| blob | 7853927482e9f2ce59e311813ff1dd21f684dd01 |
1 .file "tgammal.s"
4 // Copyright (c) 2002 - 2005, Intel Corporation
5 // All rights reserved.
6 //
7 //
8 // Redistribution and use in source and binary forms, with or without
9 // modification, are permitted provided that the following conditions are
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11 //
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13 // notice, this list of conditions and the following disclaimer.
14 //
15 // * Redistributions in binary form must reproduce the above copyright
16 // notice, this list of conditions and the following disclaimer in the
17 // documentation and/or other materials provided with the distribution.
18 //
19 // * The name of Intel Corporation may not be used to endorse or promote
20 // products derived from this software without specific prior written
21 // permission.
23 // THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
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25 // LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
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33 // SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
34 //
35 // Intel Corporation is the author of this code, and requests that all
36 // problem reports or change requests be submitted to it directly at
37 // http://www.intel.com/software/products/opensource/libraries/num.htm.
38 //
39 // History
40 //==============================================================
41 // 01/16/02 Initial version
42 // 05/20/02 Cleaned up namespace and sf0 syntax
43 // 02/10/03 Reordered header: .section, .global, .proc, .align;
44 // used data8 for long double table values
45 // 03/17/03 Moved tgammal_libm_err label into .proc region
46 // 04/10/03 Changed error codes for overflow and negative integers
47 // 03/31/05 Reformatted delimiters between data tables
48 //
49 // API
50 //==============================================================
51 // long double tgammal(long double)
52 //
53 // Resources Used:
54 //
55 // Floating-Point Registers: f8-f15
56 // f32-f127
57 //
58 // General Purpose Registers: r32-r67
59 //
60 // Predicate Registers: p6-p15
61 //
62 //*********************************************************************
63 //
64 // IEEE Special Conditions:
65 //
66 // tgammal(+inf) = +inf
67 // tgammal(-inf) = QNaN
68 // tgammal(+/-0) = +/-inf
69 // tgammal(x<0, x - integer) = QNaN
70 // tgammal(SNaN) = QNaN
71 // tgammal(QNaN) = QNaN
72 //
73 //*********************************************************************
74 // Overview of operation
75 //==============================================================
76 //
77 // Algorithm description
78 // ---------------------
79 //
80 // There are 3 main paths in the implementation
81 // (and additional special values branches)
82 //
83 // 1) |X| >= 13 - Stirling formula computation
84 // a) Positive arguments:
85 // TGAMMAL(X) = exp((X-0.5)*ln(X) - X + C + S(Z)),
86 // where C = 0.5*ln(2*Pi) , Z = 1/Z, S(Z) - Bernulli polynomial
87 // (up to 'B18' term).
88 // Some of these calculation done in multiprecision.
89 // Ln returns multiprecision result too
90 // and exp also accepts and returns pair of values.
91 //
92 // b) Negative arguments
93 // TGAMMAL(-X) = PI/(X*TGAMMAL(X)*sin(PI*X)).
94 // (X*sin(PI*X))/PI calculated in parallel with TGAMMAL.
95 // Here we use polynomial of 9th degree with 2 multiprecision steps.
96 // Argument range reduction is:
97 // N = [x] with round to nearest, r = x - N, -0.5 <= r < 0.5
98 // After ((X-0.5)*ln(X) - X + C + S(Z)) completed we just invert
99 // its result and compute exp with negative argument (1/exp(x)=exp(-x))
100 // Then we multiply exp result to PI/(X*sin(PI*X)).
101 //
102 // 2) 1 <= |X| < 13 - Polynomial part
103 // a) Positive arguments:
104 // All values are splitted to such intervals as:
105 // #0->[2;3], #1->[3,4], #2->[5,6]...
106 // For even intervals we just use polynomial computation with degree 20
107 // and first 6 multiprecision computations.
108 // Range reduction looks like
109 // N = [x] with truncate, r = x - N - 0.5, -0.5 <= r < 0.5
110 // For odd intervals we use reccurent formula:
111 // TGAMMAL(X) = TGAMMA(X-1)*(X-1)
112 // [1;2] interval is splitted to 3 subranges:
113 // [1;1.25], [1.25;1.75], [1.75;2] with the same polynomial forms
114 //
115 // b) Negative arguments
116 // TGAMMAL(-X) = PI/(X*TGAMMAL(X)*sin(PI*X)).
117 // (X*sin(PI*X))/PI calculated in parallel with TGAMMAL.
118 // After multiplication by TGAMMAL(X) result we calculate reciprocal
119 // and get final result.
120 //
121 // 3) 0 < |X| < 1 - Near 0 part
122 // a) Here we use reccurent formula TGAMMAL(X) = TGAMMAL(X+1)/X
123 // TGAMMAL(X+1) calculated as shown above,
124 // 1/X result obtained in parallel. Then we just multiply these values.
125 // There is only additional separated subrange: [0;0.125] with specific
126 // polynomial constants set.
127 //
128 // b) Negative arguments
129 // TGAMMAL(-X) = PI/(TGAMMAL(X+1)*sin(PI*X)).
130 // There is no need to compute 1/X.
134 RODATA
136 .align 16
137 LOCAL_OBJECT_START(Constants_Tgammal_log_80_Q)
138 // log2_hi, log2_lo, Q_6, Q_5, Q_4, Q_3, Q_2, Q_1
139 data4 0x00000000,0xB1721800,0x00003FFE,0x00000000
140 data4 0x4361C4C6,0x82E30865,0x0000BFE2,0x00000000
141 data4 0xA51BE0AF,0x92492453,0x00003FFC,0x00000000
142 data4 0xA0CFD29F,0xAAAAAB73,0x0000BFFC,0x00000000
143 data4 0xCCCE3872,0xCCCCCCCC,0x00003FFC,0x00000000
144 data4 0xFFFFB4FB,0xFFFFFFFF,0x0000BFFC,0x00000000
145 data4 0xAAAAAAAB,0xAAAAAAAA,0x00003FFD,0x00000000
146 data4 0x00000000,0x80000000,0x0000BFFE,0x00000000
147 LOCAL_OBJECT_END(Constants_Tgammal_log_80_Q)
149 .align 64
150 LOCAL_OBJECT_START(Constants_Tgammal_log_80_Z_G_H_h1)
151 // Z1 - 16 bit fixed, G1 and H1 IEEE single, h1 IEEE double
152 data4 0x00008000,0x3F800000,0x00000000,0x00000000
153 data4 0x00000000,0x00000000,0x00000000,0x00000000
154 data4 0x00007879,0x3F70F0F0,0x3D785196,0x00000000
155 data4 0xEBA0E0D1,0x8B1D330B,0x00003FDA,0x00000000
156 data4 0x000071C8,0x3F638E38,0x3DF13843,0x00000000
157 data4 0x9EADD553,0xE2AF365E,0x00003FE2,0x00000000
158 data4 0x00006BCB,0x3F579430,0x3E2FF9A0,0x00000000
159 data4 0x752F34A2,0xF585FEC3,0x0000BFE3,0x00000000
160 data4 0x00006667,0x3F4CCCC8,0x3E647FD6,0x00000000
161 data4 0x893B03F3,0xF3546435,0x00003FE2,0x00000000
162 data4 0x00006187,0x3F430C30,0x3E8B3AE7,0x00000000
163 data4 0x39CDD2AC,0xBABA62E0,0x00003FE4,0x00000000
164 data4 0x00005D18,0x3F3A2E88,0x3EA30C68,0x00000000
165 data4 0x457978A1,0x8718789F,0x00003FE2,0x00000000
166 data4 0x0000590C,0x3F321640,0x3EB9CEC8,0x00000000
167 data4 0x3185E56A,0x9442DF96,0x0000BFE4,0x00000000
168 data4 0x00005556,0x3F2AAAA8,0x3ECF9927,0x00000000
169 data4 0x2BBE2CBD,0xCBF9A4BF,0x00003FE4,0x00000000
170 data4 0x000051EC,0x3F23D708,0x3EE47FC5,0x00000000
171 data4 0x852D5935,0xF3537535,0x00003FE3,0x00000000
172 data4 0x00004EC5,0x3F1D89D8,0x3EF8947D,0x00000000
173 data4 0x46CDF32F,0xA1F1E699,0x0000BFDF,0x00000000
174 data4 0x00004BDB,0x3F17B420,0x3F05F3A1,0x00000000
175 data4 0xD8484CE3,0x84A61856,0x00003FE4,0x00000000
176 data4 0x00004925,0x3F124920,0x3F0F4303,0x00000000
177 data4 0xFF28821B,0xC7DD97E0,0x0000BFE2,0x00000000
178 data4 0x0000469F,0x3F0D3DC8,0x3F183EBF,0x00000000
179 data4 0xEF1FD32F,0xD3C4A887,0x00003FE3,0x00000000
180 data4 0x00004445,0x3F088888,0x3F20EC80,0x00000000
181 data4 0x464C76DA,0x84672BE6,0x00003FE5,0x00000000
182 data4 0x00004211,0x3F042108,0x3F29516A,0x00000000
183 data4 0x18835FB9,0x9A43A511,0x0000BFE5,0x00000000
184 LOCAL_OBJECT_END(Constants_Tgammal_log_80_Z_G_H_h1)
186 .align 64
187 LOCAL_OBJECT_START(Constants_Tgammal_log_80_Z_G_H_h2)
188 // Z2 - 16 bit fixed, G2 and H2 IEEE single, h2 IEEE double
189 data4 0x00008000,0x3F800000,0x00000000,0x00000000
190 data4 0x00000000,0x00000000,0x00000000,0x00000000
191 data4 0x00007F81,0x3F7F00F8,0x3B7F875D,0x00000000
192 data4 0x211398BF,0xAD08B116,0x00003FDB,0x00000000
193 data4 0x00007F02,0x3F7E03F8,0x3BFF015B,0x00000000
194 data4 0xC376958E,0xB106790F,0x00003FDE,0x00000000
195 data4 0x00007E85,0x3F7D08E0,0x3C3EE393,0x00000000
196 data4 0x79A7679A,0xFD03F242,0x0000BFDA,0x00000000
197 data4 0x00007E08,0x3F7C0FC0,0x3C7E0586,0x00000000
198 data4 0x05E7AE08,0xF03F81C3,0x0000BFDF,0x00000000
199 data4 0x00007D8D,0x3F7B1880,0x3C9E75D2,0x00000000
200 data4 0x049EB22F,0xD1B87D3C,0x00003FDE,0x00000000
201 data4 0x00007D12,0x3F7A2328,0x3CBDC97A,0x00000000
202 data4 0x3A9E81E0,0xFABC8B95,0x00003FDF,0x00000000
203 data4 0x00007C98,0x3F792FB0,0x3CDCFE47,0x00000000
204 data4 0x7C4B5443,0xF5F3653F,0x00003FDF,0x00000000
205 data4 0x00007C20,0x3F783E08,0x3CFC15D0,0x00000000
206 data4 0xF65A1773,0xE78AB204,0x00003FE0,0x00000000
207 data4 0x00007BA8,0x3F774E38,0x3D0D874D,0x00000000
208 data4 0x7B8EF695,0xDB7CBFFF,0x0000BFE0,0x00000000
209 data4 0x00007B31,0x3F766038,0x3D1CF49B,0x00000000
210 data4 0xCF773FB3,0xC0241AEA,0x0000BFE0,0x00000000
211 data4 0x00007ABB,0x3F757400,0x3D2C531D,0x00000000
212 data4 0xC9539FDF,0xFC8F4D48,0x00003FE1,0x00000000
213 data4 0x00007A45,0x3F748988,0x3D3BA322,0x00000000
214 data4 0x954665C2,0x9CD035FB,0x0000BFE1,0x00000000
215 data4 0x000079D1,0x3F73A0D0,0x3D4AE46F,0x00000000
216 data4 0xDD367A30,0xEC9017C7,0x00003FE1,0x00000000
217 data4 0x0000795D,0x3F72B9D0,0x3D5A1756,0x00000000
218 data4 0xCB11189C,0xEE6625D3,0x0000BFE1,0x00000000
219 data4 0x000078EB,0x3F71D488,0x3D693B9D,0x00000000
220 data4 0xBE11C424,0xA49C8DB5,0x0000BFE0,0x00000000
221 LOCAL_OBJECT_END(Constants_Tgammal_log_80_Z_G_H_h2)
223 .align 64
224 LOCAL_OBJECT_START(Constants_Tgammal_log_80_h3_G_H)
225 // h3 IEEE double extended, H3 and G3 IEEE single
226 data4 0x112666B0,0xAAACAAB1,0x00003FD3,0x3F7FFC00
227 data4 0x9B7FAD21,0x90051030,0x00003FD8,0x3F7FF400
228 data4 0xF4D783C4,0xA6B46F46,0x00003FDA,0x3F7FEC00
229 data4 0x11C6DDCA,0xDA148D88,0x0000BFD8,0x3F7FE400
230 data4 0xCA964D95,0xCE65C1D8,0x0000BFD8,0x3F7FDC00
231 data4 0x23412D13,0x883838EE,0x0000BFDB,0x3F7FD400
232 data4 0x983ED687,0xB7E5CFA1,0x00003FDB,0x3F7FCC08
233 data4 0xE3C3930B,0xDBE23B16,0x0000BFD9,0x3F7FC408
234 data4 0x48AA4DFC,0x9B92F1FC,0x0000BFDC,0x3F7FBC10
235 data4 0xCE9C8F7E,0x9A8CEB15,0x0000BFD9,0x3F7FB410
236 data4 0x0DECE74A,0x8C220879,0x00003FDC,0x3F7FAC18
237 data4 0x2F053150,0xB25CA912,0x0000BFDA,0x3F7FA420
238 data4 0xD9A5BE20,0xA5876555,0x00003FDB,0x3F7F9C20
239 data4 0x2053F087,0xC919BB6E,0x00003FD9,0x3F7F9428
240 data4 0x041E9A77,0xB70BDA79,0x00003FDC,0x3F7F8C30
241 data4 0xEA1C9C30,0xF18A5C08,0x00003FDA,0x3F7F8438
242 data4 0x796D89E5,0xA3790D84,0x0000BFDD,0x3F7F7C40
243 data4 0xA2915A3A,0xE1852369,0x0000BFDD,0x3F7F7448
244 data4 0xA39ED868,0xD803858F,0x00003FDC,0x3F7F6C50
245 data4 0x9417EBB7,0xB2EEE356,0x0000BFDD,0x3F7F6458
246 data4 0x9BB0D07F,0xED5C1F8A,0x0000BFDC,0x3F7F5C68
247 data4 0xE87C740A,0xD6D201A0,0x0000BFDD,0x3F7F5470
248 data4 0x1CA74025,0xE8DEBF5E,0x00003FDC,0x3F7F4C78
249 data4 0x1F34A7EB,0x9A995A97,0x0000BFDC,0x3F7F4488
250 data4 0x359EED97,0x9CB0F742,0x0000BFDA,0x3F7F3C90
251 data4 0xBBC6A1C8,0xD6F833C2,0x0000BFDD,0x3F7F34A0
252 data4 0xE71090EC,0xE1F68F2A,0x00003FDC,0x3F7F2CA8
253 data4 0xC160A74F,0xD1881CF1,0x0000BFDB,0x3F7F24B8
254 data4 0xD78CB5A4,0x9AD05AE2,0x00003FD6,0x3F7F1CC8
255 data4 0x9A77DC4B,0xE658CB8E,0x0000BFDD,0x3F7F14D8
256 data4 0x6BD6D312,0xBA281296,0x00003FDC,0x3F7F0CE0
257 data4 0xF95210D0,0xB478BBEB,0x0000BFDB,0x3F7F04F0
258 data4 0x38800100,0x39400480,0x39A00640,0x39E00C41 // H's start here
259 data4 0x3A100A21,0x3A300F22,0x3A4FF51C,0x3A6FFC1D
260 data4 0x3A87F20B,0x3A97F68B,0x3AA7EB86,0x3AB7E101
261 data4 0x3AC7E701,0x3AD7DD7B,0x3AE7D474,0x3AF7CBED
262 data4 0x3B03E1F3,0x3B0BDE2F,0x3B13DAAA,0x3B1BD766
263 data4 0x3B23CC5C,0x3B2BC997,0x3B33C711,0x3B3BBCC6
264 data4 0x3B43BAC0,0x3B4BB0F4,0x3B53AF6D,0x3B5BA620
265 data4 0x3B639D12,0x3B6B9444,0x3B7393BC,0x3B7B8B6D
266 LOCAL_OBJECT_END(Constants_Tgammal_log_80_h3_G_H)
268 .align 64
269 LOCAL_OBJECT_START(Constants_Tgammal_stirling)
270 //0.5*ln(2*Pi)=9.1893853320467266954096885e-01 + 7.2239360881843238220057778e-17
271 data8 0x3FED67F1C864BEB4, 0x3C94D252F2400510
272 // Bernulli numbers
273 data8 0xAAAAAAAAAAAAAAAB, 0x00003FFB //B2 = 8.3333333333333333333333333333e-02
274 data8 0xBF66C16C16C16C17 //B4 = -2.7777777777777777777777777778e-03
275 data8 0x3F4A01A01A01A01A //B6 = 7.9365079365079365079365079365e-04
276 data8 0xBF43813813813814 //B8 = -5.9523809523809523809523809524e-04
277 data8 0x3F4B951E2B18FF23 //B10 = 8.4175084175084175084175084175e-04
278 data8 0xBF5F6AB0D9993C7D //B12 = -1.9175269175269175269175269175e-03
279 data8 0x3F7A41A41A41A41A //B14 = 6.4102564102564102564102564103e-03
280 data8 0xBF9E4286CB0F5398 //B16 = -2.9550653594771241830065359477e-02
281 data8 0x3FC6FE96381E0680 //B18 = 1.7964437236883057316493849002e-01
282 data8 0x3FE0000000000000 // 0.5
283 LOCAL_OBJECT_END(Constants_Tgammal_stirling)
285 .align 64
286 LOCAL_OBJECT_START(Constants_Tgammal_sin)
287 // Polynomial coefficients for the sin(Pi*x)/Pi, 0 <= |x| < 0.5
288 //A2 = 8.1174242528335360802316245099e-01 + 5.1302254650266899774269946201e-18
289 data8 0x3FE9F9CB402BC46C, 0x3C57A8B3819B7CEC
290 //A1 = -1.6449340668482264060656916627e+00 + -3.0210280454695477893051351574e-17
291 data8 0xBFFA51A6625307D3, 0xBC816A402079D0EF
292 data8 0xF3AEF1FFCCE6C813, 0x0000BFE3 //A9 = -7.0921197799923779127089910470e-09
293 data8 0x87D54408E6D4BB9D, 0x00003FE9 //A8 = 2.5300880778252693946712766029e-07
294 data8 0xEA12033DCE7B8ED9, 0x0000BFED //A7 = -6.9758403885461690048189307819e-06
295 data8 0x9BA38C952A59D1A8, 0x00003FF2 //A6 = 1.4842878710882320255092707181e-04
296 data8 0x99C0B55178FF0E38, 0x0000BFF6 //A5 = -2.3460810348048124421268761990e-03
297 data8 0xD63402E798FEC896, 0x00003FF9 //A4 = 2.6147847817611456327417812320e-02
298 data8 0xC354723906D95E92, 0x0000BFFC //A3 = -1.9075182412208257558294507774e-01
299 LOCAL_OBJECT_END(Constants_Tgammal_sin)
301 .align 64
302 LOCAL_OBJECT_START(Constants_Tgammal_exp_64_Arg)
303 data4 0x00000000,0xB17217F4,0x00003FF2,0x00000000 // L_hi = hi part log(2)/2^12
304 data4 0xF278ECE6,0xF473DE6A,0x00003FD4,0x00000000 // L_lo = lo part log(2)/2^12
305 LOCAL_OBJECT_END(Constants_Tgammal_exp_64_Arg)
307 LOCAL_OBJECT_START(Constants_Tgammal_exp_64_A)
308 data4 0xB1B736A0,0xAAAAAAAB,0x00003FFA,0x00000000 // A3
309 data4 0x90CD6327,0xAAAAAAAB,0x00003FFC,0x00000000 // A2
310 data4 0xFFFFFFFF,0xFFFFFFFF,0x00003FFD,0x00000000 // A1
311 LOCAL_OBJECT_END(Constants_Tgammal_exp_64_A)
313 LOCAL_OBJECT_START(Constants_Tgammal_exp_64_T1)
314 data4 0x3F800000,0x3F8164D2,0x3F82CD87,0x3F843A29
315 data4 0x3F85AAC3,0x3F871F62,0x3F88980F,0x3F8A14D5
316 data4 0x3F8B95C2,0x3F8D1ADF,0x3F8EA43A,0x3F9031DC
317 data4 0x3F91C3D3,0x3F935A2B,0x3F94F4F0,0x3F96942D
318 data4 0x3F9837F0,0x3F99E046,0x3F9B8D3A,0x3F9D3EDA
319 data4 0x3F9EF532,0x3FA0B051,0x3FA27043,0x3FA43516
320 data4 0x3FA5FED7,0x3FA7CD94,0x3FA9A15B,0x3FAB7A3A
321 data4 0x3FAD583F,0x3FAF3B79,0x3FB123F6,0x3FB311C4
322 data4 0x3FB504F3,0x3FB6FD92,0x3FB8FBAF,0x3FBAFF5B
323 data4 0x3FBD08A4,0x3FBF179A,0x3FC12C4D,0x3FC346CD
324 data4 0x3FC5672A,0x3FC78D75,0x3FC9B9BE,0x3FCBEC15
325 data4 0x3FCE248C,0x3FD06334,0x3FD2A81E,0x3FD4F35B
326 data4 0x3FD744FD,0x3FD99D16,0x3FDBFBB8,0x3FDE60F5
327 data4 0x3FE0CCDF,0x3FE33F89,0x3FE5B907,0x3FE8396A
328 data4 0x3FEAC0C7,0x3FED4F30,0x3FEFE4BA,0x3FF28177
329 data4 0x3FF5257D,0x3FF7D0DF,0x3FFA83B3,0x3FFD3E0C
330 LOCAL_OBJECT_END(Constants_Tgammal_exp_64_T1)
332 LOCAL_OBJECT_START(Constants_Tgammal_exp_64_T2)
333 data4 0x3F800000,0x3F80058C,0x3F800B18,0x3F8010A4
334 data4 0x3F801630,0x3F801BBD,0x3F80214A,0x3F8026D7
335 data4 0x3F802C64,0x3F8031F2,0x3F803780,0x3F803D0E
336 data4 0x3F80429C,0x3F80482B,0x3F804DB9,0x3F805349
337 data4 0x3F8058D8,0x3F805E67,0x3F8063F7,0x3F806987
338 data4 0x3F806F17,0x3F8074A8,0x3F807A39,0x3F807FCA
339 data4 0x3F80855B,0x3F808AEC,0x3F80907E,0x3F809610
340 data4 0x3F809BA2,0x3F80A135,0x3F80A6C7,0x3F80AC5A
341 data4 0x3F80B1ED,0x3F80B781,0x3F80BD14,0x3F80C2A8
342 data4 0x3F80C83C,0x3F80CDD1,0x3F80D365,0x3F80D8FA
343 data4 0x3F80DE8F,0x3F80E425,0x3F80E9BA,0x3F80EF50
344 data4 0x3F80F4E6,0x3F80FA7C,0x3F810013,0x3F8105AA
345 data4 0x3F810B41,0x3F8110D8,0x3F81166F,0x3F811C07
346 data4 0x3F81219F,0x3F812737,0x3F812CD0,0x3F813269
347 data4 0x3F813802,0x3F813D9B,0x3F814334,0x3F8148CE
348 data4 0x3F814E68,0x3F815402,0x3F81599C,0x3F815F37
349 LOCAL_OBJECT_END(Constants_Tgammal_exp_64_T2)
351 LOCAL_OBJECT_START(Constants_Tgammal_exp_64_W1)
352 data8 0x0000000000000000, 0xBE384454171EC4B4
353 data8 0xBE6947414AA72766, 0xBE5D32B6D42518F8
354 data8 0x3E68D96D3A319149, 0xBE68F4DA62415F36
355 data8 0xBE6DDA2FC9C86A3B, 0x3E6B2E50F49228FE
356 data8 0xBE49C0C21188B886, 0x3E64BFC21A4C2F1F
357 data8 0xBE6A2FBB2CB98B54, 0x3E5DC5DE9A55D329
358 data8 0x3E69649039A7AACE, 0x3E54728B5C66DBA5
359 data8 0xBE62B0DBBA1C7D7D, 0x3E576E0409F1AF5F
360 data8 0x3E6125001A0DD6A1, 0xBE66A419795FBDEF
361 data8 0xBE5CDE8CE1BD41FC, 0xBE621376EA54964F
362 data8 0x3E6370BE476E76EE, 0x3E390D1A3427EB92
363 data8 0x3E1336DE2BF82BF8, 0xBE5FF1CBD0F7BD9E
