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sbignum.c
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sbignum.c
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/* antirez's arbitrary precision integer math library.
*
* $Id: sbignum.c,v 1.3 2003/10/02 08:21:42 antirez Exp $
*
* This library was implemented only to joke a bit with the bignum issues,
* don't expect this is very fast or well tested.
* Note that in many applications you should check that the arbitrary
* precision math implementation is very reliable.
*
* (news! actually I'm using it for hping3, so starting from
* now it is something like a real project.)
*
* NOTE: if you need a very good bignums implementation check-out GMP
* at http://swox.com/gmp/ it is very fast and reliable.
*
* This library API is almost GMP compatible for the subset of
* functions exported.
*
* COPYRIGHT NOTICE
* ----------------
*
* Copyright(C) 2002-2003 Salvatore Sanfilippo <antirez@invece.org>
* All rights reserved.
*
* This code and the documentation is released under the GPL license
* version 2 of the license. You can get a copy of the license at
* http://www.gnu.org/licenses/gpl.html
* A copy of the license is distributed with this code,
* see the file COPYING. */
/* History of important bugs:
*
* 28 Feb 2002: Bad casting in low-level subtraction generated bad results
* for particular pairs of numbers. It was a bit hard to
* discover the real origin of the bug since all started
* with a strange behaviour of the Fermat little theorem.
* This was since the modular reduction uses the low-level
* subtraction to perform its work. Of course now it's fixed.
*
* 12 Sep 2003: Fixed a memory leak in mpz_tostr().
*/
#include <stdlib.h>
#include <string.h>
#include <stdio.h>
#include <sys/types.h>
#include <ctype.h>
#include "sbignum.h"
#include "sbignum-tables.h"
/* All the function with the _raw suffix don't care about the sign
* and works if the last operand, that's specified as a mpz_atom_t pointer
* and a u_int32_t length is stored in statically allocated memory, while
* higher level functions expect operands declared as mpz_t and initialized
* with mpz_init(). */
/* Macros and functions starting with the '_' character are usually not
* exported faster versions of normal functions, that do some unsane assumption
* like there is enough memory to store the result and so on.
* They are used to build more complex functions */
/* --------------------------- Low level functions -------------------------- */
/* For the actual list of supported functions see sbignum.h */
/* inititialization/allocation */
static int mpz_zero_realloc(mpz_ptr z, u_int32_t i);
static void mpz_zero(mpz_ptr z);
/* shifting */
static int mpz_lshiftword(mpz_ptr r, u_int32_t i);
static int mpz_rshiftword(mpz_ptr r, u_int32_t i);
/* comparision */
static int32_t mpz_cmpabsi_raw(mpz_ptr a, mpz_atom_t *d, u_int32_t l);
static int32_t mpz_cmpabs(mpz_ptr a, mpz_ptr b);
/* addition */
static int mpz_addi_raw(mpz_ptr r, mpz_ptr z, mpz_atom_t *d, u_int32_t l);
/* subtraction */
static int mpz_subi_raw(mpz_ptr r, mpz_ptr z, mpz_atom_t *d, u_int32_t l);
