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diff --git a/sysdeps/ia64/fpu/libm_lgammal.S b/sysdeps/ia64/fpu/libm_lgammal.S new file mode 100644 index 0000000000..056171b7d2 --- /dev/null +++ b/sysdeps/ia64/fpu/libm_lgammal.S @@ -0,0 +1,7676 @@ +.file "libm_lgammal.s" + + +// Copyright (c) 2002 - 2003, Intel Corporation +// All rights reserved. +// +// Contributed 2002 by the Intel Numerics Group, Intel Corporation +// +// Redistribution and use in source and binary forms, with or without +// modification, are permitted provided that the following conditions are +// met: +// +// * Redistributions of source code must retain the above copyright +// notice, this list of conditions and the following disclaimer. +// +// * Redistributions in binary form must reproduce the above copyright +// notice, this list of conditions and the following disclaimer in the +// documentation and/or other materials provided with the distribution. +// +// * The name of Intel Corporation may not be used to endorse or promote +// products derived from this software without specific prior written +// permission. + +// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS +// "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES,INCLUDING,BUT NOT +// LIMITED TO,THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR +// A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL INTEL OR ITS +// CONTRIBUTORS BE LIABLE FOR ANY DIRECT,INDIRECT,INCIDENTAL,SPECIAL, +// EXEMPLARY,OR CONSEQUENTIAL DAMAGES (INCLUDING,BUT NOT LIMITED TO, +// PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,DATA,OR +// PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY +// OF LIABILITY,WHETHER IN CONTRACT,STRICT LIABILITY OR TORT (INCLUDING +// NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS +// SOFTWARE,EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. +// +// Intel Corporation is the author of this code,and requests that all +// problem reports or change requests be submitted to it directly at +// http://www.intel.com/software/products/opensource/libraries/num.htm. +// +//********************************************************************* +// +// History: +// 03/28/02 Original version +// 05/20/02 Cleaned up namespace and sf0 syntax +// 08/21/02 Added support of SIGN(GAMMA(x)) calculation +// 09/26/02 Algorithm description improved +// 10/21/02 Now it returns SIGN(GAMMA(x))=-1 for negative zero +// 02/10/03 Reordered header: .section, .global, .proc, .align +// +//********************************************************************* +// +// Function: __libm_lgammal(long double x, int* signgam, int szsigngam) +// computes the principal 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: f8 (Input and Return Value) +// f9-f15 +// f32-f127 +// +// General Purpose Registers: +// r2, r3, r8-r11, r14-r31 +// r32-r65 +// r66-r69 (Used to pass arguments to error handling routine) +// +// Predicate Registers: p6-p15 +// +//********************************************************************* +// +// IEEE Special Conditions: +// +// __libm_lgammal(+inf) = +inf +// __libm_lgammal(-inf) = QNaN +// __libm_lgammal(+/-0) = +inf +// __libm_lgammal(x<0, x - integer) = QNaN +// __libm_lgammal(SNaN) = QNaN +// __libm_lgammal(QNaN) = QNaN +// +//********************************************************************* +// +// ALGORITHM DESCRIPTION +// +// Below we suppose that there is log(z) function which takes an long +// double argument and returns result as a pair of long double numbers +// lnHi and lnLo (such that sum lnHi + lnLo provides ~80 correct bits +// of significand). Algorithm description for such log(z) function +// see below. +// Also, it this algorithm description we use the following notational +// conventions: +// a) pair A = (Ahi, Alo) means number A represented as sum of Ahi and Alo +// b) C = A + B = (Ahi, Alo) + (Bhi, Blo) means multi-precision addition. +// The result would be C = (Chi, Clo). Notice, that Clo shouldn't be +// equal to Alo + Blo +// c) D = A*B = (Ahi, Alo)*(Bhi, Blo) = (Dhi, Dlo) multi-precisiion +// multiplication. +// +// So, lgammal has the following computational paths: +// 1) |x| < 0.5 +// P = A1*|x| + A2*|x|^2 + ... + A22*|x|^22 +// A1, A2, A3 represented as a sum of two double precision +// numbers and multi-precision computations are used for 3 higher +// terms of the polynomial. We get polynomial as a sum of two +// double extended numbers: P = (Phi, Plo) +// 1.1) x > 0 +// lgammal(x) = P - log(|x|) = (Phi, Plo) - (lnHi(|x|), lnLo(|x|)) +// 1.2) x < 0 +// lgammal(x) = -P - log(|x|) - log(sin(Pi*x)/(Pi*x)) +// P and log(|x|) are computed by the same way as in 1.1; +// - log(sin(Pi*x)/(Pi*x)) is approximated by a polynomial Plnsin. +// Plnsin:= fLnSin2*|x|^2 + fLnSin4*|x|^4 + ... + fLnSin36*|x|^36 +// The first coefficient of Plnsin is represented as sum of two +// double precision numbers (fLnSin2, fLnSin2L). Multi-precision +// computations for higher two terms of Plnsin are used. +// So, the final result is reconstructed by the following formula +// lgammal(x) = (-(Phi, Plo) - (lnHi(|x|), lnLo(|x|))) - +// - (PlnsinHi,PlnsinLo) +// +// 2) 0.5 <= x < 0.75 -> t = x - 0.625 +// -0.75 < x <= -0.5 -> t = x + 0.625 +// 2.25 <= x < 4.0 -> t = x/2 - 1.5 +// 4.0 <= x < 8.0 -> t = x/4 - 1.5 +// -0.5 < x <= -0.40625 -> t = x + 0.5 +// -2.6005859375 < x <= -2.5 -> t = x + 2.5 +// 1.3125 <= x < 1.5625 -> t = x - LOC_MIN, where LOC_MIN is point in +// which lgammal has local minimum. Exact +// value can be found in the table below, +// approximate value is ~1.46 +// +// lgammal(x) is approximated by the polynomial of 25th degree: P25(t) +// P25(t) = A0 + A1*t + ... + A25*t^25 = (Phi, Plo) + t^4*P21(t), +// where +// (Phi, Plo) is sum of four highest terms of the polynomial P25(t): +// (Phi, Plo) = ((A0, A0L) + (A1, A1L)*t) + t^2 *((A2, A2L) + (A3, A3L)*t), +// (Ai, AiL) - coefficients represented as pairs of DP numbers. +// +// P21(t) = (PolC(t)*t^8 + PolD(t))*t^8 + PolE(t), +// where +// PolC(t) = C21*t^5 + C20*t^4 + ... + C16, +// C21 = A25, C20 = A24, ..., C16 = A20 +// +// PolD(t) = D7*t^7 + D6*t^6 + ... + D0, +// D7 = A19, D6 = A18, ..., D0 = A12 +// +// PolE(t) = E7*t^7 + E6*t^6 + ... + E0, +// E7 = A11, E6 = A10, ..., E0 = A4 +// +// Cis and Dis are represented as double precision numbers, +// Eis are represented as double extended numbers. +// +// 3) 0.75 <= x < 1.3125 -> t = x - 1.0 +// 1.5625 <= x < 2.25 -> t = x - 2.0 +// lgammal(x) is approximated by the polynomial of 25th degree: P25(t) +// P25(t) = A1*t + ... + A25*t^25, and computations are carried out +// by similar way as in the previous case +// +// 4) 10.0 < x <= Overflow Bound ("positive Sterling" range) +// lgammal(x) is approximated using Sterling's formula: +// lgammal(x) ~ ((x*(lnHi(x) - 1, lnLo(x))) - 0.5*(lnHi(x), lnLo(x))) + +// + ((Chi, Clo) + S(1/x)) +// where +// C = (Chi, Clo) - pair of double precision numbers representing constant +// 0.5*ln(2*Pi); +// S(1/x) = 1/x * (B2 + B4*(1/x)^2 + ... + B20*(1/x)^18), B2, ..., B20 are +// Bernulli numbers. S is computed in native precision and then added to +// Clo; +// lnHi(x) - 1 is computed in native precision and the multiprecision +// multiplication (x, 0) *(lnHi(x) - 1, lnLo(x)) is used. +// +// 5) -INF < x <= -2^63, any negative integer < 0 +// All numbers in this range are integers -> error handler is called +// +// 6) -2^63 < x <= -0.75 ("negative Sterling" range), x is "far" from root, +// lgammal(-t) for positive t is approximated using the following formula: +// lgammal(-t) = -lgammal(t)-log(t)-log(|dT|)+log(sin(Pi*|dT|)/(Pi*|dT|)) +// where dT = -t -round_to_nearest_integer(-t) +// Last item is approximated by the same polynomial as described in 1.2. +// We split the whole range into three subranges due to different ways of +// approximation of the first terms. +// 6.1) -2^63 < x < -6.0 ("negative Sterling" range) +// lgammal(t) is approximated exactly as in #4. The only difference that +// for -13.0 < x < -6.0 subrange instead of Bernulli numbers we use their +// minimax approximation on this range. +// log(t), log(|dT|) are approximated by the log routine mentioned above. +// 6.2) -6.0 < x <= -0.75, |x + 1|> 2^(-7) +// log(t), log(|dT|) are approximated by the log routine mentioned above, +// lgammal(t) is approximated by polynomials of the 25th degree similar +// to ones from #2. Arguments z of the polynomials are as follows +// a) 0.75 <= t < 1.0 - 2^(-7), z = 2*t - 1.5 +// b) 1.0 - 2^(-7) < t < 2.0, z = t - 1.5 +// c) 2.0 < t < 3.0, z = t/2 - 1.5 +// d) 3.0 < t < 4.0, z = t/2 - 1.5. Notice, that range reduction is +// the same as in case c) but the set of coefficients is different +// e) 4.0 < t < 6.0, z = t/4 - 1.5 +// 6.3) |x + 1| <= 2^(-7) +// log(1 + (x-1)) is approximated by Taylor series, +// log(sin(Pi*|dT|)/(Pi*|dT|)) is still approximated by polynomial but +// it has just 4th degree. +// log(|dT|) is approximated by the log routine mentioned above. +// lgammal(-x) is approximated by polynomial of 8th degree from (-x + 1). +// +// 7) -20.0 < x < -2.0, x falls in root "neighbourhood". +// "Neighbourhood" means that |lgammal(x)| < epsilon, where epsilon is +// different for every root (and it is stored in the table), but typically +// it is ~ 0.15. There are 35 roots significant from "double extended" +// point of view. We split all the roots into two subsets: "left" and "right" +// roots. Considering [-(N+1), -N] range we call root as "left" one if it +// lies closer to -(N+1) and "right" otherwise. There is no "left" root in +// the [-20, -19] range (it exists, but is insignificant for double extended +// precision). To determine if x falls in root "neighbourhood" we store +// significands of all the 35 roots as well as epsilon values (expressed +// by the left and right bound). +// In these ranges we approximate lgammal(x) by polynomial series of 19th +// degree: +// lgammal(x) = P19(t) = A0 + A1*t + ...+ A19*t^19, where t = x - EDP_Root, +// EDP_Root is the exact value of the corresponding root rounded to double +// extended precision. So, we have 35 different polynomials which make our +// table rather big. We may hope that x falls in root "neighbourhood" +// quite rarely -> ther might be no need in frequent use of different +// polynomials. +// A0, A1, A2, A3 are represented as pairs of double precision numbers, +// A4, A5 are long doubles, and to decrease the size of the table we +// keep the rest of coefficients in just double precision +// +//********************************************************************* +// Algorithm for log(X) = (lnHi(X), lnLo(X)) +// +// ALGORITHM +// +// Here we use a table lookup method. The basic idea is that in +// order to compute logl(Arg) for an argument Arg in [1,2), we +// construct a value G such that G*Arg is close to 1 and that +// logl(1/G) is obtainable easily from a table of values calculated +// beforehand. Thus +// +// logl(Arg) = logl(1/G) + logl(G*Arg) +// = logl(1/G) + logl(1 + (G*Arg - 1)) +// +// Because |G*Arg - 1| is small, the second term on the right hand +// side can be approximated by a short polynomial. We elaborate +// this method in four steps. +// +// Step 0: Initialization +// +// We need to calculate logl( X ). Obtain N, S_hi such that +// +// X = 2^N * S_hi exactly +// +// where S_hi in [1,2) +// +// Step 1: Argument Reduction +// +// Based on S_hi, obtain G_1, G_2, G_3 from a table and calculate +// +// G := G_1 * G_2 * G_3 +// r := (G * S_hi - 1) +// +// These G_j's have the property that the product is exactly +// representable and that |r| < 2^(-12) as a result. +// +// Step 2: Approximation +// +// +// logl(1 + r) is approximated by a short polynomial poly(r). +// +// Step 3: Reconstruction +// +// +// Finally, logl( X ) is given by +// +// logl( X ) = logl( 2^N * S_hi ) +// ~=~ N*logl(2) + logl(1/G) + logl(1 + r) +// ~=~ N*logl(2) + logl(1/G) + poly(r). +// +// IMPLEMENTATION +// +// Step 0. Initialization +// ---------------------- +// +// Z := X +// N := unbaised exponent of Z +// S_hi := 2^(-N) * Z +// +// Step 1. Argument Reduction +// -------------------------- +// +// Let +// +// Z = 2^N * S_hi = 2^N * 1.d_1 d_2 d_3 ... d_63 +// +// We obtain G_1, G_2, G_3 by the following steps. +// +// +// Define X_0 := 1.d_1 d_2 ... d_14. This is extracted +// from S_hi. +// +// Define A_1 := 1.d_1 d_2 d_3 d_4. This is X_0 truncated +// to lsb = 2^(-4). +// +// Define index_1 := [ d_1 d_2 d_3 d_4 ]. +// +// Fetch Z_1 := (1/A_1) rounded UP in fixed point with +// fixed point lsb = 2^(-15). +// Z_1 looks like z_0.z_1 z_2 ... z_15 +// Note that the fetching is done using index_1. +// A_1 is actually not needed in the implementation +// and is used here only to explain how is the value +// Z_1 defined. +// +// Fetch G_1 := (1/A_1) truncated to 21 sig. bits. +// floating pt. Again, fetching is done using index_1. A_1 +// explains how G_1 is defined. +// +// Calculate X_1 := X_0 * Z_1 truncated to lsb = 2^(-14) +// = 1.0 0 0 0 d_5 ... d_14 +// This is accomplised by integer multiplication. +// It is proved that X_1 indeed always begin +// with 1.0000 in fixed point. +// +// +// Define A_2 := 1.0 0 0 0 d_5 d_6 d_7 d_8. This is X_1 +// truncated to lsb = 2^(-8). Similar to A_1, +// A_2 is not needed in actual implementation. It +// helps explain how some of the values are defined. +// +// Define index_2 := [ d_5 d_6 d_7 d_8 ]. +// +// Fetch Z_2 := (1/A_2) rounded UP in fixed point with +// fixed point lsb = 2^(-15). Fetch done using index_2. +// Z_2 looks like z_0.z_1 z_2 ... z_15 +// +// Fetch G_2 := (1/A_2) truncated to 21 sig. bits. +// floating pt. +// +// Calculate X_2 := X_1 * Z_2 truncated to lsb = 2^(-14) +// = 1.0 0 0 0 0 0 0 0 d_9 d_10 ... d_14 +// This is accomplised by integer multiplication. +// It is proved that X_2 indeed always begin +// with 1.00000000 in fixed point. +// +// +// Define A_3 := 1.0 0 0 0 0 0 0 0 d_9 d_10 d_11 d_12 d_13 1. +// This is 2^(-14) + X_2 truncated to lsb = 2^(-13). +// +// Define index_3 := [ d_9 d_10 d_11 d_12 d_13 ]. +// +// Fetch G_3 := (1/A_3) truncated to 21 sig. bits. +// floating pt. Fetch is done using index_3. +// +// Compute G := G_1 * G_2 * G_3. +// +// This is done exactly since each of G_j only has 21 sig. bits. +// +// Compute +// +// r := (G*S_hi - 1) +// +// +// Step 2. Approximation +// --------------------- +// +// This step computes an approximation to logl( 1 + r ) where r is the +// reduced argument just obtained. It is proved that |r| <= 1.9*2^(-13); +// thus logl(1+r) can be approximated by a short polynomial: +// +// logl(1+r) ~=~ poly = r + Q1 r^2 + ... + Q4 r^5 +// +// +// Step 3. Reconstruction +// ---------------------- +// +// This step computes the desired result of logl(X): +// +// logl(X) = logl( 2^N * S_hi ) +// = N*logl(2) + logl( S_hi ) +// = N*logl(2) + logl(1/G) + +// logl(1 + G*S_hi - 1 ) +// +// logl(2), logl(1/G_j) are stored as pairs of (single,double) numbers: +// log2_hi, log2_lo, log1byGj_hi, log1byGj_lo. The high parts are +// single-precision numbers and the low parts are double precision +// numbers. These have the property that +// +// N*log2_hi + SUM ( log1byGj_hi ) +// +// is computable exactly in double-extended precision (64 sig. bits). +// Finally +// +// lnHi(X) := N*log2_hi + SUM ( log1byGj_hi ) +// lnLo(X) := poly_hi + [ poly_lo + +// ( SUM ( log1byGj_lo ) + N*log2_lo ) ] +// +// +//********************************************************************* +// General Purpose Registers +// scratch registers +rPolDataPtr = r2 +rLnSinDataPtr = r3 +rExpX = r8 +rSignifX = r9 +rDelta = r10 +rSignExpX = r11 +GR_ad_z_1 = r14 +r17Ones = r15 +GR_Index1 = r16 +rSignif1andQ = r17 +GR_X_0 = r18 +GR_X_1 = r19 +GR_X_2 = r20 +GR_Z_1 = r21 +GR_Z_2 = r22 +GR_N = r23 +rExpHalf = r24 +rExp8 = r25 +rX0Dx = r25 +GR_ad_tbl_1 = r26 +GR_ad_tbl_2 = r27 +GR_ad_tbl_3 = r28 +GR_ad_q = r29 +GR_ad_z_1 = r30 +GR_ad_z_2 = r31 +// stacked registers +rPFS_SAVED = r32 +GR_ad_z_3 = r33 +rSgnGamAddr = r34 +rSgnGamSize = r35 +rLogDataPtr = r36 +rZ1offsett = r37 +rTmpPtr = r38 +rTmpPtr2 = r39 +rTmpPtr3 = r40 +rExp2 = r41 +rExp2tom7 = r42 +rZ625 = r42 +rExpOne = r43 +rNegSingularity = r44 +rXint = r45 +rTbl1Addr = r46 +rTbl2Addr = r47 +rTbl3Addr = r48 +rZ2Addr = r49 +rRootsAddr = r50 +rRootsBndAddr = r51 +rRoot = r52 +rRightBound = r53 +rLeftBound = r54 +rSignifDx = r55 +rBernulliPtr = r56 +rLnSinTmpPtr = r56 +rIndex1Dx = r57 +rIndexPol = r58 +GR_Index3 = r59 +GR_Index2 = r60 +rSgnGam = r61 +rXRnd = r62 + +GR_SAVE_B0 = r63 +GR_SAVE_GP = r64 +GR_SAVE_PFS = r65 +// output parameters when calling error handling routine +GR_Parameter_X = r66 +GR_Parameter_Y = r67 +GR_Parameter_RESULT = r68 +GR_Parameter_TAG = r69 + +//******************************************************************** +// Floating Point Registers +// CAUTION: due to the lack of registers there exist (below in the code) +// sometimes "unconventional" use of declared registers +// +fAbsX = f6 +fDelX4 = f6 +fSignifX = f7 +// macros for error handling routine +FR_X = f10 // first argument +FR_Y = f1 // second argument (lgammal has just one) +FR_RESULT = f8 // result + +// First 7 Bernulli numbers +fB2 = f9 +fLnDeltaL = f9 +fXSqr = f9 +fB4 = f10 +fX4 = f10 +fB6 = f11 +fX6 = f11 +fB8 = f12 +fXSqrL = f12 +fB10 = f13 +fRes7H = f13 +fB12 = f14 +fRes7L = f14 +fB14 = f15 + +// stack registers +// Polynomial coefficients: A0, ..., A25 +fA0 = f32 +fA0L = f33 +fInvXL = f33 +fA1 = f34 +fA1L = f35 +fA2 = f36 +fA2L = f37 +fA3 = f38 +fA3L = f39 +fA4 = f40 +fA4L = f41 +fRes6H = f41 +fA5 = f42 +fB2L = f42 +fA5L = f43 +fMinNegStir = f43 +fRes6L = f43 +fA6 = f44 +fMaxNegStir = f44 +fA7 = f45 +fLnDeltaH = f45 +fA8 = f46 +fBrnL = f46 +fA9 = f47 +fBrnH = f47 +fA10 = f48 +fRes5L = f48 +fA11 = f49 +fRes5H = f49 +fA12 = f50 +fDx6 = f50 +fA13 = f51 +fDx8 = f51 +fA14 = f52 +fDx4 = f52 +fA15 = f53 +fYL = f53 +fh3Dx = f53 +fA16 = f54 +fYH = f54 +fH3Dx = f54 +fA17 = f55 +fResLnDxL = f55 +fG3Dx = f55 +fA18 = f56 +fResLnDxH = f56 +fh2Dx = f56 +fA19 = f57 +fFloatNDx = f57 +fA20 = f58 +fPolyHiDx = f58 +fhDx = f58 +fA21 = f59 +fRDxCub = f59 +fHDx = f59 +fA22 = f60 +fRDxSq = f60 +fGDx = f60 +fA23 = f61 +fPolyLoDx = f61 +fInvX3 = f61 +fA24 = f62 +fRDx = f62 +fInvX8 = f62 +fA25 = f63 +fInvX4 = f63 +fPol = f64 +fPolL = f65 +// Coefficients of ln(sin(Pi*x)/Pi*x) +fLnSin2 = f66 +fLnSin2L = f67 +fLnSin4 = f68 +fLnSin6 = f69 +fLnSin8 = f70 +fLnSin10 = f71 +fLnSin12 = f72 +fLnSin14 = f73 +fLnSin16 = f74 +fLnSin18 = f75 +fDelX8 = f75 +fLnSin20 = f76 +fLnSin22 = f77 +fDelX6 = f77 +fLnSin24 = f78 +fLnSin26 = f79 +fLnSin28 = f80 +fLnSin30 = f81 +fhDelX = f81 +fLnSin32 = f82 +fLnSin34 = f83 +fLnSin36 = f84 +fXint = f85 +fDxSqr = f85 +fRes3L = f86 +fRes3H = f87 +fRes4H = f88 +fRes4L = f89 +fResH = f90 +fResL = f91 +fDx = f92 +FR_MHalf = f93 +fRes1H = f94 +fRes1L = f95 +fRes2H = f96 +fRes2L = f97 +FR_FracX = f98 +fRcpX = f99 +fLnSinH = f99 +fTwo = f100 +fMOne = f100 +FR_G = f101 +FR_H = f102 +FR_h = f103 +FR_G2 = f104 +FR_H2 = f105 +FR_poly_lo = f106 +FR_poly_hi = f107 +FR_h2 = f108 +FR_rsq = f109 +FR_r = f110 +FR_log2_hi = f111 +FR_log2_lo = f112 +fFloatN = f113 +FR_Q4 = f114 +FR_G3 = f115 +FR_H3 = f116 +FR_h3 = f117 +FR_Q3 = f118 +FR_Q2 = f119 +FR_Q1 = f120 +fThirteen = f121 +fSix = f121 +FR_rcub = f121 +// Last three Bernulli numbers +fB16 = f122 +fB18 = f123 +fB20 = f124 +fInvX = f125 +fLnSinL = f125 +fDxSqrL = f126 +fFltIntX = f126 +fRoot = f127 +fNormDx = f127 + +// Data tables +//============================================================== +RODATA +// ************* DO NOT CHANGE THE ORDER OF THESE TABLES ************* +.align 16 +LOCAL_OBJECT_START(lgammal_right_roots_data) +// List of all right roots themselves +data8 0x9D3FE4B007C360AB, 0x0000C000 // Range [-3, -2] +data8 0xC9306DE4F2CD7BEE, 0x0000C000 // Range [-4, -3] +data8 0x814273C2CCAC0618, 0x0000C001 // Range [-5, -4] +data8 0xA04352BF85B6C865, 0x0000C001 // Range [-6, -5] +data8 0xC00B592C4BE4676C, 0x0000C001 // Range [-7, -6] +data8 0xE0019FEF6FF0F5BF, 0x0000C001 // Range [-8, -7] +data8 0x80001A01459FC9F6, 0x0000C002 // Range [-9, -8] +data8 0x900002E3BB47D86D, 0x0000C002 // Range [-10, -9] +data8 0xA0000049F93BB992, 0x0000C002 // Range [-11, -10] +data8 0xB0000006B9915316, 0x0000C002 // Range [-12, -11] +data8 0xC00000008F76C773, 0x0000C002 // Range [-13, -12] +data8 0xD00000000B09230A, 0x0000C002 // Range [-14, -13] +data8 0xE000000000C9CBA5, 0x0000C002 // Range [-15, -14] +data8 0xF0000000000D73FA, 0x0000C002 // Range [-16, -15] +data8 0x8000000000006BA0, 0x0000C003 // Range [-17, -16] +data8 0x8800000000000655, 0x0000C003 // Range [-18, -17] +data8 0x900000000000005A, 0x0000C003 // Range [-19, -18] +data8 0x9800000000000005, 0x0000C003 // Range [-20, -19] +// List of bounds of ranges with special polynomial approximation near root +// Only significands of bounds are actually stored +data8 0xA000000000000000, 0x9800000000000000 // Bounds for root on [-3, -2] +data8 0xCAB88035C5EFBB41, 0xC7E05E31F4B02115 // Bounds for root on [-4, -3] +data8 0x817831B899735C72, 0x8114633941B8053A // Bounds for root on [-5, -4] +data8 0xA04E8B34C6AA9476, 0xA039B4A42978197B // Bounds for root on [-6, -5] +data8 0xC00D3D5E588A78A9, 0xC009BA25F7E858A6 // Bounds for root on [-7, -6] +data8 0xE001E54202991EB4, 0xE001648416CE897F // Bounds for root on [-8, -7] +data8 0x80001E56D13A6B9F, 0x8000164A3BAD888A // Bounds for root on [-9, -8] +data8 0x9000035F0529272A, 0x9000027A0E3D94F0 // Bounds for root on [-10, -9] +data8 0xA00000564D705880, 0xA000003F67EA0CC7 // Bounds for root on [-11, -10] +data8 0xB0000007D87EE0EF, 0xB0000005C3A122A5 // Bounds for root on [-12, -11] +data8 0xC0000000A75FE8B1, 0xC00000007AF818AC // Bounds for root on [-13, -12] +data8 0xD00000000CDFFE36, 0xD000000009758BBF // Bounds for root on [-14, -13] +data8 0xE000000000EB6D96, 0xE000000000ACF7B2 // Bounds for root on [-15, -14] +data8 0xF0000000000FB1F9, 0xF0000000000B87FB // Bounds for root on [-16, -15] +data8 0x8000000000007D90, 0x8000000000005C40 // Bounds for root on [-17, -16] +data8 0x8800000000000763, 0x880000000000056D // Bounds for root on [-18, -17] +data8 0x9000000000000069, 0x900000000000004D // Bounds for root on [-19, -18] +data8 0x9800000000000006, 0x9800000000000005 // Bounds for root on [-20, -19] +// List of all left roots themselves +data8 0xAFDA0850DEC8065E, 0x0000C000 // Range [-3, -2] +data8 0xFD238AA3E17F285C, 0x0000C000 // Range [-4, -3] +data8 0x9FBABBD37757E6A2, 0x0000C001 // Range [-5, -4] +data8 0xBFF497AC8FA06AFC, 0x0000C001 // Range [-6, -5] +data8 0xDFFE5FBB5C377FE8, 0x0000C001 // Range [-7, -6] +data8 