| blob | 83cffd60fa9f3f52930028fa7c932b0e6cac2cc1 |
1 .file "libm_lgammaf.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 parameter store, load, and tag for __libm_error_support
45 // 02/01/02 Added support of SIGN(GAMMA(x)) calculation
46 // 05/20/02 Cleaned up namespace and sf0 syntax
47 // 09/16/02 Improved accuracy on intervals reduced to [1;1.25]
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_lgammaf(float 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-f97
66 //
67 // General Purpose Registers:
68 // r8-r11
69 // r14-r30
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 // lgamma(+inf) = +inf
80 // lgamma(-inf) = +inf
81 // lgamma(+/-0) = +inf
82 // lgamma(x<0, x - integer) = +inf
83 // lgamma(SNaN) = QNaN
84 // lgamma(QNaN) = QNaN
85 //
86 //*********************************************************************
87 //
88 // Overview
89 //
90 // The method consists of three cases.
91 //
92 // If 2^13 <= x < OVERFLOW_BOUNDARY use case lgammaf_pstirling;
93 // else if 1 < x < 2^13 use case lgammaf_regular;
94 // else if -9 < x < 1 use case lgammaf_negrecursion;
95 // else if -2^13 < x < -9 use case lgammaf_negpoly;
96 // else if x < -2^13 use case lgammaf_negstirling;
97 // else if x is close to negative
98 // roots of ln(GAMMA(x)) use case lgammaf_negroots;
99 //
100 //
101 // Case 2^13 <= 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
105 //
106 // Case 1 < x < 2^13
107 // -----------------
108 // To calculate ln(GAMMA(x)) for such arguments we use polynomial
109 // approximation on following intervals: [1.0; 1.25), [1.25; 1.5),
110 // [1.5, 1.75), [1.75; 2), [2; 4), [2^i; 2^(i+1)), i=1..8
111 //
112 // Following variants of approximation and argument reduction are used:
113 // 1. [1.0; 1.25)
114 // ln(GAMMA(x)) ~ (x-1.0)*P7(x)
115 //
116 // 2. [1.25; 1.5)
117 // ln(GAMMA(x)) ~ ln(GAMMA(x0))+(x-x0)*P8(x-x0),
118 // where x0 - point of local minimum on [1;2] rounded to nearest double
119 // precision number.
120 //
121 // 3. [1.5; 1.75)
122 // ln(GAMMA(x)) ~ P8(x)
123 //
124 // 4. [1.75; 2.0)
125 // ln(GAMMA(x)) ~ (x-2)*P7(x)
126 //
127 // 5. [2; 4)
128 // ln(GAMMA(x)) ~ (x-2)*P10(x)
129 //
130 // 6. [2^i; 2^(i+1)), i=2..8
131 // ln(GAMMA(x)) ~ P10((x-2^i)/2^i)
132 //
133 // Case -9 < x < 1
134 // ---------------
135 // Here we use the recursive formula:
136 // ln(GAMMA(x)) = ln(GAMMA(x+1)) - ln(x)
137 //
138 // Using this formula we reduce argument to base interval [1.0; 2.0]
139 //
140 // Case -2^13 < x < -9
141 // --------------------
142 // Here we use the formula:
143 // ln(GAMMA(x)) = ln(Pi/(|x|*GAMMA(|x|)*sin(Pi*|x|))) =
144 // = -ln(|x|) - ln((GAMMA(|x|)) - ln(sin(Pi*r)/(Pi*r)) - ln(|r|)
145 // where r = x - rounded_to_nearest(x), i.e |r| <= 0.5 and
146 // ln(sin(Pi*r)/(Pi*r)) is approximated by 8-degree polynomial of r^2
147 //
148 // Case x < -2^13
149 // --------------
150 // Here we use algorithm based on the Stirling formula:
151 // ln(GAMMA(x)) = -ln(sqrt(2*Pi)) + (|x|-0.5)ln(x) - |x| -
152 // - ln(sin(Pi*r)/(Pi*r)) - ln(|r|)
153 // where r = x - rounded_to_nearest(x).
154 //
155 // Neighbourhoods of negative roots
156 // --------------------------------
157 // Here we use polynomial approximation
158 // ln(GAMMA(x-x0)) = ln(GAMMA(x0)) + (x-x0)*P14(x-x0),
159 // where x0 is a root of ln(GAMMA(x)) rounded to nearest double
160 // precision number.
161 //
162 //
163 // Claculation of logarithm
164 // ------------------------
165 // Consider x = 2^N * xf so
166 // ln(x) = ln(frcpa(x)*x/frcpa(x))
167 // = ln(1/frcpa(x)) + ln(frcpa(x)*x)
168 //
169 // frcpa(x) = 2^(-N) * frcpa(xf)
170 //
171 // ln(1/frcpa(x)) = -ln(2^(-N)) - ln(frcpa(xf))
172 // = N*ln(2) - ln(frcpa(xf))
173 // = N*ln(2) + ln(1/frcpa(xf))
174 //
175 // ln(x) = ln(1/frcpa(x)) + ln(frcpa(x)*x) =
176 // = N*ln(2) + ln(1/frcpa(xf)) + ln(frcpa(x)*x)
177 // = N*ln(2) + T + ln(frcpa(x)*x)
178 //
179 // Let r = 1 - frcpa(x)*x, note that r is quite small by
180 // absolute value so
181 //
182 // ln(x) = N*ln(2) + T + ln(1+r) ~ N*ln(2) + T + Series(r),
183 // where T - is precomputed tabular value,
184 // Series(r) = (P3*r + P2)*r^2 + (P1*r + 1)
185 //
186 //*********************************************************************
188 GR_TAG = r8
189 GR_ad_Data = r8
190 GR_ad_Co = r9
191 GR_ad_SignGam = r10
192 GR_ad_Ce = r10
193 GR_SignExp = r11
195 GR_ad_C650 = r14
196 GR_ad_RootCo = r14
197 GR_ad_C0 = r15
198 GR_Dx = r15
199 GR_Ind = r16
200 GR_Offs = r17
201 GR_IntNum = r17
202 GR_ExpBias = r18
203 GR_ExpMask = r19
204 GR_Ind4T = r20
205 GR_RootInd = r20
206 GR_Sig = r21
207 GR_Exp = r22
208 GR_PureExp = r23
209 GR_ad_C43 = r24
210 GR_StirlBound = r25
211 GR_ad_T = r25
212 GR_IndX8 = r25
213 GR_Neg2 = r25
214 GR_2xDx = r25
215 GR_SingBound = r26
216 GR_IndX2 = r26
217 GR_Neg4 = r26
218 GR_ad_RootCe = r26
219 GR_Arg = r27
220 GR_ExpOf2 = r28
221 GR_fff7 = r28
222 GR_Root = r28
223 GR_ReqBound = r28
224 GR_N = r29
225 GR_ad_Root = r30
226 GR_ad_OvfBound = r30
227 GR_SignOfGamma = r31
229 GR_SAVE_B0 = r33
230 GR_SAVE_PFS = r34
231 GR_SAVE_GP = r35
232 GR_SAVE_SP = r36
234 GR_Parameter_X = r37
235 GR_Parameter_Y = r38
236 GR_Parameter_RESULT = r39
237 GR_Parameter_TAG = r40
239 //*********************************************************************
241 FR_X = f10
242 FR_Y = f1 // lgammaf is single argument function
243 FR_RESULT = f8
245 FR_x = f6
246 FR_x2 = f7
248 FR_x3 = f9
249 FR_x4 = f10
250 FR_xm2 = f11
251 FR_w = f11
252 FR_w2 = f12
253 FR_Q32 = f13
254 FR_Q10 = f14
255 FR_InvX = f15
257 FR_NormX = f32
259 FR_A0 = f33
260 FR_A1 = f34
261 FR_A2 = f35
262 FR_A3 = f36
263 FR_A4 = f37
264 FR_A5 = f38
265 FR_A6 = f39
266 FR_A7 = f40
267 FR_A8 = f41
268 FR_A9 = f42
269 FR_A10 = f43
271 FR_int_N = f44
272 FR_P3 = f45
273 FR_P2 = f46
274 FR_P1 = f47
275 FR_LocalMin = f48
276 FR_Ln2 = f49
277 FR_05 = f50
278 FR_LnSqrt2Pi = f51
279 FR_3 = f52
280 FR_r = f53
281 FR_r2 = f54
282 FR_T = f55
283 FR_N = f56
284 FR_xm05 = f57
285 FR_int_Ln = f58
286 FR_P32 = f59
287 FR_P10 = f60
289 FR_Xf = f61
290 FR_InvXf = f62
291 FR_rf = f63
292 FR_rf2 = f64
293 FR_Tf = f65
294 FR_Nf = f66
295 FR_xm05f = f67
296 FR_P32f = f68
297 FR_P10f = f69
298 FR_Lnf = f70
299 FR_Xf2 = f71
300 FR_Xf4 = f72
301 FR_Xf8 = f73
302 FR_Ln = f74
303 FR_xx = f75
304 FR_Root = f75
305 FR_Req = f76
306 FR_1pXf = f77
308 FR_S16 = f78
309 FR_R3 = f78
310 FR_S14 = f79
311 FR_R2 = f79
312 FR_S12 = f80
313 FR_R1 = f80
314 FR_S10 = f81
315 FR_R0 = f81
316 FR_S8 = f82
317 FR_rx = f82
318 FR_S6 = f83
319 FR_rx2 = f84
320 FR_S4 = f84
321 FR_S2 = f85
323 FR_Xp1 = f86
324 FR_Xp2 = f87
325 FR_Xp3 = f88
326 FR_Xp4 = f89
327 FR_Xp5 = f90
328 FR_Xp6 = f91
329 FR_Xp7 = f92
330 FR_Xp8 = f93
331 FR_OverflowBound = f93
333 FR_2 = f94
334 FR_tmp = f95
335 FR_int_Ntrunc = f96
336 FR_Ntrunc = f97
338 //*********************************************************************
340 RODATA
341 .align 32
342 LOCAL_OBJECT_START(lgammaf_data)
343 log_table_1:
344 data8 0xbfd0001008f39d59 // P3
345 data8 0x3fd5556073e0c45a // P2
346 data8 0x3fe62e42fefa39ef // ln(2)
347 data8 0x3fe0000000000000 // 0.5
348 //
349 data8 0x3F60040155D5889E //ln(1/frcpa(1+ 0/256)
350 data8 0x3F78121214586B54 //ln(1/frcpa(1+ 1/256)
351 data8 0x3F841929F96832F0 //ln(1/frcpa(1+ 2/256)
352 data8 0x3F8C317384C75F06 //ln(1/frcpa(1+ 3/256)
353 data8 0x3F91A6B91AC73386 //ln(1/frcpa(1+ 4/256)
354 data8 0x3F95BA9A5D9AC039 //ln(1/frcpa(1+ 5/256)
355 data8 0x3F99D2A8074325F4 //ln(1/frcpa(1+ 6/256)
356 data8 0x3F9D6B2725979802 //ln(1/frcpa(1+ 7/256)
357 data8 0x3FA0C58FA19DFAAA //ln(1/frcpa(1+ 8/256)
358 data8 0x3FA2954C78CBCE1B //ln(1/frcpa(1+ 9/256)
359 data8 0x3FA4A94D2DA96C56 //ln(1/frcpa(1+ 10/256)
360 data8 0x3FA67C94F2D4BB58 //ln(1/frcpa(1+ 11/256)
361 data8 0x3FA85188B630F068 //ln(1/frcpa(1+ 12/256)
362 data8 0x3FAA6B8ABE73AF4C //ln(1/frcpa(1+ 13/256)
363 data8 0x3FAC441E06F72A9E //ln(1/frcpa(1+ 14/256)
364 data8 0x3FAE1E6713606D07 //ln(1/frcpa(1+ 15/256)
365 data8 0x3FAFFA6911AB9301 //ln(1/frcpa(1+ 16/256)
366 data8 0x3FB0EC139C5DA601 //ln(1/frcpa(1+ 17/256)
367 data8 0x3FB1DBD2643D190B //ln(1/frcpa(1+ 18/256)
368 data8 0x3FB2CC7284FE5F1C //ln(1/frcpa(1+ 19/256)
369 data8 0x3FB3BDF5A7D1EE64 //ln(1/frcpa(1+ 20/256)
370 data8 0x3FB4B05D7AA012E0 //ln(1/frcpa(1+ 21/256)
371 data8 0x3FB580DB7CEB5702 //ln(1/frcpa(1+ 22/256)