/* multiplication */
static int mpz_muli_raw(mpz_ptr r, mpz_ptr z, mpz_atom_t *d, u_int32_t l);
/* division */
static int mpz_divi_qr_raw(mpz_ptr q, mpz_ptr r, mpz_ptr z, mpz_atom_t *d,
u_int32_t l);
static int mpz_divi_r_raw(mpz_ptr r, mpz_ptr z, mpz_atom_t *d, u_int32_t l);
/* number theoretic functions */
static int mpz_gcd_raw(mpz_ptr g, mpz_ptr a, mpz_atom_t *b, u_int32_t l);
/* to/from mpz conversions */
static int mpz_tostr(mpz_ptr z, u_int32_t b, void *s, size_t l);
/* random numbers */
static void sbn_rand_init(void);
/* ================================== MPZ =================================== */
#define MAX(a,b) ((a)>(b)?(a):(b))
#define MIN(a,b) ((a)<(b)?(a):(b))
/* 32bit integer to mpz conversion */
#if ATOMBYTES == 4
#define u32tompz(t,u,l) \
mpz_atom_t t[1]; \
u_int32_t l = 0; \
t[0] = u; \
if (t[0]) l = 1
#elif ATOMBYTES == 2
#define u32tompz(t,u,l) \
mpz_atom_t t[2]; \
u_int32_t l = 0; \
t[0] = u & MPZ_MASK; u >>= MPZ_SHIFT; \
t[1] = u & MPZ_MASK; u >>= MPZ_SHIFT; \
if (t[1]) l = 1; \
else if (t[0]) l = 2
#elif ATOMBYTES == 1
#define u32tompz(t,u,l) \
mpz_atom_t t[4]; \
u_int32_t l = 0; \
t[0] = u & MPZ_MASK; u >>= MPZ_SHIFT; \
t[1] = u & MPZ_MASK; u >>= MPZ_SHIFT; \
t[2] = u & MPZ_MASK; u >>= MPZ_SHIFT; \
t[3] = u & MPZ_MASK; u >>= MPZ_SHIFT; \
if (t[3]) l = 4; \
else if (t[2]) l = 3; \
else if (t[1]) l = 2; \
else if (t[0]) l = 1
#endif
/* shift/andmask needed to division and modulo operation for ATOMBITS:
* a / ATOMBITS == A >> DIVATOMBITS_SHIFT
* a % ATOMBITS == A & MODATOMBITS_MASK */
#if ATOMBYTES == 4
#define DIVATOMBITS_SHIFT 5
#elif ATOMBYTES == 2
#define DIVATOMBITS_SHIFT 4
#elif ATOMBYTES == 1
#define DIVATOMBITS_SHIFT 3
#endif
#define MODATOMBITS_MASK ((1<<DIVATOMBITS_SHIFT)-1)
#define u32pack(mpz,t,l) \
do { \
(mpz)->l = l; \
(mpz)->a = l; \
(mpz)->s = 0; \
(mpz)->d = t; \
} while(0)
/* Raw inizialization of mpz_t elements */
#define _mpz_raw_init(z, d, l, a, s) \
do { \
(z)->d = d; \
(z)->l = l; \
(z)->a = a; \
(z)->s = s; \
}
#define _mpz_neg(z) \
do { \
(z)->s ^= 1; \
} while(0)
/* ------------------------ debugging macros -------------------------------- */
#define debugprint(m,z) do { \
char *_s = mpz_get_str(NULL, 10, z); \
printf("[%d]%s\n", m, _s); \
free(_s); \
} while(0)
#define debugprint2(m,z) do { \
char *_s = mpz_get_str(NULL, 2, z); \
printf("[%d]%s\n", m, _s); \
free(_s); \
} while(0)
/* ---------------------- initialization/allocation ------------------------- */
/* Initialize a relative bignum.
* return values: none, can't fail */
void mpz_init(mpz_ptr z)
{
z->d = NULL;
z->a = z->l = z->s = 0;
}
/* This function is used every time we need to set the z->d[l] word in the
* z->d array of the mpz_t type. It performs the allocation when
* needed. So if you call it with l = 0, there is anyway at least
* one word allocated. Warning: the normalization inside some function
* relies on this behaviour.
*
* return values:
* SBN_OK on success
* SBN_MEM on out of memory
*
* On error the previous memory configuration and memory of 'z'
* is untouched.
*
* The new words are initialized to zero.
