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| author | Zack Weinberg <zackw@panix.com> | 2017-06-08 15:39:03 -0400 |
|---|---|---|
| committer | Zack Weinberg <zackw@panix.com> | 2017-06-08 15:39:03 -0400 |
| commit | 5046dbb4a7eba5eccfd258f92f4735c9ffc8d069 (patch) | |
| tree | 4470480d904b65cf14ca524f96f79eca818c3eaf /REORG.TODO/sysdeps/ia64/fpu/libm_lgamma.S | |
| parent | 199fc19d3aaaf57944ef036e15904febe877fc93 (diff) | |
| download | glibc-zack/build-layout-experiment.tar.gz glibc-zack/build-layout-experiment.tar.xz glibc-zack/build-layout-experiment.zip | |
Prepare for radical source tree reorganization. zack/build-layout-experiment
All top-level files and directories are moved into a temporary storage directory, REORG.TODO, except for files that will certainly still exist in their current form at top level when we're done (COPYING, COPYING.LIB, LICENSES, NEWS, README), all old ChangeLog files (which are moved to the new directory OldChangeLogs, instead), and the generated file INSTALL (which is just deleted; in the new order, there will be no generated files checked into version control).
Diffstat (limited to 'REORG.TODO/sysdeps/ia64/fpu/libm_lgamma.S')
| -rw-r--r-- | REORG.TODO/sysdeps/ia64/fpu/libm_lgamma.S | 3623 |
1 files changed, 3623 insertions, 0 deletions
diff --git a/REORG.TODO/sysdeps/ia64/fpu/libm_lgamma.S b/REORG.TODO/sysdeps/ia64/fpu/libm_lgamma.S new file mode 100644 index 0000000000..6096319ba5 --- /dev/null +++ b/REORG.TODO/sysdeps/ia64/fpu/libm_lgamma.S @@ -0,0 +1,3623 @@ +.file "libm_lgamma.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 error tag numbers +// 02/04/02 Added support of SIGN(GAMMA(x)) calculation +// 05/20/02 Cleaned up namespace and sf0 syntax +// 09/15/02 Fixed bug on the branch lgamma_negrecursion +// 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_lgamma(double 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-f122 +// +// General Purpose Registers: +// r8-r11 +// r14-r31 +// r32-r36 +// r37-r40 (Used to pass arguments to error handling routine) +// +// Predicate Registers: p6-p15 +// +//********************************************************************* +// +// IEEE Special Conditions: +// +// __libm_lgamma(+inf) = +inf +// __libm_lgamma(-inf) = QNaN +// __libm_lgamma(+/-0) = +inf +// __libm_lgamma(x<0, x - integer) = +inf +// __libm_lgamma(SNaN) = QNaN +// __libm_lgamma(QNaN) = QNaN +// +//********************************************************************* +// +// Overview +// +// The method consists of three cases. +// +// If 512 <= x < OVERFLOW_BOUNDARY use case lgamma_pstirling; +// else if 1 < x < 512 use case lgamma_regular; +// else if -17 < x < 1 use case lgamma_negrecursion; +// else if -512 < x < -17 use case lgamma_negpoly; +// else if x < -512 use case lgamma_negstirling; +// else if x is close to negative +// roots of ln(GAMMA(x)) use case lgamma_negroots; +// +// +// Case 512 <= 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 + (W2 + W4/x^2)/x +// +// Case 1 < x < 512 +// ---------------- +// To calculate GAMMA(x) on this interval we use polynomial approximation +// on following intervals [0.875; 1.25), [1.25; 1.75), [1.75, 2.25), +// [2.25; 4), [2^i; 2^(i+1)), i=2..8 +// +// Following variants of approximation and argument reduction are used: +// 1. [0.875; 1.25) +// ln(GAMMA(x)) ~ (x-1.0)*P17(x-1.0) +// +// 2. [1.25; 1.75) +// ln(GAMMA(x)) ~ (x-LocalMinimun)*P17(x-LocalMinimun) +// +// 3. [1.75, 2.25) +// ln(GAMMA(x)) ~ (x-2.0)*P17(x-2.0) +// +// 4. [2.25; 4) +// ln(GAMMA(x)) ~ P22(x) +// +// 5. [2^i; 2^(i+1)), i=2..8 +// ln(GAMMA(x)) ~ P22((x-2^i)/2^i) +// +// Case -17 < 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 -512 < x < -17 +// -------------------- +// 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 14-degree polynomial of r^2 +// +// +// Case x < -512 +// ------------- +// Here we use algorithm based on the Stirling formula: +// ln(GAMMA(-x)) = -ln(sqrt(2*Pi)) + (-x-0.5)ln(x) + x - (W2 + W4/x^2)/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. +// + +//********************************************************************* + +FR_X = f10 +FR_Y = f1 // __libm_lgamma is single argument function +FR_RESULT = f8 + +FR_B11 = f6 +FR_B10 = f7 + +FR_int_N = f9 +FR_N = f10 +FR_P5 = f11 +FR_P4 = f12 +FR_P3 = f13 +FR_P2 = f14 +FR_NormX = f15 + +FR_Ln2 = f32 +FR_C01 = f33 +FR_A17 = f33 +FR_C00 = f34 +FR_Xp2 = f34 +FR_A00 = f34 +FR_A16 = f34 +FR_C11 = f35 +FR_A15 = f35 +FR_C10 = f36 +FR_Xp3 = f36 +FR_A14 = f36 +FR_B1 = f36 +FR_C21 = f37 +FR_A13 = f37 +FR_PR01 = f37 +FR_C20 = f38 +FR_Xp6 = f38 +FR_A12 = f38 +FR_C31 = f39 +FR_Xp7 = f39 +FR_B0 = f39 +FR_A11 = f39 +FR_C30 = f40 +FR_Xp8 = f40 +FR_A10 = f40 +FR_PR00 = f40 +FR_C41 = f41 +FR_Xp9 = f41 +FR_A9 = f41 +FR_PR11 = f41 +FR_C40 = f42 +FR_A8 = f42 +FR_C51 = f43 +FR_Xp11 = f43 +FR_A7 = f43 +FR_C50 = f44 +FR_C = f44 +FR_Xp12 = f44 +FR_A6 = f44 +FR_Xm2 = f45 +FR_Xp13 = f45 +FR_A5 = f45 +FR_PR10 = f45 +FR_C61 = f46 +FR_Xp14 = f46 +FR_A4 = f46 +FR_PR21 = f46 +FR_C60 = f47 +FR_Xp15 = f47 +FR_A3 = f47 +FR_PR20 = f47 +FR_C71 = f48 +FR_Xp16 = f48 +FR_A2 = f48 +FR_PR31 = f48 +FR_C70 = f49 +FR_Xp17 = f49 +FR_A1 = f49 +FR_PR30 = f49 +FR_C81 = f50 +FR_B17 = f50 +FR_A0 = f50 +FR_C80 = f51 +FR_B16 = f51 +FR_C91 = f52 +FR_B15 = f52 +FR_C90 = f53 +FR_B14 = f53 +FR_CA1 = f54 +FR_B13 = f54 +FR_CA0 = f55 +FR_B12 = f55 +FR_CN = f56 +FR_Qlo = f56 +FR_PRN = f56 +FR_B7 = f57 +FR_B6 = f58 +FR_Qhi = f59 +FR_x = f60 +FR_x2 = f61 +FR_TpNxLn2 = f62 +FR_W2 = f63 +FR_x4 = f64 +FR_r4 = f64 +FR_x8 = f65 +FR_r8 = f65 +FR_r05 = f66 +FR_Xm05 = f66 +FR_B5 = f66 +FR_LnSqrt2Pi = f67 +FR_B4 = f67 +FR_InvX = f68 +FR_B3 = f68 +FR_InvX2 = f69 +FR_B2 = f69 +FR_W4 = f70 +FR_OvfBound = f71 +FR_05 = f72 +FR_LocalMin = f73 +FR_tmp = f73 +FR_LnX = f74 +FR_Xf = f75 +FR_InvXf = f76 +FR_rf = f77 +FR_rf2 = f78 +FR_P54f = f79 +FR_P32f = f80 +FR_rf3 = f81 +FR_P10f = f82 +FR_TpNxLn2f = f83 +FR_Nf = f84 +FR_LnXf = f85 +FR_int_Nf = f86 +FR_Tf = f87 +FR_Xf2 = f88 +FR_Xp10 = f89 +FR_w3 = f90 +FR_S28 = f90 +FR_w2 = f91 +FR_S26 = f91 +FR_w6 = f92 +FR_S24 = f92 +FR_w4 = f93 +FR_S22 = f93 +FR_w = f94 +FR_S20 = f94 +FR_Q8 = f95 +FR_S18 = f95 +FR_Q7 = f96 +FR_S16 = f96 +FR_Q4 = f97 +FR_S14 = f97 +FR_Q3 = f98 +FR_S12 = f98 +FR_Q6 = f99 +FR_S10 = f99 +FR_Q5 = f100 +FR_S8 = f100 +FR_Q2 = f101 +FR_S6 = f101 +FR_Root = f101 +FR_S4 = f102 +FR_Q1 = f102 +FR_S2 = f103 +FR_Xp1 = f104 +FR_Xf4 = f105 +FR_Xf8 = f106 +FR_Xfr = f107 +FR_Xf6 = f108 +FR_Ntrunc = f109 +FR_B9 = f110 +FR_2 = f110 +FR_B8 = f111 +FR_3 = f111 +FR_5 = f112 +FR_Xp4 = f113 +FR_Xp5 = f114 +FR_P54 = f115 +FR_P32 = f116 +FR_P10 = f117 +FR_r = f118 +FR_r2 = f119 +FR_r3 = f120 +FR_T = f121 +FR_int_Ntrunc = f122 + +//=================================== + +GR_TAG = r8 +GR_ExpMask = r8 +GR_ExpBias = r9 +GR_ad_Roots = r9 +GR_Expf = r10 +GR_Arg = r10 +GR_SignExp = r11 +GR_ArgXfr = r11 + +GR_Exp = r14 +GR_Arg125 = r14 +GR_RootInd = r14 +GR_ArgAsIs = r15 +GR_Arg175 = r15 +GR_Sig = r16 +GR_Ind = r17 +GR_ad_Dx = r17 +GR_ad_1 = r18 +GR_SignExp_w = r19 +GR_2_25 = r19 +GR_Arg025 = r19 +GR_Arg15 = r19 +GR_Arg17 = r19 +GR_Exp_w = r19//21 +GR_ad_2 = r20 +GR_2xDx = r21 +GR_SignOfGamma = r21 +GR_fff9 = r22 +GR_Offs = r22 +GR_ad_Co7 = r23 +GR_Arg075 = r23 +GR_Arg0875 = r23 +GR_ad_T = r24 +GR_ad_Root = r24 +GR_Ind = r24 +GR_ad_Co = r25 +GR_ad_Ce = r26 +GR_ad_Ce7 = r27 +GR_Arg05 = r27 +GR_Offs7 = r28 +GR_ArgXfrAsIs = r28 +GR_ExpOf2 = r29 +GR_ad_LnT = r29 +GR_Dx = r29 +GR_ExpOf256 = r30 +GR_0x30033 = r30 +GR_Root = r30 +GR_PseudoRoot = r30 +GR_ad_Data = r31 +GR_ad_SignGam = 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 + + + +// Data tables +//============================================================== + +RODATA +.align 16 +LOCAL_OBJECT_START(lgamma_data) +// polynomial approximation of ln(GAMMA(x)), 2.25 <= x < 512 +// [2.25; 4) +data8 0xF888E8D7892718A2,0xC001 // C01 +data8 0xF62F273BA12A4639,0x3FFD // C11 +data8 0xA93AC50A37EC8D38,0xBFFC // C21 +data8 0xB4CC43D2C161E057,0xBFFF // C31 +data8 0xC6AC672F0C1392C7,0xC000 // C41 +data8 0xA292B9AE3276942E,0xC001 // C51 +data8 0xE554E4CCCA6C7B7B,0xC001 // C61 +data8 0x92F0F55FBC87F860,0xC002 // C71 +data8 0xAF60D0112843F6C1,0xC002 // C81 +data8 0xC5956500FA3D92E7,0xC002 // C91 +data8 0xD3B22CCBD8587750,0xC002 // CA1 +data8 0xD888B6CF34159B54,0x4001 // C00 +data8 0xBCB79C8329FD9F44,0x3FFE // C10 +data8 0xCB8896FAD69C455D,0x4000 // C20 +data8 0xE510A424639EBF5E,0x4001 // C30 +data8 0xC65ED41B097486B3,0x4002 // C40 +// [4; 8) +data8 0x9F1F3C822D03080E,0xC001 // C01 +data8 0x941CACFA9C0FA8A6,0xC001 // C11 +data8 0xFE34336391D99CB7,0xC000 // C21 +data8 0xC40BAEAA165F81A1,0xC000 // C31 +data8 0xFE3AE166E9B4DE8F,0xBFFF // C41 +data8 0xD744F91AF7DAF873,0xBFFE // C51 +data8 0x87871851E9C32D02,0x3FFD // C61 +data8 0x9C93C03C502E808F,0x3FFF // C71 +data8 0xF78BED07501D6A8E,0x3FFF // C81 +data8 0x92FE41BA8BEADF70,0x4000 // C91 +data8 0xA021878E1903A2C6,0x3FFF // CA1 +data8 0xC85EFAC379FAFEE2,0x4001 // C00 +data8 0xC10D7AAB7CEC7FF2,0x4001 // C10 +data8 0xB3537BDF603E454C,0x4001 // C20 +data8 0xA0D44E3D5BBE44C4,0x4001 // C30 +data8 0x8B9C229B6241E7B3,0x4001 // C40 +// [8; 16) +data8 0xD16AB33AEC220DF6,0x3FFF // C01 +data8 0x987483646E150BCD,0x4000 // C11 +data8 0x80C10A24C863999B,0x4000 // C21 +data8 0xA39A8EB6F8AACE75,0x3FFF // C31 +data8 0x93E04A1379BEC764,0x3FFD // C41 +data8 0xD9F59C4BD3A69BD1,0xBFFE // C51 +data8 0x82094EC891179B1A,0xC000 // C61 +data8 0xC90CFE3A24F70659,0xC000 // C71 +data8 0x827984EA7C155184,0xC001 // C81 +data8 0x981BFDF79D1E0D80,0xC001 // C91 +data8 0xA37209A8B97D230D,0xC001 // CA1 +data8 0xAA1989737D6BA66D,0x3FFE // C00 +data8 0xDBC013A351630AF8,0x3FFF // C10 +data8 0x8B8D47698299389D,0x4000 // C20 +data8 0xACCDD1315DE06EB0,0x4000 // C30 +data8 0xD3414A5AC81BBB2D,0x4000 // C40 +// [16; 32) +data8 0xECB2B0BE75C5F995,0x3FFF // C01 +data8 0x9DD28BD6DBC96500,0x4000 // C11 +data8 0x8521431B99C6244F,0x4000 // C21 +data8 0xA95F92612B8413C3,0x3FFF // C31 +data8 0x9C76E643B22D9544,0x3FFD // C41 +data8 0xDD90EA99417C8038,0xBFFE // C51 +data8 0x84EA6B6D32E5F906,0xC000 // C61 +data8 0xCDBFE499E05AA622,0xC000 // C71 +data8 0x8594A7DE35427100,0xC001 // C81 +data8 0x9BC1CB2C10DC702F,0xC001 // C91 +data8 0xA7602268762666B0,0xC001 // CA1 +data8 0xDA082BCC6BDB8F7B,0x3FFE // C00 +data8 0xEEBFE1C99322B85E,0x3FFF // C10 +data8 0x96FED4C785361946,0x4000 // C20 +data8 0xB9E3A7207C16B2FE,0x4000 // C30 +data8 0xE1E8170CED48E2C7,0x4000 // C40 +// [32; 64) +data8 0xFD481EB9AEDD53E7,0x3FFF // C01 +data8 0xA216FB66AC8C53E1,0x4000 // C11 +data8 0x885FF935787553BA,0x4000 // C21 +data8 0xAD471CD89A313327,0x3FFF // C31 +data8 0x9FF13FBA139D21E0,0x3FFD // C41 +data8 0xE25E1663A6EE0266,0xBFFE // C51 +data8 0x87BE51DD5D262FA2,0xC000 // C61 +data8 0xD211A9D4CCE55696,0xC000 // C71 +data8 0x885BEFC29FDED3C9,0xC001 // C81 +data8 0x9EFA48E6367A67F6,0xC001 // C91 +data8 0xAAD3978FC0791297,0xC001 // CA1 +data8 0xF96D210DF37A0AEA,0x3FFE // C00 +data8 0xFE11DC6783917C82,0x3FFF // C10 +data8 0x9FFCD928291B7DDE,0x4000 // C20 +data8 0xC4518F4A80E09AE1,0x4000 // C30 +data8 0xEDDFE9E0FD297C63,0x4000 // C40 +// [64; 128) +data8 0x840E2E62609B0AD3,0x4000 // C01 +data8 0xA5275A0DD0D3DDF8,0x4000 // C11 +data8 0x8AADC6ABFC441731,0x4000 // C21 +data8 0xB041C6696BE90E50,0x3FFF // C31 +data8 0xA4A8C9153F4B037E,0x3FFD // C41 +data8 0xE3C6A461A7B86736,0xBFFE // C51 +data8 0x89047681C6DE7673,0xC000 // C61 +data8 0xD42DF77A480092DF,0xC000 // C71 +data8 0x89C25D17F086FB20,0xC001 // C81 +data8 0xA09F907D02E34EC7,0xC001 // C91 +data8 0xAC998A9CB79805B7,0xC001 // CA1 +data8 0x875CC9B69AE964CC,0x3FFF // C00 +data8 0x847836BA85DD4C12,0x4000 // C10 +data8 0xA5F3CB2B32E74936,0x4000 // C20 +data8 0xCAE2197C96CB5A0F,0x4000 // C30 +data8 0xF50F7EB60DE5CD09,0x4000 // C40 +// [128; 256) +data8 0x87D9065DD1876926,0x4000 // C01 +data8 0xA781C28FDAD7CC25,0x4000 // C11 +data8 0x8C6A4FCE35A7EC8D,0x4000 // C21 +data8 0xB27BA081728354F9,0x3FFF // C31 +data8 0xA82FEA7124B0EB2B,0x3FFD // C41 +data8 0xE4C996E42ECBF77A,0xBFFE // C51 +data8 0x89F1A92C84FA538F,0xC000 // C61 +data8 0xD5B6CFF7DB7F6070,0xC000 // C71 +data8 0x8AC6B561FAE38B66,0xC001 // C81 +data8 0xA1D1505C438D8F46,0xC001 // C91 +data8 0xADE2DC1C924FEC81,0xC001 // CA1 +data8 0x8EF6CC62A7E0EB5A,0x3FFF // C00 +data8 0x88A2FFC0ABCB00C0,0x4000 // C10 +data8 0xAA6EA8FCB75B065B,0x4000 // C20 +data8 0xCFC4B82B3D5C9363,0x4000 // C30 +data8 0xFA60FD85DE861771,0x4000 // C40 +// [256; 512) +data8 0x8AAA7CE4ED5C1EFD,0x4000 // C01 +data8 0xA9679234FB56F1E1,0x4000 // C11 +data8 0x8DCE02287789D841,0x4000 // C21 +data8 0xB44328EF30A8DE7E,0x3FFF // C31 +data8 0xAB0DC564BFA1AB12,0x3FFD // C41 +data8 0xE5882B16FCF2D3CB,0xBFFE // C51 +data8 0x8AA7F48993006A86,0xC000 // C61 +data8 0xD6E63752D192750D,0xC000 // C71 +data8 0x8B90080B17853295,0xC001 // C81 +data8 0xA2BDD4253128D1AB,0xC001 // C91 +data8 0xAEE1A042F96B8121,0xC001 // CA1 +data8 0x94A9C37A42E43BA7,0x3FFF // C00 +data8 0x8BFA54E703878F5A,0x4000 // C10 +data8 0xADFA426DDF14647B,0x4000 // C20 +data8 0xD39C7F7B3958EAF0,0x4000 // C30 +data8 0xFE8C3987853C01E3,0x4000 // C40 +// +// [2.25; 4) +data8 0x943AF77763601441,0x4003 // C50 +data8 0xC8A93F9ECB06E891,0x4003 // C60 +data8 0xFC2E5A4AD33DE19D,0x4003 // C70 +data8 0x9526B75B38670119,0x4004 // C80 +data8 0xA7675879D68B587E,0x4004 // C90 +data8 0xB31DFA672D7FB8C0,0x4004 // CA0 +data8 0x83A27775D86F9A81,0xBFD7 // CN +// [4; 8) +data8 0xEB8049BA5E79ADA3,0x4000 // C50 +data8 0xC20C95EA99037228,0x4000 // C60 +data8 0x9D4A8C864053CEB8,0x4000 // C70 +data8 0xFC7716544AB0C5C9,0x3FFF // C80 +data8 0xC7EB985259EABA5F,0x3FFF // C90 +data8 0xC042FB3B4C95096D,0x3FFD // CA0 +data8 0xCC2A7F930856177B,0x3FEE // CN +// [8; 16) +data8 0xFE1903679D078C7A,0x4000 // C50 +data8 0x957C221AB90171F1,0x4001 // C60 +data8 0xAB2C53B2A78F4031,0x4001 // C70 +data8 0xBE080AE6063AE387,0x4001 // C80 +data8 0xCC019A0311605CB9,0x4001 // C90 +data8 0xD3739D85A12C8ADF,0x4001 // CA0 +data8 0x81FA4D2B7BD7A82D,0x3FEF // CN +// [16; 32) +data8 0x871F69E2DD221F02,0x4001 // C50 +data8 0x9E3EF2D477442A9C,0x4001 // C60 +data8 0xB48733582B3C82C5,0x4001 // C70 +data8 0xC7DB9B3C25854A2A,0x4001 // C80 +data8 0xD628B87975BE898F,0x4001 // C90 +data8 0xDDC569C321FF119C,0x4001 // CA0 +data8 0xB27B65560DF7ADA7,0x3FEF // CN +// [32; 64) +data8 0x8DE4127349719B22,0x4001 // C50 +data8 0xA5C30A7760F5FBB2,0x4001 // C60 +data8 0xBCB4096055AA2A4E,0x4001 // C70 +data8 0xD08F5F2FB4E7B899,0x4001 // C80 +data8 0xDF39ED39DC91F9CF,0x4001 // C90 +data8 0xE7063E45322F072E,0x4001 // CA0 +data8 0x85A9E11DDDDE67C8,0x3FF0 // CN +// [64; 128) +data8 0x91CA191EB80E8893,0x4001 // C50 +data8 0xA9F1D5A55397334A,0x4001 // C60 +data8 0xC1222710295094E3,0x4001 // C70 +data8 0xD52FFABBA6CBE5C6,0x4001 // C80 +data8 0xE3FD9D5282052E1D,0x4001 // C90 +data8 0xEBDBE47BB662F3EF,0x4001 // CA0 +data8 0xEF889F489D88FD31,0x3FF0 // CN +// [128; 256) +data8 0x94AA029C2286F8D2,0x4001 // C50 +data8 0xAD0549E55A72389F,0x4001 // C60 +data8 0xC4628899DAF94BA4,0x4001 // C70 +data8 0xD89432A4161C72CB,0x4001 // C80 +data8 0xE77ABA75E9C38F3A,0x4001 // C90 +data8 0xEF65BFFFF71347FF,0x4001 // CA0 +data8 0xE2627460064D918D,0x3FF1 // CN +// [256; 512) +data8 0x96E9890D722C2FC1,0x4001 // C50 +data8 0xAF6C2236F6A1CEC4,0x4001 // C60 +data8 0xC6EBB8C9F987D20D,0x4001 // C70 +data8 0xDB38CEFD5EF328CC,0x4001 // C80 +data8 0xEA3265DC66C9A0B4,0x4001 // C90 +data8 0xF2272D6B368C70B1,0x4001 // CA0 +data8 0xDBFF93ECEBCEF1F3,0x3FF2 // CN +// +data8 0x3FDD8B618D5AF8FE // point of local minimum on [1;2] +data8 0x3FE0000000000000 // 0.5 +data8 0xBFC5555DA7212371 // P5 +data8 0x3FC999A19EEF5826 // P4 +data8 0xb17217f7d1cf79ac,0x3ffe // ln(2) +data8 0xEB3F8E4325F5A535,0x3FFE // ln(sqrt(4*arcsin(1))) +// +data8 0xBFCFFFFFFFFEF009 // P3 +data8 0x3FD555555554ECB2 // P2 +data8 0xBF66C16C16C16C17 // W4=B4/12=-1/360 +data8 0x7F5754D9278B51A8 // overflow boundary (first inf result) +data8 0xAAAAAAAAAAAAAAAB,0x3FFB // W2=B2/2=1/12 +// +data8 0x3FBC756AC654273B // Q8 +data8 0xBFC001A42489AB4D // Q7 +data8 0x3FC99999999A169B // Q4 +data8 0xBFD00000000019AC // Q3 +data8 0x3FC2492479AA0DF8 // Q6 +data8 0xBFC5555544986F52 // Q5 +data8 0x3FD5555555555555 // Q2 +data8 0xBFE0000000000000 // Q1, P1 = -0.5 +// +data8 0x80200aaeac44ef38,0x3ff6 // ln(1/frcpa(1+ 0/2^-8)) +data8 0xc09090a2c35aa070,0x3ff7 // ln(1/frcpa(1+ 1/2^-8)) +data8 0xa0c94fcb41977c75,0x3ff8 // ln(1/frcpa(1+ 2/2^-8)) +data8 0xe18b9c263af83301,0x3ff8 // ln(1/frcpa(1+ 3/2^-8)) +data8 0x8d35c8d6399c30ea,0x3ff9 // ln(1/frcpa(1+ 4/2^-8)) +data8 0xadd4d2ecd601cbb8,0x3ff9 // ln(1/frcpa(1+ 5/2^-8)) +data8 0xce95403a192f9f01,0x3ff9 // ln(1/frcpa(1+ 6/2^-8)) +data8 0xeb59392cbcc01096,0x3ff9 // ln(1/frcpa(1+ 7/2^-8)) +data8 0x862c7d0cefd54c5d,0x3ffa // ln(1/frcpa(1+ 8/2^-8)) +data8 0x94aa63c65e70d499,0x3ffa // ln(1/frcpa(1+ 9/2^-8)) +data8 0xa54a696d4b62b382,0x3ffa // ln(1/frcpa(1+ 10/2^-8)) +data8 0xb3e4a796a5dac208,0x3ffa // ln(1/frcpa(1+ 11/2^-8)) +data8 0xc28c45b1878340a9,0x3ffa // ln(1/frcpa(1+ 12/2^-8)) +data8 0xd35c55f39d7a6235,0x3ffa // ln(1/frcpa(1+ 13/2^-8)) +data8 0xe220f037b954f1f5,0x3ffa // ln(1/frcpa(1+ 14/2^-8)) +data8 0xf0f3389b036834f3,0x3ffa // ln(1/frcpa(1+ 15/2^-8)) +data8 0xffd3488d5c980465,0x3ffa // ln(1/frcpa(1+ 16/2^-8)) +data8 0x87609ce2ed300490,0x3ffb // ln(1/frcpa(1+ 17/2^-8)) +data8 0x8ede9321e8c85927,0x3ffb // ln(1/frcpa(1+ 18/2^-8)) +data8 0x96639427f2f8e2f4,0x3ffb // ln(1/frcpa(1+ 19/2^-8)) +data8 0x9defad3e8f73217b,0x3ffb // ln(1/frcpa(1+ 20/2^-8)) +data8 0xa582ebd50097029c,0x3ffb // ln(1/frcpa(1+ 21/2^-8)) +data8 0xac06dbe75ab80fee,0x3ffb // ln(1/frcpa(1+ 22/2^-8)) +data8 0xb3a78449b2d3ccca,0x3ffb // ln(1/frcpa(1+ 23/2^-8)) +data8 0xbb4f79635ab46bb2,0x3ffb // ln(1/frcpa(1+ 24/2^-8)) +data8 0xc2fec93a83523f3f,0x3ffb // ln(1/frcpa(1+ 25/2^-8)) +data8 0xc99af2eaca4c4571,0x3ffb // ln(1/frcpa(1+ 26/2^-8)) +data8 0xd1581106472fa653,0x3ffb // ln(1/frcpa(1+ 27/2^-8)) +data8 0xd8002560d4355f2e,0x3ffb // ln(1/frcpa(1+ 28/2^-8)) +data8 0xdfcb43b4fe508632,0x3ffb // ln(1/frcpa(1+ 29/2^-8)) +data8 0xe67f6dff709d4119,0x3ffb // ln(1/frcpa(1+ 30/2^-8)) +data8 0xed393b1c22351280,0x3ffb // ln(1/frcpa(1+ 31/2^-8)) +data8 0xf5192bff087bcc35,0x3ffb // ln(1/frcpa(1+ 32/2^-8)) +data8 0xfbdf4ff6dfef2fa3,0x3ffb // ln(1/frcpa(1+ 33/2^-8)) +data8 0x81559a97f92f9cc7,0x3ffc // ln(1/frcpa(1+ 34/2^-8)) +data8 0x84be72bce90266e8,0x3ffc // ln(1/frcpa(1+ 35/2^-8)) +data8 0x88bc74113f23def2,0x3ffc // ln(1/frcpa(1+ 36/2^-8)) +data8 0x8c2ba3edf6799d11,0x3ffc // ln(1/frcpa(1+ 37/2^-8)) +data8 0x8f9dc92f92ea08b1,0x3ffc // ln(1/frcpa(1+ 38/2^-8)) +data8 0x9312e8f36efab5a7,0x3ffc // ln(1/frcpa(1+ 39/2^-8)) +data8 0x968b08643409ceb6,0x3ffc // ln(1/frcpa(1+ 40/2^-8)) +data8 0x9a062cba08a1708c,0x3ffc // ln(1/frcpa(1+ 41/2^-8)) +data8 0x9d845b3abf95485c,0x3ffc // ln(1/frcpa(1+ 42/2^-8)) +data8 0xa06fd841bc001bb4,0x3ffc // ln(1/frcpa(1+ 43/2^-8)) +data8 0xa3f3a74652fbe0db,0x3ffc // ln(1/frcpa(1+ 44/2^-8)) +data8 0xa77a8fb2336f20f5,0x3ffc // ln(1/frcpa(1+ 45/2^-8)) +data8 0xab0497015d28b0a0,0x3ffc // ln(1/frcpa(1+ 46/2^-8)) +data8 0xae91c2be6ba6a615,0x3ffc // ln(1/frcpa(1+ 47/2^-8)) +data8 0xb189d1b99aebb20b,0x3ffc // ln(1/frcpa(1+ 48/2^-8)) +data8 0xb51cced5de9c1b2c,0x3ffc // ln(1/frcpa(1+ 49/2^-8)) +data8 0xb819bee9e720d42f,0x3ffc // ln(1/frcpa(1+ 50/2^-8)) +data8 0xbbb2a0947b093a5d,0x3ffc // ln(1/frcpa(1+ 51/2^-8)) +data8 0xbf4ec1505811684a,0x3ffc // ln(1/frcpa(1+ 52/2^-8)) +data8 0xc2535bacfa8975ff,0x3ffc // ln(1/frcpa(1+ 53/2^-8)) +data8 0xc55a3eafad187eb8,0x3ffc // ln(1/frcpa(1+ 54/2^-8)) +data8 0xc8ff2484b2c0da74,0x3ffc // ln(1/frcpa(1+ 55/2^-8)) +data8 0xcc0b1a008d53ab76,0x3ffc // ln(1/frcpa(1+ 56/2^-8)) +data8 0xcfb6203844b3209b,0x3ffc // ln(1/frcpa(1+ 57/2^-8)) +data8 0xd2c73949a47a19f5,0x3ffc // ln(1/frcpa(1+ 58/2^-8)) +data8 0xd5daae18b49d6695,0x3ffc // ln(1/frcpa(1+ 59/2^-8)) +data8 0xd8f08248cf7e8019,0x3ffc // ln(1/frcpa(1+ 60/2^-8)) +data8 0xdca7749f1b3e540e,0x3ffc // ln(1/frcpa(1+ 61/2^-8)) +data8 0xdfc28e033aaaf7c7,0x3ffc // ln(1/frcpa(1+ 62/2^-8)) +data8 0xe2e012a5f91d2f55,0x3ffc // ln(1/frcpa(1+ 63/2^-8)) +data8 0xe600064ed9e292a8,0x3ffc // ln(1/frcpa(1+ 64/2^-8)) +data8 0xe9226cce42b39f60,0x3ffc // ln(1/frcpa(1+ 65/2^-8)) +data8 0xec4749fd97a28360,0x3ffc // ln(1/frcpa(1+ 66/2^-8)) +data8 0xef6ea1bf57780495,0x3ffc // ln(1/frcpa(1+ 67/2^-8)) +data8 0xf29877ff38809091,0x3ffc // ln(1/frcpa(1+ 68/2^-8)) +data8 0xf5c4d0b245cb89be,0x3ffc // ln(1/frcpa(1+ 69/2^-8)) +data8 0xf8f3afd6fcdef3aa,0x3ffc // ln(1/frcpa(1+ 70/2^-8)) +data8 0xfc2519756be1abc7,0x3ffc // ln(1/frcpa(1+ 71/2^-8)) +data8 0xff59119f503e6832,0x3ffc // ln(1/frcpa(1+ 72/2^-8)) +data8 0x8147ce381ae0e146,0x3ffd // ln(1/frcpa(1+ 73/2^-8)) +data8 0x82e45f06cb1ad0f2,0x3ffd // ln(1/frcpa(1+ 74/2^-8)) +data8 0x842f5c7c573cbaa2,0x3ffd // ln(1/frcpa(1+ 75/2^-8)) +data8 0x85ce471968c8893a,0x3ffd // ln(1/frcpa(1+ 76/2^-8)) +data8 0x876e8305bc04066d,0x3ffd // ln(1/frcpa(1+ 77/2^-8)) +data8 0x891012678031fbb3,0x3ffd // ln(1/frcpa(1+ 78/2^-8)) +data8 0x8a5f1493d766a05f,0x3ffd // ln(1/frcpa(1+ 79/2^-8)) +data8 0x8c030c778c56fa00,0x3ffd // ln(1/frcpa(1+ 80/2^-8)) +data8 0x8da85df17e31d9ae,0x3ffd // ln(1/frcpa(1+ 81/2^-8)) +data8 0x8efa663e7921687e,0x3ffd // ln(1/frcpa(1+ 82/2^-8)) +data8 0x90a22b6875c6a1f8,0x3ffd // ln(1/frcpa(1+ 83/2^-8)) +data8 0x91f62cc8f5d24837,0x3ffd // ln(1/frcpa(1+ 84/2^-8)) +data8 0x93a06cfc3857d980,0x3ffd // ln(1/frcpa(1+ 85/2^-8)) +data8 0x94f66d5e6fd01ced,0x3ffd // ln(1/frcpa(1+ 86/2^-8)) +data8 0x96a330156e6772f2,0x3ffd // ln(1/frcpa(1+ 87/2^-8)) +data8 0x97fb3582754ea25b,0x3ffd // ln(1/frcpa(1+ 88/2^-8)) +data8 0x99aa8259aad1bbf2,0x3ffd // ln(1/frcpa(1+ 89/2^-8)) +data8 0x9b0492f6227ae4a8,0x3ffd // ln(1/frcpa(1+ 90/2^-8)) +data8 0x9c5f8e199bf3a7a5,0x3ffd // ln(1/frcpa(1+ 91/2^-8)) +data8 0x9e1293b9998c1daa,0x3ffd // ln(1/frcpa(1+ 92/2^-8)) +data8 0x9f6fa31e0b41f308,0x3ffd // ln(1/frcpa(1+ 93/2^-8)) +data8 0xa0cda11eaf46390e,0x3ffd // ln(1/frcpa(1+ 94/2^-8)) +data8 0xa22c8f029cfa45aa,0x3ffd // ln(1/frcpa(1+ 95/2^-8)) +data8 0xa3e48badb7856b34,0x3ffd // ln(1/frcpa(1+ 96/2^-8)) +data8 0xa5459a0aa95849f9,0x3ffd // ln(1/frcpa(1+ 97/2^-8)) +data8 0xa6a79c84480cfebd,0x3ffd // ln(1/frcpa(1+ 98/2^-8)) +data8 0xa80a946d0fcb3eb2,0x3ffd // ln(1/frcpa(1+ 99/2^-8)) +data8 0xa96e831a3ea7b314,0x3ffd // ln(1/frcpa(1+100/2^-8)) +data8 0xaad369e3dc544e3b,0x3ffd // ln(1/frcpa(1+101/2^-8)) +data8 0xac92e9588952c815,0x3ffd // ln(1/frcpa(1+102/2^-8)) +data8 0xadfa035aa1ed8fdc,0x3ffd // ln(1/frcpa(1+103/2^-8)) +data8 0xaf6219eae1ad6e34,0x3ffd // ln(1/frcpa(1+104/2^-8)) +data8 0xb0cb2e6d8160f753,0x3ffd // ln(1/frcpa(1+105/2^-8)) +data8 0xb2354249ad950f72,0x3ffd // ln(1/frcpa(1+106/2^-8)) +data8 0xb3a056e98ef4a3b4,0x3ffd // ln(1/frcpa(1+107/2^-8)) +data8 0xb50c6dba52c6292a,0x3ffd // ln(1/frcpa(1+108/2^-8)) +data8 0xb679882c33876165,0x3ffd // ln(1/frcpa(1+109/2^-8)) +data8 0xb78c07429785cedc,0x3ffd // ln(1/frcpa(1+110/2^-8)) +data8 0xb8faeb8dc4a77d24,0x3ffd // ln(1/frcpa(1+111/2^-8)) +data8 0xba6ad77eb36ae0d6,0x3ffd // ln(1/frcpa(1+112/2^-8)) +data8 0xbbdbcc915e9bee50,0x3ffd // ln(1/frcpa(1+113/2^-8)) +data8 0xbd4dcc44f8cf12ef,0x3ffd // ln(1/frcpa(1+114/2^-8)) +data8 0xbec0d81bf5b531fa,0x3ffd // ln(1/frcpa(1+115/2^-8)) +data8 0xc034f19c139186f4,0x3ffd // ln(1/frcpa(1+116/2^-8)) +data8 0xc14cb69f7c5e55ab,0x3ffd // ln(1/frcpa(1+117/2^-8)) +data8 0xc2c2abbb6e5fd56f,0x3ffd // ln(1/frcpa(1+118/2^-8)) +data8 0xc439b2c193e6771e,0x3ffd // ln(1/frcpa(1+119/2^-8)) +data8 0xc553acb9d5c67733,0x3ffd // ln(1/frcpa(1+120/2^-8)) +data8 0xc6cc96e441272441,0x3ffd // ln(1/frcpa(1+121/2^-8)) +data8 0xc8469753eca88c30,0x3ffd // ln(1/frcpa(1+122/2^-8)) +data8 0xc962cf3ce072b05c,0x3ffd // ln(1/frcpa(1+123/2^-8)) +data8 0xcadeba8771f694aa,0x3ffd // ln(1/frcpa(1+124/2^-8)) +data8 0xcc5bc08d1f72da94,0x3ffd // ln(1/frcpa(1+125/2^-8)) +data8 0xcd7a3f99ea035c29,0x3ffd // ln(1/frcpa(1+126/2^-8)) +data8 0xcef93860c8a53c35,0x3ffd // ln(1/frcpa(1+127/2^-8)) +data8 0xd0192f68a7ed23df,0x3ffd // ln(1/frcpa(1+128/2^-8)) +data8 0xd19a201127d3c645,0x3ffd // ln(1/frcpa(1+129/2^-8)) +data8 0xd2bb92f4061c172c,0x3ffd // ln(1/frcpa(1+130/2^-8)) +data8 0xd43e80b2ee8cc8fc,0x3ffd // ln(1/frcpa(1+131/2^-8)) +data8 0xd56173601fc4ade4,0x3ffd // ln(1/frcpa(1+132/2^-8)) +data8 0xd6e6637efb54086f,0x3ffd // ln(1/frcpa(1+133/2^-8)) +data8 0xd80ad9f58f3c8193,0x3ffd // ln(1/frcpa(1+134/2^-8)) +data8 0xd991d1d31aca41f8,0x3ffd // ln(1/frcpa(1+135/2^-8)) +data8 0xdab7d02231484a93,0x3ffd // ln(1/frcpa(1+136/2^-8)) +data8 0xdc40d532cde49a54,0x3ffd // ln(1/frcpa(1+137/2^-8)) +data8 0xdd685f79ed8b265e,0x3ffd // ln(1/frcpa(1+138/2^-8)) +data8 0xde9094bbc0e17b1d,0x3ffd // ln(1/frcpa(1+139/2^-8)) +data8 0xe01c91b78440c425,0x3ffd // ln(1/frcpa(1+140/2^-8)) +data8 0xe14658f26997e729,0x3ffd // ln(1/frcpa(1+141/2^-8)) +data8 0xe270cdc2391e0d23,0x3ffd // ln(1/frcpa(1+142/2^-8)) +data8 0xe3ffce3a2aa64922,0x3ffd // ln(1/frcpa(1+143/2^-8)) +data8 0xe52bdb274ed82887,0x3ffd // ln(1/frcpa(1+144/2^-8)) +data8 0xe6589852e75d7df6,0x3ffd // ln(1/frcpa(1+145/2^-8)) +data8 0xe786068c79937a7d,0x3ffd // ln(1/frcpa(1+146/2^-8)) +data8 0xe91903adad100911,0x3ffd // ln(1/frcpa(1+147/2^-8)) +data8 0xea481236f7d35bb0,0x3ffd // ln(1/frcpa(1+148/2^-8)) +data8 0xeb77d48c692e6b14,0x3ffd // ln(1/frcpa(1+149/2^-8)) +data8 0xeca84b83d7297b87,0x3ffd // ln(1/frcpa(1+150/2^-8)) +data8 0xedd977f4962aa158,0x3ffd // ln(1/frcpa(1+151/2^-8)) +data8 0xef7179a22f257754,0x3ffd // ln(1/frcpa(1+152/2^-8)) +data8 0xf0a450d139366ca7,0x3ffd // ln(1/frcpa(1+153/2^-8)) +data8 0xf1d7e0524ff9ffdb,0x3ffd // ln(1/frcpa(1+154/2^-8)) +data8 0xf30c29036a8b6cae,0x3ffd // ln(1/frcpa(1+155/2^-8)) +data8 0xf4412bc411ea8d92,0x3ffd // ln(1/frcpa(1+156/2^-8)) +data8 0xf576e97564c8619d,0x3ffd // ln(1/frcpa(1+157/2^-8)) +data8 0xf6ad62fa1b5f172f,0x3ffd // ln(1/frcpa(1+158/2^-8)) +data8 0xf7e499368b55c542,0x3ffd // ln(1/frcpa(1+159/2^-8)) +data8 0xf91c8d10abaffe22,0x3ffd // ln(1/frcpa(1+160/2^-8)) +data8 0xfa553f7018c966f3,0x3ffd // ln(1/frcpa(1+161/2^-8)) +data8 0xfb8eb13e185d802c,0x3ffd // ln(1/frcpa(1+162/2^-8)) +data8 0xfcc8e3659d9bcbed,0x3ffd // ln(1/frcpa(1+163/2^-8)) +data8 0xfe03d6d34d487fd2,0x3ffd // ln(1/frcpa(1+164/2^-8)) +data8 0xff3f8c7581e9f0ae,0x3ffd // ln(1/frcpa(1+165/2^-8)) +data8 0x803e029e280173ae,0x3ffe // ln(1/frcpa(1+166/2^-8)) +data8 0x80dca10cc52d0757,0x3ffe // ln(1/frcpa(1+167/2^-8)) +data8 0x817ba200632755a1,0x3ffe // ln(1/frcpa(1+168/2^-8)) +data8 0x821b05f3b01d6774,0x3ffe // ln(1/frcpa(1+169/2^-8)) +data8 0x82bacd623ff19d06,0x3ffe // ln(1/frcpa(1+170/2^-8)) +data8 0x835af8c88e7a8f47,0x3ffe // ln(1/frcpa(1+171/2^-8)) +data8 0x83c5f8299e2b4091,0x3ffe // ln(1/frcpa(1+172/2^-8)) +data8 0x8466cb43f3d87300,0x3ffe // ln(1/frcpa(1+173/2^-8)) +data8 0x850803a67c80ca4b,0x3ffe // ln(1/frcpa(1+174/2^-8)) +data8 0x85a9a1d11a23b461,0x3ffe // ln(1/frcpa(1+175/2^-8)) +data8 0x864ba644a18e6e05,0x3ffe // ln(1/frcpa(1+176/2^-8)) +data8 0x86ee1182dcc432f7,0x3ffe // ln(1/frcpa(1+177/2^-8)) +data8 0x875a925d7e48c316,0x3ffe // ln(1/frcpa(1+178/2^-8)) +data8 0x87fdaa109d23aef7,0x3ffe // ln(1/frcpa(1+179/2^-8)) +data8 0x88a129ed4becfaf2,0x3ffe // ln(1/frcpa(1+180/2^-8)) +data8 0x89451278ecd7f9cf,0x3ffe // ln(1/frcpa(1+181/2^-8)) +data8 0x89b29295f8432617,0x3ffe // ln(1/frcpa(1+182/2^-8)) +data8 0x8a572ac5a5496882,0x3ffe // ln(1/frcpa(1+183/2^-8)) +data8 0x8afc2d0ce3b2dadf,0x3ffe // ln(1/frcpa(1+184/2^-8)) +data8 0x8b6a69c608cfd3af,0x3ffe // ln(1/frcpa(1+185/2^-8)) +data8 0x8c101e106e899a83,0x3ffe // ln(1/frcpa(1+186/2^-8)) +data8 0x8cb63de258f9d626,0x3ffe // ln(1/frcpa(1+187/2^-8)) +data8 0x8d2539c5bd19e2b1,0x3ffe // ln(1/frcpa(1+188/2^-8)) +data8 0x8dcc0e064b29e6f1,0x3ffe // ln(1/frcpa(1+189/2^-8)) +data8 0x8e734f45d88357ae,0x3ffe // ln(1/frcpa(1+190/2^-8)) +data8 0x8ee30cef034a20db,0x3ffe // ln(1/frcpa(1+191/2^-8)) +data8 0x8f8b0515686d1d06,0x3ffe // ln(1/frcpa(1+192/2^-8)) +data8 0x90336bba039bf32f,0x3ffe // ln(1/frcpa(1+193/2^-8)) +data8 0x90a3edd23d1c9d58,0x3ffe // ln(1/frcpa(1+194/2^-8)) +data8 0x914d0de2f5d61b32,0x3ffe // ln(1/frcpa(1+195/2^-8)) +data8 0x91be0c20d28173b5,0x3ffe // ln(1/frcpa(1+196/2^-8)) +data8 0x9267e737c06cd34a,0x3ffe // ln(1/frcpa(1+197/2^-8)) +data8 0x92d962ae6abb1237,0x3ffe // ln(1/frcpa(1+198/2^-8)) +data8 0x9383fa6afbe2074c,0x3ffe // ln(1/frcpa(1+199/2^-8)) +data8 0x942f0421651c1c4e,0x3ffe // ln(1/frcpa(1+200/2^-8)) +data8 0x94a14a3845bb985e,0x3ffe // ln(1/frcpa(1+201/2^-8)) +data8 0x954d133857f861e7,0x3ffe // ln(1/frcpa(1+202/2^-8)) +data8 0x95bfd96468e604c4,0x3ffe // ln(1/frcpa(1+203/2^-8)) +data8 0x9632d31cafafa858,0x3ffe // ln(1/frcpa(1+204/2^-8)) +data8 0x96dfaabd86fa1647,0x3ffe // ln(1/frcpa(1+205/2^-8)) +data8 0x9753261fcbb2a594,0x3ffe // ln(1/frcpa(1+206/2^-8)) +data8 0x9800c11b426b996d,0x3ffe // ln(1/frcpa(1+207/2^-8)) +data8 0x9874bf4d45ae663c,0x3ffe // ln(1/frcpa(1+208/2^-8)) +data8 0x99231f5ee9a74f79,0x3ffe // ln(1/frcpa(1+209/2^-8)) +data8 0x9997a18a56bcad28,0x3ffe // ln(1/frcpa(1+210/2^-8)) +data8 0x9a46c873a3267e79,0x3ffe // ln(1/frcpa(1+211/2^-8)) +data8 0x9abbcfc621eb6cb6,0x3ffe // ln(1/frcpa(1+212/2^-8)) +data8 0x9b310cb0d354c990,0x3ffe // ln(1/frcpa(1+213/2^-8)) +data8 0x9be14cf9e1b3515c,0x3ffe // ln(1/frcpa(1+214/2^-8)) +data8 0x9c5710b8cbb73a43,0x3ffe // ln(1/frcpa(1+215/2^-8)) +data8 0x9ccd0abd301f399c,0x3ffe // ln(1/frcpa(1+216/2^-8)) +data8 0x9d7e67f3bdce8888,0x3ffe // ln(1/frcpa(1+217/2^-8)) +data8 0x9df4ea81a99daa01,0x3ffe // ln(1/frcpa(1+218/2^-8)) +data8 0x9e6ba405a54514ba,0x3ffe // ln(1/frcpa(1+219/2^-8)) +data8 0x9f1e21c8c7bb62b3,0x3ffe // ln(1/frcpa(1+220/2^-8)) +data8 0x9f956593f6b6355c,0x3ffe // ln(1/frcpa(1+221/2^-8)) +data8 0xa00ce1092e5498c3,0x3ffe // ln(1/frcpa(1+222/2^-8)) +data8 0xa0c08309c4b912c1,0x3ffe // ln(1/frcpa(1+223/2^-8)) +data8 0xa1388a8c6faa2afa,0x3ffe // ln(1/frcpa(1+224/2^-8)) +data8 0xa1b0ca7095b5f985,0x3ffe // ln(1/frcpa(1+225/2^-8)) +data8 0xa22942eb47534a00,0x3ffe // ln(1/frcpa(1+226/2^-8)) +data8 0xa2de62326449d0a3,0x3ffe // ln(1/frcpa(1+227/2^-8)) +data8 0xa357690f88bfe345,0x3ffe // ln(1/frcpa(1+228/2^-8)) +data8 0xa3d0a93f45169a4b,0x3ffe // ln(1/frcpa(1+229/2^-8)) +data8 0xa44a22f7ffe65f30,0x3ffe // ln(1/frcpa(1+230/2^-8)) +data8 0xa500c5e5b4c1aa36,0x3ffe // ln(1/frcpa(1+231/2^-8)) +data8 0xa57ad064eb2ebbc2,0x3ffe // ln(1/frcpa(1+232/2^-8)) +data8 0xa5f5152dedf4384e,0x3ffe // ln(1/frcpa(1+233/2^-8)) +data8 0xa66f9478856233ec,0x3ffe // ln(1/frcpa(1+234/2^-8)) +data8 0xa6ea4e7cca02c32e,0x3ffe // ln(1/frcpa(1+235/2^-8)) +data8 0xa765437325341ccf,0x3ffe // ln(1/frcpa(1+236/2^-8)) +data8 0xa81e21e6c75b4020,0x3ffe // ln(1/frcpa(1+237/2^-8)) +data8 0xa899ab333fe2b9ca,0x3ffe // ln(1/frcpa(1+238/2^-8)) +data8 0xa9157039c51ebe71,0x3ffe // ln(1/frcpa(1+239/2^-8)) +data8 0xa991713433c2b999,0x3ffe // ln(1/frcpa(1+240/2^-8)) +data8 0xaa0dae5cbcc048b3,0x3ffe // ln(1/frcpa(1+241/2^-8)) +data8 0xaa8a27ede5eb13ad,0x3ffe // ln(1/frcpa(1+242/2^-8)) +data8 0xab06de228a9e3499,0x3ffe // ln(1/frcpa(1+243/2^-8)) +data8 0xab83d135dc633301,0x3ffe // ln(1/frcpa(1+244/2^-8)) +data8 0xac3fb076adc7fe7a,0x3ffe // ln(1/frcpa(1+245/2^-8)) +data8 0xacbd3cbbe47988f1,0x3ffe // ln(1/frcpa(1+246/2^-8)) +data8 0xad3b06b1a5dc57c3,0x3ffe // ln(1/frcpa(1+247/2^-8)) +data8 0xadb90e94af887717,0x3ffe // ln(1/frcpa(1+248/2^-8)) +data8 0xae3754a218f7c816,0x3ffe // ln(1/frcpa(1+249/2^-8)) +data8 0xaeb5d9175437afa2,0x3ffe // ln(1/frcpa(1+250/2^-8)) +data8 0xaf349c322e9c7cee,0x3ffe // ln(1/frcpa(1+251/2^-8)) +data8 0xafb39e30d1768d1c,0x3ffe // ln(1/frcpa(1+252/2^-8)) +data8 0xb032df51c2c93116,0x3ffe // ln(1/frcpa(1+253/2^-8)) +data8 0xb0b25fd3e6035ad9,0x3ffe // ln(1/frcpa(1+254/2^-8)) +data8 0xb1321ff67cba178c,0x3ffe // ln(1/frcpa(1+255/2^-8)) +// +data8 0xC7DC2985D3B44557,0x3FCA // A00 +// +// polynomial approximation of ln(GAMMA(x)), 1 <= x < 2.25 +// [0.875,1.25) +data8 0xBF9A04F7E40C8498,0x3FAB79D8D9380F03 // C17,C16 +data8 0xBFB3B63609CA0CBD,0x3FB5564EA1675539 // C13,C12 +data8 0xBFBC806766F48C41,0x3FC010B36CDA773A // C9,C8 +data8 0xD45CE0BD54BE3D67,0xBFFC // C5 +data8 0xCD26AADF559676D0,0xBFFD // C3 +data8 0x93C467E37DB0C7A7,0xBFFE // C1 +data8 0xBFB10C251723B123,0x3FB2669DAD69A12D // C15,C14 +data8 0xBFB748A3CFCE4717,0x3FB9A01DEE29966A // C11,C10 +data8 0xBFC2703A1D85497E,0x3FC5B40CB0FD353C // C7,C6 +data8 0x8A8991563ECBBA5D,0x3FFD // C4 +data8 0xD28D3312983E9844,0x3FFE // C2 +data8 0,0 // C0 +// [1.25,1.75) +data8 0xBF12680486396DE6,0x3F23C51FC332CD9D // C17,C16 +data8 0xBF422633DA3A1496,0x3F4CC70680768857 // C13,C12 +data8 0xBF6E2F1A1F804B5D,0x3F78FCE02A032428 // C9,C8 +data8 0x864D46FA895985C1,0xBFFA // C5 +data8 0x97213C6E35E12043,0xBFFC // C3 +data8 0x8A8A42A401D979B7,0x3FC7 // C1 +data8 0xBF2E098A8A2332A8,0x3F370E61B73B205C // C15,C14 +data8 0xBF56F9849D3BC6CC,0x3F6283126F58D7F4 // C11,C10 +data8 0xBF851F9F9516A98F,0x3F9266E797A1433F // C7,C6 +data8 0x845A14A6A81B0638,0x3FFB // C4 +data8 0xF7B95E4771C55C99,0x3FFD // C2 +data8 0xF8CDCDE61C520E0F,0xBFFB // C0 +// [1.75,2.25) +data8 0xBEA01D7AFA5D8F52,0x3EB1010986E60253 // C17,C16 +data8 0xBEE3CBEDB4C918AA,0x3EF580F6D9D0F72D // C13,C12 +data8 0xBF2D3FD4C7F68563,0x3F40B36AF884AE9A // C9,C8 +data8 0xF2027E10C7B051EC,0xBFF7 // C5 +data8 0x89F000D2ABB03401,0xBFFB // C3 +data8 0xD8773039049E70B6,0x3FFD // C1 +data8 0xBEC112CD07CFC31A,0x3ED2528A428D30E1 // C15,C14 +data8 0xBF078DE5618D8C9F,0x3F1A127AD811A53D // C11,C10 +data8 0xBF538AC5C2BF540D,0x3F67ADD6EADB5718 // C7,C6 +data8 0xA8991563EC243383,0x3FF9 // C4 +data8 0xA51A6625307D3230,0x3FFD // C2 +data8 0,0 // C0 +// +// polynomial approximation of ln(sin(Pi*x)/(Pi*x)), 9 <= x <= 0.5 +data8 0xBFDC1BF0931AE591,0x3FD36D6D6CE263D7 //S28,S26 +data8 0xBFBD516F4FD9FB18,0xBFBBE1703F315086 //S20,S18 +data8 0xAAB5A3CCEFCD3628,0xBFFC //S12 +data8 0x80859B5C318E19A5,0xBFFD //S8 +data8 0x8A8991563EC7EB33,0xBFFE //S4 +data8 0xBFD23AB9E6CC88AC,0xBF9957F5146FC7AF //S24,S22 +data8 0xBFC007B324E23040,0xBFC248DEC29CAC4A //S16,S14 +data8 0xCD00EFF2F8F86899,0xBFFC //S10 +data8 0xADA06587FACD668B,0xBFFD //S6 +data8 0xD28D3312983E98A0,0xBFFF //S2 +// +data8 0x8090F777D7942F73,0x4001 // PR01 +data8 0xE5B521193CF61E63,0x4000 // PR11 +data8 0xC02C000000001939 // (-15;-14) +data8 0x0000000000000233 // (-15;-14) +data8 0xC02A000000016124 // (-14;-13) +data8 0x0000000000002BFB // (-14;-13) +data8 0xC02800000011EED9 // (-13;-12) +data8 0x0000000000025CBB // (-13;-12) +data8 0xC026000000D7322A // (-12;-11) +data8 0x00000000001E1095 // (-12;-11) +data8 0xC0240000093F2777 // (-11;-10) +data8 0x00000000013DD3DC // (-11;-10) +data8 0xC02200005C7768FB // (-10;-9) +data8 0x000000000C9539B9 // (-10;-9) +data8 0xC02000034028B3F9 // (-9;-8) +data8 0x000000007570C565 // (-9;-8) +data8 0xC01C0033FDEDFE1F // (-8;-7) +data8 0x00000007357E670E // (-8;-7) +data8 0xC018016B25897C8D // (-7;-6) +data8 0x000000346DC5D639 // (-7;-6) +data8 0xC014086A57F0B6D9 // (-6;-5) +data8 0x0000010624DD2F1B // (-6;-5) +data8 0xC010284E78599581 // (-5;-4) +data8 0x0000051EB851EB85 // (-5;-4) +data8 0xC009260DBC9E59AF // (-4;-3) +data8 