/* -------------------------------------------------------------- */ /* (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 _ATANHD2_H_ #define _ATANHD2_H_ 1 #include #include "logd2.h" /* * FUNCTION * vector double _atanhd2(vector double x) * * DESCRIPTION * The atanhd2 function returns a vector containing the hyperbolic * arctangents of the corresponding elements of the input vector. * * We are using the formula: * atanh x = 1/2 * ln((1 + x)/(1 - x)) = 1/2 * [ln(1+x) - ln(1-x)] * and the anti-symmetry of atanh. * * For x near 0, we use the Taylor series: * atanh x = x + x^3/3 + x^5/5 + x^7/7 + x^9/9 + ... * * Special Cases: * - atanh(1) = Infinity * - atanh(-1) = -Infinity * - atanh(x) for |x| > 1 = Undefined * */ /* * Maclaurin Series Coefficients * for x near 0. */ #define SMD_DP_ATANH_MAC01 1.000000000000000000000000000000E0 #define SMD_DP_ATANH_MAC03 3.333333333333333333333333333333E-1 #define SMD_DP_ATANH_MAC05 2.000000000000000000000000000000E-1 #define SMD_DP_ATANH_MAC07 1.428571428571428571428571428571E-1 #define SMD_DP_ATANH_MAC09 1.111111111111111111111111111111E-1 #define SMD_DP_ATANH_MAC11 9.090909090909090909090909090909E-2 #define SMD_DP_ATANH_MAC13 7.692307692307692307692307692308E-2 #define SMD_DP_ATANH_MAC15 6.666666666666666666666666666667E-2 #define SMD_DP_ATANH_MAC17 5.882352941176470588235294117647E-2 #if 0 #define SMD_DP_ATANH_MAC19 5.263157894736842105263157894737E-2 #define SMD_DP_ATANH_MAC21 4.761904761904761904761904761905E-2 #define SMD_DP_ATANH_MAC23 4.347826086956521739130434782609E-2 #define SMD_DP_ATANH_MAC25 4.000000000000000000000000000000E-2 #define SMD_DP_ATANH_MAC27 3.703703703703703703703703703704E-2 #define SMD_DP_ATANH_MAC29 3.448275862068965517241379310345E-2 #define SMD_DP_ATANH_MAC31 3.225806451612903225806451612903E-2 #define SMD_DP_ATANH_MAC33 3.030303030303030303030303030303E-2 #define SMD_DP_ATANH_MAC35 2.857142857142857142857142857143E-2 #define SMD_DP_ATANH_MAC37 2.702702702702702702702702702703E-2 #define SMD_DP_ATANH_MAC39 2.564102564102564102564102564103E-2 #endif static __inline vector double _atanhd2(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 sign_mask = spu_splats(-0.0); vec_double2 oned = spu_splats(1.0); vec_double2 onehalfd = spu_splats(0.5); vec_double2 xabs, xsqu; /* Where we switch from maclaurin to formula */ vec_float4 switch_approx = spu_splats(0.125f); 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: * atanh = 1/2 * ln((1 + x)/(1 - x)) = 1/2 * [ln(1+x) - ln(1-x)] */ fresult = spu_sub(_logd2(spu_add(oned, xabs)), _logd2(spu_sub(oned, xabs))); fresult = spu_mul(fresult, onehalfd); /* * Taylor Series */ mresult = spu_madd(xsqu, spu_splats(SMD_DP_ATANH_MAC17), spu_splats(SMD_DP_ATANH_MAC15)); mresult = spu_madd(xsqu, mresult, spu_splats(SMD_DP_ATANH_MAC13)); mresult = spu_madd(xsqu, mresult, spu_splats(SMD_DP_ATANH_MAC11)); mresult = spu_madd(xsqu, mresult, spu_splats(SMD_DP_ATANH_MAC09)); mresult = spu_madd(xsqu, mresult, spu_splats(SMD_DP_ATANH_MAC07)); mresult = spu_madd(xsqu, mresult, spu_splats(SMD_DP_ATANH_MAC05)); mresult = spu_madd(xsqu, mresult, spu_splats(SMD_DP_ATANH_MAC03)); mresult = spu_madd(xsqu, mresult, spu_splats(SMD_DP_ATANH_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); /* * Spec says results are undefined for |x| > 1, so * no boundary tests needed here. */ /* Restore sign - atanh is an anti-symmetric */ result = spu_sel(result, x, (vec_ullong2)sign_mask); return result; } #endif /* _ATANHD2_H_ */ #endif /* __SPU__ */