* Note that this function relies on an ANSI-C realloc() that
* acts like free if the 'size' = 0, and return NULL in such a case,
* and also acts like malloc if the ptr = NULL. */
int mpz_realloc(mpz_ptr z, u_int32_t i)
{
void *new;
u_int32_t j;
if (i < z->a)
return SBN_OK;
new = realloc(z->d, (i+1)*MPZ_ATOMSZ);
if (new == NULL)
return SBN_MEM;
z->d = new;
/* set the new words to zero */
for (j = z->a; j <= i; j++)
z->d[j] = 0;
z->a = j; /* j = i+1 here */
return SBN_OK;
}
/* Normalize the length of z, that's to set z->l accordly to the
* most non-zero significant digit. Assume that all the storage
* is initialized to zero (that's a global assuption). */
void mpz_normalize(mpz_ptr z)
{
int32_t j;
if (!z->a)
return;
j = z->a-1;
while(j >= 0) {
if (z->d[j])
break;
j--;
}
z->l = j+1;
if (z->l == 0)
z->s = 0;
}
/* If z == 0, make it positive */
void mpz_normalize_sign(mpz_ptr z)
{
if (z->l == 0)
z->s = 0;
}
/* inline version of mpz_normalize() that assumes z->a > 0 */
#define _mpz_normalize(z) \
do { \
int32_t j = (z)->a-1; \
while(j >=0 && !(z)->d[j]) \
j--; \
(z)->l = j+1; \
} while(0)
/* Free a bignum, can't fail */
void mpz_clear(mpz_ptr z)
{
free(z->d);
}
/* Free a bignum and prepare it to accept up to i+1 digits (base 256)
* Note: not GMP compatible. Don't alter the sign */
int mpz_zero_realloc(mpz_ptr z, u_int32_t i)
{
int err;
if ((err = mpz_realloc(z, i)) != SBN_OK)
return err;
mpz_zero(z);
return SBN_OK;
}
/* raw z = 0
* Note: not GMP compatible. Don't alter the sign */
void mpz_zero(mpz_ptr z)
{
if (!z->l)
return;
memset(z->d, 0, z->l*MPZ_ATOMSZ);
z->l = 0;
}
/* Create a stack-allocated clone of the bignum pointed by 'z' and make
* 'z' pointing to the clone. This is used when the different operators
* of some operations point to the same object. */
#define _mpz_clone_stack(z) \
do { \
mpz_ptr t = alloca(sizeof(mpz_t)); \
t->d = alloca((z)->a*MPZ_ATOMSZ); \
t->s = (z)->s; \
t->l = (z)->l; \
t->a = (z)->a; \
memcpy(t->d, (z)->d, (z)->a*MPZ_ATOMSZ); \
(z) = t; \
} while(0)
/* Clone 'z' using the 'L' atoms pointed by 'D' using stack-allocated memory */
#define _mpz_rawclone_stack(z, D, L) \
do { \
(z)->d = alloca((L)*MPZ_ATOMSZ); \
(z)->l = z->a = (L); \
(z)->s = 0; \
memcpy((z)->d, (D), (L)*MPZ_ATOMSZ); \
} while(0)
/* Create a stack-allocated copy of 'z' in 'r'. 'r' is an mpz_ptr type */
#define _mpz_copy_stack(r, z) \
do { \
r = alloca(sizeof(mpz_t)); \
(r)->d = alloca((z)->a*MPZ_ATOMSZ); \
(r)->s = (z)->s; \
(r)->l = (z)->l; \
(r)->a = (z)->a; \
memcpy((r)->d, (z)->d, (z)->a*MPZ_ATOMSZ); \
} while(0)
/* ----------------------- basic raw operations ----------------------------- */
/* clear the sign flag, so 'z' will be ABS(z) */
#define _mpz_abs(z) \
do { \
(z)->s = 0; \
} while(0)
/* ---------------------------- bits operations ----------------------------- */
/* compute the number of bits needed to rappresent the number 'z' */
u_int32_t mpz_bits(mpz_ptr z)
{
u_int32_t bits = (z->l-1) * ATOMBITS;
mpz_atom_t x = z->d[z->l-1];
while(x) {
bits++;
x >>= 1;
}
return bits;
}
/* Set the bit 'i' in 'z' */
int mpz_setbit(mpz_ptr z, u_int32_t i)
{
u_int32_t atom = i >> DIVATOMBITS_SHIFT;
u_int32_t bit = i & MODATOMBITS_MASK;
int err;
if ((err = mpz_realloc(z, atom)) != SBN_OK)
return err;
z->d[atom] |= (mpz_atom_t) 1 << bit;
if (z->l < atom+1)
z->l = atom+1;
return SBN_OK;
}
/* Inline bit pusher that expects the user know what is doing.
