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jeremybenn |
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/* (C)Copyright 2007,2008, */
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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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/* */
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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 = Undefined
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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 SMD_DP_ATANH_MAC01 1.000000000000000000000000000000E0
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#define SMD_DP_ATANH_MAC03 3.333333333333333333333333333333E-1
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#define SMD_DP_ATANH_MAC05 2.000000000000000000000000000000E-1
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#define SMD_DP_ATANH_MAC07 1.428571428571428571428571428571E-1
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#define SMD_DP_ATANH_MAC09 1.111111111111111111111111111111E-1
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#define SMD_DP_ATANH_MAC11 9.090909090909090909090909090909E-2
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#define SMD_DP_ATANH_MAC13 7.692307692307692307692307692308E-2
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#define SMD_DP_ATANH_MAC15 6.666666666666666666666666666667E-2
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#define SMD_DP_ATANH_MAC17 5.882352941176470588235294117647E-2
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#if 0
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#define SMD_DP_ATANH_MAC19 5.263157894736842105263157894737E-2
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#define SMD_DP_ATANH_MAC21 4.761904761904761904761904761905E-2
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#define SMD_DP_ATANH_MAC23 4.347826086956521739130434782609E-2
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#define SMD_DP_ATANH_MAC25 4.000000000000000000000000000000E-2
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#define SMD_DP_ATANH_MAC27 3.703703703703703703703703703704E-2
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#define SMD_DP_ATANH_MAC29 3.448275862068965517241379310345E-2
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#define SMD_DP_ATANH_MAC31 3.225806451612903225806451612903E-2
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#define SMD_DP_ATANH_MAC33 3.030303030303030303030303030303E-2
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#define SMD_DP_ATANH_MAC35 2.857142857142857142857142857143E-2
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#define SMD_DP_ATANH_MAC37 2.702702702702702702702702702703E-2
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#define SMD_DP_ATANH_MAC39 2.564102564102564102564102564103E-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_double2 xabs, xsqu;
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/* Where we switch from maclaurin to formula */
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vec_float4 switch_approx = spu_splats(0.125f);
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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(SMD_DP_ATANH_MAC17), spu_splats(SMD_DP_ATANH_MAC15));
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mresult = spu_madd(xsqu, mresult, spu_splats(SMD_DP_ATANH_MAC13));
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mresult = spu_madd(xsqu, mresult, spu_splats(SMD_DP_ATANH_MAC11));
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mresult = spu_madd(xsqu, mresult, spu_splats(SMD_DP_ATANH_MAC09));
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mresult = spu_madd(xsqu, mresult, spu_splats(SMD_DP_ATANH_MAC07));
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mresult = spu_madd(xsqu, mresult, spu_splats(SMD_DP_ATANH_MAC05));
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mresult = spu_madd(xsqu, mresult, spu_splats(SMD_DP_ATANH_MAC03));
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mresult = spu_madd(xsqu, mresult, spu_splats(SMD_DP_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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/*
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* Spec says results are undefined for |x| > 1, so
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* no boundary tests needed here.
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*/
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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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