364 data8 0xBE60A3550CEB09DD, 0xBE5CA37E0980F30D
365 data8 0xBE5C541B4C082D25, 0xBE5BBECA3B467D29
366 data8 0xBE400D8AB9D946C5, 0xBE5E2A0807ED374A
367 data8 0xBE66CB28365C8B0A, 0x3E3AAD5BD3403BCA
368 data8 0x3E526055C7EA21E0, 0xBE442C75E72880D6
369 data8 0x3E58B2BB85222A43, 0xBE5AAB79522C42BF
370 data8 0xBE605CB4469DC2BC, 0xBE589FA7A48C40DC
371 data8 0xBE51C2141AA42614, 0xBE48D087C37293F4
372 data8 0x3E367A1CA2D673E0, 0xBE51BEBB114F7A38
373 data8 0xBE6348E5661A4B48, 0xBDF526431D3B9962
374 data8 0x3E3A3B5E35A78A53, 0xBE46C46C1CECD788
375 data8 0xBE60B7EC7857D689, 0xBE594D3DD14F1AD7
376 data8 0xBE4F9C304C9A8F60, 0xBE52187302DFF9D2
377 data8 0xBE5E4C8855E6D68F, 0xBE62140F667F3DC4
378 data8 0xBE36961B3BF88747, 0x3E602861C96EC6AA
379 data8 0xBE3B5151D57FD718, 0x3E561CD0FC4A627B
380 data8 0xBE3A5217CA913FEA, 0x3E40A3CC9A5D193A
381 data8 0xBE5AB71310A9C312, 0x3E4FDADBC5F57719
382 data8 0x3E361428DBDF59D5, 0x3E5DB5DB61B4180D
383 data8 0xBE42AD5F7408D856, 0x3E2A314831B2B707
384 LOCAL_OBJECT_END(Constants_Tgammal_exp_64_W1)
386 LOCAL_OBJECT_START(Constants_Tgammal_exp_64_W2)
387 data8 0x0000000000000000, 0xBE641F2537A3D7A2
388 data8 0xBE68DD57AD028C40, 0xBE5C77D8F212B1B6
389 data8 0x3E57878F1BA5B070, 0xBE55A36A2ECAE6FE
390 data8 0xBE620608569DFA3B, 0xBE53B50EA6D300A3
391 data8 0x3E5B5EF2223F8F2C, 0xBE56A0D9D6DE0DF4
392 data8 0xBE64EEF3EAE28F51, 0xBE5E5AE2367EA80B
393 data8 0x3E47CB1A5FCBC02D, 0xBE656BA09BDAFEB7
394 data8 0x3E6E70C6805AFEE7, 0xBE6E0509A3415EBA
395 data8 0xBE56856B49BFF529, 0x3E66DD3300508651
396 data8 0x3E51165FC114BC13, 0x3E53333DC453290F
397 data8 0x3E6A072B05539FDA, 0xBE47CD877C0A7696
398 data8 0xBE668BF4EB05C6D9, 0xBE67C3E36AE86C93
399 data8 0xBE533904D0B3E84B, 0x3E63E8D9556B53CE
400 data8 0x3E212C8963A98DC8, 0xBE33138F032A7A22
401 data8 0x3E530FA9BC584008, 0xBE6ADF82CCB93C97
402 data8 0x3E5F91138370EA39, 0x3E5443A4FB6A05D8
403 data8 0x3E63DACD181FEE7A, 0xBE62B29DF0F67DEC
404 data8 0x3E65C4833DDE6307, 0x3E5BF030D40A24C1
405 data8 0x3E658B8F14E437BE, 0xBE631C29ED98B6C7
406 data8 0x3E6335D204CF7C71, 0x3E529EEDE954A79D
407 data8 0x3E5D9257F64A2FB8, 0xBE6BED1B854ED06C
408 data8 0x3E5096F6D71405CB, 0xBE3D4893ACB9FDF5
409 data8 0xBDFEB15801B68349, 0x3E628D35C6A463B9
410 data8 0xBE559725ADE45917, 0xBE68C29C042FC476
411 data8 0xBE67593B01E511FA, 0xBE4A4313398801ED
412 data8 0x3E699571DA7C3300, 0x3E5349BE08062A9E
413 data8 0x3E5229C4755BB28E, 0x3E67E42677A1F80D
414 data8 0xBE52B33F6B69C352, 0xBE6B3550084DA57F
415 data8 0xBE6DB03FD1D09A20, 0xBE60CBC42161B2C1
416 data8 0x3E56ED9C78A2B771, 0xBE508E319D0FA795
417 data8 0xBE59482AFD1A54E9, 0xBE2A17CEB07FD23E
418 data8 0x3E68BF5C17365712, 0x3E3956F9B3785569
419 LOCAL_OBJECT_END(Constants_Tgammal_exp_64_W2)
423 LOCAL_OBJECT_START(Constants_Tgammal_poly)
425 // Polynomial coefficients for the tgammal(x), 2 <= |x| < 3
426 //A5 = 2.8360780594841213109180699803e-02 + 2.2504152891014320704380000000e-19
427 data8 0x3F9D0A9BC49353D2, 0x3C109AEA0F23CE2D
428 //A4 = 1.0967323400216015538699565468e-01 + 9.9225166000430644587276000000e-18
429 data8 0x3FBC138B89492C5B, 0x3C66E138506D5652
430 //A3 = 2.5387124684114281691904579930e-01 + 2.2667777637607113205546600000e-17
431 data8 0x3FD03F6D2FA4F4F8, 0x3C7A2258DA8CD8B1
432 data8 0xC5866457328BC39B, 0x00003FE3 //A20 = 5.7487331964156762795056629138e-09
433 data8 0xE93D9F1ACD59C929, 0x0000BFE4 //A19= -1.3576396100397317396956445658e-08
434 data8 0xE33389C8F6CBA813, 0x00003FE5 //A18 = 2.6449714924964597501721434271e-08
435 data8 0x8FE7B25B9CD26D2A, 0x0000BFE7 //A17= -6.7011017946055513660266853311e-08
436 data8 0xB89F4721BFBC15B0, 0x00003FE8 //A16 = 1.7194280320370423615174419192e-07
437 data8 0xE49CBDC1874EBABA, 0x0000BFE9 //A15= -4.2582353660153782928729466776e-07
438 data8 0x913AF50A336129CA, 0x00003FEB //A14 = 1.0820500665257088283172211622e-06
439 data8 0xABCF0F7313B3B332, 0x0000BFEC //A13= -2.5601510627710417669568115706e-06
440 //A2 = 6.5455857798133676439533701341e-01 + 1.3292075193155190798867000000e-18
441 data8 0x3FE4F224D4B7E01C, 0x3C3885014A2B8319
442 //A1 = 9.3473452162608550164435428087e-01 + 3.2785154201417136611642400000e-17
443 data8 0x3FEDE9585F1A7093, 0x3C82E63C1B5028BF
444 //A0 = 1.3293403881791368004172682049e+00 + 2.2005689328949279282607500000e-16
445 data8 0x3FF544FA6D47B38F, 0x3CAFB6AA9829E81F
446 data8 0xF3668F799997C76D, 0x00003FED //A12 = 7.2539039479124273660331538367e-06
447 data8 0xD6C6BBD54CDEAEB1, 0x0000BFEE //A11= -1.2801665282681088568639378920e-05
448 data8 0x809E4763B06F6883, 0x00003FF1 //A10 = 6.1329973609906572700697893187e-05
449 data8 0x8443B000F8F9A71A, 0x00003FED //A9 = 3.9417864189995544394564413428e-06
450 data8 0xC5C7E6D62A6991D8, 0x00003FF4 //A8 = 7.5447412886334708803357581519e-04
451 data8 0xD2AF690725C62D88, 0x00003FF5 //A7 = 1.6074004848394703022110823298e-03
452 data8 0xAA44E635D4B7B682, 0x00003FF8 //A6 = 1.0392403425906843901680697839e-02
453 //
454 // Polynomial coefficients for the tgammal(x), 4 <= |x| < 5
455 //A5 = 1.1600674810589555185913468449e+00 + 3.0229979112715124660731000000e-17
456 data8 0x3FF28FA2EB44D22E, 0x3C816D285234C815
457 //A4 = 3.1374268565470946334983182169e+00 + 1.3694868953995008497659600000e-16
458 data8 0x400919734073B1E1, 0x3CA3BC83CD7E9565
459 //A3 = 7.0834593993741057360580271052e+00 + 3.3899702569039156457249800000e-16
460 data8 0x401C5576617B6C1F, 0x3CB86D6431213296
461 data8 0xA4A5FB49C094966B, 0x00003FDA //A20 = 9.3591760106637809309720130828e-12
462 data8 0xA9260DA0F51D7ED8, 0x00003FDD //A19 = 7.6919898428091669411809372180e-11
463 data8 0xA16441DFB14BD6E1, 0x00003FE0 //A18 = 5.8713933014370867331213494535e-10
464 data8 0x95F098D9C2234849, 0x00003FE3 //A17 = 4.3638234584169302324461091035e-09
465 data8 0x8581817400E5AD2B, 0x00003FE6 //A16 = 3.1084260332429955234755367839e-08
466 data8 0xE272940E373EBE15, 0x00003FE8 //A15 = 2.1089573544273993580820317236e-07
467 data8 0xB6B3391145D226FB, 0x00003FEB //A14 = 1.3612217421122787182942706259e-06
468 data8 0x8B9428C4DF95FCD5, 0x00003FEE //A13 = 8.3195416382628990683949003789e-06
469 //A2 = 1.2665135075272345943631080445e+01 + 9.8721896915973874255877000000e-16
470 data8 0x4029548C95A76F38, 0x3CD1C8BE715B8E13
471 //A1 = 1.6154969393303069580269948347e+01 + 9.6850518810678379641029000000e-16
472 data8 0x403027AC12FC1E1E, 0x3CD172711C15501B
473 //A0 = 1.1631728396567448058362970187e+01 + 8.7078125362814179268673000000e-16
474 data8 0x40274371E7866C65, 0x3CCF5F8A1A5FACA0
475 data8 0xC94A903114272C03, 0x00003FF0 //A12 = 4.7991576836334427243159066630e-05
476 data8 0x8844262960E04BE6, 0x00003FF3 //A11 = 2.5990716419283017929486175141e-04
477 data8 0xAC5418A76767678D, 0x00003FF5 //A10 = 1.3147621245497801180184809726e-03
478 data8 0xCA231B6EFE959132, 0x00003FF7 //A9 = 6.1687358811367989146517222415e-03
479 data8 0xDA38E39C13819D2A, 0x00003FF9 //A8 = 2.6638454961912040754759086920e-02
480 data8 0xD696DF8D8389FE53, 0x00003FFB //A7 = 1.0477995539298934056097943975e-01
481 data8 0xBDD5C153048BC435, 0x00003FFD //A6 = 3.7077144754791605130056406006e-01
482 //
483 // Polynomial coefficients for the tgammal(x), 6 <= |x| < 7
484 //A5 = 6.7169398121054200601065531373e+01 + 2.9481001527213915901489600000e-15
485 data8 0x4050CAD76B377BA0, 0x3CEA8DDB2B2DE93E
486 //A4 = 1.6115104376855398982115730178e+02 + 1.3422421925418824418257300000e-14
487 data8 0x406424D559BDC687, 0x3D0E397FDB5B33DC
488 //A3 = 3.1812194028053562533386866562e+02 + 3.9881709875858650942409600000e-14
489 data8 0x4073E1F377A6CF73, 0x3D26738F63FE9C4C
490 data8 0xD6E1B5FF90CAABD3, 0x00003FE1 //A20 = 1.5634700199277480081025480635e-09
491 data8 0xD451987B925DD37E, 0x00003FE4 //A19 = 1.2358576813211397717382327174e-08
492 data8 0xBFC151B67FA58E6B, 0x00003FE7 //A18 = 8.9292951435632759686382657901e-08
493 data8 0xA9034C5E1D67572E, 0x00003FEA //A17 = 6.2962205718327848327368724720e-07
494 data8 0x8E40F6EAA30A71EC, 0x00003FED //A16 = 4.2394926442967995119170095258e-06
495 data8 0xE3C3541B03A1C350, 0x00003FEF //A15 = 2.7151465666109594512258841637e-05
496 data8 0xACE2E58436B2DDCE, 0x00003FF2 //A14 = 1.6487723793339152877117376243e-04
497 data8 0xF7EAF8D8D1CAA3D1, 0x00003FF4 //A13 = 9.4573158112768812533636022369e-04
498 //A2 = 4.8664351544258869353143381886e+02 + 4.7424047995944376868895400000e-14
499 data8 0x407E6A4BD6D9463B, 0x3D2AB2868D79E192
500 //A1 = 5.1615277644992545447166776285e+02 + 3.0901956935588717379242200000e-14
501 data8 0x40802138E2DC003B, 0x3D216570FB601AEA
502 //A0 = 2.8788527781504433278314536437e+02 + 2.8213174117085164944959600000e-14
503 data8 0x4071FE2A1911F7D6, 0x3D1FC3E4CF4DB5AF
504 data8 0xA72B88E48D3D1BAB, 0x00003FF7 //A12 = 5.1016252919939028020562237471e-03
505 data8 0xD2EFB1067DB4FFB2, 0x00003FF9 //A11 = 2.5749059441230515023024615917e-02
506 data8 0xF788AF9522205C24, 0x00003FFB //A10 = 1.2086617635601742290221382521e-01
507 data8 0x861A6CE06CB29EAF, 0x00003FFE //A9 = 5.2384071807018493367136112163e-01
508 data8 0x84FBDE0947718B58, 0x00004000 //A8 = 2.0778727617851237754568261869e+00
509 data8 0xEEC1371E265A2C3A, 0x00004001 //A7 = 7.4610858525146049022238037342e+00
510 data8 0xBF514B9BE68ED59D, 0x00004003 //A6 = 2.3914694993947572859629197920e+01
511 //
512 // Polynomial coefficients for the tgammal(x), 8 <= |x| < 9
513 //A5 = 5.8487447114416836484451778233e+03 + 4.7365465221455983144182900000e-13
514 data8 0x40B6D8BEA568B6FD, 0x3D60AA4D44C2589B
515 //A4 = 1.2796464063087094473303295672e+04 + 1.2373341702514898266244200000e-12
516 data8 0x40C8FE3B666B532D, 0x3D75C4752C5B4783
517 //A3 = 2.2837606581322281272150576115e+04 + 2.6598064610627891398831000000e-13
518 data8 0x40D64D66D23A7764, 0x3D52B77B3A10EA5C
519 data8 0xB23418F75B0BE22A, 0x00003FE9 //A20 = 3.3192989594206801808678663868e-07
520 data8 0xA984A7BC8B856ED2, 0x00003FEC //A19 = 2.5260177918662350066375115788e-06
521 data8 0x921A49729416372C, 0x00003FEF //A18 = 1.7416797068239475136398213598e-05
522 data8 0xF5BB9415CC399CA4, 0x00003FF1 //A17 = 1.1717449586392814601938207599e-04
523 data8 0xC50B91A40B81F9DF, 0x00003FF4 //A16 = 7.5166775151159345732094429036e-04
524 data8 0x96002572326DB203, 0x00003FF7 //A15 = 4.5776541559407384162139204300e-03
525 data8 0xD81A1A595E4157BA, 0x00003FF9 //A14 = 2.6379634345126284099420760736e-02
526 data8 0x92B700D0CFECADD8, 0x00003FFC //A13 = 1.4327622675407940907282658100e-01
527 //A2 = 3.1237895525940199149772524834e+04 + 3.1280450505163186432331700000e-12
528 data8 0x40DE8179504C0878, 0x3D8B83BB33FBB766
529 //A1 = 2.9192841741344487672904506326e+04 + 7.9300780509779689630767000000e-13
530 data8 0x40DC8235DF171691, 0x3D6BE6C780EE54DF
531 //A0 = 1.4034407293483411194756627083e+04 + 1.4038139346291543309253700000e-12
532 data8 0x40CB693422315F90, 0x3D78B23746113FCE
533 data8 0xBAE50807548BC711, 0x00003FFE //A12 = 7.3005724123917935346868107005e-01
534 data8 0xDE28B1F57E68CFB6, 0x00004000 //A11 = 3.4712338349724065462763671443e+00
535 data8 0xF4DCA5A5FF901118, 0x00004002 //A10 = 1.5303868912154033908205911714e+01
536 data8 0xF85AAA1AD5E84E5E, 0x00004004 //A9 = 6.2088539523416399361048051373e+01
537 data8 0xE5AA8BB1BF02934D, 0x00004006 //A8 = 2.2966619406617480799195651466e+02
538 data8 0xBF6CFEFD67F59845, 0x00004008 //A7 = 7.6570306334640770654588802417e+02
539 data8 0x8DB5D2F001635C29, 0x0000400A //A6 = 2.2673639984182571062068713002e+03
540 //
541 // Polynomial coefficients for the tgammal(x), 10 <= |x| < 11
542 //A5 = 7.2546009516580589115619659424e+05 + 1.0343348865365065212891728822e-10
543 data8 0x412623A830B99290, 0x3DDC6E7C157611C4
544 //A4 = 1.4756292870840241666883230209e+06 + 8.1516565365333844166705674775e-11
545 data8 0x4136842D497E56AF, 0x3DD66837E4C3F9EE
546 //A3 = 2.4356116926500420086085796356e+06 + 3.5508860076560925641351069404e-10
547 data8 0x4142950DD8A8C1AF, 0x3DF866C8E3DD0980
548 data8 0xB7FD0D1EEAC38EB4, 0x00003FF1 //A20 = 8.7732544640091602721643775932e-05
549 data8 0xA9345C64AC750AE9, 0x00003FF4 //A19 = 6.4546407626804942279126469603e-04
550 data8 0x8BEABC81BE1E93C9, 0x00003FF7 //A18 = 4.2699261134524096128048819443e-03
551 data8 0xE1CD281EDD7315F8, 0x00003FF9 //A17 = 2.7563646660310313164706189622e-02
552 data8 0xAD8A5BA6D0FD9758, 0x00003FFC //A16 = 1.6947310643831556048460963841e-01
553 data8 0xFCDDA464AD3F182E, 0x00003FFE //A15 = 9.8775699098518676937088606052e-01
554 data8 0xAE0DCE2F7B60D1AE, 0x00004001 //A14 = 5.4391852309591064073782104822e+00
555 data8 0xE1745D9ABEB8D1A7, 0x00004003 //A13 = 2.8181819161363002758615770457e+01
556 //A2 = 3.0619656223573554307222366333e+06 + 1.0819940302945474471259520006e-10
557 data8 0x41475C66CFA967E4, 0x3DDDBDDB2A27334B
558 //A1 = 2.6099413018962685018777847290e+06 + 3.6851882860056025385268615240e-10
559 data8 0x4143E98AA6A48974, 0x3DF9530D42589AB6
560 //A0 = 1.1332783889487853739410638809e+06 + 1.9339350553312096248591829758e-10
561 data8 0x41314ADE639225C9, 0x3DEA946DD6C2C8D3
562 data8 0x88BCFAAE71812A1C, 0x00004006 //A12 = 1.3673820009490115307300592012e+02
563 data8 0x9A770F5AB540A326, 0x00004008 //A11 = 6.1786031215382040427126476507e+02
564 data8 0xA170C1D2C6B413FC, 0x0000400A //A10 = 2.5830473201524594051391525170e+03
565 data8 0x9AE56061CB02EB55, 0x0000400C //A9 = 9.9133441230507404119297200255e+03
566 data8 0x872390769650FBE2, 0x0000400E //A8 = 3.4595564309496661629764193479e+04
567 data8 0xD3E5E8D6923910C1, 0x0000400F //A7 = 1.0849181904819284819615140521e+05
568 data8 0x930D70602F50B754, 0x00004011 //A6 = 3.0116351174131169193070583741e+05
569 //
570 // Polynomial coefficients for the tgammal(x), 12 <= |x| < 13
571 //A5 = 1.2249876249976964294910430908e+08 + 6.0051348061679753770848000000e-09
572 data8 0x419D34BB29FFC39D, 0x3E39CAB72E01818D
573 //A4 = 2.3482765927605420351028442383e+08 + 1.1874729051592862323641700000e-08
574 data8 0x41ABFE5F168D56FA, 0x3E4980338AA7B04B
575 //A3 = 3.6407329688125067949295043945e+08 + 2.6657200942150363994658700000e-08
576 data8 0x41B5B35150E199A5, 0x3E5C9F79C0EB5300
577 data8 0xE89AE0F8D726329D, 0x00003FF9 //A20 = 2.8394164465429105626588451540e-02
578 data8 0xCF90981F86E38013, 0x00003FFC //A19 = 2.0270002071785908652476845915e-01
579 data8 0xA56C658079CA8C4A, 0x00003FFF //A18 = 1.2923704984019263122675412350e+00
580 data8 0x80AEF96A67C5615A, 0x00004002 //A17 = 8.0427183300456238315262463506e+00
581 data8 0xBE886D7529678931, 0x00004004 //A16 = 4.7633230047847868242503413461e+01
582 data8 0x858EDBA4CE2F7508, 0x00004007 //A15 = 2.6711607799594541057655957154e+02
583 data8 0xB0B0A3AF388274F0, 0x00004009 //A14 = 1.4135199810126975119809102782e+03
584 data8 0xDBA87137988751EF, 0x0000400B //A13 = 7.0290552818218513870879313985e+03
585 //A2 = 4.2828433593031734228134155273e+08 + 3.9760422293645854535247300000e-08
586 data8 0x41B98719AFEE2947, 0x3E6558A17E0D3007
587 //A1 = 3.4008253676084774732589721680e+08 + 1.2558352335001093116071000000e-09
588 data8 0x41B4453F68C2C6EB, 0x3E159338C5BC7EC3
589 //A0 = 1.3684336546556583046913146973e+08 + 2.6786516700381562934240300000e-08
590 data8 0x41A05020CAEE5EA5, 0x3E5CC3058A858579
591 data8 0xFF5E3940FB4BA576, 0x0000400D //A12 = 3.2687111823895439312116108631e+04
592 data8 0x8A08C124C7F74B6C, 0x00004010 //A11 = 1.4134701786994123329786229006e+05
593 data8 0x89D701953540BFFB, 0x00004012 //A10 = 5.6459209892773907605385652281e+05
594 data8 0xFC46344B3116C3AD, 0x00004013 //A9 = 2.0666305367147234406757715163e+06
595 data8 0xD183EBD7A400151F, 0x00004015 //A8 = 6.8653979211730981618367536737e+06
596 data8 0x9C083A40742112F4, 0x00004017 //A7 = 2.0451444503543981795037456447e+07
597 data8 0xCD3C475B1A8B6662, 0x00004018 //A6 = 5.3801245423495149598177886823e+07
598 LOCAL_OBJECT_END(Constants_Tgammal_poly)
601 LOCAL_OBJECT_START(Constants_Tgammal_poly_splitted)
603 // Polynomial coefficients for the tgammal(x), 1 <= |x| < 1.25
604 //A5 = -9.8199506890310417350775651357e-01+ -3.2546247786122976510752200000e-17
605 data8 0xBFEF6C80EC38B509, 0xBC82C2FA7A3DE3BD
606 //A4 = 9.8172808683439960475425323239e-01 + 4.4847611775298520359811400000e-17
607 data8 0x3FEF6A51055096B0, 0x3C89DA56DE95EFE4
608 //A3 = -9.0747907608088618225394839101e-01 +-1.0244057366544064435443970000e-16
609 data8 0xBFED0A118F324B62, 0xBC9D86C7B9EBCFFF
610 data8 0xB8E3FDAA66CC738E, 0x00003FFB //A20 = 9.0278608095877488976217714815e-02
611 data8 0xA76067AE1738699C, 0x0000BFFD //A19 =-3.2690738678103132837070881737e-01
612 data8 0x9D66B13718408C44, 0x00003FFE //A18 = 6.1484820933424283818320582920e-01
613 data8 0xD4AC67BBB4AE5599, 0x0000BFFE //A17 =-8.3075569470082063491389474937e-01
614 data8 0xF1426ED1C1488DB3, 0x00003FFE //A16 = 9.4241993542644505594957058785e-01
615 data8 0xFC12EB07AA6F4B6B, 0x0000BFFE //A15 =-9.8466366707947121954333549690e-01
616 data8 0xFF2B32CFE5B0DDC8, 0x00003FFE //A14 = 9.9675290656677214804168895915e-01
617 data8 0xFFD8E7E6FF3662EA, 0x0000BFFE //A13 =-9.9940347089360552383472582319e-01
618 //A2 = 9.8905599532797250361682017683e-01 + 5.1760162410376024240867300000e-17
619 data8 0x3FEFA658C23B1578, 0x3C8DD673A61F6FE7
620 //A1 = -5.7721566490153275452712478000e-01+ -1.0607935612223465065923310000e-16
621 data8 0xBFE2788CFC6FB618, 0xBC9E9346622D53B7