* Used in the division algorithm. */
#define _mpz_setbit(z, i) \
do { \
u_int32_t _atom = (i)>>DIVATOMBITS_SHIFT; \
(z)->d[_atom] |= (mpz_atom_t) 1<<((i)&MODATOMBITS_MASK);\
if ((z)->l < _atom+1) (z)->l = _atom+1; \
} while(0)
/* Faster version without normalization */
#define __mpz_setbit(z, i) \
do { \
u_int32_t _atom = (i)>>DIVATOMBITS_SHIFT; \
(z)->d[_atom] |= (mpz_atom_t) 1<<((i)&MODATOMBITS_MASK);\
} while(0)
/* Clear the bit 'i' in 'z' */
int mpz_clrbit(mpz_ptr z, u_int32_t i)
{
u_int32_t atom = i >> DIVATOMBITS_SHIFT;
u_int32_t bit = i & MODATOMBITS_MASK;
if (atom >= z->l)
return SBN_OK; /* nothing to clear */
z->d[atom] &= ~((mpz_atom_t) 1 << bit);
if (atom == z->l-1)
mpz_normalize(z);
return SBN_OK;
}
/* Fast clear-bit with normalization */
#define _mpz_clrbit(z, i) \
do { \
u_int32_t _atom = (i)>>DIVATOMBITS_SHIFT; \
(z)->d[_atom] &= ~((mpz_atom_t) 1<<((i)&MODATOMBITS_MASK)); \
if (_atom == z->l-1) \
_mpz_normalize(z); \
} while(0)
/* Fast clear-bit without normalization */
#define __mpz_clrbit(z, i) \
do { \
u_int32_t _atom = (i)>>DIVATOMBITS_SHIFT; \
(z)->d[_atom] &= ~((mpz_atom_t) 1<<((i)&MODATOMBITS_MASK));\
} while(0)
/* test the bit 'i' of 'z' and return:
* 0 if the bit 'i' is not set or out of range
* > 0 if the bit 'i' is set */
int mpz_testbit(mpz_ptr z, u_int32_t i)
{
u_int32_t atom = i >> DIVATOMBITS_SHIFT;
u_int32_t bit = i & MODATOMBITS_MASK;
if (atom >= z->l)
return 0;
return (z->d[atom] & ((mpz_atom_t) 1 << bit));
}
/* inline bit tester that expects the user know what is doing.
* It's used in the division algorithm. Return 0 if the bit is set,
* non zero if the bit isn't zet */
#define _mpz_testbit(z, i) \
((z)->d[(i)>>DIVATOMBITS_SHIFT] & ((mpz_atom_t)1<<((i)&MODATOMBITS_MASK)))
/* Return 1 if 'z' is odd, 0 if it's even. */
#define mpz_is_odd(z) (((z)->l) ? ((z)->d[0] & 1) : 0)
/* The same of mpz_odd() but assume there is at least an word allocated */
#define _mpz_is_odd(z) ((z)->d[0] & 1)
#define _mpz_is_even(z) (!_mpz_is_odd(z))
/* -------------------------------- shifting -------------------------------- */
/* Left shift of 'i' words */
int mpz_lshiftword(mpz_ptr r, u_int32_t i)
{
int err;
if (!i)
return SBN_OK;
if ((err = mpz_realloc(r, (r->l+i)-1)) != SBN_OK)
return err;
memmove(r->d+i, r->d, r->l*MPZ_ATOMSZ);
memset(r->d, 0, i*MPZ_ATOMSZ);
r->l += i;
return SBN_OK;
}
/* Right shift of 'i' words */
int mpz_rshiftword(mpz_ptr r, u_int32_t i)
{
if (!i)
return SBN_OK;
if (i >= r->l) {
mpz_zero(r);
return SBN_OK;
}
memmove(r->d, r->d+i, (r->l-i)*MPZ_ATOMSZ);
r->l -= i;
memset(r->d+r->l, 0, i);
return SBN_OK;
}
/* Left shift of 'i' bits */
int mpz_lshift(mpz_ptr r, mpz_ptr z, u_int32_t i)
{
u_int32_t rawshift = i >> DIVATOMBITS_SHIFT;
u_int32_t bitshift = i & MODATOMBITS_MASK;
int32_t j;
mpz_carry_t x;
int err;
/* clone 'z' in 'r' */
if (r != z && ((err = mpz_set(r, z)) != SBN_OK))
return err;
if (rawshift && ((err = mpz_lshiftword(r, rawshift)) != SBN_OK))
return err;
if (!bitshift)
return SBN_OK;
/* We need an additional word */
if ((err = mpz_realloc(r, r->l+1)) != SBN_OK)
