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/*
* IBM Accurate Mathematical Library
* written by International Business Machines Corp.
* Copyright (C) 2001-2013 Free Software Foundation, Inc.
*
* This program is free software; you can redistribute it and/or modify
* it under the terms of the GNU Lesser General Public License as published by
* the Free Software Foundation; either version 2.1 of the License, or
* (at your option) any later version.
*
* This program is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
* GNU Lesser General Public License for more details.
*
* You should have received a copy of the GNU Lesser General Public License
* along with this program; if not, see <http://www.gnu.org/licenses/>.
*/
/*************************************************************************/
/* MODULE_NAME:mpexp.c */
/* */
/* FUNCTIONS: mpexp */
/* */
/* FILES NEEDED: mpa.h endian.h mpexp.h */
/* mpa.c */
/* */
/* Multi-Precision exponential function subroutine */
/* ( for p >= 4, 2**(-55) <= abs(x) <= 1024 ). */
/*************************************************************************/
#include "endian.h"
#include "mpa.h"
#include "mpexp.h"
#include <assert.h>
#ifndef SECTION
# define SECTION
#endif
/* Multi-Precision exponential function subroutine (for p >= 4, */
/* 2**(-55) <= abs(x) <= 1024). */
void
SECTION
__mpexp(mp_no *x, mp_no *y, int p) {
int i,j,k,m,m1,m2,n;
double a,b;
static const int np[33] = {0,0,0,0,3,3,4,4,5,4,4,5,5,5,6,6,6,6,6,6,
6,6,6,6,7,7,7,7,8,8,8,8,8};
static const int m1p[33]= {0,0,0,0,17,23,23,28,27,38,42,39,43,47,43,47,50,54,
57,60,64,67,71,74,68,71,74,77,70,73,76,78,81};
static const int m1np[7][18] = {
{ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
{ 0, 0, 0, 0,36,48,60,72, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
{ 0, 0, 0, 0,24,32,40,48,56,64,72, 0, 0, 0, 0, 0, 0, 0},
{ 0, 0, 0, 0,17,23,29,35,41,47,53,59,65, 0, 0, 0, 0, 0},
{ 0, 0, 0, 0, 0, 0,23,28,33,38,42,47,52,57,62,66, 0, 0},
{ 0, 0, 0, 0, 0, 0, 0, 0,27, 0, 0,39,43,47,51,55,59,63},
{ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,43,47,50,54}};
mp_no mpk = {0,{0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,
0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,
0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0}};
mp_no mps,mpak,mpt1,mpt2;
/* Choose m,n and compute a=2**(-m) */
n = np[p]; m1 = m1p[p]; a = __mpexp_twomm1[p].d;
for (i=0; i<EX; i++) a *= RADIXI;
for ( ; i>EX; i--) a *= RADIX;
b = X[1]*RADIXI; m2 = 24*EX;
for (; b<HALF; m2--) { a *= TWO; b *= TWO; }
if (b == HALF) {
for (i=2; i<=p; i++) { if (X[i]!=ZERO) break; }
if (i==p+1) { m2--; a *= TWO; }
}
m = m1 + m2;
if (__glibc_unlikely (m <= 0))
{
/* The m1np array which is used to determine if we can reduce the
polynomial expansion iterations, has only 18 elements. Besides,
numbers smaller than those required by p >= 18 should not come here
at all since the fast phase of exp returns 1.0 for anything less
than 2^-55. */
assert (p < 18);
m = 0;
a = ONE;
for (i = n - 1; i > 0; i--, n--)
if (m1np[i][p] + m2 > 0)
break;
}
/* Compute s=x*2**(-m). Put result in mps */
__dbl_mp(a,&mpt1,p);
__mul(x,&mpt1,&mps,p);
/* Evaluate the polynomial. Put result in mpt2 */
mpk.e = 1; mpk.d[0] = ONE; mpk.d[1]=n;
__dvd(&mps,&mpk,&mpt1,p);
__add(&mpone,&mpt1,&mpak,p);
for (k=n-1; k>1; k--) {
__mul(&mps,&mpak,&mpt1,p);
mpk.d[1] = k;
__dvd(&mpt1,&mpk,&mpt2,p);
__add(&mpone,&mpt2,&mpak,p);
}
__mul(&mps,&mpak,&mpt1,p);
__add(&mpone,&mpt1,&mpt2,p);
/* Raise polynomial value to the power of 2**m. Put result in y */
for (k=0,j=0; k<m; ) {
__mul(&mpt2,&mpt2,&mpt1,p); k++;
if (k==m) { j=1; break; }
__mul(&mpt1,&mpt1,&mpt2,p); k++;
}
if (j) __cpy(&mpt1,y,p);
else __cpy(&mpt2,y,p);
return;
}
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