622 //A0 = 9.9999999999999988897769753748e-01 + 1.1102230245372554544790880000e-16
623 data8 0x3FEFFFFFFFFFFFFF, 0x3C9FFFFFFFF51E4E
624 data8 0xFFF360DF628F0BC9, 0x00003FFE //A12 = 9.9980740979895815468216470840e-01
625 data8 0xFFEF8F9A72B40480, 0x0000BFFE //A11 = -9.9974916001038145045939523470e-01
626 data8 0xFFE037B8C7E39952, 0x00003FFE //A10 = 9.9951504002809911822597567307e-01
627 data8 0xFFC01E08F348BED2, 0x0000BFFE //A9 = -9.9902522772325406705059517941e-01
628 data8 0xFF83DAC83119B52C, 0x00003FFE //A8 = 9.9810569179053383842734164901e-01
629 data8 0xFEF9F8AB891ABB24, 0x0000BFFE //A7 = -9.9600176036720260345608796766e-01
630 data8 0xFE3F0537573C8235, 0x00003FFE //A6 = 9.9314911461918778676646301341e-01
631 //
632 // Polynomial coefficients for the tgammal(x), 1.25 <= |x| < 1.75
633 //A5 = -7.7523052299853054125655660300e-02+ -1.2693512521686721504433600000e-17
634 data8 0xBFB3D88CFE50601B, 0xBC6D44ED60EE2170
635 //A4 = 1.4464535904462152982041800442e-01 + 2.5426820829345729856648800000e-17
636 data8 0x3FC283BD374EB2A9, 0x3C7D50AC436187C3
637 //A3 = -1.0729480456477220873257039102e-01+ -6.2429894945456418196551000000e-18
638 data8 0xBFBB77AC1CA2EBA5, 0xBC5CCA6BCC422D41
639 data8 0xF732D2689F323283, 0x00003FF2 //A20 = 2.3574688251652899567587145422e-04
640 data8 0xB6B00E23DE89D13A, 0x0000BFF3 //A19 =-3.4844916488842618776630058875e-04
641 data8 0xE98396FE4A1B2799, 0x00003FF3 //A18 =4.4539265198744452020440735977e-04
642 data8 0xAF8D235A640DB1A2, 0x0000BFF4 //A17 =-6.6967514303333563295261178346e-04
643 data8 0x8513B736C918B261, 0x00003FF5 //A16 = 1.0152970456990865810615917715e-03
644 data8 0xC790A1A2C78D8E17, 0x0000BFF5 //A15 =-1.5225598630329403515321688394e-03
645 data8 0x959706CFA638CDE2, 0x00003FF6 //A14 = 2.2825614575133879623648932383e-03
646 data8 0xE050A6021E129860, 0x0000BFF6 //A13 =-3.4227757733947066666295285936e-03
647 //A2 = 4.1481345368830113695679528973e-01 + 3.1252439808354284892632100000e-17
648 data8 0x3FDA8C4DBA620D56, 0x3C82040BCB483C76
649 //A1 = 3.2338397448885010387886751460e-02 + 3.4437825798552300531443100000e-18
650 data8 0x3FA08EA88EE561B1, 0x3C4FC366D6C64806
651 //A0 = 8.8622692545275794095971377828e-01 + 7.2689375867553992399219000000e-17
652 data8 0x3FEC5BF891B4EF6A, 0x3C94F3877D311C0C
653 data8 0xA8275AADC09D16FC, 0x00003FF7 //A12 = 5.1316445128621071486146117136e-03
654 data8 0xFBFE2CE9215267A2, 0x0000BFF7 //A11= -7.6902121820788373000579382408e-03
655 data8 0xBCC8EEAB67ECD91D, 0x00003FF8 //A10 = 1.1522515369164312742737727262e-02
656 data8 0x8D1614BB97E5E8C2, 0x0000BFF9 //A9 = -1.7222443097804730395560633583e-02
657 data8 0xD3A963578BE291E3, 0x00003FF9 //A8 = 2.5837606456090186343624210891e-02
658 data8 0x9BA7EAE64C42FDF7, 0x0000BFFA //A7 = -3.8001935555045161419575037512e-02
659 data8 0xF0115BA1A77607E7, 0x00003FFA //A6 = 5.8610303817173477119764956736e-02
660 //
661 // Polynomial coefficients for the tgammal(x), 1.75 <= |x| < 2.0
662 //A5 = 2.6698206874501426502654943818e-04 + 3.4033756836921062797887300000e-20
663 data8 0x3F317F3740FE2A68, 0x3BE417093234B06E
664 //A4 = 7.4249010753513894345090307070e-02 + 3.9810018444482764697014200000e-18
665 data8 0x3FB301FBB0F25A92, 0x3C525BEFFABB622F
666 //A3 = -8.1576919247086265851720554565e-02+ -5.2716624487804746360745000000e-19
667 data8 0xBFB4E239984650AC, 0xBC2372F1C4F276FF
668 data8 0xFEF3AEE71038E9A3, 0x00003FEB //A20 = 1.8995395865421509009969188571e-06
669 data8 0xA11CFA2672BF876A, 0x0000BFEB //A19 =-1.2003868221414015771269244270e-06
670 data8 0xF8E107215DAE2164, 0x00003FEC //A18 = 3.7085863210303833432006027217e-06
671 data8 0xBCDDD3FC011EF7D6, 0x00003FEC //A17 = 2.8143303971756051015245433043e-06
672 data8 0x8683C4687FA22E68, 0x00003FEE //A16 = 8.0177018464360416764308252462e-06
673 data8 0xFDA09E5D33E32968, 0x00003FEE //A15 = 1.5117372062443781157389064848e-05
674 data8 0xFFB00D0CFF4089B4, 0x00003FEF //A14 = 3.0480348961227424242198174995e-05
675 data8 0xFEF6C39566785085, 0x00003FF0 //A13 = 6.0788135974125244644334004947e-05
676 //A2 = 4.1184033042643969357854416558e-01 + 1.2103396182129232634761000000e-18
677 data8 0x3FDA5B978B96BEBF, 0x3C3653AAD0A139E4
678 //A1 = -4.2278433509846713445057275749e-01+ -4.9429151528135657430413000000e-18
679 data8 0xBFDB0EE6072093CE, 0xBC56CB907027554F
680 //A0 = 1.0000000000000000000000000000e+00 + 1.0969171200000000000000000000e-31
681 data8 0x3FF0000000000000, 0x3981CC6A5B20B4D5
682 data8 0xFF2B7BA9A8D68C37, 0x00003FF1 //A12 = 1.2167446884801403650547161615e-04
683 data8 0xFCA53468E3692EF1, 0x00003FF2 //A11 = 2.4094136329542400976250900707e-04
684 data8 0x808D698A9C993615, 0x00003FF4 //A10 = 4.9038845704938303659791698883e-04
685 data8 0xF10F8E3FB8BB4AFB, 0x00003FF4 //A9 = 9.1957383840999861214472423976e-04
686 data8 0x89E224E42F93F005, 0x00003FF6 //A8 = 2.1039333407187324139473634747e-03
687 data8 0xBAF374824937A323, 0x00003FF6 //A7 = 2.8526458211545152218493600470e-03
688 data8 0xB6BF7564F52140C6, 0x00003FF8 //A6 = 1.1154045718131014476684982178e-02
689 //
690 // Polynomial coefficients for the tgammal(x), 0.0 <= |x| < 0.125
691 //A5 = -9.8199506890314514073736518185e-01+ -5.9363811993837985890950900000e-17
692 data8 0xBFEF6C80EC38B67A, 0xBC911C46B447C81F
693 //A4 = 9.8172808683440015986576554496e-01 + 2.7457414262802803699834200000e-17
694 data8 0x3FEF6A51055096B5, 0x3C7FA7FF90ACAD1F
695 //A3 = -9.0747907608088618225394839101e-01 + -1.0676255850934306734701780000e-16
696 data8 0xBFED0A118F324B62, 0xBC9EC5AFB633438D
697 data8 0x9217E83FA207CB80, 0x00003FFD //A20 = 2.8533864762086088781083621561e-01
698 data8 0xA8DABFA52FDF03EC, 0x0000BFFE //A19= -6.5958783896337186303285832783e-01
699 data8 0xE331ED293AF39F9B, 0x00003FFE //A18 = 8.8748056656454687449654731184e-01
700 data8 0xF9163C5DDB52419D, 0x0000BFFE //A17= -9.7299554149078295602977718525e-01
701 data8 0xFEC0A1C672CB9265, 0x00003FFE //A16 = 9.9512683005268190987854104489e-01
702 data8 0xFFD2D65B8EA7B5F4, 0x0000BFFE //A15= -9.9931087241443958201592847861e-01
703 data8 0xFFF93AA39EE53445, 0x00003FFE //A14 = 9.9989668364186884793382816496e-01
704 data8 0xFFFB99A9A3F5F480, 0x0000BFFE //A13= -9.9993286506283835663204999212e-01
705 //A2 = 9.8905599532797250361682017683e-01 + 5.1778575360788420716540100000e-17
706 data8 0x3FEFA658C23B1578, 0x3C8DD92B45408D07
707 //A1 = -5.7721566490153275452712478000e-01+ -1.0607938730998824663273110000e-16
708 data8 0xBFE2788CFC6FB618, 0xBC9E9346F8FDE55B
709 //A0 = 9.9999999999999988897769753748e-01 + 1.1102230246251564036631420000e-16
710 data8 0x3FEFFFFFFFFFFFFF, 0x3C9FFFFFFFFFFFFF
711 data8 0xFFF7FEBB545812C1, 0x00003FFE //A12 = 9.9987785409425126648628395084e-01
712 data8 0xFFF00C02E943A3F2, 0x0000BFFE //A11= -9.9975657530855116454438747397e-01
713 data8 0xFFE0420AADC53820, 0x00003FFE //A10 = 9.9951565514290485919027183699e-01
714 data8 0xFFC01EB42EF27EEB, 0x0000BFFE //A9 = -9.9902526759155739377365522320e-01
715 data8 0xFF83DAD0BF23FF12, 0x00003FFE //A8 = 9.9810569378236378800364235948e-01
716 data8 0xFEF9F8ABDBCDB2F3, 0x0000BFFE //A7 = -9.9600176044241699109053158187e-01
717 data8 0xFE3F05375988491D, 0x00003FFE //A6 = 9.9314911462127599008937257662e-01
718 LOCAL_OBJECT_END(Constants_Tgammal_poly_splitted)
720 .align 64
721 LOCAL_OBJECT_START(Constants_Tgammal_common)
722 // Positive overflow value
723 data8 0x3FE0000000000000 // 0.5
724 data8 0x3FF8000000000000 // 1.5
725 data8 0x3FD0000000000000 // 0.25
726 data8 0x0000000000000000 // 0
727 data8 0xDB718C066B352E21, 0x00004009 // Positive overflow value
728 LOCAL_OBJECT_END(Constants_Tgammal_common)
732 //=======================================================
733 // Lgamma registers
735 // General Purpose Registers
736 GR_l_Log_Table = r33
737 GR_l_Log_Table1 = r34
738 GR_l_BIAS = r34
739 GR_l_Index1 = r35
740 GR_l_Index2 = r36
741 GR_l_signif_Z = r37
742 GR_l_X_0 = r38
743 GR_l_X_1 = r39
744 GR_l_X_2 = r40
745 GR_l_Z_1 = r41
746 GR_l_Z_2 = r42
747 GR_l_N = r43
748 GR_l_Index3 = r44
749 GR_l_Stirling_Table = r45
750 GR_l_N_Unbiased = r46
752 // Floating Point Registers
753 FR_l_logl_X = f8
755 FR_l_h_3 = f10
756 FR_l_poly_hi = f10
757 FR_l_W = f11
758 FR_l_S = f12
759 FR_l_GS_hi = f13
760 FR_l_Y_lo = f13
761 FR_l_r_cor = f14
762 FR_l_G_1 = f15
763 FR_l_G = f15
764 FR_l_H_1 = f32
765 FR_l_H = f32
766 FR_l_h = f33
767 FR_l_h_1 = f33
768 FR_l_N = f33
769 FR_l_G_2 = f34
770 FR_l_H_2 = f35
771 FR_l_h_2 = f36
772 FR_l_G_3 = f37
773 FR_l_log2_hi = f38
774 FR_l_GS_lo = f39
775 FR_l_H_3 = f40
776 FR_l_float_N = f41
777 FR_l_Q_4 = f42
778 FR_l_Q_3 = f43
779 FR_l_Q_2 = f44
780 FR_l_Q_1 = f45
781 FR_l_Q_5 = f46
782 FR_l_Q_6 = f47
783 FR_l_log2_lo = f48
784 FR_l_r = f49
785 FR_l_poly_lo = f50
786 FR_l_poly = f51
787 FR_l_rsq = f52
788 FR_l_Y_lo_res = f53
790 FR_l_Y0 = f55
791 FR_l_Q0 = f56
792 FR_l_E0 = f57
793 FR_l_E2 = f58
794 FR_l_E1 = f59
795 FR_l_Y1 = f60
796 FR_l_E3 = f61
797 FR_l_Y2 = f62
799 FR_l_Z = f63
800 FR_l_Z2 = f64
801 FR_l_Z4 = f65
802 FR_l_Z8 = f66
804 FR_l_CH = f67
805 FR_l_CL = f68
807 FR_l_B2 = f69
808 FR_l_B4 = f70
809 FR_l_B6 = f71
810 FR_l_B8 = f72
811 FR_l_B10 = f73
812 FR_l_B12 = f74
813 FR_l_B14 = f75
814 FR_l_B16 = f76
815 FR_l_B18 = f77
816 FR_l_Half = f78
817 FR_l_SS = f79
818 FR_l_AbsX_m_Half = f80
819 FR_l_CXH = f81
820 FR_l_CXL = f82
821 FR_l_SSCXH = f83
822 FR_l_SSCXL = f84
823 FR_l_XYH = f85
824 FR_l_XYL = f86
825 FR_l_Temp = f87
827 FR_l_logl_YHi = f88
828 FR_l_logl_YLo = f89
830 FR_l_SignedXYH = f123
832 FR_l_AbsX = f127
836 //=======================================================
837 // Negative part registers
839 // General Purpose Registers
840 GR_n_sin_Table = r47
841 GR_n_XN = r48
843 // Float point registers
844 FR_n_IXNS = f125
845 FR_n_IXN = f126
847 FR_n_XNS = f90
848 FR_n_XS = f91
849 FR_n_XS2 = f92
850 FR_n_XS2L = f93
851 FR_n_XS4 = f94
852 FR_n_XS7 = f95
853 FR_n_XS8 = f96
854 FR_n_TT = f97
855 FR_n_TH = f98
856 FR_n_TL = f99
858 FR_n_A2H = f100
859 FR_n_A2L = f101
860 FR_n_A1H = f102
861 FR_n_A1L = f103
862 FR_n_A9 = f104
863 FR_n_A8 = f105
864 FR_n_A7 = f106
865 FR_n_A6 = f107
866 FR_n_A5 = f108
867 FR_n_A4 = f109
868 FR_n_A3 = f110
870 FR_n_PolyH = f111
871 FR_n_PolyL = f112
873 FR_n_Poly1H = f113
874 FR_n_SinxH = f113 // the same as FR_n_Poly1H
875 FR_n_Poly1L = f114
876 FR_n_SinxL = f114 // the same as FR_n_Poly1L
878 FR_n_Tail = f115
879 FR_n_NegOne = f116
881 FR_n_Y0 = f117
883 FR_n_Q0 = f118
884 FR_n_E0 = f119
886 FR_n_E2 = f120
887 FR_n_E1 = f121
889 FR_n_Y1 = f55
890 FR_n_E3 = f56
892 FR_n_Y2 = f57
893 FR_n_R0 = f58
895 FR_n_E4 = f59
896 FR_n_RcpResH = f60
898 FR_n_Y3 = f61
899 FR_n_R1 = f62
900 FR_n_Temp = f63
902 FR_n_RcpResL = f64
904 FR_n_ResH = f65
905 FR_n_ResL = f66
910 //=======================================================
911 // Exp registers
913 // General Purpose Registers
914 GR_e_ad_Arg = r33
915 GR_e_ad_A = r34
916 GR_e_signexp_x = r35
917 GR_e_exp_x = r35
918 GR_e_exp_mask = r36
919 GR_e_ad_W1 = r37
920 GR_e_ad_W2 = r38
921 GR_e_M2 = r39
922 GR_e_M1 = r40
923 GR_e_K = r41
924 GR_e_exp_2_mk = r42
925 GR_e_exp_2_k = r43
926 GR_e_ad_T1 = r44
927 GR_e_ad_T2 = r45
928 GR_e_N_fix = r46
929 GR_e_one = r47
930 GR_e_exp_bias = r48
931 GR_e_sig_inv_ln2 = r49
932 GR_e_rshf_2to51 = r50
933 GR_e_exp_2tom51 = r51
934 GR_e_rshf = r52
936 // Floating Point Registers
937 FR_e_RSHF_2TO51 = f10
938 FR_e_INV_LN2_2TO63 = f11
939 FR_e_W_2TO51_RSH = f12
940 FR_e_2TOM51 = f13
941 FR_e_RSHF = f14
942 FR_e_Y_hi = f15
943 FR_e_Y_lo = f32
944 FR_e_scale = f33
945 FR_e_float_N = f34
946 FR_e_N_signif = f35
947 FR_e_L_hi = f36
948 FR_e_L_lo = f37
949 FR_e_r = f38
950 FR_e_W1 = f39
951 FR_e_T1 = f40
952 FR_e_W2 = f41
953 FR_e_T2 = f42
954 FR_e_W1_p1 = f43
955 FR_e_rsq = f44
956 FR_e_A2 = f45
957 FR_e_r4 = f46
958 FR_e_A3 = f47
959 FR_e_poly = f48
960 FR_e_T = f49
961 FR_e_W = f50
962 FR_e_Wp1 = f51
963 FR_e_r6 = f52
964 FR_e_2_mk = f53
965 FR_e_A1 = f54
966 FR_e_T_scale = f55
967 FR_e_result_lo = f56
968 FR_e_W_T_scale = f57
969 FR_e_Wp1_T_scale = f58
971 FR_e_expl_Input_X = f123
972 FR_e_expl_Input_Y = f124
973 FR_e_expl_Output_X = f123
974 FR_e_expl_Output_Y = f124
977 FR_e_expl_Input_AbsX = f122
981 //=======================================================
982 // Common registers
984 // General Purpose Registers
985 GR_c_Table = r53
986 GR_c_NegUnderflow = r54
987 GR_c_NegSingularity = r55
988 GR_c_X = r56
989 GR_c_SignBit = r57
990 GR_c_13 = r58
993 // Floating Point Registers
994 FR_c_PosOverflow = f123
995 FR_c_XN = f124
998 //=======================================================
999 // Polynomial part registers
1001 // General Purpose Registers
1002 GR_p_Table = r59
1003 GR_p_XN = r33
1004 GR_p_Table2 = r34
1005 GR_p_Int = r35
1006 GR_p_Offset = r36
1007 GR_p_Offset2 = r38
1008 GR_p_X_Sgnd = GR_l_signif_Z // = r37
1009 GR_p_Exp = r61
1010 GR_p_Bias = r62
1011 GR_p_0p75 = r63
1013 // Floating Point Registers
1014 FR_p_AbsX = FR_l_AbsX // = f127
1015 FR_p_IXN = FR_n_IXN // = f126
1016 FR_p_XN = f32
1017 FR_p_0p5 = f33
1018 FR_p_1p5 = f34
1019 FR_p_AbsXM1 = f35
1020 FR_p_2 = f36
1022 FR_p_A20 = f37
1023 FR_p_A19 = f38
1024 FR_p_A18 = f39
1025 FR_p_A17 = f40
1026 FR_p_A16 = f41
1027 FR_p_A15 = f42
1028 FR_p_A14 = f43
1029 FR_p_A13 = f44
1030 FR_p_A12 = f45
1031 FR_p_A11 = f46
1032 FR_p_A10 = f47
1033 FR_p_A9 = f48
1034 FR_p_A8 = f49
1035 FR_p_A7 = f50
1036 FR_p_A6 = f51
1037 FR_p_A5H = f52
1038 FR_p_A5L = f53
1039 FR_p_A4H = f54
1040 FR_p_A4L = f55
1041 FR_p_A3H = f56
1042 FR_p_A3L = f57
1043 FR_p_A2H = f58
1044 FR_p_A2L = f59
1045 FR_p_A1H = f60
1046 FR_p_A1L = f61
1047 FR_p_A0H = f62
1048 FR_p_A0L = f63
1050 FR_p_XR = f64
1051 FR_p_XR2 = f65
1052 FR_p_XR2L = f52
1054 FR_p_XR3 = f58
1055 FR_p_XR3L = f38
1057 FR_p_XR4 = f42
1058 FR_p_XR6 = f40
1059 FR_p_XR8 = f37
1061 FR_p_Poly5H = f66
1062 FR_p_Poly5L = f67
1063 FR_p_Poly4H = f53
1064 FR_p_Poly4L = f44
1065 FR_p_Poly3H = f41
1066 FR_p_Poly3L = f47
1067 FR_p_Poly2H = f68
1068 FR_p_Poly2L = f54
1069 FR_p_Poly1H = f55
1070 FR_p_Poly1L = f46
1071 FR_p_Poly0H = f39
1072 FR_p_Poly0L = f43
1074 FR_p_Temp5H = f69
1075 FR_p_Temp5L = f70
1076 FR_p_Temp4H = f71
1077 FR_p_Temp4L = f60
1078 FR_p_Temp2H = f72
1079 FR_p_Temp2L = f73
1080 FR_p_Temp1H = f59
1081 FR_p_Temp1L = f61
1082 FR_p_Temp0H = f49
1083 FR_p_Temp0L = f48
1084 FR_p_PolyTail = f45
1085 FR_p_OddPoly0H = f56
1086 FR_p_OddPoly0L = f51
1088 FR_p_0p25 = f73
1091 //=======================================================
1092 // Negative polynomial part registers
1093 // General Purpose Registers
1094 GR_r_sin_Table = r47
1095 GR_r_sin_Table2 = r60
1097 // Floating Point Registers
1098 FR_r_IXNS = FR_n_IXNS
1099 FR_r_IXN = FR_n_IXN
1101 FR_r_AbsX = FR_l_AbsX
1103 FR_r_A9 = f74
1104 FR_r_A8 = f75
1105 FR_r_A7 = f76
1106 FR_r_A6 = f77
1107 FR_r_A5 = f78
1108 FR_r_A4 = f79
1109 FR_r_A3 = f80
1110 FR_r_A2H = f81
1111 FR_r_A2L = f82
1112 FR_r_A1H = f83
1113 FR_r_A1L = f84
1115 FR_r_XNS = f85
1116 FR_r_XS = f86
1117 FR_r_XS2 = f87
1118 FR_r_XS2L = f88
1119 FR_r_XS4 = f89
1120 FR_r_XS7 = f90
1121 FR_r_XS8 = f91
1123 FR_r_Tail = f92
1125 FR_r_TT = f93
1126 FR_r_TH = f94
1127 FR_r_TL = f95
1129 FR_r_ResH = f96
1130 FR_r_ResL = f97
1132 FR_r_Res3H = f98
1133 FR_r_Res3L = f99
1135 FR_r_Res1H = f100
1136 FR_r_Res1L = f101
1140 FR_r_Y0 = f102
1141 FR_r_Q0 = f103
1142 FR_r_E0 = f104
1143 FR_r_E2 = f105
1144 FR_r_E1 = f106
1145 FR_r_Y1 = f107
1146 FR_r_E3 = f108
1147 FR_r_Y2 = f109
1148 FR_r_R0 = f110
1149 FR_r_E4 = f111
1150 FR_r_ZH = f112
1151 FR_r_Y3 = f113
1152 FR_r_R1 = f114
1153 FR_r_ZHN = f115
1154 FR_r_ZL = f115
1155 FR_r_NegOne = f116
1157 FR_z_Y0 = f102
1158 FR_z_Q0 = f103
1159 FR_z_E0 = f104
1160 FR_z_E2 = f105
1161 FR_z_E1 = f106
1162 FR_z_Y1 = f107
1163 FR_z_E3 = f108
1164 FR_z_Y2 = f109
1165 FR_z_R0 = f110
1166 FR_z_E4 = f111
1167 FR_z_ZH = f112
1168 FR_z_Y3 = f113
1169 FR_z_R1 = f114
1170 FR_z_ZL = f115
1173 // General Purpose Registers
1174 GR_SAVE_PFS = r32
1175 GR_DenOverflow = r33
1176 GR_u_XN = r34
1178 GR_SAVE_B0 = r35
1179 GR_SAVE_GP = r36
1180 GR_SAVE_SP = r37
1182 // Floating Point Registers
1183 FR_u_IXN = f34
1186 // ERROR HANDLER REGISTERS
1187 GR_Parameter_X = r64
1188 GR_Parameter_Y = r65
1189 GR_Parameter_RESULT = r66
1190 GR_Parameter_TAG = r67
1192 FR_RESULT = f8
1193 FR_X = f32
1194 FR_Y = f1
1197 .section .text
1198 GLOBAL_LIBM_ENTRY(tgammal)
1199 { .mfi
1200 alloc r32 = ar.pfs,0,32,4,0
1201 fabs FR_l_AbsX = f8 // Get absolute value of X
1202 addl GR_n_sin_Table = @ltoff(Constants_Tgammal_sin), gp
1203 }
1204 { .mfi
1205 addl GR_l_Log_Table=@ltoff(Constants_Tgammal_log_80_Z_G_H_h1#),gp
1206 nop.f 0
1207 addl GR_l_Stirling_Table = @ltoff(Constants_Tgammal_stirling), gp
1208 };;
1210 { .mfi
1211 getf.sig GR_l_signif_Z = f8 // Significand of X
1212 fcvt.fx.s1 FR_n_IXNS = f8 // Convert to fixed point
1213 addl GR_c_Table = @ltoff(Constants_Tgammal_common), gp
1214 }
1215 { .mfi
1216 ld8 GR_l_Log_Table = [GR_l_Log_Table]
1217 nop.f 0
1218 addl GR_p_Table = @ltoff(Constants_Tgammal_poly), gp
1219 };;
1221 { .mfi
1222 ld8 GR_n_sin_Table = [GR_n_sin_Table]
1223 fclass.m p6,p0 = f8,0x1EF // Check x for NaN, 0, INF, denorm
1224 // NatVal.
