/* -------------------------------------------------------------- */ /* (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 _ASINHF4_H_ #define _ASINHF4_H_ 1 #include #include "logf4.h" #include "sqrtf4.h" /* * FUNCTION * vector float _asinhf4(vector float x) * * DESCRIPTION * The asinhf4 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 * - Normally, asinh(+/- infinity) returns +/- infinity, * but on the SPU, single-precision infinity is not supported, * so it is treated as a normal number here. * */ /* * 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 #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 #if 0 #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 float _asinhf4(vector float x) { vec_float4 sign_mask = spu_splats(-0.0f); vec_float4 onef = spu_splats(1.0f); vec_uint4 oneu = spu_splats(1u); vec_uint4 twou = spu_splats(2u); vec_uint4 threeu = spu_splats(3u); vec_float4 ln2 = spu_splats(6.931471805599453094172321E-1f); vec_float4 largef = spu_splats(9.21e18f); vec_float4 result, fresult, mresult; vec_float4 xabs, xsqu; /* Where we switch from maclaurin to formula */ vec_float4 switch_approx = spu_splats(0.74f); vec_float4 trunc_part2 = spu_splats(20.0f); vec_uint4 truncadd; vec_uint4 islarge; vec_uint4 use_form; xabs = spu_andc(x, sign_mask); xsqu = spu_mul(x, x); islarge = spu_cmpgt(xabs, largef); /* * Formula: * asinh = ln(|x| + sqrt(x^2 + 1)) */ vec_float4 logarg = spu_add(xabs, _sqrtf4(spu_madd(xabs, xabs, onef))); logarg = spu_sel(logarg, xabs, islarge); fresult = _logf4(logarg); fresult = spu_sel(fresult, spu_add(fresult, ln2), islarge); /* * Maclaurin Series */ mresult = spu_madd(xsqu, spu_splats((float)ASINH_MAC31), spu_splats((float)ASINH_MAC29)); mresult = spu_madd(xsqu, mresult, spu_splats((float)ASINH_MAC27)); mresult = spu_madd(xsqu, mresult, spu_splats((float)ASINH_MAC25)); mresult = spu_madd(xsqu, mresult, spu_splats((float)ASINH_MAC23)); mresult = spu_madd(xsqu, mresult, spu_splats((float)ASINH_MAC21)); mresult = spu_madd(xsqu, mresult, spu_splats((float)ASINH_MAC19)); mresult = spu_madd(xsqu, mresult, spu_splats((float)ASINH_MAC17)); mresult = spu_madd(xsqu, mresult, spu_splats((float)ASINH_MAC15)); mresult = spu_madd(xsqu, mresult, spu_splats((float)ASINH_MAC13)); mresult = spu_madd(xsqu, mresult, spu_splats((float)ASINH_MAC11)); mresult = spu_madd(xsqu, mresult, spu_splats((float)ASINH_MAC09)); mresult = spu_madd(xsqu, mresult, spu_splats((float)ASINH_MAC07)); mresult = spu_madd(xsqu, mresult, spu_splats((float)ASINH_MAC05)); mresult = spu_madd(xsqu, mresult, spu_splats((float)ASINH_MAC03)); mresult = spu_madd(xsqu, mresult, spu_splats((float)ASINH_MAC01)); mresult = spu_mul(xabs, mresult); /* * Choose between series and formula */ use_form = spu_cmpgt(xabs, switch_approx); result = spu_sel(mresult, fresult, use_form); /* * Truncation correction on spu */ truncadd = spu_sel(oneu, threeu, use_form); truncadd = spu_sel(truncadd, twou, spu_cmpgt(xabs, trunc_part2)); result = (vec_float4)spu_add((vec_uint4)result, truncadd); /* Preserve sign - asinh is anti-symmetric */ result = spu_sel(result, x, (vec_uint4)sign_mask); return result; } #endif /* _ASINHF4_H_ */ #endif /* __SPU__ */