C11 = FR_C11,FR_r,FR_C10
700 cmp.eq p6,p7 = r0,GR_Sig // p6 if |x| from one of base intervals
701 };;
702 { .mfi
703 nop.m 0
704 fma.s1 FR_C21 = FR_C21,FR_r,FR_C20
705 nop.i 0
706 }
707 { .mfi
708 nop.m 0
709 fma.s1 FR_C31 = FR_C31,FR_r,FR_C30
710 (p7) cmp.lt.unc p9,p0 = 2,GR_RqDeg
711 };;
712 { .mfi
713 nop.m 0
714 (p14) fma.s1 FR_S11 = FR_rs,FR_rs,FR_S11
715 nop.i 0
716 }
717 { .mfi
718 nop.m 0
719 (p14) fma.s1 FR_S21 = FR_rs,FR_rs,FR_S21
720 nop.i 0
721 };;
722 { .mfi
723 nop.m 0
724 fma.s1 FR_C41 = FR_C41,FR_r,FR_C40
725 nop.i 0
726 }
727 { .mfi
728 nop.m 0
729 (p14) fma.s1 FR_S32 = FR_rs2,FR_S32,FR_S31
730 nop.i 0
731 };;
732 { .mfi
733 nop.m 0
734 (p9) fma.s1 FR_Rq1 = FR_Rq1,FR_Rq2,f0
735 nop.i 0
736 }
737 { .mfi
738 nop.m 0
739 fma.s1 FR_C51 = FR_C51,FR_r,FR_C50
740 nop.i 0
741 };;
742 { .mfi
743 (p14) getf.exp GR_SignExp = FR_rs
744 fma.s1 FR_C01 = FR_C01,FR_C11,f0
745 nop.i 0
746 }
747 { .mfi
748 nop.m 0
749 (p14) fma.s1 FR_S01 = FR_S01,FR_rs2,FR_S00
750 nop.i 0
751 };;
752 { .mfi
753 nop.m 0
754 fma.s1 FR_C21 = FR_C21,FR_C31,f0
755 nop.i 0
756 }
757 { .mfi
758 nop.m 0
759 // NR-iteration
760 (p14) fnma.s1 FR_InvNormX1 = FR_Rcp0,FR_NormX,f1
761 nop.i 0
762 };;
763 { .mfi
764 nop.m 0
765 (p14) fma.s1 FR_S11 = FR_S11,FR_rs2,FR_S10
766 (p14) tbit.z.unc p11,p12 = GR_SignExp,17
767 }
768 { .mfi
769 nop.m 0
770 (p14) fma.s1 FR_S21 = FR_S21,FR_rs2,FR_S20
771 nop.i 0
772 };;
773 { .mfi
774 nop.m 0
775 (p15) fcmp.lt.unc.s1 p0,p13 = FR_NormX,FR_OvfBound
776 nop.i 0
777 }
778 { .mfi
779 nop.m 0
780 (p14) fma.s1 FR_S32 = FR_rs2,FR_S32,f0
781 nop.i 0
782 };;
783 { .mfi
784 nop.m 0
785 fma.s1 FR_C41 = FR_C41,FR_C51,f0
786 nop.i 0
787 }
788 { .mfi
789 nop.m 0
790 (p7) fma.s1 FR_An = FR_Rq1,FR_An,f0
791 nop.i 0
792 };;
793 { .mfb
794 nop.m 0
795 nop.f 0
796 // jump if x > 35.04010009765625
797 (p13) br.cond.spnt tgammaf_overflow
798 };;
799 { .mfi
800 nop.m 0
801 // NR-iteration
802 (p14) fma.s1 FR_InvNormX1 = FR_Rcp0,FR_InvNormX1,FR_Rcp0
803 nop.i 0
804 };;
805 { .mfi
806 nop.m 0
807 (p14) fma.s1 FR_S01 = FR_S01,FR_S11,f0
808 nop.i 0
809 };;
810 { .mfi
811 nop.m 0
812 (p14) fma.s1 FR_S21 = FR_S21,FR_S32,f0
813 nop.i 0
814 };;
815 { .mfi
816 (p14) getf.exp GR_SignExp = FR_NormX
817 fma.s1 FR_C01 = FR_C01,FR_C21,f0