1225 addl GR_c_NegSingularity = 0x1003E, r0
1226 }
1227 { .mlx
1228 ld8 GR_l_Stirling_Table = [GR_l_Stirling_Table]
1229 movl GR_c_13 = 0x402A000000000000 // 13.0
1230 };;
1232 { .mfi
1233 getf.d GR_c_X = f8 // Double prec. X to general register
1234 frcpa.s1 FR_z_Y0,p0 = f1,f8 // y = frcpa(x) (for negatives)
1235 extr.u GR_l_Index1 = GR_l_signif_Z, 59, 4 // = High 4 bits of Z
1236 }
1237 { .mlx
1238 ld8 GR_c_Table = [GR_c_Table]
1239 movl GR_c_SignBit = 0x8000000000000000 // High bit (sign)
1240 };;
1242 { .mfi
1243 ld8 GR_p_Table = [GR_p_Table]
1244 fcmp.lt.s1 p15, p14 = f8,f0 // p14 - positive arg, p15 - negative
1245 shl GR_l_Index1 = GR_l_Index1,5 // Adjust Index1 ptr (x32)
1246 }
1247 { .mfb
1248 adds GR_c_NegUnderflow = 1765, r0
1249 nop.f 0
1250 (p6) br.cond.spnt tgammal_spec // Spec. values processing branch ////////////
1251 // (0s, INFs, NANs, NatVals, denormals) //////
1252 };;
1254 { .mfi
1255 ldfpd FR_l_CH,FR_l_CL= [GR_l_Stirling_Table], 16 // Load CH, CL
1256 fcvt.fx.trunc.s1 FR_n_IXN = FR_l_AbsX // Abs arg to int by trunc
1257 extr.u GR_l_X_0 = GR_l_signif_Z, 49, 15 // High 15 bit of Z
1258 }
1259 { .mfi
1260 add GR_l_Index1 = GR_l_Index1,GR_l_Log_Table // Add offset
1261 fma.s1 FR_p_2 = f1, f1, f1 // 2.0
1262 andcm GR_c_X = GR_c_X, GR_c_SignBit // Remove sign
1263 };;
1265 { .mfi
1266 addl GR_l_Log_Table = @ltoff(Constants_Tgammal_log_80_Z_G_H_h2#), gp
1267 fcmp.lt.s1 p10, p0 = FR_l_AbsX, f1 // If |X|<1 then p10 = 1
1268 nop.i 0
1269 }
1270 { .mlx
1271 ld2 GR_l_Z_1 = [GR_l_Index1],4 // load Z_1 from Index1
1272 movl GR_l_BIAS = 0x000000000000FFFF // Bias for exponent
1273 };;
1275 { .mfi
1276 ld8 GR_l_Log_Table = [GR_l_Log_Table]
1277 frcpa.s1 FR_l_Y0, p0 = f1, FR_l_AbsX // y = frcpa(x)
1278 nop.i 0
1279 }
1280 { .mfi
1281 ldfs FR_l_G_1 = [GR_l_Index1],4 // Load G_1
1282 fsub.s1 FR_l_W = FR_l_AbsX, f1 // W = |X|-1
1283 nop.i 0
1284 };;
1286 { .mfi
1287 getf.exp GR_l_N_Unbiased= FR_l_AbsX // exponent of |X|
1288 fmerge.se FR_l_S = f1, FR_l_AbsX // S = merging of X and 1.0
1289 cmp.gtu p11, p0 = GR_c_13, GR_c_X // If 1 <= |X| < 13
1290 // then p11 = 1
1291 }
1292 { .mfb
1293 ldfs FR_l_H_1 = [GR_l_Index1],8 // Load H_1
1294 fcvt.xf FR_n_XNS = FR_n_IXNS // Convert to FP repr. of int X
1295 (p10) br.cond.spnt tgamma_lt_1 // Branch to |X| < 1 path ///////////////////
1296 };;
1298 { .mfi
1299 ldfpd FR_n_A2H, FR_n_A2L = [GR_n_sin_Table], 16
1300 nop.f 0
1301 pmpyshr2.u GR_l_X_1 = GR_l_X_0,GR_l_Z_1,15 // Adjust Index2 (x32)
1302 }
1303 { .mfb
1304 ldfe FR_l_B2 = [GR_l_Stirling_Table], 16
1305 nop.f 0
1306 (p11) br.cond.spnt tgamma_lt_13 // Branch to 1 <= |X| < 13 path ///////////////
1307 };;
1309 { .mfi
1310 ldfe FR_l_h_1 = [GR_l_Index1],0
1311 nop.f 0
1312 sub GR_l_N = GR_l_N_Unbiased, GR_l_BIAS // N - BIAS
1313 }
1314 { .mib
1315 ldfpd FR_l_B4,FR_l_B6= [GR_l_Stirling_Table], 16 // Load C
1316 (p15) cmp.geu.unc p8,p0 = GR_l_N_Unbiased, GR_c_NegSingularity
1317 (p8) br.cond.spnt tgammal_singularity // Singularity for arg < to -2^63 //////
1318 };;
1320 { .mmi
1321 (p15) ldfpd FR_n_A1H, FR_n_A1L = [GR_n_sin_Table], 16
1322 ldfpd FR_l_B8, FR_l_B10 = [GR_l_Stirling_Table], 16
1323 add GR_c_Table = 0x20, GR_c_Table
1324 };;
1326 { .mfi
1327 (p15) ldfe FR_n_A9 = [GR_n_sin_Table], 16
1328 fma.s1 FR_l_Q0 = f1,FR_l_Y0,f0 // Q0 = Y0
1329 nop.i 0
1330 }
1331 { .mfi
1332 ldfpd FR_l_B12, FR_l_B14 = [GR_l_Stirling_Table], 16
1333 fnma.s1 FR_l_E0 = FR_l_Y0,FR_l_AbsX,f1 // e = 1-b*y
1334 nop.i 0
1335 };;
1337 { .mfi
1338 (p15) ldfe FR_n_A8 = [GR_n_sin_Table], 16
1339 fcvt.xf FR_c_XN = FR_n_IXN // Convert to FP repr. of int X
1340 extr.u GR_l_Index2 = GR_l_X_1, 6, 4 // Extract Index2
1341 }
1342 { .mfi
1343 ldfpd FR_l_B16, FR_l_B18 = [GR_l_Stirling_Table], 16
1344 nop.f 0
1345 nop.i 0
1346 };;
1348 { .mfi
1349 (p15) ldfe FR_n_A7 = [GR_n_sin_Table], 16
1350 fms.s1 FR_l_CXH = FR_l_CH, f1, FR_l_AbsX // CXH = CH+|X|
1351 shl GR_l_Index2 = GR_l_Index2,5
1352 }
1353 { .mfi
1354 ldfd FR_l_Half = [GR_l_Stirling_Table] // Load 0.5
1355 nop.f 0
1356 nop.i 0
1357 };;
1359 { .mfi
1360 add GR_l_Index2 = GR_l_Index2, GR_l_Log_Table // Add offset
1361 nop.f 0
1362 nop.i 0
1363 }
1364 { .mfi
1365 (p15) ldfe FR_n_A6 = [GR_n_sin_Table], 16
1366 (p15) fma.s1 FR_n_XS = FR_l_AbsX , f1, FR_n_XNS // xs = x - int(x)
1367 nop.i 0
1368 };;
1370 { .mmi
1371 ld2 GR_l_Z_2 = [GR_l_Index2],4
1372 addl GR_l_Log_Table = @ltoff(Constants_Tgammal_log_80_h3_G_H#),gp
1373 nop.i 0
1374 };;
1376 { .mfi
1377 ld8 GR_l_Log_Table = [GR_l_Log_Table]
1378 fma.s1 FR_l_E2 = FR_l_E0,FR_l_E0,FR_l_E0 // e2 = e+e^2
1379 nop.i 0
1380 }
1381 { .mfi
1382 ldfs FR_l_G_2 = [GR_l_Index2],4
1383 fma.s1 FR_l_E1 = FR_l_E0,FR_l_E0,f0 // e1 = e^2
1384 nop.i 0
1385 };;
1387 { .mmi
1388 ldfs FR_l_H_2 = [GR_l_Index2],8
1389 (p15) ldfe FR_n_A5 = [GR_n_sin_Table], 16
1390 nop.i 0
1391 };;
1393 { .mfi
1394 setf.sig FR_l_float_N = GR_l_N // float_N = Make N a fp number
1395 nop.f 0
1396 pmpyshr2.u GR_l_X_2 = GR_l_X_1,GR_l_Z_2,15 // X_2 = X_1 * Z_2
1397 }
1398 { .mfi
1399 ldfe FR_l_h_2 = [GR_l_Index2],0
1400 fma.s1 FR_l_CXL = FR_l_AbsX, f1, FR_l_CXH // CXL = |X|+CXH
1401 add GR_l_Log_Table1= 0x200, GR_l_Log_Table
1402 };;
1404 { .mfi
1405 (p15) ldfe FR_n_A4 = [GR_n_sin_Table], 16
1406 (p15) fcmp.eq.unc.s1 p9,p0 = FR_l_AbsX, FR_c_XN //if argument is integer
1407 // and negative
1408 nop.i 0
1409 }
1410 { .mfi
1411 ldfe FR_c_PosOverflow = [GR_c_Table],16 //Load pos overflow value
1412 (p15) fma.s1 FR_n_XS2 = FR_n_XS, FR_n_XS, f0 // xs^2 = xs*xs
1413 nop.i 0
1414 };;
1416 { .mfi
1417 (p15) ldfe FR_n_A3 = [GR_n_sin_Table], 16
1418 nop.f 0
1419 nop.i 0
1420 };;
1422 { .mfi
1423 (p15) getf.sig GR_n_XN = FR_n_IXN // int(x) to general reg
1424 fma.s1 FR_l_Y1 = FR_l_Y0,FR_l_E2,FR_l_Y0 // y1 = y+y*e2
1425 nop.i 0
1426 }
1427 { .mfb
1428 nop.m 0
1429 fma.s1 FR_l_E3 = FR_l_E1,FR_l_E1,FR_l_E0 // e3 = e+e1^2
1430 (p9) br.cond.spnt tgammal_singularity // Singularity for integer /////////////
1431 // and negative arguments //////////////
1432 };;
1434 { .mfi
1435 nop.m 0
1436 fms.s1 FR_l_AbsX_m_Half = FR_l_AbsX, f1, FR_l_Half // |x|-0.5
1437 extr.u GR_l_Index2 = GR_l_X_2, 1, 5 // Get Index3
1438 };;
1440 { .mfi
1441 shladd GR_l_Log_Table1= GR_l_Index2, 2, GR_l_Log_Table1
1442 nop.f 0
1443 shladd GR_l_Index3 = GR_l_Index2,4, GR_l_Log_Table // Index3
1444 }
1445 { .mfb
1446 (p15) cmp.gtu.unc p11, p0 = GR_n_XN, GR_c_NegUnderflow // X < -1765
1447 fms.s1 FR_l_CXL = FR_l_CH, f1, FR_l_CXL // CXL = CH - CXL
1448 (p11) br.cond.spnt tgammal_underflow // Singularity for negative argument //////
1449 // at underflow domain (X < -1765) //////
1450 };;
1452 { .mfi
1453 addl GR_l_Log_Table = @ltoff(Constants_Tgammal_log_80_Q#), gp
1454 (p15) fma.s1 FR_n_TT = FR_n_A2L, FR_n_XS2, f0 // T=A2L*x^2
1455 tbit.nz.unc p13, p12 = GR_n_XN, 0x0 // whether [X] odd or even
1456 }
1457 { .mfi
1458 nop.m 0
1459 (p15) fms.s1 FR_n_XS2L = FR_n_XS, FR_n_XS, FR_n_XS2 // xs^2 Low part
1460 nop.i 0
1461 };;
1463 { .mfi
1464 ld8 GR_l_Log_Table = [GR_l_Log_Table]
1465 (p15) fma.s1 FR_n_A7 = FR_n_A8, FR_n_XS2, FR_n_A7 // poly tail
1466 nop.i 0
1467 }
1468 { .mfi
1469 ldfe FR_l_h_3 = [GR_l_Index3],12
1470 (p15) fma.s1 FR_n_XS4 = FR_n_XS2, FR_n_XS2, f0 // xs^4 = xs^2*xs^2
1471 nop.i 0
1472 };;
1474 { .mfi
1475 ldfs FR_l_H_3 = [GR_l_Log_Table1], 0
1476 fma.s1 FR_l_Y2 = FR_l_Y1, FR_l_E3, FR_l_Y0 // y2 = y+y1*e3
1477 nop.i 0
1478 }
1479 { .mfi
1480 ldfs FR_l_G_3 = [GR_l_Index3], 0
1481 fnma.s1 FR_l_Z = FR_l_AbsX,FR_l_Q0,f1 // r = a-b*q
1482 nop.i 0
1483 };;
1485 { .mfi
1486 nop.m 0
1487 fmpy.s1 FR_l_G = FR_l_G_1, FR_l_G_2 // G = G1 * G_2
1488 nop.i 0
1489 }
1490 { .mfi
1491 nop.m 0
1492 fadd.s1 FR_l_H = FR_l_H_1, FR_l_H_2 // H = H_1 + H_2
1493 nop.i 0
1494 };;
1496 { .mfi
1497 ldfe FR_l_log2_hi = [GR_l_Log_Table],16 // load log2_hi part
1498 fadd.s1 FR_l_h = FR_l_h_1, FR_l_h_2 // h = h_1 + h_2
1499 nop.i 0
1500 }
1501 { .mfi
1502 nop.m 0
1503 fcvt.xf FR_l_float_N = FR_l_float_N // int(N)
1504 nop.i 0
1505 };;
1507 { .mfi
1508 ldfe FR_l_log2_lo = [GR_l_Log_Table],16 // Load log2_lo part
1509 fma.s1 FR_l_CXL = FR_l_CXL, f1, FR_l_CL
1510 nop.i 0
1511 }
1512 { .mfi
1513 nop.m 0
1514 (p15) fma.s1 FR_n_TT = FR_n_A2H, FR_n_XS2L, FR_n_TT // T=A2H*x2L+T
1515 nop.i 0
1516 };;
1518 { .mfi
1519 ldfe FR_l_Q_6 = [GR_l_Log_Table],16
1520 (p15) fma.s1 FR_n_A3 = FR_n_A4, FR_n_XS2, FR_n_A3 // poly tail
1521 nop.i 0
1522 }
1523 { .mfi
1524 nop.m 0
1525 (p15) fma.s1 FR_n_A5 = FR_n_A6, FR_n_XS2, FR_n_A5 // poly tail
1526 nop.i 0
1527 };;
1529 { .mfi
1530 ldfe FR_l_Q_5 = [GR_l_Log_Table],16
1531 (p15) fabs FR_n_XS = FR_n_XS // abs(xs)
1532 nop.i 0
1533 }
1534 { .mfi
1535 nop.m 0
1536 fma.s1 FR_l_Z = FR_l_Z,FR_l_Y2,FR_l_Q0 // x_hi = q+r*y2
1537 nop.i 0
1538 };;
1540 { .mfi
1541 ldfe FR_l_Q_4 = [GR_l_Log_Table],16
1542 (p15) fma.s1 FR_n_A7 = FR_n_A9, FR_n_XS4, FR_n_A7 // poly tail
1543 nop.i 0
1544 }
1545 { .mfi
1546 nop.m 0
1547 (p15) fma.s1 FR_n_XS7 = FR_n_XS4, FR_n_XS2, f0 // = x^4*x^2
1548 nop.i 0
1549 };;
1551 { .mfi
1552 ldfe FR_l_Q_3 = [GR_l_Log_Table],16
1553 fneg FR_n_NegOne = f1 // -1.0
1554 nop.i 0
1555 }
1556 { .mfi
1557 nop.m 0
1558 (p15) fma.s1 FR_n_XS8 = FR_n_XS4, FR_n_XS4, f0 // xs^8 = xs^4*xs^4
1559 nop.i 0
1560 };;
1562 { .mfi
1563 ldfe FR_l_Q_2 = [GR_l_Log_Table],16
1564 fadd.s1 FR_l_h = FR_l_h, FR_l_h_3 // h = h_1 + h_2 + h_3
1565 nop.i 0
1566 }
1567 { .mfi
1568 nop.m 0
1569 (p15) fma.s1 FR_n_TH = FR_n_A2H, FR_n_XS2, FR_n_TT // A2H*xs2+T
1570 nop.i 0
1571 };;
1573 { .mfi
1574 ldfe FR_l_Q_1 = [GR_l_Log_Table],16
1575 fmpy.s1 FR_l_G = FR_l_G, FR_l_G_3 // G = G_1 * G_2 * G_3
1576 nop.i 0
1577 }
1578 { .mfi
1579 nop.m 0
1580 fadd.s1 FR_l_H = FR_l_H, FR_l_H_3 // H = H_1 + H_2 + H_3
1581 nop.i 0
1582 };;
1584 { .mfi
1585 nop.m 0
1586 fma.s1 FR_l_Z2 = FR_l_Z, FR_l_Z, f0 // Z^2
1587 nop.i 0
1588 }
1589 { .mfi
1590 nop.m 0
1591 (p15) fma.s1 FR_n_A3 = FR_n_A5, FR_n_XS4, FR_n_A3 // poly tail
1592 nop.i 0
1593 };;
1595 { .mfi
1596 nop.m 0
1597 (p14) fcmp.gt.unc.s1 p7,p0 = FR_l_AbsX, FR_c_PosOverflow //X > 1755.5483
1598 // (overflow domain, result cannot be represented by normal value)
1599 nop.i 0
1600 }
1601 { .mfi
1602 nop.m 0
1603 (p15) fma.s1 FR_n_XS7 = FR_n_XS7, FR_n_XS, f0 // x^7 construction
1604 nop.i 0
1605 };;
1607 { .mfi
1608 nop.m 0
1609 (p15) fms.s1 FR_n_TL = FR_n_A2H, FR_n_XS2, FR_n_TH // A2H*xs2+TH
1610 nop.i 0
1611 }
1612 { .mfi
1613 nop.m 0
1614 (p15) fma.s1 FR_n_PolyH = FR_n_TH, f1, FR_n_A1H // PolyH=TH+A1H
1615 nop.i 0
1616 };;
1618 { .mfi
1619 nop.m 0
1620 fmpy.s1 FR_l_GS_hi = FR_l_G, FR_l_S // GS_hi = G*S
1621 nop.i 0
1622 }
1623 { .mfb
1624 nop.m 0
1625 fms.s1 FR_l_r = FR_l_G, FR_l_S, f1 // r = G*S -1
1626 (p7) br.cond.spnt tgammal_overflow // Overflow path for arg > 1755.5483 //////
1627 };;
1629 { .mfi
1630 nop.m 0
1631 fma.s1 FR_l_B14 = FR_l_B16, FR_l_Z2, FR_l_B14// Bernoulli tail
1632 nop.i 0
1633 }
1634 { .mfi
1635 nop.m 0
1636 fma.s1 FR_l_Z4 = FR_l_Z2, FR_l_Z2, f0 // Z^4 = Z^2*Z^2
1637 nop.i 0
1638 };;
1640 { .mfi
1641 nop.m 0
1642 fma.s1 FR_l_B2 = FR_l_B4, FR_l_Z2, FR_l_B2 // Bernoulli tail
1643 nop.i 0
1644 }
1645 { .mfi
1646 nop.m 0
1647 fma.s1 FR_l_B6 = FR_l_B8, FR_l_Z2, FR_l_B6 // Bernoulli tail
1648 nop.i 0
1649 };;
1651 { .mfi
1652 nop.m 0
1653 fma.s1 FR_l_B10 = FR_l_B12, FR_l_Z2, FR_l_B10// Bernoulli tail
1654 nop.i 0
1655 }
1656 { .mfi
1657 nop.m 0
1658 (p15) fma.s1 FR_n_Tail = FR_n_A7, FR_n_XS8, FR_n_A3 // poly tail
1659 nop.i 0
1660 };;
1662 { .mfi
1663 nop.m 0
1664 (p15) fma.s1 FR_n_TL = FR_n_TL, f1, FR_n_TT // TL = TL+T
1665 nop.i 0
1666 }
1667 { .mfi
1668 nop.m 0
1669 (p15) fms.s1 FR_n_PolyL = FR_n_A1H, f1, FR_n_PolyH // polyH+A1H
1670 nop.i 0
1671 };;
1673 { .mfi
1674 nop.m 0
1675 fma.s1 FR_l_poly_lo = FR_l_r, FR_l_Q_6, FR_l_Q_5 // Q_5+r*Q_6
1676 nop.i 0
1677 }
1678 { .mfi
1679 nop.m 0
1680 fsub.s1 FR_l_r_cor = FR_l_GS_hi, f1 // r_cor = GS_hi -1
1681 nop.i 0
1682 };;
1684 { .mfi
1685 nop.m 0
1686 fms.s1 FR_l_GS_lo = FR_l_G, FR_l_S, FR_l_GS_hi // G*S-GS_hi
1687 nop.i 0
1688 }
1689 { .mfi
1690 nop.m 0
1691 fma.s1 FR_l_poly = FR_l_r, FR_l_Q_2, FR_l_Q_1 //poly=r*Q2+Q1
1692 nop.i 0
1693 };;
1695 { .mfi
1696 nop.m 0
1697 fmpy.s1 FR_l_rsq = FR_l_r, FR_l_r // rsq = r * r
1698 nop.i 0
1699 }
1700 { .mfi
1701 nop.m 0
1702 fma.s1 FR_l_G = FR_l_float_N, FR_l_log2_hi, FR_l_H // Tbl =
1703 // float_N*log2_hi + H
1704 nop.i 0
1705 };;
1707 { .mfi
1708 nop.m 0
1709 fma.s1 FR_l_Y_lo = FR_l_float_N, FR_l_log2_lo, FR_l_h // Y_lo=
1710 // float_N*log2_lo + h
1711 nop.i 0
1712 }
1713 { .mfi
1714 nop.m 0
1715 fma.s1 FR_l_B14 = FR_l_B18, FR_l_Z4, FR_l_B14 //bernulli tail
1716 nop.i 0
1717 };;
1719 { .mfi
1720 nop.m 0
1721 fma.s1 FR_l_B2 = FR_l_B6, FR_l_Z4, FR_l_B2 //bernulli tail
1722 nop.i 0
1723 }
1724 { .mfi
1725 nop.m 0
1726 fma.s1 FR_l_Z8 = FR_l_Z4, FR_l_Z4, f0 //bernulli tail
1727 nop.i 0
1728 };;
1730 { .mfi
1731 nop.m 0
1732 fma.s1 FR_l_poly_lo = FR_l_r, FR_l_poly_lo, FR_l_Q_4 // poly_lo =
1733 // Q_4 + r * poly_lo
1734 nop.i 0
1735 }
1736 { .mfi
1737 nop.m 0
1738 fsub.s1 FR_l_r_cor = FR_l_r_cor, FR_l_r // r_cor = r_cor - r
1739 nop.i 0
1740 };;
1742 { .mfi
1743 nop.m 0
1744 (p15) fma.s1 FR_n_PolyL = FR_n_PolyL, f1, FR_n_TH // polyL+TH
1745 nop.i 0
1746 }
1747 { .mfi
1748 nop.m 0
1749 (p15) fma.s1 FR_n_TT = FR_n_TL, f1, FR_n_A1L // TL+A1L
1750 nop.i 0
1751 };;
1753 { .mfi
1754 nop.m 0
1755 fadd.s1 FR_l_logl_YHi = FR_l_G, FR_l_r // Y_hi = Tbl + r
1756 nop.i 0
1757 };;
1759 { .mfi
1760 nop.m 0
1761 fma.s1 FR_l_B10 = FR_l_B14, FR_l_Z4, FR_l_B10 //bernulli tail
1762 nop.i 0
1763 };;
1765 { .mfi
1766 nop.m 0
1767 fma.s1 FR_l_poly_lo = FR_l_r, FR_l_poly_lo, FR_l_Q_3 // poly_lo =
1768 // Q_3 + r * poly_lo
1769 nop.i 0
1770 }
1771 { .mfi
1772 nop.m 0
1773 fadd.s1 FR_l_r_cor = FR_l_r_cor, FR_l_GS_lo // r_cor=r_cor+GS_lo
1774 nop.i 0
1775 };;
1777 { .mfi
1778 nop.m 0
