| blob | 5c13fc3febf780fa28dfb3cbea0532f288ed6551 |
1 .file "libm_lgamma.s"
4 // Copyright (c) 2002 - 2003, Intel Corporation
5 // All rights reserved.
6 //
7 // Contributed 2002 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,
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 // 01/10/02 Initial version
44 // 01/25/02 Corrected error tag numbers
45 // 02/04/02 Added support of SIGN(GAMMA(x)) calculation
46 // 05/20/02 Cleaned up namespace and sf0 syntax
47 // 09/15/02 Fixed bug on the branch lgamma_negrecursion
48 // 10/21/02 Now it returns SIGN(GAMMA(x))=-1 for negative zero
49 // 02/10/03 Reordered header: .section, .global, .proc, .align
50 //
51 //*********************************************************************
52 //
53 //*********************************************************************
54 //
55 // Function: __libm_lgamma(double x, int* signgam, int szsigngam)
56 // computes the principle value of the logarithm of the GAMMA function
57 // of x. Signum of GAMMA(x) is stored to memory starting at the address
58 // specified by the signgam.
59 //
60 //*********************************************************************
61 //
62 // Resources Used:
63 //
64 // Floating-Point Registers: f6-f15
65 // f32-f122
66 //
67 // General Purpose Registers:
68 // r8-r11
69 // r14-r31
70 // r32-r36
71 // r37-r40 (Used to pass arguments to error handling routine)
72 //
73 // Predicate Registers: p6-p15
74 //
75 //*********************************************************************
76 //
77 // IEEE Special Conditions:
78 //
79 // __libm_lgamma(+inf) = +inf
80 // __libm_lgamma(-inf) = QNaN
81 // __libm_lgamma(+/-0) = +inf
82 // __libm_lgamma(x<0, x - integer) = +inf
83 // __libm_lgamma(SNaN) = QNaN
84 // __libm_lgamma(QNaN) = QNaN
85 //
86 //*********************************************************************
87 //
88 // Overview
89 //
90 // The method consists of three cases.
91 //
92 // If 512 <= x < OVERFLOW_BOUNDARY use case lgamma_pstirling;
93 // else if 1 < x < 512 use case lgamma_regular;
94 // else if -17 < x < 1 use case lgamma_negrecursion;
95 // else if -512 < x < -17 use case lgamma_negpoly;
96 // else if x < -512 use case lgamma_negstirling;
97 // else if x is close to negative
98 // roots of ln(GAMMA(x)) use case lgamma_negroots;
99 //
100 //
101 // Case 512 <= x < OVERFLOW_BOUNDARY
102 // ---------------------------------
103 // Here we use algorithm based on the Stirling formula:
104 // ln(GAMMA(x)) = ln(sqrt(2*Pi)) + (x-0.5)ln(x) - x + (W2 + W4/x^2)/x
105 //
106 // Case 1 < x < 512
107 // ----------------
108 // To calculate GAMMA(x) on this interval we use polynomial approximation
109 // on following intervals [0.875; 1.25), [1.25; 1.75), [1.75, 2.25),
110 // [2.25; 4), [2^i; 2^(i+1)), i=2..8
111 //
112 // Following variants of approximation and argument reduction are used:
113 // 1. [0.875; 1.25)
114 // ln(GAMMA(x)) ~ (x-1.0)*P17(x-1.0)
115 //
116 // 2. [1.25; 1.75)
117 // ln(GAMMA(x)) ~ (x-LocalMinimun)*P17(x-LocalMinimun)
118 //
119 // 3. [1.75, 2.25)
120 // ln(GAMMA(x)) ~ (x-2.0)*P17(x-2.0)
121 //
122 // 4. [2.25; 4)
123 // ln(GAMMA(x)) ~ P22(x)
124 //
125 // 5. [2^i; 2^(i+1)), i=2..8
126 // ln(GAMMA(x)) ~ P22((x-2^i)/2^i)
127 //
128 // Case -17 < x < 1
129 // ----------------
130 // Here we use the recursive formula:
131 // ln(GAMMA(x)) = ln(GAMMA(x+1)) - ln(x)
132 //
133 // Using this formula we reduce argument to base interval [1.0; 2.0]
134 //
135 // Case -512 < x < -17
136 // --------------------
137 // Here we use the formula:
138 // ln(GAMMA(-x)) = ln(Pi/(x*GAMMA(x)*sin(Pi*x))) =
139 // = -ln(x) - ln((GAMMA(x)) - ln(sin(Pi*r)/(Pi*r)) - ln(|r|)
140 // where r = x - rounded_to_nearest(x), i.e |r| <= 0.5 and
141 // ln(sin(Pi*r)/(Pi*r)) is approximated by 14-degree polynomial of r^2
142 //
143 //
144 // Case x < -512
145 // -------------
146 // Here we use algorithm based on the Stirling formula:
147 // ln(GAMMA(-x)) = -ln(sqrt(2*Pi)) + (-x-0.5)ln(x) + x - (W2 + W4/x^2)/x -
148 // - ln(sin(Pi*r)/(Pi*r)) - ln(|r|)
149 // where r = x - rounded_to_nearest(x).
150 //
151 // Neighbourhoods of negative roots
152 // --------------------------------
153 // Here we use polynomial approximation
154 // ln(GAMMA(x-x0)) = ln(GAMMA(x0)) + (x-x0)*P14(x-x0),
155 // where x0 is a root of ln(GAMMA(x)) rounded to nearest double
156 // precision number.
157 //
159 //*********************************************************************
161 FR_X = f10
162 FR_Y = f1 // __libm_lgamma is single argument function
163 FR_RESULT = f8
165 FR_B11 = f6
166 FR_B10 = f7
168 FR_int_N = f9
169 FR_N = f10
170 FR_P5 = f11
171 FR_P4 = f12
172 FR_P3 = f13
173 FR_P2 = f14
174 FR_NormX = f15
176 FR_Ln2 = f32
177 FR_C01 = f33
178 FR_A17 = f33
179 FR_C00 = f34
180 FR_Xp2 = f34
181 FR_A00 = f34
182 FR_A16 = f34
183 FR_C11 = f35
184 FR_A15 = f35
185 FR_C10 = f36
186 FR_Xp3 = f36
187 FR_A14 = f36
188 FR_B1 = f36
189 FR_C21 = f37
190 FR_A13 = f37
191 FR_PR01 = f37
192 FR_C20 = f38
193 FR_Xp6 = f38
194 FR_A12 = f38
195 FR_C31 = f39
196 FR_Xp7 = f39
197 FR_B0 = f39
198 FR_A11 = f39
199 FR_C30 = f40
200 FR_Xp8 = f40
201 FR_A10 = f40
202 FR_PR00 = f40
203 FR_C41 = f41
204 FR_Xp9 = f41
205 FR_A9 = f41
206 FR_PR11 = f41
207 FR_C40 = f42
208 FR_A8 = f42
209 FR_C51 = f43
210 FR_Xp11 = f43
211 FR_A7 = f43
212 FR_C50 = f44
213 FR_C = f44
214 FR_Xp12 = f44
215 FR_A6 = f44
216 FR_Xm2 = f45
217 FR_Xp13 = f45
218 FR_A5 = f45
219 FR_PR10 = f45
220 FR_C61 = f46
221 FR_Xp14 = f46
222 FR_A4 = f46
223 FR_PR21 = f46
224 FR_C60 = f47
225 FR_Xp15 = f47
226 FR_A3 = f47
227 FR_PR20 = f47
228 FR_C71 = f48
229 FR_Xp16 = f48
230 FR_A2 = f48
231 FR_PR31 = f48
232 FR_C70 = f49
233 FR_Xp17 = f49
234 FR_A1 = f49
235 FR_PR30 = f49
236 FR_C81 = f50
237 FR_B17 = f50
238 FR_A0 = f50
239 FR_C80 = f51
240 FR_B16 = f51
241 FR_C91 = f52
242 FR_B15 = f52
243 FR_C90 = f53
244 FR_B14 = f53
245 FR_CA1 = f54
246 FR_B13 = f54
247 FR_CA0 = f55
248 FR_B12 = f55
249 FR_CN = f56
250 FR_Qlo = f56
251 FR_PRN = f56
252 FR_B7 = f57
253 FR_B6 = f58
254 FR_Qhi = f59
255 FR_x = f60
256 FR_x2 = f61
257 FR_TpNxLn2 = f62
258 FR_W2 = f63
259 FR_x4 = f64
260 FR_r4 = f64
261 FR_x8 = f65
262 FR_r8 = f65
263 FR_r05 = f66
264 FR_Xm05 = f66
265 FR_B5 = f66
266 FR_LnSqrt2Pi = f67
267 FR_B4 = f67
268 FR_InvX = f68
269 FR_B3 = f68
270 FR_InvX2 = f69
271 FR_B2 = f69
272 FR_W4 = f70
273 FR_OvfBound = f71
274 FR_05 = f72
275 FR_LocalMin = f73
276 FR_tmp = f73
277 FR_LnX = f74
278 FR_Xf = f75
279 FR_InvXf = f76
280 FR_rf = f77
281 FR_rf2 = f78
282 FR_P54f = f79
283 FR_P32f = f80
284 FR_rf3 = f81
285 FR_P10f = f82
286 FR_TpNxLn2f = f83
287 FR_Nf = f84
288 FR_LnXf = f85
289 FR_int_Nf = f86
290 FR_Tf = f87
291 FR_Xf2 = f88
292 FR_Xp10 = f89
293 FR_w3 = f90
294 FR_S28 = f90
295 FR_w2 = f91
296 FR_S26 = f91
297 FR_w6 = f92
298 FR_S24 = f92
299 FR_w4 = f93
300 FR_S22 = f93
301 FR_w = f94
302 FR_S20 = f94
303 FR_Q8 = f95
304 FR_S18 = f95
305 FR_Q7 = f96
306 FR_S16 = f96
307 FR_Q4 = f97
308 FR_S14 = f97
309 FR_Q3 = f98
310 FR_S12 = f98
311 FR_Q6 = f99
312 FR_S10 = f99
313 FR_Q5 = f100
314 FR_S8 = f100
315 FR_Q2 = f101
316 FR_S6 = f101
317 FR_Root = f101
318 FR_S4 = f102
319 FR_Q1 = f102
320 FR_S2 = f103
321 FR_Xp1 = f104
322 FR_Xf4 = f105
323 FR_Xf8 = f106
324 FR_Xfr = f107
325 FR_Xf6 = f108
326 FR_Ntrunc = f109
327 FR_B9 = f110
328 FR_2 = f110
329 FR_B8 = f111
330 FR_3 = f111
331 FR_5 = f112
332 FR_Xp4 = f113
333 FR_Xp5 = f114
334 FR_P54 = f115
335 FR_P32 = f116
336 FR_P10 = f117
337 FR_r = f118
338 FR_r2 = f119
339 FR_r3 = f120
340 FR_T = f121
341 FR_int_Ntrunc = f122
343 //===================================
345 GR_TAG = r8
346 GR_ExpMask = r8
347 GR_ExpBias = r9
348 GR_ad_Roots = r9
349 GR_Expf = r10
350 GR_Arg = r10
351 GR_SignExp = r11
352 GR_ArgXfr = r11
354 GR_Exp = r14
355 GR_Arg125 = r14
356 GR_RootInd = r14
357 GR_ArgAsIs = r15
358 GR_Arg175 = r15
359 GR_Sig = r16
360 GR_Ind = r17
361 GR_ad_Dx = r17
362 GR_ad_1 = r18
363 GR_SignExp_w = r19
364 GR_2_25 = r19
365 GR_Arg025 = r19
366 GR_Arg15 = r19
367 GR_Arg17 = r19
368 GR_Exp_w = r19//21
369 GR_ad_2 = r20
370 GR_2xDx = r21
371 GR_SignOfGamma = r21
372 GR_fff9 = r22
373 GR_Offs = r22
374 GR_ad_Co7 = r23
375 GR_Arg075 = r23
376 GR_Arg0875 = r23
377 GR_ad_T = r24
378 GR_ad_Root = r24
379 GR_Ind = r24
380 GR_ad_Co = r25
381 GR_ad_Ce = r26
382 GR_ad_Ce7 = r27
383 GR_Arg05 = r27
384 GR_Offs7 = r28
385 GR_ArgXfrAsIs = r28
386 GR_ExpOf2 = r29
387 GR_ad_LnT = r29
388 GR_Dx = r29
389 GR_ExpOf256 = r30
390 GR_0x30033 = r30
391 GR_Root = r30
392 GR_PseudoRoot = r30
393 GR_ad_Data = r31
394 GR_ad_SignGam = r31
397 GR_SAVE_B0 = r33
398 GR_SAVE_PFS = r34
399 GR_SAVE_GP = r35
400 GR_SAVE_SP = r36
402 GR_Parameter_X = r37
403 GR_Parameter_Y = r38
404 GR_Parameter_RESULT = r39
405 GR_Parameter_TAG = r40
409 // Data tables
410 //==============================================================
412 RODATA
413 .align 16
414 LOCAL_OBJECT_START(lgamma_data)
415 // polynomial approximation of ln(GAMMA(x)), 2.25 <= x < 512
416 // [2.25; 4)
417 data8 0xF888E8D7892718A2,0xC001 // C01
418 data8 0xF62F273BA12A4639,0x3FFD // C11
419 data8 0xA93AC50A37EC8D38,0xBFFC // C21
420 data8 0xB4CC43D2C161E057,0xBFFF // C31
421 data8 0xC6AC672F0C1392C7,0xC000 // C41
422 data8 0xA292B9AE3276942E,0xC001 // C51
423 data8 0xE554E4CCCA6C7B7B,0xC001 // C61
424 data8 0x92F0F55FBC87F860,0xC002 // C71
425 data8 0xAF60D0112843F6C1,0xC002 // C81
426 data8 0xC5956500FA3D92E7,0xC002 // C91
427 data8 0xD3B22CCBD8587750,0xC002 // CA1
428 data8 0xD888B6CF34159B54,0x4001 // C00
429 data8 0xBCB79C8329FD9F44,0x3FFE // C10
430 data8 0xCB8896FAD69C455D,0x4000 // C20
431 data8 0xE510A424639EBF5E,0x4001 // C30
432 data8 0xC65ED41B097486B3,0x4002 // C40
433 // [4; 8)
434 data8 0x9F1F3C822D03080E,0xC001 // C01
435 data8 0x941CACFA9C0FA8A6,0xC001 // C11
436 data8 0xFE34336391D99CB7,0xC000 // C21
437 data8 0xC40BAEAA165F81A1,0xC000 // C31
438 data8 0xFE3AE166E9B4DE8F,0xBFFF // C41
439 data8 0xD744F91AF7DAF873,0xBFFE // C51
440 data8 0x87871851E9C32D02,0x3FFD // C61
441 data8 0x9C93C03C502E808F,0x3FFF // C71
442 data8 0xF78BED07501D6A8E,0x3FFF // C81
443 data8 0x92FE41BA8BEADF70,0x4000 // C91
444 data8 0xA021878E1903A2C6,0x3FFF // CA1
445 data8 0xC85EFAC379FAFEE2,0x4001 // C00
446 data8 0xC10D7AAB7CEC7FF2,0x4001 // C10
447 data8 0xB3537BDF603E454C,0x4001 // C20
448 data8 0xA0D44E3D5BBE44C4,0x4001 // C30
449 data8 0x8B9C229B6241E7B3,0x4001 // C40
450 // [8; 16)
451 data8 0xD16AB33AEC220DF6,0x3FFF // C01
452 data8 0x987483646E150BCD,0x4000 // C11
453 data8 0x80C10A24C863999B,0x4000 // C21
454 data8 0xA39A8EB6F8AACE75,0x3FFF // C31
455 data8 0x93E04A1379BEC764,0x3FFD // C41
456 data8 0xD9F59C4BD3A69BD1,0xBFFE // C51
457 data8 0x82094EC891179B1A,0xC000 // C61
458 data8 0xC90CFE3A24F70659,0xC000 // C71
459 data8 0x827984EA7C155184,0xC001 // C81
460 data8 0x981BFDF79D1E0D80,0xC001 // C91
461 data8 0xA37209A8B97D230D,0xC001 // CA1
462 data8 0xAA1989737D6BA66D,0x3FFE // C00
463 data8 0xDBC013A351630AF8,0x3FFF // C10
464 data8 0x8B8D47698299389D,0x4000 // C20
465 data8 0xACCDD1315DE06EB0,0x4000 // C30
466 data8 0xD3414A5AC81BBB2D,0x4000 // C40
467 // [16; 32)
468 data8 0xECB2B0BE75C5F995,0x3FFF // C01
469 data8 0x9DD28BD6DBC96500,0x4000 // C11
470 data8 0x8521431B99C6244F,0x4000 // C21
471 data8 0xA95F92612B8413C3,0x3FFF // C31
472 data8 0x9C76E643B22D9544,0x3FFD // C41
473 data8 0xDD90EA99417C8038,0xBFFE // C51
474 data8 0x84EA6B6D32E5F906,0xC000 // C61
475 data8 0xCDBFE499E05AA622,0xC000 // C71
476 data8 0x8594A7DE35427100,0xC001 // C81
477 data8 0x9BC1CB2C10DC702F,0xC001 // C91
478 data8 0xA7602268762666B0,0xC001 // CA1
479 data8 0xDA082BCC6BDB8F7B,0x3FFE // C00
480 data8 0xEEBFE1C99322B85E,0x3FFF // C10
481 data8 0x96FED4C785361946,0x4000 // C20
482 data8 0xB9E3A7207C16B2FE,0x4000 // C30
483 data8 0xE1E8170CED48E2C7,0x4000 // C40
484 // [32; 64)
485 data8 0xFD481EB9AEDD53E7,0x3FFF // C01
486 data8 0xA216FB66AC8C53E1,0x4000 // C11
487 data8 0x885FF935787553BA,0x4000 // C21
488 data8 0xAD471CD89A313327,0x3FFF // C31
489 data8 0x9FF13FBA139D21E0,0x3FFD // C41
490 data8 0xE25E1663A6EE0266,0xBFFE // C51
491 data8 0x87BE51DD5D262FA2,0xC000 // C61
492 data8 0xD211A9D4CCE55696,0xC000 // C71
493 data8 0x885BEFC29FDED3C9,0xC001 // C81
494 data8 0x9EFA48E6367A67F6,0xC001 // C91
495 data8 0xAAD3978FC0791297,0xC001 // CA1
496 data8 0xF96D210DF37A0AEA,0x3FFE // C00
497 data8 0xFE11DC6783917C82,0x3FFF // C10
498 data8 0x9FFCD928291B7DDE,0x4000 // C20
499 data8 0xC4518F4A80E09AE1,0x4000 // C30
500 data8 0xEDDFE9E0FD297C63,0x4000 // C40
501 // [64; 128)
502 data8 0x840E2E62609B0AD3,0x4000 // C01
503 data8 0xA5275A0DD0D3DDF8,0x4000 // C11
504 data8 0x8AADC6ABFC441731,0x4000 // C21
505 data8 0xB041C6696BE90E50,0x3FFF // C31
506 data8 0xA4A8C9153F4B037E,0x3FFD // C41
507 data8 0xE3C6A461A7B86736,0xBFFE // C51
508 data8 0x89047681C6DE7673,0xC000 // C61
509 data8 0xD42DF77A480092DF,0xC000 // C71
510 data8 0x89C25D17F086FB20,0xC001 // C81
511 data8 0xA09F907D02E34EC7,0xC001 // C91
512 data8 0xAC998A9CB79805B7,0xC001 // CA1
513 data8 0x875CC9B69AE964CC,0x3FFF // C00
514 data8 0x847836BA85DD4C12,0x4000 // C10
515 data8 0xA5F3CB2B32E74936,0x4000 // C20
516 data8 0xCAE2197C96CB5A0F,0x4000 // C30
517 data8 0xF50F7EB60DE5CD09,0x4000 // C40
518 // [128; 256)
519 data8 0x87D9065DD1876926,0x4000 // C01
520 data8 0xA781C28FDAD7CC25,0x4000 // C11
521 data8 0x8C6A4FCE35A7EC8D,0x4000 // C21
