173 lines
8.8 KiB
C
173 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 _ACOSHD2_H_
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#define _ACOSHD2_H_ 1
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#include <spu_intrinsics.h>
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#include "logd2.h"
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#include "sqrtd2.h"
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/*
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* FUNCTION
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* vector double _acoshd2(vector double x)
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*
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* DESCRIPTION
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* The acoshd2 function returns a vector containing the hyperbolic
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* arccosines 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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* acosh = ln(x + sqrt(x^2 - 1))
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*
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* For x near one, we use the Taylor series:
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*
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* infinity
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* ------
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* - '
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* - k
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* acosh x = - C (x - 1)
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* - k
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* - ,
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* ------
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* k = 0
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*
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*
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* Special Cases:
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* - acosh(1) = +0
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* - acosh(NaN) = NaN
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* - acosh(Infinity) = Infinity
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* - acosh(x < 1) = NaN
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*
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*/
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/*
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* Taylor Series Coefficients
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* for x around 1.
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*/
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#define ACOSH_TAY01 1.0000000000000000000000000000000000000000000000000000000000000000000000E0 /* 1 / 1 */
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#define ACOSH_TAY02 -8.3333333333333333333333333333333333333333333333333333333333333333333333E-2 /* 1 / 12 */
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#define ACOSH_TAY03 1.8750000000000000000000000000000000000000000000000000000000000000000000E-2 /* 3 / 160 */
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#define ACOSH_TAY04 -5.5803571428571428571428571428571428571428571428571428571428571428571429E-3 /* 5 / 896 */
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#define ACOSH_TAY05 1.8988715277777777777777777777777777777777777777777777777777777777777778E-3 /* 35 / 18432 */
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#define ACOSH_TAY06 -6.9912997159090909090909090909090909090909090909090909090909090909090909E-4 /* 63 / 90112 */
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#define ACOSH_TAY07 2.7113694411057692307692307692307692307692307692307692307692307692307692E-4 /* 231 / 851968 */
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#define ACOSH_TAY08 -1.0910034179687500000000000000000000000000000000000000000000000000000000E-4 /* 143 / 1310720 */
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#define ACOSH_TAY09 4.5124222250545726102941176470588235294117647058823529411764705882352941E-5 /* 6435 / 142606336 */
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#define ACOSH_TAY10 -1.9065643611707185444078947368421052631578947368421052631578947368421053E-5 /* 12155 / 637534208 */
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#define ACOSH_TAY11 8.1936873140789213634672619047619047619047619047619047619047619047619048E-6 /* 46189 / 5637144576 */
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#define ACOSH_TAY12 -3.5705692742181860882302989130434782608695652173913043478260869565217391E-6 /* 88179 / 24696061952 */
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#define ACOSH_TAY13 1.5740259550511837005615234375000000000000000000000000000000000000000000E-6 /* 676039 / 429496729600 */
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#define ACOSH_TAY14 -7.0068819224144573564882631655092592592592592592592592592592592592592593E-7 /* 1300075 / 1855425871872 */
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#define ACOSH_TAY15 3.1453306166503321507881427633351293103448275862068965517241379310344828E-7 /* 5014575 / 15942918602752 */
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#if 0
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#define ACOSH_TAY16 -1.4221629293564136230176494967552923387096774193548387096774193548387097E-7 /* 9694845 / 68169720922112 */
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#define ACOSH_TAY17 6.4711106776113328206437555226412686434659090909090909090909090909090909E-8 /* 100180065 / 1548112371908608 */
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#define ACOSH_TAY18 -2.9609409781171182528071637664522443498883928571428571428571428571428571E-8 /* 116680311 / 3940649673949184 */
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#define ACOSH_TAY19 1.3615438056281793767600509061201198680980785472972972972972972972972973E-8 /* 2268783825 / 166633186212708352 */
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#endif
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static __inline vector double _acoshd2(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 minus_oned = spu_splats(-1.0);
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vec_double2 twod = spu_splats(2.0);
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vec_double2 xminus1;
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vec_float4 xf;
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/* Where we switch from taylor to formula */
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vec_float4 switch_approx = spu_splats(1.15f);
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vec_uint4 use_form;
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vec_double2 result, fresult, mresult;;
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xf = spu_roundtf(x);
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xf = spu_shuffle(xf, xf, dup_even);
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/*
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* Formula:
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* acosh = ln(x + sqrt(x^2 - 1))
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*/
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fresult = _sqrtd2(spu_madd(x, x, minus_oned));
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fresult = spu_add(x, fresult);
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fresult = _logd2(fresult);
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/*
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* Taylor Series
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*/
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xminus1 = spu_add(x, minus_oned);
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mresult = spu_madd(xminus1, spu_splats(ACOSH_TAY15), spu_splats(ACOSH_TAY14));
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mresult = spu_madd(xminus1, mresult, spu_splats(ACOSH_TAY13));
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mresult = spu_madd(xminus1, mresult, spu_splats(ACOSH_TAY12));
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mresult = spu_madd(xminus1, mresult, spu_splats(ACOSH_TAY11));
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mresult = spu_madd(xminus1, mresult, spu_splats(ACOSH_TAY10));
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mresult = spu_madd(xminus1, mresult, spu_splats(ACOSH_TAY09));
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mresult = spu_madd(xminus1, mresult, spu_splats(ACOSH_TAY08));
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mresult = spu_madd(xminus1, mresult, spu_splats(ACOSH_TAY07));
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mresult = spu_madd(xminus1, mresult, spu_splats(ACOSH_TAY06));
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mresult = spu_madd(xminus1, mresult, spu_splats(ACOSH_TAY05));
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mresult = spu_madd(xminus1, mresult, spu_splats(ACOSH_TAY04));
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mresult = spu_madd(xminus1, mresult, spu_splats(ACOSH_TAY03));
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mresult = spu_madd(xminus1, mresult, spu_splats(ACOSH_TAY02));
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mresult = spu_madd(xminus1, mresult, spu_splats(ACOSH_TAY01));
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mresult = spu_mul(mresult, _sqrtd2(spu_mul(xminus1, twod)));
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/*
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* Select series or 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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return result;
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}
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#endif /* _ACOSHD2_H_ */
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#endif /* __SPU__ */
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