.file "libm_lgammaf.s" // Copyright (c) 2002 - 2003, 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: // 01/10/02 Initial version // 01/25/02 Corrected parameter store, load, and tag for __libm_error_support // 02/01/02 Added support of SIGN(GAMMA(x)) calculation // 05/20/02 Cleaned up namespace and sf0 syntax // 09/16/02 Improved accuracy on intervals reduced to [1;1.25] // 10/21/02 Now it returns SIGN(GAMMA(x))=-1 for negative zero // 02/10/03 Reordered header: .section, .global, .proc, .align // 07/22/03 Reformatted some data tables // //********************************************************************* // //********************************************************************* // // Function: __libm_lgammaf(float x, int* signgam, int szsigngam) // computes the principle value of the logarithm of the GAMMA function // of x. Signum of GAMMA(x) is stored to memory starting at the address // specified by the signgam. // //********************************************************************* // // Resources Used: // // Floating-Point Registers: f6-f15 // f32-f97 // // General Purpose Registers: // r8-r11 // r14-r30 // r32-r36 // r37-r40 (Used to pass arguments to error handling routine) // // Predicate Registers: p6-p15 // //********************************************************************* // // IEEE Special Conditions: // // lgamma(+inf) = +inf // lgamma(-inf) = +inf // lgamma(+/-0) = +inf // lgamma(x<0, x - integer) = +inf // lgamma(SNaN) = QNaN // lgamma(QNaN) = QNaN // //********************************************************************* // // Overview // // The method consists of three cases. // // If 2^13 <= x < OVERFLOW_BOUNDARY use case lgammaf_pstirling; // else if 1 < x < 2^13 use case lgammaf_regular; // else if -9 < x < 1 use case lgammaf_negrecursion; // else if -2^13 < x < -9 use case lgammaf_negpoly; // else if x < -2^13 use case lgammaf_negstirling; // else if x is close to negative // roots of ln(GAMMA(x)) use case lgammaf_negroots; // // // Case 2^13 <= x < OVERFLOW_BOUNDARY // ---------------------------------- // Here we use algorithm based on the Stirling formula: // ln(GAMMA(x)) = ln(sqrt(2*Pi)) + (x-0.5)*ln(x) - x // // Case 1 < x < 2^13 // ----------------- // To calculate ln(GAMMA(x)) for such arguments we use polynomial // approximation on following intervals: [1.0; 1.25), [1.25; 1.5), // [1.5, 1.75), [1.75; 2), [2; 4), [2^i; 2^(i+1)), i=1..8 // // Following variants of approximation and argument reduction are used: // 1. [1.0; 1.25) // ln(GAMMA(x)) ~ (x-1.0)*P7(x) // // 2. [1.25; 1.5) // ln(GAMMA(x)) ~ ln(GAMMA(x0))+(x-x0)*P8(x-x0), // where x0 - point of local minimum on [1;2] rounded to nearest double // precision number. // // 3. [1.5; 1.75) // ln(GAMMA(x)) ~ P8(x) // // 4. [1.75; 2.0) // ln(GAMMA(x)) ~ (x-2)*P7(x) // // 5. [2; 4) // ln(GAMMA(x)) ~ (x-2)*P10(x) // // 6. [2^i; 2^(i+1)), i=2..8 // ln(GAMMA(x)) ~ P10((x-2^i)/2^i) // // Case -9 < x < 1 // --------------- // Here we use the recursive formula: // ln(GAMMA(x)) = ln(GAMMA(x+1)) - ln(x) // // Using this formula we reduce argument to base interval [1.0; 2.0] // // Case -2^13 < x < -9 // -------------------- // Here we use the formula: // ln(GAMMA(x)) = ln(Pi/(|x|*GAMMA(|x|)*sin(Pi*|x|))) = // = -ln(|x|) - ln((GAMMA(|x|)) - ln(sin(Pi*r)/(Pi*r)) - ln(|r|) // where r = x - rounded_to_nearest(x), i.e |r| <= 0.5 and // ln(sin(Pi*r)/(Pi*r)) is approximated by 8-degree polynomial of r^2 // // Case x < -2^13 // -------------- // Here we use algorithm based on the Stirling formula: // ln(GAMMA(x)) = -ln(sqrt(2*Pi)) + (|x|-0.5)ln(x) - |x| - // - ln(sin(Pi*r)/(Pi*r)) - ln(|r|) // where r = x - rounded_to_nearest(x). // // Neighbourhoods of negative roots // -------------------------------- // Here we use polynomial approximation // ln(GAMMA(x-x0)) = ln(GAMMA(x0)) + (x-x0)*P14(x-x0), // where x0 is a root of ln(GAMMA(x)) rounded to nearest double // precision number. // // // Claculation of logarithm // ------------------------ // Consider x = 2^N * xf so // ln(x) = ln(frcpa(x)*x/frcpa(x)) // = ln(1/frcpa(x)) + ln(frcpa(x)*x) // // frcpa(x) = 2^(-N) * frcpa(xf) // // ln(1/frcpa(x)) = -ln(2^(-N)) - ln(frcpa(xf)) // = N*ln(2) - ln(frcpa(xf)) // = N*ln(2) + ln(1/frcpa(xf)) // // ln(x) = ln(1/frcpa(x)) + ln(frcpa(x)*x) = // = N*ln(2) + ln(1/frcpa(xf)) + ln(frcpa(x)*x) // = N*ln(2) + T + ln(frcpa(x)*x) // // Let r = 1 - frcpa(x)*x, note that r is quite small by // absolute value so // // ln(x) = N*ln(2) + T + ln(1+r) ~ N*ln(2) + T + Series(r), // where T - is precomputed tabular value, // Series(r) = (P3*r + P2)*r^2 + (P1*r + 1) // //********************************************************************* GR_TAG = r8 GR_ad_Data = r8 GR_ad_Co = r9 GR_ad_SignGam = r10 GR_ad_Ce = r10 GR_SignExp = r11 GR_ad_C650 = r14 GR_ad_RootCo = r14 GR_ad_C0 = r15 GR_Dx = r15 GR_Ind = r16 GR_Offs = r17 GR_IntNum = r17 GR_ExpBias = r18 GR_ExpMask = r19 GR_Ind4T = r20 GR_RootInd = r20 GR_Sig = r21 GR_Exp = r22 GR_PureExp = r23 GR_ad_C43 = r24 GR_StirlBound = r25 GR_ad_T = r25 GR_IndX8 = r25 GR_Neg2 = r25 GR_2xDx = r25 GR_SingBound = r26 GR_IndX2 = r26 GR_Neg4 = r26 GR_ad_RootCe = r26 GR_Arg = r27 GR_ExpOf2 = r28 GR_fff7 = r28 GR_Root = r28 GR_ReqBound = r28 GR_N = r29 GR_ad_Root = r30 GR_ad_OvfBound = r30 GR_SignOfGamma = r31 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 // lgammaf is single argument function FR_RESULT = f8 FR_x = f6 FR_x2 = f7 FR_x3 = f9 FR_x4 = f10 FR_xm2 = f11 FR_w = f11 FR_w2 = f12 FR_Q32 = f13 FR_Q10 = f14 FR_InvX = f15 FR_NormX = f32 FR_A0 = f33 FR_A1 = f34 FR_A2 = f35 FR_A3 = f36 FR_A4 = f37 FR_A5 = f38 FR_A6 = f39 FR_A7 = f40 FR_A8 = f41 FR_A9 = f42 FR_A10 = f43 FR_int_N = f44 FR_P3 = f45 FR_P2 = f46 FR_P1 = f47 FR_LocalMin = f48 FR_Ln2 = f49 FR_05 = f50 FR_LnSqrt2Pi = f51 FR_3 = f52 FR_r = f53 FR_r2 = f54 FR_T = f55 FR_N = f56 FR_xm05 = f57 FR_int_Ln = f58 FR_P32 = f59 FR_P10 = f60 FR_Xf = f61 FR_InvXf = f62 FR_rf = f63 FR_rf2 = f64 FR_Tf = f65 FR_Nf = f66 FR_xm05f = f67 FR_P32f = f68 FR_P10f = f69 FR_Lnf = f70 FR_Xf2 = f71 FR_Xf4 = f72 FR_Xf8 = f73 FR_Ln = f74 FR_xx = f75 FR_Root = f75 FR_Req = f76 FR_1pXf = f77 FR_S16 = f78 FR_R3 = f78 FR_S14 = f79 FR_R2 = f79 FR_S12 = f80 FR_R1 = f80 FR_S10 = f81 FR_R0 = f81 FR_S8 = f82 FR_rx = f82 FR_S6 = f83 FR_rx2 = f84 FR_S4 = f84 FR_S2 = f85 FR_Xp1 = f86 FR_Xp2 = f87 FR_Xp3 = f88 FR_Xp4 = f89 FR_Xp5 = f90 FR_Xp6 = f91 FR_Xp7 = f92 FR_Xp8 = f93 FR_OverflowBound = f93 FR_2 = f94 FR_tmp = f95 FR_int_Ntrunc = f96 FR_Ntrunc = f97 //********************************************************************* RODATA .align 32 LOCAL_OBJECT_START(lgammaf_data) log_table_1: data8 0xbfd0001008f39d59 // P3 data8 0x3fd5556073e0c45a // P2 data8 0x3fe62e42fefa39ef // ln(2) data8 0x3fe0000000000000 // 0.5 // data8 0x3F60040155D5889E //ln(1/frcpa(1+ 0/256) data8 0x3F78121214586B54 //ln(1/frcpa(1+ 1/256) data8 0x3F841929F96832F0 //ln(1/frcpa(1+ 2/256) data8 0x3F8C317384C75F06 //ln(1/frcpa(1+ 3/256) data8 0x3F91A6B91AC73386 //ln(1/frcpa(1+ 4/256) data8 0x3F95BA9A5D9AC039 //ln(1/frcpa(1+ 5/256) data8 0x3F99D2A8074325F4 //ln(1/frcpa(1+ 6/256) data8 0x3F9D6B2725979802 //ln(1/frcpa(1+ 7/256) data8 0x3FA0C58FA19DFAAA //ln(1/frcpa(1+ 8/256) data8 0x3FA2954C78CBCE1B //ln(1/frcpa(1+ 9/256) data8 0x3FA4A94D2DA96C56 //ln(1/frcpa(1+ 10/256) data8 0x3FA67C94F2D4BB58 //ln(1/frcpa(1+ 11/256) data8 0x3FA85188B630F068 //ln(1/frcpa(1+ 12/256) data8 0x3FAA6B8ABE73AF4C //ln(1/frcpa(1+ 13/256) data8 0x3FAC441E06F72A9E //ln(1/frcpa(1+ 14/256) data8 0x3FAE1E6713606D07 //ln(1/frcpa(1+ 15/256) data8 0x3FAFFA6911AB9301 //ln(1/frcpa(1+ 16/256) data8 0x3FB0EC139C5DA601 //ln(1/frcpa(1+ 17/256) data8 0x3FB1DBD2643D190B //ln(1/frcpa(1+ 18/256) data8 0x3FB2CC7284FE5F1C //ln(1/frcpa(1+ 19/256) data8 0x3FB3BDF5A7D1EE64 //ln(1/frcpa(1+ 20/256) data8 0x3FB4B05D7AA012E0 //ln(1/frcpa(1+ 21/256) data8 0x3FB580DB7CEB5702 //ln(1/frcpa(1+ 22/256) data8 0x3FB674F089365A7A //ln(1/frcpa(1+ 23/256) data8 0x3FB769EF2C6B568D //ln(1/frcpa(1+ 24/256) data8 0x3FB85FD927506A48 //ln(1/frcpa(1+ 25/256) data8 0x3FB9335E5D594989 //ln(1/frcpa(1+ 26/256) data8 0x3FBA2B0220C8E5F5 //ln(1/frcpa(1+ 27/256) data8 0x3FBB0004AC1A86AC //ln(1/frcpa(1+ 28/256) data8 0x3FBBF968769FCA11 //ln(1/frcpa(1+ 29/256) data8 0x3FBCCFEDBFEE13A8 //ln(1/frcpa(1+ 30/256) data8 0x3FBDA727638446A2 //ln(1/frcpa(1+ 31/256) data8 0x3FBEA3257FE10F7A //ln(1/frcpa(1+ 32/256) data8 0x3FBF7BE9FEDBFDE6 //ln(1/frcpa(1+ 33/256) data8 0x3FC02AB352FF25F4 //ln(1/frcpa(1+ 34/256) data8 0x3FC097CE579D204D //ln(1/frcpa(1+ 35/256) data8 0x3FC1178E8227E47C //ln(1/frcpa(1+ 36/256) data8 0x3FC185747DBECF34 //ln(1/frcpa(1+ 37/256) data8 0x3FC1F3B925F25D41 //ln(1/frcpa(1+ 38/256) data8 0x3FC2625D1E6DDF57 //ln(1/frcpa(1+ 39/256) data8 0x3FC2D1610C86813A //ln(1/frcpa(1+ 40/256) data8 0x3FC340C59741142E //ln(1/frcpa(1+ 41/256) data8 0x3FC3B08B6757F2A9 //ln(1/frcpa(1+ 42/256) data8 0x3FC40DFB08378003 //ln(1/frcpa(1+ 43/256) data8 0x3FC47E74E8CA5F7C //ln(1/frcpa(1+ 44/256) data8 0x3FC4EF51F6466DE4 //ln(1/frcpa(1+ 45/256) data8 0x3FC56092E02BA516 //ln(1/frcpa(1+ 46/256) data8 0x3FC5D23857CD74D5 //ln(1/frcpa(1+ 47/256) data8 0x3FC6313A37335D76 //ln(1/frcpa(1+ 48/256) data8 0x3FC6A399DABBD383 //ln(1/frcpa(1+ 49/256) data8 0x3FC70337DD3CE41B //ln(1/frcpa(1+ 50/256) data8 0x3FC77654128F6127 //ln(1/frcpa(1+ 51/256) data8 0x3FC7E9D82A0B022D //ln(1/frcpa(1+ 52/256) data8 0x3FC84A6B759F512F //ln(1/frcpa(1+ 53/256) data8 0x3FC8AB47D5F5A310 //ln(1/frcpa(1+ 54/256) data8 0x3FC91FE49096581B //ln(1/frcpa(1+ 55/256) data8 0x3FC981634011AA75 //ln(1/frcpa(1+ 56/256) data8 0x3FC9F6C407089664 //ln(1/frcpa(1+ 57/256) data8 0x3FCA58E729348F43 //ln(1/frcpa(1+ 58/256) data8 0x3FCABB55C31693AD //ln(1/frcpa(1+ 59/256) data8 0x3FCB1E104919EFD0 //ln(1/frcpa(1+ 60/256) data8 0x3FCB94EE93E367CB //ln(1/frcpa(1+ 61/256) data8 0x3FCBF851C067555F //ln(1/frcpa(1+ 62/256) data8 0x3FCC5C0254BF23A6 //ln(1/frcpa(1+ 63/256) data8 0x3FCCC000C9DB3C52 //ln(1/frcpa(1+ 64/256) data8 0x3FCD244D99C85674 //ln(1/frcpa(1+ 65/256) data8 0x3FCD88E93FB2F450 //ln(1/frcpa(1+ 66/256) data8 0x3FCDEDD437EAEF01 //ln(1/frcpa(1+ 67/256) data8 0x3FCE530EFFE71012 //ln(1/frcpa(1+ 68/256) data8 0x3FCEB89A1648B971 //ln(1/frcpa(1+ 69/256) data8 0x3FCF1E75FADF9BDE //ln(1/frcpa(1+ 70/256) data8 0x3FCF84A32EAD7C35 //ln(1/frcpa(1+ 71/256) data8 0x3FCFEB2233EA07CD //ln(1/frcpa(1+ 72/256) data8 0x3FD028F9C7035C1C //ln(1/frcpa(1+ 73/256) data8 0x3FD05C8BE0D9635A //ln(1/frcpa(1+ 74/256) data8 0x3FD085EB8F8AE797 //ln(1/frcpa(1+ 75/256) data8 0x3FD0B9C8E32D1911 //ln(1/frcpa(1+ 76/256) data8 0x3FD0EDD060B78081 //ln(1/frcpa(1+ 77/256) data8 0x3FD122024CF0063F //ln(1/frcpa(1+ 78/256) data8 0x3FD14BE2927AECD4 //ln(1/frcpa(1+ 79/256) data8 0x3FD180618EF18ADF //ln(1/frcpa(1+ 80/256) data8 0x3FD1B50BBE2FC63B //ln(1/frcpa(1+ 81/256) data8 0x3FD1DF4CC7CF242D //ln(1/frcpa(1+ 82/256) data8 0x3FD214456D0EB8D4 //ln(1/frcpa(1+ 83/256) data8 0x3FD23EC5991EBA49 //ln(1/frcpa(1+ 84/256) data8 0x3FD2740D9F870AFB //ln(1/frcpa(1+ 85/256) data8 0x3FD29ECDABCDFA04 //ln(1/frcpa(1+ 86/256) data8 0x3FD2D46602ADCCEE //ln(1/frcpa(1+ 87/256) data8 0x3FD2FF66B04EA9D4 //ln(1/frcpa(1+ 88/256) data8 0x3FD335504B355A37 //ln(1/frcpa(1+ 89/256) data8 0x3FD360925EC44F5D //ln(1/frcpa(1+ 90/256) data8 0x3FD38BF1C3337E75 //ln(1/frcpa(1+ 91/256) data8 0x3FD3C25277333184 //ln(1/frcpa(1+ 92/256) data8 0x3FD3EDF463C1683E //ln(1/frcpa(1+ 93/256) data8 0x3FD419B423D5E8C7 //ln(1/frcpa(1+ 94/256) data8 0x3FD44591E0539F49 //ln(1/frcpa(1+ 95/256) data8 0x3FD47C9175B6F0AD //ln(1/frcpa(1+ 96/256) data8 0x3FD4A8B341552B09 //ln(1/frcpa(1+ 97/256) data8 0x3FD4D4F3908901A0 //ln(1/frcpa(1+ 98/256) data8 0x3FD501528DA1F968 //ln(1/frcpa(1+ 99/256) data8 0x3FD52DD06347D4F6 //ln(1/frcpa(1+ 100/256) data8 0x3FD55A6D3C7B8A8A //ln(1/frcpa(1+ 101/256) data8 0x3FD5925D2B112A59 //ln(1/frcpa(1+ 102/256) data8 0x3FD5BF406B543DB2 //ln(1/frcpa(1+ 103/256) data8 0x3FD5EC433D5C35AE //ln(1/frcpa(1+ 104/256) data8 0x3FD61965CDB02C1F //ln(1/frcpa(1+ 105/256) data8 0x3FD646A84935B2A2 //ln(1/frcpa(1+ 106/256) data8 0x3FD6740ADD31DE94 //ln(1/frcpa(1+ 107/256) data8 0x3FD6A18DB74A58C5 //ln(1/frcpa(1+ 108/256) data8 0x3FD6CF31058670EC //ln(1/frcpa(1+ 109/256) data8 0x3FD6F180E852F0BA //ln(1/frcpa(1+ 110/256) data8 0x3FD71F5D71B894F0 //ln(1/frcpa(1+ 111/256) data8 0x3FD74D5AEFD66D5C //ln(1/frcpa(1+ 112/256) data8 0x3FD77B79922BD37E //ln(1/frcpa(1+ 113/256) data8 0x3FD7A9B9889F19E2 //ln(1/frcpa(1+ 114/256) data8 0x3FD7D81B037EB6A6 //ln(1/frcpa(1+ 115/256) data8 0x3FD8069E33827231 //ln(1/frcpa(1+ 116/256) data8 0x3FD82996D3EF8BCB //ln(1/frcpa(1+ 117/256) data8 0x3FD85855776DCBFB //ln(1/frcpa(1+ 118/256) data8 0x3FD8873658327CCF //ln(1/frcpa(1+ 119/256) data8 0x3FD8AA75973AB8CF //ln(1/frcpa(1+ 120/256) data8 0x3FD8D992DC8824E5 //ln(1/frcpa(1+ 121/256) data8 0x3FD908D2EA7D9512 //ln(1/frcpa(1+ 122/256) data8 0x3FD92C59E79C0E56 //ln(1/frcpa(1+ 123/256) data8 0x3FD95BD750EE3ED3 //ln(1/frcpa(1+ 