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Diffstat (limited to 'sysdeps/ia64/fpu/libm_lgammaf.S')
| -rw-r--r-- | sysdeps/ia64/fpu/libm_lgammaf.S | 2189 |
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diff --git a/sysdeps/ia64/fpu/libm_lgammaf.S b/sysdeps/ia64/fpu/libm_lgammaf.S new file mode 100644 index 0000000000..83cffd60fa --- /dev/null +++ b/sysdeps/ia64/fpu/libm_lgammaf.S @@ -0,0 +1,2189 @@ +.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 +// +//********************************************************************* +// +//********************************************************************* +// +// 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,0 // A0 +data8 0x40101476B38FD501,0xC0199DE7B387C0FC // A6,A5 +data8 0x407EB8DAEC83D759,0 // A0 +data8 0x401FDB008D65125A,0xC0296B506E665581 // A6,A5 +data8 0x409226D93107EF66,0 // A0 +data8 0x402FB3EAAF3E7B2D,0xC039521142AD8E0D // A6,A5 +data8 0x40A4EFA4F072792E,0 // A0 +data8 0x403FA024C66B2563,0xC0494569F250E691 // A6,A5 +data8 0x40B7B747C9235BB8,0 // A0 +data8 0x404F9607D6DA512C,0xC0593F0B2EDDB4BC // A6,A5 +data8 0x40CA7E29C5F16DE2,0 // A0 +data8 0x405F90C5F613D98D,0xC0693BD130E50AAF // A6,A5 +data8 0x40DD4495238B190C,0 // A0 +// +// 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# |