818 nop.i 0
819 }
820 { .mfi
821 nop.m 0
822 fma.s1 FR_C41 = FR_C41,FR_An,f0
823 (p14) mov GR_ExpOf1 = 0x2FFFF
824 };;
825 { .mfi
826 nop.m 0
827 // NR-iteration
828 (p14) fnma.s1 FR_InvNormX2 = FR_InvNormX1,FR_NormX,f1
829 nop.i 0
830 };;
831 .pred.rel "mutex",p11,p12
832 { .mfi
833 nop.m 0
834 (p12) fnma.s1 FR_S01 = FR_S01,FR_S21,f0
835 nop.i 0
836 }
837 { .mfi
838 nop.m 0
839 (p11) fma.s1 FR_S01 = FR_S01,FR_S21,f0
840 nop.i 0
841 };;
842
843 { .mfi
844 nop.m 0
845 (p14) fma.s1 FR_GAMMA = FR_C01,FR_C41,f0
846 (p14) tbit.z.unc p6,p7 = GR_Sig,0
847 }
848 { .mfb
849 nop.m 0
850 (p15) fma.s.s0 f8 = FR_C01,FR_C41,f0
851 (p15) br.ret.spnt b0 // exit for positives
852 };;
853 .pred.rel "mutex",p11,p12
854 { .mfi
855 nop.m 0
856 (p12) fms.s1 FR_S01 = FR_rs,FR_S01,FR_rs
857 nop.i 0
858 }
859 { .mfi
860 nop.m 0
861 (p11) fma.s1 FR_S01 = FR_rs,FR_S01,FR_rs
862 nop.i 0
863 };;
864 { .mfi
865 nop.m 0
866 // NR-iteration
867 fma.s1 FR_InvNormX2 = FR_InvNormX1,FR_InvNormX2,FR_InvNormX1
868 cmp.eq p10,p0 = 0x23,GR_Offs
869 };;
870 .pred.rel "mutex",p6,p7
871 { .mfi
872 nop.m 0
873 (p6) fma.s1 FR_GAMMA = FR_S01,FR_GAMMA,f0
874 cmp.gtu p8,p0 = GR_SignExp,GR_ExpOf1
875 }
876 { .mfi
877 nop.m 0
878 (p7) fnma.s1 FR_GAMMA = FR_S01,FR_GAMMA,f0
879 cmp.eq p9,p0 = GR_SignExp,GR_ExpOf1
880 };;
881 { .mfi
882 nop.m 0
883 // NR-iteration
884 fnma.s1 FR_InvNormX1 = FR_InvNormX2,FR_NormX,f1
885 nop.i 0
886 }
887 { .mfi
888 nop.m 0
889 (p10) fma.s1 FR_InvNormX2 = FR_InvNormX2,FR_InvAn,f0
890 nop.i 0
891 };;
892 { .mfi
893 nop.m 0
894 frcpa.s1 FR_Rcp0,p0 = f1,FR_GAMMA
895 nop.i 0
896 };;
897 { .mfi
898 nop.m 0
899 fms.s1 FR_Multplr = FR_NormX,f1,f1 // x - 1
900 nop.i 0
901 };;
902 { .mfi
903 nop.m 0
904 // NR-iteration
905 fnma.s1 FR_Rcp1 = FR_Rcp0,FR_GAMMA,f1
906 nop.i 0
907 };;
908 .pred.rel "mutex",p8,p9
909 { .mfi
910 nop.m 0
911 // 1/x or 1/(An*x)
912 (p8) fma.s1 FR_Multplr = FR_InvNormX2,FR_InvNormX1,FR_InvNormX2
913 nop.i 0
914 }
915 { .mfi
916 nop.m 0
917 (p9) fma.s1 FR_Multplr = f1,f1,f0
918 nop.i 0
919 };;
920 { .mfi
921 nop.m 0
922 // NR-iteration
923 fma.s1 FR_Rcp1 = FR_Rcp0,FR_Rcp1,FR_Rcp0
924 nop.i 0
925 };;
926 { .mfi
927 nop.m 0
928 // NR-iteration
929 fnma.s1 FR_Rcp2 = FR_Rcp1,FR_GAMMA,f1
930 nop.i 0
931 }
932 { .mfi
