161 lines
7.6 KiB
C
161 lines
7.6 KiB
C
/* -------------------------------------------------------------- */
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/* (C)Copyright 2007,2008, */
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/* International Business Machines Corporation */
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/* All Rights Reserved. */
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/* */
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/* Redistribution and use in source and binary forms, with or */
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/* without modification, are permitted provided that the */
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/* following conditions are met: */
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/* */
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/* - Redistributions of source code must retain the above copyright*/
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/* notice, this list of conditions and the following disclaimer. */
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/* */
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/* - Redistributions in binary form must reproduce the above */
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/* copyright notice, this list of conditions and the following */
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/* disclaimer in the documentation and/or other materials */
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/* provided with the distribution. */
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/* */
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/* - Neither the name of IBM Corporation nor the names of its */
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/* contributors may be used to endorse or promote products */
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/* derived from this software without specific prior written */
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/* permission. */
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/* */
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/* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND */
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/* CONTRIBUTORS "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, */
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/* INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF */
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/* MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE */
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/* DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR */
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/* CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, */
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/* SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT */
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/* NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; */
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/* LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) */
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/* HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN */
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/* CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR */
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/* OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, */
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/* EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. */
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/* -------------------------------------------------------------- */
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/* PROLOG END TAG zYx */
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#ifdef __SPU__
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#ifndef _ACOSHF4_H_
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#define _ACOSHF4_H_ 1
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#include <spu_intrinsics.h>
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#include "logf4.h"
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#include "sqrtf4.h"
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/*
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* FUNCTION
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* vector float _acoshf4(vector float x)
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*
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* DESCRIPTION
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* The acoshf4 function returns a vector containing the hyperbolic
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* arccosines of the corresponding elements of the input vector.
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*
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* We are using the formula:
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* acosh = ln(x + sqrt(x^2 - 1))
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*
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* For x near one, we use the Taylor series:
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*
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* infinity
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* ------
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* - '
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* - k
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* acosh x = - C (x - 1)
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* - k
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* - ,
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* ------
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* k = 0
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*
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*
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* Special Cases:
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* - acosh(1) = +0
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* - NaNs and Infinity aren't supported for single-precision on SPU.
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*
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*/
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/*
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* Taylor Series Coefficients
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* for x around 1.
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*/
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#define SDM_ACOSHF4_TAY01 1.00000000000000000000000000000000000E0f /* 1 / 1 */
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#define SDM_ACOSHF4_TAY02 -8.33333333333333333333333333333333333E-2f /* 1 / 12 */
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#define SDM_ACOSHF4_TAY03 1.87500000000000000000000000000000000E-2f /* 3 / 160 */
