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Diffstat (limited to 'newlib/libm/machine/spu/headers/lgammad2.h')
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diff --git a/newlib/libm/machine/spu/headers/lgammad2.h b/newlib/libm/machine/spu/headers/lgammad2.h new file mode 100644 index 000000000..2644c770e --- /dev/null +++ b/newlib/libm/machine/spu/headers/lgammad2.h @@ -0,0 +1,330 @@ +/* -------------------------------------------------------------- */ +/* (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 _LGAMMAD2_H_ +#define _LGAMMAD2_H_ 1 + +#include <spu_intrinsics.h> +#include "divd2.h" +#include "recipd2.h" +#include "logd2.h" +#include "sind2.h" +#include "truncd2.h" + + +/* + * FUNCTION + * vector double _lgammad2(vector double x) - Natural Log of Gamma Function + * + * DESCRIPTION + * _lgammad2 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 + * + */ + +#define PI 3.1415926535897932384626433832795028841971693993751058209749445923078164 +#define HALFLOG2PI 9.1893853320467274178032973640561763986139747363778341281715154048276570E-1 + +#define EULER_MASCHERONI 0.5772156649015328606065 + +/* + * Zeta constants for Maclaurin approx. near zero + */ +#define ZETA_02_DIV_02 8.2246703342411321823620758332301E-1 +#define ZETA_03_DIV_03 -4.0068563438653142846657938717048E-1 +#define ZETA_04_DIV_04 2.7058080842778454787900092413529E-1 +#define ZETA_05_DIV_05 -2.0738555102867398526627309729141E-1 +#define ZETA_06_DIV_06 1.6955717699740818995241965496515E-1 + +/* + * More Maclaurin coefficients + */ +/* +#define ZETA_07_DIV_07 -1.4404989676884611811997107854997E-1 +#define ZETA_08_DIV_08 1.2550966952474304242233565481358E-1 +#define ZETA_09_DIV_09 -1.1133426586956469049087252991471E-1 +#define ZETA_10_DIV_10 1.0009945751278180853371459589003E-1 +#define ZETA_11_DIV_11 -9.0954017145829042232609298411497E-2 +#define ZETA_12_DIV_12 8.3353840546109004024886499837312E-2 +#define ZETA_13_DIV_13 -7.6932516411352191472827064348181E-2 +#define ZETA_14_DIV_14 7.1432946295361336059232753221795E-2 +#define ZETA_15_DIV_15 -6.6668705882420468032903448567376E-2 +#define ZETA_16_DIV_16 6.2500955141213040741983285717977E-2 +#define ZETA_17_DIV_17 -5.8823978658684582338957270605504E-2 +#define ZETA_18_DIV_18 5.5555767627403611102214247869146E-2 +#define ZETA_19_DIV_19 -5.2631679379616660733627666155673E-2 +#define ZETA_20_DIV_20 5.0000047698101693639805657601934E-2 + */ + +/* + * Coefficients for Stirling's Series for Lgamma() + */ +#define STIRLING_01 8.3333333333333333333333333333333333333333333333333333333333333333333333E-2 +#define STIRLING_02 -2.7777777777777777777777777777777777777777777777777777777777777777777778E-3 +#define STIRLING_03 7.9365079365079365079365079365079365079365079365079365079365079365079365E-4 +#define STIRLING_04 -5.9523809523809523809523809523809523809523809523809523809523809523809524E-4 +#define STIRLING_05 8.4175084175084175084175084175084175084175084175084175084175084175084175E-4 +#define STIRLING_06 -1.9175269175269175269175269175269175269175269175269175269175269175269175E-3 +#define STIRLING_07 6.4102564102564102564102564102564102564102564102564102564102564102564103E-3 +#define STIRLING_08 -2.9550653594771241830065359477124183006535947712418300653594771241830065E-2 +#define STIRLING_09 1.7964437236883057316493849001588939669435025472177174963552672531000704E-1 +#define STIRLING_10 -1.3924322169059011164274322169059011164274322169059011164274322169059011E0 +#define STIRLING_11 1.3402864044168391994478951000690131124913733609385783298826777087646653E1 +#define STIRLING_12 -1.5684828462600201730636513245208897382810426288687158252375643679991506E2 +#define STIRLING_13 2.1931033333333333333333333333333333333333333333333333333333333333333333E3 +#define STIRLING_14 -3.6108771253724989357173265219242230736483610046828437633035334184759472E4 +#define STIRLING_15 6.9147226885131306710839525077567346755333407168779805042318946657100161E5 +/* + * More Stirling's coefficients + */ +/* +#define STIRLING_16 -1.5238221539407416192283364958886780518659076533839342188488298545224541E7 +#define STIRLING_17 3.8290075139141414141414141414141414141414141414141414141414141414141414E8 +#define STIRLING_18 -1.0882266035784391089015149165525105374729434879810819660443720594096534E10 +#define STIRLING_19 3.4732028376500225225225225225225225225225225225225225225225225225225225E11 +#define STIRLING_20 -1.2369602142269274454251710349271324881080978641954251710349271324881081E13 +#define STIRLING_21 4.8878806479307933507581516251802290210847053890567382180703629532735764E14 +*/ + + +static __inline vector double _lgammad2(vector double x) +{ + vec_uchar16 dup_even = ((vec_uchar16) { 0,1,2,3, 0,1,2,3, 8, 9,10,11, 8, 9,10,11 }); + vec_uchar16 dup_odd = ((vec_uchar16) { 4,5,6,7, 4,5,6,7, 12,13,14,15, 12,13,14,15 }); + vec_uchar16 swap_word = ((vec_uchar16) { 4,5,6,7, 0,1,2,3, 12,13,14,15, 8, 9,10,11 }); + vec_double2 infinited = (vec_double2)spu_splats(0x7FF0000000000000ull); + vec_double2 zerod = spu_splats(0.0); + vec_double2 oned = spu_splats(1.0); + vec_double2 twod = spu_splats(2.0); + vec_double2 pi = spu_splats(PI); + vec_double2 sign_maskd = spu_splats(-0.0); + + /* This is where we switch from near zero approx. */ + vec_float4 zero_switch = spu_splats(0.001f); + vec_float4 shift_switch = spu_splats(6.0f); + + vec_float4 xf; + vec_double2 inv_x, inv_xsqu; + vec_double2 xtrunc, xstirling; + vec_double2 sum, xabs; + vec_uint4 xhigh, xlow, xthigh, xtlow; + vec_uint4 x1, isnaninf, isnposint, iszero, isint, isneg, isshifted, is1, is2; + vec_double2 result, stresult, shresult, mresult, nresult; + + + /* Force Denorms to 0 */ + x = spu_add(x, zerod); + + xabs = spu_andc(x, sign_maskd); + xf = spu_roundtf(xabs); + xf = spu_shuffle(xf, xf, dup_even); + + + /* + * For 0 < x <= 0.001. + * 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(ZETA_06_DIV_06), spu_splats(ZETA_05_DIV_05)); + mresult = spu_madd(xabs, mresult, spu_splats(ZETA_04_DIV_04)); + mresult = spu_madd(xabs, mresult, spu_splats(ZETA_03_DIV_03)); + mresult = spu_madd(xabs, mresult, spu_splats(ZETA_02_DIV_02)); + mresult = spu_mul(xabs, spu_mul(xabs, mresult)); + mresult = spu_sub(mresult, spu_add(_logd2(xabs), spu_mul(xabs, spu_splats(EULER_MASCHERONI)))); + + + /* + * For 0.001 < 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, xf); + xstirling = spu_sel(xabs, spu_add(xabs, spu_splats(6.0)), (vec_ullong2)isshifted); + inv_x = _recipd2(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 + * + * Taking 10 terms of the sum