135 lines
5.0 KiB
C
135 lines
5.0 KiB
C
/*
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(C) Copyright 2001,2006,
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International Business Machines Corporation,
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Sony Computer Entertainment, Incorporated,
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Toshiba Corporation,
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All rights reserved.
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Redistribution and use in source and binary forms, with or without
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modification, are permitted provided that the following conditions are met:
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* Redistributions of source code must retain the above copyright notice,
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this list of conditions and the following disclaimer.
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* Redistributions in binary form must reproduce the above copyright
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notice, this list of conditions and the following disclaimer in the
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documentation and/or other materials provided with the distribution.
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* Neither the names of the copyright holders nor the names of their
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contributors may be used to endorse or promote products derived from this
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software without specific prior written permission.
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THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS
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IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED
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TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A
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PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER
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OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
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EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
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PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
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PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
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LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
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NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
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SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
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*/
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#ifndef _CBRT_H_
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#define _CBRT_H_ 1
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#include <spu_intrinsics.h>
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#include "headers/vec_literal.h"
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static double cbrt_factors[5] = {
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0.629960524947436484311, /* 2^(-2/3) */
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0.793700525984099680699, /* 2^(-1/3) */
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1.0, /* 2^(0) */
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1.259921049894873164666, /* 2^(1/3) */
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1.587401051968199583441 /* 2^(2/3) */
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};
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/* Compute the cube root of x to double precision.
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*/
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static __inline double _cbrt(double x)
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{
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vec_int4 exp, bias;
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vec_uint4 e_div_3, e_mod_3;
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vec_float4 bf, inv_bf;
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vec_float4 onef = VEC_SPLAT_F32(1.0f);
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vec_ullong2 mask;
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vec_ullong2 mant_mask = VEC_SPLAT_U64(0xFFFFFFFFFFFFFULL);
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vec_double2 one = VEC_SPLAT_F64(1.0);
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vec_double2 two = VEC_SPLAT_F64(2.0);
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vec_double2 half = VEC_SPLAT_F64(0.5);
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/* Polynomial coefficients */
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vec_double2 c0 = VEC_SPLAT_F64(0.354895765043919860);
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vec_double2 c1 = VEC_SPLAT_F64(1.50819193781584896);
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vec_double2 c2 = VEC_SPLAT_F64(-2.11499494167371287);
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vec_double2 c3 = VEC_SPLAT_F64(2.44693122563534430);
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vec_double2 c4 = VEC_SPLAT_F64(-1.83469277483613086);
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vec_double2 c5 = VEC_SPLAT_F64(0.784932344976639262);
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vec_double2 c6 = VEC_SPLAT_F64(0.145263899385486377);
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vec_double2 in, out, mant, u, u3, ym, a, b, factor, inv_b;
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in = spu_promote(x, 0);
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/* Normalize the mantissa (fraction part) into the range [0.5, 1.0) and
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* extract the exponent.
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*/
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mant = spu_sel(half, in, mant_mask);
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exp = spu_and(spu_rlmask((vec_int4)in, -20), 0x7FF);
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/* Generate mask used to zero result if the exponent is zero (ie, <in> is
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* either zero or a denorm
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*/
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mask = (vec_ullong2)spu_cmpeq(exp, 0);
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mask = spu_shuffle(mask, mask, VEC_LITERAL(vec_uchar16, 0,1,2,3,0,1,2,3,8,9,10,11,8,9,10,11));
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exp = spu_add(exp, -1022);
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u = spu_madd(mant, spu_madd(mant, spu_madd(mant, spu_madd(mant, spu_madd(mant, spu_nmsub(mant, c6, c5), c4), c3), c2), c1), c0);
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u3 = spu_mul(spu_mul(u, u), u);
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/* Compute: e_div_3 = exp/3
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*
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* Fetch: factor = factor[2+exp%3]
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*
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* The factors array contains 5 values: 2^(-2/3), 2^(-1/3), 2^0, 2^(1/3),
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* 2^(2/3), 2^1.
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* The fetch is done using shuffle bytes so that is can easily be extended
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* to support SIMD compution.
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*/
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bias = spu_rlmask(spu_rlmaska(exp, -15), -16);
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e_div_3 = (vec_uint4)spu_rlmaska(spu_madd((vec_short8)exp, VEC_SPLAT_S16(0x5556), bias), -16);
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e_mod_3 = (vec_uint4)spu_sub((vec_int4)(exp), spu_mulo((vec_short8)e_div_3, VEC_SPLAT_S16(3)));
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factor = spu_promote(cbrt_factors[2+spu_extract(e_mod_3, 0)], 0);
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/* Compute the estimated mantissa cube root (ym) equals:
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* ym = (u * factor * (2.0 * mant + u3)) / (2.0 * u3 + mant);
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*/
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a = spu_mul(spu_mul(factor, u), spu_madd(two, mant, u3));
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b = spu_madd(two, u3, mant);
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bf = spu_roundtf(b);
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inv_bf = spu_re(bf);
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inv_bf = spu_madd(spu_nmsub(bf, inv_bf, onef), inv_bf, inv_bf);
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inv_b = spu_extend(inv_bf);
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inv_b = spu_madd(spu_nmsub(b, inv_b, one), inv_b, inv_b);
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ym = spu_mul(a, inv_b);
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ym = spu_madd(spu_nmsub(b, ym, a), inv_b, ym);
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/* Merge sign, computed exponent, and computed mantissa.
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*/
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exp = spu_rl(spu_add((vec_int4)e_div_3, 1023), 20);
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exp = spu_andc(exp, (vec_int4)mant_mask);
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out = spu_sel((vec_double2)exp, in, VEC_SPLAT_U64(0x8000000000000000ULL));
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out = spu_mul(out, ym);
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out = spu_andc(out, (vec_double2)mask);
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return (spu_extract(out, 0));
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}
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#endif /* _CBRT_H_ */
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