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Diffstat (limited to 'newlib/libm/machine/spu/headers/expd2.h')
| -rw-r--r-- | newlib/libm/machine/spu/headers/expd2.h | 165 |
1 files changed, 165 insertions, 0 deletions
diff --git a/newlib/libm/machine/spu/headers/expd2.h b/newlib/libm/machine/spu/headers/expd2.h new file mode 100644 index 000000000..19d77dd51 --- /dev/null +++ b/newlib/libm/machine/spu/headers/expd2.h @@ -0,0 +1,165 @@ +/* -------------------------------------------------------------- */ +/* (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 _EXPD2_H_ +#define _EXPD2_H_ 1 + +#include <spu_intrinsics.h> +#include "floord2.h" +#include "ldexpd2.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) +{ + vec_uchar16 even2odd = ((vec_uchar16){0x80, 0x80, 0x80, 0x80, 0, 1, 2, 3, + 0x80, 0x80, 0x80, 0x80, 8, 9, 10, 11}); + + // 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 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 nint = spu_convts(spu_roundtf(rx),0); + vec_llong2 n = spu_extend(spu_shuffle(nint, nint, even2odd)); + + // 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 = 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)); + + // Scale the result + result = _ldexpd2(result, n); + + return result; + + +} + + +#endif /* _EXPD2_H_ */ +#endif /* __SPU__ */ |