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Diffstat (limited to 'sysdeps/ia64/fpu/w_tgammal.S')
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diff --git a/sysdeps/ia64/fpu/w_tgammal.S b/sysdeps/ia64/fpu/w_tgammal.S new file mode 100644 index 0000000000..b10c5dc276 --- /dev/null +++ b/sysdeps/ia64/fpu/w_tgammal.S @@ -0,0 +1,4487 @@ +.file "tgammal.s" + + +// Copyright (c) 2002 - 2005, Intel Corporation +// All rights reserved. +// +// Contributed 2002 by the Intel Numerics Group, Intel Corporation +// +// Redistribution and use in source and binary forms, with or without +// modification, are permitted provided that the following conditions are +// met: +// +// * Redistributions of source code must retain the above copyright +// notice, this list of conditions and the following disclaimer. +// +// * Redistributions in binary form must reproduce the above copyright +// notice, this list of conditions and the following disclaimer in the +// documentation and/or other materials provided with the distribution. +// +// * The name of Intel Corporation may not be used to endorse or promote +// products derived from this software without specific prior written +// permission. + +// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS +// "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT +// LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR +// A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL INTEL OR ITS +// CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, +// EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, +// PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR +// PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY +// OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY OR TORT (INCLUDING +// NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS +// SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. +// +// Intel Corporation is the author of this code, and requests that all +// problem reports or change requests be submitted to it directly at +// http://www.intel.com/software/products/opensource/libraries/num.htm. +// +// History +//============================================================== +// 01/16/02 Initial version +// 05/20/02 Cleaned up namespace and sf0 syntax +// 02/10/03 Reordered header: .section, .global, .proc, .align; +// used data8 for long double table values +// 03/17/03 Moved tgammal_libm_err label into .proc region +// 04/10/03 Changed error codes for overflow and negative integers +// 03/31/05 Reformatted delimiters between data tables +// +// API +//============================================================== +// long double tgammal(long double) +// +// Resources Used: +// +// Floating-Point Registers: f8-f15 +// f32-f127 +// +// General Purpose Registers: r32-r67 +// +// Predicate Registers: p6-p15 +// +//********************************************************************* +// +// IEEE Special Conditions: +// +// tgammal(+inf) = +inf +// tgammal(-inf) = QNaN +// tgammal(+/-0) = +/-inf +// tgammal(x<0, x - integer) = QNaN +// tgammal(SNaN) = QNaN +// tgammal(QNaN) = QNaN +// +//********************************************************************* +// Overview of operation +//============================================================== +// +// Algorithm description +// --------------------- +// +// There are 3 main paths in the implementation +// (and additional special values branches) +// +// 1) |X| >= 13 - Stirling formula computation +// a) Positive arguments: +// TGAMMAL(X) = exp((X-0.5)*ln(X) - X + C + S(Z)), +// where C = 0.5*ln(2*Pi) , Z = 1/Z, S(Z) - Bernulli polynomial +// (up to 'B18' term). +// Some of these calculation done in multiprecision. +// Ln returns multiprecision result too +// and exp also accepts and returns pair of values. +// +// b) Negative arguments +// TGAMMAL(-X) = PI/(X*TGAMMAL(X)*sin(PI*X)). +// (X*sin(PI*X))/PI calculated in parallel with TGAMMAL. +// Here we use polynomial of 9th degree with 2 multiprecision steps. +// Argument range reduction is: +// N = [x] with round to nearest, r = x - N, -0.5 <= r < 0.5 +// After ((X-0.5)*ln(X) - X + C + S(Z)) completed we just invert +// its result and compute exp with negative argument (1/exp(x)=exp(-x)) +// Then we multiply exp result to PI/(X*sin(PI*X)). +// +// 2) 1 <= |X| < 13 - Polynomial part +// a) Positive arguments: +// All values are splitted to such intervals as: +// #0->[2;3], #1->[3,4], #2->[5,6]... +// For even intervals we just use polynomial computation with degree 20 +// and first 6 multiprecision computations. +// Range reduction looks like +// N = [x] with truncate, r = x - N - 0.5, -0.5 <= r < 0.5 +// For odd intervals we use reccurent formula: +// TGAMMAL(X) = TGAMMA(X-1)*(X-1) +// [1;2] interval is splitted to 3 subranges: +// [1;1.25], [1.25;1.75], [1.75;2] with the same polynomial forms +// +// b) Negative arguments +// TGAMMAL(-X) = PI/(X*TGAMMAL(X)*sin(PI*X)). +// (X*sin(PI*X))/PI calculated in parallel with TGAMMAL. +// After multiplication by TGAMMAL(X) result we calculate reciprocal +// and get final result. +// +// 3) 0 < |X| < 1 - Near 0 part +// a) Here we use reccurent formula TGAMMAL(X) = TGAMMAL(X+1)/X +// TGAMMAL(X+1) calculated as shown above, +// 1/X result obtained in parallel. Then we just multiply these values. +// There is only additional separated subrange: [0;0.125] with specific +// polynomial constants set. +// +// b) Negative arguments +// TGAMMAL(-X) = PI/(TGAMMAL(X+1)*sin(PI*X)). +// There is no need to compute 1/X. + + + +RODATA + +.align 16 +LOCAL_OBJECT_START(Constants_Tgammal_log_80_Q) +// log2_hi, log2_lo, Q_6, Q_5, Q_4, Q_3, Q_2, Q_1 +data4 0x00000000,0xB1721800,0x00003FFE,0x00000000 +data4 0x4361C4C6,0x82E30865,0x0000BFE2,0x00000000 +data4 0xA51BE0AF,0x92492453,0x00003FFC,0x00000000 +data4 0xA0CFD29F,0xAAAAAB73,0x0000BFFC,0x00000000 +data4 0xCCCE3872,0xCCCCCCCC,0x00003FFC,0x00000000 +data4 0xFFFFB4FB,0xFFFFFFFF,0x0000BFFC,0x00000000 +data4 0xAAAAAAAB,0xAAAAAAAA,0x00003FFD,0x00000000 +data4 0x00000000,0x80000000,0x0000BFFE,0x00000000 +LOCAL_OBJECT_END(Constants_Tgammal_log_80_Q) + +.align 64 +LOCAL_OBJECT_START(Constants_Tgammal_log_80_Z_G_H_h1) +// Z1 - 16 bit fixed, G1 and H1 IEEE single, h1 IEEE double +data4 0x00008000,0x3F800000,0x00000000,0x00000000 +data4 0x00000000,0x00000000,0x00000000,0x00000000 +data4 0x00007879,0x3F70F0F0,0x3D785196,0x00000000 +data4 0xEBA0E0D1,0x8B1D330B,0x00003FDA,0x00000000 +data4 0x000071C8,0x3F638E38,0x3DF13843,0x00000000 +data4 0x9EADD553,0xE2AF365E,0x00003FE2,0x00000000 +data4 0x00006BCB,0x3F579430,0x3E2FF9A0,0x00000000 +data4 0x752F34A2,0xF585FEC3,0x0000BFE3,0x00000000 +data4 0x00006667,0x3F4CCCC8,0x3E647FD6,0x00000000 +data4 0x893B03F3,0xF3546435,0x00003FE2,0x00000000 +data4 0x00006187,0x3F430C30,0x3E8B3AE7,0x00000000 +data4 0x39CDD2AC,0xBABA62E0,0x00003FE4,0x00000000 +data4 0x00005D18,0x3F3A2E88,0x3EA30C68,0x00000000 +data4 0x457978A1,0x8718789F,0x00003FE2,0x00000000 +data4 0x0000590C,0x3F321640,0x3EB9CEC8,0x00000000 +data4 0x3185E56A,0x9442DF96,0x0000BFE4,0x00000000 +data4 0x00005556,0x3F2AAAA8,0x3ECF9927,0x00000000 +data4 0x2BBE2CBD,0xCBF9A4BF,0x00003FE4,0x00000000 +data4 0x000051EC,0x3F23D708,0x3EE47FC5,0x00000000 +data4 0x852D5935,0xF3537535,0x00003FE3,0x00000000 +data4 0x00004EC5,0x3F1D89D8,0x3EF8947D,0x00000000 +data4 0x46CDF32F,0xA1F1E699,0x0000BFDF,0x00000000 +data4 0x00004BDB,0x3F17B420,0x3F05F3A1,0x00000000 +data4 0xD8484CE3,0x84A61856,0x00003FE4,0x00000000 +data4 0x00004925,0x3F124920,0x3F0F4303,0x00000000 +data4 0xFF28821B,0xC7DD97E0,0x0000BFE2,0x00000000 +data4 0x0000469F,0x3F0D3DC8,0x3F183EBF,0x00000000 +data4 0xEF1FD32F,0xD3C4A887,0x00003FE3,0x00000000 +data4 0x00004445,0x3F088888,0x3F20EC80,0x00000000 +data4 0x464C76DA,0x84672BE6,0x00003FE5,0x00000000 +data4 0x00004211,0x3F042108,0x3F29516A,0x00000000 +data4 0x18835FB9,0x9A43A511,0x0000BFE5,0x00000000 +LOCAL_OBJECT_END(Constants_Tgammal_log_80_Z_G_H_h1) + +.align 64 +LOCAL_OBJECT_START(Constants_Tgammal_log_80_Z_G_H_h2) +// Z2 - 16 bit fixed, G2 and H2 IEEE single, h2 IEEE double +data4 0x00008000,0x3F800000,0x00000000,0x00000000 +data4 0x00000000,0x00000000,0x00000000,0x00000000 +data4 0x00007F81,0x3F7F00F8,0x3B7F875D,0x00000000 +data4 0x211398BF,0xAD08B116,0x00003FDB,0x00000000 +data4 0x00007F02,0x3F7E03F8,0x3BFF015B,0x00000000 +data4 0xC376958E,0xB106790F,0x00003FDE,0x00000000 +data4 0x00007E85,0x3F7D08E0,0x3C3EE393,0x00000000 +data4 0x79A7679A,0xFD03F242,0x0000BFDA,0x00000000 +data4 0x00007E08,0x3F7C0FC0,0x3C7E0586,0x00000000 +data4 0x05E7AE08,0xF03F81C3,0x0000BFDF,0x00000000 +data4 0x00007D8D,0x3F7B1880,0x3C9E75D2,0x00000000 +data4 0x049EB22F,0xD1B87D3C,0x00003FDE,0x00000000 +data4 0x00007D12,0x3F7A2328,0x3CBDC97A,0x00000000 +data4 0x3A9E81E0,0xFABC8B95,0x00003FDF,0x00000000 +data4 0x00007C98,0x3F792FB0,0x3CDCFE47,0x00000000 +data4 0x7C4B5443,0xF5F3653F,0x00003FDF,0x00000000 +data4 0x00007C20,0x3F783E08,0x3CFC15D0,0x00000000 +data4 0xF65A1773,0xE78AB204,0x00003FE0,0x00000000 +data4 0x00007BA8,0x3F774E38,0x3D0D874D,0x00000000 +data4 0x7B8EF695,0xDB7CBFFF,0x0000BFE0,0x00000000 +data4 0x00007B31,0x3F766038,0x3D1CF49B,0x00000000 +data4 0xCF773FB3,0xC0241AEA,0x0000BFE0,0x00000000 +data4 0x00007ABB,0x3F757400,0x3D2C531D,0x00000000 +data4 0xC9539FDF,0xFC8F4D48,0x00003FE1,0x00000000 +data4 0x00007A45,0x3F748988,0x3D3BA322,0x00000000 +data4 0x954665C2,0x9CD035FB,0x0000BFE1,0x00000000 +data4 0x000079D1,0x3F73A0D0,0x3D4AE46F,0x00000000 +data4 0xDD367A30,0xEC9017C7,0x00003FE1,0x00000000 +data4 0x0000795D,0x3F72B9D0,0x3D5A1756,0x00000000 +data4 0xCB11189C,0xEE6625D3,0x0000BFE1,0x00000000 +data4 0x000078EB,0x3F71D488,0x3D693B9D,0x00000000 +data4 0xBE11C424,0xA49C8DB5,0x0000BFE0,0x00000000 +LOCAL_OBJECT_END(Constants_Tgammal_log_80_Z_G_H_h2) + +.align 64 +LOCAL_OBJECT_START(Constants_Tgammal_log_80_h3_G_H) +// h3 IEEE double extended, H3 and G3 IEEE single +data4 0x112666B0,0xAAACAAB1,0x00003FD3,0x3F7FFC00 +data4 0x9B7FAD21,0x90051030,0x00003FD8,0x3F7FF400 +data4 0xF4D783C4,0xA6B46F46,0x00003FDA,0x3F7FEC00 +data4 0x11C6DDCA,0xDA148D88,0x0000BFD8,0x3F7FE400 +data4 0xCA964D95,0xCE65C1D8,0x0000BFD8,0x3F7FDC00 +data4 0x23412D13,0x883838EE,0x0000BFDB,0x3F7FD400 +data4 0x983ED687,0xB7E5CFA1,0x00003FDB,0x3F7FCC08 +data4 0xE3C3930B,0xDBE23B16,0x0000BFD9,0x3F7FC408 +data4 0x48AA4DFC,0x9B92F1FC,0x0000BFDC,0x3F7FBC10 +data4 0xCE9C8F7E,0x9A8CEB15,0x0000BFD9,0x3F7FB410 +data4 0x0DECE74A,0x8C220879,0x00003FDC,0x3F7FAC18 +data4 0x2F053150,0xB25CA912,0x0000BFDA,0x3F7FA420 +data4 0xD9A5BE20,0xA5876555,0x00003FDB,0x3F7F9C20 +data4 0x2053F087,0xC919BB6E,0x00003FD9,0x3F7F9428 +data4 0x041E9A77,0xB70BDA79,0x00003FDC,0x3F7F8C30 +data4 0xEA1C9C30,0xF18A5C08,0x00003FDA,0x3F7F8438 +data4 0x796D89E5,0xA3790D84,0x0000BFDD,0x3F7F7C40 +data4 0xA2915A3A,0xE1852369,0x0000BFDD,0x3F7F7448 +data4 0xA39ED868,0xD803858F,0x00003FDC,0x3F7F6C50 +data4 0x9417EBB7,0xB2EEE356,0x0000BFDD,0x3F7F6458 +data4 0x9BB0D07F,0xED5C1F8A,0x0000BFDC,0x3F7F5C68 +data4 0xE87C740A,0xD6D201A0,0x0000BFDD,0x3F7F5470 +data4 0x1CA74025,0xE8DEBF5E,0x00003FDC,0x3F7F4C78 +data4 0x1F34A7EB,0x9A995A97,0x0000BFDC,0x3F7F4488 +data4 0x359EED97,0x9CB0F742,0x0000BFDA,0x3F7F3C90 +data4 0xBBC6A1C8,0xD6F833C2,0x0000BFDD,0x3F7F34A0 +data4 0xE71090EC,0xE1F68F2A,0x00003FDC,0x3F7F2CA8 +data4 0xC160A74F,0xD1881CF1,0x0000BFDB,0x3F7F24B8 +data4 0xD78CB5A4,0x9AD05AE2,0x00003FD6,0x3F7F1CC8 +data4 0x9A77DC4B,0xE658CB8E,0x0000BFDD,0x3F7F14D8 +data4 0x6BD6D312,0xBA281296,0x00003FDC,0x3F7F0CE0 +data4 0xF95210D0,0xB478BBEB,0x0000BFDB,0x3F7F04F0 +data4 0x38800100,0x39400480,0x39A00640,0x39E00C41 // H's start here +data4 0x3A100A21,0x3A300F22,0x3A4FF51C,0x3A6FFC1D +data4 0x3A87F20B,0x3A97F68B,0x3AA7EB86,0x3AB7E101 +data4 0x3AC7E701,0x3AD7DD7B,0x3AE7D474,0x3AF7CBED +data4 0x3B03E1F3,0x3B0BDE2F,0x3B13DAAA,0x3B1BD766 +data4 0x3B23CC5C,0x3B2BC997,0x3B33C711,0x3B3BBCC6 +data4 0x3B43BAC0,0x3B4BB0F4,0x3B53AF6D,0x3B5BA620 +data4 0x3B639D12,0x3B6B9444,0x3B7393BC,0x3B7B8B6D +LOCAL_OBJECT_END(Constants_Tgammal_log_80_h3_G_H) + +.align 64 +LOCAL_OBJECT_START(Constants_Tgammal_stirling) +//0.5*ln(2*Pi)=9.1893853320467266954096885e-01 + 7.2239360881843238220057778e-17 +data8 0x3FED67F1C864BEB4, 0x3C94D252F2400510 +// Bernulli numbers +data8 0xAAAAAAAAAAAAAAAB, 0x00003FFB //B2 = 8.3333333333333333333333333333e-02 +data8 0xBF66C16C16C16C17 //B4 = -2.7777777777777777777777777778e-03 +data8 0x3F4A01A01A01A01A //B6 = 7.9365079365079365079365079365e-04 +data8 0xBF43813813813814 //B8 = -5.9523809523809523809523809524e-04 +data8 0x3F4B951E2B18FF23 //B10 = 8.4175084175084175084175084175e-04 +data8 0xBF5F6AB0D9993C7D //B12 = -1.9175269175269175269175269175e-03 +data8 0x3F7A41A41A41A41A //B14 = 6.4102564102564102564102564103e-03 +data8 0xBF9E4286CB0F5398 //B16 = -2.9550653594771241830065359477e-02 +data8 0x3FC6FE96381E0680 //B18 = 1.7964437236883057316493849002e-01 +data8 0x3FE0000000000000 // 0.5 +LOCAL_OBJECT_END(Constants_Tgammal_stirling) + +.align 64 +LOCAL_OBJECT_START(Constants_Tgammal_sin) +// Polynomial coefficients for the sin(Pi*x)/Pi, 0 <= |x| < 0.5 +//A2 = 8.1174242528335360802316245099e-01 + 5.1302254650266899774269946201e-18 +data8 0x3FE9F9CB402BC46C, 0x3C57A8B3819B7CEC +//A1 = -1.6449340668482264060656916627e+00 + -3.0210280454695477893051351574e-17 +data8 0xBFFA51A6625307D3, 0xBC816A402079D0EF +data8 0xF3AEF1FFCCE6C813, 0x0000BFE3 //A9 = -7.0921197799923779127089910470e-09 +data8 0x87D54408E6D4BB9D, 0x00003FE9 //A8 = 2.5300880778252693946712766029e-07 +data8 0xEA12033DCE7B8ED9, 0x0000BFED //A7 = -6.9758403885461690048189307819e-06 +data8 0x9BA38C952A59D1A8, 0x00003FF2 //A6 = 1.4842878710882320255092707181e-04 +data8 0x99C0B55178FF0E38, 0x0000BFF6 //A5 = -2.3460810348048124421268761990e-03 +data8 0xD63402E798FEC896, 0x00003FF9 //A4 = 2.6147847817611456327417812320e-02 +data8 0xC354723906D95E92, 0x0000BFFC //A3 = -1.9075182412208257558294507774e-01 +LOCAL_OBJECT_END(Constants_Tgammal_sin) + +.align 64 +LOCAL_OBJECT_START(Constants_Tgammal_exp_64_Arg) +data4 0x00000000,0xB17217F4,0x00003FF2,0x00000000 // L_hi = hi part log(2)/2^12 +data4 0xF278ECE6,0xF473DE6A,0x00003FD4,0x00000000 // L_lo = lo part log(2)/2^12 +LOCAL_OBJECT_END(Constants_Tgammal_exp_64_Arg) + +LOCAL_OBJECT_START(Constants_Tgammal_exp_64_A) +data4 