147 lines
5.7 KiB
C
147 lines
5.7 KiB
C
/* -------------------------------------------------------------- */
|
|
/* (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 _ATANHF4_H_
|
|
#define _ATANHF4_H_ 1
|
|
|
|
#include <spu_intrinsics.h>
|
|
#include <math.h>
|
|
#include "logf4.h"
|
|
|
|
/*
|
|
* FUNCTION
|
|
* vector float _atanhf4(vector float x)
|
|
*
|
|
* DESCRIPTION
|
|
* The atanhf4 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) = HUGE_VALF
|
|
* - atanh(-1) = -HUGE_VALF
|
|
* - The result is undefined for x outside of the domain [-1,1].
|
|
*
|
|
*/
|
|
|
|
/*
|
|
* Maclaurin Series Coefficients
|
|
* for x near 0.
|
|
*/
|
|
#define SDM_SP_ATANH_MAC01 1.000000000000000000000000000000E0
|
|
#define SDM_SP_ATANH_MAC03 3.333333333333333333333333333333E-1
|
|
#define SDM_SP_ATANH_MAC05 2.000000000000000000000000000000E-1
|
|
#define SDM_SP_ATANH_MAC07 1.428571428571428571428571428571E-1
|
|
#if 0
|
|
#define SDM_SP_ATANH_MAC09 1.111111111111111111111111111111E-1
|
|
#define SDM_SP_ATANH_MAC11 9.090909090909090909090909090909E-2
|
|
#define SDM_SP_ATANH_MAC13 7.692307692307692307692307692308E-2
|
|
#define SDM_SP_ATANH_MAC15 6.666666666666666666666666666667E-2
|
|
#endif
|
|
|
|
|
|
static __inline vector float _atanhf4(vector float x)
|
|
{
|
|
vec_uint4 one = spu_splats(1u);
|
|
vec_float4 sign_mask = spu_splats(-0.0f);
|
|
vec_float4 onef = spu_splats(1.0f);
|
|
vec_float4 onehalff = spu_splats(0.5f);
|
|
vec_float4 huge = spu_splats(HUGE_VALF);
|
|
vec_float4 result, fresult, mresult;;
|
|
vec_float4 xabs, xsqu;
|
|
/* Where we switch from maclaurin to formula */
|
|
vec_float4 switch_approx = spu_splats(0.165f);
|
|
vec_uint4 use_form;
|
|
|
|
xabs = spu_andc(x, sign_mask);
|
|
xsqu = spu_mul(x, x);
|
|
|
|
/*
|
|
* Formula:
|
|
* atanh = 1/2 * ln((1 + x)/(1 - x)) = 1/2 * [ln(1+x) - ln(1-x)]
|
|
*/
|
|
fresult = spu_sub(_logf4(spu_add(onef, xabs)), _logf4(spu_sub(onef, xabs)));
|
|
fresult = spu_mul(fresult, onehalff);
|
|
|
|
|
|
/*
|
|
* Taylor Series
|
|
*/
|
|
mresult = spu_madd(xsqu, spu_splats((float)SDM_SP_ATANH_MAC07), spu_splats((float)SDM_SP_ATANH_MAC05));
|
|
mresult = spu_madd(xsqu, mresult, spu_splats((float)SDM_SP_ATANH_MAC03));
|
|
mresult = spu_madd(xsqu, mresult, spu_splats((float)SDM_SP_ATANH_MAC01));
|
|
mresult = spu_mul(xabs, mresult);
|
|
|
|
/*
|
|
* Choose between series and formula
|
|
*/
|
|
use_form = spu_cmpgt(xabs, switch_approx);
|
|
result = spu_sel(mresult, fresult, use_form);
|
|
|
|
/*
|
|
* Correct for accumulated truncation error. Currently reduces rms of
|
|
* absolute error by about 50%
|
|
*/
|
|
result = (vec_float4)spu_add((vec_uint4)result, spu_and(one, spu_cmpgt(xabs, spu_splats(0.0f))));
|
|
result = (vec_float4)spu_add((vec_uint4)result, spu_and(one, spu_cmpgt(xabs, spu_splats(0.25f))));
|
|
|
|
/*
|
|
* Check Boundary Conditions
|
|
*/
|
|
result = spu_sel(result, huge, spu_cmpeq(xabs, onef));
|
|
|
|
/*
|
|
* Spec says |x| > 1, result is undefined, so no additional
|
|
* boundary checks needed.
|
|
*/
|
|
|
|
/* Preserve sign - atanh is anti-symmetric */
|
|
result = spu_sel(result, x, (vec_uint4)sign_mask);
|
|
|
|
return result;
|
|
}
|
|
|
|
#endif /* _ATANHF4_H_ */
|
|
#endif /* __SPU__ */
|