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Diffstat (limited to 'newlib/libm/machine/spu/headers/asinhd2.h')
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1 files changed, 189 insertions, 0 deletions
diff --git a/newlib/libm/machine/spu/headers/asinhd2.h b/newlib/libm/machine/spu/headers/asinhd2.h new file mode 100644 index 000000000..542d59858 --- /dev/null +++ b/newlib/libm/machine/spu/headers/asinhd2.h @@ -0,0 +1,189 @@ +/* -------------------------------------------------------------- */ +/* (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 _ASINHD2_H_ +#define _ASINHD2_H_ 1 + +#include <spu_intrinsics.h> + +#include "logd2.h" +#include "sqrtd2.h" + +/* + * FUNCTION + * vector double _asinhd2(vector double x) + * + * DESCRIPTION + * The asinhd2 function returns a vector containing the hyperbolic + * arcsines of the corresponding elements of the input vector. + * + * We are using the formula: + * asinh = ln(|x| + sqrt(x^2 + 1)) + * and the anti-symmetry of asinh. + * + * For x near zero, we use the Taylor series: + * + * infinity + * ------ + * - ' P (0) + * - k-1 k + * asinh x = - ----- x + * - k + * - , + * ------ + * k = 1 + * + * Special Cases: + * asinh(+0) returns +0 + * asinh(-0) returns -0 + * asinh(+infinity) returns +infinity + * asinh(-infinity) returns -infinity + * asinh(NaN) returns NaN + * + */ + +/* + * Maclaurin Series Coefficients + * for x near 0. + */ +#define ASINH_MAC01 1.0000000000000000000000000000000000000000000000000000000000000000000000E0 +#define ASINH_MAC03 -1.6666666666666666666666666666666666666666666666666666666666666666666667E-1 +#define ASINH_MAC05 7.5000000000000000000000000000000000000000000000000000000000000000000000E-2 +#define ASINH_MAC07 -4.4642857142857142857142857142857142857142857142857142857142857142857143E-2 +#define ASINH_MAC09 3.0381944444444444444444444444444444444444444444444444444444444444444444E-2 +#define ASINH_MAC11 -2.2372159090909090909090909090909090909090909090909090909090909090909091E-2 +#define ASINH_MAC13 1.7352764423076923076923076923076923076923076923076923076923076923076923E-2 +#define ASINH_MAC15 -1.3964843750000000000000000000000000000000000000000000000000000000000000E-2 +#define ASINH_MAC17 1.1551800896139705882352941176470588235294117647058823529411764705882353E-2 +#if 0 +#define ASINH_MAC19 -9.7616095291940789473684210526315789473684210526315789473684210526315789E-3 +#define ASINH_MAC21 8.3903358096168154761904761904761904761904761904761904761904761904761905E-3 +#define ASINH_MAC23 -7.3125258735988451086956521739130434782608695652173913043478260869565217E-3 +#define ASINH_MAC25 6.4472103118896484375000000000000000000000000000000000000000000000000000E-3 +#define ASINH_MAC27 -5.7400376708419234664351851851851851851851851851851851851851851851851852E-3 +#define ASINH_MAC29 5.1533096823199041958512931034482758620689655172413793103448275862068966E-3 +#define ASINH_MAC31 -4.6601434869150961599042338709677419354838709677419354838709677419354839E-3 +#define ASINH_MAC33 4.2409070936793630773370916193181818181818181818181818181818181818181818E-3 +#define ASINH_MAC35 -3.8809645588376692363194056919642857142857142857142857142857142857142857E-3 +#define ASINH_MAC37 3.5692053938259345454138678473395270270270270270270270270270270270270270E-3 +#define ASINH_MAC39 -3.2970595034734847453924325796274038461538461538461538461538461538461538E-3 +#define ASINH_MAC41 3.0578216492580306693548109473251714939024390243902439024390243902439024E-3 +#define ASINH_MAC43 -2.8461784011089421678767647854117460029069767441860465116279069767441860E-3 +#endif + + +static __inline vector double _asinhd2(vector double x) +{ + vec_double2 sign_mask = spu_splats(-0.0); + vec_double2 oned = spu_splats(1.0); + vec_uchar16 dup_even = ((vec_uchar16) { 0,1,2,3, 0,1,2,3, 8,9,10,11, 8,9,10,11 }); + vec_uint4 infminus1 = spu_splats(0x7FEFFFFFU); + vec_uint4 isinfnan; + vec_double2 xabs, xsqu; + vec_uint4 xabshigh; + /* Where we switch from maclaurin to formula */ + vec_float4 switch_approx = spu_splats(0.165f); + vec_uint4 use_form; + vec_float4 xf; + vec_double2 result, fresult, mresult; + + + xabs = spu_andc(x, sign_mask); + xsqu = spu_mul(x, x); + + xf = spu_roundtf(xabs); + xf = spu_shuffle(xf, xf, dup_even); + + /* + * Formula: + * asinh = ln(|x| + sqrt(x^2 + 1)) + */ + fresult = _sqrtd2(spu_add(xsqu, oned)); + fresult = spu_add(xabs, fresult); + fresult = _logd2(fresult); + + + /* + * Maclaurin Series approximation + */ + mresult = spu_madd(xsqu, spu_splats(ASINH_MAC17), spu_splats(ASINH_MAC15)); + mresult = spu_madd(xsqu, mresult, spu_splats(ASINH_MAC13)); + mresult = spu_madd(xsqu, mresult, spu_splats(ASINH_MAC11)); + mresult = spu_madd(xsqu, mresult, spu_splats(ASINH_MAC09)); + mresult = spu_madd(xsqu, mresult, spu_splats(ASINH_MAC07)); + mresult = spu_madd(xsqu, mresult, spu_splats(ASINH_MAC05)); + mresult = spu_madd(xsqu, mresult, spu_splats(ASINH_MAC03)); + mresult = spu_madd(xsqu, mresult, spu_splats(ASINH_MAC01)); + mresult = spu_mul(xabs, mresult); + + + /* + * Choose between series and formula + */ + use_form = spu_cmpgt(xf, switch_approx); + result = spu_sel(mresult, fresult, (vec_ullong2)use_form); + + + /* Special Cases */ + + /* Infinity and NaN */ + xabshigh = (vec_uint4)spu_shuffle(xabs, xabs, dup_even); + isinfnan = spu_cmpgt(xabshigh, infminus1); + result = spu_sel(result, x, (vec_ullong2)isinfnan); + + + /* Restore sign - asinh is an anti-symmetric */ + result = spu_sel(result, x, (vec_ullong2)sign_mask); + + return result; +} + +#endif /* _ASINHD2_H_ */ +#endif /* __SPU__ */ |