1779 (p15) fma.s1 FR_n_PolyL = FR_n_PolyL, f1, FR_n_TT // polyL+TT
1780 nop.i 0
1781 };;
1783 { .mfi
1784 nop.m 0
1785 fsub.s1 FR_l_Y_lo_res = FR_l_G, FR_l_logl_YHi // Y_lo = Tbl - Y_hi
1786 nop.i 0
1787 }
1788 { .mfi
1789 nop.m 0
1790 fma.s1 FR_l_XYH = FR_l_logl_YHi, FR_l_AbsX_m_Half, f0 // XYH=
1791 // YHi*|x-0.5|
1792 nop.i 0
1793 };;
1795 { .mfi
1796 nop.m 0
1797 fma.s1 FR_l_SS = FR_l_B10, FR_l_Z8, FR_l_B2 // Bernoulli tail
1798 nop.i 0
1799 };;
1801 { .mfi
1802 nop.m 0
1803 fadd.s1 FR_l_r_cor = FR_l_r_cor, FR_l_Y_lo // r_cor = r_cor+Y_lo
1804 nop.i 0
1805 }
1806 { .mfi
1807 nop.m 0
1808 fma.s1 FR_l_poly = FR_l_rsq, FR_l_poly_lo, FR_l_poly //poly=
1809 // r^2*polyLo+poly
1810 nop.i 0
1811 };;
1813 { .mfi
1814 nop.m 0
1815 (p15) fma.s1 FR_n_TT = FR_n_PolyL, FR_n_XS2, f0 // T=polyL*xs^2
1816 nop.i 0
1817 };;
1819 { .mfi
1820 nop.m 0
1821 fadd.s1 FR_l_Y_lo = FR_l_Y_lo_res, FR_l_r // Y_lo = Y_lo + r
1822 nop.i 0
1823 }
1824 { .mfi
1825 nop.m 0
1826 fms.s1 FR_l_XYL = FR_l_logl_YHi, FR_l_AbsX_m_Half, FR_l_XYH
1827 // XYL = YHi*|x-0.5|-XYH
1828 nop.i 0
1829 };;
1831 { .mfi
1832 nop.m 0
1833 fma.s1 FR_l_SSCXH = FR_l_SS, FR_l_Z, FR_l_CXH // SS*Z+CXH
1834 nop.i 0
1835 }
1836 { .mfi
1837 mov GR_e_exp_2tom51= 0xffff-51 // 2^-51
1838 (p15) fma.s1 FR_l_SignedXYH = FR_l_XYH, FR_n_NegOne, f0 // XYH = -XYH
1839 // for negatives
1840 nop.i 0
1841 };;
1843 { .mlx
1844 nop.m 0
1845 movl GR_e_rshf_2to51 = 0x4718000000000000 // 1.10000 2^(63+51)
1846 }
1847 { .mlx
1848 nop.m 0
1849 movl GR_e_sig_inv_ln2 = 0xb8aa3b295c17f0bc //significand of 1/ln2
1850 };;
1852 { .mfi
1853 nop.m 0
1854 fma.s1 FR_l_poly = FR_l_rsq, FR_l_poly, FR_l_r_cor // poly =
1855 // rsq * poly + r_cor
1856 nop.i 0
1857 };;
1859 { .mfi
1860 addl GR_e_ad_Arg = @ltoff(Constants_Tgammal_exp_64_Arg#),gp
1861 (p15) fma.s1 FR_n_TT = FR_n_PolyH, FR_n_XS2L, FR_n_TT
1862 mov GR_e_exp_mask = 0x1FFFF // Form exponent mask
1863 }
1864 { .mlx
1865 nop.m 0
1866 movl GR_e_rshf = 0x43e8000000000000 // 1.10000 2^63 rshift
1867 };;
1870 { .mmi
1871 setf.sig FR_e_INV_LN2_2TO63 = GR_e_sig_inv_ln2 // form 1/ln2 * 2^63
1872 setf.d FR_e_RSHF_2TO51 = GR_e_rshf_2to51 // 1.1000 * 2^(63+51)
1873 nop.i 0
1874 };;
1876 { .mfi
1877 nop.m 0
1878 fms.s1 FR_l_SSCXL = FR_l_CXH, f1, FR_l_SSCXH // CXH+SS*CXH
1879 nop.i 0
1880 }
1881 { .mfi
1882 nop.m 0
1883 fma.s1 FR_e_expl_Input_AbsX = FR_l_XYH, f1, FR_l_SSCXH // HI EXP
1884 nop.i 0
1885 };;
1887 .pred.rel "mutex",p14,p15
1888 { .mfi
1889 nop.m 0
1890 (p14) fma.s1 FR_e_expl_Input_X = FR_l_XYH, f1, FR_l_SSCXH // HI EXP
1891 mov GR_e_exp_bias = 0x0FFFF // Set exponent bias
1892 }
1893 { .mfi
1894 ld8 GR_e_ad_Arg = [GR_e_ad_Arg] // Point to Arg table
1895 (p15) fms.s1 FR_e_expl_Input_X = FR_l_SignedXYH, f1, FR_l_SSCXH // HI EXP
1896 nop.i 0
1897 };;
1899 { .mfi
1900 nop.m 0
1901 fadd.s1 FR_l_logl_YLo = FR_l_Y_lo, FR_l_poly // YLo = YLo+poly
1902 nop.i 0
1903 };;
1905 { .mfi
1906 setf.exp FR_e_2TOM51 = GR_e_exp_2tom51 //2^-51 for scaling float_N
1907 (p15) fma.s1 FR_n_TH = FR_n_PolyH, FR_n_XS2, FR_n_TT // TH=
1908 // polyH*xs^2+T
1909 nop.i 0
1910 }
1911 { .mib
1912 setf.d FR_e_RSHF = GR_e_rshf // Right shift const 1.1000*2^63
1913 nop.i 0
1914 nop.b 0
1915 };;
1917 { .mfi
1918 add GR_e_ad_A = 0x20, GR_e_ad_Arg // Point to A table
1919 nop.f 0
1920 add GR_e_ad_T1 = 0x50, GR_e_ad_Arg // Point to T1 table
1921 }
1922 { .mfi
1923 add GR_e_ad_T2 = 0x150, GR_e_ad_Arg // Point to T2 table
1924 nop.f 0
1925 nop.i 0
1926 };;
1928 { .mfi
1929 nop.m 0
1930 fma.s1 FR_l_SSCXL = FR_l_SS, FR_l_Z, FR_l_SSCXL
1931 nop.i 0
1932 }
1933 { .mfi
1934 nop.m 0
1935 fms.s1 FR_e_expl_Input_Y = FR_l_XYH, f1, FR_e_expl_Input_AbsX
1936 nop.i 0
1937 };;
1939 { .mfi
1940 ldfe FR_e_L_hi = [GR_e_ad_Arg],16 // Get L_hi
1941 nop.f 0
1942 nop.i 0
1943 };;
1945 { .mfi
1946 nop.m 0
1947 fma.s1 FR_l_XYL = FR_l_logl_YLo, FR_l_AbsX_m_Half, FR_l_XYL
1948 // XYL = YLo*|x-0.5|+XYL
1949 nop.i 0
1950 };;
1952 { .mfi
1953 ldfe FR_e_L_lo = [GR_e_ad_Arg],16 // Get L_lo
1954 (p15) fms.s1 FR_n_TL = FR_n_PolyH, FR_n_XS2, FR_n_TH // TL =
1955 // = polyH*xs^2-TH
1956 add GR_e_ad_W1 = 0x100, GR_e_ad_T2 // Point to W1 table
1957 }
1958 { .mfi
1959 nop.m 0
1960 (p15) fma.s1 FR_n_Poly1H = FR_n_TH, f1, f1 // poly1H = TH+1
1961 add GR_e_ad_W2 = 0x300, GR_e_ad_T2 // Point to W2 table
1962 };;
1964 { .mmi
1965 getf.exp GR_e_signexp_x = FR_e_expl_Input_X // Extract sign and exp
1966 ldfe FR_e_A3 = [GR_e_ad_A],16 // Get A3
1967 nop.i 0
1968 };;
1970 { .mfi
1971 nop.m 0
1972 fma.s1 FR_l_SSCXL = FR_l_SSCXL, f1, FR_l_CXL
1973 nop.i 0
1974 }
1975 { .mfi
1976 nop.m 0
1977 fma.s1 FR_e_expl_Input_Y = FR_e_expl_Input_Y, f1, FR_l_SSCXH
1978 nop.i 0
1979 };;
1981 { .mfi
1982 nop.m 0
1983 fma.s1 FR_e_N_signif=FR_e_expl_Input_X,FR_e_INV_LN2_2TO63,FR_e_RSHF_2TO51
1984 and GR_e_exp_x = GR_e_signexp_x, GR_e_exp_mask
1985 };;
1987 { .mmi
1988 sub GR_e_exp_x = GR_e_exp_x, GR_e_exp_bias // Get exponent
1989 ldfe FR_e_A2 = [GR_e_ad_A],16 // Get A2 for main path
1990 nop.i 0
1991 };;
1993 { .mfi
1994 nop.m 0
1995 (p15) fma.s1 FR_n_PolyH = FR_n_Poly1H, FR_n_XS, f0//sin(Pi*x) poly
1996 nop.i 0
1997 }
1998 { .mfi
1999 nop.m 0
2000 (p15) fms.s1 FR_n_Poly1L = f1, f1, FR_n_Poly1H//sin(Pi*x) poly
2001 nop.i 0
2002 };;
2004 { .mfi
2005 nop.m 0
2006 (p15) fma.s1 FR_n_TL = FR_n_TL, f1, FR_n_TT//sin(Pi*x) poly
2007 nop.i 0
2008 };;
2010 { .mfi
2011 nop.m 0
2012 fma.s1 FR_l_Temp = FR_l_XYL, f1, FR_l_SSCXL // XYL+SS*CXL
2013 nop.i 0
2014 }
2015 { .mfi
2016 nop.m 0
2017 (p15) fma.s1 FR_e_expl_Input_Y = FR_e_expl_Input_Y, FR_n_NegOne, f0
2018 // Negate lo part of exp argument for negative input values
2019 nop.i 0
2020 };;
2022 { .mfi
2023 ldfe FR_e_A1 = [GR_e_ad_A],16 // Get A1
2024 nop.f 0
2025 nop.i 0
2026 }
2027 { .mfi
2028 nop.m 0
2029 fms.s1 FR_e_float_N = FR_e_N_signif, FR_e_2TOM51, FR_e_RSHF
2030 // Get float N = signd*2^51-RSHIFTER
2031 nop.i 0
2032 };;
2034 { .mfi
2035 nop.m 0
2036 (p15) fma.s1 FR_n_Poly1L = FR_n_Poly1L, f1, FR_n_TH //sin(Pi*x) poly
2037 nop.i 0
2038 }
2039 { .mfi
2040 nop.m 0
2041 (p15) fms.s1 FR_n_PolyL = FR_n_Poly1H, FR_n_XS, FR_n_PolyH//sin(Pi*x)
2042 nop.i 0
2043 };;
2045 { .mfi
2046 getf.sig GR_e_N_fix = FR_e_N_signif // Get N from significand
2047 nop.f 0
2048 nop.i 0
2049 };;
2051 .pred.rel "mutex",p14,p15
2052 { .mfi
2053 nop.m 0
2054 (p14) fma.s1 FR_e_expl_Input_Y = FR_e_expl_Input_Y, f1, FR_l_Temp
2055 nop.i 0
2056 }
2057 { .mfi
2058 nop.m 0
2059 (p15) fms.s1 FR_e_expl_Input_Y = FR_e_expl_Input_Y, f1, FR_l_Temp
2060 // arguments for exp computation
2061 nop.i 0
2062 };;
2064 { .mfi
2065 nop.m 0
2066 fnma.s1 FR_e_r = FR_e_L_hi, FR_e_float_N, FR_e_expl_Input_X
2067 // r = -L_hi * float_N + x
2068 extr.u GR_e_M1 = GR_e_N_fix, 6, 6 // Extract index M_1
2069 };;
2071 { .mfi
2072 nop.m 0
2073 (p15) fma.s1 FR_n_Poly1L = FR_n_Poly1L, f1, FR_n_TL //sin(Pi*x) poly
2074 nop.i 0
2075 };;
2078 { .mmf
2079 nop.m 0
2080 nop.m 0
2081 fma.s1 FR_e_r = FR_e_r, f1, FR_e_expl_Input_Y
2082 // r = r + FR_e_expl_Input_Y
2083 };;
2085 { .mmi
2086 shladd GR_e_ad_W1 = GR_e_M1,3,GR_e_ad_W1 // Point to W1
2087 shladd GR_e_ad_T1 = GR_e_M1,2,GR_e_ad_T1 // Point to T1
2088 extr.u GR_e_M2 = GR_e_N_fix, 0, 6 // Extract index M_2
2089 };;
2092 { .mfi
2093 ldfs FR_e_T1 = [GR_e_ad_T1],0 // Get T1
2094 nop.f 0
2095 extr GR_e_K = GR_e_N_fix, 12, 32 //Extract limit range K
2096 }
2097 { .mfi
2098 shladd GR_e_ad_T2 = GR_e_M2,2,GR_e_ad_T2 // Point to T2
2099 (p15) fma.s1 FR_n_PolyL = FR_n_Poly1L, FR_n_XS, FR_n_PolyL
2100 //sin(Pi*x) poly
2101 shladd GR_e_ad_W2 = GR_e_M2,3,GR_e_ad_W2 // Point to W2
2102 };;
2104 { .mfi
2105 ldfs FR_e_T2 = [GR_e_ad_T2],0 // Get T2
2106 nop.f 0
2107 add GR_e_exp_2_k = GR_e_exp_bias, GR_e_K // exp of 2^k
2108 }
2109 { .mfi
2110 ldfd FR_e_W1 = [GR_e_ad_W1],0 // Get W1
2111 nop.f 0
2112 sub GR_e_exp_2_mk = GR_e_exp_bias, GR_e_K // exp of 2^-k
2113 };;
2115 { .mmi
2116 ldfd FR_e_W2 = [GR_e_ad_W2],0 // Get W2
2117 nop.m 0
2118 nop.i 0
2119 };;
2121 { .mmf
2122 setf.exp FR_e_scale = GR_e_exp_2_k // Set scale = 2^k
2123 setf.exp FR_e_2_mk = GR_e_exp_2_mk // Form 2^-k
2124 fnma.s1 FR_e_r = FR_e_L_lo, FR_e_float_N, FR_e_r
2125 // r = -L_lo * float_N + r
2126 };;
2128 { .mfi
2129 nop.m 0
2130 (p15) fma.s1 FR_n_PolyL = FR_n_Tail, FR_n_XS7, FR_n_PolyL
2131 //sin(Pi*x) poly
2132 nop.i 0
2133 };;
2135 { .mfi
2136 nop.m 0
2137 fma.s1 FR_e_poly = FR_e_r, FR_e_A3, FR_e_A2 // poly=r*A3+A2
2138 nop.i 0
2139 }
2140 { .mfi
2141 nop.m 0
2142 fmpy.s1 FR_e_rsq = FR_e_r, FR_e_r // rsq = r * r
2143 nop.i 0
2144 };;
2146 { .mfi
2147 nop.m 0
2148 fmpy.s1 FR_e_T = FR_e_T1, FR_e_T2 // T = T1 * T2
2149 nop.i 0
2150 }
2151 { .mfi
2152 nop.m 0
2153 fadd.s1 FR_e_W1_p1 = FR_e_W1, f1 // W1_p1 = W1 + 1.0
2154 nop.i 0
2155 };;
2157 { .mfi
2158 nop.m 0
2159 (p15) fma.s1 FR_n_TT = FR_n_PolyL, FR_l_AbsX, f0 //sin(Pi*x) poly
2160 nop.i 0
2161 };;
2163 { .mfi
2164 nop.m 0
2165 fma.s1 FR_e_poly = FR_e_r, FR_e_poly, FR_e_A1
2166 // poly = r * poly + A1
2167 nop.i 0
2168 };;
2170 { .mfi
2171 nop.m 0
2172 fma.s1 FR_e_T_scale = FR_e_T, FR_e_scale, f0 // T_scale=T*scale
2173 nop.i 0
2174 }
2175 { .mfi
2176 nop.m 0
2177 fma.s1 FR_e_W = FR_e_W2, FR_e_W1_p1, FR_e_W1
2178 // W = W2 * (W1+1.0) + W1
2179 nop.i 0
2180 };;
2182 { .mfi
2183 nop.m 0
2184 (p15) fma.s1 FR_n_SinxH = FR_n_PolyH, FR_l_AbsX, FR_n_TT
2185 // sin(Pi*x) poly
2186 nop.i 0
2187 };;
2189 { .mfi
2190 nop.m 0
2191 mov FR_e_Y_hi = FR_e_T // Assume Y_hi = T
2192 nop.i 0
2193 };;
2195 { .mfi
2196 nop.m 0
2197 fma.s1 FR_e_poly = FR_e_rsq, FR_e_poly, FR_e_r
2198 // poly = rsq * poly + r
2199 nop.i 0
2200 };;
2202 { .mfi
2203 nop.m 0
2204 fma.s1 FR_e_Wp1_T_scale = FR_e_W, FR_e_T_scale, FR_e_T_scale
2205 // (W+1)*T*scale
2206 nop.i 0
2207 }
2208 { .mfi
2209 nop.m 0
2210 fma.s1 FR_e_W_T_scale = FR_e_W, FR_e_T_scale, f0 // W*T*scale
2211 nop.i 0
2212 };;
2214 { .mfi
2215 nop.m 0
2216 (p15) fms.s1 FR_n_SinxL = FR_n_PolyH, FR_l_AbsX, FR_n_SinxH
2217 // Low part of sin
2218 nop.i 0
2219 };;
2221 { .mfi
2222 nop.m 0
2223 (p15) frcpa.s1 FR_n_Y0, p0 = f1, FR_n_SinxH // y = frcpa(b)
2224 nop.i 0
2225 };;
2227 { .mfi
2228 nop.m 0
2229 fma.s1 FR_e_result_lo = FR_e_Wp1_T_scale, FR_e_poly, FR_e_W_T_scale
2230 // Low part of exp result
2231 nop.i 0
2232 };;
2234 { .mfi
2235 nop.m 0
2236 (p15) fma.s1 FR_n_SinxL = FR_n_SinxL, f1, FR_n_TT // sin low result
2237 nop.i 0
2238 };;
2240 { .mfi
2241 nop.m 0
2242 (p15) fma.s1 FR_n_Q0 = f1,FR_n_Y0,f0 // q = y
2243 nop.i 0
2244 }
2245 { .mfi
2246 nop.m 0
2247 (p15) fnma.s1 FR_n_E0 = FR_n_Y0, FR_n_SinxH, f1 // e = 1-b*y
2248 nop.i 0
2249 };;
2252 { .mfb
2253 nop.m 0
2254 (p14) fma.s0 f8 = FR_e_Y_hi, FR_e_scale, FR_e_result_lo
2255 (p14) br.ret.spnt b0 // Exit for positive Stirling path //////////////////////
2256 };;
2258 { .mfi
2259 nop.m 0
2260 fma.s1 FR_e_expl_Output_X = FR_e_Y_hi, FR_e_scale, f0 // exp result
2261 nop.i 0
2262 }
2263 { .mfi
2264 nop.m 0
2265 fma.s1 FR_e_expl_Output_Y = FR_e_result_lo, f1, f0// exp lo result
2266 nop.i 0
2267 };;
2269 { .mfi
2270 nop.m 0
2271 fma.s1 FR_n_E2 = FR_n_E0,FR_n_E0,FR_n_E0 // e2 = e+e^2
2272 nop.i 0
2273 }
2274 { .mfi
2275 nop.m 0
2276 fma.s1 FR_n_E1 = FR_n_E0,FR_n_E0,f0 // e1 = e^2
2277 nop.i 0
2278 };;
2280 { .mfi
2281 nop.m 0
2282 fma.s1 FR_n_Y1 = FR_n_Y0,FR_n_E2,FR_n_Y0 // y1 = y+y*e2
2283 nop.i 0
2284 }
2285 { .mfi
2286 nop.m 0
2287 fma.s1 FR_n_E3 = FR_n_E1,FR_n_E1,FR_n_E0 // e3 = e+e1^2
2288 nop.i 0
2289 };;
2291 { .mfi
2292 nop.m 0
2293 fma.s1 FR_n_Y2 = FR_n_Y1,FR_n_E3,FR_n_Y0 // y2 = y+y1*e3
2294 nop.i 0
2295 }
2296 { .mfi
2297 nop.m 0
2298 fnma.s1 FR_n_R0 = FR_n_SinxH,FR_n_Q0,f1 // r = a-b*q
2299 nop.i 0
2300 };;
2302 { .mfi
2303 nop.m 0
2304 fnma.s1 FR_n_E4 = FR_n_SinxH,FR_n_Y2,f1 // e4 = 1-b*y2
2305 nop.i 0
2306 }
2307 { .mfi
2308 nop.m 0
2309 fma.s1 FR_n_RcpResH = FR_n_R0,FR_n_Y2,FR_n_Q0 // x = q+r*y2
2310 nop.i 0
2311 };;
2313 { .mfi
2314 nop.m 0
2315 fma.s1 FR_n_Y3 = FR_n_Y2,FR_n_E4,FR_n_Y2 // y3 = y2+y2*e4
2316 nop.i 0
2317 }
2318 { .mfi
2319 nop.m 0
2320 fnma.s1 FR_n_R1 = FR_n_SinxH,FR_n_RcpResH,f1 // r1 = a-b*x
2321 nop.i 0
2322 };;
2324 { .mfi
2325 nop.m 0
2326 fnma.s1 FR_n_R1 = FR_n_SinxL,FR_n_RcpResH,FR_n_R1
2327 // r1 = r1 - b_lo*X
2328 nop.i 0
2329 };;
2331 { .mfi
2332 nop.m 0
2333 fma.s1 FR_n_RcpResL = FR_n_R1,FR_n_Y3,f0 // x_lo = r1*y3
2334 nop.i 0
2335 }
2336 { .mfi
2337 nop.m 0
2338 fma.s1 FR_n_Temp = FR_n_RcpResH, FR_e_expl_Output_Y, f0
2339 // Multiplying exp and sin result
2340 nop.i 0
2341 };;
2343 { .mfi
2344 nop.m 0
2345 fma.s1 FR_n_Temp = FR_n_RcpResL, FR_e_expl_Output_X, FR_n_Temp
2346 // Multiplying exp and sin result
2347 nop.i 0
2348 };;
2350 { .mfi
2351 nop.m 0
2352 fma.s1 FR_n_ResH = FR_n_RcpResH, FR_e_expl_Output_X, FR_n_Temp
2353 // Multiplying exp and sin result
2354 nop.i 0
2355 };;
2357 { .mfi
2358 nop.m 0
2359 fms.s1 FR_n_ResL = FR_n_RcpResH, FR_e_expl_Output_X, FR_n_ResH
2360 // Multiplying exp and sin result
2361 nop.i 0
2362 }
2363 { .mfi
2364 nop.m 0
2365 (p12) fma.s1 FR_n_ResH = FR_n_ResH, FR_n_NegOne, f0 // Negate
2366 nop.i 0
2367 };;
2369 { .mfi
2370 nop.m 0
2371 fma.s1 FR_n_ResL = FR_n_ResL, f1, FR_n_Temp
2372 // Multiplying exp and sin result - low result obtained
2373 nop.i 0
2374 };;
2376 .pred.rel "mutex",p12,p13
2377 { .mfi
2378 nop.m 0
2379 (p13) fma.s0 f8 = FR_n_ResH, f1, FR_n_ResL // For odd
2380 nop.i 0
2381 }
2382 { .mfb
2383 nop.m 0
2384 (p12) fms.s0 f8 = FR_n_ResH, f1, FR_n_ResL // For even
2385 br.ret.sptk b0 // Exit for negative Stirling path //////////////////////
2386 };;
2389 //////////// 1 <= |X| < 13 path ////////////////////////////////////////////////
2390 //------------------------------------------------------------------------------
2391 .align 64
2392 tgamma_lt_13:
2393 { .mfi
2394 getf.sig GR_p_XN = FR_p_IXN // Get significand
2395 fcvt.xf FR_p_XN = FR_p_IXN // xn = [x]
2396 add GR_r_sin_Table2= 0x40, GR_r_sin_Table // Shifted table addr.
