151 lines
6.0 KiB
C
151 lines
6.0 KiB
C
/* -------------------------------------------------------------- */
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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 _ERFCD2_H_
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#define _ERFCD2_H_ 1
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#include <spu_intrinsics.h>
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#include "expd2.h"
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#include "recipd2.h"
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#include "divd2.h"
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#include "erf_utils.h"
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/*
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* FUNCTION
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* vector double _erfcd2(vector double x)
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*
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* DESCRIPTION
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* The erfcd2 function computes the complement error function of each element of x.
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*
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* Accuracy Note: We would benefit from a rational approximation in the domain
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* 1.2 < x < 2.0 and also around x = 2.5.
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*
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* C99 Special Cases:
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* - erfc(+0) returns +1
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* - erfc(-0) returns +1
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* - erfc(+infinite) returns +0
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* - erfc(-infinite) returns +2
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*
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* Other Cases:
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* - erfc(Nan) returns Nan
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*
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*/
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static __inline vector double _erfcd2(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 onehalfd = spu_splats(0.5);
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vec_double2 zerod = spu_splats(0.0);
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vec_double2 oned = spu_splats(1.0);
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vec_double2 twod = spu_splats(2.0);
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vec_double2 sign_mask = spu_splats(-0.0);
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/* This is where we switch from near zero approx. */
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vec_float4 approx_point = spu_splats(1.71f);
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vec_double2 xabs, xsqu, xsign;
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vec_uint4 xhigh, xabshigh;
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vec_uint4 isnan, isneg;
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vec_double2 tresult, presult, result;
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xsign = spu_and(x, sign_mask);
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/* Force Denorms to 0 */
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x = spu_add(x, zerod);
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xabs = spu_andc(x, sign_mask);
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xsqu = spu_mul(x, x);
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/*
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* Use Taylor Series for x near 0
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* Preserve sign of x in result, since erf(-x) = -erf(x)
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* This approximation is for erf, so adjust for erfc.
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*/
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TAYLOR_ERF(xabs, xsqu, tresult);
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tresult = spu_or(tresult, xsign);
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tresult = spu_sub(oned, tresult);
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/*
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* Now, use the Continued Fractions approximation away
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* from 0. If x < 0, use erfc(-x) = 2 - erfc(x)
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*/
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CONTFRAC_ERFC(xabs, xsqu, presult);
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isneg = (vec_uint4)spu_shuffle(x, x, dup_even);
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isneg = spu_rlmaska(isneg, -32);
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presult = spu_sel(presult, spu_sub(twod, presult), (vec_ullong2)isneg);
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/*
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* Select the appropriate approximation.
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*/
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vec_float4 xf = spu_roundtf(xabs);
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xf = spu_shuffle(xf, xf, dup_even);
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result = spu_sel(tresult, presult, (vec_ullong2)spu_cmpgt(xf, approx_point));
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/*
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* Special cases/errors.
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*/
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xhigh = (vec_uint4)spu_shuffle(x, x, dup_even);
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xabshigh = (vec_uint4)spu_shuffle(xabs, xabs, dup_even);
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/* x = +/- infinite */
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result = spu_sel(result, zerod, (vec_ullong2)spu_cmpeq(xhigh, 0x7FF00000));
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result = spu_sel(result, twod, (vec_ullong2)spu_cmpeq(xhigh, 0xFFF00000));
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/* x = nan, return x */
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isnan = spu_cmpgt(xabshigh, 0x7FF00000);
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result = spu_sel(result, x, (vec_ullong2)isnan);
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return result;
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}
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#endif /* _ERFCD2_H_ */
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#endif /* __SPU__ */
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