933 nop.m 0
934 // NR-iteration
935 fma.s1 FR_Rcp1 = FR_Rcp1,FR_Multplr,f0
936 nop.i 0
937 };;
938 { .mfb
939 nop.m 0
940 fma.s.s0 f8 = FR_Rcp1,FR_Rcp2,FR_Rcp1
941 br.ret.sptk b0
942 };;
943
944 // here if 0 < x < 1
945 //--------------------------------------------------------------------
946 .align 32
947 tgammaf_from_0_to_1:
948 { .mfi
949 cmp.lt p7,p0 = GR_Arg,GR_ExpOf05
950 // NR-iteration
951 fnma.s1 FR_Rcp1 = FR_Rcp0,FR_NormX,f1
952 cmp.eq p8,p0 = GR_Arg,GR_ExpOf05
953 }
954 { .mfi
955 cmp.gt p9,p0 = GR_Arg,GR_ExpOf05
956 fma.s1 FR_r = f0,f0,FR_NormX // reduced arg for (0;1)
957 mov GR_ExpOf025 = 0x7FA
958 };;
959 { .mfi
960 getf.s GR_ArgNz = f8
961 fma.d.s0 FR_X = f0,f0,f8 // set deno flag
962 shl GR_OvfNzBound = GR_OvfNzBound,20
963 }
964 { .mfi
965 (p8) mov GR_Tbl12Offs = 0x80 // 0.5 <= x < 0.75
966 nop.f 0
967 (p7) cmp.ge.unc p6,p0 = GR_Arg,GR_ExpOf025
968 };;
969 .pred.rel "mutex",p6,p9
970 { .mfi
971 (p9) mov GR_Tbl12Offs = 0xC0 // 0.75 <= x < 1
972 nop.f 0
973 (p6) mov GR_Tbl12Offs = 0x40 // 0.25 <= x < 0.5
974 }
975 { .mfi
976 add GR_ad_Ce = 0x2C0,GR_ad_Data
977 nop.f 0
978 add GR_ad_Co = 0x2A0,GR_ad_Data
979 };;
980 { .mfi
981 add GR_ad_Co = GR_ad_Co,GR_Tbl12Offs
982 nop.f 0
983 cmp.lt p12,p0 = GR_ArgNz,GR_OvfNzBound
984 }
985 { .mib
986 add GR_ad_Ce = GR_ad_Ce,GR_Tbl12Offs
987 cmp.eq p7,p0 = GR_ArgNz,GR_OvfNzBound
988 // jump if argument is 0x00200000
989 (p7) br.cond.spnt tgammaf_overflow_near0_bound
990 };;
991 { .mmb
992 ldfpd FR_A7,FR_A6 = [GR_ad_Co],16
993 ldfpd FR_A5,FR_A4 = [GR_ad_Ce],16
994 // jump if argument is close to 0 positive
995 (p12) br.cond.spnt tgammaf_overflow
996 };;
997 { .mfi
998 ldfpd FR_A3,FR_A2 = [GR_ad_Co],16
999 // NR-iteration
1000 fma.s1 FR_Rcp1 = FR_Rcp0,FR_Rcp1,FR_Rcp0
1001 nop.i 0
1002 }
1003 { .mfb
1004 ldfpd FR_A1,FR_A0 = [GR_ad_Ce],16
1005 nop.f 0
1006 br.cond.sptk tgamma_from_0_to_2
1007 };;
1008
1009 // here if 1 < x < 2
1010 //--------------------------------------------------------------------
1011 .align 32
1012 tgammaf_from_1_to_2:
1013 { .mfi
1014 add GR_ad_Co = 0x2A0,GR_ad_Data
1015 fms.s1 FR_r = f0,f0,FR_1mX
1016 shr GR_TblOffs = GR_Arg,47
1017 }
1018 { .mfi
1019 add GR_ad_Ce = 0x2C0,GR_ad_Data
1020 nop.f 0
1021 mov GR_TblOffsMask = 0x18
1022 };;
