178 lines
7.4 KiB
C
178 lines
7.4 KiB
C
/* -------------------------------------------------------------- */
|
|
/* (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 _ACOSD2_H_
|
|
#define _ACOSD2_H_ 1
|
|
|
|
#include <spu_intrinsics.h>
|
|
|
|
#include "simdmath.h"
|
|
#include "sqrtd2.h"
|
|
#include "divd2.h"
|
|
|
|
/*
|
|
* FUNCTION
|
|
* vector double _acosd2(vector double x)
|
|
*
|
|
* DESCRIPTION
|
|
* Compute the arc cosine 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 cosine using PI/2 - asind2(x).
|
|
* However, as |x| approaches 1, there is a cancellation error in
|
|
* subtracting asind2(x) from PI/2, so we simplify the evaluation
|
|
* instead of layering acosd2 on top of asind2.
|
|
*
|
|
* This yields the basic algorithm of:
|
|
*
|
|
* absx = (x < 0.0) ? -x : x;
|
|
*
|
|
* if (absx > 0.5) {
|
|
* if (x < 0) {
|
|
* addend = SM_PI;
|
|
* multiplier = -2.0;
|
|
* } else {
|
|
* addend = 0.0;
|
|
* multiplier = 2.0;
|
|
* }
|
|
*
|
|
* x = sqrt(-0.5 * absx + 0.5);
|
|
* } else {
|
|
* addend = SM_PI_2;
|
|
* 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 = (x3*pq + x)*multiplier - addend;
|
|
*
|
|
* Where P5-P0 and Q5-Q0 are the polynomial coeficients. See asind2
|
|
* for additional details.
|
|
*/
|
|
static __inline vector double _acosd2(vector double x)
|
|
{
|
|
vec_uint4 x_gt_half, x_eq_half;
|
|
vec_double2 x_neg; // input x is negative
|
|
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_neg = (vec_double2)spu_rlmaska((vec_int4)spu_shuffle(x, x, splat_hi), -31);
|
|
|
|
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_sel(spu_splats(SM_PI_2), spu_and(spu_splats(SM_PI), x_neg), (vec_ullong2)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_madd(spu_madd(x3, pq, x), multiplier, addend);
|
|
|
|
return (result);
|
|
}
|
|
|
|
#endif /* _ACOSD2_H_ */
|
|
#endif /* __SPU__ */
|
|
|