522 data8 0xB27BA081728354F9,0x3FFF // C31
523 data8 0xA82FEA7124B0EB2B,0x3FFD // C41
524 data8 0xE4C996E42ECBF77A,0xBFFE // C51
525 data8 0x89F1A92C84FA538F,0xC000 // C61
526 data8 0xD5B6CFF7DB7F6070,0xC000 // C71
527 data8 0x8AC6B561FAE38B66,0xC001 // C81
528 data8 0xA1D1505C438D8F46,0xC001 // C91
529 data8 0xADE2DC1C924FEC81,0xC001 // CA1
530 data8 0x8EF6CC62A7E0EB5A,0x3FFF // C00
531 data8 0x88A2FFC0ABCB00C0,0x4000 // C10
532 data8 0xAA6EA8FCB75B065B,0x4000 // C20
533 data8 0xCFC4B82B3D5C9363,0x4000 // C30
534 data8 0xFA60FD85DE861771,0x4000 // C40
535 // [256; 512)
536 data8 0x8AAA7CE4ED5C1EFD,0x4000 // C01
537 data8 0xA9679234FB56F1E1,0x4000 // C11
538 data8 0x8DCE02287789D841,0x4000 // C21
539 data8 0xB44328EF30A8DE7E,0x3FFF // C31
540 data8 0xAB0DC564BFA1AB12,0x3FFD // C41
541 data8 0xE5882B16FCF2D3CB,0xBFFE // C51
542 data8 0x8AA7F48993006A86,0xC000 // C61
543 data8 0xD6E63752D192750D,0xC000 // C71
544 data8 0x8B90080B17853295,0xC001 // C81
545 data8 0xA2BDD4253128D1AB,0xC001 // C91
546 data8 0xAEE1A042F96B8121,0xC001 // CA1
547 data8 0x94A9C37A42E43BA7,0x3FFF // C00
548 data8 0x8BFA54E703878F5A,0x4000 // C10
549 data8 0xADFA426DDF14647B,0x4000 // C20
550 data8 0xD39C7F7B3958EAF0,0x4000 // C30
551 data8 0xFE8C3987853C01E3,0x4000 // C40
552 //
553 // [2.25; 4)
554 data8 0x943AF77763601441,0x4003 // C50
555 data8 0xC8A93F9ECB06E891,0x4003 // C60
556 data8 0xFC2E5A4AD33DE19D,0x4003 // C70
557 data8 0x9526B75B38670119,0x4004 // C80
558 data8 0xA7675879D68B587E,0x4004 // C90
559 data8 0xB31DFA672D7FB8C0,0x4004 // CA0
560 data8 0x83A27775D86F9A81,0xBFD7 // CN
561 // [4; 8)
562 data8 0xEB8049BA5E79ADA3,0x4000 // C50
563 data8 0xC20C95EA99037228,0x4000 // C60
564 data8 0x9D4A8C864053CEB8,0x4000 // C70
565 data8 0xFC7716544AB0C5C9,0x3FFF // C80
566 data8 0xC7EB985259EABA5F,0x3FFF // C90
567 data8 0xC042FB3B4C95096D,0x3FFD // CA0
568 data8 0xCC2A7F930856177B,0x3FEE // CN
569 // [8; 16)
570 data8 0xFE1903679D078C7A,0x4000 // C50
571 data8 0x957C221AB90171F1,0x4001 // C60
572 data8 0xAB2C53B2A78F4031,0x4001 // C70
573 data8 0xBE080AE6063AE387,0x4001 // C80
574 data8 0xCC019A0311605CB9,0x4001 // C90
575 data8 0xD3739D85A12C8ADF,0x4001 // CA0
576 data8 0x81FA4D2B7BD7A82D,0x3FEF // CN
577 // [16; 32)
578 data8 0x871F69E2DD221F02,0x4001 // C50
579 data8 0x9E3EF2D477442A9C,0x4001 // C60
580 data8 0xB48733582B3C82C5,0x4001 // C70
581 data8 0xC7DB9B3C25854A2A,0x4001 // C80
582 data8 0xD628B87975BE898F,0x4001 // C90
583 data8 0xDDC569C321FF119C,0x4001 // CA0
584 data8 0xB27B65560DF7ADA7,0x3FEF // CN
585 // [32; 64)
586 data8 0x8DE4127349719B22,0x4001 // C50
587 data8 0xA5C30A7760F5FBB2,0x4001 // C60
588 data8 0xBCB4096055AA2A4E,0x4001 // C70
589 data8 0xD08F5F2FB4E7B899,0x4001 // C80
590 data8 0xDF39ED39DC91F9CF,0x4001 // C90
591 data8 0xE7063E45322F072E,0x4001 // CA0
592 data8 0x85A9E11DDDDE67C8,0x3FF0 // CN
593 // [64; 128)
594 data8 0x91CA191EB80E8893,0x4001 // C50
595 data8 0xA9F1D5A55397334A,0x4001 // C60
596 data8 0xC1222710295094E3,0x4001 // C70
597 data8 0xD52FFABBA6CBE5C6,0x4001 // C80
598 data8 0xE3FD9D5282052E1D,0x4001 // C90
599 data8 0xEBDBE47BB662F3EF,0x4001 // CA0
600 data8 0xEF889F489D88FD31,0x3FF0 // CN
601 // [128; 256)
602 data8 0x94AA029C2286F8D2,0x4001 // C50
603 data8 0xAD0549E55A72389F,0x4001 // C60
604 data8 0xC4628899DAF94BA4,0x4001 // C70
605 data8 0xD89432A4161C72CB,0x4001 // C80
606 data8 0xE77ABA75E9C38F3A,0x4001 // C90
607 data8 0xEF65BFFFF71347FF,0x4001 // CA0
608 data8 0xE2627460064D918D,0x3FF1 // CN
609 // [256; 512)
610 data8 0x96E9890D722C2FC1,0x4001 // C50
611 data8 0xAF6C2236F6A1CEC4,0x4001 // C60
612 data8 0xC6EBB8C9F987D20D,0x4001 // C70
613 data8 0xDB38CEFD5EF328CC,0x4001 // C80
614 data8 0xEA3265DC66C9A0B4,0x4001 // C90
615 data8 0xF2272D6B368C70B1,0x4001 // CA0
616 data8 0xDBFF93ECEBCEF1F3,0x3FF2 // CN
617 //
618 data8 0x3FDD8B618D5AF8FE // point of local minimum on [1;2]
619 data8 0x3FE0000000000000 // 0.5
620 data8 0xBFC5555DA7212371 // P5
621 data8 0x3FC999A19EEF5826 // P4
622 data8 0xb17217f7d1cf79ac,0x3ffe // ln(2)
623 data8 0xEB3F8E4325F5A535,0x3FFE // ln(sqrt(4*arcsin(1)))
624 //
625 data8 0xBFCFFFFFFFFEF009 // P3
626 data8 0x3FD555555554ECB2 // P2
627 data8 0xBF66C16C16C16C17 // W4=B4/12=-1/360
628 data8 0x7F5754D9278B51A8 // overflow boundary (first inf result)
629 data8 0xAAAAAAAAAAAAAAAB,0x3FFB // W2=B2/2=1/12
630 //
631 data8 0x3FBC756AC654273B // Q8
632 data8 0xBFC001A42489AB4D // Q7 ;
633 data8 0x3FC99999999A169B // Q4
634 data8 0xBFD00000000019AC // Q3
635 data8 0x3FC2492479AA0DF8 // Q6
636 data8 0xBFC5555544986F52 // Q5
637 data8 0x3FD5555555555555 // Q2
638 data8 0xBFE0000000000000 // Q1, P1 = -0.5
639 //
640 data8 0x80200aaeac44ef38,0x3ff6 // ln(1/frcpa(1+ 0/2^-8))
641 data8 0xc09090a2c35aa070,0x3ff7 // ln(1/frcpa(1+ 1/2^-8))
642 data8 0xa0c94fcb41977c75,0x3ff8 // ln(1/frcpa(1+ 2/2^-8))
643 data8 0xe18b9c263af83301,0x3ff8 // ln(1/frcpa(1+ 3/2^-8))
644 data8 0x8d35c8d6399c30ea,0x3ff9 // ln(1/frcpa(1+ 4/2^-8))
645 data8 0xadd4d2ecd601cbb8,0x3ff9 // ln(1/frcpa(1+ 5/2^-8))
646 data8 0xce95403a192f9f01,0x3ff9 // ln(1/frcpa(1+ 6/2^-8))
647 data8 0xeb59392cbcc01096,0x3ff9 // ln(1/frcpa(1+ 7/2^-8))
648 data8 0x862c7d0cefd54c5d,0x3ffa // ln(1/frcpa(1+ 8/2^-8))
649 data8 0x94aa63c65e70d499,0x3ffa // ln(1/frcpa(1+ 9/2^-8))
650 data8 0xa54a696d4b62b382,0x3ffa // ln(1/frcpa(1+ 10/2^-8))
651 data8 0xb3e4a796a5dac208,0x3ffa // ln(1/frcpa(1+ 11/2^-8))
652 data8 0xc28c45b1878340a9,0x3ffa // ln(1/frcpa(1+ 12/2^-8))
653 data8 0xd35c55f39d7a6235,0x3ffa // ln(1/frcpa(1+ 13/2^-8))
654 data8 0xe220f037b954f1f5,0x3ffa // ln(1/frcpa(1+ 14/2^-8))
655 data8 0xf0f3389b036834f3,0x3ffa // ln(1/frcpa(1+ 15/2^-8))
656 data8 0xffd3488d5c980465,0x3ffa // ln(1/frcpa(1+ 16/2^-8))
657 data8 0x87609ce2ed300490,0x3ffb // ln(1/frcpa(1+ 17/2^-8))
658 data8 0x8ede9321e8c85927,0x3ffb // ln(1/frcpa(1+ 18/2^-8))
659 data8 0x96639427f2f8e2f4,0x3ffb // ln(1/frcpa(1+ 19/2^-8))
660 data8 0x9defad3e8f73217b,0x3ffb // ln(1/frcpa(1+ 20/2^-8))
661 data8 0xa582ebd50097029c,0x3ffb // ln(1/frcpa(1+ 21/2^-8))
662 data8 0xac06dbe75ab80fee,0x3ffb // ln(1/frcpa(1+ 22/2^-8))
663 data8 0xb3a78449b2d3ccca,0x3ffb // ln(1/frcpa(1+ 23/2^-8))
664 data8 0xbb4f79635ab46bb2,0x3ffb // ln(1/frcpa(1+ 24/2^-8))
665 data8 0xc2fec93a83523f3f,0x3ffb // ln(1/frcpa(1+ 25/2^-8))
666 data8 0xc99af2eaca4c4571,0x3ffb // ln(1/frcpa(1+ 26/2^-8))
667 data8 0xd1581106472fa653,0x3ffb // ln(1/frcpa(1+ 27/2^-8))
668 data8 0xd8002560d4355f2e,0x3ffb // ln(1/frcpa(1+ 28/2^-8))
669 data8 0xdfcb43b4fe508632,0x3ffb // ln(1/frcpa(1+ 29/2^-8))
670 data8 0xe67f6dff709d4119,0x3ffb // ln(1/frcpa(1+ 30/2^-8))
671 data8 0xed393b1c22351280,0x3ffb // ln(1/frcpa(1+ 31/2^-8))
672 data8 0xf5192bff087bcc35,0x3ffb // ln(1/frcpa(1+ 32/2^-8))
673 data8 0xfbdf4ff6dfef2fa3,0x3ffb // ln(1/frcpa(1+ 33/2^-8))
674 data8 0x81559a97f92f9cc7,0x3ffc // ln(1/frcpa(1+ 34/2^-8))
675 data8 0x84be72bce90266e8,0x3ffc // ln(1/frcpa(1+ 35/2^-8))
676 data8 0x88bc74113f23def2,0x3ffc // ln(1/frcpa(1+ 36/2^-8))
677 data8 0x8c2ba3edf6799d11,0x3ffc // ln(1/frcpa(1+ 37/2^-8))
678 data8 0x8f9dc92f92ea08b1,0x3ffc // ln(1/frcpa(1+ 38/2^-8))
679 data8 0x9312e8f36efab5a7,0x3ffc // ln(1/frcpa(1+ 39/2^-8))
680 data8 0x968b08643409ceb6,0x3ffc // ln(1/frcpa(1+ 40/2^-8))
681 data8 0x9a062cba08a1708c,0x3ffc // ln(1/frcpa(1+ 41/2^-8))
682 data8 0x9d845b3abf95485c,0x3ffc // ln(1/frcpa(1+ 42/2^-8))
683 data8 0xa06fd841bc001bb4,0x3ffc // ln(1/frcpa(1+ 43/2^-8))
684 data8 0xa3f3a74652fbe0db,0x3ffc // ln(1/frcpa(1+ 44/2^-8))
685 data8 0xa77a8fb2336f20f5,0x3ffc // ln(1/frcpa(1+ 45/2^-8))
686 data8 0xab0497015d28b0a0,0x3ffc // ln(1/frcpa(1+ 46/2^-8))
687 data8 0xae91c2be6ba6a615,0x3ffc // ln(1/frcpa(1+ 47/2^-8))
688 data8 0xb189d1b99aebb20b,0x3ffc // ln(1/frcpa(1+ 48/2^-8))
689 data8 0xb51cced5de9c1b2c,0x3ffc // ln(1/frcpa(1+ 49/2^-8))
690 data8 0xb819bee9e720d42f,0x3ffc // ln(1/frcpa(1+ 50/2^-8))
691 data8 0xbbb2a0947b093a5d,0x3ffc // ln(1/frcpa(1+ 51/2^-8))
692 data8 0xbf4ec1505811684a,0x3ffc // ln(1/frcpa(1+ 52/2^-8))
693 data8 0xc2535bacfa8975ff,0x3ffc // ln(1/frcpa(1+ 53/2^-8))
694 data8 0xc55a3eafad187eb8,0x3ffc // ln(1/frcpa(1+ 54/2^-8))
695 data8 0xc8ff2484b2c0da74,0x3ffc // ln(1/frcpa(1+ 55/2^-8))
696 data8 0xcc0b1a008d53ab76,0x3ffc // ln(1/frcpa(1+ 56/2^-8))
697 data8 0xcfb6203844b3209b,0x3ffc // ln(1/frcpa(1+ 57/2^-8))
698 data8 0xd2c73949a47a19f5,0x3ffc // ln(1/frcpa(1+ 58/2^-8))
699 data8 0xd5daae18b49d6695,0x3ffc // ln(1/frcpa(1+ 59/2^-8))
700 data8 0xd8f08248cf7e8019,0x3ffc // ln(1/frcpa(1+ 60/2^-8))
701 data8 0xdca7749f1b3e540e,0x3ffc // ln(1/frcpa(1+ 61/2^-8))
702 data8 0xdfc28e033aaaf7c7,0x3ffc // ln(1/frcpa(1+ 62/2^-8))
703 data8 0xe2e012a5f91d2f55,0x3ffc // ln(1/frcpa(1+ 63/2^-8))
704 data8 0xe600064ed9e292a8,0x3ffc // ln(1/frcpa(1+ 64/2^-8))
705 data8 0xe9226cce42b39f60,0x3ffc // ln(1/frcpa(1+ 65/2^-8))
706 data8 0xec4749fd97a28360,0x3ffc // ln(1/frcpa(1+ 66/2^-8))
707 data8 0xef6ea1bf57780495,0x3ffc // ln(1/frcpa(1+ 67/2^-8))
708 data8 0xf29877ff38809091,0x3ffc // ln(1/frcpa(1+ 68/2^-8))
709 data8 0xf5c4d0b245cb89be,0x3ffc // ln(1/frcpa(1+ 69/2^-8))
710 data8 0xf8f3afd6fcdef3aa,0x3ffc // ln(1/frcpa(1+ 70/2^-8))
711 data8 0xfc2519756be1abc7,0x3ffc // ln(1/frcpa(1+ 71/2^-8))
712 data8 0xff59119f503e6832,0x3ffc // ln(1/frcpa(1+ 72/2^-8))
713 data8 0x8147ce381ae0e146,0x3ffd // ln(1/frcpa(1+ 73/2^-8))
714 data8 0x82e45f06cb1ad0f2,0x3ffd // ln(1/frcpa(1+ 74/2^-8))
715 data8 0x842f5c7c573cbaa2,0x3ffd // ln(1/frcpa(1+ 75/2^-8))
716 data8 0x85ce471968c8893a,0x3ffd // ln(1/frcpa(1+ 76/2^-8))
717 data8 0x876e8305bc04066d,0x3ffd // ln(1/frcpa(1+ 77/2^-8))
718 data8 0x891012678031fbb3,0x3ffd // ln(1/frcpa(1+ 78/2^-8))
719 data8 0x8a5f1493d766a05f,0x3ffd // ln(1/frcpa(1+ 79/2^-8))
720 data8 0x8c030c778c56fa00,0x3ffd // ln(1/frcpa(1+ 80/2^-8))
721 data8 0x8da85df17e31d9ae,0x3ffd // ln(1/frcpa(1+ 81/2^-8))
722 data8 0x8efa663e7921687e,0x3ffd // ln(1/frcpa(1+ 82/2^-8))
723 data8 0x90a22b6875c6a1f8,0x3ffd // ln(1/frcpa(1+ 83/2^-8))
724 data8 0x91f62cc8f5d24837,0x3ffd // ln(1/frcpa(1+ 84/2^-8))
725 data8 0x93a06cfc3857d980,0x3ffd // ln(1/frcpa(1+ 85/2^-8))
726 data8 0x94f66d5e6fd01ced,0x3ffd // ln(1/frcpa(1+ 86/2^-8))
727 data8 0x96a330156e6772f2,0x3ffd // ln(1/frcpa(1+ 87/2^-8))
728 data8 0x97fb3582754ea25b,0x3ffd // ln(1/frcpa(1+ 88/2^-8))
729 data8 0x99aa8259aad1bbf2,0x3ffd // ln(1/frcpa(1+ 89/2^-8))
730 data8 0x9b0492f6227ae4a8,0x3ffd // ln(1/frcpa(1+ 90/2^-8))
731 data8 0x9c5f8e199bf3a7a5,0x3ffd // ln(1/frcpa(1+ 91/2^-8))
732 data8 0x9e1293b9998c1daa,0x3ffd // ln(1/frcpa(1+ 92/2^-8))
733 data8 0x9f6fa31e0b41f308,0x3ffd // ln(1/frcpa(1+ 93/2^-8))
734 data8 0xa0cda11eaf46390e,0x3ffd // ln(1/frcpa(1+ 94/2^-8))
735 data8 0xa22c8f029cfa45aa,0x3ffd // ln(1/frcpa(1+ 95/2^-8))
736 data8 0xa3e48badb7856b34,0x3ffd // ln(1/frcpa(1+ 96/2^-8))
737 data8 0xa5459a0aa95849f9,0x3ffd // ln(1/frcpa(1+ 97/2^-8))
738 data8 0xa6a79c84480cfebd,0x3ffd // ln(1/frcpa(1+ 98/2^-8))
739 data8 0xa80a946d0fcb3eb2,0x3ffd // ln(1/frcpa(1+ 99/2^-8))
740 data8 0xa96e831a3ea7b314,0x3ffd // ln(1/frcpa(1+100/2^-8))
741 data8 0xaad369e3dc544e3b,0x3ffd // ln(1/frcpa(1+101/2^-8))
742 data8 0xac92e9588952c815,0x3ffd // ln(1/frcpa(1+102/2^-8))
743 data8 0xadfa035aa1ed8fdc,0x3ffd // ln(1/frcpa(1+103/2^-8))
744 data8 0xaf6219eae1ad6e34,0x3ffd // ln(1/frcpa(1+104/2^-8))
745 data8 0xb0cb2e6d8160f753,0x3ffd // ln(1/frcpa(1+105/2^-8))
746 data8 0xb2354249ad950f72,0x3ffd // ln(1/frcpa(1+106/2^-8))
747 data8 0xb3a056e98ef4a3b4,0x3ffd // ln(1/frcpa(1+107/2^-8))
748 data8 0xb50c6dba52c6292a,0x3ffd // ln(1/frcpa(1+108/2^-8))
749 data8 0xb679882c33876165,0x3ffd // ln(1/frcpa(1+109/2^-8))
750 data8 0xb78c07429785cedc,0x3ffd // ln(1/frcpa(1+110/2^-8))
751 data8 0xb8faeb8dc4a77d24,0x3ffd // ln(1/frcpa(1+111/2^-8))
752 data8 0xba6ad77eb36ae0d6,0x3ffd // ln(1/frcpa(1+112/2^-8))
753 data8 0xbbdbcc915e9bee50,0x3ffd // ln(1/frcpa(1+113/2^-8))
754 data8 0xbd4dcc44f8cf12ef,0x3ffd // ln(1/frcpa(1+114/2^-8))
755 data8 0xbec0d81bf5b531fa,0x3ffd // ln(1/frcpa(1+115/2^-8))
756 data8 0xc034f19c139186f4,0x3ffd // ln(1/frcpa(1+116/2^-8))
757 data8 0xc14cb69f7c5e55ab,0x3ffd // ln(1/frcpa(1+117/2^-8))
758 data8 0xc2c2abbb6e5fd56f,0x3ffd // ln(1/frcpa(1+118/2^-8))
759 data8 0xc439b2c193e6771e,0x3ffd // ln(1/frcpa(1+119/2^-8))
760 data8 0xc553acb9d5c67733,0x3ffd // ln(1/frcpa(1+120/2^-8))
761 data8 0xc6cc96e441272441,0x3ffd // ln(1/frcpa(1+121/2^-8))
762 data8 0xc8469753eca88c30,0x3ffd // ln(1/frcpa(1+122/2^-8))
763 data8 0xc962cf3ce072b05c,0x3ffd // ln(1/frcpa(1+123/2^-8))
764 data8 0xcadeba8771f694aa,0x3ffd // ln(1/frcpa(1+124/2^-8))
765 data8 0xcc5bc08d1f72da94,0x3ffd // ln(1/frcpa(1+125/2^-8))
766 data8 0xcd7a3f99ea035c29,0x3ffd // ln(1/frcpa(1+126/2^-8))
767 data8 0xcef93860c8a53c35,0x3ffd // ln(1/frcpa(1+127/2^-8))
768 data8 0xd0192f68a7ed23df,0x3ffd // ln(1/frcpa(1+128/2^-8))
769 data8 0xd19a201127d3c645,0x3ffd // ln(1/frcpa(1+129/2^-8))
770 data8 0xd2bb92f4061c172c,0x3ffd // ln(1/frcpa(1+130/2^-8))
771 data8 0xd43e80b2ee8cc8fc,0x3ffd // ln(1/frcpa(1+131/2^-8))
772 data8 0xd56173601fc4ade4,0x3ffd // ln(1/frcpa(1+132/2^-8))
773 data8 0xd6e6637efb54086f,0x3ffd // ln(1/frcpa(1+133/2^-8))
774 data8 0xd80ad9f58f3c8193,0x3ffd // ln(1/frcpa(1+134/2^-8))
775 data8 0xd991d1d31aca41f8,0x3ffd // ln(1/frcpa(1+135/2^-8))
776 data8 0xdab7d02231484a93,0x3ffd // ln(1/frcpa(1+136/2^-8))