124/256) data8 0x3FD98B7811A3EE5B //ln(1/frcpa(1+ 125/256) data8 0x3FD9AF47F33D406C //ln(1/frcpa(1+ 126/256) data8 0x3FD9DF270C1914A8 //ln(1/frcpa(1+ 127/256) data8 0x3FDA0325ED14FDA4 //ln(1/frcpa(1+ 128/256) data8 0x3FDA33440224FA79 //ln(1/frcpa(1+ 129/256) data8 0x3FDA57725E80C383 //ln(1/frcpa(1+ 130/256) data8 0x3FDA87D0165DD199 //ln(1/frcpa(1+ 131/256) data8 0x3FDAAC2E6C03F896 //ln(1/frcpa(1+ 132/256) data8 0x3FDADCCC6FDF6A81 //ln(1/frcpa(1+ 133/256) data8 0x3FDB015B3EB1E790 //ln(1/frcpa(1+ 134/256) data8 0x3FDB323A3A635948 //ln(1/frcpa(1+ 135/256) data8 0x3FDB56FA04462909 //ln(1/frcpa(1+ 136/256) data8 0x3FDB881AA659BC93 //ln(1/frcpa(1+ 137/256) data8 0x3FDBAD0BEF3DB165 //ln(1/frcpa(1+ 138/256) data8 0x3FDBD21297781C2F //ln(1/frcpa(1+ 139/256) data8 0x3FDC039236F08819 //ln(1/frcpa(1+ 140/256) data8 0x3FDC28CB1E4D32FD //ln(1/frcpa(1+ 141/256) data8 0x3FDC4E19B84723C2 //ln(1/frcpa(1+ 142/256) data8 0x3FDC7FF9C74554C9 //ln(1/frcpa(1+ 143/256) data8 0x3FDCA57B64E9DB05 //ln(1/frcpa(1+ 144/256) data8 0x3FDCCB130A5CEBB0 //ln(1/frcpa(1+ 145/256) data8 0x3FDCF0C0D18F326F //ln(1/frcpa(1+ 146/256) data8 0x3FDD232075B5A201 //ln(1/frcpa(1+ 147/256) data8 0x3FDD490246DEFA6B //ln(1/frcpa(1+ 148/256) data8 0x3FDD6EFA918D25CD //ln(1/frcpa(1+ 149/256) data8 0x3FDD9509707AE52F //ln(1/frcpa(1+ 150/256) data8 0x3FDDBB2EFE92C554 //ln(1/frcpa(1+ 151/256) data8 0x3FDDEE2F3445E4AF //ln(1/frcpa(1+ 152/256) data8 0x3FDE148A1A2726CE //ln(1/frcpa(1+ 153/256) data8 0x3FDE3AFC0A49FF40 //ln(1/frcpa(1+ 154/256) data8 0x3FDE6185206D516E //ln(1/frcpa(1+ 155/256) data8 0x3FDE882578823D52 //ln(1/frcpa(1+ 156/256) data8 0x3FDEAEDD2EAC990C //ln(1/frcpa(1+ 157/256) data8 0x3FDED5AC5F436BE3 //ln(1/frcpa(1+ 158/256) data8 0x3FDEFC9326D16AB9 //ln(1/frcpa(1+ 159/256) data8 0x3FDF2391A2157600 //ln(1/frcpa(1+ 160/256) data8 0x3FDF4AA7EE03192D //ln(1/frcpa(1+ 161/256) data8 0x3FDF71D627C30BB0 //ln(1/frcpa(1+ 162/256) data8 0x3FDF991C6CB3B379 //ln(1/frcpa(1+ 163/256) data8 0x3FDFC07ADA69A910 //ln(1/frcpa(1+ 164/256) data8 0x3FDFE7F18EB03D3E //ln(1/frcpa(1+ 165/256) data8 0x3FE007C053C5002E //ln(1/frcpa(1+ 166/256) data8 0x3FE01B942198A5A1 //ln(1/frcpa(1+ 167/256) data8 0x3FE02F74400C64EB //ln(1/frcpa(1+ 168/256) data8 0x3FE04360BE7603AD //ln(1/frcpa(1+ 169/256) data8 0x3FE05759AC47FE34 //ln(1/frcpa(1+ 170/256) data8 0x3FE06B5F1911CF52 //ln(1/frcpa(1+ 171/256) data8 0x3FE078BF0533C568 //ln(1/frcpa(1+ 172/256) data8 0x3FE08CD9687E7B0E //ln(1/frcpa(1+ 173/256) data8 0x3FE0A10074CF9019 //ln(1/frcpa(1+ 174/256) data8 0x3FE0B5343A234477 //ln(1/frcpa(1+ 175/256) data8 0x3FE0C974C89431CE //ln(1/frcpa(1+ 176/256) data8 0x3FE0DDC2305B9886 //ln(1/frcpa(1+ 177/256) data8 0x3FE0EB524BAFC918 //ln(1/frcpa(1+ 178/256) data8 0x3FE0FFB54213A476 //ln(1/frcpa(1+ 179/256) data8 0x3FE114253DA97D9F //ln(1/frcpa(1+ 180/256) data8 0x3FE128A24F1D9AFF //ln(1/frcpa(1+ 181/256) data8 0x3FE1365252BF0865 //ln(1/frcpa(1+ 182/256) data8 0x3FE14AE558B4A92D //ln(1/frcpa(1+ 183/256) data8 0x3FE15F85A19C765B //ln(1/frcpa(1+ 184/256) data8 0x3FE16D4D38C119FA //ln(1/frcpa(1+ 185/256) data8 0x3FE18203C20DD133 //ln(1/frcpa(1+ 186/256) data8 0x3FE196C7BC4B1F3B //ln(1/frcpa(1+ 187/256) data8 0x3FE1A4A738B7A33C //ln(1/frcpa(1+ 188/256) data8 0x3FE1B981C0C9653D //ln(1/frcpa(1+ 189/256) data8 0x3FE1CE69E8BB106B //ln(1/frcpa(1+ 190/256) data8 0x3FE1DC619DE06944 //ln(1/frcpa(1+ 191/256) data8 0x3FE1F160A2AD0DA4 //ln(1/frcpa(1+ 192/256) data8 0x3FE2066D7740737E //ln(1/frcpa(1+ 193/256) data8 0x3FE2147DBA47A394 //ln(1/frcpa(1+ 194/256) data8 0x3FE229A1BC5EBAC3 //ln(1/frcpa(1+ 195/256) data8 0x3FE237C1841A502E //ln(1/frcpa(1+ 196/256) data8 0x3FE24CFCE6F80D9A //ln(1/frcpa(1+ 197/256) data8 0x3FE25B2C55CD5762 //ln(1/frcpa(1+ 198/256) data8 0x3FE2707F4D5F7C41 //ln(1/frcpa(1+ 199/256) data8 0x3FE285E0842CA384 //ln(1/frcpa(1+ 200/256) data8 0x3FE294294708B773 //ln(1/frcpa(1+ 201/256) data8 0x3FE2A9A2670AFF0C //ln(1/frcpa(1+ 202/256) data8 0x3FE2B7FB2C8D1CC1 //ln(1/frcpa(1+ 203/256) data8 0x3FE2C65A6395F5F5 //ln(1/frcpa(1+ 204/256) data8 0x3FE2DBF557B0DF43 //ln(1/frcpa(1+ 205/256) data8 0x3FE2EA64C3F97655 //ln(1/frcpa(1+ 206/256) data8 0x3FE3001823684D73 //ln(1/frcpa(1+ 207/256) data8 0x3FE30E97E9A8B5CD //ln(1/frcpa(1+ 208/256) data8 0x3FE32463EBDD34EA //ln(1/frcpa(1+ 209/256) data8 0x3FE332F4314AD796 //ln(1/frcpa(1+ 210/256) data8 0x3FE348D90E7464D0 //ln(1/frcpa(1+ 211/256) data8 0x3FE35779F8C43D6E //ln(1/frcpa(1+ 212/256) data8 0x3FE36621961A6A99 //ln(1/frcpa(1+ 213/256) data8 0x3FE37C299F3C366A //ln(1/frcpa(1+ 214/256) data8 0x3FE38AE2171976E7 //ln(1/frcpa(1+ 215/256) data8 0x3FE399A157A603E7 //ln(1/frcpa(1+ 216/256) data8 0x3FE3AFCCFE77B9D1 //ln(1/frcpa(1+ 217/256) data8 0x3FE3BE9D503533B5 //ln(1/frcpa(1+ 218/256) data8 0x3FE3CD7480B4A8A3 //ln(1/frcpa(1+ 219/256) data8 0x3FE3E3C43918F76C //ln(1/frcpa(1+ 220/256) data8 0x3FE3F2ACB27ED6C7 //ln(1/frcpa(1+ 221/256) data8 0x3FE4019C2125CA93 //ln(1/frcpa(1+ 222/256) data8 0x3FE4181061389722 //ln(1/frcpa(1+ 223/256) data8 0x3FE42711518DF545 //ln(1/frcpa(1+ 224/256) data8 0x3FE436194E12B6BF //ln(1/frcpa(1+ 225/256) data8 0x3FE445285D68EA69 //ln(1/frcpa(1+ 226/256) data8 0x3FE45BCC464C893A //ln(1/frcpa(1+ 227/256) data8 0x3FE46AED21F117FC //ln(1/frcpa(1+ 228/256) data8 0x3FE47A1527E8A2D3 //ln(1/frcpa(1+ 229/256) data8 0x3FE489445EFFFCCC //ln(1/frcpa(1+ 230/256) data8 0x3FE4A018BCB69835 //ln(1/frcpa(1+ 231/256) data8 0x3FE4AF5A0C9D65D7 //ln(1/frcpa(1+ 232/256) data8 0x3FE4BEA2A5BDBE87 //ln(1/frcpa(1+ 233/256) data8 0x3FE4CDF28F10AC46 //ln(1/frcpa(1+ 234/256) data8 0x3FE4DD49CF994058 //ln(1/frcpa(1+ 235/256) data8 0x3FE4ECA86E64A684 //ln(1/frcpa(1+ 236/256) data8 0x3FE503C43CD8EB68 //ln(1/frcpa(1+ 237/256) data8 0x3FE513356667FC57 //ln(1/frcpa(1+ 238/256) data8 0x3FE522AE0738A3D8 //ln(1/frcpa(1+ 239/256) data8 0x3FE5322E26867857 //ln(1/frcpa(1+ 240/256) data8 0x3FE541B5CB979809 //ln(1/frcpa(1+ 241/256) data8 0x3FE55144FDBCBD62 //ln(1/frcpa(1+ 242/256) data8 0x3FE560DBC45153C7 //ln(1/frcpa(1+ 243/256) data8 0x3FE5707A26BB8C66 //ln(1/frcpa(1+ 244/256) data8 0x3FE587F60ED5B900 //ln(1/frcpa(1+ 245/256) data8 0x3FE597A7977C8F31 //ln(1/frcpa(1+ 246/256) data8 0x3FE5A760D634BB8B //ln(1/frcpa(1+ 247/256) data8 0x3FE5B721D295F10F //ln(1/frcpa(1+ 248/256) data8 0x3FE5C6EA94431EF9 //ln(1/frcpa(1+ 249/256) data8 0x3FE5D6BB22EA86F6 //ln(1/frcpa(1+ 250/256) data8 0x3FE5E6938645D390 //ln(1/frcpa(1+ 251/256) data8 0x3FE5F673C61A2ED2 //ln(1/frcpa(1+ 252/256) data8 0x3FE6065BEA385926 //ln(1/frcpa(1+ 253/256) data8 0x3FE6164BFA7CC06B //ln(1/frcpa(1+ 254/256) data8 0x3FE62643FECF9743 //ln(1/frcpa(1+ 255/256) // // [2;4) data8 0xBEB2CC7A38B9355F,0x3F035F2D1833BF4C // A10,A9 data8 0xBFF51BAA7FD27785,0x3FFC9D5D5B6CDEFF // A2,A1 data8 0xBF421676F9CB46C7,0x3F7437F2FA1436C6 // A8,A7 data8 0xBFD7A7041DE592FE,0x3FE9F107FEE8BD29 // A4,A3 // [4;8) data8 0x3F6BBBD68451C0CD,0xBF966EC3272A16F7 // A10,A9 data8 0x40022A24A39AD769,0x4014190EDF49C8C5 // A2,A1 data8 0x3FB130FD016EE241,0xBFC151B46E635248 // A8,A7 data8 0x3FDE8F611965B5FE,0xBFEB5110EB265E3D // A4,A3 // [8;16) data8 0x3F736EF93508626A,0xBF9FE5DBADF58AF1 // A10,A9 data8 0x40110A9FC5192058,0x40302008A6F96B29 // A2,A1 data8 0x3FB8E74E0CE1E4B5,0xBFC9B5DA78873656 // A8,A7 data8 0x3FE99D0DF10022DC,0xBFF829C0388F9484 // A4,A3 // [16;32) data8 0x3F7FFF9D6D7E9269,0xBFAA780A249AEDB1 // A10,A9 data8 0x402082A807AEA080,0x4045ED9868408013 // A2,A1 data8 0x3FC4E1E54C2F99B7,0xBFD5DE2D6FFF1490 // A8,A7 data8 0x3FF75FC89584AE87,0xC006B4BADD886CAE // A4,A3 // [32;64) data8 0x3F8CE54375841A5F,0xBFB801ABCFFA1BE2 // A10,A9 data8 0x403040A8B1815BDA,0x405B99A917D24B7A // A2,A1 data8 0x3FD30CAB81BFFA03,0xBFE41AEF61ECF48B // A8,A7 data8 0x400650CC136BEC43,0xC016022046E8292B // A4,A3 // [64;128) data8 0x3F9B69BD22CAA8B8,0xBFC6D48875B7A213 // A10,A9 data8 0x40402028CCAA2F6D,0x40709AACEB3CBE0F // A2,A1 data8 0x3FE22C6A5924761E,0xBFF342F5F224523D // A8,A7 data8 0x4015CD405CCA331F,0xC025AAD10482C769 // A4,A3 // [128;256) data8 0x3FAAAD9CD0E40D06,0xBFD63FC8505D80CB // A10,A9 data8 0x40501008D56C2648,0x408364794B0F4376 // A2,A1 data8 0x3FF1BE0126E00284,0xC002D8E3F6F7F7CA // A8,A7 data8 0x40258C757E95D860,0xC0357FA8FD398011 // A4,A3 // [256;512) data8 0x3FBA4DAC59D49FEB,0xBFE5F476D1C43A77 // A10,A9 data8 0x40600800D890C7C6,0x40962C42AAEC8EF0 // A2,A1 data8 0x40018680ECF19B89,0xC012A3EB96FB7BA4 // A8,A7 data8 0x40356C4CDD3B60F9,0xC0456A34BF18F440 // A4,A3 // [512;1024) data8 0x3FCA1B54F6225A5A,0xBFF5CD67BA10E048 // A10,A9 data8 0x407003FED94C58C2,0x40A8F30B4ACBCD22 // A2,A1 data8 0x40116A135EB66D8C,0xC022891B1CED527E // A8,A7 data8 0x40455C4617FDD8BC,0xC0555F82729E59C4 // A4,A3 // [1024;2048) data8 0x3FD9FFF9095C6EC9,0xC005B88CB25D76C9 // A10,A9 data8 0x408001FE58FA734D,0x40BBB953BAABB0F3 // A2,A1 data8 0x40215B2F9FEB5D87,0xC0327B539DEA5058 // A8,A7 data8 0x40555444B3E8D64D,0xC0655A2B26F9FC8A // A4,A3 // [2048;4096) data8 0x3FE9F065A1C3D6B1,0xC015ACF6FAE8D78D // A10,A9 data8 0x409000FE383DD2B7,0x40CE7F5C1E8BCB8B // A2,A1 data8 0x40315324E5DB2EBE,0xC04274194EF70D18 // A8,A7 data8 0x4065504353FF2207,0xC075577FE1BFE7B6 // A4,A3 // [4096;8192) data8 0x3FF9E6FBC6B1C70D,0xC025A62DAF76F85D // A10,A9 data8 0x40A0007E2F61EBE8,0x40E0A2A23FB5F6C3 // A2,A1 data8 0x40414E9BC0A0141A,0xC0527030F2B69D43 // A8,A7 data8 0x40754E417717B45B,0xC085562A447258E5 // A4,A3 // data8 0xbfdffffffffaea15 // P1 data8 0x3FDD8B618D5AF8FE // point of local minimum on [1;2] data8 0x3FED67F1C864BEB5 // ln(sqrt(2*Pi)) data8 0x4008000000000000 // 3.0 // data8 0xBF9E1C289FB224AB,0x3FBF7422445C9460 // A6,A5 data8 0xBFF01E76D66F8D8A // A0 data8 0xBFE2788CFC6F91DA // A1 [1.0;1.25) data8 0x3FCB8CC69000EB5C,0xBFD41997A0C2C641 // A6,A5 data8 0x3FFCAB0BFA0EA462 // A0 data8 0xBFBF19B9BCC38A42 // A0 [1.25;1.5) data8 0x3FD51EE4DE0A364C,0xBFE00D7F98A16E4B // A6,A5 data8 0x40210CE1F327E9E4 // A0 data8 0x4001DB08F9DFA0CC // A0 [1.5;1.75) data8 0x3FE24F606742D252,0xBFEC81D7D12574EC // A6,A5 data8 0x403BE636A63A9C27 // A0 data8 0x4000A0CB38D6CF0A // A0 [1.75;2.0) data8 0x3FF1029A9DD542B4,0xBFFAD37C209D3B25 // A6,A5 data8 0x405385E6FD9BE7EA // A0 data8 0x478895F1C0000000 // Overflow boundary data8 0x400062D97D26B523,0xC00A03E1529FF023 // A6,A5 data8 0x4069204C51E566CE // A0 data8 0x0000000000000000 // pad data8 0x40101476B38FD501,0xC0199DE7B387C0FC // A6,A5 data8 0x407EB8DAEC83D759 // A0 data8 0x0000000000000000 // pad data8 0x401FDB008D65125A,0xC0296B506E665581 // A6,A5 data8 0x409226D93107EF66 // A0 data8 0x0000000000000000 // pad data8 0x402FB3EAAF3E7B2D,0xC039521142AD8E0D // A6,A5 data8 0x40A4EFA4F072792E // A0 data8 0x0000000000000000 // pad data8 0x403FA024C66B2563,0xC0494569F250E691 // A6,A5 data8 0x40B7B747C9235BB8 // A0 data8 0x0000000000000000 // pad data8 0x404F9607D6DA512C,0xC0593F0B2EDDB4BC // A6,A5 data8 0x40CA7E29C5F16DE2 // A0 data8 0x0000000000000000 // pad data8 0x405F90C5F613D98D,0xC0693BD130E50AAF // A6,A5 data8 0x40DD4495238B190C // A0 data8 0x0000000000000000 // pad // // polynomial approximation of ln(sin(Pi*x)/(Pi*x)), |x| <= 0.5 data8 0xBFD58731A486E820,0xBFA4452CC28E15A9 // S16,S14 data8 0xBFD013F6E1B86C4F,0xBFD5B3F19F7A341F // S8,S6 data8 0xBFC86A0D5252E778,0xBFC93E08C9EE284B // S12,S10 data8 0xBFE15132555C9EDD,0xBFFA51A662480E35 // S4,S2 // // [1.0;1.25) data8 0xBFA697D6775F48EA,0x3FB9894B682A98E7 // A9,A8 data8 0xBFCA8969253CFF55,0x3FD15124EFB35D9D // A5,A4 data8 0xBFC1B00158AB719D,0x3FC5997D04E7F1C1 // A7,A6 data8 0xBFD9A4D50BAFF989,0x3FEA51A661F5176A // A3,A2 // [1.25;1.5) data8 0x3F838E0D35A6171A,0xBF831BBBD61313B7 // A8,A7 data8 0x3FB08B40196425D0,0xBFC2E427A53EB830 // A4,A3 data8 0x3F9285DDDC20D6C3,0xBFA0C90C9C223044 // A6,A5 data8 0x3FDEF72BC8F5287C,0x3D890B3DAEBC1DFC // A2,A1 // [1.5;1.75) data8 0x3F65D5A7EB31047F,0xBFA44EAC9BFA7FDE // A8,A7 data8 0x40051FEFE7A663D8,0xC012A5CFE00A2522 // A4,A3 data8 0x3FD0E1583AB00E08,0xBFF084AF95883BA5 // A6,A5 data8 0x40185982877AE0A2,0xC015F83DB73B57B7 // A2,A1 // [1.75;2.0) data8 0x3F4A9222032EB39A,0xBF8CBC9587EEA5A3 // A8,A7 data8 0x3FF795400783BE49,0xC00851BC418B8A25 // A4,A3 data8 0x3FBBC992783E8C5B,0xBFDFA67E65E89B29 // A6,A5 data8 0x4012B408F02FAF88,0xC013284CE7CB0C39 // A2,A1 // // roots data8 0xC003A7FC9600F86C // -2.4570247382208005860 data8 0xC009260DBC9E59AF // -3.1435808883499798405 data8 0xC005FB410A1BD901 // -2.7476826467274126919 data8 0xC00FA471547C2FE5 // -3.9552942848585979085 // // polynomial approximation of ln(GAMMA(x)) near roots // near -2.4570247382208005860 data8 0x3FF694A6058D9592,0x40136EEBB003A92B // R3,R2 data8 0x3FF83FE966AF5360,0x3C90323B6D1FE86D // R1,R0 // near -3.1435808883499798405 data8 0x405C11371268DA38,0x4039D4D2977D2C23 // R3,R2 data8 0x401F20A65F2FAC62,0x3CDE9605E3AE7A62 // R1,R0 // near -2.7476826467274126919 data8 0xC034185AC31314FF,0x4023267F3C28DFE3 // R3,R2 data8 0xBFFEA12DA904B194,0x3CA8FB8530BA7689 // R1,R0 // near -2.7476826467274126919 data8 0xC0AD25359E70C888,0x406F76DEAEA1B8C6 // R3,R2 data8 0xC034B99D966C5644,0xBCBDDC0336980B58 // R1,R0 LOCAL_OBJECT_END(lgammaf_data) //********************************************************************* .section .text GLOBAL_LIBM_ENTRY(__libm_lgammaf) { .mfi getf.exp GR_SignExp = f8 frcpa.s1 FR_InvX,p0 = f1,f8 mov GR_ExpOf2 = 0x10000 } { .mfi addl GR_ad_Data = @ltoff(lgammaf_data),gp fcvt.fx.s1 FR_int_N = f8 mov GR_ExpMask = 0x1ffff };; { .mfi getf.sig GR_Sig = f8 fclass.m p13,p0 = f8,0x1EF // is x NaTVal, NaN, // +/-0, +/-INF or +/-deno? mov GR_ExpBias = 0xffff } { .mfi ld8 GR_ad_Data = [GR_ad_Data] fma.s1 FR_Xp1 = f8,f1,f1 mov GR_StirlBound = 0x1000C };; { .mfi setf.exp FR_2 = GR_ExpOf2 fmerge.se FR_x = f1,f8 dep.z GR_Ind = GR_SignExp,3,4 } { .mfi cmp.eq p8,p0 = GR_SignExp,GR_ExpBias fcvt.fx.trunc.s1 FR_int_Ntrunc = f8 and GR_Exp = GR_ExpMask,GR_SignExp };; { .mfi add GR_ad_C650 = 0xB20,GR_ad_Data fcmp.lt.s1 p14,p15 = f8,f0 extr.u GR_Ind4T = GR_Sig,55,8 } { .mfb sub GR_PureExp = GR_Exp,GR_ExpBias fnorm.s1 FR_NormX = f8 // jump if x is NaTVal, NaN, +/-0, +/-INF or +/-deno (p13) br.cond.spnt lgammaf_spec };; lgammaf_core: { .mfi ldfpd FR_P1,FR_LocalMin = [GR_ad_C650],16 fms.s1 FR_xm2 = f8,f1,f1 add GR_ad_Co = 0x820,GR_ad_Data } { .mib ldfpd FR_P3,FR_P2 = [GR_ad_Data],16 cmp.ltu p9,p0 = GR_SignExp,GR_ExpBias // jump if x is from the interval [1; 2) (p8) br.cond.spnt lgammaf_1_2 };; { .mfi setf.sig FR_int_Ln = GR_PureExp fms.s1 FR_r = FR_InvX,f8,f1 shladd GR_ad_Co = GR_Ind,3,GR_ad_Co } { .mib ldfpd FR_LnSqrt2Pi,FR_3 = [GR_ad_C650],16 cmp.lt p13,p12 = GR_Exp,GR_StirlBound // jump if x is from the interval (0; 1) (p9) br.cond.spnt lgammaf_0_1 };; { .mfi ldfpd FR_Ln2,FR_05 = [GR_ad_Data],16 fma.s1 FR_Xp2 = f1,f1,FR_Xp1 // (x+2) shladd GR_ad_C650 = GR_Ind,2,GR_ad_C650 } { .mfi add GR_ad_Ce = 0x20,GR_ad_Co nop.f 0 add GR_ad_C43 = 0x30,GR_ad_Co };; { .mfi // load coefficients of polynomial approximation // of ln(GAMMA(x)), 2 <= x < 2^13 (p13) ldfpd FR_A10,FR_A9 = [GR_ad_Co],16 fcvt.xf FR_N = FR_int_N cmp.eq.unc p6,p7 = GR_ExpOf2,GR_SignExp } { .mib (p13) ldfpd FR_A8,FR_A7 = [GR_ad_Ce] (p14) cmp.le.unc p9,p0 = GR_StirlBound,GR_Exp // jump if x is less or equal to -2^13 (p9) br.cond.spnt lgammaf_negstirling };; .pred.rel "mutex",p6,p7 { .mfi (p13) ldfpd FR_A6,FR_A5 = [GR_ad_C650],16 (p6) fma.s1 FR_x = f0,f0,FR_NormX shladd GR_ad_T = GR_Ind4T,3,GR_ad_Data } { .mfi (p13) ldfpd FR_A4,FR_A3 = [GR_ad_C43] (p7) fms.s1 FR_x = FR_x,f1,f1 (p14) mov GR_ReqBound = 0x20005 };; { .mfi (p13) ldfpd FR_A2,FR_A1 = [GR_ad_Co],16 fms.s1 FR_xm2 = FR_xm2,f1,f1 (p14) extr.u GR_Arg = GR_Sig,60,4 } { .mfi mov GR_SignOfGamma = 1 // set sign of gamma(x) to 1 fcvt.xf FR_Ntrunc = FR_int_Ntrunc nop.i 0 };; { .mfi ldfd FR_T = [GR_ad_T] fma.s1 FR_r2 = FR_r,FR_r,f0 shl GR_ReqBound = GR_ReqBound,3 } { .mfi add GR_ad_Co = 0xCA0,GR_ad_Data fnma.s1 FR_Req = FR_Xp1,FR_NormX,f0 // -x*(x+1) (p14) shladd GR_Arg = GR_Exp,4,GR_Arg };; { .mfi (p13) ldfd FR_A0 = [GR_ad_C650] fma.s1 FR_Xp3 = FR_2,f1,FR_Xp1 // (x+3) (p14) cmp.le.unc p9,p0 = GR_Arg,GR_ReqBound } { .mfi (p14) add GR_ad_Ce = 0x20,GR_ad_Co fma.s1 FR_Xp4 = FR_2,FR_2,FR_NormX // (x+4) (p15) add GR_ad_OvfBound = 0xBB8,GR_ad_Data };; { .mfi // load coefficients of polynomial approximation // of ln(sin(Pi*xf)/(Pi*xf)), |xf| <= 0.5 (p14) ldfpd FR_S16,FR_S14 = [GR_ad_Co],16 (p14) fms.s1 FR_Xf = FR_NormX,f1,FR_N // xf = x - [x] (p14) sub GR_SignOfGamma = r0,GR_SignOfGamma // set sign of // gamma(x) to -1 } { .mfb (p14) ldfpd FR_S12,FR_S10 = [GR_ad_Ce],16 fma.s1 FR_Xp5 = FR_2,FR_2,FR_Xp1 // (x+5) // jump if x is from the interval (-9; 0) (p9) br.cond.spnt lgammaf_negrecursion };; { .mfi (p14) ldfpd FR_S8,FR_S6 = [GR_ad_Co],16 fma.s1 FR_P32 = FR_P3,FR_r,FR_P2 nop.i 0 } { .mfb (p14) ldfpd FR_S4,FR_S2 = [GR_ad_Ce],16 fma.s1 FR_x2 = FR_x,FR_x,f0 // jump if x is from the interval (-2^13; -9) (p14) br.cond.spnt lgammaf_negpoly };; { .mfi ldfd FR_OverflowBound = [GR_ad_OvfBound] (p12) fcvt.xf FR_N = FR_int_Ln // set p9 if signgum is 32-bit int // set p10 if signgum is 64-bit int cmp.eq p10,p9 = 8,r34 } { .mfi nop.m 0 (p12) fma.s1 FR_P10 = FR_P1,FR_r,f1 nop.i 0 };; .pred.rel "mutex",p6,p7 .pred.rel "mutex",p9,p10 { .mfi // store sign of gamma(x) as 32-bit int (p9) st4 [r33] = GR_SignOfGamma (p6) fma.s1 FR_xx = FR_x,FR_xm2,f0 nop.i 0 } { .mfi // store sign of gamma(x) as 64-bit int (p10) st8 [r33] = GR_SignOfGamma (p7) fma.s1 FR_xx = f0,f0,FR_x nop.i 0 };; { .mfi nop.m 0 (p13) fma.s1 FR_A9 = FR_A10,FR_x,FR_A9 nop.i 0 } { .mfi nop.m 0 (p13) fma.s1 FR_A7 = FR_A8,FR_x,FR_A7 nop.i 0 };; { .mfi nop.m 0 (p13) fma.s1 FR_A5 = FR_A6,FR_x,FR_A5 nop.i 0 } { .mfi nop.m 0 (p13) fma.s1 FR_A3 = FR_A4,FR_x,FR_A3 nop.i 0 };; { .mfi nop.m 0 (p15) fcmp.eq.unc.s1 p8,p0 = FR_NormX,FR_2 // is input argument 2.0? nop.i 0 } { .mfi nop.m 0 (p13) fma.s1 FR_A1 = FR_A2,FR_x,FR_A1 nop.i 0 };; { .mfi nop.m 0 (p12) fma.s1 FR_T = FR_N,FR_Ln2,FR_T nop.i 0 } { .mfi nop.m 0 (p12) fma.s1 FR_P32 = FR_P32,FR_r2,FR_P10 nop.i 0 };; { .mfi nop.m 0 (p13) fma.s1 FR_x4 = FR_x2,FR_x2,f0 nop.i 0 } { .mfi nop.m 0 (p13) fma.s1 FR_x3 = FR_x2,FR_xx,f0 nop.i 0 };; { .mfi nop.m 0 (p13) fma.s1 FR_A7 = FR_A9,FR_x2,FR_A7 nop.i 0 } { .mfb nop.m 0 (p8) fma.s.s0 f8 = f0,f0,f0 (p8) br.ret.spnt b0 // fast exit for 2.0 };; { .mfi nop.m 0 (p6) fma.s1 FR_A0 = FR_A0,FR_xm2,f0 nop.i 0 } { .mfi nop.m 0 (p13) fma.s1 FR_A3 = FR_A5,FR_x2,FR_A3 nop.i 0 };; { .mfi nop.m 0 (p15) fcmp.le.unc.s1 p8,p0 = FR_OverflowBound,FR_NormX // overflow test nop.i 0 } { .mfi nop.m 0 (p12) fms.s1 FR_xm05 = FR_NormX,f1,FR_05 nop.i 0 };; { .mfi nop.m 0 (p12) fma.s1 FR_Ln = FR_P32,FR_r,FR_T nop.i 0 } { .mfi nop.m 0 (p12) fms.s1 FR_LnSqrt2Pi = FR_LnSqrt2Pi,f1,FR_NormX nop.i 0 };; { .mfi nop.m 0 (p13) fma.s1 FR_A0 = FR_A1,FR_xx,FR_A0 nop.i 0 } { .mfb nop.m 0 (p13) fma.s1 FR_A3 = FR_A7,FR_x4,FR_A3 // jump if result overflows (p8) br.cond.spnt lgammaf_overflow };; .pred.rel "mutex",p12,p13 { .mfi nop.m 0 (p12) fma.s.s0 f8 = FR_Ln,FR_xm05,FR_LnSqrt2Pi nop.i 0 } { .mfb nop.m 0 (p13) fma.s.s0 f8 = FR_A3,FR_x3,FR_A0 br.ret.sptk b0 };; // branch for calculating of ln(GAMMA(x)) for 0 < x < 1 //--------------------------------------------------------------------- .align 32 lgammaf_0_1: { .mfi getf.sig GR_Ind = FR_Xp1 fma.s1 FR_r2 = FR_r,FR_r,f0 mov GR_fff7 = 0xFFF7 } { .mfi ldfpd FR_Ln2,FR_05 = [GR_ad_Data],16 fma.s1 FR_P32 = FR_P3,FR_r,FR_P2 // input argument cann't be equal to 1.0 cmp.eq p0,p14 = r0,r0 };; { .mfi getf.exp GR_Exp = FR_w fcvt.xf FR_N = FR_int_Ln add GR_ad_Co = 0xCE0,GR_ad_Data } { .mfi shladd