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/* -------------------------------------------------------------- */
/* (C)Copyright 2007,2008, */
/* 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. */
/* */
/* 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 _ERFCD2_H_
#define _ERFCD2_H_ 1
#include <spu_intrinsics.h>
#include "expd2.h"
#include "recipd2.h"
#include "divd2.h"
#include "erf_utils.h"
/*
* FUNCTION
* vector double _erfcd2(vector double x)
*
* DESCRIPTION
* The erfcd2 function computes the complement error function of each element of x.
*
* Accuracy Note: We would benefit from a rational approximation in the domain
* 1.2 < x < 2.0 and also around x = 2.5.
*
* C99 Special Cases:
* - erfc(+0) returns +1
* - erfc(-0) returns +1
* - erfc(+infinite) returns +0
* - erfc(-infinite) returns +2
*
* Other Cases:
* - erfc(Nan) returns Nan
*
*/
static __inline vector double _erfcd2(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 onehalfd = spu_splats(0.5);
vec_double2 zerod = spu_splats(0.0);
vec_double2 oned = spu_splats(1.0);
vec_double2 twod = spu_splats(2.0);
vec_double2 sign_mask = spu_splats(-0.0);
/* This is where we switch from near zero approx. */
vec_float4 approx_point = spu_splats(1.71f);
vec_double2 xabs, xsqu, xsign;
vec_uint4 xhigh, xabshigh;
vec_uint4 isnan, isneg;
vec_double2 tresult, presult, result;
xsign = spu_and(x, sign_mask);
/* Force Denorms to 0 */
x = spu_add(x, zerod);
xabs = spu_andc(x, sign_mask);
xsqu = spu_mul(x, x);
/*
* Use Taylor Series for x near 0
* Preserve sign of x in result, since erf(-x) = -erf(x)
* This approximation is for erf, so adjust for erfc.
*/
TAYLOR_ERF(xabs, xsqu, tresult);
tresult = spu_or(tresult, xsign);
tresult = spu_sub(oned, tresult);
/*
* Now, use the Continued Fractions approximation away
* from 0. If x < 0, use erfc(-x) = 2 - erfc(x)
*/
CONTFRAC_ERFC(xabs, xsqu, presult);
isneg = (vec_uint4)spu_shuffle(x, x, dup_even);
isneg = spu_rlmaska(isneg, -32);
presult = spu_sel(presult, spu_sub(twod, presult), (vec_ullong2)isneg);
/*
* Select the appropriate approximation.
*/
vec_float4 xf = spu_roundtf(xabs);
xf = spu_shuffle(xf, xf, dup_even);
result = spu_sel(tresult, presult, (vec_ullong2)spu_cmpgt(xf, approx_point));
/*
* Special cases/errors.
*/
xhigh = (vec_uint4)spu_shuffle(x, x, dup_even);
xabshigh = (vec_uint4)spu_shuffle(xabs, xabs, dup_even);
/* x = +/- infinite */
result = spu_sel(result, zerod, (vec_ullong2)spu_cmpeq(xhigh, 0x7FF00000));
result = spu_sel(result, twod, (vec_ullong2)spu_cmpeq(xhigh, 0xFFF00000));
/* x = nan, return x */
isnan = spu_cmpgt(xabshigh, 0x7FF00000);
result = spu_sel(result, x, (vec_ullong2)isnan);
return result;
}
#endif /* _ERFCD2_H_ */
#endif /* __SPU__ */
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