777 data8 0xdc40d532cde49a54,0x3ffd // ln(1/frcpa(1+137/2^-8))
778 data8 0xdd685f79ed8b265e,0x3ffd // ln(1/frcpa(1+138/2^-8))
779 data8 0xde9094bbc0e17b1d,0x3ffd // ln(1/frcpa(1+139/2^-8))
780 data8 0xe01c91b78440c425,0x3ffd // ln(1/frcpa(1+140/2^-8))
781 data8 0xe14658f26997e729,0x3ffd // ln(1/frcpa(1+141/2^-8))
782 data8 0xe270cdc2391e0d23,0x3ffd // ln(1/frcpa(1+142/2^-8))
783 data8 0xe3ffce3a2aa64922,0x3ffd // ln(1/frcpa(1+143/2^-8))
784 data8 0xe52bdb274ed82887,0x3ffd // ln(1/frcpa(1+144/2^-8))
785 data8 0xe6589852e75d7df6,0x3ffd // ln(1/frcpa(1+145/2^-8))
786 data8 0xe786068c79937a7d,0x3ffd // ln(1/frcpa(1+146/2^-8))
787 data8 0xe91903adad100911,0x3ffd // ln(1/frcpa(1+147/2^-8))
788 data8 0xea481236f7d35bb0,0x3ffd // ln(1/frcpa(1+148/2^-8))
789 data8 0xeb77d48c692e6b14,0x3ffd // ln(1/frcpa(1+149/2^-8))
790 data8 0xeca84b83d7297b87,0x3ffd // ln(1/frcpa(1+150/2^-8))
791 data8 0xedd977f4962aa158,0x3ffd // ln(1/frcpa(1+151/2^-8))
792 data8 0xef7179a22f257754,0x3ffd // ln(1/frcpa(1+152/2^-8))
793 data8 0xf0a450d139366ca7,0x3ffd // ln(1/frcpa(1+153/2^-8))
794 data8 0xf1d7e0524ff9ffdb,0x3ffd // ln(1/frcpa(1+154/2^-8))
795 data8 0xf30c29036a8b6cae,0x3ffd // ln(1/frcpa(1+155/2^-8))
796 data8 0xf4412bc411ea8d92,0x3ffd // ln(1/frcpa(1+156/2^-8))
797 data8 0xf576e97564c8619d,0x3ffd // ln(1/frcpa(1+157/2^-8))
798 data8 0xf6ad62fa1b5f172f,0x3ffd // ln(1/frcpa(1+158/2^-8))
799 data8 0xf7e499368b55c542,0x3ffd // ln(1/frcpa(1+159/2^-8))
800 data8 0xf91c8d10abaffe22,0x3ffd // ln(1/frcpa(1+160/2^-8))
801 data8 0xfa553f7018c966f3,0x3ffd // ln(1/frcpa(1+161/2^-8))
802 data8 0xfb8eb13e185d802c,0x3ffd // ln(1/frcpa(1+162/2^-8))
803 data8 0xfcc8e3659d9bcbed,0x3ffd // ln(1/frcpa(1+163/2^-8))
804 data8 0xfe03d6d34d487fd2,0x3ffd // ln(1/frcpa(1+164/2^-8))
805 data8 0xff3f8c7581e9f0ae,0x3ffd // ln(1/frcpa(1+165/2^-8))
806 data8 0x803e029e280173ae,0x3ffe // ln(1/frcpa(1+166/2^-8))
807 data8 0x80dca10cc52d0757,0x3ffe // ln(1/frcpa(1+167/2^-8))
808 data8 0x817ba200632755a1,0x3ffe // ln(1/frcpa(1+168/2^-8))
809 data8 0x821b05f3b01d6774,0x3ffe // ln(1/frcpa(1+169/2^-8))
810 data8 0x82bacd623ff19d06,0x3ffe // ln(1/frcpa(1+170/2^-8))
811 data8 0x835af8c88e7a8f47,0x3ffe // ln(1/frcpa(1+171/2^-8))
812 data8 0x83c5f8299e2b4091,0x3ffe // ln(1/frcpa(1+172/2^-8))
813 data8 0x8466cb43f3d87300,0x3ffe // ln(1/frcpa(1+173/2^-8))
814 data8 0x850803a67c80ca4b,0x3ffe // ln(1/frcpa(1+174/2^-8))
815 data8 0x85a9a1d11a23b461,0x3ffe // ln(1/frcpa(1+175/2^-8))
816 data8 0x864ba644a18e6e05,0x3ffe // ln(1/frcpa(1+176/2^-8))
817 data8 0x86ee1182dcc432f7,0x3ffe // ln(1/frcpa(1+177/2^-8))
818 data8 0x875a925d7e48c316,0x3ffe // ln(1/frcpa(1+178/2^-8))
819 data8 0x87fdaa109d23aef7,0x3ffe // ln(1/frcpa(1+179/2^-8))
820 data8 0x88a129ed4becfaf2,0x3ffe // ln(1/frcpa(1+180/2^-8))
821 data8 0x89451278ecd7f9cf,0x3ffe // ln(1/frcpa(1+181/2^-8))
822 data8 0x89b29295f8432617,0x3ffe // ln(1/frcpa(1+182/2^-8))
823 data8 0x8a572ac5a5496882,0x3ffe // ln(1/frcpa(1+183/2^-8))
824 data8 0x8afc2d0ce3b2dadf,0x3ffe // ln(1/frcpa(1+184/2^-8))
825 data8 0x8b6a69c608cfd3af,0x3ffe // ln(1/frcpa(1+185/2^-8))
826 data8 0x8c101e106e899a83,0x3ffe // ln(1/frcpa(1+186/2^-8))
827 data8 0x8cb63de258f9d626,0x3ffe // ln(1/frcpa(1+187/2^-8))
828 data8 0x8d2539c5bd19e2b1,0x3ffe // ln(1/frcpa(1+188/2^-8))
829 data8 0x8dcc0e064b29e6f1,0x3ffe // ln(1/frcpa(1+189/2^-8))
830 data8 0x8e734f45d88357ae,0x3ffe // ln(1/frcpa(1+190/2^-8))
831 data8 0x8ee30cef034a20db,0x3ffe // ln(1/frcpa(1+191/2^-8))
832 data8 0x8f8b0515686d1d06,0x3ffe // ln(1/frcpa(1+192/2^-8))
833 data8 0x90336bba039bf32f,0x3ffe // ln(1/frcpa(1+193/2^-8))
834 data8 0x90a3edd23d1c9d58,0x3ffe // ln(1/frcpa(1+194/2^-8))
835 data8 0x914d0de2f5d61b32,0x3ffe // ln(1/frcpa(1+195/2^-8))
836 data8 0x91be0c20d28173b5,0x3ffe // ln(1/frcpa(1+196/2^-8))
837 data8 0x9267e737c06cd34a,0x3ffe // ln(1/frcpa(1+197/2^-8))
838 data8 0x92d962ae6abb1237,0x3ffe // ln(1/frcpa(1+198/2^-8))
839 data8 0x9383fa6afbe2074c,0x3ffe // ln(1/frcpa(1+199/2^-8))
840 data8 0x942f0421651c1c4e,0x3ffe // ln(1/frcpa(1+200/2^-8))
841 data8 0x94a14a3845bb985e,0x3ffe // ln(1/frcpa(1+201/2^-8))
842 data8 0x954d133857f861e7,0x3ffe // ln(1/frcpa(1+202/2^-8))
843 data8 0x95bfd96468e604c4,0x3ffe // ln(1/frcpa(1+203/2^-8))
844 data8 0x9632d31cafafa858,0x3ffe // ln(1/frcpa(1+204/2^-8))
845 data8 0x96dfaabd86fa1647,0x3ffe // ln(1/frcpa(1+205/2^-8))
846 data8 0x9753261fcbb2a594,0x3ffe // ln(1/frcpa(1+206/2^-8))
847 data8 0x9800c11b426b996d,0x3ffe // ln(1/frcpa(1+207/2^-8))
848 data8 0x9874bf4d45ae663c,0x3ffe // ln(1/frcpa(1+208/2^-8))
849 data8 0x99231f5ee9a74f79,0x3ffe // ln(1/frcpa(1+209/2^-8))
850 data8 0x9997a18a56bcad28,0x3ffe // ln(1/frcpa(1+210/2^-8))
851 data8 0x9a46c873a3267e79,0x3ffe // ln(1/frcpa(1+211/2^-8))
852 data8 0x9abbcfc621eb6cb6,0x3ffe // ln(1/frcpa(1+212/2^-8))
853 data8 0x9b310cb0d354c990,0x3ffe // ln(1/frcpa(1+213/2^-8))
854 data8 0x9be14cf9e1b3515c,0x3ffe // ln(1/frcpa(1+214/2^-8))
855 data8 0x9c5710b8cbb73a43,0x3ffe // ln(1/frcpa(1+215/2^-8))
856 data8 0x9ccd0abd301f399c,0x3ffe // ln(1/frcpa(1+216/2^-8))
857 data8 0x9d7e67f3bdce8888,0x3ffe // ln(1/frcpa(1+217/2^-8))
858 data8 0x9df4ea81a99daa01,0x3ffe // ln(1/frcpa(1+218/2^-8))
859 data8 0x9e6ba405a54514ba,0x3ffe // ln(1/frcpa(1+219/2^-8))
860 data8 0x9f1e21c8c7bb62b3,0x3ffe // ln(1/frcpa(1+220/2^-8))
861 data8 0x9f956593f6b6355c,0x3ffe // ln(1/frcpa(1+221/2^-8))
862 data8 0xa00ce1092e5498c3,0x3ffe // ln(1/frcpa(1+222/2^-8))
863 data8 0xa0c08309c4b912c1,0x3ffe // ln(1/frcpa(1+223/2^-8))
864 data8 0xa1388a8c6faa2afa,0x3ffe // ln(1/frcpa(1+224/2^-8))
865 data8 0xa1b0ca7095b5f985,0x3ffe // ln(1/frcpa(1+225/2^-8))
866 data8 0xa22942eb47534a00,0x3ffe // ln(1/frcpa(1+226/2^-8))
867 data8 0xa2de62326449d0a3,0x3ffe // ln(1/frcpa(1+227/2^-8))
868 data8 0xa357690f88bfe345,0x3ffe // ln(1/frcpa(1+228/2^-8))
869 data8 0xa3d0a93f45169a4b,0x3ffe // ln(1/frcpa(1+229/2^-8))
870 data8 0xa44a22f7ffe65f30,0x3ffe // ln(1/frcpa(1+230/2^-8))
871 data8 0xa500c5e5b4c1aa36,0x3ffe // ln(1/frcpa(1+231/2^-8))
872 data8 0xa57ad064eb2ebbc2,0x3ffe // ln(1/frcpa(1+232/2^-8))
873 data8 0xa5f5152dedf4384e,0x3ffe // ln(1/frcpa(1+233/2^-8))
874 data8 0xa66f9478856233ec,0x3ffe // ln(1/frcpa(1+234/2^-8))
875 data8 0xa6ea4e7cca02c32e,0x3ffe // ln(1/frcpa(1+235/2^-8))
876 data8 0xa765437325341ccf,0x3ffe // ln(1/frcpa(1+236/2^-8))
877 data8 0xa81e21e6c75b4020,0x3ffe // ln(1/frcpa(1+237/2^-8))
878 data8 0xa899ab333fe2b9ca,0x3ffe // ln(1/frcpa(1+238/2^-8))
879 data8 0xa9157039c51ebe71,0x3ffe // ln(1/frcpa(1+239/2^-8))
880 data8 0xa991713433c2b999,0x3ffe // ln(1/frcpa(1+240/2^-8))
881 data8 0xaa0dae5cbcc048b3,0x3ffe // ln(1/frcpa(1+241/2^-8))
882 data8 0xaa8a27ede5eb13ad,0x3ffe // ln(1/frcpa(1+242/2^-8))
883 data8 0xab06de228a9e3499,0x3ffe // ln(1/frcpa(1+243/2^-8))
884 data8 0xab83d135dc633301,0x3ffe // ln(1/frcpa(1+244/2^-8))
885 data8 0xac3fb076adc7fe7a,0x3ffe // ln(1/frcpa(1+245/2^-8))
886 data8 0xacbd3cbbe47988f1,0x3ffe // ln(1/frcpa(1+246/2^-8))
887 data8 0xad3b06b1a5dc57c3,0x3ffe // ln(1/frcpa(1+247/2^-8))
888 data8 0xadb90e94af887717,0x3ffe // ln(1/frcpa(1+248/2^-8))
889 data8 0xae3754a218f7c816,0x3ffe // ln(1/frcpa(1+249/2^-8))
890 data8 0xaeb5d9175437afa2,0x3ffe // ln(1/frcpa(1+250/2^-8))
891 data8 0xaf349c322e9c7cee,0x3ffe // ln(1/frcpa(1+251/2^-8))
892 data8 0xafb39e30d1768d1c,0x3ffe // ln(1/frcpa(1+252/2^-8))
893 data8 0xb032df51c2c93116,0x3ffe // ln(1/frcpa(1+253/2^-8))
894 data8 0xb0b25fd3e6035ad9,0x3ffe // ln(1/frcpa(1+254/2^-8))
895 data8 0xb1321ff67cba178c,0x3ffe // ln(1/frcpa(1+255/2^-8))
896 //
897 data8 0xC7DC2985D3B44557,0x3FCA // A00
898 //
899 // polynomial approximation of ln(GAMMA(x)), 1 <= x < 2.25
900 // [0.875,1.25)
901 data8 0xBF9A04F7E40C8498,0x3FAB79D8D9380F03 // C17,C16
902 data8 0xBFB3B63609CA0CBD,0x3FB5564EA1675539 // C13,C12
903 data8 0xBFBC806766F48C41,0x3FC010B36CDA773A // C9,C8
904 data8 0xD45CE0BD54BE3D67,0xBFFC // C5
905 data8 0xCD26AADF559676D0,0xBFFD // C3
906 data8 0x93C467E37DB0C7A7,0xBFFE // C1
907 data8 0xBFB10C251723B123,0x3FB2669DAD69A12D // C15,C14
908 data8 0xBFB748A3CFCE4717,0x3FB9A01DEE29966A // C11,C10
909 data8 0xBFC2703A1D85497E,0x3FC5B40CB0FD353C // C7,C6
910 data8 0x8A8991563ECBBA5D,0x3FFD // C4
911 data8 0xD28D3312983E9844,0x3FFE // C2
912 data8 0,0 // C0
913 // [1.25,1.75)
914 data8 0xBF12680486396DE6,0x3F23C51FC332CD9D // C17,C16
915 data8 0xBF422633DA3A1496,0x3F4CC70680768857 // C13,C12
916 data8 0xBF6E2F1A1F804B5D,0x3F78FCE02A032428 // C9,C8
917 data8 0x864D46FA895985C1,0xBFFA // C5
918 data8 0x97213C6E35E12043,0xBFFC // C3
919 data8 0x8A8A42A401D979B7,0x3FC7 // C1
920 data8 0xBF2E098A8A2332A8,0x3F370E61B73B205C // C15,C14
921 data8 0xBF56F9849D3BC6CC,0x3F6283126F58D7F4 // C11,C10
922 data8 0xBF851F9F9516A98F,0x3F9266E797A1433F // C7,C6
923 data8 0x845A14A6A81B0638,0x3FFB // C4
924 data8 0xF7B95E4771C55C99,0x3FFD // C2
925 data8 0xF8CDCDE61C520E0F,0xBFFB // C0
926 // [1.75,2.25)
927 data8 0xBEA01D7AFA5D8F52,0x3EB1010986E60253 // C17,C16
928 data8 0xBEE3CBEDB4C918AA,0x3EF580F6D9D0F72D // C13,C12
929 data8 0xBF2D3FD4C7F68563,0x3F40B36AF884AE9A // C9,C8
930 data8 0xF2027E10C7B051EC,0xBFF7 // C5
931 data8 0x89F000D2ABB03401,0xBFFB // C3
932 data8 0xD8773039049E70B6,0x3FFD // C1
933 data8 0xBEC112CD07CFC31A,0x3ED2528A428D30E1 // C15,C14
934 data8 0xBF078DE5618D8C9F,0x3F1A127AD811A53D // C11,C10
935 data8 0xBF538AC5C2BF540D,0x3F67ADD6EADB5718 // C7,C6
936 data8 0xA8991563EC243383,0x3FF9 // C4
937 data8 0xA51A6625307D3230,0x3FFD // C2
938 data8 0,0 // C0
939 //
940 // polynomial approximation of ln(sin(Pi*x)/(Pi*x)), 9 <= x <= 0.5
941 data8 0xBFDC1BF0931AE591,0x3FD36D6D6CE263D7 //S28,S26
942 data8 0xBFBD516F4FD9FB18,0xBFBBE1703F315086 //S20,S18
943 data8 0xAAB5A3CCEFCD3628,0xBFFC //S12
944 data8 0x80859B5C318E19A5,0xBFFD //S8
945 data8 0x8A8991563EC7EB33,0xBFFE //S4
946 data8 0xBFD23AB9E6CC88AC,0xBF9957F5146FC7AF //S24,S22
947 data8 0xBFC007B324E23040,0xBFC248DEC29CAC4A //S16,S14
948 data8 0xCD00EFF2F8F86899,0xBFFC //S10
949 data8 0xADA06587FACD668B,0xBFFD //S6
950 data8 0xD28D3312983E98A0,0xBFFF //S2
951 //
952 data8 0x8090F777D7942F73,0x4001 // PR01
953 data8 0xE5B521193CF61E63,0x4000 // PR11
954 data8 0xC02C000000001939,0x0000000000000233 // (-15;-14)
955 data8 0xC02A000000016124,0x0000000000002BFB // (-14;-13)
956 data8 0xC02800000011EED9,0x0000000000025CBB // (-13;-12)
957 data8 0xC026000000D7322A,0x00000000001E1095 // (-12;-11)
958 data8 0xC0240000093F2777,0x00000000013DD3DC // (-11;-10)
959 data8 0xC02200005C7768FB,0x000000000C9539B9 // (-10;-9)
960 data8 0xC02000034028B3F9,0x000000007570C565 // (-9;-8)
961 data8 0xC01C0033FDEDFE1F,0x00000007357E670E // (-8;-7)
962 data8 0xC018016B25897C8D,0x000000346DC5D639 // (-7;-6)
963 data8 0xC014086A57F0B6D9,0x0000010624DD2F1B // (-6;-5)
964 data8 0xC010284E78599581,0x0000051EB851EB85 // (-5;-4)
965 data8 0xC009260DBC9E59AF,0x000028F5C28F5C29 // (-4;-3)
966 data8 0xC003A7FC9600F86C,0x0000666666666666 // (-3;-2)
967 data8 0xCC15879606130890,0x4000 // PR21
968 data8 0xB42FE3281465E1CC,0x4000 // PR31
969 //
970 data8 0x828185F0B95C9916,0x4001 // PR00
971 //
972 data8 0xD4D3C819E4E5654B,0x4000 // PR10
973 data8 0xA82FBBA4FCC75298,0x4000 // PR20
974 data8 0xC02DFFFFFFFFFE52,0x000000000000001C // (-15;-14)
975 data8 0xC02BFFFFFFFFE6C7,0x00000000000001A6 // (-14;-13)
976 data8 0xC029FFFFFFFE9EDC,0x0000000000002BFB // (-13;-12)
977 data8 0xC027FFFFFFEE1127,0x000000000001EEC8 // (-12;-11)
978 data8 0xC025FFFFFF28CDD4,0x00000000001E1095 // (-11;-10)
979 data8 0xC023FFFFF6C0D7C0,0x000000000101B2B3 // (-10;-9)
980 data8 0xC021FFFFA3884BD0,0x000000000D6BF94D // (-9;-8)
981 data8 0xC01FFFF97F8159CF,0x00000000C9539B89 // (-8;-7)
982 data8 0xC01BFFCBF76B86F0,0x00000007357E670E // (-7;-6)
983 data8 0xC017FE92F591F40D,0x000000346DC5D639 // (-6;-5)
984 data8 0xC013F7577A6EEAFD,0x00000147AE147AE1 // (-5;-4)
985 data8 0xC00FA471547C2FE5,0x00000C49BA5E353F // (-4;-3)
986 data8 0xC005FB410A1BD901,0x000053F7CED91687 // (-3;-2)
987 data8 0x80151BB918A293AA,0x4000 // PR30
988 data8 0xB3C9F8F47422A314,0x400B // PRN
989 //
990 // right negative roots
991 //(-3;-2)
992 data8 0x40BFCF8B90BE7F6B,0x40B237623345EFC3 // A15,A14
993 data8 0x407A92EFB03B281E,0x40728700C7819759 // A11,A10
994 data8 0x403809F04EF4D0F2,0x4038D32F682D9593 // A7,A6
995 data8 0xB4A5302C53C2F2D8,0x3FFF // A3
996 data8 0xC1FF4B357A9B0383,0x3FFF // A1
997 data8 0x409C46632EB4B2D3,0x4091A72AFA2148F5 // A13,A12
998 data8 0x4059297AC79A88DB,0x40548EAA7BE7FA6B // A9,A8
999 data8 0x4017339FE04B227F,0x4021718D7CA09E02 // A5,A4
1000 data8 0x9B775D8017AAE668,0x4001 // A2
1001 data8 0x8191DB68FF4366A1,0x3FC9 // A0
1002 //(-4;-3)
1003 data8 0x425260910D35307B,0x422668F5BE7983BB // A15,A14
1004 data8 0x41A4454DBE4BEE43,0x41799CA93F6EA817 // A11,A10
1005 data8 0x40FBB97AA1400F31,0x40D293C3F7ADAB15 // A7,A6
1006 data8 0xE089B8926AE4517B,0x4005 // A3
1007 data8 0xF90532F97D630C69,0x4001 // A1
1008 data8 0x41F9F0CF98C5F2EA,0x41D026336C6BF394 // A13,A12
1009 data8 0x415057F61156D5B8,0x41251EA3055CB754 // A9,A8
1010 data8 0x40A99A6337D9FC2B,0x408267203D776151 // A5,A4
1011 data8 0xCEA694BB8A8827A9,0x4003 // A2
1012 data8 0xF4B02F1D73D30EED,0x3FCD // A0
1013 //(-5;-4)
1014 data8 0x4412365489340979,0x43C86441BAFDEE39 // A15,A14
1015 data8 0x42ED68FCB19352DD,0x42A45FCE3905CD6F // A11,A10
1016 data8 0x41CD14FE49FD4FCA,0x41855E3DBFA89744 // A7,A6
1017 data8 0xAACD88D954E0EC16,0x400B // A3