0x000028F5C28F5C29 // (-4;-3) +data8 0xC003A7FC9600F86C // (-3;-2) +data8 0x0000666666666666 // (-3;-2) +data8 0xCC15879606130890,0x4000 // PR21 +data8 0xB42FE3281465E1CC,0x4000 // PR31 +// +data8 0x828185F0B95C9916,0x4001 // PR00 +// +data8 0xD4D3C819E4E5654B,0x4000 // PR10 +data8 0xA82FBBA4FCC75298,0x4000 // PR20 +data8 0xC02DFFFFFFFFFE52 // (-15;-14) +data8 0x000000000000001C // (-15;-14) +data8 0xC02BFFFFFFFFE6C7 // (-14;-13) +data8 0x00000000000001A6 // (-14;-13) +data8 0xC029FFFFFFFE9EDC // (-13;-12) +data8 0x0000000000002BFB // (-13;-12) +data8 0xC027FFFFFFEE1127 // (-12;-11) +data8 0x000000000001EEC8 // (-12;-11) +data8 0xC025FFFFFF28CDD4 // (-11;-10) +data8 0x00000000001E1095 // (-11;-10) +data8 0xC023FFFFF6C0D7C0 // (-10;-9) +data8 0x000000000101B2B3 // (-10;-9) +data8 0xC021FFFFA3884BD0 // (-9;-8) +data8 0x000000000D6BF94D // (-9;-8) +data8 0xC01FFFF97F8159CF // (-8;-7) +data8 0x00000000C9539B89 // (-8;-7) +data8 0xC01BFFCBF76B86F0 // (-7;-6) +data8 0x00000007357E670E // (-7;-6) +data8 0xC017FE92F591F40D // (-6;-5) +data8 0x000000346DC5D639 // (-6;-5) +data8 0xC013F7577A6EEAFD // (-5;-4) +data8 0x00000147AE147AE1 // (-5;-4) +data8 0xC00FA471547C2FE5 // (-4;-3) +data8 0x00000C49BA5E353F // (-4;-3) +data8 0xC005FB410A1BD901 // (-3;-2) +data8 0x000053F7CED91687 // (-3;-2) +data8 0x80151BB918A293AA,0x4000 // PR30 +data8 0xB3C9F8F47422A314,0x400B // PRN +// +// right negative roots +//(-3;-2) +data8 0x40BFCF8B90BE7F6B,0x40B237623345EFC3 // A15,A14 +data8 0x407A92EFB03B281E,0x40728700C7819759 // A11,A10 +data8 0x403809F04EF4D0F2,0x4038D32F682D9593 // A7,A6 +data8 0xB4A5302C53C2F2D8,0x3FFF // A3 +data8 0xC1FF4B357A9B0383,0x3FFF // A1 +data8 0x409C46632EB4B2D3,0x4091A72AFA2148F5 // A13,A12 +data8 0x4059297AC79A88DB,0x40548EAA7BE7FA6B // A9,A8 +data8 0x4017339FE04B227F,0x4021718D7CA09E02 // A5,A4 +data8 0x9B775D8017AAE668,0x4001 // A2 +data8 0x8191DB68FF4366A1,0x3FC9 // A0 +//(-4;-3) +data8 0x425260910D35307B,0x422668F5BE7983BB // A15,A14 +data8 0x41A4454DBE4BEE43,0x41799CA93F6EA817 // A11,A10 +data8 0x40FBB97AA1400F31,0x40D293C3F7ADAB15 // A7,A6 +data8 0xE089B8926AE4517B,0x4005 // A3 +data8 0xF90532F97D630C69,0x4001 // A1 +data8 0x41F9F0CF98C5F2EA,0x41D026336C6BF394 // A13,A12 +data8 0x415057F61156D5B8,0x41251EA3055CB754 // A9,A8 +data8 0x40A99A6337D9FC2B,0x408267203D776151 // A5,A4 +data8 0xCEA694BB8A8827A9,0x4003 // A2 +data8 0xF4B02F1D73D30EED,0x3FCD // A0 +//(-5;-4) +data8 0x4412365489340979,0x43C86441BAFDEE39 // A15,A14 +data8 0x42ED68FCB19352DD,0x42A45FCE3905CD6F // A11,A10 +data8 0x41CD14FE49FD4FCA,0x41855E3DBFA89744 // A7,A6 +data8 0xAACD88D954E0EC16,0x400B // A3 +data8 0xD652E7A490B0DCDF,0x4003 // A1 +data8 0x437F52608E0E752A,0x433560E0633E33D5 // A13,A12 +data8 0x425C83998976DE3D,0x421433DCCD3B473B // A9,A8 +data8 0x4140261EB5732106,0x40F96D18E21AE6CC // A5,A4 +data8 0xA220AE6C09FA8A0E,0x4007 // A2 +data8 0xCC1682D17A2B5A58,0xBFCF // A0 +//(-6;-5) +data8 0x4630E41D6386CF5A,0x45C2E7992C628C8C // A15,A14 +data8 0x447AABEC714F913A,0x440EDCAB45339F3A // A11,A10 +data8 0x42C9A8D00C97E3CE,0x425F7D8D5BEAB44D // A7,A6 +data8 0x929EC2B1FB95BB5B,0x4012 // A3 +data8 0xF6B970414D717D38,0x4005 // A1 +data8 0x45545E578976F6A2,0x44E738288DD52686 // A13,A12 +data8 0x43A20921FEC49492,0x433557FD7C6A41B3 // A9,A8 +data8 0x41F3E01773761DB4,0x418A225DF2DA6C47 // A5,A4 +data8 0xE7661976117F9312,0x400B // A2 +data8 0xC33C13FEE07494DE,0x3FCF // A0 +//(-7;-6) +data8 0x4898F1E6133305AD,0x4802C5306FE4A850 // A15,A14 +data8 0x463FD37946B44094,0x45A8D489B784C2DD // A11,A10 +data8 0x43E9500995815F06,0x4354F21E2FEE6DF5 // A7,A6 +data8 0xEF281D1E1BBE10BD,0x4019 // A3 +data8 0xB4EF24F1D78C2029,0x4008 // A1 +data8 0x476AB1D5930011E5,0x46D4867E77BFB622 // A13,A12 +data8 0x45139151ECDEF7C5,0x447F3A2BC6BF466F // A9,A8 +data8 0x42C1D3D50713FA40,0x422F9C7B52556A1B // A5,A4 +data8 0xFE711A4267CEA83A,0x4010 // A2 +data8 0xD11E91B3FF8F4B94,0xBFD2 // A0 +//(-8;-7) +data8 0x4B39E57569811B6E,0x4A7656073EB1FA21 // A15,A14 +data8 0x482C9B24A516B0BB,0x47698FF55139C62B // A11,A10 +data8 0x452393E2BC8E8D04,0x44628E1C710DA478 // A7,A6 +data8 0x9F2A95AF1B7A773F,0x4022 // A3 +data8 0x9DA03D51C303C918,0x400B // A1 +data8 0x49B24C241A3D5BCB,0x48F01CB936ECDA67 // A13,A12 +data8 0x46A712B3425C6797,0x45E5164114BD6DA1 // A9,A8 +data8 0x43A216A356069D01,0x42E25E42A45E2108 // A5,A4 +data8 0xC1F42ED57BBC2529,0x4016 // A2 +data8 0xB1C7B615A7DCA8A9,0xBFD7 // A0 +//(-9;-8) +data8 0x4E09D478E5EE857D,0x4D1647782106E9AB // A15,A14 +data8 0x4A3C7F4D51927548,0x49497954796D743A // A11,A10 +data8 0x467387BD6AF0CBDF,0x4582843E134111D2 // A7,A6 +data8 0x9F003C6DE9666513,0x402B // A3 +data8 0x9D8447F6BF99950A,0x400E // A1 +data8 0x4C22364D238C61A9,0x4B300B18050AB940 // A13,A12 +data8 0x4857004D64215772,0x4765074E448C3C9A // A9,A8 +data8 0x44920E9EA07BF624,0x43A257BEC94BBF48 // A5,A4 +data8 0xC1D1C49AC5B2A4B4,0x401C // A2 +data8 0x9A749AF9F2D2E688,0x3FDB // A0 +//(-10;-9) +data8 0x5102C7C43EA26C83,0x4FDCD174DEB0426B // A15,A14 +data8 0x4C6A036195CD5BAD,0x4B44ABB52B65628A // A11,A10 +data8 0x47D6439374B98FED,0x46B2C3903EF44D7D // A7,A6 +data8 0xE25BAF73AB8A7DB3,0x4034 // A3 +data8 0xB130901CA6D81B61,0x4011 // A1 +data8 0x4EB50BB0726AE206,0x4D907A96E6D2B6E2 // A13,A12 +data8 0x4A20975D78EAF01A,0x48FAF79C9C3E7908 // A9,A8 +data8 0x459044144129A247,0x446D6043FA3150A3 // A5,A4 +data8 0xF547997E083D9BA7,0x4022 // A2 +data8 0x977AF525A6ECA1BC,0x3FDC // A0 +//(-11;-10) +data8 0x5420A5D5E90C6D73,0x52C4710A503DC67A // A15,A14 +data8 0x4EB2ED07BA88D2A8,0x4D581001ED9A5ECE // A11,A10 +data8 0x494A8A28E9E3DFEF,0x47F1E4E1E476793E // A7,A6 +data8 0xDD0C97E12D4A3378,0x403E // A3 +data8 0xDD7C12D5182FD543,0x4014 // A1 +data8 0x5167ED536877A072,0x500DF9AF21DDC0B6 // A13,A12 +data8 0x4BFEE6F04BC34FF8,0x4AA4175CEF736A5E // A9,A8 +data8 0x4698D1B4388FEC78,0x4541EDE7607A600D // A5,A4 +data8 0xBF9F645F282AC552,0x4029 // A2 +data8 0xAE1BBE4D3CDACCF4,0x3FE1 // A0 +//(-12;-11) +data8 0x575F0EEF5FB7D4C0,0x55CBB7302B211A7C // A15,A14 +data8 0x5113A4F1825C7CB2,0x4F822A0D46E0605A // A11,A10 +data8 0x4ACED38FC8BE069A,0x493E3B56D2649F18 // A7,A6 +data8 0x8FA8FF5DF8B72D5E,0x4049 // A3 +data8 0x9845417E8598D642,0x4018 // A1 +data8 0x5437780541C3F2D3,0x52A56279B563C1B2 // A13,A12 +data8 0x4DF0F71A48C50188,0x4C600B358988DEBF // A9,A8 +data8 0x47AE7EE95BDA3DE9,0x46200599DC16B18F // A5,A4 +data8 0xB5249F914932E55D,0x4030 // A2 +data8 0xEAE760CD2C086094,0x3FE5 // A0 +//(-13;-12) +data8 0x5ABA5848651F6D18,0x58EF60D8A817650B // A15,A14 +data8 0x538A8CA86E13EFB1,0x51C05DBD4D01076D // A11,A10 +data8 0x4C607594C339D259,0x4A9585BD5BF932BB // A7,A6 +data8 0xF26D282C36EC3611,0x4053 // A3 +data8 0xE467DF4810EE7EEE,0x401B // A1 +data8 0x5721D9BA485E8CC3,0x5555AF2CCFB2104D // A13,A12 +data8 0x4FF4619A17B14EA6,0x4E29B2F29EB9F8C4 // A9,A8 +data8 0x48CCF27629D46E79,0x47044715F991A63D // A5,A4 +data8 0xCBC92FB9BDAA95A9,0x4037 // A2 +data8 0xFB743A426163665B,0xBFE6 // A0 +//(-14;-13) +data8 0x5E3295B24B353EAA,0x5C2B447E29796F20 // A15,A14 +data8 0x5615A35CB5EAFAE5,0x54106AB089C95CAF // A11,A10 +data8 0x4DFEC7D93501900A,0x4BF8C4C685F01B83 // A7,A6 +data8 0x820899603D9A74D5,0x405F // A3 +data8 0xB9949919933821CB,0x401F // A1 +data8 0x5A23373DB9A995AC,0x581CBA0AF7F53009 // A13,A12 +data8 0x520929836BB304CD,0x500386409A7076DA // A9,A8 +data8 0x49F480173FEAF90B,0x47F1ACB14B810793 // A5,A4 +data8 0x86881B8674DBF205,0x403F // A2 +data8 0x8CF3CC35AA2C5F90,0x3FED // A0 +//(-15;-14) +data8 0x61C37D53BE0029D6,0x5F80667CD9D68354 // A15,A14 +data8 0x58B3F01898E6605B,0x567149652116DB6A // A11,A10 +data8 0x4FA82FA4F5D35B00,0x4D663DB00832DF8F // A7,A6 +data8 0xAE426731C9B94996,0x406A // A3 +data8 0xA264C84BE3708F3F,0x4023 // A1 +data8 0x5D3B254BC1C806A8,0x5AF72E736048B553 // A13,A12 +data8 0x542E476505104BB0,0x51EAD96CDC4FB48F // A9,A8 +data8 0x4B25095F498DB134,0x48E4B9FDEBFE24AB // A5,A4 +data8 0xCE076A5A116C1D34,0x4046 // A2 +data8 0x940013871A15050B,0x3FF1 // A0 +// +// left negative roots +//(-3;-2) +data8 0x41AEB7998DBE2B2C,0xC19053D8FAC05DF7 // A16,A15 +data8 0x4133197BF1ADEAF9,0xC1150728B9B82072 // A12,A11 +data8 0x40BDBA65E74F4526,0xC0A12239BEEF8F72 // A8,A7 +data8 0xFA8256664F99E2AA,0x4004 // A4 +data8 0x9933F9E132D2A5DB,0x4002 // A2 +data8 0x416FFB167B85F77C,0xC15166AE0ACCF87C // A14,A13 +data8 0x40F75815106322C0,0xC0DA2D23C59C348D // A10,A9 +data8 0x4084373F7CC42043,0xC0685884581F8C61 // A6,A5 +data8 0xA0C2D6186460FF9D,0xC003 // A3 +data8 0xF5096D48258CA0AD,0xBFFF // A1 +//(-4;-3) +data8 0xC3E5BD233016D4B9,0x43A084DAD2D94AB1 // A15,A14 +data8 0xC2CCFFF5E5AED722,0x4286D143AC7D29A6 // A11,A10 +data8 0xC1B7DBBE0680D07B,0x4173E8F3ABB79CED // A7,A6 +data8 0xE929ACEA59799BAF,0xC00A // A3 +data8 0xA5CCECB362B21E1C,0xC003 // A1 +data8 0xC357EED873871B81,0x43128E0B873204FC // A13,A12 +data8 0xC242225FA76E8450,0x41FD2F76AE7386CE // A9,A8 +data8 0xC13116F7806D0C7A,0x40EE8F829F141025 // A5,A4 +data8 0xFBB6F57021B5B397,0x4006 // A2 +data8 0xEEE019B4C05AC269,0xBFCB // A0 +//(-5;-4) +data8 0xC626A52FE8AAA100,0x45B9FD1F4DDFE31E // A15,A14 +data8 0xC473812A5675F08B,0x440738530AECC254 // A11,A10 +data8 0xC2C5068B3F94AC27,0x425A8C5C539A500B // A7,A6 +data8 0x869FBFF732F20C3A,0xC012 // A3 +data8 0xE91251F7CF25A655,0xC005 // A1 +data8 0xC54C18CB48E5DA0F,0x44E07BD36FF561DF // A13,A12 +data8 0xC39BEC120D2FEBEA,0x4330FFA5388435BE // A9,A8 +data8 0xC1F13D5D163B7FB5,0x418752A6F5AC0F39 // A5,A4 +data8 0xDA99E33C51D360F0,0x400B // A2 +data8 0x9F47A66A2F53D9B9,0x3FD1 // A0 +//(-6;-5) +data8 0xC8970DAC16B6D59E,0x480170728306FD76 // A15,A14 +data8 0xC63E0E5030604CF3,0x45A7924D74D57C65 // A11,A10 +data8 0xC3E8684E41730FC6,0x43544D54EA2E5B9A // A7,A6 +data8 0xEB7404450C47C5F4,0xC019 // A3 +data8 0xB30FB521D2C19F8B,0xC008 // A1 +data8 0xC768F34D35DF6320,0x46D348B3BB2E68B8 // A13,A12 +data8 0xC512AC2FE5EA638E,0x447DF44BC7FC5E17 // A9,A8 +data8 0xC2C15EA6B0AAFEF9,0x422EF5D308DBC420 // A5,A4 +data8 0xFBCEE5BCA70FD3A3,0x4010 // A2 +data8 0x8589A7CFFE0A3E86,0xBFD5 // A0 +//(-7;-6) +data8 0xCB3995A0CC961E5A,0x4A7615C6C7116ADD // A15,A14 +data8 0xC82C5AFE0BF9C427,0x47695BD2F367668B // A11,A10 +data8 0xC52377E70BA14CF5,0x4462775E859E4392 // A7,A6 +data8 0x9EC8ED6E4C3D4DBE,0xC022 // A3 +data8 0x9D5FBD2E75520E65,0xC00B // A1 +data8 0xC9B21BB881A4DDF8,0x48EFEAB06FBA0207 // A13,A12 +data8 0xC6A6E8550CBC188F,0x45E4F3D26238B099 // A9,A8 +data8 0xC3A20427DF1B110A,0x42E24F3D636F2E4E // A5,A4 +data8 0xC1A4D12A82280CFB,0x4016 // A2 +data8 0xEF46D8DCCA9E8197,0x3FD2 // A0 +//(-8;-7) +data8 0xCE0946982B27DE5B,0x4D15DBC6664E2DD2 // A15,A14 +data8 0xCA3C769F6B3B2B93,0x49497251CD0C4363 // A11,A10 +data8 0xC67384066C47F489,0x458281393433AB28 // A7,A6 +data8 0x9EF3459926D0F14F,0xC02B // A3 +data8 0x9D7BB7F2600DFF0B,0xC00E // A1 +data8 0xCC22351326C939A7,0x4B3009431C4F1D3F // A13,A12 +data8 0xC856FAADDD48815D,0x476502BC3ECA040C // A9,A8 +data8 0xC4920C2A84173810,0x43A255C052525F99 // A5,A4 +data8 0xC1C73B6554011EFA,0x401C // A2 +data8 0x954612700ADF8317,0xBFD8 // A0 +//(-9;-8) +data8 0xD102F5CC7B590D3A,0x4FDD0F1C30E4EB22 // A15,A14 +data8 0xCC6A02912B0DF650,0x4B44AB18E4FCC159 // A11,A10 +data8 0xC7D64314B4A2FAAB,0x46B2C334AE5E2D34 // A7,A6 +data8 0xE2598724F7E28E99,0xC034 // A3 +data8 0xB12F6FE2E195452C,0xC011 // A1 +data8 0xCEB507747AF9356A,0x4D907802C08BA48F // A13,A12 +data8 0xCA2096E3DC29516F,0x48FAF6ED046A1DB7 // A9,A8 +data8 0xC59043D21BA5EE56,0x446D5FE468B30450 // A5,A4 +data8 0xF5460A8196B59C83,0x4022 // A2 +data8 0xB108F35A8EDA92D5,0xBFDD // A0 +//(-10;-9) +data8 0xD420430D91F8265B,0x52C406CAAAC9E0EE // A15,A14 +data8 0xCEB2ECDDDAA3DAD1,0x4D580FDA97F92E3A // A11,A10 +data8 0xC94A8A192341B5D4,0x47F1E4D8C690D07B // A7,A6 +data8 