436 lines
12 KiB
C
436 lines
12 KiB
C
/*
|
|
* Copyright (c) 2002 by The XFree86 Project, Inc.
|
|
*
|
|
* Permission is hereby granted, free of charge, to any person obtaining a
|
|
* copy of this software and associated documentation files (the "Software"),
|
|
* to deal in the Software without restriction, including without limitation
|
|
* the rights to use, copy, modify, merge, publish, distribute, sublicense,
|
|
* and/or sell copies of the Software, and to permit persons to whom the
|
|
* Software is furnished to do so, subject to the following conditions:
|
|
*
|
|
* The above copyright notice and this permission notice shall be included in
|
|
* all copies or substantial portions of the Software.
|
|
*
|
|
* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
|
|
* IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
|
|
* FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
|
|
* THE XFREE86 PROJECT BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY,
|
|
* WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF
|
|
* OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
|
|
* SOFTWARE.
|
|
*
|
|
* Except as contained in this notice, the name of the XFree86 Project shall
|
|
* not be used in advertising or otherwise to promote the sale, use or other
|
|
* dealings in this Software without prior written authorization from the
|
|
* XFree86 Project.
|
|
*
|
|
* Author: Paulo César Pereira de Andrade
|
|
*/
|
|
|
|
/* $XFree86: xc/programs/xedit/lisp/mp/mp.h,v 1.5tsi Exp $ */
|
|
|
|
#include <stdio.h>
|
|
#include <math.h>
|
|
#ifdef sun
|
|
#include <ieeefp.h>
|
|
#endif
|
|
#include <float.h>
|
|
#include <stdlib.h>
|
|
#include <limits.h>
|
|
#include <ctype.h>
|
|
#include <string.h>
|
|
|
|
#ifndef __mp_h_
|
|
#define __mp_h_
|
|
|
|
#ifdef __GNUC__
|
|
#define INLINE __inline__
|
|
#else
|
|
#define INLINE /**/
|
|
#endif
|
|
|
|
/* this normally is better for multiplication and also
|
|
* simplify addition loops putting the larger value first */
|
|
#define MP_SWAP(op1, op2, len1, len2) { \
|
|
BNS *top = op1; \
|
|
BNI tlen = len1; \
|
|
\
|
|
op1 = op2; \
|
|
len1 = len2; \
|
|
op2 = top; \
|
|
len2 = tlen; \
|
|
}
|
|
|
|
/*
|
|
* At least this length to use Karatsuba multiplication method
|
|
*/
|
|
#define KARATSUBA 32
|
|
|
|
/*
|
|
* At least this length to use Toom multiplication method
|
|
*/
|
|
#define TOOM 128
|
|
|
|
#if ULONG_MAX > 4294967295UL
|
|
/* sizeof(long) == 8 and sizeof(int) == 4 */
|
|
# define BNI unsigned long
|
|
# define BNS unsigned int
|
|
# define MINSLONG 0x8000000000000000UL
|
|
# define CARRY 0x100000000
|
|
# define LMASK 0xffffffff00000000UL
|
|
# define SMASK 0x00000000ffffffffUL
|
|
# define BNIBITS 64
|
|
# define BNSBITS 32
|
|
# ifndef LONG64
|
|
# define LONG64
|
|
# endif
|
|
#else
|
|
/* sizeof(long) == 4 and sizeof(short) == 2 */
|
|
# define BNI unsigned long
|
|
# define BNS unsigned short
|
|
# define MINSLONG 0x80000000UL
|
|
# define CARRY 0x10000
|
|
# define LMASK 0xffff0000UL
|
|
# define SMASK 0x0000ffffUL
|
|
# define BNIBITS 32
|
|
# define BNSBITS 16
|
|
#endif
|
|
|
|
#ifdef MAX
|
|
#undef MAX
|
|
#endif
|
|
#define MAX(a, b) ((a) > (b) ? (a) : (b))
|
|
|
|
#ifdef MIN
|
|
#undef MIN
|
|
#endif
|
|
#define MIN(a, b) ((a) < (b) ? (a) : (b))
|
|
|
|
/*
|
|
* Types
|
|
*/
|
|
typedef struct _mpi {
|
|
unsigned int size : 31;
|
|
unsigned int sign : 1;
|
|
BNI alloc;
|
|
BNS *digs; /* LSF format */
|
|
} mpi;
|
|
|
|
typedef struct _mpr {
|
|
mpi num;
|
|
mpi den;
|
|
} mpr;
|
|
|
|
typedef void *(*mp_malloc_fun)(size_t);
|
|
typedef void *(*mp_calloc_fun)(size_t, size_t);
|
|
typedef void *(*mp_realloc_fun)(void*, size_t);
|
|
typedef void (*mp_free_fun)(void*);
|
|
|
|
/*
|
|
* Prototypes
|
|
*/
|
|
/* GENERIC FUNCTIONS */
