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Diffstat (limited to 'newlib/libm/machine/spu/headers/acoshf4.h')
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1 files changed, 167 insertions, 0 deletions
diff --git a/newlib/libm/machine/spu/headers/acoshf4.h b/newlib/libm/machine/spu/headers/acoshf4.h new file mode 100644 index 000000000..3efc35ffc --- /dev/null +++ b/newlib/libm/machine/spu/headers/acoshf4.h @@ -0,0 +1,167 @@ +/* -------------------------------------------------------------- */ +/* (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 _ACOSHF4_H_ +#define _ACOSHF4_H_ 1 + +#include <spu_intrinsics.h> +#include "logf4.h" +#include "sqrtf4.h" + +/* + * FUNCTION + * vector float _acoshf4(vector float x) + * + * DESCRIPTION + * The acoshf4 function returns a vector containing the hyperbolic + * arccosines of the corresponding elements of the input vector. + * + * We are using the formula: + * acosh = ln(x + sqrt(x^2 - 1)) + * + * For x near one, we use the Taylor series: + * + * infinity + * ------ + * - ' + * - k + * acosh x = - C (x - 1) + * - k + * - , + * ------ + * k = 0 + * + * + * Special Cases: + * - acosh(1) = +0 + * - NaNs and Infinity aren't supported for single-precision on SPU. + * + */ + +/* + * Taylor Series Coefficients + * for x around 1. + */ +#define ACOSH_TAY01 1.0000000000000000000000000000000000000000000000000000000000000000000000E0 /* 1 / 1 */ +#define ACOSH_TAY02 -8.3333333333333333333333333333333333333333333333333333333333333333333333E-2 /* 1 / 12 */ +#define ACOSH_TAY03 1.8750000000000000000000000000000000000000000000000000000000000000000000E-2 /* 3 / 160 */ +#define ACOSH_TAY04 -5.5803571428571428571428571428571428571428571428571428571428571428571429E-3 /* 5 / 896 */ +#define ACOSH_TAY05 1.8988715277777777777777777777777777777777777777777777777777777777777778E-3 /* 35 / 18432 */ +#define ACOSH_TAY06 -6.9912997159090909090909090909090909090909090909090909090909090909090909E-4 /* 63 / 90112 */ +#define ACOSH_TAY07 2.7113694411057692307692307692307692307692307692307692307692307692307692E-4 /* 231 / 851968 */ +#define ACOSH_TAY08 -1.0910034179687500000000000000000000000000000000000000000000000000000000E-4 /* 143 / 1310720 */ +#define ACOSH_TAY09 4.5124222250545726102941176470588235294117647058823529411764705882352941E-5 /* 6435 / 142606336 */ +#define ACOSH_TAY10 -1.9065643611707185444078947368421052631578947368421052631578947368421053E-5 /* 12155 / 637534208 */ +#define ACOSH_TAY11 8.1936873140789213634672619047619047619047619047619047619047619047619048E-6 /* 46189 / 5637144576 */ +#define ACOSH_TAY12 -3.5705692742181860882302989130434782608695652173913043478260869565217391E-6 /* 88179 / 24696061952 */ +#define ACOSH_TAY13 1.5740259550511837005615234375000000000000000000000000000000000000000000E-6 /* 676039 / 429496729600 */ +#define ACOSH_TAY14 -7.0068819224144573564882631655092592592592592592592592592592592592592593E-7 /* 1300075 / 1855425871872 */ +#define ACOSH_TAY15 3.1453306166503321507881427633351293103448275862068965517241379310344828E-7 /* 5014575 / 15942918602752 */ +#if 0 +#define ACOSH_TAY16 -1.4221629293564136230176494967552923387096774193548387096774193548387097E-7 /* 9694845 / 68169720922112 */ +#define ACOSH_TAY17 6.4711106776113328206437555226412686434659090909090909090909090909090909E-8 /* 100180065 / 1548112371908608 */ +#define ACOSH_TAY18 -2.9609409781171182528071637664522443498883928571428571428571428571428571E-8 /* 116680311 / 3940649673949184 */ +#define ACOSH_TAY19 1.3615438056281793767600509061201198680980785472972972972972972972972973E-8 /* 2268783825 / 166633186212708352 */ +#endif + + + +static __inline vector float _acoshf4(vector float x) +{ + vec_float4 minus_onef = spu_splats(-1.0f); + vec_float4 twof = spu_splats(2.0f); + vec_float4 xminus1; + /* Where we switch from taylor to formula */ + vec_float4 switch_approx = spu_splats(2.0f); + vec_uint4 use_form; + vec_float4 result, fresult, mresult;; + + + /* + * Formula: + * acosh = ln(x + sqrt(x^2 - 1)) + */ + fresult = _sqrtf4(spu_madd(x, x, minus_onef)); + fresult = spu_add(x, fresult); + fresult = _logf4(fresult); + + /* + * Taylor Series + */ + xminus1 = spu_add(x, minus_onef); + + mresult = spu_madd(xminus1, spu_splats((float)ACOSH_TAY15), spu_splats((float)ACOSH_TAY14)); + mresult = spu_madd(xminus1, mresult, spu_splats((float)ACOSH_TAY13)); + mresult = spu_madd(xminus1, mresult, spu_splats((float)ACOSH_TAY12)); + mresult = spu_madd(xminus1, mresult, spu_splats((float)ACOSH_TAY11)); + mresult = spu_madd(xminus1, mresult, spu_splats((float)ACOSH_TAY10)); + mresult = spu_madd(xminus1, mresult, spu_splats((float)ACOSH_TAY09)); + mresult = spu_madd(xminus1, mresult, spu_splats((float)ACOSH_TAY08)); + mresult = spu_madd(xminus1, mresult, spu_splats((float)ACOSH_TAY07)); + mresult = spu_madd(xminus1, mresult, spu_splats((float)ACOSH_TAY06)); + mresult = spu_madd(xminus1, mresult, spu_splats((float)ACOSH_TAY05)); + mresult = spu_madd(xminus1, mresult, spu_splats((float)ACOSH_TAY04)); + mresult = spu_madd(xminus1, mresult, spu_splats((float)ACOSH_TAY03)); + mresult = spu_madd(xminus1, mresult, spu_splats((float)ACOSH_TAY02)); + mresult = spu_madd(xminus1, mresult, spu_splats((float)ACOSH_TAY01)); + + mresult = spu_mul(mresult, _sqrtf4(spu_mul(xminus1, twof))); + + /* + * Select series or formula + */ + use_form = spu_cmpgt(x, switch_approx); + result = spu_sel(mresult, fresult, use_form); + + return result; +} + +#endif /* _ACOSHF4_H_ */ +#endif /* __SPU__ */ |