ports/sysdeps/ia64/fpu/w_tgammal.S

   1 .file "tgammal.s"
   2
   3
   4 // Copyright (c) 2002 - 2005, Intel Corporation
   5 // All rights reserved.
   6 //
   7 // Contributed 2002 by the Intel Numerics Group, Intel Corporation
   8 //
   9 // Redistribution and use in source and binary forms, with or without
  10 // modification, are permitted provided that the following conditions are
  11 // met:
  12 //
  13 // * Redistributions of source code must retain the above copyright
  14 // notice, this list of conditions and the following disclaimer.
  15 //
  16 // * Redistributions in binary form must reproduce the above copyright
  17 // notice, this list of conditions and the following disclaimer in the
  18 // documentation and/or other materials provided with the distribution.
  19 //
  20 // * The name of Intel Corporation may not be used to endorse or promote
  21 // products derived from this software without specific prior written
  22 // permission.
  23
  24 // THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
  25 // "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
  26 // LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
  27 // A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL INTEL OR ITS
  28 // CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
  29 // EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
  30 // PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
  31 // PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY
  32 // OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY OR TORT (INCLUDING
  33 // NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
  34 // SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
  35 //
  36 // Intel Corporation is the author of this code, and requests that all
  37 // problem reports or change requests be submitted to it directly at
  38 // http://www.intel.com/software/products/opensource/libraries/num.htm.
  39 //
  40 // History
  41 //==============================================================
  42 // 01/16/02  Initial version
  43 // 05/20/02  Cleaned up namespace and sf0 syntax
  44 // 02/10/03  Reordered header: .section, .global, .proc, .align;
  45 //           used data8 for long double table values
  46 // 03/17/03  Moved tgammal_libm_err label into .proc region
  47 // 04/10/03  Changed error codes for overflow and negative integers
  48 // 03/31/05  Reformatted delimiters between data tables
  49 //
  50 // API
  51 //==============================================================
  52 // long double tgammal(long double)
  53 //
  54 // Resources Used:
  55 //
  56 //    Floating-Point Registers:  f8-f15
  57 //                               f32-f127
  58 //
  59 //    General Purpose Registers: r32-r67
  60 //
  61 //    Predicate Registers:       p6-p15
  62 //
  63 //*********************************************************************
  64 //
  65 // IEEE Special Conditions:
  66 //
  67 //    tgammal(+inf) = +inf
  68 //    tgammal(-inf) = QNaN
  69 //    tgammal(+/-0) = +/-inf
  70 //    tgammal(x<0, x - integer) = QNaN
  71 //    tgammal(SNaN) = QNaN
  72 //    tgammal(QNaN) = QNaN
  73 //
  74 //*********************************************************************
  75 // Overview of operation
  76 //==============================================================
  77 //
  78 // Algorithm description
  79 // ---------------------
  80 //
  81 // There are 3 main paths in the implementation
  82 // (and additional special values branches)
  83 //
  84 // 1) |X| >= 13 - Stirling formula computation
  85 //    a) Positive arguments:
  86 //       TGAMMAL(X) = exp((X-0.5)*ln(X) - X + C + S(Z)),
  87 //       where C = 0.5*ln(2*Pi) , Z = 1/Z, S(Z) - Bernulli polynomial
  88 //       (up to 'B18' term).
  89 //       Some of these calculation done in multiprecision.
  90 //       Ln returns multiprecision result too
  91 //       and exp also accepts and returns pair of values.
  92 //
  93 //    b) Negative arguments
  94 //       TGAMMAL(-X) = PI/(X*TGAMMAL(X)*sin(PI*X)).
  95 //       (X*sin(PI*X))/PI calculated in parallel with TGAMMAL.
  96 //       Here we use polynomial of 9th degree with 2 multiprecision steps.
  97 //       Argument range reduction is:
  98 //       N = [x] with round to nearest, r = x - N, -0.5 <= r < 0.5
  99 //       After ((X-0.5)*ln(X) - X + C + S(Z)) completed we just invert
 100 //       its result and compute exp with negative argument (1/exp(x)=exp(-x))
 101 //       Then we multiply exp result to PI/(X*sin(PI*X)).
 102 //
 103 // 2) 1 <= |X| < 13 - Polynomial part
 104 //    a) Positive arguments:
 105 //       All values are splitted to such intervals as:
 106 //       #0->[2;3], #1->[3,4], #2->[5,6]...
 107 //       For even intervals we just use polynomial computation with degree 20
 108 //       and first 6 multiprecision computations.
 109 //       Range reduction looks like
 110 //       N = [x] with truncate, r = x - N - 0.5, -0.5 <= r < 0.5
 111 //       For odd intervals we use reccurent formula:
 112 //       TGAMMAL(X) = TGAMMA(X-1)*(X-1)
 113 //       [1;2] interval is splitted to 3 subranges:
 114 //       [1;1.25], [1.25;1.75], [1.75;2] with the same polynomial forms
 115 //
 116 //    b) Negative arguments
 117 //       TGAMMAL(-X) = PI/(X*TGAMMAL(X)*sin(PI*X)).
 118 //       (X*sin(PI*X))/PI calculated in parallel with TGAMMAL.
 119 //       After multiplication by TGAMMAL(X) result we calculate reciprocal
 120 //       and get final result.
 121 //
 122 // 3) 0 < |X| < 1 - Near 0 part
 123 //    a) Here we use reccurent formula TGAMMAL(X) = TGAMMAL(X+1)/X
 124 //       TGAMMAL(X+1) calculated as shown above,
 125 //       1/X result obtained in parallel. Then we just multiply these values.
 126 //       There is only additional separated subrange: [0;0.125] with specific
 127 //       polynomial constants set.
 128 //
 129 //    b) Negative arguments
 130 //       TGAMMAL(-X) = PI/(TGAMMAL(X+1)*sin(PI*X)).
 131 //       There is no need to compute 1/X.
 132
 133
 134
 135 RODATA
 136
 137 .align 16
 138 LOCAL_OBJECT_START(Constants_Tgammal_log_80_Q)
 139 // log2_hi, log2_lo, Q_6, Q_5, Q_4, Q_3, Q_2, Q_1
 140 data4 0x00000000,0xB1721800,0x00003FFE,0x00000000
 141 data4 0x4361C4C6,0x82E30865,0x0000BFE2,0x00000000
 142 data4 0xA51BE0AF,0x92492453,0x00003FFC,0x00000000
 143 data4 0xA0CFD29F,0xAAAAAB73,0x0000BFFC,0x00000000
 144 data4 0xCCCE3872,0xCCCCCCCC,0x00003FFC,0x00000000
 145 data4 0xFFFFB4FB,0xFFFFFFFF,0x0000BFFC,0x00000000
 146 data4 0xAAAAAAAB,0xAAAAAAAA,0x00003FFD,0x00000000
 147 data4 0x00000000,0x80000000,0x0000BFFE,0x00000000
 148 LOCAL_OBJECT_END(Constants_Tgammal_log_80_Q)
 149
 150 .align 64
 151 LOCAL_OBJECT_START(Constants_Tgammal_log_80_Z_G_H_h1)
 152 // Z1 - 16 bit fixed, G1 and H1 IEEE single, h1 IEEE double
 153 data4 0x00008000,0x3F800000,0x00000000,0x00000000
 154 data4 0x00000000,0x00000000,0x00000000,0x00000000
 155 data4 0x00007879,0x3F70F0F0,0x3D785196,0x00000000
 156 data4 0xEBA0E0D1,0x8B1D330B,0x00003FDA,0x00000000
 157 data4 0x000071C8,0x3F638E38,0x3DF13843,0x00000000
 158 data4 0x9EADD553,0xE2AF365E,0x00003FE2,0x00000000
 159 data4 0x00006BCB,0x3F579430,0x3E2FF9A0,0x00000000
 160 data4 0x752F34A2,0xF585FEC3,0x0000BFE3,0x00000000
 161 data4 0x00006667,0x3F4CCCC8,0x3E647FD6,0x00000000
 162 data4 0x893B03F3,0xF3546435,0x00003FE2,0x00000000
 163 data4 0x00006187,0x3F430C30,0x3E8B3AE7,0x00000000
 164 data4 0x39CDD2AC,0xBABA62E0,0x00003FE4,0x00000000
 165 data4 0x00005D18,0x3F3A2E88,0x3EA30C68,0x00000000
 166 data4 0x457978A1,0x8718789F,0x00003FE2,0x00000000
 167 data4 0x0000590C,0x3F321640,0x3EB9CEC8,0x00000000
 168 data4 0x3185E56A,0x9442DF96,0x0000BFE4,0x00000000
 169 data4 0x00005556,0x3F2AAAA8,0x3ECF9927,0x00000000
 170 data4 0x2BBE2CBD,0xCBF9A4BF,0x00003FE4,0x00000000
 171 data4 0x000051EC,0x3F23D708,0x3EE47FC5,0x00000000
 172 data4 0x852D5935,0xF3537535,0x00003FE3,0x00000000
 173 data4 0x00004EC5,0x3F1D89D8,0x3EF8947D,0x00000000
 174 data4 0x46CDF32F,0xA1F1E699,0x0000BFDF,0x00000000
 175 data4 0x00004BDB,0x3F17B420,0x3F05F3A1,0x00000000
 176 data4 0xD8484CE3,0x84A61856,0x00003FE4,0x00000000
 177 data4 0x00004925,0x3F124920,0x3F0F4303,0x00000000
 178 data4 0xFF28821B,0xC7DD97E0,0x0000BFE2,0x00000000
 179 data4 0x0000469F,0x3F0D3DC8,0x3F183EBF,0x00000000
 180 data4 0xEF1FD32F,0xD3C4A887,0x00003FE3,0x00000000
 181 data4 0x00004445,0x3F088888,0x3F20EC80,0x00000000
 182 data4 0x464C76DA,0x84672BE6,0x00003FE5,0x00000000
 183 data4 0x00004211,0x3F042108,0x3F29516A,0x00000000
 184 data4 0x18835FB9,0x9A43A511,0x0000BFE5,0x00000000
 185 LOCAL_OBJECT_END(Constants_Tgammal_log_80_Z_G_H_h1)
 186
 187 .align 64
 188 LOCAL_OBJECT_START(Constants_Tgammal_log_80_Z_G_H_h2)
 189 // Z2 - 16 bit fixed, G2 and H2 IEEE single, h2 IEEE double
 190 data4 0x00008000,0x3F800000,0x00000000,0x00000000
 191 data4 0x00000000,0x00000000,0x00000000,0x00000000
 192 data4 0x00007F81,0x3F7F00F8,0x3B7F875D,0x00000000
 193 data4 0x211398BF,0xAD08B116,0x00003FDB,0x00000000
 194 data4 0x00007F02,0x3F7E03F8,0x3BFF015B,0x00000000
 195 data4 0xC376958E,0xB106790F,0x00003FDE,0x00000000
 196 data4 0x00007E85,0x3F7D08E0,0x3C3EE393,0x00000000
 197 data4 0x79A7679A,0xFD03F242,0x0000BFDA,0x00000000
 198 data4 0x00007E08,0x3F7C0FC0,0x3C7E0586,0x00000000
 199 data4 0x05E7AE08,0xF03F81C3,0x0000BFDF,0x00000000
 200 data4 0x00007D8D,0x3F7B1880,0x3C9E75D2,0x00000000
 201 data4 0x049EB22F,0xD1B87D3C,0x00003FDE,0x00000000
 202 data4 0x00007D12,0x3F7A2328,0x3CBDC97A,0x00000000
 203 data4 0x3A9E81E0,0xFABC8B95,0x00003FDF,0x00000000
 204 data4 0x00007C98,0x3F792FB0,0x3CDCFE47,0x00000000
 205 data4 0x7C4B5443,0xF5F3653F,0x00003FDF,0x00000000
 206 data4 0x00007C20,0x3F783E08,0x3CFC15D0,0x00000000
 207 data4 0xF65A1773,0xE78AB204,0x00003FE0,0x00000000
 208 data4 0x00007BA8,0x3F774E38,0x3D0D874D,0x00000000
 209 data4 0x7B8EF695,0xDB7CBFFF,0x0000BFE0,0x00000000
 210 data4 0x00007B31,0x3F766038,0x3D1CF49B,0x00000000
 211 data4 0xCF773FB3,0xC0241AEA,0x0000BFE0,0x00000000
 212 data4 0x00007ABB,0x3F757400,0x3D2C531D,0x00000000
 213 data4 0xC9539FDF,0xFC8F4D48,0x00003FE1,0x00000000
 214 data4 0x00007A45,0x3F748988,0x3D3BA322,0x00000000
 215 data4 0x954665C2,0x9CD035FB,0x0000BFE1,0x00000000
 216 data4 0x000079D1,0x3F73A0D0,0x3D4AE46F,0x00000000
 217 data4 0xDD367A30,0xEC9017C7,0x00003FE1,0x00000000
 218 data4 0x0000795D,0x3F72B9D0,0x3D5A1756,0x00000000
 219 data4 0xCB11189C,0xEE6625D3,0x0000BFE1,0x00000000
 220 data4 0x000078EB,0x3F71D488,0x3D693B9D,0x00000000
 221 data4 0xBE11C424,0xA49C8DB5,0x0000BFE0,0x00000000
 222 LOCAL_OBJECT_END(Constants_Tgammal_log_80_Z_G_H_h2)
 223
 224 .align 64
 225 LOCAL_OBJECT_START(Constants_Tgammal_log_80_h3_G_H)
 226 // h3 IEEE double extended, H3 and G3 IEEE single
 227 data4 0x112666B0,0xAAACAAB1,0x00003FD3,0x3F7FFC00
 228 data4 0x9B7FAD21,0x90051030,0x00003FD8,0x3F7FF400
 229 data4 0xF4D783C4,0xA6B46F46,0x00003FDA,0x3F7FEC00
 230 data4 0x11C6DDCA,0xDA148D88,0x0000BFD8,0x3F7FE400
 231 data4 0xCA964D95,0xCE65C1D8,0x0000BFD8,0x3F7FDC00
 232 data4 0x23412D13,0x883838EE,0x0000BFDB,0x3F7FD400
 233 data4 0x983ED687,0xB7E5CFA1,0x00003FDB,0x3F7FCC08
 234 data4 0xE3C3930B,0xDBE23B16,0x0000BFD9,0x3F7FC408
 235 data4 0x48AA4DFC,0x9B92F1FC,0x0000BFDC,0x3F7FBC10
 236 data4 0xCE9C8F7E,0x9A8CEB15,0x0000BFD9,0x3F7FB410
 237 data4 0x0DECE74A,0x8C220879,0x00003FDC,0x3F7FAC18
 238 data4 0x2F053150,0xB25CA912,0x0000BFDA,0x3F7FA420
 239 data4 0xD9A5BE20,0xA5876555,0x00003FDB,0x3F7F9C20
 240 data4 0x2053F087,0xC919BB6E,0x00003FD9,0x3F7F9428
 241 data4 0x041E9A77,0xB70BDA79,0x00003FDC,0x3F7F8C30
 242 data4 0xEA1C9C30,0xF18A5C08,0x00003FDA,0x3F7F8438
 243 data4 0x796D89E5,0xA3790D84,0x0000BFDD,0x3F7F7C40
 244 data4 0xA2915A3A,0xE1852369,0x0000BFDD,0x3F7F7448
 245 data4 0xA39ED868,0xD803858F,0x00003FDC,0x3F7F6C50
 246 data4 0x9417EBB7,0xB2EEE356,0x0000BFDD,0x3F7F6458
 247 data4 0x9BB0D07F,0xED5C1F8A,0x0000BFDC,0x3F7F5C68
 248 data4 0xE87C740A,0xD6D201A0,0x0000BFDD,0x3F7F5470
 249 data4 0x1CA74025,0xE8DEBF5E,0x00003FDC,0x3F7F4C78
 250 data4 0x1F34A7EB,0x9A995A97,0x0000BFDC,0x3F7F4488
 251 data4 0x359EED97,0x9CB0F742,0x0000BFDA,0x3F7F3C90
 252 data4 0xBBC6A1C8,0xD6F833C2,0x0000BFDD,0x3F7F34A0
 253 data4 0xE71090EC,0xE1F68F2A,0x00003FDC,0x3F7F2CA8
 254 data4 0xC160A74F,0xD1881CF1,0x0000BFDB,0x3F7F24B8
 255 data4 0xD78CB5A4,0x9AD05AE2,0x00003FD6,0x3F7F1CC8
 256 data4 0x9A77DC4B,0xE658CB8E,0x0000BFDD,0x3F7F14D8
 257 data4 0x6BD6D312,0xBA281296,0x00003FDC,0x3F7F0CE0
 258 data4 0xF95210D0,0xB478BBEB,0x0000BFDB,0x3F7F04F0
 259 data4 0x38800100,0x39400480,0x39A00640,0x39E00C41 // H's start here
 260 data4 0x3A100A21,0x3A300F22,0x3A4FF51C,0x3A6FFC1D
 261 data4 0x3A87F20B,0x3A97F68B,0x3AA7EB86,0x3AB7E101
 262 data4 0x3AC7E701,0x3AD7DD7B,0x3AE7D474,0x3AF7CBED
 263 data4 0x3B03E1F3,0x3B0BDE2F,0x3B13DAAA,0x3B1BD766
 264 data4 0x3B23CC5C,0x3B2BC997,0x3B33C711,0x3B3BBCC6
 265 data4 0x3B43BAC0,0x3B4BB0F4,0x3B53AF6D,0x3B5BA620
 266 data4 0x3B639D12,0x3B6B9444,0x3B7393BC,0x3B7B8B6D
 267 LOCAL_OBJECT_END(Constants_Tgammal_log_80_h3_G_H)
 268
 269 .align 64
 270 LOCAL_OBJECT_START(Constants_Tgammal_stirling)
 271 //0.5*ln(2*Pi)=9.1893853320467266954096885e-01 + 7.2239360881843238220057778e-17
 272 data8 0x3FED67F1C864BEB4, 0x3C94D252F2400510
 273 // Bernulli numbers
 274 data8 0xAAAAAAAAAAAAAAAB, 0x00003FFB //B2 = 8.3333333333333333333333333333e-02
 275 data8 0xBF66C16C16C16C17 //B4 = -2.7777777777777777777777777778e-03
 276 data8 0x3F4A01A01A01A01A //B6 = 7.9365079365079365079365079365e-04
 277 data8 0xBF43813813813814 //B8 = -5.9523809523809523809523809524e-04
 278 data8 0x3F4B951E2B18FF23 //B10 = 8.4175084175084175084175084175e-04
 279 data8 0xBF5F6AB0D9993C7D //B12 = -1.9175269175269175269175269175e-03
 280 data8 0x3F7A41A41A41A41A //B14 = 6.4102564102564102564102564103e-03
 281 data8 0xBF9E4286CB0F5398 //B16 = -2.9550653594771241830065359477e-02
 282 data8 0x3FC6FE96381E0680 //B18 = 1.7964437236883057316493849002e-01
 283 data8 0x3FE0000000000000 // 0.5
 284 LOCAL_OBJECT_END(Constants_Tgammal_stirling)
 285
 286 .align 64
 287 LOCAL_OBJECT_START(Constants_Tgammal_sin)
 288 // Polynomial coefficients for the sin(Pi*x)/Pi, 0 <= |x| < 0.5
 289 //A2 = 8.1174242528335360802316245099e-01 + 5.1302254650266899774269946201e-18
 290 data8 0x3FE9F9CB402BC46C, 0x3C57A8B3819B7CEC
 291 //A1 = -1.6449340668482264060656916627e+00 + -3.0210280454695477893051351574e-17
 292 data8 0xBFFA51A6625307D3, 0xBC816A402079D0EF
 293 data8 0xF3AEF1FFCCE6C813, 0x0000BFE3 //A9 = -7.0921197799923779127089910470e-09
 294 data8 0x87D54408E6D4BB9D, 0x00003FE9 //A8 = 2.5300880778252693946712766029e-07
 295 data8 0xEA12033DCE7B8ED9, 0x0000BFED //A7 = -6.9758403885461690048189307819e-06
 296 data8 0x9BA38C952A59D1A8, 0x00003FF2 //A6 = 1.4842878710882320255092707181e-04
 297 data8 0x99C0B55178FF0E38, 0x0000BFF6 //A5 = -2.3460810348048124421268761990e-03
 298 data8 0xD63402E798FEC896, 0x00003FF9 //A4 = 2.6147847817611456327417812320e-02
 299 data8 0xC354723906D95E92, 0x0000BFFC //A3 = -1.9075182412208257558294507774e-01
 300 LOCAL_OBJECT_END(Constants_Tgammal_sin)
 301
 302 .align 64
 303 LOCAL_OBJECT_START(Constants_Tgammal_exp_64_Arg)
 304 data4 0x00000000,0xB17217F4,0x00003FF2,0x00000000 // L_hi = hi part log(2)/2^12
 305 data4 0xF278ECE6,0xF473DE6A,0x00003FD4,0x00000000 // L_lo = lo part log(2)/2^12
 306 LOCAL_OBJECT_END(Constants_Tgammal_exp_64_Arg)
 307
 308 LOCAL_OBJECT_START(Constants_Tgammal_exp_64_A)
 309 data4 0xB1B736A0,0xAAAAAAAB,0x00003FFA,0x00000000 // A3
 310 data4 0x90CD6327,0xAAAAAAAB,0x00003FFC,0x00000000 // A2
 311 data4 0xFFFFFFFF,0xFFFFFFFF,0x00003FFD,0x00000000 // A1
 312 LOCAL_OBJECT_END(Constants_Tgammal_exp_64_A)
 313
 314 LOCAL_OBJECT_START(Constants_Tgammal_exp_64_T1)
 315 data4 0x3F800000,0x3F8164D2,0x3F82CD87,0x3F843A29
 316 data4 0x3F85AAC3,0x3F871F62,0x3F88980F,0x3F8A14D5
 317 data4 0x3F8B95C2,0x3F8D1ADF,0x3F8EA43A,0x3F9031DC
 318 data4 0x3F91C3D3,0x3F935A2B,0x3F94F4F0,0x3F96942D
 319 data4 0x3F9837F0,0x3F99E046,0x3F9B8D3A,0x3F9D3EDA
 320 data4 0x3F9EF532,0x3FA0B051,0x3FA27043,0x3FA43516
 321 data4 0x3FA5FED7,0x3FA7CD94,0x3FA9A15B,0x3FAB7A3A
 322 data4 0x3FAD583F,0x3FAF3B79,0x3FB123F6,0x3FB311C4
 323 data4 0x3FB504F3,0x3FB6FD92,0x3FB8FBAF,0x3FBAFF5B
 324 data4 0x3FBD08A4,0x3FBF179A,0x3FC12C4D,0x3FC346CD
 325 data4 0x3FC5672A,0x3FC78D75,0x3FC9B9BE,0x3FCBEC15
 326 data4 0x3FCE248C,0x3FD06334,0x3FD2A81E,0x3FD4F35B
 327 data4 0x3FD744FD,0x3FD99D16,0x3FDBFBB8,0x3FDE60F5
 328 data4 0x3FE0CCDF,0x3FE33F89,0x3FE5B907,0x3FE8396A
 329 data4 0x3FEAC0C7,0x3FED4F30,0x3FEFE4BA,0x3FF28177
 330 data4 0x3FF5257D,0x3FF7D0DF,0x3FFA83B3,0x3FFD3E0C
 331 LOCAL_OBJECT_END(Constants_Tgammal_exp_64_T1)
 332
 333 LOCAL_OBJECT_START(Constants_Tgammal_exp_64_T2)
 334 data4 0x3F800000,0x3F80058C,0x3F800B18,0x3F8010A4
 335 data4 0x3F801630,0x3F801BBD,0x3F80214A,0x3F8026D7
 336 data4 0x3F802C64,0x3F8031F2,0x3F803780,0x3F803D0E
 337 data4 0x3F80429C,0x3F80482B,0x3F804DB9,0x3F805349
 338 data4 0x3F8058D8,0x3F805E67,0x3F8063F7,0x3F806987
 339 data4 0x3F806F17,0x3F8074A8,0x3F807A39,0x3F807FCA
 340 data4 0x3F80855B,0x3F808AEC,0x3F80907E,0x3F809610
 341 data4 0x3F809BA2,0x3F80A135,0x3F80A6C7,0x3F80AC5A
 342 data4 0x3F80B1ED,0x3F80B781,0x3F80BD14,0x3F80C2A8
 343 data4 0x3F80C83C,0x3F80CDD1,0x3F80D365,0x3F80D8FA
 344 data4 0x3F80DE8F,0x3F80E425,0x3F80E9BA,0x3F80EF50
 345 data4 0x3F80F4E6,0x3F80FA7C,0x3F810013,0x3F8105AA
 346 data4 0x3F810B41,0x3F8110D8,0x3F81166F,0x3F811C07
 347 data4 0x3F81219F,0x3F812737,0x3F812CD0,0x3F813269
 348 data4 0x3F813802,0x3F813D9B,0x3F814334,0x3F8148CE
 349 data4 0x3F814E68,0x3F815402,0x3F81599C,0x3F815F37
 350 LOCAL_OBJECT_END(Constants_Tgammal_exp_64_T2)
 351
 352 LOCAL_OBJECT_START(Constants_Tgammal_exp_64_W1)
 353 data8 0x0000000000000000, 0xBE384454171EC4B4
 354 data8 0xBE6947414AA72766, 0xBE5D32B6D42518F8
 355 data8 0x3E68D96D3A319149, 0xBE68F4DA62415F36
 356 data8 0xBE6DDA2FC9C86A3B, 0x3E6B2E50F49228FE
 357 data8 0xBE49C0C21188B886, 0x3E64BFC21A4C2F1F
 358 data8 0xBE6A2FBB2CB98B54, 0x3E5DC5DE9A55D329
 359 data8 0x3E69649039A7AACE, 0x3E54728B5C66DBA5
 360 data8 0xBE62B0DBBA1C7D7D, 0x3E576E0409F1AF5F
 361 data8 0x3E6125001A0DD6A1, 0xBE66A419795FBDEF
 362 data8 0xBE5CDE8CE1BD41FC, 0xBE621376EA54964F
 363 data8 0x3E6370BE476E76EE, 0x3E390D1A3427EB92
 364 data8 0x3E1336DE2BF82BF8, 0xBE5FF1CBD0F7BD9E
 365 data8 0xBE60A3550CEB09DD, 0xBE5CA37E0980F30D
 366 data8 0xBE5C541B4C082D25, 0xBE5BBECA3B467D29
 367 data8 0xBE400D8AB9D946C5, 0xBE5E2A0807ED374A
 368 data8 0xBE66CB28365C8B0A, 0x3E3AAD5BD3403BCA
 369 data8 0x3E526055C7EA21E0, 0xBE442C75E72880D6
 370 data8 0x3E58B2BB85222A43, 0xBE5AAB79522C42BF
 371 data8 0xBE605CB4469DC2BC, 0xBE589FA7A48C40DC
 372 data8 0xBE51C2141AA42614, 0xBE48D087C37293F4
 373 data8 0x3E367A1CA2D673E0, 0xBE51BEBB114F7A38
 374 data8 0xBE6348E5661A4B48, 0xBDF526431D3B9962
 375 data8 0x3E3A3B5E35A78A53, 0xBE46C46C1CECD788
 376 data8 0xBE60B7EC7857D689, 0xBE594D3DD14F1AD7
 377 data8 0xBE4F9C304C9A8F60, 0xBE52187302DFF9D2
 378 data8 0xBE5E4C8855E6D68F, 0xBE62140F667F3DC4
 379 data8 0xBE36961B3BF88747, 0x3E602861C96EC6AA
 380 data8 0xBE3B5151D57FD718, 0x3E561CD0FC4A627B
 381 data8 0xBE3A5217CA913FEA, 0x3E40A3CC9A5D193A
 382 data8 0xBE5AB71310A9C312, 0x3E4FDADBC5F57719
 383 data8 0x3E361428DBDF59D5, 0x3E5DB5DB61B4180D
 384 data8 0xBE42AD5F7408D856, 0x3E2A314831B2B707