0xFFFFCBFC0ACE7879, 0x0000C001 // Range [-8, -7] +data8 0x8FFFFD1C425E8100, 0x0000C002 // Range [-9, -8] +data8 0x9FFFFFB606BDFDCD, 0x0000C002 // Range [-10, -9] +data8 0xAFFFFFF9466E9F1B, 0x0000C002 // Range [-11, -10] +data8 0xBFFFFFFF70893874, 0x0000C002 // Range [-12, -11] +data8 0xCFFFFFFFF4F6DCF6, 0x0000C002 // Range [-13, -12] +data8 0xDFFFFFFFFF36345B, 0x0000C002 // Range [-14, -13] +data8 0xEFFFFFFFFFF28C06, 0x0000C002 // Range [-15, -14] +data8 0xFFFFFFFFFFFF28C0, 0x0000C002 // Range [-16, -15] +data8 0x87FFFFFFFFFFF9AB, 0x0000C003 // Range [-17, -16] +data8 0x8FFFFFFFFFFFFFA6, 0x0000C003 // Range [-18, -17] +data8 0x97FFFFFFFFFFFFFB, 0x0000C003 // Range [-19, -18] +data8 0x0000000000000000, 0x00000000 // pad to keep logic in the main path +// List of bounds of ranges with special polynomial approximation near root +// Only significands of bounds are actually stored +data8 0xB235880944CC758E, 0xADD2F1A9FBE76C8B // Bounds for root on [-3, -2] +data8 0xFD8E7844F307B07C, 0xFCA655C2152BDE4D // Bounds for root on [-4, -3] +data8 0x9FC4D876EE546967, 0x9FAEE4AF68BC4292 // Bounds for root on [-5, -4] +data8 0xBFF641FFBFCC44F1, 0xBFF2A47919F4BA89 // Bounds for root on [-6, -5] +data8 0xDFFE9C803DEFDD59, 0xDFFE18932EB723FE // Bounds for root on [-7, -6] +data8 0xFFFFD393FA47AFC3, 0xFFFFC317CF638AE1 // Bounds for root on [-8, -7] +data8 0x8FFFFD8840279925, 0x8FFFFC9DCECEEE92 // Bounds for root on [-9, -8] +data8 0x9FFFFFC0D34E2AF8, 0x9FFFFFA9619AA3B7 // Bounds for root on [-10, -9] +data8 0xAFFFFFFA41C18246, 0xAFFFFFF82025A23C // Bounds for root on [-11, -10] +data8 0xBFFFFFFF857ACB4E, 0xBFFFFFFF58032378 // Bounds for root on [-12, -11] +data8 0xCFFFFFFFF6934AB8, 0xCFFFFFFFF313EF0A // Bounds for root on [-13, -12] +data8 0xDFFFFFFFFF53A9E9, 0xDFFFFFFFFF13B5A5 // Bounds for root on [-14, -13] +data8 0xEFFFFFFFFFF482CB, 0xEFFFFFFFFFF03F4F // Bounds for root on [-15, -14] +data8 0xFFFFFFFFFFFF482D, 0xFFFFFFFFFFFF03F5 // Bounds for root on [-16, -15] +data8 0x87FFFFFFFFFFFA98, 0x87FFFFFFFFFFF896 // Bounds for root on [-17, -16] +data8 0x8FFFFFFFFFFFFFB3, 0x8FFFFFFFFFFFFF97 // Bounds for root on [-18, -17] +data8 0x97FFFFFFFFFFFFFC, 0x97FFFFFFFFFFFFFB // Bounds for root on [-19, -18] +LOCAL_OBJECT_END(lgammal_right_roots_data) + +LOCAL_OBJECT_START(lgammal_0_Half_data) +// Polynomial coefficients for the lgammal(x), 0.0 < |x| < 0.5 +data8 0xBFD9A4D55BEAB2D6, 0xBC8AA3C097746D1F //A3 +data8 0x3FEA51A6625307D3, 0x3C7180E7BD2D0DCC //A2 +data8 0xBFE2788CFC6FB618, 0xBC9E9346C4692BCC //A1 +data8 0x8A8991563EC1BD13, 0x00003FFD //A4 +data8 0xD45CE0BD52C27EF2, 0x0000BFFC //A5 +data8 0xADA06587FA2BBD47, 0x00003FFC //A6 +data8 0x9381D0ED2194902A, 0x0000BFFC //A7 +data8 0x80859B3CF92D4192, 0x00003FFC //A8 +data8 0xE4033517C622A946, 0x0000BFFB //A9 +data8 0xCD00CE67A51FC82A, 0x00003FFB //A10 +data8 0xBA44E2A96C3B5700, 0x0000BFFB //A11 +data8 0xAAAD008FA46DBD99, 0x00003FFB //A12 +data8 0x9D604AC65A41153D, 0x0000BFFB //A13 +data8 0x917CECB864B5A861, 0x00003FFB //A14 +data8 0x85A4810EB730FDE4, 0x0000BFFB //A15 +data8 0xEF2761C38BD21F77, 0x00003FFA //A16 +data8 0xC913043A128367DA, 0x0000BFFA //A17 +data8 0x96A29B71FF7AFFAA, 0x00003FFA //A18 +data8 0xBB9FFA1A5FE649BB, 0x0000BFF9 //A19 +data8 0xB17982CD2DAA0EE3, 0x00003FF8 //A20 +data8 0xDE1DDCBFFB9453F0, 0x0000BFF6 //A21 +data8 0x87FBF5D7ACD9FA9D, 0x00003FF4 //A22 +LOCAL_OBJECT_END(lgammal_0_Half_data) + +LOCAL_OBJECT_START(Constants_Q) +// log2_hi, log2_lo, Q_4, Q_3, Q_2, and Q_1 +data4 0x00000000,0xB1721800,0x00003FFE,0x00000000 +data4 0x4361C4C6,0x82E30865,0x0000BFE2,0x00000000 +data4 0x328833CB,0xCCCCCAF2,0x00003FFC,0x00000000 +data4 0xA9D4BAFB,0x80000077,0x0000BFFD,0x00000000 +data4 0xAAABE3D2,0xAAAAAAAA,0x00003FFD,0x00000000 +data4 0xFFFFDAB7,0xFFFFFFFF,0x0000BFFD,0x00000000 +LOCAL_OBJECT_END(Constants_Q) + +LOCAL_OBJECT_START(Constants_Z_1) +// Z1 - 16 bit fixed +data4 0x00008000 +data4 0x00007879 +data4 0x000071C8 +data4 0x00006BCB +data4 0x00006667 +data4 0x00006187 +data4 0x00005D18 +data4 0x0000590C +data4 0x00005556 +data4 0x000051EC +data4 0x00004EC5 +data4 0x00004BDB +data4 0x00004925 +data4 0x0000469F +data4 0x00004445 +data4 0x00004211 +LOCAL_OBJECT_END(Constants_Z_1) + +LOCAL_OBJECT_START(Constants_G_H_h1) +// G1 and H1 - IEEE single and h1 - IEEE double +data4 0x3F800000,0x00000000,0x00000000,0x00000000 +data4 0x3F70F0F0,0x3D785196,0x617D741C,0x3DA163A6 +data4 0x3F638E38,0x3DF13843,0xCBD3D5BB,0x3E2C55E6 +data4 0x3F579430,0x3E2FF9A0,0xD86EA5E7,0xBE3EB0BF +data4 0x3F4CCCC8,0x3E647FD6,0x86B12760,0x3E2E6A8C +data4 0x3F430C30,0x3E8B3AE7,0x5C0739BA,0x3E47574C +data4 0x3F3A2E88,0x3EA30C68,0x13E8AF2F,0x3E20E30F +data4 0x3F321640,0x3EB9CEC8,0xF2C630BD,0xBE42885B +data4 0x3F2AAAA8,0x3ECF9927,0x97E577C6,0x3E497F34 +data4 0x3F23D708,0x3EE47FC5,0xA6B0A5AB,0x3E3E6A6E +data4 0x3F1D89D8,0x3EF8947D,0xD328D9BE,0xBDF43E3C +data4 0x3F17B420,0x3F05F3A1,0x0ADB090A,0x3E4094C3 +data4 0x3F124920,0x3F0F4303,0xFC1FE510,0xBE28FBB2 +data4 0x3F0D3DC8,0x3F183EBF,0x10FDE3FA,0x3E3A7895 +data4 0x3F088888,0x3F20EC80,0x7CC8C98F,0x3E508CE5 +data4 0x3F042108,0x3F29516A,0xA223106C,0xBE534874 +LOCAL_OBJECT_END(Constants_G_H_h1) + +LOCAL_OBJECT_START(Constants_Z_2) +// Z2 - 16 bit fixed +data4 0x00008000 +data4 0x00007F81 +data4 0x00007F02 +data4 0x00007E85 +data4 0x00007E08 +data4 0x00007D8D +data4 0x00007D12 +data4 0x00007C98 +data4 0x00007C20 +data4 0x00007BA8 +data4 0x00007B31 +data4 0x00007ABB +data4 0x00007A45 +data4 0x000079D1 +data4 0x0000795D +data4 0x000078EB +LOCAL_OBJECT_END(Constants_Z_2) + +LOCAL_OBJECT_START(Constants_G_H_h2) +// G2 and H2 - IEEE single and h2 - IEEE double +data4 0x3F800000,0x00000000,0x00000000,0x00000000 +data4 0x3F7F00F8,0x3B7F875D,0x22C42273,0x3DB5A116 +data4 0x3F7E03F8,0x3BFF015B,0x21F86ED3,0x3DE620CF +data4 0x3F7D08E0,0x3C3EE393,0x484F34ED,0xBDAFA07E +data4 0x3F7C0FC0,0x3C7E0586,0x3860BCF6,0xBDFE07F0 +data4 0x3F7B1880,0x3C9E75D2,0xA78093D6,0x3DEA370F +data4 0x3F7A2328,0x3CBDC97A,0x72A753D0,0x3DFF5791 +data4 0x3F792FB0,0x3CDCFE47,0xA7EF896B,0x3DFEBE6C +data4 0x3F783E08,0x3CFC15D0,0x409ECB43,0x3E0CF156 +data4 0x3F774E38,0x3D0D874D,0xFFEF71DF,0xBE0B6F97 +data4 0x3F766038,0x3D1CF49B,0x5D59EEE8,0xBE080483 +data4 0x3F757400,0x3D2C531D,0xA9192A74,0x3E1F91E9 +data4 0x3F748988,0x3D3BA322,0xBF72A8CD,0xBE139A06 +data4 0x3F73A0D0,0x3D4AE46F,0xF8FBA6CF,0x3E1D9202 +data4 0x3F72B9D0,0x3D5A1756,0xBA796223,0xBE1DCCC4 +data4 0x3F71D488,0x3D693B9D,0xB6B7C239,0xBE049391 +LOCAL_OBJECT_END(Constants_G_H_h2) + +LOCAL_OBJECT_START(Constants_G_H_h3) +// G3 and H3 - IEEE single and h3 - IEEE double +data4 0x3F7FFC00,0x38800100,0x562224CD,0x3D355595 +data4 0x3F7FF400,0x39400480,0x06136FF6,0x3D8200A2 +data4 0x3F7FEC00,0x39A00640,0xE8DE9AF0,0x3DA4D68D +data4 0x3F7FE400,0x39E00C41,0xB10238DC,0xBD8B4291 +data4 0x3F7FDC00,0x3A100A21,0x3B1952CA,0xBD89CCB8 +data4 0x3F7FD400,0x3A300F22,0x1DC46826,0xBDB10707 +data4 0x3F7FCC08,0x3A4FF51C,0xF43307DB,0x3DB6FCB9 +data4 0x3F7FC408,0x3A6FFC1D,0x62DC7872,0xBD9B7C47 +data4 0x3F7FBC10,0x3A87F20B,0x3F89154A,0xBDC3725E +data4 0x3F7FB410,0x3A97F68B,0x62B9D392,0xBD93519D +data4 0x3F7FAC18,0x3AA7EB86,0x0F21BD9D,0x3DC18441 +data4 0x3F7FA420,0x3AB7E101,0x2245E0A6,0xBDA64B95 +data4 0x3F7F9C20,0x3AC7E701,0xAABB34B8,0x3DB4B0EC +data4 0x3F7F9428,0x3AD7DD7B,0x6DC40A7E,0x3D992337 +data4 0x3F7F8C30,0x3AE7D474,0x4F2083D3,0x3DC6E17B +data4 0x3F7F8438,0x3AF7CBED,0x811D4394,0x3DAE314B +data4 0x3F7F7C40,0x3B03E1F3,0xB08F2DB1,0xBDD46F21 +data4 0x3F7F7448,0x3B0BDE2F,0x6D34522B,0xBDDC30A4 +data4 0x3F7F6C50,0x3B13DAAA,0xB1F473DB,0x3DCB0070 +data4 0x3F7F6458,0x3B1BD766,0x6AD282FD,0xBDD65DDC +data4 0x3F7F5C68,0x3B23CC5C,0xF153761A,0xBDCDAB83 +data4 0x3F7F5470,0x3B2BC997,0x341D0F8F,0xBDDADA40 +data4 0x3F7F4C78,0x3B33C711,0xEBC394E8,0x3DCD1BD7 +data4 0x3F7F4488,0x3B3BBCC6,0x52E3E695,0xBDC3532B +data4 0x3F7F3C90,0x3B43BAC0,0xE846B3DE,0xBDA3961E +data4 0x3F7F34A0,0x3B4BB0F4,0x785778D4,0xBDDADF06 +data4 0x3F7F2CA8,0x3B53AF6D,0xE55CE212,0x3DCC3ED1 +data4 0x3F7F24B8,0x3B5BA620,0x9E382C15,0xBDBA3103 +data4 0x3F7F1CC8,0x3B639D12,0x5C5AF197,0x3D635A0B +data4 0x3F7F14D8,0x3B6B9444,0x71D34EFC,0xBDDCCB19 +data4 0x3F7F0CE0,0x3B7393BC,0x52CD7ADA,0x3DC74502 +data4 0x3F7F04F0,0x3B7B8B6D,0x7D7F2A42,0xBDB68F17 +LOCAL_OBJECT_END(Constants_G_H_h3) + +LOCAL_OBJECT_START(lgammal_data) +// Positive overflow value +data8 0xB8D54C8BFFFDEBF4, 0x00007FF1 +LOCAL_OBJECT_END(lgammal_data) + +LOCAL_OBJECT_START(lgammal_Stirling) +// Coefficients needed for Strirling's formula +data8 0x3FED67F1C864BEB4 // High part of 0.5*ln(2*Pi) +data8 0x3C94D252F2400510 // Low part of 0.5*ln(2*Pi) +// +// Bernulli numbers used in Striling's formula for -2^63 < |x| < -13.0 +//(B1H, B1L) = 8.3333333333333333333262747254e-02 +data8 0x3FB5555555555555, 0x3C55555555555555 +data8 0xB60B60B60B60B60B, 0x0000BFF6 //B2 = -2.7777777777777777777777777778e-03 +data8 0xD00D00D00D00D00D, 0x00003FF4 //B3 = 7.9365079365079365079365079365e-04 +data8 0x9C09C09C09C09C0A, 0x0000BFF4 //B4 = -5.9523809523809523809523809524e-04 +data8 0xDCA8F158C7F91AB8, 0x00003FF4 //B5 = 8.4175084175084175084175084175e-04 +data8 0xFB5586CCC9E3E410, 0x0000BFF5 //B6 = -1.9175269175269175269175269175e-03 +data8 0xD20D20D20D20D20D, 0x00003FF7 //B7 = 6.4102564102564102564102564103e-03 +data8 0xF21436587A9CBEE1, 0x0000BFF9 //B8 = -2.9550653594771241830065359477e-02 +data8 0xB7F4B1C0F033FFD1, 0x00003FFC //B9 = 1.7964437236883057316493849002e-01 +data8 0xB23B3808C0F9CF6E, 0x0000BFFF //B10 = -1.3924322169059011164274322169e+00 +// Polynomial coefficients for Stirling's formula, -13.0 < x < -6.0 +data8 0x3FB5555555555555, 0x3C4D75060289C58B //A0 +data8 0xB60B60B60B0F0876, 0x0000BFF6 //A1 +data8 0xD00D00CE54B1256C, 0x00003FF4 //A2 +data8 0x9C09BF46B58F75E1, 0x0000BFF4 //A3 +data8 0xDCA8483BC91ACC6D, 0x00003FF4 //A4 +data8 0xFB3965C939CC9FEE, 0x0000BFF5 //A5 +data8 0xD0723ADE3F0BC401, 0x00003FF7 //A6 +data8 0xE1ED7434E81F0B73, 0x0000BFF9 //A7 +data8 0x8069C6982F993283, 0x00003FFC //A8 +data8 0xC271F65BFA5BEE3F, 0x0000BFFD //A9 +LOCAL_OBJECT_END(lgammal_Stirling) + +LOCAL_OBJECT_START(lgammal_lnsin_data) +// polynomial approximation of -ln(sin(Pi*x)/(Pi*x)), 0 < x <= 0.5 +data8 0x3FFA51A6625307D3, 0x3C81873332FAF94C //A2 +data8 0x8A8991563EC241C3, 0x00003FFE //A4 +data8 0xADA06588061805DF, 0x00003FFD //A6 +data8 0x80859B57C338D0F7, 0x00003FFD //A8 +data8 0xCD00F1C2D78754BD, 0x00003FFC //A10 +data8 0xAAB56B1D3A1F4655, 0x00003FFC //A12 +data8 0x924B6F2FBBED12B1, 0x00003FFC //A14 +data8 0x80008E58765F43FC, 0x00003FFC //A16 +data8 0x3FBC718EC115E429//A18 +data8 0x3FB99CE544FE183E//A20 +data8 0x3FB7251C09EAAD89//A22 +data8 0x3FB64A970733628C//A24 +data8 0x3FAC92D6802A3498//A26 +data8 0x3FC47E1165261586//A28 +data8 0xBFCA1BAA434750D4//A30 +data8 0x3FE460001C4D5961//A32 +data8 0xBFE6F06A3E4908AD//A34 +data8 0x3FE300889EBB203A//A36 +LOCAL_OBJECT_END(lgammal_lnsin_data) + +LOCAL_OBJECT_START(lgammal_half_3Q_data) +// Polynomial coefficients for the lgammal(x), 0.5 <= x < 0.75 +data8 0xBFF7A648EE90C62E, 0x3C713F326857E066 // A3, A0L +data8 0xBFF73E4B8BA780AE, 0xBCA953BC788877EF // A1, A1L +data8 0x403774DCD58D0291, 0xC0415254D5AE6623 // D0, D1 +data8 0x40B07213855CBFB0, 0xC0B8855E25D2D229 // C20, C21 +data8 0x3FFB359F85FF5000, 0x3C9BAECE6EF9EF3A // A2, A2L +data8 0x3FD717D498A3A8CC, 0xBC9088E101CFEDFA // A0, A3L +data8 0xAFEF36CC5AEC3FF0, 0x00004002 // E6 +data8 0xABE2054E1C34E791, 0x00004001 // E4 +data8 0xB39343637B2900D1, 0x00004000 // E2 +data8 0xD74FB710D53F58F6, 0x00003FFF // E0 +data8 0x4070655963BA4256, 0xC078DA9D263C4EA3 // D6, D7 +data8 0x405CD2B6A9B90978, 0xC065B3B9F4F4F171 // D4, D5 +data8 0x4049BC2204CF61FF, 0xC05337227E0BA152 // D2, D3 +data8 0x4095509A50C07A96, 0xC0A0747949D2FB45 // C18, C19 +data8 0x4082ECCBAD709414, 0xC08CD02FB088A702 // C16, C17 +data8 0xFFE4B2A61B508DD5, 0x0000C002 // E7 +data8 0xF461ADB8AE17E0A5, 0x0000C001 // E5 +data8 0xF5BE8B0B90325F20, 0x0000C000 // E3 +data8 0x877B275F3FB78DCA, 0x0000C000 // E1 +LOCAL_OBJECT_END(lgammal_half_3Q_data) + +LOCAL_OBJECT_START(lgammal_half_3Q_neg_data) +// Polynomial coefficients for the lgammal(x), -0.75 < x <= -0.5 +data8 0xC014836EFD94899C, 0x3C9835679663B44F // A3, A0L +data8 0xBFF276C7B4FB1875, 0xBC92D3D9FA29A1C0 // A1, A1L +data8 0x40C5178F24E1A435, 0xC0D9DE84FBC5D76A // D0, D1 +data8 0x41D4D1B236BF6E93, 0xC1EBB0445CE58550 // C20, C21 +data8 0x4015718CD67F63D3, 0x3CC5354B6F04B59C // A2, A2L +data8 0x3FF554493087E1ED, 0xBCB72715E37B02B9 // A0, A3L +data8 0xE4AC7E915FA72229, 0x00004009 // E6 +data8 0xA28244206395FCC6, 0x00004007 // E4 +data8 0xFB045F19C07B2544, 0x00004004 // E2 +data8 0xE5C8A6E6A9BA7D7B, 0x00004002 // E0 +data8 0x4143943B55BF5118, 0xC158AC05EA675406 // D6, D7 +data8 0x4118F6833D19717C, 0xC12F51A6F375CC80 // D4, D5 +data8 0x40F00C209483481C, 0xC103F1DABF750259 // D2, D3 +data8 0x4191038F2D8F9E40, 0xC1A413066DA8AE4A // C18, C19 +data8 0x4170B537EDD833DE, 0xC1857E79424C61CE // C16, C17 +data8 0x8941D8AB4855DB73, 0x0000C00B // E7 +data8 0xBB822B131BD2E813, 0x0000C008 // E5 +data8 0x852B4C03B83D2D4F, 0x0000C006 // E3 +data8 0xC754CA7E2DDC0F1F, 0x0000C003 // E1 +LOCAL_OBJECT_END(lgammal_half_3Q_neg_data) + +LOCAL_OBJECT_START(lgammal_2Q_4_data) +// Polynomial coefficients for the lgammal(x), 2.25 <= |x| < 4.0 +data8 0xBFCA4D55BEAB2D6F, 0x3C7ABC9DA14141F5 // A3, A0L +data8 0x3FFD8773039049E7, 0x3C66CB7957A95BA4 // A1, A1L +data8 0x3F45C3CC79E91E7D, 0xBF3A8E5005937E97 // D0, D1 +data8 0x3EC951E35E1C9203, 0xBEB030A90026C5DF // C20, C21 +data8 0x3FE94699894C1F4C, 0x3C91884D21D123F1 // A2, A2L +data8 0x3FE62E42FEFA39EF, 0xBC66480CEB70870F // A0, A3L +data8 0xF1C2EAFF0B3A7579, 0x00003FF5 // E6 +data8 0xB36AF863926B55A3, 0x00003FF7 // E4 +data8 0x9620656185BB44CA, 0x00003FF9 // E2 +data8 0xA264558FB0906AFF, 0x00003FFB // E0 +data8 0x3F03D59E9666C961, 0xBEF91115893D84A6 // D6, D7 +data8 0x3F19333611C46225, 0xBF0F89EB7D029870 // D4, D5 +data8 0x3F3055A96B347AFE, 0xBF243B5153E178A8 // D2, D3 +data8 0x3ED9A4AEF30C4BB2, 0xBED388138B1CEFF2 // C18, C19 +data8 0x3EEF7945A3C3A254, 0xBEE36F32A938EF11 // C16, C17 +data8 0x9028923F47C82118, 0x0000BFF5 // E7 +data8 0xCE0DAAFB6DC93B22, 0x0000BFF6 // E5 +data8 0xA0D0983B34AC4C8D, 0x0000BFF8 // E3 +data8 0x94D6C50FEB8B0CE7, 0x0000BFFA // E1 +LOCAL_OBJECT_END(lgammal_2Q_4_data) + +LOCAL_OBJECT_START(lgammal_4_8_data) +// Polynomial coefficients for the lgammal(x), 4.0 <= |x| < 8.0 +data8 0xBFD6626BC9B31B54, 0x3CAA53C82493A92B // A3, A0L +data8 0x401B4C420A50AD7C, 0x3C8C6E9929F789A3 // A1, A1L +data8 0x3F49410427E928C2, 0xBF3E312678F8C146 // D0, D1 +data8 0x3ED51065F7CD5848, 0xBED052782A03312F // C20, C21 +data8 0x3FF735973273D5EC, 0x3C831DFC65BF8CCF // A2, A2L +data8 0x401326643C4479C9, 0xBC6FA0498C5548A6 // A0, A3L +data8 0x9382D8B3CD4EB7E3, 0x00003FF6 // E6 +data8 0xE9F92CAD8A85CBCD, 0x00003FF7 // E4 +data8 0xD58389FE38258CEC, 0x00003FF9 // E2 +data8 0x81310136363AE8AA, 0x00003FFC // E0 +data8 0x3F04F0AE38E78570, 0xBEF9E2144BB8F03C // D6, D7 +data8 0x3F1B5E992A6CBC2A, 0xBF10F3F400113911 // D4, D5 +data8 0x3F323EE00AAB7DEE, 0xBF2640FDFA9FB637 // D2, D3 +data8 0x3ED2143EBAFF067A, 0xBEBBDEB92D6FF35D // C18, C19 +data8 0x3EF173A42B69AAA4, 0xBEE78B9951A2EAA5 // C16, C17 +data8 0xAB3CCAC6344E52AA, 0x0000BFF5 // E7 +data8 0x81ACCB8915B16508, 0x0000BFF7 // E5 +data8 0xDA62C7221102C426, 0x0000BFF8 // E3 +data8 0xDF1BD44C4083580A, 0x0000BFFA // E1 +LOCAL_OBJECT_END(lgammal_4_8_data) + +LOCAL_OBJECT_START(lgammal_loc_min_data) +// Polynomial coefficients for the lgammal(x), 1.3125 <= x < 1.5625 +data8 0xBB16C31AB5F1FB71, 0x00003FFF // xMin - point of local minimum +data8 0xBFC2E4278DC6BC23, 0xBC683DA8DDCA9650 // A3, A0L +data8 0x3BD4DB7D0CA61D5F, 0x386E719EDD01D801 // A1, A1L +data8 0x3F4CC72638E1D93F, 0xBF4228EC9953CCB9 // D0, D1 +data8 0x3ED222F97A04613E,0xBED3DDD58095CB6C // C20, C21 +data8 0x3FDEF72BC8EE38AB, 0x3C863AFF3FC48940 // A2, A2L +data8 0xBFBF19B9BCC38A41, 0xBC7425F1BFFC1442// A0, A3L +data8 0x941890032BEB34C3, 0x00003FF6 // E6 +data8 0xC7E701591CE534BC, 0x00003FF7 // E4 +data8 0x93373CBD05138DD4, 0x00003FF9 // E2 +data8 0x845A14A6A81C05D6, 0x00003FFB // E0 +data8 0x3F0F6C4DF6D47A13, 0xBF045DCDB5B49E19 // D6, D7 +data8 0x3F22E23345DDE59C, 0xBF1851159AFB1735 // D4, D5 +data8 0x3F37101EA4022B78, 0xBF2D721E6323AF13 // D2, D3 +data8 0x3EE691EBE82DF09D, 0xBEDD42550961F730 // C18, C19 +data8 0x3EFA793EDE99AD85, 0xBEF14000108E70BE // C16, C17 +data8 0xB7CBC033ACE0C99C, 0x0000BFF5 // E7 +data8 0xF178D1F7B1A45E27, 0x0000BFF6 // E5 +data8 0xA8FCFCA8106F471C, 0x0000BFF8 // E3 +data8 0x864D46FA898A9AD2, 0x0000BFFA // E1 +LOCAL_OBJECT_END(lgammal_loc_min_data) + +LOCAL_OBJECT_START(lgammal_03Q_1Q_data) +// Polynomial coefficients for the lgammal(x), 0.75 <= |x| < 1.3125 +data8 0x3FD151322AC7D848, 0x3C7184DE0DB7B4EE // A4, A2L +data8 0x3FD9A4D55BEAB2D6, 0x3C9E934AAB10845F // A3, A1L +data8 0x3FB111289C381259, 0x3FAFFFCFB32AE18D // D2, D3 +data8 0x3FB3B1D9E0E3E00D, 0x3FB2496F0D3768DF // D0, D1 +data8 0xBA461972C057D439, 0x00003FFB // E6 +data8 0x3FEA51A6625307D3, 0x3C76ABC886A72DA2 // A2, A4L +data8 0x3FA8EFE46B32A70E, 0x3F8F31B3559576B6 // C17, C20 +data8 0xE403383700387D85, 0x00003FFB // E4 +data8 0x9381D0EE74BF7251, 0x00003FFC // E2 +data8 0x3FAA2177A6D28177, 0x3FA4895E65FBD995 // C18, C19 +data8 0x3FAAED2C77DBEE5D, 0x3FA94CA59385512C // D6, D7 +data8 0x3FAE1F522E8A5941, 0x3FAC785EF56DD87E // D4, D5 +data8 0x3FB556AD5FA56F0A, 0x3FA81F416E87C783 // E7, C16 +data8 0xCD00F1C2DC2C9F1E, 0x00003FFB // E5 +data8 0x3FE2788CFC6FB618, 0x3C8E52519B5B17CB // A1, A3L +data8 0x80859B57C3E7F241, 0x00003FFC // E3 +data8 0xADA065880615F401, 0x00003FFC // E1 +data8 0xD45CE0BD530AB50E, 0x00003FFC // E0 +LOCAL_OBJECT_END(lgammal_03Q_1Q_data) + +LOCAL_OBJECT_START(lgammal_13Q_2Q_data) +// Polynomial coefficients for the lgammal(x), 1.5625 <= |x| < 2.25 +data8 0x3F951322AC7D8483, 0x3C71873D88C6539D // A4, A2L +data8 0xBFB13E001A557606, 0x3C56CB907018A101 // A3, A1L +data8 0xBEC11B2EC1E7F6FC, 0x3EB0064ED9824CC7 // D2, D3 +data8 0xBEE3CBC963EC103A, 0x3ED2597A330C107D // D0, D1 +data8 0xBC6F2DEBDFE66F38, 0x0000BFF0 // E6 +data8 0x3FD4A34CC4A60FA6, 0x3C3AFC9BF775E8A0 // A2, A4L +data8 0x3E48B0C542F85B32, 0xBE347F12EAF787AB // C17, C20 +data8 0xE9FEA63B6984FA1E, 0x0000BFF2 // E4 +data8 0x9C562E15FC703BBF, 0x0000BFF5 // E2 +data8 0xBE3C12A50AB0355E, 0xBE1C941626AE4717 // C18, C19 +data8 0xBE7AFA8714342BC4,0x3E69A12D2B7761CB // D6, D7 +data8 0xBE9E25EF1D526730, 0x3E8C762291889B99 // D4, D5 +data8 0x3EF580DCEE754733, 0xBE57C811D070549C // E7, C16 +data8 0xD093D878BE209C98, 0x00003FF1 // E5 +data8 0x3FDB0EE6072093CE, 0xBC6024B9E81281C4 // A1, A3L +data8 0x859B57C31CB77D96, 0x00003FF4 // E3 +data8 0xBD6EB756DB617E8D, 0x00003FF6 // E1 +data8 0xF2027E10C7AF8C38, 0x0000BFF7 // E0 +LOCAL_OBJECT_END(lgammal_13Q_2Q_data) + +LOCAL_OBJECT_START(lgammal_8_10_data) +// Polynomial coefficients for the lgammal(x), 8.0 <= |x| < 10.0 +// Multi Precision terms +data8 0x40312008A3A23E5C, 0x3CE020B4F2E4083A //A1 +data8 0x4025358E82FCB70C, 0x3CD4A5A74AF7B99C //A0 +// Native precision terms +data8 0xF0AA239FFBC616D2, 0x00004000 //A2 +data8 0x96A8EA798FE57D66, 0x0000BFFF //A3 +data8 0x8D501B7E3B9B9BDB, 0x00003FFE //A4 +data8 0x9EE062401F4B1DC2, 0x0000BFFD //A5 +data8 0xC63FD8CD31E93431, 0x00003FFC //A6 +data8 0x8461101709C23C30, 0x0000BFFC //A7 +data8 0xB96D7EA7EF3648B2, 0x00003FFB //A8 +data8 0x86886759D2ACC906, 0x0000BFFB //A9 +data8 0xC894B6E28265B183, 0x00003FFA //A10 +data8 0x98C4348CAD821662, 0x0000BFFA //A11 +data8 0xEC9B092226A94DF2, 0x00003FF9 //A12 +data8 0xB9F169FF9B98CDDC, 0x0000BFF9 //A13 +data8 0x9A3A32BB040894D3, 0x00003FF9 //A14 +data8 0xF9504CCC1003B3C3, 0x0000BFF8 //A15 +LOCAL_OBJECT_END(lgammal_8_10_data) + +LOCAL_OBJECT_START(lgammal_03Q_6_data) +// Polynomial coefficients for the lgammal(x), 0.75 <= |x| < 1.0 +data8 0xBFBC47DCA479E295, 0xBC607E6C1A379D55 //A3 +data8 0x3FCA051C372609ED, 0x3C7B02D73EB7D831 //A0 +data8 0xBFE15FAFA86B04DB, 0xBC3F52EE4A8945B5 //A1 +data8 0x3FD455C4FF28F0BF, 0x3C75F8C6C99F30BB //A2 +data8 0xD2CF04CD934F03E1, 0x00003FFA //A4 +data8 0xDB4ED667E29256E1, 0x0000BFF9 //A5 +data8 0xF155A33A5B6021BF, 0x00003FF8 //A6 +data8 0x895E9B9D386E0338, 0x0000BFF8 //A7 +data8 0xA001BE94B937112E, 0x00003FF7 //A8 +data8 0xBD82846E490ED048, 0x0000BFF6 //A9 +data8 0xE358D24EC30DBB5D, 0x00003FF5 //A10 +data8 0x89C4F3652446B78B, 0x0000BFF5 //A11 +data8 0xA86043E10280193D, 0x00003FF4 //A12 +data8 0xCF3A2FBA61EB7682, 0x0000BFF3 //A13 +data8 0x3F300900CC9200EC //A14 +data8 0xBF23F42264B94AE8 //A15 +data8 0x3F18EEF29895FE73 //A16 +data8 0xBF0F3C4563E3EDFB //A17 +data8 0x3F0387DBBC385056 //A18 +data8 0xBEF81B4004F92900 //A19 +data8 0x3EECA6692A9A5B81 //A20 +data8 0xBEDF61A0059C15D3 //A21 +data8 0x3ECDA9F40DCA0111 //A22 +data8 0xBEB60FE788217BAF //A23 +data8 0x3E9661D795DFC8C6 //A24 +data8 0xBE66C7756A4EDEE5 //A25 +// Polynomial coefficients for the lgammal(x), 1.0 <= |x| < 2.0 +data8 0xBFC1AE55B180726B, 0xBC7DE1BC478453F5 //A3 +data8 0xBFBEEB95B094C191, 0xBC53456FF6F1C9D9 //A0 +data8 0x3FA2AED059BD608A, 0x3C0B65CC647D557F //A1 +data8 0x3FDDE9E64DF22EF2, 0x3C8993939A8BA8E4 //A2 +data8 0xF07C206D6B100CFF, 0x00003FFA //A4 +data8 0xED2CEA9BA52FE7FB, 0x0000BFF9 //A5 +data8 0xFCE51CED52DF3602, 0x00003FF8 //A6 +data8 0x8D45D27872326619, 0x0000BFF8 //A7 +data8 0xA2B78D6BCEBE27F7, 0x00003FF7 //A8 +data8 0xBF6DC0996A895B6F, 0x0000BFF6 //A9 +data8 0xE4B9AD335AF82D79, 0x00003FF5 //A10 +data8 0x8A451880195362A1, 0x0000BFF5 //A11 +data8 0xA8BE35E63089A7A9, 0x00003FF4 //A12 +data8 0xCF7FA175FA11C40C, 0x0000BFF3 //A13 +data8 0x3F300C282FAA3B02 //A14 +data8 0xBF23F6AEBDA68B80 //A15 +data8 0x3F18F6860E2224DD //A16 +data8 0xBF0F542B3CE32F28 //A17 +data8 0x3F039436218C9BF8 //A18 +data8 0xBEF8AE6307677AEC //A19 +data8 0x3EF0B55527B3A211 //A20 +data8 0xBEE576AC995E7605 //A21 +data8 0x3ED102DDC1365D2D //A22 +data8 0xBEC442184F97EA54 //A23 +data8 0x3ED4D2283DFE5FC6 //A24 +data8 0xBECB9219A9B46787 //A25 +// Polynomial coefficients for the lgammal(x), 2.0 <= |x| < 3.0 +data8 0xBFCA4D55BEAB2D6F, 0xBC66F80E5BFD5AF5 //A3 +data8 0x3FE62E42FEFA39EF, 0x3C7ABC9E3B347E3D //A0 +data8 0x3FFD8773039049E7, 0x3C66CB9007C426EA //A1 +data8 0x3FE94699894C1F4C, 0x3C918726EB111663 //A2 +data8 0xA264558FB0906209, 0x00003FFB //A4 +data8 0x94D6C50FEB902ADC, 0x0000BFFA //A5 +data8 0x9620656184243D17, 0x00003FF9 //A6 +data8 0xA0D0983B8BCA910B, 0x0000BFF8 //A7 +data8 0xB36AF8559B222BD3, 0x00003FF7 //A8 +data8 0xCE0DACB3260AE6E5, 0x0000BFF6 //A9 +data8 0xF1C2C0BF0437C7DB, 0x00003FF5 //A10 +data8 0x902A2F2F3AB74A92, 0x0000BFF5 //A11 +data8 0xAE05009B1B2C6E4C, 0x00003FF4 //A12 +data8 0xD5B71F6456D7D4CB, 0x0000BFF3 //A13 +data8 0x3F2F0351D71BC9C6 //A14 +data8 0xBF2B53BC56A3B793 //A15 +data8 