gives good results for x > 6.0 + * + */ + sum = spu_madd(inv_xsqu, spu_splats(STIRLING_15), spu_splats(STIRLING_14)); + sum = spu_madd(sum, inv_xsqu, spu_splats(STIRLING_13)); + sum = spu_madd(sum, inv_xsqu, spu_splats(STIRLING_12)); + sum = spu_madd(sum, inv_xsqu, spu_splats(STIRLING_11)); + sum = spu_madd(sum, inv_xsqu, spu_splats(STIRLING_10)); + sum = spu_madd(sum, inv_xsqu, spu_splats(STIRLING_09)); + sum = spu_madd(sum, inv_xsqu, spu_splats(STIRLING_08)); + sum = spu_madd(sum, inv_xsqu, spu_splats(STIRLING_07)); + sum = spu_madd(sum, inv_xsqu, spu_splats(STIRLING_06)); + sum = spu_madd(sum, inv_xsqu, spu_splats(STIRLING_05)); + sum = spu_madd(sum, inv_xsqu, spu_splats(STIRLING_04)); + sum = spu_madd(sum, inv_xsqu, spu_splats(STIRLING_03)); + sum = spu_madd(sum, inv_xsqu, spu_splats(STIRLING_02)); + sum = spu_madd(sum, inv_xsqu, spu_splats(STIRLING_01)); + sum = spu_mul(sum, inv_x); + + stresult = spu_madd(spu_sub(xstirling, spu_splats(0.5)), _logd2(xstirling), spu_splats(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(1.0))); + shresult = spu_mul(shresult, spu_add(xabs, spu_splats(2.0))); + shresult = spu_mul(shresult, spu_add(xabs, spu_splats(3.0))); + shresult = spu_mul(shresult, spu_add(xabs, spu_splats(4.0))); + shresult = spu_mul(shresult, spu_add(xabs, spu_splats(5.0))); + shresult = _logd2(shresult); + shresult = spu_sub(stresult, shresult); + stresult = spu_sel(stresult, shresult, (vec_ullong2)isshifted); + + + /* + * Select either Maclaurin or Stirling result before Negative X calc. + */ + xf = spu_shuffle(xf, xf, dup_even); + vec_uint4 useStirlings = spu_cmpgt(xf, zero_switch); + result = spu_sel(mresult, stresult, (vec_ullong2)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, _sind2(spu_mul(x, pi))); + nresult = spu_andc(nresult, sign_maskd); + nresult = _logd2(_divd2(pi, nresult)); + nresult = spu_sub(nresult, result); + + + /* + * Select between the negative or positive x approximations. + */ + isneg = (vec_uint4)spu_shuffle(x, x, dup_even); + isneg = spu_rlmaska(isneg, -32); + result = spu_sel(result, nresult, (vec_ullong2)isneg); + + + /* + * Finally, special cases/errors. + */ + xhigh = (vec_uint4)spu_shuffle(xabs, xabs, dup_even); + xlow = (vec_uint4)spu_shuffle(xabs, xabs, dup_odd); + + /* x = zero, return infinite */ + x1 = spu_or(xhigh, xlow); + iszero = spu_cmpeq(x1, 0); + + /* x = negative integer, return infinite */ + xtrunc = _truncd2(xabs); + xthigh = (vec_uint4)spu_shuffle(xtrunc, xtrunc, dup_even); + xtlow = (vec_uint4)spu_shuffle(xtrunc, xtrunc, dup_odd); + isint = spu_and(spu_cmpeq(xthigh, xhigh), spu_cmpeq(xtlow, xlow)); + isnposint = spu_or(spu_and(isint, isneg), iszero); + result = spu_sel(result, infinited, (vec_ullong2)isnposint); + + /* x = 1.0 or 2.0, return 0.0 */ + is1 = spu_cmpeq((vec_uint4)x, (vec_uint4)oned); + is1 = spu_and(is1, spu_shuffle(is1, is1, swap_word)); + is2 = spu_cmpeq((vec_uint4)x, (vec_uint4)twod); + is2 = spu_and(is2, spu_shuffle(is2, is2, swap_word)); + result = spu_sel(result, zerod, (vec_ullong2)spu_or(is1,is2)); + + /* x = +/- infinite or nan, return |x| */ + isnaninf = spu_cmpgt(xhigh, 0x7FEFFFFF); + result = spu_sel(result, xabs, (vec_ullong2)isnaninf); + + return result; +} + +#endif /* _LGAMMAD2_H_ */ +#endif /* __SPU__ */ |