178 lines
8.8 KiB
C
178 lines
8.8 KiB
C
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/* -------------------------------------------------------------- */
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/* (C)Copyright 2006,2007, */
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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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/* 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 _ATANHD2_H_
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#define _ATANHD2_H_ 1
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#include <spu_intrinsics.h>
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#include "logd2.h"
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/*
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* FUNCTION
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* vector double _atanhd2(vector double x)
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*
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* DESCRIPTION
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* The atanhd2 function returns a vector containing the hyperbolic
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* arctangents 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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* atanh x = 1/2 * ln((1 + x)/(1 - x)) = 1/2 * [ln(1+x) - ln(1-x)]
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* and the anti-symmetry of atanh.
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*
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* For x near 0, we use the Taylor series:
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* atanh x = x + x^3/3 + x^5/5 + x^7/7 + x^9/9 + ...
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*
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* Special Cases:
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* - atanh(1) = Infinity
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* - atanh(-1) = -Infinity
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* - atanh(x) for |x| > 1 = NaN
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*
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*/
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/*
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* Maclaurin Series Coefficients
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* for x near 0.
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*/
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#define ATANH_MAC01 1.0000000000000000000000000000000000000000000000000000000000000000000000E0
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#define ATANH_MAC03 3.3333333333333333333333333333333333333333333333333333333333333333333333E-1
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#define ATANH_MAC05 2.0000000000000000000000000000000000000000000000000000000000000000000000E-1
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#define ATANH_MAC07 1.4285714285714285714285714285714285714285714285714285714285714285714286E-1
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#define ATANH_MAC09 1.1111111111111111111111111111111111111111111111111111111111111111111111E-1
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#define ATANH_MAC11 9.0909090909090909090909090909090909090909090909090909090909090909090909E-2
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#define ATANH_MAC13 7.6923076923076923076923076923076923076923076923076923076923076923076923E-2
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#if 0
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#define ATANH_MAC15 6.6666666666666666666666666666666666666666666666666666666666666666666667E-2
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#define ATANH_MAC17 5.8823529411764705882352941176470588235294117647058823529411764705882353E-2
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#define ATANH_MAC19 5.2631578947368421052631578947368421052631578947368421052631578947368421E-2
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#define ATANH_MAC21 4.7619047619047619047619047619047619047619047619047619047619047619047619E-2
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#define ATANH_MAC23 4.3478260869565217391304347826086956521739130434782608695652173913043478E-2
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#define ATANH_MAC25 4.0000000000000000000000000000000000000000000000000000000000000000000000E-2
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#define ATANH_MAC27 3.7037037037037037037037037037037037037037037037037037037037037037037037E-2
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#define ATANH_MAC29 3.4482758620689655172413793103448275862068965517241379310344827586206897E-2
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#define ATANH_MAC31 3.2258064516129032258064516129032258064516129032258064516129032258064516E-2
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#define ATANH_MAC33 3.0303030303030303030303030303030303030303030303030303030303030303030303E-2
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#define ATANH_MAC35 2.8571428571428571428571428571428571428571428571428571428571428571428571E-2
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#define ATANH_MAC37 2.7027027027027027027027027027027027027027027027027027027027027027027027E-2
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#define ATANH_MAC39 2.5641025641025641025641025641025641025641025641025641025641025641025641E-2
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#define ATANH_MAC41 2.4390243902439024390243902439024390243902439024390243902439024390243902E-2
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#define ATANH_MAC43 2.3255813953488372093023255813953488372093023255813953488372093023255814E-2
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#define ATANH_MAC45 2.2222222222222222222222222222222222222222222222222222222222222222222222E-2
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#define ATANH_MAC47 2.1276595744680851063829787234042553191489361702127659574468085106382979E-2
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#define ATANH_MAC49 2.0408163265306122448979591836734693877551020408163265306122448979591837E-2
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#define ATANH_MAC51 1.9607843137254901960784313725490196078431372549019607843137254901960784E-2
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#define ATANH_MAC53 1.8867924528301886792452830188679245283018867924528301886792452830188679E-2
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#define ATANH_MAC55 1.8181818181818181818181818181818181818181818181818181818181818181818182E-2
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#define ATANH_MAC57 1.7543859649122807017543859649122807017543859649122807017543859649122807E-2
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#define ATANH_MAC59 1.6949152542372881355932203389830508474576271186440677966101694915254237E-2
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#endif
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static __inline vector double _atanhd2(vector double x)
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{
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vec_uchar16 dup_even = ((vec_uchar16) { 0,1,2,3, 0,1,2,3, 8,9,10,11, 8,9,10,11 });
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vec_double2 sign_mask = spu_splats(-0.0);
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vec_double2 oned = spu_splats(1.0);
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vec_double2 onehalfd = spu_splats(0.5);
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vec_uint4 infminus1 = spu_splats(0x7FEFFFFFU);
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vec_uint4 isinfnan;
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vec_uint4 xabshigh;
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vec_double2 xabs, xsqu;
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/* Where we switch from maclaurin to formula */
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vec_float4 switch_approx = spu_splats(0.08f);
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vec_uint4 use_form;
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vec_float4 xf;
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vec_double2 result, fresult, mresult;;
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xabs = spu_andc(x, sign_mask);
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xsqu = spu_mul(x, x);
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xf = spu_roundtf(xabs);
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xf = spu_shuffle(xf, xf, dup_even);
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/*
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* Formula:
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* atanh = 1/2 * ln((1 + x)/(1 - x)) = 1/2 * [ln(1+x) - ln(1-x)]
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*/
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fresult = spu_sub(_logd2(spu_add(oned, xabs)), _logd2(spu_sub(oned, xabs)));
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fresult = spu_mul(fresult, onehalfd);
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/*
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* Taylor Series
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*/
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mresult = spu_madd(xsqu, spu_splats(ATANH_MAC13), spu_splats(ATANH_MAC11));
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mresult = spu_madd(xsqu, mresult, spu_splats(ATANH_MAC09));
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mresult = spu_madd(xsqu, mresult, spu_splats(ATANH_MAC07));
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mresult = spu_madd(xsqu, mresult, spu_splats(ATANH_MAC05));
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mresult = spu_madd(xsqu, mresult, spu_splats(ATANH_MAC03));
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mresult = spu_madd(xsqu, mresult, spu_splats(ATANH_MAC01));
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mresult = spu_mul(xabs, mresult);
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/*
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* Choose between series and formula
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*/
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use_form = spu_cmpgt(xf, switch_approx);
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result = spu_sel(mresult, fresult, (vec_ullong2)use_form);
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/* Infinity and NaN */
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xabshigh = (vec_uint4)spu_shuffle(xabs, xabs, dup_even);
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isinfnan = spu_cmpgt(xabshigh, infminus1);
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result = spu_sel(result, x, (vec_ullong2)isinfnan);
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/* Restore sign - atanh is an anti-symmetric */
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result = spu_sel(result, x, (vec_ullong2)sign_mask);
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return result;
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}
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#endif /* _ATANHD2_H_ */
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#endif /* __SPU__ */
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