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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: mpa.h */
/* */
/* FUNCTIONS: */
/* mcr */
/* acr */
/* cpy */
/* mp_dbl */
/* dbl_mp */
/* add */
/* sub */
/* mul */
/* dvd */
/* */
/* Arithmetic functions for multiple precision numbers. */
/* Common types and definition */
/************************************************************************/
#include <mpa-arch.h>
/* The mp_no structure holds the details of a multi-precision floating point
number.
- The radix of the number (R) is 2 ^ 24.
- E: The exponent of the number.
- D[0]: The sign (-1, 1) or 0 if the value is 0. In the latter case, the
values of the remaining members of the structure are ignored.
- D[1] - D[p]: The mantissa of the number where:
0 <= D[i] < R and
P is the precision of the number and 1 <= p <= 32
D[p+1] ... D[39] have no significance.
- The value of the number is:
D[1] * R ^ (E - 1) + D[2] * R ^ (E - 2) ... D[p] * R ^ (E - p)
*/
typedef struct
{
int e;
mantissa_t d[40];
} mp_no;
typedef union
{
int i[2];
double d;
} number;
extern const mp_no mpone;
extern const mp_no mptwo;
#define X x->d
#define Y y->d
#define Z z->d
#define EX x->e
#define EY y->e
#define EZ z->e
#define ABS(x) ((x) < 0 ? -(x) : (x))
#ifndef RADIXI
# define RADIXI 0x1.0p-24 /* 2^-24 */
#endif
#ifndef TWO52
# define TWO52 0x1.0p52 /* 2^52 */
#endif
#define TWO5 TWOPOW (5) /* 2^5 */
#define TWO8 TWOPOW (8) /* 2^52 */
#define TWO10 TWOPOW (10) /* 2^10 */
#define TWO18 TWOPOW (18) /* 2^18 */
#define TWO19 TWOPOW (19) /* 2^19 */
#define TWO23 TWOPOW (23) /* 2^23 */
#define HALFRAD TWO23
#define TWO57 0x1.0p57 /* 2^57 */
#define TWO71 0x1.0p71 /* 2^71 */
#define TWOM1032 0x1.0p-1032 /* 2^-1032 */
#define TWOM1022 0x1.0p-1022 /* 2^-1022 */
#define HALF 0x1.0p-1 /* 1/2 */
#define MHALF -0x1.0p-1 /* -1/2 */
int __acr (const mp_no *, const mp_no *, int);
void __cpy (const mp_no *, mp_no *, int);
void __mp_dbl (const mp_no *, double *, int);
void __dbl_mp (double, mp_no *, int);
void __add (const mp_no *, const mp_no *, mp_no *, int);
void __sub (const mp_no *, const mp_no *, mp_no *, int);
void __mul (const mp_no *, const mp_no *, mp_no *, int);
void __sqr (const mp_no *, mp_no *, int);
void __dvd (const mp_no *, const mp_no *, mp_no *, int);
extern void __mpatan (mp_no *, mp_no *, int);
extern void __mpatan2 (mp_no *, mp_no *, mp_no *, int);
extern void __mpsqrt (mp_no *, mp_no *, int);
extern void __mpexp (mp_no *, mp_no *, int);
extern void __c32 (mp_no *, mp_no *, mp_no *, int);
extern int __mpranred (double, mp_no *, int);
/* Given a power POW, build a multiprecision number 2^POW. */
static inline void
__pow_mp (int pow, mp_no *y, int p)
{
int i, rem;
/* The exponent is E such that E is a factor of 2^24. The remainder (of the
form 2^x) goes entirely into the first digit of the mantissa as it is
always less than 2^24. */
EY = pow / 24;
rem = pow - EY * 24;
EY++;
/* If the remainder is negative, it means that POW was negative since
|EY * 24| <= |pow|. Adjust so that REM is positive and still less than
24 because of which, the mantissa digit is less than 2^24. */
if (rem < 0)
{
EY--;
rem += 24;
}
/* The sign of any 2^x is always positive. */
Y[0] = 1;
Y[1] = 1 << rem;
/* Everything else is 0. */
for (i = 2; i <= p; i++)
Y[i] = 0;
}
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