1023 { .mfi
1024 nop.m 0
1025 nop.f 0
1026 and GR_TblOffs = GR_TblOffs,GR_TblOffsMask
1027 };;
1028 { .mfi
1029 shladd GR_ad_Co = GR_TblOffs,3,GR_ad_Co
1030 nop.f 0
1031 nop.i 0
1032 }
1033 { .mfi
1034 shladd GR_ad_Ce = GR_TblOffs,3,GR_ad_Ce
1035 nop.f 0
1036 cmp.eq p6,p7 = 8,GR_TblOffs
1037 };;
1038 { .mmi
1039 ldfpd FR_A7,FR_A6 = [GR_ad_Co],16
1040 ldfpd FR_A5,FR_A4 = [GR_ad_Ce],16
1041 nop.i 0
1042 };;
1043 { .mmi
1044 ldfpd FR_A3,FR_A2 = [GR_ad_Co],16
1045 ldfpd FR_A1,FR_A0 = [GR_ad_Ce],16
1046 nop.i 0
1047 };;
1048
1049 .align 32
1050 tgamma_from_0_to_2:
1051 { .mfi
1052 nop.m 0
1053 (p6) fms.s1 FR_r = FR_r,f1,FR_LocalMin
1054 nop.i 0
1055 };;
1056 { .mfi
1057 nop.m 0
1058 // NR-iteration
1059 (p10) fnma.s1 FR_Rcp2 = FR_Rcp1,FR_NormX,f1
1060 nop.i 0
1061 };;
1062 { .mfi
1063 nop.m 0
1064 fms.s1 FR_r2 = FR_r,FR_r,f0
1065 nop.i 0
1066 };;
1067 { .mfi
1068 nop.m 0
1069 fma.s1 FR_A7 = FR_A7,FR_r,FR_A6
1070 nop.i 0
1071 }
1072 { .mfi
1073 nop.m 0
1074 fma.s1 FR_A5 = FR_A5,FR_r,FR_A4
1075 nop.i 0
1076 };;
1077 { .mfi
1078 nop.m 0
1079 fma.s1 FR_A3 = FR_A3,FR_r,FR_A2
1080 nop.i 0
1081 }
1082 { .mfi
1083 nop.m 0
1084 fma.s1 FR_A1 = FR_A1,FR_r,FR_A0
1085 nop.i 0
1086 };;
1087 { .mfi
1088 nop.m 0
1089 // NR-iteration
1090 (p10) fma.s1 FR_Rcp2 = FR_Rcp1,FR_Rcp2,FR_Rcp1
1091 nop.i 0
1092 };;
1093 { .mfi
1094 nop.m 0
1095 fma.s1 FR_A7 = FR_A7,FR_r2,FR_A5
1096 nop.i 0
1097 }
1098 { .mfi
1099 nop.m 0
1100 fma.s1 FR_r4 = FR_r2,FR_r2,f0
1101 nop.i 0
1102 };;
1103 { .mfi
1104 nop.m 0
1105 fma.s1 FR_A3 = FR_A3,FR_r2,FR_A1
1106 nop.i 0
1107 };;
1108 { .mfi
1109 nop.m 0
1110 (p10) fma.s1 FR_GAMMA = FR_A7,FR_r4,FR_A3
1111 nop.i 0
1112 }
1113 { .mfi
1114 nop.m 0
1115 (p11) fma.s.s0 f8 = FR_A7,FR_r4,FR_A3
1116 nop.i 0
1117 };;
1118 { .mfb
1119 nop.m 0
1120 (p10) fma.s.s0 f8 = FR_GAMMA,FR_Rcp2,f0
1121 br.ret.sptk b0
1122 };;
1123
1124
1125 // overflow
1126 //--------------------------------------------------------------------
1127 .align 32
1128 tgammaf_overflow_near0_bound:
1129 .pred.rel "mutex",p14,p15
1130 { .mfi
1131 mov GR_fpsr = ar.fpsr
1132 nop.f 0
1133 (p15) mov r8 = 0x7f8
1134 }
1135 { .mfi
1136 nop.m 0
1137 nop.f 0
1138 (p14) mov r8 = 0xff8
1139 };;
1140 { .mfi
1141 nop.m 0
1142 nop.f 0
1143 shl r8 = r8,20
1144 };;