0xB1B736A0,0xAAAAAAAB,0x00003FFA,0x00000000 // A3 +data4 0x90CD6327,0xAAAAAAAB,0x00003FFC,0x00000000 // A2 +data4 0xFFFFFFFF,0xFFFFFFFF,0x00003FFD,0x00000000 // A1 +LOCAL_OBJECT_END(Constants_Tgammal_exp_64_A) + +LOCAL_OBJECT_START(Constants_Tgammal_exp_64_T1) +data4 0x3F800000,0x3F8164D2,0x3F82CD87,0x3F843A29 +data4 0x3F85AAC3,0x3F871F62,0x3F88980F,0x3F8A14D5 +data4 0x3F8B95C2,0x3F8D1ADF,0x3F8EA43A,0x3F9031DC +data4 0x3F91C3D3,0x3F935A2B,0x3F94F4F0,0x3F96942D +data4 0x3F9837F0,0x3F99E046,0x3F9B8D3A,0x3F9D3EDA +data4 0x3F9EF532,0x3FA0B051,0x3FA27043,0x3FA43516 +data4 0x3FA5FED7,0x3FA7CD94,0x3FA9A15B,0x3FAB7A3A +data4 0x3FAD583F,0x3FAF3B79,0x3FB123F6,0x3FB311C4 +data4 0x3FB504F3,0x3FB6FD92,0x3FB8FBAF,0x3FBAFF5B +data4 0x3FBD08A4,0x3FBF179A,0x3FC12C4D,0x3FC346CD +data4 0x3FC5672A,0x3FC78D75,0x3FC9B9BE,0x3FCBEC15 +data4 0x3FCE248C,0x3FD06334,0x3FD2A81E,0x3FD4F35B +data4 0x3FD744FD,0x3FD99D16,0x3FDBFBB8,0x3FDE60F5 +data4 0x3FE0CCDF,0x3FE33F89,0x3FE5B907,0x3FE8396A +data4 0x3FEAC0C7,0x3FED4F30,0x3FEFE4BA,0x3FF28177 +data4 0x3FF5257D,0x3FF7D0DF,0x3FFA83B3,0x3FFD3E0C +LOCAL_OBJECT_END(Constants_Tgammal_exp_64_T1) + +LOCAL_OBJECT_START(Constants_Tgammal_exp_64_T2) +data4 0x3F800000,0x3F80058C,0x3F800B18,0x3F8010A4 +data4 0x3F801630,0x3F801BBD,0x3F80214A,0x3F8026D7 +data4 0x3F802C64,0x3F8031F2,0x3F803780,0x3F803D0E +data4 0x3F80429C,0x3F80482B,0x3F804DB9,0x3F805349 +data4 0x3F8058D8,0x3F805E67,0x3F8063F7,0x3F806987 +data4 0x3F806F17,0x3F8074A8,0x3F807A39,0x3F807FCA +data4 0x3F80855B,0x3F808AEC,0x3F80907E,0x3F809610 +data4 0x3F809BA2,0x3F80A135,0x3F80A6C7,0x3F80AC5A +data4 0x3F80B1ED,0x3F80B781,0x3F80BD14,0x3F80C2A8 +data4 0x3F80C83C,0x3F80CDD1,0x3F80D365,0x3F80D8FA +data4 0x3F80DE8F,0x3F80E425,0x3F80E9BA,0x3F80EF50 +data4 0x3F80F4E6,0x3F80FA7C,0x3F810013,0x3F8105AA +data4 0x3F810B41,0x3F8110D8,0x3F81166F,0x3F811C07 +data4 0x3F81219F,0x3F812737,0x3F812CD0,0x3F813269 +data4 0x3F813802,0x3F813D9B,0x3F814334,0x3F8148CE +data4 0x3F814E68,0x3F815402,0x3F81599C,0x3F815F37 +LOCAL_OBJECT_END(Constants_Tgammal_exp_64_T2) + +LOCAL_OBJECT_START(Constants_Tgammal_exp_64_W1) +data8 0x0000000000000000, 0xBE384454171EC4B4 +data8 0xBE6947414AA72766, 0xBE5D32B6D42518F8 +data8 0x3E68D96D3A319149, 0xBE68F4DA62415F36 +data8 0xBE6DDA2FC9C86A3B, 0x3E6B2E50F49228FE +data8 0xBE49C0C21188B886, 0x3E64BFC21A4C2F1F +data8 0xBE6A2FBB2CB98B54, 0x3E5DC5DE9A55D329 +data8 0x3E69649039A7AACE, 0x3E54728B5C66DBA5 +data8 0xBE62B0DBBA1C7D7D, 0x3E576E0409F1AF5F +data8 0x3E6125001A0DD6A1, 0xBE66A419795FBDEF +data8 0xBE5CDE8CE1BD41FC, 0xBE621376EA54964F +data8 0x3E6370BE476E76EE, 0x3E390D1A3427EB92 +data8 0x3E1336DE2BF82BF8, 0xBE5FF1CBD0F7BD9E +data8 0xBE60A3550CEB09DD, 0xBE5CA37E0980F30D +data8 0xBE5C541B4C082D25, 0xBE5BBECA3B467D29 +data8 0xBE400D8AB9D946C5, 0xBE5E2A0807ED374A +data8 0xBE66CB28365C8B0A, 0x3E3AAD5BD3403BCA +data8 0x3E526055C7EA21E0, 0xBE442C75E72880D6 +data8 0x3E58B2BB85222A43, 0xBE5AAB79522C42BF +data8 0xBE605CB4469DC2BC, 0xBE589FA7A48C40DC +data8 0xBE51C2141AA42614, 0xBE48D087C37293F4 +data8 0x3E367A1CA2D673E0, 0xBE51BEBB114F7A38 +data8 0xBE6348E5661A4B48, 0xBDF526431D3B9962 +data8 0x3E3A3B5E35A78A53, 0xBE46C46C1CECD788 +data8 0xBE60B7EC7857D689, 0xBE594D3DD14F1AD7 +data8 0xBE4F9C304C9A8F60, 0xBE52187302DFF9D2 +data8 0xBE5E4C8855E6D68F, 0xBE62140F667F3DC4 +data8 0xBE36961B3BF88747, 0x3E602861C96EC6AA +data8 0xBE3B5151D57FD718, 0x3E561CD0FC4A627B +data8 0xBE3A5217CA913FEA, 0x3E40A3CC9A5D193A +data8 0xBE5AB71310A9C312, 0x3E4FDADBC5F57719 +data8 0x3E361428DBDF59D5, 0x3E5DB5DB61B4180D +data8 0xBE42AD5F7408D856, 0x3E2A314831B2B707 +LOCAL_OBJECT_END(Constants_Tgammal_exp_64_W1) + +LOCAL_OBJECT_START(Constants_Tgammal_exp_64_W2) +data8 0x0000000000000000, 0xBE641F2537A3D7A2 +data8 0xBE68DD57AD028C40, 0xBE5C77D8F212B1B6 +data8 0x3E57878F1BA5B070, 0xBE55A36A2ECAE6FE +data8 0xBE620608569DFA3B, 0xBE53B50EA6D300A3 +data8 0x3E5B5EF2223F8F2C, 0xBE56A0D9D6DE0DF4 +data8 0xBE64EEF3EAE28F51, 0xBE5E5AE2367EA80B +data8 0x3E47CB1A5FCBC02D, 0xBE656BA09BDAFEB7 +data8 0x3E6E70C6805AFEE7, 0xBE6E0509A3415EBA +data8 0xBE56856B49BFF529, 0x3E66DD3300508651 +data8 0x3E51165FC114BC13, 0x3E53333DC453290F +data8 0x3E6A072B05539FDA, 0xBE47CD877C0A7696 +data8 0xBE668BF4EB05C6D9, 0xBE67C3E36AE86C93 +data8 0xBE533904D0B3E84B, 0x3E63E8D9556B53CE +data8 0x3E212C8963A98DC8, 0xBE33138F032A7A22 +data8 0x3E530FA9BC584008, 0xBE6ADF82CCB93C97 +data8 0x3E5F91138370EA39, 0x3E5443A4FB6A05D8 +data8 0x3E63DACD181FEE7A, 0xBE62B29DF0F67DEC +data8 0x3E65C4833DDE6307, 0x3E5BF030D40A24C1 +data8 0x3E658B8F14E437BE, 0xBE631C29ED98B6C7 +data8 0x3E6335D204CF7C71, 0x3E529EEDE954A79D +data8 0x3E5D9257F64A2FB8, 0xBE6BED1B854ED06C +data8 0x3E5096F6D71405CB, 0xBE3D4893ACB9FDF5 +data8 0xBDFEB15801B68349, 0x3E628D35C6A463B9 +data8 0xBE559725ADE45917, 0xBE68C29C042FC476 +data8 0xBE67593B01E511FA, 0xBE4A4313398801ED +data8 0x3E699571DA7C3300, 0x3E5349BE08062A9E +data8 0x3E5229C4755BB28E, 0x3E67E42677A1F80D +data8 0xBE52B33F6B69C352, 0xBE6B3550084DA57F +data8 0xBE6DB03FD1D09A20, 0xBE60CBC42161B2C1 +data8 0x3E56ED9C78A2B771, 0xBE508E319D0FA795 +data8 0xBE59482AFD1A54E9, 0xBE2A17CEB07FD23E +data8 0x3E68BF5C17365712, 0x3E3956F9B3785569 +LOCAL_OBJECT_END(Constants_Tgammal_exp_64_W2) + + + +LOCAL_OBJECT_START(Constants_Tgammal_poly) + +// Polynomial coefficients for the tgammal(x), 2 <= |x| < 3 +//A5 = 2.8360780594841213109180699803e-02 + 2.2504152891014320704380000000e-19 +data8 0x3F9D0A9BC49353D2, 0x3C109AEA0F23CE2D +//A4 = 1.0967323400216015538699565468e-01 + 9.9225166000430644587276000000e-18 +data8 0x3FBC138B89492C5B, 0x3C66E138506D5652 +//A3 = 2.5387124684114281691904579930e-01 + 2.2667777637607113205546600000e-17 +data8 0x3FD03F6D2FA4F4F8, 0x3C7A2258DA8CD8B1 +data8 0xC5866457328BC39B, 0x00003FE3 //A20 = 5.7487331964156762795056629138e-09 +data8 0xE93D9F1ACD59C929, 0x0000BFE4 //A19= -1.3576396100397317396956445658e-08 +data8 0xE33389C8F6CBA813, 0x00003FE5 //A18 = 2.6449714924964597501721434271e-08 +data8 0x8FE7B25B9CD26D2A, 0x0000BFE7 //A17= -6.7011017946055513660266853311e-08 +data8 0xB89F4721BFBC15B0, 0x00003FE8 //A16 = 1.7194280320370423615174419192e-07 +data8 0xE49CBDC1874EBABA, 0x0000BFE9 //A15= -4.2582353660153782928729466776e-07 +data8 0x913AF50A336129CA, 0x00003FEB //A14 = 1.0820500665257088283172211622e-06 +data8 0xABCF0F7313B3B332, 0x0000BFEC //A13= -2.5601510627710417669568115706e-06 +//A2 = 6.5455857798133676439533701341e-01 + 1.3292075193155190798867000000e-18 +data8 0x3FE4F224D4B7E01C, 0x3C3885014A2B8319 +//A1 = 9.3473452162608550164435428087e-01 + 3.2785154201417136611642400000e-17 +data8 0x3FEDE9585F1A7093, 0x3C82E63C1B5028BF +//A0 = 1.3293403881791368004172682049e+00 + 2.2005689328949279282607500000e-16 +data8 0x3FF544FA6D47B38F, 0x3CAFB6AA9829E81F +data8 0xF3668F799997C76D, 0x00003FED //A12 = 7.2539039479124273660331538367e-06 +data8 0xD6C6BBD54CDEAEB1, 0x0000BFEE //A11= -1.2801665282681088568639378920e-05 +data8 0x809E4763B06F6883, 0x00003FF1 //A10 = 6.1329973609906572700697893187e-05 +data8 0x8443B000F8F9A71A, 0x00003FED //A9 = 3.9417864189995544394564413428e-06 +data8 0xC5C7E6D62A6991D8, 0x00003FF4 //A8 = 7.5447412886334708803357581519e-04 +data8 0xD2AF690725C62D88, 0x00003FF5 //A7 = 1.6074004848394703022110823298e-03 +data8 0xAA44E635D4B7B682, 0x00003FF8 //A6 = 1.0392403425906843901680697839e-02 +// +// Polynomial coefficients for the tgammal(x), 4 <= |x| < 5 +//A5 = 1.1600674810589555185913468449e+00 + 3.0229979112715124660731000000e-17 +data8 0x3FF28FA2EB44D22E, 0x3C816D285234C815 +//A4 = 3.1374268565470946334983182169e+00 + 1.3694868953995008497659600000e-16 +data8 0x400919734073B1E1, 0x3CA3BC83CD7E9565 +//A3 = 7.0834593993741057360580271052e+00 + 3.3899702569039156457249800000e-16 +data8 0x401C5576617B6C1F, 0x3CB86D6431213296 +data8 0xA4A5FB49C094966B, 0x00003FDA //A20 = 9.3591760106637809309720130828e-12 +data8 0xA9260DA0F51D7ED8, 0x00003FDD //A19 = 7.6919898428091669411809372180e-11 +data8 0xA16441DFB14BD6E1, 0x00003FE0 //A18 = 5.8713933014370867331213494535e-10 +data8 0x95F098D9C2234849, 0x00003FE3 //A17 = 4.3638234584169302324461091035e-09 +data8 0x8581817400E5AD2B, 0x00003FE6 //A16 = 3.1084260332429955234755367839e-08 +data8 0xE272940E373EBE15, 0x00003FE8 //A15 = 2.1089573544273993580820317236e-07 +data8 0xB6B3391145D226FB, 0x00003FEB //A14 = 1.3612217421122787182942706259e-06 +data8 0x8B9428C4DF95FCD5, 0x00003FEE //A13 = 8.3195416382628990683949003789e-06 +//A2 = 1.2665135075272345943631080445e+01 + 9.8721896915973874255877000000e-16 +data8 0x4029548C95A76F38, 0x3CD1C8BE715B8E13 +//A1 = 1.6154969393303069580269948347e+01 + 9.6850518810678379641029000000e-16 +data8 0x403027AC12FC1E1E, 0x3CD172711C15501B +//A0 = 1.1631728396567448058362970187e+01 + 8.7078125362814179268673000000e-16 +data8 0x40274371E7866C65, 0x3CCF5F8A1A5FACA0 +data8 0xC94A903114272C03, 0x00003FF0 //A12 = 4.7991576836334427243159066630e-05 +data8 0x8844262960E04BE6, 0x00003FF3 //A11 = 2.5990716419283017929486175141e-04 +data8 0xAC5418A76767678D, 0x00003FF5 //A10 = 1.3147621245497801180184809726e-03 +data8 0xCA231B6EFE959132, 0x00003FF7 //A9 = 6.1687358811367989146517222415e-03 +data8 0xDA38E39C13819D2A, 0x00003FF9 //A8 = 2.6638454961912040754759086920e-02 +data8 0xD696DF8D8389FE53, 0x00003FFB //A7 = 1.0477995539298934056097943975e-01 +data8 0xBDD5C153048BC435, 0x00003FFD //A6 = 3.7077144754791605130056406006e-01 +// +// Polynomial coefficients for the tgammal(x), 6 <= |x| < 7 +//A5 = 6.7169398121054200601065531373e+01 + 2.9481001527213915901489600000e-15 +data8 0x4050CAD76B377BA0, 0x3CEA8DDB2B2DE93E +//A4 = 1.6115104376855398982115730178e+02 + 1.3422421925418824418257300000e-14 +data8 0x406424D559BDC687, 0x3D0E397FDB5B33DC +//A3 = 3.1812194028053562533386866562e+02 + 3.9881709875858650942409600000e-14 +data8 0x4073E1F377A6CF73, 0x3D26738F63FE9C4C +data8 0xD6E1B5FF90CAABD3, 0x00003FE1 //A20 = 1.5634700199277480081025480635e-09 +data8 0xD451987B925DD37E, 0x00003FE4 //A19 = 1.2358576813211397717382327174e-08 +data8 0xBFC151B67FA58E6B, 0x00003FE7 //A18 = 8.9292951435632759686382657901e-08 +data8 0xA9034C5E1D67572E, 0x00003FEA //A17 = 6.2962205718327848327368724720e-07 +data8 0x8E40F6EAA30A71EC, 0x00003FED //A16 = 4.2394926442967995119170095258e-06 +data8 0xE3C3541B03A1C350, 0x00003FEF //A15 = 2.7151465666109594512258841637e-05 +data8 0xACE2E58436B2DDCE, 0x00003FF2 //A14 = 1.6487723793339152877117376243e-04 +data8 0xF7EAF8D8D1CAA3D1, 0x00003FF4 //A13 = 9.4573158112768812533636022369e-04 +//A2 = 4.8664351544258869353143381886e+02 + 4.7424047995944376868895400000e-14 +data8 0x407E6A4BD6D9463B, 0x3D2AB2868D79E192 +//A1 = 5.1615277644992545447166776285e+02 + 3.0901956935588717379242200000e-14 +data8 0x40802138E2DC003B, 0x3D216570FB601AEA +//A0 = 2.8788527781504433278314536437e+02 + 2.8213174117085164944959600000e-14 +data8 0x4071FE2A1911F7D6, 0x3D1FC3E4CF4DB5AF +data8 0xA72B88E48D3D1BAB, 0x00003FF7 //A12 = 5.1016252919939028020562237471e-03 +data8 0xD2EFB1067DB4FFB2, 0x00003FF9 //A11 = 2.5749059441230515023024615917e-02 +data8 0xF788AF9522205C24, 0x00003FFB //A10 = 1.2086617635601742290221382521e-01 +data8 0x861A6CE06CB29EAF, 0x00003FFE //A9 = 5.2384071807018493367136112163e-01 +data8 0x84FBDE0947718B58, 0x00004000 //A8 = 2.0778727617851237754568261869e+00 +data8 0xEEC1371E265A2C3A, 0x00004001 //A7 = 7.4610858525146049022238037342e+00 +data8 0xBF514B9BE68ED59D, 0x00004003 //A6 = 2.3914694993947572859629197920e+01 +// +// Polynomial coefficients for the tgammal(x), 8 <= |x| < 9 +//A5 = 5.8487447114416836484451778233e+03 + 4.7365465221455983144182900000e-13 +data8 0x40B6D8BEA568B6FD, 0x3D60AA4D44C2589B +//A4 = 1.2796464063087094473303295672e+04 + 1.2373341702514898266244200000e-12 +data8 0x40C8FE3B666B532D, 0x3D75C4752C5B4783 +//A3 = 2.2837606581322281272150576115e+04 + 2.6598064610627891398831000000e-13 +data8 0x40D64D66D23A7764, 0x3D52B77B3A10EA5C +data8 0xB23418F75B0BE22A, 0x00003FE9 //A20 = 3.3192989594206801808678663868e-07 +data8 0xA984A7BC8B856ED2, 0x00003FEC //A19 = 2.5260177918662350066375115788e-06 +data8 0x921A49729416372C, 0x00003FEF //A18 = 1.7416797068239475136398213598e-05 +data8 0xF5BB9415CC399CA4, 0x00003FF1 //A17 = 1.1717449586392814601938207599e-04 +data8 0xC50B91A40B81F9DF, 0x00003FF4 //A16 = 7.5166775151159345732094429036e-04 +data8 0x96002572326DB203, 0x00003FF7 //A15 = 4.5776541559407384162139204300e-03 +data8 0xD81A1A595E4157BA, 0x00003FF9 //A14 = 2.6379634345126284099420760736e-02 +data8 0x92B700D0CFECADD8, 0x00003FFC //A13 = 1.4327622675407940907282658100e-01 +//A2 = 3.1237895525940199149772524834e+04 + 3.1280450505163186432331700000e-12 +data8 0x40DE8179504C0878, 0x3D8B83BB33FBB766 +//A1 = 2.9192841741344487672904506326e+04 + 7.9300780509779689630767000000e-13 +data8 0x40DC8235DF171691, 0x3D6BE6C780EE54DF +//A0 = 1.4034407293483411194756627083e+04 + 1.4038139346291543309253700000e-12 +data8 0x40CB693422315F90, 0x3D78B23746113FCE +data8 0xBAE50807548BC711, 0x00003FFE //A12 = 7.3005724123917935346868107005e-01 +data8 0xDE28B1F57E68CFB6, 0x00004000 //A11 = 3.4712338349724065462763671443e+00 +data8 0xF4DCA5A5FF901118, 0x00004002 //A10 = 1.5303868912154033908205911714e+01 +data8 0xF85AAA1AD5E84E5E, 0x00004004 //A9 = 6.2088539523416399361048051373e+01 +data8 0xE5AA8BB1BF02934D, 0x00004006 //A8 = 2.2966619406617480799195651466e+02 +data8 0xBF6CFEFD67F59845, 0x00004008 //A7 = 7.6570306334640770654588802417e+02 +data8 0x8DB5D2F001635C29, 0x0000400A //A6 = 2.2673639984182571062068713002e+03 +// +// Polynomial coefficients for the tgammal(x), 10 <= |x| < 11 +//A5 = 7.2546009516580589115619659424e+05 + 1.0343348865365065212891728822e-10 +data8 0x412623A830B99290, 0x3DDC6E7C157611C4 +//A4 = 1.4756292870840241666883230209e+06 + 8.1516565365333844166705674775e-11 +data8 0x4136842D497E56AF, 0x3DD66837E4C3F9EE +//A3 = 2.4356116926500420086085796356e+06 + 3.5508860076560925641351069404e-10 +data8 0x4142950DD8A8C1AF, 0x3DF866C8E3DD0980 +data8 0xB7FD0D1EEAC38EB4, 0x00003FF1 //A20 = 8.7732544640091602721643775932e-05 +data8 0xA9345C64AC750AE9, 0x00003FF4 //A19 = 6.4546407626804942279126469603e-04 +data8 0x8BEABC81BE1E93C9, 0x00003FF7 //A18 = 4.2699261134524096128048819443e-03 +data8 0xE1CD281EDD7315F8, 0x00003FF9 //A17 = 2.7563646660310313164706189622e-02 +data8 0xAD8A5BA6D0FD9758, 