372 data8 0x3FB674F089365A7A //ln(1/frcpa(1+ 23/256)
373 data8 0x3FB769EF2C6B568D //ln(1/frcpa(1+ 24/256)
374 data8 0x3FB85FD927506A48 //ln(1/frcpa(1+ 25/256)
375 data8 0x3FB9335E5D594989 //ln(1/frcpa(1+ 26/256)
376 data8 0x3FBA2B0220C8E5F5 //ln(1/frcpa(1+ 27/256)
377 data8 0x3FBB0004AC1A86AC //ln(1/frcpa(1+ 28/256)
378 data8 0x3FBBF968769FCA11 //ln(1/frcpa(1+ 29/256)
379 data8 0x3FBCCFEDBFEE13A8 //ln(1/frcpa(1+ 30/256)
380 data8 0x3FBDA727638446A2 //ln(1/frcpa(1+ 31/256)
381 data8 0x3FBEA3257FE10F7A //ln(1/frcpa(1+ 32/256)
382 data8 0x3FBF7BE9FEDBFDE6 //ln(1/frcpa(1+ 33/256)
383 data8 0x3FC02AB352FF25F4 //ln(1/frcpa(1+ 34/256)
384 data8 0x3FC097CE579D204D //ln(1/frcpa(1+ 35/256)
385 data8 0x3FC1178E8227E47C //ln(1/frcpa(1+ 36/256)
386 data8 0x3FC185747DBECF34 //ln(1/frcpa(1+ 37/256)
387 data8 0x3FC1F3B925F25D41 //ln(1/frcpa(1+ 38/256)
388 data8 0x3FC2625D1E6DDF57 //ln(1/frcpa(1+ 39/256)
389 data8 0x3FC2D1610C86813A //ln(1/frcpa(1+ 40/256)
390 data8 0x3FC340C59741142E //ln(1/frcpa(1+ 41/256)
391 data8 0x3FC3B08B6757F2A9 //ln(1/frcpa(1+ 42/256)
392 data8 0x3FC40DFB08378003 //ln(1/frcpa(1+ 43/256)
393 data8 0x3FC47E74E8CA5F7C //ln(1/frcpa(1+ 44/256)
394 data8 0x3FC4EF51F6466DE4 //ln(1/frcpa(1+ 45/256)
395 data8 0x3FC56092E02BA516 //ln(1/frcpa(1+ 46/256)
396 data8 0x3FC5D23857CD74D5 //ln(1/frcpa(1+ 47/256)
397 data8 0x3FC6313A37335D76 //ln(1/frcpa(1+ 48/256)
398 data8 0x3FC6A399DABBD383 //ln(1/frcpa(1+ 49/256)
399 data8 0x3FC70337DD3CE41B //ln(1/frcpa(1+ 50/256)
400 data8 0x3FC77654128F6127 //ln(1/frcpa(1+ 51/256)
401 data8 0x3FC7E9D82A0B022D //ln(1/frcpa(1+ 52/256)
402 data8 0x3FC84A6B759F512F //ln(1/frcpa(1+ 53/256)
403 data8 0x3FC8AB47D5F5A310 //ln(1/frcpa(1+ 54/256)
404 data8 0x3FC91FE49096581B //ln(1/frcpa(1+ 55/256)
405 data8 0x3FC981634011AA75 //ln(1/frcpa(1+ 56/256)
406 data8 0x3FC9F6C407089664 //ln(1/frcpa(1+ 57/256)
407 data8 0x3FCA58E729348F43 //ln(1/frcpa(1+ 58/256)
408 data8 0x3FCABB55C31693AD //ln(1/frcpa(1+ 59/256)
409 data8 0x3FCB1E104919EFD0 //ln(1/frcpa(1+ 60/256)
410 data8 0x3FCB94EE93E367CB //ln(1/frcpa(1+ 61/256)
411 data8 0x3FCBF851C067555F //ln(1/frcpa(1+ 62/256)
412 data8 0x3FCC5C0254BF23A6 //ln(1/frcpa(1+ 63/256)
413 data8 0x3FCCC000C9DB3C52 //ln(1/frcpa(1+ 64/256)
414 data8 0x3FCD244D99C85674 //ln(1/frcpa(1+ 65/256)
415 data8 0x3FCD88E93FB2F450 //ln(1/frcpa(1+ 66/256)
416 data8 0x3FCDEDD437EAEF01 //ln(1/frcpa(1+ 67/256)
417 data8 0x3FCE530EFFE71012 //ln(1/frcpa(1+ 68/256)
418 data8 0x3FCEB89A1648B971 //ln(1/frcpa(1+ 69/256)
419 data8 0x3FCF1E75FADF9BDE //ln(1/frcpa(1+ 70/256)
420 data8 0x3FCF84A32EAD7C35 //ln(1/frcpa(1+ 71/256)
421 data8 0x3FCFEB2233EA07CD //ln(1/frcpa(1+ 72/256)
422 data8 0x3FD028F9C7035C1C //ln(1/frcpa(1+ 73/256)
423 data8 0x3FD05C8BE0D9635A //ln(1/frcpa(1+ 74/256)
424 data8 0x3FD085EB8F8AE797 //ln(1/frcpa(1+ 75/256)
425 data8 0x3FD0B9C8E32D1911 //ln(1/frcpa(1+ 76/256)
426 data8 0x3FD0EDD060B78081 //ln(1/frcpa(1+ 77/256)
427 data8 0x3FD122024CF0063F //ln(1/frcpa(1+ 78/256)
428 data8 0x3FD14BE2927AECD4 //ln(1/frcpa(1+ 79/256)
429 data8 0x3FD180618EF18ADF //ln(1/frcpa(1+ 80/256)
430 data8 0x3FD1B50BBE2FC63B //ln(1/frcpa(1+ 81/256)
431 data8 0x3FD1DF4CC7CF242D //ln(1/frcpa(1+ 82/256)
432 data8 0x3FD214456D0EB8D4 //ln(1/frcpa(1+ 83/256)
433 data8 0x3FD23EC5991EBA49 //ln(1/frcpa(1+ 84/256)
434 data8 0x3FD2740D9F870AFB //ln(1/frcpa(1+ 85/256)
435 data8 0x3FD29ECDABCDFA04 //ln(1/frcpa(1+ 86/256)
436 data8 0x3FD2D46602ADCCEE //ln(1/frcpa(1+ 87/256)
437 data8 0x3FD2FF66B04EA9D4 //ln(1/frcpa(1+ 88/256)
438 data8 0x3FD335504B355A37 //ln(1/frcpa(1+ 89/256)
439 data8 0x3FD360925EC44F5D //ln(1/frcpa(1+ 90/256)
440 data8 0x3FD38BF1C3337E75 //ln(1/frcpa(1+ 91/256)
441 data8 0x3FD3C25277333184 //ln(1/frcpa(1+ 92/256)
442 data8 0x3FD3EDF463C1683E //ln(1/frcpa(1+ 93/256)
443 data8 0x3FD419B423D5E8C7 //ln(1/frcpa(1+ 94/256)
444 data8 0x3FD44591E0539F49 //ln(1/frcpa(1+ 95/256)
445 data8 0x3FD47C9175B6F0AD //ln(1/frcpa(1+ 96/256)
446 data8 0x3FD4A8B341552B09 //ln(1/frcpa(1+ 97/256)
447 data8 0x3FD4D4F3908901A0 //ln(1/frcpa(1+ 98/256)
448 data8 0x3FD501528DA1F968 //ln(1/frcpa(1+ 99/256)
449 data8 0x3FD52DD06347D4F6 //ln(1/frcpa(1+ 100/256)
450 data8 0x3FD55A6D3C7B8A8A //ln(1/frcpa(1+ 101/256)
451 data8 0x3FD5925D2B112A59 //ln(1/frcpa(1+ 102/256)
452 data8 0x3FD5BF406B543DB2 //ln(1/frcpa(1+ 103/256)
453 data8 0x3FD5EC433D5C35AE //ln(1/frcpa(1+ 104/256)
454 data8 0x3FD61965CDB02C1F //ln(1/frcpa(1+ 105/256)
455 data8 0x3FD646A84935B2A2 //ln(1/frcpa(1+ 106/256)
456 data8 0x3FD6740ADD31DE94 //ln(1/frcpa(1+ 107/256)
457 data8 0x3FD6A18DB74A58C5 //ln(1/frcpa(1+ 108/256)
458 data8 0x3FD6CF31058670EC //ln(1/frcpa(1+ 109/256)
459 data8 0x3FD6F180E852F0BA //ln(1/frcpa(1+ 110/256)
460 data8 0x3FD71F5D71B894F0 //ln(1/frcpa(1+ 111/256)
461 data8 0x3FD74D5AEFD66D5C //ln(1/frcpa(1+ 112/256)
462 data8 0x3FD77B79922BD37E //ln(1/frcpa(1+ 113/256)
463 data8 0x3FD7A9B9889F19E2 //ln(1/frcpa(1+ 114/256)
464 data8 0x3FD7D81B037EB6A6 //ln(1/frcpa(1+ 115/256)
465 data8 0x3FD8069E33827231 //ln(1/frcpa(1+ 116/256)
466 data8 0x3FD82996D3EF8BCB //ln(1/frcpa(1+ 117/256)
467 data8 0x3FD85855776DCBFB //ln(1/frcpa(1+ 118/256)
468 data8 0x3FD8873658327CCF //ln(1/frcpa(1+ 119/256)
469 data8 0x3FD8AA75973AB8CF //ln(1/frcpa(1+ 120/256)
470 data8 0x3FD8D992DC8824E5 //ln(1/frcpa(1+ 121/256)
471 data8 0x3FD908D2EA7D9512 //ln(1/frcpa(1+ 122/256)
472 data8 0x3FD92C59E79C0E56 //ln(1/frcpa(1+ 123/256)
473 data8 0x3FD95BD750EE3ED3 //ln(1/frcpa(1+ 124/256)
474 data8 0x3FD98B7811A3EE5B //ln(1/frcpa(1+ 125/256)
475 data8 0x3FD9AF47F33D406C //ln(1/frcpa(1+ 126/256)
476 data8 0x3FD9DF270C1914A8 //ln(1/frcpa(1+ 127/256)
477 data8 0x3FDA0325ED14FDA4 //ln(1/frcpa(1+ 128/256)
478 data8 0x3FDA33440224FA79 //ln(1/frcpa(1+ 129/256)
479 data8 0x3FDA57725E80C383 //ln(1/frcpa(1+ 130/256)
480 data8 0x3FDA87D0165DD199 //ln(1/frcpa(1+ 131/256)
481 data8 0x3FDAAC2E6C03F896 //ln(1/frcpa(1+ 132/256)
482 data8 0x3FDADCCC6FDF6A81 //ln(1/frcpa(1+ 133/256)
483 data8 0x3FDB015B3EB1E790 //ln(1/frcpa(1+ 134/256)
484 data8 0x3FDB323A3A635948 //ln(1/frcpa(1+ 135/256)
485 data8 0x3FDB56FA04462909 //ln(1/frcpa(1+ 136/256)
486 data8 0x3FDB881AA659BC93 //ln(1/frcpa(1+ 137/256)
487 data8 0x3FDBAD0BEF3DB165 //ln(1/frcpa(1+ 138/256)
488 data8 0x3FDBD21297781C2F //ln(1/frcpa(1+ 139/256)
489 data8 0x3FDC039236F08819 //ln(1/frcpa(1+ 140/256)
490 data8 0x3FDC28CB1E4D32FD //ln(1/frcpa(1+ 141/256)
491 data8 0x3FDC4E19B84723C2 //ln(1/frcpa(1+ 142/256)
492 data8 0x3FDC7FF9C74554C9 //ln(1/frcpa(1+ 143/256)
493 data8 0x3FDCA57B64E9DB05 //ln(1/frcpa(1+ 144/256)
494 data8 0x3FDCCB130A5CEBB0 //ln(1/frcpa(1+ 145/256)
495 data8 0x3FDCF0C0D18F326F //ln(1/frcpa(1+ 146/256)
496 data8 0x3FDD232075B5A201 //ln(1/frcpa(1+ 147/256)
497 data8 0x3FDD490246DEFA6B //ln(1/frcpa(1+ 148/256)
498 data8 0x3FDD6EFA918D25CD //ln(1/frcpa(1+ 149/256)
499 data8 0x3FDD9509707AE52F //ln(1/frcpa(1+ 150/256)
500 data8 0x3FDDBB2EFE92C554 //ln(1/frcpa(1+ 151/256)
501 data8 0x3FDDEE2F3445E4AF //ln(1/frcpa(1+ 152/256)
502 data8 0x3FDE148A1A2726CE //ln(1/frcpa(1+ 153/256)
503 data8 0x3FDE3AFC0A49FF40 //ln(1/frcpa(1+ 154/256)
504 data8 0x3FDE6185206D516E //ln(1/frcpa(1+ 155/256)
505 data8 0x3FDE882578823D52 //ln(1/frcpa(1+ 156/256)
506 data8 0x3FDEAEDD2EAC990C //ln(1/frcpa(1+ 157/256)
507 data8 0x3FDED5AC5F436BE3 //ln(1/frcpa(1+ 158/256)
508 data8 0x3FDEFC9326D16AB9 //ln(1/frcpa(1+ 159/256)
509 data8 0x3FDF2391A2157600 //ln(1/frcpa(1+ 160/256)
510 data8 0x3FDF4AA7EE03192D //ln(1/frcpa(1+ 161/256)
511 data8 0x3FDF71D627C30BB0 //ln(1/frcpa(1+ 162/256)
512 data8 0x3FDF991C6CB3B379 //ln(1/frcpa(1+ 163/256)
513 data8 0x3FDFC07ADA69A910 //ln(1/frcpa(1+ 164/256)
514 data8 0x3FDFE7F18EB03D3E //ln(1/frcpa(1+ 165/256)
515 data8 0x3FE007C053C5002E //ln(1/frcpa(1+ 166/256)
516 data8 0x3FE01B942198A5A1 //ln(1/frcpa(1+ 167/256)
517 data8 0x3FE02F74400C64EB //ln(1/frcpa(1+ 168/256)
518 data8 0x3FE04360BE7603AD //ln(1/frcpa(1+ 169/256)
519 data8 0x3FE05759AC47FE34 //ln(1/frcpa(1+ 170/256)
520 data8 0x3FE06B5F1911CF52 //ln(1/frcpa(1+ 171/256)
521 data8 0x3FE078BF0533C568 //ln(1/frcpa(1+ 172/256)
522 data8 0x3FE08CD9687E7B0E //ln(1/frcpa(1+ 173/256)
523 data8 0x3FE0A10074CF9019 //ln(1/frcpa(1+ 174/256)
524 data8 0x3FE0B5343A234477 //ln(1/frcpa(1+ 175/256)
525 data8 0x3FE0C974C89431CE //ln(1/frcpa(1+ 176/256)