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#define SDM_ACOSHF4_TAY04 -5.58035714285714285714285714285714286E-3f /* 5 / 896 */
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#define SDM_ACOSHF4_TAY05 1.89887152777777777777777777777777778E-3f /* 35 / 18432 */
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#define SDM_ACOSHF4_TAY06 -6.99129971590909090909090909090909091E-4f /* 63 / 90112 */
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#define SDM_ACOSHF4_TAY07 2.71136944110576923076923076923076923E-4f /* 231 / 851968 */
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#define SDM_ACOSHF4_TAY08 -1.09100341796875000000000000000000000E-4f /* 143 / 1310720 */
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#define SDM_ACOSHF4_TAY09 4.51242222505457261029411764705882353E-5f /* 6435 / 142606336 */
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#define SDM_ACOSHF4_TAY10 -1.90656436117071854440789473684210526E-5f /* 12155 / 637534208 */
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#define SDM_ACOSHF4_TAY11 8.19368731407892136346726190476190476E-6f /* 46189 / 5637144576 */
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#define SDM_ACOSHF4_TAY12 -3.57056927421818608823029891304347826E-6f /* 88179 / 24696061952 */
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#define SDM_ACOSHF4_TAY13 1.57402595505118370056152343750000000E-6f /* 676039 / 429496729600 */
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#define SDM_ACOSHF4_TAY14 -7.00688192241445735648826316550925926E-7f /* 1300075 / 1855425871872 */
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#define SDM_ACOSHF4_TAY15 3.14533061665033215078814276333512931E-7f /* 5014575 / 15942918602752 */
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#if 0
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#define SDM_ACOSHF4_TAY16 -1.42216292935641362301764949675529234E-7f /* 9694845 / 68169720922112 */
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#define SDM_ACOSHF4_TAY17 6.47111067761133282064375552264126864E-8f /* 100180065 / 1548112371908608 */
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#define SDM_ACOSHF4_TAY18 -2.96094097811711825280716376645224435E-8f /* 116680311 / 3940649673949184 */
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#define SDM_ACOSHF4_TAY19 1.36154380562817937676005090612011987E-8f /* 2268783825 / 166633186212708352 */
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#endif
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static __inline vector float _acoshf4(vector float x)
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{
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vec_float4 minus_onef = spu_splats(-1.0f);
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vec_float4 twof = spu_splats(2.0f);
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vec_float4 largef = spu_splats(2.5e19f);
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vec_float4 xminus1;
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/* Where we switch from taylor to formula */
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vec_float4 switch_approx = spu_splats(2.0f);
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vec_uint4 use_form;
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vec_float4 result, fresult, mresult;;
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/*
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* Formula:
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* acosh = ln(x + sqrt(x^2 - 1))
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*/
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fresult = _sqrtf4(spu_madd(x, x, minus_onef));
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fresult = spu_add(x, spu_sel(fresult, x, spu_cmpgt(x, largef)));
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fresult = _logf4(fresult);
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fresult = (vec_float4)spu_add((vec_uint4)fresult, spu_splats(2u));
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/*
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* Taylor Series
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*/
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xminus1 = spu_add(x, minus_onef);
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mresult = spu_splats(SDM_ACOSHF4_TAY15);
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mresult = spu_madd(xminus1, mresult, spu_splats(SDM_ACOSHF4_TAY14));
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mresult = spu_madd(xminus1, mresult, spu_splats(SDM_ACOSHF4_TAY13));
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mresult = spu_madd(xminus1, mresult, spu_splats(SDM_ACOSHF4_TAY12));
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mresult = spu_madd(xminus1, mresult, spu_splats(SDM_ACOSHF4_TAY11));
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mresult = spu_madd(xminus1, mresult, spu_splats(SDM_ACOSHF4_TAY10));
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mresult = spu_madd(xminus1, mresult, spu_splats(SDM_ACOSHF4_TAY09));
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mresult = spu_madd(xminus1, mresult, spu_splats(SDM_ACOSHF4_TAY08));
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mresult = spu_madd(xminus1, mresult, spu_splats(SDM_ACOSHF4_TAY07));
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mresult = spu_madd(xminus1, mresult, spu_splats(SDM_ACOSHF4_TAY06));
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mresult = spu_madd(xminus1, mresult, spu_splats(SDM_ACOSHF4_TAY05));
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mresult = spu_madd(xminus1, mresult, spu_splats(SDM_ACOSHF4_TAY04));
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mresult = spu_madd(xminus1, mresult, spu_splats(SDM_ACOSHF4_TAY03));
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mresult = spu_madd(xminus1, mresult, spu_splats(SDM_ACOSHF4_TAY02));
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mresult = spu_madd(xminus1, mresult, spu_splats(SDM_ACOSHF4_TAY01));
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mresult = spu_mul(mresult, _sqrtf4(spu_mul(xminus1, twof)));
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mresult = (vec_float4)spu_add((vec_uint4)mresult, spu_splats(1u));
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/*
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* Select series or formula
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*/
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use_form = spu_cmpgt(x, switch_approx);
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result = spu_sel(mresult, fresult, use_form);
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return result;
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}
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#endif /* _ACOSHF4_H_ */
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#endif /* __SPU__ */
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