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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 <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
};
/* Stored values for 2^-m, where values of m are defined in M1P above. */
static const double __mpexp_twomm1[33] =
{
0x1.0p0, 0x1.0p0, 0x1.0p0, 0x1.0p0,
0x1.0p-17, 0x1.0p-23, 0x1.0p-23, 0x1.0p-28,
0x1.0p-27, 0x1.0p-38, 0x1.0p-42, 0x1.0p-39,
0x1.0p-43, 0x1.0p-47, 0x1.0p-43, 0x1.0p-47,
0x1.0p-50, 0x1.0p-54, 0x1.0p-57, 0x1.0p-60,
0x1.0p-64, 0x1.0p-67, 0x1.0p-71, 0x1.0p-74,
0x1.0p-68, 0x1.0p-71, 0x1.0p-74, 0x1.0p-77,
0x1.0p-70, 0x1.0p-73, 0x1.0p-76, 0x1.0p-78,
0x1.0p-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];
for (i = 0; i < EX; i++)
a *= RADIXI;
for (; i > EX; i--)
a *= RADIX;
b = X[1];
m2 = 24 * EX;
for (; b < HALFRAD; m2--)
{
a *= TWO;
b *= TWO;
}
if (b == HALFRAD)
{
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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