return err;
/* note that here we are sure that 'bitshift' <= ATOMBITS */
if (r->l) {
for (j = r->l-1; j >= 0; j--) {
x = (mpz_carry_t) r->d[j] << bitshift;
r->d[j] = x & MPZ_MASK;
r->d[j+1] |= x >> ATOMBITS;
}
if (r->d[r->l])
r->l++;
}
return SBN_OK;
}
/* Fast 'z' 1 bit left shift. Assume there is allocated space for
* an additional atom. Handle normalization */
#define _mpz_self_lshift1(z) \
do { \
int32_t j; \
for (j = (z)->l-1; j >= 0; j--) { \
(z)->d[j+1] |= ((z)->d[j] & (1<<(ATOMBITS-1))) >> (ATOMBITS-1);\
(z)->d[j] <<= 1; \
} \
if ((z)->d[(z)->l]) \
(z)->l++; \
} while(0);
/* Fast 'z' 1 bit left shift + set bit 0 to 'b'. Assume there is allocated
* space for an additional atom. Handle normalization */
#define _mpz_self_lshift1_setbit0(z, b) \
do { \
int32_t j; \
for (j = (z)->l-1; j >= 0; j--) { \
(z)->d[j+1] |= ((z)->d[j] & (1<<(ATOMBITS-1))) >> (ATOMBITS-1);\
(z)->d[j] <<= 1; \
} \
(z)->d[0] |= b; \
if ((z)->d[(z)->l]) \
(z)->l++; \
} while(0);
/* Right shift of 'i' bits */
int mpz_rshift(mpz_ptr r, mpz_ptr z, u_int32_t i)
{
u_int32_t rawshift = i >> DIVATOMBITS_SHIFT;
u_int32_t bitshift = i & MODATOMBITS_MASK;
u_int32_t j;
mpz_carry_t x;
int err;
/* clone 'z' in 'r' */
if (r != z && ((err = mpz_set(r, z)) != SBN_OK))
return err;
if (rawshift && ((err = mpz_rshiftword(r, rawshift)) != SBN_OK))
return err;
if (!bitshift)
return SBN_OK;
/* note that here we are sure that 'bitshift' <= ATOMBITS */
if (r->l) {
r->d[0] >>= bitshift;
for (j = 1; j < r->l; j++) {
x = (mpz_carry_t) r->d[j] << (ATOMBITS-bitshift);
r->d[j] = x >> ATOMBITS;
r->d[j-1] |= x & MPZ_MASK;
}
if (!r->d[r->l-1])
r->l--;
}
return SBN_OK;
}
/* Fast 'z' 1 bit right shift. Handle normalization. Assume z->a != 0
* (so z->d != NULL), that's: don't call it without a reallocation. */
#define _mpz_self_rshift1(z) \
do { \
u_int32_t j; \
(z)->d[0] >>= 1; \
for (j = 1; j < (z)->l; j++) { \
(z)->d[j-1] |= ((z)->d[j] & 1) << (ATOMBITS-1); \
(z)->d[j] >>= 1; \
} \
if (!(z)->d[(z)->l-1]) \
(z)->l--; \
} while(0);
/* -------------------------- bitwise AND OR XOR NOT ------------------------ */
/* 'r' = 'z' bit-AND 'm' */
int mpz_and(mpz_ptr r, mpz_ptr z, mpz_ptr m)
{
int err;
u_int32_t j;
u_int32_t len;
if (z == m) { /* A AND A = A */
mpz_set(r, z);
return SBN_OK;
}
len = MIN(z->l, m->l);
if ((err = mpz_realloc(r, len)) != SBN_OK)
return err;
for (j = 0; j < len; j++)
r->d[j] = z->d[j] & m->d[j];
memset(r->d+j, 0, r->a - j); /* clear not-used words before normalize */
mpz_normalize(r);
return SBN_OK;
}
/* -------------------------------- compare --------------------------------- */
/* The same as mpz_cmpabs() for immediate.
* Relies on the fact that mpz_cmpabs() don't perform any allocation-related
* operation on the second operand. */
int32_t mpz_cmpabsi_raw(mpz_ptr a, mpz_atom_t *d, u_int32_t l)
{
mpz_t b;
b->d = d;
b->l = b->a = l;
b->s = 0;
return mpz_cmpabs(a, b);
}
/* compare ABS('a') and ABS('b'), return values:
* >0 if a > b
* 0 if a == b
* <0 if a < b
*
* 'a->d' and 'b->d' can point to statically allocated memory.
