.file "tgamma.s" // Copyright (c) 2001 - 2005, Intel Corporation // All rights reserved. // // Contributed 2001 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: // 10/12/01 Initial version // 05/20/02 Cleaned up namespace and sf0 syntax // 02/10/03 Reordered header: .section, .global, .proc, .align // 04/04/03 Changed error codes for overflow and negative integers // 04/10/03 Changed code for overflow near zero handling // 03/31/05 Reformatted delimiters between data tables // //********************************************************************* // //********************************************************************* // // Function: tgamma(x) computes the principle value of the GAMMA // function of x. // //********************************************************************* // // Resources Used: // // Floating-Point Registers: f8-f15 // f33-f87 // // General Purpose Registers: // r8-r11 // r14-r28 // r32-r36 // r37-r40 (Used to pass arguments to error handling routine) // // Predicate Registers: p6-p15 // //********************************************************************* // // IEEE Special Conditions: // // tgamma(+inf) = +inf // tgamma(-inf) = QNaN // tgamma(+/-0) = +/-inf // tgamma(x<0, x - integer) = QNaN // tgamma(SNaN) = QNaN // tgamma(QNaN) = QNaN // //********************************************************************* // // Overview // // The method consists of three cases. // // If 2 <= x < OVERFLOW_BOUNDARY use case tgamma_regular; // else if 0 < x < 2 use case tgamma_from_0_to_2; // else if -(i+1) < x < -i, i = 0...184 use case tgamma_negatives; // // Case 2 <= x < OVERFLOW_BOUNDARY // ------------------------------- // Here we use algorithm based on the recursive formula // GAMMA(x+1) = x*GAMMA(x). For that we subdivide interval // [2; OVERFLOW_BOUNDARY] into intervals [16*n; 16*(n+1)] and // approximate GAMMA(x) by polynomial of 22th degree on each // [16*n; 16*n+1], recursive formula is used to expand GAMMA(x) // to [16*n; 16*n+1]. In other words we need to find n, i and r // such that x = 16 * n + i + r where n and i are integer numbers // and r is fractional part of x. So GAMMA(x) = GAMMA(16*n+i+r) = // = (x-1)*(x-2)*...*(x-i)*GAMMA(x-i) = // = (x-1)*(x-2)*...*(x-i)*GAMMA(16*n+r) ~ // ~ (x-1)*(x-2)*...*(x-i)*P22n(r). // // Step 1: Reduction // ----------------- // N = [x] with truncate // r = x - N, note 0 <= r < 1 // // n = N & ~0xF - index of table that contains coefficient of // polynomial approximation // i = N & 0xF - is used in recursive formula // // // Step 2: Approximation // --------------------- // We use factorized minimax approximation polynomials // P22n(r) = A22*(r^2+C01(n)*R+C00(n))* // *(r^2+C11(n)*R+C10(n))*...*(r^2+CA1(n)*R+CA0(n)) // // Step 3: Recursion // ----------------- // In case when i > 0 we need to multiply P22n(r) by product // R(i)=(x-1)*(x-2)*...*(x-i). To reduce number of fp-instructions // we can calculate R as follow: // R(i) = ((x-1)*(x-2))*((x-3)*(x-4))*...*((x-(i-1))*(x-i)) if i is // even or R = ((x-1)*(x-2))*((x-3)*(x-4))*...*((x-(i-2))*(x-(i-1)))* // *(i-1) if i is odd. In both cases we need to calculate // R2(i) = (x^2-3*x+2)*(x^2-7*x+12)*...*(x^2+x+2*j*(2*j-1)) = // = (x^2-3*x+2)*(x^2-7*x+12)*...*((x^2+x)+2*j*(2*(j-1)+(1-2*x))) = // = (RA+2*(2-RB))*(RA+4*(4-RB))*...*(RA+2*j*(2*(j-1)+RB)) // where j = 1..[i/2], RA = x^2+x, RB = 1-2*x. // // Step 4: Reconstruction // ---------------------- // Reconstruction is just simple multiplication i.e. // GAMMA(x) = P22n(r)*R(i) // // Case 0 < x < 2 // -------------- // To calculate GAMMA(x) on this interval we do following // if 1 <= x < 1.25 than GAMMA(x) = P15(x-1) // if 1.25 <= x < 1.5 than GAMMA(x) = P15(x-x_min) where // x_min is point of local minimum on [1; 2] interval. // if 1.5 <= x < 2.0 than GAMMA(x) = P15(x-1.5) // and // if 0 < x < 1 than GAMMA(x) = GAMMA(x+1)/x // // Case -(i+1) < x < -i, i = 0...184 // ---------------------------------- // Here we use the fact that GAMMA(-x) = PI/(x*GAMMA(x)*sin(PI*x)) and // so we need to calculate GAMMA(x), sin(PI*x)/PI. Calculation of // GAMMA(x) is described above. // // Step 1: Reduction // ----------------- // Note that period of sin(PI*x) is 2 and range reduction for // sin(PI*x) is like to range reduction for GAMMA(x) // i.e r = x - [x] with exception of cases // when r > 0.5 (in such cases r = 1 - (x - [x])). // // Step 2: Approximation // --------------------- // To approximate sin(PI*x)/PI = sin(PI*(2*n+r))/PI = // = (-1)^n*sin(PI*r)/PI Taylor series is used. // sin(PI*r)/PI ~ S21(r). // // Step 3: Division // ---------------- // To calculate 1/(x*GAMMA(x)*S21(r)) we use frcpa instruction // with following Newton-Raphson interations. // // //********************************************************************* GR_Sig = r8 GR_TAG = r8 GR_ad_Data = r9 GR_SigRqLin = r10 GR_iSig = r11 GR_ExpOf1 = r11 GR_ExpOf8 = r11 GR_Sig2 = r14 GR_Addr_Mask1 = r15 GR_Sign_Exp = r16 GR_Tbl_Offs = r17 GR_Addr_Mask2 = r18 GR_ad_Co = r19 GR_Bit2 = r19 GR_ad_Ce = r20 GR_ad_Co7 = r21 GR_NzOvfBound = r21 GR_ad_Ce7 = r22 GR_Tbl_Ind = r23 GR_Tbl_16xInd = r24 GR_ExpOf025 = r24 GR_ExpOf05 = r25 GR_0x30033 = r26 GR_10 = r26 GR_12 = r27 GR_185 = r27 GR_14 = r28 GR_2 = r28 GR_fpsr = r28 GR_SAVE_B0 = r33 GR_SAVE_PFS = r34 GR_SAVE_GP = r35 GR_SAVE_SP = r36 GR_Parameter_X = r37 GR_Parameter_Y = r38 GR_Parameter_RESULT = r39 GR_Parameter_TAG = r40 FR_X = f10 FR_Y = f1 // tgamma is single argument function FR_RESULT = f8 FR_AbsX = f9 FR_NormX = f9 FR_r02 = f11 FR_AbsXp1 = f12 FR_X2pX = f13 FR_1m2X = f14 FR_Rq1 = f14 FR_Xt = f15 FR_r = f33 FR_OvfBound = f34 FR_Xmin = f35 FR_2 = f36 FR_Rcp1 = f36 FR_Rcp3 = f36 FR_4 = f37 FR_5 = f38 FR_6 = f39 FR_8 = f40 FR_10 = f41 FR_12 = f42 FR_14 = f43 FR_GAMMA = f43 FR_05 = f44 FR_Rq2 = f45 FR_Rq3 = f46 FR_Rq4 = f47 FR_Rq5 = f48 FR_Rq6 = f49 FR_Rq7 = f50 FR_RqLin = f51 FR_InvAn = f52 FR_C01 = f53 FR_A15 = f53 FR_C11 = f54 FR_A14 = f54 FR_C21 = f55 FR_A13 = f55 FR_C31 = f56 FR_A12 = f56 FR_C41 = f57 FR_A11 = f57 FR_C51 = f58 FR_A10 = f58 FR_C61 = f59 FR_A9 = f59 FR_C71 = f60 FR_A8 = f60 FR_C81 = f61 FR_A7 = f61 FR_C91 = f62 FR_A6 = f62 FR_CA1 = f63 FR_A5 = f63 FR_C00 = f64 FR_A4 = f64 FR_rs2 = f64 FR_C10 = f65 FR_A3 = f65 FR_rs3 = f65 FR_C20 = f66 FR_A2 = f66 FR_rs4 = f66 FR_C30 = f67 FR_A1 = f67 FR_rs7 = f67 FR_C40 = f68 FR_A0 = f68 FR_rs8 = f68 FR_C50 = f69 FR_r2 = f69 FR_C60 = f70 FR_r3 = f70 FR_C70 = f71 FR_r4 = f71 FR_C80 = f72 FR_r7 = f72 FR_C90 = f73 FR_r8 = f73 FR_CA0 = f74 FR_An = f75 FR_S21 = f76 FR_S19 = f77 FR_Rcp0 = f77 FR_Rcp2 = f77 FR_S17 = f78 FR_S15 = f79 FR_S13 = f80 FR_S11 = f81 FR_S9 = f82 FR_S7 = f83 FR_S5 = f84 FR_S3 = f85 FR_iXt = f86 FR_rs = f87 // Data tables //============================================================== RODATA .align 16 LOCAL_OBJECT_START(tgamma_data) data8 0x406573FAE561F648 // overflow boundary (171.624376956302739927196) data8 0x3FDD8B618D5AF8FE // point of local minium (0.461632144968362356785) // //[2; 3] data8 0xEF0E85C9AE40ABE2,0x00004000 // C01 data8 0xCA2049DDB4096DD8,0x00004000 // C11 data8 0x99A203B4DC2D1A8C,0x00004000 // C21 data8 0xBF5D9D9C0C295570,0x00003FFF // C31 data8 0xE8DD037DEB833BAB,0x00003FFD // C41 data8 0xB6AE39A2A36AA03A,0x0000BFFE // C51 data8 0x804960DC2850277B,0x0000C000 // C61 data8 0xD9F3973841C09F80,0x0000C000 // C71 data8 0x9C198A676F8A2239,0x0000C001 // C81 data8 0xC98B7DAE02BE3226,0x0000C001 // C91 data8 0xE9CAF31AC69301BA,0x0000C001 // CA1 data8 0xFBBDD58608A0D172,0x00004000 // C00 data8 0xFDD0316D1E078301,0x00004000 // C10 data8 0x8630B760468C15E4,0x00004001 // C20 data8 0x93EDE20E47D9152E,0x00004001 // C30 data8 0xA86F3A38C77D6B19,0x00004001 // C40 //[16; 17] data8 0xF87F757F365EE813,0x00004000 // C01 data8 0xECA84FBA92759DA4,0x00004000 // C11 data8 0xD4E0A55E07A8E913,0x00004000 // C21 data8 0xB0EB45E94C8A5F7B,0x00004000 // C31 data8 0x8050D6B4F7C8617D,0x00004000 // C41 data8 0x8471B111AA691E5A,0x00003FFF // C51 data8 0xADAF462AF96585C9,0x0000BFFC // C61 data8 0xD327C7A587A8C32B,0x0000BFFF // C71 data8 0xDEF5192B4CF5E0F1,0x0000C000 // C81 data8 0xBADD64BB205AEF02,0x0000C001 // C91 data8 0x9330A24AA67D6860,0x0000C002 // CA1 data8 0xF57EEAF36D8C47BE,0x00004000 // C00 data8 0x807092E12A251B38,0x00004001 // C10 data8 0x8C458F80DEE7ED1C,0x00004001 // C20 data8 0x9F30C731DC77F1A6,0x00004001 // C30 data8 0xBAC4E7E099C3A373,0x00004001 // C40 //[32; 33] data8 0xC3059A415F142DEF,0x00004000 // C01 data8 0xB9C1DAC24664587A,0x00004000 // C11 data8 0xA7101D910992FFB2,0x00004000 // C21 data8 0x8A9522B8E4AA0AB4,0x00004000 // C31 data8 0xC76A271E4BA95DCC,0x00003FFF // C41 data8 0xC5D6DE2A38DB7FF2,0x00003FFE // C51 data8 0xDBA42086997818B2,0x0000BFFC // C61 data8 0xB8EDDB1424C1C996,0x0000BFFF // C71 data8 0xBF7372FB45524B5D,0x0000C000 // C81 data8 0xA03DDE759131580A,0x0000C001 // C91 data8 0xFDA6FC4022C1FFE3,0x0000C001 // CA1 data8 0x9759ABF797B2533D,0x00004000 // C00 data8 0x9FA160C6CF18CEC5,0x00004000 // C10 data8 0xB0EFF1E3530E0FCD,0x00004000 // C20 data8 0xCCD60D5C470165D1,0x00004000 // C30 data8 0xF5E53F6307B0B1C1,0x00004000 // C40 //[48; 49] data8 0xAABE577FBCE37F5E,0x00004000 // C01 data8 0xA274CAEEB5DF7172,0x00004000 // C11 data8 0x91B90B6646C1B924,0x00004000 // C21 data8 0xF06718519CA256D9,0x00003FFF // C31 data8 0xAA9EE181C0E30263,0x00003FFF // C41 data8 0xA07BDB5325CB28D2,0x00003FFE // C51 data8 0x86C8B873204F9219,0x0000BFFD // C61 data8 0xB0192C5D3E4787D6,0x0000BFFF // C71 data8 0xB1E0A6263D4C19EF,0x0000C000 // C81 data8 0x93BA32A118EAC9AE,0x0000C001 // C91 data8 0xE942A39CD9BEE887,0x0000C001 // CA1 data8 0xE838B0957B0D3D0D,0x00003FFF // C00 data8 0xF60E0F00074FCF34,0x00003FFF // C10 data8 0x89869936AE00C2A5,0x00004000 // C20 data8 0xA0FE4E8AA611207F,0x00004000 // C30 data8 0xC3B1229CFF1DDAFE,0x00004000 // C40 //[64; 65] data8 0x9C00DDF75CDC6183,0x00004000 // C01 data8 0x9446AE9C0F6A833E,0x00004000 // C11 data8 0x84ABC5083310B774,0x00004000 // C21 data8 0xD9BA3A0977B1ED83,0x00003FFF // C31 data8 0x989B18C99411D300,0x00003FFF // C41 data8 0x886E66402318CE6F,0x00003FFE // C51 data8 0x99028C2468F18F38,0x0000BFFD // C61 data8 0xAB72D17DCD40CCE1,0x0000BFFF // C71 data8 0xA9D9AC9BE42C2EF9,0x0000C000 // C81 data8 0x8C11D983AA177AD2,0x0000C001 // C91 data8 0xDC779E981C1F0F06,0x0000C001 // CA1 data8 0xC1FD4AC85965E8D6,0x00003FFF // C00 data8 0xCE3D2D909D389EC2,0x00003FFF // C10 data8 0xE7F79980AD06F5D8,0x00003FFF // C20 data8 0x88DD9F73C8680B5D,0x00004000 // C30 data8 0xA7D6CB2CB2D46F9D,0x00004000 // C40 //[80; 81] data8 0x91C7FF4E993430D0,0x00004000 // C01 data8 0x8A6E7AB83E45A7E9,0x00004000 // C11 data8 0xF72D6382E427BEA9,0x00003FFF // C21 data8 0xC9E2E4F9B3B23ED6,0x00003FFF // C31 data8 0x8BEFEF56AE05D775,0x00003FFF // C41 data8 0xEE9666AB6A185560,0x00003FFD // C51 data8 0xA6AFAF5CEFAEE04D,0x0000BFFD // C61 data8 0xA877EAFEF1F9C880,0x0000BFFF // C71 data8 0xA45BD433048ECA15,0x0000C000 // C81 data8 0x86BD1636B774CC2E,0x0000C001 // C91 data8 0xD3721BE006E10823,0x0000C001 // CA1 data8 0xA97EFABA91854208,0x00003FFF // C00 data8 0xB4AF0AEBB3F97737,0x00003FFF // C10 data8 0xCC38241936851B0B,0x00003FFF // C20 data8 0xF282A6261006EA84,0x00003FFF // C30 data8 0x95B8E9DB1BD45BAF,0x00004000 // C40 //[96; 97] data8 0x8A1FA3171B35A106,0x00004000 // C01 data8 0x830D5B8843890F21,0x00004000 // C11 data8 0xE98B0F1616677A23,0x00003FFF // C21 data8 0xBDF8347F5F67D4EC,0x00003FFF // C31 data8 0x825F15DE34EC055D,0x00003FFF // C41 data8 0xD4846186B8AAC7BE,0x00003FFD // C51 data8 0xB161093AB14919B1,0x0000BFFD // C61 data8 0xA65758EEA4800EF4,0x0000BFFF // C71 data8 0xA046B67536FA329C,0x0000C000 // C81 data8 0x82BBEC1BCB9E9068,0x0000C001 // C91 data8 0xCC9DE2B23BA91B0B,0x0000C001 // CA1 data8 0x983B16148AF77F94,0x00003FFF // C00 data8 0xA2A4D8EE90FEE5DD,0x00003FFF // C10 data8 0xB89446FA37FF481C,0x00003FFF // C20 data8 0xDC5572648485FB01,0x00003FFF // C30 data8 0x88CD5D7DB976129A,0x00004000 // C40 //[112; 113] data8 0x8417098FD62AC5E3,0x00004000 // C01 data8 0xFA7896486B779CBB,0x00003FFF // C11 data8 0xDEC98B14AF5EEBD1,0x00003FFF // C21 data8 0xB48E153C6BF0B5A3,0x00003FFF // C31 data8 0xF597B038BC957582,0x00003FFE // C41 data8 0xBFC6F0884A415694,0x00003FFD // C51 data8 0xBA075A1392BDB5E5,0x0000BFFD // C61 data8 0xA4B79E01B44C7DB4,0x0000BFFF // C71 data8 0x9D12FA7711BFAB0F,0x0000C000 // C81 data8 0xFF24C47C8E108AB4,0x0000C000 // C91 data8 0xC7325EC86562606A,0x0000C001 // CA1 data8 0x8B47DCD9E1610938,0x00003FFF // C00 data8 0x9518B111B70F88B8,0x00003FFF // C10 data8 0xA9CC197206F68682,0x00003FFF // C20 data8 0xCB98294CC0D7A6A6,0x00003FFF // C30 data8 0xFE09493EA9165181,0x00003FFF // C40 //[128; 129] data8 0xFE53D03442270D90,0x00003FFF // C01 data8 0xF0F857BAEC1993E4,0x00003FFF // C11 data8 0xD5FF6D70DBBC2FD3,0x00003FFF // C21 data8 0xACDAA5F4988B1074,0x00003FFF // C31 data8 0xE92E069F8AD75B54,0x00003FFE // C41 data8 0xAEBB64645BD94234,0x00003FFD // C51 data8 0xC13746249F39B43C,0x0000BFFD // C61 data8 0xA36B74F5B6297A1F,0x0000BFFF // C71 data8 0x9A77860DF180F6E5,0x0000C000 // C81 data8 0xF9F8457D84410A0C,0x0000C000 // C91 data8 0xC2BF44C649EB8597,0x0000C001 // CA1 data8 0x81225E7489BCDC0E,0x00003FFF // C00 data8 0x8A788A09CE0EED11,0x00003FFF // C10 data8 0x9E2E6F86D1B1D89C,0x00003FFF // C20 data8 0xBE6866B21CF6CCB5,0x00003FFF // C30 data8 0xEE94426EC1486AAE,0x00003FFF // C40 //[144; 145] data8 0xF6113E09732A6497,0x00003FFF // C01 data8 0xE900D45931B04FC8,0x00003FFF // C11 data8 0xCE9FD58F745EBA5D,0x00003FFF // C21 data8 0xA663A9636C864C86,0x00003FFF // C31 data8 0xDEBF5315896CE629,0x00003FFE // C41 data8 0xA05FEA415EBD7737,0x00003FFD // C51 data8 0xC750F112BD9C4031,0x0000BFFD // C61 data8 0xA2593A35C51C6F6C,0x0000BFFF // C71 data8 0x9848E1DA7FB40C8C,0x0000C000 // C81 data8 0xF59FEE87A5759A4B,0x0000C000 // C91 data8 0xBF00203909E45A1D,0x0000C001 // CA1 data8 0xF1D8E157200127E5,0x00003FFE // C00 data8 0x81DD5397CB08D487,0x00003FFF // C10 data8 0x94C1DC271A8B766F,0x00003FFF // C20 data8 0xB3AFAF9B5D6EDDCF,0x00003FFF // C30 data8 0xE1FB4C57CA81BE1E,0x00003FFF // C40 //[160; 161] data8 0xEEFFE5122AC72FFD,0x00003FFF // C01 data8 0xE22F70BB52AD54B3,0x00003FFF // C11 data8 0xC84FF021FE993EEA,0x00003FFF // C21 data8 0xA0DA2208EB5B2752,0x00003FFF // C31 data8 0xD5CDD2FCF8AD2DF5,0x00003FFE // C41 data8 0x940BEC6DCD811A59,0x00003FFD // C51 data8 0xCC954EF4FD4EBB81,0x0000BFFD // C61 data8 0xA1712E29A8C04554,0x0000BFFF // C71 data8 0x966B55DFB243521A,0x0000C000 // C81 data8 0xF1E6A2B9CEDD0C4C,0x0000C000 // C91 data8 0xBBC87BCC031012DB,0x0000C001 // CA1 data8 0xE43974E6D2818583,0x00003FFE // C00 data8 0xF5702A516B64C5B7,0x00003FFE // C10 data8 0x8CEBCB1B32E19471,0x00003FFF // C20 data8 0xAAC10F05BB77E0AF,0x00003FFF // C30 data8 0xD776EFCAB205CC58,0x00003FFF // C40 //[176; 177] data8 0xE8DA614119811E5D,0x00003FFF // C01 data8 0xDC415E0288B223D8,0x00003FFF // C11 data8 0xC2D2243E44EC970E,0x00003FFF // C21 data8 0x9C086664B5307BEA,0x00003FFF // C31 data8 0xCE03D7A08B461156,0x00003FFE // C41 data8 0x894BE3BAAAB66ADC,0x00003FFD // C51 data8 0xD131EDD71A702D4D,0x0000BFFD // C61 data8 0xA0A907CDDBE10898,0x0000BFFF // C71 data8 0x94CC3CD9C765C808,0x0000C000 // C81 data8 0xEEA85F237815FC0D,0x0000C000 // C91 data8 0xB8FA04B023E43F91,0x0000C001 // CA1 data8 0xD8B2C7D9FCBD7EF9,0x00003FFE // C00 data8 0xE9566E93AAE7E38F,0x00003FFE // C10 data8 0x8646E78AABEF0255,0x00003FFF // C20 data8 0xA32AEDB62E304345,0x00003FFF // C30 data8 0xCE83E40280EE7DF0,0x00003FFF // C40 // //[2; 3] data8 0xC44FB47E90584083,0x00004001 // C50 data8 0xE863EE77E1C45981,0x00004001 // C60 data8 0x8AC15BE238B9D70E,0x00004002 // C70 data8 0xA5D94B6592350EF4,0x00004002 // C80 data8 0xC379DB3E20A148B3,0x00004002 // C90 data8 0xDACA49B73974F6C9,0x00004002 // CA0 data8 0x810E496A1AFEC895,0x00003FE1 // An //[16; 17] data8 0xE17C0357AAF3F817,0x00004001 // C50 data8 0x8BA8804750FBFBFE,0x00004002 // C60 data8 0xB18EAB3CB64BEBEE,0x00004002 // C70 data8 0xE90AB7015AF1C28F,0x00004002 // C80 data8 0xA0AB97CE9E259196,0x00004003 // C90 data8 0xF5E0E0A000C2D720,0x00004003 // CA0 data8 0xD97F0F87EC791954,0x00004005 // An //[32; 33] data8 0x980C293F3696040D,0x00004001 // C50 data8 0xC0DBFFBB948A9A4E,0x00004001 // C60 data8 0xFAB54625E9A588A2,0x00004001 // C70 data8 0xA7E08176D6050FBF,0x00004002 // C80 data8 0xEBAAEC4952270A9F,0x00004002 // C90 data8 0xB7479CDAD20550FE,0x00004003 // CA0 data8 0xAACD45931C3FF634,0x00004054 // An //[48; 49] data8 0xF5180F0000419AD5,0x00004000 // C50 data8 0x9D507D07BFBB2273,0x00004001 // C60 data8 0xCEB53F7A13A383E3,0x00004001 // C70 data8 0x8BAFEF9E0A49128F,0x00004002 // C80 data8 0xC58EF912D39E228C,0x00004002 // C90 data8 0x9A88118422BA208E,0x00004003 // CA0 data8 0xBD6C0E2477EC12CB,0x000040AC // An //[64; 65] data8 0xD410AC48BF7748DA,0x00004000 // C50 data8 0x89399B90AFEBD931,0x00004001 // C60 data8 0xB596DF8F77EB8560,0x00004001 // C70 data8 0xF6D9445A047FB4A6,0x00004001 // C80 data8 0xAF52F0DD65221357,0x00004002 // C90 data8 0x8989B45BFC881989,0x00004003 // CA0 data8 0xB7FCAE86E6E10D5A,0x0000410B // An //[80; 81] data8 0xBE759740E3B5AA84,0x00004000 // C50 data8 0xF8037B1B07D27609,0x00004000 // C60 data8 0xA4F6F6C7F0977D4F,0x00004001 // C70 data8 0xE131960233BF02C4,0x00004001 // C80 data8 0xA06DF43D3922BBE2,0x00004002 // C90 data8 0xFC266AB27255A360,0x00004002 // CA0 data8 0xD9F4B012EDAFEF2F,0x0000416F // An //[96; 97] data8 0xAEFC84CDA8E1EAA6,0x00004000 // C50 data8 0xE5009110DB5F3C8A,0x00004000 // C60 data8 0x98F5F48738E7B232,0x00004001 // C70 data8 0xD17EE64E21FFDC6B,0x00004001 // C80 data8 0x9596F7A7E36145CC,0x00004002 // C90 data8 0xEB64DBE50E125CAF,0x00004002 // CA0 data8 0xA090530D79E32D2E,0x000041D8 // An //[112; 113] data8 0xA33AEA22A16B2655,0x00004000 // C50 data8 0xD682B93BD7D7945C,0x00004000 // C60 data8 0x8FC854C6E6E30CC3,0x00004001 // C70 data8 0xC5754D828AFFDC7A,0x00004001 // C80 data8 0x8D41216B397139C2,0x00004002 // C90 data8 0xDE78D746848116E5,0x00004002 // CA0 data8 0xB8A297A2DC0630DB,0x00004244 // An //[128; 129] data8 0x99EB00F11D95E292,0x00004000 // C50 data8 0xCB005CB911EB779A,0x00004000 // C60 data8 0x8879AA2FDFF3A37A,0x00004001 // C70 data8 0xBBDA538AD40CAC2C,0x00004001 // C80 data8 0x8696D849D311B9DE,0x00004002 // C90 data8 0xD41E1C041481199F,0x00004002 // CA0 data8 0xEBA1A43D34EE61EE,0x000042B3 // An //[144; 145] data8 0x924F822578AA9F3D,0x00004000 // C50 data8 0xC193FAF9D3B36960,0x00004000 // C60 data8 0x827AE3A6B68ED0CA,0x00004001 // C70 data8 0xB3F52A27EED23F0B,0x00004001 // C80 data8 0x811A079FB3C94D79,0x00004002 // C90 data8 0xCB94415470B6F8D2,0x00004002 // CA0 data8 0x80A0260DCB3EC9AC,0x00004326 // An //[160; 161] data8 0x8BF24091E88B331D,0x00004000 // C50 data8 0xB9ADE01187E65201,0x00004000 // C60 data8 0xFAE4508F6E7625FE,0x00004000 // C70 data8 0xAD516668AD6D7367,0x00004001 // C80 data8 0xF8F5FF171154F637,0x00004001 // C90 data8 0xC461321268990C82,0x00004002 // CA0 data8 0xC3B693F344B0E6FE,0x0000439A // An // //[176; 177] data8 0x868545EB42A258ED,0x00004000 // C50 data8 0xB2EF04ACE8BA0E6E,0x00004000 // C60 data8 0xF247D22C22E69230,0x00004000 // C70 data8 0xA7A1AB93E3981A90,0x00004001 // C80 data8 0xF10951733E2C697F,0x00004001 // C90 data8 0xBE3359BFAD128322,0x00004002 // CA0 data8 0x8000000000000000,0x00003fff // //[160; 161] for negatives data8 0xA76DBD55B2E32D71,0x00003C63 // 1/An // // sin(pi*x)/pi data8 0xBCBC4342112F52A2,0x00003FDE // S21 data8 0xFAFCECB86536F655,0x0000BFE3 // S19 data8 0x87E4C97F9CF09B92,0x00003FE9 // S17 data8 0xEA124C68E704C5CB,0x0000BFED // S15 data8 0x9BA38CFD59C8AA1D,0x00003FF2 // S13 data8 0x99C0B552303D5B21,0x0000BFF6 // S11 // //[176; 177] for negatives data8 0xBA5D5869211696FF,0x00003BEC // 1/An // // sin(pi*x)/pi data8 0xD63402E79A853175,0x00003FF9 // S9 data8 0xC354723906DB36BA,0x0000BFFC // S7 data8 0xCFCE5A015E236291,0x00003FFE // S5 data8 0xD28D3312983E9918,0x0000BFFF // S3 // // // [1.0;1.25] data8 0xA405530B067ECD3C,0x0000BFFC // A15 data8 0xF5B5413F95E1C282,0x00003FFD // A14 data8 0xC4DED71C782F76C8,0x0000BFFE // A13 data8 0xECF7DDDFD27C9223,0x00003FFE // A12 data8 0xFB73D31793068463,0x0000BFFE // A11 data8 0xFF173B7E66FD1D61,0x00003FFE // A10 data8 0xFFA5EF3959089E94,0x0000BFFE // A9 data8 0xFF8153BD42E71A4F,0x00003FFE // A8 data8 0xFEF9CAEE2CB5B533,0x0000BFFE // A7 data8 0xFE3F02E5EDB6811E,0x00003FFE // A6 data8 0xFB64074CED2658FB,0x0000BFFE // A5 data8 0xFB52882A095B18A4,0x00003FFE // A4 data8 0xE8508C7990A0DAC0,0x0000BFFE // A3 data8 0xFD32C611D8A881D0,0x00003FFE // A2 data8 0x93C467E37DB0C536,0x0000BFFE // A1 data8 0x8000000000000000,0x00003FFF // A0 // // [1.25;1.5] data8 0xD038092400619677,0x0000BFF7 // A15 data8 0xEA6DE925E6EB8C8F,0x00003FF3 // A14 data8 0xC53F83645D4597FC,0x0000BFF7 // A13 data8 0xE366DB2FB27B7ECD,0x00003FF7 // A12 data8 0xAC8FD5E11F6EEAD8,0x0000BFF8 // A11 data8 0xFB14010FB3697785,0x00003FF8 // A10 data8 