 385 LOCAL_OBJECT_END(Constants_Tgammal_exp_64_W1)
 386
 387 LOCAL_OBJECT_START(Constants_Tgammal_exp_64_W2)
 388 data8 0x0000000000000000, 0xBE641F2537A3D7A2
 389 data8 0xBE68DD57AD028C40, 0xBE5C77D8F212B1B6
 390 data8 0x3E57878F1BA5B070, 0xBE55A36A2ECAE6FE
 391 data8 0xBE620608569DFA3B, 0xBE53B50EA6D300A3
 392 data8 0x3E5B5EF2223F8F2C, 0xBE56A0D9D6DE0DF4
 393 data8 0xBE64EEF3EAE28F51, 0xBE5E5AE2367EA80B
 394 data8 0x3E47CB1A5FCBC02D, 0xBE656BA09BDAFEB7
 395 data8 0x3E6E70C6805AFEE7, 0xBE6E0509A3415EBA
 396 data8 0xBE56856B49BFF529, 0x3E66DD3300508651
 397 data8 0x3E51165FC114BC13, 0x3E53333DC453290F
 398 data8 0x3E6A072B05539FDA, 0xBE47CD877C0A7696
 399 data8 0xBE668BF4EB05C6D9, 0xBE67C3E36AE86C93
 400 data8 0xBE533904D0B3E84B, 0x3E63E8D9556B53CE
 401 data8 0x3E212C8963A98DC8, 0xBE33138F032A7A22
 402 data8 0x3E530FA9BC584008, 0xBE6ADF82CCB93C97
 403 data8 0x3E5F91138370EA39, 0x3E5443A4FB6A05D8
 404 data8 0x3E63DACD181FEE7A, 0xBE62B29DF0F67DEC
 405 data8 0x3E65C4833DDE6307, 0x3E5BF030D40A24C1
 406 data8 0x3E658B8F14E437BE, 0xBE631C29ED98B6C7
 407 data8 0x3E6335D204CF7C71, 0x3E529EEDE954A79D
 408 data8 0x3E5D9257F64A2FB8, 0xBE6BED1B854ED06C
 409 data8 0x3E5096F6D71405CB, 0xBE3D4893ACB9FDF5
 410 data8 0xBDFEB15801B68349, 0x3E628D35C6A463B9
 411 data8 0xBE559725ADE45917, 0xBE68C29C042FC476
 412 data8 0xBE67593B01E511FA, 0xBE4A4313398801ED
 413 data8 0x3E699571DA7C3300, 0x3E5349BE08062A9E
 414 data8 0x3E5229C4755BB28E, 0x3E67E42677A1F80D
 415 data8 0xBE52B33F6B69C352, 0xBE6B3550084DA57F
 416 data8 0xBE6DB03FD1D09A20, 0xBE60CBC42161B2C1
 417 data8 0x3E56ED9C78A2B771, 0xBE508E319D0FA795
 418 data8 0xBE59482AFD1A54E9, 0xBE2A17CEB07FD23E
 419 data8 0x3E68BF5C17365712, 0x3E3956F9B3785569
 420 LOCAL_OBJECT_END(Constants_Tgammal_exp_64_W2)
 421
 422
 423
 424 LOCAL_OBJECT_START(Constants_Tgammal_poly)
 425
 426 // Polynomial coefficients for the tgammal(x), 2 <= |x| < 3
 427 //A5 = 2.8360780594841213109180699803e-02 + 2.2504152891014320704380000000e-19
 428 data8 0x3F9D0A9BC49353D2, 0x3C109AEA0F23CE2D
 429 //A4 = 1.0967323400216015538699565468e-01 + 9.9225166000430644587276000000e-18
 430 data8 0x3FBC138B89492C5B, 0x3C66E138506D5652
 431 //A3 = 2.5387124684114281691904579930e-01 + 2.2667777637607113205546600000e-17
 432 data8 0x3FD03F6D2FA4F4F8, 0x3C7A2258DA8CD8B1
 433 data8 0xC5866457328BC39B, 0x00003FE3 //A20 = 5.7487331964156762795056629138e-09
 434 data8 0xE93D9F1ACD59C929, 0x0000BFE4 //A19= -1.3576396100397317396956445658e-08
 435 data8 0xE33389C8F6CBA813, 0x00003FE5 //A18 = 2.6449714924964597501721434271e-08
 436 data8 0x8FE7B25B9CD26D2A, 0x0000BFE7 //A17= -6.7011017946055513660266853311e-08
 437 data8 0xB89F4721BFBC15B0, 0x00003FE8 //A16 = 1.7194280320370423615174419192e-07
 438 data8 0xE49CBDC1874EBABA, 0x0000BFE9 //A15= -4.2582353660153782928729466776e-07
 439 data8 0x913AF50A336129CA, 0x00003FEB //A14 = 1.0820500665257088283172211622e-06
 440 data8 0xABCF0F7313B3B332, 0x0000BFEC //A13= -2.5601510627710417669568115706e-06
 441 //A2 = 6.5455857798133676439533701341e-01 + 1.3292075193155190798867000000e-18
 442 data8 0x3FE4F224D4B7E01C, 0x3C3885014A2B8319
 443 //A1 = 9.3473452162608550164435428087e-01 + 3.2785154201417136611642400000e-17
 444 data8 0x3FEDE9585F1A7093, 0x3C82E63C1B5028BF
 445 //A0 = 1.3293403881791368004172682049e+00 + 2.2005689328949279282607500000e-16
 446 data8 0x3FF544FA6D47B38F, 0x3CAFB6AA9829E81F
 447 data8 0xF3668F799997C76D, 0x00003FED //A12 = 7.2539039479124273660331538367e-06
 448 data8 0xD6C6BBD54CDEAEB1, 0x0000BFEE //A11= -1.2801665282681088568639378920e-05
 449 data8 0x809E4763B06F6883, 0x00003FF1 //A10 = 6.1329973609906572700697893187e-05
 450 data8 0x8443B000F8F9A71A, 0x00003FED //A9 = 3.9417864189995544394564413428e-06
 451 data8 0xC5C7E6D62A6991D8, 0x00003FF4 //A8 = 7.5447412886334708803357581519e-04
 452 data8 0xD2AF690725C62D88, 0x00003FF5 //A7 = 1.6074004848394703022110823298e-03
 453 data8 0xAA44E635D4B7B682, 0x00003FF8 //A6 = 1.0392403425906843901680697839e-02
 454 //
 455 // Polynomial coefficients for the tgammal(x), 4 <= |x| < 5
 456 //A5 = 1.1600674810589555185913468449e+00 + 3.0229979112715124660731000000e-17
 457 data8 0x3FF28FA2EB44D22E, 0x3C816D285234C815
 458 //A4 = 3.1374268565470946334983182169e+00 + 1.3694868953995008497659600000e-16
 459 data8 0x400919734073B1E1, 0x3CA3BC83CD7E9565
 460 //A3 = 7.0834593993741057360580271052e+00 + 3.3899702569039156457249800000e-16
 461 data8 0x401C5576617B6C1F, 0x3CB86D6431213296
 462 data8 0xA4A5FB49C094966B, 0x00003FDA //A20 = 9.3591760106637809309720130828e-12
 463 data8 0xA9260DA0F51D7ED8, 0x00003FDD //A19 = 7.6919898428091669411809372180e-11
 464 data8 0xA16441DFB14BD6E1, 0x00003FE0 //A18 = 5.8713933014370867331213494535e-10
 465 data8 0x95F098D9C2234849, 0x00003FE3 //A17 = 4.3638234584169302324461091035e-09
 466 data8 0x8581817400E5AD2B, 0x00003FE6 //A16 = 3.1084260332429955234755367839e-08
 467 data8 0xE272940E373EBE15, 0x00003FE8 //A15 = 2.1089573544273993580820317236e-07
 468 data8 0xB6B3391145D226FB, 0x00003FEB //A14 = 1.3612217421122787182942706259e-06
 469 data8 0x8B9428C4DF95FCD5, 0x00003FEE //A13 = 8.3195416382628990683949003789e-06
 470 //A2 = 1.2665135075272345943631080445e+01 + 9.8721896915973874255877000000e-16
 471 data8 0x4029548C95A76F38, 0x3CD1C8BE715B8E13
 472 //A1 = 1.6154969393303069580269948347e+01 + 9.6850518810678379641029000000e-16
 473 data8 0x403027AC12FC1E1E, 0x3CD172711C15501B
 474 //A0 = 1.1631728396567448058362970187e+01 + 8.7078125362814179268673000000e-16
 475 data8 0x40274371E7866C65, 0x3CCF5F8A1A5FACA0
 476 data8 0xC94A903114272C03, 0x00003FF0 //A12 = 4.7991576836334427243159066630e-05
 477 data8 0x8844262960E04BE6, 0x00003FF3 //A11 = 2.5990716419283017929486175141e-04
 478 data8 0xAC5418A76767678D, 0x00003FF5 //A10 = 1.3147621245497801180184809726e-03
 479 data8 0xCA231B6EFE959132, 0x00003FF7 //A9 = 6.1687358811367989146517222415e-03
 480 data8 0xDA38E39C13819D2A, 0x00003FF9 //A8 = 2.6638454961912040754759086920e-02
 481 data8 0xD696DF8D8389FE53, 0x00003FFB //A7 = 1.0477995539298934056097943975e-01
 482 data8 0xBDD5C153048BC435, 0x00003FFD //A6 = 3.7077144754791605130056406006e-01
 483 //
 484 // Polynomial coefficients for the tgammal(x), 6 <= |x| < 7
 485 //A5 = 6.7169398121054200601065531373e+01 + 2.9481001527213915901489600000e-15
 486 data8 0x4050CAD76B377BA0, 0x3CEA8DDB2B2DE93E
 487 //A4 = 1.6115104376855398982115730178e+02 + 1.3422421925418824418257300000e-14
 488 data8 0x406424D559BDC687, 0x3D0E397FDB5B33DC
 489 //A3 = 3.1812194028053562533386866562e+02 + 3.9881709875858650942409600000e-14
 490 data8 0x4073E1F377A6CF73, 0x3D26738F63FE9C4C
 491 data8 0xD6E1B5FF90CAABD3, 0x00003FE1 //A20 = 1.5634700199277480081025480635e-09
 492 data8 0xD451987B925DD37E, 0x00003FE4 //A19 = 1.2358576813211397717382327174e-08
 493 data8 0xBFC151B67FA58E6B, 0x00003FE7 //A18 = 8.9292951435632759686382657901e-08
 494 data8 0xA9034C5E1D67572E, 0x00003FEA //A17 = 6.2962205718327848327368724720e-07
 495 data8 0x8E40F6EAA30A71EC, 0x00003FED //A16 = 4.2394926442967995119170095258e-06
 496 data8 0xE3C3541B03A1C350, 0x00003FEF //A15 = 2.7151465666109594512258841637e-05
 497 data8 0xACE2E58436B2DDCE, 0x00003FF2 //A14 = 1.6487723793339152877117376243e-04
 498 data8 0xF7EAF8D8D1CAA3D1, 0x00003FF4 //A13 = 9.4573158112768812533636022369e-04
 499 //A2 = 4.8664351544258869353143381886e+02 + 4.7424047995944376868895400000e-14
 500 data8 0x407E6A4BD6D9463B, 0x3D2AB2868D79E192
 501 //A1 = 5.1615277644992545447166776285e+02 + 3.0901956935588717379242200000e-14
 502 data8 0x40802138E2DC003B, 0x3D216570FB601AEA
 503 //A0 = 2.8788527781504433278314536437e+02 + 2.8213174117085164944959600000e-14
 504 data8 0x4071FE2A1911F7D6, 0x3D1FC3E4CF4DB5AF
 505 data8 0xA72B88E48D3D1BAB, 0x00003FF7 //A12 = 5.1016252919939028020562237471e-03
 506 data8 0xD2EFB1067DB4FFB2, 0x00003FF9 //A11 = 2.5749059441230515023024615917e-02
 507 data8 0xF788AF9522205C24, 0x00003FFB //A10 = 1.2086617635601742290221382521e-01
 508 data8 0x861A6CE06CB29EAF, 0x00003FFE //A9 = 5.2384071807018493367136112163e-01
 509 data8 0x84FBDE0947718B58, 0x00004000 //A8 = 2.0778727617851237754568261869e+00
 510 data8 0xEEC1371E265A2C3A, 0x00004001 //A7 = 7.4610858525146049022238037342e+00
 511 data8 0xBF514B9BE68ED59D, 0x00004003 //A6 = 2.3914694993947572859629197920e+01
 512 //
 513 // Polynomial coefficients for the tgammal(x), 8 <= |x| < 9
 514 //A5 = 5.8487447114416836484451778233e+03 + 4.7365465221455983144182900000e-13
 515 data8 0x40B6D8BEA568B6FD, 0x3D60AA4D44C2589B
 516 //A4 = 1.2796464063087094473303295672e+04 + 1.2373341702514898266244200000e-12
 517 data8 0x40C8FE3B666B532D, 0x3D75C4752C5B4783
 518 //A3 = 2.2837606581322281272150576115e+04 + 2.6598064610627891398831000000e-13
 519 data8 0x40D64D66D23A7764, 0x3D52B77B3A10EA5C
 520 data8 0xB23418F75B0BE22A, 0x00003FE9 //A20 = 3.3192989594206801808678663868e-07
 521 data8 0xA984A7BC8B856ED2, 0x00003FEC //A19 = 2.5260177918662350066375115788e-06
 522 data8 0x921A49729416372C, 0x00003FEF //A18 = 1.7416797068239475136398213598e-05
 523 data8 0xF5BB9415CC399CA4, 0x00003FF1 //A17 = 1.1717449586392814601938207599e-04
 524 data8 0xC50B91A40B81F9DF, 0x00003FF4 //A16 = 7.5166775151159345732094429036e-04
 525 data8 0x96002572326DB203, 0x00003FF7 //A15 = 4.5776541559407384162139204300e-03
 526 data8 0xD81A1A595E4157BA, 0x00003FF9 //A14 = 2.6379634345126284099420760736e-02
 527 data8 0x92B700D0CFECADD8, 0x00003FFC //A13 = 1.4327622675407940907282658100e-01
 528 //A2 = 3.1237895525940199149772524834e+04 + 3.1280450505163186432331700000e-12
 529 data8 0x40DE8179504C0878, 0x3D8B83BB33FBB766
 530 //A1 = 2.9192841741344487672904506326e+04 + 7.9300780509779689630767000000e-13
 531 data8 0x40DC8235DF171691, 0x3D6BE6C780EE54DF
 532 //A0 = 1.4034407293483411194756627083e+04 + 1.4038139346291543309253700000e-12
 533 data8 0x40CB693422315F90, 0x3D78B23746113FCE
 534 data8 0xBAE50807548BC711, 0x00003FFE //A12 = 7.3005724123917935346868107005e-01
 535 data8 0xDE28B1F57E68CFB6, 0x00004000 //A11 = 3.4712338349724065462763671443e+00
 536 data8 0xF4DCA5A5FF901118, 0x00004002 //A10 = 1.5303868912154033908205911714e+01
 537 data8 0xF85AAA1AD5E84E5E, 0x00004004 //A9 = 6.2088539523416399361048051373e+01
 538 data8 0xE5AA8BB1BF02934D, 0x00004006 //A8 = 2.2966619406617480799195651466e+02
 539 data8 0xBF6CFEFD67F59845, 0x00004008 //A7 = 7.6570306334640770654588802417e+02
 540 data8 0x8DB5D2F001635C29, 0x0000400A //A6 = 2.2673639984182571062068713002e+03
 541 //
 542 // Polynomial coefficients for the tgammal(x), 10 <= |x| < 11
 543 //A5 = 7.2546009516580589115619659424e+05 + 1.0343348865365065212891728822e-10
 544 data8 0x412623A830B99290, 0x3DDC6E7C157611C4
 545 //A4 = 1.4756292870840241666883230209e+06 + 8.1516565365333844166705674775e-11
 546 data8 0x4136842D497E56AF, 0x3DD66837E4C3F9EE
 547 //A3 = 2.4356116926500420086085796356e+06 + 3.5508860076560925641351069404e-10
 548 data8 0x4142950DD8A8C1AF, 0x3DF866C8E3DD0980
 549 data8 0xB7FD0D1EEAC38EB4, 0x00003FF1 //A20 = 8.7732544640091602721643775932e-05
 550 data8 0xA9345C64AC750AE9, 0x00003FF4 //A19 = 6.4546407626804942279126469603e-04
 551 data8 0x8BEABC81BE1E93C9, 0x00003FF7 //A18 = 4.2699261134524096128048819443e-03
 552 data8 0xE1CD281EDD7315F8, 0x00003FF9 //A17 = 2.7563646660310313164706189622e-02
 553 data8 0xAD8A5BA6D0FD9758, 0x00003FFC //A16 = 1.6947310643831556048460963841e-01
 554 data8 0xFCDDA464AD3F182E, 0x00003FFE //A15 = 9.8775699098518676937088606052e-01
 555 data8 0xAE0DCE2F7B60D1AE, 0x00004001 //A14 = 5.4391852309591064073782104822e+00
 556 data8 0xE1745D9ABEB8D1A7, 0x00004003 //A13 = 2.8181819161363002758615770457e+01
 557 //A2 = 3.0619656223573554307222366333e+06 + 1.0819940302945474471259520006e-10
 558 data8 0x41475C66CFA967E4, 0x3DDDBDDB2A27334B
 559 //A1 = 2.6099413018962685018777847290e+06 + 3.6851882860056025385268615240e-10
 560 data8 0x4143E98AA6A48974, 0x3DF9530D42589AB6
 561 //A0 = 1.1332783889487853739410638809e+06 + 1.9339350553312096248591829758e-10
 562 data8 0x41314ADE639225C9, 0x3DEA946DD6C2C8D3
 563 data8 0x88BCFAAE71812A1C, 0x00004006 //A12 = 1.3673820009490115307300592012e+02
 564 data8 0x9A770F5AB540A326, 0x00004008 //A11 = 6.1786031215382040427126476507e+02
 565 data8 0xA170C1D2C6B413FC, 0x0000400A //A10 = 2.5830473201524594051391525170e+03
 566 data8 0x9AE56061CB02EB55, 0x0000400C //A9 = 9.9133441230507404119297200255e+03
 567 data8 0x872390769650FBE2, 0x0000400E //A8 = 3.4595564309496661629764193479e+04
 568 data8 0xD3E5E8D6923910C1, 0x0000400F //A7 = 1.0849181904819284819615140521e+05
 569 data8 0x930D70602F50B754, 0x00004011 //A6 = 3.0116351174131169193070583741e+05
 570 //
 571 // Polynomial coefficients for the tgammal(x), 12 <= |x| < 13
 572 //A5 = 1.2249876249976964294910430908e+08 + 6.0051348061679753770848000000e-09
 573 data8 0x419D34BB29FFC39D, 0x3E39CAB72E01818D
 574 //A4 = 2.3482765927605420351028442383e+08 + 1.1874729051592862323641700000e-08
 575 data8 0x41ABFE5F168D56FA, 0x3E4980338AA7B04B
 576 //A3 = 3.6407329688125067949295043945e+08 + 2.6657200942150363994658700000e-08
 577 data8 0x41B5B35150E199A5, 0x3E5C9F79C0EB5300
 578 data8 0xE89AE0F8D726329D, 0x00003FF9 //A20 = 2.8394164465429105626588451540e-02
 579 data8 0xCF90981F86E38013, 0x00003FFC //A19 = 2.0270002071785908652476845915e-01
 580 data8 0xA56C658079CA8C4A, 0x00003FFF //A18 = 1.2923704984019263122675412350e+00
 581 data8 0x80AEF96A67C5615A, 0x00004002 //A17 = 8.0427183300456238315262463506e+00
 582 data8 0xBE886D7529678931, 0x00004004 //A16 = 4.7633230047847868242503413461e+01
 583 data8 0x858EDBA4CE2F7508, 0x00004007 //A15 = 2.6711607799594541057655957154e+02
 584 data8 0xB0B0A3AF388274F0, 0x00004009 //A14 = 1.4135199810126975119809102782e+03
 585 data8 0xDBA87137988751EF, 0x0000400B //A13 = 7.0290552818218513870879313985e+03
 586 //A2 = 4.2828433593031734228134155273e+08 + 3.9760422293645854535247300000e-08
 587 data8 0x41B98719AFEE2947, 0x3E6558A17E0D3007
 588 //A1 = 3.4008253676084774732589721680e+08 + 1.2558352335001093116071000000e-09
 589 data8 0x41B4453F68C2C6EB, 0x3E159338C5BC7EC3
 590 //A0 = 1.3684336546556583046913146973e+08 + 2.6786516700381562934240300000e-08
 591 data8 0x41A05020CAEE5EA5, 0x3E5CC3058A858579
 592 data8 0xFF5E3940FB4BA576, 0x0000400D //A12 = 3.2687111823895439312116108631e+04
 593 data8 0x8A08C124C7F74B6C, 0x00004010 //A11 = 1.4134701786994123329786229006e+05
 594 data8 0x89D701953540BFFB, 0x00004012 //A10 = 5.6459209892773907605385652281e+05
 595 data8 0xFC46344B3116C3AD, 0x00004013 //A9 = 2.0666305367147234406757715163e+06
 596 data8 0xD183EBD7A400151F, 0x00004015 //A8 = 6.8653979211730981618367536737e+06
 597 data8 0x9C083A40742112F4, 0x00004017 //A7 = 2.0451444503543981795037456447e+07
 598 data8 0xCD3C475B1A8B6662, 0x00004018 //A6 = 5.3801245423495149598177886823e+07
 599 LOCAL_OBJECT_END(Constants_Tgammal_poly)
 600
 601
 602 LOCAL_OBJECT_START(Constants_Tgammal_poly_splitted)
 603
 604 // Polynomial coefficients for the tgammal(x), 1 <= |x| < 1.25
 605 //A5 = -9.8199506890310417350775651357e-01+ -3.2546247786122976510752200000e-17
 606 data8 0xBFEF6C80EC38B509, 0xBC82C2FA7A3DE3BD
 607 //A4 = 9.8172808683439960475425323239e-01 + 4.4847611775298520359811400000e-17
 608 data8 0x3FEF6A51055096B0, 0x3C89DA56DE95EFE4
 609 //A3 = -9.0747907608088618225394839101e-01 +-1.0244057366544064435443970000e-16
 610 data8 0xBFED0A118F324B62, 0xBC9D86C7B9EBCFFF
 611 data8 0xB8E3FDAA66CC738E, 0x00003FFB //A20 = 9.0278608095877488976217714815e-02
 612 data8 0xA76067AE1738699C, 0x0000BFFD //A19 =-3.2690738678103132837070881737e-01
 613 data8 0x9D66B13718408C44, 0x00003FFE //A18 = 6.1484820933424283818320582920e-01
 614 data8 0xD4AC67BBB4AE5599, 0x0000BFFE //A17 =-8.3075569470082063491389474937e-01
 615 data8 0xF1426ED1C1488DB3, 0x00003FFE //A16 = 9.4241993542644505594957058785e-01
 616 data8 0xFC12EB07AA6F4B6B, 0x0000BFFE //A15 =-9.8466366707947121954333549690e-01
 617 data8 0xFF2B32CFE5B0DDC8, 0x00003FFE //A14 = 9.9675290656677214804168895915e-01
 618 data8 0xFFD8E7E6FF3662EA, 0x0000BFFE //A13 =-9.9940347089360552383472582319e-01
 619 //A2 = 9.8905599532797250361682017683e-01 + 5.1760162410376024240867300000e-17
 620 data8 0x3FEFA658C23B1578, 0x3C8DD673A61F6FE7
 621 //A1 = -5.7721566490153275452712478000e-01+ -1.0607935612223465065923310000e-16
 622 data8 0xBFE2788CFC6FB618, 0xBC9E9346622D53B7
 623 //A0 = 9.9999999999999988897769753748e-01 + 1.1102230245372554544790880000e-16
 624 data8 0x3FEFFFFFFFFFFFFF, 0x3C9FFFFFFFF51E4E
 625 data8 0xFFF360DF628F0BC9, 0x00003FFE //A12 = 9.9980740979895815468216470840e-01
 626 data8 0xFFEF8F9A72B40480, 0x0000BFFE //A11 = -9.9974916001038145045939523470e-01
 627 data8 0xFFE037B8C7E39952, 0x00003FFE //A10 = 9.9951504002809911822597567307e-01
 628 data8 0xFFC01E08F348BED2, 0x0000BFFE //A9 = -9.9902522772325406705059517941e-01
 629 data8 0xFF83DAC83119B52C, 0x00003FFE //A8 = 9.9810569179053383842734164901e-01
 630 data8 0xFEF9F8AB891ABB24, 0x0000BFFE //A7 = -9.9600176036720260345608796766e-01
 631 data8 0xFE3F0537573C8235, 0x00003FFE //A6 = 9.9314911461918778676646301341e-01
 632 //
 633 // Polynomial coefficients for the tgammal(x), 1.25 <= |x| < 1.75
 634 //A5 = -7.7523052299853054125655660300e-02+ -1.2693512521686721504433600000e-17
 635 data8 0xBFB3D88CFE50601B, 0xBC6D44ED60EE2170
 636 //A4 = 1.4464535904462152982041800442e-01 + 2.5426820829345729856648800000e-17
 637 data8 0x3FC283BD374EB2A9, 0x3C7D50AC436187C3
 638 //A3 = -1.0729480456477220873257039102e-01+ -6.2429894945456418196551000000e-18
 639 data8 0xBFBB77AC1CA2EBA5, 0xBC5CCA6BCC422D41
 640 data8 0xF732D2689F323283, 0x00003FF2 //A20 = 2.3574688251652899567587145422e-04
 641 data8 0xB6B00E23DE89D13A, 0x0000BFF3 //A19 =-3.4844916488842618776630058875e-04
 642 data8 0xE98396FE4A1B2799, 0x00003FF3 //A18 =4.4539265198744452020440735977e-04
 643 data8 0xAF8D235A640DB1A2, 0x0000BFF4 //A17 =-6.6967514303333563295261178346e-04
 644 data8 0x8513B736C918B261, 0x00003FF5 //A16 = 1.0152970456990865810615917715e-03
 645 data8 0xC790A1A2C78D8E17, 0x0000BFF5 //A15 =-1.5225598630329403515321688394e-03
 646 data8 0x959706CFA638CDE2, 0x00003FF6 //A14 = 2.2825614575133879623648932383e-03
 647 data8 0xE050A6021E129860, 0x0000BFF6 //A13 =-3.4227757733947066666295285936e-03
 648 //A2 = 4.1481345368830113695679528973e-01 + 3.1252439808354284892632100000e-17
 649 data8 0x3FDA8C4DBA620D56, 0x3C82040BCB483C76
 650 //A1 = 3.2338397448885010387886751460e-02 + 3.4437825798552300531443100000e-18
 651 data8 0x3FA08EA88EE561B1, 0x3C4FC366D6C64806
 652 //A0 = 8.8622692545275794095971377828e-01 + 7.2689375867553992399219000000e-17
 653 data8 0x3FEC5BF891B4EF6A, 0x3C94F3877D311C0C
 654 data8 0xA8275AADC09D16FC, 0x00003FF7 //A12 = 5.1316445128621071486146117136e-03
 655 data8 0xFBFE2CE9215267A2, 0x0000BFF7 //A11= -7.6902121820788373000579382408e-03
 656 data8 0xBCC8EEAB67ECD91D, 0x00003FF8 //A10 = 1.1522515369164312742737727262e-02
 657 data8 0x8D1614BB97E5E8C2, 0x0000BFF9 //A9 = -1.7222443097804730395560633583e-02
 658 data8 0xD3A963578BE291E3, 0x00003FF9 //A8 = 2.5837606456090186343624210891e-02
 659 data8 0x9BA7EAE64C42FDF7, 0x0000BFFA //A7 = -3.8001935555045161419575037512e-02
 660 data8 0xF0115BA1A77607E7, 0x00003FFA //A6 = 5.8610303817173477119764956736e-02
 661 //
 662 // Polynomial coefficients for the tgammal(x), 1.75 <= |x| < 2.0
 663 //A5 = 2.6698206874501426502654943818e-04 + 3.4033756836921062797887300000e-20
