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/* -------------------------------------------------------------- */
/* (C)Copyright 2006,2007, */
/* 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. */
/* 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 _SQRTD2_H_
#define _SQRTD2_H_ 1
#include <spu_intrinsics.h>
/*
* FUNCTION
* vector double _sqrtd2(vector double in)
*
* DESCRIPTION
* The _sqrtd2 function computes the square root of the vector input "in"
* and returns the result.
*
*/
static __inline vector double _sqrtd2(vector double in)
{
vec_int4 bias_exp;
vec_uint4 exp;
vec_float4 fx, fg, fy, fd, fe, fy2, fhalf;
vec_ullong2 nochange, denorm;
vec_ullong2 mask = spu_splats(0x7FE0000000000000ULL);
vec_double2 dx, de, dd, dy, dg, dy2, dhalf;
vec_double2 neg;
vec_double2 one = spu_splats(1.0);
vec_double2 two_pow_52 = (vec_double2)spu_splats(0x4330000000000000ULL);
/* If the input is a denorm, then multiply it by 2^52 so that the input is no
* longer denormal.
*/
exp = (vec_uint4)spu_and((vec_ullong2)in, spu_splats(0xFFF0000000000000ULL));
denorm = (vec_ullong2)spu_cmpeq(exp,0);
in = spu_mul(in, spu_sel(one, two_pow_52, denorm));
fhalf = spu_splats(0.5f);
dhalf = spu_splats(0.5);
/* Coerce the input, in, into the argument reduced space [0.5, 2.0).
*/
dx = spu_sel(in, dhalf, mask);
/* Compute an initial single precision guess for the square root (fg)
* and half reciprocal (fy2).
*/
fx = spu_roundtf(dx);
fy2 = spu_rsqrte(fx);
fy = spu_mul(fy2, fhalf);
fg = spu_mul(fy2, fx); /* 12-bit approximation to sqrt(cx) */
/* Perform one single precision Newton-Raphson iteration to improve
* accuracy to about 22 bits.
*/
fe = spu_nmsub(fy, fg, fhalf);
fd = spu_nmsub(fg, fg, fx);
fy = spu_madd(fy2, fe, fy);
fg = spu_madd(fy, fd, fg); /* 22-bit approximation */
dy = spu_extend(fy);
dg = spu_extend(fg);
/* Perform two double precision Newton-Raphson iteration to improve
* accuracy to about 44 and 88 bits repectively.
*/
dy2 = spu_add(dy, dy);
de = spu_nmsub(dy, dg, dhalf);
dd = spu_nmsub(dg, dg, dx);
dy = spu_madd(dy2, de, dy);
dg = spu_madd(dy, dd, dg); /* 44 bit approximation */
dd = spu_nmsub(dg, dg, dx);
dg = spu_madd(dy, dd, dg); /* full double precision approximation */
/* Compute the expected exponent assuming that it is not a special value.
* See special value handling below.
*/
bias_exp = spu_rlmaska(spu_sub((vec_int4)spu_and((vec_ullong2)in, mask),
(vec_int4)spu_splats(0x3FE0000000000000ULL)),
-1);
/* Adjust the exponent bias if the input was denormalized */
bias_exp = spu_sub(bias_exp, (vec_int4)spu_and(spu_splats(0x01A0000000000000ULL), denorm));
dg = (vec_double2)spu_add((vec_int4)dg, bias_exp);
/* Handle special inputs. These include:
*
* input output
* ========= =========
* -0 -0
* 0 0
* +infinity +infinity
* NaN NaN
* <0 NaN
*/
exp = spu_shuffle(exp, exp, ((vec_uchar16) { 0,1,2,3,0,1,2,3, 8,9,10,11,8,9,10,11 }));
neg = (vec_double2)spu_rlmaska((vec_int4)exp, -31);
nochange = spu_or((vec_ullong2)spu_cmpeq(exp, 0x7FF00000),
spu_cmpeq(in, spu_splats(0.0)));
dg = spu_sel(spu_or(dg, neg), in, nochange);
return (dg);
}
#endif /* _SQRTD2_H_ */
#endif /* __SPU__ */
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