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Diffstat (limited to 'newlib/libm/machine/spu/headers/tgammad2.h')
| -rw-r--r-- | newlib/libm/machine/spu/headers/tgammad2.h | 289 |
1 files changed, 0 insertions, 289 deletions
diff --git a/newlib/libm/machine/spu/headers/tgammad2.h b/newlib/libm/machine/spu/headers/tgammad2.h deleted file mode 100644 index fa0f2f325..000000000 --- a/newlib/libm/machine/spu/headers/tgammad2.h +++ /dev/null @@ -1,289 +0,0 @@ -/* -------------------------------------------------------------- */ -/* (C)Copyright 2007,2008, */ -/* International Business Machines Corporation */ -/* All Rights Reserved. */ -/* */ -/* 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. */ -/* */ -/* - Neither the name of IBM Corporation nor the names of its */ -/* contributors may 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 THE COPYRIGHT OWNER OR */ -/* 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. */ -/* -------------------------------------------------------------- */ -/* PROLOG END TAG zYx */ -#ifdef __SPU__ - -#ifndef _TGAMMAD2_H_ -#define _TGAMMAD2_H_ 1 - -#include <spu_intrinsics.h> -#include "simdmath.h" - -#include "recipd2.h" -#include "truncd2.h" -#include "expd2.h" -#include "logd2.h" -#include "divd2.h" -#include "sind2.h" -#include "powd2.h" - - -/* - * FUNCTION - * vector double _tgammad2(vector double x) - * - * DESCRIPTION - * _tgammad2 - * - * This is an interesting function to approximate fast - * and accurately. We take a fairly standard approach - break - * the domain into 5 separate regions: - * - * 1. [-infinity, 0) - use - * 2. [0, 1) - push x into [1,2), then adjust the - * result. - * 3. [1, 2) - use a rational approximation. - * 4. [2, 10) - pull back into [1, 2), then adjust - * the result. - * 5. [10, +infinity] - use Stirling's Approximation. - * - * - * Special Cases: - * - tgamma(+/- 0) returns +/- infinity - * - tgamma(negative integer) returns NaN - * - tgamma(-infinity) returns NaN - * - tgamma(infinity) returns infinity - * - */ - - -/* - * Coefficients for Stirling's Series for Gamma() - */ -/* 1/ 1 */ -#define STIRLING_00 1.000000000000000000000000000000000000E0 -/* 1/ 12 */ -#define STIRLING_01 8.333333333333333333333333333333333333E-2 -/* 1/ 288 */ -#define STIRLING_02 3.472222222222222222222222222222222222E-3 -/* -139/ 51840 */ -#define STIRLING_03 -2.681327160493827160493827160493827160E-3 -/* -571/ 2488320 */ -#define STIRLING_04 -2.294720936213991769547325102880658436E-4 -/* 163879/ 209018880 */ -#define STIRLING_05 7.840392217200666274740348814422888497E-4 -/* 5246819/ 75246796800 */ -#define STIRLING_06 6.972813758365857774293988285757833083E-5 -/* -534703531/ 902961561600 */ -#define STIRLING_07 -5.921664373536938828648362256044011874E-4 -/* -4483131259/ 86684309913600 */ -#define STIRLING_08 -5.171790908260592193370578430020588228E-5 -/* 432261921612371/ 514904800886784000 */ -#define STIRLING_09 8.394987206720872799933575167649834452E-4 -/* 6232523202521089/ 86504006548979712000 */ -#define STIRLING_10 7.204895416020010559085719302250150521E-5 -/* -25834629665134204969/ 13494625021640835072000 */ -#define STIRLING_11 -1.914438498565477526500898858328522545E-3 -/* -1579029138854919086429/ 9716130015581401251840000 */ -#define STIRLING_12 -1.625162627839158168986351239802709981E-4 -/* 746590869962651602203151/ 116593560186976815022080000 */ -#define STIRLING_13 6.403362833808069794823638090265795830E-3 -/* 1511513601028097903631961/ 2798245444487443560529920000 */ -#define STIRLING_14 5.401647678926045151804675085702417355E-4 -/* -8849272268392873147705987190261/ 299692087104605205332754432000000 */ -#define STIRLING_15 -2.952788094569912050544065105469382445E-2 -/* -142801712490607530608130701097701/ 57540880724084199423888850944000000 */ -#define STIRLING_16 -2.481743600264997730915658368743464324E-3 - - -/* - * Rational Approximation Coefficients for the - * domain [1, 2). - */ -#define TGD2_P00 -1.8211798563156931777484715e+05 -#define TGD2_P01 -8.7136501560410004458390176e+04 -#define TGD2_P02 -3.9304030489789496641606092e+04 -#define TGD2_P03 -1.2078833505605729442322627e+04 -#define TGD2_P04 -2.2149136023607729839568492e+03 -#define TGD2_P05 -7.2672456596961114883015398e+02 -#define TGD2_P06 -2.2126466212611862971471055e+01 -#define TGD2_P07 -2.0162424149396112937893122e+01 - -#define TGD2_Q00 1.0000000000000000000000000 -#define TGD2_Q01 -1.8212849094205905566923320e+05 -#define TGD2_Q02 -1.9220660507239613798446953e+05 -#define TGD2_Q03 2.9692670736656051303725690e+04 -#define TGD2_Q04 3.0352658363629092491464689e+04 -#define TGD2_Q05 -1.0555895821041505769244395e+04 -#define TGD2_Q06 1.2786642579487202056043316e+03 -#define TGD2_Q07 -5.5279768804094054246434098e+01 - -static __inline vector double _tgammad2(vector double x) -{ - vector double signbit = spu_splats(-0.0); - vector double zerod = spu_splats(0.0); - vector double halfd = spu_splats(0.5); - vector double oned = spu_splats(1.0); - vector double ninep9d = (vec_double2)spu_splats(0x4023FFFFFFFFFFFFull); - vector double twohd = spu_splats(200.0); - vector double pi = spu_splats(SM_PI); - vector double sqrt2pi = spu_splats(2.50662827463100050241576528481); - vector double inf = (vector double)spu_splats(0x7FF0000000000000ull); - vector double nan = (vector double)spu_splats(0x7FF8000000000000ull); - - - vector double xabs; - vector double xscaled; - vector double xtrunc; - vector double xinv; - vector double nresult; - vector double rresult; /* Rational Approx result */ - vector double sresult; /* Stirling's result */ - vector double result; - vector double pr,qr; - - vector unsigned long long gt0 = spu_cmpgt(x, zerod); - vector unsigned long long gt1 = spu_cmpgt(x, oned); - vector unsigned long long gt9p9 = spu_cmpgt(x, ninep9d); - vector unsigned long long gt200 = spu_cmpgt(x, twohd); - - - xabs = spu_andc(x, signbit); - - /* - * For x in [0, 1], add 1 to x, use rational - * approximation, then use: - * - * gamma(x) = gamma(x+1)/x - * - */ - xabs = spu_sel(spu_add(xabs, oned), xabs, gt1); - xtrunc = _truncd2(xabs); - - - /* - * For x in [2, 10): - */ - xscaled = spu_add(oned, spu_sub(xabs, xtrunc)); - - /* - * For x in [1,2), use a rational approximation. - */ - pr = spu_madd(xscaled, spu_splats(TGD2_P07), spu_splats(TGD2_P06)); - pr = spu_madd(pr, xscaled, spu_splats(TGD2_P05)); - pr = spu_madd(pr, xscaled, spu_splats(TGD2_P04)); - pr = spu_madd(pr, xscaled, spu_splats(TGD2_P03)); - pr = spu_madd(pr, xscaled, spu_splats(TGD2_P02)); - pr = spu_madd(pr, xscaled, spu_splats(TGD2_P01)); - pr = spu_madd(pr, xscaled, spu_splats(TGD2_P00)); - - qr = spu_madd(xscaled, spu_splats(TGD2_Q07), spu_splats(TGD2_Q06)); - qr = spu_madd(qr, xscaled, spu_splats(TGD2_Q05)); - qr = spu_madd(qr, xscaled, spu_splats(TGD2_Q04)); - qr = spu_madd(qr, xscaled, spu_splats(TGD2_Q03)); - qr = spu_madd(qr, xscaled, spu_splats(TGD2_Q02)); - qr = spu_madd(qr, xscaled, spu_splats(TGD2_Q01)); - qr = spu_madd(qr, xscaled, spu_splats(TGD2_Q00)); - - rresult = _divd2(pr, qr); - rresult = spu_sel(_divd2(rresult, x), rresult, gt1); - - /* - * If x was in [2,10) and we pulled it into [1,2), we need to push - * it back out again. - */ - rresult = spu_sel(rresult, spu_mul(rresult, xscaled), spu_cmpgt(x, xscaled)); /* [2,3) */ - xscaled = spu_add(xscaled, oned); - rresult = spu_sel(rresult, spu_mul(rresult, xscaled), spu_cmpgt(x, xscaled)); /* [3,4) */ - xscaled = spu_add(xscaled, oned); - rresult = spu_sel(rresult, spu_mul(rresult, xscaled), spu_cmpgt(x, xscaled)); /* [4,5) */ - xscaled = spu_add(xscaled, oned); - rresult = spu_sel(rresult, spu_mul(rresult, xscaled), spu_cmpgt(x, xscaled)); /* [5,6) */ - xscaled = spu_add(xscaled, oned); - rresult = spu_sel(rresult, spu_mul(rresult, xscaled), spu_cmpgt(x, xscaled)); /* [6,7) */ - xscaled = spu_add(xscaled, oned); - rresult = spu_sel(rresult, spu_mul(rresult, xscaled), spu_cmpgt(x, xscaled)); /* [7,8) */ - xscaled = spu_add(xscaled, oned); - rresult = spu_sel(rresult, spu_mul(rresult, xscaled), spu_cmpgt(x, xscaled)); /* [8,9) */ - xscaled = spu_add(xscaled, oned); - rresult = spu_sel(rresult, spu_mul(rresult, xscaled), spu_cmpgt(x, xscaled)); /* [9,10) */ - - - /* - * For x >= 10, we use Stirling's Approximation - */ - vector double sum; - xinv = _recipd2(xabs); - sum = spu_madd(xinv, spu_splats(STIRLING_16), spu_splats(STIRLING_15)); - sum = spu_madd(sum, xinv, spu_splats(STIRLING_14)); - sum = spu_madd(sum, xinv, spu_splats(STIRLING_13)); - sum = spu_madd(sum, xinv, spu_splats(STIRLING_12)); - sum = spu_madd(sum, xinv, spu_splats(STIRLING_11)); - sum = spu_madd(sum, xinv, spu_splats(STIRLING_10)); - sum = spu_madd(sum, xinv, spu_splats(STIRLING_09)); - sum = spu_madd(sum, xinv, spu_splats(STIRLING_08)); - sum = spu_madd(sum, xinv, spu_splats(STIRLING_07)); - sum = spu_madd(sum, xinv, spu_splats(STIRLING_06)); - sum = spu_madd(sum, xinv, spu_splats(STIRLING_05)); - sum = spu_madd(sum, xinv, spu_splats(STIRLING_04)); - sum = spu_madd(sum, xinv, spu_splats(STIRLING_03)); - sum = spu_madd(sum, xinv, spu_splats(STIRLING_02)); - sum = spu_madd(sum, xinv, spu_splats(STIRLING_01)); - sum = spu_madd(sum, xinv, spu_splats(STIRLING_00)); - - sum = spu_mul(sum, sqrt2pi); - sum = spu_mul(sum, _powd2(x, spu_sub(x, halfd))); - sresult = spu_mul(sum, _expd2(spu_or(x, signbit))); - - /* - * Choose rational approximation or Stirling's result. - */ - result = spu_sel(rresult, sresult, gt9p9); - - - result = spu_sel(result, inf, gt200); - - /* For x < 0, use: - * - * gamma(x) = pi/(x*gamma(-x)*sin(x*pi)) - * or - * gamma(x) = pi/(gamma(1 - x)*sin(x*pi)) - */ - nresult = _divd2(pi, spu_mul(x, spu_mul(result, _sind2(spu_mul(x, pi))))); - result = spu_sel(nresult, result, gt0); - - /* - * x = non-positive integer, return NaN. - */ - result = spu_sel(result, nan, spu_andc(spu_cmpeq(x, xtrunc), gt0)); - - - return result; -} - -#endif /* _TGAMMAD2_H_ */ -#endif /* __SPU__ */ |