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/* -------------------------------------------------------------- */
/* (C)Copyright 2007,2008, */
/* 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. */
/* */
/* 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 _ACOSHD2_H_
#define _ACOSHD2_H_ 1
#include <spu_intrinsics.h>
#include "logd2.h"
#include "sqrtd2.h"
/*
* FUNCTION
* vector double _acoshd2(vector double x)
*
* DESCRIPTION
* The acoshd2 function returns a vector containing the hyperbolic
* arccosines of the corresponding elements of the input vector.
*
* We are using the formula:
* acosh = ln(x + sqrt(x^2 - 1))
*
* For x near one, we use the Taylor series:
*
* infinity
* ------
* - '
* - k
* acosh x = - C (x - 1)
* - k
* - ,
* ------
* k = 0
*
*
* Special Cases:
* - acosh(1) = +0
* - acosh(NaN) = NaN
* - acosh(Infinity) = Infinity
* - acosh(x < 1) = NaN
*
*/
/*
* Taylor Series Coefficients
* for x around 1.
*/
#define SDM_ACOSHD2_TAY01 1.000000000000000000000000000000000E0 /* 1 / 1 */
#define SDM_ACOSHD2_TAY02 -8.333333333333333333333333333333333E-2 /* 1 / 12 */
#define SDM_ACOSHD2_TAY03 1.875000000000000000000000000000000E-2 /* 3 / 160 */
#define SDM_ACOSHD2_TAY04 -5.580357142857142857142857142857142E-3 /* 5 / 896 */
#define SDM_ACOSHD2_TAY05 1.898871527777777777777777777777777E-3 /* 35 / 18432 */
#define SDM_ACOSHD2_TAY06 -6.991299715909090909090909090909090E-4 /* 63 / 90112 */
#define SDM_ACOSHD2_TAY07 2.711369441105769230769230769230769E-4 /* 231 / 851968 */
#define SDM_ACOSHD2_TAY08 -1.091003417968750000000000000000000E-4 /* 143 / 1310720 */
#define SDM_ACOSHD2_TAY09 4.512422225054572610294117647058823E-5 /* 6435 / 142606336 */
#define SDM_ACOSHD2_TAY10 -1.906564361170718544407894736842105E-5 /* 12155 / 637534208 */
#define SDM_ACOSHD2_TAY11 8.193687314078921363467261904761904E-6 /* 46189 / 5637144576 */
#define SDM_ACOSHD2_TAY12 -3.570569274218186088230298913043478E-6 /* 88179 / 24696061952 */
#define SDM_ACOSHD2_TAY13 1.574025955051183700561523437500000E-6 /* 676039 / 429496729600 */
#define SDM_ACOSHD2_TAY14 -7.006881922414457356488263165509259E-7 /* 1300075 / 1855425871872 */
#define SDM_ACOSHD2_TAY15 3.145330616650332150788142763335129E-7 /* 5014575 / 15942918602752 */
static __inline vector double _acoshd2(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_double2 minus_oned = spu_splats(-1.0);
vec_double2 twod = spu_splats(2.0);
/* Where we switch from taylor to formula */
vec_float4 switch_approx = spu_splats(1.15f);
vec_double2 result, fresult, mresult;;
vec_double2 xminus1 = spu_add(x, minus_oned);
vec_float4 xf = spu_roundtf(x);
xf = spu_shuffle(xf, xf, dup_even);
vec_ullong2 use_form = (vec_ullong2)spu_cmpgt(xf, switch_approx);
vec_double2 sqrtargformula = spu_madd(x, x, minus_oned);
vec_double2 sqrtargtaylor = spu_mul(xminus1, twod);
vec_double2 sqrtarg = spu_sel(sqrtargtaylor, sqrtargformula, use_form);
vec_double2 sqrtresult = _sqrtd2(sqrtarg);
/*
* Formula:
* acosh = ln(x + sqrt(x^2 - 1))
*/
fresult = spu_add(x, sqrtresult);
fresult = _logd2(fresult);
/*
* Taylor Series
*/
mresult = spu_splats(SDM_ACOSHD2_TAY15);
mresult = spu_madd(xminus1, mresult, spu_splats(SDM_ACOSHD2_TAY14));
mresult = spu_madd(xminus1, mresult, spu_splats(SDM_ACOSHD2_TAY13));
mresult = spu_madd(xminus1, mresult, spu_splats(SDM_ACOSHD2_TAY12));
mresult = spu_madd(xminus1, mresult, spu_splats(SDM_ACOSHD2_TAY11));
mresult = spu_madd(xminus1, mresult, spu_splats(SDM_ACOSHD2_TAY10));
mresult = spu_madd(xminus1, mresult, spu_splats(SDM_ACOSHD2_TAY09));
mresult = spu_madd(xminus1, mresult, spu_splats(SDM_ACOSHD2_TAY08));
mresult = spu_madd(xminus1, mresult, spu_splats(SDM_ACOSHD2_TAY07));
mresult = spu_madd(xminus1, mresult, spu_splats(SDM_ACOSHD2_TAY06));
mresult = spu_madd(xminus1, mresult, spu_splats(SDM_ACOSHD2_TAY05));
mresult = spu_madd(xminus1, mresult, spu_splats(SDM_ACOSHD2_TAY04));
mresult = spu_madd(xminus1, mresult, spu_splats(SDM_ACOSHD2_TAY03));
mresult = spu_madd(xminus1, mresult, spu_splats(SDM_ACOSHD2_TAY02));
mresult = spu_madd(xminus1, mresult, spu_splats(SDM_ACOSHD2_TAY01));
mresult = spu_mul(mresult, sqrtresult);
/*
* Select series or formula
*/
result = spu_sel(mresult, fresult, use_form);
return result;
}
#endif /* _ACOSHD2_H_ */
#endif /* __SPU__ */
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