526 data8 0x3FE0DDC2305B9886 //ln(1/frcpa(1+ 177/256)
527 data8 0x3FE0EB524BAFC918 //ln(1/frcpa(1+ 178/256)
528 data8 0x3FE0FFB54213A476 //ln(1/frcpa(1+ 179/256)
529 data8 0x3FE114253DA97D9F //ln(1/frcpa(1+ 180/256)
530 data8 0x3FE128A24F1D9AFF //ln(1/frcpa(1+ 181/256)
531 data8 0x3FE1365252BF0865 //ln(1/frcpa(1+ 182/256)
532 data8 0x3FE14AE558B4A92D //ln(1/frcpa(1+ 183/256)
533 data8 0x3FE15F85A19C765B //ln(1/frcpa(1+ 184/256)
534 data8 0x3FE16D4D38C119FA //ln(1/frcpa(1+ 185/256)
535 data8 0x3FE18203C20DD133 //ln(1/frcpa(1+ 186/256)
536 data8 0x3FE196C7BC4B1F3B //ln(1/frcpa(1+ 187/256)
537 data8 0x3FE1A4A738B7A33C //ln(1/frcpa(1+ 188/256)
538 data8 0x3FE1B981C0C9653D //ln(1/frcpa(1+ 189/256)
539 data8 0x3FE1CE69E8BB106B //ln(1/frcpa(1+ 190/256)
540 data8 0x3FE1DC619DE06944 //ln(1/frcpa(1+ 191/256)
541 data8 0x3FE1F160A2AD0DA4 //ln(1/frcpa(1+ 192/256)
542 data8 0x3FE2066D7740737E //ln(1/frcpa(1+ 193/256)
543 data8 0x3FE2147DBA47A394 //ln(1/frcpa(1+ 194/256)
544 data8 0x3FE229A1BC5EBAC3 //ln(1/frcpa(1+ 195/256)
545 data8 0x3FE237C1841A502E //ln(1/frcpa(1+ 196/256)
546 data8 0x3FE24CFCE6F80D9A //ln(1/frcpa(1+ 197/256)
547 data8 0x3FE25B2C55CD5762 //ln(1/frcpa(1+ 198/256)
548 data8 0x3FE2707F4D5F7C41 //ln(1/frcpa(1+ 199/256)
549 data8 0x3FE285E0842CA384 //ln(1/frcpa(1+ 200/256)
550 data8 0x3FE294294708B773 //ln(1/frcpa(1+ 201/256)
551 data8 0x3FE2A9A2670AFF0C //ln(1/frcpa(1+ 202/256)
552 data8 0x3FE2B7FB2C8D1CC1 //ln(1/frcpa(1+ 203/256)
553 data8 0x3FE2C65A6395F5F5 //ln(1/frcpa(1+ 204/256)
554 data8 0x3FE2DBF557B0DF43 //ln(1/frcpa(1+ 205/256)
555 data8 0x3FE2EA64C3F97655 //ln(1/frcpa(1+ 206/256)
556 data8 0x3FE3001823684D73 //ln(1/frcpa(1+ 207/256)
557 data8 0x3FE30E97E9A8B5CD //ln(1/frcpa(1+ 208/256)
558 data8 0x3FE32463EBDD34EA //ln(1/frcpa(1+ 209/256)
559 data8 0x3FE332F4314AD796 //ln(1/frcpa(1+ 210/256)
560 data8 0x3FE348D90E7464D0 //ln(1/frcpa(1+ 211/256)
561 data8 0x3FE35779F8C43D6E //ln(1/frcpa(1+ 212/256)
562 data8 0x3FE36621961A6A99 //ln(1/frcpa(1+ 213/256)
563 data8 0x3FE37C299F3C366A //ln(1/frcpa(1+ 214/256)
564 data8 0x3FE38AE2171976E7 //ln(1/frcpa(1+ 215/256)
565 data8 0x3FE399A157A603E7 //ln(1/frcpa(1+ 216/256)
566 data8 0x3FE3AFCCFE77B9D1 //ln(1/frcpa(1+ 217/256)
567 data8 0x3FE3BE9D503533B5 //ln(1/frcpa(1+ 218/256)
568 data8 0x3FE3CD7480B4A8A3 //ln(1/frcpa(1+ 219/256)
569 data8 0x3FE3E3C43918F76C //ln(1/frcpa(1+ 220/256)
570 data8 0x3FE3F2ACB27ED6C7 //ln(1/frcpa(1+ 221/256)
571 data8 0x3FE4019C2125CA93 //ln(1/frcpa(1+ 222/256)
572 data8 0x3FE4181061389722 //ln(1/frcpa(1+ 223/256)
573 data8 0x3FE42711518DF545 //ln(1/frcpa(1+ 224/256)
574 data8 0x3FE436194E12B6BF //ln(1/frcpa(1+ 225/256)
575 data8 0x3FE445285D68EA69 //ln(1/frcpa(1+ 226/256)
576 data8 0x3FE45BCC464C893A //ln(1/frcpa(1+ 227/256)
577 data8 0x3FE46AED21F117FC //ln(1/frcpa(1+ 228/256)
578 data8 0x3FE47A1527E8A2D3 //ln(1/frcpa(1+ 229/256)
579 data8 0x3FE489445EFFFCCC //ln(1/frcpa(1+ 230/256)
580 data8 0x3FE4A018BCB69835 //ln(1/frcpa(1+ 231/256)
581 data8 0x3FE4AF5A0C9D65D7 //ln(1/frcpa(1+ 232/256)
582 data8 0x3FE4BEA2A5BDBE87 //ln(1/frcpa(1+ 233/256)
583 data8 0x3FE4CDF28F10AC46 //ln(1/frcpa(1+ 234/256)
584 data8 0x3FE4DD49CF994058 //ln(1/frcpa(1+ 235/256)
585 data8 0x3FE4ECA86E64A684 //ln(1/frcpa(1+ 236/256)
586 data8 0x3FE503C43CD8EB68 //ln(1/frcpa(1+ 237/256)
587 data8 0x3FE513356667FC57 //ln(1/frcpa(1+ 238/256)
588 data8 0x3FE522AE0738A3D8 //ln(1/frcpa(1+ 239/256)
589 data8 0x3FE5322E26867857 //ln(1/frcpa(1+ 240/256)
590 data8 0x3FE541B5CB979809 //ln(1/frcpa(1+ 241/256)
591 data8 0x3FE55144FDBCBD62 //ln(1/frcpa(1+ 242/256)
592 data8 0x3FE560DBC45153C7 //ln(1/frcpa(1+ 243/256)
593 data8 0x3FE5707A26BB8C66 //ln(1/frcpa(1+ 244/256)
594 data8 0x3FE587F60ED5B900 //ln(1/frcpa(1+ 245/256)
595 data8 0x3FE597A7977C8F31 //ln(1/frcpa(1+ 246/256)
596 data8 0x3FE5A760D634BB8B //ln(1/frcpa(1+ 247/256)
597 data8 0x3FE5B721D295F10F //ln(1/frcpa(1+ 248/256)
598 data8 0x3FE5C6EA94431EF9 //ln(1/frcpa(1+ 249/256)
599 data8 0x3FE5D6BB22EA86F6 //ln(1/frcpa(1+ 250/256)
600 data8 0x3FE5E6938645D390 //ln(1/frcpa(1+ 251/256)
601 data8 0x3FE5F673C61A2ED2 //ln(1/frcpa(1+ 252/256)
602 data8 0x3FE6065BEA385926 //ln(1/frcpa(1+ 253/256)
603 data8 0x3FE6164BFA7CC06B //ln(1/frcpa(1+ 254/256)
604 data8 0x3FE62643FECF9743 //ln(1/frcpa(1+ 255/256)
605 //
606 // [2;4)
607 data8 0xBEB2CC7A38B9355F,0x3F035F2D1833BF4C // A10,A9
608 data8 0xBFF51BAA7FD27785,0x3FFC9D5D5B6CDEFF // A2,A1
609 data8 0xBF421676F9CB46C7,0x3F7437F2FA1436C6 // A8,A7
610 data8 0xBFD7A7041DE592FE,0x3FE9F107FEE8BD29 // A4,A3
611 // [4;8)
612 data8 0x3F6BBBD68451C0CD,0xBF966EC3272A16F7 // A10,A9
613 data8 0x40022A24A39AD769,0x4014190EDF49C8C5 // A2,A1
614 data8 0x3FB130FD016EE241,0xBFC151B46E635248 // A8,A7
615 data8 0x3FDE8F611965B5FE,0xBFEB5110EB265E3D // A4,A3
616 // [8;16)
617 data8 0x3F736EF93508626A,0xBF9FE5DBADF58AF1 // A10,A9
618 data8 0x40110A9FC5192058,0x40302008A6F96B29 // A2,A1
619 data8 0x3FB8E74E0CE1E4B5,0xBFC9B5DA78873656 // A8,A7
620 data8 0x3FE99D0DF10022DC,0xBFF829C0388F9484 // A4,A3
621 // [16;32)
622 data8 0x3F7FFF9D6D7E9269,0xBFAA780A249AEDB1 // A10,A9
623 data8 0x402082A807AEA080,0x4045ED9868408013 // A2,A1
624 data8 0x3FC4E1E54C2F99B7,0xBFD5DE2D6FFF1490 // A8,A7
625 data8 0x3FF75FC89584AE87,0xC006B4BADD886CAE // A4,A3
626 // [32;64)
627 data8 0x3F8CE54375841A5F,0xBFB801ABCFFA1BE2 // A10,A9
628 data8 0x403040A8B1815BDA,0x405B99A917D24B7A // A2,A1
629 data8 0x3FD30CAB81BFFA03,0xBFE41AEF61ECF48B // A8,A7
630 data8 0x400650CC136BEC43,0xC016022046E8292B // A4,A3
631 // [64;128)
632 data8 0x3F9B69BD22CAA8B8,0xBFC6D48875B7A213 // A10,A9
633 data8 0x40402028CCAA2F6D,0x40709AACEB3CBE0F // A2,A1
634 data8 0x3FE22C6A5924761E,0xBFF342F5F224523D // A8,A7
635 data8 0x4015CD405CCA331F,0xC025AAD10482C769 // A4,A3
636 // [128;256)
637 data8 0x3FAAAD9CD0E40D06,0xBFD63FC8505D80CB // A10,A9
638 data8 0x40501008D56C2648,0x408364794B0F4376 // A2,A1
639 data8 0x3FF1BE0126E00284,0xC002D8E3F6F7F7CA // A8,A7
640 data8 0x40258C757E95D860,0xC0357FA8FD398011 // A4,A3
641 // [256;512)
642 data8 0x3FBA4DAC59D49FEB,0xBFE5F476D1C43A77 // A10,A9
643 data8 0x40600800D890C7C6,0x40962C42AAEC8EF0 // A2,A1
644 data8 0x40018680ECF19B89,0xC012A3EB96FB7BA4 // A8,A7
645 data8 0x40356C4CDD3B60F9,0xC0456A34BF18F440 // A4,A3
646 // [512;1024)
647 data8 0x3FCA1B54F6225A5A,0xBFF5CD67BA10E048 // A10,A9
648 data8 0x407003FED94C58C2,0x40A8F30B4ACBCD22 // A2,A1
649 data8 0x40116A135EB66D8C,0xC022891B1CED527E // A8,A7
650 data8 0x40455C4617FDD8BC,0xC0555F82729E59C4 // A4,A3
651 // [1024;2048)
652 data8 0x3FD9FFF9095C6EC9,0xC005B88CB25D76C9 // A10,A9
653 data8 0x408001FE58FA734D,0x40BBB953BAABB0F3 // A2,A1
654 data8 0x40215B2F9FEB5D87,0xC0327B539DEA5058 // A8,A7
655 data8 0x40555444B3E8D64D,0xC0655A2B26F9FC8A // A4,A3
656 // [2048;4096)
657 data8 0x3FE9F065A1C3D6B1,0xC015ACF6FAE8D78D // A10,A9
658 data8 0x409000FE383DD2B7,0x40CE7F5C1E8BCB8B // A2,A1
659 data8 0x40315324E5DB2EBE,0xC04274194EF70D18 // A8,A7
660 data8 0x4065504353FF2207,0xC075577FE1BFE7B6 // A4,A3
661 // [4096;8192)
662 data8 0x3FF9E6FBC6B1C70D,0xC025A62DAF76F85D // A10,A9
663 data8 0x40A0007E2F61EBE8,0x40E0A2A23FB5F6C3 // A2,A1
664 data8 0x40414E9BC0A0141A,0xC0527030F2B69D43 // A8,A7
665 data8 0x40754E417717B45B,0xC085562A447258E5 // A4,A3
666 //
667 data8 0xbfdffffffffaea15 // P1
668 data8 0x3FDD8B618D5AF8FE // point of local minimum on [1;2]
669 data8 0x3FED67F1C864BEB5 // ln(sqrt(2*Pi))
670 data8 0x4008000000000000 // 3.0
671 //
672 data8 0xBF9E1C289FB224AB,0x3FBF7422445C9460 // A6,A5
673 data8 0xBFF01E76D66F8D8A // A0
674 data8 0xBFE2788CFC6F91DA // A1 [1.0;1.25)
675 data8 0x3FCB8CC69000EB5C,0xBFD41997A0C2C641 // A6,A5
676 data8 0x3FFCAB0BFA0EA462 // A0
677 data8 0xBFBF19B9BCC38A42 // A0 [1.25;1.5)
678 data8 0x3FD51EE4DE0A364C,0xBFE00D7F98A16E4B // A6,A5
679 data8 0x40210CE1F327E9E4 // A0
680 data8 0x4001DB08F9DFA0CC // A0 [1.5;1.75)
681 data8 0x3FE24F606742D252,0xBFEC81D7D12574EC // A6,A5
682 data8 0x403BE636A63A9C27 // A0
683 data8 0x4000A0CB38D6CF0A // A0 [1.75;2.0)
684 data8 0x3FF1029A9DD542B4,0xBFFAD37C209D3B25 // A6,A5
685 data8 0x405385E6FD9BE7EA // A0
686 data8 0x478895F1C0000000 // Overflow boundary
687 data8 0x400062D97D26B523,0xC00A03E1529FF023 // A6,A5
688 data8 0x4069204C51E566CE,0 // A0