 664 data8 0x3F317F3740FE2A68, 0x3BE417093234B06E
 665 //A4 = 7.4249010753513894345090307070e-02 + 3.9810018444482764697014200000e-18
 666 data8 0x3FB301FBB0F25A92, 0x3C525BEFFABB622F
 667 //A3 = -8.1576919247086265851720554565e-02+ -5.2716624487804746360745000000e-19
 668 data8 0xBFB4E239984650AC, 0xBC2372F1C4F276FF
 669 data8 0xFEF3AEE71038E9A3, 0x00003FEB //A20 = 1.8995395865421509009969188571e-06
 670 data8 0xA11CFA2672BF876A, 0x0000BFEB //A19 =-1.2003868221414015771269244270e-06
 671 data8 0xF8E107215DAE2164, 0x00003FEC //A18 = 3.7085863210303833432006027217e-06
 672 data8 0xBCDDD3FC011EF7D6, 0x00003FEC //A17 = 2.8143303971756051015245433043e-06
 673 data8 0x8683C4687FA22E68, 0x00003FEE //A16 = 8.0177018464360416764308252462e-06
 674 data8 0xFDA09E5D33E32968, 0x00003FEE //A15 = 1.5117372062443781157389064848e-05
 675 data8 0xFFB00D0CFF4089B4, 0x00003FEF //A14 = 3.0480348961227424242198174995e-05
 676 data8 0xFEF6C39566785085, 0x00003FF0 //A13 = 6.0788135974125244644334004947e-05
 677 //A2 = 4.1184033042643969357854416558e-01 + 1.2103396182129232634761000000e-18
 678 data8 0x3FDA5B978B96BEBF, 0x3C3653AAD0A139E4
 679 //A1 = -4.2278433509846713445057275749e-01+ -4.9429151528135657430413000000e-18
 680 data8 0xBFDB0EE6072093CE, 0xBC56CB907027554F
 681 //A0 = 1.0000000000000000000000000000e+00 + 1.0969171200000000000000000000e-31
 682 data8 0x3FF0000000000000, 0x3981CC6A5B20B4D5
 683 data8 0xFF2B7BA9A8D68C37, 0x00003FF1 //A12 = 1.2167446884801403650547161615e-04
 684 data8 0xFCA53468E3692EF1, 0x00003FF2 //A11 = 2.4094136329542400976250900707e-04
 685 data8 0x808D698A9C993615, 0x00003FF4 //A10 = 4.9038845704938303659791698883e-04
 686 data8 0xF10F8E3FB8BB4AFB, 0x00003FF4 //A9 = 9.1957383840999861214472423976e-04
 687 data8 0x89E224E42F93F005, 0x00003FF6 //A8 = 2.1039333407187324139473634747e-03
 688 data8 0xBAF374824937A323, 0x00003FF6 //A7 = 2.8526458211545152218493600470e-03
 689 data8 0xB6BF7564F52140C6, 0x00003FF8 //A6 = 1.1154045718131014476684982178e-02
 690 //
 691 // Polynomial coefficients for the tgammal(x), 0.0 <= |x| < 0.125
 692 //A5 = -9.8199506890314514073736518185e-01+ -5.9363811993837985890950900000e-17
 693 data8 0xBFEF6C80EC38B67A, 0xBC911C46B447C81F
 694 //A4 = 9.8172808683440015986576554496e-01 + 2.7457414262802803699834200000e-17
 695 data8 0x3FEF6A51055096B5, 0x3C7FA7FF90ACAD1F
 696 //A3 = -9.0747907608088618225394839101e-01 + -1.0676255850934306734701780000e-16
 697 data8 0xBFED0A118F324B62, 0xBC9EC5AFB633438D
 698 data8 0x9217E83FA207CB80, 0x00003FFD //A20 = 2.8533864762086088781083621561e-01
 699 data8 0xA8DABFA52FDF03EC, 0x0000BFFE //A19= -6.5958783896337186303285832783e-01
 700 data8 0xE331ED293AF39F9B, 0x00003FFE //A18 = 8.8748056656454687449654731184e-01
 701 data8 0xF9163C5DDB52419D, 0x0000BFFE //A17= -9.7299554149078295602977718525e-01
 702 data8 0xFEC0A1C672CB9265, 0x00003FFE //A16 = 9.9512683005268190987854104489e-01
 703 data8 0xFFD2D65B8EA7B5F4, 0x0000BFFE //A15= -9.9931087241443958201592847861e-01
 704 data8 0xFFF93AA39EE53445, 0x00003FFE //A14 = 9.9989668364186884793382816496e-01
 705 data8 0xFFFB99A9A3F5F480, 0x0000BFFE //A13= -9.9993286506283835663204999212e-01
 706 //A2 = 9.8905599532797250361682017683e-01 + 5.1778575360788420716540100000e-17
 707 data8 0x3FEFA658C23B1578, 0x3C8DD92B45408D07
 708 //A1 = -5.7721566490153275452712478000e-01+ -1.0607938730998824663273110000e-16
 709 data8 0xBFE2788CFC6FB618, 0xBC9E9346F8FDE55B
 710 //A0 = 9.9999999999999988897769753748e-01 + 1.1102230246251564036631420000e-16
 711 data8 0x3FEFFFFFFFFFFFFF, 0x3C9FFFFFFFFFFFFF
 712 data8 0xFFF7FEBB545812C1, 0x00003FFE //A12 = 9.9987785409425126648628395084e-01
 713 data8 0xFFF00C02E943A3F2, 0x0000BFFE //A11= -9.9975657530855116454438747397e-01
 714 data8 0xFFE0420AADC53820, 0x00003FFE //A10 = 9.9951565514290485919027183699e-01
 715 data8 0xFFC01EB42EF27EEB, 0x0000BFFE //A9 = -9.9902526759155739377365522320e-01
 716 data8 0xFF83DAD0BF23FF12, 0x00003FFE //A8 = 9.9810569378236378800364235948e-01
 717 data8 0xFEF9F8ABDBCDB2F3, 0x0000BFFE //A7 = -9.9600176044241699109053158187e-01
 718 data8 0xFE3F05375988491D, 0x00003FFE //A6 = 9.9314911462127599008937257662e-01
 719 LOCAL_OBJECT_END(Constants_Tgammal_poly_splitted)
 720
 721 .align 64
 722 LOCAL_OBJECT_START(Constants_Tgammal_common)
 723 // Positive overflow value
 724 data8 0x3FE0000000000000 // 0.5
 725 data8 0x3FF8000000000000 // 1.5
 726 data8 0x3FD0000000000000 // 0.25
 727 data8 0x0000000000000000 // 0
 728 data8 0xDB718C066B352E21, 0x00004009 // Positive overflow value
 729 LOCAL_OBJECT_END(Constants_Tgammal_common)
 730
 731
 732
 733 //=======================================================
 734 // Lgamma registers
 735
 736 // General Purpose Registers
 737 GR_l_Log_Table        = r33
 738 GR_l_Log_Table1       = r34
 739 GR_l_BIAS             = r34
 740 GR_l_Index1           = r35
 741 GR_l_Index2           = r36
 742 GR_l_signif_Z         = r37
 743 GR_l_X_0              = r38
 744 GR_l_X_1              = r39
 745 GR_l_X_2              = r40
 746 GR_l_Z_1              = r41
 747 GR_l_Z_2              = r42
 748 GR_l_N                = r43
 749 GR_l_Index3           = r44
 750 GR_l_Stirling_Table   = r45
 751 GR_l_N_Unbiased       = r46
 752
 753 // Floating Point Registers
 754 FR_l_logl_X            = f8
 755
 756 FR_l_h_3              = f10
 757 FR_l_poly_hi          = f10
 758 FR_l_W                = f11
 759 FR_l_S                = f12
 760 FR_l_GS_hi            = f13
 761 FR_l_Y_lo             = f13
 762 FR_l_r_cor            = f14
 763 FR_l_G_1              = f15
 764 FR_l_G                = f15
 765 FR_l_H_1              = f32
 766 FR_l_H                = f32
 767 FR_l_h                = f33
 768 FR_l_h_1              = f33
 769 FR_l_N                = f33
 770 FR_l_G_2              = f34
 771 FR_l_H_2              = f35
 772 FR_l_h_2              = f36
 773 FR_l_G_3              = f37
 774 FR_l_log2_hi          = f38
 775 FR_l_GS_lo            = f39
 776 FR_l_H_3              = f40
 777 FR_l_float_N          = f41
 778 FR_l_Q_4              = f42
 779 FR_l_Q_3              = f43
 780 FR_l_Q_2              = f44
 781 FR_l_Q_1              = f45
 782 FR_l_Q_5              = f46
 783 FR_l_Q_6              = f47
 784 FR_l_log2_lo          = f48
 785 FR_l_r                = f49
 786 FR_l_poly_lo          = f50
 787 FR_l_poly             = f51
 788 FR_l_rsq              = f52
 789 FR_l_Y_lo_res         = f53
 790
 791 FR_l_Y0               = f55
 792 FR_l_Q0               = f56
 793 FR_l_E0               = f57
 794 FR_l_E2               = f58
 795 FR_l_E1               = f59
 796 FR_l_Y1               = f60
 797 FR_l_E3               = f61
 798 FR_l_Y2               = f62
 799
 800 FR_l_Z                = f63
 801 FR_l_Z2               = f64
 802 FR_l_Z4               = f65
 803 FR_l_Z8               = f66
 804
 805 FR_l_CH               = f67
 806 FR_l_CL               = f68
 807
 808 FR_l_B2               = f69
 809 FR_l_B4               = f70
 810 FR_l_B6               = f71
 811 FR_l_B8               = f72
 812 FR_l_B10              = f73
 813 FR_l_B12              = f74
 814 FR_l_B14              = f75
 815 FR_l_B16              = f76
 816 FR_l_B18              = f77
 817 FR_l_Half             = f78
 818 FR_l_SS               = f79
 819 FR_l_AbsX_m_Half      = f80
 820 FR_l_CXH              = f81
 821 FR_l_CXL              = f82
 822 FR_l_SSCXH            = f83
 823 FR_l_SSCXL            = f84
 824 FR_l_XYH              = f85
 825 FR_l_XYL              = f86
 826 FR_l_Temp             = f87
 827
 828 FR_l_logl_YHi         = f88
 829 FR_l_logl_YLo         = f89
 830
 831 FR_l_SignedXYH        = f123
 832
 833 FR_l_AbsX             = f127
 834
 835
 836
 837 //=======================================================
 838 // Negative part registers
 839
 840 // General Purpose Registers
 841 GR_n_sin_Table        = r47
 842 GR_n_XN               = r48
 843
 844 // Float point registers
 845 FR_n_IXNS             = f125
 846 FR_n_IXN              = f126
 847
 848 FR_n_XNS              = f90
 849 FR_n_XS               = f91
 850 FR_n_XS2              = f92
 851 FR_n_XS2L             = f93
 852 FR_n_XS4              = f94
 853 FR_n_XS7              = f95
 854 FR_n_XS8              = f96
 855 FR_n_TT               = f97
 856 FR_n_TH               = f98
 857 FR_n_TL               = f99
 858
 859 FR_n_A2H              = f100
 860 FR_n_A2L              = f101
 861 FR_n_A1H              = f102
 862 FR_n_A1L              = f103
 863 FR_n_A9               = f104
 864 FR_n_A8               = f105
 865 FR_n_A7               = f106
 866 FR_n_A6               = f107
 867 FR_n_A5               = f108
 868 FR_n_A4               = f109
 869 FR_n_A3               = f110
 870
 871 FR_n_PolyH            = f111
 872 FR_n_PolyL            = f112
 873
 874 FR_n_Poly1H           = f113
 875 FR_n_SinxH            = f113 // the same as FR_n_Poly1H
 876 FR_n_Poly1L           = f114
 877 FR_n_SinxL            = f114 // the same as FR_n_Poly1L
 878
 879 FR_n_Tail             = f115
 880 FR_n_NegOne           = f116
 881
 882 FR_n_Y0               = f117
 883
 884 FR_n_Q0               = f118
 885 FR_n_E0               = f119
 886
 887 FR_n_E2               = f120
 888 FR_n_E1               = f121
 889
 890 FR_n_Y1               = f55
 891 FR_n_E3               = f56
 892
 893 FR_n_Y2               = f57
 894 FR_n_R0               = f58
 895
 896 FR_n_E4               = f59
 897 FR_n_RcpResH          = f60
 898
 899 FR_n_Y3               = f61
 900 FR_n_R1               = f62
 901 FR_n_Temp             = f63
 902
 903 FR_n_RcpResL          = f64
 904
 905 FR_n_ResH             = f65
 906 FR_n_ResL             = f66
 907
 908
 909
 910
 911 //=======================================================
 912 // Exp registers
 913
 914 // General Purpose Registers
 915 GR_e_ad_Arg           = r33
 916 GR_e_ad_A             = r34
 917 GR_e_signexp_x        = r35
 918 GR_e_exp_x            = r35
 919 GR_e_exp_mask         = r36
 920 GR_e_ad_W1            = r37
 921 GR_e_ad_W2            = r38
 922 GR_e_M2               = r39
 923 GR_e_M1               = r40
 924 GR_e_K                = r41
 925 GR_e_exp_2_mk         = r42
 926 GR_e_exp_2_k          = r43
 927 GR_e_ad_T1            = r44
 928 GR_e_ad_T2            = r45
 929 GR_e_N_fix            = r46
 930 GR_e_one              = r47
 931 GR_e_exp_bias         = r48
 932 GR_e_sig_inv_ln2      = r49
 933 GR_e_rshf_2to51       = r50
 934 GR_e_exp_2tom51       = r51
 935 GR_e_rshf             = r52
 936
 937 // Floating Point Registers
 938 FR_e_RSHF_2TO51       = f10
 939 FR_e_INV_LN2_2TO63    = f11
 940 FR_e_W_2TO51_RSH      = f12
 941 FR_e_2TOM51           = f13
 942 FR_e_RSHF             = f14
 943 FR_e_Y_hi             = f15
 944 FR_e_Y_lo             = f32
 945 FR_e_scale            = f33
 946 FR_e_float_N          = f34
 947 FR_e_N_signif         = f35
 948 FR_e_L_hi             = f36
 949 FR_e_L_lo             = f37
 950 FR_e_r                = f38
 951 FR_e_W1               = f39
 952 FR_e_T1               = f40
 953 FR_e_W2               = f41
 954 FR_e_T2               = f42
 955 FR_e_W1_p1            = f43
 956 FR_e_rsq              = f44
 957 FR_e_A2               = f45
 958 FR_e_r4               = f46
 959 FR_e_A3               = f47
 960 FR_e_poly             = f48
 961 FR_e_T                = f49
 962 FR_e_W                = f50
 963 FR_e_Wp1              = f51
 964 FR_e_r6               = f52
 965 FR_e_2_mk             = f53
 966 FR_e_A1               = f54
 967 FR_e_T_scale          = f55
 968 FR_e_result_lo        = f56
 969 FR_e_W_T_scale        = f57
 970 FR_e_Wp1_T_scale      = f58
 971
 972 FR_e_expl_Input_X     = f123
 973 FR_e_expl_Input_Y     = f124
 974 FR_e_expl_Output_X    = f123
 975 FR_e_expl_Output_Y    = f124
 976
 977
 978 FR_e_expl_Input_AbsX  = f122
 979
 980
 981
 982 //=======================================================
 983 // Common registers
 984
 985 // General Purpose Registers
 986 GR_c_Table            = r53
 987 GR_c_NegUnderflow     = r54
 988 GR_c_NegSingularity   = r55
 989 GR_c_X                = r56
 990 GR_c_SignBit          = r57
 991 GR_c_13               = r58
 992
 993
 994 // Floating Point Registers
 995 FR_c_PosOverflow      = f123
 996 FR_c_XN               = f124
 997
 998
 999 //=======================================================
1000 // Polynomial part registers
1001
1002 // General Purpose Registers
1003 GR_p_Table            = r59
1004 GR_p_XN               = r33
1005 GR_p_Table2           = r34
1006 GR_p_Int              = r35
1007 GR_p_Offset           = r36
1008 GR_p_Offset2          = r38
1009 GR_p_X_Sgnd           = GR_l_signif_Z // = r37
1010 GR_p_Exp              = r61
1011 GR_p_Bias             = r62
1012 GR_p_0p75             = r63
1013
1014 // Floating Point Registers
1015 FR_p_AbsX             = FR_l_AbsX // = f127
1016 FR_p_IXN              = FR_n_IXN  // = f126
1017 FR_p_XN               = f32
1018 FR_p_0p5              = f33
1019 FR_p_1p5              = f34
1020 FR_p_AbsXM1           = f35
1021 FR_p_2                = f36
1022
1023 FR_p_A20              = f37
1024 FR_p_A19              = f38
1025 FR_p_A18              = f39
1026 FR_p_A17              = f40
1027 FR_p_A16              = f41
1028 FR_p_A15              = f42
1029 FR_p_A14              = f43
1030 FR_p_A13              = f44
1031 FR_p_A12              = f45
1032 FR_p_A11              = f46
1033 FR_p_A10              = f47
1034 FR_p_A9               = f48
1035 FR_p_A8               = f49
1036 FR_p_A7               = f50
1037 FR_p_A6               = f51
1038 FR_p_A5H              = f52
1039 FR_p_A5L              = f53
1040 FR_p_A4H              = f54
1041 FR_p_A4L              = f55
1042 FR_p_A3H              = f56
1043 FR_p_A3L              = f57
1044 FR_p_A2H              = f58
1045 FR_p_A2L              = f59
1046 FR_p_A1H              = f60
1047 FR_p_A1L              = f61
1048 FR_p_A0H              = f62
1049 FR_p_A0L              = f63
1050
1051 FR_p_XR               = f64
1052 FR_p_XR2              = f65
1053 FR_p_XR2L             = f52
1054
1055 FR_p_XR3              = f58
1056 FR_p_XR3L             = f38
1057
1058 FR_p_XR4              = f42
1059 FR_p_XR6              = f40
1060 FR_p_XR8              = f37
1061
1062 FR_p_Poly5H           = f66
1063 FR_p_Poly5L           = f67
1064 FR_p_Poly4H           = f53
1065 FR_p_Poly4L           = f44
1066 FR_p_Poly3H           = f41
1067 FR_p_Poly3L           = f47
1068 FR_p_Poly2H           = f68
1069 FR_p_Poly2L           = f54
1070 FR_p_Poly1H           = f55
1071 FR_p_Poly1L           = f46
1072 FR_p_Poly0H           = f39
1073 FR_p_Poly0L           = f43
1074
1075 FR_p_Temp5H           = f69
1076 FR_p_Temp5L           = f70
1077 FR_p_Temp4H           = f71
1078 FR_p_Temp4L           = f60
1079 FR_p_Temp2H           = f72
1080 FR_p_Temp2L           = f73
1081 FR_p_Temp1H           = f59
1082 FR_p_Temp1L           = f61
1083 FR_p_Temp0H           = f49
1084 FR_p_Temp0L           = f48
1085 FR_p_PolyTail         = f45
1086 FR_p_OddPoly0H        = f56
1087 FR_p_OddPoly0L        = f51
1088
1089 FR_p_0p25             = f73
1090
1091
1092 //=======================================================
1093 // Negative polynomial part registers
1094 // General Purpose Registers
1095 GR_r_sin_Table        = r47
1096 GR_r_sin_Table2       = r60
1097
1098 // Floating Point Registers
1099 FR_r_IXNS             = FR_n_IXNS
1100 FR_r_IXN              = FR_n_IXN
1101
1102 FR_r_AbsX             = FR_l_AbsX
1103
1104 FR_r_A9               = f74
1105 FR_r_A8               = f75
1106 FR_r_A7               = f76
1107 FR_r_A6               = f77
1108 FR_r_A5               = f78
1109 FR_r_A4               = f79
1110 FR_r_A3               = f80
1111 FR_r_A2H              = f81
1112 FR_r_A2L              = f82
1113 FR_r_A1H              = f83
1114 FR_r_A1L              = f84
1115
1116 FR_r_XNS              = f85
1117 FR_r_XS               = f86
1118 FR_r_XS2              = f87
1119 FR_r_XS2L             = f88
1120 FR_r_XS4              = f89
1121 FR_r_XS7              = f90
1122 FR_r_XS8              = f91
1123
1124 FR_r_Tail             = f92
1125
1126 FR_r_TT               = f93
1127 FR_r_TH               = f94
1128 FR_r_TL               = f95
1129
1130 FR_r_ResH             = f96
1131 FR_r_ResL             = f97
1132
1133 FR_r_Res3H            = f98
1134 FR_r_Res3L            = f99
1135
1136 FR_r_Res1H            = f100
1137 FR_r_Res1L            = f101
1138
1139
1140
1141 FR_r_Y0               = f102
1142 FR_r_Q0               = f103
1143 FR_r_E0               = f104
1144 FR_r_E2               = f105
1145 FR_r_E1               = f106
1146 FR_r_Y1               = f107
1147 FR_r_E3               = f108
1148 FR_r_Y2               = f109
1149 FR_r_R0               = f110
1150 FR_r_E4               = f111
1151 FR_r_ZH               = f112
1152 FR_r_Y3               = f113
1153 FR_r_R1               = f114
1154 FR_r_ZHN              = f115
1155 FR_r_ZL               = f115
1156 FR_r_NegOne           = f116
1157
1158 FR_z_Y0               = f102
1159 FR_z_Q0               = f103
1160 FR_z_E0               = f104
1161 FR_z_E2               = f105
1162 FR_z_E1               = f106
1163 FR_z_Y1               = f107
1164 FR_z_E3               = f108
1165 FR_z_Y2               = f109
1166 FR_z_R0               = f110
1167 FR_z_E4               = f111
1168 FR_z_ZH               = f112
1169 FR_z_Y3               = f113
1170 FR_z_R1               = f114
1171 FR_z_ZL               = f115
1172
1173
1174 // General Purpose Registers
1175 GR_SAVE_PFS           = r32
1176 GR_DenOverflow        = r33
1177 GR_u_XN               = r34
1178
1179 GR_SAVE_B0            = r35
1180 GR_SAVE_GP            = r36
1181 GR_SAVE_SP            = r37
1182
1183 // Floating Point Registers
1184 FR_u_IXN              = f34
1185
1186
1187 // ERROR HANDLER REGISTERS
1188 GR_Parameter_X        = r64
1189 GR_Parameter_Y        = r65
1190 GR_Parameter_RESULT   = r66
1191 GR_Parameter_TAG      = r67
1192
1193 FR_RESULT             = f8
1194 FR_X                  = f32
1195 FR_Y                  = f1
1196
1197
1198 .section .text
1199 GLOBAL_LIBM_ENTRY(tgammal)
1200 { .mfi
1201       alloc         r32            = ar.pfs,0,32,4,0
1202       fabs          FR_l_AbsX      = f8 // Get absolute value of X
1203       addl          GR_n_sin_Table = @ltoff(Constants_Tgammal_sin), gp
1204 }
1205 { .mfi
1206       addl          GR_l_Log_Table=@ltoff(Constants_Tgammal_log_80_Z_G_H_h1#),gp
1207       nop.f         0
1208       addl          GR_l_Stirling_Table = @ltoff(Constants_Tgammal_stirling), gp
1209 };;
1210
1211 { .mfi
1212       getf.sig      GR_l_signif_Z  = f8 // Significand of X
1213       fcvt.fx.s1    FR_n_IXNS      = f8 // Convert to fixed point
1214       addl          GR_c_Table     = @ltoff(Constants_Tgammal_common), gp
1215 }
1216 { .mfi
1217       ld8           GR_l_Log_Table = [GR_l_Log_Table]
1218       nop.f         0
1219       addl          GR_p_Table     = @ltoff(Constants_Tgammal_poly), gp
1220 };;
1221
1222 { .mfi
1223       ld8           GR_n_sin_Table = [GR_n_sin_Table]
1224       fclass.m      p6,p0          = f8,0x1EF // Check x for NaN, 0, INF, denorm
1225                                               // NatVal.