1018 data8 0xD652E7A490B0DCDF,0x4003 // A1
1019 data8 0x437F52608E0E752A,0x433560E0633E33D5 // A13,A12
1020 data8 0x425C83998976DE3D,0x421433DCCD3B473B // A9,A8
1021 data8 0x4140261EB5732106,0x40F96D18E21AE6CC // A5,A4
1022 data8 0xA220AE6C09FA8A0E,0x4007 // A2
1023 data8 0xCC1682D17A2B5A58,0xBFCF // A0
1024 //(-6;-5)
1025 data8 0x4630E41D6386CF5A,0x45C2E7992C628C8C // A15,A14
1026 data8 0x447AABEC714F913A,0x440EDCAB45339F3A // A11,A10
1027 data8 0x42C9A8D00C97E3CE,0x425F7D8D5BEAB44D // A7,A6
1028 data8 0x929EC2B1FB95BB5B,0x4012 // A3
1029 data8 0xF6B970414D717D38,0x4005 // A1
1030 data8 0x45545E578976F6A2,0x44E738288DD52686 // A13,A12
1031 data8 0x43A20921FEC49492,0x433557FD7C6A41B3 // A9,A8
1032 data8 0x41F3E01773761DB4,0x418A225DF2DA6C47 // A5,A4
1033 data8 0xE7661976117F9312,0x400B // A2
1034 data8 0xC33C13FEE07494DE,0x3FCF // A0
1035 //(-7;-6)
1036 data8 0x4898F1E6133305AD,0x4802C5306FE4A850 // A15,A14
1037 data8 0x463FD37946B44094,0x45A8D489B784C2DD // A11,A10
1038 data8 0x43E9500995815F06,0x4354F21E2FEE6DF5 // A7,A6
1039 data8 0xEF281D1E1BBE10BD,0x4019 // A3
1040 data8 0xB4EF24F1D78C2029,0x4008 // A1
1041 data8 0x476AB1D5930011E5,0x46D4867E77BFB622 // A13,A12
1042 data8 0x45139151ECDEF7C5,0x447F3A2BC6BF466F // A9,A8
1043 data8 0x42C1D3D50713FA40,0x422F9C7B52556A1B // A5,A4
1044 data8 0xFE711A4267CEA83A,0x4010 // A2
1045 data8 0xD11E91B3FF8F4B94,0xBFD2 // A0
1046 //(-8;-7)
1047 data8 0x4B39E57569811B6E,0x4A7656073EB1FA21 // A15,A14
1048 data8 0x482C9B24A516B0BB,0x47698FF55139C62B // A11,A10
1049 data8 0x452393E2BC8E8D04,0x44628E1C710DA478 // A7,A6
1050 data8 0x9F2A95AF1B7A773F,0x4022 // A3
1051 data8 0x9DA03D51C303C918,0x400B // A1
1052 data8 0x49B24C241A3D5BCB,0x48F01CB936ECDA67 // A13,A12
1053 data8 0x46A712B3425C6797,0x45E5164114BD6DA1 // A9,A8
1054 data8 0x43A216A356069D01,0x42E25E42A45E2108 // A5,A4
1055 data8 0xC1F42ED57BBC2529,0x4016 // A2
1056 data8 0xB1C7B615A7DCA8A9,0xBFD7 // A0
1057 //(-9;-8)
1058 data8 0x4E09D478E5EE857D,0x4D1647782106E9AB // A15,A14
1059 data8 0x4A3C7F4D51927548,0x49497954796D743A // A11,A10
1060 data8 0x467387BD6AF0CBDF,0x4582843E134111D2 // A7,A6
1061 data8 0x9F003C6DE9666513,0x402B // A3
1062 data8 0x9D8447F6BF99950A,0x400E // A1
1063 data8 0x4C22364D238C61A9,0x4B300B18050AB940 // A13,A12
1064 data8 0x4857004D64215772,0x4765074E448C3C9A // A9,A8
1065 data8 0x44920E9EA07BF624,0x43A257BEC94BBF48 // A5,A4
1066 data8 0xC1D1C49AC5B2A4B4,0x401C // A2
1067 data8 0x9A749AF9F2D2E688,0x3FDB // A0
1068 //(-10;-9)
1069 data8 0x5102C7C43EA26C83,0x4FDCD174DEB0426B // A15,A14
1070 data8 0x4C6A036195CD5BAD,0x4B44ABB52B65628A // A11,A10
1071 data8 0x47D6439374B98FED,0x46B2C3903EF44D7D // A7,A6
1072 data8 0xE25BAF73AB8A7DB3,0x4034 // A3
1073 data8 0xB130901CA6D81B61,0x4011 // A1
1074 data8 0x4EB50BB0726AE206,0x4D907A96E6D2B6E2 // A13,A12
1075 data8 0x4A20975D78EAF01A,0x48FAF79C9C3E7908 // A9,A8
1076 data8 0x459044144129A247,0x446D6043FA3150A3 // A5,A4
1077 data8 0xF547997E083D9BA7,0x4022 // A2
1078 data8 0x977AF525A6ECA1BC,0x3FDC // A0
1079 //(-11;-10)
1080 data8 0x5420A5D5E90C6D73,0x52C4710A503DC67A // A15,A14
1081 data8 0x4EB2ED07BA88D2A8,0x4D581001ED9A5ECE // A11,A10
1082 data8 0x494A8A28E9E3DFEF,0x47F1E4E1E476793E // A7,A6
1083 data8 0xDD0C97E12D4A3378,0x403E // A3
1084 data8 0xDD7C12D5182FD543,0x4014 // A1
1085 data8 0x5167ED536877A072,0x500DF9AF21DDC0B6 // A13,A12
1086 data8 0x4BFEE6F04BC34FF8,0x4AA4175CEF736A5E // A9,A8
1087 data8 0x4698D1B4388FEC78,0x4541EDE7607A600D // A5,A4
1088 data8 0xBF9F645F282AC552,0x4029 // A2
1089 data8 0xAE1BBE4D3CDACCF4,0x3FE1 // A0
1090 //(-12;-11)
1091 data8 0x575F0EEF5FB7D4C0,0x55CBB7302B211A7C // A15,A14
1092 data8 0x5113A4F1825C7CB2,0x4F822A0D46E0605A // A11,A10
1093 data8 0x4ACED38FC8BE069A,0x493E3B56D2649F18 // A7,A6
1094 data8 0x8FA8FF5DF8B72D5E,0x4049 // A3
1095 data8 0x9845417E8598D642,0x4018 // A1
1096 data8 0x5437780541C3F2D3,0x52A56279B563C1B2 // A13,A12
1097 data8 0x4DF0F71A48C50188,0x4C600B358988DEBF // A9,A8
1098 data8 0x47AE7EE95BDA3DE9,0x46200599DC16B18F // A5,A4
1099 data8 0xB5249F914932E55D,0x4030 // A2
1100 data8 0xEAE760CD2C086094,0x3FE5 // A0
1101 //(-13;-12)
1102 data8 0x5ABA5848651F6D18,0x58EF60D8A817650B // A15,A14
1103 data8 0x538A8CA86E13EFB1,0x51C05DBD4D01076D // A11,A10
1104 data8 0x4C607594C339D259,0x4A9585BD5BF932BB // A7,A6
1105 data8 0xF26D282C36EC3611,0x4053 // A3
1106 data8 0xE467DF4810EE7EEE,0x401B // A1
1107 data8 0x5721D9BA485E8CC3,0x5555AF2CCFB2104D // A13,A12
1108 data8 0x4FF4619A17B14EA6,0x4E29B2F29EB9F8C4 // A9,A8
1109 data8 0x48CCF27629D46E79,0x47044715F991A63D // A5,A4
1110 data8 0xCBC92FB9BDAA95A9,0x4037 // A2
1111 data8 0xFB743A426163665B,0xBFE6 // A0
1112 //(-14;-13)
1113 data8 0x5E3295B24B353EAA,0x5C2B447E29796F20 // A15,A14
1114 data8 0x5615A35CB5EAFAE5,0x54106AB089C95CAF // A11,A10
1115 data8 0x4DFEC7D93501900A,0x4BF8C4C685F01B83 // A7,A6
1116 data8 0x820899603D9A74D5,0x405F // A3
1117 data8 0xB9949919933821CB,0x401F // A1
1118 data8 0x5A23373DB9A995AC,0x581CBA0AF7F53009 // A13,A12
1119 data8 0x520929836BB304CD,0x500386409A7076DA // A9,A8
1120 data8 0x49F480173FEAF90B,0x47F1ACB14B810793 // A5,A4
1121 data8 0x86881B8674DBF205,0x403F // A2
1122 data8 0x8CF3CC35AA2C5F90,0x3FED // A0
1123 //(-15;-14)
1124 data8 0x61C37D53BE0029D6,0x5F80667CD9D68354 // A15,A14
1125 data8 0x58B3F01898E6605B,0x567149652116DB6A // A11,A10
1126 data8 0x4FA82FA4F5D35B00,0x4D663DB00832DF8F // A7,A6
1127 data8 0xAE426731C9B94996,0x406A // A3
1128 data8 0xA264C84BE3708F3F,0x4023 // A1
1129 data8 0x5D3B254BC1C806A8,0x5AF72E736048B553 // A13,A12
1130 data8 0x542E476505104BB0,0x51EAD96CDC4FB48F // A9,A8
1131 data8 0x4B25095F498DB134,0x48E4B9FDEBFE24AB // A5,A4
1132 data8 0xCE076A5A116C1D34,0x4046 // A2
1133 data8 0x940013871A15050B,0x3FF1 // A0
1134 //
1135 // left negative roots
1136 //(-3;-2)
1137 data8 0x41AEB7998DBE2B2C,0xC19053D8FAC05DF7 // A16,A15
1138 data8 0x4133197BF1ADEAF9,0xC1150728B9B82072 // A12,A11
1139 data8 0x40BDBA65E74F4526,0xC0A12239BEEF8F72 // A8,A7
1140 data8 0xFA8256664F99E2AA,0x4004 // A4
1141 data8 0x9933F9E132D2A5DB,0x4002 // A2
1142 data8 0x416FFB167B85F77C,0xC15166AE0ACCF87C // A14,A13
1143 data8 0x40F75815106322C0,0xC0DA2D23C59C348D // A10,A9
1144 data8 0x4084373F7CC42043,0xC0685884581F8C61 // A6,A5
1145 data8 0xA0C2D6186460FF9D,0xC003 // A3
1146 data8 0xF5096D48258CA0AD,0xBFFF // A1
1147 //(-4;-3)
1148 data8 0xC3E5BD233016D4B9,0x43A084DAD2D94AB1 // A15,A14
1149 data8 0xC2CCFFF5E5AED722,0x4286D143AC7D29A6 // A11,A10
1150 data8 0xC1B7DBBE0680D07B,0x4173E8F3ABB79CED // A7,A6
1151 data8 0xE929ACEA59799BAF,0xC00A // A3
1152 data8 0xA5CCECB362B21E1C,0xC003 // A1
1153 data8 0xC357EED873871B81,0x43128E0B873204FC // A13,A12
1154 data8 0xC242225FA76E8450,0x41FD2F76AE7386CE // A9,A8
1155 data8 0xC13116F7806D0C7A,0x40EE8F829F141025 // A5,A4
1156 data8 0xFBB6F57021B5B397,0x4006 // A2
1157 data8 0xEEE019B4C05AC269,0xBFCB // A0
1158 //(-5;-4)
1159 data8 0xC626A52FE8AAA100,0x45B9FD1F4DDFE31E // A15,A14
1160 data8 0xC473812A5675F08B,0x440738530AECC254 // A11,A10
1161 data8 0xC2C5068B3F94AC27,0x425A8C5C539A500B // A7,A6
1162 data8 0x869FBFF732F20C3A,0xC012 // A3
1163 data8 0xE91251F7CF25A655,0xC005 // A1
1164 data8 0xC54C18CB48E5DA0F,0x44E07BD36FF561DF // A13,A12
1165 data8 0xC39BEC120D2FEBEA,0x4330FFA5388435BE // A9,A8
1166 data8 0xC1F13D5D163B7FB5,0x418752A6F5AC0F39 // A5,A4
1167 data8 0xDA99E33C51D360F0,0x400B // A2
1168 data8 0x9F47A66A2F53D9B9,0x3FD1 // A0
1169 //(-6;-5)
1170 data8 0xC8970DAC16B6D59E,0x480170728306FD76 // A15,A14
1171 data8 0xC63E0E5030604CF3,0x45A7924D74D57C65 // A11,A10
1172 data8 0xC3E8684E41730FC6,0x43544D54EA2E5B9A // A7,A6
1173 data8 0xEB7404450C47C5F4,0xC019 // A3
1174 data8 0xB30FB521D2C19F8B,0xC008 // A1
1175 data8 0xC768F34D35DF6320,0x46D348B3BB2E68B8 // A13,A12
1176 data8 0xC512AC2FE5EA638E,0x447DF44BC7FC5E17 // A9,A8
1177 data8 0xC2C15EA6B0AAFEF9,0x422EF5D308DBC420 // A5,A4
1178 data8 0xFBCEE5BCA70FD3A3,0x4010 // A2
1179 data8 0x8589A7CFFE0A3E86,0xBFD5 // A0
1180 //(-7;-6)
1181 data8 0xCB3995A0CC961E5A,0x4A7615C6C7116ADD // A15,A14
1182 data8 0xC82C5AFE0BF9C427,0x47695BD2F367668B // A11,A10
1183 data8 0xC52377E70BA14CF5,0x4462775E859E4392 // A7,A6
1184 data8 0x9EC8ED6E4C3D4DBE,0xC022 // A3
1185 data8 0x9D5FBD2E75520E65,0xC00B // A1
1186 data8 0xC9B21BB881A4DDF8,0x48EFEAB06FBA0207 // A13,A12
1187 data8 0xC6A6E8550CBC188F,0x45E4F3D26238B099 // A9,A8
1188 data8 0xC3A20427DF1B110A,0x42E24F3D636F2E4E // A5,A4
1189 data8 0xC1A4D12A82280CFB,0x4016 // A2
1190 data8 0xEF46D8DCCA9E8197,0x3FD2 // A0
1191 //(-8;-7)
1192 data8 0xCE0946982B27DE5B,0x4D15DBC6664E2DD2 // A15,A14
1193 data8 0xCA3C769F6B3B2B93,0x49497251CD0C4363 // A11,A10
1194 data8 0xC67384066C47F489,0x458281393433AB28 // A7,A6
1195 data8 0x9EF3459926D0F14F,0xC02B // A3
1196 data8 0x9D7BB7F2600DFF0B,0xC00E // A1
1197 data8 0xCC22351326C939A7,0x4B3009431C4F1D3F // A13,A12
1198 data8 0xC856FAADDD48815D,0x476502BC3ECA040C // A9,A8
1199 data8 0xC4920C2A84173810,0x43A255C052525F99 // A5,A4
1200 data8 0xC1C73B6554011EFA,0x401C // A2
1201 data8 0x954612700ADF8317,0xBFD8 // A0
1202 //(-9;-8)
1203 data8 0xD102F5CC7B590D3A,0x4FDD0F1C30E4EB22 // A15,A14
1204 data8 0xCC6A02912B0DF650,0x4B44AB18E4FCC159 // A11,A10
1205 data8 0xC7D64314B4A2FAAB,0x46B2C334AE5E2D34 // A7,A6
1206 data8 0xE2598724F7E28E99,0xC034 // A3
1207 data8 0xB12F6FE2E195452C,0xC011 // A1
1208 data8 0xCEB507747AF9356A,0x4D907802C08BA48F // A13,A12
1209 data8 0xCA2096E3DC29516F,0x48FAF6ED046A1DB7 // A9,A8
1210 data8 0xC59043D21BA5EE56,0x446D5FE468B30450 // A5,A4
1211 data8 0xF5460A8196B59C83,0x4022 // A2
1212 data8 0xB108F35A8EDA92D5,0xBFDD // A0
1213 //(-10;-9)
1214 data8 0xD420430D91F8265B,0x52C406CAAAC9E0EE // A15,A14
1215 data8 0xCEB2ECDDDAA3DAD1,0x4D580FDA97F92E3A // A11,A10
1216 data8 0xC94A8A192341B5D4,0x47F1E4D8C690D07B // A7,A6
1217 data8 0xDD0C5F920C2F0D2B,0xC03E // A3
1218 data8 0xDD7BED3631657B48,0xC014 // A1
1219 data8 0xD167F410E64E90A4,0x500DFFED20F714A7 // A13,A12
1220 data8 0xCBFEE6D9043169E9,0x4AA4174F64B40AA7 // A9,A8
1221 data8 0xC698D1A9AF0AB9C2,0x4541EDE14987A887 // A5,A4
1222 data8 0xBF9F43D461B3DE6E,0x4029 // A2
1223 data8 0xF3891A50642FAF26,0x3FE1 // A0
1224 //(-11;-10)
1225 data8 0xD75F0EEAF769D42A,0x55CBB72C8869183A // A15,A14
1226 data8 0xD113A4EF80394F77,0x4F822A0B96B3ECA9 // A11,A10
1227 data8 0xCACED38DC75763CB,0x493E3B5522D2D028 // A7,A6
1228 data8 0x8FA8FB5C92533701,0xC049 // A3
1229 data8 0x98453EDB9339C24E,0xC018 // A1
1230 data8 0xD43778026CCD4B20,0x52A5627753273B9B // A13,A12
1231 data8 0xCDF0F718DD7E1214,0x4C600B34582911EB // A9,A8
1232 data8 0xC7AE7EE7F112362C,0x46200599439C264F // A5,A4
1233 data8 0xB5249C335342B5BC,0x4030 // A2
1234 data8 0x881550711D143475,0x3FE4 // A0
1235 //(-12;-11)
1236 data8 0xDAB9C724EEEE2BBB,0x58EEC971340EDDBA // A15,A14
1237 data8 0xD38A8C8AE63BD8BF,0x51C05DB21CEE00D3 // A11,A10
1238 data8 0xCC607594C311C12D,0x4A9585BD5BE6AB57 // A7,A6
1239 data8 0xF26D282C36EC0E66,0xC053 // A3
1240 data8 0xE467DF1FA674BFAE,0xC01B // A1
1241 data8 0xD721DE506999AA9C,0x5555B34F71B45132 // A13,A12
1242 data8 0xCFF4619A476BF76F,0x4E29B2F2BBE7A67E // A9,A8
1243 data8 0xC8CCF27629D48EDC,0x47044715F991AB46 // A5,A4
1244 data8 0xCBC92FB9BDAA928D,0x4037 // A2
1245 data8 0xCE27C4F01CF53284,0xBFE6 // A0
1246 //(-13;-12)
1247 data8 0xDE3295B24355C5A1,0x5C2B447E298B562D // A15,A14
1248 data8 0xD615A35CB5E92103,0x54106AB089C95E8C // A11,A10
1249 data8 0xCDFEC7D935019005,0x4BF8C4C685F01B83 // A7,A6
1250 data8 0x820899603D9A74D5,0xC05F // A3
1251 data8 0xB9949916F8DF4AC4,0xC01F // A1
1252 data8 0xDA23373DBA0B7548,0x581CBA0AF7F45C01 // A13,A12
1253 data8 0xD20929836BB30934,0x500386409A7076D6 // A9,A8
1254 data8 0xC9F480173FEAF90B,0x47F1ACB14B810793 // A5,A4
1255 data8 0x86881B8674DBF205,0x403F // A2
1256 data8 0x8CFAFA9A142C1FF0,0x3FED // A0
1257 //(-14;-13)
1258 data8 0xE1C33F356FA2C630,0x5F8038B8AA919DD7 // A15,A14
1259 data8 0xD8B3F0167E14982D,0x5671496400BAE0DB // A11,A10
1260 data8 0xCFA82FA4F5D25C3E,0x4D663DB008328C58 // A7,A6
1261 data8 0xAE426731C9B94980,0xC06A // A3
1262 data8 0xA264C84BB8A66F86,0xC023 // A1
1263 data8 0xDD3B26E34762ED1E,0x5AF72F76E3C1B793 // A13,A12
1264 data8 0xD42E476507E3D06E,0x51EAD96CDD881DFA // A9,A8
1265 data8 0xCB25095F498DB15F,0x48E4B9FDEBFE24B5 // A5,A4
1266 data8 0xCE076A5A116C1D32,0x4046 // A2
1267 data8 0x94001BF5A24966F5,0x3FF1 // A0
1268 //(-15;-14)
1269 data8 0xE56DB8B72D7156FF,0x62EAB0CDB22539BE // A15,A14
1270 data8 0xDB63D76B0D3457E7,0x58E254823D0AE4FF // A11,A10
1271 data8 0xD15F060BF548404A,0x4EDE65C20CD4E961 // A7,A6
1272 data8 0x900DA565ED76C19D,0xC076 // A3
1273 data8 0x9868C809852DA712,0xC027 // A1
1274 data8 0xE067CCDA0408AAF0,0x5DE5A79C5C5C54AF // A13,A12
1275 data8 0xD6611ADBF5958ED0,0x53E0294092BE9677 // A9,A8
1276 data8 0xCC5EA28D90EE8C5D,0x49E014930EF336EE // A5,A4
1277 data8 0xB57930DCE7A61AE8,0x404E // A2
1278 data8 0x976BEC1F30DF151C,0x3FF5 // A0
1279 LOCAL_OBJECT_END(lgamma_data)
1282 .section .text
1283 GLOBAL_LIBM_ENTRY(__libm_lgamma)
1285 { .mfi
1286 getf.exp GR_SignExp = f8
1287 frcpa.s1 FR_C,p9 = f1,f8
1288 mov GR_ExpMask = 0x1ffff
1289 }
1290 { .mfi
1291 addl GR_ad_Data = @ltoff(lgamma_data),gp
1292 fcvt.fx.s1 FR_int_N = f8
1293 mov GR_2_25 = 0x4002 // 2.25
1294 };;
1295 { .mfi
1296 getf.d GR_ArgAsIs = f8
1297 fclass.m p13,p0 = f8,0x1EF // is x NaTVal, NaN,
1298 // +/-0, +/-INF or +/-deno?