689 data8 0x40101476B38FD501,0xC0199DE7B387C0FC // A6,A5
690 data8 0x407EB8DAEC83D759,0 // A0
691 data8 0x401FDB008D65125A,0xC0296B506E665581 // A6,A5
692 data8 0x409226D93107EF66,0 // A0
693 data8 0x402FB3EAAF3E7B2D,0xC039521142AD8E0D // A6,A5
694 data8 0x40A4EFA4F072792E,0 // A0
695 data8 0x403FA024C66B2563,0xC0494569F250E691 // A6,A5
696 data8 0x40B7B747C9235BB8,0 // A0
697 data8 0x404F9607D6DA512C,0xC0593F0B2EDDB4BC // A6,A5
698 data8 0x40CA7E29C5F16DE2,0 // A0
699 data8 0x405F90C5F613D98D,0xC0693BD130E50AAF // A6,A5
700 data8 0x40DD4495238B190C,0 // A0
701 //
702 // polynomial approximation of ln(sin(Pi*x)/(Pi*x)), |x| <= 0.5
703 data8 0xBFD58731A486E820,0xBFA4452CC28E15A9 // S16,S14
704 data8 0xBFD013F6E1B86C4F,0xBFD5B3F19F7A341F // S8,S6
705 data8 0xBFC86A0D5252E778,0xBFC93E08C9EE284B // S12,S10
706 data8 0xBFE15132555C9EDD,0xBFFA51A662480E35 // S4,S2
707 //
708 // [1.0;1.25)
709 data8 0xBFA697D6775F48EA,0x3FB9894B682A98E7 // A9,A8
710 data8 0xBFCA8969253CFF55,0x3FD15124EFB35D9D // A5,A4
711 data8 0xBFC1B00158AB719D,0x3FC5997D04E7F1C1 // A7,A6
712 data8 0xBFD9A4D50BAFF989,0x3FEA51A661F5176A // A3,A2
713 // [1.25;1.5)
714 data8 0x3F838E0D35A6171A,0xBF831BBBD61313B7 // A8,A7
715 data8 0x3FB08B40196425D0,0xBFC2E427A53EB830 // A4,A3
716 data8 0x3F9285DDDC20D6C3,0xBFA0C90C9C223044 // A6,A5
717 data8 0x3FDEF72BC8F5287C,0x3D890B3DAEBC1DFC // A2,A1
718 // [1.5;1.75)
719 data8 0x3F65D5A7EB31047F,0xBFA44EAC9BFA7FDE // A8,A7
720 data8 0x40051FEFE7A663D8,0xC012A5CFE00A2522 // A4,A3
721 data8 0x3FD0E1583AB00E08,0xBFF084AF95883BA5 // A6,A5
722 data8 0x40185982877AE0A2,0xC015F83DB73B57B7 // A2,A1
723 // [1.75;2.0)
724 data8 0x3F4A9222032EB39A,0xBF8CBC9587EEA5A3 // A8,A7
725 data8 0x3FF795400783BE49,0xC00851BC418B8A25 // A4,A3
726 data8 0x3FBBC992783E8C5B,0xBFDFA67E65E89B29 // A6,A5
727 data8 0x4012B408F02FAF88,0xC013284CE7CB0C39 // A2,A1
728 //
729 // roots
730 data8 0xC003A7FC9600F86C // -2.4570247382208005860
731 data8 0xC009260DBC9E59AF // -3.1435808883499798405
732 data8 0xC005FB410A1BD901 // -2.7476826467274126919
733 data8 0xC00FA471547C2FE5 // -3.9552942848585979085
734 //
735 // polynomial approximation of ln(GAMMA(x)) near roots
736 // near -2.4570247382208005860
737 data8 0x3FF694A6058D9592,0x40136EEBB003A92B // R3,R2
738 data8 0x3FF83FE966AF5360,0x3C90323B6D1FE86D // R1,R0
739 // near -3.1435808883499798405
740 data8 0x405C11371268DA38,0x4039D4D2977D2C23 // R3,R2
741 data8 0x401F20A65F2FAC62,0x3CDE9605E3AE7A62 // R1,R0
742 // near -2.7476826467274126919
743 data8 0xC034185AC31314FF,0x4023267F3C28DFE3 // R3,R2
744 data8 0xBFFEA12DA904B194,0x3CA8FB8530BA7689 // R1,R0
745 // near -2.7476826467274126919
746 data8 0xC0AD25359E70C888,0x406F76DEAEA1B8C6 // R3,R2
747 data8 0xC034B99D966C5644,0xBCBDDC0336980B58 // R1,R0
748 LOCAL_OBJECT_END(lgammaf_data)
750 //*********************************************************************
752 .section .text
753 GLOBAL_LIBM_ENTRY(__libm_lgammaf)
754 { .mfi
755 getf.exp GR_SignExp = f8
756 frcpa.s1 FR_InvX,p0 = f1,f8
757 mov GR_ExpOf2 = 0x10000
758 }
759 { .mfi
760 addl GR_ad_Data = @ltoff(lgammaf_data),gp
761 fcvt.fx.s1 FR_int_N = f8
762 mov GR_ExpMask = 0x1ffff
763 };;
764 { .mfi
765 getf.sig GR_Sig = f8
766 fclass.m p13,p0 = f8,0x1EF // is x NaTVal, NaN,
767 // +/-0, +/-INF or +/-deno?
768 mov GR_ExpBias = 0xffff
769 }
770 { .mfi
771 ld8 GR_ad_Data = [GR_ad_Data]
772 fma.s1 FR_Xp1 = f8,f1,f1
773 mov GR_StirlBound = 0x1000C
774 };;
775 { .mfi
776 setf.exp FR_2 = GR_ExpOf2
777 fmerge.se FR_x = f1,f8
778 dep.z GR_Ind = GR_SignExp,3,4
779 }
780 { .mfi
781 cmp.eq p8,p0 = GR_SignExp,GR_ExpBias
782 fcvt.fx.trunc.s1 FR_int_Ntrunc = f8
783 and GR_Exp = GR_ExpMask,GR_SignExp
784 };;
785 { .mfi
786 add GR_ad_C650 = 0xB20,GR_ad_Data
787 fcmp.lt.s1 p14,p15 = f8,f0
788 extr.u GR_Ind4T = GR_Sig,55,8
789 }
790 { .mfb
791 sub GR_PureExp = GR_Exp,GR_ExpBias
792 fnorm.s1 FR_NormX = f8
793 // jump if x is NaTVal, NaN, +/-0, +/-INF or +/-deno
794 (p13) br.cond.spnt lgammaf_spec
795 };;
796 lgammaf_core:
797 { .mfi
798 ldfpd FR_P1,FR_LocalMin = [GR_ad_C650],16
799 fms.s1 FR_xm2 = f8,f1,f1
800 add GR_ad_Co = 0x820,GR_ad_Data
801 }
802 { .mib
803 ldfpd FR_P3,FR_P2 = [GR_ad_Data],16
804 cmp.ltu p9,p0 = GR_SignExp,GR_ExpBias
805 // jump if x is from the interval [1; 2)
806 (p8) br.cond.spnt lgammaf_1_2
807 };;
808 { .mfi
809 setf.sig FR_int_Ln = GR_PureExp
810 fms.s1 FR_r = FR_InvX,f8,f1
811 shladd GR_ad_Co = GR_Ind,3,GR_ad_Co
812 }
813 { .mib
814 ldfpd FR_LnSqrt2Pi,FR_3 = [GR_ad_C650],16
815 cmp.lt p13,p12 = GR_Exp,GR_StirlBound
816 // jump if x is from the interval (0; 1)
817 (p9) br.cond.spnt lgammaf_0_1
818 };;
819 { .mfi
820 ldfpd FR_Ln2,FR_05 = [GR_ad_Data],16
821 fma.s1 FR_Xp2 = f1,f1,FR_Xp1 // (x+2)
822 shladd GR_ad_C650 = GR_Ind,2,GR_ad_C650
823 }
824 { .mfi
825 add GR_ad_Ce = 0x20,GR_ad_Co
826 nop.f 0
827 add GR_ad_C43 = 0x30,GR_ad_Co
828 };;
829 { .mfi
830 // load coefficients of polynomial approximation
831 // of ln(GAMMA(x)), 2 <= x < 2^13
832 (p13) ldfpd FR_A10,FR_A9 = [GR_ad_Co],16
833 fcvt.xf FR_N = FR_int_N
834 cmp.eq.unc p6,p7 = GR_ExpOf2,GR_SignExp
835 }
836 { .mib
837 (p13) ldfpd FR_A8,FR_A7 = [GR_ad_Ce]
838 (p14) cmp.le.unc p9,p0 = GR_StirlBound,GR_Exp
839 // jump if x is less or equal to -2^13
840 (p9) br.cond.spnt lgammaf_negstirling
841 };;
842 .pred.rel "mutex",p6,p7
843 { .mfi
844 (p13) ldfpd FR_A6,FR_A5 = [GR_ad_C650],16
845 (p6) fma.s1 FR_x = f0,f0,FR_NormX
846 shladd GR_ad_T = GR_Ind4T,3,GR_ad_Data
847 }
848 { .mfi
849 (p13) ldfpd FR_A4,FR_A3 = [GR_ad_C43]
850 (p7) fms.s1 FR_x = FR_x,f1,f1
851 (p14) mov GR_ReqBound = 0x20005
852 };;
853 { .mfi
854 (p13) ldfpd FR_A2,FR_A1 = [GR_ad_Co],16
855 fms.s1 FR_xm2 = FR_xm2,f1,f1
856 (p14) extr.u GR_Arg = GR_Sig,60,4
857 }
858 { .mfi
859 mov GR_SignOfGamma = 1 // set sign of gamma(x) to 1
860 fcvt.xf FR_Ntrunc = FR_int_Ntrunc
861 nop.i 0
862 };;
863 { .mfi
864 ldfd FR_T = [GR_ad_T]
865 fma.s1 FR_r2 = FR_r,FR_r,f0
866 shl GR_ReqBound = GR_ReqBound,3
867 }
868 { .mfi
869 add GR_ad_Co = 0xCA0,GR_ad_Data
870 fnma.s1 FR_Req = FR_Xp1,FR_NormX,f0 // -x*(x+1)
871 (p14) shladd GR_Arg = GR_Exp,4,GR_Arg
872 };;
873 { .mfi
874 (p13) ldfd FR_A0 = [GR_ad_C650]
875 fma.s1 FR_Xp3 = FR_2,f1,FR_Xp1 // (x+3)
876 (p14) cmp.le.unc p9,p0 = GR_Arg,GR_ReqBound
877 }
878 { .mfi
879 (p14) add GR_ad_Ce = 0x20,GR_ad_Co
880 fma.s1 FR_Xp4 = FR_2,FR_2,FR_NormX // (x+4)
881 (p15) add GR_ad_OvfBound = 0xBB8,GR_ad_Data
882 };;
883 { .mfi
884 // load coefficients of polynomial approximation
885 // of ln(sin(Pi*xf)/(Pi*xf)), |xf| <= 0.5
886 (p14) ldfpd FR_S16,FR_S14 = [GR_ad_Co],16
887 (p14) fms.s1 FR_Xf = FR_NormX,f1,FR_N // xf = x - [x]
888 (p14) sub GR_SignOfGamma = r0,GR_SignOfGamma // set sign of
889 // gamma(x) to -1
890 }
891 { .mfb
892 (p14) ldfpd FR_S12,FR_S10 = [GR_ad_Ce],16
893 fma.s1 FR_Xp5 = FR_2,FR_2,FR_Xp1 // (x+5)
894 // jump if x is from the interval (-9; 0)
895 (p9) br.cond.spnt lgammaf_negrecursion
896 };;
897 { .mfi
898 (p14) ldfpd FR_S8,FR_S6 = [GR_ad_Co],16
899 fma.s1 FR_P32 = FR_P3,FR_r,FR_P2
900 nop.i 0
901 }
902 { .mfb
903 (p14) ldfpd FR_S4,FR_S2 = [GR_ad_Ce],16
904 fma.s1 FR_x2 = FR_x,FR_x,f0
905 // jump if x is from the interval (-2^13; -9)
906 (p14) br.cond.spnt lgammaf_negpoly
907 };;
908 { .mfi
909 ldfd FR_OverflowBound = [GR_ad_OvfBound]
910 (p12) fcvt.xf FR_N = FR_int_Ln
911 // set p9 if signgum is 32-bit int
912 // set p10 if signgum is 64-bit int
913 cmp.eq p10,p9 = 8,r34
914 }
915 { .mfi
916 nop.m 0
917 (p12) fma.s1 FR_P10 = FR_P1,FR_r,f1
918 nop.i 0
919 };;
920 .pred.rel "mutex",p6,p7
921 .pred.rel "mutex",p9,p10
922 { .mfi
923 // store sign of gamma(x) as 32-bit int
924 (p9) st4 [r33] = GR_SignOfGamma
925 (p6) fma.s1 FR_xx = FR_x,FR_xm2,f0
926 nop.i 0
927 }
928 { .mfi
929 // store sign of gamma(x) as 64-bit int
930 (p10) st8 [r33] = GR_SignOfGamma
931 (p7) fma.s1 FR_xx = f0,f0,FR_x
932 nop.i 0
933 };;
934 { .mfi
935 nop.m 0
936 (p13) fma.s1 FR_A9 = FR_A10,FR_x,FR_A9
937 nop.i 0
938 }
939 { .mfi
940 nop.m 0
941 (p13) fma.s1 FR_A7 = FR_A8,FR_x,FR_A7
942 nop.i 0
943 };;
944 { .mfi
945 nop.m 0
946 (p13) fma.s1 FR_A5 = FR_A6,FR_x,FR_A5
947 nop.i 0
948 }
949 { .mfi
950 nop.m 0
951 (p13) fma.s1 FR_A3 = FR_A4,FR_x,FR_A3
952 nop.i 0
953 };;
954 { .mfi
955 nop.m 0
956 (p15) fcmp.eq.unc.s1 p8,p0 = FR_NormX,FR_2 // is input argument 2.0?