2397 }
2398 { .mfi
2399 ldfpd FR_p_0p5, FR_p_1p5 = [GR_c_Table], 16 // 0.5 & 1.5
2400 fms.s1 FR_p_AbsXM1 = FR_p_AbsX, f1, f1 // X-1
2401 add GR_p_Table2 = 0xB0, GR_p_Table
2402 };;
2404 { .mfi
2405 add GR_r_sin_Table = -16, GR_r_sin_Table // For compensation
2406 fcvt.xf FR_r_XNS = FR_r_IXNS // Convert int repr to float
2407 shr.u GR_p_X_Sgnd = GR_p_X_Sgnd, 59 // Get only 5 bit of signd
2408 };;
2410 { .mfi
2411 ldfpd FR_r_A2H,FR_r_A2L = [GR_r_sin_Table], 16 // Load A2
2412 nop.f 0
2413 add GR_p_Int = -2, GR_p_XN // int = int - 2
2414 }
2415 { .mfi
2416 ldfe FR_r_A6 = [GR_r_sin_Table2], 16
2417 nop.f 0
2418 cmp.gtu p11, p12 = 0x2, GR_p_XN // p11: x < 2 (splitted intervals),
2419 // p12: x > 2 (base intervals)
2420 };;
2422 { .mfi
2423 ldfpd FR_r_A1H, FR_r_A1L = [GR_r_sin_Table], 16
2424 nop.f 0
2425 shr GR_p_Int = GR_p_Int, 1 // int/2
2426 }
2427 { .mfi
2428 ldfe FR_r_A5 = [GR_r_sin_Table2], 16
2429 nop.f 0
2430 (p11) cmp.gtu.unc p10, p11 = 0x1C, GR_p_X_Sgnd // sgnd(x) < 0.75
2431 };;
2433 { .mfi
2434 ldfe FR_r_A9 = [GR_r_sin_Table], 16
2435 nop.f 0
2436 shl GR_p_Offset = GR_p_Int, 4 // offset = int*16
2437 }
2438 { .mfi
2439 ldfe FR_r_A4 = [GR_r_sin_Table2], 16
2440 nop.f 0
2441 (p10) cmp.gtu.unc p9, p10 = 0x14, GR_p_X_Sgnd // sgnd(x) < 0.25
2442 };;
2445 { .mfi
2446 ldfe FR_r_A8 = [GR_r_sin_Table], 16
2447 nop.f 0
2448 (p12) tbit.nz.unc p13, p12 = GR_p_XN, 0x0 // p13: reccurent computations
2449 // X is at [3;4], [5;6], [7;8]... interval
2450 }
2451 { .mfi
2452 ldfe FR_r_A3 = [GR_r_sin_Table2], 16
2453 nop.f 0
2454 shladd GR_p_Offset = GR_p_Int, 2, GR_p_Offset // +int*4
2455 };;
2457 .pred.rel "mutex",p9,p11
2458 { .mfi
2459 add GR_p_Offset = GR_p_Int, GR_p_Offset
2460 // +int, so offset = int*21
2461 (p9) fms.s1 FR_p_XR = FR_p_AbsX, f1, f1 // r = x-1
2462 nop.i 0
2463 }
2464 { .mfi
2465 ldfe FR_r_A7 = [GR_r_sin_Table], 16
2466 (p11) fms.s1 FR_p_XR = FR_p_2, f1, FR_p_AbsX
2467 // r = 2-x for 1.75 < x < 2
2468 nop.i 0
2469 };;
2471 .pred.rel "mutex",p9,p10
2472 .pred.rel "mutex",p10,p11
2473 .pred.rel "mutex",p9,p11
2474 { .mfi
2475 (p9) add GR_p_Offset = 126, r0 // 1.0 < x < 1.25 table
2476 (p15) fcmp.eq.unc.s1 p7,p0 = FR_p_AbsX, FR_p_XN
2477 // If arg is integer and negative - singularity branch
2478 nop.i 0
2479 }
2480 { .mfi
2481 (p10) add GR_p_Offset = 147, r0 // 1.25 < x < 1.75 table
2482 nop.f 0
2483 (p11) add GR_p_Offset = 168, r0 // 1.75 < x < 2.0 table
2484 };;
2486 { .mmf
2487 shladd GR_p_Table = GR_p_Offset, 4, GR_p_Table
2488 shladd GR_p_Table2 = GR_p_Offset, 4, GR_p_Table2
2489 fma.s1 FR_r_XS = FR_r_AbsX , f1, FR_r_XNS // xs = x - [x]
2490 };;
2492 { .mmb
2493 ldfpd FR_p_A5H, FR_p_A5L = [GR_p_Table], 16
2494 ldfpd FR_p_A2H, FR_p_A2L = [GR_p_Table2], 16
2495 (p7) br.cond.spnt tgammal_singularity // Singularity for integer /////////////
2496 // and negative argument ///////////////
2497 };;
2499 { .mfi
2500 ldfpd FR_p_A4H, FR_p_A4L = [GR_p_Table], 16
2501 fma.s1 FR_p_XN = FR_p_XN, f1, FR_p_0p5 // xn = xn+0.5
2502 nop.i 0
2503 }
2504 { .mfi
2505 ldfpd FR_p_A1H, FR_p_A1L = [GR_p_Table2], 16
2506 (p10) fms.s1 FR_p_XR = FR_p_AbsX, f1, FR_p_1p5 // r = x - 1.5
2507 nop.i 0
2508 };;
2510 { .mmi
2511 ldfpd FR_p_A3H, FR_p_A3L = [GR_p_Table], 16
2512 ldfpd FR_p_A0H, FR_p_A0L = [GR_p_Table2], 16
2513 nop.i 0
2514 };;
2516 { .mmi
2517 ldfe FR_p_A20 = [GR_p_Table], 16
2518 ldfe FR_p_A12 = [GR_p_Table2], 16
2519 nop.i 0
2520 };;
2522 { .mmf
2523 ldfe FR_p_A19 = [GR_p_Table], 16
2524 ldfe FR_p_A11 = [GR_p_Table2], 16
2525 fma.s1 FR_r_XS2 = FR_r_XS, FR_r_XS, f0 // xs2 = xs*xs
2526 };;
2528 { .mmi
2529 ldfe FR_p_A18 = [GR_p_Table], 16
2530 ldfe FR_p_A10 = [GR_p_Table2], 16
2531 nop.i 0
2532 };;
2534 .pred.rel "mutex",p12,p13
2535 { .mfi
2536 ldfe FR_p_A17 = [GR_p_Table], 16
2537 (p12) fms.s1 FR_p_XR = FR_p_AbsX, f1, FR_p_XN // r = x - xn
2538 nop.i 0
2539 }
2540 { .mfi
2541 ldfe FR_p_A9 = [GR_p_Table2], 16
2542 (p13) fms.s1 FR_p_XR = FR_p_AbsX, f1, FR_p_XN
2543 nop.i 0
2544 };;
2546 { .mmi
2547 ldfe FR_p_A16 = [GR_p_Table], 16
2548 ldfe FR_p_A8 = [GR_p_Table2], 16
2549 (p9) cmp.eq p12, p0 = r0, r0 // clear p12
2550 };;
2552 { .mmi
2553 ldfe FR_p_A15 = [GR_p_Table], 16
2554 ldfe FR_p_A7 = [GR_p_Table2], 16
2555 (p10) cmp.eq p12, p0 = r0, r0 // clear p12
2556 };;
2558 { .mfi
2559 ldfe FR_p_A14 = [GR_p_Table], 16
2560 fma.s1 FR_r_TH = FR_r_A2H, FR_r_XS2, f0 // sin for neg
2561 (p11) cmp.eq p12, p0 = r0, r0 // clear p12
2562 }
2563 { .mfi
2564 ldfe FR_p_A6 = [GR_p_Table2], 16
2565 fma.s1 FR_r_TL = FR_r_A2L, FR_r_XS2, f0 // sin for neg
2566 nop.i 0
2567 };;
2569 { .mfi
2570 ldfe FR_p_A13 = [GR_p_Table], 16
2571 fms.s1 FR_r_XS2L = FR_r_XS, FR_r_XS, FR_r_XS2 // x2Lo part
2572 nop.i 0
2573 };;
2575 { .mfi
2576 nop.m 0
2577 fma.s1 FR_p_Temp5H = FR_p_A5H, FR_p_XR, f0 // A5H*r
2578 // 'Low poly'
2579 nop.i 0
2580 }
2581 { .mfi
2582 nop.m 0
2583 fma.s1 FR_p_XR2 = FR_p_XR, FR_p_XR, f0 // r^2 = r*r
2584 nop.i 0
2585 };;
2587 { .mfi
2588 nop.m 0
2589 fabs FR_r_XS = FR_r_XS // abs(xs)
2590 nop.i 0
2591 }
2592 { .mfi
2593 nop.m 0
2594 fma.s1 FR_p_Temp2H = FR_p_A2H, FR_p_XR, f0 // A2H*r
2595 // 'High poly'
2596 nop.i 0
2597 };;
2599 { .mfi
2600 nop.m 0
2601 fms.s1 FR_r_TT = FR_r_A2H, FR_r_XS2, FR_r_TH // sin for neg
2602 nop.i 0
2603 }
2604 { .mfi
2605 nop.m 0
2606 fma.s1 FR_r_ResH = FR_r_TH, f1, FR_r_A1H // sin for neg
2607 nop.i 0
2608 };;
2610 { .mfi
2611 nop.m 0
2612 fma.s1 FR_r_TL = FR_r_A2H, FR_r_XS2L, FR_r_TL // sin for neg
2613 nop.i 0
2614 };;
2616 { .mfi
2617 nop.m 0
2618 fms.s1 FR_p_Temp5L = FR_p_A5H,FR_p_XR,FR_p_Temp5H //A5H*r delta
2619 // 'Low poly'
2620 nop.i 0
2621 }
2622 { .mfi
2623 nop.m 0
2624 fma.s1 FR_p_Poly5H = FR_p_Temp5H, f1, FR_p_A4H // A5H*r+A4H
2625 // 'Low poly'
2626 nop.i 0
2627 };;
2629 { .mfi
2630 nop.m 0
2631 fms.s1 FR_p_Temp2L = FR_p_A2H, FR_p_XR, FR_p_Temp2H//A2H*r delta
2632 //'High poly'
2633 nop.i 0
2634 }
2635 { .mfi
2636 nop.m 0
2637 fma.s1 FR_p_Poly2H = FR_p_Temp2H, f1, FR_p_A1H // A2H*r+A1H
2638 //'High poly'
2639 nop.i 0
2640 };;
2642 { .mfi
2643 nop.m 0
2644 fma.s1 FR_p_XR3 = FR_p_XR2, FR_p_XR, f0 // r^3 = r^2*r
2645 nop.i 0
2646 }
2647 { .mfi
2648 nop.m 0
2649 fms.s1 FR_p_XR2L = FR_p_XR, FR_p_XR, FR_p_XR2 // r^2 delta
2650 nop.i 0
2651 };;
2653 { .mfi
2654 nop.m 0
2655 fma.s1 FR_p_A18 = FR_p_A19, FR_p_XR, FR_p_A18 // Poly tail
2656 nop.i 0
2657 }
2658 { .mfi
2659 nop.m 0
2660 fma.s1 FR_p_A14 = FR_p_A15, FR_p_XR, FR_p_A14 // Poly tail
2661 nop.i 0
2662 };;
2664 { .mfi
2665 nop.m 0
2666 fma.s1 FR_p_XR4 = FR_p_XR2, FR_p_XR2, f0 // r^4 = r^2*r^2
2667 nop.i 0
2668 };;
2670 { .mfi
2671 nop.m 0
2672 fma.s1 FR_p_Temp5L = FR_p_A5L, FR_p_XR, FR_p_Temp5L// Low part
2673 // of A5*r+A4
2674 nop.i 0
2675 }
2676 { .mfi
2677 nop.m 0
2678 fms.s1 FR_p_Poly5L = FR_p_A4H, f1, FR_p_Poly5H // Low part
2679 // of A5*r+A4
2680 nop.i 0
2681 };;
2683 { .mfi
2684 nop.m 0
2685 fma.s1 FR_p_Temp4H = FR_p_Poly5H, FR_p_XR, f0 // (A5H*r+A4H)*r
2686 nop.i 0
2687 }
2688 { .mfi
2689 nop.m 0
2690 fma.s1 FR_p_Temp2L = FR_p_A2L, FR_p_XR, FR_p_Temp2L // A2*r low
2691 nop.i 0
2692 };;
2694 { .mfi
2695 nop.m 0
2696 fms.s1 FR_p_Poly2L = FR_p_A1H, f1, FR_p_Poly2H // High poly
2697 nop.i 0
2698 }
2699 { .mfi
2700 nop.m 0
2701 fma.s1 FR_p_Temp1H = FR_p_Poly2H, FR_p_XR, f0 // High poly
2702 nop.i 0
2703 };;
2705 { .mfi
2706 nop.m 0
2707 fms.s1 FR_p_XR3L = FR_p_XR2, FR_p_XR, FR_p_XR3 // x^3 delta
2708 nop.i 0
2709 }
2710 { .mfi
2711 nop.m 0
2712 fma.s1 FR_p_A16 = FR_p_A17, FR_p_XR, FR_p_A16 // Poly tail
2713 nop.i 0
2714 };;
2716 { .mfi
2717 nop.m 0
2718 fms.s1 FR_r_ResL = FR_r_A1H, f1, FR_r_ResH // sin for neg
2719 nop.i 0
2720 }
2721 { .mfi
2722 nop.m 0
2723 fma.s1 FR_r_TL = FR_r_TL, f1, FR_r_TT // sin for neg
2724 nop.i 0
2725 };;
2727 { .mfi
2728 nop.m 0
2729 fma.s1 FR_p_Temp5L = FR_p_Temp5L, f1, FR_p_A4L // Low poly
2730 nop.i 0
2731 }
2732 { .mfi
2733 nop.m 0
2734 fma.s1 FR_p_Poly5L = FR_p_Poly5L, f1, FR_p_Temp5H // Low poly
2735 nop.i 0
2736 };;
2738 { .mfi
2739 nop.m 0
2740 fms.s1 FR_p_Temp4L = FR_p_Poly5H,FR_p_XR,FR_p_Temp4H //Low poly
2741 nop.i 0
2742 }
2743 { .mfi
2744 nop.m 0
2745 fma.s1 FR_p_Poly4H = FR_p_Temp4H, f1, FR_p_A3H // Low poly
2746 nop.i 0
2747 };;
2749 { .mfi
2750 nop.m 0
2751 fma.s1 FR_p_Temp2L = FR_p_Temp2L, f1, FR_p_A1L // High poly
2752 nop.i 0
2753 }
2754 { .mfi
2755 nop.m 0
2756 fma.s1 FR_p_Poly2L = FR_p_Poly2L, f1, FR_p_Temp2H // High poly
2757 nop.i 0
2758 };;
2760 { .mfi
2761 nop.m 0
2762 fms.s1 FR_p_Temp1L = FR_p_Poly2H,FR_p_XR,FR_p_Temp1H //High poly
2763 nop.i 0
2764 }
2765 { .mfi
2766 nop.m 0
2767 fma.s1 FR_p_Poly1H = FR_p_Temp1H, f1, FR_p_A0H // High poly
2768 nop.i 0
2769 };;
2771 { .mfi
2772 nop.m 0
2773 fma.s1 FR_p_A12 = FR_p_A13, FR_p_XR, FR_p_A12 // Poly tail
2774 nop.i 0
2775 }
2776 { .mfi
2777 nop.m 0
2778 fma.s1 FR_p_XR3L = FR_p_XR2L, FR_p_XR, FR_p_XR3L // x^3 low
2779 nop.i 0
2780 };;
2782 { .mfi
2783 nop.m 0
2784 fma.s1 FR_p_Poly5L = FR_p_Poly5L, f1, FR_p_Temp5L // Low poly
2785 nop.i 0
2786 }
2787 { .mfi
2788 nop.m 0
2789 fma.s1 FR_p_A10 = FR_p_A11, FR_p_XR, FR_p_A10 // Poly tail
2790 nop.i 0
2791 };;
2793 { .mfi
2794 nop.m 0
2795 fms.s1 FR_p_Poly4L = FR_p_A3H, f1, FR_p_Poly4H // Low poly
2796 nop.i 0
2797 }
2798 { .mfi
2799 nop.m 0
2800 fma.s1 FR_p_A6 = FR_p_A7, FR_p_XR, FR_p_A6 // Poly tail
2801 nop.i 0
2802 };;
2804 { .mfi
2805 nop.m 0
2806 fma.s1 FR_p_A8 = FR_p_A9, FR_p_XR, FR_p_A8 // Poly tail
2807 nop.i 0
2808 }
2809 { .mfi
2810 nop.m 0
2811 fma.s1 FR_p_XR6 = FR_p_XR4, FR_p_XR2, f0 // Poly tail
2812 nop.i 0
2813 };;
2815 { .mfi
2816 nop.m 0
2817 fma.s1 FR_p_Poly2L = FR_p_Poly2L, f1, FR_p_Temp2L // High poly
2818 nop.i 0
2819 }
2820 { .mfi
2821 nop.m 0
2822 fms.s1 FR_p_Poly1L = FR_p_A0H, f1, FR_p_Poly1H // High poly
2823 nop.i 0
2824 };;
2826 { .mfi
2827 nop.m 0
2828 fma.s1 FR_r_ResL = FR_r_ResL, f1, FR_r_TH // sin for neg
2829 nop.i 0
2830 }
2831 { .mfi
2832 nop.m 0
2833 fma.s1 FR_r_TT = FR_r_TL, f1, FR_r_A1L // sin for neg
2834 nop.i 0
2835 };;
2837 { .mfi
2838 nop.m 0
2839 fma.s1 FR_p_Temp4L = FR_p_Poly5L,FR_p_XR,FR_p_Temp4L // Low poly
2840 nop.i 0
2841 }
2842 { .mfi
2843 nop.m 0
2844 fma.s1 FR_p_A18 = FR_p_A20, FR_p_XR2, FR_p_A18 // Poly tail
2845 nop.i 0
2846 };;
2848 { .mfi
2849 nop.m 0
2850 fma.s1 FR_p_Poly4L = FR_p_Poly4L, f1, FR_p_Temp4H // Low poly
2851 nop.i 0
2852 }
2853 { .mfi
2854 nop.m 0
2855 fma.s1 FR_p_A14 = FR_p_A16, FR_p_XR2, FR_p_A14 // Poly tail
2856 nop.i 0
2857 };;
2859 { .mfi
2860 nop.m 0
2861 fma.s1 FR_p_A6 = FR_p_A8, FR_p_XR2, FR_p_A6 // Poly tail
2862 nop.i 0
2863 }
2864 { .mfi
2865 nop.m 0
2866 fma.s1 FR_p_A10 = FR_p_A12, FR_p_XR2, FR_p_A10 // Poly tail
2867 nop.i 0
2868 };;
2870 { .mfi
2871 nop.m 0
2872 fma.s1 FR_p_Temp1L = FR_p_Poly2L,FR_p_XR,FR_p_Temp1L //High poly
2873 nop.i 0
2874 }
2875 { .mfi
2876 nop.m 0
2877 fma.s1 FR_p_Poly1L = FR_p_Poly1L, f1, FR_p_Temp1H // High poly
2878 nop.i 0
2879 };;
2881 { .mfi
2882 nop.m 0
2883 fma.s1 FR_r_ResL = FR_r_ResL, f1, FR_r_TT // sin for neg
2884 nop.i 0
2885 }
2886 { .mfi
2887 nop.m 0
2888 fma.s1 FR_r_TH = FR_r_ResH, FR_r_XS2, f0 // sin for neg
2889 nop.i 0
2890 };;
2892 { .mfi
2893 nop.m 0
2894 fma.s1 FR_p_Temp4L = FR_p_Temp4L, f1, FR_p_A3L // Low poly
2895 nop.i 0
2896 }
2897 { .mfi
2898 nop.m 0
2899 fma.s1 FR_p_Poly3H = FR_p_Poly4H, FR_p_XR3, f0 // Low poly
2900 nop.i 0
2901 };;
2903 { .mfi
2904 nop.m 0
2905 fma.s1 FR_p_A14 = FR_p_A18, FR_p_XR4, FR_p_A14 // Poly tail
2906 nop.i 0
2907 }
2908 { .mfi
2909 nop.m 0
2910 fma.s1 FR_p_XR8 = FR_p_XR4, FR_p_XR4, f0 // Poly tail
2911 nop.i 0
2912 };;
2914 { .mfi
2915 nop.m 0
2916 fma.s1 FR_r_TL = FR_r_ResH, FR_r_XS2L, f0 // sin for neg
2917 nop.i 0
2918 };;
2920 { .mfi
2921 nop.m 0
2922 fma.s1 FR_p_Temp1L = FR_p_Temp1L, f1, FR_p_A0L // High poly
2923 nop.i 0
2924 }
2925 { .mfi
2926 nop.m 0
2927 fma.s1 FR_p_A6 = FR_p_A10, FR_p_XR4, FR_p_A6 // Poly tail
2928 nop.i 0
2929 };;
2931 { .mfi
2932 nop.m 0
2933 fms.s1 FR_r_TT = FR_r_ResH, FR_r_XS2, FR_r_TH // sin for neg
2934 nop.i 0
2935 }
2936 { .mfi
2937 nop.m 0
2938 fma.s1 FR_r_Res3H = FR_r_TH, f1, f1 // sin for neg
2939 nop.i 0
2940 };;
2942 { .mfi
2943 nop.m 0
2944 fma.s1 FR_p_Poly4L = FR_p_Poly4L, f1, FR_p_Temp4L // Low poly
2945 nop.i 0
2946 }
2947 { .mfi
2948 nop.m 0
2949 fma.s1 FR_p_Poly3L = FR_p_Poly4H, FR_p_XR3L, f0 // Low poly
2950 nop.i 0
2951 };;
2953 { .mfi
2954 nop.m 0
2955 fma.s1 FR_p_Poly0H = FR_p_Poly3H,f1,FR_p_Poly1H //Low & High add
2956 nop.i 0
2957 }
2958 { .mfi
2959 nop.m 0
2960 fma.s1 FR_r_A7 = FR_r_A8, FR_r_XS2, FR_r_A7 // sin for neg
2961 nop.i 0
2962 };;
2964 { .mfi
2965 nop.m 0
2966 fma.s1 FR_r_TL = FR_r_ResL, FR_r_XS2, FR_r_TL // sin for neg
2967 nop.i 0
2968 }
2969 { .mfi
2970 nop.m 0
2971 fma.s1 FR_r_XS4 = FR_r_XS2, FR_r_XS2, f0 // sin for neg
2972 nop.i 0
2973 };;
2975 { .mfi
2976 nop.m 0
2977 fma.s1 FR_p_Poly1L = FR_p_Poly1L, f1, FR_p_Temp1L // High poly
2978 nop.i 0
2979 }
2980 { .mfi
2981 nop.m 0
2982 fma.s1 FR_p_PolyTail = FR_p_A14, FR_p_XR8, FR_p_A6 // Poly tail
2983 nop.i 0
2984 };;
2986 { .mfi
2987 nop.m 0
2988 fms.s1 FR_r_Res3L = f1, f1, FR_r_Res3H // sin for neg
2989 nop.i 0
2990 }
2991 { .mfi
2992 nop.m 0
2993 fma.s1 FR_r_ResH = FR_r_Res3H, FR_r_XS, f0 // sin for neg
2994 nop.i 0
2995 };;
2997 { .mfi
2998 nop.m 0
2999 fms.s1 FR_p_Temp0L = FR_p_Poly4H,FR_p_XR3,FR_p_Poly3H //Low poly
3000 nop.i 0
3001 }
3002 { .mfi
3003 nop.m 0
3004 fma.s1 FR_p_Poly3L = FR_p_Poly4L,FR_p_XR3,FR_p_Poly3L //Low poly
3005 nop.i 0
3006 };;
3008 { .mfi
3009 nop.m 0
3010 fms.s1 FR_p_Poly0L = FR_p_Poly1H,f1,FR_p_Poly0H //Low & High add
3011 nop.i 0
3012 }
3013 { .mfi
3014 nop.m 0
3015 (p13) fma.s1 FR_p_OddPoly0H = FR_p_Poly0H, FR_p_AbsXM1, f0
3016 // Reccurent computations - multiplying by X-1
3017 nop.i 0
3018 };;
3020 { .mfi
3021 nop.m 0
3022 fma.s1 FR_r_TL = FR_r_TL, f1, FR_r_TT // sin for neg
3023 nop.i 0
3024 }
3025 { .mfi
3026 nop.m 0
3027 fma.s1 FR_r_A3 = FR_r_A4, FR_r_XS2, FR_r_A3 // sin for neg
3028 nop.i 0
3029 };;
3031 { .mfi
3032 nop.m 0
3033 fma.s1 FR_p_Poly1L = FR_p_PolyTail,FR_p_XR6,FR_p_Poly1L//High
3034 nop.i 0
3035 }
3036 { .mfi
3037 nop.m 0
3038 fma.s1 FR_r_A5 = FR_r_A6, FR_r_XS2, FR_r_A5 // sin for neg
3039 nop.i 0
3040 };;
3042 { .mfi
3043 nop.m 0
3044 fma.s1 FR_r_Res3L = FR_r_Res3L, f1, FR_r_TH // sin for neg
3045 nop.i 0
3046 }
3047 { .mfi
3048 nop.m 0
3049 fms.s1 FR_r_ResL = FR_r_Res3H, FR_r_XS, FR_r_ResH//sin for neg
3050 nop.i 0
3051 };;
3053 { .mfi
3054 nop.m 0
3055 fma.s1 FR_p_Poly3L = FR_p_Poly3L, f1, FR_p_Temp0L // Low poly
3056 nop.i 0
3057 }
3058 { .mfi
3059 nop.m 0
3060 fma.s1 FR_r_A7 = FR_r_A9, FR_r_XS4, FR_r_A7 // sin for neg
3061 nop.i 0
3062 };;
3064 { .mfi
3065 nop.m 0
3066 fma.s1 FR_p_Poly0L = FR_p_Poly0L,f1,FR_p_Poly3H //Low & High add
3067 nop.i 0
3068 }
3069 { .mfi
3070 nop.m 0
3071 (p13) fms.s1 FR_p_OddPoly0L = FR_p_Poly0H, FR_p_AbsXM1, FR_p_OddPoly0H
3072 // Reccurent computations - multiplying by X-1 (low part)
3073 nop.i 0
3074 };;
3076 { .mfi
3077 nop.m 0
3078 fma.s1 FR_r_A3 = FR_r_A5, FR_r_XS4, FR_r_A3 // sin for neg
3079 nop.i 0
3080 }
3081 { .mfi
3082 nop.m 0
3083 fma.s1 FR_r_XS7 = FR_r_XS4, FR_r_XS2, f0 // xs^6
3084 nop.i 0
3085 };;
3087 { .mfi
3088 nop.m 0
3089 fma.s1 FR_r_Res3L = FR_r_Res3L, f1, FR_r_TL // sin for neg