0xBF18B12DC6F6B861 //A16 +data8 0xBF43EE6EB5215C2F //A17 +data8 0xBF5474787CDD455E //A18 +data8 0xBF642B503C9C060A //A19 +data8 0xBF6E07D1AA254AA3 //A20 +data8 0xBF71C785443AAEE8 //A21 +data8 0xBF6F67BF81B71052 //A22 +data8 0xBF63E4BCCF4FFABF //A23 +data8 0xBF50067F8C671D5A //A24 +data8 0xBF29C770D680A5AC //A25 +// Polynomial coefficients for the lgammal(x), 4.0 <= |x| < 6.0 +data8 0xBFD6626BC9B31B54, 0xBC85AABE08680902 //A3 +data8 0x401326643C4479C9, 0x3CAA53C26F31E364 //A0 +data8 0x401B4C420A50AD7C, 0x3C8C76D55E57DD8D //A1 +data8 0x3FF735973273D5EC, 0x3C83A0B78E09188A //A2 +data8 0x81310136363AAB6D, 0x00003FFC //A4 +data8 0xDF1BD44C4075C0E6, 0x0000BFFA //A5 +data8 0xD58389FE38D8D664, 0x00003FF9 //A6 +data8 0xDA62C7221D5B5F87, 0x0000BFF8 //A7 +data8 0xE9F92CAD0263E157, 0x00003FF7 //A8 +data8 0x81ACCB8606C165FE, 0x0000BFF7 //A9 +data8 0x9382D8D263D1C2A3, 0x00003FF6 //A10 +data8 0xAB3CCBA4C853B12C, 0x0000BFF5 //A11 +data8 0xCA0818BBCCC59296, 0x00003FF4 //A12 +data8 0xF18912691CBB5BD0, 0x0000BFF3 //A13 +data8 0x3F323EF5D8330339 //A14 +data8 0xBF2641132EA571F7 //A15 +data8 0x3F1B5D9576175CA9 //A16 +data8 0xBF10F56A689C623D //A17 +data8 0x3F04CACA9141A18D //A18 +data8 0xBEFA307AC9B4E85D //A19 +data8 0x3EF4B625939FBE32 //A20 +data8 0xBECEE6AC1420F86F //A21 +data8 0xBE9A95AE2E485964 //A22 +data8 0xBF039EF47F8C09BB //A23 +data8 0xBF05345957F7B7A9 //A24 +data8 0xBEF85AE6385D4CCC //A25 +// Polynomial coefficients for the lgammal(x), 3.0 <= |x| < 4.0 +data8 0xBFCA4D55BEAB2D6F, 0xBC667B20FF46C6A8 //A3 +data8 0x3FE62E42FEFA39EF, 0x3C7ABC9E3B398012 //A0 +data8 0x3FFD8773039049E7, 0x3C66CB9070238D77 //A1 +data8 0x3FE94699894C1F4C, 0x3C91873D8839B1CD //A2 +data8 0xA264558FB0906D7E, 0x00003FFB //A4 +data8 0x94D6C50FEB8AFD72, 0x0000BFFA //A5 +data8 0x9620656185B68F14, 0x00003FF9 //A6 +data8 0xA0D0983B34B7088A, 0x0000BFF8 //A7 +data8 0xB36AF863964AA440, 0x00003FF7 //A8 +data8 0xCE0DAAFB5497AFB8, 0x0000BFF6 //A9 +data8 0xF1C2EAFA79CC2864, 0x00003FF5 //A10 +data8 0x9028922A839572B8, 0x0000BFF5 //A11 +data8 0xAE1E62F870BA0278, 0x00003FF4 //A12 +data8 0xD4726F681E2ABA29, 0x0000BFF3 //A13 +data8 0x3F30559B9A02FADF //A14 +data8 0xBF243ADEB1266CAE //A15 +data8 0x3F19303B6F552603 //A16 +data8 0xBF0F768C288EC643 //A17 +data8 0x3F039D5356C21DE1 //A18 +data8 0xBEF81BCA8168E6BE //A19 +data8 0x3EEC74A53A06AD54 //A20 +data8 0xBEDED52D1A5DACDF //A21 +data8 0x3ECCB4C2C7087342 //A22 +data8 0xBEB4F1FAFDFF5C2F //A23 +data8 0x3E94C80B52D58904 //A24 +data8 0xBE64A328CBE92A27 //A25 +LOCAL_OBJECT_END(lgammal_03Q_6_data) + +LOCAL_OBJECT_START(lgammal_1pEps_data) +// Polynomial coefficients for the lgammal(x), 1 - 2^(-7) <= |x| < 1 + 2^(-7) +data8 0x93C467E37DB0C7A5, 0x00003FFE //A1 +data8 0xD28D3312983E9919, 0x00003FFE //A2 +data8 0xCD26AADF559A47E3, 0x00003FFD //A3 +data8 0x8A8991563EC22E81, 0x00003FFD //A4 +data8 0x3FCA8B9C168D52FE //A5 +data8 0x3FC5B40CB0696370 //A6 +data8 0x3FC270AC2229A65D //A7 +data8 0x3FC0110AF10FCBFC //A8 +// Polynomial coefficients for the log1p(x), - 2^(-7) <= |x| < 2^(-7) +data8 0x3FBC71C71C71C71C //P8 +data8 0xBFC0000000000000 //P7 +data8 0x3FC2492492492492 //P6 +data8 0xBFC5555555555555 //P5 +data8 0x3FC999999999999A //P4 +data8 0xBFD0000000000000 //P3 +data8 0x3FD5555555555555 //P2 +data8 0xBFE0000000000000 //P1 +// short version of "lnsin" polynomial +data8 0xD28D3312983E9918, 0x00003FFF //A2 +data8 0x8A8991563EC241B6, 0x00003FFE //A4 +data8 0xADA06588061830A5, 0x00003FFD //A6 +data8 0x80859B57C31CB746, 0x00003FFD //A8 +LOCAL_OBJECT_END(lgammal_1pEps_data) + +LOCAL_OBJECT_START(lgammal_neg2andHalf_data) +// Polynomial coefficients for the lgammal(x), -2.005859375 <= x < -2.5 +data8 0xBF927781D4BB093A, 0xBC511D86D85B7045 // A3, A0L +data8 0x3FF1A68793DEFC15, 0x3C9852AE2DA7DEEF // A1, A1L +data8 0x408555562D45FAFD, 0xBF972CDAFE5FEFAD // D0, D1 +data8 0xC18682331EF492A5, 0xC1845E3E0D29606B // C20, C21 +data8 0x4013141822E16979, 0x3CCF8718B6E75F6C // A2, A2L +data8 0xBFACCBF9F5ED0F15, 0xBBDD1AEB73297401 // A0, A3L +data8 0xCCCDB17423046445, 0x00004006 // E6 +data8 0x800514E230A3A452, 0x00004005 // E4 +data8 0xAAE9A48EC162E76F, 0x00004003 // E2 +data8 0x81D4F88B3F3EA0FC, 0x00004002 // E0 +data8 0x40CF3F3E35238DA0, 0xC0F8B340945F1A7E // D6, D7 +data8 0x40BF89EC0BD609C6, 0xC095897242AEFEE2 // D4, D5 +data8 0x40A2482FF01DBC5C, 0xC02095E275FDCF62 // D2, D3 +data8 0xC1641354F2312A6A, 0xC17B3657F85258E9 // C18, C19 +data8 0xC11F964E9ECBE2C9, 0xC146D7A90F70696C // C16, C17 +data8 0xE7AECDE6AF8EA816, 0x0000BFEF // E7 +data8 0xD711252FEBBE1091, 0x0000BFEB // E5 +data8 0xE648BD10F8C43391, 0x0000BFEF // E3 +data8 0x948A1E78AA00A98D, 0x0000BFF4 // E1 +LOCAL_OBJECT_END(lgammal_neg2andHalf_data) + +LOCAL_OBJECT_START(lgammal_near_neg_half_data) +// Polynomial coefficients for the lgammal(x), -0.5 < x < -0.40625 +data8 0xBFC1AE55B180726C, 0x3C8053CD734E6A1D // A3, A0L +data8 0x3FA2AED059BD608A, 0x3C0CD3D2CDBA17F4 // A1, A1L +data8 0x40855554DBCD1E1E, 0x3F96C51AC2BEE9E1 // D0, D1 +data8 0xC18682331EF4927D, 0x41845E3E0D295DFC // C20, C21 +data8 0x4011DE9E64DF22EF, 0x3CA692B70DAD6B7B // A2, A2L +data8 0x3FF43F89A3F0EDD6, 0xBC4955AED0FA087D // A0, A3L +data8 0xCCCD3F1DF4A2C1DD, 0x00004006 // E6 +data8 0x80028ADE33C7FCD9, 0x00004005 // E4 +data8 0xAACA474E485507EF, 0x00004003 // E2 +data8 0x80F07C206D6B0ECD, 0x00004002 // E0 +data8 0x40CF3F3E33E83056, 0x40F8B340944633D9 // D6, D7 +data8 0x40BF89EC059931F0, 0x409589723307AD20 // D4, D5 +data8 0x40A2482FD0054824, 0x402095CE7F19D011 // D2, D3 +data8 0xC1641354F2313614, 0x417B3657F8525354 // C18, C19 +data8 0xC11F964E9ECFD21C, 0x4146D7A90F701836 // C16, C17 +data8 0x86A9C01F0EA11E5A, 0x0000BFF5 // E7 +data8 0xBF6D8469142881C0, 0x0000BFF6 // E5 +data8 0x8D45D277BA8255F1, 0x0000BFF8 // E3 +data8 0xED2CEA9BA528BCC3, 0x0000BFF9 // E1 +LOCAL_OBJECT_END(lgammal_near_neg_half_data) + +//!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! +////////////// POLYNOMIAL COEFFICIENTS FOR "NEAR ROOTS" RANGES ///////////// +////////////// THIS PART OF TABLE SHOULD BE ADDRESSED REALLY RARE ///////////// +//!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! +LOCAL_OBJECT_START(lgammal_right_roots_polynomial_data) +// Polynomial coefficients for right root on [-3, -2] +// Lgammal is aproximated by polynomial within [-.056244 ; .158208 ] range +data8 0xBBBD5E9DCD11030B, 0xB867411D9FF87DD4 //A0 +data8 0x3FF83FE966AF535E, 0x3CAA21235B8A769A //A1 +data8 0x40136EEBB002F55C, 0x3CC3959A6029838E //A2 +data8 0xB4A5302C53C2BEDD, 0x00003FFF //A3 +data8 0x8B8C6BE504F2DA1C, 0x00004002 //A4 +data8 0xB99CFF02593B4D98, 0x00004001 //A5 +data8 0x4038D32F682AA1CF //A6 +data8 0x403809F04EE6C5B5 //A7 +data8 0x40548EAA81634CEE //A8 +data8 0x4059297ADB6BC03D //A9 +data8 0x407286FB8EC5C9DA //A10 +data8 0x407A92E05B744CFB //A11 +data8 0x4091A9D4144258CD //A12 +data8 0x409C4D01D24F367E //A13 +data8 0x40B1871B9A426A83 //A14 +data8 0x40BE51C48BD9A583 //A15 +data8 0x40D2140D0C6153E7 //A16 +data8 0x40E0FB2C989CE4A3 //A17 +data8 0x40E52739AB005641 //A18 +data8 0x41161E3E6DDF503A //A19 +// Polynomial coefficients for right root on [-4, -3] +// Lgammal is aproximated by polynomial within [-.172797 ; .171573 ] range +data8 0x3C172712B248E42E, 0x38CB8D17801A5D67 //A0 +data8 0x401F20A65F2FAC54, 0x3CCB9EA1817A824E //A1 +data8 0x4039D4D2977150EF, 0x3CDA42E149B6276A //A2 +data8 0xE089B8926AE2D9CB, 0x00004005 //A3 +data8 0x933901EBBB586C37, 0x00004008 //A4 +data8 0xCCD319BED1CFA1CD, 0x0000400A //A5 +data8 0x40D293C3F78D3C37 //A6 +data8 0x40FBB97AA0B6DD02 //A7 +data8 0x41251EA3345E5EB9 //A8 +data8 0x415057F65C92E7B0 //A9 +data8 0x41799C865241B505 //A10 +data8 0x41A445209EFE896B //A11 +data8 0x41D02D21880C953B //A12 +data8 0x41F9FFDE8C63E16D //A13 +data8 0x422504DC8302D2BE //A14 +data8 0x425111BF18C95414 //A15 +data8 0x427BCBE74A2B8EF7 //A16 +data8 0x42A7256F59B286F7 //A17 +data8 0x42D462D1586DE61F //A18 +data8 0x42FBB1228D6C5118 //A19 +// Polynomial coefficients for right root on [-5, -4] +// Lgammal is aproximated by polynomial within [-.163171 ; .161988 ] range +data8 0x3C5840FBAFDEE5BB, 0x38CAC0336E8C490A //A0 +data8 0x403ACA5CF4921642, 0x3CCEDCDDA5491E56 //A1 +data8 0x40744415CD813F8E, 0x3CFBFEBC17E39146 //A2 +data8 0xAACD88D954E3E1BD, 0x0000400B //A3 +data8 0xCB68C710D75ED802, 0x0000400F //A4 +data8 0x8130F5AB997277AC, 0x00004014 //A5 +data8 0x41855E3DBF99EBA7 //A6 +data8 0x41CD14FE49C49FC2 //A7 +data8 0x421433DCE281F07D //A8 +data8 0x425C8399C7A92B6F //A9 +data8 0x42A45FBE67840F1A //A10 +data8 0x42ED68D75F9E6C98 //A11 +data8 0x433567291C27E5BE //A12 +data8 0x437F5ED7A9D9FD28 //A13 +data8 0x43C720A65C8AB711 //A14 +data8 0x441120A6C1D40B9B //A15 +data8 0x44596F561F2D1CBE //A16 +data8 0x44A3507DA81D5C01 //A17 +data8 0x44EF06A31E39EEDF //A18 +data8 0x45333774C99F523F //A19 +// Polynomial coefficients for right root on [-6, -5] +// Lgammal is aproximated by polynomial within [-.156450 ; .156126 ] range +data8 0x3C71B82D6B2B3304, 0x3917186E3C0DC231 //A0 +data8 0x405ED72E0829AE02, 0x3C960C25157980EB //A1 +data8 0x40BCECC32EC22F9B, 0x3D5D8335A32F019C //A2 +data8 0x929EC2B1FB931F17, 0x00004012 //A3 +data8 0xD112EF96D37316DE, 0x00004018 //A4 +data8 0x9F00BB9BB13416AB, 0x0000401F //A5 +data8 0x425F7D8D5BDCB223 //A6 +data8 0x42C9A8D00C776CC6 //A7 +data8 0x433557FD8C481424 //A8 +data8 0x43A209221A953EF0 //A9 +data8 0x440EDC98D5618AB7 //A10 +data8 0x447AABD25E367378 //A11 +data8 0x44E73DE20CC3B288 //A12 +data8 0x455465257B4E0BD8 //A13 +data8 0x45C2011532085353 //A14 +data8 0x462FEE4CC191945B //A15 +data8 0x469C63AEEFEF0A7F //A16 +data8 0x4709D045390A3810 //A17 +data8 0x4778D360873C9F64 //A18 +data8 0x47E26965BE9A682A //A19 +// Polynomial coefficients for right root on [-7, -6] +// Lgammal is aproximated by polynomial within [-.154582 ; .154521 ] range +data8 0x3C75F103A1B00A48, 0x391C041C190C726D //A0 +data8 0x40869DE49E3AF2AA, 0x3D1C17E1F813063B //A1 +data8 0x410FCE23484CFD10, 0x3DB6F38C2F11DAB9 //A2 +data8 0xEF281D1E1BE2055A, 0x00004019 //A3 +data8 0xFCE3DA92AC55DFF8, 0x00004022 //A4 +data8 0x8E9EA838A20BD58E, 0x0000402C //A5 +data8 0x4354F21E2FB9E0C9 //A6 +data8 0x43E9500994CD4F09 //A7 +data8 0x447F3A2C23C033DF //A8 +data8 0x45139152656606D8 //A9 +data8 0x45A8D45F8D3BF2E8 //A10 +data8 0x463FD32110E5BFE5 //A11 +data8 0x46D490B3BDBAE0BE //A12 +data8 0x476AC3CAD905DD23 //A13 +data8 0x48018558217AD473 //A14 +data8 0x48970AF371D30585 //A15 +data8 0x492E6273A8BEFFE3 //A16 +data8 0x49C47CC9AE3F1073 //A17 +data8 0x4A5D38E8C35EFF45 //A18 +data8 0x4AF0123E89694CD8 //A19 +// Polynomial coefficients for right root on [-8, -7] +// Lgammal is aproximated by polynomial within [-.154217 ; .154208 ] range +data8 0xBCD2507D818DDD68, 0xB97F6940EA2871A0 //A0 +data8 0x40B3B407AA387BCB, 0x3D6320238F2C43D1 //A1 +data8 0x41683E85DAAFBAC7, 0x3E148D085958EA3A //A2 +data8 0x9F2A95AF1E10A548, 0x00004022 //A3 +data8 0x92F21522F482300E, 0x0000402E //A4 +data8 0x90B51AB03A1F244D, 0x0000403A //A5 +data8 0x44628E1C70EF534F //A6 +data8 0x452393E2BC32D244 //A7 +data8 0x45E5164141F4BA0B //A8 +data8 0x46A712B3A8AF5808 //A9 +data8 0x47698FD36CEDD0F2 //A10 +data8 0x482C9AE6BBAA3637 //A11 +data8 0x48F023821857C8E9 //A12 +data8 0x49B2569053FC106F //A13 +data8 0x4A74F646D5C1604B //A14 +data8 0x4B3811CF5ABA4934 //A15 +data8 0x4BFBB5DD6C84E233 //A16 +data8 0x4CC05021086F637B //A17 +data8 0x4D8450A345B0FB49 //A18 +data8 0x4E43825848865DB2 //A19 +// Polynomial coefficients for right root on [-9, -8] +// Lgammal is aproximated by polynomial within [-.154160 ; .154158 ] range +data8 0x3CDF4358564F2B46, 0x397969BEE6042F81 //A0 +data8 0x40E3B088FED67721, 0x3D82787BA937EE85 //A1 +data8 0x41C83A3893550EF4, 0x3E542ED57E244DA8 //A2 +data8 0x9F003C6DC56E0B8E, 0x0000402B //A3 +data8 0x92BDF64A3213A699, 0x0000403A //A4 +data8 0x9074F503AAD417AF, 0x00004049 //A5 +data8 0x4582843E1313C8CD //A6 +data8 0x467387BD6A7826C1 //A7 +data8 0x4765074E788CF440 //A8 +data8 0x4857004DD9D1E09D //A9 +data8 0x4949792ED7530EAF //A10 +data8 0x4A3C7F089A292ED3 //A11 +data8 0x4B30125BF0AABB86 //A12 +data8 0x4C224175195E307E //A13 +data8 0x4D14DC4C8B32C08D //A14 +data8 0x4E07F1DB2786197E //A15 +data8 0x4EFB8EA1C336DACB //A16 +data8 0x4FF03797EACD0F23 //A17 +data8 0x50E4304A8E68A730 //A18 +data8 0x51D3618FB2EC9F93 //A19 +// Polynomial coefficients for right root on [-10, -9] +// Lgammal is aproximated by polynomial within [-.154152 ; .154152 ] range +data8 0x3D42F34DA97ECF0C, 0x39FD1256F345B0D0 //A0 +data8 0x4116261203919787, 0x3DC12D44055588EB //A1 +data8 0x422EA8F32FB7FE99, 0x3ED849CE4E7B2D77 //A2 +data8 0xE25BAF73477A57B5, 0x00004034 //A3 +data8 0xEB021FD10060504A, 0x00004046 //A4 +data8 0x8220A208EE206C5F, 0x00004059 //A5 +data8 0x46B2C3903EC9DA14 //A6 +data8 0x47D64393744B9C67 //A7 +data8 0x48FAF79CCDC604DD //A8 +data8 0x4A20975DB8061EBA //A9 +data8 0x4B44AB9CBB38DB21 //A10 +data8 0x4C6A032F60094FE9 //A11 +data8 0x4D908103927634B4 //A12 +data8 0x4EB516CA21D30861 //A13 +data8 0x4FDB1BF12C58D318 //A14 +data8 0x510180AAE094A553 //A15 +data8 0x5226A8F2A2D45D57 //A16 +data8 0x534E00B6B0C8B809 //A17 +data8 0x5475022FE21215B2 //A18 +data8 0x5596B02BF6C5E19B //A19 +// Polynomial coefficients for right root on [-11, -10] +// Lgammal is aproximated by polynomial within [-.154151 ; .154151 ] range +data8 0x3D7AA9C2E2B1029C, 0x3A15FB37578544DB //A0 +data8 0x414BAF825A0C91D4, 0x3DFB9DA2CE398747 //A1 +data8 0x4297F3EC8AE0AF03, 0x3F34208B55FB8781 //A2 +data8 0xDD0C97D3197F56DE, 0x0000403E //A3 +data8 0x8F6F3AF7A5499674, 0x00004054 //A4 +data8 0xC68DA1AF6D878EEB, 0x00004069 //A5 +data8 0x47F1E4E1E2197CE0 //A6 +data8 0x494A8A28E597C3EB //A7 +data8 0x4AA4175D0D35D705 //A8 +data8 0x4BFEE6F0AF69E814 //A9 +data8 0x4D580FE7B3DBB3C6 //A10 +data8 0x4EB2ECE60E4608AF //A11 +data8 0x500E04BE3E2B4F24 //A12 +data8 0x5167F9450F0FB8FD //A13 +data8 0x52C342BDE747603F //A14 +data8 0x541F1699D557268C //A15 +data8 0x557927C5F079864E //A16 +data8 0x56D4D10FEEDB030C //A17 +data8 0x5832385DF86AD28A //A18 +data8 0x598898914B4D6523 //A19 +// Polynomial coefficients for right root on [-12, -11] +// Lgammal is aproximated by polynomial within [-.154151 ; .154151 ] range +data8 0xBD96F61647C58B03, 0xBA3ABB0C2A6C755B //A0 +data8 0x418308A82714B70D, 0x3E1088FC6A104C39 //A1 +data8 0x4306A493DD613C39, 0x3FB2341ECBF85741 //A2 +data8 0x8FA8FE98339474AB, 0x00004049 //A3 +data8 0x802CCDF570BA7942, 0x00004062 //A4 +data8 0xF3F748AF11A32890, 0x0000407A //A5 +data8 0x493E3B567EF178CF //A6 +data8 0x4ACED38F651BA362 //A7 +data8 0x4C600B357337F946 //A8 +data8 0x4DF0F71A52B54CCF //A9 +data8 0x4F8229F3B9FA2C70 //A10 +data8 0x5113A4C4979B770E //A11 +data8 0x52A56BC367F298D5 //A12 +data8 0x543785CF31842DC0 //A13 +data8 0x55C9FC37E3E40896 //A14 +data8 0x575CD5D1BA556C82 //A15 +data8 0x58F00A7AD99A9E08 //A16 +data8 0x5A824088688B008D //A17 +data8 0x5C15F75EF7E08EBD //A18 +data8 0x5DA462EA902F0C90 //A19 +// Polynomial coefficients for right root on [-13, -12] +// Lgammal is aproximated by polynomial within [-.154151 ; .154151 ] range +data8 0x3DC3191752ACFC9D, 0x3A26CB6629532DBF //A0 +data8 0x41BC8CFC051191BD, 0x3E68A84DA4E62AF2 //A1 +data8 0x43797926294A0148, 0x400F345FF3723CFF //A2 +data8 0xF26D2AF700B82625, 0x00004053 //A3 +data8 0xA238B24A4B1F7B15, 0x00004070 //A4 +data8 0xE793B5C0A41A264F, 0x0000408C //A5 +data8 0x4A9585BDDACE863D //A6 +data8 0x4C6075953448088A //A7 +data8 0x4E29B2F38D1FC670 //A8 +data8 0x4FF4619B079C440F //A9 +data8 0x51C05DAE118D8AD9 //A10 +data8 0x538A8C7F87326AD4 //A11 +data8 0x5555B6937588DAB3 //A12 +data8 0x5721E1F8B6E6A7DB //A13 +data8 0x58EDA1D7A77DD6E5 //A14 +data8 0x5AB8A9616B7DC9ED //A15 +data8 0x5C84942AA209ED17 //A16 +data8 0x5E518FC34C6F54EF //A17 +data8 0x601FB3F17BCCD9A0 //A18 +data8 0x61E61128D512FE97 //A1 +// Polynomial coefficients for right root on [-14, -13] +// Lgammal is aproximated by polynomial within [-.154151 ; .154151 ] range +data8 0xBE170D646421B3F5, 0xBAAD95F79FCB5097 //A0 +data8 0x41F7328CBFCD9AC7, 0x3E743B8B1E8AEDB1 //A1 +data8 0x43F0D0FA2DBDA237, 0x40A0422D6A227B55 //A2 +data8 0x82082DF2D32686CC, 0x0000405F //A3 +data8 0x8D64EE9B42E68B43, 0x0000407F //A4 +data8 0xA3FFD82E08C5F1F1, 0x0000409F //A5 +data8 0x4BF8C49D99123454 //A6 +data8 0x4DFEC79DDF11342F //A7 +data8 0x50038615A892F6BD //A8 +data8 0x520929453DB32EF1 //A9 +data8 0x54106A7808189A7F //A10 +data8 0x5615A302D03C207B //A11 +data8 0x581CC175AA736F5E //A12 +data8 0x5A233E071147C017 //A13 +data8 0x5C29E81917243F22 //A14 +data8 0x5E3184B0B5AC4707 //A15 +data8 0x6037C11DE62D8388 //A16 +data8 0x6240787C4B1C9D6C //A17 +data8 0x6448289235E80977 //A18 +data8 0x664B5352C6C3449E //A19 +// Polynomial coefficients for right root on [-15, -14] +// Lgammal is aproximated by polynomial within [-.154151 ; .154151 ] range +data8 0x3E562C2E34A9207D, 0x3ADC00DA3DFF7A83 //A0 +data8 0x42344C3B2F0D90AB, 0x3EB8A2E979F24536 //A1 +data8 0x4469BFFF28B50D07, 0x41181E3D05C1C294 //A2 +data8 0xAE38F64DCB24D9F8, 0x0000406A //A3 +data8 0xA5C3F52C1B350702, 0x0000408E //A4 +data8 0xA83BC857BCD67A1B, 0x000040B2 //A5 +data8 0x4D663B4727B4D80A //A6 +data8 0x4FA82C965B0F7788 //A7 +data8 0x51EAD58C02908D95 //A8 +data8 0x542E427970E073D8 //A9 +data8 0x56714644C558A818 //A10 +data8 0x58B3EC2040C77BAE //A11 +data8 0x5AF72AE6A83D45B1 //A12 +data8 0x5D3B214F611F5D12 //A13 +data8 0x5F7FF5E49C54E92A //A14 +data8 0x61C2E917AB765FB2 //A15 +data8 0x64066FD70907B4C1 //A16 +data8 0x664B3998D60D0F9B //A17 +data8 0x689178710782FA8B //A18 +data8 0x6AD14A66C1C7BEC3 //A19 +// Polynomial coefficients for right root on [-16, -15] +// Lgammal is aproximated by polynomial within [-.154151 ; .154151 ] range +data8 0xBE6D7E7192615BAE, 0xBB0137677D7CC719 //A0 +data8 0x4273077763F6628C, 0x3F09250FB8FC8EC9 //A1 +data8 0x44E6A1BF095B1AB3, 0x4178D5A74F6CB3B3 //A2 +data8 0x8F8E0D5060FCC76E, 0x00004076 //A3 +data8 0x800CC1DCFF092A63, 0x0000409E //A4 +data8 0xF3AB0BA9D14CDA72, 0x000040C5 //A5 +data8 0x4EDE3000A2F6D54F //A6 +data8 0x515EC613B9C8E241 //A7 +data8 0x53E003309FEEEA96 //A8 +data8 0x5660ED908D7C9A90 //A9 +data8 0x58E21E9B517B1A50 //A10 +data8 0x5B639745E4374EE2 //A11 +data8 0x5DE55BB626B2075D //A12 +data8 0x606772B7506BA747 //A13 +data8 0x62E9E581AB2E057B //A14 +data8 0x656CBAD1CF85D396 //A15 +data8 0x67EFF4EBD7989872 //A16 +data8 0x6A722D2B19B7E2F9 //A17 +data8 0x6CF5DEB3073B0743 //A18 +data8 0x6F744AC11550B93A //A19 +// Polynomial coefficients for right root on [-17, -16] +// Lgammal is aproximated by polynomial within [-.154151 ; .154151 ] range +data8 0xBEDCC6291188207E, 0xBB872E3FDD48F5B7 //A0 +data8 0x42B3076EE7525EF9, 0x3F6687A5038CA81C //A1 +data8 0x4566A1AAD96EBCB5, 0x421F0FEDFBF548D2 //A2 +data8 0x8F8D4D3DE9850DBA, 0x00004082 //A3 +data8 0x800BDD6DA2CE1859, 0x000040AE //A4 +data8 0xF3A8EC4C9CDC1CE5, 0x000040D9 //A5 +data8 0x505E2FAFDB812628 //A6 +data8 0x531EC5B3A7508719 //A7 +data8 0x55E002F77E99B628 //A8 +data8 0x58A0ED4C9B4DAE54 //A9 +data8 0x5B621E4A8240F90C //A10 +data8 0x5E2396E5C8849814 //A11 +data8 0x60E55B43D8C5CE71 //A12 +data8 0x63A7722F5D45D01D //A13 +data8 0x6669E4E010DCE45A //A14 +data8 0x692CBA120D5E78F6 //A15 +data8 0x6BEFF4045350B22E //A16 +data8 0x6EB22C9807C21819 //A17 +data8 0x7175DE20D04617C4 //A18 +data8 0x74344AB87C6D655F //A19 +// Polynomial coefficients for right root on [-18, -17] +// Lgammal is aproximated by polynomial within [-.154151 ; .154151 ] range +data8 0xBF28AEEE7B61D77C, 0xBBDBBB5FC57ABF79 //A0 +data8 0x42F436F56B3B8A0C, 0x3FA43EE3C5C576E9 //A1 +data8 0x45E98A22535D115D, 0x42984678BE78CC48 //A2 +data8 0xAC176F3775E6FCFC, 0x0000408E //A3 +data8 0xA3114F53A9FEB922, 0x000040BE //A4 +data8 0xA4D168A8334ABF41, 0x000040EE //A5 +data8 0x51E5B0E7EC7182BB //A6 +data8 0x54E77D67B876EAB6 //A7 +data8 0x57E9F7C30C09C4B6 //A8 +data8 0x5AED29B0488614CA //A9 +data8 0x5DF09486F87E79F9 //A10 +data8 0x60F30B199979654E //A11 +data8 0x63F60E02C7DCCC5F //A12 +data8 0x66F9B8A00EB01684 //A13 +data8 0x69FE2D3ED0700044 //A14 +data8 0x6D01C8363C7DCC84 //A15 +data8 0x700502B29C2F06E3 //A16 +data8 0x730962B4500F4A61 //A17 +data8 0x76103C6ED099192A //A18 +data8 0x79100C7132CFD6E3 //A19 +// Polynomial coefficients for right root on [-19, -18] +// Lgammal is aproximated by polynomial within [-.154151 ; .154151 ] range +data8 0x3F3C19A53328A0C3, 0x3BE04ADC3FBE1458 //A0 +data8 0x4336C16C16C16C19, 0x3FE58CE3AC4A7C28 //A1 +data8 0x46702E85C0898B70, 0x432C922E412CEC6E //A2 +data8 0xF57B99A1C034335D, 0x0000409A //A3 +data8 0x82EC9634223DF909, 0x000040CF //A4 +data8 0x94F66D7557E2EA60, 0x00004103 //A5 +data8 0x5376118B79AE34D0 //A6 +data8 0x56BAE7106D52E548 //A7 +data8 0x5A00BD48CC8E25AB //A8 +data8 0x5D4529722821B493 //A9 +data8 0x608B1654AF31BBC1 //A10 +data8 0x63D182CC98AEA859 //A11 +data8 0x6716D43D5EEB05E8 //A12 +data8 0x6A5DF884FC172E1C //A13 +data8 0x6DA3CA7EBB97976B //A14 +data8 0x70EA416D0BE6D2EF //A15 +data8 0x743176C31EBB65F2 //A16 +data8 0x7777C401A8715CF9 //A17 +data8 0x7AC1110C6D350440 //A18 +data8 0x7E02D0971CF84865 //A19 +// Polynomial coefficients for right root on [-20, -19] +// Lgammal is aproximated by polynomial within [-.154151 ; .154151 ] range +data8 0xBFAB767F9BE21803, 0xBC5ACEF5BB1BD8B5 //A0 +data8 0x4379999999999999, 0x4029241C7F5914C8 //A1 +data8 0x46F47AE147AE147A, 0x43AC2979B64B9D7E //A2 +data8 0xAEC33E1F67152993, 0x000040A7 //A3 +data8 0xD1B71758E219616F, 0x000040DF //A4 +data8 0x8637BD05AF6CF468, 0x00004118 //A5 +data8 0x55065E9F80F293DE //A6 +data8 0x588EADA78C44EE66 //A7 +data8 0x5C15798EE22DEF09 //A8 +data8 0x5F9E8ABFD644FA63 //A9 +data8 0x6325FD7FE29BD7CD //A10 +data8 0x66AFFC5C57E1F802 //A11 +data8 0x6A3774CD7D5C0181 //A12 +data8 0x6DC152724DE2A6FE //A13 +data8 0x7149BB138EB3D0C2 //A14 +data8 0x74D32FF8A70896C2 //A15 +data8 0x785D3749F9C72BD7 //A16 +data8 0x7BE5CCF65EBC4E40 //A17 +data8 0x7F641A891B5FC652 //A18 +data8 0x7FEFFFFFFFFFFFFF //A19 +LOCAL_OBJECT_END(lgammal_right_roots_polynomial_data) + +LOCAL_OBJECT_START(lgammal_left_roots_polynomial_data) +// Polynomial coefficients for left root on [-3, -2] +// Lgammal is aproximated by polynomial within [.084641 ; -.059553 ] range +data8 0xBC0844590979B82E, 0xB8BC7CE8CE2ECC3B //A0 +data8 0xBFFEA12DA904B18C, 0xBC91A6B2BAD5EF6E //A1 +data8 0x4023267F3C265A51, 0x3CD7055481D03AED //A2 +data8 0xA0C2D618645F8E00, 0x0000C003 //A3 +data8 0xFA8256664F8CD2BE, 0x00004004 //A4 +data8 0xC2C422C103F57158, 0x0000C006 //A5 +data8 0x4084373F7CC70AF5 //A6 +data8 0xC0A12239BDD6BB95 //A7 +data8 0x40BDBA65E2709397 //A8 +data8 0xC0DA2D2504DFB085 //A9 +data8 0x40F758173CA5BF3C //A10 +data8 0xC11506C65C267E72 //A11 +data8 0x413318EE3A6B05FC //A12 +data8 0xC1517767F247DA98 //A13 +data8 0x41701237B4754D73 //A14 +data8 0xC18DB8A03BC5C3D8 //A15 +data8 0x41AB80953AC14A07 //A16 +data8 0xC1C9B7B76638D0A4 //A17 +data8 0x41EA727E3033E2D9 //A18 +data8 0xC20812C297729142 //A19 +// +// Polynomial