957 nop.i 0
958 }
959 { .mfi
960 nop.m 0
961 (p13) fma.s1 FR_A1 = FR_A2,FR_x,FR_A1
962 nop.i 0
963 };;
964 { .mfi
965 nop.m 0
966 (p12) fma.s1 FR_T = FR_N,FR_Ln2,FR_T
967 nop.i 0
968 }
969 { .mfi
970 nop.m 0
971 (p12) fma.s1 FR_P32 = FR_P32,FR_r2,FR_P10
972 nop.i 0
973 };;
974 { .mfi
975 nop.m 0
976 (p13) fma.s1 FR_x4 = FR_x2,FR_x2,f0
977 nop.i 0
978 }
979 { .mfi
980 nop.m 0
981 (p13) fma.s1 FR_x3 = FR_x2,FR_xx,f0
982 nop.i 0
983 };;
984 { .mfi
985 nop.m 0
986 (p13) fma.s1 FR_A7 = FR_A9,FR_x2,FR_A7
987 nop.i 0
988 }
989 { .mfb
990 nop.m 0
991 (p8) fma.s.s0 f8 = f0,f0,f0
992 (p8) br.ret.spnt b0 // fast exit for 2.0
993 };;
994 { .mfi
995 nop.m 0
996 (p6) fma.s1 FR_A0 = FR_A0,FR_xm2,f0
997 nop.i 0
998 }
999 { .mfi
1000 nop.m 0
1001 (p13) fma.s1 FR_A3 = FR_A5,FR_x2,FR_A3
1002 nop.i 0
1003 };;
1004 { .mfi
1005 nop.m 0
1006 (p15) fcmp.le.unc.s1 p8,p0 = FR_OverflowBound,FR_NormX // overflow test
1007 nop.i 0
1008 }
1009 { .mfi
1010 nop.m 0
1011 (p12) fms.s1 FR_xm05 = FR_NormX,f1,FR_05
1012 nop.i 0
1013 };;
1014 { .mfi
1015 nop.m 0
1016 (p12) fma.s1 FR_Ln = FR_P32,FR_r,FR_T
1017 nop.i 0
1018 }
1019 { .mfi
1020 nop.m 0
1021 (p12) fms.s1 FR_LnSqrt2Pi = FR_LnSqrt2Pi,f1,FR_NormX
1022 nop.i 0
1023 };;
1024 { .mfi
1025 nop.m 0
1026 (p13) fma.s1 FR_A0 = FR_A1,FR_xx,FR_A0
1027 nop.i 0
1028 }
1029 { .mfb
1030 nop.m 0
1031 (p13) fma.s1 FR_A3 = FR_A7,FR_x4,FR_A3
1032 // jump if result overflows
1033 (p8) br.cond.spnt lgammaf_overflow
1034 };;
1035 .pred.rel "mutex",p12,p13
1036 { .mfi
1037 nop.m 0
1038 (p12) fma.s.s0 f8 = FR_Ln,FR_xm05,FR_LnSqrt2Pi
1039 nop.i 0
1040 }
1041 { .mfb
1042 nop.m 0
1043 (p13) fma.s.s0 f8 = FR_A3,FR_x3,FR_A0
1044 br.ret.sptk b0
1045 };;
1046 // branch for calculating of ln(GAMMA(x)) for 0 < x < 1
1047 //---------------------------------------------------------------------
1048 .align 32
1049 lgammaf_0_1:
1050 { .mfi
1051 getf.sig GR_Ind = FR_Xp1
1052 fma.s1 FR_r2 = FR_r,FR_r,f0
1053 mov GR_fff7 = 0xFFF7
1054 }
1055 { .mfi
1056 ldfpd FR_Ln2,FR_05 = [GR_ad_Data],16
1057 fma.s1 FR_P32 = FR_P3,FR_r,FR_P2
1058 // input argument cann't be equal to 1.0
1059 cmp.eq p0,p14 = r0,r0
1060 };;
1061 { .mfi
1062 getf.exp GR_Exp = FR_w
1063 fcvt.xf FR_N = FR_int_Ln
1064 add GR_ad_Co = 0xCE0,GR_ad_Data
1065 }
1066 { .mfi
1067 shladd GR_ad_T = GR_Ind4T,3,GR_ad_Data
1068 fma.s1 FR_P10 = FR_P1,FR_r,f1
1069 add GR_ad_Ce = 0xD00,GR_ad_Data
1070 };;
1071 { .mfi
1072 ldfd FR_T = [GR_ad_T]
1073 fma.s1 FR_w2 = FR_w,FR_w,f0
1074 extr.u GR_Ind = GR_Ind,61,2
1075 }
1076 { .mfi
1077 nop.m 0
1078 fma.s1 FR_Q32 = FR_P3,FR_w,FR_P2
1079 //// add GR_ad_C0 = 0xB30,GR_ad_Data
1080 add GR_ad_C0 = 0xB38,GR_ad_Data
1081 };;
1082 { .mfi
1083 and GR_Exp = GR_Exp,GR_ExpMask
1084 nop.f 0
1085 shladd GR_IndX8 = GR_Ind,3,r0
1086 }
1087 { .mfi
1088 shladd GR_IndX2 = GR_Ind,1,r0
1089 fma.s1 FR_Q10 = FR_P1,FR_w,f1
1090 cmp.eq p6,p15 = 0,GR_Ind
1091 };;
1092 { .mfi
1093 shladd GR_ad_Co = GR_IndX8,3,GR_ad_Co
1094 (p6) fma.s1 FR_x = f0,f0,FR_NormX
1095 shladd GR_ad_C0 = GR_IndX2,4,GR_ad_C0
1096 }
1097 { .mfi
1098 shladd GR_ad_Ce = GR_IndX8,3,GR_ad_Ce
1099 nop.f 0
1100 (p15) cmp.eq.unc p7,p8 = 1,GR_Ind
1101 };;
1102 .pred.rel "mutex",p7,p8
1103 { .mfi
1104 ldfpd FR_A8,FR_A7 = [GR_ad_Co],16
1105 (p7) fms.s1 FR_x = FR_NormX,f1,FR_LocalMin
1106 cmp.ge p10,p11 = GR_Exp,GR_fff7
1107 }
1108 { .mfb
1109 ldfpd FR_A6,FR_A5 = [GR_ad_Ce],16
1110 (p8) fma.s1 FR_x = f1,f1,FR_NormX
1111 br.cond.sptk lgamma_0_2_core
1112 };;
1113 // branch for calculating of ln(GAMMA(x)) for 1 <= x < 2
1114 //---------------------------------------------------------------------
1115 .align 32
1116 lgammaf_1_2:
1117 { .mfi
1118 add GR_ad_Co = 0xCF0,GR_ad_Data
1119 fcmp.eq.s1 p14,p0 = f1,FR_NormX // is input argument 1.0?