|
|
/* memory allocation wrappers */
|
|
void *mp_malloc(size_t size);
|
|
void *mp_calloc(size_t nmemb, size_t size);
|
|
void *mp_realloc(void *pointer, size_t size);
|
|
void mp_free(void *pointer);
|
|
mp_malloc_fun mp_set_malloc(mp_malloc_fun);
|
|
mp_calloc_fun mp_set_calloc(mp_calloc_fun);
|
|
mp_realloc_fun mp_set_realloc(mp_realloc_fun);
|
|
mp_free_fun mp_set_free(mp_free_fun);
|
|
|
|
/* adds op1 and op2, stores result in rop
|
|
* rop must pointer to at least len1 + len2 + 1 elements
|
|
* rop can be either op1 or op2 */
|
|
long mp_add(BNS *rop, BNS *op1, BNS *op2, BNI len1, BNI len2);
|
|
|
|
/* subtracts op2 from op1, stores result in rop
|
|
* rop must pointer to at least len1 + len2 elements
|
|
* op1 must be >= op2
|
|
* rop can be either op1 or op2 */
|
|
long mp_sub(BNS *rop, BNS *op1, BNS *op2, BNI len1, BNI len2);
|
|
|
|
/* shift op to the left shift bits
|
|
* rop must have enough storage for result
|
|
* rop can be op */
|
|
long mp_lshift(BNS *rop, BNS *op, BNI len, long shift);
|
|
|
|
/* shift op to the right shift bits
|
|
* shift must be positive
|
|
* rop can be op */
|
|
long mp_rshift(BNS *rop, BNS *op, BNI len, long shift);
|
|
|
|
/* use simple generic multiplication method
|
|
* rop cannot be the same as op1 or op2
|
|
* rop must be zeroed
|
|
* op1 can be op2 */
|
|
long mp_base_mul(BNS *rop, BNS *op1, BNS *op2, BNI len1, BNI len2);
|
|
|
|
/* use Karatsuba method
|
|
* MIN(len1, len2) must be larger than (MAX(len1, len2) + 1) >> 1
|
|
* MAX(len1, len2) should be at least 2
|
|
* rop cannot be the same as op1 or op2
|
|
* rop must be zeroed
|
|
* op1 can be op2 */
|
|
long mp_karatsuba_mul(BNS *rop, BNS *op1, BNS *op2, BNI len1, BNI len2);
|
|
|
|
/* use Toom method
|
|
* len1 / 3 should be equal to len2 / 3
|
|
* len1 / 3 should be at least 1
|
|
* rop cannot be the same as op1 or op2
|
|
* rop must be zeroed
|
|
* op1 can be op2 */
|
|
long mp_toom_mul(BNS *rop, BNS *op1, BNS *op2, BNI len1, BNI len2);
|
|
|
|
/* chooses the available multiplication methods based on it's input
|
|
* rop must be a pointer to len1 + len2 elements
|
|
* rop cannot be the same as op1 or op2
|
|
* rop must be zeroed
|
|
* op1 can be op2 */
|
|
long mp_mul(BNS *rop, BNS *op1, BNS *op2, BNI len1, BNI len2);
|
|
|
|
/* INTEGER FUNCTIONS */
|
|
/* initialize op and set it to 0 */
|
|
void mpi_init(mpi *op);
|
|
|
|
/* clear memory associated to op */
|
|
void mpi_clear(mpi *op);
|
|
|
|
/* set rop to the value of op */
|
|
void mpi_set(mpi *rop, mpi *op);
|
|
|
|
/* set rop to the value of si */
|
|
void mpi_seti(mpi *rop, long si);
|
|
|
|
/* set rop to the floor(fabs(d)) */
|
|
void mpi_setd(mpi *rop, double d);
|
|
|
|
/* initialize rop to number representation in str in the given base.
|
|
* leading zeros are skipped.
|
|
* if sign present, it is processed.
|
|
* base must be in the range 2 to 36. */
|
|
void mpi_setstr(mpi *rop, char *str, int base);
|
|
|
|
/* adds two mp integers */
|
|
void mpi_add(mpi *rop, mpi *op1, mpi *op2);
|
|
|
|
/* adds op1 and op2 */
|
|
void mpi_addi(mpi *rop, mpi *op1, long op2);
|
|
|
|
/* subtracts two mp integers */
|
|
void mpi_sub(mpi *rop, mpi *op1, mpi *op2);
|
|
|
|
/* subtracts op2 from op1 */
|
|
void mpi_subi(mpi *rop, mpi *op1, long op2);
|
|
|
|
/* multiply two mp integers */
|
|
void mpi_mul(mpi *rop, mpi *op1, mpi *op2);
|
|
|
|
/* multiply op1 by op2 */
|
|
void mpi_muli(mpi *rop, mpi *op1, long op2);
|
|
|
|
/* divides num by den and sets rop to result */
|
|
void mpi_div(mpi *rop, mpi *num, mpi *den);
|
|
|
|
/* divides num by den and sets rop to the remainder */
|
|
void mpi_rem(mpi *rop, mpi *num, mpi *den);
|
|
|
|
/* divides num by den, sets quotient to qrop and remainder to rrop
|
|
* qrop is truncated towards zero.