3090 nop.i 0
3091 }
3092 { .mfi
3093 nop.m 0
3094 fma.s1 FR_r_XS8 = FR_r_XS4, FR_r_XS4, f0 // sin for neg
3095 nop.i 0
3096 };;
3098 { .mfi
3099 nop.m 0
3100 fma.s1 FR_p_Temp0H = FR_p_Poly3L,f1,FR_p_Poly1L //Low & High add
3101 nop.i 0
3102 };;
3104 { .mfi
3105 nop.m 0
3106 fma.s1 FR_r_XS7 = FR_r_XS7, FR_r_XS, f0 // xs^7
3107 nop.i 0
3108 };;
3110 { .mfi
3111 nop.m 0
3112 fma.s1 FR_r_ResL = FR_r_Res3L, FR_r_XS, FR_r_ResL//sin for neg
3113 nop.i 0
3114 }
3115 { .mfi
3116 nop.m 0
3117 fma.s1 FR_r_Tail = FR_r_A7, FR_r_XS8, FR_r_A3 // sin tail res
3118 nop.i 0
3119 };;
3121 { .mfi
3122 nop.m 0
3123 fma.s1 FR_p_Poly0L = FR_p_Poly0L,f1,FR_p_Temp0H //Low & High add
3124 nop.i 0
3125 };;
3128 { .mfi
3129 nop.m 0
3130 fma.s1 FR_r_ResL = FR_r_Tail,FR_r_XS7,FR_r_ResL //sin for neg
3131 nop.i 0
3132 };;
3134 { .mfi
3135 nop.m 0
3136 (p13) fma.s1 FR_p_OddPoly0L = FR_p_Poly0L, FR_p_AbsXM1, FR_p_OddPoly0L
3137 // Reccurent computations - multiplying by X-1 (low part)
3138 nop.i 0
3139 };;
3141 { .mfi
3142 nop.m 0
3143 fma.s1 FR_r_TT = FR_r_ResL, FR_r_AbsX, f0 // X*sin
3144 nop.i 0
3145 };;
3147 .pred.rel "mutex",p12,p13
3148 { .mfi
3149 nop.m 0
3150 (p12) fma.s0 f8 = FR_p_Poly0H, f1, FR_p_Poly0L // Even
3151 nop.i 0
3152 }
3153 { .mfb
3154 nop.m 0
3155 (p13) fma.s0 f8 = FR_p_OddPoly0H, f1, FR_p_OddPoly0L // Odd
3156 (p14) br.ret.spnt b0 // Exit for 1 <= |X| < 13 path (positive arguments)/////
3157 };;
3159 { .mfi
3160 nop.m 0
3161 (p13) fma.s1 FR_p_Poly0H = FR_p_OddPoly0H, f1, f0
3162 // Reccurent computations
3163 nop.i 0
3164 }
3165 { .mfi
3166 nop.m 0
3167 (p13) fma.s1 FR_p_Poly0L = FR_p_OddPoly0L, f1, f0
3168 // Reccurent computations
3169 nop.i 0
3170 };;
3172 { .mfi
3173 nop.m 0
3174 fma.s1 FR_r_Res1H = FR_r_ResH, FR_r_AbsX, FR_r_TT // X*sin
3175 (p11) cmp.eq p13, p12 = r0, r0
3176 };;
3178 { .mfi
3179 nop.m 0
3180 fms.s1 FR_r_Res1L = FR_r_ResH,FR_r_AbsX,FR_r_Res1H// X*sin
3181 (p9) cmp.eq p13, p12 = r0, r0
3182 };;
3184 { .mfi
3185 nop.m 0
3186 fma.s1 FR_r_Res1L = FR_r_Res1L, f1, FR_r_TT // sin for neg
3187 (p10) cmp.eq p13, p12 = r0, r0
3188 }
3189 { .mfi
3190 nop.m 0
3191 fma.s1 FR_r_TL = FR_p_Poly0L, FR_r_Res1H, f0 // mult by sin
3192 nop.i 0
3193 };;
3195 { .mfi
3196 nop.m 0
3197 fma.s1 FR_r_TL = FR_p_Poly0H,FR_r_Res1L,FR_r_TL//mult by sin
3198 nop.i 0
3199 };;
3201 { .mfi
3202 nop.m 0
3203 fma.s1 FR_r_ResH = FR_p_Poly0H,FR_r_Res1H,FR_r_TL//mult by sin
3204 nop.i 0
3205 };;
3207 { .mfi
3208 nop.m 0
3209 fms.s1 FR_r_ResL = FR_p_Poly0H,FR_r_Res1H,FR_r_ResH//sin mult
3210 nop.i 0
3211 };;
3213 { .mfi
3214 nop.m 0
3215 frcpa.s1 FR_r_Y0,p0 = f1,FR_r_ResH // y = frcpa(b)
3216 nop.i 0
3217 };;
3219 { .mfi
3220 nop.m 0
3221 fneg FR_r_NegOne = f1 // Form -1.0
3222 nop.i 0
3223 }
3224 { .mfi
3225 nop.m 0
3226 fma.s1 FR_r_ResL = FR_r_ResL, f1, FR_r_TL //Low result of mult
3227 nop.i 0
3228 };;
3230 { .mfi
3231 nop.m 0
3232 fma.s1 FR_r_Q0 = f1,FR_r_Y0,f0 // q = a*y
3233 nop.i 0
3234 }
3235 { .mfi
3236 nop.m 0
3237 fnma.s1 FR_r_E0 = FR_r_Y0,FR_r_ResH,f1 // e = 1-b*y
3238 nop.i 0
3239 };;
3241 { .mfi
3242 nop.m 0
3243 fma.s1 FR_r_E2 = FR_r_E0,FR_r_E0,FR_r_E0 // e2 = e+e^2
3244 nop.i 0
3245 }
3246 { .mfi
3247 nop.m 0
3248 fma.s1 FR_r_E1 = FR_r_E0,FR_r_E0,f0 // e1 = e^2
3249 nop.i 0
3250 };;
3252 { .mfi
3253 nop.m 0
3254 fma.s1 FR_r_Y1 = FR_r_Y0,FR_r_E2,FR_r_Y0 // y1 = y+y*e2
3255 nop.i 0
3256 }
3257 { .mfi
3258 nop.m 0
3259 fma.s1 FR_r_E3 = FR_r_E1,FR_r_E1,FR_r_E0 // e3 = e+e1^2
3260 nop.i 0
3261 };;
3263 { .mfi
3264 nop.m 0
3265 fma.s1 FR_r_Y2 = FR_r_Y1,FR_r_E3,FR_r_Y0 // y2 = y+y1*e3
3266 nop.i 0
3267 }
3268 { .mfi
3269 nop.m 0
3270 fnma.s1 FR_r_R0 = FR_r_ResH,FR_r_Q0,f1 // r = a-b*q
3271 nop.i 0
3272 };;
3274 { .mfi
3275 nop.m 0
3276 fnma.s1 FR_r_E4 = FR_r_ResH,FR_r_Y2,f1 // e4 = 1-b*y2
3277 nop.i 0
3278 }
3279 { .mfi
3280 nop.m 0
3281 fma.s1 FR_r_ZH = FR_r_R0,FR_r_Y2,FR_r_Q0 // x = q+r*y2
3282 nop.i 0
3283 };;
3285 { .mfi
3286 nop.m 0
3287 fma.s1 FR_r_Y3 = FR_r_Y2,FR_r_E4,FR_r_Y2 // y3 = y2+y2*e4
3288 nop.i 0
3289 }
3290 { .mfi
3291 nop.m 0
3292 fnma.s1 FR_r_R1 = FR_r_ResH,FR_r_ZH,f1 // r1 = a-b*x
3293 nop.i 0
3294 };;
3296 { .mfi
3297 nop.m 0
3298 fnma.s1 FR_r_R1 = FR_r_ResL,FR_r_ZH,FR_r_R1 // r1=r1-b_lo*X
3299 nop.i 0
3300 }
3301 { .mfi
3302 nop.m 0
3303 (p12) fma.s1 FR_r_ZHN = FR_r_ZH,FR_r_NegOne, f0 // Negate for evens
3304 nop.i 0
3305 };;
3307 .pred.rel "mutex",p13,p12
3308 { .mfi
3309 nop.m 0
3310 (p13) fma.s0 f8 = FR_r_R1,FR_r_Y3,FR_r_ZH // Final result
3311 nop.i 0
3312 }
3313 { .mfb
3314 nop.m 0
3315 (p12) fnma.s0 f8 = FR_r_R1,FR_r_Y3,FR_r_ZHN // Final result
3316 br.ret.sptk b0 // Exit for 1 <= |X| < 13 path (negative arguments)//////
3317 };;
3320 //////////// |X| < 1 path /////////////////////////////////////////////////////
3321 //------------------------------------------------------------------------------
3322 .align 64
3323 tgamma_lt_1:
3324 { .mfi
3325 getf.exp GR_p_Exp = FR_p_AbsX // exp of abs X
3326 fma.s1 FR_z_Q0 = f1,FR_z_Y0,f0 // q = a*y
3327 add GR_r_sin_Table2= 0x50, GR_r_sin_Table
3328 }
3329 { .mfi
3330 ldfpd FR_p_0p5, FR_p_1p5 = [GR_c_Table], 16
3331 fnma.s1 FR_z_E0 = FR_z_Y0,f8,f1 // e = 1-b*y
3332 add GR_p_Table2 = 0xB0, GR_p_Table
3333 };;
3335 { .mfi
3336 ldfd FR_p_0p25 = [GR_c_Table]
3337 fcvt.xf FR_r_XNS = FR_r_IXNS // Convert int repr to float
3338 shr.u GR_p_X_Sgnd = GR_p_X_Sgnd, 60
3339 // Obtain only 4 bits of significand
3340 }
3341 { .mfi
3342 nop.m 0
3343 nop.f 0
3344 add GR_p_Bias = 0xffff, r0 // Set bias
3345 };;
3347 { .mfi
3348 ldfpd FR_r_A2H, FR_r_A2L = [GR_r_sin_Table], 16
3349 nop.f 0
3350 shl GR_p_XN = GR_p_Exp, 4
3351 // Shift exp to 4 bits left to set place for significand
3352 }
3353 { .mlx
3354 ldfe FR_r_A6 = [GR_r_sin_Table2], 16
3355 movl GR_p_0p75 = 0xfffec // 0.75
3356 };;
3358 { .mfi
3359 ldfpd FR_r_A1H, FR_r_A1L = [GR_r_sin_Table], 16
3360 nop.f 0
3361 or GR_p_XN = GR_p_XN, GR_p_X_Sgnd
3362 // Combine exp with 4 high bits of significand
3363 }
3364 { .mfi
3365 ldfe FR_r_A5 = [GR_r_sin_Table2], 16
3366 nop.f 0
3367 sub GR_p_Exp = GR_p_Exp, GR_p_Bias // Unbiased exp
3368 };;
3370 { .mmi
3371 ldfe FR_r_A9 = [GR_r_sin_Table], 16
3372 ldfe FR_r_A4 = [GR_r_sin_Table2], 16
3373 cmp.gtu.unc p10, p11 = GR_p_0p75, GR_p_XN // sgnd(x) < 0.75
3374 };;
3376 { .mfi
3377 ldfe FR_r_A8 = [GR_r_sin_Table], 16
3378 fma.s1 FR_z_E2 = FR_z_E0,FR_z_E0,FR_z_E0 // e2 = e+e^2
3379 (p10) cmp.gt.unc p9, p10 = -2, GR_p_Exp // x < 0.25
3380 }
3381 { .mfi
3382 ldfe FR_r_A3 = [GR_r_sin_Table2], 16
3383 fma.s1 FR_z_E1 = FR_z_E0,FR_z_E0,f0 // e1 = e^2
3384 (p11) add GR_p_Offset = 168, r0 // [0.75;1] interval
3385 };;
3387 { .mmi
3388 (p10) add GR_p_Offset = 147, r0 // [0.25;0.75] interval
3389 ldfe FR_r_A7 = [GR_r_sin_Table], 16
3390 (p9) cmp.gt.unc p8, p9 = -3, GR_p_Exp // x < 0.125
3391 };;
3393 .pred.rel "mutex",p9,p8
3394 { .mmi
3395 (p9) add GR_p_Offset = 126, r0 // [0.125;0.25] interval
3396 (p8) add GR_p_Offset = 189, r0 // [0.;0.125] interval
3397 nop.i 0
3398 };;
3400 { .mmf
3401 shladd GR_p_Table = GR_p_Offset, 4, GR_p_Table //Make addresses
3402 shladd GR_p_Table2 = GR_p_Offset, 4, GR_p_Table2
3403 fma.s1 FR_r_XS = FR_r_AbsX , f1, FR_r_XNS // xs = |x|-[x]
3404 };;
3406 .pred.rel "mutex",p8,p11
3407 { .mfi
3408 ldfpd FR_p_A5H, FR_p_A5L = [GR_p_Table], 16
3409 (p11) fms.s1 FR_p_XR = f1, f1, FR_p_AbsX // r = 1 - |x|
3410 // for [0.75;1] interval
3411 nop.i 0
3412 }
3413 { .mfi
3414 ldfpd FR_p_A2H, FR_p_A2L = [GR_p_Table2], 16
3415 (p8) fms.s1 FR_p_XR = FR_p_AbsX, f1, f0 // r = |x|
3416 // for [0.;0.125] interval
3417 nop.i 0
3418 };;
3420 { .mfi
3421 ldfpd FR_p_A4H, FR_p_A4L = [GR_p_Table], 16
3422 fma.s1 FR_z_Y1 = FR_z_Y0,FR_z_E2,FR_z_Y0 // y1 = y+y*e2
3423 nop.i 0
3424 }
3425 { .mfi
3426 ldfpd FR_p_A1H, FR_p_A1L = [GR_p_Table2], 16
3427 fma.s1 FR_z_E3 = FR_z_E1,FR_z_E1,FR_z_E0 // e3 = e+e1^2
3428 nop.i 0
3429 };;
3431 .pred.rel "mutex",p9,p10
3432 { .mfi
3433 ldfpd FR_p_A3H, FR_p_A3L = [GR_p_Table], 16
3434 (p9) fms.s1 FR_p_XR = FR_p_AbsX, f1, f0 // r = |x|
3435 // for [0.125;0.25] interval
3436 nop.i 0
3437 }
3438 { .mfi
3439 ldfpd FR_p_A0H, FR_p_A0L = [GR_p_Table2], 16
3440 (p10) fms.s1 FR_p_XR = FR_p_AbsX, f1, FR_p_0p5 // r = |x| - 0.5
3441 // for [0.25;0.75] interval
3442 nop.i 0
3443 };;
3445 { .mmi
3446 ldfe FR_p_A20 = [GR_p_Table], 16
3447 ldfe FR_p_A12 = [GR_p_Table2], 16
3448 nop.i 0
3449 };;
3451 { .mfi
3452 ldfe FR_p_A19 = [GR_p_Table], 16
3453 fma.s1 FR_r_XS2 = FR_r_XS, FR_r_XS, f0 // xs^2
3454 nop.i 0
3455 }
3456 { .mfi
3457 ldfe FR_p_A11 = [GR_p_Table2], 16
3458 nop.f 0
3459 nop.i 0
3460 };;
3462 { .mmi
3463 ldfe FR_p_A18 = [GR_p_Table], 16
3464 ldfe FR_p_A10 = [GR_p_Table2], 16
3465 nop.i 0
3466 };;
3468 .pred.rel "mutex",p12,p13
3469 { .mfi
3470 ldfe FR_p_A17 = [GR_p_Table], 16
3471 fma.s1 FR_z_Y2 = FR_z_Y1,FR_z_E3,FR_z_Y0 // y2 = y+y1*e3
3472 nop.i 0
3473 }
3474 { .mfi
3475 ldfe FR_p_A9 = [GR_p_Table2], 16
3476 fnma.s1 FR_z_R0 = f8,FR_z_Q0,f1 // r = a-b*q
3477 nop.i 0
3478 };;
3480 { .mmi
3481 ldfe FR_p_A16 = [GR_p_Table], 16
3482 ldfe FR_p_A8 = [GR_p_Table2], 16
3483 nop.i 0
3484 };;
3486 { .mmi
3487 ldfe FR_p_A15 = [GR_p_Table], 16
3488 ldfe FR_p_A7 = [GR_p_Table2], 16
3489 nop.i 0
3490 };;
3492 { .mfi
3493 ldfe FR_p_A14 = [GR_p_Table], 16
3494 fma.s1 FR_r_TH = FR_r_A2H, FR_r_XS2, f0 // neg sin
3495 nop.i 0
3496 }
3497 { .mfi
3498 ldfe FR_p_A6 = [GR_p_Table2], 16
3499 fma.s1 FR_r_TL = FR_r_A2L, FR_r_XS2, f0 // neg sin
3500 nop.i 0
3501 };;
3503 { .mfi
3504 ldfe FR_p_A13 = [GR_p_Table], 16
3505 fms.s1 FR_r_XS2L = FR_r_XS, FR_r_XS, FR_r_XS2 // xs^2 delta
3506 nop.i 0
3507 };;
3509 { .mfi
3510 nop.m 0
3511 fma.s1 FR_p_Temp5H = FR_p_A5H, FR_p_XR, f0 // Low poly
3512 nop.i 0
3513 }
3514 { .mfi
3515 nop.m 0
3516 fma.s1 FR_p_XR2 = FR_p_XR, FR_p_XR, f0 // poly tail
3517 nop.i 0
3518 };;
3520 { .mfi
3521 nop.m 0
3522 fabs FR_r_XS = FR_r_XS // Absolute value of xs
3523 nop.i 0
3524 }
3525 { .mfi
3526 nop.m 0
3527 fma.s1 FR_p_Temp2H = FR_p_A2H, FR_p_XR, f0 // High poly
3528 nop.i 0
3529 };;
3531 { .mfi
3532 nop.m 0
3533 fnma.s1 FR_z_E4 = f8,FR_z_Y2,f1 // e4 = 1-b*y2
3534 nop.i 0
3535 }
3536 { .mfi
3537 nop.m 0
3538 fma.s1 FR_z_ZH = FR_z_R0,FR_z_Y2,FR_z_Q0 // 1/x = q+r*y2
3539 nop.i 0
3540 };;
3542 { .mfi
3543 nop.m 0
3544 fms.s1 FR_r_TT = FR_r_A2H, FR_r_XS2, FR_r_TH // neg sin
3545 nop.i 0
3546 }
3547 { .mfi
3548 nop.m 0
3549 fma.s1 FR_r_ResH = FR_r_TH, f1, FR_r_A1H // neg sin
3550 nop.i 0
3551 };;
3553 { .mfi
3554 nop.m 0
3555 fma.s1 FR_r_TL = FR_r_A2H, FR_r_XS2L, FR_r_TL // neg sin
3556 nop.i 0
3557 };;
3559 { .mfi
3560 nop.m 0
3561 fms.s1 FR_p_Temp5L = FR_p_A5H, FR_p_XR, FR_p_Temp5H // Low poly
3562 nop.i 0
3563 }
3564 { .mfi
3565 nop.m 0
3566 fma.s1 FR_p_Poly5H = FR_p_Temp5H, f1, FR_p_A4H // Low poly
3567 nop.i 0
3568 };;
3570 { .mfi
3571 nop.m 0
3572 fms.s1 FR_p_Temp2L = FR_p_A2H, FR_p_XR, FR_p_Temp2H // High poly
3573 nop.i 0
3574 }
3575 { .mfi
3576 nop.m 0
3577 fma.s1 FR_p_Poly2H = FR_p_Temp2H, f1, FR_p_A1H // High poly
3578 nop.i 0
3579 };;
3581 { .mfi
3582 nop.m 0
3583 fma.s1 FR_p_XR3 = FR_p_XR2, FR_p_XR, f0 // r^3
3584 nop.i 0
3585 }
3586 { .mfi
3587 nop.m 0
3588 fms.s1 FR_p_XR2L = FR_p_XR, FR_p_XR, FR_p_XR2 // r^2 delta
3589 nop.i 0
3590 };;
3592 { .mfi
3593 nop.m 0
3594 fma.s1 FR_p_A18 = FR_p_A19, FR_p_XR, FR_p_A18 // poly tail
3595 nop.i 0
3596 }
3597 { .mfi
3598 nop.m 0
3599 fma.s1 FR_p_A14 = FR_p_A15, FR_p_XR, FR_p_A14 // poly tail
3600 nop.i 0
3601 };;
3603 { .mfi
3604 nop.m 0
3605 fma.s1 FR_p_XR4 = FR_p_XR2, FR_p_XR2, f0 // poly tail
3606 nop.i 0
3607 }
3608 { .mfi
3609 nop.m 0
3610 fma.s1 FR_z_Y3 = FR_z_Y2,FR_z_E4,FR_z_Y2 // y3 = y2+y2*e4
3611 nop.i 0
3612 };;
3614 { .mfi
3615 nop.m 0
3616 fma.s1 FR_p_Temp5L = FR_p_A5L, FR_p_XR, FR_p_Temp5L // Low poly
3617 nop.i 0
3618 }
3619 { .mfi
3620 nop.m 0
3621 fms.s1 FR_p_Poly5L = FR_p_A4H, f1, FR_p_Poly5H // Low poly
3622 nop.i 0
3623 };;
3625 { .mfi
3626 nop.m 0
3627 fma.s1 FR_p_Temp4H = FR_p_Poly5H, FR_p_XR, f0 // Low poly
3628 nop.i 0
3629 }
3630 { .mfi
3631 nop.m 0
3632 fma.s1 FR_p_Temp2L = FR_p_A2L, FR_p_XR, FR_p_Temp2L // High poly
3633 nop.i 0
3634 };;
3636 { .mfi
3637 nop.m 0
3638 fms.s1 FR_p_Poly2L = FR_p_A1H, f1, FR_p_Poly2H // High poly
3639 nop.i 0
3640 }
3641 { .mfi
3642 nop.m 0
3643 fma.s1 FR_p_Temp1H = FR_p_Poly2H, FR_p_XR, f0 // High poly
3644 nop.i 0
3645 };;
3647 { .mfi
3648 nop.m 0
3649 fms.s1 FR_p_XR3L = FR_p_XR2, FR_p_XR, FR_p_XR3 // x^3 delta
3650 nop.i 0
3651 }
3652 { .mfi
3653 nop.m 0
3654 fma.s1 FR_p_A16 = FR_p_A17, FR_p_XR, FR_p_A16 //poly tail
3655 nop.i 0
3656 };;
3658 { .mfi
3659 nop.m 0
3660 fms.s1 FR_r_ResL = FR_r_A1H, f1, FR_r_ResH // neg sin
3661 nop.i 0
3662 }
3663 { .mfi
3664 nop.m 0
3665 fma.s1 FR_r_TL = FR_r_TL, f1, FR_r_TT // neg sin
3666 nop.i 0
3667 };;
3669 { .mfi
3670 nop.m 0
3671 fma.s1 FR_p_Temp5L = FR_p_Temp5L, f1, FR_p_A4L // Low poly
3672 nop.i 0
3673 }
3674 { .mfi
3675 nop.m 0
3676 fma.s1 FR_p_Poly5L = FR_p_Poly5L, f1, FR_p_Temp5H //Low poly
3677 nop.i 0
3678 };;
3680 { .mfi
3681 nop.m 0
3682 fms.s1 FR_p_Temp4L = FR_p_Poly5H, FR_p_XR, FR_p_Temp4H//Low poly
3683 nop.i 0
3684 }
3685 { .mfi
3686 nop.m 0
3687 fma.s1 FR_p_Poly4H = FR_p_Temp4H, f1, FR_p_A3H // Low poly
3688 nop.i 0
3689 };;
3691 { .mfi
3692 nop.m 0
3693 fma.s1 FR_p_Temp2L = FR_p_Temp2L, f1, FR_p_A1L // High poly
3694 nop.i 0
3695 }
3696 { .mfi
3697 nop.m 0
3698 fma.s1 FR_p_Poly2L = FR_p_Poly2L, f1, FR_p_Temp2H // High poly
3699 nop.i 0
3700 };;
3702 { .mfi
3703 nop.m 0
3704 fms.s1 FR_p_Temp1L = FR_p_Poly2H,FR_p_XR,FR_p_Temp1H //High poly
3705 nop.i 0
3706 }
3707 { .mfi
3708 nop.m 0
3709 fma.s1 FR_p_Poly1H = FR_p_Temp1H, f1, FR_p_A0H // High poly
3710 nop.i 0
3711 };;
3713 { .mfi
3714 nop.m 0
3715 fma.s1 FR_p_A12 = FR_p_A13, FR_p_XR, FR_p_A12 // poly tail
3716 nop.i 0
3717 }
3718 { .mfi
3719 nop.m 0
3720 fma.s1 FR_p_XR3L = FR_p_XR2L, FR_p_XR, FR_p_XR3L // x^3 low
3721 nop.i 0
3722 };;
3724 { .mfi
3725 nop.m 0
3726 fma.s1 FR_p_Poly5L = FR_p_Poly5L, f1, FR_p_Temp5L //Low poly
3727 nop.i 0
3728 }
3729 { .mfi
3730 nop.m 0
3731 fma.s1 FR_p_A10 = FR_p_A11, FR_p_XR, FR_p_A10 //poly tail
3732 nop.i 0
3733 };;
3735 { .mfi
3736 nop.m 0
3737 fms.s1 FR_p_Poly4L = FR_p_A3H, f1, FR_p_Poly4H /// Low poly
3738 nop.i 0
3739 }
3740 { .mfi
3741 nop.m 0
3742 fma.s1 FR_p_A6 = FR_p_A7, FR_p_XR, FR_p_A6 // poly tail
3743 nop.i 0
3744 };;
3746 { .mfi
3747 nop.m 0
3748 fma.s1 FR_p_A8 = FR_p_A9, FR_p_XR, FR_p_A8 // poly tail
3749 nop.i 0
3750 }
3751 { .mfi
3752 nop.m 0
3753 fma.s1 FR_p_XR6 = FR_p_XR4, FR_p_XR2, f0 // r^6
3754 nop.i 0
3755 };;
3757 { .mfi
3758 nop.m 0
3759 fma.s1 FR_p_Poly2L = FR_p_Poly2L, f1, FR_p_Temp2L // High poly
3760 nop.i 0
3761 }
3762 { .mfi
3763 nop.m 0
3764 fms.s1 FR_p_Poly1L = FR_p_A0H, f1, FR_p_Poly1H // High poly
3765 nop.i 0
3766 };;
3768 { .mfi
3769 nop.m 0
3770 fma.s1 FR_r_ResL = FR_r_ResL, f1, FR_r_TH // neg sin
3771 nop.i 0
3772 }
3773 { .mfi
3774 nop.m 0
3775 fma.s1 FR_r_TT = FR_r_TL, f1, FR_r_A1L // neg sin
3776 nop.i 0
3777 };;
3779 { .mfi
3780 nop.m 0
3781 fma.s1 FR_p_Temp4L = FR_p_Poly5L,FR_p_XR,FR_p_Temp4L //Low poly
3782 nop.i 0
3783 }
3784 { .mfi
3785 nop.m 0
3786 fma.s1 FR_p_A18 = FR_p_A20, FR_p_XR2, FR_p_A18 // poly tail
3787 nop.i 0