0x00003FFC //A16 = 1.6947310643831556048460963841e-01 +data8 0xFCDDA464AD3F182E, 0x00003FFE //A15 = 9.8775699098518676937088606052e-01 +data8 0xAE0DCE2F7B60D1AE, 0x00004001 //A14 = 5.4391852309591064073782104822e+00 +data8 0xE1745D9ABEB8D1A7, 0x00004003 //A13 = 2.8181819161363002758615770457e+01 +//A2 = 3.0619656223573554307222366333e+06 + 1.0819940302945474471259520006e-10 +data8 0x41475C66CFA967E4, 0x3DDDBDDB2A27334B +//A1 = 2.6099413018962685018777847290e+06 + 3.6851882860056025385268615240e-10 +data8 0x4143E98AA6A48974, 0x3DF9530D42589AB6 +//A0 = 1.1332783889487853739410638809e+06 + 1.9339350553312096248591829758e-10 +data8 0x41314ADE639225C9, 0x3DEA946DD6C2C8D3 +data8 0x88BCFAAE71812A1C, 0x00004006 //A12 = 1.3673820009490115307300592012e+02 +data8 0x9A770F5AB540A326, 0x00004008 //A11 = 6.1786031215382040427126476507e+02 +data8 0xA170C1D2C6B413FC, 0x0000400A //A10 = 2.5830473201524594051391525170e+03 +data8 0x9AE56061CB02EB55, 0x0000400C //A9 = 9.9133441230507404119297200255e+03 +data8 0x872390769650FBE2, 0x0000400E //A8 = 3.4595564309496661629764193479e+04 +data8 0xD3E5E8D6923910C1, 0x0000400F //A7 = 1.0849181904819284819615140521e+05 +data8 0x930D70602F50B754, 0x00004011 //A6 = 3.0116351174131169193070583741e+05 +// +// Polynomial coefficients for the tgammal(x), 12 <= |x| < 13 +//A5 = 1.2249876249976964294910430908e+08 + 6.0051348061679753770848000000e-09 +data8 0x419D34BB29FFC39D, 0x3E39CAB72E01818D +//A4 = 2.3482765927605420351028442383e+08 + 1.1874729051592862323641700000e-08 +data8 0x41ABFE5F168D56FA, 0x3E4980338AA7B04B +//A3 = 3.6407329688125067949295043945e+08 + 2.6657200942150363994658700000e-08 +data8 0x41B5B35150E199A5, 0x3E5C9F79C0EB5300 +data8 0xE89AE0F8D726329D, 0x00003FF9 //A20 = 2.8394164465429105626588451540e-02 +data8 0xCF90981F86E38013, 0x00003FFC //A19 = 2.0270002071785908652476845915e-01 +data8 0xA56C658079CA8C4A, 0x00003FFF //A18 = 1.2923704984019263122675412350e+00 +data8 0x80AEF96A67C5615A, 0x00004002 //A17 = 8.0427183300456238315262463506e+00 +data8 0xBE886D7529678931, 0x00004004 //A16 = 4.7633230047847868242503413461e+01 +data8 0x858EDBA4CE2F7508, 0x00004007 //A15 = 2.6711607799594541057655957154e+02 +data8 0xB0B0A3AF388274F0, 0x00004009 //A14 = 1.4135199810126975119809102782e+03 +data8 0xDBA87137988751EF, 0x0000400B //A13 = 7.0290552818218513870879313985e+03 +//A2 = 4.2828433593031734228134155273e+08 + 3.9760422293645854535247300000e-08 +data8 0x41B98719AFEE2947, 0x3E6558A17E0D3007 +//A1 = 3.4008253676084774732589721680e+08 + 1.2558352335001093116071000000e-09 +data8 0x41B4453F68C2C6EB, 0x3E159338C5BC7EC3 +//A0 = 1.3684336546556583046913146973e+08 + 2.6786516700381562934240300000e-08 +data8 0x41A05020CAEE5EA5, 0x3E5CC3058A858579 +data8 0xFF5E3940FB4BA576, 0x0000400D //A12 = 3.2687111823895439312116108631e+04 +data8 0x8A08C124C7F74B6C, 0x00004010 //A11 = 1.4134701786994123329786229006e+05 +data8 0x89D701953540BFFB, 0x00004012 //A10 = 5.6459209892773907605385652281e+05 +data8 0xFC46344B3116C3AD, 0x00004013 //A9 = 2.0666305367147234406757715163e+06 +data8 0xD183EBD7A400151F, 0x00004015 //A8 = 6.8653979211730981618367536737e+06 +data8 0x9C083A40742112F4, 0x00004017 //A7 = 2.0451444503543981795037456447e+07 +data8 0xCD3C475B1A8B6662, 0x00004018 //A6 = 5.3801245423495149598177886823e+07 +LOCAL_OBJECT_END(Constants_Tgammal_poly) + + +LOCAL_OBJECT_START(Constants_Tgammal_poly_splitted) + +// Polynomial coefficients for the tgammal(x), 1 <= |x| < 1.25 +//A5 = -9.8199506890310417350775651357e-01+ -3.2546247786122976510752200000e-17 +data8 0xBFEF6C80EC38B509, 0xBC82C2FA7A3DE3BD +//A4 = 9.8172808683439960475425323239e-01 + 4.4847611775298520359811400000e-17 +data8 0x3FEF6A51055096B0, 0x3C89DA56DE95EFE4 +//A3 = -9.0747907608088618225394839101e-01 +-1.0244057366544064435443970000e-16 +data8 0xBFED0A118F324B62, 0xBC9D86C7B9EBCFFF +data8 0xB8E3FDAA66CC738E, 0x00003FFB //A20 = 9.0278608095877488976217714815e-02 +data8 0xA76067AE1738699C, 0x0000BFFD //A19 =-3.2690738678103132837070881737e-01 +data8 0x9D66B13718408C44, 0x00003FFE //A18 = 6.1484820933424283818320582920e-01 +data8 0xD4AC67BBB4AE5599, 0x0000BFFE //A17 =-8.3075569470082063491389474937e-01 +data8 0xF1426ED1C1488DB3, 0x00003FFE //A16 = 9.4241993542644505594957058785e-01 +data8 0xFC12EB07AA6F4B6B, 0x0000BFFE //A15 =-9.8466366707947121954333549690e-01 +data8 0xFF2B32CFE5B0DDC8, 0x00003FFE //A14 = 9.9675290656677214804168895915e-01 +data8 0xFFD8E7E6FF3662EA, 0x0000BFFE //A13 =-9.9940347089360552383472582319e-01 +//A2 = 9.8905599532797250361682017683e-01 + 5.1760162410376024240867300000e-17 +data8 0x3FEFA658C23B1578, 0x3C8DD673A61F6FE7 +//A1 = -5.7721566490153275452712478000e-01+ -1.0607935612223465065923310000e-16 +data8 0xBFE2788CFC6FB618, 0xBC9E9346622D53B7 +//A0 = 9.9999999999999988897769753748e-01 + 1.1102230245372554544790880000e-16 +data8 0x3FEFFFFFFFFFFFFF, 0x3C9FFFFFFFF51E4E +data8 0xFFF360DF628F0BC9, 0x00003FFE //A12 = 9.9980740979895815468216470840e-01 +data8 0xFFEF8F9A72B40480, 0x0000BFFE //A11 = -9.9974916001038145045939523470e-01 +data8 0xFFE037B8C7E39952, 0x00003FFE //A10 = 9.9951504002809911822597567307e-01 +data8 0xFFC01E08F348BED2, 0x0000BFFE //A9 = -9.9902522772325406705059517941e-01 +data8 0xFF83DAC83119B52C, 0x00003FFE //A8 = 9.9810569179053383842734164901e-01 +data8 0xFEF9F8AB891ABB24, 0x0000BFFE //A7 = -9.9600176036720260345608796766e-01 +data8 0xFE3F0537573C8235, 0x00003FFE //A6 = 9.9314911461918778676646301341e-01 +// +// Polynomial coefficients for the tgammal(x), 1.25 <= |x| < 1.75 +//A5 = -7.7523052299853054125655660300e-02+ -1.2693512521686721504433600000e-17 +data8 0xBFB3D88CFE50601B, 0xBC6D44ED60EE2170 +//A4 = 1.4464535904462152982041800442e-01 + 2.5426820829345729856648800000e-17 +data8 0x3FC283BD374EB2A9, 0x3C7D50AC436187C3 +//A3 = -1.0729480456477220873257039102e-01+ -6.2429894945456418196551000000e-18 +data8 0xBFBB77AC1CA2EBA5, 0xBC5CCA6BCC422D41 +data8 0xF732D2689F323283, 0x00003FF2 //A20 = 2.3574688251652899567587145422e-04 +data8 0xB6B00E23DE89D13A, 0x0000BFF3 //A19 =-3.4844916488842618776630058875e-04 +data8 0xE98396FE4A1B2799, 0x00003FF3 //A18 =4.4539265198744452020440735977e-04 +data8 0xAF8D235A640DB1A2, 0x0000BFF4 //A17 =-6.6967514303333563295261178346e-04 +data8 0x8513B736C918B261, 0x00003FF5 //A16 = 1.0152970456990865810615917715e-03 +data8 0xC790A1A2C78D8E17, 0x0000BFF5 //A15 =-1.5225598630329403515321688394e-03 +data8 0x959706CFA638CDE2, 0x00003FF6 //A14 = 2.2825614575133879623648932383e-03 +data8 0xE050A6021E129860, 0x0000BFF6 //A13 =-3.4227757733947066666295285936e-03 +//A2 = 4.1481345368830113695679528973e-01 + 3.1252439808354284892632100000e-17 +data8 0x3FDA8C4DBA620D56, 0x3C82040BCB483C76 +//A1 = 3.2338397448885010387886751460e-02 + 3.4437825798552300531443100000e-18 +data8 0x3FA08EA88EE561B1, 0x3C4FC366D6C64806 +//A0 = 8.8622692545275794095971377828e-01 + 7.2689375867553992399219000000e-17 +data8 0x3FEC5BF891B4EF6A, 0x3C94F3877D311C0C +data8 0xA8275AADC09D16FC, 0x00003FF7 //A12 = 5.1316445128621071486146117136e-03 +data8 0xFBFE2CE9215267A2, 0x0000BFF7 //A11= -7.6902121820788373000579382408e-03 +data8 0xBCC8EEAB67ECD91D, 0x00003FF8 //A10 = 1.1522515369164312742737727262e-02 +data8 0x8D1614BB97E5E8C2, 0x0000BFF9 //A9 = -1.7222443097804730395560633583e-02 +data8 0xD3A963578BE291E3, 0x00003FF9 //A8 = 2.5837606456090186343624210891e-02 +data8 0x9BA7EAE64C42FDF7, 0x0000BFFA //A7 = -3.8001935555045161419575037512e-02 +data8 0xF0115BA1A77607E7, 0x00003FFA //A6 = 5.8610303817173477119764956736e-02 +// +// Polynomial coefficients for the tgammal(x), 1.75 <= |x| < 2.0 +//A5 = 2.6698206874501426502654943818e-04 + 3.4033756836921062797887300000e-20 +data8 0x3F317F3740FE2A68, 0x3BE417093234B06E +//A4 = 7.4249010753513894345090307070e-02 + 3.9810018444482764697014200000e-18 +data8 0x3FB301FBB0F25A92, 0x3C525BEFFABB622F +//A3 = -8.1576919247086265851720554565e-02+ -5.2716624487804746360745000000e-19 +data8 0xBFB4E239984650AC, 0xBC2372F1C4F276FF +data8 0xFEF3AEE71038E9A3, 0x00003FEB //A20 = 1.8995395865421509009969188571e-06 +data8 0xA11CFA2672BF876A, 0x0000BFEB //A19 =-1.2003868221414015771269244270e-06 +data8 0xF8E107215DAE2164, 0x00003FEC //A18 = 3.7085863210303833432006027217e-06 +data8 0xBCDDD3FC011EF7D6, 0x00003FEC //A17 = 2.8143303971756051015245433043e-06 +data8 0x8683C4687FA22E68, 0x00003FEE //A16 = 8.0177018464360416764308252462e-06 +data8 0xFDA09E5D33E32968, 0x00003FEE //A15 = 1.5117372062443781157389064848e-05 +data8 0xFFB00D0CFF4089B4, 0x00003FEF //A14 = 3.0480348961227424242198174995e-05 +data8 0xFEF6C39566785085, 0x00003FF0 //A13 = 6.0788135974125244644334004947e-05 +//A2 = 4.1184033042643969357854416558e-01 + 1.2103396182129232634761000000e-18 +data8 0x3FDA5B978B96BEBF, 0x3C3653AAD0A139E4 +//A1 = -4.2278433509846713445057275749e-01+ -4.9429151528135657430413000000e-18 +data8 0xBFDB0EE6072093CE, 0xBC56CB907027554F +//A0 = 1.0000000000000000000000000000e+00 + 1.0969171200000000000000000000e-31 +data8 0x3FF0000000000000, 0x3981CC6A5B20B4D5 +data8 0xFF2B7BA9A8D68C37, 0x00003FF1 //A12 = 1.2167446884801403650547161615e-04 +data8 0xFCA53468E3692EF1, 0x00003FF2 //A11 = 2.4094136329542400976250900707e-04 +data8 0x808D698A9C993615, 0x00003FF4 //A10 = 4.9038845704938303659791698883e-04 +data8 0xF10F8E3FB8BB4AFB, 0x00003FF4 //A9 = 9.1957383840999861214472423976e-04 +data8 0x89E224E42F93F005, 0x00003FF6 //A8 = 2.1039333407187324139473634747e-03 +data8 0xBAF374824937A323, 0x00003FF6 //A7 = 2.8526458211545152218493600470e-03 +data8 0xB6BF7564F52140C6, 0x00003FF8 //A6 = 1.1154045718131014476684982178e-02 +// +// Polynomial coefficients for the tgammal(x), 0.0 <= |x| < 0.125 +//A5 = -9.8199506890314514073736518185e-01+ -5.9363811993837985890950900000e-17 +data8 0xBFEF6C80EC38B67A, 0xBC911C46B447C81F +//A4 = 9.8172808683440015986576554496e-01 + 2.7457414262802803699834200000e-17 +data8 0x3FEF6A51055096B5, 0x3C7FA7FF90ACAD1F +//A3 = -9.0747907608088618225394839101e-01 + -1.0676255850934306734701780000e-16 +data8 0xBFED0A118F324B62, 0xBC9EC5AFB633438D +data8 0x9217E83FA207CB80, 0x00003FFD //A20 = 2.8533864762086088781083621561e-01 +data8 0xA8DABFA52FDF03EC, 0x0000BFFE //A19= -6.5958783896337186303285832783e-01 +data8 0xE331ED293AF39F9B, 0x00003FFE //A18 = 8.8748056656454687449654731184e-01 +data8 0xF9163C5DDB52419D, 0x0000BFFE //A17= -9.7299554149078295602977718525e-01 +data8 0xFEC0A1C672CB9265, 0x00003FFE //A16 = 9.9512683005268190987854104489e-01 +data8 0xFFD2D65B8EA7B5F4, 0x0000BFFE //A15= -9.9931087241443958201592847861e-01 +data8 0xFFF93AA39EE53445, 0x00003FFE //A14 = 9.9989668364186884793382816496e-01 +data8 0xFFFB99A9A3F5F480, 0x0000BFFE //A13= -9.9993286506283835663204999212e-01 +//A2 = 9.8905599532797250361682017683e-01 + 5.1778575360788420716540100000e-17 +data8 0x3FEFA658C23B1578, 0x3C8DD92B45408D07 +//A1 = -5.7721566490153275452712478000e-01+ -1.0607938730998824663273110000e-16 +data8 0xBFE2788CFC6FB618, 0xBC9E9346F8FDE55B +//A0 = 9.9999999999999988897769753748e-01 + 1.1102230246251564036631420000e-16 +data8 0x3FEFFFFFFFFFFFFF, 0x3C9FFFFFFFFFFFFF +data8 0xFFF7FEBB545812C1, 0x00003FFE //A12 = 9.9987785409425126648628395084e-01 +data8 0xFFF00C02E943A3F2, 0x0000BFFE //A11= -9.9975657530855116454438747397e-01 +data8 0xFFE0420AADC53820, 0x00003FFE //A10 = 9.9951565514290485919027183699e-01 +data8 0xFFC01EB42EF27EEB, 0x0000BFFE //A9 = -9.9902526759155739377365522320e-01 +data8 0xFF83DAD0BF23FF12, 0x00003FFE //A8 = 9.9810569378236378800364235948e-01 +data8 0xFEF9F8ABDBCDB2F3, 0x0000BFFE //A7 = -9.9600176044241699109053158187e-01 +data8 0xFE3F05375988491D, 0x00003FFE //A6 = 9.9314911462127599008937257662e-01 +LOCAL_OBJECT_END(Constants_Tgammal_poly_splitted) + +.align 64 +LOCAL_OBJECT_START(Constants_Tgammal_common) +// Positive overflow value +data8 0x3FE0000000000000 // 0.5 +data8 0x3FF8000000000000 // 1.5 +data8 0x3FD0000000000000 // 0.25 +data8 0x0000000000000000 // 0 +data8 0xDB718C066B352E21, 0x00004009 // Positive overflow value +LOCAL_OBJECT_END(Constants_Tgammal_common) + + + +//======================================================= +// Lgamma registers + +// General Purpose Registers +GR_l_Log_Table = r33 +GR_l_Log_Table1 = r34 +GR_l_BIAS = r34 +GR_l_Index1 = r35 +GR_l_Index2 = r36 +GR_l_signif_Z = r37 +GR_l_X_0 = r38 +GR_l_X_1 = r39 +GR_l_X_2 = r40 +GR_l_Z_1 = r41 +GR_l_Z_2 = r42 +GR_l_N = r43 +GR_l_Index3 = r44 +GR_l_Stirling_Table = r45 +GR_l_N_Unbiased = r46 + +// Floating Point Registers +FR_l_logl_X = f8 + +FR_l_h_3 = f10 +FR_l_poly_hi = f10 +FR_l_W = f11 +FR_l_S = f12 +FR_l_GS_hi = f13 +FR_l_Y_lo = f13 +FR_l_r_cor = f14 +FR_l_G_1 = f15 +FR_l_G = f15 +FR_l_H_1 = f32 +FR_l_H = f32 +FR_l_h = f33 +FR_l_h_1 = f33 +FR_l_N = f33 +FR_l_G_2 = f34 +FR_l_H_2 = f35 +FR_l_h_2 = f36 +FR_l_G_3 = f37 +FR_l_log2_hi = f38 +FR_l_GS_lo = f39 +FR_l_H_3 = f40 +FR_l_float_N = f41 +FR_l_Q_4 = f42 +FR_l_Q_3 = f43 +FR_l_Q_2 = f44 +FR_l_Q_1 = f45 +FR_l_Q_5 = f46 +FR_l_Q_6 = f47 +FR_l_log2_lo = f48 +FR_l_r = f49 +FR_l_poly_lo = f50 +FR_l_poly = f51 +FR_l_rsq = f52 +FR_l_Y_lo_res = f53 + +FR_l_Y0 = f55 +FR_l_Q0 = f56 +FR_l_E0 = f57 +FR_l_E2 = f58 +FR_l_E1 = f59 +FR_l_Y1 = f60 +FR_l_E3 = f61 +FR_l_Y2 = f62 + +FR_l_Z = f63 +FR_l_Z2 = f64 +FR_l_Z4 = f65 +FR_l_Z8 = f66 + +FR_l_CH = f67 +FR_l_CL = f68 + +FR_l_B2 = f69 +FR_l_B4 = f70 +FR_l_B6 = f71 +FR_l_B8 = f72 +FR_l_B10 = f73 +FR_l_B12 = f74 +FR_l_B14 = f75 +FR_l_B16 = f76 +FR_l_B18 = f77 +FR_l_Half = f78 +FR_l_SS = f79 +FR_l_AbsX_m_Half = f80 +FR_l_CXH = f81 +FR_l_CXL = f82 +FR_l_SSCXH = f83 +FR_l_SSCXL = f84 +FR_l_XYH = f85 +FR_l_XYL = f86 +FR_l_Temp = f87 + +FR_l_logl_YHi = f88 +FR_l_logl_YLo = f89 + +FR_l_SignedXYH = f123 + +FR_l_AbsX = f127 + + + +//======================================================= +// Negative part registers + +// General Purpose Registers +GR_n_sin_Table = r47 +GR_n_XN = r48 + +// Float point registers +FR_n_IXNS = f125 +FR_n_IXN = f126 + +FR_n_XNS = f90 +FR_n_XS = f91 +FR_n_XS2 = f92 +FR_n_XS2L = f93 +FR_n_XS4 = f94 +FR_n_XS7 = f95 +FR_n_XS8 = f96 +FR_n_TT = f97 +FR_n_TH = f98 +FR_n_TL = f99 + +FR_n_A2H = f100 +FR_n_A2L = f101 +FR_n_A1H = f102 +FR_n_A1L = f103 +FR_n_A9 = f104 +FR_n_A8 = f105 +FR_n_A7 = f106 +FR_n_A6 = f107 +FR_n_A5 = f108 +FR_n_A4 = f109 +FR_n_A3 = f110 + +FR_n_PolyH = f111 +FR_n_PolyL = f112 + +FR_n_Poly1H = f113 +FR_n_SinxH = f113 // the same as FR_n_Poly1H +FR_n_Poly1L = f114 +FR_n_SinxL = f114 // the same as FR_n_Poly1L + +FR_n_Tail = f115 +FR_n_NegOne = f116 + +FR_n_Y0 = f117 + +FR_n_Q0 = f118 +FR_n_E0 = f119 + +FR_n_E2 = f120 +FR_n_E1 = f121 + +FR_n_Y1 = f55 +FR_n_E3 = f56 + +FR_n_Y2 = f57 +FR_n_R0 = f58 + +FR_n_E4 = f59 +FR_n_RcpResH = f60 + +FR_n_Y3 = f61 +FR_n_R1 = f62 +FR_n_Temp = f63 + +FR_n_RcpResL = f64 + +FR_n_ResH = f65 +FR_n_ResL = f66 + + + + +//======================================================= +// Exp registers + +// General Purpose Registers +GR_e_ad_Arg = r33 +GR_e_ad_A = r34 +GR_e_signexp_x = r35 +GR_e_exp_x = r35 +GR_e_exp_mask = r36 +GR_e_ad_W1 = r37 +GR_e_ad_W2 = r38 +GR_e_M2 = r39 +GR_e_M1 = r40 +GR_e_K = r41 +GR_e_exp_2_mk = r42 +GR_e_exp_2_k = r43 +GR_e_ad_T1 = r44 +GR_e_ad_T2 = r45 +GR_e_N_fix = r46 +GR_e_one = r47 +GR_e_exp_bias = r48 +GR_e_sig_inv_ln2 = r49 +GR_e_rshf_2to51 = r50 +GR_e_exp_2tom51 = r51 +GR_e_rshf = r52 + +// Floating Point Registers +FR_e_RSHF_2TO51 = f10 +FR_e_INV_LN2_2TO63 = f11 +FR_e_W_2TO51_RSH = f12 +FR_e_2TOM51 = f13 +FR_e_RSHF = f14 +FR_e_Y_hi = f15 +FR_e_Y_lo = f32 +FR_e_scale = f33 +FR_e_float_N = f34 +FR_e_N_signif = f35 +FR_e_L_hi = f36 +FR_e_L_lo = f37 +FR_e_r = f38 +FR_e_W1 = f39 +FR_e_T1 = f40 +FR_e_W2 = f41 +FR_e_T2 = f42 +FR_e_W1_p1 = f43 +FR_e_rsq = f44 +FR_e_A2 = f45 +FR_e_r4 = f46 +FR_e_A3 = f47 +FR_e_poly = f48 +FR_e_T = f49 +FR_e_W = f50 +FR_e_Wp1 = f51 +FR_e_r6 = f52 +FR_e_2_mk = f53 +FR_e_A1 = f54 +FR_e_T_scale = f55 +FR_e_result_lo = f56 +FR_e_W_T_scale = f57 +FR_e_Wp1_T_scale = f58 + +FR_e_expl_Input_X = f123 +FR_e_expl_Input_Y = f124 +FR_e_expl_Output_X = f123 +FR_e_expl_Output_Y = f124 + + +FR_e_expl_Input_AbsX = f122 + + + +//======================================================= +// Common registers + +// General Purpose Registers +GR_c_Table = r53 +GR_c_NegUnderflow = r54 +GR_c_NegSingularity = r55 +GR_c_X = r56 +GR_c_SignBit = r57 +GR_c_13 = r58 + + +// Floating Point Registers +FR_c_PosOverflow = f123 +FR_c_XN = f124 + + +//======================================================= +// Polynomial part registers + +// General Purpose Registers +GR_p_Table = r59 +GR_p_XN = r33 +GR_p_Table2 = r34 +GR_p_Int = r35 +GR_p_Offset = r36 +GR_p_Offset2 = r38 +GR_p_X_Sgnd = GR_l_signif_Z // = r37 +GR_p_Exp = r61 +GR_p_Bias = r62 +GR_p_0p75 = r63 + +// Floating Point Registers +FR_p_AbsX = FR_l_AbsX // = f127 +FR_p_IXN = FR_n_IXN // = f126 +FR_p_XN = f32 +FR_p_0p5 = f33 +FR_p_1p5 = f34 +FR_p_AbsXM1 = f35 +FR_p_2 = f36 + +FR_p_A20 = f37 +FR_p_A19 = f38 +FR_p_A18 = f39 +FR_p_A17 = f40 +FR_p_A16 = f41 +FR_p_A15 = f42 +FR_p_A14 = f43 +FR_p_A13 = f44 +FR_p_A12 = f45 +FR_p_A11 = f46 +FR_p_A10 = f47 +FR_p_A9 = f48 +FR_p_A8 = f49 +FR_p_A7 = f50 +FR_p_A6 = f51 +FR_p_A5H = f52 +FR_p_A5L = f53 +FR_p_A4H = f54 +FR_p_A4L = f55 +FR_p_A3H = f56 +FR_p_A3L = f57 +FR_p_A2H = f58 +FR_p_A2L = f59 +FR_p_A1H = f60 +FR_p_A1L = f61 +FR_p_A0H = f62 +FR_p_A0L = f63 + +FR_p_XR = f64 +FR_p_XR2 = f65 +FR_p_XR2L = f52 + +FR_p_XR3 = f58 +FR_p_XR3L = f38 + +FR_p_XR4 = f42 +FR_p_XR6 = f40 +FR_p_XR8 = f37 + +FR_p_Poly5H = f66 +FR_p_Poly5L = f67 +FR_p_Poly4H = f53 +FR_p_Poly4L = f44 +FR_p_Poly3H = f41 +FR_p_Poly3L = f47 +FR_p_Poly2H = f68 +FR_p_Poly2L = f54 +FR_p_Poly1H = f55 +FR_p_Poly1L = f46 +FR_p_Poly0H = f39 +FR_p_Poly0L = f43 + +FR_p_Temp5H = f69 +FR_p_Temp5L = f70 +FR_p_Temp4H = f71 +FR_p_Temp4L = f60 +FR_p_Temp2H = f72 +FR_p_Temp2L = f73 +FR_p_Temp1H = f59 +FR_p_Temp1L = f61 +FR_p_Temp0H = f49 +FR_p_Temp0L = f48 +FR_p_PolyTail = f45 +FR_p_OddPoly0H = f56 +FR_p_OddPoly0L = f51 + +FR_p_0p25 = f73 + + +//======================================================= +// Negative polynomial part registers +// General Purpose Registers +GR_r_sin_Table = r47 +GR_r_sin_Table2 = r60 + +// Floating Point Registers +FR_r_IXNS = FR_n_IXNS +FR_r_IXN = FR_n_IXN + +FR_r_AbsX = FR_l_AbsX + +FR_r_A9 = f74 +FR_r_A8 = f75 +FR_r_A7 = f76 +FR_r_A6 = f77 +FR_r_A5 = f78 +FR_r_A4 = f79 +FR_r_A3 = f80 +FR_r_A2H = f81 +FR_r_A2L = f82 +FR_r_A1H = f83 +FR_r_A1L = f84 + +FR_r_XNS = f85 +FR_r_XS = f86 +FR_r_XS2 = f87 +FR_r_XS2L = f88 +FR_r_XS4 = f89 +FR_r_XS7 = f90 +FR_r_XS8 = f91 + +FR_r_Tail = f92 + +FR_r_TT = f93 +FR_r_TH = f94 +FR_r_TL = f95 + +FR_r_ResH = f96 +FR_r_ResL = f97 + +FR_r_Res3H = f98 +FR_r_Res3L = f99 + +FR_r_Res1H = f100 +FR_r_Res1L = f101 + + + +FR_r_Y0 = f102 +FR_r_Q0 = f103 +FR_r_E0 = f104 +FR_r_E2 = f105 +FR_r_E1 = f106 +FR_r_Y1 = f107 +FR_r_E3 = f108 +FR_r_Y2 = f109 +FR_r_R0 = f110 +FR_r_E4 = f111 +FR_r_ZH = f112 +FR_r_Y3 = f113 +FR_r_R1 = f114 +FR_r_ZHN = f115 +FR_r_ZL = f115 +FR_r_NegOne = f116 + +FR_z_Y0 = f102 +FR_z_Q0 = f103 +FR_z_E0 = f104 +FR_z_E2 = f105 +FR_z_E1 = f106 +FR_z_Y1 = f107 +FR_z_E3 = f108 +FR_z_Y2 = f109 +FR_z_R0 = f110 +FR_z_E4 = f111 +FR_z_ZH = f112 +FR_z_Y3 = f113 +FR_z_R1 = f114 +FR_z_ZL = f115 + + +// General Purpose Registers +GR_SAVE_PFS = r32 +GR_DenOverflow = r33 +GR_u_XN = r34 + +GR_SAVE_B0 = r35 +GR_SAVE_GP = r36 +GR_SAVE_SP = r37 + +// Floating Point Registers +FR_u_IXN = f34 + + +// ERROR HANDLER REGISTERS +GR_Parameter_X = r64 +GR_Parameter_Y = r65 +GR_Parameter_RESULT = r66 +GR_Parameter_TAG = r67 + +FR_RESULT = f8 +FR_X = f32 +FR_Y = f1 + + +.section .text +GLOBAL_LIBM_ENTRY(tgammal) +{ .mfi + alloc r32 = ar.pfs,0,32,4,0 + fabs FR_l_AbsX = f8 // Get absolute value of X + addl GR_n_sin_Table = @ltoff(Constants_Tgammal_sin), gp +} +{ .mfi + addl GR_l_Log_Table=@ltoff(Constants_Tgammal_log_80_Z_G_H_h1#),gp + nop.f 0 + addl GR_l_Stirling_Table = @ltoff(Constants_Tgammal_stirling), gp +};; + +{ .mfi + getf.sig GR_l_signif_Z = f8 // Significand of X + fcvt.fx.s1 FR_n_IXNS = f8 // Convert to fixed point + addl GR_c_Table = @ltoff(Constants_Tgammal_common), gp +} +{ .mfi + ld8 GR_l_Log_Table = [GR_l_Log_Table] + nop.f 0 + addl GR_p_Table = @ltoff(Constants_Tgammal_poly), gp +};; + +{ .mfi + ld8 GR_n_sin_Table = [GR_n_sin_Table] + fclass.m p6,p0 = f8,0x1EF // Check x for NaN, 0, INF, denorm + // NatVal. + addl GR_c_NegSingularity = 0x1003E, r0 +} +{ .mlx + ld8 GR_l_Stirling_Table = [GR_l_Stirling_Table] + movl GR_c_13 = 0x402A000000000000 // 13.0 +};; + +{ .mfi + getf.d GR_c_X = f8 // Double prec. X to general register + frcpa.s1 FR_z_Y0,p0 = f1,f8 // y = frcpa(x) (for negatives) + extr.u GR_l_Index1 = GR_l_signif_Z, 59, 4 // = High 4 bits of Z +} +{ .mlx + ld8 GR_c_Table = [GR_c_Table] + movl GR_c_SignBit = 0x8000000000000000 // High bit (sign) +};; + +{ .mfi + ld8 GR_p_Table = [GR_p_Table] + fcmp.lt.s1 p15, p14 = f8,f0 // p14 - positive arg, p15 - negative + shl GR_l_Index1 = GR_l_Index1,5 // Adjust Index1 ptr (x32) +} +{ .mfb + adds GR_c_NegUnderflow = 1765, r0 + nop.f 0 +(p6) br.cond.spnt tgammal_spec // Spec. values processing branch //////////// + // (0s, INFs, NANs, NatVals, denormals) ////// +};; + +{ .mfi + ldfpd FR_l_CH,FR_l_CL= [GR_l_Stirling_Table], 16 // Load CH, CL + fcvt.fx.trunc.s1 FR_n_IXN = FR_l_AbsX // Abs arg to int by trunc + extr.u GR_l_X_0 = GR_l_signif_Z, 49, 15 // High 15 bit of Z +} +{ .mfi + add GR_l_Index1 = GR_l_Index1,GR_l_Log_Table // Add offset + fma.s1 FR_p_2 = f1, f1, f1 // 2.0 + andcm GR_c_X = GR_c_X, GR_c_SignBit // Remove sign +};; + +{ .mfi + addl GR_l_Log_Table = @ltoff(Constants_Tgammal_log_80_Z_G_H_h2#), gp + fcmp.lt.s1 p10, p0 = FR_l_AbsX, f1 // If |X|<1 then p10 = 1 + nop.i 0 +} +{ .mlx + ld2 GR_l_Z_1 = [GR_l_Index1],4 // load Z_1 from Index1 + movl GR_l_BIAS = 0x000000000000FFFF // Bias for exponent +};; + +{ .mfi + ld8 GR_l_Log_Table = [GR_l_Log_Table] + frcpa.s1 FR_l_Y0, p0 = f1, FR_l_AbsX // y = frcpa(x) + nop.i 0 +} +{ .mfi + ldfs FR_l_G_1 = [GR_l_Index1],4 // Load G_1 + fsub.s1 FR_l_W = FR_l_AbsX, f1 // W = |X|-1 + nop.i 0 +};; + +{ .mfi + getf.exp GR_l_N_Unbiased= FR_l_AbsX // exponent of |X| + fmerge.se FR_l_S = f1, FR_l_AbsX // S = merging of X and 1.0 + cmp.gtu p11, p0 = GR_c_13, GR_c_X // If 1 <= |X| < 13 + // then p11 = 1 +} +{ .mfb + ldfs FR_l_H_1 = [GR_l_Index1],8 // Load H_1 + fcvt.xf FR_n_XNS = FR_n_IXNS // Convert to FP repr. of int X +(p10) br.cond.spnt tgamma_lt_1 // Branch to |X| < 1 path /////////////////// +};; + +{ .mfi + ldfpd FR_n_A2H, FR_n_A2L = [GR_n_sin_Table], 16 + nop.f 0 + pmpyshr2.u GR_l_X_1 = GR_l_X_0,GR_l_Z_1,15 // Adjust Index2 (x32) +} +{ .mfb + ldfe FR_l_B2 = [GR_l_Stirling_Table], 16 + nop.f 0 +(p11) br.cond.spnt tgamma_lt_13 // Branch to 1 <= |X| < 13 path /////////////// +};; + +{ .mfi + ldfe FR_l_h_1 = [GR_l_Index1],0 + nop.f 0 + sub GR_l_N = GR_l_N_Unbiased, GR_l_BIAS // N - BIAS +} +{ .mib + ldfpd FR_l_B4,FR_l_B6= [GR_l_Stirling_Table], 16 // Load C +(p15) cmp.geu.unc p8,p0 = GR_l_N_Unbiased, GR_c_NegSingularity +(p8) br.cond.spnt tgammal_singularity // Singularity for arg < to -2^63 ////// +};; + +{ .mmi +(p15) ldfpd FR_n_A1H, FR_n_A1L = [GR_n_sin_Table], 16 + ldfpd FR_l_B8, FR_l_B10 = [GR_l_Stirling_Table], 16 + add GR_c_Table = 0x20, GR_c_Table +};; + +{ .mfi +(p15) ldfe FR_n_A9 = [GR_n_sin_Table], 16 + fma.s1 FR_l_Q0 = f1,FR_l_Y0,f0 // Q0 = Y0 + nop.i 0 +} +{ .mfi + ldfpd FR_l_B12, FR_l_B14 = [GR_l_Stirling_Table], 16 + fnma.s1 FR_l_E0 = FR_l_Y0,FR_l_AbsX,f1 // e = 1-b*y + nop.i 0 +};; + +{ .mfi +(p15) ldfe FR_n_A8 = [GR_n_sin_Table], 16 + fcvt.xf FR_c_XN = FR_n_IXN // Convert to FP repr. of int X + extr.u GR_l_Index2 = GR_l_X_1, 6, 4 // Extract Index2 +} +{ .mfi + ldfpd FR_l_B16, FR_l_B18 = [GR_l_Stirling_Table], 16 + nop.f 0 + nop.i 0 +};; + +{ .mfi +(p15) ldfe FR_n_A7 = [GR_n_sin_Table], 16 + fms.s1 FR_l_CXH = FR_l_CH, f1, FR_l_AbsX // CXH = CH+|X| + shl GR_l_Index2 = GR_l_Index2,5 +} +{ .mfi + ldfd FR_l_Half = [GR_l_Stirling_Table] // Load 0.5 + nop.f 0 + nop.i 0 +};; + +{ .mfi + add GR_l_Index2 = GR_l_Index2, GR_l_Log_Table // Add offset + nop.f 0 + nop.i 0 +} +{ .mfi +(p15) ldfe FR_n_A6 = [GR_n_sin_Table], 16 +(p15) fma.s1 FR_n_XS = FR_l_AbsX , f1, FR_n_XNS // xs = x - int(x) + nop.i 0 +};; + +{ .mmi + ld2 GR_l_Z_2 = [GR_l_Index2],4 + addl GR_l_Log_Table = @ltoff(Constants_Tgammal_log_80_h3_G_H#),gp + nop.i 0 +};; + +{ .mfi + ld8 GR_l_Log_Table = [GR_l_Log_Table] + fma.s1 FR_l_E2 = FR_l_E0,FR_l_E0,FR_l_E0 // e2 = e+e^2 + nop.i 0 +} +{ .mfi + ldfs FR_l_G_2 = [GR_l_Index2],4 + fma.s1 FR_l_E1 = FR_l_E0,FR_l_E0,f0 // e1 = e^2 + nop.i 0 +};; + +{ .mmi + ldfs FR_l_H_2 = [GR_l_Index2],8 +(p15) ldfe FR_n_A5 = [GR_n_sin_Table], 16 + nop.i 0 +};; + +{ .mfi + setf.sig FR_l_float_N = GR_l_N // float_N = Make N a fp number + nop.f 0 + pmpyshr2.u GR_l_X_2 = GR_l_X_1,GR_l_Z_2,15 // X_2 = X_1 * Z_2 +} +{ .mfi + ldfe FR_l_h_2 = [GR_l_Index2],0 + fma.s1 FR_l_CXL = FR_l_AbsX, f1, FR_l_CXH // CXL = |X|+CXH + add GR_l_Log_Table1= 0x200, GR_l_Log_Table +};; + +{ .mfi +(p15) ldfe FR_n_A4 = [GR_n_sin_Table], 16 +(p15) fcmp.eq.unc.s1 p9,p0 = FR_l_AbsX, FR_c_XN //if argument is integer + // and negative + nop.i 0 +} +{ .mfi + ldfe FR_c_PosOverflow = [GR_c_Table],16 //Load pos overflow value +(p15) fma.s1 FR_n_XS2 = FR_n_XS, FR_n_XS, f0 // xs^2 = xs*xs + nop.i 0 +};; + +{ .mfi +(p15) ldfe FR_n_A3 = [GR_n_sin_Table], 16 + nop.f 0 + nop.i 0 +};; + +{ .mfi +(p15) getf.sig GR_n_XN = FR_n_IXN // int(x) to general reg + fma.s1 FR_l_Y1 = FR_l_Y0,FR_l_E2,FR_l_Y0 // y1 = y+y*e2 + nop.i 0 +} +{ .mfb + nop.m 0 + fma.s1 FR_l_E3 = FR_l_E1,FR_l_E1,FR_l_E0 // e3 = e+e1^2 +(p9) br.cond.spnt tgammal_singularity // Singularity for integer ///////////// + // and negative arguments ////////////// +};; + +{ .mfi + nop.m 0 + fms.s1 FR_l_AbsX_m_Half = FR_l_AbsX, f1, FR_l_Half // |x|-0.5 + extr.u GR_l_Index2 = GR_l_X_2, 1, 5 // Get Index3 +};; + +{ .mfi + shladd GR_l_Log_Table1= GR_l_Index2, 2, GR_l_Log_Table1 + nop.f 0 + shladd GR_l_Index3 = GR_l_Index2,4, GR_l_Log_Table // Index3 +} +{ .mfb +(p15) cmp.gtu.unc p11, p0 = GR_n_XN, GR_c_NegUnderflow // X < -1765 + fms.s1 FR_l_CXL = FR_l_CH, f1, FR_l_CXL // CXL = CH - CXL +(p11) br.cond.spnt tgammal_underflow // Singularity for negative argument ////// + // at underflow domain (X < -1765) ////// +};; + +{ .mfi + addl GR_l_Log_Table = @ltoff(Constants_Tgammal_log_80_Q#), gp +(p15) fma.s1 FR_n_TT = FR_n_A2L, FR_n_XS2, f0 // T=A2L*x^2 + tbit.nz.unc p13, p12 = GR_n_XN, 0x0 // whether [X] odd or even +} +{ .mfi + nop.m 0 +(p15) fms.s1 FR_n_XS2L = FR_n_XS, FR_n_XS, FR_n_XS2 // xs^2 Low part + nop.i 0 +};; + +{ .mfi + ld8 GR_l_Log_Table = [GR_l_Log_Table] +(p15) fma.s1 FR_n_A7 = FR_n_A8, FR_n_XS2, FR_n_A7 // poly tail + nop.i 0 +} +{ .mfi + ldfe FR_l_h_3 = [GR_l_Index3],12 +(p15) fma.s1 FR_n_XS4 = FR_n_XS2, FR_n_XS2, f0 // xs^4 = xs^2*xs^2 + nop.i 0 +};; + +{ .mfi + ldfs FR_l_H_3 = [GR_l_Log_Table1], 0 + fma.s1 FR_l_Y2 = FR_l_Y1, FR_l_E3, FR_l_Y0 // y2 = y+y1*e3 + nop.i 0 +} +{ .mfi + ldfs FR_l_G_3 = [GR_l_Index3], 0 + fnma.s1 FR_l_Z = FR_l_AbsX,FR_l_Q0,f1 // r = a-b*q + nop.i 0 +};; + +{ .mfi + nop.m 0 + fmpy.s1 FR_l_G = FR_l_G_1, FR_l_G_2 // G = G1 * G_2 + nop.i 0 +} +{ .mfi + nop.m 0 + fadd.s1 FR_l_H = FR_l_H_1, FR_l_H_2 // H = H_1 + H_2 + nop.i 0 +};; + +{ .mfi + ldfe FR_l_log2_hi = [GR_l_Log_Table],16 // load log2_hi part + fadd.s1 FR_l_h = FR_l_h_1, FR_l_h_2 // h = h_1 + h_2 + nop.i 0 +} +{ .mfi + nop.m 0 + fcvt.xf FR_l_float_N = FR_l_float_N // int(N) + nop.i 0 +};; + +{ .mfi + ldfe FR_l_log2_lo = [GR_l_Log_Table],16 // Load log2_lo part + fma.s1 FR_l_CXL = FR_l_CXL, f1, FR_l_CL + nop.i 0 +} +{ .mfi + nop.m 0 +(p15) fma.s1 FR_n_TT = FR_n_A2H, FR_n_XS2L, FR_n_TT // T=A2H*x2L+T + nop.i 0 +};; + +{ .mfi + ldfe FR_l_Q_6 = [GR_l_Log_Table],16 +(p15) fma.s1 FR_n_A3 = FR_n_A4, FR_n_XS2, FR_n_A3 // poly tail + nop.i 0 +} +{ .mfi + nop.m 0 +(p15) fma.s1 FR_n_A5 = FR_n_A6, FR_n_XS2, FR_n_A5 // poly tail + nop.i 0 +};; + +{ .mfi + ldfe FR_l_Q_5 = [GR_l_Log_Table],16 +(p15) fabs FR_n_XS = FR_n_XS // abs(xs) + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 FR_l_Z = FR_l_Z,FR_l_Y2,FR_l_Q0 // x_hi = q+r*y2 + nop.i 0 +};; + +{ .mfi + ldfe FR_l_Q_4 = [GR_l_Log_Table],16 +(p15) fma.s1 FR_n_A7 = FR_n_A9, FR_n_XS4, FR_n_A7 // poly tail + nop.i 0 +} +{ .mfi + nop.m 0 +(p15) fma.s1 FR_n_XS7 = FR_n_XS4, FR_n_XS2, f0 // = x^4*x^2 + nop.i 0 +};; + +{ .mfi + ldfe FR_l_Q_3 = [GR_l_Log_Table],16 + fneg FR_n_NegOne = f1 // -1.0 + nop.i 0 +} +{ .mfi + nop.m 0 +(p15) fma.s1 FR_n_XS8 = FR_n_XS4, FR_n_XS4, f0 // xs^8 = xs^4*xs^4 + nop.i 0 +};; + +{ .mfi + ldfe FR_l_Q_2 = [GR_l_Log_Table],16 + fadd.s1 FR_l_h = FR_l_h, FR_l_h_3 // h = h_1 + h_2 + h_3 + nop.i 0 +} +{ .mfi + nop.m 0 +(p15) fma.s1 FR_n_TH = FR_n_A2H, FR_n_XS2, FR_n_TT // A2H*xs2+T + nop.i 0 +};; + +{ .mfi + ldfe FR_l_Q_1 = [GR_l_Log_Table],16 + fmpy.s1 FR_l_G = FR_l_G, FR_l_G_3 // G = G_1 * G_2 * G_3 + nop.i 0 +} +{ .mfi + nop.m 0 + fadd.s1 FR_l_H = FR_l_H, FR_l_H_3 // H = H_1 + H_2 + H_3 + nop.i 0 +};; + +{ .mfi + nop.m 0 + fma.s1 FR_l_Z2 = FR_l_Z, FR_l_Z, f0 // Z^2 + nop.i 0 +} +{ .mfi + nop.m 0 +(p15) fma.s1 FR_n_A3 = FR_n_A5, FR_n_XS4, FR_n_A3 // poly tail + nop.i 0 +};; + +{ .mfi + nop.m 0 +(p14) fcmp.gt.unc.s1 p7,p0 = FR_l_AbsX, FR_c_PosOverflow //X > 1755.5483 + // (overflow domain, result cannot be represented by normal value) + nop.i 0 +} +{ .mfi + nop.m 0 +(p15) fma.s1 FR_n_XS7 = FR_n_XS7, FR_n_XS, f0 // x^7 construction + nop.i 0 +};; + +{ .mfi + nop.m 0 +(p15) fms.s1 FR_n_TL = FR_n_A2H, FR_n_XS2, FR_n_TH // A2H*xs2+TH + nop.i 0 +} +{ .mfi + nop.m 0 +(p15) fma.s1 FR_n_PolyH = FR_n_TH, f1, FR_n_A1H // PolyH=TH+A1H + nop.i 0 +};; + +{ .mfi + nop.m 0 + fmpy.s1 FR_l_GS_hi = FR_l_G, FR_l_S // GS_hi = G*S + nop.i 0 +} +{ .mfb + nop.m 0 + fms.s1 FR_l_r = FR_l_G, FR_l_S, f1 // r = G*S -1 +(p7) br.cond.spnt tgammal_overflow // Overflow path for arg > 1755.5483 ////// +};; + +{ .mfi + nop.m 0 + fma.s1 FR_l_B14 = FR_l_B16, FR_l_Z2, FR_l_B14// Bernoulli tail + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 FR_l_Z4 = FR_l_Z2, FR_l_Z2, f0 // Z^4 = Z^2*Z^2 + nop.i 0 +};; + +{ .mfi + nop.m 0 + fma.s1 FR_l_B2 = FR_l_B4, FR_l_Z2, FR_l_B2 // Bernoulli tail + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 FR_l_B6 = FR_l_B8, FR_l_Z2, FR_l_B6 // Bernoulli tail + nop.i 0 +};; + +{ .mfi + nop.m 0 + fma.s1 FR_l_B10 = FR_l_B12, FR_l_Z2, FR_l_B10// Bernoulli tail + nop.i 0 +} +{ .mfi + nop.m 0 +(p15) fma.s1 FR_n_Tail = FR_n_A7, FR_n_XS8, FR_n_A3 // poly tail + nop.i 0 +};; + +{ .mfi + nop.m 0 +(p15) fma.s1 FR_n_TL = FR_n_TL, f1, FR_n_TT // TL = TL+T + nop.i 0 +} +{ .mfi + nop.m 0 +(p15) fms.s1 FR_n_PolyL = FR_n_A1H, f1, FR_n_PolyH // polyH+A1H + nop.i 0 +};; + +{ .mfi + nop.m 0 + fma.s1 FR_l_poly_lo = FR_l_r, FR_l_Q_6, FR_l_Q_5 // Q_5+r*Q_6 + nop.i 0 +} +{ .mfi + nop.m 0 + fsub.s1 FR_l_r_cor = FR_l_GS_hi, f1 // r_cor = GS_hi -1 + nop.i 0 +};; + +{ .mfi + nop.m 0 + fms.s1 FR_l_GS_lo = FR_l_G, FR_l_S, FR_l_GS_hi // G*S-GS_hi + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 FR_l_poly = FR_l_r, FR_l_Q_2, FR_l_Q_1 //poly=r*Q2+Q1 + nop.i 0 +};; + +{ .mfi + nop.m 0 + fmpy.s1 FR_l_rsq = FR_l_r, FR_l_r // rsq = r * r + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 FR_l_G = FR_l_float_N, FR_l_log2_hi, FR_l_H // Tbl = + // float_N*log2_hi + H + nop.i 0 +};; + +{ .mfi + nop.m 0 + fma.s1 FR_l_Y_lo = FR_l_float_N, FR_l_log2_lo, FR_l_h // Y_lo= + // float_N*log2_lo + h + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 FR_l_B14 = FR_l_B18, FR_l_Z4, FR_l_B14 //bernulli tail + nop.i 0 +};; + +{ .mfi + nop.m 0 + fma.s1 FR_l_B2 = FR_l_B6, FR_l_Z4, FR_l_B2 //bernulli tail + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 FR_l_Z8 = FR_l_Z4, FR_l_Z4, f0 //bernulli tail + nop.i 0 +};; + +{ .mfi + nop.m 0 + fma.s1 FR_l_poly_lo = FR_l_r, FR_l_poly_lo, FR_l_Q_4 // poly_lo = + // Q_4 + r * poly_lo + nop.i 0 +} +{ .mfi + nop.m 0 + fsub.s1 FR_l_r_cor = FR_l_r_cor, FR_l_r // r_cor = r_cor - r + nop.i 0 +};; + +{ .mfi + nop.m 0 +(p15) fma.s1 FR_n_PolyL = FR_n_PolyL, f1, FR_n_TH // polyL+TH + nop.i 0 +} +{ .mfi + nop.m 0 +(p15) fma.s1 FR_n_TT = FR_n_TL, f1, FR_n_A1L // TL+A1L + nop.i 0 +};; + +{ .mfi + nop.m 0 + fadd.s1 FR_l_logl_YHi = FR_l_G, FR_l_r // Y_hi = Tbl + r + nop.i 0 +};; + +{ .mfi + nop.m 0 + fma.s1 FR_l_B10 = FR_l_B14, FR_l_Z4, FR_l_B10 //bernulli tail + nop.i 0 +};; + +{ .mfi + nop.m 0 + fma.s1 FR_l_poly_lo = FR_l_r, FR_l_poly_lo, FR_l_Q_3 // poly_lo = + // Q_3 + r * poly_lo + nop.i 0 +} +{ .mfi + nop.m 0 + fadd.s1 FR_l_r_cor = FR_l_r_cor, FR_l_GS_lo // r_cor=r_cor+GS_lo + nop.i 0 +};; + +{ .mfi + nop.m 0 +(p15) fma.s1 FR_n_PolyL = FR_n_PolyL, f1, FR_n_TT // polyL+TT + nop.i 0 +};; + +{ .mfi + nop.m 0 + fsub.s1 FR_l_Y_lo_res = FR_l_G, FR_l_logl_YHi // Y_lo = Tbl - Y_hi + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 FR_l_XYH = FR_l_logl_YHi, FR_l_AbsX_m_Half, f0 // XYH= + // YHi*|x-0.5| + nop.i 0 +};; + +{ .mfi + nop.m 0 + fma.s1 FR_l_SS = FR_l_B10, FR_l_Z8, FR_l_B2 // Bernoulli tail + nop.i 0 +};; + +{ .mfi + nop.m 0 + fadd.s1 FR_l_r_cor = FR_l_r_cor, FR_l_Y_lo // r_cor = r_cor+Y_lo + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 FR_l_poly = FR_l_rsq, FR_l_poly_lo, FR_l_poly //poly= + // r^2*polyLo+poly + nop.i 0 +};; + +{ .mfi + nop.m 0 +(p15) fma.s1 FR_n_TT = FR_n_PolyL, FR_n_XS2, f0 // T=polyL*xs^2 + nop.i 0 +};; + +{ .mfi + nop.m 0 + fadd.s1 FR_l_Y_lo = FR_l_Y_lo_res, FR_l_r // Y_lo = Y_lo + r + nop.i 0 +} +{ .mfi + nop.m 0 + fms.s1 FR_l_XYL = FR_l_logl_YHi, FR_l_AbsX_m_Half, FR_l_XYH + // XYL = YHi*|x-0.5|-XYH + nop.i 0 +};; + +{ .mfi + nop.m 0 + fma.s1 FR_l_SSCXH = FR_l_SS, FR_l_Z, FR_l_CXH // SS*Z+CXH + nop.i 0 +} +{ .mfi + mov GR_e_exp_2tom51= 0xffff-51 // 2^-51 +(p15) fma.s1 FR_l_SignedXYH = FR_l_XYH, FR_n_NegOne, f0 // XYH = -XYH + // for negatives + nop.i 0 +};; + +{ .mlx + nop.m 0 + movl GR_e_rshf_2to51 = 0x4718000000000000 // 1.10000 2^(63+51) +} +{ .mlx + nop.m 0 + movl GR_e_sig_inv_ln2 = 0xb8aa3b295c17f0bc //significand of 1/ln2 +};; + +{ .mfi + nop.m 0 + fma.s1 FR_l_poly = FR_l_rsq, FR_l_poly, FR_l_r_cor // poly = + // rsq * poly + r_cor + nop.i 0 +};; + +{ .mfi + addl GR_e_ad_Arg = @ltoff(Constants_Tgammal_exp_64_Arg#),gp +(p15) fma.s1 FR_n_TT = FR_n_PolyH, FR_n_XS2L, FR_n_TT + mov GR_e_exp_mask = 0x1FFFF // Form exponent mask +} +{ .mlx + nop.m 0 + movl GR_e_rshf = 0x43e8000000000000 // 1.10000 2^63 rshift +};; + + +{ .mmi + setf.sig FR_e_INV_LN2_2TO63 = GR_e_sig_inv_ln2 // form 1/ln2 * 2^63 + setf.d FR_e_RSHF_2TO51 = GR_e_rshf_2to51 // 1.1000 * 2^(63+51) + nop.i 0 +};; + +{ .mfi + nop.m 0 + fms.s1 FR_l_SSCXL = FR_l_CXH, f1, FR_l_SSCXH // CXH+SS*CXH + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 FR_e_expl_Input_AbsX = FR_l_XYH, f1, FR_l_SSCXH // HI EXP + nop.i 0 +};; + +.pred.rel "mutex",p14,p15 +{ .mfi + nop.m 0 +(p14) fma.s1 FR_e_expl_Input_X = FR_l_XYH, f1, FR_l_SSCXH // HI EXP + mov GR_e_exp_bias = 0x0FFFF // Set exponent bias +} +{ .mfi + ld8 GR_e_ad_Arg = [GR_e_ad_Arg] // Point to Arg table +(p15) fms.s1 FR_e_expl_Input_X = FR_l_SignedXYH, f1, FR_l_SSCXH // HI EXP + nop.i 0 +};; + +{ .mfi + nop.m 0 + fadd.s1 FR_l_logl_YLo = FR_l_Y_lo, FR_l_poly // YLo = YLo+poly + nop.i 0 +};; + +{ .mfi + setf.exp FR_e_2TOM51 = GR_e_exp_2tom51 //2^-51 for scaling float_N +(p15) fma.s1 FR_n_TH = FR_n_PolyH, FR_n_XS2, FR_n_TT // TH= + // polyH*xs^2+T + nop.i 0 +} +{ .mib + setf.d FR_e_RSHF = GR_e_rshf // Right shift const 1.1000*2^63 + nop.i 0 + nop.b 0 +};; + +{ .mfi + add GR_e_ad_A = 0x20, GR_e_ad_Arg // Point to A table + nop.f 0 + add GR_e_ad_T1 = 0x50, GR_e_ad_Arg // Point to T1 table +} +{ .mfi + add GR_e_ad_T2 = 0x150, GR_e_ad_Arg // Point to T2 table + nop.f 0 + nop.i 0 +};; + +{ .mfi + nop.m 0 + fma.s1 FR_l_SSCXL = FR_l_SS, FR_l_Z, FR_l_SSCXL + nop.i 0 +} +{ .mfi + nop.m 0 + fms.s1 FR_e_expl_Input_Y = FR_l_XYH, f1, FR_e_expl_Input_AbsX + nop.i 0 +};; + +{ .mfi + ldfe FR_e_L_hi = [GR_e_ad_Arg],16 // Get L_hi + nop.f 0 + nop.i 0 +};; + +{ .mfi + nop.m 0 + fma.s1 FR_l_XYL = FR_l_logl_YLo, FR_l_AbsX_m_Half, FR_l_XYL + // XYL = YLo*|x-0.5|+XYL + nop.i 0 +};; + +{ .mfi + ldfe FR_e_L_lo = [GR_e_ad_Arg],16 // Get L_lo +(p15) fms.s1 FR_n_TL = FR_n_PolyH, FR_n_XS2, FR_n_TH // TL = + // = polyH*xs^2-TH + add GR_e_ad_W1 = 0x100, GR_e_ad_T2 // Point to W1 table +} +{ .mfi + nop.m 0 +(p15) fma.s1 FR_n_Poly1H = FR_n_TH, f1, f1 // poly1H = TH+1 + add GR_e_ad_W2 = 0x300, GR_e_ad_T2 // Point to W2 table +};; + +{ .mmi + getf.exp GR_e_signexp_x = FR_e_expl_Input_X // Extract sign and exp + ldfe FR_e_A3 = [GR_e_ad_A],16 // Get A3 + nop.i 0 +};; + +{ .mfi + nop.m 0 + fma.s1 FR_l_SSCXL = FR_l_SSCXL, f1, FR_l_CXL + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 FR_e_expl_Input_Y = FR_e_expl_Input_Y, f1, FR_l_SSCXH + nop.i 0 +};; + +{ .mfi + nop.m 0 + fma.s1 FR_e_N_signif=FR_e_expl_Input_X,FR_e_INV_LN2_2TO63,FR_e_RSHF_2TO51 + and GR_e_exp_x = GR_e_signexp_x, GR_e_exp_mask +};; + +{ .mmi + sub GR_e_exp_x = GR_e_exp_x, GR_e_exp_bias // Get exponent + ldfe FR_e_A2 = [GR_e_ad_A],16 // Get A2 for main path + nop.i 0 +};; + +{ .mfi + nop.m 0 +(p15) fma.s1 FR_n_PolyH = FR_n_Poly1H, FR_n_XS, f0//sin(Pi*x) poly + nop.i 0 +} +{ .mfi + nop.m 0 +(p15) fms.s1 FR_n_Poly1L = f1, f1, FR_n_Poly1H//sin(Pi*x) poly + nop.i 0 +};; + +{ .mfi + nop.m 0 +(p15) fma.s1 FR_n_TL = FR_n_TL, f1, FR_n_TT//sin(Pi*x) poly + nop.i 0 +};; + +{ .mfi + nop.m 0 + fma.s1 FR_l_Temp = FR_l_XYL, f1, FR_l_SSCXL // XYL+SS*CXL + nop.i 0 +} +{ .mfi + nop.m 0 +(p15) fma.s1 FR_e_expl_Input_Y = FR_e_expl_Input_Y, FR_n_NegOne, f0 + // Negate lo part of exp argument for negative input values + nop.i 0 +};; + +{ .mfi + ldfe FR_e_A1 = [GR_e_ad_A],16 // Get A1 + nop.f 0 + nop.i 0 +} +{ .mfi + nop.m 0 + fms.s1 FR_e_float_N = FR_e_N_signif, FR_e_2TOM51, FR_e_RSHF + // Get float N = signd*2^51-RSHIFTER + nop.i 0 +};; + +{ .mfi + nop.m 0 +(p15) fma.s1 FR_n_Poly1L = FR_n_Poly1L, f1, FR_n_TH //sin(Pi*x) poly + nop.i 0 +} +{ .mfi + nop.m 0 +(p15) fms.s1 FR_n_PolyL = FR_n_Poly1H, FR_n_XS, FR_n_PolyH//sin(Pi*x) + nop.i 0 +};; + +{ .mfi + getf.sig GR_e_N_fix = FR_e_N_signif // Get N from significand + nop.f 0 + nop.i 0 +};; + +.pred.rel "mutex",p14,p15 +{ .mfi + nop.m 0 +(p14) fma.s1 FR_e_expl_Input_Y = FR_e_expl_Input_Y, f1, FR_l_Temp + nop.i 0 +} +{ .mfi + nop.m 0 +(p15) fms.s1 FR_e_expl_Input_Y = FR_e_expl_Input_Y, f1, FR_l_Temp + // arguments for exp computation + nop.i 0 +};; + +{ .mfi + nop.m 0 + fnma.s1 FR_e_r = FR_e_L_hi, FR_e_float_N, FR_e_expl_Input_X + // r = -L_hi * float_N + x + extr.u GR_e_M1 = GR_e_N_fix, 6, 6 // Extract index M_1 +};; + +{ .mfi + nop.m 0 +(p15) fma.s1 FR_n_Poly1L = FR_n_Poly1L, f1, FR_n_TL //sin(Pi*x) poly + nop.i 0 +};; + + +{ .mmf + nop.m 0 + nop.m 0 + fma.s1 FR_e_r = FR_e_r, f1, FR_e_expl_Input_Y + // r = r + FR_e_expl_Input_Y +};; + +{ .mmi + shladd GR_e_ad_W1 = GR_e_M1,3,GR_e_ad_W1 // Point to W1 + shladd GR_e_ad_T1 = GR_e_M1,2,GR_e_ad_T1 // Point to T1 + extr.u GR_e_M2 = GR_e_N_fix, 0, 6 // Extract index M_2 +};; + + +{ .mfi + ldfs FR_e_T1 = [GR_e_ad_T1],0 // Get T1 + nop.f 0 + extr GR_e_K = GR_e_N_fix, 12, 32 //Extract limit range K +} +{ .mfi + shladd GR_e_ad_T2 = GR_e_M2,2,GR_e_ad_T2 // Point to T2 +(p15) fma.s1 FR_n_PolyL = FR_n_Poly1L, FR_n_XS, FR_n_PolyL + //sin(Pi*x) poly + shladd GR_e_ad_W2 = GR_e_M2,3,GR_e_ad_W2 // Point to W2 +};; + +{ .mfi + ldfs FR_e_T2 = [GR_e_ad_T2],0 // Get T2 + nop.f 0 + add GR_e_exp_2_k = GR_e_exp_bias, GR_e_K // exp of 2^k +} +{ .mfi + ldfd FR_e_W1 = [GR_e_ad_W1],0 // Get W1 + nop.f 0 + sub GR_e_exp_2_mk = GR_e_exp_bias, GR_e_K // exp of 2^-k +};; + +{ .mmi + ldfd FR_e_W2 = [GR_e_ad_W2],0 // Get W2 + nop.m 0 + nop.i 0 +};; + +{ .mmf + setf.exp FR_e_scale = GR_e_exp_2_k // Set scale = 2^k + setf.exp FR_e_2_mk = GR_e_exp_2_mk // Form 2^-k + fnma.s1 FR_e_r = FR_e_L_lo, FR_e_float_N, FR_e_r + // r = -L_lo * float_N + r +};; + +{ .mfi + nop.m 0 +(p15) fma.s1 FR_n_PolyL = FR_n_Tail, FR_n_XS7, FR_n_PolyL + //sin(Pi*x) poly + nop.i 0 +};; + +{ .mfi + nop.m 0 + fma.s1 FR_e_poly = FR_e_r, FR_e_A3, FR_e_A2 // poly=r*A3+A2 + nop.i 0 +} +{ .mfi + nop.m 0 + fmpy.s1 FR_e_rsq = FR_e_r, FR_e_r // rsq = r * r + nop.i 0 +};; + +{ .mfi + nop.m 0 + fmpy.s1 FR_e_T = FR_e_T1, FR_e_T2 // T = T1 * T2 + nop.i 0 +} +{ .mfi + nop.m 0 + fadd.s1 FR_e_W1_p1 = FR_e_W1, f1 // W1_p1 = W1 + 1.0 + nop.i 0 +};; + +{ .mfi + nop.m 0 +(p15) fma.s1 FR_n_TT = FR_n_PolyL, FR_l_AbsX, f0 //sin(Pi*x) poly + nop.i 0 +};; + +{ .mfi + nop.m 0 + fma.s1 FR_e_poly = FR_e_r, FR_e_poly, FR_e_A1 + // poly = r * poly + A1 + nop.i 0 +};; + +{ .mfi + nop.m 0 + fma.s1 FR_e_T_scale = FR_e_T, FR_e_scale, f0 // T_scale=T*scale + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 FR_e_W = FR_e_W2, FR_e_W1_p1, FR_e_W1 + // W = W2 * (W1+1.0) + W1 + nop.i 0 +};; + +{ .mfi + nop.m 0 +(p15) fma.s1 FR_n_SinxH = FR_n_PolyH, FR_l_AbsX, FR_n_TT + // sin(Pi*x) poly + nop.i 0 +};; + +{ .mfi + nop.m 0 + mov FR_e_Y_hi = FR_e_T // Assume Y_hi = T + nop.i 0 +};; + +{ .mfi + nop.m 0 + fma.s1 FR_e_poly = FR_e_rsq, FR_e_poly, FR_e_r + // poly = rsq * poly + r + nop.i 0 +};; + +{ .mfi + nop.m 0 + fma.s1 FR_e_Wp1_T_scale = FR_e_W, FR_e_T_scale, FR_e_T_scale + // (W+1)*T*scale + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 FR_e_W_T_scale = FR_e_W, FR_e_T_scale, f0 // W*T*scale + nop.i 0 +};; + +{ .mfi + nop.m 0 +(p15) fms.s1 FR_n_SinxL = FR_n_PolyH, FR_l_AbsX, FR_n_SinxH + // Low part of sin + nop.i 0 +};; + +{ .mfi + nop.m 0 +(p15) frcpa.s1 FR_n_Y0, p0 = f1, FR_n_SinxH // y = frcpa(b) + nop.i 0 +};; + +{ .mfi + nop.m 0 + fma.s1 FR_e_result_lo = FR_e_Wp1_T_scale, FR_e_poly, FR_e_W_T_scale + // Low part of exp result + nop.i 0 +};; + +{ .mfi + nop.m 0 +(p15) fma.s1 FR_n_SinxL = FR_n_SinxL, f1, FR_n_TT // sin low result + nop.i 0 +};; + +{ .mfi + nop.m 0 +(p15) fma.s1 FR_n_Q0 = f1,FR_n_Y0,f0 // q = y + nop.i 0 +} +{ .mfi + nop.m 0 +(p15) fnma.s1 FR_n_E0 = FR_n_Y0, FR_n_SinxH, f1 // e = 1-b*y + nop.i 0 +};; + + +{ .mfb + nop.m 0 +(p14) fma.s0 f8 = FR_e_Y_hi, FR_e_scale, FR_e_result_lo +(p14) br.ret.spnt b0 // Exit for positive Stirling path ////////////////////// +};; + +{ .mfi + nop.m 0 + fma.s1 FR_e_expl_Output_X = FR_e_Y_hi, FR_e_scale, f0 // exp result + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 FR_e_expl_Output_Y = FR_e_result_lo, f1, f0// exp lo result + nop.i 0 +};; + +{ .mfi + nop.m 0 + fma.s1 FR_n_E2 = FR_n_E0,FR_n_E0,FR_n_E0 // e2 = e+e^2 + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 FR_n_E1 = FR_n_E0,FR_n_E0,f0 // e1 = e^2 + nop.i 0 +};; + +{ .mfi + nop.m 0 + fma.s1 FR_n_Y1 = FR_n_Y0,FR_n_E2,FR_n_Y0 // y1 = y+y*e2 + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 FR_n_E3 = FR_n_E1,FR_n_E1,FR_n_E0 // e3 = e+e1^2 + nop.i 0 +};; + +{ .mfi + nop.m 0 + fma.s1 FR_n_Y2 = FR_n_Y1,FR_n_E3,FR_n_Y0 // y2 = y+y1*e3 + nop.i 0 +} +{ .mfi + nop.m 0 + fnma.s1 FR_n_R0 = FR_n_SinxH,FR_n_Q0,f1 // r = a-b*q + nop.i 0 +};; + +{ .mfi + nop.m 0 + fnma.s1 