/* -------------------------------------------------------------- */ /* (C)Copyright 2001,2008, */ /* 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 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 _RECIPD2_H_ #define _RECIPD2_H_ 1 #include /* * FUNCTION * vector double _recipd2(vector double value) * * DESCRIPTION * The _recipd2 function inverts "value" and returns the result. * Computation is performed using the single precision reciprocal * estimate and interpolate instructions to produce a 12 accurate * estimate. * * One (1) iteration of a Newton-Raphson is performed to improve * accuracy to single precision floating point. Two additional double * precision iterations are needed to achieve a full double * preicision result. * * The Newton-Raphson iteration is of the form: * a) X[i+1] = X[i] * (2.0 - b*X[i]) * or * b) X[i+1] = X[i] + X[i]*(1.0 - X[i]*b) * where b is the input value to be inverted * * The later (b) form improves the accuracy to 99.95% correctly rounded. */ static __inline vector double _recipd2(vector double value_in) { vec_float4 x0; vec_float4 value; vec_float4 one = spu_splats(1.0f); vec_double2 one_d = spu_splats(1.0); vec_double2 x1, x2, x3; vec_double2 scale; vec_double2 exp, value_d; vec_ullong2 expmask = spu_splats(0x7FF0000000000000ULL); vec_ullong2 is0inf; #ifdef __SPU_EDP__ vec_ullong2 isdenorm; vec_ullong2 expmask_minus1 = spu_splats(0x7FE0000000000000ULL); /* Determine special input values. For example, if the input is a denorm, infinity or 0 */ isdenorm = spu_testsv(value_in, (SPU_SV_POS_DENORM | SPU_SV_NEG_DENORM)); is0inf = spu_testsv(value_in, (SPU_SV_NEG_ZERO | SPU_SV_POS_ZERO | SPU_SV_NEG_INFINITY | SPU_SV_POS_INFINITY)); /* Scale the divisor to correct for double precision floating * point exponents that are out of single precision range. */ exp = spu_and(value_in, (vec_double2)expmask); scale = spu_xor(exp, (vec_double2)spu_sel(expmask, expmask_minus1, isdenorm)); value_d = spu_mul(value_in, scale); value = spu_roundtf(value_d); /* Perform reciprocal with 1 single precision and 2 double precision * Newton-Raphson iterations. */ x0 = spu_re(value); x1 = spu_extend(spu_madd(spu_nmsub(value, x0, one), x0, x0)); x2 = spu_madd(spu_nmsub(value_d, x1, one_d), x1, x1); x3 = spu_madd(spu_nmsub(value_d, x2, one_d), x2, x2); x3 = spu_sel(spu_mul(x3, scale), spu_xor(value_in, (vector double)expmask), is0inf); #else /* !__SPU_EDP__ */ vec_uint4 isinf, iszero, isdenorm0; vec_double2 value_abs; vec_double2 sign = spu_splats(-0.0); vec_double2 denorm_scale = (vec_double2)spu_splats(0x4330000000000000ULL); vec_double2 exp_53 = (vec_double2)spu_splats(0x0350000000000000ULL); vec_uchar16 splat_hi = (vec_uchar16){0,1,2,3, 0,1,2,3, 8,9,10,11, 8,9,10,11}; vec_uchar16 swap = (vec_uchar16){4,5,6,7, 0,1,2,3, 12,13,14,15, 8,9,10,11}; value_abs = spu_andc(value_in, sign); exp = spu_and(value_in, (vec_double2)expmask); /* Determine if the input is a special value. These include: * denorm - then we must coerce it to a normal value. * zero - then we must return an infinity * infinity - then we must return a zero. */ isdenorm0 = spu_cmpeq(spu_shuffle((vec_uint4)exp, (vec_uint4)exp, splat_hi), 0); isinf = spu_cmpeq((vec_uint4)value_abs, (vec_uint4)expmask); iszero = spu_cmpeq((vec_uint4)value_abs, 0); isinf = spu_and(isinf, spu_shuffle(isinf, isinf, swap)); iszero = spu_and(iszero, spu_shuffle(iszero, iszero, swap)); is0inf = (vec_ullong2)spu_or(isinf, iszero); /* If the inputs is a denorm, we must first convert it to a normal number since * arithmetic operations on denormals produces 0 on Cell/B.E. */ value_d = spu_sub(spu_or(value_abs, exp_53), exp_53); value_d = spu_sel(value_abs, value_d, (vec_ullong2)isdenorm0); /* Scale the divisor to correct for double precision floating * point exponents that are out of single precision range. */ scale = spu_xor(spu_and(value_d, (vec_double2)expmask), (vec_double2)expmask); value_d = spu_mul(value_d, scale); value = spu_roundtf(value_d); /* Perform reciprocal with 1 single precision and 2 double precision * Newton-Raphson iterations. The bias is removed after the single * precision iteration. */ x0 = spu_re(value); x1 = spu_extend(spu_madd(spu_nmsub(value, x0, one), x0, x0)); x2 = spu_madd(spu_nmsub(value_d, x1, one_d), x1, x1); x3 = spu_madd(spu_nmsub(value_d, x2, one_d), x2, x2); x3 = spu_mul(x3, spu_sel(scale, value_in, (vec_ullong2)sign)); x3 = spu_sel(x3, spu_mul(x3, denorm_scale), (vec_ullong2)isdenorm0); x3 = spu_sel(x3, spu_xor(value_in, (vector double)expmask), is0inf); #endif /* __SPU_EDP__ */ return (x3); } #endif /* _RECIPD2_H_ */ #endif /* __SPU__ */