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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 _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__ */
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