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Diffstat (limited to 'sysdeps/ia64/fpu/libm_lgamma.S')
| -rw-r--r-- | sysdeps/ia64/fpu/libm_lgamma.S | 3623 |
1 files changed, 3623 insertions, 0 deletions
diff --git a/sysdeps/ia64/fpu/libm_lgamma.S b/sysdeps/ia64/fpu/libm_lgamma.S new file mode 100644 index 0000000000..6096319ba5 --- /dev/null +++ b/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# |