/* -------------------------------------------------------------- */ /* (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 _ACOSHF4_H_ #define _ACOSHF4_H_ 1 #include #include "logf4.h" #include "sqrtf4.h" /* * FUNCTION * vector float _acoshf4(vector float x) * * DESCRIPTION * The acoshf4 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 * - NaNs and Infinity aren't supported for single-precision on SPU. * */ /* * Taylor Series Coefficients * for x around 1. */ #define SDM_ACOSHF4_TAY01 1.00000000000000000000000000000000000E0f /* 1 / 1 */ #define SDM_ACOSHF4_TAY02 -8.33333333333333333333333333333333333E-2f /* 1 / 12 */ #define SDM_ACOSHF4_TAY03 1.87500000000000000000000000000000000E-2f /* 3 / 160 */ #define SDM_ACOSHF4_TAY04 -5.58035714285714285714285714285714286E-3f /* 5 / 896 */ #define SDM_ACOSHF4_TAY05 1.89887152777777777777777777777777778E-3f /* 35 / 18432 */ #define SDM_ACOSHF4_TAY06 -6.99129971590909090909090909090909091E-4f /* 63 / 90112 */ #define SDM_ACOSHF4_TAY07 2.71136944110576923076923076923076923E-4f /* 231 / 851968 */ #define SDM_ACOSHF4_TAY08 -1.09100341796875000000000000000000000E-4f /* 143 / 1310720 */ #define SDM_ACOSHF4_TAY09 4.51242222505457261029411764705882353E-5f /* 6435 / 142606336 */ #define SDM_ACOSHF4_TAY10 -1.90656436117071854440789473684210526E-5f /* 12155 / 637534208 */ #define SDM_ACOSHF4_TAY11 8.19368731407892136346726190476190476E-6f /* 46189 / 5637144576 */ #define SDM_ACOSHF4_TAY12 -3.57056927421818608823029891304347826E-6f /* 88179 / 24696061952 */ #define SDM_ACOSHF4_TAY13 1.57402595505118370056152343750000000E-6f /* 676039 / 429496729600 */ #define SDM_ACOSHF4_TAY14 -7.00688192241445735648826316550925926E-7f /* 1300075 / 1855425871872 */ #define SDM_ACOSHF4_TAY15 3.14533061665033215078814276333512931E-7f /* 5014575 / 15942918602752 */ #if 0 #define SDM_ACOSHF4_TAY16 -1.42216292935641362301764949675529234E-7f /* 9694845 / 68169720922112 */ #define SDM_ACOSHF4_TAY17 6.47111067761133282064375552264126864E-8f /* 100180065 / 1548112371908608 */ #define SDM_ACOSHF4_TAY18 -2.96094097811711825280716376645224435E-8f /* 116680311 / 3940649673949184 */ #define SDM_ACOSHF4_TAY19 1.36154380562817937676005090612011987E-8f /* 2268783825 / 166633186212708352 */ #endif static __inline vector float _acoshf4(vector float x) { vec_float4 minus_onef = spu_splats(-1.0f); vec_float4 twof = spu_splats(2.0f); vec_float4 largef = spu_splats(2.5e19f); vec_float4 xminus1; /* Where we switch from taylor to formula */ vec_float4 switch_approx = spu_splats(2.0f); vec_uint4 use_form; vec_float4 result, fresult, mresult;; /* * Formula: * acosh = ln(x + sqrt(x^2 - 1)) */ fresult = _sqrtf4(spu_madd(x, x, minus_onef)); fresult = spu_add(x, spu_sel(fresult, x, spu_cmpgt(x, largef))); fresult = _logf4(fresult); fresult = (vec_float4)spu_add((vec_uint4)fresult, spu_splats(2u)); /* * Taylor Series */ xminus1 = spu_add(x, minus_onef); mresult = spu_splats(SDM_ACOSHF4_TAY15); mresult = spu_madd(xminus1, mresult, spu_splats(SDM_ACOSHF4_TAY14)); mresult = spu_madd(xminus1, mresult, spu_splats(SDM_ACOSHF4_TAY13)); mresult = spu_madd(xminus1, mresult, spu_splats(SDM_ACOSHF4_TAY12)); mresult = spu_madd(xminus1, mresult, spu_splats(SDM_ACOSHF4_TAY11)); mresult = spu_madd(xminus1, mresult, spu_splats(SDM_ACOSHF4_TAY10)); mresult = spu_madd(xminus1, mresult, spu_splats(SDM_ACOSHF4_TAY09)); mresult = spu_madd(xminus1, mresult, spu_splats(SDM_ACOSHF4_TAY08)); mresult = spu_madd(xminus1, mresult, spu_splats(SDM_ACOSHF4_TAY07)); mresult = spu_madd(xminus1, mresult, spu_splats(SDM_ACOSHF4_TAY06)); mresult = spu_madd(xminus1, mresult, spu_splats(SDM_ACOSHF4_TAY05)); mresult = spu_madd(xminus1, mresult, spu_splats(SDM_ACOSHF4_TAY04)); mresult = spu_madd(xminus1, mresult, spu_splats(SDM_ACOSHF4_TAY03)); mresult = spu_madd(xminus1, mresult, spu_splats(SDM_ACOSHF4_TAY02)); mresult = spu_madd(xminus1, mresult, spu_splats(SDM_ACOSHF4_TAY01)); mresult = spu_mul(mresult, _sqrtf4(spu_mul(xminus1, twof))); mresult = (vec_float4)spu_add((vec_uint4)mresult, spu_splats(1u)); /* * Select series or formula */ use_form = spu_cmpgt(x, switch_approx); result = spu_sel(mresult, fresult, use_form); return result; } #endif /* _ACOSHF4_H_ */ #endif /* __SPU__ */