|
|
* qrop and rrop are optional
|
|
* qrop and rrop cannot be the same variable */
|
|
void mpi_divqr(mpi *qrop, mpi *rrop, mpi *num, mpi *den);
|
|
|
|
/* divides num by then and stores result in rop */
|
|
void mpi_divi(mpi *rop, mpi *num, long den);
|
|
|
|
/* divides num by den and returns remainder */
|
|
long mpi_remi(mpi *num, long den);
|
|
|
|
/* divides num by den
|
|
* stores quotient in qrop and returns remainder */
|
|
long mpi_divqri(mpi *qrop, mpi *num, long den);
|
|
|
|
/* sets rop to num modulo den */
|
|
void mpi_mod(mpi *rop, mpi *num, mpi *den);
|
|
|
|
/* returns num modulo den */
|
|
long mpi_modi(mpi *num, long den);
|
|
|
|
/* sets rop to the greatest common divisor of num and den
|
|
* result is always positive */
|
|
void mpi_gcd(mpi *rop, mpi *num, mpi *den);
|
|
|
|
/* sets rop to the least common multiple of num and den
|
|
* result is always positive */
|
|
void mpi_lcm(mpi *rop, mpi *num, mpi *den);
|
|
|
|
/* sets rop to op raised to exp */
|
|
void mpi_pow(mpi *rop, mpi *op, unsigned long exp);
|
|
|
|
/* sets rop to the integer part of the nth root of op.
|
|
* returns 1 if result is exact, 0 otherwise */
|
|
int mpi_root(mpi *rop, mpi *op, unsigned long nth);
|
|
|
|
/* sets rop to the integer part of the square root of op.
|
|
* returns 1 if result is exact, 0 otherwise */
|
|
int mpi_sqrt(mpi *rop, mpi *op);
|
|
|
|
/* bit shift, left if shift positive, right if negative
|
|
* a fast way to multiply and divide by powers of two */
|
|
void mpi_ash(mpi *rop, mpi *op, long shift);
|
|
|
|
/* sets rop to op1 logand op2 */
|
|
void mpi_and(mpi *rop, mpi *op1, mpi *op2);
|
|
|
|
/* sets rop to op1 logior op2 */
|
|
void mpi_ior(mpi *rop, mpi *op1, mpi *op2);
|
|
|
|
/* sets rop to op1 logxor op2 */
|
|
void mpi_xor(mpi *rop, mpi *op1, mpi *op2);
|
|
|
|
/* sets rop to one's complement of op */
|
|
void mpi_com(mpi *rop, mpi *op);
|
|
|
|
/* sets rop to -op */
|
|
void mpi_neg(mpi *rop, mpi *op);
|
|
|
|
/* sets rop to the absolute value of op */
|
|
void mpi_abs(mpi *rop, mpi *op);
|
|
|
|
/* compares op1 and op2
|
|
* returns >0 if op1 > op2, 0 if op1 = op2, and <0 if op1 < op2 */
|
|
int mpi_cmp(mpi *op1, mpi *op2);
|
|
|
|
/* mpi_cmp with a long integer operand */
|
|
int mpi_cmpi(mpi *op1, long op2);
|
|
|
|
/* compares absolute value of op1 and op2
|
|
* returns >0 if abs(op1) > abs(op2), 0 if abs(op1) = abs(op2),
|
|
* and <0 if abs(op1) < abs(op2) */
|
|
int mpi_cmpabs(mpi *op1, mpi *op2);
|
|
|
|
/* mpi_cmpabs with a long integer operand */
|
|
int mpi_cmpabsi(mpi *op1, long op2);
|
|
|
|
/* returns 1 if op1 > 0, 0 if op1 = 0, and -1 if op1 < 0 */
|
|
int mpi_sgn(mpi *op);
|
|
|
|
/* fastly swaps contents of op1 and op2 */
|
|
void mpi_swap(mpi *op1, mpi *op2);
|
|
|
|
/* returns 1 if op fits in a signed long int, 0 otherwise */
|
|
int mpi_fiti(mpi *op);
|
|
|
|
/* converts mp integer to long int
|
|
* to know if the value will fit, call mpi_fiti */
|
|
long mpi_geti(mpi *op);
|
|
|
|
/* convert mp integer to double */
|
|
double mpi_getd(mpi *op);
|
|
|
|
/* returns exact number of characters to represent mp integer
|
|
* in given base, excluding sign and ending null character.
