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/* -------------------------------------------------------------- */
/* (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 <spu_intrinsics.h>
/*
* 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__ */
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