166 lines
6.6 KiB
C
166 lines
6.6 KiB
C
/* -------------------------------------------------------------- */
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/* (C)Copyright 2006,2008, */
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/* International Business Machines Corporation */
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/* All Rights Reserved. */
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/* */
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/* Redistribution and use in source and binary forms, with or */
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/* without modification, are permitted provided that the */
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/* following conditions are met: */
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/* */
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/* - Redistributions of source code must retain the above copyright*/
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/* notice, this list of conditions and the following disclaimer. */
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/* */
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/* - Redistributions in binary form must reproduce the above */
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/* copyright notice, this list of conditions and the following */
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/* disclaimer in the documentation and/or other materials */
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/* provided with the distribution. */
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/* */
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/* - Neither the name of IBM Corporation nor the names of its */
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/* contributors may be used to endorse or promote products */
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/* derived from this software without specific prior written */
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/* permission. */
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/* */
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/* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND */
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/* CONTRIBUTORS "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, */
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/* INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF */
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/* MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE */
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/* DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR */
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/* CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, */
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/* SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT */
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/* NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; */
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/* LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) */
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/* HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN */
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/* CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR */
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/* OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, */
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/* EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. */
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/* -------------------------------------------------------------- */
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/* PROLOG END TAG zYx */
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#ifdef __SPU__
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#ifndef _ACOSD2_H_
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#define _ACOSD2_H_ 1
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#include <spu_intrinsics.h>
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#include "simdmath.h"
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#include "sqrtd2.h"
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#include "divd2.h"
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/*
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* FUNCTION
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* vector double _acosd2(vector double x)
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*
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* DESCRIPTION
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* Compute the arc cosine of the vector of double precision elements
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* specified by x, returning the resulting angles in radians. The input
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* elements are to be in the closed interval [-1, 1]. Values outside
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* this range result in a invalid operation execption being latched in
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* the FPSCR register and a NAN is returned.
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*
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* The basic algorithm computes the arc cosine using PI/2 - asind2(x).
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* However, as |x| approaches 1, there is a cancellation error in
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* subtracting asind2(x) from PI/2, so we simplify the evaluation
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* instead of layering acosd2 on top of asind2.
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*
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* This yields the basic algorithm of:
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*
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* absx = (x < 0.0) ? -x : x;
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*
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* if (absx > 0.5) {
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* if (x < 0) {
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* addend = SM_PI;
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* multiplier = -2.0;
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* } else {
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* addend = 0.0;
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* multiplier = 2.0;
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* }
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*
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* x = sqrt(-0.5 * absx + 0.5);
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* } else {
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* addend = SM_PI_2;
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* multiplier = -1.0;
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* }
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*
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* x2 = x * x;
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* x3 = x2 * x;
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*
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* p = ((((P5 * x2 + P4)*x2 + P3)*x2 + P2)*x2 + P1)*x2 + P0;
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*
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* q = ((((Q5 * x2 + Q4)*x2 + Q3)*x2 + Q2)*x2 + Q1)*x2 + Q0;;
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*
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* pq = p / q;
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*
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* result = (x3*pq + x)*multiplier - addend;
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*
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* Where P5-P0 and Q5-Q0 are the polynomial coeficients. See asind2
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* for additional details.
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*/
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static __inline vector double _acosd2(vector double x)
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{
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vec_uint4 x_gt_half, x_eq_half;
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vec_double2 x_neg; // input x is negative
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vec_double2 x_abs; // absolute value of x
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vec_double2 x_trans; // transformed x when |x| > 0.5
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vec_double2 x2, x3; // x squared and x cubed, respectively.
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vec_double2 result;
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vec_double2 multiplier, addend;
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vec_double2 p, q, pq;
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vec_double2 half = spu_splats(0.5);
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vec_double2 sign = (vec_double2)spu_splats(0x8000000000000000ULL);
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vec_uchar16 splat_hi = ((vec_uchar16){0,1,2,3, 0,1,2,3, 8,9,10,11, 8,9,10,11});
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// Compute the absolute value of x
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x_abs = spu_andc(x, sign);
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// Perform transformation for the case where |x| > 0.5. We rely on
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// sqrtd2 producing a NAN is |x| > 1.0.
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x_trans = _sqrtd2(spu_nmsub(x_abs, half, half));
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// Determine the correct addend and multiplier.
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x_neg = (vec_double2)spu_rlmaska((vec_int4)spu_shuffle(x, x, splat_hi), -31);
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x_gt_half = spu_cmpgt((vec_uint4)x_abs, (vec_uint4)half);
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x_eq_half = spu_cmpeq((vec_uint4)x_abs, (vec_uint4)half);
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x_gt_half = spu_or(x_gt_half, spu_and(x_eq_half, spu_rlqwbyte(x_gt_half, 4)));
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x_gt_half = spu_shuffle(x_gt_half, x_gt_half, splat_hi);
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addend = spu_sel(spu_splats(SM_PI_2), spu_and(spu_splats(SM_PI), x_neg), (vec_ullong2)x_gt_half);
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multiplier = spu_sel(spu_splats(-1.0), spu_sel(spu_splats(2.0), x, (vec_ullong2)sign), (vec_ullong2)x_gt_half);
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// Select whether to use the x or the transformed x for the polygon evaluation.
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// if |x| > 0.5 use x_trans
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// else use x
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x = spu_sel(x, x_trans, (vec_ullong2)x_gt_half);
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// Compute the polynomials.
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x2 = spu_mul(x, x);
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x3 = spu_mul(x2, x);
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p = spu_madd(spu_splats(0.004253011369004428248960), x2, spu_splats(-0.6019598008014123785661));
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p = spu_madd(p, x2, spu_splats(5.444622390564711410273));
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p = spu_madd(p, x2, spu_splats(-16.26247967210700244449));
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p = spu_madd(p, x2, spu_splats(19.56261983317594739197));
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p = spu_madd(p, x2, spu_splats(-8.198089802484824371615));
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q = spu_add(x2, spu_splats(-14.74091372988853791896));
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q = spu_madd(q, x2, spu_splats(70.49610280856842141659));
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q = spu_madd(q, x2, spu_splats(-147.1791292232726029859));
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q = spu_madd(q, x2, spu_splats(139.5105614657485689735));
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q = spu_madd(q, x2, spu_splats(-49.18853881490881290097));
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// Compute the rational solution p/q and final multiplication and addend
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// correction.
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pq = _divd2(p, q);
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result = spu_madd(spu_madd(x3, pq, x), multiplier, addend);
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return (result);
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}
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#endif /* _ACOSD2_H_ */
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#endif /* __SPU__ */
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