2007-09-29 02:44:24 +08:00
|
|
|
/* -------------------------------------------------------------- */
|
|
|
|
|
/* (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 _ASINHD2_H_
|
|
|
|
|
#define _ASINHD2_H_ 1
|
|
|
|
|
|
|
|
|
|
#include <spu_intrinsics.h>
|
|
|
|
|
|
|
|
|
|
#include "logd2.h"
|
|
|
|
|
#include "sqrtd2.h"
|
|
|
|
|
|
|
|
|
|
/*
|
|
|
|
|
* FUNCTION
|
|
|
|
|
* vector double _asinhd2(vector double x)
|
|
|
|
|
*
|
|
|
|
|
* DESCRIPTION
|
|
|
|
|
* The asinhd2 function returns a vector containing the hyperbolic
|
|
|
|
|
* arcsines of the corresponding elements of the input vector.
|
|
|
|
|
*
|
|
|
|
|
* We are using the formula:
|
|
|
|
|
* asinh = ln(|x| + sqrt(x^2 + 1))
|
|
|
|
|
* and the anti-symmetry of asinh.
|
|
|
|
|
*
|
|
|
|
|
* For x near zero, we use the Taylor series:
|
|
|
|
|
*
|
|
|
|
|
* infinity
|
|
|
|
|
* ------
|
|
|
|
|
* - ' P (0)
|
|
|
|
|
* - k-1 k
|
|
|
|
|
* asinh x = - ----- x
|
|
|
|
|
* - k
|
|
|
|
|
* - ,
|
|
|
|
|
* ------
|
|
|
|
|
* k = 1
|
|
|
|
|
*
|
|
|
|
|
* Special Cases:
|
|
|
|
|
* asinh(+0) returns +0
|
|
|
|
|
* asinh(-0) returns -0
|
|
|
|
|
* asinh(+infinity) returns +infinity
|
|
|
|
|
* asinh(-infinity) returns -infinity
|
|
|
|
|
* asinh(NaN) returns NaN
|
|
|
|
|
*
|
|
|
|
|
*/
|
|
|
|
|
|
|
|
|
|
/*
|
|
|
|
|
* Maclaurin Series Coefficients
|
|
|
|
|
* for x near 0.
|
|
|
|
|
*/
|
2008-09-05 01:46:14 +08:00
|
|
|
#define SDM_ASINHD2_MAC01 1.000000000000000000000000000000000000000000E0
|
|
|
|
|
#define SDM_ASINHD2_MAC03 -1.666666666666666666666666666666666666666667E-1
|
|
|
|
|
#define SDM_ASINHD2_MAC05 7.500000000000000000000000000000000000000000E-2
|
|
|
|
|
#define SDM_ASINHD2_MAC07 -4.464285714285714285714285714285714285714286E-2
|
|
|
|
|
#define SDM_ASINHD2_MAC09 3.038194444444444444444444444444444444444444E-2
|
|
|
|
|
#define SDM_ASINHD2_MAC11 -2.237215909090909090909090909090909090909091E-2
|
|
|
|
|
#define SDM_ASINHD2_MAC13 1.735276442307692307692307692307692307692308E-2
|
|
|
|
|
#define SDM_ASINHD2_MAC15 -1.396484375000000000000000000000000000000000E-2
|
|
|
|
|
#define SDM_ASINHD2_MAC17 1.155180089613970588235294117647058823529412E-2
|
2007-09-29 02:44:24 +08:00
|
|
|
|
|
|
|
|
|
|
|
|
|
static __inline vector double _asinhd2(vector double x)
|
|
|
|
|
{
|
|
|
|
|
vec_double2 sign_mask = spu_splats(-0.0);
|
|
|
|
|
vec_double2 oned = spu_splats(1.0);
|
2008-09-05 01:46:14 +08:00
|
|
|
vec_uchar16 dup_even = ((vec_uchar16) { 0,1,2,3, 0,1,2,3, 8,9,10,11, 8,9,10,11 });
|
2007-09-29 02:44:24 +08:00
|
|
|
vec_uint4 infminus1 = spu_splats(0x7FEFFFFFU);
|
|
|
|
|
vec_uint4 isinfnan;
|
|
|
|
|
vec_double2 xabs, xsqu;
|
|
|
|
|
vec_uint4 xabshigh;
|
2008-09-05 01:46:14 +08:00
|
|
|
vec_float4 switch_approx = spu_splats(0.165f); /* Where we switch from maclaurin to formula */
|
2007-09-29 02:44:24 +08:00
|
|
|
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:
|
|
|
|
|
* asinh = ln(|x| + sqrt(x^2 + 1))
|
|
|
|
|
*/
|
|
|
|
|
fresult = _sqrtd2(spu_add(xsqu, oned));
|
|
|
|
|
fresult = spu_add(xabs, fresult);
|
|
|
|
|
fresult = _logd2(fresult);
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
/*
|
|
|
|
|
* Maclaurin Series approximation
|
|
|
|
|
*/
|
2008-09-05 01:46:14 +08:00
|
|
|
|
|
|
|
|
mresult = spu_splats(SDM_ASINHD2_MAC17);
|
|
|
|
|
mresult = spu_madd(xsqu, mresult, spu_splats(SDM_ASINHD2_MAC15));
|
|
|
|
|
mresult = spu_madd(xsqu, mresult, spu_splats(SDM_ASINHD2_MAC13));
|
|
|
|
|
mresult = spu_madd(xsqu, mresult, spu_splats(SDM_ASINHD2_MAC11));
|
|
|
|
|
mresult = spu_madd(xsqu, mresult, spu_splats(SDM_ASINHD2_MAC09));
|
|
|
|
|
mresult = spu_madd(xsqu, mresult, spu_splats(SDM_ASINHD2_MAC07));
|
|
|
|
|
mresult = spu_madd(xsqu, mresult, spu_splats(SDM_ASINHD2_MAC05));
|
|
|
|
|
mresult = spu_madd(xsqu, mresult, spu_splats(SDM_ASINHD2_MAC03));
|
|
|
|
|
mresult = spu_madd(xsqu, mresult, spu_splats(SDM_ASINHD2_MAC01));
|
2007-09-29 02:44:24 +08:00
|
|
|
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);
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
/* Special Cases */
|
|
|
|
|
|
|
|
|
|
/* 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 - asinh is an anti-symmetric */
|
|
|
|
|
result = spu_sel(result, x, (vec_ullong2)sign_mask);
|
|
|
|
|
|
|
|
|
|
return result;
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
#endif /* _ASINHD2_H_ */
|
|
|
|
|
#endif /* __SPU__ */
|