GR_ad_T = GR_Ind4T,3,GR_ad_Data fma.s1 FR_P10 = FR_P1,FR_r,f1 add GR_ad_Ce = 0xD00,GR_ad_Data };; { .mfi ldfd FR_T = [GR_ad_T] fma.s1 FR_w2 = FR_w,FR_w,f0 extr.u GR_Ind = GR_Ind,61,2 } { .mfi nop.m 0 fma.s1 FR_Q32 = FR_P3,FR_w,FR_P2 //// add GR_ad_C0 = 0xB30,GR_ad_Data add GR_ad_C0 = 0xB38,GR_ad_Data };; { .mfi and GR_Exp = GR_Exp,GR_ExpMask nop.f 0 shladd GR_IndX8 = GR_Ind,3,r0 } { .mfi shladd GR_IndX2 = GR_Ind,1,r0 fma.s1 FR_Q10 = FR_P1,FR_w,f1 cmp.eq p6,p15 = 0,GR_Ind };; { .mfi shladd GR_ad_Co = GR_IndX8,3,GR_ad_Co (p6) fma.s1 FR_x = f0,f0,FR_NormX shladd GR_ad_C0 = GR_IndX2,4,GR_ad_C0 } { .mfi shladd GR_ad_Ce = GR_IndX8,3,GR_ad_Ce nop.f 0 (p15) cmp.eq.unc p7,p8 = 1,GR_Ind };; .pred.rel "mutex",p7,p8 { .mfi ldfpd FR_A8,FR_A7 = [GR_ad_Co],16 (p7) fms.s1 FR_x = FR_NormX,f1,FR_LocalMin cmp.ge p10,p11 = GR_Exp,GR_fff7 } { .mfb ldfpd FR_A6,FR_A5 = [GR_ad_Ce],16 (p8) fma.s1 FR_x = f1,f1,FR_NormX br.cond.sptk lgamma_0_2_core };; // branch for calculating of ln(GAMMA(x)) for 1 <= x < 2 //--------------------------------------------------------------------- .align 32 lgammaf_1_2: { .mfi add GR_ad_Co = 0xCF0,GR_ad_Data fcmp.eq.s1 p14,p0 = f1,FR_NormX // is input argument 1.0? extr.u GR_Ind = GR_Sig,61,2 } { .mfi add GR_ad_Ce = 0xD10,GR_ad_Data nop.f 0 //// add GR_ad_C0 = 0xB40,GR_ad_Data add GR_ad_C0 = 0xB48,GR_ad_Data };; { .mfi shladd GR_IndX8 = GR_Ind,3,r0 nop.f 0 shladd GR_IndX2 = GR_Ind,1,r0 } { .mfi cmp.eq p6,p15 = 0,GR_Ind // p6 <- x from [1;1.25) nop.f 0 cmp.ne p9,p0 = r0,r0 };; { .mfi shladd GR_ad_Co = GR_IndX8,3,GR_ad_Co (p6) fms.s1 FR_x = FR_NormX,f1,f1 // reduced x for [1;1.25) shladd GR_ad_C0 = GR_IndX2,4,GR_ad_C0 } { .mfi shladd GR_ad_Ce = GR_IndX8,3,GR_ad_Ce (p14) fma.s.s0 f8 = f0,f0,f0 (p15) cmp.eq.unc p7,p8 = 1,GR_Ind // p7 <- x from [1.25;1.5) };; .pred.rel "mutex",p7,p8 { .mfi ldfpd FR_A8,FR_A7 = [GR_ad_Co],16 (p7) fms.s1 FR_x = FR_xm2,f1,FR_LocalMin nop.i 0 } { .mfi ldfpd FR_A6,FR_A5 = [GR_ad_Ce],16 (p8) fma.s1 FR_x = f0,f0,FR_NormX (p9) cmp.eq.unc p10,p11 = r0,r0 };; lgamma_0_2_core: { .mmi ldfpd FR_A4,FR_A3 = [GR_ad_Co],16 ldfpd FR_A2,FR_A1 = [GR_ad_Ce],16 mov GR_SignOfGamma = 1 // set sign of gamma(x) to 1 };; { .mfi // add GR_ad_C0 = 8,GR_ad_C0 ldfd FR_A0 = [GR_ad_C0] nop.f 0 // set p13 if signgum is 32-bit int // set p15 if signgum is 64-bit int cmp.eq p15,p13 = 8,r34 };; .pred.rel "mutex",p13,p15 { .mmf // store sign of gamma(x) (p13) st4 [r33] = GR_SignOfGamma // as 32-bit int (p15) st8 [r33] = GR_SignOfGamma // as 64-bit int (p11) fma.s1 FR_Q32 = FR_Q32,FR_w2,FR_Q10 };; { .mfb nop.m 0 (p10) fma.s1 FR_P32 = FR_P32,FR_r2,FR_P10 (p14) br.ret.spnt b0 // fast exit for 1.0 };; { .mfi nop.m 0 (p10) fma.s1 FR_T = FR_N,FR_Ln2,FR_T cmp.eq p6,p7 = 0,GR_Ind // p6 <- x from [1;1.25) } { .mfi nop.m 0 fma.s1 FR_x2 = FR_x,FR_x,f0 cmp.eq p8,p0 = r0,r0 // set p8 to 1 that means we on [1;2] };; { .mfi nop.m 0 (p11) fma.s1 FR_Ln = FR_Q32,FR_w,f0 nop.i 0 } { .mfi nop.m 0 nop.f 0 nop.i 0 };; .pred.rel "mutex",p6,p7 { .mfi nop.m 0 (p6) fma.s1 FR_xx = f0,f0,FR_x nop.i 0 } { .mfi nop.m 0 (p7) fma.s1 FR_xx = f0,f0,f1 nop.i 0 };; { .mfi nop.m 0 fma.s1 FR_A7 = FR_A8,FR_x,FR_A7 nop.i 0 } { .mfi nop.m 0 fma.s1 FR_A5 = FR_A6,FR_x,FR_A5 (p9) cmp.ne p8,p0 = r0,r0 // set p8 to 0 that means we on [0;1] };; { .mfi nop.m 0 fma.s1 FR_A3 = FR_A4,FR_x,FR_A3 nop.i 0 } { .mfi nop.m 0 fma.s1 FR_A1 = FR_A2,FR_x,FR_A1 nop.i 0 };; { .mfi nop.m 0 fma.s1 FR_x4 = FR_x2,FR_x2,f0 nop.i 0 } { .mfi nop.m 0 (p10) fma.s1 FR_Ln = FR_P32,FR_r,FR_T nop.i 0 };; { .mfi nop.m 0 fma.s1 FR_A5 = FR_A7,FR_x2,FR_A5 nop.i 0 } { .mfi nop.m 0 fma.s1 FR_A1 = FR_A3,FR_x2,FR_A1 nop.i 0 };; .pred.rel "mutex",p9,p8 { .mfi nop.m 0 (p9) fms.d.s1 FR_A0 = FR_A0,FR_xx,FR_Ln nop.i 0 } { .mfi nop.m 0 (p8) fms.s1 FR_A0 = FR_A0,FR_xx,f0 nop.i 0 };; { .mfi nop.m 0 fma.d.s1 FR_A1 = FR_A5,FR_x4,FR_A1 nop.i 0 } { .mfi nop.m 0 nop.f 0 nop.i 0 };; .pred.rel "mutex",p6,p7 { .mfi nop.m 0 (p6) fma.s.s0 f8 = FR_A1,FR_x2,FR_A0 nop.i 0 } { .mfb nop.m 0 (p7) fma.s.s0 f8 = FR_A1,FR_x,FR_A0 br.ret.sptk b0 };; // branch for calculating of ln(GAMMA(x)) for -9 < x < 1 //--------------------------------------------------------------------- .align 32 lgammaf_negrecursion: { .mfi getf.sig GR_N = FR_int_Ntrunc fms.s1 FR_1pXf = FR_Xp2,f1,FR_Ntrunc // 1 + (x+1) - [x] mov GR_Neg2 = 2 } { .mfi add GR_ad_Co = 0xCE0,GR_ad_Data fms.s1 FR_Xf = FR_Xp1,f1,FR_Ntrunc // (x+1) - [x] mov GR_Neg4 = 4 };; { .mfi add GR_ad_Ce = 0xD00,GR_ad_Data fma.s1 FR_Xp6 = FR_2,FR_2,FR_Xp2 // (x+6) add GR_ad_C0 = 0xB30,GR_ad_Data } { .mfi sub GR_Neg2 = r0,GR_Neg2 fma.s1 FR_Xp7 = FR_2,FR_3,FR_Xp1 // (x+7) sub GR_Neg4 = r0,GR_Neg4 };; { .mfi cmp.ne p8,p0 = r0,GR_N fcmp.eq.s1 p13,p0 = FR_NormX,FR_Ntrunc and GR_IntNum = 0xF,GR_N } { .mfi cmp.lt p6,p0 = GR_N,GR_Neg2 fma.s1 FR_Xp8 = FR_2,FR_3,FR_Xp2 // (x+8) cmp.lt p7,p0 = GR_N,GR_Neg4 };; { .mfi getf.d GR_Arg = FR_NormX (p6) fma.s1 FR_Xp2 = FR_Xp2,FR_Xp3,f0 (p8) tbit.z.unc p14,p15 = GR_IntNum,0 } { .mfi sub GR_RootInd = 0xE,GR_IntNum (p7) fma.s1 FR_Xp4 = FR_Xp4,FR_Xp5,f0 add GR_ad_Root = 0xDE0,GR_ad_Data };; { .mfi shladd GR_ad_Root = GR_RootInd,3,GR_ad_Root fms.s1 FR_x = FR_Xp1,f1,FR_Ntrunc // (x+1) - [x] nop.i 0 } { .mfb nop.m 0 nop.f 0 (p13) br.cond.spnt lgammaf_singularity };; .pred.rel "mutex",p14,p15 { .mfi cmp.gt p6,p0 = 0xA,GR_IntNum (p14) fma.s1 FR_Req = FR_Req,FR_Xf,f0 cmp.gt p7,p0 = 0xD,GR_IntNum } { .mfi (p15) mov GR_SignOfGamma = 1 // set sign of gamma(x) to 1 (p15) fnma.s1 FR_Req = FR_Req,FR_Xf,f0 cmp.leu p0,p13 = 2,GR_RootInd };; { .mfi nop.m 0 (p6) fma.s1 FR_Xp6 = FR_Xp6,FR_Xp7,f0 (p13) add GR_ad_RootCo = 0xE00,GR_ad_Data };; { .mfi nop.m 0 fcmp.eq.s1 p12,p11 = FR_1pXf,FR_2 nop.i 0 };; { .mfi getf.sig GR_Sig = FR_1pXf fcmp.le.s1 p9,p0 = FR_05,FR_Xf nop.i 0 } { .mfi (p13) shladd GR_RootInd = GR_RootInd,4,r0 (p7) fma.s1 FR_Xp2 = FR_Xp2,FR_Xp4,f0 (p8) cmp.gt.unc p10,p0 = 0x9,GR_IntNum };; .pred.rel "mutex",p11,p12 { .mfi nop.m 0 (p10) fma.s1 FR_Req = FR_Req,FR_Xp8,f0 (p11) extr.u GR_Ind = GR_Sig,61,2 } { .mfi (p13) add GR_RootInd = GR_RootInd,GR_RootInd nop.f 0 (p12) mov GR_Ind = 3 };; { .mfi shladd GR_IndX2 = GR_Ind,1,r0 nop.f 0 cmp.gt p14,p0 = 2,GR_Ind } { .mfi shladd GR_IndX8 = GR_Ind,3,r0 nop.f 0 cmp.eq p6,p0 = 1,GR_Ind };; .pred.rel "mutex",p6,p9 { .mfi shladd GR_ad_Co = GR_IndX8,3,GR_ad_Co (p6) fms.s1 FR_x = FR_Xf,f1,FR_LocalMin cmp.gt p10,p0 = 0xB,GR_IntNum } { .mfi shladd GR_ad_Ce = GR_IndX8,3,GR_ad_Ce (p9) fma.s1 FR_x = f0,f0,FR_1pXf shladd GR_ad_C0 = GR_IndX2,4,GR_ad_C0 };; { .mfi // load coefficients of polynomial approximation // of ln(GAMMA(x)), 1 <= x < 2 ldfpd FR_A8,FR_A7 = [GR_ad_Co],16 (p10) fma.s1 FR_Xp2 = FR_Xp2,FR_Xp6,f0 add GR_ad_C0 = 8,GR_ad_C0 } { .mfi ldfpd FR_A6,FR_A5 = [GR_ad_Ce],16 nop.f 0 (p14) add GR_ad_Root = 0x10,GR_ad_Root };; { .mfi ldfpd FR_A4,FR_A3 = [GR_ad_Co],16 nop.f 0 add GR_ad_RootCe = 0xE10,GR_ad_Data } { .mfi ldfpd FR_A2,FR_A1 = [GR_ad_Ce],16 nop.f 0 (p14) add GR_RootInd = 0x40,GR_RootInd };; { .mmi ldfd FR_A0 = [GR_ad_C0] (p13) add GR_ad_RootCo = GR_ad_RootCo,GR_RootInd (p13) add GR_ad_RootCe = GR_ad_RootCe,GR_RootInd };; { .mmi (p13) ld8 GR_Root = [GR_ad_Root] (p13) ldfd FR_Root = [GR_ad_Root] mov GR_ExpBias = 0xffff };; { .mfi nop.m 0 fma.s1 FR_x2 = FR_x,FR_x,f0 nop.i 0 } { .mlx (p8) cmp.gt.unc p10,p0 = 0xF,GR_IntNum movl GR_Dx = 0x000000014F8B588E };; { .mfi // load coefficients of polynomial approximation // of ln(GAMMA(x)), x is close to one of negative roots (p13) ldfpd FR_R3,FR_R2 = [GR_ad_RootCo] // argumenth for logarithm (p10) fma.s1 FR_Req = FR_Req,FR_Xp2,f0 mov GR_ExpMask = 0x1ffff } { .mfi (p13) ldfpd FR_R1,FR_R0 = [GR_ad_RootCe] nop.f 0 // set p9 if signgum is 32-bit int // set p8 if signgum is 64-bit int cmp.eq p8,p9 = 8,r34 };; .pred.rel "mutex",p9,p8 { .mfi (p9) st4 [r33] = GR_SignOfGamma // as 32-bit int fma.s1 FR_A7 = FR_A8,FR_x,FR_A7 (p13) sub GR_Root = GR_Arg,GR_Root } { .mfi (p8) st8 [r33] = GR_SignOfGamma // as 64-bit int fma.s1 FR_A5 = FR_A6,FR_x,FR_A5 nop.i 0 };; { .mfi nop.m 0 fms.s1 FR_w = FR_Req,f1,f1 (p13) add GR_Root = GR_Root,GR_Dx } { .mfi nop.m 0 nop.f 0 (p13) add GR_2xDx = GR_Dx,GR_Dx };; { .mfi nop.m 0 fma.s1 FR_A3 = FR_A4,FR_x,FR_A3 nop.i 0 } { .mfi nop.m 0 fma.s1 FR_A1 = FR_A2,FR_x,FR_A1 (p13) cmp.leu.unc p10,p0 = GR_Root,GR_2xDx };; { .mfi nop.m 0 frcpa.s1 FR_InvX,p0 = f1,FR_Req nop.i 0 } { .mfi nop.m 0 (p10) fms.s1 FR_rx = FR_NormX,f1,FR_Root nop.i 0 };; { .mfi getf.exp GR_SignExp = FR_Req fma.s1 FR_x4 = FR_x2,FR_x2,f0 nop.i 0 };; { .mfi getf.sig GR_Sig = FR_Req fma.s1 FR_A5 = FR_A7,FR_x2,FR_A5 nop.i 0 };; { .mfi sub GR_PureExp = GR_SignExp,GR_ExpBias fma.s1 FR_w2 = FR_w,FR_w,f0 nop.i 0 } { .mfi nop.m 0 fma.s1 FR_Q32 = FR_P3,FR_w,FR_P2 nop.i 0 };; { .mfi setf.sig FR_int_Ln = GR_PureExp fma.s1 FR_A1 = FR_A3,FR_x2,FR_A1 extr.u GR_Ind4T = GR_Sig,55,8 } { .mfi nop.m 0 fma.s1 FR_Q10 = FR_P1,FR_w,f1 nop.i 0 };; { .mfi shladd GR_ad_T = GR_Ind4T,3,GR_ad_Data fms.s1 FR_r = FR_InvX,FR_Req,f1 nop.i 0 } { .mfi nop.m 0 (p10) fms.s1 FR_rx2 = FR_rx,FR_rx,f0 nop.i 0 };; { .mfi ldfd FR_T = [GR_ad_T] (p10) fma.s1 FR_R2 = FR_R3,FR_rx,FR_R2 nop.i 0 } { .mfi nop.m 0 (p10) fma.s1 FR_R0 = FR_R1,FR_rx,FR_R0 nop.i 0 };; { .mfi getf.exp GR_Exp = FR_w fma.s1 FR_A1 = FR_A5,FR_x4,FR_A1 mov GR_ExpMask = 0x1ffff } { .mfi nop.m 0 fma.s1 FR_Q32 = FR_Q32, FR_w2,FR_Q10 nop.i 0 };; { .mfi nop.m 0 fma.s1 FR_r2 = FR_r,FR_r,f0 mov GR_fff7 = 0xFFF7 } { .mfi nop.m 0 fma.s1 FR_P32 = FR_P3,FR_r,FR_P2 nop.i 0 };; { .mfi nop.m 0 fma.s1 FR_P10 = FR_P1,FR_r,f1 and GR_Exp = GR_ExpMask,GR_Exp } { .mfb nop.m 0 (p10) fma.s.s0 f8 = FR_R2,FR_rx2,FR_R0 (p10) br.ret.spnt b0 // exit for arguments close to negative roots };; { .mfi nop.m 0 fcvt.xf FR_N = FR_int_Ln nop.i 0 } { .mfi cmp.ge p14,p15 = GR_Exp,GR_fff7 nop.f 0 nop.i 0 };; { .mfi nop.m 0 fma.s1 FR_A0 = FR_A1,FR_x,FR_A0 nop.i 0 } { .mfi nop.m 0 (p15) fma.s1 FR_Ln = FR_Q32,FR_w,f0 nop.i 0 };; { .mfi nop.m 0 (p14) fma.s1 FR_P32 = FR_P32,FR_r2,FR_P10 cmp.eq p6,p7 = 0,GR_Ind };; { .mfi nop.m 0 (p14) fma.s1 FR_T = FR_N,FR_Ln2,FR_T nop.i 0 };; { .mfi nop.m 0 (p14) fma.s1 FR_Ln = FR_P32,FR_r,FR_T nop.i 0 };; .pred.rel "mutex",p6,p7 { .mfi nop.m 0 (p6) fms.s.s0 f8 = FR_A0,FR_x,FR_Ln nop.i 0 } { .mfb nop.m 0 (p7) fms.s.s0 f8 = FR_A0,f1,FR_Ln br.ret.sptk b0 };; // branch for calculating of ln(GAMMA(x)) for x < -2^13 //--------------------------------------------------------------------- .align 32 lgammaf_negstirling: { .mfi shladd GR_ad_T = GR_Ind4T,3,GR_ad_Data fms.s1 FR_Xf = FR_NormX,f1,FR_N // xf = x - [x] mov GR_SingBound = 0x10016 } { .mfi add GR_ad_Co = 0xCA0,GR_ad_Data fma.s1 FR_P32 = FR_P3,FR_r,FR_P2 nop.i 0 };; { .mfi ldfd FR_T = [GR_ad_T] fcvt.xf FR_int_Ln = FR_int_Ln cmp.le p6,p0 = GR_SingBound,GR_Exp } { .mfb add GR_ad_Ce = 0x20,GR_ad_Co fma.s1 FR_r2 = FR_r,FR_r,f0 (p6) br.cond.spnt lgammaf_singularity };; { .mfi // load coefficients of polynomial approximation // of ln(sin(Pi*xf)/(Pi*xf)), |xf| <= 0.5 ldfpd FR_S16,FR_S14 = [GR_ad_Co],16 fma.s1 FR_P10 = FR_P1,FR_r,f1 nop.i 0 } { .mfi ldfpd FR_S12,FR_S10 = [GR_ad_Ce],16 fms.s1 FR_xm05 = FR_NormX,f1,FR_05 nop.i 0 };; { .mmi ldfpd FR_S8,FR_S6 = [GR_ad_Co],16 ldfpd FR_S4,FR_S2 = [GR_ad_Ce],16 nop.i 0 };; { .mfi getf.sig GR_N = FR_int_Ntrunc // signgam calculation fma.s1 FR_Xf2 = FR_Xf,FR_Xf,f0 nop.i 0 };; { .mfi nop.m 0 frcpa.s1 FR_InvXf,p0 = f1,FR_Xf nop.i 0 };; { .mfi getf.d GR_Arg = FR_Xf fcmp.eq.s1 p6,p0 = FR_NormX,FR_N mov GR_ExpBias = 0x3FF };; { .mfi nop.m 0 fma.s1 FR_T = FR_int_Ln,FR_Ln2,FR_T extr.u GR_Exp = GR_Arg,52,11 } { .mfi nop.m 0 fma.s1 FR_P32 = FR_P32,FR_r2,FR_P10 nop.i 0 };; { .mfi sub GR_PureExp = GR_Exp,GR_ExpBias fma.s1 FR_S14 = FR_S16,FR_Xf2,FR_S14 extr.u GR_Ind4T = GR_Arg,44,8 } { .mfb mov GR_SignOfGamma = 1 // set signgam to -1 fma.s1 FR_S10 = FR_S12,FR_Xf2,FR_S10 (p6) br.cond.spnt lgammaf_singularity };; { .mfi setf.sig FR_int_Ln = GR_PureExp fms.s1 FR_rf = FR_InvXf,FR_Xf,f1 // set p14 if GR_N is even tbit.z p14,p0 = GR_N,0 } { .mfi shladd GR_ad_T = GR_Ind4T,3,GR_ad_Data fma.s1 FR_Xf4 = FR_Xf2,FR_Xf2,f0 nop.i 0 };; { .mfi (p14) sub GR_SignOfGamma = r0,GR_SignOfGamma // set signgam to -1 fma.s1 FR_S6 = FR_S8,FR_Xf2,FR_S6 nop.i 0 } { .mfi // set p9 if signgum is 32-bit int // set p10 if signgum is 64-bit int cmp.eq p10,p9 = 8,r34 fma.s1 FR_S2 = FR_S4,FR_Xf2,FR_S2 nop.i 0 };; { .mfi ldfd FR_Tf = [GR_ad_T] fma.s1 FR_Ln = FR_P32,FR_r,FR_T nop.i 0 } { .mfi nop.m 0 fma.s1 FR_LnSqrt2Pi = FR_LnSqrt2Pi,f1,FR_NormX nop.i 0 };; .pred.rel "mutex",p9,p10 { .mfi (p9) st4 [r33] = GR_SignOfGamma // as 32-bit int fma.s1 FR_rf2 = FR_rf,FR_rf,f0 nop.i 0 } { .mfi (p10) st8 [r33] = GR_SignOfGamma // as 64-bit int fma.s1 FR_S10 = FR_S14,FR_Xf4,FR_S10 nop.i 0 };; { .mfi nop.m 0 fma.s1 FR_P32f = FR_P3,FR_rf,FR_P2 nop.i 0 } { .mfi nop.m 0 fma.s1 FR_Xf8 = FR_Xf4,FR_Xf4,f0 nop.i 0 };; { .mfi nop.m 0 fma.s1 FR_P10f = FR_P1,FR_rf,f1 nop.i 0 } { .mfi nop.m 0 fma.s1 FR_S2 = FR_S6,FR_Xf4,FR_S2 nop.i 0 };; { .mfi nop.m 0 fms.s1 FR_Ln = FR_Ln,FR_xm05,FR_LnSqrt2Pi nop.i 