0xB6F91CB5C371177B,0x0000BFF9 // A9 data8 0x85A262C6F8FEEF71,0x00003FFA // A8 data8 0xC038E6E3261568F9,0x0000BFFA // A7 data8 0x8F4BDE8883232364,0x00003FFB // A6 data8 0xBCFBBD5786537E9A,0x0000BFFB // A5 data8 0xA4C08BAF0A559479,0x00003FFC // A4 data8 0x85D74FA063E81476,0x0000BFFC // A3 data8 0xDB629FB9BBDC1C4E,0x00003FFD // A2 data8 0xF4F8FBC7C0C9D317,0x00003FC6 // A1 data8 0xE2B6E4153A57746C,0x00003FFE // A0 // // [1.25;1.5] data8 0x9533F9D3723B448C,0x0000BFF2 // A15 data8 0xF1F75D3C561CBBAF,0x00003FF5 // A14 data8 0xBA55A9A1FC883523,0x0000BFF8 // A13 data8 0xB5D5E9E5104FA995,0x00003FFA // A12 data8 0xFD84F35B70CD9AE2,0x0000BFFB // A11 data8 0x87445235F4688CC5,0x00003FFD // A10 data8 0xE7F236EBFB9F774E,0x0000BFFD // A9 data8 0xA6605F2721F787CE,0x00003FFE // A8 data8 0xCF579312AD7EAD72,0x0000BFFE // A7 data8 0xE96254A2407A5EAC,0x00003FFE // A6 data8 0xF41312A8572ED346,0x0000BFFE // A5 data8 0xF9535027C1B1F795,0x00003FFE // A4 data8 0xE7E82D0C613A8DE4,0x0000BFFE // A3 data8 0xFD23CD9741B460B8,0x00003FFE // A2 data8 0x93C30FD9781DBA88,0x0000BFFE // A1 data8 0xFFFFF1781FDBEE84,0x00003FFE // A0 LOCAL_OBJECT_END(tgamma_data) //============================================================== // Code //============================================================== .section .text GLOBAL_LIBM_ENTRY(tgamma) { .mfi getf.exp GR_Sign_Exp = f8 fma.s1 FR_1m2X = f8,f1,f8 // 2x addl GR_ad_Data = @ltoff(tgamma_data), gp } { .mfi mov GR_ExpOf8 = 0x10002 // 8 fcvt.fx.trunc.s1 FR_iXt = f8 // [x] mov GR_ExpOf05 = 0xFFFE // 0.5 };; { .mfi getf.sig GR_Sig = f8 fma.s1 FR_2 = f1,f1,f1 // 2 mov GR_Addr_Mask1 = 0x780 } { .mlx setf.exp FR_8 = GR_ExpOf8 movl GR_10 = 0x4024000000000000 };; { .mfi ld8 GR_ad_Data = [GR_ad_Data] fcmp.lt.s1 p14,p15 = f8,f0 tbit.z p12,p13 = GR_Sign_Exp,0x10 // p13 if x >= 2 } { .mlx and GR_Bit2 = 4,GR_Sign_Exp movl GR_12 = 0x4028000000000000 };; { .mfi setf.d FR_10 = GR_10 fma.s1 FR_r02 = f8,f1,f0 extr.u GR_Tbl_Offs = GR_Sig,58,6 } { .mfi (p12) mov GR_Addr_Mask1 = r0 fma.s1 FR_NormX = f8,f1,f0 cmp.ne p8,p0 = GR_Bit2,r0 };; { .mfi (p8) shladd GR_Tbl_Offs = GR_Tbl_Offs,4,r0 fclass.m p10,p0 = f8,0x1E7 // Test x for NaTVal, NaN, +/-0, +/-INF tbit.nz p11,p0 = GR_Sign_Exp,1 } { .mlx add GR_Addr_Mask2 = GR_Addr_Mask1,GR_Addr_Mask1 movl GR_14 = 0x402C000000000000 };; .pred.rel "mutex",p14,p15 { .mfi setf.d FR_12 = GR_12 (p14) fma.s1 FR_1m2X = f1,f1,FR_1m2X // RB=1-2|x| tbit.nz p8,p9 = GR_Sign_Exp,0 } { .mfi ldfpd FR_OvfBound,FR_Xmin = [GR_ad_Data],16 (p15) fms.s1 FR_1m2X = f1,f1,FR_1m2X // RB=1-2|x| (p11) shladd GR_Tbl_Offs = GR_Tbl_Offs,2,r0 };; .pred.rel "mutex",p9,p8 { .mfi setf.d FR_14 = GR_14 fma.s1 FR_4 = FR_2,FR_2,f0 (p8) and GR_Tbl_Offs = GR_Tbl_Offs, GR_Addr_Mask1 } { .mfi setf.exp FR_05 = GR_ExpOf05 fma.s1 FR_6 = FR_2,FR_2,FR_2 (p9) and GR_Tbl_Offs = GR_Tbl_Offs, GR_Addr_Mask2 };; .pred.rel "mutex",p9,p8 { .mfi (p8) shladd GR_ad_Co = GR_Tbl_Offs,1,GR_ad_Data fcvt.xf FR_Xt = FR_iXt // [x] (p15) tbit.z.unc p11,p0 = GR_Sign_Exp,0x10 // p11 if 0 < x < 2 } { .mfi (p9) add GR_ad_Co = GR_ad_Data,GR_Tbl_Offs fma.s1 FR_5 = FR_2,FR_2,f1 (p15) cmp.lt.unc p7,p6 = GR_ExpOf05,GR_Sign_Exp // p7 if 0 < x < 1 };; { .mfi add GR_ad_Ce = 16,GR_ad_Co (p11) frcpa.s1 FR_Rcp0,p0 = f1,f8 sub GR_Tbl_Offs = GR_ad_Co,GR_ad_Data } { .mfb ldfe FR_C01 = [GR_ad_Co],32 (p7) fms.s1 FR_r02 = FR_r02,f1,f1 // jump if x is NaTVal, NaN, +/-0, +/-INF (p10) br.cond.spnt tgamma_spec };; .pred.rel "mutex",p14,p15 { .mfi ldfe FR_C11 = [GR_ad_Ce],32 (p14) fms.s1 FR_X2pX = f8,f8,f8 // RA=x^2+|x| shr GR_Tbl_Ind = GR_Tbl_Offs,8 } { .mfb ldfe FR_C21 = [GR_ad_Co],32 (p15) fma.s1 FR_X2pX = f8,f8,f8 // RA=x^2+x // jump if 0 < x < 2 (p11) br.cond.spnt tgamma_from_0_to_2 };; { .mfi ldfe FR_C31 = [GR_ad_Ce],32 fma.s1 FR_Rq2 = FR_2,f1,FR_1m2X // 2 + B cmp.ltu p7,p0=0xB,GR_Tbl_Ind } { .mfb ldfe FR_C41 = [GR_ad_Co],32 fma.s1 FR_Rq3 = FR_2,FR_2,FR_1m2X // 4 + B // jump if GR_Tbl_Ind > 11, i.e |x| is more than 192 (p7) br.cond.spnt tgamma_spec_res };; { .mfi ldfe FR_C51 = [GR_ad_Ce],32 fma.s1 FR_Rq4 = FR_6,f1,FR_1m2X // 6 + B shr GR_Tbl_Offs = GR_Tbl_Offs,1 } { .mfi ldfe FR_C61 = [GR_ad_Co],32 fma.s1 FR_Rq5 = FR_4,FR_2,FR_1m2X // 8 + B nop.i 0 };; { .mfi ldfe FR_C71 = [GR_ad_Ce],32 (p14) fms.s1 FR_r = FR_Xt,f1,f8 // r = |x| - [|x|] shr GR_Tbl_16xInd = GR_Tbl_Offs,3 } { .mfi ldfe FR_C81 = [GR_ad_Co],32 (p15) fms.s1 FR_r = f8,f1,FR_Xt // r = x - [x] add GR_ad_Data = 0xC00,GR_ad_Data };; { .mfi ldfe FR_C91 = [GR_ad_Ce],32 fma.s1 FR_Rq6 = FR_5,FR_2,FR_1m2X // 10 + B (p14) mov GR_0x30033 = 0x30033 } { .mfi ldfe FR_CA1 = [GR_ad_Co],32 fma.s1 FR_Rq7 = FR_6,FR_2,FR_1m2X // 12 + B sub GR_Tbl_Offs = GR_Tbl_Offs,GR_Tbl_16xInd };; { .mfi ldfe FR_C00 = [GR_ad_Ce],32 fma.s1 FR_Rq1 = FR_Rq1,FR_2,FR_X2pX // (x-1)*(x-2) (p13) cmp.eq.unc p8,p0 = r0,GR_Tbl_16xInd // index is 0 i.e. arg from [2;16) } { .mfi ldfe FR_C10 = [GR_ad_Co],32 (p14) fms.s1 FR_AbsX = f0,f0,FR_NormX // absolute value of argument add GR_ad_Co7 = GR_ad_Data,GR_Tbl_Offs };; { .mfi ldfe FR_C20 = [GR_ad_Ce],32 fma.s1 FR_Rq2 = FR_Rq2,FR_4,FR_X2pX // (x-3)*(x-4) add GR_ad_Ce7 = 16,GR_ad_Co7 } { .mfi ldfe FR_C30 = [GR_ad_Co],32 fma.s1 FR_Rq3 = FR_Rq3,FR_6,FR_X2pX // (x-5)*(x-6) nop.i 0 };; { .mfi