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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 _EXPD2_H_
#define _EXPD2_H_ 1
#include <spu_intrinsics.h>
#include "floord2.h"
#define LOG2E 1.4426950408889634073599 // 1/log(2)
/*
* FUNCTION
* vector double _expd2(vector double x)
*
* DESCRIPTION
* _expd2 computes e raised to the input x for
* each of the element of the double word vector.
*
* Calculation is performed by reducing the input argument
* to within a managable range, and then computing the power
* series to the 11th degree.
*
* Range reduction is performed using the property:
*
* exp(x) = 2^n * exp(r)
*
* Values for "n" and "r" are determined such that:
*
* x = n * ln(2) + r, |r| <= ln(2)/2
*
* n = floor( (x/ln(2)) + 1/2 )
* r = x - (n * ln(2))
*
* To enhance the precision for "r", computation is performed
* using a two part representation of ln(2).
*
* Once the input is reduced, the power series is computed:
*
* __12_
* \
* exp(x) = 1 + \ (x^i)/i!
* /
* /____
* i=2
*
* The resulting value is scaled by 2^n and returned.
*
*/
static __inline vector double _expd2(vector double x)
{
// log(2) in extended machine representable precision
vec_double2 ln2_hi = spu_splats(6.9314575195312500E-1); // 3FE62E4000000000
vec_double2 ln2_lo = spu_splats(1.4286068203094172E-6); // 3EB7F7D1CF79ABCA
// coefficients for the power series
// vec_double2 f01 = spu_splats(1.00000000000000000000E0); // 1/(1!)
vec_double2 f02 = spu_splats(5.00000000000000000000E-1); // 1/(2!)
vec_double2 f03 = spu_splats(1.66666666666666666667E-1); // 1/(3!)
vec_double2 f04 = spu_splats(4.16666666666666666667E-2); // 1/(4!)
vec_double2 f05 = spu_splats(8.33333333333333333333E-3); // 1/(5!)
vec_double2 f06 = spu_splats(1.38888888888888888889E-3); // 1/(6!)
vec_double2 f07 = spu_splats(1.98412698412698412698E-4); // 1/(7!)
vec_double2 f08 = spu_splats(2.48015873015873015873E-5); // 1/(8!)
vec_double2 f09 = spu_splats(2.75573192239858906526E-6); // 1/(9!)
vec_double2 f10 = spu_splats(2.75573192239858906526E-7); // 1/(10!)
vec_double2 f11 = spu_splats(2.50521083854417187751E-8); // 1/(11!)
vec_double2 f12 = spu_splats(2.08767569878680989792E-9); // 1/(12!)
// rx = floor(1/2 + x/log(2))
vec_double2 rx = _floord2(spu_madd(x,spu_splats(LOG2E),spu_splats(0.5)));
// extract the exponent of reduction
vec_int4 exp = spu_convts(spu_roundtf(rx),0);
// reduce the input to within [ -ln(2)/2 ... ln(2)/2 ]
vec_double2 r;
r = spu_nmsub(rx,ln2_hi,x);
r = spu_nmsub(rx,ln2_lo,r);
vec_double2 result;
vec_double2 r2 = spu_mul(r,r);
// Use Horner's method on the power series
/* result = ((((c12*x + c11)*x + c10)*x + c9)*x + c8)*x + c7)*x + c6)*x^6 +
((((((c5*x + c4)*x + c3)*x + c2)*x + c1)*x + c0
*/
#ifdef __SPU_EDP__
vec_double2 p1, p2, r4, r6;
p1 = spu_madd(f12, r, f11);
p2 = spu_madd(f05, r, f04);
r4 = spu_mul(r2, r2);
p1 = spu_madd(p1, r, f10);
p2 = spu_madd(p2, r, f03);
p1 = spu_madd(p1, r, f09);
p2 = spu_madd(p2, r, f02);
p1 = spu_madd(p1, r, f08);
r6 = spu_mul(r2, r4);
p1 = spu_madd(p1, r, f07);
p2 = spu_madd(p2, r2, r);
p1 = spu_madd(p1, r, f06);
result = spu_madd(r6, p1, p2);
result = spu_add(result, spu_splats(1.0));
#else
result = spu_madd(r,f12,f11);
result = spu_madd(result,r,f10);
result = spu_madd(result,r,f09);
result = spu_madd(result,r,f08);
result = spu_madd(result,r,f07);
result = spu_madd(result,r,f06);
result = spu_madd(result,r,f05);
result = spu_madd(result,r,f04);
result = spu_madd(result,r,f03);
result = spu_madd(result,r,f02);
result = spu_madd(result,r2,r);
result = spu_add(result,spu_splats(1.0));
#endif /* __SPU_EDP__ */
// Scale the result - basically a call to ldexpd2()
vec_int4 e1, e2;
vec_int4 min = spu_splats(-2044);
vec_int4 max = spu_splats(2046);
vec_uint4 cmp_min, cmp_max;
vec_uint4 shift = (vec_uint4) { 20, 32, 20, 32 };
vec_double2 f1, f2;
/* Clamp the specified exponent to the range -2044 to 2046.
*/
cmp_min = spu_cmpgt(exp, min);
cmp_max = spu_cmpgt(exp, max);
exp = spu_sel(min, exp, cmp_min);
exp = spu_sel(exp, max, cmp_max);
/* Generate the factors f1 = 2^e1 and f2 = 2^e2
*/
e1 = spu_rlmaska(exp, -1);
e2 = spu_sub(exp, e1);
f1 = (vec_double2)spu_sl(spu_add(e1, 1023), shift);
f2 = (vec_double2)spu_sl(spu_add(e2, 1023), shift);
/* Compute the product x * 2^e1 * 2^e2
*/
result = spu_mul(spu_mul(result, f1), f2);
return result;
}
#endif /* _EXPD2_H_ */
#endif /* __SPU__ */
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