| /* -------------------------------------------------------------- */ |
| /* (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__ */ |