*
* Note that we can't use subtraction to return >0 or <0 if a-b != 0
* since the type for length and atom is unsigned so it may overflow.
*/
int32_t mpz_cmpabs(mpz_ptr a, mpz_ptr b)
{
int32_t i;
if (a->l > b->l) return 1;
if (a->l < b->l) return -1;
i = a->l;
while(i--) {
if (a->d[i] > b->d[i]) return 1;
if (a->d[i] < b->d[i]) return -1;
}
return 0;
}
/* the same as mpz_cmpabs() but 'b' is a 32bit unsigned immediate */
int32_t mpz_cmpabs_ui(mpz_ptr a, u_int32_t u)
{
mpz_t mpz;
u32tompz(t,u,l);
u32pack(mpz,t,l);
return mpz_cmpabs(a, mpz);
}
/* compare 'a' and 'b'. Return values are the same as mpz_cmpabs() */
int32_t mpz_cmp(mpz_ptr a, mpz_ptr b)
{
if (!a->l && !b->l) /* 0 == 0 */
return 0;
if (a->s == b->s) { /* same sign */
if (a->s) return mpz_cmpabs(b,a); /* both negative */
return mpz_cmpabs(a,b); /* both positive */
}
/* one negative, one positive */
if (a->s)
return -1;
return 1;
}
/* The same as mpz_cmp() with unsigned 32bit immediate */
int32_t mpz_cmp_ui(mpz_ptr a, u_int32_t u)
{
mpz_t mpz;
u32tompz(t,u,l);
u32pack(mpz,t,l);
return mpz_cmp(a, mpz);
}
/* signed integer version */
int32_t mpz_cmp_si(mpz_ptr a, int32_t s)
{
mpz_t mpz;
u_int32_t u = (s > 0) ? s : -s;
u32tompz(t,u,l);
u32pack(mpz,t,l);
mpz->s = s < 0;
return mpz_cmp(a, mpz);
}
/* ---------------------------- addition ------------------------------------ */
/* Raw add of immediate, don't care about the sign since
* it's up to the caller */
int mpz_addi_raw(mpz_ptr r, mpz_ptr z, mpz_atom_t *d, u_int32_t l)
{
int err;
u_int32_t maxi = MAX(z->l, l);
mpz_atom_t car = 0;
mpz_carry_t sum;
u_int32_t j;
mpz_atom_t *t = NULL;
if (r->d == d) {
if ((t = malloc(l*MPZ_ATOMSZ)) == NULL)
return SBN_MEM;
memcpy(t, d, l*MPZ_ATOMSZ);
d = t;
}
/* two sum of a,b requires at max MAX(len(a),len(b))+1 bytes */
if (r != z && ((err = mpz_zero_realloc(r, maxi)) != SBN_OK))
return err;
if ((err = mpz_realloc(z, (r == z) ? maxi : l)) != SBN_OK)
return err;
for(j = 0; j < l; j++) {
sum = (mpz_carry_t) d[j] + z->d[j] + car;
car = sum >> MPZ_SHIFT;
sum &= MPZ_MASK;
r->d[j] = sum;
}
for (j = l; j < z->l; j++) {
sum = (mpz_carry_t) z->d[j] + car;
car = sum >> MPZ_SHIFT;
sum &= MPZ_MASK;
r->d[j] = sum;
}
if (car) {
r->d[j] = car;
j++;
}
r->l = j; /* mpz_normalize() not needed */
if (t)
free(t);
return SBN_OK;
}
/* Add 'z' and a 32bit unsigned integer 'u' and put the result in 'r'
* Relies on the ability of mpz_add() to accept the last operator
* statically allocated */
int mpz_add_ui(mpz_ptr r, mpz_ptr z, u_int32_t u)
{
mpz_t mpz;
u32tompz(t,u,l);
u32pack(mpz,t,l);
return mpz_add(r, z, mpz);
}
/* The same as mpz_add_ui but with signed integer */