1120 extr.u GR_Ind = GR_Sig,61,2
1121 }
1122 { .mfi
1123 add GR_ad_Ce = 0xD10,GR_ad_Data
1124 nop.f 0
1125 //// add GR_ad_C0 = 0xB40,GR_ad_Data
1126 add GR_ad_C0 = 0xB48,GR_ad_Data
1127 };;
1128 { .mfi
1129 shladd GR_IndX8 = GR_Ind,3,r0
1130 nop.f 0
1131 shladd GR_IndX2 = GR_Ind,1,r0
1132 }
1133 { .mfi
1134 cmp.eq p6,p15 = 0,GR_Ind // p6 <- x from [1;1.25)
1135 nop.f 0
1136 cmp.ne p9,p0 = r0,r0
1137 };;
1138 { .mfi
1139 shladd GR_ad_Co = GR_IndX8,3,GR_ad_Co
1140 (p6) fms.s1 FR_x = FR_NormX,f1,f1 // reduced x for [1;1.25)
1141 shladd GR_ad_C0 = GR_IndX2,4,GR_ad_C0
1142 }
1143 { .mfi
1144 shladd GR_ad_Ce = GR_IndX8,3,GR_ad_Ce
1145 (p14) fma.s.s0 f8 = f0,f0,f0
1146 (p15) cmp.eq.unc p7,p8 = 1,GR_Ind // p7 <- x from [1.25;1.5)
1147 };;
1148 .pred.rel "mutex",p7,p8
1149 { .mfi
1150 ldfpd FR_A8,FR_A7 = [GR_ad_Co],16
1151 (p7) fms.s1 FR_x = FR_xm2,f1,FR_LocalMin
1152 nop.i 0
1153 }
1154 { .mfi
1155 ldfpd FR_A6,FR_A5 = [GR_ad_Ce],16
1156 (p8) fma.s1 FR_x = f0,f0,FR_NormX
1157 (p9) cmp.eq.unc p10,p11 = r0,r0
1158 };;
1159 lgamma_0_2_core:
1160 { .mmi
1161 ldfpd FR_A4,FR_A3 = [GR_ad_Co],16
1162 ldfpd FR_A2,FR_A1 = [GR_ad_Ce],16
1163 mov GR_SignOfGamma = 1 // set sign of gamma(x) to 1
1164 };;
1165 { .mfi
1166 // add GR_ad_C0 = 8,GR_ad_C0
1167 ldfd FR_A0 = [GR_ad_C0]
1168 nop.f 0
1169 // set p13 if signgum is 32-bit int
1170 // set p15 if signgum is 64-bit int
1171 cmp.eq p15,p13 = 8,r34
1172 };;
1173 .pred.rel "mutex",p13,p15
1174 { .mmf
1175 // store sign of gamma(x)
1176 (p13) st4 [r33] = GR_SignOfGamma // as 32-bit int
1177 (p15) st8 [r33] = GR_SignOfGamma // as 64-bit int
1178 (p11) fma.s1 FR_Q32 = FR_Q32,FR_w2,FR_Q10
1179 };;
1180 { .mfb
1181 nop.m 0
1182 (p10) fma.s1 FR_P32 = FR_P32,FR_r2,FR_P10
1183 (p14) br.ret.spnt b0 // fast exit for 1.0
1184 };;
1185 { .mfi
1186 nop.m 0
1187 (p10) fma.s1 FR_T = FR_N,FR_Ln2,FR_T
1188 cmp.eq p6,p7 = 0,GR_Ind // p6 <- x from [1;1.25)
1189 }
1190 { .mfi
1191 nop.m 0
1192 fma.s1 FR_x2 = FR_x,FR_x,f0
1193 cmp.eq p8,p0 = r0,r0 // set p8 to 1 that means we on [1;2]
1194 };;
1195 { .mfi
1196 nop.m 0
1197 (p11) fma.s1 FR_Ln = FR_Q32,FR_w,f0
1198 nop.i 0
1199 }
1200 { .mfi
1201 nop.m 0
1202 nop.f 0
1203 nop.i 0
1204 };;
1205 .pred.rel "mutex",p6,p7
1206 { .mfi
1207 nop.m 0
1208 (p6) fma.s1 FR_xx = f0,f0,FR_x
1209 nop.i 0
1210 }
1211 { .mfi
1212 nop.m 0
1213 (p7) fma.s1 FR_xx = f0,f0,f1
1214 nop.i 0
1215 };;
1216 { .mfi
1217 nop.m 0
1218 fma.s1 FR_A7 = FR_A8,FR_x,FR_A7
1219 nop.i 0
1220 }
1221 { .mfi
1222 nop.m 0
1223 fma.s1 FR_A5 = FR_A6,FR_x,FR_A5
1224 (p9) cmp.ne p8,p0 = r0,r0 // set p8 to 0 that means we on [0;1]
1225 };;
1226 { .mfi
1227 nop.m 0
1228 fma.s1 FR_A3 = FR_A4,FR_x,FR_A3
1229 nop.i 0
1230 }
1231 { .mfi
1232 nop.m 0
1233 fma.s1 FR_A1 = FR_A2,FR_x,FR_A1
1234 nop.i 0
1235 };;
1236 { .mfi
1237 nop.m 0
1238 fma.s1 FR_x4 = FR_x2,FR_x2,f0
1239 nop.i 0
1240 }
1241 { .mfi
1242 nop.m 0
1243 (p10) fma.s1 FR_Ln = FR_P32,FR_r,FR_T
1244 nop.i 0
1245 };;
1246 { .mfi
1247 nop.m 0
1248 fma.s1 FR_A5 = FR_A7,FR_x2,FR_A5
1249 nop.i 0
1250 }
1251 { .mfi
1252 nop.m 0
1253 fma.s1 FR_A1 = FR_A3,FR_x2,FR_A1
1254 nop.i 0
1255 };;
1256 .pred.rel "mutex",p9,p8
1257 { .mfi
1258 nop.m 0
1259 (p9) fms.d.s1 FR_A0 = FR_A0,FR_xx,FR_Ln
1260 nop.i 0
1261 }
1262 { .mfi
1263 nop.m 0
1264 (p8) fms.s1 FR_A0 = FR_A0,FR_xx,f0
1265 nop.i 0
1266 };;
1267 { .mfi
1268 nop.m 0
1269 fma.d.s1 FR_A1 = FR_A5,FR_x4,FR_A1
1270 nop.i 0
1271 }
1272 { .mfi
1273 nop.m 0
1274 nop.f 0
1275 nop.i 0
1276 };;
1277 .pred.rel "mutex",p6,p7
1278 { .mfi
1279 nop.m 0
1280 (p6) fma.s.s0 f8 = FR_A1,FR_x2,FR_A0
1281 nop.i 0
1282 }
1283 { .mfb
1284 nop.m 0
1285 (p7) fma.s.s0 f8 = FR_A1,FR_x,FR_A0
1286 br.ret.sptk b0
1287 };;
1288 // branch for calculating of ln(GAMMA(x)) for -9 < x < 1
1289 //---------------------------------------------------------------------
1290 .align 32
1291 lgammaf_negrecursion:
1292 { .mfi
1293 getf.sig GR_N = FR_int_Ntrunc
1294 fms.s1 FR_1pXf = FR_Xp2,f1,FR_Ntrunc // 1 + (x+1) - [x]
1295 mov GR_Neg2 = 2
1296 }
1297 { .mfi
1298 add GR_ad_Co = 0xCE0,GR_ad_Data
1299 fms.s1 FR_Xf = FR_Xp1,f1,FR_Ntrunc // (x+1) - [x]
1300 mov GR_Neg4 = 4
1301 };;
1302 { .mfi
1303 add GR_ad_Ce = 0xD00,GR_ad_Data
1304 fma.s1 FR_Xp6 = FR_2,FR_2,FR_Xp2 // (x+6)
1305 add GR_ad_C0 = 0xB30,GR_ad_Data
1306 }
1307 { .mfi
1308 sub GR_Neg2 = r0,GR_Neg2
1309 fma.s1 FR_Xp7 = FR_2,FR_3,FR_Xp1 // (x+7)
1310 sub GR_Neg4 = r0,GR_Neg4
1311 };;
1312 { .mfi
1313 cmp.ne p8,p0 = r0,GR_N
1314 fcmp.eq.s1 p13,p0 = FR_NormX,FR_Ntrunc
1315 and GR_IntNum = 0xF,GR_N
1316 }
1317 { .mfi
1318 cmp.lt p6,p0 = GR_N,GR_Neg2
1319 fma.s1 FR_Xp8 = FR_2,FR_3,FR_Xp2 // (x+8)
1320 cmp.lt p7,p0 = GR_N,GR_Neg4
1321 };;
1322 { .mfi
1323 getf.d GR_Arg = FR_NormX
1324 (p6) fma.s1 FR_Xp2 = FR_Xp2,FR_Xp3,f0
1325 (p8) tbit.z.unc p14,p15 = GR_IntNum,0
1326 }
1327 { .mfi
1328 sub GR_RootInd = 0xE,GR_IntNum
1329 (p7) fma.s1 FR_Xp4 = FR_Xp4,FR_Xp5,f0
1330 add GR_ad_Root = 0xDE0,GR_ad_Data
1331 };;
1332 { .mfi
1333 shladd GR_ad_Root = GR_RootInd,3,GR_ad_Root
1334 fms.s1 FR_x = FR_Xp1,f1,FR_Ntrunc // (x+1) - [x]
1335 nop.i 0
1336 }
1337 { .mfb
1338 nop.m 0
1339 nop.f 0
1340 (p13) br.cond.spnt lgammaf_singularity
1341 };;
1342 .pred.rel "mutex",p14,p15
1343 { .mfi
1344 cmp.gt p6,p0 = 0xA,GR_IntNum
1345 (p14) fma.s1 FR_Req = FR_Req,FR_Xf,f0
1346 cmp.gt p7,p0 = 0xD,GR_IntNum
1347 }
1348 { .mfi
1349 (p15) mov GR_SignOfGamma = 1 // set sign of gamma(x) to 1
1350 (p15) fnma.s1 FR_Req = FR_Req,FR_Xf,f0
1351 cmp.leu p0,p13 = 2,GR_RootInd
1352 };;
1353 { .mfi
1354 nop.m 0
1355 (p6) fma.s1 FR_Xp6 = FR_Xp6,FR_Xp7,f0
1356 (p13) add GR_ad_RootCo = 0xE00,GR_ad_Data
1357 };;
1358 { .mfi
1359 nop.m 0
1360 fcmp.eq.s1 p12,p11 = FR_1pXf,FR_2
1361 nop.i 0
1362 };;
1363 { .mfi
1364 getf.sig GR_Sig = FR_1pXf
1365 fcmp.le.s1 p9,p0 = FR_05,FR_Xf
1366 nop.i 0
1367 }
1368 { .mfi
1369 (p13) shladd GR_RootInd = GR_RootInd,4,r0
1370 (p7) fma.s1 FR_Xp2 = FR_Xp2,FR_Xp4,f0
1371 (p8) cmp.gt.unc p10,p0 = 0x9,GR_IntNum
1372 };;
1373 .pred.rel "mutex",p11,p12
1374 { .mfi
1375 nop.m 0
1376 (p10) fma.s1 FR_Req = FR_Req,FR_Xp8,f0
1377 (p11) extr.u GR_Ind = GR_Sig,61,2
1378 }
1379 { .mfi
1380 (p13) add GR_RootInd = GR_RootInd,GR_RootInd
1381 nop.f 0
1382 (p12) mov GR_Ind = 3
1383 };;
1384 { .mfi
1385 shladd GR_IndX2 = GR_Ind,1,r0
1386 nop.f 0
1387 cmp.gt p14,p0 = 2,GR_Ind
1388 }
1389 { .mfi
1390 shladd GR_IndX8 = GR_Ind,3,r0
1391 nop.f 0
1392 cmp.eq p6,p0 = 1,GR_Ind
1393 };;
1394 .pred.rel "mutex",p6,p9
1395 { .mfi
1396 shladd GR_ad_Co = GR_IndX8,3,GR_ad_Co
1397 (p6) fms.s1 FR_x = FR_Xf,f1,FR_LocalMin
1398 cmp.gt p10,p0 = 0xB,GR_IntNum
1399 }
1400 { .mfi
1401 shladd GR_ad_Ce = GR_IndX8,3,GR_ad_Ce
1402 (p9) fma.s1 FR_x = f0,f0,FR_1pXf
1403 shladd GR_ad_C0 = GR_IndX2,4,GR_ad_C0
1404 };;
1405 { .mfi
1406 // load coefficients of polynomial approximation
1407 // of ln(GAMMA(x)), 1 <= x < 2
1408 ldfpd FR_A8,FR_A7 = [GR_ad_Co],16
1409 (p10) fma.s1 FR_Xp2 = FR_Xp2,FR_Xp6,f0
1410 add GR_ad_C0 = 8,GR_ad_C0
1411 }
1412 { .mfi
1413 ldfpd FR_A6,FR_A5 = [GR_ad_Ce],16
1414 nop.f 0
1415 (p14) add GR_ad_Root = 0x10,GR_ad_Root
1416 };;
1417 { .mfi
1418 ldfpd FR_A4,FR_A3 = [GR_ad_Co],16
1419 nop.f 0
1420 add GR_ad_RootCe = 0xE10,GR_ad_Data
1421 }
1422 { .mfi
1423 ldfpd FR_A2,FR_A1 = [GR_ad_Ce],16
1424 nop.f 0
1425 (p14) add GR_RootInd = 0x40,GR_RootInd
1426 };;
1427 { .mmi
1428 ldfd FR_A0 = [GR_ad_C0]
1429 (p13) add GR_ad_RootCo = GR_ad_RootCo,GR_RootInd
1430 (p13) add GR_ad_RootCe = GR_ad_RootCe,GR_RootInd
1431 };;
1432 { .mmi
1433 (p13) ld8 GR_Root = [GR_ad_Root]
1434 (p13) ldfd FR_Root = [GR_ad_Root]
1435 mov GR_ExpBias = 0xffff
1436 };;
1437 { .mfi
1438 nop.m 0
1439 fma.s1 FR_x2 = FR_x,FR_x,f0
1440 nop.i 0
1441 }
1442 { .mlx
