| /* |
| (C) Copyright 2001,2006, |
| International Business Machines Corporation, |
| Sony Computer Entertainment, Incorporated, |
| Toshiba 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 names of the copyright holders nor the names of their |
| 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. |
| */ |
| |
| #ifndef _CBRT_H_ |
| #define _CBRT_H_ 1 |
| |
| #include <spu_intrinsics.h> |
| #include "headers/vec_literal.h" |
| |
| static double cbrt_factors[5] = { |
| 0.629960524947436484311, /* 2^(-2/3) */ |
| 0.793700525984099680699, /* 2^(-1/3) */ |
| 1.0, /* 2^(0) */ |
| 1.259921049894873164666, /* 2^(1/3) */ |
| 1.587401051968199583441 /* 2^(2/3) */ |
| }; |
| |
| /* Compute the cube root of x to double precision. |
| */ |
| |
| static __inline double _cbrt(double x) |
| { |
| vec_int4 exp, bias; |
| vec_uint4 e_div_3, e_mod_3; |
| vec_float4 bf, inv_bf; |
| vec_float4 onef = VEC_SPLAT_F32(1.0f); |
| vec_ullong2 mask; |
| vec_ullong2 mant_mask = VEC_SPLAT_U64(0xFFFFFFFFFFFFFULL); |
| vec_double2 one = VEC_SPLAT_F64(1.0); |
| vec_double2 two = VEC_SPLAT_F64(2.0); |
| vec_double2 half = VEC_SPLAT_F64(0.5); |
| /* Polynomial coefficients */ |
| vec_double2 c0 = VEC_SPLAT_F64(0.354895765043919860); |
| vec_double2 c1 = VEC_SPLAT_F64(1.50819193781584896); |
| vec_double2 c2 = VEC_SPLAT_F64(-2.11499494167371287); |
| vec_double2 c3 = VEC_SPLAT_F64(2.44693122563534430); |
| vec_double2 c4 = VEC_SPLAT_F64(-1.83469277483613086); |
| vec_double2 c5 = VEC_SPLAT_F64(0.784932344976639262); |
| vec_double2 c6 = VEC_SPLAT_F64(0.145263899385486377); |
| vec_double2 in, out, mant, u, u3, ym, a, b, factor, inv_b; |
| |
| in = spu_promote(x, 0); |
| |
| /* Normalize the mantissa (fraction part) into the range [0.5, 1.0) and |
| * extract the exponent. |
| */ |
| mant = spu_sel(half, in, mant_mask); |
| exp = spu_and(spu_rlmask((vec_int4)in, -20), 0x7FF); |
| |
| /* Generate mask used to zero result if the exponent is zero (ie, <in> is |
| * either zero or a denorm |
| */ |
| mask = (vec_ullong2)spu_cmpeq(exp, 0); |
| 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)); |
| exp = spu_add(exp, -1022); |
| |
| 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); |
| u3 = spu_mul(spu_mul(u, u), u); |
| |
| /* Compute: e_div_3 = exp/3 |
| * |
| * Fetch: factor = factor[2+exp%3] |
| * |
| * The factors array contains 5 values: 2^(-2/3), 2^(-1/3), 2^0, 2^(1/3), |
| * 2^(2/3), 2^1. |
| * The fetch is done using shuffle bytes so that is can easily be extended |
| * to support SIMD compution. |
| */ |
| bias = spu_rlmask(spu_rlmaska(exp, -15), -16); |
| e_div_3 = (vec_uint4)spu_rlmaska(spu_madd((vec_short8)exp, VEC_SPLAT_S16(0x5556), bias), -16); |
| |
| e_mod_3 = (vec_uint4)spu_sub((vec_int4)(exp), spu_mulo((vec_short8)e_div_3, VEC_SPLAT_S16(3))); |
| |
| factor = spu_promote(cbrt_factors[2+spu_extract(e_mod_3, 0)], 0); |
| |
| /* Compute the estimated mantissa cube root (ym) equals: |
| * ym = (u * factor * (2.0 * mant + u3)) / (2.0 * u3 + mant); |
| */ |
| a = spu_mul(spu_mul(factor, u), spu_madd(two, mant, u3)); |
| b = spu_madd(two, u3, mant); |
| |
| bf = spu_roundtf(b); |
| inv_bf = spu_re(bf); |
| inv_bf = spu_madd(spu_nmsub(bf, inv_bf, onef), inv_bf, inv_bf); |
| |
| inv_b = spu_extend(inv_bf); |
| inv_b = spu_madd(spu_nmsub(b, inv_b, one), inv_b, inv_b); |
| |
| ym = spu_mul(a, inv_b); |
| ym = spu_madd(spu_nmsub(b, ym, a), inv_b, ym); |
| |
| /* Merge sign, computed exponent, and computed mantissa. |
| */ |
| exp = spu_rl(spu_add((vec_int4)e_div_3, 1023), 20); |
| exp = spu_andc(exp, (vec_int4)mant_mask); |
| out = spu_sel((vec_double2)exp, in, VEC_SPLAT_U64(0x8000000000000000ULL)); |
| out = spu_mul(out, ym); |
| |
| out = spu_andc(out, (vec_double2)mask); |
| |
| return (spu_extract(out, 0)); |
| } |
| |
| #endif /* _CBRT_H_ */ |