1226       addl          GR_c_NegSingularity = 0x1003E, r0
1227 }
1228 { .mlx
1229       ld8           GR_l_Stirling_Table = [GR_l_Stirling_Table]
1230       movl          GR_c_13        = 0x402A000000000000 // 13.0
1231 };;
1232
1233 { .mfi
1234       getf.d        GR_c_X         = f8 // Double prec. X to general register
1235       frcpa.s1      FR_z_Y0,p0     = f1,f8 // y = frcpa(x) (for negatives)
1236       extr.u        GR_l_Index1    = GR_l_signif_Z, 59, 4 // = High 4 bits of Z
1237 }
1238 { .mlx
1239       ld8           GR_c_Table     = [GR_c_Table]
1240       movl          GR_c_SignBit   = 0x8000000000000000 // High bit (sign)
1241 };;
1242
1243 { .mfi
1244       ld8           GR_p_Table     = [GR_p_Table]
1245       fcmp.lt.s1    p15, p14       = f8,f0 // p14 - positive arg, p15 - negative
1246       shl           GR_l_Index1    = GR_l_Index1,5 // Adjust Index1 ptr (x32)
1247 }
1248 { .mfb
1249       adds          GR_c_NegUnderflow = 1765, r0
1250       nop.f         0
1251 (p6)  br.cond.spnt  tgammal_spec  // Spec. values processing branch ////////////
1252                                   // (0s, INFs, NANs, NatVals, denormals) //////
1253 };;
1254
1255 { .mfi
1256       ldfpd         FR_l_CH,FR_l_CL= [GR_l_Stirling_Table], 16 // Load CH, CL
1257       fcvt.fx.trunc.s1 FR_n_IXN    = FR_l_AbsX // Abs arg to int by trunc
1258       extr.u        GR_l_X_0       = GR_l_signif_Z, 49, 15  //  High 15 bit of Z
1259 }
1260 { .mfi
1261       add           GR_l_Index1    = GR_l_Index1,GR_l_Log_Table  // Add offset
1262       fma.s1        FR_p_2         = f1, f1, f1 // 2.0
1263       andcm         GR_c_X         = GR_c_X, GR_c_SignBit // Remove sign
1264 };;
1265
1266 { .mfi
1267       addl       GR_l_Log_Table = @ltoff(Constants_Tgammal_log_80_Z_G_H_h2#), gp
1268       fcmp.lt.s1    p10, p0        = FR_l_AbsX, f1 // If |X|<1 then p10 = 1
1269       nop.i         0
1270 }
1271 { .mlx
1272       ld2           GR_l_Z_1       = [GR_l_Index1],4 // load Z_1 from Index1
1273       movl          GR_l_BIAS      = 0x000000000000FFFF // Bias for exponent
1274 };;
1275
1276 { .mfi
1277       ld8           GR_l_Log_Table = [GR_l_Log_Table]
1278       frcpa.s1      FR_l_Y0, p0    = f1, FR_l_AbsX // y = frcpa(x)
1279       nop.i         0
1280 }
1281 { .mfi
1282       ldfs          FR_l_G_1       = [GR_l_Index1],4  //  Load G_1
1283       fsub.s1       FR_l_W         = FR_l_AbsX, f1 // W = |X|-1
1284       nop.i         0
1285 };;
1286
1287 { .mfi
1288       getf.exp      GR_l_N_Unbiased=  FR_l_AbsX // exponent of |X|
1289       fmerge.se     FR_l_S         = f1, FR_l_AbsX //  S = merging of X and 1.0
1290       cmp.gtu       p11, p0        = GR_c_13, GR_c_X // If 1 <= |X| < 13
1291                                                      // then p11 = 1
1292 }
1293 { .mfb
1294       ldfs          FR_l_H_1       = [GR_l_Index1],8 // Load H_1
1295       fcvt.xf       FR_n_XNS       = FR_n_IXNS // Convert to FP repr. of int X
1296 (p10) br.cond.spnt  tgamma_lt_1    // Branch to |X| < 1 path ///////////////////
1297 };;
1298
1299 { .mfi
1300       ldfpd         FR_n_A2H, FR_n_A2L = [GR_n_sin_Table], 16
1301       nop.f         0
1302       pmpyshr2.u    GR_l_X_1       = GR_l_X_0,GR_l_Z_1,15 // Adjust Index2 (x32)
1303 }
1304 { .mfb
1305       ldfe          FR_l_B2        = [GR_l_Stirling_Table], 16
1306       nop.f         0
1307 (p11) br.cond.spnt  tgamma_lt_13 // Branch to 1 <= |X| < 13 path ///////////////
1308 };;
1309
1310 { .mfi
1311       ldfe          FR_l_h_1       = [GR_l_Index1],0
1312       nop.f         0
1313       sub           GR_l_N         = GR_l_N_Unbiased, GR_l_BIAS  //  N - BIAS
1314 }
1315 { .mib
1316       ldfpd         FR_l_B4,FR_l_B6= [GR_l_Stirling_Table], 16 // Load C
1317 (p15) cmp.geu.unc   p8,p0          = GR_l_N_Unbiased, GR_c_NegSingularity
1318 (p8)  br.cond.spnt  tgammal_singularity // Singularity for arg < to -2^63 //////
1319 };;
1320
1321 { .mmi
1322 (p15) ldfpd         FR_n_A1H, FR_n_A1L = [GR_n_sin_Table], 16
1323       ldfpd         FR_l_B8, FR_l_B10  = [GR_l_Stirling_Table], 16
1324       add           GR_c_Table         = 0x20, GR_c_Table
1325 };;
1326
1327 { .mfi
1328 (p15) ldfe          FR_n_A9        = [GR_n_sin_Table], 16
1329       fma.s1        FR_l_Q0        = f1,FR_l_Y0,f0 // Q0 = Y0
1330       nop.i         0
1331 }
1332 { .mfi
1333       ldfpd         FR_l_B12, FR_l_B14 = [GR_l_Stirling_Table], 16
1334       fnma.s1       FR_l_E0        = FR_l_Y0,FR_l_AbsX,f1 // e = 1-b*y
1335       nop.i         0
1336 };;
1337
1338 { .mfi
1339 (p15) ldfe          FR_n_A8        = [GR_n_sin_Table], 16
1340       fcvt.xf       FR_c_XN        = FR_n_IXN // Convert to FP repr. of int X
1341       extr.u        GR_l_Index2    = GR_l_X_1, 6, 4  // Extract Index2
1342 }
1343 { .mfi
1344       ldfpd         FR_l_B16, FR_l_B18 = [GR_l_Stirling_Table], 16
1345       nop.f         0
1346       nop.i         0
1347 };;
1348
1349 { .mfi
1350 (p15) ldfe          FR_n_A7        = [GR_n_sin_Table], 16
1351       fms.s1        FR_l_CXH       = FR_l_CH, f1, FR_l_AbsX // CXH = CH+|X|
1352       shl           GR_l_Index2    = GR_l_Index2,5
1353 }
1354 { .mfi
1355       ldfd          FR_l_Half      = [GR_l_Stirling_Table] // Load 0.5
1356       nop.f         0
1357       nop.i         0
1358 };;
1359
1360 { .mfi
1361       add           GR_l_Index2    = GR_l_Index2, GR_l_Log_Table  // Add offset
1362       nop.f         0
1363       nop.i         0
1364 }
1365 { .mfi
1366 (p15) ldfe          FR_n_A6        = [GR_n_sin_Table], 16
1367 (p15) fma.s1        FR_n_XS        = FR_l_AbsX , f1, FR_n_XNS // xs = x - int(x)
1368       nop.i         0
1369 };;
1370
1371 { .mmi
1372       ld2           GR_l_Z_2       = [GR_l_Index2],4
1373       addl          GR_l_Log_Table = @ltoff(Constants_Tgammal_log_80_h3_G_H#),gp
1374       nop.i         0
1375 };;
1376
1377 { .mfi
1378       ld8           GR_l_Log_Table = [GR_l_Log_Table]
1379       fma.s1        FR_l_E2        = FR_l_E0,FR_l_E0,FR_l_E0 // e2 = e+e^2
1380       nop.i         0
1381 }
1382 { .mfi
1383       ldfs          FR_l_G_2       = [GR_l_Index2],4
1384       fma.s1        FR_l_E1        = FR_l_E0,FR_l_E0,f0 // e1 = e^2
1385       nop.i         0
1386 };;
1387
1388 { .mmi
1389       ldfs          FR_l_H_2       = [GR_l_Index2],8
1390 (p15) ldfe          FR_n_A5        = [GR_n_sin_Table], 16
1391       nop.i         0
1392 };;
1393
1394 { .mfi
1395       setf.sig      FR_l_float_N   = GR_l_N //    float_N = Make N a fp number
1396       nop.f         0
1397       pmpyshr2.u    GR_l_X_2       = GR_l_X_1,GR_l_Z_2,15  // X_2 = X_1 * Z_2
1398 }
1399 { .mfi
1400       ldfe          FR_l_h_2       = [GR_l_Index2],0
1401       fma.s1        FR_l_CXL       = FR_l_AbsX, f1, FR_l_CXH // CXL = |X|+CXH
1402       add           GR_l_Log_Table1= 0x200, GR_l_Log_Table
1403 };;
1404
1405 { .mfi
1406 (p15) ldfe          FR_n_A4        = [GR_n_sin_Table], 16
1407 (p15) fcmp.eq.unc.s1 p9,p0         = FR_l_AbsX, FR_c_XN //if argument is integer
1408                                                         // and negative
1409       nop.i         0
1410 }
1411 { .mfi
1412       ldfe          FR_c_PosOverflow = [GR_c_Table],16 //Load pos overflow value
1413 (p15) fma.s1        FR_n_XS2         = FR_n_XS, FR_n_XS, f0 // xs^2 = xs*xs
1414       nop.i         0
1415 };;
1416
1417 { .mfi
1418 (p15) ldfe          FR_n_A3        = [GR_n_sin_Table], 16
1419       nop.f         0
1420       nop.i         0
1421 };;
1422
1423 { .mfi
1424 (p15) getf.sig      GR_n_XN        = FR_n_IXN // int(x) to general reg
1425       fma.s1        FR_l_Y1        = FR_l_Y0,FR_l_E2,FR_l_Y0 // y1 = y+y*e2
1426       nop.i         0
1427 }
1428 { .mfb
1429       nop.m         0
1430       fma.s1        FR_l_E3        = FR_l_E1,FR_l_E1,FR_l_E0 // e3 = e+e1^2
1431 (p9)  br.cond.spnt  tgammal_singularity // Singularity for integer /////////////
1432                                         // and negative arguments //////////////
1433 };;
1434
1435 { .mfi
1436       nop.m         0
1437       fms.s1        FR_l_AbsX_m_Half = FR_l_AbsX, f1, FR_l_Half // |x|-0.5
1438       extr.u        GR_l_Index2      = GR_l_X_2, 1, 5   //  Get Index3
1439 };;
1440
1441 { .mfi
1442       shladd        GR_l_Log_Table1= GR_l_Index2, 2, GR_l_Log_Table1
1443       nop.f         0
1444       shladd        GR_l_Index3    = GR_l_Index2,4, GR_l_Log_Table  // Index3
1445 }
1446 { .mfb
1447 (p15) cmp.gtu.unc   p11, p0        = GR_n_XN, GR_c_NegUnderflow // X < -1765
1448       fms.s1        FR_l_CXL       = FR_l_CH, f1, FR_l_CXL // CXL = CH - CXL
1449 (p11) br.cond.spnt tgammal_underflow // Singularity for negative argument //////
1450                                      // at underflow domain (X < -1765) //////
1451 };;
1452
1453 { .mfi
1454       addl          GR_l_Log_Table = @ltoff(Constants_Tgammal_log_80_Q#), gp
1455 (p15) fma.s1        FR_n_TT        = FR_n_A2L, FR_n_XS2, f0 // T=A2L*x^2
1456       tbit.nz.unc   p13, p12       = GR_n_XN, 0x0 // whether [X] odd or even
1457 }
1458 { .mfi
1459       nop.m         0
1460 (p15) fms.s1        FR_n_XS2L      = FR_n_XS, FR_n_XS, FR_n_XS2 // xs^2 Low part
1461       nop.i         0
1462 };;
1463
1464 { .mfi
1465       ld8           GR_l_Log_Table = [GR_l_Log_Table]
1466 (p15) fma.s1        FR_n_A7        = FR_n_A8,  FR_n_XS2, FR_n_A7 // poly tail
1467       nop.i 0
1468 }
1469 { .mfi
1470       ldfe          FR_l_h_3       = [GR_l_Index3],12
1471 (p15) fma.s1        FR_n_XS4       = FR_n_XS2, FR_n_XS2, f0 // xs^4 = xs^2*xs^2
1472       nop.i 0
1473 };;
1474
1475 { .mfi
1476       ldfs          FR_l_H_3       = [GR_l_Log_Table1], 0
1477       fma.s1        FR_l_Y2        = FR_l_Y1, FR_l_E3, FR_l_Y0 // y2 = y+y1*e3
1478       nop.i         0
1479 }
1480 { .mfi
1481       ldfs          FR_l_G_3       = [GR_l_Index3], 0
1482       fnma.s1       FR_l_Z         = FR_l_AbsX,FR_l_Q0,f1 // r = a-b*q
1483       nop.i         0
1484 };;
1485
1486 { .mfi
1487       nop.m         0
1488       fmpy.s1       FR_l_G         = FR_l_G_1, FR_l_G_2 // G = G1 * G_2
1489       nop.i         0
1490 }
1491 { .mfi
1492       nop.m         0
1493       fadd.s1       FR_l_H         = FR_l_H_1, FR_l_H_2 // H = H_1 + H_2
1494       nop.i         0
1495 };;
1496
1497 { .mfi
1498       ldfe          FR_l_log2_hi   = [GR_l_Log_Table],16 //  load log2_hi part
1499       fadd.s1       FR_l_h         = FR_l_h_1, FR_l_h_2  //  h = h_1 + h_2
1500       nop.i         0
1501 }
1502 { .mfi
1503       nop.m         0
1504       fcvt.xf       FR_l_float_N   = FR_l_float_N // int(N)
1505       nop.i         0
1506 };;
1507
1508 { .mfi
1509       ldfe          FR_l_log2_lo   = [GR_l_Log_Table],16 //  Load log2_lo part
1510       fma.s1        FR_l_CXL       = FR_l_CXL, f1, FR_l_CL
1511       nop.i 0
1512 }
1513 { .mfi
1514       nop.m         0
1515 (p15) fma.s1        FR_n_TT        = FR_n_A2H, FR_n_XS2L, FR_n_TT // T=A2H*x2L+T
1516       nop.i         0
1517 };;
1518
1519 { .mfi
1520       ldfe          FR_l_Q_6       = [GR_l_Log_Table],16
1521 (p15) fma.s1        FR_n_A3        = FR_n_A4,  FR_n_XS2, FR_n_A3 // poly tail
1522       nop.i         0
1523 }
1524 { .mfi
1525       nop.m         0
1526 (p15) fma.s1        FR_n_A5        = FR_n_A6,  FR_n_XS2, FR_n_A5 // poly tail
1527       nop.i 0
1528 };;
1529
1530 { .mfi
1531       ldfe          FR_l_Q_5       = [GR_l_Log_Table],16
1532 (p15) fabs          FR_n_XS        = FR_n_XS // abs(xs)
1533       nop.i         0
1534 }
1535 { .mfi
1536       nop.m         0
1537       fma.s1        FR_l_Z         = FR_l_Z,FR_l_Y2,FR_l_Q0 // x_hi = q+r*y2
1538       nop.i         0
1539 };;
1540
1541 { .mfi
1542       ldfe          FR_l_Q_4       = [GR_l_Log_Table],16
1543 (p15) fma.s1        FR_n_A7        = FR_n_A9,  FR_n_XS4, FR_n_A7 // poly tail
1544       nop.i         0
1545 }
1546 { .mfi
1547       nop.m         0
1548 (p15) fma.s1        FR_n_XS7       = FR_n_XS4, FR_n_XS2, f0 // = x^4*x^2
1549       nop.i         0
1550 };;
1551
1552 { .mfi
1553       ldfe          FR_l_Q_3       = [GR_l_Log_Table],16
1554       fneg          FR_n_NegOne    = f1 // -1.0
1555       nop.i         0
1556 }
1557 { .mfi
1558       nop.m         0
1559 (p15) fma.s1        FR_n_XS8       = FR_n_XS4, FR_n_XS4, f0 // xs^8 = xs^4*xs^4
1560       nop.i         0
1561 };;
1562
1563 { .mfi
1564       ldfe          FR_l_Q_2       = [GR_l_Log_Table],16
1565       fadd.s1       FR_l_h         = FR_l_h, FR_l_h_3 //  h = h_1 + h_2 + h_3
1566       nop.i         0
1567 }
1568 { .mfi
1569       nop.m         0
1570 (p15) fma.s1        FR_n_TH        = FR_n_A2H, FR_n_XS2, FR_n_TT // A2H*xs2+T
1571       nop.i         0
1572 };;
1573
1574 { .mfi
1575       ldfe          FR_l_Q_1       = [GR_l_Log_Table],16
1576       fmpy.s1       FR_l_G         = FR_l_G, FR_l_G_3 // G = G_1 * G_2 * G_3
1577       nop.i         0
1578 }
1579 { .mfi
1580       nop.m         0
1581       fadd.s1       FR_l_H         = FR_l_H, FR_l_H_3 // H = H_1 + H_2 + H_3
1582       nop.i         0
1583 };;
1584
1585 { .mfi
1586       nop.m         0
1587       fma.s1        FR_l_Z2        = FR_l_Z, FR_l_Z, f0 // Z^2
1588       nop.i         0
1589 }
1590 { .mfi
1591       nop.m         0
1592 (p15) fma.s1        FR_n_A3        = FR_n_A5,  FR_n_XS4, FR_n_A3 // poly tail
1593       nop.i         0
1594 };;
1595
1596 { .mfi
1597       nop.m         0
1598 (p14) fcmp.gt.unc.s1 p7,p0         = FR_l_AbsX, FR_c_PosOverflow //X > 1755.5483
1599               // (overflow domain, result cannot be represented by normal value)
1600       nop.i         0
1601 }
1602 { .mfi
1603       nop.m         0
1604 (p15) fma.s1        FR_n_XS7       = FR_n_XS7, FR_n_XS,  f0 // x^7 construction
1605       nop.i         0
1606 };;
1607
1608 { .mfi
1609       nop.m         0
1610 (p15) fms.s1        FR_n_TL        = FR_n_A2H, FR_n_XS2, FR_n_TH // A2H*xs2+TH
1611       nop.i         0
1612 }
1613 { .mfi
1614       nop.m         0
1615 (p15) fma.s1        FR_n_PolyH     = FR_n_TH, f1, FR_n_A1H // PolyH=TH+A1H
1616       nop.i         0
1617 };;
1618
1619 { .mfi
1620       nop.m         0
1621       fmpy.s1       FR_l_GS_hi     = FR_l_G, FR_l_S // GS_hi = G*S
1622       nop.i         0
1623 }
1624 { .mfb
1625       nop.m         0
1626       fms.s1        FR_l_r         = FR_l_G, FR_l_S, f1 // r = G*S -1
1627 (p7)  br.cond.spnt  tgammal_overflow // Overflow path for arg > 1755.5483 //////
1628 };;
1629
1630 { .mfi
1631       nop.m         0
1632       fma.s1        FR_l_B14       = FR_l_B16, FR_l_Z2, FR_l_B14// bernulli tail
1633       nop.i         0
1634 }
1635 { .mfi
1636       nop.m         0
1637       fma.s1        FR_l_Z4        = FR_l_Z2, FR_l_Z2, f0 // Z^4 = Z^2*Z^2
1638       nop.i         0
1639 };;
1640
1641 { .mfi
1642       nop.m         0
1643       fma.s1        FR_l_B2        = FR_l_B4, FR_l_Z2, FR_l_B2 // bernulli tail
1644       nop.i         0
1645 }
1646 { .mfi
1647       nop.m         0
1648       fma.s1        FR_l_B6        = FR_l_B8, FR_l_Z2, FR_l_B6 // bernulli tail
1649       nop.i         0
1650 };;
1651
1652 { .mfi
1653       nop.m         0
1654       fma.s1        FR_l_B10       = FR_l_B12, FR_l_Z2, FR_l_B10// bernulli tail
1655       nop.i         0
1656 }
1657 { .mfi
1658       nop.m         0
1659 (p15) fma.s1        FR_n_Tail      = FR_n_A7,  FR_n_XS8, FR_n_A3 // poly tail
1660       nop.i         0
1661 };;
1662
1663 { .mfi
1664       nop.m         0
1665 (p15) fma.s1        FR_n_TL        = FR_n_TL, f1, FR_n_TT // TL = TL+T
1666       nop.i         0
1667 }
1668 { .mfi
1669       nop.m         0
1670 (p15) fms.s1        FR_n_PolyL     = FR_n_A1H, f1, FR_n_PolyH // polyH+A1H
1671       nop.i         0
1672 };;
1673
1674 { .mfi
1675       nop.m         0
1676       fma.s1        FR_l_poly_lo   = FR_l_r, FR_l_Q_6, FR_l_Q_5 // Q_5+r*Q_6
1677       nop.i         0
1678 }
1679 { .mfi
1680       nop.m         0
1681       fsub.s1       FR_l_r_cor     = FR_l_GS_hi, f1 //     r_cor = GS_hi -1
1682       nop.i         0
1683 };;
1684
1685 { .mfi
1686       nop.m         0
1687       fms.s1        FR_l_GS_lo     = FR_l_G, FR_l_S, FR_l_GS_hi // G*S-GS_hi
1688       nop.i         0
1689 }
1690 { .mfi
1691       nop.m         0
1692       fma.s1        FR_l_poly      = FR_l_r, FR_l_Q_2, FR_l_Q_1 //poly=r*Q2+Q1
1693       nop.i         0
1694 };;
1695
1696 { .mfi
1697       nop.m         0
1698       fmpy.s1       FR_l_rsq       = FR_l_r, FR_l_r // rsq = r * r
1699       nop.i         0
1700 }
1701 { .mfi
1702       nop.m         0
1703       fma.s1        FR_l_G         = FR_l_float_N, FR_l_log2_hi, FR_l_H // Tbl =
1704                                                         // float_N*log2_hi + H
1705       nop.i         0
1706 };;
1707
1708 { .mfi
1709       nop.m 0
1710       fma.s1        FR_l_Y_lo      = FR_l_float_N, FR_l_log2_lo, FR_l_h // Y_lo=
1711                                                        // float_N*log2_lo + h
1712       nop.i 0
1713 }
1714 { .mfi
1715       nop.m 0
1716       fma.s1        FR_l_B14       = FR_l_B18, FR_l_Z4, FR_l_B14 //bernulli tail
1717       nop.i 0
1718 };;
1719
1720 { .mfi
1721       nop.m 0
1722       fma.s1        FR_l_B2        = FR_l_B6, FR_l_Z4, FR_l_B2 //bernulli tail
1723       nop.i 0
1724 }
1725 { .mfi
1726       nop.m 0
1727       fma.s1        FR_l_Z8        = FR_l_Z4, FR_l_Z4, f0 //bernulli tail
1728       nop.i 0
1729 };;
1730
1731 { .mfi
1732       nop.m         0
1733       fma.s1        FR_l_poly_lo   = FR_l_r, FR_l_poly_lo, FR_l_Q_4 // poly_lo =
1734                                                             // Q_4 + r * poly_lo
1735       nop.i         0
1736 }
1737 { .mfi
1738       nop.m         0
1739       fsub.s1       FR_l_r_cor     = FR_l_r_cor, FR_l_r // r_cor = r_cor - r
1740       nop.i         0
1741 };;
1742
1743 { .mfi
1744       nop.m         0
1745 (p15) fma.s1        FR_n_PolyL     = FR_n_PolyL, f1, FR_n_TH // polyL+TH
1746       nop.i         0
1747 }
1748 { .mfi
1749       nop.m         0
1750 (p15) fma.s1        FR_n_TT        = FR_n_TL, f1, FR_n_A1L // TL+A1L
1751       nop.i         0
1752 };;
1753
1754 { .mfi
1755       nop.m         0
1756       fadd.s1       FR_l_logl_YHi  = FR_l_G, FR_l_r // Y_hi = Tbl + r
1757       nop.i         0
1758 };;
1759
1760 { .mfi
1761       nop.m         0
1762       fma.s1        FR_l_B10       = FR_l_B14, FR_l_Z4, FR_l_B10 //bernulli tail
1763       nop.i         0
1764 };;
1765
1766 { .mfi
1767       nop.m         0
1768       fma.s1        FR_l_poly_lo   = FR_l_r, FR_l_poly_lo, FR_l_Q_3 // poly_lo =
1769                                                           // Q_3 + r * poly_lo
1770       nop.i         0
1771 }
1772 { .mfi
1773       nop.m         0
1774       fadd.s1       FR_l_r_cor     = FR_l_r_cor, FR_l_GS_lo // r_cor=r_cor+GS_lo
1775       nop.i         0
1776 };;
1777
1778 { .mfi
1779       nop.m         0
1780 (p15) fma.s1        FR_n_PolyL     = FR_n_PolyL, f1, FR_n_TT // polyL+TT
1781       nop.i         0
1782 };;
1783
1784 { .mfi
1785       nop.m         0
1786       fsub.s1       FR_l_Y_lo_res  = FR_l_G, FR_l_logl_YHi // Y_lo = Tbl - Y_hi
1787       nop.i         0
1788 }
1789 { .mfi
1790       nop.m         0
1791       fma.s1        FR_l_XYH       = FR_l_logl_YHi, FR_l_AbsX_m_Half, f0 // XYH=
1792                                           // YHi*|x-0.5|
1793       nop.i         0
1794 };;
1795
1796 { .mfi
1797       nop.m         0