FR_n_E4 = FR_n_SinxH,FR_n_Y2,f1 // e4 = 1-b*y2 + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 FR_n_RcpResH = FR_n_R0,FR_n_Y2,FR_n_Q0 // x = q+r*y2 + nop.i 0 +};; + +{ .mfi + nop.m 0 + fma.s1 FR_n_Y3 = FR_n_Y2,FR_n_E4,FR_n_Y2 // y3 = y2+y2*e4 + nop.i 0 +} +{ .mfi + nop.m 0 + fnma.s1 FR_n_R1 = FR_n_SinxH,FR_n_RcpResH,f1 // r1 = a-b*x + nop.i 0 +};; + +{ .mfi + nop.m 0 + fnma.s1 FR_n_R1 = FR_n_SinxL,FR_n_RcpResH,FR_n_R1 + // r1 = r1 - b_lo*X + nop.i 0 +};; + +{ .mfi + nop.m 0 + fma.s1 FR_n_RcpResL = FR_n_R1,FR_n_Y3,f0 // x_lo = r1*y3 + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 FR_n_Temp = FR_n_RcpResH, FR_e_expl_Output_Y, f0 + // Multiplying exp and sin result + nop.i 0 +};; + +{ .mfi + nop.m 0 + fma.s1 FR_n_Temp = FR_n_RcpResL, FR_e_expl_Output_X, FR_n_Temp + // Multiplying exp and sin result + nop.i 0 +};; + +{ .mfi + nop.m 0 + fma.s1 FR_n_ResH = FR_n_RcpResH, FR_e_expl_Output_X, FR_n_Temp + // Multiplying exp and sin result + nop.i 0 +};; + +{ .mfi + nop.m 0 + fms.s1 FR_n_ResL = FR_n_RcpResH, FR_e_expl_Output_X, FR_n_ResH + // Multiplying exp and sin result + nop.i 0 +} +{ .mfi + nop.m 0 +(p12) fma.s1 FR_n_ResH = FR_n_ResH, FR_n_NegOne, f0 // Negate + nop.i 0 +};; + +{ .mfi + nop.m 0 + fma.s1 FR_n_ResL = FR_n_ResL, f1, FR_n_Temp + // Multiplying exp and sin result - low result obtained + nop.i 0 +};; + +.pred.rel "mutex",p12,p13 +{ .mfi + nop.m 0 +(p13) fma.s0 f8 = FR_n_ResH, f1, FR_n_ResL // For odd + nop.i 0 +} +{ .mfb + nop.m 0 +(p12) fms.s0 f8 = FR_n_ResH, f1, FR_n_ResL // For even + br.ret.sptk b0 // Exit for negative Stirling path ////////////////////// +};; + + +//////////// 1 <= |X| < 13 path //////////////////////////////////////////////// +//------------------------------------------------------------------------------ +.align 64 +tgamma_lt_13: +{ .mfi + getf.sig GR_p_XN = FR_p_IXN // Get significand + fcvt.xf FR_p_XN = FR_p_IXN // xn = [x] + add GR_r_sin_Table2= 0x40, GR_r_sin_Table // Shifted table addr. +} +{ .mfi + ldfpd FR_p_0p5, FR_p_1p5 = [GR_c_Table], 16 // 0.5 & 1.5 + fms.s1 FR_p_AbsXM1 = FR_p_AbsX, f1, f1 // X-1 + add GR_p_Table2 = 0xB0, GR_p_Table +};; + +{ .mfi + add GR_r_sin_Table = -16, GR_r_sin_Table // For compensation + fcvt.xf FR_r_XNS = FR_r_IXNS // Convert int repr to float + shr.u GR_p_X_Sgnd = GR_p_X_Sgnd, 59 // Get only 5 bit of signd +};; + +{ .mfi + ldfpd FR_r_A2H,FR_r_A2L = [GR_r_sin_Table], 16 // Load A2 + nop.f 0 + add GR_p_Int = -2, GR_p_XN // int = int - 2 +} +{ .mfi + ldfe FR_r_A6 = [GR_r_sin_Table2], 16 + nop.f 0 + cmp.gtu p11, p12 = 0x2, GR_p_XN // p11: x < 2 (splitted intervals), + // p12: x > 2 (base intervals) +};; + +{ .mfi + ldfpd FR_r_A1H, FR_r_A1L = [GR_r_sin_Table], 16 + nop.f 0 + shr GR_p_Int = GR_p_Int, 1 // int/2 +} +{ .mfi + ldfe FR_r_A5 = [GR_r_sin_Table2], 16 + nop.f 0 +(p11) cmp.gtu.unc p10, p11 = 0x1C, GR_p_X_Sgnd // sgnd(x) < 0.75 +};; + +{ .mfi + ldfe FR_r_A9 = [GR_r_sin_Table], 16 + nop.f 0 + shl GR_p_Offset = GR_p_Int, 4 // offset = int*16 +} +{ .mfi + ldfe FR_r_A4 = [GR_r_sin_Table2], 16 + nop.f 0 +(p10) cmp.gtu.unc p9, p10 = 0x14, GR_p_X_Sgnd // sgnd(x) < 0.25 +};; + + +{ .mfi + ldfe FR_r_A8 = [GR_r_sin_Table], 16 + nop.f 0 +(p12) tbit.nz.unc p13, p12 = GR_p_XN, 0x0 // p13: reccurent computations + // X is at [3;4], [5;6], [7;8]... interval +} +{ .mfi + ldfe FR_r_A3 = [GR_r_sin_Table2], 16 + nop.f 0 + shladd GR_p_Offset = GR_p_Int, 2, GR_p_Offset // +int*4 +};; + +.pred.rel "mutex",p9,p11 +{ .mfi + add GR_p_Offset = GR_p_Int, GR_p_Offset + // +int, so offset = int*21 +(p9) fms.s1 FR_p_XR = FR_p_AbsX, f1, f1 // r = x-1 + nop.i 0 +} +{ .mfi + ldfe FR_r_A7 = [GR_r_sin_Table], 16 +(p11) fms.s1 FR_p_XR = FR_p_2, f1, FR_p_AbsX + // r = 2-x for 1.75 < x < 2 + nop.i 0 +};; + +.pred.rel "mutex",p9,p10 +.pred.rel "mutex",p10,p11 +.pred.rel "mutex",p9,p11 +{ .mfi +(p9) add GR_p_Offset = 126, r0 // 1.0 < x < 1.25 table +(p15) fcmp.eq.unc.s1 p7,p0 = FR_p_AbsX, FR_p_XN + // If arg is integer and negative - singularity branch + nop.i 0 +} +{ .mfi +(p10) add GR_p_Offset = 147, r0 // 1.25 < x < 1.75 table + nop.f 0 +(p11) add GR_p_Offset = 168, r0 // 1.75 < x < 2.0 table +};; + +{ .mmf + shladd GR_p_Table = GR_p_Offset, 4, GR_p_Table + shladd GR_p_Table2 = GR_p_Offset, 4, GR_p_Table2 + fma.s1 FR_r_XS = FR_r_AbsX , f1, FR_r_XNS // xs = x - [x] +};; + +{ .mmb + ldfpd FR_p_A5H, FR_p_A5L = [GR_p_Table], 16 + ldfpd FR_p_A2H, FR_p_A2L = [GR_p_Table2], 16 +(p7) br.cond.spnt tgammal_singularity // Singularity for integer ///////////// + // and negative argument /////////////// +};; + +{ .mfi + ldfpd FR_p_A4H, FR_p_A4L = [GR_p_Table], 16 + fma.s1 FR_p_XN = FR_p_XN, f1, FR_p_0p5 // xn = xn+0.5 + nop.i 0 +} +{ .mfi + ldfpd FR_p_A1H, FR_p_A1L = [GR_p_Table2], 16 +(p10) fms.s1 FR_p_XR = FR_p_AbsX, f1, FR_p_1p5 // r = x - 1.5 + nop.i 0 +};; + +{ .mmi + ldfpd FR_p_A3H, FR_p_A3L = [GR_p_Table], 16 + ldfpd FR_p_A0H, FR_p_A0L = [GR_p_Table2], 16 + nop.i 0 +};; + +{ .mmi + ldfe FR_p_A20 = [GR_p_Table], 16 + ldfe FR_p_A12 = [GR_p_Table2], 16 + nop.i 0 +};; + +{ .mmf + ldfe FR_p_A19 = [GR_p_Table], 16 + ldfe FR_p_A11 = [GR_p_Table2], 16 + fma.s1 FR_r_XS2 = FR_r_XS, FR_r_XS, f0 // xs2 = xs*xs +};; + +{ .mmi + ldfe FR_p_A18 = [GR_p_Table], 16 + ldfe FR_p_A10 = [GR_p_Table2], 16 + nop.i 0 +};; + +.pred.rel "mutex",p12,p13 +{ .mfi + ldfe FR_p_A17 = [GR_p_Table], 16 +(p12) fms.s1 FR_p_XR = FR_p_AbsX, f1, FR_p_XN // r = x - xn + nop.i 0 +} +{ .mfi + ldfe FR_p_A9 = [GR_p_Table2], 16 +(p13) fms.s1 FR_p_XR = FR_p_AbsX, f1, FR_p_XN + nop.i 0 +};; + +{ .mmi + ldfe FR_p_A16 = [GR_p_Table], 16 + ldfe FR_p_A8 = [GR_p_Table2], 16 +(p9) cmp.eq p12, p0 = r0, r0 // clear p12 +};; + +{ .mmi + ldfe FR_p_A15 = [GR_p_Table], 16 + ldfe FR_p_A7 = [GR_p_Table2], 16 +(p10) cmp.eq p12, p0 = r0, r0 // clear p12 +};; + +{ .mfi + ldfe FR_p_A14 = [GR_p_Table], 16 + fma.s1 FR_r_TH = FR_r_A2H, FR_r_XS2, f0 // sin for neg +(p11) cmp.eq p12, p0 = r0, r0 // clear p12 +} +{ .mfi + ldfe FR_p_A6 = [GR_p_Table2], 16 + fma.s1 FR_r_TL = FR_r_A2L, FR_r_XS2, f0 // sin for neg + nop.i 0 +};; + +{ .mfi + ldfe FR_p_A13 = [GR_p_Table], 16 + fms.s1 FR_r_XS2L = FR_r_XS, FR_r_XS, FR_r_XS2 // x2Lo part + nop.i 0 +};; + +{ .mfi + nop.m 0 + fma.s1 FR_p_Temp5H = FR_p_A5H, FR_p_XR, f0 // A5H*r + // 'Low poly' + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 FR_p_XR2 = FR_p_XR, FR_p_XR, f0 // r^2 = r*r + nop.i 0 +};; + +{ .mfi + nop.m 0 + fabs FR_r_XS = FR_r_XS // abs(xs) + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 FR_p_Temp2H = FR_p_A2H, FR_p_XR, f0 // A2H*r + // 'High poly' + nop.i 0 +};; + +{ .mfi + nop.m 0 + fms.s1 FR_r_TT = FR_r_A2H, FR_r_XS2, FR_r_TH // sin for neg + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 FR_r_ResH = FR_r_TH, f1, FR_r_A1H // sin for neg + nop.i 0 +};; + +{ .mfi + nop.m 0 + fma.s1 FR_r_TL = FR_r_A2H, FR_r_XS2L, FR_r_TL // sin for neg + nop.i 0 +};; + +{ .mfi + nop.m 0 + fms.s1 FR_p_Temp5L = FR_p_A5H,FR_p_XR,FR_p_Temp5H //A5H*r delta + // 'Low poly' + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 FR_p_Poly5H = FR_p_Temp5H, f1, FR_p_A4H // A5H*r+A4H + // 'Low poly' + nop.i 0 +};; + +{ .mfi + nop.m 0 + fms.s1 FR_p_Temp2L = FR_p_A2H, FR_p_XR, FR_p_Temp2H//A2H*r delta + //'High poly' + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 FR_p_Poly2H = FR_p_Temp2H, f1, FR_p_A1H // A2H*r+A1H + //'High poly' + nop.i 0 +};; + +{ .mfi + nop.m 0 + fma.s1 FR_p_XR3 = FR_p_XR2, FR_p_XR, f0 // r^3 = r^2*r + nop.i 0 +} +{ .mfi + nop.m 0 + fms.s1 FR_p_XR2L = FR_p_XR, FR_p_XR, FR_p_XR2 // r^2 delta + nop.i 0 +};; + +{ .mfi + nop.m 0 + fma.s1 FR_p_A18 = FR_p_A19, FR_p_XR, FR_p_A18 // Poly tail + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 FR_p_A14 = FR_p_A15, FR_p_XR, FR_p_A14 // Poly tail + nop.i 0 +};; + +{ .mfi + nop.m 0 + fma.s1 FR_p_XR4 = FR_p_XR2, FR_p_XR2, f0 // r^4 = r^2*r^2 + nop.i 0 +};; + +{ .mfi + nop.m 0 + fma.s1 FR_p_Temp5L = FR_p_A5L, FR_p_XR, FR_p_Temp5L// Low part + // of A5*r+A4 + nop.i 0 +} +{ .mfi + nop.m 0 + fms.s1 FR_p_Poly5L = FR_p_A4H, f1, FR_p_Poly5H // Low part + // of A5*r+A4 + nop.i 0 +};; + +{ .mfi + nop.m 0 + fma.s1 FR_p_Temp4H = FR_p_Poly5H, FR_p_XR, f0 // (A5H*r+A4H)*r + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 FR_p_Temp2L = FR_p_A2L, FR_p_XR, FR_p_Temp2L // A2*r low + nop.i 0 +};; + +{ .mfi + nop.m 0 + fms.s1 FR_p_Poly2L = FR_p_A1H, f1, FR_p_Poly2H // High poly + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 FR_p_Temp1H = FR_p_Poly2H, FR_p_XR, f0 // High poly + nop.i 0 +};; + +{ .mfi + nop.m 0 + fms.s1 FR_p_XR3L = FR_p_XR2, FR_p_XR, FR_p_XR3 // x^3 delta + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 FR_p_A16 = FR_p_A17, FR_p_XR, FR_p_A16 // Poly tail + nop.i 0 +};; + +{ .mfi + nop.m 0 + fms.s1 FR_r_ResL = FR_r_A1H, f1, FR_r_ResH // sin for neg + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 FR_r_TL = FR_r_TL, f1, FR_r_TT // sin for neg + nop.i 0 +};; + +{ .mfi + nop.m 0 + fma.s1 FR_p_Temp5L = FR_p_Temp5L, f1, FR_p_A4L // Low poly + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 FR_p_Poly5L = FR_p_Poly5L, f1, FR_p_Temp5H // Low poly + nop.i 0 +};; + +{ .mfi + nop.m 0 + fms.s1 FR_p_Temp4L = FR_p_Poly5H,FR_p_XR,FR_p_Temp4H //Low poly + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 FR_p_Poly4H = FR_p_Temp4H, f1, FR_p_A3H // Low poly + nop.i 0 +};; + +{ .mfi + nop.m 0 + fma.s1 FR_p_Temp2L = FR_p_Temp2L, f1, FR_p_A1L // High poly + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 FR_p_Poly2L = FR_p_Poly2L, f1, FR_p_Temp2H // High poly + nop.i 0 +};; + +{ .mfi + nop.m 0 + fms.s1 FR_p_Temp1L = FR_p_Poly2H,FR_p_XR,FR_p_Temp1H //High poly + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 FR_p_Poly1H = FR_p_Temp1H, f1, FR_p_A0H // High poly + nop.i 0 +};; + +{ .mfi + nop.m 0 + fma.s1 FR_p_A12 = FR_p_A13, FR_p_XR, FR_p_A12 // Poly tail + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 FR_p_XR3L = FR_p_XR2L, FR_p_XR, FR_p_XR3L // x^3 low + nop.i 0 +};; + +{ .mfi + nop.m 0 + fma.s1 FR_p_Poly5L = FR_p_Poly5L, f1, FR_p_Temp5L // Low poly + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 FR_p_A10 = FR_p_A11, FR_p_XR, FR_p_A10 // Poly tail + nop.i 0 +};; + +{ .mfi + nop.m 0 + fms.s1 FR_p_Poly4L = FR_p_A3H, f1, FR_p_Poly4H // Low poly + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 FR_p_A6 = FR_p_A7, FR_p_XR, FR_p_A6 // Poly tail + nop.i 0 +};; + +{ .mfi + nop.m 0 + fma.s1 FR_p_A8 = FR_p_A9, FR_p_XR, FR_p_A8 // Poly tail + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 FR_p_XR6 = FR_p_XR4, FR_p_XR2, f0 // Poly tail + nop.i 0 +};; + +{ .mfi + nop.m 0 + fma.s1 FR_p_Poly2L = FR_p_Poly2L, f1, FR_p_Temp2L // High poly + nop.i 0 +} +{ .mfi + nop.m 0 + fms.s1 FR_p_Poly1L = FR_p_A0H, f1, FR_p_Poly1H // High poly + nop.i 0 +};; + +{ .mfi + nop.m 0 + fma.s1 FR_r_ResL = FR_r_ResL, f1, FR_r_TH // sin for neg + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 FR_r_TT = FR_r_TL, f1, FR_r_A1L // sin for neg + nop.i 0 +};; + +{ .mfi + nop.m 0 + fma.s1 FR_p_Temp4L = FR_p_Poly5L,FR_p_XR,FR_p_Temp4L // Low poly + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 FR_p_A18 = FR_p_A20, FR_p_XR2, FR_p_A18 // Poly tail + nop.i 0 +};; + +{ .mfi + nop.m 0 + fma.s1 FR_p_Poly4L = FR_p_Poly4L, f1, FR_p_Temp4H // Low poly + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 FR_p_A14 = FR_p_A16, FR_p_XR2, FR_p_A14 // Poly tail + nop.i 0 +};; + +{ .mfi + nop.m 0 + fma.s1 FR_p_A6 = FR_p_A8, FR_p_XR2, FR_p_A6 // Poly tail + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 FR_p_A10 = FR_p_A12, FR_p_XR2, FR_p_A10 // Poly tail + nop.i 0 +};; + +{ .mfi + nop.m 0 + fma.s1 FR_p_Temp1L = FR_p_Poly2L,FR_p_XR,FR_p_Temp1L //High poly + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 FR_p_Poly1L = FR_p_Poly1L, f1, FR_p_Temp1H // High poly + nop.i 0 +};; + +{ .mfi + nop.m 0 + fma.s1 FR_r_ResL = FR_r_ResL, f1, FR_r_TT // sin for neg + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 FR_r_TH = FR_r_ResH, FR_r_XS2, f0 // sin for neg + nop.i 0 +};; + +{ .mfi + nop.m 0 + fma.s1 FR_p_Temp4L = FR_p_Temp4L, f1, FR_p_A3L // Low poly + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 FR_p_Poly3H = FR_p_Poly4H, FR_p_XR3, f0 // Low poly + nop.i 0 +};; + +{ .mfi + nop.m 0 + fma.s1 FR_p_A14 = FR_p_A18, FR_p_XR4, FR_p_A14 // Poly tail + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 FR_p_XR8 = FR_p_XR4, FR_p_XR4, f0 // Poly tail + nop.i 0 +};; + +{ .mfi + nop.m 0 + fma.s1 FR_r_TL = FR_r_ResH, FR_r_XS2L, f0 // sin for neg + nop.i 0 +};; + +{ .mfi + nop.m 0 + fma.s1 FR_p_Temp1L = FR_p_Temp1L, f1, FR_p_A0L // High poly + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 FR_p_A6 = FR_p_A10, FR_p_XR4, FR_p_A6 // Poly tail + nop.i 0 +};; + +{ .mfi + nop.m 0 + fms.s1 FR_r_TT = FR_r_ResH, FR_r_XS2, FR_r_TH // sin for neg + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 FR_r_Res3H = FR_r_TH, f1, f1 // sin for neg + nop.i 0 +};; + +{ .mfi + nop.m 0 + fma.s1 FR_p_Poly4L = FR_p_Poly4L, f1, FR_p_Temp4L // Low poly + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 FR_p_Poly3L = FR_p_Poly4H, FR_p_XR3L, f0 // Low poly + nop.i 0 +};; + +{ .mfi + nop.m 0 + fma.s1 FR_p_Poly0H = FR_p_Poly3H,f1,FR_p_Poly1H //Low & High add + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 FR_r_A7 = FR_r_A8, FR_r_XS2, FR_r_A7 // sin for neg + nop.i 0 +};; + +{ .mfi + nop.m 0 + fma.s1 FR_r_TL = FR_r_ResL, FR_r_XS2, FR_r_TL // sin for neg + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 FR_r_XS4 = FR_r_XS2, FR_r_XS2, f0 // sin for neg + nop.i 0 +};; + +{ .mfi + nop.m 0 + fma.s1 FR_p_Poly1L = FR_p_Poly1L, f1, FR_p_Temp1L // High poly + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 FR_p_PolyTail = FR_p_A14, FR_p_XR8, FR_p_A6 // Poly tail + nop.i 0 +};; + +{ .mfi + nop.m 0 + fms.s1 FR_r_Res3L = f1, f1, FR_r_Res3H // sin for neg + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 FR_r_ResH = FR_r_Res3H, FR_r_XS, f0 // sin for neg + nop.i 0 +};; + +{ .mfi + nop.m 0 + fms.s1 FR_p_Temp0L = FR_p_Poly4H,FR_p_XR3,FR_p_Poly3H //Low poly + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 FR_p_Poly3L = FR_p_Poly4L,FR_p_XR3,FR_p_Poly3L //Low poly + nop.i 0 +};; + +{ .mfi + nop.m 0 + fms.s1 FR_p_Poly0L = FR_p_Poly1H,f1,FR_p_Poly0H //Low & High add + nop.i 0 +} +{ .mfi + nop.m 0 +(p13) fma.s1 FR_p_OddPoly0H = FR_p_Poly0H, FR_p_AbsXM1, f0 + // Reccurent computations - multiplying by X-1 + nop.i 0 +};; + +{ .mfi + nop.m 0 + fma.s1 FR_r_TL = FR_r_TL, f1, FR_r_TT // sin for neg + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 FR_r_A3 = FR_r_A4, FR_r_XS2, FR_r_A3 // sin for neg + nop.i 0 +};; + +{ .mfi + nop.m 0 + fma.s1 FR_p_Poly1L = FR_p_PolyTail,FR_p_XR6,FR_p_Poly1L//High + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 FR_r_A5 = FR_r_A6, FR_r_XS2, FR_r_A5 // sin for neg + nop.i 0 +};; + +{ .mfi + nop.m 0 + fma.s1 FR_r_Res3L = FR_r_Res3L, f1, FR_r_TH // sin for neg + nop.i 0 +} +{ .mfi + nop.m 0 + fms.s1 FR_r_ResL = FR_r_Res3H, FR_r_XS, FR_r_ResH//sin for neg + nop.i 0 +};; + +{ .mfi + nop.m 0 + fma.s1 FR_p_Poly3L = FR_p_Poly3L, f1, FR_p_Temp0L // Low poly + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 FR_r_A7 = FR_r_A9, FR_r_XS4, FR_r_A7 // sin for neg + nop.i 0 +};; + +{ .mfi + nop.m 0 + fma.s1 FR_p_Poly0L = FR_p_Poly0L,f1,FR_p_Poly3H //Low & High add + nop.i 0 +} +{ .mfi + nop.m 0 +(p13) fms.s1 FR_p_OddPoly0L = FR_p_Poly0H, FR_p_AbsXM1, FR_p_OddPoly0H + // Reccurent computations - multiplying by X-1 (low part) + nop.i 0 +};; + +{ .mfi + nop.m 0 + fma.s1 FR_r_A3 = FR_r_A5, FR_r_XS4, FR_r_A3 // sin for neg + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 FR_r_XS7 = FR_r_XS4, FR_r_XS2, f0 // xs^6 + nop.i 0 +};; + +{ .mfi + nop.m 0 + fma.s1 FR_r_Res3L = FR_r_Res3L, f1, FR_r_TL // sin for neg + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 FR_r_XS8 = FR_r_XS4, FR_r_XS4, f0 // sin for neg + nop.i 0 +};; + +{ .mfi + nop.m 0 + fma.s1 FR_p_Temp0H = FR_p_Poly3L,f1,FR_p_Poly1L //Low & High add + nop.i 0 +};; + +{ .mfi + nop.m 0 + fma.s1 FR_r_XS7 = FR_r_XS7, FR_r_XS, f0 // xs^7 + nop.i 0 +};; + +{ .mfi + nop.m 0 + fma.s1 FR_r_ResL = FR_r_Res3L, FR_r_XS, FR_r_ResL//sin for neg + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 FR_r_Tail = FR_r_A7, FR_r_XS8, FR_r_A3 // sin tail res + nop.i 0 +};; + +{ .mfi + nop.m 0 + fma.s1 FR_p_Poly0L = FR_p_Poly0L,f1,FR_p_Temp0H //Low & High add + nop.i 0 +};; + + +{ .mfi + nop.m 0 + fma.s1 FR_r_ResL = FR_r_Tail,FR_r_XS7,FR_r_ResL //sin for neg + nop.i 0 +};; + +{ .mfi + nop.m 0 +(p13) fma.s1 FR_p_OddPoly0L = FR_p_Poly0L, FR_p_AbsXM1, FR_p_OddPoly0L + // Reccurent computations - multiplying by X-1 (low part) + nop.i 0 +};; + +{ .mfi + nop.m 0 + fma.s1 FR_r_TT = FR_r_ResL, FR_r_AbsX, f0 // X*sin + nop.i 0 +};; + +.pred.rel "mutex",p12,p13 +{ .mfi + nop.m 0 +(p12) fma.s0 f8 = FR_p_Poly0H, f1, FR_p_Poly0L // Even + nop.i 0 +} +{ .mfb + nop.m 0 +(p13) fma.s0 f8 = FR_p_OddPoly0H, f1, FR_p_OddPoly0L // Odd +(p14) br.ret.spnt b0 // Exit for 1 <= |X| < 13 path (positive arguments)///// +};; + +{ .mfi + nop.m 0 +(p13) fma.s1 FR_p_Poly0H = FR_p_OddPoly0H, f1, f0 + // Reccurent computations + nop.i 0 +} +{ .mfi + nop.m 0 +(p13) fma.s1 FR_p_Poly0L = FR_p_OddPoly0L, f1, f0 + // Reccurent computations + nop.i 0 +};; + +{ .mfi + nop.m 0 + fma.s1 FR_r_Res1H = FR_r_ResH, FR_r_AbsX, FR_r_TT // X*sin +(p11) cmp.eq p13, p12 = r0, r0 +};; + +{ .mfi + nop.m 0 + fms.s1 FR_r_Res1L = FR_r_ResH,FR_r_AbsX,FR_r_Res1H// X*sin +(p9) cmp.eq p13, p12 = r0, r0 +};; + +{ .mfi + nop.m 0 + fma.s1 FR_r_Res1L = FR_r_Res1L, f1, FR_r_TT // sin for neg +(p10) cmp.eq p13, p12 = r0, r0 +} +{ .mfi + nop.m 0 + fma.s1 FR_r_TL = FR_p_Poly0L, FR_r_Res1H, f0 // mult by sin + nop.i 0 +};; + +{ .mfi + nop.m 0 + fma.s1 FR_r_TL = FR_p_Poly0H,FR_r_Res1L,FR_r_TL//mult by sin + nop.i 0 +};; + +{ .mfi + nop.m 0 + fma.s1 FR_r_ResH = FR_p_Poly0H,FR_r_Res1H,FR_r_TL//mult by sin + nop.i 0 +};; + +{ .mfi + nop.m 0 + fms.s1 FR_r_ResL = FR_p_Poly0H,FR_r_Res1H,FR_r_ResH//sin mult + nop.i 0 +};; + +{ .mfi + nop.m 0 + frcpa.s1 FR_r_Y0,p0 = f1,FR_r_ResH // y = frcpa(b) + nop.i 0 +};; + +{ .mfi + nop.m 0 + fneg FR_r_NegOne = f1 // Form -1.0 + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 FR_r_ResL = FR_r_ResL, f1, FR_r_TL //Low result of mult + nop.i 0 +};; + +{ .mfi + nop.m 0 + fma.s1 FR_r_Q0 = f1,FR_r_Y0,f0 // q = a*y + nop.i 0 +} +{ .mfi + nop.m 0 + fnma.s1 FR_r_E0 = FR_r_Y0,FR_r_ResH,f1 // e = 1-b*y + nop.i 0 +};; + +{ .mfi + nop.m 0 + fma.s1 FR_r_E2 = FR_r_E0,FR_r_E0,FR_r_E0 // e2 = e+e^2 + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 FR_r_E1 = FR_r_E0,FR_r_E0,f0 // e1 = e^2 + nop.i 0 +};; + +{ .mfi + nop.m 0 + fma.s1 FR_r_Y1 = FR_r_Y0,FR_r_E2,FR_r_Y0 // y1 = y+y*e2 + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 FR_r_E3 = FR_r_E1,FR_r_E1,FR_r_E0 // e3 = e+e1^2 + nop.i 0 +};; + +{ .mfi + nop.m 0 + fma.s1 FR_r_Y2 = FR_r_Y1,FR_r_E3,FR_r_Y0 // y2 = y+y1*e3 + nop.i 0 +} +{ .mfi + nop.m 0 + fnma.s1 FR_r_R0 = FR_r_ResH,FR_r_Q0,f1 // r = a-b*q + nop.i 0 +};; + +{ .mfi + nop.m 0 + fnma.s1 FR_r_E4 = FR_r_ResH,FR_r_Y2,f1 // e4 = 1-b*y2 + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 FR_r_ZH = FR_r_R0,FR_r_Y2,FR_r_Q0 // x = q+r*y2 + nop.i 0 +};; + +{ .mfi + nop.m 0 + fma.s1 FR_r_Y3 = FR_r_Y2,FR_r_E4,FR_r_Y2 // y3 = y2+y2*e4 + nop.i 0 +} +{ .mfi + nop.m 0 + fnma.s1 FR_r_R1 = FR_r_ResH,FR_r_ZH,f1 // r1 = a-b*x + nop.i 0 +};; + +{ .mfi + nop.m 0 + fnma.s1 FR_r_R1 = FR_r_ResL,FR_r_ZH,FR_r_R1 // r1=r1-b_lo*X + nop.i 0 +} +{ .mfi + nop.m 0 +(p12) fma.s1 FR_r_ZHN = FR_r_ZH,FR_r_NegOne, f0 // Negate for evens + nop.i 0 +};; + +.pred.rel "mutex",p13,p12 +{ .mfi + nop.m 0 +(p13) fma.s0 f8 = FR_r_R1,FR_r_Y3,FR_r_ZH // Final result + nop.i 0 +} +{ .mfb + nop.m 0 +(p12) fnma.s0 f8 = FR_r_R1,FR_r_Y3,FR_r_ZHN // Final result + br.ret.sptk b0 // Exit for 1 <= |X| < 13 path (negative arguments)////// +};; + + +//////////// |X| < 1 path ///////////////////////////////////////////////////// +//------------------------------------------------------------------------------ +.align 64 +tgamma_lt_1: +{ .mfi + getf.exp GR_p_Exp = FR_p_AbsX // exp of abs X + fma.s1 FR_z_Q0 = f1,FR_z_Y0,f0 // q = a*y + add GR_r_sin_Table2= 0x50, GR_r_sin_Table +} +{ .mfi + ldfpd FR_p_0p5, FR_p_1p5 = [GR_c_Table], 16 + fnma.s1 FR_z_E0 = FR_z_Y0,f8,f1 // e = 1-b*y + add GR_p_Table2 = 0xB0, GR_p_Table +};; + +{ .mfi + ldfd FR_p_0p25 = [GR_c_Table] + fcvt.xf FR_r_XNS = FR_r_IXNS // Convert int repr to float + shr.u GR_p_X_Sgnd = GR_p_X_Sgnd, 60 + // Obtain only 4 bits of significand +} +{ .mfi + nop.m 0 + nop.f 0 + add GR_p_Bias = 0xffff, r0 // Set bias +};; + +{ .mfi + ldfpd FR_r_A2H, FR_r_A2L = [GR_r_sin_Table], 16 + nop.f 0 + shl GR_p_XN = GR_p_Exp, 4 + // Shift exp to 4 bits left to set place for significand +} +{ .mlx + ldfe FR_r_A6 = [GR_r_sin_Table2], 16 + movl GR_p_0p75 = 0xfffec // 0.75 +};; + +{ .mfi + ldfpd FR_r_A1H, FR_r_A1L = [GR_r_sin_Table], 16 + nop.f 0 + or GR_p_XN = GR_p_XN, GR_p_X_Sgnd + // Combine exp with 4 high bits of significand +} +{ .mfi + ldfe FR_r_A5 = [GR_r_sin_Table2], 16 + nop.f 0 + sub GR_p_Exp = GR_p_Exp, GR_p_Bias // Unbiased exp +};; + +{ .mmi + ldfe FR_r_A9 = [GR_r_sin_Table], 16 + ldfe FR_r_A4 = [GR_r_sin_Table2], 16 + cmp.gtu.unc p10, p11 = GR_p_0p75, GR_p_XN // sgnd(x) < 0.75 +};; + +{ .mfi + ldfe FR_r_A8 = [GR_r_sin_Table], 16 + fma.s1 FR_z_E2 = FR_z_E0,FR_z_E0,FR_z_E0 // e2 = e+e^2 +(p10) cmp.gt.unc p9, p10 = -2, GR_p_Exp // x < 0.25 +} +{ .mfi + ldfe FR_r_A3 = [GR_r_sin_Table2], 16 + fma.s1 FR_z_E1 = FR_z_E0,FR_z_E0,f0 // e1 = e^2 +(p11) add GR_p_Offset = 168, r0 // [0.75;1] interval +};; + +{ .mmi +(p10) add GR_p_Offset = 147, r0 // [0.25;0.75] interval + ldfe FR_r_A7 = [GR_r_sin_Table], 16 +(p9) cmp.gt.unc p8, p9 = -3, GR_p_Exp // x < 0.125 +};; + +.pred.rel "mutex",p9,p8 +{ .mmi +(p9) add GR_p_Offset = 126, r0 // [0.125;0.25] interval +(p8) add GR_p_Offset = 189, r0 // [0.;0.125] interval + nop.i 0 +};; + +{ .mmf + shladd GR_p_Table = GR_p_Offset, 4, GR_p_Table //Make addresses + shladd GR_p_Table2 = GR_p_Offset, 4, GR_p_Table2 + fma.s1 FR_r_XS = FR_r_AbsX , f1, FR_r_XNS // xs = |x|-[x] +};; + +.pred.rel "mutex",p8,p11 +{ .mfi + ldfpd FR_p_A5H, FR_p_A5L = [GR_p_Table], 16 +(p11) fms.s1 FR_p_XR = f1, f1, FR_p_AbsX // r = 1 - |x| + // for [0.75;1] interval + nop.i 0 +} +{ .mfi + ldfpd FR_p_A2H, FR_p_A2L = [GR_p_Table2], 16 +(p8) fms.s1 FR_p_XR = FR_p_AbsX, f1, f0 // r = |x| + // for [0.;0.125] interval + nop.i 0 +};; + +{ .mfi + ldfpd FR_p_A4H, FR_p_A4L = [GR_p_Table], 16 + fma.s1 FR_z_Y1 = FR_z_Y0,FR_z_E2,FR_z_Y0 // y1 = y+y*e2 + nop.i 0 +} +{ .mfi + ldfpd FR_p_A1H, FR_p_A1L = [GR_p_Table2], 16 + fma.s1 FR_z_E3 = FR_z_E1,FR_z_E1,FR_z_E0 // e3 = e+e1^2 + nop.i 0 +};; + +.pred.rel "mutex",p9,p10 +{ .mfi + ldfpd FR_p_A3H, FR_p_A3L = [GR_p_Table], 16 +(p9) fms.s1 FR_p_XR = FR_p_AbsX, f1, f0 // r = |x| + // for [0.125;0.25] interval + nop.i 0 +} +{ .mfi + ldfpd FR_p_A0H, FR_p_A0L = [GR_p_Table2], 16 +(p10) fms.s1 FR_p_XR = FR_p_AbsX, f1, FR_p_0p5 // r = |x| - 0.5 + // for [0.25;0.75] interval + nop.i 0 +};; + +{ .mmi + ldfe FR_p_A20 = [GR_p_Table], 16 + ldfe FR_p_A12 = [GR_p_Table2], 16 + nop.i 0 +};; + +{ .mfi + ldfe FR_p_A19 = [GR_p_Table], 16 + fma.s1 FR_r_XS2 = FR_r_XS, FR_r_XS, f0 // xs^2 + nop.i 0 +} +{ .mfi + ldfe FR_p_A11 = [GR_p_Table2], 16 + nop.f 0 + nop.i 0 +};; + +{ .mmi + ldfe FR_p_A18 = [GR_p_Table], 16 + ldfe FR_p_A10 = [GR_p_Table2], 16 + nop.i 0 +};; + +.pred.rel "mutex",p12,p13 +{ .mfi + ldfe FR_p_A17 = [GR_p_Table], 16 + fma.s1 FR_z_Y2 = FR_z_Y1,FR_z_E3,FR_z_Y0 // y2 = y+y1*e3 + nop.i 0 +} +{ .mfi + ldfe FR_p_A9 = [GR_p_Table2], 16 + fnma.s1 FR_z_R0 = f8,FR_z_Q0,f1 // r = a-b*q + nop.i 0 +};; + +{ .mmi + ldfe FR_p_A16 = [GR_p_Table], 16 + ldfe FR_p_A8 = [GR_p_Table2], 16 + nop.i 0 +};; + +{ .mmi + ldfe FR_p_A15 = [GR_p_Table], 16 + ldfe FR_p_A7 = [GR_p_Table2], 16 + nop.i 0 +};; + +{ .mfi + ldfe FR_p_A14 = [GR_p_Table], 16 + fma.s1 FR_r_TH = FR_r_A2H, FR_r_XS2, f0 // neg sin + nop.i 0 +} +{ .mfi + ldfe FR_p_A6 = [GR_p_Table2], 16 + fma.s1 FR_r_TL = FR_r_A2L, FR_r_XS2, f0 // neg sin + nop.i 0 +};; + +{ .mfi + ldfe FR_p_A13 = [GR_p_Table], 16 + fms.s1 FR_r_XS2L = FR_r_XS, FR_r_XS, FR_r_XS2 // xs^2 delta + nop.i 0 +};; + +{ .mfi + nop.m 0 + fma.s1 FR_p_Temp5H = FR_p_A5H, FR_p_XR, f0 // Low poly + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 FR_p_XR2 = FR_p_XR, FR_p_XR, f0 // poly tail + nop.i 0 +};; + +{ .mfi + nop.m 0 + fabs FR_r_XS = FR_r_XS // Absolute value of xs + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 FR_p_Temp2H = FR_p_A2H, FR_p_XR, f0 // High poly + nop.i 0 +};; + +{ .mfi + nop.m 0 + fnma.s1 FR_z_E4 = f8,FR_z_Y2,f1 // e4 = 1-b*y2 + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 FR_z_ZH = FR_z_R0,FR_z_Y2,FR_z_Q0 // 1/x = q+r*y2 + nop.i 0 +};; + +{ .mfi + nop.m 0 + fms.s1 FR_r_TT = FR_r_A2H, FR_r_XS2, FR_r_TH // neg sin + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 FR_r_ResH = FR_r_TH, f1, FR_r_A1H // neg sin + nop.i 0 +};; + +{ .mfi + nop.m 0 + fma.s1 FR_r_TL = FR_r_A2H, FR_r_XS2L, FR_r_TL // neg sin + nop.i 0 +};; + +{ .mfi + nop.m 0 + fms.s1 FR_p_Temp5L = FR_p_A5H, FR_p_XR, FR_p_Temp5H // Low poly + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 FR_p_Poly5H = FR_p_Temp5H, f1, FR_p_A4H // Low poly + nop.i 0 +};; + +{ .mfi + nop.m 0 + fms.s1 FR_p_Temp2L = FR_p_A2H, FR_p_XR, FR_p_Temp2H // High poly + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 FR_p_Poly2H = FR_p_Temp2H, f1, FR_p_A1H // High poly + nop.i 0 +};; + +{ .mfi + nop.m 0 + fma.s1 FR_p_XR3 = FR_p_XR2, FR_p_XR, f0 // r^3 + nop.i 0 +} +{ .mfi + nop.m 0 + fms.s1 FR_p_XR2L = FR_p_XR, FR_p_XR, FR_p_XR2 // r^2 delta + nop.i 0 +};; + +{ .mfi + nop.m 0 + fma.s1 FR_p_A18 = FR_p_A19, FR_p_XR, FR_p_A18 // poly tail + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 FR_p_A14 = FR_p_A15, FR_p_XR, FR_p_A14 // poly tail + nop.i 0 +};; + +{ .mfi + nop.m 0 + fma.s1 FR_p_XR4 = FR_p_XR2, FR_p_XR2, f0 // poly tail + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 FR_z_Y3 = FR_z_Y2,FR_z_E4,FR_z_Y2 // y3 = y2+y2*e4 + nop.i 0 +};; + +{ .mfi + nop.m 0 + fma.s1 FR_p_Temp5L = FR_p_A5L, FR_p_XR, FR_p_Temp5L // Low poly + nop.i 0 +} +{ .mfi + nop.m 0 + fms.s1 FR_p_Poly5L = FR_p_A4H, f1, FR_p_Poly5H // Low poly + nop.i 0 +};; + +{ .mfi + nop.m 0 + fma.s1 FR_p_Temp4H = FR_p_Poly5H, FR_p_XR, f0 // Low poly + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 FR_p_Temp2L = FR_p_A2L, FR_p_XR, FR_p_Temp2L // High poly + nop.i 0 +};; + +{ .mfi + nop.m 0 + fms.s1 FR_p_Poly2L = FR_p_A1H, f1, FR_p_Poly2H // High poly + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 FR_p_Temp1H = FR_p_Poly2H, FR_p_XR, f0 // High poly + nop.i 0 +};; + +{ .mfi + nop.m 0 + fms.s1 FR_p_XR3L = FR_p_XR2, FR_p_XR, FR_p_XR3 // x^3 delta + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 FR_p_A16 = FR_p_A17, FR_p_XR, FR_p_A16 //poly tail + nop.i 0 +};; + +{ .mfi + nop.m 0 + fms.s1 FR_r_ResL = FR_r_A1H, f1, FR_r_ResH // neg sin + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 FR_r_TL = FR_r_TL, f1, FR_r_TT // neg sin + nop.i 0 +};; + +{ .mfi + nop.m 0 + fma.s1 FR_p_Temp5L = FR_p_Temp5L, f1, FR_p_A4L // Low poly + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 FR_p_Poly5L = FR_p_Poly5L, f1, FR_p_Temp5H //Low poly + nop.i 0 +};; + +{ .mfi + nop.m 0 + fms.s1 FR_p_Temp4L = FR_p_Poly5H, FR_p_XR, FR_p_Temp4H//Low poly + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 FR_p_Poly4H = FR_p_Temp4H, f1, FR_p_A3H // Low poly + nop.i 0 +};; + +{ .mfi + nop.m 0 + fma.s1 FR_p_Temp2L = FR_p_Temp2L, f1, FR_p_A1L // High poly + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 FR_p_Poly2L = FR_p_Poly2L, f1, FR_p_Temp2H // High poly + nop.i 0 +};; + +{ .mfi + nop.m 0 + fms.s1 FR_p_Temp1L = FR_p_Poly2H,FR_p_XR,FR_p_Temp1H //High poly + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 FR_p_Poly1H = FR_p_Temp1H, f1, FR_p_A0H // High poly + nop.i 0 +};; + +{ .mfi + nop.m 0 + fma.s1 FR_p_A12 = FR_p_A13, FR_p_XR, FR_p_A12 // poly tail + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 FR_p_XR3L = FR_p_XR2L, FR_p_XR, FR_p_XR3L // x^3 low + nop.i 0 +};; + +{ .mfi + nop.m 0 + fma.s1 FR_p_Poly5L = FR_p_Poly5L, f1, FR_p_Temp5L //Low poly + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 FR_p_A10 = FR_p_A11, FR_p_XR, FR_p_A10 //poly tail + nop.i 0 +};; + +{ .mfi + nop.m 0 + fms.s1 FR_p_Poly4L = FR_p_A3H, f1, FR_p_Poly4H /// Low poly + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 FR_p_A6 = FR_p_A7, FR_p_XR, FR_p_A6 // poly tail + nop.i 0 +};; + +{ .mfi + nop.m 0 + fma.s1 FR_p_A8 = FR_p_A9, FR_p_XR, FR_p_A8 // poly tail + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 FR_p_XR6 = FR_p_XR4, FR_p_XR2, f0 // r^6 + nop.i 0 +};; + +{ .mfi + nop.m 0 + fma.s1 FR_p_Poly2L = FR_p_Poly2L, f1, FR_p_Temp2L // High poly + nop.i 0 +} +{ .mfi + nop.m 0 + fms.s1 FR_p_Poly1L = FR_p_A0H, f1, FR_p_Poly1H // High poly + nop.i 0 +};; + +{ .mfi + nop.m 0 + fma.s1 FR_r_ResL = FR_r_ResL, f1, FR_r_TH // neg sin + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 FR_r_TT = FR_r_TL, f1, FR_r_A1L // neg sin + nop.i 0 +};; + +{ .mfi + nop.m 0 + fma.s1 FR_p_Temp4L = FR_p_Poly5L,FR_p_XR,FR_p_Temp4L //Low poly + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 FR_p_A18 = FR_p_A20, FR_p_XR2, FR_p_A18 // poly tail + nop.i 0 +};; + +{ .mfi + nop.m 0 + fma.s1 FR_p_Poly4L = FR_p_Poly4L, f1, FR_p_Temp4H // Low poly + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 FR_p_A14 = FR_p_A16, FR_p_XR2, FR_p_A14 // poly tail + nop.i 0 +};; + +{ .mfi + nop.m 0 + fma.s1 FR_p_A6 = FR_p_A8, FR_p_XR2, FR_p_A6 // poly tail + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 FR_p_A10 = FR_p_A12, FR_p_XR2, FR_p_A10 // poly tail + nop.i 0 +};; + +{ .mfi + nop.m 0 + fma.s1 FR_p_Temp1L = FR_p_Poly2L,FR_p_XR,FR_p_Temp1L //High poly + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 FR_p_Poly1L = FR_p_Poly1L, f1, FR_p_Temp1H // High poly + nop.i 0 +};; + +{ .mfi + nop.m 0 + fma.s1 FR_r_ResL = FR_r_ResL, f1, FR_r_TT // neg sin + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 FR_r_TH = FR_r_ResH, FR_r_XS2, f0 // neg sin + nop.i 0 +};; + +{ .mfi + nop.m 0 + fma.s1 FR_p_Temp4L = FR_p_Temp4L, f1, FR_p_A3L // Low poly + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 FR_p_Poly3H = FR_p_Poly4H, FR_p_XR3, f0 // Low poly + nop.i 0 +};; + +{ .mfi + nop.m 0 + fma.s1 FR_p_A14 = FR_p_A18, FR_p_XR4, FR_p_A14 // poly tail + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 FR_p_XR8 = FR_p_XR4, FR_p_XR4, f0 // r^8 + nop.i 0 +};; + +{ .mfi + nop.m 0 + fma.s1 FR_r_TL = FR_r_ResH, FR_r_XS2L, f0 // neg sin + nop.i 0 +} +{ .mfi + nop.m 0 + fnma.s1 FR_z_R1 = f8,FR_z_ZH,f1 // r1 = a-b*x + nop.i 0 +};; + +{ .mfi + nop.m 0 + fma.s1 FR_p_Temp1L = FR_p_Temp1L, f1, FR_p_A0L // High poly + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 FR_p_A6 = FR_p_A10, FR_p_XR4, FR_p_A6 // poly tail + nop.i 0 +};; + +{ .mfi + nop.m 0 + fms.s1 FR_r_TT = FR_r_ResH, FR_r_XS2, FR_r_TH // neg sin + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 FR_r_Res3H = FR_r_TH, f1, f1 // neg sin + nop.i 0 +};; + +{ .mfi + nop.m 0 + fma.s1 FR_p_Poly4L = FR_p_Poly4L, f1, FR_p_Temp4L // Low poly + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 FR_p_Poly3L = FR_p_Poly4H, FR_p_XR3L, f0 // Low poly + nop.i 0 +};; + +{ .mfi + nop.m 0 + fma.s1 FR_p_Poly0H = FR_p_Poly3H, f1, FR_p_Poly1H // Result + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 FR_r_A7 = FR_r_A8, FR_r_XS2, FR_r_A7 // neg sin + nop.i 0 +};; + +{ .mfi + nop.m 0 + fma.s1 FR_r_TL = FR_r_ResL, FR_r_XS2, FR_r_TL // neg sin + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 FR_r_XS4 = FR_r_XS2, FR_r_XS2, f0 // xs^4 + nop.i 0 +};; + +{ .mfi + nop.m 0 + fma.s1 FR_p_Poly1L = FR_p_Poly1L, f1, FR_p_Temp1L // High poly + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 FR_p_PolyTail = FR_p_A14, FR_p_XR8, FR_p_A6 // poly tail + nop.i 0 +};; + +{ .mfi + nop.m 0 + fms.s1 FR_r_Res3L = f1, f1, FR_r_Res3H // neg sin + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 FR_r_ResH = FR_r_Res3H, FR_r_XS, f0 // neg sin + nop.i 0 +};; + +{ .mfi + nop.m 0 + fms.s1 FR_p_Temp0L = FR_p_Poly4H,FR_p_XR3,FR_p_Poly3H //Low poly + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 FR_p_Poly3L = FR_p_Poly4L,FR_p_XR3,FR_p_Poly3L //Low poly + nop.i 0 +};; + +{ .mfi + nop.m 0 + fms.s1 FR_p_Poly0L = FR_p_Poly1H, f1, FR_p_Poly0H // Result + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 FR_z_ZL = FR_z_R1,FR_z_Y3, f0 // x_lo = r1*y3 + nop.i 0 +};; + +{ .mfi + nop.m 0 + fma.s1 FR_r_TL = FR_r_TL, f1, FR_r_TT // neg sin + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 FR_r_A3 = FR_r_A4, FR_r_XS2, FR_r_A3 /// neg sin + nop.i 0 +};; + +{ .mfi + nop.m 0 + fma.s1 FR_p_Poly1L = FR_p_PolyTail,FR_p_XR6,FR_p_Poly1L // High + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 FR_r_A5 = FR_r_A6, FR_r_XS2, FR_r_A5 // neg sin + nop.i 0 +};; + +{ .mfi + nop.m 0 + fma.s1 FR_r_Res3L = FR_r_Res3L, f1, FR_r_TH // neg sin + nop.i 0 +} +{ .mfi + nop.m 0 + fms.s1 FR_r_ResL = FR_r_Res3H, FR_r_XS, FR_r_ResH // neg sin + nop.i 0 +};; + +{ .mfi + nop.m 0 + fma.s1 FR_p_Poly3L = FR_p_Poly3L, f1, FR_p_Temp0L // Low poly + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 FR_r_A7 = FR_r_A9, FR_r_XS4, FR_r_A7 // neg sin + nop.i 0 +};; + +{ .mfi + nop.m 0 + fma.s1 FR_p_Poly0L = FR_p_Poly0L, f1, FR_p_Poly3H // result + nop.i 0 +};; + +{ .mfi + nop.m 0 +(p14) fma.s1 f8 = FR_p_Poly0H, FR_z_ZH, f0 // z*poly + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 FR_p_Temp1L = FR_p_Poly0H, FR_z_ZL, f0 // z*poly low + nop.i 0 +};; + +{ .mfi + nop.m 0 + fma.s1 FR_r_A3 = FR_r_A5, FR_r_XS4, FR_r_A3 // sin tail + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 FR_r_XS7 = FR_r_XS4, FR_r_XS2, f0 // xs^6 + nop.i 0 +};; + +{ .mfi + nop.m 0 + fma.s1 FR_r_Res3L = FR_r_Res3L, f1, FR_r_TL // sin low + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 FR_r_XS8 = FR_r_XS4, FR_r_XS4, f0 // xs^8 + nop.i 0 +};; + +{ .mfi + nop.m 0 + fma.s1 FR_p_Temp0H = FR_p_Poly3L, f1, FR_p_Poly1L // result + nop.i 0 +};; + +{ .mfi + nop.m 0 +(p14) fms.s1 FR_p_Temp1H = FR_p_Poly0H, FR_z_ZH, f8 // hi result + nop.i 0 +};; + +{ .mfi + nop.m 0 + fma.s1 FR_r_XS7 = FR_r_XS7, FR_r_XS, f0 // xs^7 + nop.i 0 +};; + +{ .mfi + nop.m 0 + fma.s1 FR_r_ResL = FR_r_Res3L, FR_r_XS, FR_r_ResL // lo result + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 FR_r_Tail = FR_r_A7, FR_r_XS8, FR_r_A3 // tail result + nop.i 0 +};; + +{ .mfi + nop.m 0 + fma.s1 FR_p_Poly0L = FR_p_Poly0L, f1, FR_p_Temp0H // lo result + nop.i 0 +};; + +{ .mfi + nop.m 0 + fma.s1 FR_r_ResL = FR_r_Tail, FR_r_XS7, FR_r_ResL // lo result + nop.i 0 +};; + +{ .mfi + nop.m 0 +(p14) fma.s1 FR_p_Temp1L = FR_p_Poly0L,FR_z_ZH,FR_p_Temp1L //hi result + nop.i 0 +};; + +{ .mfi + nop.m 0 + fma.s1 FR_r_TT = FR_r_ResL, f1, f0 // for low result + nop.i 0 +};; + +.pred.rel "mutex",p12,p13 +{ .mfi + nop.m 0 +(p14) fma.s1 FR_p_Temp1L = FR_p_Temp1L, f1, FR_p_Temp1H // for lo res + nop.i 0 +};; + +{ .mfi +(p10) cmp.eq p13, p12 = r0, r0 // set p13, clear p12 + fma.s1 FR_r_Res1H = FR_r_ResH, f1, FR_r_TT // hi res + nop.i 0 +};; + +{ .mfb +(p9) cmp.eq p13, p12 = r0, r0 // set p13, clear p12 +(p14) fma.s0 f8 = f8, f1, FR_p_Temp1L // Final result +(p14) br.ret.spnt b0 // Exit for 0 < |X| < 1 path (positive arguments)/////// +};; + +{ .mfi +(p11) cmp.eq p13, p12 = r0, r0 // set p13, clear p12 + fms.s1 FR_r_Res1L = FR_r_ResH, f1, FR_r_Res1H // Low sin result + nop.i 0 +};; + +{ .mfi + nop.m 0 + fma.s1 FR_r_Res1L = FR_r_Res1L, f1, FR_r_TT // Low sin result + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 FR_r_TL = FR_p_Poly0L,FR_r_Res1H,f0 //Low sin result + nop.i 0 +};; + +{ .mfi + nop.m 0 + fma.s1 FR_r_TL = FR_p_Poly0H, FR_r_Res1L, FR_r_TL //Low sin + nop.i 0 +};; + +{ .mfi + nop.m 0 + fma.s1 FR_r_ResH = FR_p_Poly0H, FR_r_Res1H, FR_r_TL //High sin + nop.i 0 +};; + +{ .mfi + nop.m 0 + fms.s1 FR_r_ResL = FR_p_Poly0H,FR_r_Res1H,FR_r_ResH //Low res + nop.i 0 +};; + +{ .mfi + nop.m 0 + frcpa.s1 FR_r_Y0,p0 = f1,FR_r_ResH // y = frcpa(b) + nop.i 0 +};; + +{ .mfi + nop.m 0 + fneg FR_r_NegOne = f1 // Construct -1.0 + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 FR_r_ResL = FR_r_ResL, f1, FR_r_TL // low sin + nop.i 0 +};; + +{ .mfi + nop.m 0 + fma.s1 FR_r_Q0 = f1,FR_r_Y0,f0 // q = a*y + nop.i 0 +} +{ .mfi + nop.m 0 + fnma.s1 FR_r_E0 = FR_r_Y0,FR_r_ResH,f1 // e = 1-b*y + nop.i 0 +};; + +{ .mfi + nop.m 0 + fma.s1 FR_r_E2 = FR_r_E0,FR_r_E0,FR_r_E0 // e2 = e+e^2 + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 FR_r_E1 = FR_r_E0,FR_r_E0,f0 // e1 = e^2 + nop.i 0 +};; + +{ .mfi + nop.m 0 + fma.s1 FR_r_Y1 = FR_r_Y0,FR_r_E2,FR_r_Y0 // y1 = y+y*e2 + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 FR_r_E3 = FR_r_E1,FR_r_E1,FR_r_E0 // e3 = e+e1^2 + nop.i 0 +};; + +{ .mfi + nop.m 0 + fma.s1 FR_r_Y2 = FR_r_Y1,FR_r_E3,FR_r_Y0 // y2 = y+y1*e3 + nop.i 0 +} +{ .mfi + nop.m 0 + fnma.s1 FR_r_R0 = FR_r_ResH,FR_r_Q0,f1 // r = a-b*q + nop.i 0 +};; + +{ .mfi + nop.m 0 + fnma.s1 FR_r_E4 = FR_r_ResH,FR_r_Y2,f1 // e4 = 1-b*y2 + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 FR_r_ZH = FR_r_R0,FR_r_Y2,FR_r_Q0 // x = q+r*y2 + nop.i 0 +};; + +{ .mfi + nop.m 0 + fma.s1 FR_r_Y3 = FR_r_Y2,FR_r_E4,FR_r_Y2 // y3 = y2+y2*e4 + nop.i 0 +} +{ .mfi + nop.m 0 + fnma.s1 FR_r_R1 = FR_r_ResH,FR_r_ZH,f1 // r1 = a-b*x + nop.i 0 +};; + +{ .mfi + nop.m 0 + fnma.s1 FR_r_R1 = FR_r_ResL,FR_r_ZH,FR_r_R1 // r1=r1 - b_lo*X + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 FR_r_ZHN = FR_r_ZH,FR_r_NegOne, f0 // Negate + nop.i 0 +};; + +.pred.rel "mutex",p13,p12 +{ .mfb + nop.m 0 + fnma.s0 f8 = FR_r_R1,FR_r_Y3,FR_r_ZHN // Result for neg + br.ret.sptk b0 // Exit for 0 < |X| < 1 path (negative arguments)////// +};; + + + + +// SPECIALS (x for natval, nan, +/-inf or +/-0) /////////////////////////////// +//------------------------------------------------------------------------------ +.align 32 +tgammal_spec: +{ .mlx + nop.m 0 + movl GR_DenOverflow = 0x2000000000000001 +} +{ .mfi + nop.m 0 + fclass.m p9,p0 = f8,0xB // +/-denormals + nop.i 0 +};; +{ .mfi + nop.m 0 + fclass.m p6,p0 = f8,0x1E1 // Test x for natval, nan, +inf + nop.i 0 +};; +{ .mfi + nop.m 0 + fclass.m p7,p8 = f8,0x7 // +/-0 + nop.i 0 +} + +{ .mfi +(p9) cmp.ltu.unc p10,p11 = GR_l_signif_Z, GR_DenOverflow +(p9) fnorm.s0 f8 = f8 + nop.i 0 +};; + +{ .mfb + nop.m 0 +(p9) fcvt.fx.trunc.s1 FR_n_IXN = FR_l_AbsX // Round by truncate +(p11) br.cond.sptk tgamma_lt_1 // Return to gamma ('good' denormal)//////////// +};; + +{ .mfb + nop.m 0 + nop.f 0 +(p10) br.cond.spnt tgammal_overflow // "Bad" denormal - overflow! ///////////// +};; + +{ .mfi + nop.m 0 + mov FR_X = f8 // for error handler + nop.i 0 +} +{ .mfb + nop.m 0 +(p6) fma.s0 f8 = f8,f1,f8 // res = x + x +(p6) br.ret.spnt b0 // Exit for NAN, INF and NatVals //////////////////////// +};; +.pred.rel "mutex",p7,p8 +{ .mfi +(p7) mov GR_Parameter_TAG = 256 // negative +(p7) frcpa.s0 f8,p0 = f1,f8 // Raise V flag + nop.i 0 +} +{ .mfb + nop.m 0 + nop.f 0 +(p8) br.cond.spnt tgammal_singularity // Branch for +ZERO //////////////////// +};; + +{ .mfb + nop.m 0 + nop.f 0 + br.cond.spnt tgammal_libm_err // Branch for -ZERO /////////////////////// +};; + + + + +// SINGULARITY (x is negative integer or 0) //////////////////////////////////// +//------------------------------------------------------------------------------ +.align 32 +tgammal_singularity: +{ .mfi + nop.m 0 + mov FR_X = f8 // For error handler + mov GR_Parameter_TAG = 256 // negative +} +{ .mfb + nop.m 0 + frcpa.s0 f8,p0 = f0,f0 // Raise V flag + br.cond.sptk tgammal_libm_err // Call error handler ///////////////////// + // with singularity error ///////////////// +};; + + + + +// OVERFLOW (result is too big and cannot be represented by normal value) ////// +// ( X > 1755.54 and for denormals with abs value less than 0x2000000000000001 ) +//------------------------------------------------------------------------------ +.align 32 +tgammal_overflow: +{ .mfi + addl r8 = 0x1FFFE, r0 // Exp of INF + fcmp.lt.s1 p15,p14 = f8,f0 // p14 - pos arg, p15 - neg arg + nop.i 0 +};; + +{ .mfi + setf.exp f9 = r8 + mov FR_X = f8 // For error handler + mov GR_Parameter_TAG = 255 // overflow +};; + +.pred.rel "mutex",p14,p15 +{ .mfi + nop.m 0 +(p14) fma.s0 f8 = f9,f9,f0 // Set I,O and +INF result + nop.i 0 +} +{ .mfb + nop.m 0 +(p15) fnma.s0 f8 = f9,f9,f0 // Set I,O and -INF result + br.cond.sptk tgammal_libm_err // Call error handler ///////////////////// + // with overflow error //////////////////// +};; + + + + + +// UNDERFLOW (x is negative noninteger with big absolute value) //////////////// +//------------------------------------------------------------------------------ +.align 32 +tgammal_underflow: +{ .mfi + nop.m 0 + fcvt.fx.trunc.s1 FR_u_IXN = f8 // Convert arg to int repres. in FR + nop.i 0 +};; + +{ .mmi + getf.sig GR_u_XN = FR_u_IXN + mov r11 = 0x00001 + nop.i 0 +};; + +{ .mfi + setf.exp f9 = r11 + nop.f 0 + nop.i 0 +};; + +{ .mfi + nop.m 0 + nop.f 0 + tbit.z p6,p7 = GR_u_XN,0 // even or odd +};; + +.pred.rel "mutex",p6,p7 +{ .mfi + nop.m 0 +(p6) fms.s0 f8 = f9,f9,f9 // for negatives + nop.i 0 +} +{ .mfb + nop.m 0 +(p7) fma.s0 f8 = f9,f9,f9 // for positives + br.ret.sptk b0 // Exit for underflow path ////////////////////////////// +};; + + +GLOBAL_LIBM_END(tgammal) + + + + +////////////////// Tgammal error handler /////////////////////////////////////// +//------------------------------------------------------------------------------ +LOCAL_LIBM_ENTRY(__libm_error_region) +tgammal_libm_err: +.prologue +{ .mfi + add GR_Parameter_Y=-32,sp // Parameter 2 value + nop.f 0 +.save ar.pfs,GR_SAVE_PFS + mov GR_SAVE_PFS=ar.pfs // Save ar.pfs +} +{ .mfi +.fframe 64 + add sp=-64,sp // Create new stack + nop.f 0 + mov GR_SAVE_GP=gp // Save gp +};; +{ .mmi + stfe [GR_Parameter_Y] = FR_Y,16 // Save Parameter 2 on stack + add GR_Parameter_X = 16,sp // Parameter 1 address +.save b0, GR_SAVE_B0 + mov GR_SAVE_B0=b0 // Save b0 +};; +.body +{ .mib + stfe [GR_Parameter_X] = FR_X // Store Parameter 1 on stack + add GR_Parameter_RESULT = 0,GR_Parameter_Y + nop.b 0 // Parameter 3 address +} +{ .mib + stfe [GR_Parameter_Y] = FR_RESULT // Store Parameter 3 on stack + add GR_Parameter_Y = -16,GR_Parameter_Y + br.call.sptk b0=__libm_error_support# // Call error handling function +};; +{ .mmi + nop.m 999 + nop.m 999 + add GR_Parameter_RESULT = 48,sp +};; +{ .mmi + ldfe f8 = [GR_Parameter_RESULT] // Get return result off stack +.restore sp + add sp = 64,sp // Restore stack pointer + mov b0 = GR_SAVE_B0 // Restore return address +};; +{ .mib + mov gp = GR_SAVE_GP // Restore gp + mov ar.pfs = GR_SAVE_PFS // Restore ar.pfs + br.ret.sptk b0 // Return +};; + +LOCAL_LIBM_END(__libm_error_region#) + +.type __libm_error_support#,@function +.global __libm_error_support# |