1299 mov GR_ExpBias = 0xFFFF
1300 }
1301 { .mfi
1302 ld8 GR_ad_Data = [GR_ad_Data]
1303 fcvt.fx.trunc.s1 FR_int_Ntrunc = f8
1304 mov GR_ExpOf256 = 0x10007
1305 };;
1306 { .mfi
1307 mov GR_ExpOf2 = 0x10000
1308 fcmp.lt.s1 p14,p15 = f8,f0 // p14 if x<0
1309 dep.z GR_Ind = GR_SignExp,8,4
1310 }
1311 { .mfi
1312 and GR_Exp = GR_SignExp,GR_ExpMask
1313 fma.s1 FR_2 = f1,f1,f1
1314 cmp.lt p10,p0 = GR_SignExp,GR_ExpBias
1315 };;
1316 { .mfi
1317 add GR_ad_1 = 0xB80,GR_ad_Data
1318 fnorm.s1 FR_NormX = f8
1319 shr.u GR_Arg = GR_ArgAsIs,48
1320 }
1321 { .mib
1322 add GR_ad_Co = GR_Ind,GR_ad_Data
1323 add GR_ad_Ce = 0x10,GR_ad_Data
1324 // jump if the input argument is NaTVal, NaN, +/-0, +/-INF or +/-deno
1325 (p13) br.cond.spnt lgamma_spec
1326 };;
1327 lgamma_common:
1328 { .mfi
1329 ldfpd FR_LocalMin,FR_05 = [GR_ad_1],16
1330 fmerge.se FR_x = f1,f8
1331 add GR_ad_2 = 0xBC0,GR_ad_Data
1332 }
1333 { .mfb
1334 add GR_ad_Ce = GR_Ind,GR_ad_Ce
1335 fms.s1 FR_w = f8,f1,f1 // x-1
1336 // jump if the input argument is positive and less than 1.0
1337 (p10) br.cond.spnt lgamma_0_1
1338 };;
1339 { .mfi
1340 ldfe FR_C01 = [GR_ad_Co],32
1341 fnma.s1 FR_InvX = FR_C,f8,f1 // NR iteration #1
1342 (p15) cmp.lt.unc p8,p0 = GR_ExpOf256,GR_SignExp
1343 }
1344 { .mib
1345 ldfe FR_C11 = [GR_ad_Ce],32
1346 (p15) cmp.lt.unc p11,p0 = GR_Arg,GR_2_25
1347 // jump if the input argument isn't less than 512.0
1348 (p8) br.cond.spnt lgamma_pstirling
1349 };;
1350 { .mfi
1351 ldfe FR_C21 = [GR_ad_Co],32
1352 (p14) fms.s1 FR_r = FR_C,f8,f1 // reduced arg for log(x)
1353 (p14) cmp.lt.unc p0,p9 = GR_Exp,GR_ExpOf256
1354 }
1355 { .mib
1356 ldfe FR_C31 = [GR_ad_Ce],32
1357 add GR_ad_Co7 = 0x12C0,GR_ad_2
1358 // jump if the input argument is from range [1.0; 2.25)
1359 (p11) br.cond.spnt lgamma_1_2
1360 };;
1361 { .mfi
1362 ldfe FR_C41 = [GR_ad_Co],32
1363 fcvt.xf FR_N = FR_int_N
1364 add GR_ad_Ce7 = 0x1310,GR_ad_2
1365 }
1366 { .mfb
1367 ldfe FR_C51 = [GR_ad_Ce],32
1368 (p14) fma.s1 FR_5 = FR_2,FR_2,f1
1369 // jump if the input argument is less or equal to -512.0
1370 (p9) br.cond.spnt lgamma_negstirling
1371 };;
1372 { .mfi
1373 ldfe FR_C61 = [GR_ad_Co],32
1374 (p14) fcvt.xf FR_Ntrunc = FR_int_Ntrunc
1375 shr GR_Ind = GR_Ind,4
1376 }
1377 { .mfi
1378 ldfe FR_C71 = [GR_ad_Ce],32
1379 (p14) fma.s1 FR_Xp1 = f1,f1,FR_NormX // x+1
1380 cmp.eq p6,p7 = GR_ExpOf2,GR_SignExp
1381 };;
1382 .pred.rel "mutex",p6,p7
1383 { .mfi
1384 ldfe FR_C81 = [GR_ad_Co],32
1385 (p6) fma.s1 FR_x = f0,f0,FR_NormX
1386 shladd GR_Offs7 = GR_Ind,2,GR_Ind // (ind*16)*5
1387 }
1388 { .mfi
1389 ldfe FR_C91 = [GR_ad_Ce],32
1390 (p7) fms.s1 FR_x = FR_x,f1,f1
1391 add GR_ad_Co7 = 0x800,GR_ad_Data
1392 };;
1393 { .mfi
1394 ldfe FR_CA1 = [GR_ad_Co],32
1395 (p14) fma.s1 FR_3 = f1,f1,FR_2
1396 shladd GR_Offs7 = GR_Ind,1,GR_Offs7 // (ind*16)*7
1397 }
1398 { .mfi
1399 ldfe FR_C00 = [GR_ad_Ce],32
1400 (p14) fma.s1 FR_Xp4 = FR_2,FR_2,FR_NormX
1401 add GR_ad_Ce7 = 0x810,GR_ad_Data
1402 };;
1403 { .mfi
1404 ldfe FR_C10 = [GR_ad_Co],32
1405 (p6) fms.s1 FR_Xm2 = FR_w,f1,f1
1406 add GR_ad_Co7 = GR_ad_Co7,GR_Offs7
1407 }
1408 { .mfi
1409 ldfe FR_C20 = [GR_ad_Ce],32
1410 (p14) fma.s1 FR_r2 = FR_r,FR_r,f0 // log(x)
1411 add GR_ad_Ce7 = GR_ad_Ce7,GR_Offs7
1412 };;
1413 { .mfi
1414 ldfe FR_C30 = [GR_ad_Co],32
1415 (p14) fms.s1 FR_Xf = FR_NormX,f1,FR_N // xf = x - [x]
1416 (p14) mov GR_Arg17 = 0xC031 // -17
1417 }
1418 { .mfi
1419 ldfe FR_C40 = [GR_ad_Ce],32
1420 (p14) fma.s1 FR_Xp5 = FR_5,f1,FR_NormX
1421 (p14) sub GR_Exp = GR_Exp,GR_ExpBias
1422 };;
1423 { .mfi
1424 ldfe FR_C50 = [GR_ad_Co7],32
1425 (p14) fms.s1 FR_Xfr = FR_Xp1,f1,FR_Ntrunc // xfr = (x+1) - [x]
1426 (p14) cmp.lt.unc p13,p0 = GR_Arg,GR_Arg17
1427 }
1428 { .mfb
1429 ldfe FR_C60 = [GR_ad_Ce7],32
1430 (p14) fma.s1 FR_Xp10 = FR_5,FR_2,FR_NormX
1431 // jump if the input argument is negative and great than -17.0
1432 (p13) br.cond.spnt lgamma_negrecursion
1433 };;
1434 { .mfi
1435 ldfe FR_C70 = [GR_ad_Co7],32
1436 fma.s1 FR_C01 = FR_x,f1,FR_C01
1437 (p14) add GR_ad_Ce = 0x1310,GR_ad_2
1438 }
1439 { .mfi
1440 ldfe FR_C80 = [GR_ad_Ce7],32
1441 fma.s1 FR_C11 = FR_x,f1,FR_C11
1442 (p14) add GR_ad_Co = 0x12C0,GR_ad_2
1443 };;
1444 { .mfi
1445 ldfe FR_C90 = [GR_ad_Co7],32
1446 fma.s1 FR_C21 = FR_x,f1,FR_C21
1447 nop.i 0
1448 }
1449 { .mfi
1450 ldfe FR_CA0 = [GR_ad_Ce7],32
1451 fma.s1 FR_C31 = FR_x,f1,FR_C31
1452 nop.i 0
1453 };;
1454 { .mfi
1455 ldfe FR_CN = [GR_ad_Co7],32
1456 fma.s1 FR_C41 = FR_x,f1,FR_C41
1457 nop.i 0
1458 }
1459 { .mfi
1460 (p14) ldfpd FR_P5,FR_P4 = [GR_ad_1],16
1461 fma.s1 FR_C51 = FR_x,f1,FR_C51
1462 nop.i 0
1463 };;
1464 { .mfi
1465 (p14) ldfpd FR_P3,FR_P2 = [GR_ad_2],16
1466 fma.s1 FR_C61 = FR_x,f1,FR_C61
1467 nop.i 0
1468 }
1469 { .mfi
1470 (p14) ldfe FR_Ln2 = [GR_ad_1]
1471 fma.s1 FR_C71 = FR_x,f1,FR_C71
1472 nop.i 0
1473 };;
1474 { .mfi
1475 (p14) ldfpd FR_S28,FR_S26 = [GR_ad_Co],16
1476 fma.s1 FR_C81 = FR_x,f1,FR_C81
1477 add GR_ad_2 = 0x60,GR_ad_2
1478 }
1479 { .mfi
1480 (p14) ldfpd FR_S24,FR_S22 = [GR_ad_Ce],16
1481 fma.s1 FR_C91 = FR_x,f1,FR_C91
1482 nop.i 0
1483 };;
1484 { .mfi
1485 (p14) ldfpd FR_S20,FR_S18 = [GR_ad_Co],16
1486 fma.s1 FR_CA1 = FR_x,f1,FR_CA1
1487 nop.i 0
1488 }
1489 { .mfi
1490 (p14) ldfpd FR_S16,FR_S14 = [GR_ad_Ce],16
1491 fma.s1 FR_C01 = FR_C01,FR_x,FR_C00
1492 nop.i 0
1493 };;
1494 { .mfi
1495 (p14) getf.exp GR_SignExp = FR_Xf
1496 fma.s1 FR_C11 = FR_C11,FR_x,FR_C10
1497 nop.i 0
1498 }
1499 { .mfi
1500 (p14) ldfe FR_S12 = [GR_ad_Co],16
1501 fma.s1 FR_C21 = FR_C21,FR_x,FR_C20
1502 nop.i 0
1503 };;
1504 { .mfi
1505 (p14) getf.sig GR_Sig = FR_Xf
1506 (p14) frcpa.s1 FR_InvXf,p0 = f1,FR_Xf
1507 nop.i 0
1508 }
1509 { .mfi
1510 (p14) ldfe FR_S10 = [GR_ad_Ce],16
1511 fma.s1 FR_C41 = FR_C41,FR_x,FR_C40
1512 nop.i 0
1513 };;
1514 { .mfi
1515 (p14) ldfe FR_S8 = [GR_ad_Co],16
1516 fma.s1 FR_C51 = FR_C51,FR_x,FR_C50
1517 nop.i 0
1518 }
1519 { .mfi
1520 (p14) ldfe FR_S6 = [GR_ad_Ce],16
1521 fma.s1 FR_C61 = FR_C61,FR_x,FR_C60
1522 (p14) and GR_Expf = GR_SignExp,GR_ExpMask
1523 };;
1524 { .mfi
1525 (p14) sub GR_Expf = GR_Expf,GR_ExpBias
1526 fma.s1 FR_C71 = FR_C71,FR_x,FR_C70
1527 (p14) shl GR_Ind = GR_Sig,1
1528 }
1529 { .mfi
1530 (p14) ldfe FR_S4 = [GR_ad_Co],16
1531 fma.s1 FR_C81 = FR_C81,FR_x,FR_C80
1532 (p14) cmp.eq.unc p8,p0 = 0,GR_Sig
1533 };;
1534 { .mfi
1535 (p14) setf.sig FR_int_Nf = GR_Expf
1536 fma.s1 FR_C91 = FR_C91,FR_x,FR_C90
1537 (p14) shr.u GR_Ind = GR_Ind,56
1538 }
1539 { .mfb
1540 (p14) ldfe FR_S2 = [GR_ad_Ce],16
1541 fma.s1 FR_CA1 = FR_CA1,FR_x,FR_CA0
1542 // jump if the input argument is integer number from range (-512.0;-17.0]
1543 (p8) br.cond.spnt lgamma_singularity
1544 };;
1545 { .mfi
1546 (p14) getf.sig GR_Sig = FR_int_Ntrunc
1547 fma.s1 FR_C01 = FR_C01,FR_C11,f0
1548 nop.i 0
1549 }
1550 { .mfi
1551 (p14) shladd GR_ad_T = GR_Ind,4,GR_ad_2
1552 fma.s1 FR_C31 = FR_C31,FR_x,FR_C30
1553 nop.i 0
1554 };;
1555 { .mfi
1556 (p14) ldfe FR_Tf = [GR_ad_T]
1557 (p14) fms.s1 FR_rf = FR_InvXf,FR_Xf,f1 // reduced arg for log({x})
1558 (p14) extr.u GR_Ind = GR_ArgAsIs,44,8
1559 }
1560 { .mfi
1561 // set p9 if signgum is 32-bit int
1562 // set p10 if signgum is 64-bit int
1563 cmp.eq p10,p9 = 8,r34
1564 fma.s1 FR_C21 = FR_C21,FR_C41,f0
1565 mov GR_SignOfGamma = 1
1566 };;
1567 { .mfi
1568 nop.m 0
1569 fma.s1 FR_C51 = FR_C51,FR_C61,f0
1570 (p14) tbit.z.unc p8,p0 = GR_Sig,0
1571 }
1572 { .mfi
1573 (p14) shladd GR_ad_T = GR_Ind,4,GR_ad_2
1574 (p6) fma.s1 FR_CN = FR_CN,FR_Xm2,f0
1575 nop.i 0
1576 };;
1577 { .mfi
1578 (p14) setf.sig FR_int_N = GR_Exp
1579 fma.s1 FR_C71 = FR_C71,FR_C81,f0
1580 (p8) sub GR_SignOfGamma = r0,GR_SignOfGamma
1581 }
1582 { .mfi
1583 nop.m 0
1584 (p14) fma.s1 FR_Xf2 = FR_Xf,FR_Xf,f0
1585 nop.i 0
1586 };;
1587 { .mfi
1588 (p14) ldfe FR_T = [GR_ad_T]
1589 fma.s1 FR_C91 = FR_C91,FR_CA1,f0
1590 nop.i 0
1591 }
1592 { .mfi
1593 nop.m 0
1594 (p14) fma.s1 FR_r2 = FR_r,FR_r,f0
1595 nop.i 0
1596 };;
1597 .pred.rel "mutex",p9,p10
1598 { .mfi
1599 // store sign of gamma(x) as 32-bit int
1600 (p9) st4 [r33] = GR_SignOfGamma
1601 fma.s1 FR_C01 = FR_C01,FR_C31,f0
1602 nop.i 0
1603 }
1604 { .mfi
1605 // store sign of gamma(x) as 64-bit int
1606 (p10) st8 [r33] = GR_SignOfGamma
1607 (p14) fma.s1 FR_P54 = FR_P5,FR_r,FR_P4
1608 nop.i 0
1609 };;
1610 { .mfi
1611 nop.m 0
1612 (p14) fma.s1 FR_P32 = FR_P3,FR_r,FR_P2
1613 nop.i 0
1614 }
1615 { .mfb
1616 nop.m 0
1617 (p14) fma.s1 FR_P54f = FR_P5,FR_rf,FR_P4
1618 // jump if the input argument is non-integer from range (-512.0;-17.0]
1619 (p14) br.cond.spnt lgamma_negpoly
1620 };;
1621 { .mfi
1622 nop.m 0
1623 fma.s1 FR_C21 = FR_C21,FR_C51,f0
1624 nop.i 0
1625 };;
1626 { .mfi
1627 nop.m 0
1628 fma.s1 FR_C71 = FR_C71,FR_C91,f0
1629 nop.i 0
1630 };;
1631 { .mfi
1632 nop.m 0
1633 fma.s1 FR_CN = FR_C01,FR_CN,f0
1634 nop.i 0
1635 };;
1636 { .mfi
1637 nop.m 0
1638 fma.s1 FR_C21 = FR_C21,FR_C71,f0
1639 nop.i 0
1640 };;
1641 { .mfb
1642 nop.m 0
1643 fma.d.s0 f8 = FR_C21,FR_CN,f0
1644 br.ret.sptk b0 // exit for arguments from range [2.25; 512.0)
1645 };;
1646 // branch for calculating of ln(GAMMA(x)) for -512 < x < -17
1647 //---------------------------------------------------------------------
1648 .align 32
1649 lgamma_negpoly:
1650 { .mfi
1651 nop.m 0
1652 fma.s1 FR_Xf4 = FR_Xf2,FR_Xf2,f0
1653 nop.i 0
1654 }
1655 { .mfi
1656 nop.m 0
1657 fma.s1 FR_S28 = FR_S28,FR_Xf2,FR_S26
1658 nop.i 0
1659 };;
1660 { .mfi
1661 nop.m 0
1662 fma.s1 FR_S24 = FR_S24,FR_Xf2,FR_S22
1663 nop.i 0
1664 }
1665 { .mfi
1666 nop.m 0
1667 fma.s1 FR_S20 = FR_S20,FR_Xf2,FR_S18
1668 nop.i 0
1669 };;
1670 { .mfi
1671 nop.m 0
1672 fma.s1 FR_S16 = FR_S16,FR_Xf2,FR_S14
1673 nop.i 0
1674 }
1675 { .mfi
1676 nop.m 0
1677 fma.s1 FR_S12 = FR_S12,FR_Xf2,FR_S10
1678 nop.i 0
1679 };;
1680 { .mfi
1681 nop.m 0
1682 fma.s1 FR_S8 = FR_S8,FR_Xf2,FR_S6
1683 nop.i 0
1684 }
1685 { .mfi
1686 nop.m 0
1687 fma.s1 FR_S4 = FR_S4,FR_Xf2,FR_S2
1688 nop.i 0
1689 };;
1690 { .mfi
1691 nop.m 0
1692 fma.s1 FR_rf2 = FR_rf,FR_rf,f0
1693 nop.i 0
1694 }
1695 { .mfi
1696 nop.m 0
1697 fma.s1 FR_P32f = FR_P3,FR_rf,FR_P2 // log(x)
1698 nop.i 0
1699 };;
1700 { .mfi
1701 nop.m 0
1702 fma.s1 FR_r3 = FR_r2,FR_r,f0 // log(x)
1703 nop.i 0
1704 }
1705 { .mfi
1706 nop.m 0
1707 fcvt.xf FR_Nf = FR_int_Nf // log({x})
1708 nop.i 0
1709 };;
1710 { .mfi
1711 nop.m 0
1712 fma.s1 FR_S28 = FR_S28,FR_Xf4,FR_S24
1713 nop.i 0
1714 }
1715 { .mfi
1716 nop.m 0
1717 fma.s1 FR_Xf8 = FR_Xf4,FR_Xf4,f0
1718 nop.i 0
1719 };;
1720 { .mfi
1721 nop.m 0
1722 fma.s1 FR_S20 = FR_S20,FR_Xf4,FR_S16
1723 nop.i 0
1724 }
1725 { .mfi
1726 nop.m 0
1727 fma.s1 FR_C21 = FR_C21,FR_C51,f0
1728 nop.i 0
1729 };;
1730 { .mfi
1731 nop.m 0
1732 fma.s1 FR_S12 = FR_S12,FR_Xf4,FR_S8
1733 nop.i 0
1734 }
1735 { .mfi
1736 nop.m 0
1737 fma.s1 FR_C71 = FR_C71,FR_C91,f0
1738 nop.i 0
1739 };;
1740 { .mfi
1741 nop.m 0
1742 fnma.s1 FR_P10 = FR_r2,FR_05,FR_r // log(x)
1743 nop.i 0
1744 }
1745 { .mfi
1746 nop.m 0
1747 fma.s1 FR_P54 = FR_P54,FR_r2,FR_P32 // log(x)
1748 nop.i 0
1749 };;
1750 { .mfi
1751 nop.m 0
1752 fnma.s1 FR_P10f = FR_rf2,FR_05,FR_rf // log({x})
1753 nop.i 0
1754 }
1755 { .mfi
1756 nop.m 0
1757 fcvt.xf FR_N = FR_int_N // log(x)
1758 nop.i 0
1759 };;
1760 { .mfi
1761 nop.m 0
1762 fma.s1 FR_rf3 = FR_rf2,FR_rf,f0 // log({x})
1763 nop.i 0
1764 }
1765 { .mfi
1766 nop.m 0
1767 fma.s1 FR_P54f = FR_P54f,FR_rf2,FR_P32f // log({x})
1768 nop.i 0
1769 };;
1770 { .mfi
1771 nop.m 0
1772 fma.s1 FR_S28 = FR_S28,FR_Xf8,FR_S20
1773 nop.i 0
1774 }
1775 { .mfi
1776 nop.m 0
1777 fma.s1 FR_TpNxLn2f = FR_Nf,FR_Ln2,FR_Tf // log({x})
1778 nop.i 0
1779 };;
1780 { .mfi
1781 nop.m 0
1782 fma.s1 FR_CN = FR_C01,FR_CN,f0
1783 nop.i 0
1784 }
1785 { .mfi
1786 nop.m 0
1787 fma.s1 FR_C21 = FR_C21,FR_C71,f0
1788 nop.i 0
1789 };;
1790 { .mfi
1791 nop.m 0
1792 fma.s1 FR_P54 = FR_P54,FR_r3,FR_P10 // log(x)
1793 nop.i 0
1794 };;
1795 { .mfi
1796 nop.m 0
1797 fma.s1 FR_TpNxLn2 = FR_N,FR_Ln2,FR_T // log(x)
1798 nop.i 0
1799 };;
1800 { .mfi
1801 nop.m 0
1802 fma.s1 FR_P54f = FR_P54f,FR_rf3,FR_P10f // log({x})
1803 nop.i 0
1804 };;
1805 { .mfi
1806 nop.m 0
1807 fma.s1 FR_S28 = FR_S28,FR_Xf8,FR_S12
1808 nop.i 0
1809 };;
1810 { .mfi
1811 nop.m 0
1812 fnma.s1 FR_C21 = FR_C21,FR_CN,f0
1813 nop.i 0
1814 };;
1815 { .mfi
1816 nop.m 0
1817 fma.s1 FR_LnX = FR_TpNxLn2,f1,FR_P54 // log(x)
1818 nop.i 0
1819 };;
1820 { .mfi
1821 nop.m 0
1822 fma.s1 FR_LnXf = FR_TpNxLn2f,f1,FR_P54f // log({x})
1823 nop.i 0
1824 };;
1825 { .mfi
1826 nop.m 0
1827 fma.s1 FR_S28 = FR_S28,FR_Xf4,FR_S4
1828 nop.i 0
1829 };;
1830 { .mfi
1831 nop.m 0
1832 fma.s1 FR_LnX = FR_LnX,f1,FR_LnXf
1833 nop.i 0
1834 };;
1835 { .mfi
1836 nop.m 0
1837 fnma.s1 FR_S28 = FR_S28,FR_Xf2,FR_C21
1838 nop.i 0
1839 };;
1840 { .mfb
1841 nop.m 0
1842 fms.d.s0 f8 = FR_S28,f1,FR_LnX
1843 br.ret.sptk b0
1844 };;
1845 // branch for calculating of ln(GAMMA(x)) for x >= 512
1846 //---------------------------------------------------------------------
1847 .align 32
1848 lgamma_pstirling:
1849 { .mfi
1850 ldfpd FR_P5,FR_P4 = [GR_ad_1],16
1851 nop.f 0
1852 and GR_Exp = GR_SignExp,GR_ExpMask
1853 }
1854 { .mfi
1855 ldfpd FR_P3,FR_P2 = [GR_ad_2],16
1856 fma.s1 FR_InvX = FR_C,FR_InvX,FR_C // NR iteration #1