1145 { .mfi
1146 sub r8 = r8,r0,1
1147 nop.f 0
1148 extr.u GR_fpsr = GR_fpsr,10,2 // rounding mode
1149 };;
1150 .pred.rel "mutex",p14,p15
1151 { .mfi
1152 // set p8 to 0 in case of overflow and to 1 otherwise
1153 // for negative arg:
1154 // no overflow if rounding mode either Z or +Inf, i.e.
1155 // GR_fpsr > 1
1156 (p14) cmp.lt p8,p0 = 1,GR_fpsr
1157 nop.f 0
1158 // for positive arg:
1159 // no overflow if rounding mode either Z or -Inf, i.e.
1160 // (GR_fpsr & 1) == 0
1161 (p15) tbit.z p0,p8 = GR_fpsr,0
1162 };;
1163 { .mib
1164 (p8) setf.s f8 = r8 // set result to 0x7f7fffff without
1165 // OVERFLOW flag raising
1166 nop.i 0
1167 (p8) br.ret.sptk b0
1168 };;
1169
1170 .align 32
1171 tgammaf_overflow:
1172 { .mfi
1173 nop.m 0
1174 nop.f 0
1175 mov r8 = 0x1FFFE
1176 };;
1177 { .mfi
1178 setf.exp f9 = r8
1179 fmerge.s FR_X = f8,f8
1180 nop.i 0
1181 };;
1182 .pred.rel "mutex",p14,p15
1183 { .mfi
1184 nop.m 0
1185 (p14) fnma.s.s0 f8 = f9,f9,f0 // set I,O and -INF result
1186 mov GR_TAG = 261 // overflow
1187 }
1188 { .mfb
1189 nop.m 0
1190 (p15) fma.s.s0 f8 = f9,f9,f0 // set I,O and +INF result
1191 br.cond.sptk tgammaf_libm_err
1192 };;
1193
1194 // x is negative integer or +/-0
1195 //--------------------------------------------------------------------
1196 .align 32
1197 tgammaf_singularity:
1198 { .mfi
1199 nop.m 0
1200 fmerge.s FR_X = f8,f8
1201 mov GR_TAG = 262 // negative
1202 }
1203 { .mfb
1204 nop.m 0
1205 frcpa.s0 f8,p0 = f0,f0
1206 br.cond.sptk tgammaf_libm_err
1207 };;
1208 // x is negative noninteger with big absolute value
1209 //--------------------------------------------------------------------
1210 .align 32
1211 tgammaf_underflow:
1212 { .mfi
1213 mov r8 = 0x00001
1214 nop.f 0
1215 tbit.z p6,p7 = GR_Sig,0
1216 };;
1217 { .mfi
1218 setf.exp f9 = r8
1219 nop.f 0
1220 nop.i 0
1221 };;
1222 .pred.rel "mutex",p6,p7
1223 { .mfi
1224 nop.m 0
1225 (p6) fms.s.s0 f8 = f9,f9,f9
1226 nop.i 0
1227 }
1228 { .mfb
1229 nop.m 0
1230 (p7) fma.s.s0 f8 = f9,f9,f9
1231 br.ret.sptk b0
1232 };;
1233
1234 // x for natval, nan, +/-inf or +/-0
1235 //--------------------------------------------------------------------
1236 .align 32
1237 tgammaf_spec_args:
1238 { .mfi
1239 nop.m 0