ldfe FR_C40 = [GR_ad_Ce],32 fma.s1 FR_Rq4 = FR_Rq4,FR_8,FR_X2pX // (x-7)*(x-8) (p14) cmp.leu.unc p7,p0 = GR_0x30033,GR_Sign_Exp } { .mfb ldfe FR_C50 = [GR_ad_Co7],32 fma.s1 FR_Rq5 = FR_Rq5,FR_10,FR_X2pX // (x-9)*(x-10) // jump if x is less or equal to -2^52, i.e. x is big negative integer (p7) br.cond.spnt tgamma_singularity };; { .mfi ldfe FR_C60 = [GR_ad_Ce7],32 fma.s1 FR_C01 = FR_C01,f1,FR_r add GR_ad_Ce = 0x560,GR_ad_Data } { .mfi ldfe FR_C70 = [GR_ad_Co7],32 fma.s1 FR_rs = f0,f0,FR_r // reduced arg for sin(pi*x) add GR_ad_Co = 0x550,GR_ad_Data };; { .mfi ldfe FR_C80 = [GR_ad_Ce7],32 fma.s1 FR_C11 = FR_C11,f1,FR_r nop.i 0 } { .mfi ldfe FR_C90 = [GR_ad_Co7],32 fma.s1 FR_C21 = FR_C21,f1,FR_r nop.i 0 };; .pred.rel "mutex",p12,p13 { .mfi (p13) getf.sig GR_iSig = FR_iXt fcmp.lt.s1 p11,p0 = FR_05,FR_r mov GR_185 = 185 } { .mfi nop.m 0 fma.s1 FR_Rq6 = FR_Rq6,FR_12,FR_X2pX // (x-11)*(x-12) nop.i 0 };; { .mfi ldfe FR_CA0 = [GR_ad_Ce7],32 fma.s1 FR_C31 = FR_C31,f1,FR_r (p12) mov GR_iSig = 0 } { .mfi ldfe FR_An = [GR_ad_Co7],0x80 fma.s1 FR_C41 = FR_C41,f1,FR_r nop.i 0 };; { .mfi (p14) getf.sig GR_Sig = FR_r fma.s1 FR_C51 = FR_C51,f1,FR_r (p14) sub GR_iSig = r0,GR_iSig } { .mfi ldfe FR_S21 = [GR_ad_Co],32 fma.s1 FR_C61 = FR_C61,f1,FR_r nop.i 0 };; { .mfi ldfe FR_S19 = [GR_ad_Ce],32 fma.s1 FR_C71 = FR_C71,f1,FR_r and GR_SigRqLin = 0xF,GR_iSig } { .mfi ldfe FR_S17 = [GR_ad_Co],32 fma.s1 FR_C81 = FR_C81,f1,FR_r mov GR_2 = 2 };; { .mfi (p14) ldfe FR_InvAn = [GR_ad_Co7] fma.s1 FR_C91 = FR_C91,f1,FR_r // if significand of r is 0 tnan argument is negative integer (p14) cmp.eq.unc p12,p0 = r0,GR_Sig } { .mfb (p8) sub GR_SigRqLin = GR_SigRqLin,GR_2 // subtract 2 if 2 <= x < 16 fma.s1 FR_CA1 = FR_CA1,f1,FR_r // jump if x is negative integer such that -2^52 < x < -185 (p12) br.cond.spnt tgamma_singularity };; { .mfi setf.sig FR_Xt = GR_SigRqLin (p11) fms.s1 FR_rs = f1,f1,FR_r (p14) cmp.ltu.unc p7,p0 = GR_185,GR_iSig } { .mfb ldfe FR_S15 = [GR_ad_Ce],32 fma.s1 FR_Rq7 = FR_Rq7,FR_14,FR_X2pX // (x-13)*(x-14) // jump if x is noninteger such that -2^52 < x < -185 (p7) br.cond.spnt tgamma_underflow };; { .mfi ldfe FR_S13 = [GR_ad_Co],48 fma.s1 FR_C01 = FR_C01,FR_r,FR_C00 and GR_Sig2 = 0xE,GR_SigRqLin } { .mfi ldfe FR_S11 = [GR_ad_Ce],48 fma.s1 FR_C11 = FR_C11,FR_r,FR_C10 nop.i 0 };; { .mfi ldfe FR_S9 = [GR_ad_Co],32 fma.s1 FR_C21 = FR_C21,FR_r,FR_C20 // should we mul by polynomial of recursion? cmp.eq p13,p12 = r0,GR_SigRqLin } { .mfi ldfe FR_S7 = [GR_ad_Ce],32 fma.s1 FR_C31 = FR_C31,FR_r,FR_C30 nop.i 0 };; { .mfi ldfe FR_S5 = [GR_ad_Co],32 fma.s1 FR_C41 = FR_C41,FR_r,FR_C40 nop.i 0 } { .mfi ldfe FR_S3 = [GR_ad_Ce],32 fma.s1 FR_C51 = FR_C51,FR_r,FR_C50 nop.i 0 };; { .mfi nop.m 0 fma.s1 FR_C61 = FR_C61,FR_r,FR_C60 nop.i 0 } { .mfi nop.m 0 fma.s1 FR_C71 = FR_C71,FR_r,FR_C70 nop.i 0 };; { .mfi nop.m 0 fma.s1 FR_C81 = FR_C81,FR_r,FR_C80 nop.i 0 } { .mfi nop.m 0 fma.s1 FR_C91 = FR_C91,FR_r,FR_C90 nop.i 0 };; { .mfi nop.m 0 fma.s1 FR_CA1 = FR_CA1,FR_r,FR_CA0 nop.i 0 } { .mfi nop.m 0 fma.s1 FR_C01 = FR_C01,FR_C11,f0 nop.i 0 };; { .mfi nop.m 0 fma.s1 FR_C21 = FR_C21,FR_C31,f0 nop.i 0 } { .mfi nop.m 0 fma.s1 FR_rs2 = FR_rs,FR_rs,f0 (p12) cmp.lt.unc p7,p0 = 2,GR_Sig2 // should mul by FR_Rq2? };; { .mfi nop.m 0 fma.s1 FR_C41 = FR_C41,FR_C51,f0 nop.i 0 } { .mfi nop.m 0 (p7) fma.s1 FR_Rq1 = FR_Rq1,FR_Rq2,f0 (p12) cmp.lt.unc p9,p0 = 6,GR_Sig2 // should mul by FR_Rq4? };; { .mfi nop.m 0 fma.s1 FR_C61 = FR_C61,FR_C71,f0 (p15) cmp.eq p11,p0 = r0,r0 } { .mfi nop.m 0 (p9) fma.s1 FR_Rq3 = FR_Rq3,FR_Rq4,f0 (p12) cmp.lt.unc p8,p0 = 10,GR_Sig2 // should mul by FR_Rq6? };; { .mfi nop.m 0 fma.s1 FR_C81 = FR_C81,FR_C91,f0 nop.i 0 } { .mfi nop.m 0 (p8) fma.s1 FR_Rq5 = FR_Rq5,FR_Rq6,f0 (p14) cmp.ltu p0,p11 = 0x9,GR_Tbl_Ind };; { .mfi nop.m 0 fcvt.xf FR_RqLin = FR_Xt nop.i 0 } { .mfi nop.m 0 (p11) fma.s1 FR_CA1 = FR_CA1,FR_An,f0 nop.i 0 };; { .mfi nop.m 0 fma.s1 FR_S21 = FR_S21,FR_rs2,FR_S19 nop.i 0 } { .mfi nop.m 0 fma.s1 FR_S17 = FR_S17,FR_rs2,FR_S15 nop.i 0 };; { .mfi nop.m 0 fma.s1 FR_C01 = FR_C01,FR_C21,f0 nop.i 0 } { .mfi nop.m 0 fma.s1 FR_rs4 = FR_rs2,FR_rs2,f0 (p12) cmp.lt.unc p8,p0 = 4,GR_Sig2 // should mul by FR_Rq3? };; { .mfi nop.m 0 (p8) fma.s1 FR_Rq1 = FR_Rq1,FR_Rq3,f0 nop.i 0 } { .mfi nop.m 0 fma.s1 FR_S13 = FR_S13,FR_rs2,FR_S11 (p12) cmp.lt.unc p9,p0 = 12,GR_Sig2 // should mul by FR_Rq7? };; { .mfi nop.m 0 fma.s1 FR_C41 = FR_C41,FR_C61,f0 nop.i 0 } { .mfi nop.m 0 (p9) fma.s1 FR_Rq5 = FR_Rq5,FR_Rq7,f0 nop.i 0 };; { .mfi nop.m 0 fma.s1 FR_C81 = FR_C81,FR_CA1,f0 nop.i 0 } { .mfi nop.m 0 fma.s1 FR_S9 = FR_S9,FR_rs2,FR_S7 nop.i 0 };; { .mfi nop.m 0 fma.s1 FR_S5 = FR_S5,FR_rs2,FR_S3 nop.i 0 };; { .mfi nop.m 0 fma.s1 FR_rs3 = FR_rs2,FR_rs,f0 (p12) tbit.nz.unc p6,p0 = GR_SigRqLin,0 } { .mfi nop.m 0 fma.s1 FR_rs8 = FR_rs4,FR_rs4,f0 nop.i 0 };; { .mfi nop.m 0 fma.s1 FR_S21 = FR_S21,FR_rs4,FR_S17 mov GR_ExpOf1 = 0x2FFFF } { .mfi nop.m 0 (p6) fms.s1 FR_RqLin = FR_AbsX,f1,FR_RqLin (p12) cmp.lt.unc p8,p0 = 8,GR_Sig2 // should mul by FR_Rq5? };; { .mfi nop.m 0 fma.s1 FR_C01 = FR_C01,FR_C41,f0 nop.i 0 } { .mfi nop.m 0 (p8) fma.s1 FR_Rq1 = FR_Rq1,FR_Rq5,f0 (p14) cmp.gtu.unc p7,p0 = GR_Sign_Exp,GR_ExpOf1 };; { .mfi nop.m 0 fma.s1 