1857 mov GR_ExpBias = 0xffff
1858 };;
1859 { .mfi
1860 ldfe FR_Ln2 = [GR_ad_1],16
1861 nop.f 0
1862 sub GR_Exp = GR_Exp,GR_ExpBias
1863 };;
1864 { .mfi
1865 ldfpd FR_W4,FR_OvfBound = [GR_ad_2],16
1866 nop.f 0
1867 nop.i 0
1868 };;
1869 { .mfi
1870 setf.sig FR_int_N = GR_Exp
1871 fms.s1 FR_r = FR_C,f8,f1
1872 nop.i 0
1873 };;
1874 { .mmf
1875 getf.sig GR_Sig = FR_NormX
1876 ldfe FR_LnSqrt2Pi = [GR_ad_1],16
1877 nop.f 0
1878 };;
1879 { .mmf
1880 ldfe FR_W2 = [GR_ad_2],16
1881 nop.m 0
1882 fnma.s1 FR_InvX2 = FR_InvX,FR_NormX,f1 // NR iteration #2
1883 };;
1884 { .mfi
1885 add GR_ad_2 = 0x40,GR_ad_2
1886 nop.f 0
1887 shl GR_Ind = GR_Sig,1
1888 };;
1889 { .mfi
1890 mov GR_SignOfGamma = 1
1891 nop.f 0
1892 shr.u GR_Ind = GR_Ind,56
1893 };;
1894 { .mfi
1895 shladd GR_ad_2 = GR_Ind,4,GR_ad_2
1896 fma.s1 FR_r2 = FR_r,FR_r,f0
1897 // set p9 if signgum is 32-bit int
1898 // set p10 if signgum is 64-bit int
1899 cmp.eq p10,p9 = 8,r34
1900 };;
1901 { .mfi
1902 ldfe FR_T = [GR_ad_2]
1903 fma.s1 FR_P54 = FR_P5,FR_r,FR_P4
1904 nop.i 0
1905 }
1906 { .mfi
1907 nop.m 0
1908 fma.s1 FR_P32 = FR_P3,FR_r,FR_P2
1909 nop.i 0
1910 };;
1911 { .mfi
1912 nop.m 0
1913 fcmp.le.s1 p6,p0 = FR_OvfBound,FR_NormX
1914 nop.i 0
1915 }
1916 { .mfi
1917 nop.m 0
1918 fma.s1 FR_InvX2 = FR_InvX,FR_InvX2,FR_InvX // NR iteration #2
1919 nop.i 0
1920 };;
1921 { .mfi
1922 nop.m 0
1923 fcvt.xf FR_N = FR_int_N
1924 nop.i 0
1925 }
1926 { .mfb
1927 nop.m 0
1928 nop.f 0
1929 // jump if x is great than OVERFLOW_BOUNDARY
1930 (p6) br.cond.spnt lgamma_overflow
1931 };;
1932 .pred.rel "mutex",p9,p10
1933 { .mfi
1934 // store sign of gamma(x) as 32-bit int
1935 (p9) st4 [r33] = GR_SignOfGamma
1936 fma.s1 FR_r3 = FR_r2,FR_r,f0
1937 nop.i 0
1938 }
1939 { .mfi
1940 // store sign of gamma(x) as 64-bit int
1941 (p10) st8 [r33] = GR_SignOfGamma
1942 fnma.s1 FR_P10 = FR_r2,FR_05,FR_r
1943 nop.i 0
1944 };;
1945 { .mfi
1946 nop.m 0
1947 fma.s1 FR_P54 = FR_P54,FR_r2,FR_P32
1948 nop.i 0
1949 };;
1950 { .mfi
1951 nop.m 0
1952 fnma.s1 FR_InvX = FR_InvX2,FR_NormX,f1 // NR iteration #3
1953 nop.i 0
1954 };;
1955 { .mfi
1956 nop.m 0
1957 fms.s1 FR_Xm05 = FR_NormX,f1,FR_05 // (x-1/2)
1958 nop.i 0
1959 };;
1960 { .mfi
1961 nop.m 0
1962 fma.s1 FR_TpNxLn2 = FR_N,FR_Ln2,FR_T
1963 nop.i 0
1964 };;
1965 { .mfi
1966 nop.m 0
1967 fma.s1 FR_P54 = FR_P54,FR_r3,FR_P10
1968 nop.i 0
1969 };;
1970 { .mfi
1971 nop.m 0
1972 fma.s1 FR_InvX = FR_InvX2,FR_InvX,FR_InvX2 // NR iteration #3
1973 nop.i 0
1974 }
1975 { .mfi
1976 nop.m 0
1977 fms.s1 FR_LnSqrt2Pi = FR_LnSqrt2Pi,f1,FR_NormX // ln(sqrt(2*Pi))-x
1978 nop.i 0
1979 };;
1980 { .mfi
1981 nop.m 0
1982 fma.s1 FR_LnX = FR_TpNxLn2,f1,FR_P54
1983 nop.i 0
1984 };;
1985 { .mfi
1986 nop.m 0
1987 fma.s1 FR_InvX2 = FR_InvX,FR_InvX,f0
1988 nop.i 0
1989 };;
1990 { .mfi
1991 nop.m 0
1992 // (x-1/2)*ln(x)+ln(sqrt(2*Pi))-x
1993 fma.s1 FR_LnX = FR_LnX,FR_Xm05,FR_LnSqrt2Pi
1994 nop.i 0
1995 };;
1996 { .mfi
1997 nop.m 0
1998 fma.s1 FR_W2 = FR_W4,FR_InvX2,FR_W2 // W2 + W4/x^2
1999 nop.i 0
2000 };;
2001 { .mfb
2002 nop.m 0
2003 fma.d.s0 f8 = FR_InvX,FR_W2,FR_LnX
2004 br.ret.sptk b0
2005 };;
2006 // branch for calculating of ln(GAMMA(x)) for x < -512
2007 //---------------------------------------------------------------------
2008 .align 32
2009 lgamma_negstirling:
2010 { .mfi
2011 ldfpd FR_P5,FR_P4 = [GR_ad_1],16
2012 fms.s1 FR_Xf = FR_NormX,f1,FR_N // xf = x - [x]
2013 and GR_Exp = GR_SignExp,GR_ExpMask
2014 }
2015 { .mfi
2016 ldfpd FR_P3,FR_P2 = [GR_ad_2],16
2017 fma.s1 FR_InvX = FR_C,FR_InvX,FR_C // NR iteration #1
2018 mov GR_0x30033 = 0x30033
2019 };;
2020 { .mfi
2021 ldfe FR_Ln2 = [GR_ad_1],16
2022 nop.f 0
2023 extr.u GR_Ind = GR_ArgAsIs,44,8
2024 }
2025 { .mib
2026 ldfd FR_W4 = [GR_ad_2],16
2027 // jump if x is less or equal to -2^52, i.e. x is big negative integer
2028 cmp.leu.unc p7,p0 = GR_0x30033,GR_SignExp
2029 (p7) br.cond.spnt lgamma_singularity
2030 };;
2031 { .mfi
2032 ldfpd FR_S28,FR_S26 = [GR_ad_Co7],16
2033 nop.f 0
2034 add GR_ad_LnT = 0x50,GR_ad_2
2035 }
2036 { .mfi
2037 ldfpd FR_S24,FR_S22 = [GR_ad_Ce7],16
2038 nop.f 0
2039 mov GR_ExpBias = 0xffff
2040 };;
2041 { .mfi
2042 ldfpd FR_S20,FR_S18 = [GR_ad_Co7],16
2043 nop.f 0
2044 shladd GR_ad_T = GR_Ind,4,GR_ad_LnT
2045 }
2046 { .mfi
2047 ldfpd FR_S16,FR_S14 = [GR_ad_Ce7],16
2048 nop.f 0
2049 sub GR_Exp = GR_Exp,GR_ExpBias
2050 };;
2051 { .mfi
2052 ldfe FR_S12 = [GR_ad_Co7],16
2053 nop.f 0
2054 nop.i 0
2055 }
2056 { .mfi
2057 ldfe FR_S10 = [GR_ad_Ce7],16
2058 fms.s1 FR_r = FR_C,f8,f1
2059 nop.i 0
2060 };;
2061 { .mmf
2062 ldfe FR_S8 = [GR_ad_Co7],16
2063 ldfe FR_S6 = [GR_ad_Ce7],16
2064 nop.f 0
2065 };;
2066 { .mfi
2067 ldfe FR_S4 = [GR_ad_Co7],16
2068 fma.s1 FR_Xf2 = FR_Xf,FR_Xf,f0
2069 nop.i 0
2070 }
2071 { .mfi
2072 ldfe FR_S2 = [GR_ad_Ce7],16
2073 fnma.s1 FR_InvX2 = FR_InvX,FR_NormX,f1 // NR iteration #2
2074 nop.i 0
2075 };;
2076 { .mfi
2077 setf.sig FR_int_N = GR_Exp
2078 frcpa.s1 FR_InvXf,p9 = f1,FR_Xf // 1/xf
2079 nop.i 0
2080 }
2081 { .mfi
2082 ldfe FR_LnSqrt2Pi = [GR_ad_1],16
2083 nop.f 0
2084 nop.i 0
2085 };;
2086 { .mfi
2087 getf.exp GR_SignExp = FR_Xf
2088 nop.f 0
2089 nop.i 0
2090 }
2091 { .mfi
2092 ldfe FR_W2 = [GR_ad_2],16
2093 nop.f 0
2094 nop.i 0
2095 };;
2096 { .mfi
2097 getf.sig GR_Sig = FR_Xf
2098 fma.s1 FR_P54 = FR_P5,FR_r,FR_P4
2099 nop.i 0
2100 }
2101 { .mfi
2102 ldfe FR_T = [GR_ad_T]
2103 fma.s1 FR_P32 = FR_P3,FR_r,FR_P2
2104 nop.i 0
2105 };;
2106 { .mfi
2107 and GR_Exp = GR_SignExp,GR_ExpMask
2108 fma.s1 FR_r2 = FR_r,FR_r,f0
2109 nop.i 0
2110 }
2111 { .mfi
2112 nop.m 0
2113 fms.s1 FR_Xm05 = FR_NormX,f1,FR_05 // (x-1/2)
2114 nop.i 0
2115 };;
2116 { .mfi
2117 nop.m 0
2118 fma.s1 FR_InvX2 = FR_InvX,FR_InvX2,FR_InvX // NR iteration #2
2119 extr.u GR_Ind = GR_Sig,55,8
2120 }
2121 { .mfi
2122 sub GR_Exp = GR_Exp,GR_ExpBias
2123 fma.s1 FR_Xf4 = FR_Xf2,FR_Xf2,f0
2124 cmp.eq p6,p0 = 0,GR_Sig
2125 };;
2126 { .mfi
2127 setf.sig FR_int_Nf = GR_Exp
2128 fma.s1 FR_S28 = FR_S28,FR_Xf2,FR_S26
2129 shladd GR_ad_T = GR_Ind,4,GR_ad_LnT
2130 }
2131 { .mfb
2132 nop.m 0
2133 fma.s1 FR_S24 = FR_S24,FR_Xf2,FR_S22
2134 // jump if the input argument is integer number from range (-512.0;-17.0]
2135 (p6) br.cond.spnt lgamma_singularity
2136 };;
2137 { .mfi
2138 getf.sig GR_Sig = FR_int_Ntrunc
2139 fma.s1 FR_S20 = FR_S20,FR_Xf2,FR_S18
2140 nop.i 0
2141 }
2142 { .mfi
2143 nop.m 0
2144 fma.s1 FR_S16 = FR_S16,FR_Xf2,FR_S14
2145 nop.i 0
2146 };;
2147 { .mfi
2148 ldfe FR_Tf = [GR_ad_T]
2149 fma.s1 FR_S12 = FR_S12,FR_Xf2,FR_S10
2150 nop.i 0
2151 }
2152 { .mfi
2153 nop.m 0
2154 fma.s1 FR_S8 = FR_S8,FR_Xf2,FR_S6
2155 mov GR_SignOfGamma = 1
2156 };;
2157 { .mfi
2158 nop.m 0
2159 fms.s1 FR_rf = FR_InvXf,FR_Xf,f1 // reduced arg rf
2160 tbit.z p8,p0 = GR_Sig,0
2161 }
2162 { .mfi
2163 nop.m 0
2164 fma.s1 FR_r3 = FR_r2,FR_r,f0
2165 // set p9 if signgum is 32-bit int
2166 // set p10 if signgum is 64-bit int
2167 cmp.eq p10,p9 = 8,r34
2168 };;
2169 { .mfi
2170 nop.m 0
2171 fcvt.xf FR_N = FR_int_N
2172 (p8) sub GR_SignOfGamma = r0,GR_SignOfGamma
2173 }
2174 { .mfi
2175 nop.m 0
2176 fnma.s1 FR_InvX = FR_InvX2,FR_NormX,f1 // NR iteration #3
2177 nop.i 0
2178 };;
2179 .pred.rel "mutex",p9,p10
2180 { .mfi
2181 // store sign of gamma(x) as 32-bit int
2182 (p9) st4 [r33] = GR_SignOfGamma
2183 fma.s1 FR_P54 = FR_P54,FR_r2,FR_P32
2184 nop.i 0
2185 }
2186 { .mfi
2187 // store sign of gamma(x) as 64-bit int
2188 (p10) st8 [r33] = GR_SignOfGamma
2189 fnma.s1 FR_P10 = FR_r2,FR_05,FR_r
2190 nop.i 0
2191 };;
2192 { .mfi
2193 nop.m 0
2194 fma.s1 FR_Xf8 = FR_Xf4,FR_Xf4,f0
2195 nop.i 0
2196 }
2197 { .mfi
2198 nop.m 0
2199 fma.s1 FR_S28 = FR_S28,FR_Xf4,FR_S24
2200 nop.i 0
2201 };;
2202 { .mfi
2203 nop.m 0
2204 fma.s1 FR_S20 = FR_S20,FR_Xf4,FR_S16
2205 nop.i 0
2206 }
2207 { .mfi
2208 nop.m 0
2209 fma.s1 FR_S12 = FR_S12,FR_Xf4,FR_S8
2210 nop.i 0
2211 };;
2212 { .mfi
2213 nop.m 0
2214 fma.s1 FR_rf2 = FR_rf,FR_rf,f0
2215 nop.i 0
2216 }
2217 { .mfi
2218 nop.m 0
2219 fma.s1 FR_P54f = FR_P5,FR_rf,FR_P4
2220 nop.i 0
2221 };;
2222 { .mfi
2223 nop.m 0
2224 fma.s1 FR_P32f = FR_P3,FR_rf,FR_P2
2225 nop.i 0
2226 }
2227 { .mfi
2228 nop.m 0
2229 fma.s1 FR_InvX = FR_InvX2,FR_InvX,FR_InvX2 // NR iteration #3
2230 nop.i 0
2231 };;
2232 { .mfi
2233 nop.m 0
2234 fcvt.xf FR_Nf = FR_int_Nf
2235 nop.i 0
2236 }
2237 { .mfi
2238 nop.m 0
2239 fma.s1 FR_LnSqrt2Pi = FR_NormX,f1,FR_LnSqrt2Pi // x+ln(sqrt(2*Pi))
2240 nop.i 0
2241 };;
2242 { .mfi
2243 nop.m 0
2244 fma.s1 FR_P54 = FR_P54,FR_r3,FR_P10
2245 nop.i 0
2246 };;
2247 { .mfi
2248 nop.m 0
2249 fma.s1 FR_S28 = FR_S28,FR_Xf8,FR_S20
2250 nop.i 0
2251 };;
2252 { .mfi
2253 nop.m 0
2254 fma.s1 FR_rf3 = FR_rf2,FR_rf,f0
2255 nop.i 0
2256 }
2257 { .mfi
2258 nop.m 0
2259 fnma.s1 FR_P10f = FR_rf2,FR_05,FR_rf
2260 nop.i 0
2261 };;
2262 { .mfi
2263 nop.m 0
2264 fma.s1 FR_TpNxLn2 = FR_N,FR_Ln2,FR_T
2265 nop.i 0
2266 }
2267 { .mfi
2268 nop.m 0
2269 fma.s1 FR_P54f = FR_P54f,FR_rf2,FR_P32f
2270 nop.i 0
2271 };;
2272 { .mfi
2273 nop.m 0
2274 fma.s1 FR_InvX2 = FR_InvX,FR_InvX,f0
2275 nop.i 0
2276 };;
2277 { .mfi
2278 nop.m 0
2279 fma.s1 FR_S28 = FR_S28,FR_Xf8,FR_S12
2280 nop.i 0
2281 }
2282 { .mfi
2283 nop.m 0
2284 fma.s1 FR_S4 = FR_S4,FR_Xf2,FR_S2
2285 nop.i 0
2286 };;
2287 { .mfi
2288 nop.m 0
2289 fma.s1 FR_P54f = FR_P54f,FR_rf3,FR_P10f
2290 nop.i 0
2291 }
2292 { .mfi
2293 nop.m 0
2294 fma.s1 FR_TpNxLn2f = FR_Nf,FR_Ln2,FR_Tf
2295 nop.i 0
2296 };;
2297 { .mfi
2298 nop.m 0
2299 fma.s1 FR_LnX = FR_TpNxLn2,f1,FR_P54
2300 nop.i 0
2301 }
2302 { .mfi
2303 nop.m 0
2304 fma.s1 FR_W2 = FR_W4,FR_InvX2,FR_W2
2305 nop.i 0
2306 };;
2307 { .mfi
2308 nop.m 0
2309 fma.s1 FR_S28 = FR_S28,FR_Xf4,FR_S4
2310 nop.i 0
2311 };;
2312 { .mfi
2313 nop.m 0
2314 fma.s1 FR_LnXf = FR_TpNxLn2f,f1,FR_P54f
2315 nop.i 0
2316 };;
2317 { .mfi
2318 nop.m 0
2319 fms.s1 FR_LnX = FR_LnX,FR_Xm05,FR_LnSqrt2Pi
2320 nop.i 0
2321 };;
2322 { .mfi
2323 nop.m 0
2324 fma.s1 FR_LnX = FR_InvX,FR_W2,FR_LnX
2325 nop.i 0
2326 };;
2327 { .mfi
2328 nop.m 0
2329 fnma.s1 FR_LnX = FR_S28,FR_Xf2,FR_LnX
2330 nop.i 0
2331 };;
2332 { .mfb
2333 nop.m 0
2334 fms.d.s0 f8 = FR_LnX,f1,FR_LnXf
2335 br.ret.sptk b0
2336 };;
2337 // branch for calculating of ln(GAMMA(x)) for 0 <= x < 1
2338 //---------------------------------------------------------------------
2339 .align 32
2340 lgamma_0_1:
2341 { .mfi
2342 ldfpd FR_P5,FR_P4 = [GR_ad_1],16
2343 fms.s1 FR_x = FR_NormX,f1,f0 // x
2344 mov GR_Arg025 = 0x3FD0
2345 }
2346 { .mfi
2347 ldfpd FR_P3,FR_P2 = [GR_ad_2],16
2348 nop.f 0
2349 add GR_ad_Co = 0x1C40,GR_ad_Data
2350 };;
2351 { .mfi
2352 ldfe FR_Ln2 = [GR_ad_1],0x50
2353 nop.f 0
2354 // p6 if arg < 0.25
2355 cmp.lt p6,p9 = GR_Arg,GR_Arg025
2356 }
2357 { .mfi
2358 add GR_ad_2 = 0x40,GR_ad_2
2359 nop.f 0
2360 mov GR_Arg075 = 0x3FE8
2361 };;
2362 { .mfi
2363 ldfpd FR_Q8,FR_Q7 = [GR_ad_1],16
2364 fma.s1 FR_w2 = FR_w,FR_w,f0
2365 // p7 if 0.25 <= arg < 0.75
2366 // p8 if 0.75 <= arg < 1.0
2367 (p9) cmp.lt.unc p7,p8 = GR_Arg,GR_Arg075
2368 }
2369 { .mfi
2370 mov GR_Arg0875 = 0x3FEC
2371 nop.f 0
2372 sub GR_Exp = GR_Exp,GR_ExpBias
2373 };;
2374 { .mfi
2375 ldfpd FR_Q6,FR_Q5 = [GR_ad_2],16
2376 nop.f 0
2377 (p8) cmp.lt p9,p0 = GR_Arg,GR_Arg0875
2378 }
2379 { .mfi
2380 ldfpd FR_Q4,FR_Q3 = [GR_ad_1],16
2381 nop.f 0
2382 add GR_ad_Ce = 0x60,GR_ad_Co
2383 };;
2384 .pred.rel "mutex",p7,p8
2385 { .mfi
2386 ldfd FR_Q2 = [GR_ad_2],16
2387 fms.s1 FR_r = FR_C,f8,f1
2388 (p7) mov GR_Offs = 0xC0
2389 }
2390 { .mfi
2391 setf.sig FR_int_N = GR_Exp
2392 nop.f 0
2393 (p8) mov GR_Offs = 0x180
2394 };;
2395 .pred.rel "mutex",p6,p7
2396 { .mfi
2397 (p9) add GR_ad_Co = GR_Offs,GR_ad_Co
2398 (p8) fms.s1 FR_x = FR_NormX,f1,f1 // x-1
2399 nop.i 0
2400 }
2401 { .mfi
2402 (p9) add GR_ad_Ce = GR_Offs,GR_ad_Ce
2403 (p7) fms.s1 FR_x = FR_NormX,f1,FR_LocalMin // x-LocalMin
2404 cmp.lt p10,p0 = GR_Arg,GR_Arg0875
2405 };;
2406 lgamma_common_0_2:
2407 { .mfi
2408 ldfpd FR_A17,FR_A16 = [GR_ad_Co],16
2409 nop.f 0
2410 nop.i 0
2411 }
2412 { .mfi
2413 ldfpd FR_A15,FR_A14 = [GR_ad_Ce],16
2414 nop.f 0
2415 nop.i 0
2416 };;
2417 { .mfi
2418 ldfpd FR_A13,FR_A12 = [GR_ad_Co],16
2419 nop.f 0
2420 (p10) extr.u GR_Ind = GR_ArgAsIs,44,8
2421 }
2422 { .mfi
2423 ldfpd FR_A11,FR_A10 = [GR_ad_Ce],16
2424 nop.f 0
2425 nop.i 0
2426 };;
2427 { .mfi
2428 ldfpd FR_A9,FR_A8 = [GR_ad_Co],16
2429 (p10) fnma.s1 FR_Q1 = FR_05,FR_w2,FR_w
2430 nop.i 0
2431 }
2432 { .mfi
2433 ldfpd FR_A7,FR_A6 = [GR_ad_Ce],16
2434 (p10) fma.s1 FR_w3 = FR_w2,FR_w,f0
2435 nop.i 0
2436 };;
2437 { .mfi
2438 (p10) getf.exp GR_SignExp_w = FR_w
2439 (p10) fma.s1 FR_w4 = FR_w2,FR_w2,f0
2440 nop.i 0
2441 }
2442 { .mfi
2443 (p10) shladd GR_ad_2 = GR_Ind,4,GR_ad_2
2444 (p10) fma.s1 FR_r2 = FR_r,FR_r,f0
2445 nop.i 0
2446 };;
2447 { .mfi
2448 (p10) ldfe FR_T = [GR_ad_2]
2449 (p10) fma.s1 FR_P54 = FR_P5,FR_r,FR_P4
2450 nop.i 0
2451 }
2452 { .mfi
2453 ldfe FR_A5 = [GR_ad_Co],16
2454 (p10) fma.s1 FR_P32 = FR_P3,FR_r,FR_P2
2455 nop.i 0
2456 };;
2457 { .mfi
2458 ldfe FR_A4 = [GR_ad_Ce],16
2459 fma.s1 FR_x2 = FR_x,FR_x,f0
2460 (p10) and GR_Exp_w = GR_ExpMask, GR_SignExp_w
2461 }
2462 { .mfi
2463 ldfe FR_A3 = [GR_ad_Co],16
2464 nop.f 0
2465 (p10) mov GR_fff9 = 0xfff9
