mirror of
https://github.com/autc04/Retro68.git
synced 2024-12-04 16:50:57 +00:00
230 lines
9.2 KiB
C
230 lines
9.2 KiB
C
/* -------------------------------------------------------------- */
|
|
/* (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__ */
|