1240 fclass.m p6,p0 = f8,0x1E1 // Test x for natval, nan, +inf
1241 nop.i 0
1242 };;
1243 { .mfi
1244 nop.m 0
1245 fclass.m p7,p8 = f8,0x7 // +/-0
1246 nop.i 0
1247 };;
1248 { .mfi
1249 nop.m 0
1250 fmerge.s FR_X = f8,f8
1251 nop.i 0
1252 }
1253 { .mfb
1254 nop.m 0
1255 (p6) fma.s.s0 f8 = f8,f1,f8
1256 (p6) br.ret.spnt b0
1257 };;
1258 .pred.rel "mutex",p7,p8
1259 { .mfi
1260 (p7) mov GR_TAG = 262 // negative
1261 (p7) frcpa.s0 f8,p0 = f1,f8
1262 nop.i 0
1263 }
1264 { .mib
1265 nop.m 0
1266 nop.i 0
1267 (p8) br.cond.spnt tgammaf_singularity
1268 };;
1269
1270 .align 32
1271 tgammaf_libm_err:
1272 { .mfi
1273 alloc r32 = ar.pfs,1,4,4,0
1274 nop.f 0
1275 mov GR_Parameter_TAG = GR_TAG
1276 };;
1277
1278 GLOBAL_LIBM_END(tgammaf)
1279
1280 LOCAL_LIBM_ENTRY(__libm_error_region)
1281 .prologue
1282 { .mfi
1283 add GR_Parameter_Y=-32,sp // Parameter 2 value
1284 nop.f 0
1285 .save ar.pfs,GR_SAVE_PFS
1286 mov GR_SAVE_PFS=ar.pfs // Save ar.pfs
1287 }
1288 { .mfi
1289 .fframe 64
1290 add sp=-64,sp // Create new stack
1291 nop.f 0
1292 mov GR_SAVE_GP=gp // Save gp
1293 };;
1294 { .mmi
1295 stfs [GR_Parameter_Y] = FR_Y,16 // STORE Parameter 2 on stack
1296 add GR_Parameter_X = 16,sp // Parameter 1 address
1297 .save b0, GR_SAVE_B0
1298 mov GR_SAVE_B0=b0 // Save b0
1299 };;
1300 .body
1301 { .mib
1302 stfs [GR_Parameter_X] = FR_X // STORE Parameter 1 on stack
1303 add GR_Parameter_RESULT = 0,GR_Parameter_Y // Parameter 3 address
1304 nop.b 0
1305 }
1306 { .mib
1307 stfs [GR_Parameter_Y] = FR_RESULT // STORE Parameter 3 on stack
1308 add GR_Parameter_Y = -16,GR_Parameter_Y
1309 br.call.sptk b0=__libm_error_support# // Call error handling function
1310 };;
1311 { .mmi
1312 nop.m 0
1313 nop.m 0
1314 add GR_Parameter_RESULT = 48,sp
1315 };;
1316 { .mmi
1317 ldfs f8 = [GR_Parameter_RESULT] // Get return result off stack
1318 .restore sp
1319 add sp = 64,sp // Restore stack pointer
1320 mov b0 = GR_SAVE_B0 // Restore return address
1321 };;
1322 { .mib
1323 mov gp = GR_SAVE_GP // Restore gp
1324 mov ar.pfs = GR_SAVE_PFS // Restore ar.pfs
1325 br.ret.sptk b0 // Return
1326 };;
1327
1328 LOCAL_LIBM_END(__libm_error_region)
1329 .type __libm_error_support#,@function
1330 .global __libm_error_support#
1331
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