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Diffstat (limited to 'newlib/libm/machine/spu/headers/atanhd2.h')
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1 files changed, 177 insertions, 0 deletions
diff --git a/newlib/libm/machine/spu/headers/atanhd2.h b/newlib/libm/machine/spu/headers/atanhd2.h new file mode 100644 index 000000000..b1bc33ef9 --- /dev/null +++ b/newlib/libm/machine/spu/headers/atanhd2.h @@ -0,0 +1,177 @@ +/* -------------------------------------------------------------- */ +/* (C)Copyright 2006,2007, */ +/* 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. */ +/* 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 <spu_intrinsics.h> +#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 = NaN + * + */ + +/* + * Maclaurin Series Coefficients + * for x near 0. + */ +#define ATANH_MAC01 1.0000000000000000000000000000000000000000000000000000000000000000000000E0 +#define ATANH_MAC03 3.3333333333333333333333333333333333333333333333333333333333333333333333E-1 +#define ATANH_MAC05 2.0000000000000000000000000000000000000000000000000000000000000000000000E-1 +#define ATANH_MAC07 1.4285714285714285714285714285714285714285714285714285714285714285714286E-1 +#define ATANH_MAC09 1.1111111111111111111111111111111111111111111111111111111111111111111111E-1 +#define ATANH_MAC11 9.0909090909090909090909090909090909090909090909090909090909090909090909E-2 +#define ATANH_MAC13 7.6923076923076923076923076923076923076923076923076923076923076923076923E-2 +#if 0 +#define ATANH_MAC15 6.6666666666666666666666666666666666666666666666666666666666666666666667E-2 +#define ATANH_MAC17 5.8823529411764705882352941176470588235294117647058823529411764705882353E-2 +#define ATANH_MAC19 5.2631578947368421052631578947368421052631578947368421052631578947368421E-2 +#define ATANH_MAC21 4.7619047619047619047619047619047619047619047619047619047619047619047619E-2 +#define ATANH_MAC23 4.3478260869565217391304347826086956521739130434782608695652173913043478E-2 +#define ATANH_MAC25 4.0000000000000000000000000000000000000000000000000000000000000000000000E-2 +#define ATANH_MAC27 3.7037037037037037037037037037037037037037037037037037037037037037037037E-2 +#define ATANH_MAC29 3.4482758620689655172413793103448275862068965517241379310344827586206897E-2 +#define ATANH_MAC31 3.2258064516129032258064516129032258064516129032258064516129032258064516E-2 +#define ATANH_MAC33 3.0303030303030303030303030303030303030303030303030303030303030303030303E-2 +#define ATANH_MAC35 2.8571428571428571428571428571428571428571428571428571428571428571428571E-2 +#define ATANH_MAC37 2.7027027027027027027027027027027027027027027027027027027027027027027027E-2 +#define ATANH_MAC39 2.5641025641025641025641025641025641025641025641025641025641025641025641E-2 +#define ATANH_MAC41 2.4390243902439024390243902439024390243902439024390243902439024390243902E-2 +#define ATANH_MAC43 2.3255813953488372093023255813953488372093023255813953488372093023255814E-2 +#define ATANH_MAC45 2.2222222222222222222222222222222222222222222222222222222222222222222222E-2 +#define ATANH_MAC47 2.1276595744680851063829787234042553191489361702127659574468085106382979E-2 +#define ATANH_MAC49 2.0408163265306122448979591836734693877551020408163265306122448979591837E-2 +#define ATANH_MAC51 1.9607843137254901960784313725490196078431372549019607843137254901960784E-2 +#define ATANH_MAC53 1.8867924528301886792452830188679245283018867924528301886792452830188679E-2 +#define ATANH_MAC55 1.8181818181818181818181818181818181818181818181818181818181818181818182E-2 +#define ATANH_MAC57 1.7543859649122807017543859649122807017543859649122807017543859649122807E-2 +#define ATANH_MAC59 1.6949152542372881355932203389830508474576271186440677966101694915254237E-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_uint4 infminus1 = spu_splats(0x7FEFFFFFU); + vec_uint4 isinfnan; + vec_uint4 xabshigh; + vec_double2 xabs, xsqu; + /* Where we switch from maclaurin to formula */ + vec_float4 switch_approx = spu_splats(0.08f); + 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(ATANH_MAC13), spu_splats(ATANH_MAC11)); + mresult = spu_madd(xsqu, mresult, spu_splats(ATANH_MAC09)); + mresult = spu_madd(xsqu, mresult, spu_splats(ATANH_MAC07)); + mresult = spu_madd(xsqu, mresult, spu_splats(ATANH_MAC05)); + mresult = spu_madd(xsqu, mresult, spu_splats(ATANH_MAC03)); + mresult = spu_madd(xsqu, mresult, spu_splats(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); + + /* 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 - atanh is an anti-symmetric */ + result = spu_sel(result, x, (vec_ullong2)sign_mask); + + return result; +} + +#endif /* _ATANHD2_H_ */ +#endif /* __SPU__ */ |