2466 };;
2467 // p13 <== large w __libm_lgamma
2468 // p14 <== small w __libm_lgamma
2469 { .mfi
2470 ldfe FR_A2 = [GR_ad_Ce],16
2471 (p10) fma.s1 FR_Q8 = FR_Q8,FR_w,FR_Q7
2472 (p10) cmp.ge.unc p13,p14 = GR_Exp_w,GR_fff9
2473 }
2474 { .mfi
2475 ldfe FR_A1 = [GR_ad_Co],16
2476 (p10) fma.s1 FR_Q6 = FR_Q6,FR_w,FR_Q5
2477 nop.i 0
2478 };;
2479 { .mfi
2480 ldfe FR_A0 = [GR_ad_Ce],16
2481 (p10) fma.s1 FR_Q4 = FR_Q4,FR_w,FR_Q3
2482 nop.i 0
2483 }
2484 { .mfi
2485 nop.m 0
2486 (p10) fma.s1 FR_Q2 = FR_Q2,FR_w3,FR_Q1
2487 nop.i 0
2488 };;
2489 { .mfi
2490 // set p11 if signgum is 32-bit int
2491 // set p12 if signgum is 64-bit int
2492 cmp.eq p12,p11 = 8,r34
2493 (p10) fma.s1 FR_r3 = FR_r2,FR_r,f0
2494 nop.i 0
2495 }
2496 { .mfi
2497 nop.m 0
2498 (p10) fnma.s1 FR_P10 = FR_r2,FR_05,FR_r
2499 mov GR_SignOfGamma = 1
2500 };;
2501 .pred.rel "mutex",p11,p12
2502 { .mfi
2503 // store sign of gamma(x) as 32-bit int
2504 (p11) st4 [r33] = GR_SignOfGamma
2505 fma.s1 FR_A17 = FR_A17,FR_x,FR_A16
2506 nop.i 0
2507 }
2508 { .mfi
2509 // store sign of gamma(x) as 64-bit int
2510 (p12) st8 [r33] = GR_SignOfGamma
2511 fma.s1 FR_A15 = FR_A15,FR_x,FR_A14
2512 nop.i 0
2513 };;
2514 { .mfi
2515 nop.m 0
2516 (p10) fcvt.xf FR_N = FR_int_N
2517 nop.i 0
2518 }
2519 { .mfi
2520 nop.m 0
2521 (p10) fma.s1 FR_P54 = FR_P54,FR_r2,FR_P32
2522 nop.i 0
2523 };;
2524 { .mfi
2525 nop.m 0
2526 fma.s1 FR_A13 = FR_A13,FR_x,FR_A12
2527 nop.i 0
2528 }
2529 { .mfi
2530 nop.m 0
2531 fma.s1 FR_A11 = FR_A11,FR_x,FR_A10
2532 nop.i 0
2533 };;
2534 { .mfi
2535 nop.m 0
2536 fma.s1 FR_A9 = FR_A9,FR_x,FR_A8
2537 nop.i 0
2538 }
2539 { .mfi
2540 nop.m 0
2541 fma.s1 FR_A7 = FR_A7,FR_x,FR_A6
2542 nop.i 0
2543 };;
2544 { .mfi
2545 nop.m 0
2546 (p10) fma.s1 FR_Qlo = FR_Q8,FR_w2,FR_Q6
2547 nop.i 0
2548 }
2549 { .mfi
2550 nop.m 0
2551 (p10) fma.s1 FR_w6 = FR_w3,FR_w3,f0
2552 nop.i 0
2553 };;
2554 { .mfi
2555 nop.m 0
2556 (p10) fma.s1 FR_Qhi = FR_Q4,FR_w4,FR_Q2
2557 nop.i 0
2558 }
2559 { .mfi
2560 nop.m 0
2561 fma.s1 FR_A5 = FR_A5,FR_x,FR_A4
2562 nop.i 0
2563 };;
2564 { .mfi
2565 nop.m 0
2566 (p10) fma.s1 FR_TpNxLn2 = FR_N,FR_Ln2,FR_T
2567 nop.i 0
2568 }
2569 { .mfi
2570 nop.m 0
2571 fma.s1 FR_A3 = FR_A3,FR_x,FR_A2
2572 nop.i 0
2573 };;
2574 { .mfi
2575 nop.m 0
2576 (p10) fma.s1 FR_P54 = FR_P54,FR_r3,FR_P10
2577 nop.i 0
2578 }
2579 { .mfi
2580 nop.m 0
2581 fma.s1 FR_A1 = FR_A1,FR_x,FR_A0
2582 nop.i 0
2583 };;
2584 { .mfi
2585 nop.m 0
2586 fma.s1 FR_A17 = FR_A17,FR_x2,FR_A15
2587 nop.i 0
2588 }
2589 { .mfi
2590 nop.m 0
2591 fma.s1 FR_A13 = FR_A13,FR_x2,FR_A11
2592 nop.i 0
2593 };;
2594 { .mfi
2595 nop.m 0
2596 fma.s1 FR_A9 = FR_A9,FR_x2,FR_A7
2597 nop.i 0
2598 }
2599 { .mfi
2600 nop.m 0
2601 fma.s1 FR_x4 = FR_x2,FR_x2,f0
2602 nop.i 0
2603 };;
2604 { .mfi
2605 nop.m 0
2606 (p14) fma.s1 FR_LnX = FR_Qlo,FR_w6,FR_Qhi
2607 nop.i 0
2608 };;
2609 { .mfi
2610 nop.m 0
2611 fma.s1 FR_A5 = FR_A5,FR_x2,FR_A3
2612 nop.i 0
2613 };;
2614 { .mfi
2615 nop.m 0
2616 (p13) fma.s1 FR_LnX = FR_TpNxLn2,f1,FR_P54
2617 nop.i 0
2618 };;
2619 { .mfi
2620 nop.m 0
2621 fma.s1 FR_A17 = FR_A17,FR_x4,FR_A13
2622 nop.i 0
2623 }
2624 { .mfi
2625 nop.m 0
2626 fma.s1 FR_x8 = FR_x4,FR_x4,f0
2627 nop.i 0
2628 };;
2629 { .mfi
2630 nop.m 0
2631 fma.s1 FR_A9 = FR_A9,FR_x4,FR_A5
2632 nop.i 0
2633 };;
2634 { .mfi
2635 nop.m 0
2636 fma.s1 FR_A17 = FR_A17,FR_x8,FR_A9
2637 nop.i 0
2638 };;
2639 { .mfi
2640 nop.m 0
2641 (p10) fms.s1 FR_A1 = FR_A1,f1,FR_LnX
2642 nop.i 0
2643 };;
2644 { .mfb
2645 nop.m 0
2646 fma.d.s0 f8 = FR_A17,FR_x2,FR_A1
2647 br.ret.sptk b0
2648 };;
2649 // branch for calculating of ln(GAMMA(x)) for 1.0 <= x < 2.25
2650 //---------------------------------------------------------------------
2651 .align 32
2652 lgamma_1_2:
2653 { .mfi
2654 add GR_ad_Co = 0x10B0,GR_ad_1
2655 fcmp.eq.s1 p12,p0 = f1,FR_w
2656 mov GR_Arg125 = 0x3FF4
2657 }
2658 { .mfi
2659 add GR_ad_Ce = 0x1110,GR_ad_1
2660 nop.f 0
2661 mov GR_Arg175 = 0x3FFC
2662 };;
2663 { .mfi
2664 mov GR_SignOfGamma = 1
2665 fcmp.eq.s1 p13,p0 = f1,FR_NormX
2666 cmp.lt p6,p9 = GR_Arg,GR_Arg125 // 1.0 <= x < 1.25
2667 }
2668 { .mfi
2669 // set p10 if signgum is 32-bit int
2670 // set p11 if signgum is 64-bit int
2671 cmp.eq p11,p10 = 8,r34
2672 nop.f 0
2673 cmp.ge p8,p0 = GR_Arg,GR_Arg175 // x >= 1.75
2674 };;
2675 .pred.rel "mutex",p10,p11
2676 { .mfi
2677 // store sign of gamma(x) as 32-bit int
2678 (p10) st4 [r33] = GR_SignOfGamma
2679 (p12) fma.d.s0 f8 = f0,f0,f0
2680 (p9) cmp.lt.unc p7,p0 = GR_Arg,GR_Arg175 // 1.25 <= x < 1.75
2681 }
2682 { .mib
2683 // store sign of gamma(x) as 64-bit int
2684 (p11) st8 [r33] = GR_SignOfGamma
2685 mov GR_Offs = 0
2686 (p12) br.ret.spnt b0 // fast exit for 2.0
2687 };;
2688 .pred.rel "mutex",p7,p8
2689 { .mfi
2690 (p7) mov GR_Offs = 0xC0
2691 (p7) fms.s1 FR_x = FR_w,f1,FR_LocalMin
2692 nop.i 0
2693 }
2694 { .mfb
2695 (p8) mov GR_Offs = 0x180
2696 (p13) fma.d.s0 f8 = f0,f0,f0
2697 (p13) br.ret.spnt b0 // fast exit for 1.0
2698 };;
2699 .pred.rel "mutex",p6,p8
2700 { .mfi
2701 add GR_ad_Co = GR_ad_Co,GR_Offs
2702 (p8) fms.s1 FR_x = FR_w,f1,f1
2703 cmp.eq p0,p10 = r0,r0
2704 }
2705 { .mfb
2706 add GR_ad_Ce = GR_ad_Ce,GR_Offs
2707 (p6) fma.s1 FR_x = f0,f0,FR_w
2708 br.cond.sptk lgamma_common_0_2
2709 };;
2710 // branch for calculating of ln(GAMMA(x)) for -17 < x < 0
2711 //---------------------------------------------------------------------
2712 .align 32
2713 lgamma_negrecursion:
2714 { .mfi
2715 getf.d GR_ArgXfrAsIs = FR_Xfr
2716 fma.s1 FR_Xp2 = FR_2,f1,FR_NormX
2717 mov GR_Arg05 = 0x3FE
2718 }
2719 { .mfi
2720 add GR_ad_Roots = 0x1390,GR_ad_1
2721 fma.s1 FR_NormX = FR_NormX,FR_Xfr,f0
2722 mov GR_Arg075 = 0x3FE8
2723 };;
2724 { .mfi
2725 getf.sig GR_Sig = FR_int_Ntrunc
2726 fma.s1 FR_Xp3 = FR_2,f1,FR_Xp1
2727 shl GR_Arg05 = GR_Arg05,52
2728 }
2729 { .mfi
2730 mov GR_Arg025 = 0x3FD0
2731 fma.s1 FR_Xp6 = FR_5,f1,FR_Xp1
2732 add GR_ad_Co = 0x1C40,GR_ad_Data
2733 };;
2734 { .mfi
2735 add GR_ad_Dx = 8,GR_ad_Roots
2736 fma.s1 FR_Xp7 = FR_2,f1,FR_Xp5
2737 shr.u GR_ArgXfr = GR_ArgXfrAsIs,48
2738 }
2739 { .mfi
2740 add GR_ad_Ce = 0x60,GR_ad_Co
2741 fma.s1 FR_Xp8 = FR_3,f1,FR_Xp5
2742 cmp.lt p6,p0 = GR_ArgXfrAsIs,GR_Arg05
2743 };;
2744 { .mfi
2745 and GR_RootInd = 0xF,GR_Sig
2746 fma.s1 FR_Xp9 = FR_2,FR_2,FR_Xp5
2747 // p10 if arg < 0.25
2748 cmp.lt p10,p14 = GR_ArgXfr,GR_Arg025
2749 }
2750 { .mfi
2751 (p6) add GR_ad_Roots = 0x120,GR_ad_Roots
2752 fma.s1 FR_Xp11 = f1,f1,FR_Xp10
2753 (p6) add GR_ad_Dx = 0x120,GR_ad_Dx
2754 };;
2755 { .mfi
2756 shladd GR_ad_Root = GR_RootInd,4,GR_ad_Roots
2757 fma.s1 FR_Xp12 = FR_2,f1,FR_Xp10
2758 // p11 if 0.25 <= arg < 0.75
2759 // p12 if 0.75 <= arg < 1.0
2760 (p14) cmp.lt.unc p11,p12 = GR_ArgXfr,GR_Arg075
2761 }
2762 { .mfi
2763 shladd GR_ad_Dx = GR_RootInd,4,GR_ad_Dx
2764 fma.s1 FR_Xp13 = FR_3,f1,FR_Xp10
2765 cmp.eq p0,p13 = 0,GR_Sig
2766 };;
2767 { .mfi
2768 ld8 GR_Root = [GR_ad_Root]
2769 fma.s1 FR_Xp14 = FR_2,FR_2,FR_Xp10
2770 (p12) mov GR_Offs = 0x180
2771 }
2772 { .mfi
2773 ldfd FR_Root = [GR_ad_Root]
2774 fma.s1 FR_Xp15 = FR_5,f1,FR_Xp10
2775 and GR_Sig = 0xF,GR_Sig
2776 };;
2777 { .mfi
2778 ld8 GR_Dx = [GR_ad_Dx]
2779 fma.s1 FR_Xp16 = FR_3,FR_2,FR_Xp10
2780 (p13) cmp.ge.unc p6,p0 = 0xD,GR_Sig
2781 }
2782 { .mfi
2783 (p11) mov GR_Offs = 0xC0
2784 (p13) fma.s1 FR_NormX = FR_NormX,FR_Xp1,f0
2785 (p13) cmp.ge.unc p7,p0 = 0xB,GR_Sig
2786 };;
2787 { .mfi
2788 (p14) add GR_ad_Co = GR_Offs,GR_ad_Co
2789 (p6) fma.s1 FR_Xp2 = FR_Xp2,FR_Xp3,f0
2790 (p13) cmp.ge.unc p8,p0 = 0x9,GR_Sig
2791 }
2792 { .mfi
2793 (p14) add GR_ad_Ce = GR_Offs,GR_ad_Ce
2794 (p7) fma.s1 FR_Xp4 = FR_Xp4,FR_Xp5,f0
2795 (p13) cmp.ge.unc p9,p0 = 0x7,GR_Sig
2796 };;
2797 { .mfi
2798 ldfpd FR_B17,FR_B16 = [GR_ad_Co],16
2799 (p8) fma.s1 FR_Xp6 = FR_Xp6,FR_Xp7,f0
2800 (p13) cmp.ge.unc p6,p0 = 0x5,GR_Sig
2801 }
2802 { .mfi
2803 ldfpd FR_B15,FR_B14 = [GR_ad_Ce],16
2804 (p9) fma.s1 FR_Xp8 = FR_Xp8,FR_Xp9,f0
2805 (p13) cmp.ge.unc p7,p0 = 0x3,GR_Sig
2806 };;
2807 { .mfi
2808 ldfpd FR_B13,FR_B12 = [GR_ad_Co],16
2809 (p6) fma.s1 FR_Xp10 = FR_Xp10,FR_Xp11,f0
2810 (p13) cmp.ge.unc p8,p0 = 0x1,GR_Sig
2811 }
2812 { .mfi
2813 ldfpd FR_B11,FR_B10 = [GR_ad_Ce],16
2814 (p7) fma.s1 FR_Xp12 = FR_Xp12,FR_Xp13,f0
2815 (p13) cmp.eq.unc p9,p0 = 0,GR_Sig
2816 };;
2817 { .mfi
2818 ldfpd FR_B9,FR_B8 = [GR_ad_Co],16
2819 (p8) fma.s1 FR_Xp14 = FR_Xp14,FR_Xp15,f0
2820 mov GR_Arg15 = 0xC02E // -15
2821 }
2822 { .mfi
2823 ldfpd FR_B7,FR_B6 = [GR_ad_Ce],16
2824 fcmp.eq.s1 p15,p0 = f0,FR_Xf
2825 (p13) cmp.ge.unc p6,p0 = 0xC,GR_Sig
2826 };;
2827 { .mfi
2828 ldfe FR_B5 = [GR_ad_Co],16
2829 (p9) fma.s1 FR_NormX = FR_NormX,FR_Xp16,f0
2830 sub GR_Root = GR_ArgAsIs,GR_Root
2831 }
2832 { .mfi
2833 sub GR_RootInd = 0xE,GR_RootInd
2834 (p11) fms.s1 FR_x = FR_Xfr,f1,FR_LocalMin // x-LocalMin
2835 (p13) cmp.ge.unc p7,p0 = 0x8,GR_Sig
2836 };;
2837 .pred.rel "mutex",p10,p12
2838 { .mfi
2839 ldfe FR_B4 = [GR_ad_Ce],16
2840 (p10) fms.s1 FR_x = FR_Xfr,f1,f0 // x
2841 add GR_Root = GR_Root,GR_Dx
2842 }
2843 { .mfb
2844 cmp.gtu p14,p0 = 0xE,GR_RootInd
2845 (p12) fms.s1 FR_x = FR_Xfr,f1,f1 // x-1
2846 (p15) br.cond.spnt lgamma_singularity
2847 };;
2848 { .mfi
2849 ldfe FR_B3 = [GR_ad_Co],16
2850 (p6) fma.s1 FR_Xp2 = FR_Xp2,FR_Xp4,f0
2851 (p14) cmp.lt.unc p11,p0 = GR_Arg,GR_Arg15
2852 }
2853 { .mfi
2854 ldfe FR_B2 = [GR_ad_Ce],16
2855 (p7) fma.s1 FR_Xp6 = FR_Xp6,FR_Xp8,f0
2856 add GR_2xDx = GR_Dx,GR_Dx
2857 };;
2858 { .mfi
2859 ldfe FR_B1 = [GR_ad_Co],16
2860 fms.s1 FR_r = f8,f1,FR_Root
2861 (p13) cmp.ge.unc p6,p0 = 0x4,GR_Sig
2862 }
2863 { .mib
2864 ldfe FR_B0 = [GR_ad_Ce],16
2865 (p11) cmp.leu.unc p10,p0 = GR_Root,GR_2xDx
2866 (p10) br.cond.spnt lgamma_negroots
2867 };;
2868 { .mfi
2869 ldfpd FR_P5,FR_P4 = [GR_ad_1],16
2870 (p6) fma.s1 FR_Xp10 = FR_Xp10,FR_Xp12,f0
2871 tbit.z p14,p15 = GR_Sig,0
2872 }
2873 { .mfi
2874 ldfpd FR_P3,FR_P2 = [GR_ad_2],16
2875 fnma.d.s0 FR_T = f1,f1,f8 // nop.f 0
2877 (p13) cmp.ge.unc p7,p0 = 0x2,GR_Sig
2878 };;
2879 { .mfi
2880 ldfe FR_Ln2 = [GR_ad_1],0x50
2881 (p7) fma.s1 FR_NormX = FR_NormX,FR_Xp14,f0
2882 mov GR_PseudoRoot = 0xBFFBC
2883 }
2884 { .mlx
2885 add GR_ad_2 = 0x40,GR_ad_2
2886 movl GR_2xDx = 0x00002346DC5D6389
2887 };;
2888 { .mfi
2889 ldfpd FR_Q8,FR_Q7 = [GR_ad_1],16
2890 fma.s1 FR_x2 = FR_x,FR_x,f0
2891 shl GR_PseudoRoot = GR_PseudoRoot,44
2892 }
2893 { .mfi
2894 ldfpd FR_Q6,FR_Q5 = [GR_ad_2],16
2895 fma.s1 FR_B17 = FR_B17,FR_x,FR_B16
2896 (p13) cmp.ge.unc p6,p0 = 0xA,GR_Sig
2897 };;
2898 { .mfi
2899 ldfpd FR_Q4,FR_Q3 = [GR_ad_1],16
2900 (p6) fma.s1 FR_Xp2 = FR_Xp2,FR_Xp6,f0
2901 sub GR_PseudoRoot = GR_ArgAsIs,GR_PseudoRoot
2902 }
2903 { .mfi
2904 ldfpd FR_Q2,FR_Q1 = [GR_ad_2],16
2905 fma.s1 FR_B15 = FR_B15,FR_x,FR_B14
2906 (p13) cmp.ge.unc p7,p0 = 0x6,GR_Sig
2907 };;
2908 { .mfi
2909 add GR_ad_Co = 0x12F0,GR_ad_2
2910 fma.s1 FR_B13 = FR_B13,FR_x,FR_B12
2911 cmp.leu.unc p10,p0 = GR_PseudoRoot,GR_2xDx
2912 }
2913 { .mfi
2914 add GR_ad_Ce = 0x1300,GR_ad_2
2915 fma.s1 FR_B11 = FR_B11,FR_x,FR_B10
2916 mov GR_ExpMask = 0x1ffff
2917 };;
2918 { .mfi
2919 (p10) ldfe FR_PR01 = [GR_ad_Co],0xF0
2920 fma.s1 FR_B9 = FR_B9,FR_x,FR_B8
2921 mov GR_ExpBias = 0xFFFF
2922 }
2923 { .mfb
2924 (p10) ldfe FR_PR11 = [GR_ad_Ce],0xF0
2925 fma.s1 FR_B7 = FR_B7,FR_x,FR_B6
2926 (p10) br.cond.spnt lgamma_pseudoroot
2927 };;
2928 { .mfi
2929 (p13) cmp.ge.unc p6,p0 = 0xE,GR_Sig
2930 (p7) fma.s1 FR_NormX = FR_NormX,FR_Xp10,f0
2931 tbit.z.unc p8,p0 = GR_Sig,0
2932 }
2933 { .mfi
2934 mov GR_SignOfGamma = 1
2935 fma.s1 FR_B5 = FR_B5,FR_x,FR_B4
2936 // set p9 if signgum is 32-bit int
2937 // set p10 if signgum is 64-bit int
2938 cmp.eq p10,p9 = 8,r34
2939 };;
2940 { .mfi
2941 nop.m 0
2942 fma.s1 FR_B3 = FR_B3,FR_x,FR_B2
2943 (p8) sub GR_SignOfGamma = r0,GR_SignOfGamma
2944 }
2945 { .mfi
2946 nop.m 0
2947 (p14) fms.s1 FR_w = f0,f0,f1
2948 nop.i 0
2949 };;
2950 .pred.rel "mutex",p9,p10
2951 { .mfi
2952 // store sign of gamma(x) as 32-bit int
2953 (p9) st4 [r33] = GR_SignOfGamma
2954 fma.s1 FR_B1 = FR_B1,FR_x,FR_B0
2955 nop.i 0
2956 }
2957 { .mfi
2958 // store sign of gamma(x) as 64-bit int
2959 (p10) st8 [r33] = GR_SignOfGamma
2960 fma.s1 FR_B17 = FR_B17,FR_x2,FR_B15
2961 nop.i 0
2962 };;
2963 { .mfi
2964 nop.m 0
2965 fma.s1 FR_B13 = FR_B13,FR_x2,FR_B11
2966 nop.i 0
2967 };;
2968 { .mfi
2969 nop.m 0
2970 fma.s1 FR_B9 = FR_B9,FR_x2,FR_B7
2971 nop.i 0
2972 }
2973 { .mfi
2974 nop.m 0
2975 fma.s1 FR_x4 = FR_x2,FR_x2,f0
2976 nop.i 0
2977 };;
2978 { .mfi
2979 nop.m 0
2980 (p6) fma.s1 FR_NormX = FR_NormX,FR_Xp2,f0
2981 nop.i 0
2982 };;
2983 { .mfi
2984 nop.m 0
2985 fma.s1 FR_B5 = FR_B5,FR_x2,FR_B3
2986 nop.i 0
2987 };;
2988 { .mfi
2989 nop.m 0
2990 fma.s1 FR_B17 = FR_B17,FR_x4,FR_B13
2991 nop.i 0
2992 }
2993 { .mfi
2994 nop.m 0
2995 fma.s1 FR_x8 = FR_x4,FR_x4,f0
2996 nop.i 0
2997 };;
2998 .pred.rel "mutex",p14,p15
2999 { .mfi
3000 nop.m 0
3001 (p15) fms.s1 FR_w = FR_NormX,f1,f1
3002 nop.i 0
3003 }
3004 { .mfi
3005 nop.m 0
3006 (p14) fnma.s1 FR_w = FR_NormX,f1,FR_w
3007 nop.i 0
3008 };;
3009 { .mfi
3010 nop.m 0
3011 fma.s1 FR_B9 = FR_B9,FR_x4,FR_B5
3012 nop.i 0
3013 };;
3014 { .mfi
3015 nop.m 0
3016 frcpa.s1 FR_C,p0 = f1,FR_NormX
3017 nop.i 0
3018 };;
