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Diffstat (limited to 'newlib/libm/machine/spu/headers/lgammaf4.h')
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diff --git a/newlib/libm/machine/spu/headers/lgammaf4.h b/newlib/libm/machine/spu/headers/lgammaf4.h new file mode 100644 index 000000000..956a0e1c4 --- /dev/null +++ b/newlib/libm/machine/spu/headers/lgammaf4.h @@ -0,0 +1,232 @@ +/* -------------------------------------------------------------- */ +/* (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__ */ |