1443 (p8) cmp.gt.unc p10,p0 = 0xF,GR_IntNum
1444 movl GR_Dx = 0x000000014F8B588E
1445 };;
1446 { .mfi
1447 // load coefficients of polynomial approximation
1448 // of ln(GAMMA(x)), x is close to one of negative roots
1449 (p13) ldfpd FR_R3,FR_R2 = [GR_ad_RootCo]
1450 // argumenth for logarithm
1451 (p10) fma.s1 FR_Req = FR_Req,FR_Xp2,f0
1452 mov GR_ExpMask = 0x1ffff
1453 }
1454 { .mfi
1455 (p13) ldfpd FR_R1,FR_R0 = [GR_ad_RootCe]
1456 nop.f 0
1457 // set p9 if signgum is 32-bit int
1458 // set p8 if signgum is 64-bit int
1459 cmp.eq p8,p9 = 8,r34
1460 };;
1461 .pred.rel "mutex",p9,p8
1462 { .mfi
1463 (p9) st4 [r33] = GR_SignOfGamma // as 32-bit int
1464 fma.s1 FR_A7 = FR_A8,FR_x,FR_A7
1465 (p13) sub GR_Root = GR_Arg,GR_Root
1466 }
1467 { .mfi
1468 (p8) st8 [r33] = GR_SignOfGamma // as 64-bit int
1469 fma.s1 FR_A5 = FR_A6,FR_x,FR_A5
1470 nop.i 0
1471 };;
1472 { .mfi
1473 nop.m 0
1474 fms.s1 FR_w = FR_Req,f1,f1
1475 (p13) add GR_Root = GR_Root,GR_Dx
1476 }
1477 { .mfi
1478 nop.m 0
1479 nop.f 0
1480 (p13) add GR_2xDx = GR_Dx,GR_Dx
1481 };;
1482 { .mfi
1483 nop.m 0
1484 fma.s1 FR_A3 = FR_A4,FR_x,FR_A3
1485 nop.i 0
1486 }
1487 { .mfi
1488 nop.m 0
1489 fma.s1 FR_A1 = FR_A2,FR_x,FR_A1
1490 (p13) cmp.leu.unc p10,p0 = GR_Root,GR_2xDx
1491 };;
1492 { .mfi
1493 nop.m 0
1494 frcpa.s1 FR_InvX,p0 = f1,FR_Req
1495 nop.i 0
1496 }
1497 { .mfi
1498 nop.m 0
1499 (p10) fms.s1 FR_rx = FR_NormX,f1,FR_Root
1500 nop.i 0
1501 };;
1502 { .mfi
1503 getf.exp GR_SignExp = FR_Req
1504 fma.s1 FR_x4 = FR_x2,FR_x2,f0
1505 nop.i 0
1506 };;
1507 { .mfi
1508 getf.sig GR_Sig = FR_Req
1509 fma.s1 FR_A5 = FR_A7,FR_x2,FR_A5
1510 nop.i 0
1511 };;
1512 { .mfi
1513 sub GR_PureExp = GR_SignExp,GR_ExpBias
1514 fma.s1 FR_w2 = FR_w,FR_w,f0
1515 nop.i 0
1516 }
1517 { .mfi
1518 nop.m 0
1519 fma.s1 FR_Q32 = FR_P3,FR_w,FR_P2
1520 nop.i 0
1521 };;
1522 { .mfi
1523 setf.sig FR_int_Ln = GR_PureExp
1524 fma.s1 FR_A1 = FR_A3,FR_x2,FR_A1
1525 extr.u GR_Ind4T = GR_Sig,55,8
1526 }
1527 { .mfi
1528 nop.m 0
1529 fma.s1 FR_Q10 = FR_P1,FR_w,f1
1530 nop.i 0
1531 };;
1532 { .mfi
1533 shladd GR_ad_T = GR_Ind4T,3,GR_ad_Data
1534 fms.s1 FR_r = FR_InvX,FR_Req,f1
1535 nop.i 0
1536 }
1537 { .mfi
1538 nop.m 0
1539 (p10) fms.s1 FR_rx2 = FR_rx,FR_rx,f0
1540 nop.i 0
1541 };;
1542 { .mfi
1543 ldfd FR_T = [GR_ad_T]
1544 (p10) fma.s1 FR_R2 = FR_R3,FR_rx,FR_R2
1545 nop.i 0
1546 }
1547 { .mfi
1548 nop.m 0
1549 (p10) fma.s1 FR_R0 = FR_R1,FR_rx,FR_R0
1550 nop.i 0
1551 };;
1552 { .mfi
1553 getf.exp GR_Exp = FR_w
1554 fma.s1 FR_A1 = FR_A5,FR_x4,FR_A1
1555 mov GR_ExpMask = 0x1ffff
1556 }
1557 { .mfi
1558 nop.m 0
1559 fma.s1 FR_Q32 = FR_Q32, FR_w2,FR_Q10
1560 nop.i 0
1561 };;
1562 { .mfi
1563 nop.m 0
1564 fma.s1 FR_r2 = FR_r,FR_r,f0
1565 mov GR_fff7 = 0xFFF7
1566 }
1567 { .mfi
1568 nop.m 0
1569 fma.s1 FR_P32 = FR_P3,FR_r,FR_P2
1570 nop.i 0
1571 };;
1572 { .mfi
1573 nop.m 0
1574 fma.s1 FR_P10 = FR_P1,FR_r,f1
1575 and GR_Exp = GR_ExpMask,GR_Exp
1576 }
1577 { .mfb
1578 nop.m 0
1579 (p10) fma.s.s0 f8 = FR_R2,FR_rx2,FR_R0
1580 (p10) br.ret.spnt b0 // exit for arguments close to negative roots
1581 };;
1582 { .mfi
1583 nop.m 0
1584 fcvt.xf FR_N = FR_int_Ln
1585 nop.i 0
1586 }
1587 { .mfi
1588 cmp.ge p14,p15 = GR_Exp,GR_fff7
1589 nop.f 0
1590 nop.i 0
1591 };;
1592 { .mfi
1593 nop.m 0
1594 fma.s1 FR_A0 = FR_A1,FR_x,FR_A0
1595 nop.i 0
1596 }
1597 { .mfi
1598 nop.m 0
1599 (p15) fma.s1 FR_Ln = FR_Q32,FR_w,f0
1600 nop.i 0
1601 };;
1602 { .mfi
1603 nop.m 0
1604 (p14) fma.s1 FR_P32 = FR_P32,FR_r2,FR_P10
1605 cmp.eq p6,p7 = 0,GR_Ind
1606 };;
1607 { .mfi
1608 nop.m 0
1609 (p14) fma.s1 FR_T = FR_N,FR_Ln2,FR_T
1610 nop.i 0
1611 };;
1612 { .mfi
1613 nop.m 0
1614 (p14) fma.s1 FR_Ln = FR_P32,FR_r,FR_T
1615 nop.i 0
1616 };;
1617 .pred.rel "mutex",p6,p7
1618 { .mfi
1619 nop.m 0
1620 (p6) fms.s.s0 f8 = FR_A0,FR_x,FR_Ln
1621 nop.i 0
1622 }
1623 { .mfb
1624 nop.m 0
1625 (p7) fms.s.s0 f8 = FR_A0,f1,FR_Ln
1626 br.ret.sptk b0
1627 };;
1629 // branch for calculating of ln(GAMMA(x)) for x < -2^13
1630 //---------------------------------------------------------------------
1631 .align 32
1632 lgammaf_negstirling:
1633 { .mfi
1634 shladd GR_ad_T = GR_Ind4T,3,GR_ad_Data
1635 fms.s1 FR_Xf = FR_NormX,f1,FR_N // xf = x - [x]
1636 mov GR_SingBound = 0x10016
1637 }
1638 { .mfi
1639 add GR_ad_Co = 0xCA0,GR_ad_Data
1640 fma.s1 FR_P32 = FR_P3,FR_r,FR_P2
1641 nop.i 0
1642 };;
1643 { .mfi
1644 ldfd FR_T = [GR_ad_T]
1645 fcvt.xf FR_int_Ln = FR_int_Ln
1646 cmp.le p6,p0 = GR_SingBound,GR_Exp
1647 }
1648 { .mfb
1649 add GR_ad_Ce = 0x20,GR_ad_Co
1650 fma.s1 FR_r2 = FR_r,FR_r,f0
1651 (p6) br.cond.spnt lgammaf_singularity
1652 };;
1653 { .mfi
1654 // load coefficients of polynomial approximation
1655 // of ln(sin(Pi*xf)/(Pi*xf)), |xf| <= 0.5
1656 ldfpd FR_S16,FR_S14 = [GR_ad_Co],16
1657 fma.s1 FR_P10 = FR_P1,FR_r,f1
1658 nop.i 0
1659 }
1660 { .mfi
1661 ldfpd FR_S12,FR_S10 = [GR_ad_Ce],16
1662 fms.s1 FR_xm05 = FR_NormX,f1,FR_05
1663 nop.i 0
1664 };;
1665 { .mmi
1666 ldfpd FR_S8,FR_S6 = [GR_ad_Co],16
1667 ldfpd FR_S4,FR_S2 = [GR_ad_Ce],16
1668 nop.i 0
1669 };;
1670 { .mfi
1671 getf.sig GR_N = FR_int_Ntrunc // signgam calculation
1672 fma.s1 FR_Xf2 = FR_Xf,FR_Xf,f0
1673 nop.i 0
1674 };;
1675 { .mfi
1676 nop.m 0
1677 frcpa.s1 FR_InvXf,p0 = f1,FR_Xf
1678 nop.i 0
1679 };;
1680 { .mfi
1681 getf.d GR_Arg = FR_Xf
1682 fcmp.eq.s1 p6,p0 = FR_NormX,FR_N
1683 mov GR_ExpBias = 0x3FF
1684 };;
1685 { .mfi
1686 nop.m 0
1687 fma.s1 FR_T = FR_int_Ln,FR_Ln2,FR_T
1688 extr.u GR_Exp = GR_Arg,52,11
1689 }
1690 { .mfi
1691 nop.m 0
1692 fma.s1 FR_P32 = FR_P32,FR_r2,FR_P10
1693 nop.i 0
1694 };;
1695 { .mfi
1696 sub GR_PureExp = GR_Exp,GR_ExpBias
1697 fma.s1 FR_S14 = FR_S16,FR_Xf2,FR_S14
1698 extr.u GR_Ind4T = GR_Arg,44,8
1699 }
1700 { .mfb
1701 mov GR_SignOfGamma = 1 // set signgam to -1
1702 fma.s1 FR_S10 = FR_S12,FR_Xf2,FR_S10
1703 (p6) br.cond.spnt lgammaf_singularity
1704 };;
1705 { .mfi
1706 setf.sig FR_int_Ln = GR_PureExp
1707 fms.s1 FR_rf = FR_InvXf,FR_Xf,f1
1708 // set p14 if GR_N is even
1709 tbit.z p14,p0 = GR_N,0
1710 }
1711 { .mfi
1712 shladd GR_ad_T = GR_Ind4T,3,GR_ad_Data
1713 fma.s1 FR_Xf4 = FR_Xf2,FR_Xf2,f0
1714 nop.i 0
1715 };;
1716 { .mfi
1717 (p14) sub GR_SignOfGamma = r0,GR_SignOfGamma // set signgam to -1
1718 fma.s1 FR_S6 = FR_S8,FR_Xf2,FR_S6
1719 nop.i 0
1720 }
1721 { .mfi
1722 // set p9 if signgum is 32-bit int
1723 // set p10 if signgum is 64-bit int
1724 cmp.eq p10,p9 = 8,r34
1725 fma.s1 FR_S2 = FR_S4,FR_Xf2,FR_S2
1726 nop.i 0
1727 };;
1728 { .mfi
1729 ldfd FR_Tf = [GR_ad_T]
1730 fma.s1 FR_Ln = FR_P32,FR_r,FR_T
1731 nop.i 0
1732 }
1733 { .mfi
1734 nop.m 0
1735 fma.s1 FR_LnSqrt2Pi = FR_LnSqrt2Pi,f1,FR_NormX
1736 nop.i 0
1737 };;
1738 .pred.rel "mutex",p9,p10
1739 { .mfi
1740 (p9) st4 [r33] = GR_SignOfGamma // as 32-bit int
1741 fma.s1 FR_rf2 = FR_rf,FR_rf,f0
1742 nop.i 0
1743 }
1744 { .mfi
1745 (p10) st8 [r33] = GR_SignOfGamma // as 64-bit int
1746 fma.s1 FR_S10 = FR_S14,FR_Xf4,FR_S10
1747 nop.i 0
1748 };;
1749 { .mfi
1750 nop.m 0
1751 fma.s1 FR_P32f = FR_P3,FR_rf,FR_P2
1752 nop.i 0
1753 }
1754 { .mfi
1755 nop.m 0
1756 fma.s1 FR_Xf8 = FR_Xf4,FR_Xf4,f0
1757 nop.i 0
1758 };;
1759 { .mfi
1760 nop.m 0
1761 fma.s1 FR_P10f = FR_P1,FR_rf,f1
1762 nop.i 0
1763 }
1764 { .mfi
1765 nop.m 0
1766 fma.s1 FR_S2 = FR_S6,FR_Xf4,FR_S2
1767 nop.i 0
1768 };;
1769 { .mfi
1770 nop.m 0
1771 fms.s1 FR_Ln = FR_Ln,FR_xm05,FR_LnSqrt2Pi
1772 nop.i 0
1773 };;
1774 { .mfi
1775 nop.m 0
1776 fcvt.xf FR_Nf = FR_int_Ln
1777 nop.i 0
1778 };;
1779 { .mfi
1780 nop.m 0
1781 fma.s1 FR_S2 = FR_S10,FR_Xf8,FR_S2
1782 nop.i 0
1783 };;
1784 { .mfi
1785 nop.m 0
1786 fma.s1 FR_Tf = FR_Nf,FR_Ln2,FR_Tf
1787 nop.i 0
1788 }
1789 { .mfi
1790 nop.m 0
1791 fma.s1 FR_P32f = FR_P32f,FR_rf2,FR_P10f // ??????