|
|
* base must be in the range 2 to 36 */
|
|
unsigned long mpi_getsize(mpi *op, int base);
|
|
|
|
/* returns pointer to string with representation of mp integer
|
|
* if str is not NULL, it must have enough space to store integer
|
|
* representation, if NULL a newly allocated string is returned.
|
|
* base must be in the range 2 to 36 */
|
|
char *mpi_getstr(char *str, mpi *op, int base);
|
|
|
|
/* RATIO FUNCTIONS */
|
|
#define mpr_num(op) (&((op)->num))
|
|
#define mpr_den(op) (&((op)->den))
|
|
|
|
/* initialize op and set it to 0/1 */
|
|
void mpr_init(mpr *op);
|
|
|
|
/* clear memory associated to op */
|
|
void mpr_clear(mpr *op);
|
|
|
|
/* set rop to the value of op */
|
|
void mpr_set(mpr *rop, mpr *op);
|
|
|
|
/* set rop to num/den */
|
|
void mpr_seti(mpr *rop, long num, long den);
|
|
|
|
/* set rop to the value of d */
|
|
void mpr_setd(mpr *rop, double d);
|
|
|
|
/* initialize rop to number representation in str in the given base.
|
|
* leading zeros are skipped.
|
|
* if sign present, it is processed.
|
|
* base must be in the range 2 to 36. */
|
|
void mpr_setstr(mpr *rop, char *str, int base);
|
|
|
|
/* remove common factors of op */
|
|
void mpr_canonicalize(mpr *op);
|
|
|
|
/* adds two mp rationals */
|
|
void mpr_add(mpr *rop, mpr *op1, mpr *op2);
|
|
|
|
/* adds op1 and op2 */
|
|
void mpr_addi(mpr *rop, mpr *op1, long op2);
|
|
|
|
/* subtracts two mp rationals */
|
|
void mpr_sub(mpr *rop, mpr *op1, mpr *op2);
|
|
|
|
/* subtracts op2 from op1 */
|
|
void mpr_subi(mpr *rop, mpr *op1, long op2);
|
|
|
|
/* multiply two mp rationals */
|
|
void mpr_mul(mpr *rop, mpr *op1, mpr *op2);
|
|
|
|
/* multiply op1 by op2 */
|
|
void mpr_muli(mpr *rop, mpr *op1, long op2);
|
|
|
|
/* divide two mp rationals */
|
|
void mpr_div(mpr *rop, mpr *op1, mpr *op2);
|
|
|
|
/* divides op1 by op2 */
|
|
void mpr_divi(mpr *rop, mpr *op1, long op2);
|
|
|
|
/* sets rop to 1/op */
|
|
void mpr_inv(mpr *rop, mpr *op);
|
|
|
|
/* sets rop to -op */
|
|
void mpr_neg(mpr *rop, mpr *op);
|
|
|
|
/* sets rop to the absolute value of op */
|
|
void mpr_abs(mpr *rop, mpr *op);
|
|
|
|
/* compares op1 and op2
|
|
* returns >0 if op1 > op2, 0 if op1 = op2, and <0 if op1 < op2 */
|
|
int mpr_cmp(mpr *op1, mpr *op2);
|
|
|
|
/* mpr_cmp with a long integer operand */
|
|
int mpr_cmpi(mpr *op1, long op2);
|
|
|
|
/* compares absolute value of op1 and op2
|
|
* returns >0 if abs(op1) > abs(op2), 0 if abs(op1) = abs(op2),
|
|
* and <0 if abs(op1) < abs(op2) */
|
|
int mpr_cmpabs(mpr *op1, mpr *op2);
|
|
|
|
/* mpr_cmpabs with a long integer operand */
|
|
int mpr_cmpabsi(mpr *op1, long op2);
|
|
|
|
/* fastly swaps contents of op1 and op2 */
|
|
void mpr_swap(mpr *op1, mpr *op2);
|
|
|
|
/* returns 1 if op fits in a signed long int, 0 otherwise */
|
|
int mpr_fiti(mpr *op);
|
|
|
|
/* convert mp rational to double */
|
|
double mpr_getd(mpr *op);
|
|
|
|
/* returns pointer to string with representation of mp rational
|
|
* if str is not NULL, it must have enough space to store rational
|
|
* representation, if NULL a newly allocated string is returned.
|
|
* base must be in the range 2 to 36 */
|
|
char *mpr_getstr(char *str, mpr *op, int base);
|
|
|
|
#endif /* __mp_h_ */
|