3019 { .mfi
3020 getf.exp GR_Exp = FR_NormX
3021 nop.f 0
3022 nop.i 0
3023 };;
3024 { .mfi
3025 getf.d GR_ArgAsIs = FR_NormX
3026 nop.f 0
3027 nop.i 0
3028 };;
3029 { .mfi
3030 nop.m 0
3031 fma.s1 FR_w2 = FR_w,FR_w,f0
3032 nop.i 0
3033 }
3034 { .mfi
3035 and GR_Exp = GR_Exp,GR_ExpMask
3036 fma.s1 FR_Q8 = FR_Q8,FR_w,FR_Q7
3037 nop.i 0
3038 };;
3039 { .mfi
3040 sub GR_Exp = GR_Exp,GR_ExpBias
3041 fma.s1 FR_B17 = FR_B17,FR_x8,FR_B9
3042 extr.u GR_Ind = GR_ArgAsIs,44,8
3043 }
3044 { .mfi
3045 nop.m 0
3046 fma.s1 FR_Q6 = FR_Q6,FR_w,FR_Q5
3047 nop.i 0
3048 };;
3049 { .mfi
3050 setf.sig FR_int_N = GR_Exp
3051 fms.s1 FR_r = FR_C,FR_NormX,f1
3052 nop.i 0
3053 }
3054 { .mfi
3055 shladd GR_ad_2 = GR_Ind,4,GR_ad_2
3056 nop.f 0
3057 nop.i 0
3058 };;
3059 { .mfi
3060 getf.exp GR_SignExp_w = FR_w
3061 fma.s1 FR_Q4 = FR_Q4,FR_w,FR_Q3
3062 nop.i 0
3063 }
3064 { .mfi
3065 ldfe FR_T = [GR_ad_2]
3066 nop.f 0
3067 nop.i 0
3068 };;
3069 { .mfi
3070 and GR_Exp_w = GR_ExpMask, GR_SignExp_w
3071 fnma.s1 FR_Q1 = FR_05,FR_w2,FR_w
3072 mov GR_fff9 = 0xfff9
3073 }
3074 { .mfi
3075 nop.m 0
3076 fma.s1 FR_w3 = FR_w2,FR_w,f0
3077 nop.i 0
3078 };;
3079 { .mfi
3080 nop.m 0
3081 fma.s1 FR_w4 = FR_w2,FR_w2,f0
3082 // p13 <== large w __libm_lgamma
3083 // p14 <== small w __libm_lgamma
3084 cmp.ge p13,p14 = GR_Exp_w,GR_fff9
3085 }
3086 { .mfi
3087 nop.m 0
3088 fma.s1 FR_Qlo = FR_Q8,FR_w2,FR_Q6
3089 nop.i 0
3090 };;
3091 { .mfi
3092 nop.m 0
3093 (p13) fma.s1 FR_r2 = FR_r,FR_r,f0
3094 nop.i 0
3095 }
3096 { .mfi
3097 nop.m 0
3098 fma.s1 FR_B17 = FR_B17,FR_x2,FR_B1
3099 nop.i 0
3100 };;
3101 { .mfi
3102 nop.m 0
3103 (p13) fma.s1 FR_P32 = FR_P3,FR_r,FR_P2
3104 nop.i 0
3105 }
3106 { .mfi
3107 nop.m 0
3108 (p13) fma.s1 FR_P54 = FR_P5,FR_r,FR_P4
3109 nop.i 0
3110 };;
3111 { .mfi
3112 nop.m 0
3113 (p14) fma.s1 FR_Q2 = FR_Q2,FR_w3,FR_Q1
3114 nop.i 0
3115 }
3116 { .mfi
3117 nop.m 0
3118 (p14) fma.s1 FR_w6 = FR_w3,FR_w3,f0
3119 nop.i 0
3120 };;
3121 { .mfi
3122 nop.m 0
3123 (p13) fcvt.xf FR_N = FR_int_N
3124 nop.i 0
3125 };;
3126 { .mfi
3127 nop.m 0
3128 (p13) fma.s1 FR_r3 = FR_r2,FR_r,f0
3129 nop.i 0
3130 }
3131 { .mfi
3132 nop.m 0
3133 (p13) fnma.s1 FR_P10 = FR_r2,FR_05,FR_r
3134 nop.i 0
3135 };;
3136 { .mfi
3137 nop.m 0
3138 (p13) fma.s1 FR_P54 = FR_P54,FR_r2,FR_P32
3139 nop.i 0
3140 };;
3141 { .mfi
3142 nop.m 0
3143 (p14) fma.s1 FR_Qhi = FR_Q4,FR_w4,FR_Q2
3144 nop.i 0
3145 }
3146 { .mfi
3147 nop.m 0
3148 (p14) fnma.s1 FR_Qlo = FR_Qlo,FR_w6,FR_B17
3149 nop.i 0
3150 };;
3151 { .mfi
3152 nop.m 0
3153 (p13) fma.s1 FR_TpNxLn2 = FR_N,FR_Ln2,FR_T
3154 nop.i 0
3155 };;
3156 { .mfi
3157 nop.m 0
3158 (p13) fma.s1 FR_P54 = FR_P54,FR_r3,FR_P10
3159 nop.i 0
3160 };;
3161 .pred.rel "mutex",p13,p14
3162 { .mfi
3163 nop.m 0
3164 (p14) fms.d.s0 f8 = FR_Qlo,f1,FR_Qhi
3165 nop.i 0
3166 }
3167 { .mfi
3168 nop.m 0
3169 (p13) fma.s1 FR_LnX = FR_TpNxLn2,f1,FR_P54
3170 nop.i 0
3171 };;
3172 { .mfb
3173 nop.m 0
3174 (p13) fms.d.s0 f8 = FR_B17,f1,FR_LnX
3175 br.ret.sptk b0
3176 };;
3177 // branch for calculating of ln(GAMMA(x)) near negative roots
3178 //---------------------------------------------------------------------
3179 .align 32
3180 lgamma_negroots:
3181 { .mfi
3182 shladd GR_Offs = GR_RootInd,3,r0 //GR_RootInd*8
3183 fma.s1 FR_r2 = FR_r,FR_r,f0
3184 add GR_ad_Co = 0x15C0,GR_ad_1//0x1590,GR_ad_1
3185 }
3186 { .mfi
3187 add GR_ad_Ce = 0x1610,GR_ad_1//0x15E0,GR_ad_1
3188 nop.f 0
3189 cmp.lt p6,p0 = GR_ArgXfrAsIs,GR_Arg05
3190 };;
3191 { .mfi
3192 add GR_ad_Roots = 0x10A0,GR_ad_1
3193 nop.f 0
3194 (p6) add GR_ad_Co = 0x820,GR_ad_Co
3195 }
3196 { .mfi
3197 (p6) add GR_ad_Ce = 0x820,GR_ad_Ce
3198 nop.f 0
3199 shladd GR_Offs = GR_RootInd,1,GR_Offs //GR_RootInd*10
3200 };;
3201 { .mmi
3202 shladd GR_ad_Co = GR_Offs,4,GR_ad_Co
3203 shladd GR_ad_Ce = GR_Offs,4,GR_ad_Ce
3204 cmp.eq p8,p7 = r0,r0
3205 };;
3206 { .mmi
3207 ldfpd FR_A15,FR_A14 = [GR_ad_Co],16
3208 ldfpd FR_A13,FR_A12 = [GR_ad_Ce],16
3209 mov GR_SignOfGamma = 1
3210 };;
3211 { .mmi
3212 ldfpd FR_A11,FR_A10 = [GR_ad_Co],16
3213 ldfpd FR_A9,FR_A8 = [GR_ad_Ce],16
3214 (p6) cmp.eq p7,p8 = r0,GR_RootInd
3215 };;
3216 { .mmi
3217 ldfpd FR_A7,FR_A6 = [GR_ad_Co],16
3218 ldfpd FR_A5,FR_A4 = [GR_ad_Ce],16
3219 tbit.z p11,p0 = GR_Sig,0
3220 };;
3221 { .mmi
3222 ldfe FR_A3 = [GR_ad_Co],16
3223 ldfe FR_A2 = [GR_ad_Ce],16
3224 // set p9 if signgum is 32-bit int
3225 // set p10 if signgum is 64-bit int
3226 cmp.eq p10,p9 = 8,r34
3227 };;
3228 { .mmi
3229 ldfe FR_A1 = [GR_ad_Co],16
3230 ldfe FR_A0 = [GR_ad_Ce],16
3231 (p11) sub GR_SignOfGamma = r0,GR_SignOfGamma
3232 };;
3233 { .mfi
3234 ldfe FR_A00 = [GR_ad_Roots]
3235 fma.s1 FR_r4 = FR_r2,FR_r2,f0
3236 nop.i 0
3237 };;
3238 { .mfi
3239 nop.m 0
3240 fma.s1 FR_A15 = FR_A15,FR_r,FR_A14
3241 nop.i 0
3242 }
3243 { .mfi
3244 nop.m 0
3245 fma.s1 FR_A13 = FR_A13,FR_r,FR_A12
3246 nop.i 0
3247 };;
3248 .pred.rel "mutex",p9,p10
3249 { .mfi
3250 // store sign of gamma(x) as 32-bit int
3251 (p9) st4 [r33] = GR_SignOfGamma
3252 fma.s1 FR_A11 = FR_A11,FR_r,FR_A10
3253 nop.i 0
3254 }
3255 { .mfi
3256 // store sign of gamma(x) as 64-bit int
3257 (p10) st8 [r33] = GR_SignOfGamma
3258 fma.s1 FR_A9 = FR_A9,FR_r,FR_A8
3259 nop.i 0
3260 };;
3261 { .mfi
3262 nop.m 0
3263 fma.s1 FR_A7 = FR_A7,FR_r,FR_A6
3264 nop.i 0
3265 }
3266 { .mfi
3267 nop.m 0
3268 fma.s1 FR_A5 = FR_A5,FR_r,FR_A4
3269 nop.i 0
3270 };;
3271 { .mfi
3272 nop.m 0
3273 fma.s1 FR_A3 = FR_A3,FR_r,FR_A2
3274 nop.i 0
3275 }
3276 { .mfi
3277 nop.m 0
3278 fma.s1 FR_r8 = FR_r4,FR_r4,f0
3279 nop.i 0
3280 };;
3281 { .mfi
3282 nop.m 0
3283 fma.s1 FR_A1 = FR_A1,FR_r,FR_A0
3284 nop.i 0
3285 };;
3286 { .mfi
3287 nop.m 0
3288 fma.s1 FR_A15 = FR_A15,FR_r2,FR_A13
3289 nop.i 0
3290 };;
3291 { .mfi
3292 nop.m 0
3293 fma.s1 FR_A11 = FR_A11,FR_r2,FR_A9
3294 nop.i 0
3295 };;
3296 { .mfi
3297 nop.m 0
3298 fma.s1 FR_A7 = FR_A7,FR_r2,FR_A5
3299 nop.i 0
3300 };;
3301 { .mfi
3302 nop.m 0
3303 fma.s1 FR_A3 = FR_A3,FR_r2,FR_A1
3304 nop.i 0
3305 };;
3306 { .mfi
3307 nop.m 0
3308 fma.s1 FR_A15 = FR_A15,FR_r4,FR_A11
3309 nop.i 0
3310 };;
3311 { .mfi
3312 nop.m 0
3313 fma.s1 FR_A7 = FR_A7,FR_r4,FR_A3
3314 nop.i 0
3315 };;
3316 .pred.rel "mutex",p7,p8
3317 { .mfi
3318 nop.m 0
3319 (p7) fma.s1 FR_A1 = FR_A15,FR_r8,FR_A7
3320 nop.i 0
3321 }
3322 { .mfi
3323 nop.m 0
3324 (p8) fma.d.s0 f8 = FR_A15,FR_r8,FR_A7
3325 nop.i 0
3326 };;
3327 { .mfb
3328 nop.m 0
3329 (p7) fma.d.s0 f8 = FR_A1,FR_r,FR_A00
3330 br.ret.sptk b0
3331 };;
3332 // branch for handling pseudo root on (-2;-1)
3333 //---------------------------------------------------------------------
3334 .align 32
3335 lgamma_pseudoroot:
3336 { .mmi
3337 ldfe FR_PR21 = [GR_ad_Co],32
3338 ldfe FR_PR31 = [GR_ad_Ce],32
3339 // set p9 if signgum is 32-bit int
3340 // set p10 if signgum is 64-bit int
3341 cmp.eq p10,p9 = 8,r34
3342 };;
3343 { .mmi
3344 ldfe FR_PR00 = [GR_ad_Co],32
3345 ldfe FR_PR10 = [GR_ad_Ce],0xF0
3346 mov GR_SignOfGamma = 1
3347 };;
3348 { .mmi
3349 ldfe FR_PR20 = [GR_ad_Co],0xF0
3350 ldfe FR_PR30 = [GR_ad_Ce]
3351 tbit.z p8,p0 = GR_Sig,0
3352 };;
3353 { .mfi
3354 ldfe FR_PRN = [GR_ad_Co]
3355 fma.s1 FR_PR01 = f8,f1,FR_PR01
3356 nop.i 0
3357 }
3358 { .mfi
3359 nop.m 0
3360 fma.s1 FR_PR11 = f8,f1,FR_PR11
3361 (p8) sub GR_SignOfGamma = r0,GR_SignOfGamma
3362 };;
3363 .pred.rel "mutex",p9,p10
3364 { .mfi
3365 // store sign of gamma(x) as 32-bit int
3366 (p9) st4 [r33] = GR_SignOfGamma
3367 fma.s1 FR_PR21 = f8,f1,FR_PR21
3368 nop.i 0
3369 }
3370 { .mfi
3371 // store sign of gamma(x) as 64-bit int
3372 (p10) st8 [r33] = GR_SignOfGamma
3373 fma.s1 FR_PR31 = f8,f1,FR_PR31
3374 nop.i 0
3375 };;
3376 { .mfi
3377 nop.m 0
3378 fma.s1 FR_PR01 = f8,FR_PR01,FR_PR00
3379 nop.i 0
3380 }
3381 { .mfi
3382 nop.m 0
3383 fma.s1 FR_PR11 = f8,FR_PR11,FR_PR10
3384 nop.i 0
3385 };;
3386 { .mfi
3387 nop.m 0
3388 fma.s1 FR_PR21 = f8,FR_PR21,FR_PR20
3389 nop.i 0
3390 }
3391 { .mfi
3392 nop.m 0
3393 fma.s1 FR_PR31 = f8,FR_PR31,FR_PR30
3394 nop.i 0
3395 };;
3396 { .mfi
3397 nop.m 0
3398 fma.s1 FR_PR01 = FR_PR11,FR_PR01,f0
3399 nop.i 0
3400 };;
3401 { .mfi
3402 nop.m 0
3403 fma.s1 FR_PR21 = FR_PR31,FR_PR21,f0
3404 nop.i 0
3405 };;
3406 { .mfi
3407 nop.m 0
3408 fma.s1 FR_PR01 = FR_PR21,FR_PR01,f0
3409 nop.i 0
3410 };;
3411 { .mfb
3412 nop.m 0
3413 fma.d.s0 f8 = FR_PR01,FR_PRN,f0
3414 br.ret.sptk b0
3415 };;
3416 // branch for handling +/-0, NaT, QNaN, +/-INF and denormalised numbers
3417 //---------------------------------------------------------------------
3418 .align 32
3419 lgamma_spec:
3420 { .mfi
3421 getf.exp GR_SignExp = FR_NormX
3422 fclass.m p6,p0 = f8,0x21 // is arg +INF?
3423 mov GR_SignOfGamma = 1
3424 };;
3425 { .mfi
3426 getf.sig GR_ArgAsIs = FR_NormX
3427 fclass.m p7,p0 = f8,0xB // is x deno?
3428 // set p11 if signgum is 32-bit int
3429 // set p12 if signgum is 64-bit int
3430 cmp.eq p12,p11 = 8,r34
3431 };;
3432 .pred.rel "mutex",p11,p12
3433 { .mfi
3434 // store sign of gamma(x) as 32-bit int
3435 (p11) st4 [r33] = GR_SignOfGamma
3436 fclass.m p8,p0 = f8,0x1C0 // is arg NaT or NaN?
3437 dep.z GR_Ind = GR_SignExp,8,4
3438 }
3439 { .mib
3440 // store sign of gamma(x) as 64-bit int
3441 (p12) st8 [r33] = GR_SignOfGamma
3442 cmp.lt p10,p0 = GR_SignExp,GR_ExpBias
3443 (p6) br.ret.spnt b0 // exit for +INF
3444 };;
3445 { .mfi
3446 and GR_Exp = GR_SignExp,GR_ExpMask
3447 fclass.m p9,p0 = f8,0x22 // is arg -INF?
3448 nop.i 0
3449 };;
3450 { .mfi
3451 add GR_ad_Co = GR_Ind,GR_ad_Data
3452 (p7) fma.s0 FR_tmp = f8,f8,f8
3453 extr.u GR_ArgAsIs = GR_ArgAsIs,11,52
3454 }
3455 { .mfb
3456 nop.m 0
3457 (p8) fms.d.s0 f8 = f8,f1,f8
3458 (p8) br.ret.spnt b0 // exit for NaT and NaN
3459 };;
3460 { .mib
3461 nop.m 0
3462 shr.u GR_Arg = GR_ArgAsIs,48
3463 (p7) br.cond.sptk lgamma_common
3464 };;
3465 { .mfb
3466 nop.m 0
3467 (p9) fmerge.s f8 = f1,f8
3468 (p9) br.ret.spnt b0 // exit -INF
3469 };;
3470 // branch for handling negative integers and +/-0
3471 //---------------------------------------------------------------------
3472 .align 32
3473 lgamma_singularity:
3474 { .mfi
3475 mov GR_ad_SignGam = r33
3476 fclass.m p6,p0 = f8, 0x6 // is x -0?
3477 mov GR_SignOfGamma = 1
3478 }
3479 { .mfi
3480 // set p9 if signgum is 32-bit int
3481 // set p10 if signgum is 64-bit int
3482 cmp.eq p10,p9 = 8,r34
3483 fma.s1 FR_X = f0,f0,f8
3484 nop.i 0
3485 };;
3486 { .mfi
3487 nop.m 0
3488 frcpa.s0 f8,p0 = f1,f0
3489 mov GR_TAG = 106 // negative
3490 }
3491 { .mib
3492 nop.m 0
3493 (p6) sub GR_SignOfGamma = r0,GR_SignOfGamma
3494 br.cond.sptk lgamma_libm_err
3495 };;
3496 // overflow (x > OVERFLOV_BOUNDARY)
3497 //---------------------------------------------------------------------
3498 .align 32
3499 lgamma_overflow:
3500 { .mfi
3501 mov GR_SignOfGamma = 1
3502 nop.f 0
3503 mov r8 = 0x1FFFE
3504 };;
3505 { .mfi
3506 setf.exp f9 = r8
3507 fmerge.s FR_X = f8,f8
3508 mov GR_TAG = 105 // overflow
3509 };;
3510 { .mfi
3511 mov GR_ad_SignGam = r33
3512 nop.f 0
3513 // set p9 if signgum is 32-bit int
3514 // set p10 if signgum is 64-bit int
3515 cmp.eq p10,p9 = 8,r34
3516 }
3517 { .mfi
3518 nop.m 0
3519 fma.d.s0 f8 = f9,f9,f0 // Set I,O and +INF result
3520 nop.i 0
3521 };;
3522 //
3523 //---------------------------------------------------------------------
3524 .align 32
3525 lgamma_libm_err:
3526 { .mmi
3527 alloc r32 = ar.pfs,1,4,4,0
3528 mov GR_Parameter_TAG = GR_TAG
3529 nop.i 0
3530 };;
3531 .pred.rel "mutex",p9,p10
3532 { .mmi
3533 // store sign of gamma(x) as 32-bit int
3534 (p9) st4 [GR_ad_SignGam] = GR_SignOfGamma
3535 // store sign of gamma(x) as 64-bit int
3536 (p10) st8 [GR_ad_SignGam] = GR_SignOfGamma
3537 nop.i 0
3538 };;
3539 GLOBAL_LIBM_END(__libm_lgamma)
3541 LOCAL_LIBM_ENTRY(__libm_error_region)
3542 .prologue
3543 { .mfi
3544 add GR_Parameter_Y=-32,sp // Parameter 2 value
3545 nop.f 0
3546 .save ar.pfs,GR_SAVE_PFS
3547 mov GR_SAVE_PFS=ar.pfs // Save ar.pfs
3548 }
3549 { .mfi
3550 .fframe 64
3551 add sp=-64,sp // Create new stack
3552 nop.f 0
3553 mov GR_SAVE_GP=gp // Save gp
3554 };;
3555 { .mmi
3556 stfd [GR_Parameter_Y] = FR_Y,16 // STORE Parameter 2 on stack
3557 add GR_Parameter_X = 16,sp // Parameter 1 address
3558 .save b0, GR_SAVE_B0
3559 mov GR_SAVE_B0=b0 // Save b0
3560 };;
3561 .body
3562 { .mib
3563 stfd [GR_Parameter_X] = FR_X // STORE Parameter 1
3564 // on stack
3565 add GR_Parameter_RESULT = 0,GR_Parameter_Y // Parameter 3 address
3566 nop.b 0
3567 }
3568 { .mib
3569 stfd [GR_Parameter_Y] = FR_RESULT // STORE Parameter 3
3570 // on stack
3571 add GR_Parameter_Y = -16,GR_Parameter_Y
3572 br.call.sptk b0=__libm_error_support# // Call error handling
3573 // function
3574 };;
3575 { .mmi
3576 nop.m 0
3577 nop.m 0
3578 add GR_Parameter_RESULT = 48,sp
3579 };;
3580 { .mmi
3581 ldfd f8 = [GR_Parameter_RESULT] // Get return result off stack
3582 .restore sp
3583 add sp = 64,sp // Restore stack pointer
3584 mov b0 = GR_SAVE_B0 // Restore return address
3585 };;
3586 { .mib
3587 mov gp = GR_SAVE_GP // Restore gp
3588 mov ar.pfs = GR_SAVE_PFS // Restore ar.pfs
3589 br.ret.sptk b0 // Return
3590 };;
3592 LOCAL_LIBM_END(__libm_error_region)
3593 .type __libm_error_support#,@function
3594 .global __libm_error_support#