1798       fma.s1        FR_l_SS        = FR_l_B10, FR_l_Z8, FR_l_B2 // bernulli tail
1799       nop.i         0
1800 };;
1801
1802 { .mfi
1803       nop.m         0
1804       fadd.s1       FR_l_r_cor     = FR_l_r_cor, FR_l_Y_lo // r_cor = r_cor+Y_lo
1805       nop.i         0
1806 }
1807 { .mfi
1808       nop.m         0
1809       fma.s1        FR_l_poly      = FR_l_rsq, FR_l_poly_lo, FR_l_poly //poly=
1810                                                             // r^2*polyLo+poly
1811       nop.i         0
1812 };;
1813
1814 { .mfi
1815       nop.m         0
1816 (p15) fma.s1        FR_n_TT        = FR_n_PolyL, FR_n_XS2, f0 // T=polyL*xs^2
1817       nop.i         0
1818 };;
1819
1820 { .mfi
1821       nop.m         0
1822       fadd.s1       FR_l_Y_lo      = FR_l_Y_lo_res, FR_l_r // Y_lo =  Y_lo + r
1823       nop.i         0
1824 }
1825 { .mfi
1826       nop.m         0
1827       fms.s1        FR_l_XYL       = FR_l_logl_YHi, FR_l_AbsX_m_Half, FR_l_XYH
1828                                                       // XYL = YHi*|x-0.5|-XYH
1829       nop.i         0
1830 };;
1831
1832 { .mfi
1833       nop.m         0
1834       fma.s1        FR_l_SSCXH     = FR_l_SS, FR_l_Z, FR_l_CXH // SS*Z+CXH
1835       nop.i         0
1836 }
1837 { .mfi
1838       mov           GR_e_exp_2tom51= 0xffff-51 // 2^-51
1839 (p15) fma.s1        FR_l_SignedXYH = FR_l_XYH, FR_n_NegOne, f0 // XYH = -XYH
1840                                                             // for negatives
1841       nop.i         0
1842 };;
1843
1844 { .mlx
1845       nop.m         0
1846       movl          GR_e_rshf_2to51  = 0x4718000000000000   // 1.10000 2^(63+51)
1847 }
1848 { .mlx
1849       nop.m         0
1850       movl          GR_e_sig_inv_ln2 = 0xb8aa3b295c17f0bc //significand of 1/ln2
1851 };;
1852
1853 { .mfi
1854       nop.m         0
1855       fma.s1        FR_l_poly      = FR_l_rsq, FR_l_poly, FR_l_r_cor // poly =
1856                                                         // rsq * poly + r_cor
1857       nop.i         0
1858 };;
1859
1860 { .mfi
1861       addl          GR_e_ad_Arg    = @ltoff(Constants_Tgammal_exp_64_Arg#),gp
1862 (p15) fma.s1        FR_n_TT        = FR_n_PolyH, FR_n_XS2L, FR_n_TT
1863       mov           GR_e_exp_mask  = 0x1FFFF          // Form exponent mask
1864 }
1865 { .mlx
1866       nop.m         0
1867       movl          GR_e_rshf      = 0x43e8000000000000  // 1.10000 2^63 rshift
1868 };;
1869
1870
1871 { .mmi
1872       setf.sig      FR_e_INV_LN2_2TO63 = GR_e_sig_inv_ln2 // form 1/ln2 * 2^63
1873       setf.d        FR_e_RSHF_2TO51    = GR_e_rshf_2to51 //  1.1000 * 2^(63+51)
1874       nop.i         0
1875 };;
1876
1877 { .mfi
1878       nop.m         0
1879       fms.s1        FR_l_SSCXL     = FR_l_CXH, f1, FR_l_SSCXH // CXH+SS*CXH
1880       nop.i         0
1881 }
1882 { .mfi
1883       nop.m         0
1884       fma.s1        FR_e_expl_Input_AbsX = FR_l_XYH, f1, FR_l_SSCXH // HI EXP
1885       nop.i         0
1886 };;
1887
1888 .pred.rel "mutex",p14,p15
1889 { .mfi
1890       nop.m         0
1891 (p14) fma.s1        FR_e_expl_Input_X = FR_l_XYH, f1, FR_l_SSCXH // HI EXP
1892       mov           GR_e_exp_bias     = 0x0FFFF  // Set exponent bias
1893 }
1894 { .mfi
1895       ld8           GR_e_ad_Arg       = [GR_e_ad_Arg] // Point to Arg table
1896 (p15) fms.s1        FR_e_expl_Input_X = FR_l_SignedXYH, f1, FR_l_SSCXH // HI EXP
1897       nop.i         0
1898 };;
1899
1900 { .mfi
1901       nop.m         0
1902       fadd.s1       FR_l_logl_YLo  = FR_l_Y_lo, FR_l_poly // YLo = YLo+poly
1903       nop.i         0
1904 };;
1905
1906 { .mfi
1907       setf.exp      FR_e_2TOM51    = GR_e_exp_2tom51 //2^-51 for scaling float_N
1908 (p15) fma.s1        FR_n_TH        = FR_n_PolyH, FR_n_XS2, FR_n_TT // TH=
1909                                                            // polyH*xs^2+T
1910       nop.i         0
1911 }
1912 { .mib
1913       setf.d        FR_e_RSHF     = GR_e_rshf // Right shift const 1.1000*2^63
1914       nop.i 0
1915       nop.b 0
1916 };;
1917
1918 { .mfi
1919       add           GR_e_ad_A      = 0x20, GR_e_ad_Arg // Point to A table
1920       nop.f         0
1921       add           GR_e_ad_T1     = 0x50, GR_e_ad_Arg // Point to T1 table
1922 }
1923 { .mfi
1924       add           GR_e_ad_T2     = 0x150, GR_e_ad_Arg // Point to T2 table
1925       nop.f         0
1926       nop.i         0
1927 };;
1928
1929 { .mfi
1930       nop.m         0
1931       fma.s1        FR_l_SSCXL     =   FR_l_SS, FR_l_Z,  FR_l_SSCXL
1932       nop.i         0
1933 }
1934 { .mfi
1935       nop.m         0
1936       fms.s1        FR_e_expl_Input_Y = FR_l_XYH, f1, FR_e_expl_Input_AbsX
1937       nop.i         0
1938 };;
1939
1940 { .mfi
1941       ldfe          FR_e_L_hi      = [GR_e_ad_Arg],16 // Get L_hi
1942       nop.f         0
1943       nop.i         0
1944 };;
1945
1946 { .mfi
1947       nop.m         0
1948       fma.s1        FR_l_XYL       = FR_l_logl_YLo, FR_l_AbsX_m_Half, FR_l_XYL
1949                                                      // XYL = YLo*|x-0.5|+XYL
1950       nop.i         0
1951 };;
1952
1953 { .mfi
1954       ldfe          FR_e_L_lo      = [GR_e_ad_Arg],16     // Get L_lo
1955 (p15) fms.s1        FR_n_TL        = FR_n_PolyH, FR_n_XS2, FR_n_TH // TL =
1956                                                           // = polyH*xs^2-TH
1957       add           GR_e_ad_W1     = 0x100, GR_e_ad_T2   // Point to W1 table
1958 }
1959 { .mfi
1960       nop.m         0
1961 (p15) fma.s1        FR_n_Poly1H    = FR_n_TH, f1, f1 // poly1H = TH+1
1962       add           GR_e_ad_W2     = 0x300, GR_e_ad_T2 // Point to W2 table
1963 };;
1964
1965 { .mmi
1966       getf.exp      GR_e_signexp_x = FR_e_expl_Input_X // Extract sign and exp
1967       ldfe          FR_e_A3        = [GR_e_ad_A],16     // Get A3
1968       nop.i         0
1969 };;
1970
1971 { .mfi
1972       nop.m         0
1973       fma.s1        FR_l_SSCXL     = FR_l_SSCXL, f1, FR_l_CXL
1974       nop.i         0
1975 }
1976 { .mfi
1977       nop.m         0
1978       fma.s1        FR_e_expl_Input_Y = FR_e_expl_Input_Y, f1, FR_l_SSCXH
1979       nop.i         0
1980 };;
1981
1982 { .mfi
1983       nop.m         0
1984       fma.s1  FR_e_N_signif=FR_e_expl_Input_X,FR_e_INV_LN2_2TO63,FR_e_RSHF_2TO51
1985       and           GR_e_exp_x     = GR_e_signexp_x, GR_e_exp_mask
1986 };;
1987
1988 { .mmi
1989       sub           GR_e_exp_x     = GR_e_exp_x, GR_e_exp_bias // Get exponent
1990       ldfe          FR_e_A2        = [GR_e_ad_A],16     // Get A2 for main path
1991       nop.i         0
1992 };;
1993
1994 { .mfi
1995       nop.m         0
1996 (p15) fma.s1        FR_n_PolyH     =    FR_n_Poly1H, FR_n_XS, f0//sin(Pi*x) poly
1997       nop.i         0
1998 }
1999 { .mfi
2000       nop.m         0
2001 (p15) fms.s1        FR_n_Poly1L    =    f1, f1, FR_n_Poly1H//sin(Pi*x) poly
2002       nop.i         0
2003 };;
2004
2005 { .mfi
2006       nop.m         0
2007 (p15) fma.s1        FR_n_TL        =    FR_n_TL, f1, FR_n_TT//sin(Pi*x) poly
2008       nop.i         0
2009 };;
2010
2011 { .mfi
2012       nop.m         0
2013       fma.s1        FR_l_Temp      =   FR_l_XYL, f1, FR_l_SSCXL // XYL+SS*CXL
2014       nop.i         0
2015 }
2016 { .mfi
2017       nop.m         0
2018 (p15) fma.s1        FR_e_expl_Input_Y = FR_e_expl_Input_Y, FR_n_NegOne, f0
2019                      // Negate lo part of exp argument for negative input values
2020       nop.i         0
2021 };;
2022
2023 { .mfi
2024       ldfe          FR_e_A1        = [GR_e_ad_A],16   // Get A1
2025       nop.f         0
2026       nop.i         0
2027 }
2028 { .mfi
2029       nop.m 0
2030       fms.s1        FR_e_float_N   = FR_e_N_signif, FR_e_2TOM51, FR_e_RSHF
2031                                            // Get float N = signd*2^51-RSHIFTER
2032       nop.i 0
2033 };;
2034
2035 { .mfi
2036       nop.m         0
2037 (p15) fma.s1        FR_n_Poly1L    = FR_n_Poly1L, f1, FR_n_TH //sin(Pi*x) poly
2038       nop.i         0
2039 }
2040 { .mfi
2041       nop.m         0
2042 (p15) fms.s1        FR_n_PolyL     = FR_n_Poly1H, FR_n_XS, FR_n_PolyH//sin(Pi*x)
2043       nop.i         0
2044 };;
2045
2046 { .mfi
2047       getf.sig      GR_e_N_fix     = FR_e_N_signif // Get N from significand
2048       nop.f         0
2049       nop.i         0
2050 };;
2051
2052 .pred.rel "mutex",p14,p15
2053 { .mfi
2054       nop.m 0
2055 (p14) fma.s1        FR_e_expl_Input_Y = FR_e_expl_Input_Y, f1, FR_l_Temp
2056       nop.i         0
2057 }
2058 { .mfi
2059       nop.m 0
2060 (p15) fms.s1        FR_e_expl_Input_Y = FR_e_expl_Input_Y, f1, FR_l_Temp
2061       // arguments for exp computation
2062       nop.i         0
2063 };;
2064
2065 { .mfi
2066       nop.m         0
2067       fnma.s1       FR_e_r         = FR_e_L_hi, FR_e_float_N, FR_e_expl_Input_X
2068                                                    // r = -L_hi * float_N + x
2069       extr.u        GR_e_M1        = GR_e_N_fix, 6, 6   // Extract index M_1
2070 };;
2071
2072 { .mfi
2073       nop.m         0
2074 (p15) fma.s1        FR_n_Poly1L    =   FR_n_Poly1L, f1, FR_n_TL //sin(Pi*x) poly
2075       nop.i         0
2076 };;
2077
2078
2079 { .mmf
2080       nop.m         0
2081       nop.m         0
2082       fma.s1        FR_e_r         = FR_e_r, f1, FR_e_expl_Input_Y
2083                                                  // r =  r + FR_e_expl_Input_Y
2084 };;
2085
2086 { .mmi
2087       shladd        GR_e_ad_W1     = GR_e_M1,3,GR_e_ad_W1 // Point to W1
2088       shladd        GR_e_ad_T1     = GR_e_M1,2,GR_e_ad_T1 // Point to T1
2089       extr.u        GR_e_M2        = GR_e_N_fix, 0, 6      // Extract index M_2
2090 };;
2091
2092
2093 { .mfi
2094       ldfs          FR_e_T1        = [GR_e_ad_T1],0         // Get T1
2095       nop.f         0
2096       extr          GR_e_K         = GR_e_N_fix, 12, 32 //Extract limit range K
2097 }
2098 { .mfi
2099       shladd        GR_e_ad_T2     = GR_e_M2,2,GR_e_ad_T2 // Point to T2
2100 (p15) fma.s1        FR_n_PolyL     = FR_n_Poly1L, FR_n_XS, FR_n_PolyL
2101                                                               //sin(Pi*x) poly
2102       shladd        GR_e_ad_W2     = GR_e_M2,3,GR_e_ad_W2 // Point to W2
2103 };;
2104
2105 { .mfi
2106       ldfs          FR_e_T2        = [GR_e_ad_T2],0         // Get T2
2107       nop.f         0
2108       add           GR_e_exp_2_k   = GR_e_exp_bias, GR_e_K // exp of 2^k
2109 }
2110 { .mfi
2111       ldfd          FR_e_W1        = [GR_e_ad_W1],0         // Get W1
2112       nop.f         0
2113       sub           GR_e_exp_2_mk  = GR_e_exp_bias, GR_e_K // exp of 2^-k
2114 };;
2115
2116 { .mmi
2117       ldfd          FR_e_W2        = [GR_e_ad_W2],0         // Get W2
2118       nop.m 0
2119       nop.i 0
2120 };;
2121
2122 { .mmf
2123       setf.exp      FR_e_scale     = GR_e_exp_2_k     // Set scale = 2^k
2124       setf.exp      FR_e_2_mk      = GR_e_exp_2_mk     // Form 2^-k
2125       fnma.s1       FR_e_r         = FR_e_L_lo, FR_e_float_N, FR_e_r
2126                                                // r = -L_lo * float_N + r
2127 };;
2128
2129 { .mfi
2130       nop.m         0
2131 (p15) fma.s1        FR_n_PolyL     = FR_n_Tail, FR_n_XS7, FR_n_PolyL
2132                                                                //sin(Pi*x) poly
2133       nop.i         0
2134 };;
2135
2136 { .mfi
2137       nop.m 0
2138       fma.s1        FR_e_poly      = FR_e_r, FR_e_A3, FR_e_A2 // poly=r*A3+A2
2139       nop.i 0
2140 }
2141 { .mfi
2142       nop.m 0
2143       fmpy.s1       FR_e_rsq       = FR_e_r, FR_e_r // rsq = r * r
2144       nop.i 0
2145 };;
2146
2147 { .mfi
2148       nop.m 0
2149       fmpy.s1       FR_e_T         = FR_e_T1, FR_e_T2         // T = T1 * T2
2150       nop.i 0
2151 }
2152 { .mfi
2153       nop.m 0
2154       fadd.s1       FR_e_W1_p1     = FR_e_W1, f1        // W1_p1 = W1 + 1.0
2155       nop.i 0
2156 };;
2157
2158 { .mfi
2159       nop.m 0
2160 (p15) fma.s1        FR_n_TT        = FR_n_PolyL, FR_l_AbsX, f0 //sin(Pi*x) poly
2161       nop.i 0
2162 };;
2163
2164 { .mfi
2165       nop.m         0
2166       fma.s1        FR_e_poly      = FR_e_r, FR_e_poly, FR_e_A1
2167                                                  // poly = r * poly + A1
2168       nop.i 0
2169 };;
2170
2171 { .mfi
2172       nop.m         0
2173       fma.s1        FR_e_T_scale   = FR_e_T, FR_e_scale, f0 // T_scale=T*scale
2174       nop.i         0
2175 }
2176 { .mfi
2177       nop.m         0
2178       fma.s1        FR_e_W         = FR_e_W2, FR_e_W1_p1, FR_e_W1
2179                                                      // W = W2 * (W1+1.0) + W1
2180       nop.i         0
2181 };;
2182
2183 { .mfi
2184       nop.m         0
2185 (p15) fma.s1        FR_n_SinxH     =    FR_n_PolyH, FR_l_AbsX, FR_n_TT
2186                                                               // sin(Pi*x) poly
2187       nop.i         0
2188 };;
2189
2190 { .mfi
2191       nop.m         0
2192       mov           FR_e_Y_hi      = FR_e_T  // Assume Y_hi = T
2193       nop.i         0
2194 };;
2195
2196 { .mfi
2197       nop.m 0
2198       fma.s1        FR_e_poly      = FR_e_rsq, FR_e_poly, FR_e_r
2199                                                      // poly = rsq * poly + r
2200       nop.i 0
2201 };;
2202
2203 { .mfi
2204       nop.m 0
2205       fma.s1        FR_e_Wp1_T_scale = FR_e_W, FR_e_T_scale, FR_e_T_scale
2206                                                               // (W+1)*T*scale
2207       nop.i 0
2208 }
2209 { .mfi
2210       nop.m 0
2211       fma.s1        FR_e_W_T_scale = FR_e_W, FR_e_T_scale, f0 // W*T*scale
2212       nop.i 0
2213 };;
2214
2215 { .mfi
2216       nop.m 0
2217 (p15) fms.s1        FR_n_SinxL     =   FR_n_PolyH, FR_l_AbsX, FR_n_SinxH
2218                                                              // Low part of sin
2219       nop.i 0
2220 };;
2221
2222 { .mfi
2223       nop.m         0
2224 (p15) frcpa.s1      FR_n_Y0, p0    = f1, FR_n_SinxH //  y = frcpa(b)
2225       nop.i         0
2226 };;
2227
2228 { .mfi
2229       nop.m         0
2230       fma.s1        FR_e_result_lo = FR_e_Wp1_T_scale, FR_e_poly, FR_e_W_T_scale
2231                                                        // Low part of exp result
2232       nop.i         0
2233 };;
2234
2235 { .mfi
2236       nop.m         0
2237 (p15) fma.s1        FR_n_SinxL     = FR_n_SinxL, f1, FR_n_TT // sin low result
2238       nop.i         0
2239 };;
2240
2241 { .mfi
2242       nop.m         0
2243 (p15) fma.s1        FR_n_Q0        = f1,FR_n_Y0,f0 // q = y
2244       nop.i         0
2245 }
2246 { .mfi
2247       nop.m         0
2248 (p15) fnma.s1       FR_n_E0        = FR_n_Y0, FR_n_SinxH, f1 // e = 1-b*y
2249       nop.i         0
2250 };;
2251
2252
2253 { .mfb
2254       nop.m         0
2255 (p14) fma.s0        f8             = FR_e_Y_hi, FR_e_scale, FR_e_result_lo
2256 (p14) br.ret.spnt   b0 // Exit for positive Stirling path //////////////////////
2257 };;
2258
2259 { .mfi
2260       nop.m 0
2261       fma.s1        FR_e_expl_Output_X = FR_e_Y_hi, FR_e_scale, f0 // exp result
2262       nop.i         0
2263 }
2264 { .mfi
2265       nop.m 0
2266       fma.s1        FR_e_expl_Output_Y = FR_e_result_lo, f1, f0// exp lo result
2267       nop.i         0
2268 };;
2269
2270 { .mfi
2271       nop.m         0
2272       fma.s1        FR_n_E2        = FR_n_E0,FR_n_E0,FR_n_E0 //  e2 = e+e^2
2273       nop.i         0
2274 }
2275 { .mfi
2276       nop.m         0
2277       fma.s1        FR_n_E1        = FR_n_E0,FR_n_E0,f0 //  e1 = e^2
2278       nop.i         0
2279 };;
2280
2281 { .mfi
2282       nop.m         0
2283       fma.s1        FR_n_Y1        = FR_n_Y0,FR_n_E2,FR_n_Y0 //  y1 = y+y*e2
2284       nop.i         0
2285 }
2286 { .mfi
2287       nop.m         0
2288       fma.s1        FR_n_E3        = FR_n_E1,FR_n_E1,FR_n_E0 //  e3 = e+e1^2
2289       nop.i         0
2290 };;
2291
2292 { .mfi
2293       nop.m         0
2294       fma.s1        FR_n_Y2        = FR_n_Y1,FR_n_E3,FR_n_Y0 //  y2 = y+y1*e3
2295       nop.i         0
2296 }
2297 { .mfi
2298       nop.m         0
2299       fnma.s1       FR_n_R0        = FR_n_SinxH,FR_n_Q0,f1 //  r = a-b*q
2300       nop.i         0
2301 };;
2302
2303 { .mfi
2304       nop.m         0
2305       fnma.s1       FR_n_E4        = FR_n_SinxH,FR_n_Y2,f1 //  e4 = 1-b*y2
2306       nop.i         0
2307 }
2308 { .mfi
2309       nop.m         0
2310       fma.s1        FR_n_RcpResH   = FR_n_R0,FR_n_Y2,FR_n_Q0 //  x = q+r*y2
2311       nop.i         0
2312 };;
2313
2314 { .mfi
2315       nop.m         0
2316       fma.s1        FR_n_Y3        = FR_n_Y2,FR_n_E4,FR_n_Y2 //  y3 = y2+y2*e4
2317       nop.i         0
2318 }
2319 { .mfi
2320       nop.m         0
2321       fnma.s1       FR_n_R1        = FR_n_SinxH,FR_n_RcpResH,f1 //  r1 = a-b*x
2322       nop.i         0
2323 };;
2324
2325 { .mfi
2326       nop.m         0
2327       fnma.s1       FR_n_R1        = FR_n_SinxL,FR_n_RcpResH,FR_n_R1
2328                                                           // r1 = r1 - b_lo*X
2329       nop.i         0
2330 };;
2331
2332 { .mfi
2333       nop.m         0
2334       fma.s1        FR_n_RcpResL   = FR_n_R1,FR_n_Y3,f0 //  x_lo = r1*y3
2335       nop.i         0
2336 }
2337 { .mfi
2338       nop.m         0
2339       fma.s1        FR_n_Temp      = FR_n_RcpResH, FR_e_expl_Output_Y, f0
2340                                               // Multiplying exp and sin result
2341       nop.i         0
2342 };;
2343
2344 { .mfi
2345       nop.m         0
2346       fma.s1        FR_n_Temp      = FR_n_RcpResL, FR_e_expl_Output_X, FR_n_Temp
2347                                               // Multiplying exp and sin result
2348       nop.i         0
2349 };;
2350
2351 { .mfi
2352       nop.m         0
2353       fma.s1        FR_n_ResH      = FR_n_RcpResH, FR_e_expl_Output_X, FR_n_Temp
2354                                               // Multiplying exp and sin result
2355       nop.i         0
2356 };;
2357
2358 { .mfi
2359       nop.m         0
2360       fms.s1        FR_n_ResL      = FR_n_RcpResH, FR_e_expl_Output_X, FR_n_ResH
2361                                               // Multiplying exp and sin result
2362       nop.i         0
2363 }
2364 { .mfi
2365       nop.m         0
2366 (p12) fma.s1        FR_n_ResH      = FR_n_ResH, FR_n_NegOne, f0 // Negate
2367       nop.i         0
2368 };;
2369
2370 { .mfi
2371       nop.m         0
2372       fma.s1        FR_n_ResL  = FR_n_ResL, f1, FR_n_Temp
2373                       // Multiplying exp and sin result - low result obtained
2374       nop.i         0
2375 };;
2376
2377 .pred.rel "mutex",p12,p13
2378 { .mfi
2379       nop.m         0
2380 (p13) fma.s0        f8             = FR_n_ResH, f1, FR_n_ResL // For odd
2381       nop.i         0
2382 }
2383 { .mfb
2384       nop.m         0
2385 (p12) fms.s0        f8             = FR_n_ResH, f1, FR_n_ResL // For even
2386       br.ret.sptk   b0 // Exit for negative Stirling path //////////////////////
2387 };;
2388
2389
2390 //////////// 1 <= |X| < 13 path ////////////////////////////////////////////////
2391 //------------------------------------------------------------------------------
2392 .align 64
2393 tgamma_lt_13:
2394 { .mfi
2395       getf.sig      GR_p_XN        = FR_p_IXN // Get significand
2396       fcvt.xf       FR_p_XN        = FR_p_IXN  // xn = [x]
2397       add           GR_r_sin_Table2= 0x40, GR_r_sin_Table // Shifted table addr.