int mpz_add_si(mpz_ptr r, mpz_ptr z, int32_t s)
{
mpz_t mpz;
u_int32_t u = (s > 0) ? s : -s;
u32tompz(t,u,l);
u32pack(mpz,t,l);
mpz->s = s < 0;
return mpz_add(r, z, mpz);
}
/* 'r' = 'a' + 'b'
* b->d can point to statically allocated data */
int mpz_add(mpz_ptr r, mpz_ptr a, mpz_ptr b)
{
int cmp = mpz_cmpabs(a, b);
int err;
/* both positive or negative */
if (a->s == b->s) {
err = mpz_addi_raw(r, a, b->d, b->l);
r->s = a->s;
return err;
}
/* different signs if we are here */
if (a->s) { /* a negative, b positive */
if (cmp >= 0) { /* a >= b */
err = mpz_subi_raw(r, a, b->d, b->l);
r->s = (r->l == 0) ? 0 : 1; /* negative */
return err;
} else { /* a < b */
err = mpz_subi_raw(r, b, a->d, a->l);
r->s = 0; /* positive */
return err;
}
} else { /* a positive, b negative */
if (cmp >= 0) { /* a >= b */
err = mpz_subi_raw(r, a, b->d, b->l);
r->s = 0; /* positive */
return err;
} else { /* a < b */
err = mpz_subi_raw(r, b, a->d, a->l);
r->s = (r->l == 0) ? 0 : 1; /* negative */
return err;
}
}
return SBN_OK; /* not reached */
}
/* ---------------------------- subtraction --------------------------------- */
/* WARNING: assume z > d */
int mpz_subi_raw(mpz_ptr r, mpz_ptr z, mpz_atom_t *d, u_int32_t l)
{
int err;
mpz_scarry_t sub;
mpz_atom_t car = 0;
u_int32_t j;
mpz_atom_t *t = NULL;
if (r->d == d) {
if ((t = malloc(l*MPZ_ATOMSZ)) == NULL)
return SBN_MEM;
memcpy(t, d, l*MPZ_ATOMSZ);
d = t;
}
if (r != z && ((err = mpz_set(r, z)) != SBN_OK))
return err;
for (j = 0; j < l; j++) {
sub = (mpz_scarry_t) z->d[j] - car - d[j];
car = 0;
if (sub < 0) {
sub += MPZ_BASE;
car = 1;
}
r->d[j] = sub;
}
for (j = l; j < z->l; j++) {
sub = (mpz_scarry_t) z->d[j] - car;
car = 0;
if (sub < 0) {
sub += MPZ_BASE;
car = 1;
}
r->d[j] = sub;
}
r->l = j;
mpz_normalize(r);
if (t)
free(t);
return SBN_OK;
}
/* 'r' = 'a' - 'b'
* b->d can be statically allocated data */
int mpz_sub(mpz_ptr r, mpz_ptr a, mpz_ptr b)
{
int cmp = mpz_cmpabs(a, b);
int err;
/* different signs? */
if (a->s != b->s) {
err = mpz_addi_raw(r, a, b->d, b->l);
r->s = a->s;
return err;
}
/* both positive or negative if we are here */
if (a->s) { /* both negative */
if (cmp >= 0) { /* a >= b */
err = mpz_subi_raw(r, a, b->d, b->l);
r->s = (r->l == 0) ? 0 : 1; /* negative */
return err;
} else { /* a < b */
err = mpz_subi_raw(r, b, a->d, a->l);
r->s = 0; /* positive */
return err;
}
} else { /* both positive */
if (cmp >= 0) { /* a >= b */
err = mpz_subi_raw(r, a, b->d, b->l);
r->s = 0; /* positive */
return err;
} else { /* a < b */
err = mpz_subi_raw(r, b, a->d, a->l);
r->s = (r->l == 0) ? 0 : 1; /* negative */
return err;
}
}
return SBN_OK; /* not reached */
}
/* mpz_sub() with immediate.