FR_S13 = FR_S13,FR_rs4,FR_S9 nop.i 0 } { .mfi nop.m 0 (p7) fma.s1 FR_C81 = FR_C81,FR_AbsX,f0 nop.i 0 };; { .mfi nop.m 0 (p14) fma.s1 FR_AbsXp1 = f1,f1,FR_AbsX // |x|+1 nop.i 0 } { .mfi nop.m 0 (p15) fcmp.lt.unc.s1 p0,p10 = FR_AbsX,FR_OvfBound // x >= overflow_boundary nop.i 0 };; { .mfi nop.m 0 fma.s1 FR_rs7 = FR_rs4,FR_rs3,f0 nop.i 0 } { .mfi nop.m 0 fma.s1 FR_S5 = FR_S5,FR_rs3,FR_rs nop.i 0 };; { .mib (p14) cmp.lt p13,p0 = r0,r0 // set p13 to 0 if x < 0 (p12) cmp.eq.unc p8,p9 = 1,GR_SigRqLin (p10) br.cond.spnt tgamma_spec_res };; { .mfi getf.sig GR_Sig = FR_iXt (p6) fma.s1 FR_Rq1 = FR_Rq1,FR_RqLin,f0 // should we mul by polynomial of recursion? (p15) cmp.eq.unc p0,p11 = r0,GR_SigRqLin } { .mfb nop.m 0 fma.s1 FR_GAMMA = FR_C01,FR_C81,f0 (p11) br.cond.spnt tgamma_positives };; { .mfi nop.m 0 fma.s1 FR_S21 = FR_S21,FR_rs8,FR_S13 nop.i 0 } { .mfb nop.m 0 (p13) fma.d.s0 f8 = FR_C01,FR_C81,f0 (p13) br.ret.spnt b0 };; .pred.rel "mutex",p8,p9 { .mfi nop.m 0 (p9) fma.s1 FR_GAMMA = FR_GAMMA,FR_Rq1,f0 tbit.z p6,p7 = GR_Sig,0 // p6 if sin<0, p7 if sin>0 } { .mfi nop.m 0 (p8) fma.s1 FR_GAMMA = FR_GAMMA,FR_RqLin,f0 nop.i 0 };; { .mfi nop.m 0 fma.s1 FR_S21 = FR_S21,FR_rs7,FR_S5 nop.i 0 };; .pred.rel "mutex",p6,p7 { .mfi nop.m 0 (p6) fnma.s1 FR_GAMMA = FR_GAMMA,FR_S21,f0 nop.i 0 } { .mfi nop.m 0 (p7) fma.s1 FR_GAMMA = FR_GAMMA,FR_S21,f0 mov GR_Sig2 = 1 };; { .mfi nop.m 0 frcpa.s1 FR_Rcp0,p0 = f1,FR_GAMMA cmp.ltu p13,p0 = GR_Sign_Exp,GR_ExpOf1 };; // NR method: ineration #1 { .mfi (p13) getf.exp GR_Sign_Exp = FR_AbsX fnma.s1 FR_Rcp1 = FR_Rcp0,FR_GAMMA,f1 // t = 1 - r0*x (p13) shl GR_Sig2 = GR_Sig2,63 };; { .mfi (p13) getf.sig GR_Sig = FR_AbsX nop.f 0 (p13) mov GR_NzOvfBound = 0xFBFF };; { .mfi (p13) cmp.ltu.unc p8,p0 = GR_Sign_Exp,GR_NzOvfBound // p8 <- overflow nop.f 0 (p13) cmp.eq.unc p9,p0 = GR_Sign_Exp,GR_NzOvfBound };; { .mfb nop.m 0 (p13) fma.d.s0 FR_X = f1,f1,f8 // set deno & inexact flags (p8) br.cond.spnt tgamma_ovf_near_0 //tgamma_neg_overflow };; { .mib nop.m 0 (p9) cmp.eq.unc p8,p0 = GR_Sig,GR_Sig2 (p8) br.cond.spnt tgamma_ovf_near_0_boundary //tgamma_neg_overflow };; { .mfi nop.m 0 fma.s1 FR_Rcp1 = FR_Rcp0,FR_Rcp1,FR_Rcp0 nop.i 0 };; // NR method: ineration #2 { .mfi nop.m 0 fnma.s1 FR_Rcp2 = FR_Rcp1,FR_GAMMA,f1 // t = 1 - r1*x nop.i 0 };; { .mfi nop.m 0 fma.s1 FR_Rcp2 = FR_Rcp1,FR_Rcp2,FR_Rcp1 nop.i 0 };; // NR method: ineration #3 { .mfi nop.m 0 fnma.s1 FR_Rcp3 = FR_Rcp2,FR_GAMMA,f1 // t = 1 - r2*x nop.i 0 } { .mfi nop.m 0 (p13) fma.s1 FR_Rcp2 = FR_Rcp2,FR_AbsXp1,f0 (p14) cmp.ltu p10,p11 = 0x9,GR_Tbl_Ind };; .pred.rel "mutex",p10,p11 { .mfi nop.m 0 (p10) fma.s1 FR_GAMMA = FR_Rcp2,FR_Rcp3,FR_Rcp2 nop.i 0 } { .mfi nop.m 0 (p11) fma.d.s0 f8 = FR_Rcp2,FR_Rcp3,FR_Rcp2 nop.i 0 };; { .mfb nop.m 0 (p10) fma.d.s0 f8 = FR_GAMMA,FR_InvAn,f0 br.ret.sptk b0 };; // here if x >= 3 //-------------------------------------------------------------------- .align 32 tgamma_positives: .pred.rel "mutex",p8,p9 { .mfi nop.m 0 (p9) fma.d.s0 f8 = FR_GAMMA,FR_Rq1,f0 nop.i 0 } { .mfb nop.m 0 (p8) fma.d.s0 f8 = FR_GAMMA,FR_RqLin,f0 br.ret.sptk b0 };; // here if 0 < x < 1 //-------------------------------------------------------------------- .align 32 tgamma_from_0_to_2: { .mfi getf.exp GR_Sign_Exp = FR_r02 fms.s1 FR_r = FR_r02,f1,FR_Xmin mov GR_ExpOf025 = 0xFFFD } { .mfi add GR_ad_Co = 0x1200,GR_ad_Data (p6) fnma.s1 FR_Rcp1 = FR_Rcp0,FR_NormX,f1 // t = 1 - r0*x (p6) mov GR_Sig2 = 1 };; { .mfi (p6) getf.sig GR_Sig = FR_NormX nop.f 0 (p6) shl GR_Sig2 = GR_Sig2,63 } { .mfi add GR_ad_Ce = 0x1210,GR_ad_Data nop.f 0 (p6) mov GR_NzOvfBound = 0xFBFF };; { .mfi cmp.eq p8,p0 = GR_Sign_Exp,GR_ExpOf05 // r02 >= 1/2 nop.f 0 cmp.eq p9,p10 = GR_Sign_Exp,GR_ExpOf025 // r02 >= 1/4 } { .mfi (p6) cmp.ltu.unc p11,p0 = GR_Sign_Exp,GR_NzOvfBound // p11 <- overflow nop.f 0 (p6) cmp.eq.unc p12,p0 = GR_Sign_Exp,GR_NzOvfBound };; .pred.rel "mutex",p8,p9 { .mfi (p8) add GR_ad_Co = 0x200,GR_ad_Co (p6) fma.d.s0 FR_X = f1,f1,f8 // set deno & inexact flags (p9) add GR_ad_Co = 0x100,GR_ad_Co } { .mib (p8) add GR_ad_Ce = 0x200,GR_ad_Ce (p9) add GR_ad_Ce = 0x100,GR_ad_Ce (p11) br.cond.spnt tgamma_ovf_near_0 //tgamma_spec_res };; { .mfi ldfe FR_A15 = [GR_ad_Co],32 nop.f 0 (p12) cmp.eq.unc p13,p0 = GR_Sig,GR_Sig2 } { .mfb ldfe FR_A14 = [GR_ad_Ce],32 nop.f 0 (p13) br.cond.spnt tgamma_ovf_near_0_boundary //tgamma_spec_res };; { .mfi ldfe FR_A13 = [GR_ad_Co],32 nop.f 0 nop.i 0 } { .mfi ldfe FR_A12 = [GR_ad_Ce],32 nop.f 0 nop.i 0 };; .pred.rel "mutex",p9,p10 { .mfi ldfe FR_A11 = [GR_ad_Co],32 (p10) fma.s1 FR_r2 = FR_r02,FR_r02,f0 nop.i 0 } { .mfi ldfe FR_A10 = [GR_ad_Ce],32 (p9) fma.s1 FR_r2 = FR_r,FR_r,f0 nop.i 0 };; { .mfi ldfe FR_A9 = [GR_ad_Co],32 (p6) fma.s1 FR_Rcp1 = FR_Rcp0,FR_Rcp1,FR_Rcp0 nop.i 0 } { .mfi ldfe FR_A8 = [GR_ad_Ce],32 (p10) fma.s1 FR_r = f0,f0,FR_r02 nop.i 0 };; { .mfi ldfe FR_A7 = [GR_ad_Co],32 nop.f 0 nop.i 0 } { .mfi ldfe FR_A6 = [GR_ad_Ce],32 nop.f 0 nop.i 0 };; { .mfi ldfe FR_A5 = [GR_ad_Co],32 nop.f 0 nop.i 0 } { .mfi ldfe FR_A4 = [GR_ad_Ce],32 nop.f 0 nop.i 0 };; { .mfi ldfe FR_A3 = [GR_ad_Co],32 nop.f 0 nop.i 0 } { .mfi ldfe FR_A2 = [GR_ad_Ce],32 nop.f 0 nop.i 0 };; { .mfi ldfe FR_A1 = [GR_ad_Co],32 fma.s1 FR_r4 = FR_r2,FR_r2,f0 nop.i 0 } { .mfi ldfe FR_A0 = [GR_ad_Ce],32 nop.f 0 nop.i 0 };; { .mfi nop.m 0 (p6) fnma.s1 FR_Rcp2 = FR_Rcp1,FR_NormX,f1 // t = 1 - r1*x nop.i 0 };; { .mfi nop.m 0 fma.s1 FR_A15 = FR_A15,FR_r,FR_A14 nop.i 0 } { .mfi nop.m 0 fma.s1 FR_A11 = FR_A11,FR_r,FR_A10 nop.i 0 };; { .mfi nop.m 0 fma.s1 FR_r8 = FR_r4,FR_r4,f0 nop.i 0 };; { .mfi nop.m 0 (p6) fma.s1 FR_Rcp2 = FR_Rcp1,FR_Rcp2,FR_Rcp1 nop.i 0 };; { .mfi nop.m 0 fma.s1 FR_A7 = FR_A7,FR_r,FR_A6 nop.i 0 } { .mfi nop.m 0 fma.s1 FR_A3 = FR_A3,FR_r,FR_A2 nop.i 0 };; { .mfi nop.m 0 fma.s1 FR_A15 = FR_A15,FR_r,FR_A13 nop.i 0 } { .mfi nop.m 0 fma.s1 FR_A11 = FR_A11,FR_r,FR_A9 nop.i 0 };; { .mfi nop.m 0 (p6) fnma.s1 FR_Rcp3 = FR_Rcp2,FR_NormX,f1 // t = 1 - r1*x nop.i 0 };; { .mfi nop.m 0 fma.s1 FR_A7 = FR_A7,FR_r,FR_A5 nop.i 0 } { .mfi nop.m 0 fma.s1 FR_A3 = FR_A3,FR_r,FR_A1 nop.i 0 };; { .mfi nop.m 0 fma.s1 FR_A15 = FR_A15,FR_r,FR_A12 nop.i 0 } { .mfi nop.m 0 fma.s1 FR_A11 = FR_A11,FR_r,FR_A8 nop.i 0 };; { .mfi nop.m 0 (p6) fma.s1 FR_Rcp3 = FR_Rcp2,FR_Rcp3,FR_Rcp2 nop.i 0 };; { .mfi nop.m 0 fma.s1 FR_A7 = FR_A7,FR_r,FR_A4 nop.i 0 } { .mfi nop.m 0 fma.s1 FR_A3 = FR_A3,FR_r,FR_A0 nop.i 0 };; { .mfi nop.m 0 fma.s1 FR_A15 = FR_A15,FR_r4,FR_A11 nop.i 0 } { .mfi nop.m 0 fma.s1 FR_A7 = FR_A7,FR_r4,FR_A3 nop.i 0 };; .pred.rel "mutex",p6,p7 { .mfi nop.m 0 (p6) fma.s1 FR_A15 = FR_A15,FR_r8,FR_A7 nop.i 0 } { .mfi nop.m 0 (p7) fma.d.s0 f8 = FR_A15,FR_r8,FR_A7 nop.i 0 };; { .mfb nop.m 0 (p6) fma.d.s0 f8 = FR_A15,FR_Rcp3,f0 br.ret.sptk b0 };; // overflow //-------------------------------------------------------------------- .align 32 tgamma_ovf_near_0_boundary: .pred.rel "mutex",p14,p15 { .mfi mov GR_fpsr = ar.fpsr nop.f 0 (p15) mov r8 = 0x7ff } { .mfi nop.m 0 nop.f 0 (p14) mov r8 = 0xfff };; { .mfi nop.m 0 nop.f 0 shl r8 = r8,52 };; { .mfi sub r8 = r8,r0,1 nop.f 0 extr.u GR_fpsr = GR_fpsr,10,2 // rounding mode };; .pred.rel "mutex",p14,p15 { .mfi // set p8 to 0 in case of overflow and to 1 otherwise // for negative arg: // no overflow if rounding mode either Z or +Inf, i.e. // GR_fpsr > 1 (p14) cmp.lt p8,p0 = 1,GR_fpsr nop.f 0 // for positive arg: // no overflow if rounding mode either Z or -Inf, i.e. // (GR_fpsr & 1) == 0 (p15) tbit.z p0,p8 = GR_fpsr,0 };; { .mib (p8) setf.d f8 = r8 // set result to 0x7fefffffffffffff without // OVERFLOW flag raising nop.i 0 (p8) br.ret.sptk b0 };; .align 32 tgamma_ovf_near_0: { .mfi mov r8 = 0x1FFFE nop.f 0 nop.i 0 };; { .mfi setf.exp f9 = r8 fmerge.s FR_X = f8,f8 mov GR_TAG = 258 // overflow };; .pred.rel "mutex",p14,p15 { .mfi nop.m 0 (p15) fma.d.s0 f8 = f9,f9,f0 // Set I,O and +INF result nop.i 0 } { .mfb nop.m 0 (p14) fnma.d.s0 f8 = f9,f9,f0 // Set I,O and -INF result br.cond.sptk tgamma_libm_err };; // overflow or absolute value of x is too big //-------------------------------------------------------------------- .align 32 tgamma_spec_res: { .mfi mov GR_0x30033 = 0x30033 (p14) fcmp.eq.unc.s1 p10,p11 = f8,FR_Xt (p15) mov r8 = 0x1FFFE };; { .mfi (p15) setf.exp f9 = r8 nop.f 0 nop.i 0 };; { .mfb (p11) cmp.ltu.unc p7,p8 = GR_0x30033,GR_Sign_Exp nop.f 0 (p10) br.cond.spnt tgamma_singularity };; .pred.rel "mutex",p7,p8 { .mbb nop.m 0 (p7) br.cond.spnt tgamma_singularity (p8) br.cond.spnt tgamma_underflow };; { .mfi nop.m 0 fmerge.s FR_X = f8,f8 mov GR_TAG = 258 // overflow } { .mfb nop.m 0 (p15) fma.d.s0 f8 = f9,f9,f0 // Set I,O and +INF result br.cond.sptk tgamma_libm_err };; // x is negative integer or +/-0 //-------------------------------------------------------------------- .align 32 tgamma_singularity: { .mfi nop.m 0 fmerge.s FR_X = f8,f8 mov GR_TAG = 259 // negative } { .mfb nop.m 0 frcpa.s0 f8,p0 = f0,f0 br.cond.sptk tgamma_libm_err };; // x is negative noninteger with big absolute value //-------------------------------------------------------------------- .align 32 tgamma_underflow: { .mmi getf.sig GR_Sig = FR_iXt 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_Sig,0 };; .pred.rel "mutex",p6,p7 { .mfi nop.m 0 (p6) fms.d.s0 f8 = f9,f9,f9 nop.i 0 } { .mfb nop.m 0 (p7) fma.d.s0 f8 = f9,f9,f9 br.ret.sptk b0 };; // x for natval, nan, +/-inf or +/-0 //-------------------------------------------------------------------- .align 32 tgamma_spec: { .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 nop.m 0 fmerge.s FR_X = f8,f8 nop.i 0 } { .mfb nop.m 0 (p6) fma.d.s0 f8 = f8,f1,f8 (p6) br.ret.spnt b0 };; .pred.rel "mutex",p7,p8 { .mfi (p7) mov GR_TAG = 259 // negative (p7) frcpa.s0 f8,p0 = f1,f8 nop.i 0 } { .mib nop.m 0 nop.i 0 (p8) br.cond.spnt tgamma_singularity };; .align 32 tgamma_libm_err: { .mfi alloc r32 = ar.pfs,1,4,4,0 nop.f 0 mov GR_Parameter_TAG = GR_TAG };; GLOBAL_LIBM_END(tgamma) LOCAL_LIBM_ENTRY(__libm_error_region) .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 stfd [GR_Parameter_Y] = FR_Y,16 // STORE 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 stfd [GR_Parameter_X] = FR_X // STORE Parameter 1 on stack add GR_Parameter_RESULT = 0,GR_Parameter_Y // Parameter 3 address nop.b 0 } { .mib stfd [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 0 nop.m 0 add GR_Parameter_RESULT = 48,sp };; { .mmi ldfd 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#