coefficients for left root on [-4, -3] +// Lgammal is aproximated by polynomial within [.147147 ; -.145158 ] range +data8 0xBC3130AE5C4F54DB, 0xB8ED23294C13398A //A0 +data8 0xC034B99D966C5646, 0xBCE2E5FE3BC3DBB9 //A1 +data8 0x406F76DEAE0436BD, 0x3D14974DDEC057BD //A2 +data8 0xE929ACEA5979BE96, 0x0000C00A //A3 +data8 0xF47C14F8A0D52771, 0x0000400E //A4 +data8 0x88B7BC036937481C, 0x0000C013 //A5 +data8 0x4173E8F3AB9FC266 //A6 +data8 0xC1B7DBBE062FB11B //A7 +data8 0x41FD2F76DE7A47A7 //A8 +data8 0xC242225FE53B124D //A9 +data8 0x4286D12AE2FBFA30 //A10 +data8 0xC2CCFFC267A3C4C0 //A11 +data8 0x431294E10008E014 //A12 +data8 0xC357FAC8C9A2DF6A //A13 +data8 0x439F2190AB9FAE01 //A14 +data8 0xC3E44C1D8E8C67C3 //A15 +data8 0x442A8901105D5A38 //A16 +data8 0xC471C4421E908C3A //A17 +data8 0x44B92CD4D59D6D17 //A18 +data8 0xC4FB3A078B5247FA //A19 +// Polynomial coefficients for left root on [-5, -4] +// Lgammal is aproximated by polynomial within [.155671 ; -.155300 ] range +data8 0xBC57BF3C6E8A94C1, 0xB902FB666934AC9E //A0 +data8 0xC05D224A3EF9E41F, 0xBCF6F5713913E440 //A1 +data8 0x40BB533C678A3955, 0x3D688E53E3C72538 //A2 +data8 0x869FBFF732E99B84, 0x0000C012 //A3 +data8 0xBA9537AD61392DEC, 0x00004018 //A4 +data8 0x89EAE8B1DEA06B05, 0x0000C01F //A5 +data8 0x425A8C5C53458D3C //A6 +data8 0xC2C5068B3ED6509B //A7 +data8 0x4330FFA575E99B4E //A8 +data8 0xC39BEC12DDDF7669 //A9 +data8 0x44073825725F74F9 //A10 +data8 0xC47380EBCA299047 //A11 +data8 0x44E084DD9B666437 //A12 +data8 0xC54C2DA6BF787ACF //A13 +data8 0x45B82D65C8D6FA42 //A14 +data8 0xC624D62113FE950A //A15 +data8 0x469200CC19B45016 //A16 +data8 0xC6FFDDC6DD938E2E //A17 +data8 0x476DD7C07184B9F9 //A18 +data8 0xC7D554A30085C052 //A19 +// Polynomial coefficients for left root on [-6, -5] +// Lgammal is aproximated by polynomial within [.157425 ; -.157360 ] range +data8 0x3C9E20A87C8B79F1, 0x39488BE34B2427DB //A0 +data8 0xC08661F6A43A5E12, 0xBD3D912526D759CC //A1 +data8 0x410F79DCB794F270, 0x3DB9BEE7CD3C1BF5 //A2 +data8 0xEB7404450D0005DB, 0x0000C019 //A3 +data8 0xF7AE9846DFE4D4AB, 0x00004022 //A4 +data8 0x8AF535855A95B6DA, 0x0000C02C //A5 +data8 0x43544D54E9FE240E //A6 +data8 0xC3E8684E40CE6CFC //A7 +data8 0x447DF44C1D803454 //A8 +data8 0xC512AC305439B2BA //A9 +data8 0x45A79226AF79211A //A10 +data8 0xC63E0DFF7244893A //A11 +data8 0x46D35216C3A83AF3 //A12 +data8 0xC76903BE0C390E28 //A13 +data8 0x48004A4DECFA4FD5 //A14 +data8 0xC8954FBD243DB8BE //A15 +data8 0x492BF3A31EB18DDA //A16 +data8 0xC9C2C6A864521F3A //A17 +data8 0x4A5AB127C62E8DA1 //A18 +data8 0xCAECF60EF3183C57 //A19 +// Polynomial coefficients for left root on [-7, -6] +// Lgammal is aproximated by polynomial within [.157749 ; -.157739 ] range +data8 0x3CC9B9E8B8D551D6, 0x3961813C8E1E10DB //A0 +data8 0xC0B3ABF7A5CEA91F, 0xBD55638D4BCB4CC4 //A1 +data8 0x4168349A25504236, 0x3E0287ECE50CCF76 //A2 +data8 0x9EC8ED6E4C219E67, 0x0000C022 //A3 +data8 0x9279EB1B799A3FF3, 0x0000402E //A4 +data8 0x90213EF8D9A5DBCF, 0x0000C03A //A5 +data8 0x4462775E857FB71C //A6 +data8 0xC52377E70B45FDBF //A7 +data8 0x45E4F3D28EDA8C28 //A8 +data8 0xC6A6E85571BD2D0B //A9 +data8 0x47695BB17E74DF74 //A10 +data8 0xC82C5AC0ED6A662F //A11 +data8 0x48EFF8159441C2E3 //A12 +data8 0xC9B22602C1B68AE5 //A13 +data8 0x4A74BA8CE7B34100 //A14 +data8 0xCB37C7E208482E4B //A15 +data8 0x4BFB5A1D57352265 //A16 +data8 0xCCC01CB3021212FF //A17 +data8 0x4D841613AC3431D1 //A18 +data8 0xCE431C9E9EE43AD9 //A19 +// Polynomial coefficients for left root on [-8, -7] +// Lgammal is aproximated by polynomial within [.157799 ; -.157798 ] range +data8 0xBCF9C7A33AD9478C, 0xB995B0470F11E5ED //A0 +data8 0xC0E3AF76FE4C2F8B, 0xBD8DBCD503250511 //A1 +data8 0x41C838E76CAAF0D5, 0x3E5D79F5E2E069C3 //A2 +data8 0x9EF345992B262CE0, 0x0000C02B //A3 +data8 0x92AE0292985FD559, 0x0000403A //A4 +data8 0x90615420C08F7D8C, 0x0000C049 //A5 +data8 0x45828139342CEEB7 //A6 +data8 0xC67384066C31E2D3 //A7 +data8 0x476502BC4DAC2C35 //A8 +data8 0xC856FAADFF22ADC6 //A9 +data8 0x49497243255AB3CE //A10 +data8 0xCA3C768489520F6B //A11 +data8 0x4B300D1EA47AF838 //A12 +data8 0xCC223B0508AC620E //A13 +data8 0x4D14D46583338CD8 //A14 +data8 0xCE07E7A87AA068E4 //A15 +data8 0x4EFB811AD2F8BEAB //A16 +data8 0xCFF0351B51508523 //A17 +data8 0x50E4364CCBF53100 //A18 +data8 0xD1D33CFD0BF96FA6 //A19 +// Polynomial coefficients for left root on [-9, -8] +// Lgammal is aproximated by polynomial within [.157806 ; -.157806 ] range +data8 0x3D333E4438B1B9D4, 0x39E7B956B83964C1 //A0 +data8 0xC11625EDFC63DCD8, 0xBDCF39625709EFAC //A1 +data8 0x422EA8C150480F16, 0x3EC16ED908AB7EDD //A2 +data8 0xE2598725E2E11646, 0x0000C034 //A3 +data8 0xEAFF2346DE3EBC98, 0x00004046 //A4 +data8 0x821E90DE12A0F05F, 0x0000C059 //A5 +data8 0x46B2C334AE5366FE //A6 +data8 0xC7D64314B43191B6 //A7 +data8 0x48FAF6ED5899E01B //A8 +data8 0xCA2096E4472AF37D //A9 +data8 0x4B44AAF49FB7E4C8 //A10 +data8 0xCC6A02469F2BD920 //A11 +data8 0x4D9080626D2EFC07 //A12 +data8 0xCEB515EDCF0695F7 //A13 +data8 0x4FDB1AC69BF36960 //A14 +data8 0xD1017F8274339270 //A15 +data8 0x5226A684961BAE2F //A16 +data8 0xD34E085C088404A5 //A17 +data8 0x547511892FF8960E //A18 +data8 0xD5968FA3B1ED67A9 //A19 +// Polynomial coefficients for left root on [-10, -9] +// Lgammal is aproximated by polynomial within [.157807 ; -.157807 ] range +data8 0xBD355818A2B42BA2, 0xB9B7320B6A0D61EA //A0 +data8 0xC14BAF7DA5F3770E, 0xBDE64AF9A868F719 //A1 +data8 0x4297F3E8791F9CD3, 0x3F2A553E59B4835E //A2 +data8 0xDD0C5F7E551BD13C, 0x0000C03E //A3 +data8 0x8F6F0A3B2EB08BBB, 0x00004054 //A4 +data8 0xC68D4D5AD230BA08, 0x0000C069 //A5 +data8 0x47F1E4D8C35D1A3E //A6 +data8 0xC94A8A191DB0A466 //A7 +data8 0x4AA4174F65FE6AE8 //A8 +data8 0xCBFEE6D90F94E9DD //A9 +data8 0x4D580FD3438BE16C //A10 +data8 0xCEB2ECD456D50224 //A11 +data8 0x500E049F7FE64546 //A12 +data8 0xD167F92D9600F378 //A13 +data8 0x52C342AE2B43261A //A14 +data8 0xD41F15DEEDA4B67E //A15 +data8 0x55792638748AFB7D //A16 +data8 0xD6D4D760074F6E6B //A17 +data8 0x5832469D58ED3FA9 //A18 +data8 0xD988769F3DC76642 //A19 +// Polynomial coefficients for left root on [-11, -10] +// Lgammal is aproximated by polynomial within [.157807 ; -.157807 ] range +data8 0xBDA050601F39778A, 0xBA0D4D1CE53E8241 //A0 +data8 0xC18308A7D8EA4039, 0xBE370C379D3EAD41 //A1 +data8 0x4306A49380644E6C, 0x3FBBB143C0E7B5C8 //A2 +data8 0x8FA8FB233E4AA6D2, 0x0000C049 //A3 +data8 0x802CC9D8AEAC207D, 0x00004062 //A4 +data8 0xF3F73EE651A37A13, 0x0000C07A //A5 +data8 0x493E3B550A7B9568 //A6 +data8 0xCACED38DAA060929 //A7 +data8 0x4C600B346BAB3BC6 //A8 +data8 0xCDF0F719193E3D26 //A9 +data8 0x4F8229F24528B151 //A10 +data8 0xD113A4C2D32FBBE2 //A11 +data8 0x52A56BC13DC4474D //A12 +data8 0xD43785CFAF5E3CE3 //A13 +data8 0x55C9FC3EA5941202 //A14 +data8 0xD75CD545A3341AF5 //A15 +data8 0x58F009911F77C282 //A16 +data8 0xDA8246294D210BEC //A17 +data8 0x5C1608AAC32C3A8E //A18 +data8 0xDDA446E570A397D5 //A19 +// Polynomial coefficients for left root on [-12, -11] +// Lgammal is aproximated by polynomial within [.157807 ; -.157807 ] range +data8 0x3DEACBB3081C502E, 0x3A8AA6F01DEDF745 //A0 +data8 0xC1BC8CFBFB0A9912, 0xBE6556B6504A2AE6 //A1 +data8 0x43797926206941D7, 0x40289A9644C2A216 //A2 +data8 0xF26D2A78446D0839, 0x0000C053 //A3 +data8 0xA238B1D937FFED38, 0x00004070 //A4 +data8 0xE793B4F6DE470538, 0x0000C08C //A5 +data8 0x4A9585BDC44DC45D //A6 +data8 0xCC60759520342C47 //A7 +data8 0x4E29B2F3694C0404 //A8 +data8 0xCFF4619AE7B6BBAB //A9 +data8 0x51C05DADF52B89E8 //A10 +data8 0xD38A8C7F48819A4A //A11 +data8 0x5555B6932D687860 //A12 +data8 0xD721E1FACB6C1B5B //A13 +data8 0x58EDA1E2677C8F91 //A14 +data8 0xDAB8A8EC523C1F71 //A15 +data8 0x5C84930133F30411 //A16 +data8 0xDE51952FDFD1EC49 //A17 +data8 0x601FCCEC1BBD25F1 //A18 +data8 0xE1E5F2D76B610920 //A19 +// Polynomial coefficients for left root on [-13, -12] +// Lgammal is aproximated by polynomial within [.157807 ; -.157807 ] range +data8 0xBE01612F373268ED, 0xBA97B7A18CDF103B //A0 +data8 0xC1F7328CBF7A4FAC, 0xBE89A25A6952F481 //A1 +data8 0x43F0D0FA2DBDA237, 0x40A0422EC1CE6084 //A2 +data8 0x82082DF2D32686C5, 0x0000C05F //A3 +data8 0x8D64EE9B42E68B36, 0x0000407F //A4 +data8 0xA3FFD82E08C630C9, 0x0000C09F //A5 +data8 0x4BF8C49D99123466 //A6 +data8 0xCDFEC79DDF1119ED //A7 +data8 0x50038615A892D242 //A8 +data8 0xD20929453DC8B537 //A9 +data8 0x54106A78083BA1EE //A10 +data8 0xD615A302C69E27B2 //A11 +data8 0x581CC175870FF16F //A12 +data8 0xDA233E0979E12B74 //A13 +data8 0x5C29E822BC568C80 //A14 +data8 0xDE31845DB5340FBC //A15 +data8 0x6037BFC6D498D5F9 //A16 +data8 0xE2407D92CD613E82 //A17 +data8 0x64483B9B62367EB7 //A18 +data8 0xE64B2DC830E8A799 //A1 +// Polynomial coefficients for left root on [-14, -13] +// Lgammal is aproximated by polynomial within [.157807 ; -.157807 ] range +data8 0x3E563D0B930B371F, 0x3AE779957E14F012 //A0 +data8 0xC2344C3B2F083767, 0xBEC0B7769AA3DD66 //A1 +data8 0x4469BFFF28B50D07, 0x41181E3F13ED2401 //A2 +data8 0xAE38F64DCB24D9EE, 0x0000C06A //A3 +data8 0xA5C3F52C1B3506F2, 0x0000408E //A4 +data8 0xA83BC857BCD6BA92, 0x0000C0B2 //A5 +data8 0x4D663B4727B4D81A //A6 +data8 0xCFA82C965B0F62E9 //A7 +data8 0x51EAD58C02905B71 //A8 +data8 0xD42E427970FA56AD //A9 +data8 0x56714644C57D8476 //A10 +data8 0xD8B3EC2037EC95F2 //A11 +data8 0x5AF72AE68BBA5B3D //A12 +data8 0xDD3B2152C67AA6B7 //A13 +data8 0x5F7FF5F082861B8B //A14 +data8 0xE1C2E8BE125A5B7A //A15 +data8 0x64066E92FE9EBE7D //A16 +data8 0xE64B4201CDF9F138 //A17 +data8 0x689186351E58AA88 //A18 +data8 0xEAD132A585DFC60A //A19 +// Polynomial coefficients for left root on [-15, -14] +// Lgammal is aproximated by polynomial within [.157807 ; -.157807 ] range +data8 0xBE6D7DDE12700AC1, 0xBB1E025BF1667FB5 //A0 +data8 0xC273077763F60AD5, 0xBF2A1698184C7A9A //A1 +data8 0x44E6A1BF095B1AB3, 0x4178D5AE8A4A2874 //A2 +data8 0x8F8E0D5060FCC767, 0x0000C076 //A3 +data8 0x800CC1DCFF092A57, 0x0000409E //A4 +data8 0xF3AB0BA9D14D37D1, 0x0000C0C5 //A5 +data8 0x4EDE3000A2F6D565 //A6 +data8 0xD15EC613B9C8C800 //A7 +data8 0x53E003309FEECCAA //A8 +data8 0xD660ED908D8B15C4 //A9 +data8 0x58E21E9B51A1C4AE //A10 +data8 0xDB639745DB82210D //A11 +data8 0x5DE55BB60C68FCF6 //A12 +data8 0xE06772BA3FCA23C6 //A13 +data8 0x62E9E58B4F702C31 //A14 +data8 0xE56CBA49B071ABE2 //A15 +data8 0x67EFF31E4F2BA36A //A16 +data8 0xEA7232C8804F32C3 //A17 +data8 0x6CF5EFEE929A0928 //A18 +data8 0xEF742EE03EC3E8FF //A19 +// Polynomial coefficients for left root on [-16, -15] +// Lgammal is aproximated by polynomial within [.157807 ; -.157807 ] range +data8 0xBEDCC628FEAC7A1B, 0xBB80582C8BEBB198 //A0 +data8 0xC2B3076EE752595E, 0xBF5388F55AFAE53E //A1 +data8 0x4566A1AAD96EBCB5, 0x421F0FEFE2444293 //A2 +data8 0x8F8D4D3DE9850DB2, 0x0000C082 //A3 +data8 0x800BDD6DA2CE184C, 0x000040AE //A4 +data8 0xF3A8EC4C9CDC7A43, 0x0000C0D9 //A5 +data8 0x505E2FAFDB81263F //A6 +data8 0xD31EC5B3A7506CD9 //A7 +data8 0x55E002F77E999810 //A8 +data8 0xD8A0ED4C9B5C2900 //A9 +data8 0x5B621E4A8267C401 //A10 +data8 0xDE2396E5BFCFDA7A //A11 +data8 0x60E55B43BE6F9A79 //A12 +data8 0xE3A772324C7405FA //A13 +data8 0x6669E4E9B7E57A2D //A14 +data8 0xE92CB989F8A8FB37 //A15 +data8 0x6BEFF2368849A36E //A16 +data8 0xEEB23234FE191D55 //A17 +data8 0x7175EF5D1080B105 //A18 +data8 0xF4342ED7B1B7BE31 //A19 +// Polynomial coefficients for left root on [-17, -16] +// Lgammal is aproximated by polynomial within [.157807 ; -.157807 ] range +data8 0xBF28AEEE7B58C790, 0xBBC4448DE371FA0A //A0 +data8 0xC2F436F56B3B89B1, 0xBF636755245AC63A //A1 +data8 0x45E98A22535D115D, 0x4298467DA93DB784 //A2 +data8 0xAC176F3775E6FCF2, 0x0000C08E //A3 +data8 0xA3114F53A9FEB908, 0x000040BE //A4 +data8 0xA4D168A8334AFE5A, 0x0000C0EE //A5 +data8 0x51E5B0E7EC7182CF //A6 +data8 0xD4E77D67B876D6B4 //A7 +data8 0x57E9F7C30C098C83 //A8 +data8 0xDAED29B0489EF7A7 //A9 +data8 0x5DF09486F8A524B8 //A10 +data8 0xE0F30B19910A2393 //A11 +data8 0x63F60E02AB3109F4 //A12 +data8 0xE6F9B8A3431854D5 //A13 +data8 0x69FE2D4A6D94218E //A14 +data8 0xED01C7E272A73560 //A15 +data8 0x7005017D82B186B6 //A16 +data8 0xF3096A81A69BD8AE //A17 +data8 0x76104951BAD67D5C //A18 +data8 0xF90FECC99786FD5B //A19 +// Polynomial coefficients for left root on [-18, -17] +// Lgammal is aproximated by polynomial within [.157807 ; -.157807 ] range +data8 0x3F3C19A53328E26A, 0x3BE238D7BA036B3B //A0 +data8 0xC336C16C16C16C13, 0xBFEACE245DEC56F3 //A1 +data8 0x46702E85C0898B70, 0x432C922B64FD1DA4 //A2 +data8 0xF57B99A1C0343350, 0x0000C09A //A3 +data8 0x82EC9634223DF90D, 0x000040CF //A4 +data8 0x94F66D7557E3237D, 0x0000C103 //A5 +data8 0x5376118B79AE34D6 //A6 +data8 0xD6BAE7106D52CE49 //A7 +data8 0x5A00BD48CC8E11AB //A8 +data8 0xDD4529722833E2DF //A9 +data8 0x608B1654AF5F46AF //A10 +data8 0xE3D182CC90D8723F //A11 +data8 0x6716D43D46706AA0 //A12 +data8 0xEA5DF888C5B428D3 //A13 +data8 0x6DA3CA85888931A6 //A14 +data8 0xF0EA40EF2AC7E070 //A15 +data8 0x743175D1A251AFCD //A16 +data8 0xF777CB6E2B550D73 //A17 +data8 0x7AC11E468A134A51 //A18 +data8 0xFE02B6BDD0FC40AA //A19 +// Polynomial coefficients for left root on [-19, -18] +// Lgammal is aproximated by polynomial within [.157807 ; -.157807 ] range +data8 0xBFAB767F9BE217FC, 0xBC4A5541CE0D8D0D //A0 +data8 0xC379999999999999, 0xC01A84981B490BE8 //A1 +data8 0x46F47AE147AE147A, 0x43AC2987BBC466EB //A2 +data8 0xAEC33E1F67152987, 0x0000C0A7 //A3 +data8 0xD1B71758E2196153, 0x000040DF //A4 +data8 0x8637BD05AF6D420E, 0x0000C118 //A5 +data8 0x55065E9F80F293B2 //A6 +data8 0xD88EADA78C44BFA7 //A7 +data8 0x5C15798EE22EC6CD //A8 +data8 0xDF9E8ABFD67895CF //A9 +data8 0x6325FD7FE13B0DE0 //A10 +data8 0xE6AFFC5C3DE70858 //A11 +data8 0x6A3774CE81C70D43 //A12 +data8 0xEDC1527412D8129F //A13 +data8 0x7149BABCDA8B7A72 //A14 +data8 0xF4D330AD49071BB5 //A15 +data8 0x785D4046F4C5F1FD //A16 +data8 0xFBE59BFEDBA73FAF //A17 +data8 0x7F64BEF2B2EC8DA1 //A18 +data8 0xFFEFFFFFFFFFFFFF //A19 +LOCAL_OBJECT_END(lgammal_left_roots_polynomial_data) + + +//============================================================== +// Code +//============================================================== + +.section .text +GLOBAL_LIBM_ENTRY(__libm_lgammal) +{ .mfi + getf.exp rSignExpX = f8 + // Test x for NaTVal, NaN, +/-0, +/-INF, denormals + fclass.m p6,p0 = f8,0x1EF + addl r17Ones = 0x1FFFF, r0 // exponent mask +} +{ .mfi + addl GR_ad_z_1 = @ltoff(Constants_Z_1#),gp + fcvt.fx.s1 fXint = f8 // Convert arg to int (int repres. in FR) + adds rDelta = 0x3FC, r0 +} +;; +{ .mfi + getf.sig rSignifX = f8 + fcmp.lt.s1 p15, p14 = f8, f0 + shl rDelta = rDelta, 20 // single precision 1.5 +} +{ .mfi + ld8 GR_ad_z_1 = [GR_ad_z_1]// get pointer to Constants_Z_1 + fma.s1 fTwo = f1, f1, f1 // 2.0 + addl rExp8 = 0x10002, r0 // exponent of 8.0 +} +;; +{ .mfi + alloc rPFS_SAVED = ar.pfs, 0, 34, 4, 0 // get some registers + fmerge.s fAbsX = f1, f8 // |x| + and rExpX = rSignExpX, r17Ones // mask sign bit +} +{ .mib + addl rExpHalf = 0xFFFE, r0 // exponent of 0.5 + addl rExp2 = 0x10000, r0 // exponent of 2.0 + // branch out if x is NaTVal, NaN, +/-0, +/-INF, or denormalized number +(p6) br.cond.spnt lgammal_spec +} +;; +_deno_back_to_main_path: +{ .mfi + // Point to Constants_G_H_h1 + add rTbl1Addr = 0x040, GR_ad_z_1 + frcpa.s1 fRcpX, p0 = f1, f8 // initial approximation of 1/x + extr.u GR_Index1 = rSignifX, 59, 4 +} +{ .mib +(p14) cmp.ge.unc p8, p0 = rExpX, rExp8 // p8 = 1 if x >= 8.0 + adds rZ625 = 0x3F2, r0 +(p8) br.cond.spnt lgammal_big_positive // branch out if x >= 8.0 +} +;; +{ .mfi + shladd rZ1offsett = GR_Index1, 2, GR_ad_z_1 // Point to Z_1 + fmerge.se fSignifX = f1, f8 // sifnificand of x + // Get high 15 bits of significand + extr.u GR_X_0 = rSignifX, 49, 15 +} +{ .mib + cmp.lt.unc p9, p0 = rExpX, rExpHalf // p9 = 1 if |x| < 0.5 + // set p11 if 2 <= x < 4 +(p14) cmp.eq.unc p11, p0 = rExpX, rExp2 +(p9) br.cond.spnt lgammal_0_half // branch out if |x| < 0.5 +} +;; +{ .mfi + ld4 GR_Z_1 = [rZ1offsett] // Load Z_1 + fms.s1 fA5L = f1, f1, f8 // for 0.75 <= x < 1.3125 path + shl rZ625 = rZ625, 20 // sinfle precision 0.625 +} +{ .mib + setf.s FR_MHalf = rDelta + // set p10 if x >= 4.0 +(p14) cmp.gt.unc p10, p0 = rExpX, rExp2 + // branch to special path for 4.0 <= x < 8 +(p10) br.cond.spnt lgammal_4_8 +} +;; +{ .mfi + // for 1.3125 <= x < 1.5625 path + addl rPolDataPtr= @ltoff(lgammal_loc_min_data),gp + // argument of polynomial approximation for 1.5625 <= x < 2.25 + fms.s1 fB4 = f8, f1, fTwo + cmp.eq p12, p0 = rExpX, rExpHalf +} +{ .mib + addl rExpOne = 0xFFFF, r0 // exponent of 1.0 + // set p10 if significand of x >= 1.125 +(p11) cmp.le p11, p0 = 2, GR_Index1 +(p11) br.cond.spnt lgammal_2Q_4 +} +;; +{ .mfi + // point to xMin for 1.3125 <= x < 1.5625 path + ld8 rPolDataPtr = [rPolDataPtr] + fcvt.xf fFltIntX = fXint // RTN(x) +(p14) cmp.eq.unc p13, p7 = rExpX, rExpOne // p13 set if 1.0 <= x < 2.0 +} +{ .mib + setf.s FR_FracX = rZ625 + // set p12 if |x| < 0.75 +(p12) cmp.gt.unc p12, p0 = 8, GR_Index1 + // branch out to special path for |x| < 0.75 +(p12) br.cond.spnt lgammal_half_3Q +} +;; +.pred.rel "mutex", p7, p13 +{ .mfi + getf.sig rXRnd = fXint // integer part of the input value + fnma.s1 fInvX = f8, fRcpX, f1 // start of 1st NR iteration + // Get bits 30-15 of X_0 * Z_1 + pmpyshr2.u GR_X_1 = GR_X_0,GR_Z_1,15 +} +{ .mib +(p7) cmp.eq p6, p0 = rExpX, rExp2 // p6 set if 2.0 <= x < 2.25 +(p13) cmp.le p6, p0 = 9, GR_Index1 + // branch to special path 1.5625 <= x < 2.25 +(p6) br.cond.spnt lgammal_13Q_2Q +} +;; +// +// For performance, don't use result of pmpyshr2.u for 4 cycles. +// +{ .mfi + shladd GR_ad_tbl_1 = GR_Index1, 4, rTbl1Addr // Point to G_1 + fma.s1 fSix = fTwo, fTwo, fTwo // 6.0 + add GR_ad_q = -0x60, GR_ad_z_1 // Point to Constants_Q +} +{ .mib + add rTmpPtr3 = -0x50, GR_ad_z_1 +(p13) cmp.gt p7, p0 = 5, GR_Index1 + // branch to special path 0.75 <= x < 1.3125 +(p7) br.cond.spnt lgammal_03Q_1Q +} +;; +{ .mfi + add rTmpPtr = 8, GR_ad_tbl_1 + fma.s1 fRoot = f8, f1, f1 // x + 1 + // Absolute value of int arg. Will be used as index in table with roots + sub rXRnd = r0, rXRnd +} +{ .mib + ldfe fA5L = [rPolDataPtr], 16 // xMin + addl rNegSingularity = 0x3003E, r0 +(p14) br.cond.spnt lgammal_loc_min +} +;; +{ .mfi + ldfps FR_G, FR_H = [GR_ad_tbl_1], 8 // Load G_1, H_1 + nop.f 0 + add rZ2Addr = 0x140, GR_ad_z_1 // Point to Constants_Z_2 +} +{ .mib + ldfd FR_h = [rTmpPtr] // Load h_1 + // If arg is less or equal to -2^63 + cmp.geu.unc p8,p0 = rSignExpX, rNegSingularity + // Singularity for x < -2^63 since all such arguments are integers + // branch to special code which deals with singularity +(p8) br.cond.spnt lgammal_singularity +} +;; +{ .mfi + ldfe FR_log2_hi = [GR_ad_q], 32 // Load log2_hi + nop.f 0 + extr.u GR_Index2 = GR_X_1, 6, 4 // Extract bits 6-9 of X_1 +} +{ .mfi + ldfe FR_log2_lo = [rTmpPtr3], 32 // Load log2_lo + fms.s1 fDx = f8, f1, fFltIntX // x - RTN(x) + // index in table with roots and bounds + adds rXint = -2, rXRnd +} +;; +{ .mfi + ldfe FR_Q4 = [GR_ad_q], 32 // Load Q4 + nop.f 0 + // set p12 if x may be close to negative root: -19.5 < x < -2.0 + cmp.gtu p12, p0 = 18, rXint +} +{ .mfi + shladd GR_ad_z_2 = GR_Index2, 2, rZ2Addr // Point to Z_2 + fma.s1 fRcpX = fInvX, fRcpX, fRcpX // end of 1st NR iteration + // Point to Constants_G_H_h2 + add rTbl2Addr = 0x180, GR_ad_z_1 +} +;; +{ .mfi + shladd GR_ad_tbl_2 = GR_Index2, 4, rTbl2Addr // Point to G_2 + // set p9 if x is integer and negative + fcmp.eq.s1 p9, p0 = f8,fFltIntX + // Point to Constants_G_H_h3 + add rTbl3Addr = 0x280, GR_ad_z_1 +} +{ .mfi + ld4 GR_Z_2 = [GR_ad_z_2] // Load Z_2 + nop.f 0 + sub GR_N = rExpX, rExpHalf, 1 +} +;; +{ .mfi + ldfe FR_Q3 = [rTmpPtr3], 32 // Load Q3 + nop.f 0 + // Point to lnsin polynomial coefficients + adds rLnSinDataPtr = 864, rTbl3Addr +} +{ .mfi + ldfe FR_Q2 = [GR_ad_q],32 // Load Q2 + nop.f 0 + add rTmpPtr = 8, GR_ad_tbl_2 +} +;; +{ .mfi + ldfe FR_Q1 = [rTmpPtr3] // Load Q1 + fcmp.lt.s1 p0, p15 = fAbsX, fSix // p15 is set when x < -6.0 + // point to table with roots and bounds + adds rRootsBndAddr = -1296, GR_ad_z_1 +} +{ .mfb + // Put integer N into rightmost significand + setf.sig fFloatN = GR_N + fma.s1 fThirteen = fSix, fTwo, f1 // 13.0 + // Singularity if -2^63 < x < 0 and x is integer + // branch to special code which deals with singularity +(p9) br.cond.spnt lgammal_singularity +} +;; +{ .mfi + ldfps FR_G2, FR_H2 = [GR_ad_tbl_2] // Load G_2, H_2 + // y = |x|/2^(exponent(x)) - 1.5 + fms.s1 FR_FracX = fSignifX, f1, FR_MHalf + // Get bits 30-15 of X_1 * Z_2 + pmpyshr2.u GR_X_2 = GR_X_1,GR_Z_2,15 +} +{ .mfi + ldfd FR_h2 = [rTmpPtr] // Load h_2 + fma.s1 fDxSqr = fDx, fDx, f0 // deltaX^2 + adds rTmpPtr3 = 128, rLnSinDataPtr +} +;; +// +// For performance, don't use result of pmpyshr2.u for 4 cycles. +// +{ .mfi + getf.exp rRoot = fRoot // sign and biased exponent of (x + 1) + nop.f 0 + // set p6 if -4 < x <= -2 + cmp.eq p6, p0 = rExpX, rExp2 +} +{ .mfi + ldfpd fLnSin2, fLnSin2L = [rLnSinDataPtr], 16 + fnma.s1 fInvX = f8, fRcpX, f1 // start of 2nd NR iteration + sub rIndexPol = rExpX, rExpHalf // index of polynom +} +;; +{ .mfi + ldfe fLnSin4 = [rLnSinDataPtr], 96 + // p10 is set if x is potential "right" root + // p11 set for possible "left" root + fcmp.lt.s1 p10, p11 = fDx, f0 + shl rIndexPol = rIndexPol, 6 // (i*16)*4 +} +{ .mfi + ldfpd fLnSin18, fLnSin20 = [rTmpPtr3], 16 + nop.f 0 + mov rExp2tom7 = 0x0fff8 // Exponent of 2^-7 +} +;; +{ .mfi + getf.sig rSignifDx = fDx // Get significand of RTN(x) + nop.f 0 + // set p6 if -4 < x <= -3.0 +(p6) cmp.le.unc p6, p0 = 0x8, GR_Index1 +} +{ .mfi + ldfpd fLnSin22, fLnSin24 = [rTmpPtr3], 16 + nop.f 0 + // mask sign bit in the exponent of (x + 1) + and rRoot = rRoot, r17Ones +} +;; +{ .mfi + ldfe fLnSin16 = [rLnSinDataPtr], -80 + nop.f 0 + extr.u GR_Index3 = GR_X_2, 1, 5 // Extract bits 1-5 of X_2 +} +{ .mfi + ldfpd fLnSin26, fLnSin28 = [rTmpPtr3], 16 + nop.f 0 + and rXRnd = 1, rXRnd +} +;; +{ .mfi + shladd GR_ad_tbl_3 = GR_Index3, 4, rTbl3Addr // Point to G_3 + fms.s1 fDxSqrL = fDx, fDx, fDxSqr // low part of deltaX^2 + // potential "left" root +(p11) adds rRootsBndAddr = 560, rRootsBndAddr +} +{ .mib + ldfpd fLnSin30, fLnSin32 = [rTmpPtr3], 16 + // set p7 if |x+1| < 2^-7 + cmp.lt p7, p0 = rRoot, rExp2tom7 + // branch to special path for |x+1| < 2^-7 +(p7) br.cond.spnt _closeToNegOne +} +;; +{ .mfi + ldfps FR_G3, FR_H3 = [GR_ad_tbl_3], 8 // Load G_3, H_3 + fcmp.lt.s1 p14, p0 = fAbsX, fThirteen // set p14 if x > -13.0 + // base address of polynomial on range [-6.0, -0.75] + adds rPolDataPtr = 3440, rTbl3Addr +} +{ .mfi + // (i*16)*4 + (i*16)*8 - offsett of polynomial on range [-6.0, -0.75] + shladd rTmpPtr = rIndexPol, 2, rIndexPol + fma.s1 fXSqr = FR_FracX, FR_FracX, f0 // y^2 + // point to left "near root" bound +(p12) shladd rRootsBndAddr = rXint, 