166 lines
6.9 KiB
C
166 lines
6.9 KiB
C
/* -------------------------------------------------------------- */
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/* (C)Copyright 2006,2007, */
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/* International Business Machines Corporation, */
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/* Sony Computer Entertainment, Incorporated, */
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/* Toshiba Corporation, */
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/* */
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/* All Rights Reserved. */
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/* */
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/* Redistribution and use in source and binary forms, with or */
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/* without modification, are permitted provided that the */
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/* following conditions are met: */
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/* */
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/* - Redistributions of source code must retain the above copyright*/
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/* notice, this list of conditions and the following disclaimer. */
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/* */
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/* - Redistributions in binary form must reproduce the above */
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/* copyright notice, this list of conditions and the following */
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/* disclaimer in the documentation and/or other materials */
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/* provided with the distribution. */
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/* */
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/* - Neither the name of IBM Corporation nor the names of its */
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/* contributors may be used to endorse or promote products */
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/* derived from this software without specific prior written */
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/* permission. */
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/* Redistributions of source code must retain the above copyright */
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/* notice, this list of conditions and the following disclaimer. */
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/* */
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/* Redistributions in binary form must reproduce the above */
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/* copyright notice, this list of conditions and the following */
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/* disclaimer in the documentation and/or other materials */
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/* provided with the distribution. */
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/* */
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/* Neither the name of IBM Corporation nor the names of its */
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/* contributors may be used to endorse or promote products */
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/* derived from this software without specific prior written */
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/* permission. */
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/* */
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/* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND */
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/* CONTRIBUTORS "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, */
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/* INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF */
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/* MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE */
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/* DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR */
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/* CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, */
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/* SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT */
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/* NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; */
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/* LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) */
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/* HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN */
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/* CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR */
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/* OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, */
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/* EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. */
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/* -------------------------------------------------------------- */
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/* PROLOG END TAG zYx */
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#ifdef __SPU__
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#ifndef _EXPD2_H_
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#define _EXPD2_H_ 1
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#include <spu_intrinsics.h>
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#include "floord2.h"
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#include "ldexpd2.h"
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#define LOG2E 1.4426950408889634073599 // 1/log(2)
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/*
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* FUNCTION
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* vector double _expd2(vector double x)
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*
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* DESCRIPTION
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* _expd2 computes e raised to the input x for
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* each of the element of the double word vector.
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*
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* Calculation is performed by reducing the input argument
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* to within a managable range, and then computing the power
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* series to the 11th degree.
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*
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* Range reduction is performed using the property:
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*
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* exp(x) = 2^n * exp(r)
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*
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* Values for "n" and "r" are determined such that:
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*
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* x = n * ln(2) + r, |r| <= ln(2)/2
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*
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* n = floor( (x/ln(2)) + 1/2 )
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* r = x - (n * ln(2))
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*
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* To enhance the precision for "r", computation is performed
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* using a two part representation of ln(2).
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*
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* Once the input is reduced, the power series is computed:
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*
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* __12_
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* \
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* exp(x) = 1 + \ (x^i)/i!
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* /
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* /____
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* i=2
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*
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* The resulting value is scaled by 2^n and returned.
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*
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*/
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static __inline vector double _expd2(vector double x)
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{
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vec_uchar16 even2odd = ((vec_uchar16){0x80, 0x80, 0x80, 0x80, 0, 1, 2, 3,
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0x80, 0x80, 0x80, 0x80, 8, 9, 10, 11});
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// log(2) in extended machine representable precision
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vec_double2 ln2_hi = spu_splats(6.9314575195312500E-1); // 3FE62E4000000000
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vec_double2 ln2_lo = spu_splats(1.4286068203094172E-6); // 3EB7F7D1CF79ABCA
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// coefficients for the power series
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vec_double2 f02 = spu_splats(5.00000000000000000000E-1); // 1/(2!)
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vec_double2 f03 = spu_splats(1.66666666666666666667E-1); // 1/(3!)
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vec_double2 f04 = spu_splats(4.16666666666666666667E-2); // 1/(4!)
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vec_double2 f05 = spu_splats(8.33333333333333333333E-3); // 1/(5!)
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vec_double2 f06 = spu_splats(1.38888888888888888889E-3); // 1/(6!)
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vec_double2 f07 = spu_splats(1.98412698412698412698E-4); // 1/(7!)
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vec_double2 f08 = spu_splats(2.48015873015873015873E-5); // 1/(8!)
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vec_double2 f09 = spu_splats(2.75573192239858906526E-6); // 1/(9!)
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vec_double2 f10 = spu_splats(2.75573192239858906526E-7); // 1/(10!)
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vec_double2 f11 = spu_splats(2.50521083854417187751E-8); // 1/(11!)
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vec_double2 f12 = spu_splats(2.08767569878680989792E-9); // 1/(12!)
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// rx = floor(1/2 + x/log(2))
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vec_double2 rx = _floord2(spu_madd(x,spu_splats(LOG2E),spu_splats(0.5)));
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// extract the exponent of reduction
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vec_int4 nint = spu_convts(spu_roundtf(rx),0);
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vec_llong2 n = spu_extend(spu_shuffle(nint, nint, even2odd));
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// reduce the input to within [ -ln(2)/2 ... ln(2)/2 ]
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vec_double2 r;
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r = spu_nmsub(rx,ln2_hi,x);
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r = spu_nmsub(rx,ln2_lo,r);
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vec_double2 result;
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vec_double2 r2 = spu_mul(r,r);
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// Use Horner's method on the power series
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result = spu_madd(r,f12,f11);
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result = spu_madd(result,r,f10);
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result = spu_madd(result,r,f09);
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result = spu_madd(result,r,f08);
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result = spu_madd(result,r,f07);
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result = spu_madd(result,r,f06);
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result = spu_madd(result,r,f05);
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result = spu_madd(result,r,f04);
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result = spu_madd(result,r,f03);
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result = spu_madd(result,r,f02);
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result = spu_madd(result,r2,r);
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result = spu_add(result,spu_splats(1.0));
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// Scale the result
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result = _ldexpd2(result, n);
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return result;
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}
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#endif /* _EXPD2_H_ */
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#endif /* __SPU__ */
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