2398 }
2399 { .mfi
2400       ldfpd         FR_p_0p5, FR_p_1p5 = [GR_c_Table], 16  // 0.5 & 1.5
2401       fms.s1        FR_p_AbsXM1    = FR_p_AbsX, f1, f1 // X-1
2402       add           GR_p_Table2    = 0xB0, GR_p_Table
2403 };;
2404
2405 { .mfi
2406       add           GR_r_sin_Table = -16, GR_r_sin_Table // For compensation
2407       fcvt.xf       FR_r_XNS       = FR_r_IXNS // Convert int repr to float
2408       shr.u         GR_p_X_Sgnd    = GR_p_X_Sgnd, 59 // Get only 5 bit of signd
2409 };;
2410
2411 { .mfi
2412       ldfpd         FR_r_A2H,FR_r_A2L = [GR_r_sin_Table], 16 // Load A2
2413       nop.f         0
2414       add           GR_p_Int       = -2, GR_p_XN // int = int - 2
2415 }
2416 { .mfi
2417       ldfe          FR_r_A6 = [GR_r_sin_Table2], 16
2418       nop.f         0
2419       cmp.gtu       p11, p12 = 0x2, GR_p_XN // p11: x < 2 (splitted intervals),
2420                                             // p12: x > 2 (base intervals)
2421 };;
2422
2423 { .mfi
2424       ldfpd         FR_r_A1H, FR_r_A1L = [GR_r_sin_Table], 16
2425       nop.f         0
2426       shr           GR_p_Int       = GR_p_Int, 1 // int/2
2427 }
2428 { .mfi
2429       ldfe          FR_r_A5        = [GR_r_sin_Table2], 16
2430       nop.f         0
2431 (p11) cmp.gtu.unc   p10, p11       = 0x1C, GR_p_X_Sgnd // sgnd(x) < 0.75
2432 };;
2433
2434 { .mfi
2435       ldfe          FR_r_A9        = [GR_r_sin_Table], 16
2436       nop.f         0
2437       shl           GR_p_Offset    = GR_p_Int, 4 // offset = int*16
2438 }
2439 { .mfi
2440       ldfe          FR_r_A4        = [GR_r_sin_Table2], 16
2441       nop.f         0
2442 (p10) cmp.gtu.unc   p9, p10        = 0x14, GR_p_X_Sgnd // sgnd(x) < 0.25
2443 };;
2444
2445
2446 { .mfi
2447       ldfe          FR_r_A8        = [GR_r_sin_Table], 16
2448       nop.f         0
2449 (p12) tbit.nz.unc   p13, p12       = GR_p_XN, 0x0 // p13: reccurent computations
2450                                       // X is at [3;4], [5;6], [7;8]... interval
2451 }
2452 { .mfi
2453       ldfe          FR_r_A3        = [GR_r_sin_Table2], 16
2454       nop.f         0
2455       shladd        GR_p_Offset    = GR_p_Int, 2, GR_p_Offset // +int*4
2456 };;
2457
2458 .pred.rel "mutex",p9,p11
2459 { .mfi
2460       add           GR_p_Offset    = GR_p_Int, GR_p_Offset
2461                                                     // +int, so offset = int*21
2462 (p9)  fms.s1        FR_p_XR        = FR_p_AbsX, f1, f1 // r = x-1
2463       nop.i         0
2464 }
2465 { .mfi
2466       ldfe          FR_r_A7        = [GR_r_sin_Table], 16
2467 (p11) fms.s1        FR_p_XR        = FR_p_2, f1, FR_p_AbsX
2468                                                     // r = 2-x for 1.75 < x < 2
2469       nop.i         0
2470 };;
2471
2472 .pred.rel "mutex",p9,p10
2473 .pred.rel "mutex",p10,p11
2474 .pred.rel "mutex",p9,p11
2475 { .mfi
2476 (p9)  add           GR_p_Offset    = 126, r0 // 1.0 < x < 1.25 table
2477 (p15) fcmp.eq.unc.s1 p7,p0         = FR_p_AbsX, FR_p_XN
2478                           // If arg is integer and negative - singularity branch
2479       nop.i         0
2480 }
2481 { .mfi
2482 (p10) add           GR_p_Offset    = 147, r0 // 1.25 < x < 1.75 table
2483       nop.f         0
2484 (p11) add           GR_p_Offset    = 168, r0 // 1.75 < x < 2.0 table
2485 };;
2486
2487 { .mmf
2488       shladd        GR_p_Table     = GR_p_Offset, 4, GR_p_Table
2489       shladd        GR_p_Table2    = GR_p_Offset, 4, GR_p_Table2
2490       fma.s1        FR_r_XS        = FR_r_AbsX , f1, FR_r_XNS // xs = x - [x]
2491 };;
2492
2493 { .mmb
2494       ldfpd         FR_p_A5H, FR_p_A5L = [GR_p_Table], 16
2495       ldfpd         FR_p_A2H, FR_p_A2L = [GR_p_Table2], 16
2496 (p7)  br.cond.spnt  tgammal_singularity // Singularity for integer /////////////
2497                                         // and negative argument ///////////////
2498 };;
2499
2500 { .mfi
2501       ldfpd         FR_p_A4H, FR_p_A4L = [GR_p_Table], 16
2502       fma.s1        FR_p_XN        = FR_p_XN, f1, FR_p_0p5 // xn = xn+0.5
2503       nop.i         0
2504 }
2505 { .mfi
2506       ldfpd         FR_p_A1H, FR_p_A1L = [GR_p_Table2], 16
2507 (p10) fms.s1        FR_p_XR        = FR_p_AbsX, f1, FR_p_1p5 // r = x - 1.5
2508       nop.i         0
2509 };;
2510
2511 { .mmi
2512       ldfpd         FR_p_A3H, FR_p_A3L = [GR_p_Table], 16
2513       ldfpd         FR_p_A0H, FR_p_A0L = [GR_p_Table2], 16
2514       nop.i         0
2515 };;
2516
2517 { .mmi
2518       ldfe         FR_p_A20        = [GR_p_Table], 16
2519       ldfe         FR_p_A12        = [GR_p_Table2], 16
2520       nop.i         0
2521 };;
2522
2523 { .mmf
2524       ldfe         FR_p_A19        = [GR_p_Table], 16
2525       ldfe         FR_p_A11        = [GR_p_Table2], 16
2526       fma.s1       FR_r_XS2        = FR_r_XS, FR_r_XS, f0 // xs2 = xs*xs
2527 };;
2528
2529 { .mmi
2530       ldfe          FR_p_A18       = [GR_p_Table], 16
2531       ldfe          FR_p_A10       = [GR_p_Table2], 16
2532       nop.i         0
2533 };;
2534
2535 .pred.rel "mutex",p12,p13
2536 { .mfi
2537       ldfe          FR_p_A17       = [GR_p_Table], 16
2538 (p12) fms.s1        FR_p_XR        = FR_p_AbsX, f1, FR_p_XN // r = x - xn
2539       nop.i         0
2540 }
2541 { .mfi
2542       ldfe          FR_p_A9        = [GR_p_Table2], 16
2543 (p13) fms.s1        FR_p_XR        = FR_p_AbsX, f1, FR_p_XN
2544       nop.i         0
2545 };;
2546
2547 { .mmi
2548       ldfe          FR_p_A16       = [GR_p_Table], 16
2549       ldfe          FR_p_A8        = [GR_p_Table2], 16
2550 (p9)  cmp.eq        p12, p0        = r0, r0 // clear p12
2551 };;
2552
2553 { .mmi
2554       ldfe          FR_p_A15       = [GR_p_Table], 16
2555       ldfe          FR_p_A7        = [GR_p_Table2], 16
2556 (p10) cmp.eq        p12, p0        = r0, r0 // clear p12
2557 };;
2558
2559 { .mfi
2560       ldfe          FR_p_A14       = [GR_p_Table], 16
2561       fma.s1        FR_r_TH        = FR_r_A2H, FR_r_XS2, f0 // sin for neg
2562 (p11) cmp.eq        p12, p0        = r0, r0 // clear p12
2563 }
2564 { .mfi
2565       ldfe          FR_p_A6        = [GR_p_Table2], 16
2566       fma.s1        FR_r_TL        = FR_r_A2L, FR_r_XS2, f0 // sin for neg
2567       nop.i         0
2568 };;
2569
2570 { .mfi
2571       ldfe          FR_p_A13       = [GR_p_Table], 16
2572       fms.s1        FR_r_XS2L      = FR_r_XS, FR_r_XS, FR_r_XS2 // x2Lo part
2573       nop.i         0
2574 };;
2575
2576 { .mfi
2577       nop.m         0
2578       fma.s1        FR_p_Temp5H    = FR_p_A5H, FR_p_XR, f0 // A5H*r
2579                                                            // 'Low poly'
2580       nop.i         0
2581 }
2582 { .mfi
2583       nop.m         0
2584       fma.s1        FR_p_XR2       = FR_p_XR, FR_p_XR, f0 // r^2 = r*r
2585       nop.i         0
2586 };;
2587
2588 { .mfi
2589       nop.m         0
2590       fabs          FR_r_XS        = FR_r_XS // abs(xs)
2591       nop.i         0
2592 }
2593 { .mfi
2594       nop.m         0
2595       fma.s1        FR_p_Temp2H    = FR_p_A2H, FR_p_XR, f0 // A2H*r
2596                                                            // 'High poly'
2597       nop.i         0
2598 };;
2599
2600 { .mfi
2601       nop.m         0
2602       fms.s1        FR_r_TT        = FR_r_A2H, FR_r_XS2, FR_r_TH // sin for neg
2603       nop.i         0
2604 }
2605 { .mfi
2606       nop.m         0
2607       fma.s1        FR_r_ResH      = FR_r_TH, f1, FR_r_A1H // sin for neg
2608       nop.i         0
2609 };;
2610
2611 { .mfi
2612       nop.m         0
2613       fma.s1        FR_r_TL        = FR_r_A2H, FR_r_XS2L, FR_r_TL // sin for neg
2614       nop.i         0
2615 };;
2616
2617 { .mfi
2618       nop.m         0
2619       fms.s1        FR_p_Temp5L    = FR_p_A5H,FR_p_XR,FR_p_Temp5H //A5H*r delta
2620                                                                   // 'Low poly'
2621       nop.i         0
2622 }
2623 { .mfi
2624       nop.m         0
2625       fma.s1        FR_p_Poly5H    = FR_p_Temp5H, f1, FR_p_A4H // A5H*r+A4H
2626                                                                // 'Low poly'
2627       nop.i         0
2628 };;
2629
2630 { .mfi
2631       nop.m         0
2632       fms.s1        FR_p_Temp2L    = FR_p_A2H, FR_p_XR, FR_p_Temp2H//A2H*r delta
2633                                                                    //'High poly'
2634       nop.i         0
2635 }
2636 { .mfi
2637       nop.m         0
2638       fma.s1        FR_p_Poly2H    = FR_p_Temp2H, f1, FR_p_A1H // A2H*r+A1H
2639                                                                //'High poly'
2640       nop.i         0
2641 };;
2642
2643 { .mfi
2644       nop.m         0
2645       fma.s1        FR_p_XR3       = FR_p_XR2, FR_p_XR,  f0 // r^3 = r^2*r
2646       nop.i         0
2647 }
2648 { .mfi
2649       nop.m         0
2650       fms.s1        FR_p_XR2L      = FR_p_XR, FR_p_XR, FR_p_XR2 // r^2 delta
2651       nop.i         0
2652 };;
2653
2654 { .mfi
2655       nop.m         0
2656       fma.s1        FR_p_A18       = FR_p_A19, FR_p_XR, FR_p_A18 // Poly tail
2657       nop.i         0
2658 }
2659 { .mfi
2660       nop.m         0
2661       fma.s1        FR_p_A14       = FR_p_A15, FR_p_XR, FR_p_A14 // Poly tail
2662       nop.i         0
2663 };;
2664
2665 { .mfi
2666       nop.m         0
2667       fma.s1        FR_p_XR4       = FR_p_XR2, FR_p_XR2, f0 // r^4 = r^2*r^2
2668       nop.i         0
2669 };;
2670
2671 { .mfi
2672       nop.m         0
2673       fma.s1        FR_p_Temp5L    = FR_p_A5L, FR_p_XR, FR_p_Temp5L// Low part
2674                                                                    // of A5*r+A4
2675       nop.i         0
2676 }
2677 { .mfi
2678       nop.m         0
2679       fms.s1        FR_p_Poly5L    = FR_p_A4H, f1, FR_p_Poly5H // Low part
2680                                                                // of A5*r+A4
2681       nop.i         0
2682 };;
2683
2684 { .mfi
2685       nop.m         0
2686       fma.s1        FR_p_Temp4H    = FR_p_Poly5H, FR_p_XR, f0 // (A5H*r+A4H)*r
2687       nop.i         0
2688 }
2689 { .mfi
2690       nop.m         0
2691       fma.s1        FR_p_Temp2L    = FR_p_A2L, FR_p_XR, FR_p_Temp2L // A2*r low
2692       nop.i         0
2693 };;
2694
2695 { .mfi
2696       nop.m         0
2697       fms.s1        FR_p_Poly2L    = FR_p_A1H, f1, FR_p_Poly2H // High poly
2698       nop.i         0
2699 }
2700 { .mfi
2701       nop.m         0
2702       fma.s1        FR_p_Temp1H    = FR_p_Poly2H, FR_p_XR, f0 // High poly
2703       nop.i         0
2704 };;
2705
2706 { .mfi
2707       nop.m         0
2708       fms.s1        FR_p_XR3L      = FR_p_XR2, FR_p_XR, FR_p_XR3 // x^3 delta
2709       nop.i         0
2710 }
2711 { .mfi
2712       nop.m         0
2713       fma.s1        FR_p_A16       = FR_p_A17, FR_p_XR, FR_p_A16 // Poly tail
2714       nop.i         0
2715 };;
2716
2717 { .mfi
2718       nop.m         0
2719       fms.s1        FR_r_ResL      = FR_r_A1H, f1, FR_r_ResH // sin for neg
2720       nop.i         0
2721 }
2722 { .mfi
2723       nop.m         0
2724       fma.s1        FR_r_TL        = FR_r_TL, f1, FR_r_TT // sin for neg
2725       nop.i         0
2726 };;
2727
2728 { .mfi
2729       nop.m         0
2730       fma.s1        FR_p_Temp5L    = FR_p_Temp5L, f1, FR_p_A4L // Low poly
2731       nop.i         0
2732 }
2733 { .mfi
2734       nop.m         0
2735       fma.s1        FR_p_Poly5L    = FR_p_Poly5L, f1, FR_p_Temp5H // Low poly
2736       nop.i         0
2737 };;
2738
2739 { .mfi
2740       nop.m         0
2741       fms.s1        FR_p_Temp4L    = FR_p_Poly5H,FR_p_XR,FR_p_Temp4H //Low poly
2742       nop.i         0
2743 }
2744 { .mfi
2745       nop.m         0
2746       fma.s1        FR_p_Poly4H    = FR_p_Temp4H, f1, FR_p_A3H // Low poly
2747       nop.i         0
2748 };;
2749
2750 { .mfi
2751       nop.m         0
2752       fma.s1        FR_p_Temp2L    = FR_p_Temp2L, f1, FR_p_A1L // High poly
2753       nop.i         0
2754 }
2755 { .mfi
2756       nop.m         0
2757       fma.s1        FR_p_Poly2L    = FR_p_Poly2L, f1, FR_p_Temp2H // High poly
2758       nop.i         0
2759 };;
2760
2761 { .mfi
2762       nop.m         0
2763       fms.s1        FR_p_Temp1L    = FR_p_Poly2H,FR_p_XR,FR_p_Temp1H //High poly
2764       nop.i         0
2765 }
2766 { .mfi
2767       nop.m         0
2768       fma.s1        FR_p_Poly1H    = FR_p_Temp1H, f1, FR_p_A0H // High poly
2769       nop.i         0
2770 };;
2771
2772 { .mfi
2773       nop.m         0
2774       fma.s1        FR_p_A12       = FR_p_A13, FR_p_XR, FR_p_A12 // Poly tail
2775       nop.i         0
2776 }
2777 { .mfi
2778       nop.m         0
2779       fma.s1        FR_p_XR3L      = FR_p_XR2L, FR_p_XR, FR_p_XR3L // x^3 low
2780       nop.i         0
2781 };;
2782
2783 { .mfi
2784       nop.m         0
2785       fma.s1        FR_p_Poly5L    = FR_p_Poly5L, f1, FR_p_Temp5L // Low poly
2786       nop.i         0
2787 }
2788 { .mfi
2789       nop.m         0
2790       fma.s1        FR_p_A10       = FR_p_A11, FR_p_XR, FR_p_A10 // Poly tail
2791       nop.i         0
2792 };;
2793
2794 { .mfi
2795       nop.m         0
2796       fms.s1        FR_p_Poly4L    = FR_p_A3H, f1, FR_p_Poly4H // Low poly
2797       nop.i         0
2798 }
2799 { .mfi
2800       nop.m         0
2801       fma.s1        FR_p_A6        = FR_p_A7, FR_p_XR, FR_p_A6 // Poly tail
2802       nop.i         0
2803 };;
2804
2805 { .mfi
2806       nop.m         0
2807       fma.s1        FR_p_A8        = FR_p_A9, FR_p_XR, FR_p_A8 // Poly tail
2808       nop.i         0
2809 }
2810 { .mfi
2811       nop.m         0
2812       fma.s1        FR_p_XR6       = FR_p_XR4, FR_p_XR2, f0 // Poly tail
2813       nop.i         0
2814 };;
2815
2816 { .mfi
2817       nop.m         0
2818       fma.s1        FR_p_Poly2L    = FR_p_Poly2L, f1, FR_p_Temp2L // High poly
2819       nop.i         0
2820 }
2821 { .mfi
2822       nop.m         0
2823       fms.s1        FR_p_Poly1L    = FR_p_A0H, f1, FR_p_Poly1H // High poly
2824       nop.i         0
2825 };;
2826
2827 { .mfi
2828       nop.m         0
2829       fma.s1        FR_r_ResL      = FR_r_ResL, f1, FR_r_TH // sin for neg
2830       nop.i         0
2831 }
2832 { .mfi
2833       nop.m         0
2834       fma.s1        FR_r_TT        = FR_r_TL, f1, FR_r_A1L // sin for neg
2835       nop.i         0
2836 };;
2837
2838 { .mfi
2839       nop.m         0
2840       fma.s1        FR_p_Temp4L    = FR_p_Poly5L,FR_p_XR,FR_p_Temp4L // Low poly
2841       nop.i         0
2842 }
2843 { .mfi
2844       nop.m         0
2845       fma.s1        FR_p_A18       = FR_p_A20, FR_p_XR2, FR_p_A18 // Poly tail
2846       nop.i         0
2847 };;
2848
2849 { .mfi
2850       nop.m         0
2851       fma.s1        FR_p_Poly4L    = FR_p_Poly4L, f1, FR_p_Temp4H // Low poly
2852       nop.i         0
2853 }
2854 { .mfi
2855       nop.m         0
2856       fma.s1        FR_p_A14       = FR_p_A16, FR_p_XR2, FR_p_A14 // Poly tail
2857       nop.i         0
2858 };;
2859
2860 { .mfi
2861       nop.m         0
2862       fma.s1        FR_p_A6        = FR_p_A8, FR_p_XR2, FR_p_A6 // Poly tail
2863       nop.i         0
2864 }
2865 { .mfi
2866       nop.m         0
2867       fma.s1        FR_p_A10       = FR_p_A12, FR_p_XR2, FR_p_A10 // Poly tail
2868       nop.i         0
2869 };;
2870
2871 { .mfi
2872       nop.m         0
2873       fma.s1        FR_p_Temp1L    = FR_p_Poly2L,FR_p_XR,FR_p_Temp1L //High poly
2874       nop.i         0
2875 }
2876 { .mfi
2877       nop.m         0
2878       fma.s1        FR_p_Poly1L    = FR_p_Poly1L, f1, FR_p_Temp1H // High poly
2879       nop.i         0
2880 };;
2881
2882 { .mfi
2883       nop.m         0
2884       fma.s1        FR_r_ResL      = FR_r_ResL, f1, FR_r_TT // sin for neg
2885       nop.i         0
2886 }
2887 { .mfi
2888       nop.m         0
2889       fma.s1        FR_r_TH        = FR_r_ResH, FR_r_XS2, f0 // sin for neg
2890       nop.i         0
2891 };;
2892
2893 { .mfi
2894       nop.m         0
2895       fma.s1        FR_p_Temp4L    = FR_p_Temp4L, f1, FR_p_A3L // Low poly
2896       nop.i         0
2897 }
2898 { .mfi
2899       nop.m         0
2900       fma.s1        FR_p_Poly3H    = FR_p_Poly4H, FR_p_XR3, f0 // Low poly
2901       nop.i         0
2902 };;
2903
2904 { .mfi
2905       nop.m         0
2906       fma.s1        FR_p_A14       = FR_p_A18, FR_p_XR4, FR_p_A14 // Poly tail
2907       nop.i         0
2908 }
2909 { .mfi
2910       nop.m         0
2911       fma.s1        FR_p_XR8       = FR_p_XR4, FR_p_XR4, f0 // Poly tail
2912       nop.i         0
2913 };;
2914
2915 { .mfi
2916       nop.m         0
2917       fma.s1        FR_r_TL        = FR_r_ResH, FR_r_XS2L, f0 // sin for neg
2918       nop.i         0
2919 };;
2920
2921 { .mfi
2922       nop.m         0
2923       fma.s1        FR_p_Temp1L    = FR_p_Temp1L, f1, FR_p_A0L // High poly
2924       nop.i         0
2925 }
2926 { .mfi
2927       nop.m         0
2928       fma.s1        FR_p_A6        = FR_p_A10, FR_p_XR4, FR_p_A6 // Poly tail
2929       nop.i         0
2930 };;
2931
2932 { .mfi
2933       nop.m         0
2934       fms.s1        FR_r_TT        = FR_r_ResH, FR_r_XS2, FR_r_TH // sin for neg
2935       nop.i         0
2936 }
2937 { .mfi
2938       nop.m         0
2939       fma.s1        FR_r_Res3H     = FR_r_TH, f1, f1 // sin for neg
2940       nop.i         0
2941 };;
2942
2943 { .mfi
2944       nop.m         0
2945       fma.s1        FR_p_Poly4L    = FR_p_Poly4L, f1, FR_p_Temp4L // Low poly
2946       nop.i         0
2947 }
2948 { .mfi
2949       nop.m         0
2950       fma.s1        FR_p_Poly3L    = FR_p_Poly4H, FR_p_XR3L, f0 // Low poly
2951       nop.i         0
2952 };;
2953
2954 { .mfi
2955       nop.m         0
2956       fma.s1        FR_p_Poly0H    = FR_p_Poly3H,f1,FR_p_Poly1H //Low & High add
2957       nop.i         0
2958 }
2959 { .mfi
2960       nop.m         0
2961       fma.s1        FR_r_A7        = FR_r_A8,  FR_r_XS2, FR_r_A7 // sin for neg
2962       nop.i         0
2963 };;
2964
2965 { .mfi
2966       nop.m         0
2967       fma.s1        FR_r_TL        = FR_r_ResL, FR_r_XS2, FR_r_TL // sin for neg
2968       nop.i         0
2969 }
2970 { .mfi
2971       nop.m         0
2972       fma.s1        FR_r_XS4       = FR_r_XS2, FR_r_XS2, f0 // sin for neg
2973       nop.i         0
2974 };;
2975
2976 { .mfi
2977       nop.m         0
2978       fma.s1        FR_p_Poly1L    = FR_p_Poly1L, f1, FR_p_Temp1L // High poly
2979       nop.i         0
2980 }
2981 { .mfi
2982       nop.m         0
2983       fma.s1        FR_p_PolyTail  = FR_p_A14, FR_p_XR8, FR_p_A6 // Poly tail
2984       nop.i         0
2985 };;
2986
2987 { .mfi
2988       nop.m         0
2989       fms.s1        FR_r_Res3L     = f1, f1, FR_r_Res3H // sin for neg
2990       nop.i         0
2991 }
2992 { .mfi
2993       nop.m         0
2994       fma.s1        FR_r_ResH      = FR_r_Res3H, FR_r_XS, f0 // sin for neg
2995       nop.i         0
2996 };;
2997
2998 { .mfi
2999       nop.m         0
3000       fms.s1        FR_p_Temp0L    = FR_p_Poly4H,FR_p_XR3,FR_p_Poly3H //Low poly
3001       nop.i         0
3002 }
3003 { .mfi
3004       nop.m         0
3005       fma.s1        FR_p_Poly3L    = FR_p_Poly4L,FR_p_XR3,FR_p_Poly3L //Low poly
3006       nop.i         0
3007 };;
3008
3009 { .mfi
3010       nop.m         0
3011       fms.s1        FR_p_Poly0L    = FR_p_Poly1H,f1,FR_p_Poly0H //Low & High add
3012       nop.i         0
3013 }
3014 { .mfi
3015       nop.m         0
3016 (p13) fma.s1        FR_p_OddPoly0H = FR_p_Poly0H, FR_p_AbsXM1, f0
3017                                  // Reccurent computations - multiplying by X-1
3018       nop.i         0
3019 };;
3020
3021 { .mfi
3022       nop.m         0
3023       fma.s1        FR_r_TL        = FR_r_TL, f1, FR_r_TT // sin for neg
3024       nop.i         0
3025 }
3026 { .mfi
3027       nop.m         0
3028       fma.s1        FR_r_A3        = FR_r_A4,  FR_r_XS2, FR_r_A3 // sin for neg
3029       nop.i         0
3030 };;
3031
3032 { .mfi
3033       nop.m         0
3034       fma.s1        FR_p_Poly1L    = FR_p_PolyTail,FR_p_XR6,FR_p_Poly1L//High
3035       nop.i         0
3036 }
3037 { .mfi
3038       nop.m         0
3039       fma.s1        FR_r_A5        = FR_r_A6, FR_r_XS2, FR_r_A5 // sin for neg
3040       nop.i         0
3041 };;
3042
3043 { .mfi
3044       nop.m         0
3045       fma.s1        FR_r_Res3L     = FR_r_Res3L, f1, FR_r_TH // sin for neg
3046       nop.i         0
3047 }
3048 { .mfi
3049       nop.m         0
3050       fms.s1        FR_r_ResL      = FR_r_Res3H, FR_r_XS, FR_r_ResH//sin for neg
3051       nop.i         0
3052 };;
3053
3054 { .mfi
3055       nop.m         0
3056       fma.s1        FR_p_Poly3L    = FR_p_Poly3L, f1, FR_p_Temp0L // Low poly