3788 };;
3790 { .mfi
3791 nop.m 0
3792 fma.s1 FR_p_Poly4L = FR_p_Poly4L, f1, FR_p_Temp4H // Low poly
3793 nop.i 0
3794 }
3795 { .mfi
3796 nop.m 0
3797 fma.s1 FR_p_A14 = FR_p_A16, FR_p_XR2, FR_p_A14 // poly tail
3798 nop.i 0
3799 };;
3801 { .mfi
3802 nop.m 0
3803 fma.s1 FR_p_A6 = FR_p_A8, FR_p_XR2, FR_p_A6 // poly tail
3804 nop.i 0
3805 }
3806 { .mfi
3807 nop.m 0
3808 fma.s1 FR_p_A10 = FR_p_A12, FR_p_XR2, FR_p_A10 // poly tail
3809 nop.i 0
3810 };;
3812 { .mfi
3813 nop.m 0
3814 fma.s1 FR_p_Temp1L = FR_p_Poly2L,FR_p_XR,FR_p_Temp1L //High poly
3815 nop.i 0
3816 }
3817 { .mfi
3818 nop.m 0
3819 fma.s1 FR_p_Poly1L = FR_p_Poly1L, f1, FR_p_Temp1H // High poly
3820 nop.i 0
3821 };;
3823 { .mfi
3824 nop.m 0
3825 fma.s1 FR_r_ResL = FR_r_ResL, f1, FR_r_TT // neg sin
3826 nop.i 0
3827 }
3828 { .mfi
3829 nop.m 0
3830 fma.s1 FR_r_TH = FR_r_ResH, FR_r_XS2, f0 // neg sin
3831 nop.i 0
3832 };;
3834 { .mfi
3835 nop.m 0
3836 fma.s1 FR_p_Temp4L = FR_p_Temp4L, f1, FR_p_A3L // Low poly
3837 nop.i 0
3838 }
3839 { .mfi
3840 nop.m 0
3841 fma.s1 FR_p_Poly3H = FR_p_Poly4H, FR_p_XR3, f0 // Low poly
3842 nop.i 0
3843 };;
3845 { .mfi
3846 nop.m 0
3847 fma.s1 FR_p_A14 = FR_p_A18, FR_p_XR4, FR_p_A14 // poly tail
3848 nop.i 0
3849 }
3850 { .mfi
3851 nop.m 0
3852 fma.s1 FR_p_XR8 = FR_p_XR4, FR_p_XR4, f0 // r^8
3853 nop.i 0
3854 };;
3856 { .mfi
3857 nop.m 0
3858 fma.s1 FR_r_TL = FR_r_ResH, FR_r_XS2L, f0 // neg sin
3859 nop.i 0
3860 }
3861 { .mfi
3862 nop.m 0
3863 fnma.s1 FR_z_R1 = f8,FR_z_ZH,f1 // r1 = a-b*x
3864 nop.i 0
3865 };;
3867 { .mfi
3868 nop.m 0
3869 fma.s1 FR_p_Temp1L = FR_p_Temp1L, f1, FR_p_A0L // High poly
3870 nop.i 0
3871 }
3872 { .mfi
3873 nop.m 0
3874 fma.s1 FR_p_A6 = FR_p_A10, FR_p_XR4, FR_p_A6 // poly tail
3875 nop.i 0
3876 };;
3878 { .mfi
3879 nop.m 0
3880 fms.s1 FR_r_TT = FR_r_ResH, FR_r_XS2, FR_r_TH // neg sin
3881 nop.i 0
3882 }
3883 { .mfi
3884 nop.m 0
3885 fma.s1 FR_r_Res3H = FR_r_TH, f1, f1 // neg sin
3886 nop.i 0
3887 };;
3889 { .mfi
3890 nop.m 0
3891 fma.s1 FR_p_Poly4L = FR_p_Poly4L, f1, FR_p_Temp4L // Low poly
3892 nop.i 0
3893 }
3894 { .mfi
3895 nop.m 0
3896 fma.s1 FR_p_Poly3L = FR_p_Poly4H, FR_p_XR3L, f0 // Low poly
3897 nop.i 0
3898 };;
3900 { .mfi
3901 nop.m 0
3902 fma.s1 FR_p_Poly0H = FR_p_Poly3H, f1, FR_p_Poly1H // Result
3903 nop.i 0
3904 }
3905 { .mfi
3906 nop.m 0
3907 fma.s1 FR_r_A7 = FR_r_A8, FR_r_XS2, FR_r_A7 // neg sin
3908 nop.i 0
3909 };;
3911 { .mfi
3912 nop.m 0
3913 fma.s1 FR_r_TL = FR_r_ResL, FR_r_XS2, FR_r_TL // neg sin
3914 nop.i 0
3915 }
3916 { .mfi
3917 nop.m 0
3918 fma.s1 FR_r_XS4 = FR_r_XS2, FR_r_XS2, f0 // xs^4
3919 nop.i 0
3920 };;
3922 { .mfi
3923 nop.m 0
3924 fma.s1 FR_p_Poly1L = FR_p_Poly1L, f1, FR_p_Temp1L // High poly
3925 nop.i 0
3926 }
3927 { .mfi
3928 nop.m 0
3929 fma.s1 FR_p_PolyTail = FR_p_A14, FR_p_XR8, FR_p_A6 // poly tail
3930 nop.i 0
3931 };;
3933 { .mfi
3934 nop.m 0
3935 fms.s1 FR_r_Res3L = f1, f1, FR_r_Res3H // neg sin
3936 nop.i 0
3937 }
3938 { .mfi
3939 nop.m 0
3940 fma.s1 FR_r_ResH = FR_r_Res3H, FR_r_XS, f0 // neg sin
3941 nop.i 0
3942 };;
3944 { .mfi
3945 nop.m 0
3946 fms.s1 FR_p_Temp0L = FR_p_Poly4H,FR_p_XR3,FR_p_Poly3H //Low poly
3947 nop.i 0
3948 }
3949 { .mfi
3950 nop.m 0
3951 fma.s1 FR_p_Poly3L = FR_p_Poly4L,FR_p_XR3,FR_p_Poly3L //Low poly
3952 nop.i 0
3953 };;
3955 { .mfi
3956 nop.m 0
3957 fms.s1 FR_p_Poly0L = FR_p_Poly1H, f1, FR_p_Poly0H // Result
3958 nop.i 0
3959 }
3960 { .mfi
3961 nop.m 0
3962 fma.s1 FR_z_ZL = FR_z_R1,FR_z_Y3, f0 // x_lo = r1*y3
3963 nop.i 0
3964 };;
3966 { .mfi
3967 nop.m 0
3968 fma.s1 FR_r_TL = FR_r_TL, f1, FR_r_TT // neg sin
3969 nop.i 0
3970 }
3971 { .mfi
3972 nop.m 0
3973 fma.s1 FR_r_A3 = FR_r_A4, FR_r_XS2, FR_r_A3 /// neg sin
3974 nop.i 0
3975 };;
3977 { .mfi
3978 nop.m 0
3979 fma.s1 FR_p_Poly1L = FR_p_PolyTail,FR_p_XR6,FR_p_Poly1L // High
3980 nop.i 0
3981 }
3982 { .mfi
3983 nop.m 0
3984 fma.s1 FR_r_A5 = FR_r_A6, FR_r_XS2, FR_r_A5 // neg sin
3985 nop.i 0
3986 };;
3988 { .mfi
3989 nop.m 0
3990 fma.s1 FR_r_Res3L = FR_r_Res3L, f1, FR_r_TH // neg sin
3991 nop.i 0
3992 }
3993 { .mfi
3994 nop.m 0
3995 fms.s1 FR_r_ResL = FR_r_Res3H, FR_r_XS, FR_r_ResH // neg sin
3996 nop.i 0
3997 };;
3999 { .mfi
4000 nop.m 0
4001 fma.s1 FR_p_Poly3L = FR_p_Poly3L, f1, FR_p_Temp0L // Low poly
4002 nop.i 0
4003 }
4004 { .mfi
4005 nop.m 0
4006 fma.s1 FR_r_A7 = FR_r_A9, FR_r_XS4, FR_r_A7 // neg sin
4007 nop.i 0
4008 };;
4010 { .mfi
4011 nop.m 0
4012 fma.s1 FR_p_Poly0L = FR_p_Poly0L, f1, FR_p_Poly3H // result
4013 nop.i 0
4014 };;
4016 { .mfi
4017 nop.m 0
4018 (p14) fma.s1 f8 = FR_p_Poly0H, FR_z_ZH, f0 // z*poly
4019 nop.i 0
4020 }
4021 { .mfi
4022 nop.m 0
4023 fma.s1 FR_p_Temp1L = FR_p_Poly0H, FR_z_ZL, f0 // z*poly low
4024 nop.i 0
4025 };;
4027 { .mfi
4028 nop.m 0
4029 fma.s1 FR_r_A3 = FR_r_A5, FR_r_XS4, FR_r_A3 // sin tail
4030 nop.i 0
4031 }
4032 { .mfi
4033 nop.m 0
4034 fma.s1 FR_r_XS7 = FR_r_XS4, FR_r_XS2, f0 // xs^6
4035 nop.i 0
4036 };;
4038 { .mfi
4039 nop.m 0
4040 fma.s1 FR_r_Res3L = FR_r_Res3L, f1, FR_r_TL // sin low
4041 nop.i 0
4042 }
4043 { .mfi
4044 nop.m 0
4045 fma.s1 FR_r_XS8 = FR_r_XS4, FR_r_XS4, f0 // xs^8
4046 nop.i 0
4047 };;
4049 { .mfi
4050 nop.m 0
4051 fma.s1 FR_p_Temp0H = FR_p_Poly3L, f1, FR_p_Poly1L // result
4052 nop.i 0
4053 };;
4055 { .mfi
4056 nop.m 0
4057 (p14) fms.s1 FR_p_Temp1H = FR_p_Poly0H, FR_z_ZH, f8 // hi result
4058 nop.i 0
4059 };;
4061 { .mfi
4062 nop.m 0
4063 fma.s1 FR_r_XS7 = FR_r_XS7, FR_r_XS, f0 // xs^7
4064 nop.i 0
4065 };;
4067 { .mfi
4068 nop.m 0
4069 fma.s1 FR_r_ResL = FR_r_Res3L, FR_r_XS, FR_r_ResL // lo result
4070 nop.i 0
4071 }
4072 { .mfi
4073 nop.m 0
4074 fma.s1 FR_r_Tail = FR_r_A7, FR_r_XS8, FR_r_A3 // tail result
4075 nop.i 0
4076 };;
4078 { .mfi
4079 nop.m 0
4080 fma.s1 FR_p_Poly0L = FR_p_Poly0L, f1, FR_p_Temp0H // lo result
4081 nop.i 0
4082 };;
4084 { .mfi
4085 nop.m 0
4086 fma.s1 FR_r_ResL = FR_r_Tail, FR_r_XS7, FR_r_ResL // lo result
4087 nop.i 0
4088 };;
4090 { .mfi
4091 nop.m 0
4092 (p14) fma.s1 FR_p_Temp1L = FR_p_Poly0L,FR_z_ZH,FR_p_Temp1L //hi result
4093 nop.i 0
4094 };;
4096 { .mfi
4097 nop.m 0
4098 fma.s1 FR_r_TT = FR_r_ResL, f1, f0 // for low result
4099 nop.i 0
4100 };;
4102 .pred.rel "mutex",p12,p13
4103 { .mfi
4104 nop.m 0
4105 (p14) fma.s1 FR_p_Temp1L = FR_p_Temp1L, f1, FR_p_Temp1H // for lo res
4106 nop.i 0
4107 };;
4109 { .mfi
4110 (p10) cmp.eq p13, p12 = r0, r0 // set p13, clear p12
4111 fma.s1 FR_r_Res1H = FR_r_ResH, f1, FR_r_TT // hi res
4112 nop.i 0
4113 };;
4115 { .mfb
4116 (p9) cmp.eq p13, p12 = r0, r0 // set p13, clear p12
4117 (p14) fma.s0 f8 = f8, f1, FR_p_Temp1L // Final result
4118 (p14) br.ret.spnt b0 // Exit for 0 < |X| < 1 path (positive arguments)///////
4119 };;
4121 { .mfi
4122 (p11) cmp.eq p13, p12 = r0, r0 // set p13, clear p12
4123 fms.s1 FR_r_Res1L = FR_r_ResH, f1, FR_r_Res1H // Low sin result
4124 nop.i 0
4125 };;
4127 { .mfi
4128 nop.m 0
4129 fma.s1 FR_r_Res1L = FR_r_Res1L, f1, FR_r_TT // Low sin result
4130 nop.i 0
4131 }
4132 { .mfi
4133 nop.m 0
4134 fma.s1 FR_r_TL = FR_p_Poly0L,FR_r_Res1H,f0 //Low sin result
4135 nop.i 0
4136 };;
4138 { .mfi
4139 nop.m 0
4140 fma.s1 FR_r_TL = FR_p_Poly0H, FR_r_Res1L, FR_r_TL //Low sin
4141 nop.i 0
4142 };;
4144 { .mfi
4145 nop.m 0
4146 fma.s1 FR_r_ResH = FR_p_Poly0H, FR_r_Res1H, FR_r_TL //High sin
4147 nop.i 0
4148 };;
4150 { .mfi
4151 nop.m 0
4152 fms.s1 FR_r_ResL = FR_p_Poly0H,FR_r_Res1H,FR_r_ResH //Low res
4153 nop.i 0
4154 };;
4156 { .mfi
4157 nop.m 0
4158 frcpa.s1 FR_r_Y0,p0 = f1,FR_r_ResH // y = frcpa(b)
4159 nop.i 0
4160 };;
4162 { .mfi
4163 nop.m 0
4164 fneg FR_r_NegOne = f1 // Construct -1.0
4165 nop.i 0
4166 }
4167 { .mfi
4168 nop.m 0
4169 fma.s1 FR_r_ResL = FR_r_ResL, f1, FR_r_TL // low sin
4170 nop.i 0
4171 };;
4173 { .mfi
4174 nop.m 0
4175 fma.s1 FR_r_Q0 = f1,FR_r_Y0,f0 // q = a*y
4176 nop.i 0
4177 }
4178 { .mfi
4179 nop.m 0
4180 fnma.s1 FR_r_E0 = FR_r_Y0,FR_r_ResH,f1 // e = 1-b*y
4181 nop.i 0
4182 };;
4184 { .mfi
4185 nop.m 0
4186 fma.s1 FR_r_E2 = FR_r_E0,FR_r_E0,FR_r_E0 // e2 = e+e^2
4187 nop.i 0
4188 }
4189 { .mfi
4190 nop.m 0
4191 fma.s1 FR_r_E1 = FR_r_E0,FR_r_E0,f0 // e1 = e^2
4192 nop.i 0
4193 };;
4195 { .mfi
4196 nop.m 0
4197 fma.s1 FR_r_Y1 = FR_r_Y0,FR_r_E2,FR_r_Y0 // y1 = y+y*e2
4198 nop.i 0
4199 }
4200 { .mfi
4201 nop.m 0
4202 fma.s1 FR_r_E3 = FR_r_E1,FR_r_E1,FR_r_E0 // e3 = e+e1^2
4203 nop.i 0
4204 };;
4206 { .mfi
4207 nop.m 0
4208 fma.s1 FR_r_Y2 = FR_r_Y1,FR_r_E3,FR_r_Y0 // y2 = y+y1*e3
4209 nop.i 0
4210 }
4211 { .mfi
4212 nop.m 0
4213 fnma.s1 FR_r_R0 = FR_r_ResH,FR_r_Q0,f1 // r = a-b*q
4214 nop.i 0
4215 };;
4217 { .mfi
4218 nop.m 0
4219 fnma.s1 FR_r_E4 = FR_r_ResH,FR_r_Y2,f1 // e4 = 1-b*y2
4220 nop.i 0
4221 }
4222 { .mfi
4223 nop.m 0
4224 fma.s1 FR_r_ZH = FR_r_R0,FR_r_Y2,FR_r_Q0 // x = q+r*y2
4225 nop.i 0
4226 };;
4228 { .mfi
4229 nop.m 0
4230 fma.s1 FR_r_Y3 = FR_r_Y2,FR_r_E4,FR_r_Y2 // y3 = y2+y2*e4
4231 nop.i 0
4232 }
4233 { .mfi
4234 nop.m 0
4235 fnma.s1 FR_r_R1 = FR_r_ResH,FR_r_ZH,f1 // r1 = a-b*x
4236 nop.i 0
4237 };;
4239 { .mfi
4240 nop.m 0
4241 fnma.s1 FR_r_R1 = FR_r_ResL,FR_r_ZH,FR_r_R1 // r1=r1 - b_lo*X
4242 nop.i 0
4243 }
4244 { .mfi
4245 nop.m 0
4246 fma.s1 FR_r_ZHN = FR_r_ZH,FR_r_NegOne, f0 // Negate
4247 nop.i 0
4248 };;
4250 .pred.rel "mutex",p13,p12
4251 { .mfb
4252 nop.m 0
4253 fnma.s0 f8 = FR_r_R1,FR_r_Y3,FR_r_ZHN // Result for neg
4254 br.ret.sptk b0 // Exit for 0 < |X| < 1 path (negative arguments)//////
4255 };;
4260 // SPECIALS (x for natval, nan, +/-inf or +/-0) ///////////////////////////////
4261 //------------------------------------------------------------------------------
4262 .align 32
4263 tgammal_spec:
4264 { .mlx
4265 nop.m 0
4266 movl GR_DenOverflow = 0x2000000000000001
4267 }
4268 { .mfi
4269 nop.m 0
4270 fclass.m p9,p0 = f8,0xB // +/-denormals
4271 nop.i 0
4272 };;
4273 { .mfi
4274 nop.m 0
4275 fclass.m p6,p0 = f8,0x1E1 // Test x for natval, nan, +inf
4276 nop.i 0
4277 };;
4278 { .mfi
4279 nop.m 0
4280 fclass.m p7,p8 = f8,0x7 // +/-0
4281 nop.i 0
4282 }
4284 { .mfi
4285 (p9) cmp.ltu.unc p10,p11 = GR_l_signif_Z, GR_DenOverflow
4286 (p9) fnorm.s0 f8 = f8
4287 nop.i 0
4288 };;
4290 { .mfb
4291 nop.m 0
4292 (p9) fcvt.fx.trunc.s1 FR_n_IXN = FR_l_AbsX // Round by truncate
4293 (p11) br.cond.sptk tgamma_lt_1 // Return to gamma ('good' denormal)////////////
4294 };;
4296 { .mfb
4297 nop.m 0
4298 nop.f 0
4299 (p10) br.cond.spnt tgammal_overflow // "Bad" denormal - overflow! /////////////
4300 };;
4302 { .mfi
4303 nop.m 0
4304 mov FR_X = f8 // for error handler
4305 nop.i 0
4306 }
4307 { .mfb
4308 nop.m 0
4309 (p6) fma.s0 f8 = f8,f1,f8 // res = x + x
4310 (p6) br.ret.spnt b0 // Exit for NAN, INF and NatVals ////////////////////////
4311 };;
4312 .pred.rel "mutex",p7,p8
4313 { .mfi
4314 (p7) mov GR_Parameter_TAG = 256 // negative
4315 (p7) frcpa.s0 f8,p0 = f1,f8 // Raise V flag
4316 nop.i 0
4317 }
4318 { .mfb
4319 nop.m 0
4320 nop.f 0
4321 (p8) br.cond.spnt tgammal_singularity // Branch for +ZERO ////////////////////
4322 };;
4324 { .mfb
4325 nop.m 0
4326 nop.f 0
4327 br.cond.spnt tgammal_libm_err // Branch for -ZERO ///////////////////////
4328 };;
4333 // SINGULARITY (x is negative integer or 0) ////////////////////////////////////
4334 //------------------------------------------------------------------------------
4335 .align 32
4336 tgammal_singularity:
4337 { .mfi
4338 nop.m 0
4339 mov FR_X = f8 // For error handler
4340 mov GR_Parameter_TAG = 256 // negative
4341 }
4342 { .mfb
4343 nop.m 0
4344 frcpa.s0 f8,p0 = f0,f0 // Raise V flag
4345 br.cond.sptk tgammal_libm_err // Call error handler /////////////////////
4346 // with singularity error /////////////////
4347 };;
4352 // OVERFLOW (result is too big and cannot be represented by normal value) //////
4353 // ( X > 1755.54 and for denormals with abs value less than 0x2000000000000001 )
4354 //------------------------------------------------------------------------------
4355 .align 32
4356 tgammal_overflow:
4357 { .mfi
4358 addl r8 = 0x1FFFE, r0 // Exp of INF
4359 fcmp.lt.s1 p15,p14 = f8,f0 // p14 - pos arg, p15 - neg arg
4360 nop.i 0
4361 };;
4363 { .mfi
4364 setf.exp f9 = r8
4365 mov FR_X = f8 // For error handler
4366 mov GR_Parameter_TAG = 255 // overflow
4367 };;
4369 .pred.rel "mutex",p14,p15
4370 { .mfi
4371 nop.m 0
4372 (p14) fma.s0 f8 = f9,f9,f0 // Set I,O and +INF result
4373 nop.i 0
4374 }
4375 { .mfb
4376 nop.m 0
4377 (p15) fnma.s0 f8 = f9,f9,f0 // Set I,O and -INF result
4378 br.cond.sptk tgammal_libm_err // Call error handler /////////////////////
4379 // with overflow error ////////////////////
4380 };;
4386 // UNDERFLOW (x is negative noninteger with big absolute value) ////////////////
4387 //------------------------------------------------------------------------------
4388 .align 32
4389 tgammal_underflow:
4390 { .mfi
4391 nop.m 0
4392 fcvt.fx.trunc.s1 FR_u_IXN = f8 // Convert arg to int repres. in FR
4393 nop.i 0
4394 };;
4396 { .mmi
4397 getf.sig GR_u_XN = FR_u_IXN
4398 mov r11 = 0x00001
4399 nop.i 0
4400 };;
4402 { .mfi
4403 setf.exp f9 = r11
4404 nop.f 0
4405 nop.i 0
4406 };;
4408 { .mfi
4409 nop.m 0
4410 nop.f 0
4411 tbit.z p6,p7 = GR_u_XN,0 // even or odd
4412 };;
4414 .pred.rel "mutex",p6,p7
4415 { .mfi
4416 nop.m 0
4417 (p6) fms.s0 f8 = f9,f9,f9 // for negatives
4418 nop.i 0
4419 }
4420 { .mfb
4421 nop.m 0
4422 (p7) fma.s0 f8 = f9,f9,f9 // for positives
4423 br.ret.sptk b0 // Exit for underflow path //////////////////////////////
4424 };;
4427 GLOBAL_LIBM_END(tgammal)
4428 libm_alias_ldouble_other (tgamma, tgamma)
4433 ////////////////// Tgammal error handler ///////////////////////////////////////
4434 //------------------------------------------------------------------------------
4435 LOCAL_LIBM_ENTRY(__libm_error_region)
4436 tgammal_libm_err:
4437 .prologue
4438 { .mfi
4439 add GR_Parameter_Y=-32,sp // Parameter 2 value
4440 nop.f 0
4441 .save ar.pfs,GR_SAVE_PFS
4442 mov GR_SAVE_PFS=ar.pfs // Save ar.pfs
4443 }
4444 { .mfi
4445 .fframe 64
4446 add sp=-64,sp // Create new stack
4447 nop.f 0
4448 mov GR_SAVE_GP=gp // Save gp
4449 };;
4450 { .mmi
4451 stfe [GR_Parameter_Y] = FR_Y,16 // Save Parameter 2 on stack
4452 add GR_Parameter_X = 16,sp // Parameter 1 address
4453 .save b0, GR_SAVE_B0
4454 mov GR_SAVE_B0=b0 // Save b0
4455 };;
4456 .body
4457 { .mib
4458 stfe [GR_Parameter_X] = FR_X // Store Parameter 1 on stack
4459 add GR_Parameter_RESULT = 0,GR_Parameter_Y
4460 nop.b 0 // Parameter 3 address
4461 }
4462 { .mib
4463 stfe [GR_Parameter_Y] = FR_RESULT // Store Parameter 3 on stack
4464 add GR_Parameter_Y = -16,GR_Parameter_Y
4465 br.call.sptk b0=__libm_error_support# // Call error handling function
4466 };;
4467 { .mmi
4468 nop.m 999
4469 nop.m 999
4470 add GR_Parameter_RESULT = 48,sp
4471 };;
4472 { .mmi
4473 ldfe f8 = [GR_Parameter_RESULT] // Get return result off stack
4474 .restore sp
4475 add sp = 64,sp // Restore stack pointer
4476 mov b0 = GR_SAVE_B0 // Restore return address
4477 };;
4478 { .mib
4479 mov gp = GR_SAVE_GP // Restore gp
4480 mov ar.pfs = GR_SAVE_PFS // Restore ar.pfs
4481 br.ret.sptk b0 // Return
4482 };;
4484 LOCAL_LIBM_END(__libm_error_region#)
4486 .type __libm_error_support#,@function
4487 .global __libm_error_support#