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/*
* IBM Accurate Mathematical Library
* written by International Business Machines Corp.
* Copyright (C) 2001-2017 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:halfulp.c */
/* */
/* FUNCTIONS:halfulp */
/* FILES NEEDED: mydefs.h dla.h endian.h */
/* uroot.c */
/* */
/*Routine halfulp(double x, double y) computes x^y where result does */
/*not need rounding. If the result is closer to 0 than can be */
/*represented it returns 0. */
/* In the following cases the function does not compute anything */
/*and returns a negative number: */
/*1. if the result needs rounding, */
/*2. if y is outside the interval [0, 2^20-1], */
/*3. if x can be represented by x=2**n for some integer n. */
/************************************************************************/
#include "endian.h"
#include "mydefs.h"
#include <dla.h>
#include <math_private.h>
#ifndef SECTION
# define SECTION
#endif
static const int4 tab54[32] = {
262143, 11585, 1782, 511, 210, 107, 63, 42,
30, 22, 17, 14, 12, 10, 9, 7,
7, 6, 5, 5, 5, 4, 4, 4,
3, 3, 3, 3, 3, 3, 3, 3
};
double
SECTION
__halfulp (double x, double y)
{
mynumber v;
double z, u, uu;
#ifndef DLA_FMS
double j1, j2, j3, j4, j5;
#endif
int4 k, l, m, n;
if (y <= 0) /*if power is negative or zero */
{
v.x = y;
if (v.i[LOW_HALF] != 0)
return -10.0;
v.x = x;
if (v.i[LOW_HALF] != 0)
return -10.0;
if ((v.i[HIGH_HALF] & 0x000fffff) != 0)
return -10; /* if x =2 ^ n */
k = ((v.i[HIGH_HALF] & 0x7fffffff) >> 20) - 1023; /* find this n */
z = (double) k;
return (z * y == -1075.0) ? 0 : -10.0;
}
/* if y > 0 */
v.x = y;
if (v.i[LOW_HALF] != 0)
return -10.0;
v.x = x;
/* case where x = 2**n for some integer n */
if (((v.i[HIGH_HALF] & 0x000fffff) | v.i[LOW_HALF]) == 0)
{
k = (v.i[HIGH_HALF] >> 20) - 1023;
return (((double) k) * y == -1075.0) ? 0 : -10.0;
}
v.x = y;
k = v.i[HIGH_HALF];
m = k << 12;
l = 0;
while (m)
{
m = m << 1; l++;
}
n = (k & 0x000fffff) | 0x00100000;
n = n >> (20 - l); /* n is the odd integer of y */
k = ((k >> 20) - 1023) - l; /* y = n*2**k */
if (k > 5)
return -10.0;
if (k > 0)
for (; k > 0; k--)
n *= 2;
if (n > 34)
return -10.0;
k = -k;
if (k > 5)
return -10.0;
/* now treat x */
while (k > 0)
{
z = __ieee754_sqrt (x);
EMULV (z, z, u, uu, j1, j2, j3, j4, j5);
if (((u - x) + uu) != 0)
break;
x = z;
k--;
}
if (k)
return -10.0;
/* it is impossible that n == 2, so the mantissa of x must be short */
v.x = x;
if (v.i[LOW_HALF])
return -10.0;
k = v.i[HIGH_HALF];
m = k << 12;
l = 0;
while (m)
{
m = m << 1; l++;
}
m = (k & 0x000fffff) | 0x00100000;
m = m >> (20 - l); /* m is the odd integer of x */
/* now check whether the length of m**n is at most 54 bits */
if (m > tab54[n - 3])
return -10.0;
/* yes, it is - now compute x**n by simple multiplications */
u = x;
for (k = 1; k < n; k++)
u = u * x;
return u;
}
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