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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 _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 SDM_ASINHD2_MAC01 1.000000000000000000000000000000000000000000E0 #define SDM_ASINHD2_MAC03 -1.666666666666666666666666666666666666666667E-1 #define SDM_ASINHD2_MAC05 7.500000000000000000000000000000000000000000E-2 #define SDM_ASINHD2_MAC07 -4.464285714285714285714285714285714285714286E-2 #define SDM_ASINHD2_MAC09 3.038194444444444444444444444444444444444444E-2 #define SDM_ASINHD2_MAC11 -2.237215909090909090909090909090909090909091E-2 #define SDM_ASINHD2_MAC13 1.735276442307692307692307692307692307692308E-2 #define SDM_ASINHD2_MAC15 -1.396484375000000000000000000000000000000000E-2 #define SDM_ASINHD2_MAC17 1.155180089613970588235294117647058823529412E-2 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; vec_float4 switch_approx = spu_splats(0.165f); /* Where we switch from maclaurin to formula */ 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_splats(SDM_ASINHD2_MAC17); mresult = spu_madd(xsqu, mresult, spu_splats(SDM_ASINHD2_MAC15)); mresult = spu_madd(xsqu, mresult, spu_splats(SDM_ASINHD2_MAC13)); mresult = spu_madd(xsqu, mresult, spu_splats(SDM_ASINHD2_MAC11)); mresult = spu_madd(xsqu, mresult, spu_splats(SDM_ASINHD2_MAC09)); mresult = spu_madd(xsqu, mresult, spu_splats(SDM_ASINHD2_MAC07)); mresult = spu_madd(xsqu, mresult, spu_splats(SDM_ASINHD2_MAC05)); mresult = spu_madd(xsqu, mresult, spu_splats(SDM_ASINHD2_MAC03)); mresult = spu_madd(xsqu, mresult, spu_splats(SDM_ASINHD2_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__ */