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/* -------------------------------------------------------------- */
/* (C)Copyright 2006,2008, */
/* 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 _ASIND2_H_
#define _ASIND2_H_ 1
#include "simdmath.h"
#include <spu_intrinsics.h>
#include "sqrtd2.h"
#include "divd2.h"
/*
* FUNCTION
* vector double _asind2(vector double x)
*
* DESCRIPTION
* Compute the arc sine of the vector of double precision elements
* specified by x, returning the resulting angles in radians. The input
* elements are to be in the closed interval [-1, 1]. Values outside
* this range result in a invalid operation execption being latched in
* the FPSCR register and a NAN is returned.
*
* The basic algorithm computes the arc sine using a rational polynomial
* of the form x + x^3 * P(x^2) / Q(x^2) for inputs |x| in the interval
* [0, 0.5]. Values outsize this range are transformed as by:
*
* asin(x) = PI/2 - 2*asin(sqrt((1-x)/2)) for x in the range (0.5, 1.0]
*
* asin(x) = -PI/2 + 2*asin(sqrt((1+x)/2)) for x in the range [-1.0, -0.5)
*
* This yields the basic algorithm of:
*
* absx = (x < 0.0) ? -x : x;
*
* if (absx > 0.5) {
* if (x < 0) {
* addend = -SM_PI_2;
* multiplier = -2.0;
* } else {
* addend = SM_PI_2;
* multiplier = 2.0;
* }
*
* x = sqrt(-0.5 * absx + 0.5);
* } else {
* addend = 0.0;
* multiplier = 1.0;
* }
*
* x2 = x * x;
* x3 = x2 * x;
*
* p = ((((P5 * x2 + P4)*x2 + P3)*x2 + P2)*x2 + P1)*x2 + P0;
*
* q = ((((Q5 * x2 + Q4)*x2 + Q3)*x2 + Q2)*x2 + Q1)*x2 + Q0;;
*
* pq = p / q;
*
* result = addend - (x3*pq + x)*multiplier;
*
* Where P5-P0 and Q5-Q0 are the polynomial coeficients.
*/
static __inline vector double _asind2(vector double x)
{
vec_uint4 x_gt_half, x_eq_half;
vec_double2 x_abs; // absolute value of x
vec_double2 x_trans; // transformed x when |x| > 0.5
vec_double2 x2, x3; // x squared and x cubed, respectively.
vec_double2 result;
vec_double2 multiplier, addend;
vec_double2 p, q, pq;
vec_double2 half = spu_splats(0.5);
vec_double2 sign = (vec_double2)spu_splats(0x8000000000000000ULL);
vec_uchar16 splat_hi = ((vec_uchar16){0,1,2,3, 0,1,2,3, 8,9,10,11, 8,9,10,11});
// Compute the absolute value of x
x_abs = spu_andc(x, sign);
// Perform transformation for the case where |x| > 0.5. We rely on
// sqrtd2 producing a NAN is |x| > 1.0.
x_trans = _sqrtd2(spu_nmsub(x_abs, half, half));
// Determine the correct addend and multiplier.
x_gt_half = spu_cmpgt((vec_uint4)x_abs, (vec_uint4)half);
x_eq_half = spu_cmpeq((vec_uint4)x_abs, (vec_uint4)half);
x_gt_half = spu_or(x_gt_half, spu_and(x_eq_half, spu_rlqwbyte(x_gt_half, 4)));
x_gt_half = spu_shuffle(x_gt_half, x_gt_half, splat_hi);
addend = spu_and(spu_sel(spu_splats((double)SM_PI_2), x, (vec_ullong2)sign), (vec_double2)x_gt_half);
multiplier = spu_sel(spu_splats(-1.0), spu_sel(spu_splats(2.0), x, (vec_ullong2)sign), (vec_ullong2)x_gt_half);
// Select whether to use the x or the transformed x for the polygon evaluation.
// if |x| > 0.5 use x_trans
// else use x
x = spu_sel(x, x_trans, (vec_ullong2)x_gt_half);
// Compute the polynomials.
x2 = spu_mul(x, x);
x3 = spu_mul(x2, x);
p = spu_madd(spu_splats(0.004253011369004428248960), x2, spu_splats(-0.6019598008014123785661));
p = spu_madd(p, x2, spu_splats(5.444622390564711410273));
p = spu_madd(p, x2, spu_splats(-16.26247967210700244449));
p = spu_madd(p, x2, spu_splats(19.56261983317594739197));
p = spu_madd(p, x2, spu_splats(-8.198089802484824371615));
q = spu_add(x2, spu_splats(-14.74091372988853791896));
q = spu_madd(q, x2, spu_splats(70.49610280856842141659));
q = spu_madd(q, x2, spu_splats(-147.1791292232726029859));
q = spu_madd(q, x2, spu_splats(139.5105614657485689735));
q = spu_madd(q, x2, spu_splats(-49.18853881490881290097));
// Compute the rational solution p/q and final multiplication and addend
// correction.
pq = _divd2(p, q);
result = spu_nmsub(spu_madd(x3, pq, x), multiplier, addend);
return (result);
}
#endif /* _ASIND2_H_ */
#endif /* __SPU__ */
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