1792 nop.i 0
1793 };;
1794 { .mfi
1795 nop.m 0
1796 fnma.s1 FR_Ln = FR_S2,FR_Xf2,FR_Ln
1797 nop.i 0
1798 };;
1799 { .mfi
1800 nop.m 0
1801 fma.s1 FR_Lnf = FR_P32f,FR_rf,FR_Tf
1802 nop.i 0
1803 };;
1804 { .mfb
1805 nop.m 0
1806 fms.s.s0 f8 = FR_Ln,f1,FR_Lnf
1807 br.ret.sptk b0
1808 };;
1809 // branch for calculating of ln(GAMMA(x)) for -2^13 < x < -9
1810 //---------------------------------------------------------------------
1811 .align 32
1812 lgammaf_negpoly:
1813 { .mfi
1814 getf.d GR_Arg = FR_Xf
1815 frcpa.s1 FR_InvXf,p0 = f1,FR_Xf
1816 mov GR_ExpBias = 0x3FF
1817 }
1818 { .mfi
1819 nop.m 0
1820 fma.s1 FR_Xf2 = FR_Xf,FR_Xf,f0
1821 nop.i 0
1822 };;
1823 { .mfi
1824 getf.sig GR_N = FR_int_Ntrunc
1825 fcvt.xf FR_N = FR_int_Ln
1826 mov GR_SignOfGamma = 1
1827 }
1828 { .mfi
1829 nop.m 0
1830 fma.s1 FR_A9 = FR_A10,FR_x,FR_A9
1831 nop.i 0
1832 };;
1833 { .mfi
1834 nop.m 0
1835 fma.s1 FR_P10 = FR_P1,FR_r,f1
1836 extr.u GR_Exp = GR_Arg,52,11
1837 }
1838 { .mfi
1839 nop.m 0
1840 fma.s1 FR_x4 = FR_x2,FR_x2,f0
1841 nop.i 0
1842 };;
1843 { .mfi
1844 sub GR_PureExp = GR_Exp,GR_ExpBias
1845 fma.s1 FR_A7 = FR_A8,FR_x,FR_A7
1846 tbit.z p14,p0 = GR_N,0
1847 }
1848 { .mfi
1849 nop.m 0
1850 fma.s1 FR_A5 = FR_A6,FR_x,FR_A5
1851 nop.i 0
1852 };;
1853 { .mfi
1854 setf.sig FR_int_Ln = GR_PureExp
1855 fma.s1 FR_A3 = FR_A4,FR_x,FR_A3
1856 nop.i 0
1857 }
1858 { .mfi
1859 nop.m 0
1860 fma.s1 FR_A1 = FR_A2,FR_x,FR_A1
1861 (p14) sub GR_SignOfGamma = r0,GR_SignOfGamma
1862 };;
1863 { .mfi
1864 nop.m 0
1865 fms.s1 FR_rf = FR_InvXf,FR_Xf,f1
1866 nop.i 0
1867 }
1868 { .mfi
1869 nop.m 0
1870 fma.s1 FR_Xf4 = FR_Xf2,FR_Xf2,f0
1871 nop.i 0
1872 };;
1873 { .mfi
1874 nop.m 0
1875 fma.s1 FR_S14 = FR_S16,FR_Xf2,FR_S14
1876 nop.i 0
1877 }
1878 { .mfi
1879 nop.m 0
1880 fma.s1 FR_S10 = FR_S12,FR_Xf2,FR_S10
1881 nop.i 0
1882 };;
1883 { .mfi
1884 nop.m 0
1885 fma.s1 FR_T = FR_N,FR_Ln2,FR_T
1886 nop.i 0
1887 }
1888 { .mfi
1889 nop.m 0
1890 fma.s1 FR_P32 = FR_P32,FR_r2,FR_P10
1891 nop.i 0
1892 };;
1893 { .mfi
1894 nop.m 0
1895 fma.s1 FR_S6 = FR_S8,FR_Xf2,FR_S6
1896 extr.u GR_Ind4T = GR_Arg,44,8
1897 }
1898 { .mfi
1899 nop.m 0
1900 fma.s1 FR_S2 = FR_S4,FR_Xf2,FR_S2
1901 nop.i 0
1902 };;
1903 { .mfi
1904 nop.m 0
1905 fma.s1 FR_A7 = FR_A9,FR_x2,FR_A7
1906 nop.i 0
1907 }
1908 { .mfi
1909 shladd GR_ad_T = GR_Ind4T,3,GR_ad_Data
1910 fma.s1 FR_A3 = FR_A5,FR_x2,FR_A3
1911 nop.i 0
1912 };;
1913 { .mfi
1914 nop.m 0
1915 fma.s1 FR_Xf8 = FR_Xf4,FR_Xf4,f0
1916 nop.i 0
1917 }
1918 { .mfi
1919 nop.m 0
1920 fma.s1 FR_rf2 = FR_rf,FR_rf,f0
1921 nop.i 0
1922 };;
1923 { .mfi
1924 nop.m 0
1925 fma.s1 FR_P32f = FR_P3,FR_rf,FR_P2
1926 nop.i 0
1927 }
1928 { .mfi
1929 nop.m 0
1930 fma.s1 FR_P10f = FR_P1,FR_rf,f1
1931 nop.i 0
1932 };;
1933 { .mfi
1934 ldfd FR_Tf = [GR_ad_T]
1935 fma.s1 FR_Ln = FR_P32,FR_r,FR_T
1936 nop.i 0
1937 }
1938 { .mfi
1939 nop.m 0
1940 fma.s1 FR_A0 = FR_A1,FR_x,FR_A0
1941 nop.i 0
1942 };;
1943 { .mfi
1944 nop.m 0
1945 fma.s1 FR_S10 = FR_S14,FR_Xf4,FR_S10
1946 nop.i 0
1947 }
1948 { .mfi
1949 nop.m 0
1950 fma.s1 FR_S2 = FR_S6,FR_Xf4,FR_S2
1951 nop.i 0
1952 };;
1953 { .mfi
1954 nop.m 0
1955 fcvt.xf FR_Nf = FR_int_Ln
1956 nop.i 0
1957 }
1958 { .mfi
1959 nop.m 0
1960 fma.s1 FR_A3 = FR_A7,FR_x4,FR_A3
1961 nop.i 0
1962 };;
1963 { .mfi
1964 nop.m 0
1965 fcmp.eq.s1 p13,p0 = FR_NormX,FR_Ntrunc
1966 nop.i 0
1967 }
1968 { .mfi
1969 nop.m 0
1970 fnma.s1 FR_x3 = FR_x2,FR_x,f0 // -x^3
1971 nop.i 0
1972 };;
1973 { .mfi
1974 nop.m 0
1975 fma.s1 FR_P32f = FR_P32f,FR_rf2,FR_P10f
1976 nop.i 0
1977 };;
1978 { .mfb
1979 // set p9 if signgum is 32-bit int
1980 // set p10 if signgum is 64-bit int
1981 cmp.eq p10,p9 = 8,r34
1982 fma.s1 FR_S2 = FR_S10,FR_Xf8,FR_S2
1983 (p13) br.cond.spnt lgammaf_singularity
1984 };;
1985 .pred.rel "mutex",p9,p10
1986 { .mmf
1987 (p9) st4 [r33] = GR_SignOfGamma // as 32-bit int
1988 (p10) st8 [r33] = GR_SignOfGamma // as 64-bit int
1989 fms.s1 FR_A0 = FR_A3,FR_x3,FR_A0 // -A3*x^3-A0
1990 };;
1991 { .mfi
1992 nop.m 0
1993 fma.s1 FR_Tf = FR_Nf,FR_Ln2,FR_Tf
1994 nop.i 0
1995 };;
1996 { .mfi
1997 nop.m 0
1998 fma.s1 FR_Ln = FR_S2,FR_Xf2,FR_Ln // S2*Xf^2+Ln
1999 nop.i 0
2000 };;
2001 { .mfi
2002 nop.m 0
2003 fma.s1 FR_Lnf = FR_P32f,FR_rf,FR_Tf
2004 nop.i 0
2005 };;
2006 { .mfi
2007 nop.m 0
2008 fms.s1 FR_Ln = FR_A0,f1,FR_Ln
2009 nop.i 0
2010 };;
2011 { .mfb
2012 nop.m 0
2013 fms.s.s0 f8 = FR_Ln,f1,FR_Lnf
2014 br.ret.sptk b0
2015 };;
2016 // branch for handling +/-0, NaT, QNaN, +/-INF and denormalised numbers
2017 //---------------------------------------------------------------------
2018 .align 32
2019 lgammaf_spec:
2020 { .mfi
2021 getf.exp GR_SignExp = FR_NormX
2022 fclass.m p6,p0 = f8,0x21 // is arg +INF?
2023 mov GR_SignOfGamma = 1 // set signgam to 1
2024 };;
2025 { .mfi
2026 getf.sig GR_Sig = FR_NormX
2027 fclass.m p7,p0 = f8,0xB // is x deno?
2028 // set p11 if signgum is 32-bit int
2029 // set p12 if signgum is 64-bit int
2030 cmp.eq p12,p11 = 8,r34
2031 };;
2032 .pred.rel "mutex",p11,p12
2033 { .mfi
2034 // store sign of gamma(x) as 32-bit int
2035 (p11) st4 [r33] = GR_SignOfGamma
2036 fclass.m p8,p0 = f8,0x1C0 // is arg NaT or NaN?
2037 dep.z GR_Ind = GR_SignExp,3,4
2038 }
2039 { .mib
2040 // store sign of gamma(x) as 64-bit int
2041 (p12) st8 [r33] = GR_SignOfGamma
2042 and GR_Exp = GR_ExpMask,GR_SignExp
2043 (p6) br.ret.spnt b0 // exit for +INF
2044 };;
2045 { .mfi
2046 sub GR_PureExp = GR_Exp,GR_ExpBias
2047 fclass.m p9,p0 = f8,0x22 // is arg -INF?
2048 extr.u GR_Ind4T = GR_Sig,55,8
2049 }
2050 { .mfb
2051 nop.m 0
2052 (p7) fma.s0 FR_tmp = f1,f1,f8
2053 (p7) br.cond.sptk lgammaf_core
2054 };;
2055 { .mfb
2056 nop.m 0
2057 (p8) fms.s.s0 f8 = f8,f1,f8
2058 (p8) br.ret.spnt b0 // exit for NaT and NaN
2059 };;
2060 { .mfb
2061 nop.m 0
2062 (p9) fmerge.s f8 = f1,f8
2063 (p9) br.ret.spnt b0 // exit -INF
2064 };;
2065 // branch for handling negative integers and +/-0
2066 //---------------------------------------------------------------------
2067 .align 32
2068 lgammaf_singularity:
2069 { .mfi
2070 mov GR_SignOfGamma = 1 // set signgam to 1
2071 fclass.m p6,p0 = f8,0x6 // is x -0?
2072 mov GR_TAG = 109 // negative
2073 }
2074 { .mfi
2075 mov GR_ad_SignGam = r33
2076 fma.s1 FR_X = f0,f0,f8
2077 nop.i 0
2078 };;
2079 { .mfi
2080 nop.m 0
2081 frcpa.s0 f8,p0 = f1,f0
2082 // set p9 if signgum is 32-bit int
2083 // set p10 if signgum is 64-bit int
2084 cmp.eq p10,p9 = 8,r34
2085 }
2086 { .mib
2087 nop.m 0
2088 (p6) sub GR_SignOfGamma = r0,GR_SignOfGamma
2089 br.cond.sptk lgammaf_libm_err
2090 };;
2091 // overflow (x > OVERFLOV_BOUNDARY)
2092 //---------------------------------------------------------------------
2093 .align 32
2094 lgammaf_overflow:
2095 { .mfi
2096 nop.m 0
2097 nop.f 0
2098 mov r8 = 0x1FFFE
2099 };;
2100 { .mfi
2101 setf.exp f9 = r8
2102 fmerge.s FR_X = f8,f8
2103 mov GR_TAG = 108 // overflow
2104 };;
2105 { .mfi
2106 mov GR_ad_SignGam = r33
2107 nop.f 0
2108 // set p9 if signgum is 32-bit int
2109 // set p10 if signgum is 64-bit int
2110 cmp.eq p10,p9 = 8,r34
2111 }
2112 { .mfi
2113 nop.m 0
2114 fma.s.s0 f8 = f9,f9,f0 // Set I,O and +INF result
2115 nop.i 0
2116 };;
2117 // gate to __libm_error_support#
2118 //---------------------------------------------------------------------
2119 .align 32
2120 lgammaf_libm_err:
2121 { .mmi
2122 alloc r32 = ar.pfs,1,4,4,0
2123 mov GR_Parameter_TAG = GR_TAG
2124 nop.i 0
2125 };;
2126 .pred.rel "mutex",p9,p10
2127 { .mmi
2128 // store sign of gamma(x) as 32-bit int
2129 (p9) st4 [GR_ad_SignGam] = GR_SignOfGamma
2130 // store sign of gamma(x) as 64-bit int
2131 (p10) st8 [GR_ad_SignGam] = GR_SignOfGamma
2132 nop.i 0
2133 };;
2134 GLOBAL_LIBM_END(__libm_lgammaf)
2136 LOCAL_LIBM_ENTRY(__libm_error_region)
2137 .prologue
2138 { .mfi
2139 add GR_Parameter_Y=-32,sp // Parameter 2 value
2140 nop.f 0
2141 .save ar.pfs,GR_SAVE_PFS
2142 mov GR_SAVE_PFS=ar.pfs // Save ar.pfs
2143 }
2144 { .mfi
2145 .fframe 64
2146 add sp=-64,sp // Create new stack
2147 nop.f 0
2148 mov GR_SAVE_GP=gp // Save gp
2149 };;
2150 { .mmi
2151 stfs [GR_Parameter_Y] = FR_Y,16 // STORE Parameter 2 on stack
2152 add GR_Parameter_X = 16,sp // Parameter 1 address
2153 .save b0, GR_SAVE_B0
2154 mov GR_SAVE_B0=b0 // Save b0
2155 };;
2156 .body
2157 { .mib
2158 stfs [GR_Parameter_X] = FR_X // STORE Parameter 1
2159 // on stack
2160 add GR_Parameter_RESULT = 0,GR_Parameter_Y // Parameter 3 address
2161 nop.b 0
2162 }
2163 { .mib
2164 stfs [GR_Parameter_Y] = FR_RESULT // STORE Parameter 3
2165 // on stack
2166 add GR_Parameter_Y = -16,GR_Parameter_Y
2167 br.call.sptk b0=__libm_error_support# // Call error handling
2168 // function
2169 };;
2170 { .mmi
2171 nop.m 0
2172 nop.m 0
2173 add GR_Parameter_RESULT = 48,sp
2174 };;
2175 { .mmi
2176 ldfs f8 = [GR_Parameter_RESULT] // Get return result off stack
2177 .restore sp
2178 add sp = 64,sp // Restore stack pointer
2179 mov b0 = GR_SAVE_B0 // Restore return address
2180 };;
2181 { .mib
2182 mov gp = GR_SAVE_GP // Restore gp
2183 mov ar.pfs = GR_SAVE_PFS // Restore ar.pfs
2184 br.ret.sptk b0 // Return
2185 };;
2187 LOCAL_LIBM_END(__libm_error_region)
2188 .type __libm_error_support#,@function
2189 .global __libm_error_support#