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libc/newlib/libm/machine/spu/headers/lgammaf4.h

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/* -------------------------------------------------------------- */
/* (C)Copyright 2006,2007, */
/* 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. */
/* 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 _LGAMMAF4_H_
#define _LGAMMAF4_H_ 1
#include <spu_intrinsics.h>
#include "lgammad2.h"
#include "recipf4.h"
#include "logf4.h"
#include "sinf4.h"
#include "truncf4.h"
/*
* FUNCTION
* vector float _lgammaf4(vector float x) - Natural Log of Gamma Function
*
* DESCRIPTION
* _lgammaf4 calculates the natural logarithm of the absolute value of the gamma
* function for the corresponding elements of the input vector.
*
* C99 Special Cases:
* lgamma(0) returns +infinite
* lgamma(1) returns +0
* lgamma(2) returns +0
* lgamma(negative integer) returns +infinite
* lgamma(+infinite) returns +infinite
* lgamma(-infinite) returns +infinite
*
* Other Cases:
* lgamma(Nan) returns Nan
* lgamma(Denorm) treated as lgamma(0) and returns +infinite
*
*/
static __inline vector float _lgammaf4(vector float x)
{
vec_float4 inff = (vec_float4)spu_splats(0x7F800000);
vec_float4 zerof = spu_splats(0.0f);
vec_float4 pi = spu_splats((float)PI);
vec_float4 sign_maskf = spu_splats(-0.0f);
vector unsigned int gt0;
/* This is where we switch from near zero approx. */
vec_float4 mac_switch = spu_splats(0.16f);
vec_float4 shift_switch = spu_splats(6.0f);
vec_float4 inv_x, inv_xsqu;
vec_float4 xtrunc, xstirling;
vec_float4 sum, xabs;
vec_uint4 isnaninf, isshifted;
vec_float4 result, stresult, shresult, mresult, nresult;
/* Force Denorms to 0 */
x = spu_add(x, zerof);
xabs = spu_andc(x, sign_maskf);
gt0 = spu_cmpgt(x, zerof);
xtrunc = _truncf4(x);
/*
* For 0 < x <= 0.16.
* Approximation Near Zero
*
* Use Maclaurin Expansion of lgamma()
*
* lgamma(z) = -ln(z) - z * EulerMascheroni + Sum[(-1)^n * z^n * Zeta(n)/n]
*/
mresult = spu_madd(xabs, spu_splats((float)ZETA_06_DIV_06), spu_splats((float)ZETA_05_DIV_05));
mresult = spu_madd(xabs, mresult, spu_splats((float)ZETA_04_DIV_04));
mresult = spu_madd(xabs, mresult, spu_splats((float)ZETA_03_DIV_03));
mresult = spu_madd(xabs, mresult, spu_splats((float)ZETA_02_DIV_02));
mresult = spu_mul(xabs, spu_mul(xabs, mresult));
mresult = spu_sub(mresult, spu_add(_logf4(xabs), spu_mul(xabs, spu_splats((float)EULER_MASCHERONI))));
/*
* For 0.16 < x <= 6.0, we are going to push value
* out to an area where Stirling's approximation is
* accurate. Let's use a constant of 6.
*
* Use the recurrence relation:
* lgamma(x + 1) = ln(x) + lgamma(x)
*
* Note that we shift x here, before Stirling's calculation,
* then after Stirling's, we adjust the result.
*
*/
isshifted = spu_cmpgt(shift_switch, x);
xstirling = spu_sel(xabs, spu_add(xabs, spu_splats(6.0f)), isshifted);
inv_x = _recipf4(xstirling);
inv_xsqu = spu_mul(inv_x, inv_x);
/*
* For 6.0 < x < infinite
*
* Use Stirling's Series.
*
* 1 1 1 1 1
* lgamma(x) = --- ln (2*pi) + (z - ---) ln(x) - x + --- - ----- + ------ ...
* 2 2 12x 360x^3 1260x^5
*
*
*/
sum = spu_madd(inv_xsqu, spu_splats((float)STIRLING_10), spu_splats((float)STIRLING_09));
sum = spu_madd(sum, inv_xsqu, spu_splats((float)STIRLING_08));
sum = spu_madd(sum, inv_xsqu, spu_splats((float)STIRLING_07));
sum = spu_madd(sum, inv_xsqu, spu_splats((float)STIRLING_06));
sum = spu_madd(sum, inv_xsqu, spu_splats((float)STIRLING_05));
sum = spu_madd(sum, inv_xsqu, spu_splats((float)STIRLING_04));
sum = spu_madd(sum, inv_xsqu, spu_splats((float)STIRLING_03));
sum = spu_madd(sum, inv_xsqu, spu_splats((float)STIRLING_02));
sum = spu_madd(sum, inv_xsqu, spu_splats((float)STIRLING_01));
sum = spu_mul(sum, inv_x);
stresult = spu_madd(spu_sub(xstirling, spu_splats(0.5f)), _logf4(xstirling), spu_splats((float)HALFLOG2PI));
stresult = spu_sub(stresult, xstirling);
stresult = spu_add(stresult, sum);
/*
* Adjust result if we shifted x into Stirling range.
*
* lgamma(x) = lgamma(x + n) - ln(x(x+1)(x+2)...(x+n-1)
*
*/
shresult = spu_mul(xabs, spu_add(xabs, spu_splats(1.0f)));
shresult = spu_mul(shresult, spu_add(xabs, spu_splats(2.0f)));
shresult = spu_mul(shresult, spu_add(xabs, spu_splats(3.0f)));
shresult = spu_mul(shresult, spu_add(xabs, spu_splats(4.0f)));
shresult = spu_mul(shresult, spu_add(xabs, spu_splats(5.0f)));
shresult = _logf4(shresult);
shresult = spu_sub(stresult, shresult);
stresult = spu_sel(stresult, shresult, isshifted);
/*
* Select either Maclaurin or Stirling result before Negative X calc.
*/
vec_uint4 useStirlings = spu_cmpgt(xabs, mac_switch);
result = spu_sel(mresult, stresult, useStirlings);
/*
* Approximation for Negative X
*
* Use reflection relation:
*
* gamma(x) * gamma(-x) = -pi/(x sin(pi x))
*
* lgamma(x) = log(pi/(-x sin(pi x))) - lgamma(-x)
*
*/
nresult = spu_mul(x, _sinf4(spu_mul(x, pi)));
nresult = spu_andc(nresult, sign_maskf);
nresult = spu_sub(_logf4(pi), spu_add(result, _logf4(nresult)));
/*
* Select between the negative or positive x approximations.
*/
result = spu_sel(nresult, result, gt0);
/*
* Finally, special cases/errors.
*/
/*
* x = non-positive integer, return infinity.
*/
result = spu_sel(result, inff, spu_andc(spu_cmpeq(x, xtrunc), gt0));
/* x = +/- infinite or nan, return |x| */
isnaninf = spu_cmpgt((vec_uint4)xabs, 0x7FEFFFFF);
result = spu_sel(result, xabs, isnaninf);
return result;
}
#endif /* _LGAMMAF4_H_ */
#endif /* __SPU__ */
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