4, rRootsBndAddr +} +;; +{ .mfi + ldfpd fLnSin34, fLnSin36 = [rTmpPtr3], 16 + fma.s1 fRcpX = fInvX, fRcpX, fRcpX // end of 2nd NR iteration + // add special offsett if -4 < x <= -3.0 +(p6) adds rPolDataPtr = 640, rPolDataPtr +} +{ .mfi + // point to right "near root" bound + adds rTmpPtr2 = 8, rRootsBndAddr + fnma.s1 fMOne = f1, f1, f0 // -1.0 + // Point to Bernulli numbers + adds rBernulliPtr = 544, rTbl3Addr +} +;; +{ .mfi + // left bound of "near root" range +(p12) ld8 rLeftBound = [rRootsBndAddr] + fmerge.se fNormDx = f1, fDx // significand of DeltaX + // base address + offsett for polynomial coeff. on range [-6.0, -0.75] + add rPolDataPtr = rPolDataPtr, rTmpPtr +} +{ .mfi + // right bound of "near root" range +(p12) ld8 rRightBound = [rTmpPtr2] + fcvt.xf fFloatN = fFloatN + // special "Bernulli" numbers for Stirling's formula for -13 < x < -6 +(p14) adds rBernulliPtr = 160, rBernulliPtr +} +;; +{ .mfi + ldfd FR_h3 = [GR_ad_tbl_3] // Load h_3 + fmpy.s1 FR_G = FR_G, FR_G2 // G = G_1 * G_2 + adds rTmpPtr3 = -160, rTmpPtr3 +} +{ .mfb + adds rTmpPtr = 80, rPolDataPtr + fadd.s1 FR_H = FR_H, FR_H2 // H = H_1 + H_2 + // p15 is set if -2^63 < x < 6.0 and x is not an integer + // branch to path with implementation using Stirling's formula for neg. x +(p15) br.cond.spnt _negStirling +} +;; +{ .mfi + ldfpd fA3, fA3L = [rPolDataPtr], 16 // A3 + fma.s1 fDelX4 = fDxSqr, fDxSqr, f0 // deltaX^4 + // Get high 4 bits of signif + extr.u rIndex1Dx = rSignifDx, 59, 4 +} +{ .mfi + ldfe fA5 = [rTmpPtr], -16 // A5 + fadd.s1 FR_h = FR_h, FR_h2 // h = h_1 + h_2 + adds rLnSinTmpPtr = 16, rLnSinDataPtr +} +;; +{ .mfi + ldfpd fA0, fA0L = [rPolDataPtr], 16 // A0 + fma.s1 fLnSin20 = fLnSin20, fDxSqr, fLnSin18 + // Get high 15 bits of significand + extr.u rX0Dx = rSignifDx, 49, 15 +} +{ .mfi + ldfe fA4 = [rTmpPtr], 192 // A4 + fms.s1 fXSqrL = FR_FracX, FR_FracX, fXSqr // low part of y^2 + shladd GR_ad_z_1 = rIndex1Dx, 2, GR_ad_z_1 // Point to Z_1 +} +;; +{ .mfi + ldfpd fA1, fA1L = [rPolDataPtr], 16 // A1 + fma.s1 fX4 = fXSqr, fXSqr, f0 // y^4 + adds rTmpPtr2 = 32, rTmpPtr +} +{ .mfi + ldfpd fA18, fA19 = [rTmpPtr], 16 // A18, A19 + fma.s1 fLnSin24 = fLnSin24, fDxSqr, fLnSin22 + nop.i 0 +} +;; +{ .mfi + ldfe fLnSin6 = [rLnSinDataPtr], 32 + fma.s1 fLnSin28 = fLnSin28, fDxSqr, fLnSin26 + nop.i 0 +} +{ .mfi + ldfe fLnSin8 = [rLnSinTmpPtr], 32 + nop.f 0 + nop.i 0 +} +;; +{ .mfi + ldfpd fA20, fA21 = [rTmpPtr], 16 // A20, A21 + fma.s1 fLnSin32 = fLnSin32, fDxSqr, fLnSin30 + nop.i 0 +} +{ .mfi + ldfpd fA22, fA23 = [rTmpPtr2], 16 // A22, A23 + fma.s1 fB20 = f1, f1, FR_MHalf // 2.5 +(p12) cmp.ltu.unc p6, p0 = rSignifX, rLeftBound +} +;; +{ .mfi + ldfpd fA2, fA2L = [rPolDataPtr], 16 // A2 + fmpy.s1 FR_G = FR_G, FR_G3 // G = (G_1 * G_2) * G_3 + // set p6 if x falls in "near root" range +(p6) cmp.geu.unc p6, p0 = rSignifX, rRightBound +} +{ .mfb + adds rTmpPtr3 = -64, rTmpPtr + fadd.s1 FR_H = FR_H, FR_H3 // H = (H_1 + H_2) + H_3 + // branch to special path if x falls in "near root" range +(p6) br.cond.spnt _negRoots +} +;; +{ .mfi + ldfpd fA24, fA25 = [rTmpPtr2], 16 // A24, A25 + fma.s1 fLnSin36 = fLnSin36, fDxSqr, fLnSin34 +(p11) cmp.eq.unc p7, p0 = 1,rXint // p7 set if -3.0 < x < -2.5 +} +{ .mfi + adds rTmpPtr = -48, rTmpPtr + fma.s1 fLnSin20 = fLnSin20, fDxSqr, fLnSin16 + addl rDelta = 0x5338, r0 // significand of -2.605859375 +} +;; +{ .mfi + getf.exp GR_N = fDx // Get N = exponent of DeltaX + fma.s1 fX6 = fX4, fXSqr, f0 // y^6 + // p7 set if -2.605859375 <= x < -2.5 +(p7) cmp.gt.unc p7, p0 = rDelta, GR_X_0 +} +{ .mfb + ld4 GR_Z_1 = [GR_ad_z_1] // Load Z_1 + fma.s1 fDelX8 = fDelX4, fDelX4, f0 // deltaX^8 + // branch to special path for -2.605859375 <= x < -2.5 +(p7) br.cond.spnt _neg2andHalf +} +;; +{ .mfi + ldfpd fA14, fA15 = [rTmpPtr3], 16 // A14, A15 + fadd.s1 FR_h = FR_h, FR_h3 // h = (h_1 + h_2) + h_3 + adds rTmpPtr2 = 128 , rPolDataPtr +} +{ .mfi + ldfpd fA16, fA17 = [rTmpPtr], 16 // A16, A17 + fma.s1 fLnSin28 = fLnSin28, fDelX4, fLnSin24 + adds rPolDataPtr = 144 , rPolDataPtr +} +;; +{ .mfi + ldfe fLnSin10 = [rLnSinDataPtr], 32 + fma.s1 fRes1H = fA3, FR_FracX, f0 // (A3*y)hi + and GR_N = GR_N, r17Ones // mask sign bit +} +{ .mfi + ldfe fLnSin12 = [rLnSinTmpPtr] + fma.s1 fDelX6 = fDxSqr, fDelX4, f0 // DeltaX^6 + shladd GR_ad_tbl_1 = rIndex1Dx, 4, rTbl1Addr // Point to G_1 +} +;; +{ .mfi + ldfe fA13 = [rPolDataPtr], -32 // A13 + fma.s1 fA4 = fA5, FR_FracX, fA4 // A5*y + A4 + // Get bits 30-15 of X_0 * Z_1 + pmpyshr2.u GR_X_1 = rX0Dx, GR_Z_1, 15 +} +{ .mfi + ldfe fA12 = [rTmpPtr2], -32 // A12 + fms.s1 FR_r = FR_G, fSignifX, f1 // r = G * S_hi - 1 + sub GR_N = GR_N, rExpHalf, 1 // unbisaed exponent of DeltaX +} +;; +// +// For performance, don't use result of pmpyshr2.u for 4 cycles. +// +.pred.rel "mutex",p10,p11 +{ .mfi + ldfe fA11 = [rPolDataPtr], -32 // A11 + // High part of log(|x|) = Y_hi = N * log2_hi + H + fma.s1 fResH = fFloatN, FR_log2_hi, FR_H +(p10) cmp.eq p8, p9 = rXRnd, r0 +} +{ .mfi + ldfe fA10 = [rTmpPtr2], -32 // A10 + fma.s1 fRes6H = fA1, FR_FracX, f0 // (A1*y)hi +(p11) cmp.eq p9, p8 = rXRnd, r0 +} +;; +{ .mfi + ldfe fA9 = [rPolDataPtr], -32 // A9 + fma.s1 fB14 = fLnSin6, fDxSqr, f0 // (LnSin6*deltaX^2)hi + cmp.eq p6, p7 = 4, rSgnGamSize +} +{ .mfi + ldfe fA8 = [rTmpPtr2], -32 // A8 + fma.s1 fA18 = fA19, FR_FracX, fA18 + nop.i 0 +} +;; +{ .mfi + ldfe fA7 = [rPolDataPtr] // A7 + fma.s1 fA23 = fA23, FR_FracX, fA22 + nop.i 0 +} +{ .mfi + ldfe fA6 = [rTmpPtr2] // A6 + fma.s1 fA21 = fA21, FR_FracX, fA20 + nop.i 0 +} +;; +{ .mfi + ldfe fLnSin14 = [rLnSinDataPtr] + fms.s1 fRes1L = fA3, FR_FracX, fRes1H // delta((A3*y)hi) + extr.u GR_Index2 = GR_X_1, 6, 4 // Extract bits 6-9 of X_1 +} +{ .mfi + setf.sig fFloatNDx = GR_N + fadd.s1 fPol = fRes1H, fA2 // (A3*y + A2)hi + nop.i 0 +} +;; +{ .mfi + ldfps FR_G, FR_H = [GR_ad_tbl_1], 8 // Load G_1, H_1 + fma.s1 fRes2H = fA4, fXSqr, f0 // ((A5 + A4*y)*y^2)hi + nop.i 0 +} +{ .mfi + shladd GR_ad_z_2 = GR_Index2, 2, rZ2Addr // Point to Z_2 + fma.s1 fA25 = fA25, FR_FracX, fA24 + shladd GR_ad_tbl_2 = GR_Index2, 4, rTbl2Addr // Point to G_2 +} +;; +.pred.rel "mutex",p8,p9 +{ .mfi + ld4 GR_Z_2 = [GR_ad_z_2] // Load Z_2 + fms.s1 fRes6L = fA1, FR_FracX, fRes6H // delta((A1*y)hi) + // sign of GAMMA(x) is negative +(p8) adds rSgnGam = -1, r0 +} +{ .mfi + adds rTmpPtr = 8, GR_ad_tbl_2 + fadd.s1 fRes3H = fRes6H, fA0 // (A1*y + A0)hi + // sign of GAMMA(x) is positive +(p9) adds rSgnGam = 1, r0 +} +;; +{ .mfi + ldfps FR_G2, FR_H2 = [GR_ad_tbl_2] // Load G_2, H_2 + // (LnSin6*deltaX^2 + LnSin4)hi + fadd.s1 fLnSinH = fB14, fLnSin4 + nop.i 0 +} +{ .mfi + ldfd FR_h2 = [rTmpPtr] // Load h_2 + fms.s1 fB16 = fLnSin6, fDxSqr, fB14 // delta(LnSin6*deltaX^2) + nop.i 0 +} +;; +{ .mfi + ldfd fhDelX = [GR_ad_tbl_1] // Load h_1 + fma.s1 fA21 = fA21, fXSqr, fA18 + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 fLnSin36 = fLnSin36, fDelX4, fLnSin32 + nop.i 0 +} +;; +{ .mfi + nop.m 0 + fma.s1 fRes1L = fA3L, FR_FracX, fRes1L // (A3*y)lo + // Get bits 30-15 of X_1 * Z_ + pmpyshr2.u GR_X_2 = GR_X_1,GR_Z_2,15 +} +{ .mfi + nop.m 0 + fsub.s1 fPolL = fA2, fPol + nop.i 0 +} +;; +// +// For performance, don't use result of pmpyshr2.u for 4 cycles. +// +{ .mfi + nop.m 0 + // delta(((A5 + A4*y)*y^2)hi) + fms.s1 fRes2L = fA4, fXSqr, fRes2H + nop.i 0 +} +{ .mfi + nop.m 0 + // (((A5 + A4*y)*y^2) + A3*y + A2)hi + fadd.s1 fRes4H = fRes2H, fPol + nop.i 0 +} +;; +{ .mfi + // store signgam if size of variable is 4 bytes +(p6) st4 [rSgnGamAddr] = rSgnGam + fma.s1 fRes6L = fA1L, FR_FracX, fRes6L // (A1*y)lo + nop.i 0 +} +{ .mfi + // store signgam if size of variable is 8 bytes +(p7) st8 [rSgnGamAddr] = rSgnGam + fsub.s1 fRes3L = fA0, fRes3H + nop.i 0 +} +;; +{ .mfi + nop.m 0 + fsub.s1 fLnSinL = fLnSin4, fLnSinH + nop.i 0 +} +{ .mfi + nop.m 0 + // ((LnSin6*deltaX^2 + LnSin4)*deltaX^2)hi + fma.s1 fB18 = fLnSinH, fDxSqr, f0 + nop.i 0 +} +;; +{ .mfi + adds rTmpPtr = 8, rTbl3Addr + fma.s1 fB16 = fLnSin6, fDxSqrL, fB16 // (LnSin6*deltaX^2)lo + extr.u GR_Index3 = GR_X_2, 1, 5 // Extract bits 1-5 of X_2 +} +{ .mfi + nop.m 0 + fma.s1 fA25 = fA25, fXSqr, fA23 + nop.i 0 +} +;; +{ .mfi + shladd GR_ad_tbl_3 = GR_Index3, 4, rTbl3Addr // Point to G_3 + fadd.s1 fPolL = fPolL, fRes1H + nop.i 0 +} +{ .mfi + shladd rTmpPtr = GR_Index3, 4, rTmpPtr // Point to G_3 + fadd.s1 fRes1L = fRes1L, fA2L // (A3*y)lo + A2lo + nop.i 0 +} +;; +{ .mfi + ldfps FR_G3, FR_H3 = [GR_ad_tbl_3] // Load G_3, H_3 + fma.s1 fRes2L = fA4, fXSqrL, fRes2L // ((A5 + A4*y)*y^2)lo + nop.i 0 +} +{ .mfi + ldfd FR_h3 = [rTmpPtr] // Load h_3 + fsub.s1 fRes4L = fPol, fRes4H + nop.i 0 +} +;; +{ .mfi + nop.m 0 + // ((((A5 + A4*y)*y^2) + A3*y + A2)*y^2)hi + fma.s1 fRes7H = fRes4H, fXSqr, f0 + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 fA15 = fA15, FR_FracX, fA14 + nop.i 0 +} +;; +{ .mfi + nop.m 0 + fadd.s1 fRes3L = fRes3L, fRes6H + nop.i 0 +} +{ .mfi + nop.m 0 + fadd.s1 fRes6L = fRes6L, fA0L // (A1*y)lo + A0lo + nop.i 0 +} +;; +{ .mfi + nop.m 0 + fadd.s1 fLnSinL = fLnSinL, fB14 + + nop.i 0 +} +{ .mfi + nop.m 0 + // delta((LnSin6*deltaX^2 + LnSin4)*deltaX^2) + fms.s1 fB20 = fLnSinH, fDxSqr, fB18 + nop.i 0 +} +;; +{ .mfi + nop.m 0 + fadd.s1 fPolL = fPolL, fRes1L // (A3*y + A2)lo + + nop.i 0 +} +{ .mfi + nop.m 0 + // ((LnSin6*deltaX^2 + LnSin4)*deltaX^2 + LnSin2)hi + fadd.s1 fLnSin6 = fB18, fLnSin2 + nop.i 0 +} +;; +{ .mfi + nop.m 0 + fadd.s1 fRes4L = fRes4L, fRes2H + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 fA17 = fA17, FR_FracX, fA16 + nop.i 0 +} +;; +{ .mfi + nop.m 0 + // delta(((((A5 + A4*y)*y^2) + A3*y + A2)*y^2) + fms.s1 fRes7L = fRes4H, fXSqr, fRes7H + nop.i 0 +} +{ .mfi + nop.m 0 + fadd.s1 fPol = fRes7H, fRes3H + nop.i 0 +} +;; +{ .mfi + nop.m 0 + fadd.s1 fRes3L = fRes3L, fRes6L // (A1*y + A0)lo + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 fA25 = fA25, fX4, fA21 + nop.i 0 +} +;; +{ .mfi + nop.m 0 + // (LnSin6*deltaX^2 + LnSin4)lo + fadd.s1 fLnSinL = fLnSinL, fB16 + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 fB20 = fLnSinH, fDxSqrL, fB20 + nop.i 0 +} +;; +{ .mfi + nop.m 0 + fsub.s1 fLnSin4 = fLnSin2, fLnSin6 + nop.i 0 +} +{ .mfi + nop.m 0 + // (((LnSin6*deltaX^2 + LnSin4)*deltaX^2 + LnSin2)*DeltaX^2)hi + fma.s1 fLnSinH = fLnSin6, fDxSqr, f0 + nop.i 0 +} +;; +{ .mfi + nop.m 0 + // ((A5 + A4*y)*y^2)lo + (A3*y + A2)lo + fadd.s1 fRes2L = fRes2L, fPolL + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 fA17 = fA17, fXSqr, fA15 + nop.i 0 +} +;; +{ .mfi + nop.m 0 + // ((((A5 + A4*y)*y^2) + A3*y + A2)*y^2)lo + fma.s1 fRes7L = fRes4H, fXSqrL, fRes7L + nop.i 0 +} +{ .mfi + nop.m 0 + fsub.s1 fPolL = fRes3H, fPol + nop.i 0 +} +;; +{ .mfi + nop.m 0 + fma.s1 fA13 = fA13, FR_FracX, fA12 + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 fA11 = fA11, FR_FracX, fA10 + nop.i 0 +} +;; +{ .mfi + nop.m 0 + // ((LnSin6*deltaX^2 + LnSin4)*deltaX^2)lo + fma.s1 fB20 = fLnSinL, fDxSqr, fB20 + nop.i 0 +} +{ .mfi + nop.m 0 + fmpy.s1 FR_G = FR_G, FR_G2 // G = G_1 * G_2 + nop.i 0 +} +;; +{ .mfi + nop.m 0 + fadd.s1 fLnSin4 = fLnSin4, fB18 + nop.i 0 +} +{ .mfi + nop.m 0 + fms.s1 fLnSinL = fLnSin6, fDxSqr, fLnSinH + nop.i 0 +} +;; +{ .mfi + nop.m 0 + // (((A5 + A4*y)*y^2) + A3*y + A2)lo + fadd.s1 fRes4L = fRes4L, fRes2L + nop.i 0 +} +{ .mfi + nop.m 0 + fadd.s1 fhDelX = fhDelX, FR_h2 // h = h_1 + h_2 + nop.i 0 +} +;; +{ .mfi + nop.m 0 + fadd.s1 fRes7L = fRes7L, fRes3L + nop.i 0 +} +{ .mfi + nop.m 0 + fadd.s1 fPolL = fPolL, fRes7H + nop.i 0 +} +;; +{ .mfi + nop.m 0 + fcvt.xf fFloatNDx = fFloatNDx + nop.i 0 +} +{ .mfi + nop.m 0 + fadd.s1 FR_H = FR_H, FR_H2 // H = H_1 + H_2 + nop.i 0 +} +;; +{ .mfi + nop.m 0 + fmpy.s1 FR_G = FR_G, FR_G3 // G = (G_1 * G_2) * G_3 + nop.i 0 +} +{ .mfi + nop.m 0 + // ((LnSin6*deltaX^2 + LnSin4)*deltaX^2)lo + (LnSin2)lo + fadd.s1 fLnSin2L = fLnSin2L, fB20 + nop.i 0 +} +;; +{ .mfi + nop.m 0 + fma.s1 fA25 = fA25, fX4, fA17 + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 fA13 = fA13, fXSqr, fA11 + nop.i 0 +} +;; +{ .mfi + nop.m 0 + fma.s1 fA9 = fA9, FR_FracX, fA8 + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 fA7 = fA7, FR_FracX, fA6 + nop.i 0 +} +;; +{ .mfi + nop.m 0 + fma.s1 fLnSin36 = fLnSin36, fDelX8, fLnSin28 + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 fLnSin14 = fLnSin14, fDxSqr, fLnSin12 + nop.i 0 +} +;; +{ .mfi + nop.m 0 + fma.s1 fLnSin10 = fLnSin10, fDxSqr, fLnSin8 + nop.i 0 +} +{ .mfi + nop.m 0 + fadd.s1 FR_H = FR_H, FR_H3 // H = (H_1 + H_2) + H_3 + nop.i 0 +} +;; +{ .mfi + nop.m 0 + fms.s1 fRDx = FR_G, fNormDx, f1 // r = G * S_hi - 1 + nop.i 0 +} +{ .mfi + nop.m 0 + // poly_lo = r * Q4 + Q3 + fma.s1 FR_poly_lo = FR_r, FR_Q4, FR_Q3 + nop.i 0 +} +;; +{ .mfi + nop.m 0 + fmpy.s1 FR_rsq = FR_r, FR_r // rsq = r * r + nop.i 0 +} +{ .mfi + nop.m 0 + // ((((A5 + A4*y)*y^2) + A3*y + A2)*y^2)lo + (A1*y + A0)lo + fma.s1 fRes7L = fRes4L, fXSqr, fRes7L + nop.i 0 +} +;; +{ .mfi + nop.m 0 + fma.s1 fA25 = fA25, fX4, fA13 + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 fA9 = fA9, fXSqr, fA7 + nop.i 0 +} +;; +{ .mfi + nop.m 0 + // h = N * log2_lo + h + fma.s1 FR_h = fFloatN, FR_log2_lo, FR_h + nop.i 0 +} +{ .mfi + nop.m 0 + fadd.s1 fhDelX = fhDelX, FR_h3 // h = (h_1 + h_2) + h_3 + nop.i 0 +} +;; +{ .mfi + nop.m 0 + fma.s1 fLnSin36 = fLnSin36, fDelX6, fLnSin20 + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 fLnSin14 = fLnSin14, fDelX4, fLnSin10 + nop.i 0 +} +;; +{ .mfi + nop.m 0 + // poly_lo = r * Q4 + Q3 + fma.s1 fPolyLoDx = fRDx, FR_Q4, FR_Q3 + nop.i 0 +} +{ .mfi + nop.m 0 + fmpy.s1 fRDxSq = fRDx, fRDx // rsq = r * r + nop.i 0 +} +;; +{ .mfi + nop.m 0 + // Y_hi = N * log2_hi + H + fma.s1 fResLnDxH = fFloatNDx, FR_log2_hi, FR_H + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 FR_rcub = FR_rsq, FR_r, f0 // rcub = r^3 + nop.i 0 +} +;; +{ .mfi + nop.m 0 + fma.s1 fA9 = fA25, fX4, fA9 + nop.i 0 +} +{ .mfi + nop.m 0 + fadd.s1 fPolL = fPolL, fRes7L + nop.i 0 +} +;; +{ .mfi + nop.m 0 + fadd.s1 fLnSin4 = fLnSin4, fLnSin2L + nop.i 0 +} +{ .mfi + nop.m 0 + // h = N * log2_lo + h + fma.s1 fhDelX = fFloatNDx, FR_log2_lo, fhDelX + nop.i 0 +} +;; +{ .mfi + nop.m 0 + fma.s1 fLnSin36 = fLnSin36, fDelX8, fLnSin14 + nop.i 0 +} +{ .mfi + nop.m 0 + // ((LnSin6*deltaX^2 + LnSin4)*deltaX^2 + LnSin2)lo + fma.s1 fLnSinL = fLnSin6, fDxSqrL, fLnSinL + nop.i 0 +} +;; +{ .mfi + nop.m 0 + // poly_lo = poly_lo * r + Q2 + fma.s1 fPolyLoDx = fPolyLoDx, fRDx, FR_Q2 + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 fRDxCub = fRDxSq, fRDx, f0 // rcub = r^3 + nop.i 0 +} +;; +{ .mfi + nop.m 0 + famax.s0 fRes5H = fPol, fResH + nop.i 0 +} +{ .mfi + nop.m 0 + // High part of (lgammal(|x|) + log(|x|)) + fadd.s1 fRes1H = fPol, fResH + nop.i 0 +} +;; +{ .mfi + nop.m 0 + // poly_lo = poly_lo * r + Q2 + fma.s1 FR_poly_lo = FR_poly_lo, FR_r, FR_Q2 + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 fPolL = fA9, fX6, fPolL // P25lo + nop.i 0 +} +;; + +{ .mfi + nop.m 0 + famin.s0 fRes5L = fPol, fResH + nop.i 0 +} +{ .mfi + nop.m 0 + // High part of -(LnSin + log(|DeltaX|)) + fnma.s1 fRes2H = fResLnDxH, f1, fLnSinH + nop.i 0 +} +;; + +{ .mfi + nop.m 0 + // (((LnSin6*deltaX^2 + LnSin4)*deltaX^2 + LnSin2)*DeltaX^2)lo + fma.s1 fLnSinL = fLnSin4, fDxSqr, fLnSinL + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 fLnSin36 = fLnSin36, fDelX6, f0 + nop.i 0 +} +;; +{ .mfi + nop.m 0 + // poly_hi = Q1 * rsq + r + fma.s1 fPolyHiDx = FR_Q1, fRDxSq, fRDx + nop.i 0 +} +{ .mfi + nop.m 0 + // poly_lo = poly_lo*r^3 + h + fma.s1 fPolyLoDx = fPolyLoDx, fRDxCub, fhDelX + nop.i 0 +} +;; +{ .mfi + nop.m 0 + fsub.s1 fRes1L = fRes5H, fRes1H + nop.i 0 +} +{ .mfi + nop.m 0 + // -(lgammal(|x|) + log(|x|))hi + fnma.s1 fRes1H = fRes1H, f1, f0 + + nop.i 0 +} +;; +{ .mfi + nop.m 0 + // poly_hi = Q1 * rsq + r + fma.s1 FR_poly_hi = FR_Q1, FR_rsq, FR_r + nop.i 0 +} +{ .mfi + nop.m 0 + // poly_lo = poly_lo*r^3 + h + fma.s1 FR_poly_lo = FR_poly_lo, FR_rcub, FR_h + nop.i 0 +} +;; +{ .mfi + nop.m 0 + fms.s1 fRes2L = fResLnDxH, fMOne, fRes2H + nop.i 0 +} +;; +{ .mfi + nop.m 0 + fma.s1 fLnSinL = fLnSin36, fDxSqr, fLnSinL + nop.i 0 +} +{ .mfi + nop.m 0 + // Y_lo = poly_hi + poly_lo + fadd.s1 fResLnDxL = fPolyHiDx, fPolyLoDx + nop.i 0 +} +;; +{ .mfi + nop.m 0 + fadd.s1 fRes1L = fRes1L, fRes5L + nop.i 0 +} +{ .mfi + nop.m 0 + // high part of the final result + fadd.s1 fYH = fRes2H, fRes1H + nop.i 0 +} +;; +{ .mfi + nop.m 0 + // Y_lo = poly_hi + poly_lo + fadd.s1 fResL = FR_poly_hi, FR_poly_lo + nop.i 0 +} +;; +{ .mfi + nop.m 0 + famax.s0 fRes4H = fRes2H, fRes1H + nop.i 0 +} +;; +{ .mfi + nop.m 0 + famin.s0 fRes4L = fRes2H, fRes1H + nop.i 0 +} +;; +{ .mfi + nop.m 0 + // (LnSin)lo + (log(|DeltaX|))lo + fsub.s1 fLnSinL = fLnSinL, fResLnDxL + nop.i 0 +} +{ .mfi + nop.m 0 + fadd.s1 fRes2L = fRes2L, fLnSinH + nop.i 0 +} +;; +{ .mfi + nop.m 0 + //(lgammal(|x|))lo + (log(|x|))lo + fadd.s1 fPolL = fResL, fPolL + nop.i 0 +} +;; +{ .mfi + nop.m 0 + fsub.s1 fYL = fRes4H, fYH + nop.i 0 +} +;; +{ .mfi + nop.m 0 + // Low part of -(LnSin + log(|DeltaX|)) + fadd.s1 fRes2L = fRes2L, fLnSinL + nop.i 0 +} +{ .mfi + nop.m 0 + // High part of (lgammal(|x|) + log(|x|)) + fadd.s1 fRes1L = fRes1L, fPolL + nop.i 0 +} +;; +{ .mfi + nop.m 0 + fadd.s1 fYL = fYL, fRes4L + nop.i 0 +} +{ .mfi + nop.m 0 + fsub.s1 fRes2L = fRes2L, fRes1L + nop.i 0 +} +;; +{ .mfi + nop.m 0 + // low part of the final result + fadd.s1 fYL = fYL, fRes2L + nop.i 0 +} +;; +{ .mfb + nop.m 0 + // final result for -6.0 < x <= -0.75, non-integer, "far" from roots + fma.s0 f8 = fYH, f1, fYL + // exit here for -6.0 < x <= -0.75, non-integer, "far" from roots + br.ret.sptk b0 +} +;; + +// here if |x+1| < 2^(-7) +.align 32 +_closeToNegOne: +{ .mfi + getf.exp GR_N = fDx // Get N = exponent of x + fmerge.se fAbsX = f1, fDx // Form |deltaX| + // Get high 4 bits of significand of deltaX + extr.u rIndex1Dx = rSignifDx, 59, 4 +} +{ .mfi + addl rPolDataPtr= @ltoff(lgammal_1pEps_data),gp + fma.s1 fA0L = fDxSqr, fDxSqr, f0 // deltaX^4 + // sign of GAMMA is positive if p10 is set to 1 +(p10) adds rSgnGam = 1, r0 +} +;; +{ .mfi + shladd GR_ad_z_1 = rIndex1Dx, 2, GR_ad_z_1 // Point to Z_1 + fnma.s1 fResL = fDx, f1, f0 // -(x+1) + // Get high 15 bits of significand + extr.u GR_X_0 = rSignifDx, 49, 15 +} +{ .mfi + ld8 rPolDataPtr = [rPolDataPtr] + nop.f 0 + shladd GR_ad_tbl_1 = rIndex1Dx, 4, rTbl1Addr // Point to G_1 +} +;; +{ .mfi + ld4 GR_Z_1 = [GR_ad_z_1] // Load Z_1 + nop.f 0 + and GR_N = GR_N, r17Ones // mask sign bit +} +{ .mfi + adds rTmpPtr = 8, GR_ad_tbl_1 + nop.f 0 + cmp.eq p6, p7 = 4, rSgnGamSize +} +;; +{ .mfi + ldfps FR_G, FR_H = [GR_ad_tbl_1],8 // Load G_1, H_1 + nop.f 0 + adds rTmpPtr2 = 96, rPolDataPtr +} +{ .mfi + ldfd FR_h = [rTmpPtr] // Load h_1 + nop.f 0 + // unbiased exponent of deltaX + sub GR_N = GR_N, rExpHalf, 1 +} +;; +{ .mfi + adds rTmpPtr3 = 192, rPolDataPtr + nop.f 0 + // sign of GAMMA is negative if p11 is set to 1 +(p11) adds rSgnGam = -1, r0 +} +{ .mfi + ldfe fA1 = [rPolDataPtr], 16 // A1 + nop.f 0 + nop.i 0 +} +;; +{.mfi + ldfe fA2 = [rPolDataPtr], 16 // A2 + nop.f 0 + // Get bits 30-15 of X_0 * Z_1 + pmpyshr2.u GR_X_1 = GR_X_0,GR_Z_1,15 +} +{ .mfi + ldfpd fA20, fA19 = [rTmpPtr2], 16 // P8, P7 + nop.f 0 + nop.i 0 +} +;; +// +// For performance, don't use result of pmpyshr2.u for 4 cycles. +// +{ .mfi + ldfe fA3 = [rPolDataPtr], 16 // A3 + nop.f 0 + nop.i 0 +} +{ .mfi + ldfpd fA18, fA17 = [rTmpPtr2], 16 // P6, P5 + nop.f 0 + nop.i 0 +} +;; +{ .mfi + ldfe fA4 = [rPolDataPtr], 16 // A4 + nop.f 0 + nop.i 0 +} +{ .mfi + ldfpd fA16, fA15 = [rTmpPtr2], 16 // P4, p3 + nop.f 0 + nop.i 0 +} +;; +{ .mfi + ldfpd fA5L, fA6 = [rPolDataPtr], 16 // A5, A6 + nop.f 0 + nop.i 0 +} +{ .mfi + ldfpd fA14, fA13 = [rTmpPtr2], 16 // P2, P1 + nop.f 0 + nop.i 0 +} +;; +{ .mfi + ldfpd fA7, fA8 = [rPolDataPtr], 16 // A7, A8 + nop.f 0 + extr.u GR_Index2 = GR_X_1, 6, 4 // Extract bits 6-9 of X_1 +} +{ .mfi + ldfe fLnSin2 = [rTmpPtr2], 16 + nop.f 0 + nop.i 0 +} +;; +{ .mfi + shladd GR_ad_z_2 = GR_Index2, 2, rZ2Addr // Point to Z_2 + nop.f 0 + shladd GR_ad_tbl_2 = GR_Index2, 4, rTbl2Addr // Point to G_2 +} +{ .mfi + ldfe fLnSin4 = [rTmpPtr2], 32 + nop.f 0 + nop.i 0 +} +;; +{ .mfi + ld4 GR_Z_2 = [GR_ad_z_2] // Load Z_2 + nop.f 0 + adds rTmpPtr = 8, GR_ad_tbl_2 +} +{ .mfi + // Put integer N into rightmost significand + setf.sig fFloatN = GR_N + nop.f 0 + nop.i 0 +} +;; +{ .mfi + ldfe fLnSin6 = [rTmpPtr3] + nop.f 0 + nop.i 0 +} +{ .mfi + ldfe fLnSin8 = [rTmpPtr2] + nop.f 0 + nop.i 0 +} +;; +{ .mfi + ldfps FR_G2, FR_H2 = [GR_ad_tbl_2],8 // Load G_2, H_2 + nop.f 0 + nop.i 0 +} +{ .mfi + ldfd FR_h2 = [rTmpPtr] // Load h_2 + nop.f 0 + nop.i 0 +} +;; +{ .mfi + // store signgam if size of variable is 4 bytes +(p6) st4 [rSgnGamAddr] = rSgnGam + fma.s1 fResH = fA20, fResL, fA19 //polynomial for log(|x|) + // Get bits 30-15 of X_1 * Z_2 + pmpyshr2.u GR_X_2 = GR_X_1,GR_Z_2,15 +} +{ .mfi + // store signgam if size of variable is 8 bytes +(p7) st8 [rSgnGamAddr] = rSgnGam + fma.s1 fA2 = fA2, fDx, fA1 // polynomial for lgammal(|x|) + nop.i 0 +} +;; +// +// For performance, don't use result of pmpyshr2.u for 4 cycles. +// +{ .mfi + nop.m 0 + fma.s1 fA18 = fA18, fResL, fA17 //polynomial for log(|x|) + nop.i 0 +} +;; +{ .mfi + nop.m 0 + fma.s1 fA16 = fA16, fResL, fA15 //polynomial for log(|x|) + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 fA4 = fA4, fDx, fA3 // polynomial for lgammal(|x|) + nop.i 0 +} +;; +{ .mfi + nop.m 0 + fma.s1 fA14 = fA14, fResL, fA13 //polynomial for log(|x|) + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 fA6 = fA6, fDx, fA5L // polynomial for lgammal(|x|) + nop.i 0 +} +;; +{ .mfi + nop.m 0 + fma.s1 fPol = fA8, fDx, fA7 // polynomial for lgammal(|x|) + extr.u GR_Index3 = GR_X_2, 1, 5 // Extract bits 1-5 of X_2 +} +;; +{ .mfi + shladd GR_ad_tbl_3 = GR_Index3, 4, rTbl3Addr // Point to G_3 + // loqw part of lnsin polynomial + fma.s1 fRes3L = fLnSin4, fDxSqr, fLnSin2 + nop.i 0 +} +;; +{ .mfi + ldfps FR_G3, FR_H3 = [GR_ad_tbl_3], 8 // Load G_3, H_3 + fcvt.xf fFloatN = fFloatN // N as FP number + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 fResH = fResH, fDxSqr, fA18 // High part of log(|x|) + nop.i 0 +} +;; +{ .mfi + ldfd FR_h3 = [GR_ad_tbl_3] // Load h_3 + fma.s1 fA4 = fA4, fDxSqr, fA2 // Low part of lgammal(|x|) + nop.i 0 +} +{ .mfi + nop.m 0 + // high part of lnsin polynomial + fma.s1 fRes3H = fLnSin8, fDxSqr, fLnSin6 + nop.i 0 +} +;; +{ .mfi + nop.m 0 + fmpy.s1 FR_G = FR_G, FR_G2 // G = G_1 * G_2 + nop.i 0 +} +{ .mfi + nop.m 0 + fadd.s1 FR_H = FR_H, FR_H2 // H = H_1 + H_2 + nop.i 0 +} +;; +{ .mfi + nop.m 0 + fadd.s1 FR_h = FR_h, FR_h2 // h = h_1 + h_2 + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 fA16 = fA16, fDxSqr, fA14 // Low part of log(|x|) + nop.i 0 +} +;; +{ .mfi + nop.m 0 + fma.s1 fPol = fPol, fDxSqr, fA6 // High part of lgammal(|x|) + nop.i 0 +} +;; +{ .mfi + nop.m 0 + fma.s1 fResH = fResH, fA0L, fA16 // log(|x|)/deltaX^2 - deltaX + nop.i 0 +} +;; +{ .mfi + nop.m 0 + fmpy.s1 FR_G = FR_G, FR_G3 // G = (G_1 * G_2) * G_3 + nop.i 0 +} +{ .mfi + nop.m 0 + fadd.s1 FR_H = FR_H, FR_H3 // H = (H_1 + H_2) + H_3 + nop.i 0 +} +;; +{ .mfi + nop.m 0 + fadd.s1 FR_h = FR_h, FR_h3 // h = (h_1 + h_2) + h_3 + nop.i 0 +} +;; +{ .mfi + nop.m 0 + fma.s1 fResH = fResH, fDxSqr, fResL // log(|x|) + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 fPol = fPol, fA0L, fA4 // lgammal(|x|)/|x| + nop.i 0 +} +;; +{ .mfi + nop.m 0 + fms.s1 FR_r = FR_G, fAbsX, f1 // r = G * S_hi - 1 + nop.i 0 +} +{ .mfi + nop.m 0 + // high part of log(deltaX)= Y_hi = N * log2_hi + H + fma.s1 fRes4H = fFloatN, FR_log2_hi, FR_H + nop.i 0 +} +;; +{ .mfi + nop.m 0 + // h = N * log2_lo + h + fma.s1 FR_h = fFloatN, FR_log2_lo, FR_h + nop.i 0 +} +;; +{ .mfi + nop.m 0 + fma.s1 fResH = fPol, fDx, fResH // lgammal(|x|) + log(|x|) + nop.i 0 +} +{ .mfi + nop.m 0 + // lnsin/deltaX^2 + fma.s1 fRes3H = fRes3H, fA0L, fRes3L + nop.i 0 +} +;; +{ .mfi + nop.m 0 + // poly_lo = r * Q4 + Q3 + fma.s1 FR_poly_lo = FR_r, FR_Q4, FR_Q3 + nop.i 0 +} +{ .mfi + nop.m 0 + fmpy.s1 FR_rsq = FR_r, FR_r // rsq = r * r + nop.i 0 +} +;; +{ .mfi + nop.m 0 + // lnSin - log(|x|) - lgammal(|x|) + fms.s1 fResH = fRes3H, fDxSqr, fResH + nop.i 0 +} +;; + +{ .mfi + nop.m 0 + // poly_lo = poly_lo * r + Q2 + fma.s1 FR_poly_lo = FR_poly_lo, FR_r, FR_Q2 + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 FR_rcub = FR_rsq, FR_r, f0 // rcub = r^3 + nop.i 0 +} +;; + +{ .mfi + nop.m 0 + // poly_hi = Q1 * rsq + r + fma.s1 FR_poly_hi = FR_Q1, FR_rsq, FR_r + nop.i 0 +} +;; + +{ .mfi + nop.m 0 + // poly_lo = poly_lo*r^3 + h + fma.s1 FR_poly_lo = FR_poly_lo, FR_rcub, FR_h + nop.i 0 +} +;; + +{ .mfi + nop.m 0 + // low part of log(|deltaX|) = Y_lo = poly_hi + poly_lo + fadd.s1 fRes4L = FR_poly_hi, FR_poly_lo + nop.i 0 +} +;; +{ .mfi + nop.m 0 + fsub.s1 fResH = fResH, fRes4L + nop.i 0 +} +;; +{ .mfb + nop.m 0 + // final result for |x+1|< 2^(-7) path + fsub.s0 f8 = fResH, fRes4H + // exit for |x+1|< 2^(-7) path + br.ret.sptk b0 +} +;; + + +// here if -2^63 < x < -6.0 and x is not an integer +// Also we are going to filter out cases when x falls in +// range which is "close enough" to negative root. Rhis case +// may occur only for -19.5 < x since other roots of lgamma are +// insignificant from double extended point of view (they are closer +// to RTN(x) than one ulp(x). +.align 32 +_negStirling: +{ .mfi + ldfe fLnSin6 = [rLnSinDataPtr], 32 + fnma.s1 fInvX = f8, fRcpX, f1 // start of 3rd NR iteration + // Get high 4 bits of significand of deltaX + extr.u rIndex1Dx = rSignifDx, 59, 4 +} +{ .mfi + ldfe fLnSin8 = [rTmpPtr3], 32 + fadd.s1 FR_h = FR_h, FR_h2 // h = h_1 + h_2 +(p12) cmp.ltu.unc p6, p0 = rSignifX, rLeftBound +} +;; +{ .mfi + ldfe fLnSin10 = [rLnSinDataPtr], 32 + fmpy.s1 FR_G = FR_G, FR_G3 // G = (G_1 * G_2) * G_3 + // Get high 15 bits of significand + extr.u GR_X_0 = rSignifDx, 49, 15 +} +{ .mfi + shladd GR_ad_z_1 = rIndex1Dx, 2, GR_ad_z_1 // Point to Z_1 + fadd.s1 FR_H = FR_H, FR_H3 // H = (H_1 + H_2) + H_3 + // set p6 if x falls in "near root" range +(p6) cmp.geu.unc p6, p0 = rSignifX, rRightBound +} +;; +{ .mfi + getf.exp GR_N = fDx // Get N = exponent of x + fma.s1 fDx4 = fDxSqr, fDxSqr, f0 // deltaX^4 + adds rTmpPtr = 96, rBernulliPtr +} +{ .mfb + ld4 GR_Z_1 = [GR_ad_z_1] // Load Z_1 + fma.s1 fLnSin34 = fLnSin34, fDxSqr, fLnSin32 + // branch to special path if x falls in "near root" range +(p6) br.cond.spnt _negRoots +} +;; +.pred.rel "mutex",p10,p11 +{ .mfi + ldfe fLnSin12 = [rTmpPtr3] + fma.s1 fLnSin26 = fLnSin26, fDxSqr, fLnSin24 +(p10) cmp.eq p8, p9 = rXRnd, r0 +} +{ .mfi + ldfe fLnSin14 = [rLnSinDataPtr] + fma.s1 fLnSin30 = fLnSin30, fDxSqr, fLnSin28 +(p11) cmp.eq p9, p8 = rXRnd, r0 +} +;; +{ .mfi + ldfpd fB2, fB2L = [rBernulliPtr], 16 + fma.s1 fLnSin18 = fLnSin18, fDxSqr, fLnSin16 + shladd GR_ad_tbl_1 = rIndex1Dx, 4, rTbl1Addr // Point to G_1 + +} +{ .mfi + ldfe fB14 = [rTmpPtr], 16 + fma.s1 fLnSin22 = fLnSin22, fDxSqr, fLnSin20 + and GR_N = GR_N, r17Ones // mask sign bit +} +;; +{ .mfi + ldfe fB4 = [rBernulliPtr], 16 + fma.s1 fInvX = fInvX, fRcpX, fRcpX // end of 3rd NR iteration + // Get bits 30-15 of X_0 * Z_1 + pmpyshr2.u GR_X_1 = GR_X_0,GR_Z_1,15 +} +{ .mfi + ldfe fB16 = [rTmpPtr], 16 + fadd.s1 FR_h = FR_h, FR_h3 // h = (h_1 + h_2) + h_3 + adds rTmpPtr2 = 8, GR_ad_tbl_1 +} +;; +// +// For performance, don't use result of pmpyshr2.u for 4 cycles. +// +{ .mfi + ldfe fB6 = [rBernulliPtr], 16 + fms.s1 FR_r = FR_G, fSignifX, f1 // r = G * S_hi - 1 + adds rTmpPtr3 = -48, rTmpPtr +} +{ .mfi + ldfe fB18 = [rTmpPtr], 16 + // High part of the log(|x|) = Y_hi = N * log2_hi + H + fma.s1 fResH = fFloatN, FR_log2_hi, FR_H + sub GR_N = GR_N, rExpHalf, 1 // unbiased exponent of deltaX +} +;; +.pred.rel "mutex",p8,p9 +{ .mfi + ldfe fB8 = [rBernulliPtr], 16 + fma.s1 fLnSin36 = fLnSin36, fDx4, fLnSin34 + // sign of GAMMA(x) is negative +(p8) adds rSgnGam = -1, r0 +} +{ .mfi + ldfe fB20 = [rTmpPtr], -160 + fma.s1 fRes5H = fLnSin4, fDxSqr, f0 + // sign of GAMMA(x) is positive +(p9) adds rSgnGam = 1, r0 + +} +;; +{ .mfi + ldfe fB10 = [rBernulliPtr], 16 + fma.s1 fLnSin30 = fLnSin30, fDx4, fLnSin26 +(p14) adds rTmpPtr = -160, rTmpPtr +} +{ .mfi + ldfe fB12 = [rTmpPtr3], 16 + fma.s1 fDx8 = fDx4, fDx4, f0 // deltaX^8 + cmp.eq p6, p7 = 4, rSgnGamSize +} +;; +{ .mfi + ldfps fGDx, fHDx = [GR_ad_tbl_1], 8 // Load G_1, H_1 + fma.s1 fDx6 = fDx4, fDxSqr, f0 // deltaX^6 + extr.u GR_Index2 = GR_X_1, 6, 4 // Extract bits 6-9 of X_1 +} +{ .mfi + ldfd fhDx = [rTmpPtr2] // Load h_1 + fma.s1 fLnSin22 = fLnSin22, fDx4, fLnSin18 + nop.i 0 +} +;; +{ .mfi + // Load two parts of C + ldfpd fRes1H, fRes1L = [rTmpPtr], 16 + fma.s1 fRcpX = fInvX, fInvX, f0 // (1/x)^2 + shladd GR_ad_tbl_2 = GR_Index2, 4, rTbl2Addr // Point to G_2 +} +{ .mfi + shladd GR_ad_z_2 = GR_Index2, 2, rZ2Addr // Point to Z_2 + fma.s1 FR_h = fFloatN, FR_log2_lo, FR_h// h = N * log2_lo + h + nop.i 0 +} +;; +{ .mfi + ld4 GR_Z_2 = [GR_ad_z_2] // Load Z_2 + fnma.s1 fInvXL = f8, fInvX, f1 // relative error of 1/x + nop.i 0 +} +{ .mfi + adds rTmpPtr2 = 8, GR_ad_tbl_2 + fma.s1 fLnSin8 = fLnSin8, fDxSqr, fLnSin6 + nop.i 0 +} +;; +{ .mfi + ldfps FR_G2, FR_H2 = [GR_ad_tbl_2],8 // Load G_2, H_2 + // poly_lo = r * Q4 + Q3 + fma.s1 FR_poly_lo = FR_r, FR_Q4, FR_Q3 + nop.i 0 +} +{ .mfi + ldfd fh2Dx = [rTmpPtr2] // Load h_2 + fmpy.s1 FR_rsq = FR_r, FR_r // rsq = r * r + nop.i 0 +} +;; +{ .mfi + nop.m 0 + fma.s1 fA1L = fB2, fInvX, f0 // (B2*(1/x))hi + nop.i 0 +} +{ .mfi + // Put integer N into rightmost significand + setf.sig fFloatNDx = GR_N + fms.s1 fRes4H = fResH, f1, f1 // ln(|x|)hi - 1 + nop.i 0 +} +;; +{ .mfi + nop.m 0 + fadd.s1 fRes2H = fRes5H, fLnSin2//(lnSin4*DeltaX^2 + lnSin2)hi + // Get bits 30-15 of X_1 * Z_2 + pmpyshr2.u GR_X_2 = GR_X_1,GR_Z_2,15 +} +{ .mfi + nop.m 0 + fms.s1 fRes5L = fLnSin4, fDxSqr, fRes5H + nop.i 0 +} +;; +// +// For performance, don't use result of pmpyshr2.u for 4 cycles. +// +{ .mfi + nop.m 0 + fma.s1 fInvX4 = fRcpX, fRcpX, f0 // (1/x)^4 + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 fB6 = fB6, fRcpX, fB4 + nop.i 0 +} +;; +{ .mfi + // store signgam if size of variable is 4 bytes +(p6) st4 [rSgnGamAddr] = rSgnGam + fma.s1 fB18 = fB18, fRcpX, fB16 + nop.i 0 +} +{ .mfi + // store signgam if size of variable is 8 bytes +(p7) st8 [rSgnGamAddr] = rSgnGam + fma.s1 fInvXL = fInvXL, fInvX, f0 // low part of 1/x + nop.i 0 +} +;; +{ .mfi + nop.m 0 + // poly_lo = poly_lo * r + Q2 + fma.s1 FR_poly_lo = FR_poly_lo, FR_r, FR_Q2 + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 FR_rcub = FR_rsq, FR_r, f0 // rcub = r^3 + nop.i 0 +} +;; +{ .mfi + nop.m 0 + fma.s1 fRes3H = fRes4H, f8, f0 // (-|x|*(ln(|x|)-1))hi + extr.u GR_Index3 = GR_X_2, 1, 5 // Extract bits 1-5 of X_2 +} +{ .mfi + nop.m 0 + // poly_hi = Q1 * rsq + r + fma.s1 FR_poly_hi = FR_Q1, FR_rsq, FR_r + nop.i 0 +} +;; +{ .mfi + shladd GR_ad_tbl_3 = GR_Index3, 4, rTbl3Addr // Point to G_3 + fms.s1 fA2L = fB2, fInvX, fA1L // delta(B2*(1/x)) + nop.i 0 +} +{ .mfi + nop.m 0 + fnma.s1 fBrnH = fRes1H, f1, fA1L // (-C - S(1/x))hi + nop.i 0 +} +;; +{ .mfi + ldfps fG3Dx, fH3Dx = [GR_ad_tbl_3],8 // Load G_3, H_3 + fma.s1 fInvX8 = fInvX4, fInvX4, f0 // (1/x)^8 + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 fB10 = fB10, fRcpX, fB8 + nop.i 0 +} +;; + +{ .mfi + ldfd fh3Dx = [GR_ad_tbl_3] // Load h_3 + fma.s1 fB20 = fB20, fInvX4, fB18 + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 fB14 = fB14, fRcpX, fB12 + nop.i 0 +} +;; +{ .mfi + nop.m 0 + fma.s1 fLnSin36 = fLnSin36, fDx8, fLnSin30 + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 fLnSin12 = fLnSin12, fDxSqr, fLnSin10 + nop.i 0 +} +;; +{ .mfi + nop.m 0 + fsub.s1 fRes2L = fLnSin2, fRes2H + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 fPol = fRes2H, fDxSqr, f0 // high part of LnSin + nop.i 0 +} +;; +{ .mfi + nop.m 0 + fnma.s1 fResH = fResH, FR_MHalf, fResH // -0.5*ln(|x|)hi + nop.i 0 +} +{ .mfi + nop.m 0 + fmpy.s1 fGDx = fGDx, FR_G2 // G = G_1 * G_2 + nop.i 0 +} +;; +{ .mfi + nop.m 0 + // poly_lo = poly_lo*r^3 + h + fma.s1 FR_poly_lo = FR_poly_lo, FR_rcub, FR_h + nop.i 0 +} +{ .mfi + nop.m 0 + // B2lo*(1/x)hi+ delta(B2*(1/x)) + fma.s1 fA2L = fB2L, fInvX, fA2L + nop.i 0 +} +;; +{ .mfi + nop.m 0 + fma.s1 fB20 = fB20, fInvX4, fB14 + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 fB10 = fB10, fInvX4, fB6 + nop.i 0 +} +;; +{ .mfi + nop.m 0 + fcvt.xf fFloatNDx = fFloatNDx + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 fLnSin14 = fLnSin14, fDx4, fLnSin12 + nop.i 0 +} +;; +{ .mfi + nop.m 0 + fma.s1 fLnSin36 = fLnSin36, fDx8, fLnSin22 + nop.i 0 +} +{ .mfi + nop.m 0 + fms.s1 fRes3L = fRes4H, f8, fRes3H // delta(-|x|*(ln(|x|)-1)) + nop.i 0 +} +;; +{ .mfi + nop.m 0 + fmpy.s1 fGDx = fGDx, fG3Dx // G = (G_1 * G_2) * G_3 + nop.i 0 +} +{ .mfi + nop.m 0 + // (-|x|*(ln(|x|)-1) - 0.5ln(|x|))hi + fadd.s1 fRes4H = fRes3H, fResH + nop.i 0 +} +;; +{ .mfi + nop.m 0 + fma.s1 fA2L = fInvXL, fB2, fA2L //(B2*(1/x))lo + nop.i 0 +} +{ .mfi + nop.m 0 + // low part of log(|x|) = Y_lo = poly_hi + poly_lo + fadd.s1 fResL = FR_poly_hi, FR_poly_lo + nop.i 0 +} +;; +{ .mfi + nop.m 0 + fma.s1 fB20 = fB20, fInvX8, fB10 + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 fInvX3 = fInvX, fRcpX, f0 // (1/x)^3 + nop.i 0 +} +;; +{ .mfi + nop.m 0 + fadd.s1 fHDx = fHDx, FR_H2 // H = H_1 + H_2 + nop.i 0 +} +{ .mfi + nop.m 0 + fadd.s1 fRes5L = fRes5L, fLnSin2L + nop.i 0 +} +;; +{ .mfi + nop.m 0 + fadd.s1 fRes2L = fRes2L, fRes5H + nop.i 0 +} +{ .mfi + nop.m 0 + fadd.s1 fhDx = fhDx, fh2Dx // h = h_1 + h_2 + nop.i 0 +} +;; +{ .mfi + nop.m 0 + fms.s1 fBrnL = fRes1H, fMOne, fBrnH + nop.i 0 +} +{ .mfi + nop.m 0 + fms.s1 FR_r = fGDx, fNormDx, f1 // r = G * S_hi - 1 + nop.i 0 +} +;; +{ .mfi + nop.m 0 + fma.s1 fRes3L = fResL, f8 , fRes3L // (-|x|*(ln(|x|)-1))lo + nop.i 0 +} +{ .mfi + nop.m 0 + fsub.s1 fRes4L = fRes3H, fRes4H + nop.i 0 +} +;; +{ .mfi + nop.m 0 + // low part of "Bernulli" polynomial + fma.s1 fB20 = fB20, fInvX3, fA2L + nop.i 0 +} +{ .mfi + nop.m 0 + fnma.s1 fResL = fResL, FR_MHalf, fResL // -0.5*ln(|x|)lo + nop.i 0 +} +;; +{ .mfi + nop.m 0 + fadd.s1 fHDx = fHDx, fH3Dx // H = (H_1 + H_2) + H_3 + nop.i 0 +} +{ .mfi + nop.m 0 + fms.s1 fPolL = fRes2H, fDxSqr, fPol + nop.i 0 +} +;; +{ .mfi + nop.m 0 + fadd.s1 fhDx = fhDx, fh3Dx // h = (h_1 + h_2) + h_3 + nop.i 0 +} +{ .mfi + nop.m 0 + // (-|x|*(ln(|x|)-1) - 0.5ln(|x|) - C - S(1/x))hi + fadd.s1 fB14 = fRes4H, fBrnH + nop.i 0 +} +;; +{ .mfi + nop.m 0 + // poly_lo = r * Q4 + Q3 + fma.s1 FR_poly_lo = FR_r, FR_Q4, FR_Q3 + nop.i 0 +} +{ .mfi + nop.m 0 + fmpy.s1 FR_rsq = FR_r, FR_r // rsq = r * r + nop.i 0 +} +;; +{ .mfi + nop.m 0 + fadd.s1 fRes4L = fRes4L, fResH + nop.i 0 +} +{ .mfi + nop.m 0 + fadd.s1 fBrnL = fBrnL, fA1L + nop.i 0 +} +;; +{ .mfi + nop.m 0 + // (-|x|*(ln(|x|)-1))lo + (-0.5ln(|x|))lo + fadd.s1 fRes3L = fRes3L, fResL + nop.i 0 +} +{ .mfi + nop.m 0 + fnma.s1 fB20 = fRes1L, f1, fB20 // -Clo - S(1/x)lo + nop.i 0 +} +;; +{ .mfi + nop.m 0 + fadd.s1 fRes2L = fRes2L, fRes5L // (lnSin4*DeltaX^2 + lnSin2)lo + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 fPolL = fDxSqrL, fRes2H, fPolL + nop.i 0 +} +;; +{ .mfi + nop.m 0 + fma.s1 fLnSin14 = fLnSin14, fDx4, fLnSin8 + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 fLnSin36 = fLnSin36, fDx8, f0 + nop.i 0 +} +;; +{ .mfi + nop.m 0 + // poly_lo = poly_lo * r + Q2 + fma.s1 FR_poly_lo = FR_poly_lo, FR_r, FR_Q2 + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 FR_rcub = FR_rsq, FR_r, f0 // rcub = r^3 + nop.i 0 +} +;; +{ .mfi + nop.m 0 + // poly_hi = Q1 * rsq + r + fma.s1 FR_poly_hi = FR_Q1, FR_rsq, FR_r + nop.i 0 +} +{ .mfi + nop.m 0 + fsub.s1 fB12 = fRes4H, fB14 + nop.i 0 +} +;; +{ .mfi + nop.m 0 + // (-|x|*(ln(|x|)-1) - 0.5ln(|x|))lo + fadd.s1 fRes4L = fRes4L, fRes3L + nop.i 0 +} +{ .mfi + nop.m 0 + fadd.s1 fBrnL = fBrnL, fB20 // (-C - S(1/x))lo + nop.i 0 +} +;; +{ .mfi + nop.m 0 + // high part of log(|DeltaX|) = Y_hi = N * log2_hi + H + fma.s1 fLnDeltaH = fFloatNDx, FR_log2_hi, fHDx + nop.i 0 +} +{ .mfi + nop.m 0 + // h = N * log2_lo + h + fma.s1 fhDx = fFloatNDx, FR_log2_lo, fhDx + nop.i 0 +} +;; +{ .mfi + nop.m 0 + fma.s1 fPolL = fRes2L, fDxSqr, fPolL + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 fLnSin14 = fLnSin36, fDxSqr, fLnSin14 + nop.i 0 +} +;; +{ .mfi + nop.m 0 + // (-|x|*(ln(|x|)-1) - 0.5ln(|x|))lo + (- C - S(1/x))lo + fadd.s1 fBrnL = fBrnL, fRes4L + nop.i 0 +} +{ .mfi + nop.m 0 + fadd.s1 fB12 = fB12, fBrnH + nop.i 0 +} +;; +{ .mfi + nop.m 0 + // poly_lo = poly_lo*r^3 + h + fma.s1 FR_poly_lo = FR_poly_lo, FR_rcub, fhDx + nop.i 0 +} +{ .mfi + nop.m 0 + fnma.s1 fRes1H = fLnDeltaH, f1, fPol//(-ln(|DeltaX|) + LnSin)hi + nop.i 0 +} +;; +{ .mfi + nop.m 0 + fma.s1 fPolL = fDxSqrL, fRes2L, fPolL + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 fLnSin36 = fLnSin14, fDx6, f0 + nop.i 0 +} +;; +{ .mfi + nop.m 0 + // (-|x|*(ln(|x|)-1) - 0.5ln(|x|) - C - S(1/x))lo + fadd.s1 fB12 = fB12, fBrnL + nop.i 0 +} +;; +{ .mfi + nop.m 0 + // low part of log(|DeltaX|) = Y_lo = poly_hi + poly_lo + fadd.s1 fLnDeltaL= FR_poly_hi, FR_poly_lo + nop.i 0 +} +{ .mfi + nop.m 0 + fms.s1 fRes1L = fLnDeltaH, fMOne, fRes1H + nop.i 0 +} +;; +{ .mfi + nop.m 0 + fadd.s1 fPolL = fPolL, fLnSin36 + nop.i 0 +} +{ .mfi + nop.m 0 + //(-|x|*(ln(|x|)-1)-0.5ln(|x|) - C - S(1/x))hi + (-ln(|DeltaX|) + LnSin)hi + fadd.s1 f8 = fRes1H, fB14 + nop.i 0 +} +;; +{ .mfi + nop.m 0 + //max((-|x|*(ln(|x|)-1)-0.5ln(|x|) - C - S(1/x))hi, + // (-ln(|DeltaX|) + LnSin)hi) + famax.s1 fMaxNegStir = fRes1H, fB14 + nop.i 0 +} +{ .mfi + nop.m 0 + //min((-|x|*(ln(|x|)-1)-0.5ln(|x|) - C - S(1/x))hi, + // (-ln(|DeltaX|) + LnSin)hi) + famin.s1 fMinNegStir = fRes1H, fB14 + nop.i 0 +} +;; +{ .mfi + nop.m 0 + fadd.s1 fRes1L = fRes1L, fPol + nop.i 0 +} +{ .mfi + nop.m 0 + // (-ln(|DeltaX|))lo + (LnSin)lo + fnma.s1 fPolL = fLnDeltaL, f1, fPolL + nop.i 0 +} +;; +{ .mfi + nop.m 0 + fsub.s1 f9 = fMaxNegStir, f8 // delta1 + nop.i 0 +} +;; +{ .mfi + nop.m 0 + fadd.s1 fRes1L = fRes1L, fPolL // (-ln(|DeltaX|) + LnSin)lo + nop.i 0 +} +;; +{ .mfi + nop.m 0 + fadd.s1 f9 = f9, fMinNegStir + nop.i 0 +} +;; +{ .mfi + nop.m 0 + fadd.s1 fRes1L = fRes1L, fB12 + nop.i 0 +} +;; +{ .mfi + // low part of the result + fadd.s1 f9 = f9, fRes1L + nop.i 0 +} +;; +{ .mfb + nop.m 0 + // final result for -2^63 < x < -6.0 path + fma.s0 f8 = f8, f1, f9 + // exit here for -2^63 < x < -6.0 path + br.ret.sptk b0 +} +;; + +// here if x falls in neighbourhood of any negative root +// "neighbourhood" typically means that |lgammal(x)| < 0.17 +// on the [-3.0,-2.0] range |lgammal(x)| has even less +// magnitude +// rXint contains index of the root +// p10 is set if root belongs to "right" ones +// p11 is set if root belongs to "left" ones +// lgammal(x) is approximated by polynomial of +// 19th degree from (x - root) argument +.align 32 +_negRoots: +{ .mfi + addl rPolDataPtr= @ltoff(lgammal_right_roots_polynomial_data),gp + nop.f 0 + shl rTmpPtr2 = rXint, 7 // (i*16)*8 +} +{ .mfi + adds rRootsAddr = -288, rRootsBndAddr + nop.f 0 + nop.i 0 +} +;; +{ .mfi + ldfe fRoot = [rRootsAddr] // FP representation of root + nop.f 0 + shl rTmpPtr = rXint, 6 // (i*16)*4 +} +{ .mfi +(p11) adds rTmpPtr2 = 3536, rTmpPtr2 + nop.f 0 + nop.i 0 +} +;; +{ .mfi + ld8 rPolDataPtr = [rPolDataPtr] + nop.f 0 + shladd rTmpPtr = rXint, 4, rTmpPtr // (i*16) + (i*16)*4 +} +{ .mfi + adds rTmpPtr3 = 32, rTmpPtr2 + nop.f 0 + nop.i 0 +} +;; +.pred.rel "mutex",p10,p11 +{ .mfi + add rTmpPtr3 = rTmpPtr, rTmpPtr3 + nop.f 0 +(p10) cmp.eq p8, p9 = rXRnd, r0 +} +{ .mfi + // (i*16) + (i*16)*4 + (i*16)*8 + add rTmpPtr = rTmpPtr, rTmpPtr2 + nop.f 0 +(p11) cmp.eq p9, p8 = rXRnd, r0 +} +;; +{ .mfi + add rTmpPtr2 = rPolDataPtr, rTmpPtr3 + nop.f 0 + nop.i 0 +} +{ .mfi + add rPolDataPtr = rPolDataPtr, rTmpPtr // begin + offsett + nop.f 0 + nop.i 0 +} +;; +{ .mfi + ldfpd fA0, fA0L = [rPolDataPtr], 16 // A0 + nop.f 0 + adds rTmpPtr = 112, rTmpPtr2 +} +{ .mfi + ldfpd fA2, fA2L = [rTmpPtr2], 16 // A2 + nop.f 0 + cmp.eq p12, p13 = 4, rSgnGamSize +} +;; +{ .mfi + ldfpd fA1, fA1L = [rPolDataPtr], 16 // A1 + nop.f 0 + nop.i 0 +} +{ .mfi + ldfe fA3 = [rTmpPtr2], 128 // A4 + nop.f 0 + nop.i 0 +} +;; +{ .mfi + ldfpd fA12, fA13 = [rTmpPtr], 16 // A12, A13 + nop.f 0 + adds rTmpPtr3 = 64, rPolDataPtr +} +{ .mfi + ldfpd fA16, fA17 = [rTmpPtr2], 16 // A16, A17 + nop.f 0 + adds rPolDataPtr = 32, rPolDataPtr +} +;; +.pred.rel "mutex",p8,p9 +{ .mfi + ldfpd fA14, fA15 = [rTmpPtr], 16 // A14, A15 + nop.f 0 + // sign of GAMMA(x) is negative +(p8) adds rSgnGam = -1, r0 +} +{ .mfi + ldfpd fA18, fA19 = [rTmpPtr2], 16 // A18, A19 + nop.f 0 + // sign of GAMMA(x) is positive +(p9) adds rSgnGam = 1, r0 +} +;; +{ .mfi + ldfe fA4 = [rPolDataPtr], 16 // A4 + nop.f 0 + nop.i 0 +} +{ .mfi + ldfpd fA6, fA7 = [rTmpPtr3], 16 // A6, A7 + nop.f 0 + nop.i 0 +} +;; +{ .mfi + ldfe fA5 = [rPolDataPtr], 16 // A5 + // if x equals to (rounded) root exactly + fcmp.eq.s1 p6, p0 = f8, fRoot + nop.i 0 +} +{ .mfi + ldfpd fA8, fA9 = [rTmpPtr3], 16 // A8, A9 + fms.s1 FR_FracX = f8, f1, fRoot + nop.i 0 +} +;; +{ .mfi + // store signgam if size of variable is 4 bytes +(p12) st4 [rSgnGamAddr] = rSgnGam + nop.f 0 + nop.i 0 +} +{ .mfb + // store signgam if size of variable is 8 bytes +(p13) st8 [rSgnGamAddr] = rSgnGam + // answer if x equals to (rounded) root exactly +(p6) fadd.s0 f8 = fA0, fA0L + // exit if x equals to (rounded) root exactly +(p6) br.ret.spnt b0 +} +;; +{ .mmf + ldfpd fA10, fA11 = [rTmpPtr3], 16 // A10, A11 + nop.m 0 + nop.f 0 +} +;; +{ .mfi + nop.m 0 + fma.s1 fResH = fA2, FR_FracX, f0 // (A2*x)hi + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 fA4L = FR_FracX, FR_FracX, f0 // x^2 + nop.i 0 +} +;; +{ .mfi + nop.m 0 + fma.s1 fA17 = fA17, FR_FracX, fA16 + nop.i 0 +} +{.mfi + nop.m 0 + fma.s1 fA13 = fA13, FR_FracX, fA12 + nop.i 0 +} +;; +{ .mfi + nop.m 0 + fma.s1 fA19 = fA19, FR_FracX, fA18 + nop.i 0 +} +{.mfi + nop.m 0 + fma.s1 fA15 = fA15, FR_FracX, fA14 + nop.i 0 +} +;; +{.mfi + nop.m 0 + fma.s1 fPol = fA7, FR_FracX, fA6 + nop.i 0 +} +;; +{.mfi + nop.m 0 + fma.s1 fA9 = fA9, FR_FracX, fA8 + nop.i 0 +} +;; +{ .mfi + nop.m 0 + fms.s1 fResL = fA2, FR_FracX, fResH // delta(A2*x) + nop.i 0 +} +{.mfi + nop.m 0 + fadd.s1 fRes1H = fResH, fA1 // (A2*x + A1)hi + nop.i 0 +} +;; +{ .mfi + nop.m 0 + fma.s1 fA11 = fA11, FR_FracX, fA10 + nop.i 0 +} +{.mfi + nop.m 0 + fma.s1 fA5L = fA4L, fA4L, f0 // x^4 + nop.i 0 +} +;; +{ .mfi + nop.m 0 + fma.s1 fA19 = fA19, fA4L, fA17 + nop.i 0 +} +{.mfi + nop.m 0 + fma.s1 fA15 = fA15, fA4L, fA13 + nop.i 0 +} +;; +{ .mfi + nop.m 0 + fma.s1 fPol = fPol, FR_FracX, fA5 + nop.i 0 +} +{.mfi + nop.m 0 + fma.s1 fA3L = fA4L, FR_FracX, f0 // x^3 + nop.i 0 +} +;; +{ .mfi + nop.m 0 + // delta(A2*x) + A2L*x = (A2*x)lo + fma.s1 fResL = fA2L, FR_FracX, fResL + nop.i 0 +} +{.mfi + nop.m 0 + fsub.s1 fRes1L = fA1, fRes1H + nop.i 0 +} +;; +{ .mfi + nop.m 0 + fma.s1 fA11 = fA11, fA4L, fA9 + nop.i 0 +} +{.mfi + nop.m 0 + fma.s1 fA19 = fA19, fA5L, fA15 + nop.i 0 +} +;; +{.mfi + nop.m 0 + fma.s1 fPol = fPol, FR_FracX, fA4 + nop.i 0 +} +;; +{ .mfi + nop.m 0 + fadd.s1 fResL = fResL, fA1L // (A2*x)lo + A1 + nop.i 0 +} +{.mfi + nop.m 0 + fadd.s1 fRes1L = fRes1L, fResH + nop.i 0 +} +;; +{ .mfi + nop.m 0 + fma.s1 fRes2H = fRes1H, FR_FracX, f0 // ((A2*x + A1)*x)hi + nop.i 0 +} +;; +{.mfi + nop.m 0 + fma.s1 fA19 = fA19, fA5L, fA11 + nop.i 0 +} +;; +{.mfi + nop.m 0 + fma.s1 fPol = fPol, FR_FracX, fA3 + nop.i 0 +} +;; +{ .mfi + nop.m 0 + fadd.s1 fRes1L = fRes1L, fResL // (A2*x + A1)lo + nop.i 0 +} +;; +{ .mfi + nop.m 0 + // delta((A2*x + A1)*x) + fms.s1 fRes2L = fRes1H, FR_FracX, fRes2H + nop.i 0 +} +{.mfi + nop.m 0 + fadd.s1 fRes3H = fRes2H, fA0 // ((A2*x + A1)*x + A0)hi + nop.i 0 +} +;; +{ .mfi + nop.m 0 + fma.s1 fA19 = fA19, fA5L, f0 + nop.i 0 +} + +;; +{ .mfi + nop.m 0 + fma.s1 fRes2L = fRes1L, FR_FracX, fRes2L // ((A2*x + A1)*x)lo + nop.i 0 +} +{.mfi + nop.m 0 + fsub.s1 fRes3L = fRes2H, fRes3H + nop.i 0 +} +;; +{.mfi + nop.m 0 + fma.s1 fPol = fA19, FR_FracX, fPol + nop.i 0 +} +;; +{ .mfi + nop.m 0 + fadd.s1 fRes3L = fRes3L, fA0 + nop.i 0 +} +{.mfi + nop.m 0 + fadd.s1 fRes2L = fRes2L, fA0L // ((A2*x + A1)*x)lo + A0L + nop.i 0 +} +;; +{ .mfi + nop.m 0 + fadd.s1 fRes3L = fRes3L, fRes2L // (((A2*x + A1)*x) + A0)lo + nop.i 0 +} +;; +{.mfi + nop.m 0 + fma.s1 fRes3L = fPol, fA3L, fRes3L + nop.i 0 +} +;; +{ .mfb + nop.m 0 + // final result for arguments which are close to negative roots + fma.s0 f8 = fRes3H, f1, fRes3L + // exit here for arguments which are close to negative roots + br.ret.sptk b0 +} +;; + +// here if |x| < 0.5 +.align 32 +lgammal_0_half: +{ .mfi + ld4 GR_Z_1 = [rZ1offsett] // Load Z_1 + fma.s1 fA4L = f8, f8, f0 // x^2 + addl rPolDataPtr = @ltoff(lgammal_0_Half_data), gp +} +{ .mfi + shladd GR_ad_tbl_1 = GR_Index1, 4, rTbl1Addr// Point to G_1 + nop.f 0 + addl rLnSinDataPtr = @ltoff(lgammal_lnsin_data), gp +} +;; +{ .mfi + ldfps FR_G, FR_H = [GR_ad_tbl_1],8 // Load G_1, H_1 + nop.f 0 + // Point to Constants_Z_2 + add GR_ad_z_2 = 0x140, GR_ad_z_1 +} +{ .mfi + add GR_ad_q = -0x60, GR_ad_z_1 // Point to Constants_Q + nop.f 0 + // Point to Constants_G_H_h2 + add GR_ad_tbl_2 = 0x180, GR_ad_z_1 +} +;; +{ .mfi + ld8 rPolDataPtr = [rPolDataPtr] + nop.f 0 + // Point to Constants_G_H_h3 + add GR_ad_tbl_3 = 0x280, GR_ad_z_1 +} +{ .mfi + ldfd FR_h = [GR_ad_tbl_1] // Load h_1 + nop.f 0 + sub GR_N = rExpX, rExpHalf, 1 +} +;; +{ .mfi + ld8 rLnSinDataPtr = [rLnSinDataPtr] + nop.f 0 + // Get bits 30-15 