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Diffstat (limited to 'newlib/libm/machine/spu/headers/asind2.h')
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diff --git a/newlib/libm/machine/spu/headers/asind2.h b/newlib/libm/machine/spu/headers/asind2.h new file mode 100644 index 000000000..8f86db307 --- /dev/null +++ b/newlib/libm/machine/spu/headers/asind2.h @@ -0,0 +1,177 @@ +/* -------------------------------------------------------------- */ +/* (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 _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__ */ |