| /* -------------------------------------------------------------- */ |
| /* (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 _ACOSD2_H_ |
| #define _ACOSD2_H_ 1 |
| |
| #include "simdmath.h" |
| #include <spu_intrinsics.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__ */ |
| |