3057       nop.i         0
3058 }
3059 { .mfi
3060       nop.m         0
3061       fma.s1        FR_r_A7        = FR_r_A9, FR_r_XS4, FR_r_A7 // sin for neg
3062       nop.i         0
3063 };;
3064
3065 { .mfi
3066       nop.m         0
3067       fma.s1        FR_p_Poly0L    = FR_p_Poly0L,f1,FR_p_Poly3H //Low & High add
3068       nop.i         0
3069 }
3070 { .mfi
3071       nop.m         0
3072 (p13) fms.s1        FR_p_OddPoly0L = FR_p_Poly0H, FR_p_AbsXM1, FR_p_OddPoly0H
3073                        // Reccurent computations - multiplying by X-1 (low part)
3074       nop.i         0
3075 };;
3076
3077 { .mfi
3078       nop.m         0
3079       fma.s1        FR_r_A3        = FR_r_A5,  FR_r_XS4, FR_r_A3 // sin for neg
3080       nop.i         0
3081 }
3082 { .mfi
3083       nop.m         0
3084       fma.s1        FR_r_XS7       = FR_r_XS4, FR_r_XS2, f0 // xs^6
3085       nop.i         0
3086 };;
3087
3088 { .mfi
3089       nop.m         0
3090       fma.s1        FR_r_Res3L     = FR_r_Res3L, f1, FR_r_TL // sin for neg
3091       nop.i         0
3092 }
3093 { .mfi
3094       nop.m         0
3095       fma.s1        FR_r_XS8       = FR_r_XS4, FR_r_XS4, f0 // sin for neg
3096       nop.i         0
3097 };;
3098
3099 { .mfi
3100       nop.m         0
3101       fma.s1        FR_p_Temp0H    = FR_p_Poly3L,f1,FR_p_Poly1L //Low & High add
3102       nop.i         0
3103 };;
3104
3105 { .mfi
3106       nop.m         0
3107       fma.s1        FR_r_XS7       = FR_r_XS7, FR_r_XS,  f0 // xs^7
3108       nop.i         0
3109 };;
3110
3111 { .mfi
3112       nop.m         0
3113       fma.s1        FR_r_ResL      = FR_r_Res3L, FR_r_XS, FR_r_ResL//sin for neg
3114       nop.i         0
3115 }
3116 { .mfi
3117       nop.m         0
3118       fma.s1        FR_r_Tail      = FR_r_A7, FR_r_XS8, FR_r_A3 // sin tail res
3119       nop.i         0
3120 };;
3121
3122 { .mfi
3123       nop.m         0
3124       fma.s1        FR_p_Poly0L    = FR_p_Poly0L,f1,FR_p_Temp0H //Low & High add
3125       nop.i         0
3126 };;
3127
3128
3129 { .mfi
3130       nop.m         0
3131       fma.s1        FR_r_ResL      = FR_r_Tail,FR_r_XS7,FR_r_ResL //sin for neg
3132       nop.i         0
3133 };;
3134
3135 { .mfi
3136       nop.m         0
3137 (p13) fma.s1        FR_p_OddPoly0L  = FR_p_Poly0L, FR_p_AbsXM1, FR_p_OddPoly0L
3138                        // Reccurent computations - multiplying by X-1 (low part)
3139       nop.i         0
3140 };;
3141
3142 { .mfi
3143       nop.m         0
3144       fma.s1        FR_r_TT        = FR_r_ResL, FR_r_AbsX, f0 // X*sin
3145       nop.i         0
3146 };;
3147
3148 .pred.rel "mutex",p12,p13
3149 { .mfi
3150       nop.m         0
3151 (p12) fma.s0        f8             =   FR_p_Poly0H, f1, FR_p_Poly0L // Even
3152       nop.i         0
3153 }
3154 { .mfb
3155       nop.m         0
3156 (p13) fma.s0        f8             =   FR_p_OddPoly0H, f1, FR_p_OddPoly0L // Odd
3157 (p14) br.ret.spnt   b0  // Exit for 1 <= |X| < 13 path (positive arguments)/////
3158 };;
3159
3160 { .mfi
3161       nop.m         0
3162 (p13) fma.s1        FR_p_Poly0H    = FR_p_OddPoly0H, f1, f0
3163                                                        // Reccurent computations
3164       nop.i         0
3165 }
3166 { .mfi
3167       nop.m         0
3168 (p13) fma.s1        FR_p_Poly0L    = FR_p_OddPoly0L, f1, f0
3169                                                        // Reccurent computations
3170       nop.i         0
3171 };;
3172
3173 { .mfi
3174       nop.m         0
3175       fma.s1        FR_r_Res1H     = FR_r_ResH, FR_r_AbsX, FR_r_TT // X*sin
3176 (p11) cmp.eq        p13, p12       = r0, r0
3177 };;
3178
3179 { .mfi
3180       nop.m         0
3181       fms.s1        FR_r_Res1L     = FR_r_ResH,FR_r_AbsX,FR_r_Res1H// X*sin
3182 (p9)  cmp.eq        p13, p12       = r0, r0
3183 };;
3184
3185 { .mfi
3186       nop.m         0
3187       fma.s1        FR_r_Res1L     = FR_r_Res1L, f1, FR_r_TT // sin for neg
3188 (p10) cmp.eq        p13, p12       = r0, r0
3189 }
3190 { .mfi
3191       nop.m         0
3192       fma.s1        FR_r_TL        = FR_p_Poly0L, FR_r_Res1H, f0 // mult by sin
3193       nop.i         0
3194 };;
3195
3196 { .mfi
3197       nop.m         0
3198       fma.s1        FR_r_TL        = FR_p_Poly0H,FR_r_Res1L,FR_r_TL//mult by sin
3199       nop.i         0
3200 };;
3201
3202 { .mfi
3203       nop.m         0
3204       fma.s1        FR_r_ResH      = FR_p_Poly0H,FR_r_Res1H,FR_r_TL//mult by sin
3205       nop.i         0
3206 };;
3207
3208 { .mfi
3209       nop.m         0
3210       fms.s1        FR_r_ResL      = FR_p_Poly0H,FR_r_Res1H,FR_r_ResH//sin mult
3211       nop.i         0
3212 };;
3213
3214 { .mfi
3215       nop.m         0
3216       frcpa.s1      FR_r_Y0,p0     = f1,FR_r_ResH //  y = frcpa(b)
3217       nop.i         0
3218 };;
3219
3220 { .mfi
3221       nop.m         0
3222       fneg          FR_r_NegOne    = f1 // Form -1.0
3223       nop.i         0
3224 }
3225 { .mfi
3226       nop.m         0
3227       fma.s1        FR_r_ResL      = FR_r_ResL, f1, FR_r_TL //Low result of mult
3228       nop.i         0
3229 };;
3230
3231 { .mfi
3232       nop.m         0
3233       fma.s1        FR_r_Q0        = f1,FR_r_Y0,f0 //  q = a*y
3234       nop.i         0
3235 }
3236 { .mfi
3237       nop.m         0
3238       fnma.s1       FR_r_E0        = FR_r_Y0,FR_r_ResH,f1 //  e = 1-b*y
3239       nop.i         0
3240 };;
3241
3242 { .mfi
3243       nop.m         0
3244       fma.s1        FR_r_E2        = FR_r_E0,FR_r_E0,FR_r_E0 //  e2 = e+e^2
3245       nop.i         0
3246 }
3247 { .mfi
3248       nop.m         0
3249       fma.s1        FR_r_E1        = FR_r_E0,FR_r_E0,f0 //  e1 = e^2
3250       nop.i         0
3251 };;
3252
3253 { .mfi
3254       nop.m         0
3255       fma.s1        FR_r_Y1        = FR_r_Y0,FR_r_E2,FR_r_Y0 //  y1 = y+y*e2
3256       nop.i         0
3257 }
3258 { .mfi
3259       nop.m         0
3260       fma.s1        FR_r_E3        = FR_r_E1,FR_r_E1,FR_r_E0 //  e3 = e+e1^2
3261       nop.i         0
3262 };;
3263
3264 { .mfi
3265       nop.m         0
3266       fma.s1        FR_r_Y2        = FR_r_Y1,FR_r_E3,FR_r_Y0 //  y2 = y+y1*e3
3267       nop.i         0
3268 }
3269 { .mfi
3270       nop.m         0
3271       fnma.s1       FR_r_R0        = FR_r_ResH,FR_r_Q0,f1 //  r = a-b*q
3272       nop.i         0
3273 };;
3274
3275 { .mfi
3276       nop.m         0
3277       fnma.s1       FR_r_E4        = FR_r_ResH,FR_r_Y2,f1 //  e4 = 1-b*y2
3278       nop.i         0
3279 }
3280 { .mfi
3281       nop.m         0
3282       fma.s1        FR_r_ZH        = FR_r_R0,FR_r_Y2,FR_r_Q0 //  x = q+r*y2
3283       nop.i         0
3284 };;
3285
3286 { .mfi
3287       nop.m         0
3288       fma.s1        FR_r_Y3        = FR_r_Y2,FR_r_E4,FR_r_Y2 //  y3 = y2+y2*e4
3289       nop.i         0
3290 }
3291 { .mfi
3292       nop.m         0
3293       fnma.s1       FR_r_R1        = FR_r_ResH,FR_r_ZH,f1 //  r1 = a-b*x
3294       nop.i         0
3295 };;
3296
3297 { .mfi
3298       nop.m         0
3299       fnma.s1       FR_r_R1        = FR_r_ResL,FR_r_ZH,FR_r_R1 // r1=r1-b_lo*X
3300       nop.i         0
3301 }
3302 { .mfi
3303       nop.m         0
3304 (p12) fma.s1        FR_r_ZHN       = FR_r_ZH,FR_r_NegOne, f0 // Negate for evens
3305       nop.i         0
3306 };;
3307
3308 .pred.rel "mutex",p13,p12
3309 { .mfi
3310       nop.m         0
3311 (p13) fma.s0        f8             = FR_r_R1,FR_r_Y3,FR_r_ZH // Final result
3312       nop.i         0
3313 }
3314 { .mfb
3315       nop.m         0
3316 (p12) fnma.s0       f8             = FR_r_R1,FR_r_Y3,FR_r_ZHN // Final result
3317       br.ret.sptk   b0 // Exit for 1 <= |X| < 13 path (negative arguments)//////
3318 };;
3319
3320
3321 ////////////  |X| < 1 path /////////////////////////////////////////////////////
3322 //------------------------------------------------------------------------------
3323 .align 64
3324 tgamma_lt_1:
3325 { .mfi
3326       getf.exp      GR_p_Exp       = FR_p_AbsX // exp of abs X
3327       fma.s1        FR_z_Q0        = f1,FR_z_Y0,f0 // q = a*y
3328       add           GR_r_sin_Table2= 0x50, GR_r_sin_Table
3329 }
3330 { .mfi
3331       ldfpd         FR_p_0p5, FR_p_1p5 = [GR_c_Table], 16
3332       fnma.s1       FR_z_E0        = FR_z_Y0,f8,f1 //  e = 1-b*y
3333       add           GR_p_Table2    = 0xB0, GR_p_Table
3334 };;
3335
3336 { .mfi
3337       ldfd          FR_p_0p25      = [GR_c_Table]
3338       fcvt.xf       FR_r_XNS       = FR_r_IXNS // Convert int repr to float
3339       shr.u         GR_p_X_Sgnd    = GR_p_X_Sgnd, 60
3340                                        // Obtain only 4 bits of significand
3341 }
3342 { .mfi
3343       nop.m        0
3344       nop.f        0
3345       add          GR_p_Bias           = 0xffff, r0 // Set bias
3346 };;
3347
3348 { .mfi
3349       ldfpd        FR_r_A2H, FR_r_A2L  = [GR_r_sin_Table], 16
3350       nop.f        0
3351       shl          GR_p_XN             = GR_p_Exp, 4
3352                        // Shift exp to 4 bits left to set place for significand
3353 }
3354 { .mlx
3355       ldfe         FR_r_A6         = [GR_r_sin_Table2], 16
3356       movl         GR_p_0p75       = 0xfffec // 0.75
3357 };;
3358
3359 { .mfi
3360       ldfpd        FR_r_A1H, FR_r_A1L = [GR_r_sin_Table], 16
3361       nop.f        0
3362       or           GR_p_XN         = GR_p_XN, GR_p_X_Sgnd
3363                                  // Combine exp with 4 high bits of significand
3364 }
3365 { .mfi
3366       ldfe         FR_r_A5         = [GR_r_sin_Table2], 16
3367       nop.f        0
3368       sub          GR_p_Exp        = GR_p_Exp, GR_p_Bias // Unbiased exp
3369 };;
3370
3371 { .mmi
3372       ldfe         FR_r_A9         = [GR_r_sin_Table], 16
3373       ldfe         FR_r_A4         = [GR_r_sin_Table2], 16
3374       cmp.gtu.unc  p10, p11        = GR_p_0p75, GR_p_XN // sgnd(x) < 0.75
3375 };;
3376
3377 { .mfi
3378       ldfe          FR_r_A8        = [GR_r_sin_Table], 16
3379       fma.s1        FR_z_E2        = FR_z_E0,FR_z_E0,FR_z_E0 //  e2 = e+e^2
3380 (p10) cmp.gt.unc    p9, p10        = -2, GR_p_Exp //  x < 0.25
3381 }
3382 { .mfi
3383       ldfe          FR_r_A3        = [GR_r_sin_Table2], 16
3384       fma.s1        FR_z_E1        = FR_z_E0,FR_z_E0,f0 // e1 = e^2
3385 (p11) add           GR_p_Offset    = 168, r0 // [0.75;1] interval
3386 };;
3387
3388 { .mmi
3389 (p10) add           GR_p_Offset    = 147, r0 // [0.25;0.75] interval
3390       ldfe          FR_r_A7        = [GR_r_sin_Table], 16
3391 (p9)  cmp.gt.unc    p8, p9         = -3, GR_p_Exp // x < 0.125
3392 };;
3393
3394 .pred.rel "mutex",p9,p8
3395 { .mmi
3396 (p9)  add           GR_p_Offset    = 126, r0 // [0.125;0.25] interval
3397 (p8)  add           GR_p_Offset    = 189, r0 // [0.;0.125] interval
3398       nop.i         0
3399 };;
3400
3401 { .mmf
3402       shladd        GR_p_Table     = GR_p_Offset, 4, GR_p_Table //Make addresses
3403       shladd        GR_p_Table2    = GR_p_Offset, 4, GR_p_Table2
3404       fma.s1        FR_r_XS        = FR_r_AbsX , f1, FR_r_XNS // xs = |x|-[x]
3405 };;
3406
3407 .pred.rel "mutex",p8,p11
3408 { .mfi
3409       ldfpd         FR_p_A5H, FR_p_A5L = [GR_p_Table], 16
3410 (p11) fms.s1        FR_p_XR            = f1, f1, FR_p_AbsX // r = 1 - |x|
3411                                                  // for [0.75;1] interval
3412       nop.i         0
3413 }
3414 { .mfi
3415       ldfpd        FR_p_A2H, FR_p_A2L = [GR_p_Table2], 16
3416 (p8)  fms.s1       FR_p_XR            = FR_p_AbsX, f1, f0 // r = |x|
3417                                                       // for [0.;0.125] interval
3418       nop.i         0
3419 };;
3420
3421 { .mfi
3422       ldfpd         FR_p_A4H, FR_p_A4L = [GR_p_Table], 16
3423       fma.s1        FR_z_Y1        = FR_z_Y0,FR_z_E2,FR_z_Y0 // y1 = y+y*e2
3424       nop.i         0
3425 }
3426 { .mfi
3427       ldfpd         FR_p_A1H, FR_p_A1L = [GR_p_Table2], 16
3428       fma.s1        FR_z_E3        = FR_z_E1,FR_z_E1,FR_z_E0 // e3 = e+e1^2
3429       nop.i         0
3430 };;
3431
3432 .pred.rel "mutex",p9,p10
3433 { .mfi
3434       ldfpd         FR_p_A3H, FR_p_A3L = [GR_p_Table], 16
3435 (p9)  fms.s1        FR_p_XR        = FR_p_AbsX, f1, f0 // r = |x|
3436                                                   // for [0.125;0.25] interval
3437       nop.i         0
3438 }
3439 { .mfi
3440       ldfpd         FR_p_A0H, FR_p_A0L  = [GR_p_Table2], 16
3441 (p10) fms.s1        FR_p_XR        = FR_p_AbsX, f1, FR_p_0p5 // r = |x| - 0.5
3442                                                  // for [0.25;0.75] interval
3443       nop.i         0
3444 };;
3445
3446 { .mmi
3447       ldfe          FR_p_A20       = [GR_p_Table], 16
3448       ldfe          FR_p_A12       = [GR_p_Table2], 16
3449       nop.i         0
3450 };;
3451
3452 { .mfi
3453       ldfe          FR_p_A19       = [GR_p_Table], 16
3454       fma.s1        FR_r_XS2       = FR_r_XS, FR_r_XS, f0 // xs^2
3455       nop.i         0
3456 }
3457 { .mfi
3458       ldfe          FR_p_A11       = [GR_p_Table2], 16
3459       nop.f         0
3460       nop.i         0
3461 };;
3462
3463 { .mmi
3464       ldfe          FR_p_A18       = [GR_p_Table], 16
3465       ldfe          FR_p_A10       = [GR_p_Table2], 16
3466       nop.i         0
3467 };;
3468
3469 .pred.rel "mutex",p12,p13
3470 { .mfi
3471       ldfe          FR_p_A17       = [GR_p_Table], 16
3472       fma.s1        FR_z_Y2        = FR_z_Y1,FR_z_E3,FR_z_Y0 // y2 = y+y1*e3
3473       nop.i         0
3474 }
3475 { .mfi
3476       ldfe          FR_p_A9        = [GR_p_Table2], 16
3477       fnma.s1       FR_z_R0        = f8,FR_z_Q0,f1 //  r = a-b*q
3478       nop.i         0
3479 };;
3480
3481 { .mmi
3482       ldfe          FR_p_A16       = [GR_p_Table], 16
3483       ldfe          FR_p_A8        = [GR_p_Table2], 16
3484       nop.i         0
3485 };;
3486
3487 { .mmi
3488       ldfe          FR_p_A15       = [GR_p_Table], 16
3489       ldfe          FR_p_A7        = [GR_p_Table2], 16
3490       nop.i         0
3491 };;
3492
3493 { .mfi
3494       ldfe          FR_p_A14       = [GR_p_Table], 16
3495       fma.s1        FR_r_TH        = FR_r_A2H, FR_r_XS2, f0 // neg sin
3496       nop.i         0
3497 }
3498 { .mfi
3499       ldfe          FR_p_A6        = [GR_p_Table2], 16
3500       fma.s1        FR_r_TL        =   FR_r_A2L, FR_r_XS2, f0 // neg sin
3501       nop.i         0
3502 };;
3503
3504 { .mfi
3505       ldfe          FR_p_A13       = [GR_p_Table], 16
3506       fms.s1        FR_r_XS2L      = FR_r_XS, FR_r_XS, FR_r_XS2 // xs^2 delta
3507       nop.i         0
3508 };;
3509
3510 { .mfi
3511       nop.m         0
3512       fma.s1        FR_p_Temp5H     = FR_p_A5H, FR_p_XR, f0 // Low poly
3513       nop.i         0
3514 }
3515 { .mfi
3516       nop.m         0
3517       fma.s1        FR_p_XR2       = FR_p_XR, FR_p_XR, f0 // poly tail
3518       nop.i         0
3519 };;
3520
3521 { .mfi
3522       nop.m         0
3523       fabs          FR_r_XS        = FR_r_XS // Absolute value of xs
3524       nop.i         0
3525 }
3526 { .mfi
3527       nop.m         0
3528       fma.s1        FR_p_Temp2H    = FR_p_A2H, FR_p_XR, f0 // High poly
3529       nop.i         0
3530 };;
3531
3532 { .mfi
3533       nop.m         0
3534       fnma.s1       FR_z_E4        = f8,FR_z_Y2,f1 //  e4 = 1-b*y2
3535       nop.i         0
3536 }
3537 { .mfi
3538       nop.m         0
3539       fma.s1        FR_z_ZH        = FR_z_R0,FR_z_Y2,FR_z_Q0 // 1/x = q+r*y2
3540       nop.i         0
3541 };;
3542
3543 { .mfi
3544       nop.m         0
3545       fms.s1        FR_r_TT        = FR_r_A2H, FR_r_XS2, FR_r_TH // neg sin
3546       nop.i         0
3547 }
3548 { .mfi
3549       nop.m         0
3550       fma.s1        FR_r_ResH      = FR_r_TH, f1, FR_r_A1H // neg sin
3551       nop.i         0
3552 };;
3553
3554 { .mfi
3555       nop.m         0
3556       fma.s1        FR_r_TL        = FR_r_A2H, FR_r_XS2L, FR_r_TL // neg sin
3557       nop.i         0
3558 };;
3559
3560 { .mfi
3561       nop.m         0
3562       fms.s1        FR_p_Temp5L    = FR_p_A5H, FR_p_XR, FR_p_Temp5H // Low poly
3563       nop.i         0
3564 }
3565 { .mfi
3566       nop.m         0
3567       fma.s1        FR_p_Poly5H    = FR_p_Temp5H, f1, FR_p_A4H // Low poly
3568       nop.i         0
3569 };;
3570
3571 { .mfi
3572       nop.m         0
3573       fms.s1        FR_p_Temp2L    = FR_p_A2H, FR_p_XR, FR_p_Temp2H // High poly
3574       nop.i         0
3575 }
3576 { .mfi
3577       nop.m         0
3578       fma.s1        FR_p_Poly2H    = FR_p_Temp2H, f1, FR_p_A1H // High poly
3579       nop.i         0
3580 };;
3581
3582 { .mfi
3583       nop.m         0
3584       fma.s1        FR_p_XR3       = FR_p_XR2, FR_p_XR,  f0 // r^3
3585       nop.i         0
3586 }
3587 { .mfi
3588       nop.m         0
3589       fms.s1        FR_p_XR2L      = FR_p_XR, FR_p_XR, FR_p_XR2 // r^2 delta
3590       nop.i         0
3591 };;
3592
3593 { .mfi
3594       nop.m         0
3595       fma.s1        FR_p_A18       = FR_p_A19, FR_p_XR, FR_p_A18 // poly tail
3596       nop.i         0
3597 }
3598 { .mfi
3599       nop.m         0
3600       fma.s1        FR_p_A14       = FR_p_A15, FR_p_XR, FR_p_A14 // poly tail
3601       nop.i         0
3602 };;
3603
3604 { .mfi
3605       nop.m         0
3606       fma.s1        FR_p_XR4       = FR_p_XR2, FR_p_XR2, f0 // poly tail
3607       nop.i         0
3608 }
3609 { .mfi
3610       nop.m         0
3611       fma.s1        FR_z_Y3        = FR_z_Y2,FR_z_E4,FR_z_Y2 //  y3 = y2+y2*e4
3612       nop.i         0
3613 };;
3614
3615 { .mfi
3616       nop.m         0
3617       fma.s1        FR_p_Temp5L    = FR_p_A5L, FR_p_XR, FR_p_Temp5L // Low poly
3618       nop.i         0
3619 }
3620 { .mfi
3621       nop.m         0
3622       fms.s1        FR_p_Poly5L    = FR_p_A4H, f1, FR_p_Poly5H // Low poly
3623       nop.i         0
3624 };;
3625
3626 { .mfi
3627       nop.m         0
3628       fma.s1        FR_p_Temp4H    = FR_p_Poly5H, FR_p_XR, f0 // Low poly
3629       nop.i         0
3630 }
3631 { .mfi
3632       nop.m         0
3633       fma.s1        FR_p_Temp2L    = FR_p_A2L, FR_p_XR, FR_p_Temp2L // High poly
3634       nop.i         0
3635 };;
3636
3637 { .mfi
3638       nop.m         0
3639       fms.s1        FR_p_Poly2L    = FR_p_A1H, f1, FR_p_Poly2H // High poly
3640       nop.i         0
3641 }
3642 { .mfi
3643       nop.m         0
3644       fma.s1        FR_p_Temp1H    = FR_p_Poly2H, FR_p_XR, f0 // High poly
3645       nop.i         0
3646 };;
3647
3648 { .mfi
3649       nop.m         0
3650       fms.s1        FR_p_XR3L      = FR_p_XR2, FR_p_XR, FR_p_XR3 // x^3 delta
3651       nop.i         0
3652 }
3653 { .mfi
3654       nop.m         0
3655       fma.s1        FR_p_A16       = FR_p_A17, FR_p_XR, FR_p_A16 //poly tail
3656       nop.i         0
3657 };;
3658
3659 { .mfi
3660       nop.m         0
3661       fms.s1        FR_r_ResL      = FR_r_A1H, f1, FR_r_ResH // neg sin
3662       nop.i         0
3663 }
3664 { .mfi
3665       nop.m         0
3666       fma.s1        FR_r_TL        = FR_r_TL, f1, FR_r_TT // neg sin
3667       nop.i         0
3668 };;
3669
3670 { .mfi
3671       nop.m         0
3672       fma.s1        FR_p_Temp5L    = FR_p_Temp5L, f1, FR_p_A4L // Low poly
3673       nop.i         0
3674 }
3675 { .mfi
3676       nop.m         0
3677       fma.s1        FR_p_Poly5L    = FR_p_Poly5L, f1, FR_p_Temp5H //Low poly
3678       nop.i         0
3679 };;
3680
3681 { .mfi
3682       nop.m         0
3683       fms.s1        FR_p_Temp4L    = FR_p_Poly5H, FR_p_XR, FR_p_Temp4H//Low poly
3684       nop.i         0
3685 }
3686 { .mfi
3687       nop.m         0
3688       fma.s1        FR_p_Poly4H    = FR_p_Temp4H, f1, FR_p_A3H // Low poly
3689       nop.i         0
3690 };;
3691
3692 { .mfi
3693       nop.m         0
3694       fma.s1        FR_p_Temp2L    = FR_p_Temp2L, f1, FR_p_A1L // High poly
3695       nop.i         0
3696 }
3697 { .mfi
3698       nop.m         0
3699       fma.s1        FR_p_Poly2L    = FR_p_Poly2L, f1, FR_p_Temp2H // High poly
3700       nop.i         0
3701 };;
3702
3703 { .mfi
3704       nop.m         0
3705       fms.s1        FR_p_Temp1L    = FR_p_Poly2H,FR_p_XR,FR_p_Temp1H //High poly
3706       nop.i         0
3707 }
3708 { .mfi
3709       nop.m         0
3710       fma.s1        FR_p_Poly1H    = FR_p_Temp1H, f1, FR_p_A0H // High poly
3711       nop.i         0
3712 };;
3713
3714 { .mfi
3715       nop.m         0
3716       fma.s1        FR_p_A12       = FR_p_A13, FR_p_XR, FR_p_A12 // poly tail
3717       nop.i         0
3718 }
3719 { .mfi
3720       nop.m         0
3721       fma.s1        FR_p_XR3L      = FR_p_XR2L, FR_p_XR, FR_p_XR3L // x^3 low
3722       nop.i         0
3723 };;
