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Diffstat (limited to 'sysdeps/ia64/fpu/libm_lgammaf.S')
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diff --git a/sysdeps/ia64/fpu/libm_lgammaf.S b/sysdeps/ia64/fpu/libm_lgammaf.S deleted file mode 100644 index 4bd92c3b26..0000000000 --- a/sysdeps/ia64/fpu/libm_lgammaf.S +++ /dev/null @@ -1,2199 +0,0 @@ -.file "libm_lgammaf.s" - - -// Copyright (c) 2002 - 2005, Intel Corporation -// All rights reserved. -// -// Contributed 2002 by the Intel Numerics Group, Intel Corporation -// -// Redistribution and use in source and binary forms, with or without -// modification, are permitted provided that the following conditions are -// met: -// -// * Redistributions of source code must retain the above copyright -// notice, this list of conditions and the following disclaimer. -// -// * Redistributions in binary form must reproduce the above copyright -// notice, this list of conditions and the following disclaimer in the -// documentation and/or other materials provided with the distribution. -// -// * The name of Intel Corporation may not be used to endorse or promote -// products derived from this software without specific prior written -// permission. - -// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS -// "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES,INCLUDING,BUT NOT -// LIMITED TO,THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR -// A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL INTEL OR ITS -// CONTRIBUTORS BE LIABLE FOR ANY DIRECT,INDIRECT,INCIDENTAL,SPECIAL, -// EXEMPLARY,OR CONSEQUENTIAL DAMAGES (INCLUDING,BUT NOT LIMITED TO, -// PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,DATA,OR -// PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY -// OF LIABILITY,WHETHER IN CONTRACT,STRICT LIABILITY OR TORT (INCLUDING -// NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS -// SOFTWARE,EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. -// -// Intel Corporation is the author of this code,and requests that all -// problem reports or change requests be submitted to it directly at -// http://www.intel.com/software/products/opensource/libraries/num.htm. -// -//********************************************************************* -// -// History: -// 01/10/02 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 -// 03/31/05 Reformatted delimiters between 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# |