233 lines
8.8 KiB
C
233 lines
8.8 KiB
C
/* -------------------------------------------------------------- */
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/* (C)Copyright 2006,2007, */
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/* International Business Machines Corporation */
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/* All Rights Reserved. */
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/* */
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/* Redistribution and use in source and binary forms, with or */
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/* without modification, are permitted provided that the */
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/* following conditions are met: */
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/* */
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/* - Redistributions of source code must retain the above copyright*/
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/* notice, this list of conditions and the following disclaimer. */
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/* */
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/* - Redistributions in binary form must reproduce the above */
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/* copyright notice, this list of conditions and the following */
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/* disclaimer in the documentation and/or other materials */
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/* provided with the distribution. */
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/* */
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/* - Neither the name of IBM Corporation nor the names of its */
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/* contributors may be used to endorse or promote products */
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/* derived from this software without specific prior written */
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/* permission. */
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/* Redistributions of source code must retain the above copyright */
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/* notice, this list of conditions and the following disclaimer. */
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/* */
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/* Redistributions in binary form must reproduce the above */
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/* copyright notice, this list of conditions and the following */
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/* disclaimer in the documentation and/or other materials */
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/* provided with the distribution. */
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/* */
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/* Neither the name of IBM Corporation nor the names of its */
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/* contributors may be used to endorse or promote products */
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/* derived from this software without specific prior written */
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/* permission. */
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/* */
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/* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND */
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/* CONTRIBUTORS "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, */
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/* INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF */
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/* MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE */
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/* DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR */
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/* CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, */
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/* SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT */
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/* NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; */
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/* LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) */
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/* HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN */
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/* CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR */
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/* OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, */
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/* EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. */
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/* -------------------------------------------------------------- */
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/* PROLOG END TAG zYx */
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#ifdef __SPU__
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#ifndef _LGAMMAF4_H_
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#define _LGAMMAF4_H_ 1
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#include <spu_intrinsics.h>
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#include "lgammad2.h"
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#include "recipf4.h"
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#include "logf4.h"
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#include "sinf4.h"
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#include "truncf4.h"
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/*
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* FUNCTION
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* vector float _lgammaf4(vector float x) - Natural Log of Gamma Function
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*
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* DESCRIPTION
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* _lgammaf4 calculates the natural logarithm of the absolute value of the gamma
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* function for the corresponding elements of the input vector.
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*
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* C99 Special Cases:
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* lgamma(0) returns +infinite
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* lgamma(1) returns +0
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* lgamma(2) returns +0
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* lgamma(negative integer) returns +infinite
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* lgamma(+infinite) returns +infinite
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* lgamma(-infinite) returns +infinite
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*
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* Other Cases:
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* lgamma(Nan) returns Nan
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* lgamma(Denorm) treated as lgamma(0) and returns +infinite
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*
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*/
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static __inline vector float _lgammaf4(vector float x)
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{
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vec_float4 inff = (vec_float4)spu_splats(0x7F800000);
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vec_float4 zerof = spu_splats(0.0f);
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vec_float4 pi = spu_splats((float)PI);
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vec_float4 sign_maskf = spu_splats(-0.0f);
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vector unsigned int gt0;
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/* This is where we switch from near zero approx. */
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vec_float4 mac_switch = spu_splats(0.16f);
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vec_float4 shift_switch = spu_splats(6.0f);
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vec_float4 inv_x, inv_xsqu;
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vec_float4 xtrunc, xstirling;
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vec_float4 sum, xabs;
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vec_uint4 isnaninf, isshifted;
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vec_float4 result, stresult, shresult, mresult, nresult;
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/* Force Denorms to 0 */
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x = spu_add(x, zerof);
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xabs = spu_andc(x, sign_maskf);
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gt0 = spu_cmpgt(x, zerof);
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xtrunc = _truncf4(x);
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/*
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* For 0 < x <= 0.16.
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* Approximation Near Zero
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*
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* Use Maclaurin Expansion of lgamma()
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*
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* lgamma(z) = -ln(z) - z * EulerMascheroni + Sum[(-1)^n * z^n * Zeta(n)/n]
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*/
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mresult = spu_madd(xabs, spu_splats((float)ZETA_06_DIV_06), spu_splats((float)ZETA_05_DIV_05));
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mresult = spu_madd(xabs, mresult, spu_splats((float)ZETA_04_DIV_04));
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mresult = spu_madd(xabs, mresult, spu_splats((float)ZETA_03_DIV_03));
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mresult = spu_madd(xabs, mresult, spu_splats((float)ZETA_02_DIV_02));
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mresult = spu_mul(xabs, spu_mul(xabs, mresult));
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mresult = spu_sub(mresult, spu_add(_logf4(xabs), spu_mul(xabs, spu_splats((float)EULER_MASCHERONI))));
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/*
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* For 0.16 < x <= 6.0, we are going to push value
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* out to an area where Stirling's approximation is
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* accurate. Let's use a constant of 6.