0 };; { .mfi nop.m 0 fcvt.xf FR_Nf = FR_int_Ln nop.i 0 };; { .mfi nop.m 0 fma.s1 FR_S2 = FR_S10,FR_Xf8,FR_S2 nop.i 0 };; { .mfi nop.m 0 fma.s1 FR_Tf = FR_Nf,FR_Ln2,FR_Tf nop.i 0 } { .mfi nop.m 0 fma.s1 FR_P32f = FR_P32f,FR_rf2,FR_P10f // ?????? nop.i 0 };; { .mfi nop.m 0 fnma.s1 FR_Ln = FR_S2,FR_Xf2,FR_Ln nop.i 0 };; { .mfi nop.m 0 fma.s1 FR_Lnf = FR_P32f,FR_rf,FR_Tf nop.i 0 };; { .mfb nop.m 0 fms.s.s0 f8 = FR_Ln,f1,FR_Lnf br.ret.sptk b0 };; // branch for calculating of ln(GAMMA(x)) for -2^13 < x < -9 //--------------------------------------------------------------------- .align 32 lgammaf_negpoly: { .mfi getf.d GR_Arg = FR_Xf frcpa.s1 FR_InvXf,p0 = f1,FR_Xf mov GR_ExpBias = 0x3FF } { .mfi nop.m 0 fma.s1 FR_Xf2 = FR_Xf,FR_Xf,f0 nop.i 0 };; { .mfi getf.sig GR_N = FR_int_Ntrunc fcvt.xf FR_N = FR_int_Ln mov GR_SignOfGamma = 1 } { .mfi nop.m 0 fma.s1 FR_A9 = FR_A10,FR_x,FR_A9 nop.i 0 };; { .mfi nop.m 0 fma.s1 FR_P10 = FR_P1,FR_r,f1 extr.u GR_Exp = GR_Arg,52,11 } { .mfi nop.m 0 fma.s1 FR_x4 = FR_x2,FR_x2,f0 nop.i 0 };; { .mfi sub GR_PureExp = GR_Exp,GR_ExpBias fma.s1 FR_A7 = FR_A8,FR_x,FR_A7 tbit.z p14,p0 = GR_N,0 } { .mfi nop.m 0 fma.s1 FR_A5 = FR_A6,FR_x,FR_A5 nop.i 0 };; { .mfi setf.sig FR_int_Ln = GR_PureExp fma.s1 FR_A3 = FR_A4,FR_x,FR_A3 nop.i 0 } { .mfi nop.m 0 fma.s1 FR_A1 = FR_A2,FR_x,FR_A1 (p14) sub GR_SignOfGamma = r0,GR_SignOfGamma };; { .mfi nop.m 0 fms.s1 FR_rf = FR_InvXf,FR_Xf,f1 nop.i 0 } { .mfi nop.m 0 fma.s1 FR_Xf4 = FR_Xf2,FR_Xf2,f0 nop.i 0 };; { .mfi nop.m 0 fma.s1 FR_S14 = FR_S16,FR_Xf2,FR_S14 nop.i 0 } { .mfi nop.m 0 fma.s1 FR_S10 = FR_S12,FR_Xf2,FR_S10 nop.i 0 };; { .mfi nop.m 0 fma.s1 FR_T = FR_N,FR_Ln2,FR_T nop.i 0 } { .mfi nop.m 0 fma.s1 FR_P32 = FR_P32,FR_r2,FR_P10 nop.i 0 };; { .mfi nop.m 0 fma.s1 FR_S6 = FR_S8,FR_Xf2,FR_S6 extr.u GR_Ind4T = GR_Arg,44,8 } { .mfi nop.m 0 fma.s1 FR_S2 = FR_S4,FR_Xf2,FR_S2 nop.i 0 };; { .mfi nop.m 0 fma.s1 FR_A7 = FR_A9,FR_x2,FR_A7 nop.i 0 } { .mfi shladd GR_ad_T = GR_Ind4T,3,GR_ad_Data fma.s1 FR_A3 = FR_A5,FR_x2,FR_A3 nop.i 0 };; { .mfi nop.m 0 fma.s1 FR_Xf8 = FR_Xf4,FR_Xf4,f0 nop.i 0 } { .mfi nop.m 0 fma.s1 FR_rf2 = FR_rf,FR_rf,f0 nop.i 0 };; { .mfi nop.m 0 fma.s1 FR_P32f = FR_P3,FR_rf,FR_P2 nop.i 0 } { .mfi nop.m 0 fma.s1 FR_P10f = FR_P1,FR_rf,f1 nop.i 0 };; { .mfi ldfd FR_Tf = [GR_ad_T] fma.s1 FR_Ln = FR_P32,FR_r,FR_T nop.i 0 } { .mfi nop.m 0 fma.s1 FR_A0 = FR_A1,FR_x,FR_A0 nop.i 0 };; { .mfi nop.m 0 fma.s1 FR_S10 = FR_S14,FR_Xf4,FR_S10 nop.i 0 } { .mfi nop.m 0 fma.s1 FR_S2 = FR_S6,FR_Xf4,FR_S2 nop.i 0 };; { .mfi nop.m 0 fcvt.xf FR_Nf = FR_int_Ln nop.i 0 } { .mfi nop.m 0 fma.s1 FR_A3 = FR_A7,FR_x4,FR_A3 nop.i 0 };; { .mfi nop.m 0 fcmp.eq.s1 p13,p0 = FR_NormX,FR_Ntrunc nop.i 0 } { .mfi nop.m 0 fnma.s1 FR_x3 = FR_x2,FR_x,f0 // -x^3 nop.i 0 };; { .mfi nop.m 0 fma.s1 FR_P32f = FR_P32f,FR_rf2,FR_P10f nop.i 0 };; { .mfb // set p9 if signgum is 32-bit int // set p10 if signgum is 64-bit int cmp.eq p10,p9 = 8,r34 fma.s1 FR_S2 = FR_S10,FR_Xf8,FR_S2 (p13) br.cond.spnt lgammaf_singularity };; .pred.rel "mutex",p9,p10 { .mmf (p9) st4 [r33] = GR_SignOfGamma // as 32-bit int (p10) st8 [r33] = GR_SignOfGamma // as 64-bit int fms.s1 FR_A0 = FR_A3,FR_x3,FR_A0 // -A3*x^3-A0 };; { .mfi nop.m 0 fma.s1 FR_Tf = FR_Nf,FR_Ln2,FR_Tf nop.i 0 };; { .mfi nop.m 0 fma.s1 FR_Ln = FR_S2,FR_Xf2,FR_Ln // S2*Xf^2+Ln nop.i 0 };; { .mfi nop.m 0 fma.s1 FR_Lnf = FR_P32f,FR_rf,FR_Tf nop.i 0 };; { .mfi nop.m 0 fms.s1 FR_Ln = FR_A0,f1,FR_Ln nop.i 0 };; { .mfb nop.m 0 fms.s.s0 f8 = FR_Ln,f1,FR_Lnf br.ret.sptk b0 };; // branch for handling +/-0, NaT, QNaN, +/-INF and denormalised numbers //--------------------------------------------------------------------- .align 32 lgammaf_spec: { .mfi getf.exp GR_SignExp = FR_NormX fclass.m p6,p0 = f8,0x21 // is arg +INF? mov GR_SignOfGamma = 1 // set signgam to 1 };; { .mfi getf.sig GR_Sig = FR_NormX fclass.m p7,p0 = f8,0xB // is x deno? // set p11 if signgum is 32-bit int // set p12 if signgum is 64-bit int cmp.eq p12,p11 = 8,r34 };; .pred.rel "mutex",p11,p12 { .mfi // store sign of gamma(x) as 32-bit int (p11) st4 [r33] = GR_SignOfGamma fclass.m p8,p0 = f8,0x1C0 // is arg NaT or NaN? dep.z GR_Ind = GR_SignExp,3,4 } { .mib // store sign of gamma(x) as 64-bit int (p12) st8 [r33] = GR_SignOfGamma and GR_Exp = GR_ExpMask,GR_SignExp (p6) br.ret.spnt b0 // exit for +INF };; { .mfi sub GR_PureExp = GR_Exp,GR_ExpBias fclass.m p9,p0 = f8,0x22 // is arg -INF? extr.u GR_Ind4T = GR_Sig,55,8 } { .mfb nop.m 0 (p7) fma.s0 FR_tmp = f1,f1,f8 (p7) br.cond.sptk lgammaf_core };; { .mfb nop.m 0 (p8) fms.s.s0 f8 = f8,f1,f8 (p8) br.ret.spnt b0 // exit for NaT and NaN };; { .mfb nop.m 0 (p9) fmerge.s f8 = f1,f8 (p9) br.ret.spnt b0 // exit -INF };; // branch for handling negative integers and +/-0 //--------------------------------------------------------------------- .align 32 lgammaf_singularity: { .mfi mov GR_SignOfGamma = 1 // set signgam to 1 fclass.m p6,p0 = f8,0x6 // is x -0? mov GR_TAG = 109 // negative } { .mfi mov GR_ad_SignGam = r33 fma.s1 FR_X = f0,f0,f8 nop.i 0 };; { .mfi nop.m 0 frcpa.s0 f8,p0 = f1,f0 // set p9 if signgum is 32-bit int // set p10 if signgum is 64-bit int cmp.eq p10,p9 = 8,r34 } { .mib nop.m 0 (p6) sub GR_SignOfGamma = r0,GR_SignOfGamma br.cond.sptk lgammaf_libm_err };; // overflow (x > OVERFLOV_BOUNDARY) //--------------------------------------------------------------------- .align 32 lgammaf_overflow: { .mfi nop.m 0 nop.f 0 mov r8 = 0x1FFFE };; { .mfi setf.exp f9 = r8 fmerge.s FR_X = f8,f8 mov GR_TAG = 108 // overflow };; { .mfi mov GR_ad_SignGam = r33 nop.f 0 // set p9 if signgum is 32-bit int // set p10 if signgum is 64-bit int cmp.eq p10,p9 = 8,r34 } { .mfi nop.m 0 fma.s.s0 f8 = f9,f9,f0 // Set I,O and +INF result nop.i 0 };; // gate to __libm_error_support# //--------------------------------------------------------------------- .align 32 lgammaf_libm_err: { .mmi alloc r32 = ar.pfs,1,4,4,0 mov GR_Parameter_TAG = GR_TAG nop.i 0 };; .pred.rel "mutex",p9,p10 { .mmi // store sign of gamma(x) as 32-bit int (p9) st4 [GR_ad_SignGam] = GR_SignOfGamma // store sign of gamma(x) as 64-bit int (p10) st8 [GR_ad_SignGam] = GR_SignOfGamma nop.i 0 };; GLOBAL_LIBM_END(__libm_lgammaf) 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 stfs [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 stfs [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 stfs [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 ldfs 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#