0xDD0C5F920C2F0D2B,0xC03E // A3 +data8 0xDD7BED3631657B48,0xC014 // A1 +data8 0xD167F410E64E90A4,0x500DFFED20F714A7 // A13,A12 +data8 0xCBFEE6D9043169E9,0x4AA4174F64B40AA7 // A9,A8 +data8 0xC698D1A9AF0AB9C2,0x4541EDE14987A887 // A5,A4 +data8 0xBF9F43D461B3DE6E,0x4029 // A2 +data8 0xF3891A50642FAF26,0x3FE1 // A0 +//(-11;-10) +data8 0xD75F0EEAF769D42A,0x55CBB72C8869183A // A15,A14 +data8 0xD113A4EF80394F77,0x4F822A0B96B3ECA9 // A11,A10 +data8 0xCACED38DC75763CB,0x493E3B5522D2D028 // A7,A6 +data8 0x8FA8FB5C92533701,0xC049 // A3 +data8 0x98453EDB9339C24E,0xC018 // A1 +data8 0xD43778026CCD4B20,0x52A5627753273B9B // A13,A12 +data8 0xCDF0F718DD7E1214,0x4C600B34582911EB // A9,A8 +data8 0xC7AE7EE7F112362C,0x46200599439C264F // A5,A4 +data8 0xB5249C335342B5BC,0x4030 // A2 +data8 0x881550711D143475,0x3FE4 // A0 +//(-12;-11) +data8 0xDAB9C724EEEE2BBB,0x58EEC971340EDDBA // A15,A14 +data8 0xD38A8C8AE63BD8BF,0x51C05DB21CEE00D3 // A11,A10 +data8 0xCC607594C311C12D,0x4A9585BD5BE6AB57 // A7,A6 +data8 0xF26D282C36EC0E66,0xC053 // A3 +data8 0xE467DF1FA674BFAE,0xC01B // A1 +data8 0xD721DE506999AA9C,0x5555B34F71B45132 // A13,A12 +data8 0xCFF4619A476BF76F,0x4E29B2F2BBE7A67E // A9,A8 +data8 0xC8CCF27629D48EDC,0x47044715F991AB46 // A5,A4 +data8 0xCBC92FB9BDAA928D,0x4037 // A2 +data8 0xCE27C4F01CF53284,0xBFE6 // A0 +//(-13;-12) +data8 0xDE3295B24355C5A1,0x5C2B447E298B562D // A15,A14 +data8 0xD615A35CB5E92103,0x54106AB089C95E8C // A11,A10 +data8 0xCDFEC7D935019005,0x4BF8C4C685F01B83 // A7,A6 +data8 0x820899603D9A74D5,0xC05F // A3 +data8 0xB9949916F8DF4AC4,0xC01F // A1 +data8 0xDA23373DBA0B7548,0x581CBA0AF7F45C01 // A13,A12 +data8 0xD20929836BB30934,0x500386409A7076D6 // A9,A8 +data8 0xC9F480173FEAF90B,0x47F1ACB14B810793 // A5,A4 +data8 0x86881B8674DBF205,0x403F // A2 +data8 0x8CFAFA9A142C1FF0,0x3FED // A0 +//(-14;-13) +data8 0xE1C33F356FA2C630,0x5F8038B8AA919DD7 // A15,A14 +data8 0xD8B3F0167E14982D,0x5671496400BAE0DB // A11,A10 +data8 0xCFA82FA4F5D25C3E,0x4D663DB008328C58 // A7,A6 +data8 0xAE426731C9B94980,0xC06A // A3 +data8 0xA264C84BB8A66F86,0xC023 // A1 +data8 0xDD3B26E34762ED1E,0x5AF72F76E3C1B793 // A13,A12 +data8 0xD42E476507E3D06E,0x51EAD96CDD881DFA // A9,A8 +data8 0xCB25095F498DB15F,0x48E4B9FDEBFE24B5 // A5,A4 +data8 0xCE076A5A116C1D32,0x4046 // A2 +data8 0x94001BF5A24966F5,0x3FF1 // A0 +//(-15;-14) +data8 0xE56DB8B72D7156FF,0x62EAB0CDB22539BE // A15,A14 +data8 0xDB63D76B0D3457E7,0x58E254823D0AE4FF // A11,A10 +data8 0xD15F060BF548404A,0x4EDE65C20CD4E961 // A7,A6 +data8 0x900DA565ED76C19D,0xC076 // A3 +data8 0x9868C809852DA712,0xC027 // A1 +data8 0xE067CCDA0408AAF0,0x5DE5A79C5C5C54AF // A13,A12 +data8 0xD6611ADBF5958ED0,0x53E0294092BE9677 // A9,A8 +data8 0xCC5EA28D90EE8C5D,0x49E014930EF336EE // A5,A4 +data8 0xB57930DCE7A61AE8,0x404E // A2 +data8 0x976BEC1F30DF151C,0x3FF5 // A0 +LOCAL_OBJECT_END(lgamma_data) + + +.section .text +GLOBAL_LIBM_ENTRY(__libm_lgamma) + +{ .mfi + getf.exp GR_SignExp = f8 + frcpa.s1 FR_C,p9 = f1,f8 + mov GR_ExpMask = 0x1ffff +} +{ .mfi + addl GR_ad_Data = @ltoff(lgamma_data),gp + fcvt.fx.s1 FR_int_N = f8 + mov GR_2_25 = 0x4002 // 2.25 +};; +{ .mfi + getf.d GR_ArgAsIs = 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] + fcvt.fx.trunc.s1 FR_int_Ntrunc = f8 + mov GR_ExpOf256 = 0x10007 +};; +{ .mfi + mov GR_ExpOf2 = 0x10000 + fcmp.lt.s1 p14,p15 = f8,f0 // p14 if x<0 + dep.z GR_Ind = GR_SignExp,8,4 +} +{ .mfi + and GR_Exp = GR_SignExp,GR_ExpMask + fma.s1 FR_2 = f1,f1,f1 + cmp.lt p10,p0 = GR_SignExp,GR_ExpBias +};; +{ .mfi + add GR_ad_1 = 0xB80,GR_ad_Data + fnorm.s1 FR_NormX = f8 + shr.u GR_Arg = GR_ArgAsIs,48 +} +{ .mib + add GR_ad_Co = GR_Ind,GR_ad_Data + add GR_ad_Ce = 0x10,GR_ad_Data + // jump if the input argument is NaTVal, NaN, +/-0, +/-INF or +/-deno +(p13) br.cond.spnt lgamma_spec +};; +lgamma_common: +{ .mfi + ldfpd FR_LocalMin,FR_05 = [GR_ad_1],16 + fmerge.se FR_x = f1,f8 + add GR_ad_2 = 0xBC0,GR_ad_Data +} +{ .mfb + add GR_ad_Ce = GR_Ind,GR_ad_Ce + fms.s1 FR_w = f8,f1,f1 // x-1 + // jump if the input argument is positive and less than 1.0 +(p10) br.cond.spnt lgamma_0_1 +};; +{ .mfi + ldfe FR_C01 = [GR_ad_Co],32 + fnma.s1 FR_InvX = FR_C,f8,f1 // NR iteration #1 +(p15) cmp.lt.unc p8,p0 = GR_ExpOf256,GR_SignExp +} +{ .mib + ldfe FR_C11 = [GR_ad_Ce],32 +(p15) cmp.lt.unc p11,p0 = GR_Arg,GR_2_25 + // jump if the input argument isn't less than 512.0 +(p8) br.cond.spnt lgamma_pstirling +};; +{ .mfi + ldfe FR_C21 = [GR_ad_Co],32 +(p14) fms.s1 FR_r = FR_C,f8,f1 // reduced arg for log(x) +(p14) cmp.lt.unc p0,p9 = GR_Exp,GR_ExpOf256 +} +{ .mib + ldfe FR_C31 = [GR_ad_Ce],32 + add GR_ad_Co7 = 0x12C0,GR_ad_2 + // jump if the input argument is from range [1.0; 2.25) +(p11) br.cond.spnt lgamma_1_2 +};; +{ .mfi + ldfe FR_C41 = [GR_ad_Co],32 + fcvt.xf FR_N = FR_int_N + add GR_ad_Ce7 = 0x1310,GR_ad_2 +} +{ .mfb + ldfe FR_C51 = [GR_ad_Ce],32 +(p14) fma.s1 FR_5 = FR_2,FR_2,f1 + // jump if the input argument is less or equal to -512.0 +(p9) br.cond.spnt lgamma_negstirling +};; +{ .mfi + ldfe FR_C61 = [GR_ad_Co],32 +(p14) fcvt.xf FR_Ntrunc = FR_int_Ntrunc + shr GR_Ind = GR_Ind,4 +} +{ .mfi + ldfe FR_C71 = [GR_ad_Ce],32 +(p14) fma.s1 FR_Xp1 = f1,f1,FR_NormX // x+1 + cmp.eq p6,p7 = GR_ExpOf2,GR_SignExp +};; +.pred.rel "mutex",p6,p7 +{ .mfi + ldfe FR_C81 = [GR_ad_Co],32 +(p6) fma.s1 FR_x = f0,f0,FR_NormX + shladd GR_Offs7 = GR_Ind,2,GR_Ind // (ind*16)*5 +} +{ .mfi + ldfe FR_C91 = [GR_ad_Ce],32 +(p7) fms.s1 FR_x = FR_x,f1,f1 + add GR_ad_Co7 = 0x800,GR_ad_Data +};; +{ .mfi + ldfe FR_CA1 = [GR_ad_Co],32 +(p14) fma.s1 FR_3 = f1,f1,FR_2 + shladd GR_Offs7 = GR_Ind,1,GR_Offs7 // (ind*16)*7 +} +{ .mfi + ldfe FR_C00 = [GR_ad_Ce],32 +(p14) fma.s1 FR_Xp4 = FR_2,FR_2,FR_NormX + add GR_ad_Ce7 = 0x810,GR_ad_Data +};; +{ .mfi + ldfe FR_C10 = [GR_ad_Co],32 +(p6) fms.s1 FR_Xm2 = FR_w,f1,f1 + add GR_ad_Co7 = GR_ad_Co7,GR_Offs7 +} +{ .mfi + ldfe FR_C20 = [GR_ad_Ce],32 +(p14) fma.s1 FR_r2 = FR_r,FR_r,f0 // log(x) + add GR_ad_Ce7 = GR_ad_Ce7,GR_Offs7 +};; +{ .mfi + ldfe FR_C30 = [GR_ad_Co],32 +(p14) fms.s1 FR_Xf = FR_NormX,f1,FR_N // xf = x - [x] +(p14) mov GR_Arg17 = 0xC031 // -17 +} +{ .mfi + ldfe FR_C40 = [GR_ad_Ce],32 +(p14) fma.s1 FR_Xp5 = FR_5,f1,FR_NormX +(p14) sub GR_Exp = GR_Exp,GR_ExpBias +};; +{ .mfi + ldfe FR_C50 = [GR_ad_Co7],32 +(p14) fms.s1 FR_Xfr = FR_Xp1,f1,FR_Ntrunc // xfr = (x+1) - [x] +(p14) cmp.lt.unc p13,p0 = GR_Arg,GR_Arg17 +} +{ .mfb + ldfe FR_C60 = [GR_ad_Ce7],32 +(p14) fma.s1 FR_Xp10 = FR_5,FR_2,FR_NormX + // jump if the input argument is negative and great than -17.0 +(p13) br.cond.spnt lgamma_negrecursion +};; +{ .mfi + ldfe FR_C70 = [GR_ad_Co7],32 + fma.s1 FR_C01 = FR_x,f1,FR_C01 +(p14) add GR_ad_Ce = 0x1310,GR_ad_2 +} +{ .mfi + ldfe FR_C80 = [GR_ad_Ce7],32 + fma.s1 FR_C11 = FR_x,f1,FR_C11 +(p14) add GR_ad_Co = 0x12C0,GR_ad_2 +};; +{ .mfi + ldfe FR_C90 = [GR_ad_Co7],32 + fma.s1 FR_C21 = FR_x,f1,FR_C21 + nop.i 0 +} +{ .mfi + ldfe FR_CA0 = [GR_ad_Ce7],32 + fma.s1 FR_C31 = FR_x,f1,FR_C31 + nop.i 0 +};; +{ .mfi + ldfe FR_CN = [GR_ad_Co7],32 + fma.s1 FR_C41 = FR_x,f1,FR_C41 + nop.i 0 +} +{ .mfi +(p14) ldfpd FR_P5,FR_P4 = [GR_ad_1],16 + fma.s1 FR_C51 = FR_x,f1,FR_C51 + nop.i 0 +};; +{ .mfi +(p14) ldfpd FR_P3,FR_P2 = [GR_ad_2],16 + fma.s1 FR_C61 = FR_x,f1,FR_C61 + nop.i 0 +} +{ .mfi +(p14) ldfe FR_Ln2 = [GR_ad_1] + fma.s1 FR_C71 = FR_x,f1,FR_C71 + nop.i 0 +};; +{ .mfi +(p14) ldfpd FR_S28,FR_S26 = [GR_ad_Co],16 + fma.s1 FR_C81 = FR_x,f1,FR_C81 + add GR_ad_2 = 0x60,GR_ad_2 +} +{ .mfi +(p14) ldfpd FR_S24,FR_S22 = [GR_ad_Ce],16 + fma.s1 FR_C91 = FR_x,f1,FR_C91 + nop.i 0 +};; +{ .mfi +(p14) ldfpd FR_S20,FR_S18 = [GR_ad_Co],16 + fma.s1 FR_CA1 = FR_x,f1,FR_CA1 + nop.i 0 +} +{ .mfi +(p14) ldfpd FR_S16,FR_S14 = [GR_ad_Ce],16 + fma.s1 FR_C01 = FR_C01,FR_x,FR_C00 + nop.i 0 +};; +{ .mfi +(p14) getf.exp GR_SignExp = FR_Xf + fma.s1 FR_C11 = FR_C11,FR_x,FR_C10 + nop.i 0 +} +{ .mfi +(p14) ldfe FR_S12 = [GR_ad_Co],16 + fma.s1 FR_C21 = FR_C21,FR_x,FR_C20 + nop.i 0 +};; +{ .mfi +(p14) getf.sig GR_Sig = FR_Xf +(p14) frcpa.s1 FR_InvXf,p0 = f1,FR_Xf + nop.i 0 +} +{ .mfi +(p14) ldfe FR_S10 = [GR_ad_Ce],16 + fma.s1 FR_C41 = FR_C41,FR_x,FR_C40 + nop.i 0 +};; +{ .mfi +(p14) ldfe FR_S8 = [GR_ad_Co],16 + fma.s1 FR_C51 = FR_C51,FR_x,FR_C50 + nop.i 0 +} +{ .mfi +(p14) ldfe FR_S6 = [GR_ad_Ce],16 + fma.s1 FR_C61 = FR_C61,FR_x,FR_C60 +(p14) and GR_Expf = GR_SignExp,GR_ExpMask +};; +{ .mfi +(p14) sub GR_Expf = GR_Expf,GR_ExpBias + fma.s1 FR_C71 = FR_C71,FR_x,FR_C70 +(p14) shl GR_Ind = GR_Sig,1 +} +{ .mfi +(p14) ldfe FR_S4 = [GR_ad_Co],16 + fma.s1 FR_C81 = FR_C81,FR_x,FR_C80 +(p14) cmp.eq.unc p8,p0 = 0,GR_Sig +};; +{ .mfi +(p14) setf.sig FR_int_Nf = GR_Expf + fma.s1 FR_C91 = FR_C91,FR_x,FR_C90 +(p14) shr.u GR_Ind = GR_Ind,56 +} +{ .mfb +(p14) ldfe FR_S2 = [GR_ad_Ce],16 + fma.s1 FR_CA1 = FR_CA1,FR_x,FR_CA0 + // jump if the input argument is integer number from range (-512.0;-17.0] +(p8) br.cond.spnt lgamma_singularity +};; +{ .mfi +(p14) getf.sig GR_Sig = FR_int_Ntrunc + fma.s1 FR_C01 = FR_C01,FR_C11,f0 + nop.i 0 +} +{ .mfi +(p14) shladd GR_ad_T = GR_Ind,4,GR_ad_2 + fma.s1 FR_C31 = FR_C31,FR_x,FR_C30 + nop.i 0 +};; +{ .mfi +(p14) ldfe FR_Tf = [GR_ad_T] +(p14) fms.s1 FR_rf = FR_InvXf,FR_Xf,f1 // reduced arg for log({x}) +(p14) extr.u GR_Ind = GR_ArgAsIs,44,8 +} +{ .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_C21 = FR_C21,FR_C41,f0 + mov GR_SignOfGamma = 1 +};; +{ .mfi + nop.m 0 + fma.s1 FR_C51 = FR_C51,FR_C61,f0 +(p14) tbit.z.unc p8,p0 = GR_Sig,0 +} +{ .mfi +(p14) shladd GR_ad_T = GR_Ind,4,GR_ad_2 +(p6) fma.s1 FR_CN = FR_CN,FR_Xm2,f0 + nop.i 0 +};; +{ .mfi +(p14) setf.sig FR_int_N = GR_Exp + fma.s1 FR_C71 = FR_C71,FR_C81,f0 +(p8) sub GR_SignOfGamma = r0,GR_SignOfGamma +} +{ .mfi + nop.m 0 +(p14) fma.s1 FR_Xf2 = FR_Xf,FR_Xf,f0 + nop.i 0 +};; +{ .mfi +(p14) ldfe FR_T = [GR_ad_T] + fma.s1 FR_C91 = FR_C91,FR_CA1,f0 + nop.i 0 +} +{ .mfi + nop.m 0 +(p14) fma.s1 FR_r2 = FR_r,FR_r,f0 + nop.i 0 +};; +.pred.rel "mutex",p9,p10 +{ .mfi + // store sign of gamma(x) as 32-bit int +(p9) st4 [r33] = GR_SignOfGamma + fma.s1 FR_C01 = FR_C01,FR_C31,f0 + nop.i 0 +} +{ .mfi + // store sign of gamma(x) as 64-bit int +(p10) st8 [r33] = GR_SignOfGamma +(p14) fma.s1 FR_P54 = FR_P5,FR_r,FR_P4 + nop.i 0 +};; +{ .mfi + nop.m 0 +(p14) fma.s1 FR_P32 = FR_P3,FR_r,FR_P2 + nop.i 0 +} +{ .mfb + nop.m 0 +(p14) fma.s1 FR_P54f = FR_P5,FR_rf,FR_P4 + // jump if the input argument is non-integer from range (-512.0;-17.0] +(p14) br.cond.spnt lgamma_negpoly +};; +{ .mfi + nop.m 0 + fma.s1 FR_C21 = FR_C21,FR_C51,f0 + nop.i 0 +};; +{ .mfi + nop.m 0 + fma.s1 FR_C71 = FR_C71,FR_C91,f0 + nop.i 0 +};; +{ .mfi + nop.m 0 + fma.s1 FR_CN = FR_C01,FR_CN,f0 + nop.i 0 +};; +{ .mfi + nop.m 0 + fma.s1 FR_C21 = FR_C21,FR_C71,f0 + nop.i 0 +};; +{ .mfb + nop.m 0 + fma.d.s0 f8 = FR_C21,FR_CN,f0 + br.ret.sptk b0 // exit for arguments from range [2.25; 512.0) +};; +// branch for calculating of ln(GAMMA(x)) for -512 < x < -17 +//--------------------------------------------------------------------- +.align 32 +lgamma_negpoly: +{ .mfi + nop.m 0 + fma.s1 FR_Xf4 = FR_Xf2,FR_Xf2,f0 + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 FR_S28 = FR_S28,FR_Xf2,FR_S26 + nop.i 0 +};; +{ .mfi + nop.m 0 + fma.s1 FR_S24 = FR_S24,FR_Xf2,FR_S22 + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 FR_S20 = FR_S20,FR_Xf2,FR_S18 + nop.i 0 +};; +{ .mfi + nop.m 0 + fma.s1 FR_S16 = FR_S16,FR_Xf2,FR_S14 + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 FR_S12 = FR_S12,FR_Xf2,FR_S10 + nop.i 0 +};; +{ .mfi + nop.m 0 + fma.s1 FR_S8 = FR_S8,FR_Xf2,FR_S6 + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 FR_S4 = FR_S4,FR_Xf2,FR_S2 + 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 // log(x) + nop.i 0 +};; +{ .mfi + nop.m 0 + fma.s1 FR_r3 = FR_r2,FR_r,f0 // log(x) + nop.i 0 +} +{ .mfi + nop.m 0 + fcvt.xf FR_Nf = FR_int_Nf // log({x}) + nop.i 0 +};; +{ .mfi + nop.m 0 + fma.s1 FR_S28 = FR_S28,FR_Xf4,FR_S24 + 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_S20 = FR_S20,FR_Xf4,FR_S16 + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 FR_C21 = FR_C21,FR_C51,f0 + nop.i 0 +};; +{ .mfi + nop.m 0 + fma.s1 FR_S12 = FR_S12,FR_Xf4,FR_S8 + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 FR_C71 = FR_C71,FR_C91,f0 + nop.i 0 +};; +{ .mfi + nop.m 0 + fnma.s1 FR_P10 = FR_r2,FR_05,FR_r // log(x) + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 FR_P54 = FR_P54,FR_r2,FR_P32 // log(x) + nop.i 0 +};; +{ .mfi + nop.m 0 + fnma.s1 FR_P10f = FR_rf2,FR_05,FR_rf // log({x}) + nop.i 0 +} +{ .mfi + nop.m 0 + fcvt.xf FR_N = FR_int_N // log(x) + nop.i 0 +};; +{ .mfi + nop.m 0 + fma.s1 FR_rf3 = FR_rf2,FR_rf,f0 // log({x}) + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 FR_P54f = FR_P54f,FR_rf2,FR_P32f // log({x}) + nop.i 0 +};; +{ .mfi + nop.m 0 + fma.s1 FR_S28 = FR_S28,FR_Xf8,FR_S20 + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 FR_TpNxLn2f = FR_Nf,FR_Ln2,FR_Tf // log({x}) + nop.i 0 +};; +{ .mfi + nop.m 0 + fma.s1 FR_CN = FR_C01,FR_CN,f0 + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 FR_C21 = FR_C21,FR_C71,f0 + nop.i 0 +};; +{ .mfi + nop.m 0 + fma.s1 FR_P54 = FR_P54,FR_r3,FR_P10 // log(x) + nop.i 0 +};; +{ .mfi + nop.m 0 + fma.s1 FR_TpNxLn2 = FR_N,FR_Ln2,FR_T // log(x) + nop.i 0 +};; +{ .mfi + nop.m 0 + fma.s1 FR_P54f = FR_P54f,FR_rf3,FR_P10f // log({x}) + nop.i 0 +};; +{ .mfi + nop.m 0 + fma.s1 FR_S28 = FR_S28,FR_Xf8,FR_S12 + nop.i 0 +};; +{ .mfi + nop.m 0 + fnma.s1 FR_C21 = FR_C21,FR_CN,f0 + nop.i 0 +};; +{ .mfi + nop.m 0 + fma.s1 FR_LnX = FR_TpNxLn2,f1,FR_P54 // log(x) + nop.i 0 +};; +{ .mfi + nop.m 0 + fma.s1 FR_LnXf = FR_TpNxLn2f,f1,FR_P54f // log({x}) + nop.i 0 +};; +{ .mfi + nop.m 0 + fma.s1 FR_S28 = FR_S28,FR_Xf4,FR_S4 + nop.i 0 +};; +{ .mfi + nop.m 0 + fma.s1 FR_LnX = FR_LnX,f1,FR_LnXf + nop.i 0 +};; +{ .mfi + nop.m 0 + fnma.s1 FR_S28 = FR_S28,FR_Xf2,FR_C21 + nop.i 0 +};; +{ .mfb + nop.m 0 + fms.d.s0 f8 = FR_S28,f1,FR_LnX + br.ret.sptk b0 +};; +// branch for calculating of ln(GAMMA(x)) for x >= 512 +//--------------------------------------------------------------------- +.align 32 +lgamma_pstirling: +{ .mfi + ldfpd FR_P5,FR_P4 = [GR_ad_1],16 + nop.f 0 + and GR_Exp = GR_SignExp,GR_ExpMask +} +{ .mfi + ldfpd FR_P3,FR_P2 = [GR_ad_2],16 + fma.s1 FR_InvX = FR_C,FR_InvX,FR_C // NR iteration #1 + mov GR_ExpBias = 0xffff +};; +{ .mfi + ldfe FR_Ln2 = [GR_ad_1],16 + nop.f 0 + sub GR_Exp = GR_Exp,GR_ExpBias +};; +{ .mfi + ldfpd FR_W4,FR_OvfBound = [GR_ad_2],16 + nop.f 0 + nop.i 0 +};; +{ .mfi + setf.sig FR_int_N = GR_Exp + fms.s1 FR_r = FR_C,f8,f1 + nop.i 0 +};; +{ .mmf + getf.sig GR_Sig = FR_NormX + ldfe FR_LnSqrt2Pi = [GR_ad_1],16 + nop.f 0 +};; +{ .mmf + ldfe FR_W2 = [GR_ad_2],16 + nop.m 0 + fnma.s1 FR_InvX2 = FR_InvX,FR_NormX,f1 // NR iteration #2 +};; +{ .mfi + add GR_ad_2 = 0x40,GR_ad_2 + nop.f 0 + shl GR_Ind = GR_Sig,1 +};; +{ .mfi + mov GR_SignOfGamma = 1 + nop.f 0 + shr.u GR_Ind = GR_Ind,56 +};; +{ .mfi + shladd GR_ad_2 = GR_Ind,4,GR_ad_2 + fma.s1 FR_r2 = FR_r,FR_r,f0 + // set p9 if signgum is 32-bit int + // set p10 if signgum is 64-bit int + cmp.eq p10,p9 = 8,r34 +};; +{ .mfi + ldfe FR_T = [GR_ad_2] + fma.s1 FR_P54 = FR_P5,FR_r,FR_P4 + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 FR_P32 = FR_P3,FR_r,FR_P2 + nop.i 0 +};; +{ .mfi + nop.m 0 + fcmp.le.s1 p6,p0 = FR_OvfBound,FR_NormX + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 FR_InvX2 = FR_InvX,FR_InvX2,FR_InvX // NR iteration #2 + nop.i 0 +};; +{ .mfi + nop.m 0 + fcvt.xf FR_N = FR_int_N + nop.i 0 +} +{ .mfb + nop.m 0 + nop.f 0 + // jump if x is great than OVERFLOW_BOUNDARY +(p6) br.cond.spnt lgamma_overflow +};; +.pred.rel "mutex",p9,p10 +{ .mfi + // store sign of gamma(x) as 32-bit int +(p9) st4 [r33] = GR_SignOfGamma + fma.s1 FR_r3 = FR_r2,FR_r,f0 + nop.i 0 +} +{ .mfi + // store sign of gamma(x) as 64-bit int +(p10) st8 [r33] = GR_SignOfGamma + fnma.s1 FR_P10 = FR_r2,FR_05,FR_r + nop.i 0 +};; +{ .mfi + nop.m 0 + fma.s1 FR_P54 = FR_P54,FR_r2,FR_P32 + nop.i 0 +};; +{ .mfi + nop.m 0 + fnma.s1 FR_InvX = FR_InvX2,FR_NormX,f1 // NR iteration #3 + nop.i 0 +};; +{ .mfi + nop.m 0 + fms.s1 FR_Xm05 = FR_NormX,f1,FR_05 // (x-1/2) + nop.i 0 +};; +{ .mfi + nop.m 0 + fma.s1 FR_TpNxLn2 = FR_N,FR_Ln2,FR_T + nop.i 0 +};; +{ .mfi + nop.m 0 + fma.s1 FR_P54 = FR_P54,FR_r3,FR_P10 + nop.i 0 +};; +{ .mfi + nop.m 0 + fma.s1 FR_InvX = FR_InvX2,FR_InvX,FR_InvX2 // NR iteration #3 + nop.i 0 +} +{ .mfi + nop.m 0 + fms.s1 FR_LnSqrt2Pi = FR_LnSqrt2Pi,f1,FR_NormX // ln(sqrt(2*Pi))-x + nop.i 0 +};; +{ .mfi + nop.m 0 + fma.s1 FR_LnX = FR_TpNxLn2,f1,FR_P54 + nop.i 0 +};; +{ .mfi + nop.m 0 + fma.s1 FR_InvX2 = FR_InvX,FR_InvX,f0 + nop.i 0 +};; +{ .mfi + nop.m 0 + // (x-1/2)*ln(x)+ln(sqrt(2*Pi))-x + fma.s1 FR_LnX = FR_LnX,FR_Xm05,FR_LnSqrt2Pi + nop.i 0 +};; +{ .mfi + nop.m 0 + fma.s1 FR_W2 = FR_W4,FR_InvX2,FR_W2 // W2 + W4/x^2 + nop.i 0 +};; +{ .mfb + nop.m 0 + fma.d.s0 f8 = FR_InvX,FR_W2,FR_LnX + br.ret.sptk b0 +};; +// branch for calculating of ln(GAMMA(x)) for x < -512 +//--------------------------------------------------------------------- +.align 32 +lgamma_negstirling: +{ .mfi + ldfpd FR_P5,FR_P4 = [GR_ad_1],16 + fms.s1 FR_Xf = FR_NormX,f1,FR_N // xf = x - [x] + and GR_Exp = GR_SignExp,GR_ExpMask +} +{ .mfi + ldfpd FR_P3,FR_P2 = [GR_ad_2],16 + fma.s1 FR_InvX = FR_C,FR_InvX,FR_C // NR iteration #1 + mov GR_0x30033 = 0x30033 +};; +{ .mfi + ldfe FR_Ln2 = [GR_ad_1],16 + nop.f 0 + extr.u GR_Ind = GR_ArgAsIs,44,8 +} +{ .mib + ldfd FR_W4 = [GR_ad_2],16 + // jump if x is less or equal to -2^52, i.e. x is big negative integer + cmp.leu.unc p7,p0 = GR_0x30033,GR_SignExp +(p7) br.cond.spnt lgamma_singularity +};; +{ .mfi + ldfpd FR_S28,FR_S26 = [GR_ad_Co7],16 + nop.f 0 + add GR_ad_LnT = 0x50,GR_ad_2 +} +{ .mfi + ldfpd FR_S24,FR_S22 = [GR_ad_Ce7],16 + nop.f 0 + mov GR_ExpBias = 0xffff +};; +{ .mfi + ldfpd FR_S20,FR_S18 = [GR_ad_Co7],16 + nop.f 0 + shladd GR_ad_T = GR_Ind,4,GR_ad_LnT +} +{ .mfi + ldfpd FR_S16,FR_S14 = [GR_ad_Ce7],16 + nop.f 0 + sub GR_Exp = GR_Exp,GR_ExpBias +};; +{ .mfi + ldfe FR_S12 = [GR_ad_Co7],16 + nop.f 0 + nop.i 0 +} +{ .mfi + ldfe FR_S10 = [GR_ad_Ce7],16 + fms.s1 FR_r = FR_C,f8,f1 + nop.i 0 +};; +{ .mmf + ldfe FR_S8 = [GR_ad_Co7],16 + ldfe FR_S6 = [GR_ad_Ce7],16 + nop.f 0 +};; +{ .mfi + ldfe FR_S4 = [GR_ad_Co7],16 + fma.s1 FR_Xf2 = FR_Xf,FR_Xf,f0 + nop.i 0 +} +{ .mfi + ldfe FR_S2 = [GR_ad_Ce7],16 + fnma.s1 FR_InvX2 = FR_InvX,FR_NormX,f1 // NR iteration #2 + nop.i 0 +};; +{ .mfi + setf.sig FR_int_N = GR_Exp + frcpa.s1 FR_InvXf,p9 = f1,FR_Xf // 1/xf + nop.i 0 +} +{ .mfi + ldfe FR_LnSqrt2Pi = [GR_ad_1],16 + nop.f 0 + nop.i 0 +};; +{ .mfi + getf.exp GR_SignExp = FR_Xf + nop.f 0 + nop.i 0 +} +{ .mfi + ldfe FR_W2 = [GR_ad_2],16 + nop.f 0 + nop.i 0 +};; +{ .mfi + getf.sig GR_Sig = FR_Xf + fma.s1 FR_P54 = FR_P5,FR_r,FR_P4 + nop.i 0 +} +{ .mfi + ldfe FR_T = [GR_ad_T] + fma.s1 FR_P32 = FR_P3,FR_r,FR_P2 + nop.i 0 +};; +{ .mfi + and GR_Exp = GR_SignExp,GR_ExpMask + fma.s1 FR_r2 = FR_r,FR_r,f0 + nop.i 0 +} +{ .mfi + nop.m 0 + fms.s1 FR_Xm05 = FR_NormX,f1,FR_05 // (x-1/2) + nop.i 0 +};; +{ .mfi + nop.m 0 + fma.s1 FR_InvX2 = FR_InvX,FR_InvX2,FR_InvX // NR iteration #2 + extr.u GR_Ind = GR_Sig,55,8 +} +{ .mfi + sub GR_Exp = GR_Exp,GR_ExpBias + fma.s1 FR_Xf4 = FR_Xf2,FR_Xf2,f0 + cmp.eq p6,p0 = 0,GR_Sig +};; +{ .mfi + setf.sig FR_int_Nf = GR_Exp + fma.s1 FR_S28 = FR_S28,FR_Xf2,FR_S26 + shladd GR_ad_T = GR_Ind,4,GR_ad_LnT +} +{ .mfb + nop.m 0 + fma.s1 FR_S24 = FR_S24,FR_Xf2,FR_S22 + // jump if the input argument is integer number from range (-512.0;-17.0] +(p6) br.cond.spnt lgamma_singularity +};; +{ .mfi + getf.sig GR_Sig = FR_int_Ntrunc + fma.s1 FR_S20 = FR_S20,FR_Xf2,FR_S18 + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 FR_S16 = FR_S16,FR_Xf2,FR_S14 + nop.i 0 +};; +{ .mfi + ldfe FR_Tf = [GR_ad_T] + fma.s1 FR_S12 = FR_S12,FR_Xf2,FR_S10 + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 FR_S8 = FR_S8,FR_Xf2,FR_S6 + mov GR_SignOfGamma = 1 +};; +{ .mfi + nop.m 0 + fms.s1 FR_rf = FR_InvXf,FR_Xf,f1 // reduced arg rf + tbit.z p8,p0 = GR_Sig,0 +} +{ .mfi + nop.m 0 + fma.s1 FR_r3 = FR_r2,FR_r,f0 + // 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 + fcvt.xf FR_N = FR_int_N +(p8) sub GR_SignOfGamma = r0,GR_SignOfGamma +} +{ .mfi + nop.m 0 + fnma.s1 FR_InvX = FR_InvX2,FR_NormX,f1 // NR iteration #3 + nop.i 0 +};; +.pred.rel "mutex",p9,p10 +{ .mfi + // store sign of gamma(x) as 32-bit int +(p9) st4 [r33] = GR_SignOfGamma + fma.s1 FR_P54 = FR_P54,FR_r2,FR_P32 + nop.i 0 +} +{ .mfi + // store sign of gamma(x) as 64-bit int +(p10) st8 [r33] = GR_SignOfGamma + fnma.s1 FR_P10 = FR_r2,FR_05,FR_r + 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_S28 = FR_S28,FR_Xf4,FR_S24 + nop.i 0 +};; +{ .mfi + nop.m 0 + fma.s1 FR_S20 = FR_S20,FR_Xf4,FR_S16 + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 FR_S12 = FR_S12,FR_Xf4,FR_S8 + 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_P54f = FR_P5,FR_rf,FR_P4 + 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_InvX = FR_InvX2,FR_InvX,FR_InvX2 // NR iteration #3 + nop.i 0 +};; +{ .mfi + nop.m 0 + fcvt.xf FR_Nf = FR_int_Nf + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 FR_LnSqrt2Pi = FR_NormX,f1,FR_LnSqrt2Pi // x+ln(sqrt(2*Pi)) + nop.i 0 +};; +{ .mfi + nop.m 0 + fma.s1 FR_P54 = FR_P54,FR_r3,FR_P10 + nop.i 0 +};; +{ .mfi + nop.m 0 + fma.s1 FR_S28 = FR_S28,FR_Xf8,FR_S20 + nop.i 0 +};; +{ .mfi + nop.m 0 + fma.s1 FR_rf3 = FR_rf2,FR_rf,f0 + nop.i 0 +} +{ .mfi + nop.m 0 + fnma.s1 FR_P10f = FR_rf2,FR_05,FR_rf + nop.i 0 +};; +{ .mfi + nop.m 0 + fma.s1 FR_TpNxLn2 = FR_N,FR_Ln2,FR_T + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 FR_P54f = FR_P54f,FR_rf2,FR_P32f + nop.i 0 +};; +{ .mfi + nop.m 0 + fma.s1 FR_InvX2 = FR_InvX,FR_InvX,f0 + nop.i 0 +};; +{ .mfi + nop.m 0 + fma.s1 FR_S28 = FR_S28,FR_Xf8,FR_S12 + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 FR_S4 = FR_S4,FR_Xf2,FR_S2 + nop.i 0 +};; +{ .mfi + nop.m 0 + fma.s1 FR_P54f = FR_P54f,FR_rf3,FR_P10f + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 FR_TpNxLn2f = FR_Nf,FR_Ln2,FR_Tf + nop.i 0 +};; +{ .mfi + nop.m 0 + fma.s1 FR_LnX = FR_TpNxLn2,f1,FR_P54 + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 FR_W2 = FR_W4,FR_InvX2,FR_W2 + nop.i 0 +};; +{ .mfi + nop.m 0 + fma.s1 FR_S28 = FR_S28,FR_Xf4,FR_S4 + nop.i 0 +};; +{ .mfi + nop.m 0 + fma.s1 FR_LnXf = FR_TpNxLn2f,f1,FR_P54f + nop.i 0 +};; +{ .mfi + nop.m 0 + fms.s1 FR_LnX = FR_LnX,FR_Xm05,FR_LnSqrt2Pi + nop.i 0 +};; +{ .mfi + nop.m 0 + fma.s1 FR_LnX = FR_InvX,FR_W2,FR_LnX + nop.i 0 +};; +{ .mfi + nop.m 0 + fnma.s1 FR_LnX = FR_S28,FR_Xf2,FR_LnX + nop.i 0 +};; +{ .mfb + nop.m 0 + fms.d.s0 f8 = FR_LnX,f1,FR_LnXf + br.ret.sptk b0 +};; +// branch for calculating of ln(GAMMA(x)) for 0 <= x < 1 +//--------------------------------------------------------------------- +.align 32 +lgamma_0_1: +{ .mfi + ldfpd FR_P5,FR_P4 = [GR_ad_1],16 + fms.s1 FR_x = FR_NormX,f1,f0 // x + mov GR_Arg025 = 0x3FD0 +} +{ .mfi + ldfpd FR_P3,FR_P2 = [GR_ad_2],16 + nop.f 0 + add GR_ad_Co = 0x1C40,GR_ad_Data +};; +{ .mfi + ldfe FR_Ln2 = [GR_ad_1],0x50 + nop.f 0 + // p6 if arg < 0.25 + cmp.lt p6,p9 = GR_Arg,GR_Arg025 +} +{ .mfi + add GR_ad_2 = 0x40,GR_ad_2 + nop.f 0 + mov GR_Arg075 = 0x3FE8 +};; +{ .mfi + ldfpd FR_Q8,FR_Q7 = [GR_ad_1],16 + fma.s1 FR_w2 = FR_w,FR_w,f0 + // p7 if 0.25 <= arg < 0.75 + // p8 if 0.75 <= arg < 1.0 +(p9) cmp.lt.unc p7,p8 = GR_Arg,GR_Arg075 +} +{ .mfi + mov GR_Arg0875 = 0x3FEC + nop.f 0 + sub GR_Exp = GR_Exp,GR_ExpBias +};; +{ .mfi + ldfpd FR_Q6,FR_Q5 = [GR_ad_2],16 + nop.f 0 +(p8) cmp.lt p9,p0 = GR_Arg,GR_Arg0875 +} +{ .mfi + ldfpd FR_Q4,FR_Q3 = [GR_ad_1],16 + nop.f 0 + add GR_ad_Ce = 0x60,GR_ad_Co +};; +.pred.rel "mutex",p7,p8 +{ .mfi + ldfd FR_Q2 = [GR_ad_2],16 + fms.s1 FR_r = FR_C,f8,f1 +(p7) mov GR_Offs = 0xC0 +} +{ .mfi + setf.sig FR_int_N = GR_Exp + nop.f 0 +(p8) mov GR_Offs = 0x180 +};; +.pred.rel "mutex",p6,p7 +{ .mfi +(p9) add GR_ad_Co = GR_Offs,GR_ad_Co +(p8) fms.s1 FR_x = FR_NormX,f1,f1 // x-1 + nop.i 0 +} +{ .mfi +(p9) add GR_ad_Ce = GR_Offs,GR_ad_Ce +(p7) fms.s1 FR_x = FR_NormX,f1,FR_LocalMin // x-LocalMin + cmp.lt p10,p0 = GR_Arg,GR_Arg0875 +};; +lgamma_common_0_2: +{ .mfi + ldfpd FR_A17,FR_A16 = [GR_ad_Co],16 + nop.f 0 + nop.i 0 +} +{ .mfi + ldfpd FR_A15,FR_A14 = [GR_ad_Ce],16 + nop.f 0 + nop.i 0 +};; +{ .mfi + ldfpd FR_A13,FR_A12 = [GR_ad_Co],16 + nop.f 0 +(p10) extr.u GR_Ind = GR_ArgAsIs,44,8 +} +{ .mfi + ldfpd FR_A11,FR_A10 = [GR_ad_Ce],16 + nop.f 0 + nop.i 0 +};; +{ .mfi + ldfpd FR_A9,FR_A8 = [GR_ad_Co],16 +(p10) fnma.s1 FR_Q1 = FR_05,FR_w2,FR_w + nop.i 0 +} +{ .mfi + ldfpd FR_A7,FR_A6 = [GR_ad_Ce],16 +(p10) fma.s1 FR_w3 = FR_w2,FR_w,f0 + nop.i 0 +};; +{ .mfi +(p10) getf.exp GR_SignExp_w = FR_w +(p10) fma.s1 FR_w4 = FR_w2,FR_w2,f0 + nop.i 0 +} +{ .mfi +(p10) shladd GR_ad_2 = GR_Ind,4,GR_ad_2 +(p10) fma.s1 FR_r2 = FR_r,FR_r,f0 + nop.i 0 +};; +{ .mfi +(p10) ldfe FR_T = [GR_ad_2] +(p10) fma.s1 FR_P54 = FR_P5,FR_r,FR_P4 + nop.i 0 +} +{ .mfi + ldfe FR_A5 = [GR_ad_Co],16 +(p10) fma.s1 FR_P32 = FR_P3,FR_r,FR_P2 + nop.i 0 +};; +{ .mfi + ldfe FR_A4 = [GR_ad_Ce],16 + fma.s1 FR_x2 = FR_x,FR_x,f0 +(p10) and GR_Exp_w = GR_ExpMask, GR_SignExp_w +} +{ .mfi + ldfe FR_A3 = [GR_ad_Co],16 + nop.f 0 +(p10) mov GR_fff9 = 0xfff9 +};; +// p13 <== large w __libm_lgamma +// p14 <== small w __libm_lgamma +{ .mfi + ldfe FR_A2 = [GR_ad_Ce],16 +(p10) fma.s1 FR_Q8 = FR_Q8,FR_w,FR_Q7 +(p10) cmp.ge.unc p13,p14 = GR_Exp_w,GR_fff9 +} +{ .mfi + ldfe FR_A1 = [GR_ad_Co],16 +(p10) fma.s1 FR_Q6 = FR_Q6,FR_w,FR_Q5 + nop.i 0 +};; +{ .mfi + ldfe FR_A0 = [GR_ad_Ce],16 +(p10) fma.s1 FR_Q4 = FR_Q4,FR_w,FR_Q3 + nop.i 0 +} +{ .mfi + nop.m 0 +(p10) fma.s1 FR_Q2 = FR_Q2,FR_w3,FR_Q1 + nop.i 0 +};; +{ .mfi + // set p11 if signgum is 32-bit int + // set p12 if signgum is 64-bit int + cmp.eq p12,p11 = 8,r34 +(p10) fma.s1 FR_r3 = FR_r2,FR_r,f0 + nop.i 0 +} +{ .mfi + nop.m 0 +(p10) fnma.s1 FR_P10 = FR_r2,FR_05,FR_r + mov GR_SignOfGamma = 1 +};; +.pred.rel "mutex",p11,p12 +{ .mfi + // store sign of gamma(x) as 32-bit int +(p11) st4 [r33] = GR_SignOfGamma + fma.s1 FR_A17 = FR_A17,FR_x,FR_A16 + nop.i 0 +} +{ .mfi + // store sign of gamma(x) as 64-bit int +(p12) st8 [r33] = GR_SignOfGamma + fma.s1 FR_A15 = FR_A15,FR_x,FR_A14 + nop.i 0 +};; +{ .mfi + nop.m 0 +(p10) fcvt.xf FR_N = FR_int_N + nop.i 0 +} +{ .mfi + nop.m 0 +(p10) fma.s1 FR_P54 = FR_P54,FR_r2,FR_P32 + nop.i 0 +};; +{ .mfi + nop.m 0 + fma.s1 FR_A13 = FR_A13,FR_x,FR_A12 + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 FR_A11 = FR_A11,FR_x,FR_A10 + nop.i 0 +};; +{ .mfi + nop.m 0 + fma.s1 FR_A9 = FR_A9,FR_x,FR_A8 + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 FR_A7 = FR_A7,FR_x,FR_A6 + nop.i 0 +};; +{ .mfi + nop.m 0 +(p10) fma.s1 FR_Qlo = FR_Q8,FR_w2,FR_Q6 + nop.i 0 +} +{ .mfi + nop.m 0 +(p10) fma.s1 FR_w6 = FR_w3,FR_w3,f0 + nop.i 0 +};; +{ .mfi + nop.m 0 +(p10) fma.s1 FR_Qhi = FR_Q4,FR_w4,FR_Q2 + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 FR_A5 = FR_A5,FR_x,FR_A4 + nop.i 0 +};; +{ .mfi + nop.m 0 +(p10) fma.s1 FR_TpNxLn2 = FR_N,FR_Ln2,FR_T + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 FR_A3 = FR_A3,FR_x,FR_A2 + nop.i 0 +};; +{ .mfi + nop.m 0 +(p10) fma.s1 FR_P54 = FR_P54,FR_r3,FR_P10 + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 FR_A1 = FR_A1,FR_x,FR_A0 + nop.i 0 +};; +{ .mfi + nop.m 0 + fma.s1 FR_A17 = FR_A17,FR_x2,FR_A15 + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 FR_A13 = FR_A13,FR_x2,FR_A11 + nop.i 0 +};; +{ .mfi + nop.m 0 + fma.s1 FR_A9 = FR_A9,FR_x2,FR_A7 + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 FR_x4 = FR_x2,FR_x2,f0 + nop.i 0 +};; +{ .mfi + nop.m 0 +(p14) fma.s1 FR_LnX = FR_Qlo,FR_w6,FR_Qhi + nop.i 0 +};; +{ .mfi + nop.m 0 + fma.s1 FR_A5 = FR_A5,FR_x2,FR_A3 + nop.i 0 +};; +{ .mfi + nop.m 0 +(p13) fma.s1 FR_LnX = FR_TpNxLn2,f1,FR_P54 + nop.i 0 +};; +{ .mfi + nop.m 0 + fma.s1 FR_A17 = FR_A17,FR_x4,FR_A13 + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 FR_x8 = FR_x4,FR_x4,f0 + nop.i 0 +};; +{ .mfi + nop.m 0 + fma.s1 FR_A9 = FR_A9,FR_x4,FR_A5 + nop.i 0 +};; +{ .mfi + nop.m 0 + fma.s1 FR_A17 = FR_A17,FR_x8,FR_A9 + nop.i 0 +};; +{ .mfi + nop.m 0 +(p10) fms.s1 FR_A1 = FR_A1,f1,FR_LnX + nop.i 0 +};; +{ .mfb + nop.m 0 + fma.d.s0 f8 = FR_A17,FR_x2,FR_A1 + br.ret.sptk b0 +};; +// branch for calculating of ln(GAMMA(x)) for 1.0 <= x < 2.25 +//--------------------------------------------------------------------- +.align 32 +lgamma_1_2: +{ .mfi + add GR_ad_Co = 0x10B0,GR_ad_1 + fcmp.eq.s1 p12,p0 = f1,FR_w + mov GR_Arg125 = 0x3FF4 +} +{ .mfi + add GR_ad_Ce = 0x1110,GR_ad_1 + nop.f 0 + mov GR_Arg175 = 0x3FFC +};; +{ .mfi + mov GR_SignOfGamma = 1 + fcmp.eq.s1 p13,p0 = f1,FR_NormX + cmp.lt p6,p9 = GR_Arg,GR_Arg125 // 1.0 <= x < 1.25 +} +{ .mfi + // set p10 if signgum is 32-bit int + // set p11 if signgum is 64-bit int + cmp.eq p11,p10 = 8,r34 + nop.f 0 + cmp.ge p8,p0 = GR_Arg,GR_Arg175 // x >= 1.75 +};; +.pred.rel "mutex",p10,p11 +{ .mfi + // store sign of gamma(x) as 32-bit int +(p10) st4 [r33] = GR_SignOfGamma +(p12) fma.d.s0 f8 = f0,f0,f0 +(p9) cmp.lt.unc p7,p0 = GR_Arg,GR_Arg175 // 1.25 <= x < 1.75 +} +{ .mib + // store sign of gamma(x) as 64-bit int +(p11) st8 [r33] = GR_SignOfGamma + mov GR_Offs = 0 +(p12) br.ret.spnt b0 // fast exit for 2.0 +};; +.pred.rel "mutex",p7,p8 +{ .mfi +(p7) mov GR_Offs = 0xC0 +(p7) fms.s1 FR_x = FR_w,f1,FR_LocalMin + nop.i 0 +} +{ .mfb +(p8) mov GR_Offs = 0x180 +(p13) fma.d.s0 f8 = f0,f0,f0 +(p13) br.ret.spnt b0 // fast exit for 1.0 +};; +.pred.rel "mutex",p6,p8 +{ .mfi + add GR_ad_Co = GR_ad_Co,GR_Offs +(p8) fms.s1 FR_x = FR_w,f1,f1 + cmp.eq p0,p10 = r0,r0 +} +{ .mfb + add GR_ad_Ce = GR_ad_Ce,GR_Offs +(p6) fma.s1 FR_x = f0,f0,FR_w + br.cond.sptk lgamma_common_0_2 +};; +// branch for calculating of ln(GAMMA(x)) for -17 < x < 0 +//--------------------------------------------------------------------- +.align 32 +lgamma_negrecursion: +{ .mfi + getf.d GR_ArgXfrAsIs = FR_Xfr + fma.s1 FR_Xp2 = FR_2,f1,FR_NormX + mov GR_Arg05 = 0x3FE +} +{ .mfi + add GR_ad_Roots = 0x1390,GR_ad_1 + fma.s1 FR_NormX = FR_NormX,FR_Xfr,f0 + mov GR_Arg075 = 0x3FE8 +};; +{ .mfi + getf.sig GR_Sig = FR_int_Ntrunc + fma.s1 FR_Xp3 = FR_2,f1,FR_Xp1 + shl GR_Arg05 = GR_Arg05,52 +} +{ .mfi + mov GR_Arg025 = 0x3FD0 + fma.s1 FR_Xp6 = FR_5,f1,FR_Xp1 + add GR_ad_Co = 0x1C40,GR_ad_Data +};; +{ .mfi + add GR_ad_Dx = 8,GR_ad_Roots + fma.s1 FR_Xp7 = FR_2,f1,FR_Xp5 + shr.u GR_ArgXfr = GR_ArgXfrAsIs,48 +} +{ .mfi + add GR_ad_Ce = 0x60,GR_ad_Co + fma.s1 FR_Xp8 = FR_3,f1,FR_Xp5 + cmp.lt p6,p0 = GR_ArgXfrAsIs,GR_Arg05 +};; +{ .mfi + and GR_RootInd = 0xF,GR_Sig + fma.s1 FR_Xp9 = FR_2,FR_2,FR_Xp5 + // p10 if arg < 0.25 + cmp.lt p10,p14 = GR_ArgXfr,GR_Arg025 +} +{ .mfi +(p6) add GR_ad_Roots = 0x120,GR_ad_Roots + fma.s1 FR_Xp11 = f1,f1,FR_Xp10 +(p6) add GR_ad_Dx = 0x120,GR_ad_Dx +};; +{ .mfi + shladd GR_ad_Root = GR_RootInd,4,GR_ad_Roots + fma.s1 FR_Xp12 = FR_2,f1,FR_Xp10 + // p11 if 0.25 <= arg < 0.75 + // p12 if 0.75 <= arg < 1.0 +(p14) cmp.lt.unc p11,p12 = GR_ArgXfr,GR_Arg075 +} +{ .mfi + shladd GR_ad_Dx = GR_RootInd,4,GR_ad_Dx + fma.s1 FR_Xp13 = FR_3,f1,FR_Xp10 + cmp.eq p0,p13 = 0,GR_Sig +};; +{ .mfi + ld8 GR_Root = [GR_ad_Root] + fma.s1 FR_Xp14 = FR_2,FR_2,FR_Xp10 +(p12) mov GR_Offs = 0x180 +} +{ .mfi + ldfd FR_Root = [GR_ad_Root] + fma.s1 FR_Xp15 = FR_5,f1,FR_Xp10 + and GR_Sig = 0xF,GR_Sig +};; +{ .mfi + ld8 GR_Dx = [GR_ad_Dx] + fma.s1 FR_Xp16 = FR_3,FR_2,FR_Xp10 +(p13) cmp.ge.unc p6,p0 = 0xD,GR_Sig +} +{ .mfi +(p11) mov GR_Offs = 0xC0 +(p13) fma.s1 FR_NormX = FR_NormX,FR_Xp1,f0 +(p13) cmp.ge.unc p7,p0 = 0xB,GR_Sig +};; +{ .mfi +(p14) add GR_ad_Co = GR_Offs,GR_ad_Co +(p6) fma.s1 FR_Xp2 = FR_Xp2,FR_Xp3,f0 +(p13) cmp.ge.unc p8,p0 = 0x9,GR_Sig +} +{ .mfi +(p14) add GR_ad_Ce = GR_Offs,GR_ad_Ce +(p7) fma.s1 FR_Xp4 = FR_Xp4,FR_Xp5,f0 +(p13) cmp.ge.unc p9,p0 = 0x7,GR_Sig +};; +{ .mfi + ldfpd FR_B17,FR_B16 = [GR_ad_Co],16 +(p8) fma.s1 FR_Xp6 = FR_Xp6,FR_Xp7,f0 +(p13) cmp.ge.unc p6,p0 = 0x5,GR_Sig +} +{ .mfi + ldfpd FR_B15,FR_B14 = [GR_ad_Ce],16 +(p9) fma.s1 FR_Xp8 = FR_Xp8,FR_Xp9,f0 +(p13) cmp.ge.unc p7,p0 = 0x3,GR_Sig +};; +{ .mfi + ldfpd FR_B13,FR_B12 = [GR_ad_Co],16 +(p6) fma.s1 FR_Xp10 = FR_Xp10,FR_Xp11,f0 +(p13) cmp.ge.unc p8,p0 = 0x1,GR_Sig +} +{ .mfi + ldfpd FR_B11,FR_B10 = [GR_ad_Ce],16 +(p7) fma.s1 FR_Xp12 = FR_Xp12,FR_Xp13,f0 +(p13) cmp.eq.unc p9,p0 = 0,GR_Sig +};; +{ .mfi + ldfpd FR_B9,FR_B8 = [GR_ad_Co],16 +(p8) fma.s1 FR_Xp14 = FR_Xp14,FR_Xp15,f0 + mov GR_Arg15 = 0xC02E // -15 +} +{ .mfi + ldfpd FR_B7,FR_B6 = [GR_ad_Ce],16 + fcmp.eq.s1 p15,p0 = f0,FR_Xf +(p13) cmp.ge.unc p6,p0 = 0xC,GR_Sig +};; +{ .mfi + ldfe FR_B5 = [GR_ad_Co],16 +(p9) fma.s1 FR_NormX = FR_NormX,FR_Xp16,f0 + sub GR_Root = GR_ArgAsIs,GR_Root +} +{ .mfi + sub GR_RootInd = 0xE,GR_RootInd +(p11) fms.s1 FR_x = FR_Xfr,f1,FR_LocalMin // x-LocalMin +(p13) cmp.ge.unc p7,p0 = 0x8,GR_Sig +};; +.pred.rel "mutex",p10,p12 +{ .mfi + ldfe FR_B4 = [GR_ad_Ce],16 +(p10) fms.s1 FR_x = FR_Xfr,f1,f0 // x + add GR_Root = GR_Root,GR_Dx +} +{ .mfb + cmp.gtu p14,p0 = 0xE,GR_RootInd +(p12) fms.s1 FR_x = FR_Xfr,f1,f1 // x-1 +(p15) br.cond.spnt lgamma_singularity +};; +{ .mfi + ldfe FR_B3 = [GR_ad_Co],16 +(p6) fma.s1 FR_Xp2 = FR_Xp2,FR_Xp4,f0 +(p14) cmp.lt.unc p11,p0 = GR_Arg,GR_Arg15 +} +{ .mfi + ldfe FR_B2 = [GR_ad_Ce],16 +(p7) fma.s1 FR_Xp6 = FR_Xp6,FR_Xp8,f0 + add GR_2xDx = GR_Dx,GR_Dx +};; +{ .mfi + ldfe FR_B1 = [GR_ad_Co],16 + fms.s1 FR_r = f8,f1,FR_Root +(p13) cmp.ge.unc p6,p0 = 0x4,GR_Sig +} +{ .mib + ldfe FR_B0 = [GR_ad_Ce],16 +(p11) cmp.leu.unc p10,p0 = GR_Root,GR_2xDx +(p10) br.cond.spnt lgamma_negroots +};; +{ .mfi + ldfpd FR_P5,FR_P4 = [GR_ad_1],16 +(p6) fma.s1 FR_Xp10 = FR_Xp10,FR_Xp12,f0 + tbit.z p14,p15 = GR_Sig,0 +} +{ .mfi + ldfpd FR_P3,FR_P2 = [GR_ad_2],16 + fnma.d.s0 FR_T = f1,f1,f8 // nop.f 0 + +(p13) cmp.ge.unc p7,p0 = 0x2,GR_Sig +};; +{ .mfi + ldfe FR_Ln2 = [GR_ad_1],0x50 +(p7) fma.s1 FR_NormX = FR_NormX,FR_Xp14,f0 + mov GR_PseudoRoot = 0xBFFBC +} +{ .mlx + add GR_ad_2 = 0x40,GR_ad_2 + movl GR_2xDx = 0x00002346DC5D6389 +};; +{ .mfi + ldfpd FR_Q8,FR_Q7 = [GR_ad_1],16 + fma.s1 FR_x2 = FR_x,FR_x,f0 + shl GR_PseudoRoot = GR_PseudoRoot,44 +} +{ .mfi + ldfpd FR_Q6,FR_Q5 = [GR_ad_2],16 + fma.s1 FR_B17 = FR_B17,FR_x,FR_B16 +(p13) cmp.ge.unc p6,p0 = 0xA,GR_Sig +};; +{ .mfi + ldfpd FR_Q4,FR_Q3 = [GR_ad_1],16 +(p6) fma.s1 FR_Xp2 = FR_Xp2,FR_Xp6,f0 + sub GR_PseudoRoot = GR_ArgAsIs,GR_PseudoRoot +} +{ .mfi + ldfpd FR_Q2,FR_Q1 = [GR_ad_2],16 + fma.s1 FR_B15 = FR_B15,FR_x,FR_B14 +(p13) cmp.ge.unc p7,p0 = 0x6,GR_Sig +};; +{ .mfi + add GR_ad_Co = 0x12F0,GR_ad_2 + fma.s1 FR_B13 = FR_B13,FR_x,FR_B12 + cmp.leu.unc p10,p0 = GR_PseudoRoot,GR_2xDx +} +{ .mfi + add GR_ad_Ce = 0x1300,GR_ad_2 + fma.s1 FR_B11 = FR_B11,FR_x,FR_B10 + mov GR_ExpMask = 0x1ffff +};; +{ .mfi +(p10) ldfe FR_PR01 = [GR_ad_Co],0xF0 + fma.s1 FR_B9 = FR_B9,FR_x,FR_B8 + mov GR_ExpBias = 0xFFFF +} +{ .mfb +(p10) ldfe FR_PR11 = [GR_ad_Ce],0xF0 + fma.s1 FR_B7 = FR_B7,FR_x,FR_B6 +(p10) br.cond.spnt lgamma_pseudoroot +};; +{ .mfi +(p13) cmp.ge.unc p6,p0 = 0xE,GR_Sig +(p7) fma.s1 FR_NormX = FR_NormX,FR_Xp10,f0 + tbit.z.unc p8,p0 = GR_Sig,0 +} +{ .mfi + mov GR_SignOfGamma = 1 + fma.s1 FR_B5 = FR_B5,FR_x,FR_B4 + // 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.s1 FR_B3 = FR_B3,FR_x,FR_B2 +(p8) sub GR_SignOfGamma = r0,GR_SignOfGamma +} +{ .mfi + nop.m 0 +(p14) fms.s1 FR_w = f0,f0,f1 + nop.i 0 +};; +.pred.rel "mutex",p9,p10 +{ .mfi + // store sign of gamma(x) as 32-bit int +(p9) st4 [r33] = GR_SignOfGamma + fma.s1 FR_B1 = FR_B1,FR_x,FR_B0 + nop.i 0 +} +{ .mfi + // store sign of gamma(x) as 64-bit int +(p10) st8 [r33] = GR_SignOfGamma + fma.s1 FR_B17 = FR_B17,FR_x2,FR_B15 + nop.i 0 +};; +{ .mfi + nop.m 0 + fma.s1 FR_B13 = FR_B13,FR_x2,FR_B11 + nop.i 0 +};; +{ .mfi + nop.m 0 + fma.s1 FR_B9 = FR_B9,FR_x2,FR_B7 + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 FR_x4 = FR_x2,FR_x2,f0 + nop.i 0 +};; +{ .mfi + nop.m 0 +(p6) fma.s1 FR_NormX = FR_NormX,FR_Xp2,f0 + nop.i 0 +};; +{ .mfi + nop.m 0 + fma.s1 FR_B5 = FR_B5,FR_x2,FR_B3 + nop.i 0 +};; +{ .mfi + nop.m 0 + fma.s1 FR_B17 = FR_B17,FR_x4,FR_B13 + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 FR_x8 = FR_x4,FR_x4,f0 + nop.i 0 +};; +.pred.rel "mutex",p14,p15 +{ .mfi + nop.m 0 +(p15) fms.s1 FR_w = FR_NormX,f1,f1 + nop.i 0 +} +{ .mfi + nop.m 0 +(p14) fnma.s1 FR_w = FR_NormX,f1,FR_w + nop.i 0 +};; +{ .mfi + nop.m 0 + fma.s1 FR_B9 = FR_B9,FR_x4,FR_B5 + nop.i 0 +};; +{ .mfi + nop.m 0 + frcpa.s1 FR_C,p0 = f1,FR_NormX + nop.i 0 +};; +{ .mfi + getf.exp GR_Exp = FR_NormX + nop.f 0 + nop.i 0 +};; +{ .mfi + getf.d GR_ArgAsIs = FR_NormX + nop.f 0 + nop.i 0 +};; +{ .mfi + nop.m 0 + fma.s1 FR_w2 = FR_w,FR_w,f0 + nop.i 0 +} +{ .mfi + and GR_Exp = GR_Exp,GR_ExpMask + fma.s1 FR_Q8 = FR_Q8,FR_w,FR_Q7 + nop.i 0 +};; +{ .mfi + sub GR_Exp = GR_Exp,GR_ExpBias + fma.s1 FR_B17 = FR_B17,FR_x8,FR_B9 + extr.u GR_Ind = GR_ArgAsIs,44,8 +} +{ .mfi + nop.m 0 + fma.s1 FR_Q6 = FR_Q6,FR_w,FR_Q5 + nop.i 0 +};; +{ .mfi + setf.sig FR_int_N = GR_Exp + fms.s1 FR_r = FR_C,FR_NormX,f1 + nop.i 0 +} +{ .mfi + shladd GR_ad_2 = GR_Ind,4,GR_ad_2 + nop.f 0 + nop.i 0 +};; +{ .mfi + getf.exp GR_SignExp_w = FR_w + fma.s1 FR_Q4 = FR_Q4,FR_w,FR_Q3 + nop.i 0 +} +{ .mfi + ldfe FR_T = [GR_ad_2] + nop.f 0 + nop.i 0 +};; +{ .mfi + and GR_Exp_w = GR_ExpMask, GR_SignExp_w + fnma.s1 FR_Q1 = FR_05,FR_w2,FR_w + mov GR_fff9 = 0xfff9 +} +{ .mfi + nop.m 0 + fma.s1 FR_w3 = FR_w2,FR_w,f0 + nop.i 0 +};; +{ .mfi + nop.m 0 + fma.s1 FR_w4 = FR_w2,FR_w2,f0 +// p13 <== large w __libm_lgamma +// p14 <== small w __libm_lgamma + cmp.ge p13,p14 = GR_Exp_w,GR_fff9 +} +{ .mfi + nop.m 0 + fma.s1 FR_Qlo = FR_Q8,FR_w2,FR_Q6 + nop.i 0 +};; +{ .mfi + nop.m 0 +(p13) fma.s1 FR_r2 = FR_r,FR_r,f0 + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 FR_B17 = FR_B17,FR_x2,FR_B1 + nop.i 0 +};; +{ .mfi + nop.m 0 +(p13) fma.s1 FR_P32 = FR_P3,FR_r,FR_P2 + nop.i 0 +} +{ .mfi + nop.m 0 +(p13) fma.s1 FR_P54 = FR_P5,FR_r,FR_P4 + nop.i 0 +};; +{ .mfi + nop.m 0 +(p14) fma.s1 FR_Q2 = FR_Q2,FR_w3,FR_Q1 + nop.i 0 +} +{ .mfi + nop.m 0 +(p14) fma.s1 FR_w6 = FR_w3,FR_w3,f0 + nop.i 0 +};; +{ .mfi + nop.m 0 +(p13) fcvt.xf FR_N = FR_int_N + nop.i 0 +};; +{ .mfi + nop.m 0 +(p13) fma.s1 FR_r3 = FR_r2,FR_r,f0 + nop.i 0 +} +{ .mfi + nop.m 0 +(p13) fnma.s1 FR_P10 = FR_r2,FR_05,FR_r + nop.i 0 +};; +{ .mfi + nop.m 0 +(p13) fma.s1 FR_P54 = FR_P54,FR_r2,FR_P32 + nop.i 0 +};; +{ .mfi + nop.m 0 +(p14) fma.s1 FR_Qhi = FR_Q4,FR_w4,FR_Q2 + nop.i 0 +} +{ .mfi + nop.m 0 +(p14) fnma.s1 FR_Qlo = FR_Qlo,FR_w6,FR_B17 + nop.i 0 +};; +{ .mfi + nop.m 0 +(p13) fma.s1 FR_TpNxLn2 = FR_N,FR_Ln2,FR_T + nop.i 0 +};; +{ .mfi + nop.m 0 +(p13) fma.s1 FR_P54 = FR_P54,FR_r3,FR_P10 + nop.i 0 +};; +.pred.rel "mutex",p13,p14 +{ .mfi + nop.m 0 +(p14) fms.d.s0 f8 = FR_Qlo,f1,FR_Qhi + nop.i 0 +} +{ .mfi + nop.m 0 +(p13) fma.s1 FR_LnX = FR_TpNxLn2,f1,FR_P54 + nop.i 0 +};; +{ .mfb + nop.m 0 +(p13) fms.d.s0 f8 = FR_B17,f1,FR_LnX + br.ret.sptk b0 +};; +// branch for calculating of ln(GAMMA(x)) near negative roots +//--------------------------------------------------------------------- +.align 32 +lgamma_negroots: +{ .mfi + shladd GR_Offs = GR_RootInd,3,r0 //GR_RootInd*8 + fma.s1 FR_r2 = FR_r,FR_r,f0 + add GR_ad_Co = 0x15C0,GR_ad_1//0x1590,GR_ad_1 +} +{ .mfi + add GR_ad_Ce = 0x1610,GR_ad_1//0x15E0,GR_ad_1 + nop.f 0 + cmp.lt p6,p0 = GR_ArgXfrAsIs,GR_Arg05 +};; +{ .mfi + add GR_ad_Roots = 0x10A0,GR_ad_1 + nop.f 0 +(p6) add GR_ad_Co = 0x820,GR_ad_Co +} +{ .mfi +(p6) add GR_ad_Ce = 0x820,GR_ad_Ce + nop.f 0 + shladd GR_Offs = GR_RootInd,1,GR_Offs //GR_RootInd*10 +};; +{ .mmi + shladd GR_ad_Co = GR_Offs,4,GR_ad_Co + shladd GR_ad_Ce = GR_Offs,4,GR_ad_Ce + cmp.eq p8,p7 = r0,r0 +};; +{ .mmi + ldfpd FR_A15,FR_A14 = [GR_ad_Co],16 + ldfpd FR_A13,FR_A12 = [GR_ad_Ce],16 + mov GR_SignOfGamma = 1 +};; +{ .mmi + ldfpd FR_A11,FR_A10 = [GR_ad_Co],16 + ldfpd FR_A9,FR_A8 = [GR_ad_Ce],16 +(p6) cmp.eq p7,p8 = r0,GR_RootInd +};; +{ .mmi + ldfpd FR_A7,FR_A6 = [GR_ad_Co],16 + ldfpd FR_A5,FR_A4 = [GR_ad_Ce],16 + tbit.z p11,p0 = GR_Sig,0 +};; +{ .mmi + ldfe FR_A3 = [GR_ad_Co],16 + ldfe FR_A2 = [GR_ad_Ce],16 + // set p9 if signgum is 32-bit int + // set p10 if signgum is 64-bit int + cmp.eq p10,p9 = 8,r34 +};; +{ .mmi + ldfe FR_A1 = [GR_ad_Co],16 + ldfe FR_A0 = [GR_ad_Ce],16 +(p11) sub GR_SignOfGamma = r0,GR_SignOfGamma +};; +{ .mfi + ldfe FR_A00 = [GR_ad_Roots] + fma.s1 FR_r4 = FR_r2,FR_r2,f0 + nop.i 0 +};; +{ .mfi + nop.m 0 + fma.s1 FR_A15 = FR_A15,FR_r,FR_A14 + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 FR_A13 = FR_A13,FR_r,FR_A12 + nop.i 0 +};; +.pred.rel "mutex",p9,p10 +{ .mfi + // store sign of gamma(x) as 32-bit int +(p9) st4 [r33] = GR_SignOfGamma + fma.s1 FR_A11 = FR_A11,FR_r,FR_A10 + nop.i 0 +} +{ .mfi + // store sign of gamma(x) as 64-bit int +(p10) st8 [r33] = GR_SignOfGamma + fma.s1 FR_A9 = FR_A9,FR_r,FR_A8 + nop.i 0 +};; +{ .mfi + nop.m 0 + fma.s1 FR_A7 = FR_A7,FR_r,FR_A6 + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 FR_A5 = FR_A5,FR_r,FR_A4 + nop.i 0 +};; +{ .mfi + nop.m 0 + fma.s1 FR_A3 = FR_A3,FR_r,FR_A2 + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 FR_r8 = FR_r4,FR_r4,f0 + nop.i 0 +};; +{ .mfi + nop.m 0 + fma.s1 FR_A1 = FR_A1,FR_r,FR_A0 + nop.i 0 +};; +{ .mfi + nop.m 0 + fma.s1 FR_A15 = FR_A15,FR_r2,FR_A13 + nop.i 0 +};; +{ .mfi + nop.m 0 + fma.s1 FR_A11 = FR_A11,FR_r2,FR_A9 + nop.i 0 +};; +{ .mfi + nop.m 0 + fma.s1 FR_A7 = FR_A7,FR_r2,FR_A5 + nop.i 0 +};; +{ .mfi + nop.m 0 + fma.s1 FR_A3 = FR_A3,FR_r2,FR_A1 + nop.i 0 +};; +{ .mfi + nop.m 0 + fma.s1 FR_A15 = FR_A15,FR_r4,FR_A11 + nop.i 0 +};; +{ .mfi + nop.m 0 + fma.s1 FR_A7 = FR_A7,FR_r4,FR_A3 + nop.i 0 +};; +.pred.rel "mutex",p7,p8 +{ .mfi + nop.m 0 +(p7) fma.s1 FR_A1 = FR_A15,FR_r8,FR_A7 + nop.i 0 +} +{ .mfi + nop.m 0 +(p8) fma.d.s0 f8 = FR_A15,FR_r8,FR_A7 + nop.i 0 +};; +{ .mfb + nop.m 0 +(p7) fma.d.s0 f8 = FR_A1,FR_r,FR_A00 + br.ret.sptk b0 +};; +// branch for handling pseudo root on (-2;-1) +//--------------------------------------------------------------------- +.align 32 +lgamma_pseudoroot: +{ .mmi + ldfe FR_PR21 = [GR_ad_Co],32 + ldfe FR_PR31 = [GR_ad_Ce],32 + // set p9 if signgum is 32-bit int + // set p10 if signgum is 64-bit int + cmp.eq p10,p9 = 8,r34 +};; +{ .mmi + ldfe FR_PR00 = [GR_ad_Co],32 + ldfe FR_PR10 = [GR_ad_Ce],0xF0 + mov GR_SignOfGamma = 1 +};; +{ .mmi + ldfe FR_PR20 = [GR_ad_Co],0xF0 + ldfe FR_PR30 = [GR_ad_Ce] + tbit.z p8,p0 = GR_Sig,0 +};; +{ .mfi + ldfe FR_PRN = [GR_ad_Co] + fma.s1 FR_PR01 = f8,f1,FR_PR01 + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 FR_PR11 = f8,f1,FR_PR11 +(p8) sub GR_SignOfGamma = r0,GR_SignOfGamma +};; +.pred.rel "mutex",p9,p10 +{ .mfi + // store sign of gamma(x) as 32-bit int +(p9) st4 [r33] = GR_SignOfGamma + fma.s1 FR_PR21 = f8,f1,FR_PR21 + nop.i 0 +} +{ .mfi + // store sign of gamma(x) as 64-bit int +(p10) st8 [r33] = GR_SignOfGamma + fma.s1 FR_PR31 = f8,f1,FR_PR31 + nop.i 0 +};; +{ .mfi + nop.m 0 + fma.s1 FR_PR01 = f8,FR_PR01,FR_PR00 + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 FR_PR11 = f8,FR_PR11,FR_PR10 + nop.i 0 +};; +{ .mfi + nop.m 0 + fma.s1 FR_PR21 = f8,FR_PR21,FR_PR20 + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 FR_PR31 = f8,FR_PR31,FR_PR30 + nop.i 0 +};; +{ .mfi + nop.m 0 + fma.s1 FR_PR01 = FR_PR11,FR_PR01,f0 + nop.i 0 +};; +{ .mfi + nop.m 0 + fma.s1 FR_PR21 = FR_PR31,FR_PR21,f0 + nop.i 0 +};; +{ .mfi + nop.m 0 + fma.s1 FR_PR01 = FR_PR21,FR_PR01,f0 + nop.i 0 +};; +{ .mfb + nop.m 0 + fma.d.s0 f8 = FR_PR01,FR_PRN,f0 + br.ret.sptk b0 +};; +// branch for handling +/-0, NaT, QNaN, +/-INF and denormalised numbers +//--------------------------------------------------------------------- +.align 32 +lgamma_spec: +{ .mfi + getf.exp GR_SignExp = FR_NormX + fclass.m p6,p0 = f8,0x21 // is arg +INF? + mov GR_SignOfGamma = 1 +};; +{ .mfi + getf.sig GR_ArgAsIs = 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,8,4 +} +{ .mib + // store sign of gamma(x) as 64-bit int +(p12) st8 [r33] = GR_SignOfGamma + cmp.lt p10,p0 = GR_SignExp,GR_ExpBias +(p6) br.ret.spnt b0 // exit for +INF +};; +{ .mfi + and GR_Exp = GR_SignExp,GR_ExpMask + fclass.m p9,p0 = f8,0x22 // is arg -INF? + nop.i 0 +};; +{ .mfi + add GR_ad_Co = GR_Ind,GR_ad_Data +(p7) fma.s0 FR_tmp = f8,f8,f8 + extr.u GR_ArgAsIs = GR_ArgAsIs,11,52 +} +{ .mfb + nop.m 0 +(p8) fms.d.s0 f8 = f8,f1,f8 +(p8) br.ret.spnt b0 // exit for NaT and NaN +};; +{ .mib + nop.m 0 + shr.u GR_Arg = GR_ArgAsIs,48 +(p7) br.cond.sptk lgamma_common +};; +{ .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 +lgamma_singularity: +{ .mfi + mov GR_ad_SignGam = r33 + fclass.m p6,p0 = f8, 0x6 // is x -0? + mov GR_SignOfGamma = 1 +} +{ .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_X = f0,f0,f8 + nop.i 0 +};; +{ .mfi + nop.m 0 + frcpa.s0 f8,p0 = f1,f0 + mov GR_TAG = 106 // negative +} +{ .mib + nop.m 0 +(p6) sub GR_SignOfGamma = r0,GR_SignOfGamma + br.cond.sptk lgamma_libm_err +};; +// overflow (x > OVERFLOV_BOUNDARY) +//--------------------------------------------------------------------- +.align 32 +lgamma_overflow: +{ .mfi + mov GR_SignOfGamma = 1 + nop.f 0 + mov r8 = 0x1FFFE +};; +{ .mfi + setf.exp f9 = r8 + fmerge.s FR_X = f8,f8 + mov GR_TAG = 105 // 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.d.s0 f8 = f9,f9,f0 // Set I,O and +INF result + nop.i 0 +};; +// +//--------------------------------------------------------------------- +.align 32 +lgamma_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_lgamma) + + +LOCAL_LIBM_ENTRY(__libm_error_region) +.prologue +{ .mfi + add GR_Parameter_Y=-32,sp // Parameter 2 value + nop.f 0 +.save ar.pfs,GR_SAVE_PFS + mov GR_SAVE_PFS=ar.pfs // Save ar.pfs +} +{ .mfi +.fframe 64 + add sp=-64,sp // Create new stack + nop.f 0 + mov GR_SAVE_GP=gp // Save gp +};; +{ .mmi + stfd [GR_Parameter_Y] = FR_Y,16 // STORE Parameter 2 on stack + add GR_Parameter_X = 16,sp // Parameter 1 address +.save b0, GR_SAVE_B0 + mov GR_SAVE_B0=b0 // Save b0 +};; +.body +{ .mib + stfd [GR_Parameter_X] = FR_X // STORE Parameter 1 + // on stack + add GR_Parameter_RESULT = 0,GR_Parameter_Y // Parameter 3 address + nop.b 0 +} +{ .mib + stfd [GR_Parameter_Y] = FR_RESULT // STORE Parameter 3 + // on stack + add GR_Parameter_Y = -16,GR_Parameter_Y + br.call.sptk b0=__libm_error_support# // Call error handling + // function +};; +{ .mmi + nop.m 0 + nop.m 0 + add GR_Parameter_RESULT = 48,sp +};; +{ .mmi + ldfd f8 = [GR_Parameter_RESULT] // Get return result off stack +.restore sp + add sp = 64,sp // Restore stack pointer + mov b0 = GR_SAVE_B0 // Restore return address +};; +{ .mib + mov gp = GR_SAVE_GP // Restore gp + mov ar.pfs = GR_SAVE_PFS // Restore ar.pfs + br.ret.sptk b0 // Return +};; + +LOCAL_LIBM_END(__libm_error_region) +.type __libm_error_support#,@function +.global __libm_error_support# |