of X_0 * Z_1 + pmpyshr2.u GR_X_1 = GR_X_0,GR_Z_1,15 +} +{ .mfi + ldfe FR_log2_hi = [GR_ad_q],16 // Load log2_hi + nop.f 0 + sub GR_N = r0, GR_N +} +;; +// +// For performance, don't use result of pmpyshr2.u for 4 cycles. +// +{ .mfi + ldfe FR_log2_lo = [GR_ad_q], 16 // Load log2_lo + nop.f 0 + add rTmpPtr2 = 320, rPolDataPtr +} +{ .mfi + add rTmpPtr = 32, rPolDataPtr + nop.f 0 + // exponent of 0.25 + adds rExp2 = -1, rExpHalf +} +;; +{ .mfi + ldfpd fA3, fA3L = [rPolDataPtr], 16 // A3 + fma.s1 fA5L = fA4L, fA4L, f0 // x^4 + nop.i 0 +} +{ .mfi + ldfpd fA1, fA1L = [rTmpPtr], 16 // A1 + fms.s1 fB8 = f8, f8, fA4L // x^2 - <x^2> + // set p6 if -0.5 < x <= -0.25 +(p15) cmp.eq.unc p6, p0 = rExpX, rExp2 +} +;; +{ .mfi + ldfpd fA2, fA2L = [rPolDataPtr], 16 // A2 + nop.f 0 + // set p6 if -0.5 < x <= -0.40625 +(p6) cmp.le.unc p6, p0 = 10, GR_Index1 +} +{ .mfi + ldfe fA21 = [rTmpPtr2], -16 // A21 + // Put integer N into rightmost significand + nop.f 0 + adds rTmpPtr = 240, rTmpPtr +} +;; +{ .mfi + setf.sig fFloatN = GR_N + nop.f 0 + extr.u GR_Index2 = GR_X_1, 6, 4 // Extract bits 6-9 of X_1 +} +{ .mfi + ldfe FR_Q4 = [GR_ad_q], 16 // Load Q4 + nop.f 0 + adds rPolDataPtr = 304, rPolDataPtr +} +;; +{ .mfi + ldfe fA20 = [rTmpPtr2], -32 // A20 + nop.f 0 + shladd GR_ad_z_2 = GR_Index2, 2, GR_ad_z_2 // Point to Z_2 +} +{ .mfi + ldfe fA19 = [rTmpPtr], -32 // A19 + nop.f 0 + shladd GR_ad_tbl_2 = GR_Index2, 4, GR_ad_tbl_2// Point to G_2 +} +;; +{ .mfi + ldfe fA17 = [rTmpPtr], -32 // A17 + nop.f 0 + adds rTmpPtr3 = 8, GR_ad_tbl_2 +} +{ .mfb + ldfe fA18 = [rTmpPtr2], -32 // A18 + nop.f 0 + // branch to special path for -0.5 < x <= 0.40625 +(p6) br.cond.spnt lgammal_near_neg_half +} +;; +{ .mmf + ld4 GR_Z_2 = [GR_ad_z_2] // Load Z_2 + ldfe fA15 = [rTmpPtr], -32 // A15 + fma.s1 fB20 = fA5L, fA5L, f0 // x^8 +} +;; +{ .mmf + ldfe fA16 = [rTmpPtr2], -32 // A16 + ldfe fA13 = [rTmpPtr], -32 // A13 + fms.s1 fB16 = fA4L, fA4L, fA5L +} +;; +{ .mmf + ldfps FR_G2, FR_H2 = [GR_ad_tbl_2], 8 // Load G_2, H_2 + ldfd FR_h2 = [rTmpPtr3] // Load h_2 + fmerge.s fB10 = f8, fA5L // sign(x) * x^4 +} +;; +{ .mmi + ldfe fA14 = [rTmpPtr2], -32 // A14 + ldfe fA11 = [rTmpPtr], -32 // A11 + // Get bits 30-15 of X_1 * Z_2 + pmpyshr2.u GR_X_2 = GR_X_1,GR_Z_2,15 +} +;; +// +// For performance, don't use result of pmpyshr2.u for 4 cycles. +// +{ .mfi + ldfe fA12 = [rTmpPtr2], -32 // A12 + fma.s1 fRes4H = fA3, fAbsX, f0 + adds rTmpPtr3 = 16, GR_ad_q +} +{ .mfi + ldfe fA9 = [rTmpPtr], -32 // A9 + nop.f 0 + nop.i 0 +} +;; +{ .mmf + ldfe fA10 = [rTmpPtr2], -32 // A10 + ldfe fA7 = [rTmpPtr], -32 // A7 + fma.s1 fB18 = fB20, fB20, f0 // x^16 +} +;; +{ .mmf + ldfe fA8 = [rTmpPtr2], -32 // A8 + ldfe fA22 = [rPolDataPtr], 16 // A22 + fcvt.xf fFloatN = fFloatN +} +;; +{ .mfi + ldfe fA5 = [rTmpPtr], -32 // A5 + fma.s1 fA21 = fA21, fAbsX, fA20 // v16 + extr.u GR_Index3 = GR_X_2, 1, 5 // Extract bits 1-5 of X_2 +} +{ .mfi + ldfe fA6 = [rTmpPtr2], -32 // A6 + nop.f 0 + nop.i 0 +} +;; +{ .mmf + // Point to G_3 + shladd GR_ad_tbl_3 = GR_Index3, 4, GR_ad_tbl_3 + ldfe fA4 = [rTmpPtr2], -32 // A4 + fma.s1 fA19 = fA19, fAbsX, fA18 // v13 +} +;; +.pred.rel "mutex",p14,p15 +{ .mfi + ldfps FR_G3, FR_H3 = [GR_ad_tbl_3],8 // Load G_3, H_3 + fms.s1 fRes4L = fA3, fAbsX, fRes4H +(p14) adds rSgnGam = 1, r0 +} +{ .mfi + cmp.eq p6, p7 = 4, rSgnGamSize + fadd.s1 fRes2H = fRes4H, fA2 +(p15) adds rSgnGam = -1, r0 +} +;; + +{ .mfi + ldfd FR_h3 = [GR_ad_tbl_3] // Load h_3 + fma.s1 fA17 = fA17, fAbsX, fA16 // v12 + nop.i 0 +} +;; +{ .mfi + ldfe FR_Q3 = [GR_ad_q], 32 // Load Q3 + fmpy.s1 FR_G = FR_G, FR_G2 // G = G_1 * G_2 + nop.i 0 +} +{ .mfi + ldfe FR_Q2 = [rTmpPtr3], 16 // Load Q2 + fadd.s1 FR_H = FR_H, FR_H2 // H = H_1 + H_2 + nop.i 0 +} +;; +{ .mfi + ldfe FR_Q1 = [GR_ad_q] // Load Q1 + fma.s1 fA15 = fA15, fAbsX, fA14 // v8 + nop.i 0 +} +{ .mfi + adds rTmpPtr3 = 32, rLnSinDataPtr + fadd.s1 FR_h = FR_h, FR_h2 // h = h_1 + h_2 + nop.i 0 +} +;; +{ .mmf + ldfpd fLnSin2, fLnSin2L = [rLnSinDataPtr], 16 + ldfe fLnSin6 = [rTmpPtr3], 32 + fma.s1 fA13 = fA13, fAbsX, fA12 // v7 + +} +;; +{ .mfi + ldfe fLnSin4 = [rLnSinDataPtr], 32 + fma.s1 fRes4L = fA3L, fAbsX, fRes4L + nop.i 0 +} +{ .mfi + ldfe fLnSin10 = [rTmpPtr3], 32 + fsub.s1 fRes2L = fA2, fRes2H + nop.i 0 +} +;; +{ .mfi + ldfe fLnSin8 = [rLnSinDataPtr], 32 + fma.s1 fResH = fRes2H, fAbsX, f0 + nop.i 0 +} +{ .mfi + ldfe fLnSin14 = [rTmpPtr3], 32 + fma.s1 fA22 = fA22, fA4L, fA21 // v15 + nop.i 0 +} +;; +{ .mfi + ldfe fLnSin12 = [rLnSinDataPtr], 32 + fma.s1 fA9 = fA9, fAbsX, fA8 // v4 + nop.i 0 +} +{ .mfi + ldfd fLnSin18 = [rTmpPtr3], 16 + fma.s1 fA11 = fA11, fAbsX, fA10 // v5 + nop.i 0 +} +;; +{ .mfi + ldfe fLnSin16 = [rLnSinDataPtr], 24 + fma.s1 fA19 = fA19, fA4L, fA17 // v11 + nop.i 0 +} +{ .mfi + ldfd fLnSin22 = [rTmpPtr3], 16 + fma.s1 fPolL = fA7, fAbsX, fA6 + nop.i 0 +} +;; +{ .mfi + ldfd fLnSin20 = [rLnSinDataPtr], 16 + fmpy.s1 FR_G = FR_G, FR_G3 // G = (G_1 * G_2) * G_3 + nop.i 0 +} +{ .mfi + ldfd fLnSin26 = [rTmpPtr3], 16 + fadd.s1 FR_H = FR_H, FR_H3 // H = (H_1 + H_2) + H_3 + nop.i 0 +} +;; +{ .mfi + ldfd fLnSin24 = [rLnSinDataPtr], 16 + fadd.s1 fRes2L = fRes2L, fRes4H + nop.i 0 +} +{ .mfi + ldfd fLnSin30 = [rTmpPtr3], 16 + fadd.s1 fA2L = fA2L, fRes4L + nop.i 0 +} +;; +{ .mfi + ldfd fLnSin28 = [rLnSinDataPtr], 16 + fms.s1 fResL = fRes2H, fAbsX, fResH + nop.i 0 +} +{ .mfi + ldfd fLnSin34 = [rTmpPtr3], 8 + fadd.s1 fRes2H = fResH, fA1 + nop.i 0 +} +;; +{ .mfi + ldfd fLnSin32 = [rLnSinDataPtr] + fma.s1 fA11 = fA11, fA4L, fA9 // v3 + nop.i 0 +} +{ .mfi + ldfd fLnSin36 = [rTmpPtr3] + fma.s1 fA15 = fA15, fA4L, fA13 // v6 + nop.i 0 +} +;; + +{ .mfi + // store signgam if size of variable is 4 bytes +(p6) st4 [rSgnGamAddr] = rSgnGam + fadd.s1 FR_h = FR_h, FR_h3 // h = (h_1 + h_2) + h_3 + nop.i 0 +} +{ .mfi + // store signgam if size of variable is 8 bytes +(p7) st8 [rSgnGamAddr] = rSgnGam + fma.s1 fA5 = fA5, fAbsX, fA4 + nop.i 0 +} +;; +{ .mfi + nop.m 0 + fms.s1 FR_r = FR_G, fSignifX, f1 // r = G * S_hi - 1 + nop.i 0 +} +{ .mfi + nop.m 0 + // High part of the log(|x|): Y_hi = N * log2_hi + H + fms.s1 FR_log2_hi = fFloatN, FR_log2_hi, FR_H + nop.i 0 +} +;; +{ .mfi + nop.m 0 + fadd.s1 fA3L = fRes2L, fA2L + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 fA22 = fA22, fA5L, fA19 + nop.i 0 +} +;; +{ .mfi + nop.m 0 + fsub.s1 fRes2L = fA1, fRes2H + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 fRes3H = fRes2H, f8, f0 + nop.i 0 +} +;; +{ .mfi + nop.m 0 + fma.s1 fA15 = fA15, fA5L, fA11 // v2 + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 fLnSin18 = fLnSin18, fA4L, fLnSin16 + nop.i 0 +} +;; +{ .mfi + nop.m 0 + // h = N * log2_lo + h + fms.s1 FR_h = fFloatN, FR_log2_lo, FR_h + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 fPolL = fPolL, fA4L, fA5 + nop.i 0 +} +;; +{ .mfi + nop.m 0 + // poly_lo = r * Q4 + Q3 + fma.s1 FR_poly_lo = FR_r, FR_Q4, FR_Q3 + nop.i 0 +} +{ .mfi + nop.m 0 + fmpy.s1 FR_rsq = FR_r, FR_r // rsq = r * r + nop.i 0 +} +;; +{ .mfi + nop.m 0 + fma.s1 fResL = fA3L, fAbsX, fResL + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 fLnSin30 = fLnSin30, fA4L, fLnSin28 + nop.i 0 +} +;; +{ .mfi + nop.m 0 + fadd.s1 fRes2L = fRes2L, fResH + nop.i 0 +} +{ .mfi + nop.m 0 + fms.s1 fRes3L = fRes2H, f8, fRes3H + nop.i 0 +} +;; +{ .mfi + nop.m 0 + fadd.s1 fRes1H = fRes3H, FR_log2_hi + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 fPol = fB20, fA22, fA15 + nop.i 0 +} +;; +{ .mfi + nop.m 0 + fma.s1 fLnSin34 = fLnSin34, fA4L, fLnSin32 + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 fLnSin14 = fLnSin14, fA4L, fLnSin12 + nop.i 0 +} +;; + +{ .mfi + nop.m 0 + // poly_lo = poly_lo * r + Q2 + fma.s1 FR_poly_lo = FR_poly_lo, FR_r, FR_Q2 + nop.i 0 +} +{ .mfi + nop.m 0 + fnma.s1 FR_rcub = FR_rsq, FR_r, f0 // rcub = r^3 + nop.i 0 +} +;; +{ .mfi + nop.m 0 + // poly_hi = Q1 * rsq + r + fma.s1 FR_poly_hi = FR_Q1, FR_rsq, FR_r + nop.i 0 +} +{ .mfi + nop.m 0 + fadd.s1 fA1L = fA1L, fResL + nop.i 0 +} +;; + +{ .mfi + nop.m 0 + fma.s1 fLnSin22 = fLnSin22, fA4L, fLnSin20 + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 fLnSin26 = fLnSin26, fA4L, fLnSin24 + nop.i 0 +} +;; + +{ .mfi + nop.m 0 + fsub.s1 fRes1L = FR_log2_hi, fRes1H + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 fPol = fPol, fA5L, fPolL + nop.i 0 +} +;; +{ .mfi + nop.m 0 + fma.s1 fLnSin34 = fLnSin36, fA5L, fLnSin34 + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 fLnSin18 = fLnSin18, fA5L, fLnSin14 + nop.i 0 +} +;; +{ .mfi + nop.m 0 + fma.s1 fLnSin6 = fLnSin6, fA4L, fLnSin4 + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 fLnSin10 = fLnSin10, fA4L, fLnSin8 + nop.i 0 +} +;; +{ .mfi + nop.m 0 + // poly_hi = Q1 * rsq + r + fma.s1 FR_poly_hi = FR_Q1, FR_rsq, FR_r + nop.i 0 +} +{ .mfi + nop.m 0 + fadd.s1 fRes2L = fRes2L, fA1L + nop.i 0 +} +;; +{ .mfi + nop.m 0 + // poly_lo = poly_lo*r^3 + h + fma.s1 FR_poly_lo = FR_poly_lo, FR_rcub, FR_h + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 fB2 = fLnSin2, fA4L, f0 + nop.i 0 +} +;; +{ .mfi + nop.m 0 + fadd.s1 fRes1L = fRes1L, fRes3H + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 fPol = fPol, fB10, f0 + nop.i 0 +} +;; +{ .mfi + nop.m 0 + fma.s1 fLnSin26 = fLnSin26, fA5L, fLnSin22 + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 fLnSin34 = fLnSin34, fA5L, fLnSin30 + nop.i 0 +} +;; +{ .mfi + nop.m 0 + fma.s1 fLnSin10 = fLnSin10, fA5L, fLnSin6 + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 fLnSin2L = fLnSin2L, fA4L, f0 + nop.i 0 +} +;; + +{ .mfi + nop.m 0 + fma.s1 fRes3L = fRes2L, f8, fRes3L + nop.i 0 +} +;; +{ .mfi + nop.m 0 + // Y_lo = poly_hi + poly_lo + fsub.s1 FR_log2_lo = FR_poly_lo, FR_poly_hi + nop.i 0 +} +{ .mfi + nop.m 0 + fms.s1 fB4 = fLnSin2, fA4L, fB2 + nop.i 0 +} +;; +{ .mfi + nop.m 0 + fadd.s1 fRes2H = fRes1H, fPol + nop.i 0 +} +;; +{ .mfi + nop.m 0 + fma.s1 fLnSin34 = fLnSin34, fB20, fLnSin26 + nop.i 0 +} +;; +{ .mfi + nop.m 0 + fma.s1 fLnSin18 = fLnSin18, fB20, fLnSin10 + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 fLnSin2L = fB8, fLnSin2, fLnSin2L + nop.i 0 +} +;; + +{ .mfi + nop.m 0 + fadd.s1 FR_log2_lo = FR_log2_lo, fRes3L + nop.i 0 +} +;; +{ .mfi + nop.m 0 + fsub.s1 fRes2L = fRes1H, fRes2H + nop.i 0 +} +;; +{ .mfi + nop.m 0 + fma.s1 fB6 = fLnSin34, fB18, fLnSin18 + nop.i 0 +} +{ .mfi + nop.m 0 + fadd.s1 fB4 = fLnSin2L, fB4 + nop.i 0 +} +;; + +{ .mfi + nop.m 0 + fadd.s1 fRes1L = fRes1L, FR_log2_lo + nop.i 0 +} +;; +{ .mfi + nop.m 0 + fadd.s1 fRes2L = fRes2L, fPol + nop.i 0 +} +;; +{ .mfi + nop.m 0 + fma.s1 fB12 = fB6, fA5L, f0 + nop.i 0 +} +;; +{ .mfi + nop.m 0 + fadd.s1 fRes2L = fRes2L, fRes1L + nop.i 0 +} +;; + +{ .mfi + nop.m 0 + fms.s1 fB14 = fB6, fA5L, fB12 + nop.i 0 +} +{ .mfb + nop.m 0 + fadd.s1 fLnSin30 = fB2, fB12 + // branch out if x is negative +(p15) br.cond.spnt _O_Half_neg +} +;; +{ .mfb + nop.m 0 + // sign(x)*Pol(|x|) - log(|x|) + fma.s0 f8 = fRes2H, f1, fRes2L + // it's an answer already for positive x + // exit if 0 < x < 0.5 + br.ret.sptk b0 +} +;; + +// here if x is negative and |x| < 0.5 +.align 32 +_O_Half_neg: +{ .mfi + nop.m 0 + fma.s1 fB14 = fB16, fB6, fB14 + nop.i 0 +} +{ .mfi + nop.m 0 + fsub.s1 fLnSin16 = fB2, fLnSin30 + nop.i 0 +} +;; +{ .mfi + nop.m 0 + fadd.s1 fResH = fLnSin30, fRes2H + nop.i 0 +} +;; +{ .mfi + nop.m 0 + fadd.s1 fLnSin16 = fLnSin16, fB12 + nop.i 0 +} +{ .mfi + nop.m 0 + fadd.s1 fB4 = fB14, fB4 + nop.i 0 +} +;; +{ .mfi + nop.m 0 + fadd.s1 fLnSin16 = fB4, fLnSin16 + nop.i 0 +} +{ .mfi + nop.m 0 + fsub.s1 fResL = fRes2H, fResH + nop.i 0 +} +;; +{ .mfi + nop.m 0 + fadd.s1 fResL = fResL, fLnSin30 + nop.i 0 +} +{ .mfi + nop.m 0 + fadd.s1 fLnSin16 = fLnSin16, fRes2L + nop.i 0 +} +;; +{ .mfi + nop.m 0 + fadd.s1 fResL = fResL, fLnSin16 + nop.i 0 +} +;; +{ .mfb + nop.m 0 + // final result for -0.5 < x < 0 + fma.s0 f8 = fResH, f1, fResL + // exit for -0.5 < x < 0 + br.ret.sptk b0 +} +;; + +// here if x >= 8.0 +// there are two computational paths: +// 1) For x >10.0 Stirling's formula is used +// 2) Polynomial approximation for 8.0 <= x <= 10.0 +.align 32 +lgammal_big_positive: +{ .mfi + addl rPolDataPtr = @ltoff(lgammal_data), gp + fmerge.se fSignifX = f1, f8 + // Get high 15 bits of significand + extr.u GR_X_0 = rSignifX, 49, 15 +} +{.mfi + shladd rZ1offsett = GR_Index1, 2, GR_ad_z_1 // Point to Z_1 + fnma.s1 fInvX = f8, fRcpX, f1 // start of 1st NR iteration + adds rSignif1andQ = 0x5, r0 +} +;; +{.mfi + ld4 GR_Z_1 = [rZ1offsett] // Load Z_1 + nop.f 0 + shl rSignif1andQ = rSignif1andQ, 61 // significand of 1.25 +} +{ .mfi + cmp.eq p8, p0 = rExpX, rExp8 // p8 = 1 if 8.0 <= x < 16 + nop.f 0 + adds rSgnGam = 1, r0 // gamma is positive at this range +} +;; +{ .mfi + shladd GR_ad_tbl_1 = GR_Index1, 4, rTbl1Addr// Point to G_1 + nop.f 0 + add GR_ad_q = -0x60, GR_ad_z_1 // Point to Constants_Q +} +{ .mlx + ld8 rPolDataPtr = [rPolDataPtr] + movl rDelta = 0x3FF2000000000000 +} +;; +{ .mfi + ldfps FR_G, FR_H = [GR_ad_tbl_1],8 // Load G_1, H_1 + nop.f 0 + add GR_ad_z_2 = 0x140, GR_ad_z_1 // Point to Constants_Z_2 +} +{ .mfi + // Point to Constants_G_H_h2 + add GR_ad_tbl_2 = 0x180, GR_ad_z_1 + nop.f 0 + // p8 = 1 if 8.0 <= x <= 10.0 +(p8) cmp.leu.unc p8, p0 = rSignifX, rSignif1andQ +} +;; +{ .mfi + ldfd FR_h = [GR_ad_tbl_1] // Load h_1 + nop.f 0 + // Get bits 30-15 of X_0 * Z_1 + pmpyshr2.u GR_X_1 = GR_X_0,GR_Z_1,15 +} +{ .mfb +(p8) setf.d FR_MHalf = rDelta + nop.f 0 +(p8) br.cond.spnt lgammal_8_10 // branch out if 8.0 <= x <= 10.0 +} +;; +// +// For performance, don't use result of pmpyshr2.u for 4 cycles. +// +{ .mfi + ldfe fA1 = [rPolDataPtr], 16 // Load overflow threshold + fma.s1 fRcpX = fInvX, fRcpX, fRcpX // end of 1st NR iteration + // Point to Constants_G_H_h3 + add GR_ad_tbl_3 = 0x280, GR_ad_z_1 +} +{ .mlx + nop.m 0 + movl rDelta = 0xBFE0000000000000 // -0.5 in DP +} +;; +{ .mfi + ldfe FR_log2_hi = [GR_ad_q],16 // Load log2_hi + nop.f 0 + sub GR_N = rExpX, rExpHalf, 1 // unbiased exponent of x +} +;; +{ .mfi + ldfe FR_log2_lo = [GR_ad_q],16 // Load log2_lo + nop.f 0 + nop.i 0 +} +{ .mfi + setf.d FR_MHalf = rDelta + nop.f 0 + nop.i 0 +} +;; +{ .mfi + // Put integer N into rightmost significand + setf.sig fFloatN = GR_N + nop.f 0 + extr.u GR_Index2 = GR_X_1, 6, 4 // Extract bits 6-9 of X_1 +} +{ .mfi + ldfe FR_Q4 = [GR_ad_q], 16 // Load Q4 + nop.f 0 + nop.i 0 +} +;; +{ .mfi + shladd GR_ad_z_2 = GR_Index2, 2, GR_ad_z_2 // Point to Z_2 + nop.f 0 + shladd GR_ad_tbl_2 = GR_Index2, 4, GR_ad_tbl_2// Point to G_2 +} +{ .mfi + ldfe FR_Q3 = [GR_ad_q], 16 // Load Q3 + nop.f 0 + nop.i 0 +} +;; +{ .mfi + ld4 GR_Z_2 = [GR_ad_z_2] // Load Z_2 + fnma.s1 fInvX = f8, fRcpX, f1 // start of 2nd NR iteration + nop.i 0 +} +;; +{ .mfi + ldfps FR_G2, FR_H2 = [GR_ad_tbl_2], 8 // Load G_2, H_2 + nop.f 0 + nop.i 0 +} +;; +{ .mfi + ldfd FR_h2 = [GR_ad_tbl_2] // Load h_2 + nop.f 0 + nop.i 0 +} +;; +{ .mfi + ldfe FR_Q2 = [GR_ad_q],16 // Load Q2 + nop.f 0 + // Get bits 30-15 of X_1 * Z_2 + pmpyshr2.u GR_X_2 = GR_X_1,GR_Z_2,15 +} +;; +// +// For performance, don't use result of pmpyshr2.u for 4 cycles. +// +{ .mfi + ldfe FR_Q1 = [GR_ad_q] // Load Q1 + fcmp.gt.s1 p7,p0 = f8, fA1 // check if x > overflow threshold + nop.i 0 +} +;; +{.mfi + ldfpd fA0, fA0L = [rPolDataPtr], 16 // Load two parts of C + fma.s1 fRcpX = fInvX, fRcpX, fRcpX // end of 2nd NR iteration + nop.i 0 +} +;; +{ .mfb + ldfpd fB2, fA1 = [rPolDataPtr], 16 + nop.f 0 +(p7) br.cond.spnt lgammal_overflow // branch if x > overflow threshold +} +;; +{.mfi + ldfe fB4 = [rPolDataPtr], 16 + fcvt.xf fFloatN = fFloatN + extr.u GR_Index3 = GR_X_2, 1, 5 // Extract bits 1-5 of X_2 +} +;; +{ .mfi + shladd GR_ad_tbl_3 = GR_Index3, 4, GR_ad_tbl_3// Point to G_3 + nop.f 0 + nop.i 0 +} +{ .mfi + ldfe fB6 = [rPolDataPtr], 16 + nop.f 0 + nop.i 0 +} +;; +{ .mfi + ldfps FR_G3, FR_H3 = [GR_ad_tbl_3], 8 // Load G_3, H_3 + nop.f 0 + nop.i 0 +} +;; +{ .mfi + ldfd FR_h3 = [GR_ad_tbl_3] // Load h_3 + fmpy.s1 FR_G = FR_G, FR_G2 // G = G_1 * G_2 + nop.i 0 +} +{ .mfi + nop.m 0 + fadd.s1 FR_H = FR_H, FR_H2 // H = H_1 + H_2 + nop.i 0 +} +;; + +{ .mfi + ldfe fB8 = [rPolDataPtr], 16 + fadd.s1 FR_h = FR_h, FR_h2 // h = h_1 + h_2 + nop.i 0 +} +{ .mfi + nop.m 0 + fnma.s1 fInvX = f8, fRcpX, f1 // start of 3rd NR iteration + nop.i 0 +} +;; +{ .mfi + ldfe fB10 = [rPolDataPtr], 16 + nop.f 0 + cmp.eq p6, p7 = 4, rSgnGamSize +} +;; +{ .mfi + ldfe fB12 = [rPolDataPtr], 16 + nop.f 0 + nop.i 0 +} +;; +{ .mfi + ldfe fB14 = [rPolDataPtr], 16 + nop.f 0 + nop.i 0 +} +;; + +{ .mfi + ldfe fB16 = [rPolDataPtr], 16 + // get double extended coefficients from two doubles + // two doubles are needed in Stitling's formula for negative x + fadd.s1 fB2 = fB2, fA1 + nop.i 0 +} +;; +{ .mfi + ldfe fB18 = [rPolDataPtr], 16 + fma.s1 fInvX = fInvX, fRcpX, fRcpX // end of 3rd NR iteration + nop.i 0 +} +;; +{ .mfi + ldfe fB20 = [rPolDataPtr], 16 + nop.f 0 + nop.i 0 +} +;; +{ .mfi + // store signgam if size of variable is 4 bytes +(p6) st4 [rSgnGamAddr] = rSgnGam + fmpy.s1 FR_G = FR_G, FR_G3 // G = (G_1 * G_2) * G_3 + nop.i 0 +} +{ .mfi + // store signgam if size of variable is 8 bytes +(p7) st8 [rSgnGamAddr] = rSgnGam + fadd.s1 FR_H = FR_H, FR_H3 // H = (H_1 + H_2) + H_3 + nop.i 0 +} +;; +{ .mfi + nop.m 0 + fadd.s1 FR_h = FR_h, FR_h3 // h = (h_1 + h_2) + h_3 + nop.i 0 +} +;; +{ .mfi + nop.m 0 + fma.s1 fRcpX = fInvX, fInvX, f0 // 1/x^2 + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 fA0L = fB2, fInvX, fA0L + nop.i 0 +} +;; +{ .mfi + nop.m 0 + fms.s1 FR_r = fSignifX, FR_G, f1 // r = G * S_hi - 1 + nop.i 0 +} +{ .mfi + nop.m 0 + // High part of the log(x): Y_hi = N * log2_hi + H + fma.s1 fRes2H = fFloatN, FR_log2_hi, FR_H + nop.i 0 +} +;; + +{ .mfi + nop.m 0 + // h = N * log2_lo + h + fma.s1 FR_h = fFloatN, FR_log2_lo, FR_h + nop.i 0 +} +{ .mfi + nop.m 0 + // High part of the log(x): Y_hi = N * log2_hi + H + fma.s1 fRes1H = fFloatN, FR_log2_hi, FR_H + nop.i 0 +} +;; +{.mfi + nop.m 0 + fma.s1 fPol = fB18, fRcpX, fB16 // v9 + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 fA2L = fRcpX, fRcpX, f0 // v10 + nop.i 0 +} +;; +{.mfi + nop.m 0 + fma.s1 fA3 = fB6, fRcpX, fB4 // v3 + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 fA4 = fB10, fRcpX, fB8 // v4 + nop.i 0 +} +;; +{ .mfi + nop.m 0 + fms.s1 fRes2H =fRes2H, f1, f1 // log_Hi(x) -1 + nop.i 0 +} +{ .mfi + nop.m 0 + // poly_lo = r * Q4 + Q3 + fma.s1 FR_poly_lo = FR_r, FR_Q4, FR_Q3 + nop.i 0 +} +;; +{ .mfi + nop.m 0 + fma.s1 fRes1H = fRes1H, FR_MHalf, f0 // -0.5*log_Hi(x) + nop.i 0 +} +{ .mfi + nop.m 0 + fmpy.s1 FR_rsq = FR_r, FR_r // rsq = r * r + nop.i 0 +} +;; +{ .mfi + nop.m 0 + fma.s1 fA7 = fB14, fRcpX, fB12 // v7 + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 fA8 = fA2L, fB20, fPol // v8 + nop.i 0 +} +;; +{ .mfi + nop.m 0 + fma.s1 fA2 = fA4, fA2L, fA3 // v2 + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 fA4L = fA2L, fA2L, f0 // v5 + nop.i 0 +} +;; +{ .mfi + nop.m 0 + fma.s1 fResH = fRes2H, f8, f0 // (x*(ln(x)-1))hi + nop.i 0 +} +{ .mfi + nop.m 0 + // poly_lo = poly_lo * r + Q2 + fma.s1 FR_poly_lo = FR_poly_lo, FR_r, FR_Q2 + nop.i 0 +} +;; +{ .mfi + nop.m 0 + fma.s1 FR_rcub = FR_rsq, FR_r, f0 // rcub = r^3 + nop.i 0 +} +{ .mfi + nop.m 0 + // poly_hi = Q1 * rsq + r + fma.s1 FR_poly_hi = FR_Q1, FR_rsq, FR_r + nop.i 0 +} +;; +{ .mfi + nop.m 0 + fma.s1 fA11 = fRcpX, fInvX, f0 // 1/x^3 + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 fA6 = fA8, fA2L, fA7 // v6 + nop.i 0 +} +;; +{ .mfi + nop.m 0 + fms.s1 fResL = fRes2H, f8, fResH // d(x*(ln(x)-1)) + nop.i 0 +} +{ .mfi + nop.m 0 + fadd.s1 fRes3H = fResH, fRes1H // (x*(ln(x)-1) -0.5ln(x))hi + nop.i 0 +} +;; +{ .mfi + nop.m 0 + // poly_lo = poly_lo*r^3 + h + fma.s1 FR_poly_lo = FR_poly_lo, FR_rcub, FR_h + nop.i 0 +} +;; +{ .mfi + nop.m 0 + fma.s1 fPol = fA4L, fA6, fA2 // v1 + nop.i 0 +} +{ .mfi + nop.m 0 + // raise inexact exception + fma.s0 FR_log2_lo = FR_log2_lo, FR_log2_lo, f0 + nop.i 0 +} +;; +{ .mfi + nop.m 0 + fadd.s1 fRes4H = fRes3H, fA0 // (x*(ln(x)-1) -0.5ln(x))hi + Chi + nop.i 0 +} +{ .mfi + nop.m 0 + fsub.s1 fRes3L = fResH, fRes3H + nop.i 0 +} +;; +{ .mfi + nop.m 0 + // Y_lo = poly_hi + poly_lo + fadd.s1 fRes2L = FR_poly_hi, FR_poly_lo + nop.i 0 +} +;; + +{ .mfi + nop.m 0 + fma.s1 fA0L = fPol, fA11, fA0L // S(1/x) + Clo + nop.i 0 +} +;; +{ .mfi + nop.m 0 + fadd.s1 fRes3L = fRes3L, fRes1H + nop.i 0 +} +{ .mfi + nop.m 0 + fsub.s1 fRes4L = fRes3H, fRes4H + nop.i 0 +} +;; +{ .mfi + nop.m 0 + fma.s1 fResL = fRes2L, f8 , fResL // lo part of x*(ln(x)-1) + nop.i 0 +} +;; +{ .mfi + nop.m 0 + // Clo + S(1/x) - 0.5*logLo(x) + fma.s1 fA0L = fRes2L, FR_MHalf, fA0L + nop.i 0 +} +;; +{ .mfi + nop.m 0 + fadd.s1 fRes4L = fRes4L, fA0 + nop.i 0 +} +;; +{ .mfi + nop.m 0 + // Clo + S(1/x) - 0.5*logLo(x) + (x*(ln(x)-1))lo + fadd.s1 fA0L = fA0L, fResL + nop.i 0 +} +;; +{ .mfi + nop.m 0 + fadd.s1 fRes4L = fRes4L, fRes3L + nop.i 0 +} +;; +{ .mfi + nop.m 0 + fadd.s1 fRes4L = fRes4L, fA0L + nop.i 0 +} +;; +{ .mfb + nop.m 0 + fma.s0 f8 = fRes4H, f1, fRes4L + // exit for x > 10.0 + br.ret.sptk b0 +} +;; +// here if 8.0 <= x <= 10.0 +// Result = P15(y), where y = x/8.0 - 1.5 +.align 32 +lgammal_8_10: +{ .mfi + addl rPolDataPtr = @ltoff(lgammal_8_10_data), gp + fms.s1 FR_FracX = fSignifX, f1, FR_MHalf // y = x/8.0 - 1.5 + cmp.eq p6, p7 = 4, rSgnGamSize +} +;; +{ .mfi + ld8 rLnSinDataPtr = [rPolDataPtr] + nop.f 0 + nop.i 0 +} +{ .mfi + ld8 rPolDataPtr = [rPolDataPtr] + nop.f 0 + nop.i 0 +} +;; +{ .mfi + adds rZ1offsett = 32, rLnSinDataPtr + nop.f 0 + nop.i 0 +} +{ .mfi + adds rLnSinDataPtr = 48, rLnSinDataPtr + nop.f 0 + nop.i 0 +} +;; +{ .mfi + ldfpd fA1, fA1L = [rPolDataPtr], 16 // A1 + nop.f 0 + nop.i 0 +} +{ .mfi + ldfe fA2 = [rZ1offsett], 32 // A5 + nop.f 0 + nop.i 0 +} +;; +{ .mfi + ldfpd fA0, fA0L = [rPolDataPtr], 16 // A0 + fma.s1 FR_rsq = FR_FracX, FR_FracX, f0 // y^2 + nop.i 0 +} +{ .mfi + ldfe fA3 = [rLnSinDataPtr],32 // A5 + nop.f 0 + nop.i 0 +} +;; +{ .mmf + ldfe fA4 = [rZ1offsett], 32 // A4 + ldfe fA5 = [rLnSinDataPtr], 32 // A5 + nop.f 0 +} +;; +{ .mmf + ldfe fA6 = [rZ1offsett], 32 // A6 + ldfe fA7 = [rLnSinDataPtr], 32 // A7 + nop.f 0 +} +;; +{ .mmf + ldfe fA8 = [rZ1offsett], 32 // A8 + ldfe fA9 = [rLnSinDataPtr], 32 // A9 + nop.f 0 +} +;; +{ .mmf + ldfe fA10 = [rZ1offsett], 32 // A10 + ldfe fA11 = [rLnSinDataPtr], 32 // A11 + nop.f 0 +} +;; +{ .mmf + ldfe fA12 = [rZ1offsett], 32 // A12 + ldfe fA13 = [rLnSinDataPtr], 32 // A13 + fma.s1 FR_Q4 = FR_rsq, FR_rsq, f0 // y^4 +} +;; +{ .mmf + ldfe fA14 = [rZ1offsett], 32 // A14 + ldfe fA15 = [rLnSinDataPtr], 32 // A15 + nop.f 0 +} +;; +{ .mfi + nop.m 0 + fma.s1 fRes1H = FR_FracX, fA1, f0 + nop.i 0 +} +;; +{ .mfi + nop.m 0 + fma.s1 fA3 = fA3, FR_FracX, fA2 // v4 + nop.i 0 +} +;; +{ .mfi + nop.m 0 + fma.s1 fA5 = fA5, FR_FracX, fA4 // v5 + nop.i 0 +} +;; +{ .mfi + // store sign of GAMMA(x) if size of variable is 4 bytes +(p6) st4 [rSgnGamAddr] = rSgnGam + fma.s1 fA3L = FR_Q4, FR_Q4, f0 // v9 = y^8 + nop.i 0 +} +{ .mfi + // store sign of GAMMA(x) if size of variable is 8 bytes +(p7) st8 [rSgnGamAddr] = rSgnGam + fma.s1 fA7 = fA7, FR_FracX, fA6 // v7 + nop.i 0 +} +;; +{ .mfi + nop.m 0 + fma.s1 fA9 = fA9, FR_FracX, fA8 // v8 + nop.i 0 +} +;; +{ .mfi + nop.m 0 + fms.s1 fRes1L = FR_FracX, fA1, fRes1H + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 fA11 = fA11, FR_FracX, fA10 // v12 + nop.i 0 +} +;; +{ .mfi + nop.m 0 + fma.s1 fA13 = fA13, FR_FracX, fA12 // v13 + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 fRes2H = fRes1H, f1, fA0 + nop.i 0 +} +;; +{ .mfi + nop.m 0 + fma.s1 fA15 = fA15, FR_FracX, fA14 // v16 + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 fA5 = fA5, FR_rsq, fA3 // v3 + nop.i 0 +} +;; +{ .mfi + nop.m 0 + fma.s1 fA9 = fA9, FR_rsq, fA7 // v6 + nop.i 0 +} +;; +{ .mfi + nop.m 0 + fma.s1 fRes1L = FR_FracX, fA1L, fRes1L + nop.i 0 +} +;; +{ .mfi + nop.m 0 + fms.s1 fRes2L = fA0, f1, fRes2H + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 fA13 = fA13, FR_rsq, fA11 // v11 + nop.i 0 +} +;; +{ .mfi + nop.m 0 + fma.s1 fA9 = fA9, FR_Q4, fA5 // v2 + nop.i 0 +} +;; +{ .mfi + nop.m 0 + fma.s1 fRes1L = fRes1L, f1, fA0L + nop.i 0 +} +;; +{ .mfi + nop.m 0 + fma.s1 fRes2L = fRes2L, f1, fRes1H + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 fA15 = fA15, FR_Q4, fA13 // v10 + nop.i 0 +} +;; +{ .mfi + nop.m 0 + fma.s1 fRes2L = fRes1L, f1, fRes2L + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 fPol = fA3L, fA15, fA9 + nop.i 0 +} +;; +{ .mfi + nop.m 0 + fma.s1 f8 = FR_rsq , fPol, fRes2H + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 fPol = fPol, FR_rsq, f0 + nop.i 0 +} +;; +{ .mfi + nop.m 0 + fms.s1 fRes1L = fRes2H, f1, f8 + nop.i 0 +} +;; +{ .mfi + nop.m 0 + fma.s1 fRes1L = fRes1L, f1, fPol + nop.i 0 +} +;; +{.mfi + nop.m 0 + fma.s1 fRes1L = fRes1L, f1, fRes2L + nop.i 0 +} +;; +{ .mfb + nop.m 0 + fma.s0 f8 = f8, f1, fRes1L + // exit for 8.0 <= x <= 10.0 + br.ret.sptk b0 +} +;; + +// here if 4.0 <=x < 8.0 +.align 32 +lgammal_4_8: +{ .mfi + addl rPolDataPtr= @ltoff(lgammal_4_8_data),gp + fms.s1 FR_FracX = fSignifX, f1, FR_MHalf + adds rSgnGam = 1, r0 +} +;; +{ .mfi + ld8 rPolDataPtr = [rPolDataPtr] + nop.f 0 + nop.i 0 +} +;; + +{ .mfb + adds rTmpPtr = 160, rPolDataPtr + nop.f 0 + // branch to special path which computes polynomial of 25th degree + br.sptk lgamma_polynom25 +} +;; + +// here if 2.25 <=x < 4.0 +.align 32 +lgammal_2Q_4: +{ .mfi + addl rPolDataPtr= @ltoff(lgammal_2Q_4_data),gp + fms.s1 FR_FracX = fSignifX, f1, FR_MHalf + adds rSgnGam = 1, r0 +} +;; +{ .mfi + ld8 rPolDataPtr = [rPolDataPtr] + nop.f 0 + nop.i 0 +} +;; + +{ .mfb + adds rTmpPtr = 160, rPolDataPtr + nop.f 0 + // branch to special path which computes polynomial of 25th degree + br.sptk lgamma_polynom25 +} +;; + +// here if 0.5 <= |x| < 0.75 +.align 32 +lgammal_half_3Q: +.pred.rel "mutex", p14, p15 +{ .mfi +(p14) addl rPolDataPtr= @ltoff(lgammal_half_3Q_data),gp + // FR_FracX = x - 0.625 for positive x +(p14) fms.s1 FR_FracX = f8, f1, FR_FracX +(p14) adds rSgnGam = 1, r0 +} +{ .mfi +(p15) addl rPolDataPtr= @ltoff(lgammal_half_3Q_neg_data),gp + // FR_FracX = x + 0.625 for negative x +(p15) fma.s1 FR_FracX = f8, f1, FR_FracX +(p15) adds rSgnGam = -1, r0 +} +;; +{ .mfi + ld8 rPolDataPtr = [rPolDataPtr] + nop.f 0 + nop.i 0 +} +;; +{ .mfb + adds rTmpPtr = 160, rPolDataPtr + nop.f 0 + // branch to special path which computes polynomial of 25th degree + br.sptk lgamma_polynom25 +} +;; +// here if 1.3125 <= x < 1.5625 +.align 32 +lgammal_loc_min: +{ .mfi + adds rSgnGam = 1, r0 + nop.f 0 + nop.i 0 +} +{ .mfb + adds rTmpPtr = 160, rPolDataPtr + fms.s1 FR_FracX = f8, f1, fA5L + br.sptk lgamma_polynom25 +} +;; +// here if -2.605859375 <= x < -2.5 +// special polynomial approximation used since neither "near root" +// approximation nor reflection formula give satisfactory accuracy on +// this range +.align 32 +_neg2andHalf: +{ .mfi + addl rPolDataPtr= @ltoff(lgammal_neg2andHalf_data),gp + fma.s1 FR_FracX = fB20, f1, f8 // 2.5 + x + adds rSgnGam = -1, r0 +} +;; +{.mfi + ld8 rPolDataPtr = [rPolDataPtr] + nop.f 0 + nop.i 0 +} +;; +{ .mfb + adds rTmpPtr = 160, rPolDataPtr + nop.f 0 + // branch to special path which computes polynomial of 25th degree + br.sptk lgamma_polynom25 +} +;; + +// here if -0.5 < x <= -0.40625 +.align 32 +lgammal_near_neg_half: +{ .mmf + addl rPolDataPtr= @ltoff(lgammal_near_neg_half_data),gp + setf.exp FR_FracX = rExpHalf + nop.f 0 +} +;; +{ .mfi + ld8 rPolDataPtr = [rPolDataPtr] + nop.f 0 + adds rSgnGam = -1, r0 +} +;; +{ .mfb + adds rTmpPtr = 160, rPolDataPtr + fma.s1 FR_FracX = FR_FracX, f1, f8 + // branch to special path which computes polynomial of 25th degree + br.sptk lgamma_polynom25 +} +;; + +// here if there an answer is P25(x) +// rPolDataPtr, rTmpPtr point to coefficients +// x is in FR_FracX register +.align 32 +lgamma_polynom25: +{ .mfi + ldfpd fA3, fA0L = [rPolDataPtr], 16 // A3 + nop.f 0 + cmp.eq p6, p7 = 4, rSgnGamSize +} +{ .mfi + ldfpd fA18, fA19 = [rTmpPtr], 16 // D7, D6 + nop.f 0 + nop.i 0 +} +;; +{ .mfi + ldfpd fA1, fA1L = [rPolDataPtr], 16 // A1 + nop.f 0 + nop.i 0 +} +{ .mfi + ldfpd fA16, fA17 = [rTmpPtr], 16 // D4, D5 + nop.f 0 +} +;; +{ .mfi + ldfpd fA12, fA13 = [rPolDataPtr], 16 // D0, D1 + nop.f 0 + nop.i 0 +} +{ .mfi + ldfpd fA14, fA15 = [rTmpPtr], 16 // D2, D3 + nop.f 0 + nop.i 0 +} +;; +{ .mfi + ldfpd fA24, fA25 = [rPolDataPtr], 16 // C21, C20 + nop.f 0 + nop.i 0 +} +{ .mfi + ldfpd fA22, fA23 = [rTmpPtr], 16 // C19, C18 + nop.f 0 + nop.i 0 +} +;; +{ .mfi + ldfpd fA2, fA2L = [rPolDataPtr], 16 // A2 + fma.s1 fA4L = FR_FracX, FR_FracX, f0 // x^2 + nop.i 0 +} +{ .mfi + ldfpd fA20, fA21 = [rTmpPtr], 16 // C17, C16 + nop.f 0 + nop.i 0 +} +;; +{ .mfi + ldfe fA11 = [rTmpPtr], 16 // E7 + nop.f 0 + nop.i 0 +} +{ .mfi + ldfpd fA0, fA3L = [rPolDataPtr], 16 // A0 + nop.f 0 + nop.i 0 +};; +{ .mfi + ldfe fA10 = [rPolDataPtr], 16 // E6 + nop.f 0 + nop.i 0 +} +{ .mfi + ldfe fA9 = [rTmpPtr], 16 // E5 + nop.f 0 + nop.i 0 +} +;; +{ .mmf + ldfe fA8 = [rPolDataPtr], 16 // E4 + ldfe fA7 = [rTmpPtr], 16 // E3 + nop.f 0 +} +;; +{ .mmf + ldfe fA6 = [rPolDataPtr], 16 // E2 + ldfe fA5 = [rTmpPtr], 16 // E1 + nop.f 0 +} +;; +{ .mfi + ldfe fA4 = [rPolDataPtr], 16 // E0 + fma.s1 fA5L = fA4L, fA4L, f0 // x^4 + nop.i 0 +} +{ .mfi + nop.m 0 + fms.s1 fB2 = FR_FracX, FR_FracX, fA4L // x^2 - <x^2> + nop.i 0 +} +;; +{ .mfi + // store signgam if size of variable is 4 bytes +(p6) st4 [rSgnGamAddr] = rSgnGam + fma.s1 fRes4H = fA3, FR_FracX, f0 // (A3*x)hi + nop.i 0 +} +{ .mfi + // store signgam if size of variable is 8 bytes +(p7) st8 [rSgnGamAddr] = rSgnGam + fma.s1 fA19 = fA19, FR_FracX, fA18 // D7*x + D6 + nop.i 0 +} +;; +{ .mfi + nop.m 0 + fma.s1 fResH = fA1, FR_FracX, f0 // (A1*x)hi + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 fB6 = fA1L, FR_FracX, fA0L // A1L*x + A0L + nop.i 0 +} +;; +{ .mfi + nop.m 0 + fma.s1 fA17 = fA17, FR_FracX, fA16 // D5*x + D4 + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 fA15 = fA15, FR_FracX, fA14 // D3*x + D2 + nop.i 0 +} +;; +{ .mfi + nop.m 0 + fma.s1 fA25 = fA25, FR_FracX, fA24 // C21*x + C20 + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 fA13 = fA13, FR_FracX, fA12 // D1*x + D0 + nop.i 0 +} +;; +{ .mfi + nop.m 0 + fma.s1 fA23 = fA23, FR_FracX, fA22 // C19*x + C18 + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 fA21 = fA21, FR_FracX, fA20 // C17*x + C16 + nop.i 0 +} +;; +{ .mfi + nop.m 0 + fms.s1 fRes4L = fA3, FR_FracX, fRes4H // delta((A3*x)hi) + nop.i 0 +} +{ .mfi + nop.m 0 + fadd.s1 fRes2H = fRes4H, fA2 // (A3*x + A2)hi + nop.i 0 +} +;; +{ .mfi + nop.m 0 + fms.s1 fResL = fA1, FR_FracX, fResH // d(A1*x) + nop.i 0 +} +{ .mfi + nop.m 0 + fadd.s1 fRes1H = fResH, fA0 // (A1*x + A0)hi + nop.i 0 +} +;; +{ .mfi + nop.m 0 + fma.s1 fA19 = fA19, fA4L, fA17 // Dhi + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 fA11 = fA11, FR_FracX, fA10 // E7*x + E6 + nop.i 0 +} +;; +{ .mfi + nop.m 0 + // Doing this to raise inexact flag + fma.s0 fA10 = fA0, fA0, f0 + nop.i 0 +} +;; +{ .mfi + nop.m 0 + fma.s1 fA15 = fA15, fA4L, fA13 // Dlo + nop.i 0 +} +{ .mfi + nop.m 0 + // (C21*x + C20)*x^2 + C19*x + C18 + fma.s1 fA25 = fA25, fA4L, fA23 + nop.i 0 +} +;; +{ .mfi + nop.m 0 + fma.s1 fA9 = fA9, FR_FracX, fA8 // E5*x + E4 + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 fA7 = fA7, FR_FracX, fA6 // E3*x + E2 + nop.i 0 +} +;; +{ .mfi + nop.m 0 + fma.s1 fRes4L = fA3L, FR_FracX, fRes4L // (A3*x)lo + nop.i 0 +} +{ .mfi + nop.m 0 + fsub.s1 fRes2L = fA2, fRes2H + nop.i 0 +} +;; +{ .mfi + nop.m 0 + fadd.s1 fResL = fResL, fB6 // (A1L*x + A0L) + d(A1*x) + nop.i 0 +} +{ .mfi + nop.m 0 + fsub.s1 fRes1L = fA0, fRes1H + nop.i 0 +} +;; +{ .mfi + nop.m 0 + fma.s1 fA5 = fA5, FR_FracX, fA4 // E1*x + E0 + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 fB8 = fA5L, fA5L, f0 // x^8 + nop.i 0 +} +;; +{ .mfi + nop.m 0 + // ((C21*x + C20)*x^2 + C19*x + C18)*x^2 + C17*x + C16 + fma.s1 fA25 = fA25, fA4L, fA21 + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 fA19 = fA19, fA5L, fA15 // D + nop.i 0 +} +;; +{ .mfi + nop.m 0 + fma.s1 fA11 = fA11, fA4L, fA9 // Ehi + nop.i 0 +} +;; +{ .mfi + nop.m 0 + fadd.s1 fRes2L = fRes2L, fRes4H + nop.i 0 +} +{ .mfi + nop.m 0 + fadd.s1 fRes4L = fRes4L, fA2L // (A3*x)lo + A2L + nop.i 0 +} +;; +{ .mfi + nop.m 0 + fma.s1 fRes3H = fRes2H, fA4L, f0 // ((A3*x + A2)*x^2)hi + nop.i 0 +} +{ .mfi + nop.m 0 + fadd.s1 fRes1L = fRes1L, fResH + nop.i 0 +} +;; +{ .mfi + nop.m 0 + fma.s1 fRes3L = fRes2H, fB2, f0 // (A3*x + A2)hi*d(x^2) + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 fA7 = fA7, fA4L, fA5 // Elo + nop.i 0 +} +;; +{ .mfi + nop.m 0 + fma.s1 fA25 = fA25, fB8, fA19 // C*x^8 + D + nop.i 0 +} +;; +{ .mfi + nop.m 0 + fadd.s1 fRes2L = fRes2L, fRes4L // (A3*x + A2)lo + nop.i 0 +} +;; +{ .mfi + nop.m 0 + fms.s1 fB4 = fRes2H, fA4L, fRes3H // d((A3*x + A2)*x^2)) + nop.i 0 +} +{ .mfi + nop.m 0 + fadd.s1 fRes1L = fRes1L, fResL // (A1*x + A0)lo + nop.i 0 +} +;; +{ .mfi + nop.m 0 + fadd.s1 fB20 = fRes3H, fRes1H // Phi + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 fA11 = fA11, fA5L, fA7 // E + nop.i 0 +} +;; +{ .mfi + nop.m 0 + // ( (A3*x + A2)lo*<x^2> + (A3*x + A2)hi*d(x^2)) + fma.s1 fRes3L = fRes2L, fA4L, fRes3L + nop.i 0 +} +;; +{ .mfi + nop.m 0 + // d((A3*x + A2)*x^2)) + (A1*x + A0)lo + fadd.s1 fRes1L = fRes1L, fB4 + nop.i 0 +} +;; +{ .mfi + nop.m 0 + fsub.s1 fB18 = fRes1H, fB20 + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 fPol = fA25, fB8, fA11 + nop.i 0 +} +;; +{ .mfi + nop.m 0 + fadd.s1 fRes1L = fRes1L, fRes3L + nop.i 0 +} +;; +{ .mfi + nop.m 0 + fadd.s1 fB18 = fB18, fRes3H + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 fRes4H = fPol, fA5L, fB20 + nop.i 0 +} +;; +{ .mfi + nop.m 0 + fma.s1 fPolL = fPol, fA5L, f0 + nop.i 0 +} +;; +{ .mfi + nop.m 0 + fadd.s1 fB18 = fB18, fRes1L // Plo + nop.i 0 +} +{ .mfi + nop.m 0 + fsub.s1 fRes4L = fB20, fRes4H + nop.i 0 +} +;; +{ .mfi + nop.m 0 + fadd.s1 fB18 = fB18, fPolL + nop.i 0 +} +;; +{ .mfi + nop.m 0 + fadd.s1 fRes4L = fRes4L, fB18 + nop.i 0 +} +;; +{ .mfb + nop.m 0 + fma.s0 f8 = fRes4H, f1, fRes4L + // P25(x) computed, exit here + br.ret.sptk b0 +} +;; + + +// here if 0.75 <= x < 1.3125 +.align 32 +lgammal_03Q_1Q: +{ .mfi + addl rPolDataPtr= @ltoff(lgammal_03Q_1Q_data),gp + fma.s1 FR_FracX = fA5L, f1, f0 // x + adds rSgnGam = 1, r0 +} +{ .mfi + nop.m 0 + fma.s1 fB4 = fA5L, fA5L, f0 // x^2 + nop.i 0 +} +;; +{ .mfi + ld8 rPolDataPtr = [rPolDataPtr] + nop.f 0 + nop.i 0 +} +;; +{ .mfb + adds rTmpPtr = 144, rPolDataPtr + nop.f 0 + br.sptk lgamma_polynom24x +} +;; + +// here if 1.5625 <= x < 2.25 +.align 32 +lgammal_13Q_2Q: +{ .mfi + addl rPolDataPtr= @ltoff(lgammal_13Q_2Q_data),gp + fma.s1 FR_FracX = fB4, f1, f0 // x + adds rSgnGam = 1, r0 +} +{ .mfi + nop.m 0 + fma.s1 fB4 = fB4, fB4, f0 // x^2 + nop.i 0 +} +;; +{ .mfi + ld8 rPolDataPtr = [rPolDataPtr] + nop.f 0 + nop.i 0 +} +;; +{ .mfb + adds rTmpPtr = 144, rPolDataPtr + nop.f 0 + br.sptk lgamma_polynom24x +} +;; + +// here if result is Pol24(x) +// x is in FR_FracX, +// rPolDataPtr, rTmpPtr point to coefficients +.align 32 +lgamma_polynom24x: +{ .mfi + ldfpd fA4, fA2L = [rPolDataPtr], 16 + nop.f 0 + cmp.eq p6, p7 = 4, rSgnGamSize +} +{ .mfi + ldfpd fA23, fA24 = [rTmpPtr], 16 // C18, C19 + nop.f 0 + nop.i 0 +} +;; +{ .mfi + ldfpd fA3, fA1L = [rPolDataPtr], 16 + fma.s1 fA5L = fB4, fB4, f0 // x^4 + nop.i 0 +} +{ .mfi + ldfpd fA19, fA20 = [rTmpPtr], 16 // D6, D7 + fms.s1 fB2 = FR_FracX, FR_FracX, fB4 // x^2 - <x^2> + nop.i 0 +} +;; +{ .mmf + ldfpd fA15, fA16 = [rPolDataPtr], 16 // D2, D3 + ldfpd fA17, fA18 = [rTmpPtr], 16 // D4, D5 + nop.f 0 +} +;; +{ .mmf + ldfpd fA13, fA14 = [rPolDataPtr], 16 // D0, D1 + ldfpd fA12, fA21 = [rTmpPtr], 16 // E7, C16 + nop.f 0 +} +;; +{ .mfi + ldfe fA11 = [rPolDataPtr], 16 // E6 + nop.f 0 + nop.i 0 +} +{ .mfi + ldfe fA10 = [rTmpPtr], 16 // E5 + nop.f 0 + nop.i 0 +} +;; +{ .mfi + ldfpd fA2, fA4L = [rPolDataPtr], 16 + nop.f 0 + nop.i 0 +} +{ .mfi + ldfpd fA1, fA3L = [rTmpPtr], 16 + nop.f 0 + nop.i 0 +} +;; +{ .mfi + ldfpd fA22, fA25 = [rPolDataPtr], 16 // C17, C20 + fma.s1 fA0 = fA5L, fA5L, f0 // x^8 + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 fA0L = fA5L, FR_FracX, f0 // x^5 + nop.i 0 +} +;; +{ .mmf + ldfe fA9 = [rPolDataPtr], 16 // E4 + ldfe fA8 = [rTmpPtr], 16 // E3 + nop.f 0 +} +;; +{ .mmf + ldfe fA7 = [rPolDataPtr], 16 // E2 + ldfe fA6 = [rTmpPtr], 16 // E1 + nop.f 0 +} +;; +{ .mfi + ldfe fA5 = [rTmpPtr], 16 // E0 + fma.s1 fRes4H = fA4, fB4, f0 // A4*<x^2> + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 fPol = fA24, FR_FracX, fA23 // C19*x + C18 + nop.i 0 +} +;; +{ .mfi + // store signgam if size of variable is 4 bytes +(p6) st4 [rSgnGamAddr] = rSgnGam + fma.s1 fRes1H = fA3, fB4, f0 // A3*<x^2> + nop.i 0 +} +{ .mfi + // store signgam if size of variable is 8 bytes +(p7) st8 [rSgnGamAddr] = rSgnGam + fma.s1 fA1L = fA3, fB2,fA1L // A3*d(x^2) + A1L + nop.i 0 +} +;; +{ .mfi + nop.m 0 + fma.s1 fA20 = fA20, FR_FracX, fA19 // D7*x + D6 + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 fA18 = fA18, FR_FracX, fA17 // D5*x + D4 + nop.i 0 +} +;; +{ .mfi + nop.m 0 + fma.s1 fA16 = fA16, FR_FracX, fA15 // D3*x + D2 + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 fA14 = fA14, FR_FracX, fA13 // D1*x + D0 + nop.i 0 +} +;; +{ .mfi + nop.m 0 + fma.s1 fA2L = fA4, fB2,fA2L // A4*d(x^2) + A2L + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 fA12 = fA12, FR_FracX, fA11 // E7*x + E6 + nop.i 0 +} +;; +{ .mfi + nop.m 0 + fms.s1 fRes2L = fA4, fB4, fRes4H // delta(A4*<x^2>) + nop.i 0 +} +{ .mfi + nop.m 0 + fadd.s1 fRes2H = fRes4H, fA2 // A4*<x^2> + A2 + nop.i 0 +} +;; +{ .mfi + nop.m 0 + fms.s1 fRes3L = fA3, fB4, fRes1H // delta(A3*<x^2>) + nop.i 0 +} +{ .mfi + nop.m 0 + fadd.s1 fRes3H = fRes1H, fA1 // A3*<x^2> + A1 + nop.i 0 +} +;; +{ .mfi + nop.m 0 + fma.s1 fA20 = fA20, fB4, fA18 // (D7*x + D6)*x^2 + D5*x + D4 + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 fA22 = fA22, FR_FracX, fA21 // C17*x + C16 + nop.i 0 +} +;; +{ .mfi + nop.m 0 + fma.s1 fA16 = fA16, fB4, fA14 // (D3*x + D2)*x^2 + D1*x + D0 + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 fPol = fA25, fB4, fPol // C20*x^2 + C19*x + C18 + nop.i 0 +} +;; +{ .mfi + nop.m 0 + fma.s1 fA2L = fA4L, fB4, fA2L // A4L*<x^2> + A4*d(x^2) + A2L + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 fA1L = fA3L, fB4, fA1L // A3L*<x^2> + A3*d(x^2) + A1L + nop.i 0 +} +;; +{ .mfi + nop.m 0 + fsub.s1 fRes4L = fA2, fRes2H // d1 + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 fResH = fRes2H, fB4, f0 // (A4*<x^2> + A2)*x^2 + nop.i 0 +} +;; +{ .mfi + nop.m 0 + fsub.s1 fRes1L = fA1, fRes3H // d1 + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 fB6 = fRes3H, FR_FracX, f0 // (A3*<x^2> + A1)*x + nop.i 0 +} +;; +{ .mfi + nop.m 0 + fma.s1 fA10 = fA10, FR_FracX, fA9 // E5*x + E4 + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 fA8 = fA8, FR_FracX, fA7 // E3*x + E2 + nop.i 0 +} +;; +{ .mfi + nop.m 0 + // (C20*x^2 + C19*x + C18)*x^2 + C17*x + C16 + fma.s1 fPol = fPol, fB4, fA22 + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 fA6 = fA6, FR_FracX, fA5 // E1*x + E0 + nop.i 0 +} +;; +{ .mfi + nop.m 0 + // A4L*<x^2> + A4*d(x^2) + A2L + delta(A4*<x^2>) + fadd.s1 fRes2L = fA2L, fRes2L + nop.i 0 +} +{ .mfi + nop.m 0 + // A3L*<x^2> + A3*d(x^2) + A1L + delta(A3*<x^2>) + fadd.s1 fRes3L = fA1L, fRes3L + nop.i 0 +} +;; +{ .mfi + nop.m 0 + fadd.s1 fRes4L = fRes4L, fRes4H // d2 + nop.i 0 +} +{ .mfi + nop.m 0 + fms.s1 fResL = fRes2H, fB4, fResH // d(A4*<x^2> + A2)*x^2) + nop.i 0 +} +;; +{ .mfi + nop.m 0 + fadd.s1 fRes1L = fRes1L, fRes1H // d2 + nop.i 0 +} +{ .mfi + nop.m 0 + fms.s1 fB8 = fRes3H, FR_FracX, fB6 // d((A3*<x^2> + A1)*x) + nop.i 0 +} +;; +{ .mfi + nop.m 0 + fadd.s1 fB10 = fResH, fB6 // (A4*x^4 + .. + A1*x)hi + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 fA12 = fA12, fB4, fA10 // Ehi + nop.i 0 +} +;; +{ .mfi + nop.m 0 + // ((D7*x + D6)*x^2 + D5*x + D4)*x^4 + (D3*x + D2)*x^2 + D1*x + D0 + fma.s1 fA20 = fA20, fA5L, fA16 + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 fA8 = fA8, fB4, fA6 // Elo + nop.i 0 +} +;; +{ .mfi + nop.m 0 + fadd.s1 fRes2L = fRes2L, fRes4L // (A4*<x^2> + A2)lo + nop.i 0 +} +{ .mfi + nop.m 0 + // d(A4*<x^2> + A2)*x^2) + A4*<x^2> + A2)*d(x^2) + fma.s1 fResL = fRes2H, fB2, fResL + nop.i 0 +} +;; +{ .mfi + nop.m 0 + fadd.s1 fRes3L = fRes3L, fRes1L // (A4*<x^2> + A2)lo + nop.i 0 +} +;; +{ .mfi + nop.m 0 + fsub.s1 fB12 = fB6, fB10 + nop.i 0 +} +;; +{ .mfi + nop.m 0 + fma.s1 fPol = fPol, fA0, fA20 // PolC*x^8 + PolD + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 fPolL = fA12, fA5L, fA8 // E + nop.i 0 +} +;; +{ .mfi + nop.m 0 + fma.s1 fResL = fB4, fRes2L, fResL // ((A4*<x^2> + A2)*x^2)lo + nop.i 0 +} +;; +{ .mfi + nop.m 0 + fma.s1 fRes3L = fRes3L, FR_FracX, fB8 // ((A3*<x^2> + A1)*x)lo + nop.i 0 +} +;; +{ .mfi + nop.m 0 + fadd.s1 fB12 = fB12, fResH + nop.i 0 +} +;; +{ .mfi + nop.m 0 + fma.s1 fPol = fPol, fA0, fPolL + nop.i 0 +} +;; +{ .mfi + nop.m 0 + fadd.s1 fRes3L = fRes3L, fResL + nop.i 0 +} +;; +{ .mfi + nop.m 0 + fma.s1 fRes2H = fPol, fA0L, fB10 + nop.i 0 +} +;; +{ .mfi + nop.m 0 + fadd.s1 fRes3L = fB12, fRes3L + nop.i 0 +} +;; +{ .mfi + nop.m 0 + fsub.s1 fRes4L = fB10, fRes2H + nop.i 0 +} +;; +{ .mfi + nop.m 0 + fma.s1 fRes4L = fPol, fA0L, fRes4L + nop.i 0 +} +;; +{ .mfi + nop.m 0 + fadd.s1 fRes4L = fRes4L, fRes3L + nop.i 0 +} +;; +{ .mfb + nop.m 0 + // final result for all paths for which the result is Pol24(x) + fma.s0 f8 = fRes2H, f1, fRes4L + // here is the exit for all paths for which the result is Pol24(x) + br.ret.sptk b0 +} +;; + + +// here if x is natval, nan, +/-inf, +/-0, or denormal +.align 32 +lgammal_spec: +{ .mfi + nop.m 0 + fclass.m p9, p0 = f8, 0xB // +/-denormals + nop.i 0 +};; +{ .mfi + nop.m 0 + fclass.m p6, p0 = f8, 0x1E1 // Test x for natval, nan, +inf + nop.i 0 +};; +{ .mfb + nop.m 0 + fclass.m p7, p0 = f8, 0x7 // +/-0 +(p9) br.cond.sptk lgammal_denormal_input +};; +{ .mfb + nop.m 0 + nop.f 0 + // branch out if if x is natval, nan, +inf +(p6) br.cond.spnt lgammal_nan_pinf +};; +{ .mfb + nop.m 0 + nop.f 0 +(p7) br.cond.spnt lgammal_singularity +};; +// if we are still here then x = -inf +{ .mfi + cmp.eq p6, p7 = 4, rSgnGamSize + nop.f 0 + adds rSgnGam = 1, r0 +};; +{ .mfi + // store signgam if size of variable is 4 bytes +(p6) st4 [rSgnGamAddr] = rSgnGam + nop.f 0 + nop.i 0 +} +{ .mfb + // store signgam if size of variable is 8 bytes +(p7) st8 [rSgnGamAddr] = rSgnGam + fma.s0 f8 = f8,f8,f0 // return +inf, no call to error support + br.ret.spnt b0 +};; + +// here if x is NaN, NatVal or +INF +.align 32 +lgammal_nan_pinf: +{ .mfi + cmp.eq p6, p7 = 4, rSgnGamSize + nop.f 0 + adds rSgnGam = 1, r0 +} +;; +{ .mfi + // store signgam if size of variable is 4 bytes +(p6) st4 [rSgnGamAddr] = rSgnGam + fma.s0 f8 = f8,f1,f8 // return x+x if x is natval, nan, +inf + nop.i 0 +} +{ .mfb + // store signgam if size of variable is 8 bytes +(p7) st8 [rSgnGamAddr] = rSgnGam + nop.f 0 + br.ret.sptk b0 +} +;; + +// here if x denormal or unnormal +.align 32 +lgammal_denormal_input: +{ .mfi + nop.m 0 + fma.s0 fResH = f1, f1, f8 // raise denormal exception + nop.i 0 +} +{ .mfi + nop.m 0 + fnorm.s1 f8 = f8 // normalize input value + nop.i 0 +} +;; +{ .mfi + getf.sig rSignifX = f8 + fmerge.se fSignifX = f1, f8 + nop.i 0 +} +{ .mfi + getf.exp rSignExpX = f8 + fcvt.fx.s1 fXint = f8 // Convert arg to int (int repres. in FR) + nop.i 0 +} +;; +{ .mfi + getf.exp rSignExpX = f8 + fcmp.lt.s1 p15, p14 = f8, f0 + nop.i 0 +} +;; +{ .mfb + and rExpX = rSignExpX, r17Ones + fmerge.s fAbsX = f1, f8 // |x| + br.cond.sptk _deno_back_to_main_path +} +;; + + +// here if overflow (x > overflow_bound) +.align 32 +lgammal_overflow: +{ .mfi + addl r8 = 0x1FFFE, r0 + nop.f 0 + cmp.eq p6, p7 = 4, rSgnGamSize +} +{ .mfi + adds rSgnGam = 1, r0 + nop.f 0 + nop.i 0 +} +;; +{ .mfi + setf.exp f9 = r8 + fmerge.s FR_X = f8,f8 + mov GR_Parameter_TAG = 102 // overflow +};; +{ .mfi + // store signgam if size of variable is 4 bytes +(p6) st4 [rSgnGamAddr] = rSgnGam + nop.f 0 + nop.i 0 +} +{ .mfb + // store signgam if size of variable is 8 bytes +(p7) st8 [rSgnGamAddr] = rSgnGam + fma.s0 FR_RESULT = f9,f9,f0 // Set I,O and +INF result + br.cond.sptk __libm_error_region +};; + +// here if x is negative integer or +/-0 (SINGULARITY) +.align 32 +lgammal_singularity: +{ .mfi + adds rSgnGam = 1, r0 + fclass.m p8,p0 = f8,0x6 // is x -0? + mov GR_Parameter_TAG = 103 // negative +} +{ .mfi + cmp.eq p6, p7 = 4, rSgnGamSize + fma.s1 FR_X = f0,f0,f8 + nop.i 0 +};; +{ .mfi +(p8) sub rSgnGam = r0, rSgnGam + nop.f 0 + nop.i 0 +} +{ .mfi + nop.m 0 + nop.f 0 + nop.i 0 +};; +{ .mfi + // store signgam if size of variable is 4 bytes +(p6) st4 [rSgnGamAddr] = rSgnGam + nop.f 0 + nop.i 0 +} +{ .mfb + // store signgam if size of variable is 8 bytes +(p7) st8 [rSgnGamAddr] = rSgnGam + frcpa.s0 FR_RESULT, p0 = f1, f0 + br.cond.sptk __libm_error_region +};; + +GLOBAL_LIBM_END(__libm_lgammal) + + +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 + stfe [GR_Parameter_Y] = FR_Y,16 // Save 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 + stfe [GR_Parameter_X] = FR_X // Store Parameter 1 on stack + add GR_Parameter_RESULT = 0,GR_Parameter_Y + nop.b 0 // Parameter 3 address +} +{ .mib + stfe [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 + add GR_Parameter_RESULT = 48,sp + nop.m 999 + nop.i 999 +};; +{ .mmi + ldfe 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# |