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/* -------------------------------------------------------------- */
/* (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 _TGAMMAF4_H_
#define _TGAMMAF4_H_ 1
#include <spu_intrinsics.h>
#include "simdmath.h"
#include "recipf4.h"
#include "truncf4.h"
#include "expf4.h"
#include "logf4.h"
#include "divf4.h"
#include "sinf4.h"
#include "powf4.h"
#include "tgammad2.h"
/*
* FUNCTION
* vector float _tgammaf4(vector float x)
*
* DESCRIPTION
* The tgammaf4 function returns a vector containing tgamma for each
* element of x
*
* We take a fairly standard approach - break the domain into 5 separate regions:
*
* 1. [-infinity, 0) - use gamma(x) = pi/(x*gamma(-x)*sin(x*pi))
* 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() are defined in
* tgammad2.h
*/
/*
* Rational Approximation Coefficients for the
* domain [1, 2) are defined in tgammad2.h
*/
static __inline vector float _tgammaf4(vector float x)
{
vector float signbit = spu_splats(-0.0f);
vector float zerof = spu_splats(0.0f);
vector float halff = spu_splats(0.5f);
vector float onef = spu_splats(1.0f);
vector float ninep9f = (vector float)spu_splats(0x411FFFFF); /* Next closest to 10.0 */
vector float t38f = spu_splats(38.0f);
vector float pi = spu_splats((float)SM_PI);
vector float sqrt2pi = spu_splats(2.506628274631000502415765284811f);
vector float inf = (vec_float4)spu_splats(0x7F800000);
vector float nan = (vec_float4)spu_splats(0x7FFFFFFF);
vector float xabs;
vector float xscaled;
vector float xtrunc;
vector float xinv;
vector float nresult; /* Negative x result */
vector float rresult; /* Rational Approx result */
vector float sresult; /* Stirling's result */
vector float result;
vector float pr,qr;
vector unsigned int gt0 = spu_cmpgt(x, zerof);
vector unsigned int gt1 = spu_cmpgt(x, onef);
vector unsigned int gt9p9 = spu_cmpgt(x, ninep9f);
vector unsigned int gt38 = spu_cmpgt(x, t38f);
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, onef), xabs, gt1);
xtrunc = _truncf4(xabs);
/*
* For x in [2, 10):
*/
xscaled = spu_add(onef, spu_sub(xabs, xtrunc));
/*
* For x in [1,2), use a rational approximation.
*/
pr = spu_madd(xscaled, spu_splats((float)TGD2_P07), spu_splats((float)TGD2_P06));
pr = spu_madd(pr, xscaled, spu_splats((float)TGD2_P05));
pr = spu_madd(pr, xscaled, spu_splats((float)TGD2_P04));
pr = spu_madd(pr, xscaled, spu_splats((float)TGD2_P03));
pr = spu_madd(pr, xscaled, spu_splats((float)TGD2_P02));
pr = spu_madd(pr, xscaled, spu_splats((float)TGD2_P01));
pr = spu_madd(pr, xscaled, spu_splats((float)TGD2_P00));
qr = spu_madd(xscaled, spu_splats((float)TGD2_Q07), spu_splats((float)TGD2_Q06));
qr = spu_madd(qr, xscaled, spu_splats((float)TGD2_Q05));
qr = spu_madd(qr, xscaled, spu_splats((float)TGD2_Q04));
qr = spu_madd(qr, xscaled, spu_splats((float)TGD2_Q03));
qr = spu_madd(qr, xscaled, spu_splats((float)TGD2_Q02));
qr = spu_madd(qr, xscaled, spu_splats((float)TGD2_Q01));
qr = spu_madd(qr, xscaled, spu_splats((float)TGD2_Q00));
rresult = _divf4(pr, qr);
rresult = spu_sel(_divf4(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, onef);
rresult = spu_sel(rresult, spu_mul(rresult, xscaled), spu_cmpgt(x, xscaled)); /* [3,4) */
xscaled = spu_add(xscaled, onef);
rresult = spu_sel(rresult, spu_mul(rresult, xscaled), spu_cmpgt(x, xscaled)); /* [4,5) */
xscaled = spu_add(xscaled, onef);
rresult = spu_sel(rresult, spu_mul(rresult, xscaled), spu_cmpgt(x, xscaled)); /* [5,6) */
xscaled = spu_add(xscaled, onef);
rresult = spu_sel(rresult, spu_mul(rresult, xscaled), spu_cmpgt(x, xscaled)); /* [6,7) */
xscaled = spu_add(xscaled, onef);
rresult = spu_sel(rresult, spu_mul(rresult, xscaled), spu_cmpgt(x, xscaled)); /* [7,8) */
xscaled = spu_add(xscaled, onef);
rresult = spu_sel(rresult, spu_mul(rresult, xscaled), spu_cmpgt(x, xscaled)); /* [8,9) */
xscaled = spu_add(xscaled, onef);
rresult = spu_sel(rresult, spu_mul(rresult, xscaled), spu_cmpgt(x, xscaled)); /* [9,10) */
/*
* For x >= 10, we use Stirling's Approximation
*/
vector float sum;
xinv = _recipf4(xabs);
sum = spu_madd(xinv, spu_splats((float)STIRLING_16), spu_splats((float)STIRLING_15));
sum = spu_madd(sum, xinv, spu_splats((float)STIRLING_14));
sum = spu_madd(sum, xinv, spu_splats((float)STIRLING_13));
sum = spu_madd(sum, xinv, spu_splats((float)STIRLING_12));
sum = spu_madd(sum, xinv, spu_splats((float)STIRLING_11));
sum = spu_madd(sum, xinv, spu_splats((float)STIRLING_10));
sum = spu_madd(sum, xinv, spu_splats((float)STIRLING_09));
sum = spu_madd(sum, xinv, spu_splats((float)STIRLING_08));
sum = spu_madd(sum, xinv, spu_splats((float)STIRLING_07));
sum = spu_madd(sum, xinv, spu_splats((float)STIRLING_06));
sum = spu_madd(sum, xinv, spu_splats((float)STIRLING_05));
sum = spu_madd(sum, xinv, spu_splats((float)STIRLING_04));
sum = spu_madd(sum, xinv, spu_splats((float)STIRLING_03));
sum = spu_madd(sum, xinv, spu_splats((float)STIRLING_02));
sum = spu_madd(sum, xinv, spu_splats((float)STIRLING_01));
sum = spu_madd(sum, xinv, spu_splats((float)STIRLING_00));
sum = spu_mul(sum, sqrt2pi);
sum = spu_mul(sum, _powf4(x, spu_sub(x, halff)));
sresult = spu_mul(sum, _expf4(spu_or(x, signbit)));
/*
* Choose rational approximation or Stirling's result.
*/
result = spu_sel(rresult, sresult, gt9p9);
result = spu_sel(result, inf, gt38);
/* For x < 0, use:
* gamma(x) = pi/(x*gamma(-x)*sin(x*pi))
*/
nresult = _divf4(pi, spu_mul(x, spu_mul(result, _sinf4(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 /* _TGAMMAF4_H_ */
#endif /* __SPU__ */
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