* Relies on the fact that mpz_sub() works if the last argument
* is statically allocated */
int mpz_sub_ui(mpz_ptr r, mpz_ptr z, u_int32_t u)
{
mpz_t mpz;
u32tompz(t,u,l);
u32pack(mpz,t,l);
return mpz_sub(r, z, mpz);
}
/* like mpz_sub_ui but with signed integer */
int mpz_sub_si(mpz_ptr r, mpz_ptr z, int32_t s)
{
mpz_t mpz;
u_int32_t u = (s > 0) ? s : -s;
u32tompz(t,u,l);
u32pack(mpz,t,l);
mpz->s = s < 0;
return mpz_sub(r, z, mpz);
}
/* ------------------------------- product ---------------------------------- */
/* Raw multiplication of immediate, don't care about the sign
* since it's up to the caller */
int mpz_muli_raw(mpz_ptr r, mpz_ptr z, mpz_atom_t *d, u_int32_t l)
{
int err;
u_int32_t maxi = z->l+l;
mpz_atom_t car;
mpz_carry_t mul;
u_int32_t j, i;
mpz_t t, rt;
mpz_ptr rbak = NULL;
int tmptarget = (r == z);
mpz_atom_t *x = NULL;
/* Make a copy of 'd' if it's == r */
if (r->d == d) {
if ((x = malloc(l*MPZ_ATOMSZ)) == NULL)
return SBN_MEM;
memcpy(x, d, l*MPZ_ATOMSZ);
d = x;
}
/* if r and z are the same we need a temp bignum target */
if (tmptarget) {
rbak = r;
r = rt;
mpz_init(r);
r->s = rbak->s; /* preserve the original sign */
}
/* two product of a,b requires at max len(a)+len(b) bytes */
if ((err = mpz_zero_realloc(r, maxi)) != SBN_OK)
goto error;
/* initialize the temp var */
mpz_init(t);
if ((err = mpz_realloc(t, maxi)) != SBN_OK)
goto error;
for(j = 0; j < l; j++) {
car = 0;
mpz_zero(t);
for (i = 0; i < z->l; i++) {
/* note that A = B * C + D + E
* with A of N*2 bits and C,D,E of N bits
* can't overflow since:
* (2^N-1)*(2^N-1)+(2^N-1)+(2^N-1) == 2^(2*N)-1 */
mul = (mpz_carry_t) d[j] * z->d[i] + car + r->d[i+j];
car = mul >> MPZ_SHIFT;
mul &= MPZ_MASK;
r->d[i+j] = mul;
}
if (car)
r->d[i+j] = car;
}
r->l = maxi;
mpz_normalize(r);
if (tmptarget && ((err = mpz_set(rbak, rt)) != SBN_OK))
goto error;
err = SBN_OK;
/* fall through */
error:
mpz_clear(t);
if (tmptarget)
mpz_clear(rt);
if (x)
free(x);
return err;
}
/* 'r' = 'z' * 'f' */
int mpz_mul(mpz_ptr r, mpz_ptr z, mpz_ptr f)
{
r->s = z->s^f->s; /* the sign is the xor of the two sings */
return mpz_muli_raw(r, z, f->d, f->l);
}
/* Mul 'z' and a 32bit unsigned integer 'u' and put the result in 'r'
* We don't need to touch the sign since the factor is >= 0 */
int mpz_mul_ui(mpz_ptr r, mpz_ptr z, u_int32_t u)
{
u32tompz(t,u,l);
r->s = z->s;
return mpz_muli_raw(r, z, t, l);
}
/* Like mpz_mul_ui but with signed integer */
int mpz_mul_si(mpz_ptr r, mpz_ptr z, int32_t s)
{
u_int32_t u = (s > 0) ? s : -s;
u32tompz(t,u,l);
r->s = z->s^(s<0);
return mpz_muli_raw(r, z, t, l);
}
/* 'r' = i! */
int mpz_fac_ui(mpz_ptr r, u_int32_t i)
{
u_int32_t j;
int err;
if (!i) {
mpz_setzero(r);
return SBN_OK;
}
if ((err = mpz_set_ui(r, 1)) != SBN_OK)
return err;
for (j = 2; j <= i; j++)
if ((err = mpz_mul_ui(r, r, j)) != SBN_OK)
return err;
return SBN_OK;
}
/* --------------------------- exponentialization --------------------------- */
/* compute b^e mod m.
* Note that there are much faster ways to do it.
* see www.nc.com for more information */
int mpz_powm(mpz_ptr r, mpz_ptr b, mpz_ptr e, mpz_ptr m)
{
int rs = 0, err;