3724
3725 { .mfi
3726       nop.m         0
3727       fma.s1        FR_p_Poly5L    = FR_p_Poly5L, f1, FR_p_Temp5L //Low poly
3728       nop.i         0
3729 }
3730 { .mfi
3731       nop.m         0
3732       fma.s1        FR_p_A10       = FR_p_A11, FR_p_XR, FR_p_A10 //poly tail
3733       nop.i         0
3734 };;
3735
3736 { .mfi
3737       nop.m         0
3738       fms.s1        FR_p_Poly4L    = FR_p_A3H, f1, FR_p_Poly4H /// Low poly
3739       nop.i         0
3740 }
3741 { .mfi
3742       nop.m         0
3743       fma.s1        FR_p_A6        = FR_p_A7, FR_p_XR, FR_p_A6 // poly tail
3744       nop.i         0
3745 };;
3746
3747 { .mfi
3748       nop.m         0
3749       fma.s1        FR_p_A8        = FR_p_A9, FR_p_XR, FR_p_A8 // poly tail
3750       nop.i         0
3751 }
3752 { .mfi
3753       nop.m         0
3754       fma.s1        FR_p_XR6       = FR_p_XR4, FR_p_XR2, f0 // r^6
3755       nop.i         0
3756 };;
3757
3758 { .mfi
3759       nop.m         0
3760       fma.s1        FR_p_Poly2L    = FR_p_Poly2L, f1, FR_p_Temp2L // High poly
3761       nop.i         0
3762 }
3763 { .mfi
3764       nop.m         0
3765       fms.s1        FR_p_Poly1L    = FR_p_A0H, f1, FR_p_Poly1H // High poly
3766       nop.i         0
3767 };;
3768
3769 { .mfi
3770       nop.m         0
3771       fma.s1        FR_r_ResL      = FR_r_ResL, f1, FR_r_TH // neg sin
3772       nop.i         0
3773 }
3774 { .mfi
3775       nop.m         0
3776       fma.s1        FR_r_TT        = FR_r_TL, f1, FR_r_A1L // neg sin
3777       nop.i         0
3778 };;
3779
3780 { .mfi
3781       nop.m         0
3782       fma.s1        FR_p_Temp4L    = FR_p_Poly5L,FR_p_XR,FR_p_Temp4L //Low poly
3783       nop.i         0
3784 }
3785 { .mfi
3786       nop.m         0
3787       fma.s1        FR_p_A18       = FR_p_A20, FR_p_XR2, FR_p_A18 // poly tail
3788       nop.i         0
3789 };;
3790
3791 { .mfi
3792       nop.m         0
3793       fma.s1        FR_p_Poly4L    = FR_p_Poly4L, f1, FR_p_Temp4H // Low poly
3794       nop.i         0
3795 }
3796 { .mfi
3797       nop.m         0
3798       fma.s1        FR_p_A14       = FR_p_A16, FR_p_XR2, FR_p_A14 // poly tail
3799       nop.i         0
3800 };;
3801
3802 { .mfi
3803       nop.m         0
3804       fma.s1        FR_p_A6        = FR_p_A8, FR_p_XR2, FR_p_A6 // poly tail
3805       nop.i         0
3806 }
3807 { .mfi
3808       nop.m         0
3809       fma.s1        FR_p_A10       = FR_p_A12, FR_p_XR2, FR_p_A10 // poly tail
3810       nop.i         0
3811 };;
3812
3813 { .mfi
3814       nop.m         0
3815       fma.s1        FR_p_Temp1L    = FR_p_Poly2L,FR_p_XR,FR_p_Temp1L //High poly
3816       nop.i         0
3817 }
3818 { .mfi
3819       nop.m         0
3820       fma.s1        FR_p_Poly1L    = FR_p_Poly1L, f1, FR_p_Temp1H // High poly
3821       nop.i         0
3822 };;
3823
3824 { .mfi
3825       nop.m         0
3826       fma.s1        FR_r_ResL      = FR_r_ResL, f1, FR_r_TT // neg sin
3827       nop.i         0
3828 }
3829 { .mfi
3830       nop.m         0
3831       fma.s1        FR_r_TH        = FR_r_ResH, FR_r_XS2, f0 // neg sin
3832       nop.i         0
3833 };;
3834
3835 { .mfi
3836       nop.m         0
3837       fma.s1        FR_p_Temp4L    = FR_p_Temp4L, f1, FR_p_A3L // Low poly
3838       nop.i         0
3839 }
3840 { .mfi
3841       nop.m         0
3842       fma.s1        FR_p_Poly3H    = FR_p_Poly4H, FR_p_XR3, f0 // Low poly
3843       nop.i         0
3844 };;
3845
3846 { .mfi
3847       nop.m         0
3848       fma.s1        FR_p_A14       = FR_p_A18, FR_p_XR4, FR_p_A14 // poly tail
3849       nop.i         0
3850 }
3851 { .mfi
3852       nop.m         0
3853       fma.s1        FR_p_XR8       = FR_p_XR4, FR_p_XR4, f0 // r^8
3854       nop.i         0
3855 };;
3856
3857 { .mfi
3858       nop.m         0
3859       fma.s1        FR_r_TL        = FR_r_ResH, FR_r_XS2L, f0 // neg sin
3860       nop.i         0
3861 }
3862 { .mfi
3863       nop.m         0
3864       fnma.s1       FR_z_R1        = f8,FR_z_ZH,f1 //  r1 = a-b*x
3865       nop.i         0
3866 };;
3867
3868 { .mfi
3869       nop.m         0
3870       fma.s1        FR_p_Temp1L    = FR_p_Temp1L, f1, FR_p_A0L // High poly
3871       nop.i         0
3872 }
3873 { .mfi
3874       nop.m         0
3875       fma.s1        FR_p_A6        = FR_p_A10, FR_p_XR4, FR_p_A6 // poly tail
3876       nop.i         0
3877 };;
3878
3879 { .mfi
3880       nop.m         0
3881       fms.s1        FR_r_TT        = FR_r_ResH, FR_r_XS2, FR_r_TH // neg sin
3882       nop.i         0
3883 }
3884 { .mfi
3885       nop.m         0
3886       fma.s1        FR_r_Res3H     = FR_r_TH, f1, f1 // neg sin
3887       nop.i         0
3888 };;
3889
3890 { .mfi
3891       nop.m         0
3892       fma.s1        FR_p_Poly4L    = FR_p_Poly4L, f1, FR_p_Temp4L // Low poly
3893       nop.i         0
3894 }
3895 { .mfi
3896       nop.m         0
3897       fma.s1        FR_p_Poly3L    = FR_p_Poly4H, FR_p_XR3L, f0 // Low poly
3898       nop.i         0
3899 };;
3900
3901 { .mfi
3902       nop.m         0
3903       fma.s1        FR_p_Poly0H    = FR_p_Poly3H, f1, FR_p_Poly1H // Result
3904       nop.i         0
3905 }
3906 { .mfi
3907       nop.m         0
3908       fma.s1        FR_r_A7        = FR_r_A8, FR_r_XS2, FR_r_A7 // neg sin
3909       nop.i         0
3910 };;
3911
3912 { .mfi
3913       nop.m         0
3914       fma.s1        FR_r_TL        = FR_r_ResL, FR_r_XS2, FR_r_TL // neg sin
3915       nop.i         0
3916 }
3917 { .mfi
3918       nop.m         0
3919       fma.s1        FR_r_XS4       = FR_r_XS2, FR_r_XS2, f0 // xs^4
3920       nop.i         0
3921 };;
3922
3923 { .mfi
3924       nop.m         0
3925       fma.s1        FR_p_Poly1L    = FR_p_Poly1L, f1, FR_p_Temp1L // High poly
3926       nop.i         0
3927 }
3928 { .mfi
3929       nop.m         0
3930       fma.s1        FR_p_PolyTail  = FR_p_A14, FR_p_XR8, FR_p_A6 // poly tail
3931       nop.i         0
3932 };;
3933
3934 { .mfi
3935       nop.m         0
3936       fms.s1        FR_r_Res3L     = f1, f1, FR_r_Res3H // neg sin
3937       nop.i         0
3938 }
3939 { .mfi
3940       nop.m         0
3941       fma.s1        FR_r_ResH      = FR_r_Res3H, FR_r_XS, f0 // neg sin
3942       nop.i         0
3943 };;
3944
3945 { .mfi
3946       nop.m         0
3947       fms.s1        FR_p_Temp0L    = FR_p_Poly4H,FR_p_XR3,FR_p_Poly3H //Low poly
3948       nop.i         0
3949 }
3950 { .mfi
3951       nop.m         0
3952       fma.s1        FR_p_Poly3L    = FR_p_Poly4L,FR_p_XR3,FR_p_Poly3L //Low poly
3953       nop.i         0
3954 };;
3955
3956 { .mfi
3957       nop.m         0
3958       fms.s1        FR_p_Poly0L    = FR_p_Poly1H, f1, FR_p_Poly0H // Result
3959       nop.i         0
3960 }
3961 { .mfi
3962       nop.m         0
3963       fma.s1        FR_z_ZL        = FR_z_R1,FR_z_Y3, f0 //  x_lo = r1*y3
3964       nop.i         0
3965 };;
3966
3967 { .mfi
3968       nop.m         0
3969       fma.s1        FR_r_TL        = FR_r_TL, f1, FR_r_TT // neg sin
3970       nop.i         0
3971 }
3972 { .mfi
3973       nop.m         0
3974       fma.s1        FR_r_A3        = FR_r_A4, FR_r_XS2, FR_r_A3 /// neg sin
3975       nop.i         0
3976 };;
3977
3978 { .mfi
3979       nop.m         0
3980       fma.s1        FR_p_Poly1L    = FR_p_PolyTail,FR_p_XR6,FR_p_Poly1L // High
3981       nop.i         0
3982 }
3983 { .mfi
3984       nop.m         0
3985       fma.s1        FR_r_A5        = FR_r_A6, FR_r_XS2, FR_r_A5 // neg sin
3986       nop.i         0
3987 };;
3988
3989 { .mfi
3990       nop.m         0
3991       fma.s1        FR_r_Res3L     = FR_r_Res3L, f1, FR_r_TH // neg sin
3992       nop.i         0
3993 }
3994 { .mfi
3995       nop.m         0
3996       fms.s1        FR_r_ResL      = FR_r_Res3H, FR_r_XS, FR_r_ResH // neg sin
3997       nop.i         0
3998 };;
3999
4000 { .mfi
4001       nop.m         0
4002       fma.s1        FR_p_Poly3L    = FR_p_Poly3L, f1, FR_p_Temp0L // Low poly
4003       nop.i         0
4004 }
4005 { .mfi
4006       nop.m         0
4007       fma.s1        FR_r_A7        = FR_r_A9,  FR_r_XS4, FR_r_A7 // neg sin
4008       nop.i         0
4009 };;
4010
4011 { .mfi
4012       nop.m         0
4013       fma.s1        FR_p_Poly0L    = FR_p_Poly0L, f1, FR_p_Poly3H // result
4014       nop.i         0
4015 };;
4016
4017 { .mfi
4018       nop.m         0
4019 (p14) fma.s1        f8             = FR_p_Poly0H, FR_z_ZH, f0 // z*poly
4020       nop.i         0
4021 }
4022 { .mfi
4023       nop.m         0
4024       fma.s1        FR_p_Temp1L    = FR_p_Poly0H, FR_z_ZL, f0 // z*poly low
4025       nop.i         0
4026 };;
4027
4028 { .mfi
4029       nop.m         0
4030       fma.s1        FR_r_A3        = FR_r_A5, FR_r_XS4, FR_r_A3 // sin tail
4031       nop.i         0
4032 }
4033 { .mfi
4034       nop.m         0
4035       fma.s1        FR_r_XS7       = FR_r_XS4, FR_r_XS2, f0  // xs^6
4036       nop.i         0
4037 };;
4038
4039 { .mfi
4040       nop.m         0
4041       fma.s1        FR_r_Res3L     = FR_r_Res3L, f1, FR_r_TL // sin low
4042       nop.i         0
4043 }
4044 { .mfi
4045       nop.m         0
4046       fma.s1        FR_r_XS8       = FR_r_XS4, FR_r_XS4, f0 // xs^8
4047       nop.i         0
4048 };;
4049
4050 { .mfi
4051       nop.m         0
4052       fma.s1        FR_p_Temp0H    = FR_p_Poly3L, f1, FR_p_Poly1L // result
4053       nop.i         0
4054 };;
4055
4056 { .mfi
4057       nop.m         0
4058 (p14) fms.s1        FR_p_Temp1H    = FR_p_Poly0H, FR_z_ZH, f8 // hi result
4059       nop.i         0
4060 };;
4061
4062 { .mfi
4063       nop.m         0
4064       fma.s1        FR_r_XS7       = FR_r_XS7, FR_r_XS,  f0 // xs^7
4065       nop.i         0
4066 };;
4067
4068 { .mfi
4069       nop.m         0
4070       fma.s1        FR_r_ResL      = FR_r_Res3L, FR_r_XS, FR_r_ResL // lo result
4071       nop.i         0
4072 }
4073 { .mfi
4074       nop.m         0
4075       fma.s1        FR_r_Tail      = FR_r_A7, FR_r_XS8, FR_r_A3 // tail result
4076       nop.i         0
4077 };;
4078
4079 { .mfi
4080       nop.m         0
4081       fma.s1        FR_p_Poly0L    = FR_p_Poly0L, f1, FR_p_Temp0H // lo result
4082       nop.i         0
4083 };;
4084
4085 { .mfi
4086       nop.m         0
4087       fma.s1        FR_r_ResL      = FR_r_Tail, FR_r_XS7, FR_r_ResL // lo result
4088       nop.i         0
4089 };;
4090
4091 { .mfi
4092       nop.m         0
4093 (p14) fma.s1        FR_p_Temp1L    = FR_p_Poly0L,FR_z_ZH,FR_p_Temp1L //hi result
4094       nop.i         0
4095 };;
4096
4097 { .mfi
4098       nop.m         0
4099       fma.s1        FR_r_TT        = FR_r_ResL, f1, f0 // for low result
4100       nop.i         0
4101 };;
4102
4103 .pred.rel "mutex",p12,p13
4104 { .mfi
4105       nop.m         0
4106 (p14) fma.s1        FR_p_Temp1L    = FR_p_Temp1L, f1, FR_p_Temp1H // for lo res
4107       nop.i         0
4108 };;
4109
4110 { .mfi
4111 (p10) cmp.eq        p13, p12       = r0, r0 // set p13, clear p12
4112       fma.s1        FR_r_Res1H     = FR_r_ResH, f1, FR_r_TT // hi res
4113       nop.i         0
4114 };;
4115
4116 { .mfb
4117 (p9)  cmp.eq        p13, p12       = r0, r0 // set p13, clear p12
4118 (p14) fma.s0        f8             =   f8, f1, FR_p_Temp1L // Final result
4119 (p14) br.ret.spnt   b0 // Exit for  0 < |X| < 1 path (positive arguments)///////
4120 };;
4121
4122 { .mfi
4123 (p11) cmp.eq        p13, p12       = r0, r0 // set p13, clear p12
4124       fms.s1        FR_r_Res1L     = FR_r_ResH, f1, FR_r_Res1H // Low sin result
4125       nop.i         0
4126 };;
4127
4128 { .mfi
4129       nop.m         0
4130       fma.s1        FR_r_Res1L     = FR_r_Res1L, f1, FR_r_TT // Low sin result
4131       nop.i         0
4132 }
4133 { .mfi
4134       nop.m         0
4135       fma.s1        FR_r_TL        = FR_p_Poly0L,FR_r_Res1H,f0 //Low sin result
4136       nop.i         0
4137 };;
4138
4139 { .mfi
4140       nop.m         0
4141       fma.s1        FR_r_TL        = FR_p_Poly0H, FR_r_Res1L, FR_r_TL //Low sin
4142       nop.i         0
4143 };;
4144
4145 { .mfi
4146       nop.m         0
4147       fma.s1        FR_r_ResH      = FR_p_Poly0H, FR_r_Res1H, FR_r_TL //High sin
4148       nop.i         0
4149 };;
4150
4151 { .mfi
4152       nop.m         0
4153       fms.s1        FR_r_ResL      = FR_p_Poly0H,FR_r_Res1H,FR_r_ResH //Low res
4154       nop.i         0
4155 };;
4156
4157 { .mfi
4158       nop.m         0
4159       frcpa.s1      FR_r_Y0,p0     = f1,FR_r_ResH //  y = frcpa(b)
4160       nop.i         0
4161 };;
4162
4163 { .mfi
4164       nop.m         0
4165       fneg          FR_r_NegOne    = f1 // Construct -1.0
4166       nop.i         0
4167 }
4168 { .mfi
4169       nop.m         0
4170       fma.s1        FR_r_ResL      = FR_r_ResL, f1, FR_r_TL // low sin
4171       nop.i         0
4172 };;
4173
4174 { .mfi
4175       nop.m         0
4176       fma.s1        FR_r_Q0        = f1,FR_r_Y0,f0 // q = a*y
4177       nop.i         0
4178 }
4179 { .mfi
4180       nop.m         0
4181       fnma.s1       FR_r_E0        = FR_r_Y0,FR_r_ResH,f1 // e = 1-b*y
4182       nop.i         0
4183 };;
4184
4185 { .mfi
4186       nop.m         0
4187       fma.s1        FR_r_E2        = FR_r_E0,FR_r_E0,FR_r_E0 // e2 = e+e^2
4188       nop.i         0
4189 }
4190 { .mfi
4191       nop.m         0
4192       fma.s1        FR_r_E1        = FR_r_E0,FR_r_E0,f0 // e1 = e^2
4193       nop.i         0
4194 };;
4195
4196 { .mfi
4197       nop.m         0
4198       fma.s1        FR_r_Y1        = FR_r_Y0,FR_r_E2,FR_r_Y0 //  y1 = y+y*e2
4199       nop.i         0
4200 }
4201 { .mfi
4202       nop.m         0
4203       fma.s1        FR_r_E3        = FR_r_E1,FR_r_E1,FR_r_E0 //  e3 = e+e1^2
4204       nop.i         0
4205 };;
4206
4207 { .mfi
4208       nop.m         0
4209       fma.s1        FR_r_Y2        = FR_r_Y1,FR_r_E3,FR_r_Y0 //  y2 = y+y1*e3
4210       nop.i         0
4211 }
4212 { .mfi
4213       nop.m         0
4214       fnma.s1       FR_r_R0        = FR_r_ResH,FR_r_Q0,f1 //  r = a-b*q
4215       nop.i         0
4216 };;
4217
4218 { .mfi
4219       nop.m         0
4220       fnma.s1       FR_r_E4        = FR_r_ResH,FR_r_Y2,f1 //  e4 = 1-b*y2
4221       nop.i         0
4222 }
4223 { .mfi
4224       nop.m         0
4225       fma.s1        FR_r_ZH        = FR_r_R0,FR_r_Y2,FR_r_Q0 //  x = q+r*y2
4226       nop.i         0
4227 };;
4228
4229 { .mfi
4230       nop.m         0
4231       fma.s1        FR_r_Y3        = FR_r_Y2,FR_r_E4,FR_r_Y2 //  y3 = y2+y2*e4
4232       nop.i         0
4233 }
4234 { .mfi
4235       nop.m         0
4236       fnma.s1       FR_r_R1        = FR_r_ResH,FR_r_ZH,f1 //  r1 = a-b*x
4237       nop.i         0
4238 };;
4239
4240 { .mfi
4241       nop.m         0
4242       fnma.s1       FR_r_R1        = FR_r_ResL,FR_r_ZH,FR_r_R1 // r1=r1 - b_lo*X
4243       nop.i         0
4244 }
4245 { .mfi
4246       nop.m         0
4247       fma.s1        FR_r_ZHN       = FR_r_ZH,FR_r_NegOne, f0 // Negate
4248       nop.i         0
4249 };;
4250
4251 .pred.rel "mutex",p13,p12
4252 { .mfb
4253       nop.m         0
4254       fnma.s0       f8             = FR_r_R1,FR_r_Y3,FR_r_ZHN // Result for neg
4255       br.ret.sptk   b0  // Exit for  0 < |X| < 1 path (negative arguments)//////
4256 };;
4257
4258
4259
4260
4261 //  SPECIALS (x for natval, nan, +/-inf or +/-0) ///////////////////////////////
4262 //------------------------------------------------------------------------------
4263 .align 32
4264 tgammal_spec:
4265 { .mlx
4266       nop.m         0
4267       movl          GR_DenOverflow = 0x2000000000000001
4268 }
4269 { .mfi
4270       nop.m         0
4271       fclass.m      p9,p0          =  f8,0xB // +/-denormals
4272       nop.i         0
4273 };;
4274 { .mfi
4275       nop.m         0
4276       fclass.m      p6,p0          =  f8,0x1E1 // Test x for natval, nan, +inf
4277       nop.i         0
4278 };;
4279 { .mfi
4280       nop.m         0
4281       fclass.m      p7,p8          = f8,0x7 // +/-0
4282       nop.i         0
4283 }
4284
4285 { .mfi
4286 (p9)  cmp.ltu.unc   p10,p11        = GR_l_signif_Z, GR_DenOverflow
4287 (p9)  fnorm.s0      f8 = f8
4288       nop.i         0
4289 };;
4290
4291 { .mfb
4292       nop.m         0
4293 (p9)  fcvt.fx.trunc.s1 FR_n_IXN    = FR_l_AbsX // Round by truncate
4294 (p11) br.cond.sptk  tgamma_lt_1 // Return to gamma ('good' denormal)////////////
4295 };;
4296
4297 { .mfb
4298       nop.m         0
4299       nop.f         0
4300 (p10) br.cond.spnt  tgammal_overflow // "Bad" denormal - overflow! /////////////
4301 };;
4302
4303 { .mfi
4304       nop.m         0
4305       mov           FR_X           = f8 // for error handler
4306       nop.i         0
4307 }
4308 { .mfb
4309       nop.m         0
4310 (p6)  fma.s0        f8             = f8,f1,f8 // res = x + x
4311 (p6)  br.ret.spnt   b0 // Exit for NAN, INF and NatVals ////////////////////////
4312 };;
4313 .pred.rel "mutex",p7,p8
4314 { .mfi
4315 (p7)  mov           GR_Parameter_TAG = 256   // negative
4316 (p7)  frcpa.s0      f8,p0            = f1,f8 // Raise V flag
4317       nop.i         0
4318 }
4319 { .mfb
4320       nop.m         0
4321       nop.f         0
4322 (p8)  br.cond.spnt  tgammal_singularity // Branch for +ZERO ////////////////////
4323 };;
4324
4325 { .mfb
4326       nop.m         0
4327       nop.f         0
4328       br.cond.spnt  tgammal_libm_err // Branch for -ZERO ///////////////////////
4329 };;
4330
4331
4332
4333
4334 // SINGULARITY (x is negative integer or 0) ////////////////////////////////////
4335 //------------------------------------------------------------------------------
4336 .align 32
4337 tgammal_singularity:
4338 { .mfi
4339       nop.m         0
4340       mov           FR_X             = f8  // For error handler
4341       mov           GR_Parameter_TAG = 256 // negative
4342 }
4343 { .mfb
4344       nop.m         0
4345       frcpa.s0      f8,p0 = f0,f0 // Raise V flag
4346       br.cond.sptk  tgammal_libm_err // Call error handler /////////////////////
4347                                      // with singularity error /////////////////
4348 };;
4349
4350
4351
4352
4353 // OVERFLOW (result is too big and cannot be represented by normal value) //////
4354 // ( X > 1755.54 and for denormals with abs value less than 0x2000000000000001 )
4355 //------------------------------------------------------------------------------
4356 .align 32
4357 tgammal_overflow:
4358 { .mfi
4359       addl          r8             = 0x1FFFE, r0 // Exp of INF
4360       fcmp.lt.s1    p15,p14        = f8,f0 // p14 - pos arg, p15 - neg arg
4361       nop.i         0
4362 };;
4363
4364 { .mfi
4365       setf.exp      f9               = r8
4366       mov           FR_X             = f8 // For error handler
4367       mov           GR_Parameter_TAG = 255 // overflow
4368 };;
4369
4370 .pred.rel "mutex",p14,p15
4371 { .mfi
4372       nop.m         0
4373 (p14) fma.s0        f8             = f9,f9,f0 // Set I,O and +INF result
4374       nop.i         0
4375 }
4376 { .mfb
4377       nop.m         0
4378 (p15) fnma.s0       f8             = f9,f9,f0 // Set I,O and -INF result
4379       br.cond.sptk  tgammal_libm_err // Call error handler /////////////////////
4380                                      // with overflow error ////////////////////
4381 };;
4382
4383
4384
4385
4386
4387 // UNDERFLOW (x is negative noninteger with big absolute value) ////////////////
4388 //------------------------------------------------------------------------------
4389 .align 32
4390 tgammal_underflow:
4391 { .mfi
4392       nop.m         0
4393       fcvt.fx.trunc.s1 FR_u_IXN    = f8 // Convert arg to int repres. in FR
4394       nop.i         0
4395 };;
4396
4397 { .mmi
4398       getf.sig      GR_u_XN        = FR_u_IXN
4399       mov           r11            = 0x00001
4400       nop.i         0
4401 };;
4402
4403 { .mfi
4404       setf.exp      f9             = r11
4405       nop.f         0
4406       nop.i         0
4407 };;
4408
4409 { .mfi
4410       nop.m         0
4411       nop.f         0
4412       tbit.z        p6,p7          = GR_u_XN,0 // even or odd
4413 };;
4414
4415 .pred.rel "mutex",p6,p7
4416 { .mfi
4417       nop.m         0
4418 (p6)  fms.s0        f8             = f9,f9,f9 // for negatives
4419       nop.i         0
4420 }
4421 { .mfb
4422       nop.m         0
4423 (p7)  fma.s0        f8             = f9,f9,f9 // for positives
4424       br.ret.sptk   b0 // Exit for underflow path //////////////////////////////
4425 };;
4426
4427
4428 GLOBAL_LIBM_END(tgammal)
4429
4430
4431
4432
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 };;
4483
4484 LOCAL_LIBM_END(__libm_error_region#)
4485
4486 .type   __libm_error_support#,@function
4487 .global __libm_error_support#