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*
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* Use the recurrence relation:
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* lgamma(x + 1) = ln(x) + lgamma(x)
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*
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* Note that we shift x here, before Stirling's calculation,
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* then after Stirling's, we adjust the result.
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*
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*/
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isshifted = spu_cmpgt(shift_switch, x);
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xstirling = spu_sel(xabs, spu_add(xabs, spu_splats(6.0f)), isshifted);
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inv_x = _recipf4(xstirling);
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inv_xsqu = spu_mul(inv_x, inv_x);
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/*
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* For 6.0 < x < infinite
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*
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* Use Stirling's Series.
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*
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* 1 1 1 1 1
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* lgamma(x) = --- ln (2*pi) + (z - ---) ln(x) - x + --- - ----- + ------ ...
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* 2 2 12x 360x^3 1260x^5
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*
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*
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*/
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sum = spu_madd(inv_xsqu, spu_splats((float)STIRLING_10), spu_splats((float)STIRLING_09));
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sum = spu_madd(sum, inv_xsqu, spu_splats((float)STIRLING_08));
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sum = spu_madd(sum, inv_xsqu, spu_splats((float)STIRLING_07));
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sum = spu_madd(sum, inv_xsqu, spu_splats((float)STIRLING_06));
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sum = spu_madd(sum, inv_xsqu, spu_splats((float)STIRLING_05));
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sum = spu_madd(sum, inv_xsqu, spu_splats((float)STIRLING_04));
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sum = spu_madd(sum, inv_xsqu, spu_splats((float)STIRLING_03));
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sum = spu_madd(sum, inv_xsqu, spu_splats((float)STIRLING_02));
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sum = spu_madd(sum, inv_xsqu, spu_splats((float)STIRLING_01));
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sum = spu_mul(sum, inv_x);
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stresult = spu_madd(spu_sub(xstirling, spu_splats(0.5f)), _logf4(xstirling), spu_splats((float)HALFLOG2PI));
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stresult = spu_sub(stresult, xstirling);
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stresult = spu_add(stresult, sum);
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/*
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* Adjust result if we shifted x into Stirling range.
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*
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* lgamma(x) = lgamma(x + n) - ln(x(x+1)(x+2)...(x+n-1)
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*
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*/
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shresult = spu_mul(xabs, spu_add(xabs, spu_splats(1.0f)));
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shresult = spu_mul(shresult, spu_add(xabs, spu_splats(2.0f)));
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shresult = spu_mul(shresult, spu_add(xabs, spu_splats(3.0f)));
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shresult = spu_mul(shresult, spu_add(xabs, spu_splats(4.0f)));
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shresult = spu_mul(shresult, spu_add(xabs, spu_splats(5.0f)));
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shresult = _logf4(shresult);
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shresult = spu_sub(stresult, shresult);
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stresult = spu_sel(stresult, shresult, isshifted);
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/*
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* Select either Maclaurin or Stirling result before Negative X calc.
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*/
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vec_uint4 useStirlings = spu_cmpgt(xabs, mac_switch);
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result = spu_sel(mresult, stresult, useStirlings);
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/*
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* Approximation for Negative X
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*
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* Use reflection relation:
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*
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* gamma(x) * gamma(-x) = -pi/(x sin(pi x))
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*
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* lgamma(x) = log(pi/(-x sin(pi x))) - lgamma(-x)
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*
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*/
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nresult = spu_mul(x, _sinf4(spu_mul(x, pi)));
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nresult = spu_andc(nresult, sign_maskf);
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nresult = spu_sub(_logf4(pi), spu_add(result, _logf4(nresult)));
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/*
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* Select between the negative or positive x approximations.
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*/
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result = spu_sel(nresult, result, gt0);
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/*
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* Finally, special cases/errors.
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*/
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/*
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* x = non-positive integer, return infinity.
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*/
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result = spu_sel(result, inff, spu_andc(spu_cmpeq(x, xtrunc), gt0));
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/* x = +/- infinite or nan, return |x| */
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isnaninf = spu_cmpgt((vec_uint4)xabs, 0x7FEFFFFF);
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result = spu_sel(result, xabs, isnaninf);
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return result;
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}
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#endif /* _LGAMMAF4_H_ */
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#endif /* __SPU__ */
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