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mpz.cpp
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mpz.cpp
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/*++
Copyright (c) 2006 Microsoft Corporation
Module Name:
mpz.cpp
Abstract:
<abstract>
Author:
Leonardo de Moura (leonardo) 2010-06-17.
Revision History:
--*/
#include <cstring>
#include <sstream>
#include <iomanip>
#include "util/mpz.h"
#include "util/buffer.h"
#include "util/trace.h"
#include "util/hash.h"
#include "util/bit_util.h"
#if defined(_MP_INTERNAL)
#include "util/mpn.h"
#elif defined(_MP_GMP)
#include<gmp.h>
#else
#error No multi-precision library selected.
#endif
// Available GCD algorithms
// #define EUCLID_GCD
// #define BINARY_GCD
// #define LS_BINARY_GCD
// #define LEHMER_GCD
#if defined(_MP_GMP)
// Use LEHMER only if not using GMP
// LEHMER assumes 32-bit digits, so it cannot be used with MSBIGNUM library + 64-bit binary
#define EUCLID_GCD
#else
#define LEHMER_GCD
#endif
#if defined(__GNUC__)
#define _trailing_zeros32(X) __builtin_ctz(X)
#elif defined(_WINDOWS) && !defined(_M_ARM) && !defined(_M_ARM64) && !defined(__MINGW32__)
// This is needed for _tzcnt_u32 and friends.
#include <immintrin.h>
#define _trailing_zeros32(X) _tzcnt_u32(X)
#else
static uint32_t _trailing_zeros32(uint32_t x) {
uint32_t r = 0;
for (; 0 == (x & 1) && r < 32; ++r, x >>= 1);
return r;
}
#endif
#if (defined(__LP64__) || defined(_WIN64)) && !defined(_M_ARM) && !defined(_M_ARM64)
#if defined(__GNUC__)
#define _trailing_zeros64(X) __builtin_ctzll(X)
#else
#define _trailing_zeros64(X) _tzcnt_u64(X)
#endif
#else
static uint64_t _trailing_zeros64(uint64_t x) {
uint64_t r = 0;
for (; 0 == (x & 1) && r < 64; ++r, x >>= 1);
return r;
}
#endif
#define _bit_min(x, y) (y + ((x - y) & ((int)(x - y) >> 31)))
#define _bit_max(x, y) (x - ((x - y) & ((int)(x - y) >> 31)))
unsigned u_gcd(unsigned u, unsigned v) {
if (u == 0) return v;
if (v == 0) return u;
unsigned shift = _trailing_zeros32(u | v);
u >>= _trailing_zeros32(u);
if (u == 1 || v == 1) return 1 << shift;
if (u == v) return u << shift;
do {
v >>= _trailing_zeros32(v);
unsigned diff = u - v;
unsigned mdiff = diff & (unsigned)((int)diff >> 31);
u = v + mdiff; // min
v = diff - 2 * mdiff; // if v <= u: u - v, if v > u: v - u = u - v - 2 * (u - v)
}
while (v != 0);
return u << shift;
}
uint64_t u64_gcd(uint64_t u, uint64_t v) {
if (u == 0) return v;
if (v == 0) return u;
if (u == 1 || v == 1) return 1;
auto shift = _trailing_zeros64(u | v);
u >>= _trailing_zeros64(u);
do {
v >>= _trailing_zeros64(v);
if (u > v) std::swap(u, v);
v -= u;
}
while (v != 0);
return u << shift;
}
template<bool SYNCH>
mpz_manager<SYNCH>::mpz_manager():
m_allocator("mpz_manager") {
#ifndef _MP_GMP
if (sizeof(digit_t) == sizeof(uint64_t)) {
// 64-bit machine
m_init_cell_capacity = 4;
}
else {
m_init_cell_capacity = 6;
}
set(m_int_min, -static_cast<int64_t>(INT_MIN));
#else
// GMP
mpz_init(m_tmp);
mpz_init(m_tmp2);
mpz_init(m_two32);
mpz_set_ui(m_two32, UINT_MAX);
mpz_set_ui(m_tmp, 1);
mpz_add(m_two32, m_two32, m_tmp);
mpz_init(m_uint64_max);
unsigned max_l = static_cast<unsigned>(UINT64_MAX);
unsigned max_h = static_cast<unsigned>(UINT64_MAX >> 32);
mpz_set_ui(m_uint64_max, max_h);
mpz_mul(m_uint64_max, m_two32, m_uint64_max);
mpz_set_ui(m_tmp, max_l);
mpz_add(m_uint64_max, m_uint64_max, m_tmp);
mpz_init(m_int64_max);
mpz_init(m_int64_min);
max_l = static_cast<unsigned>(INT64_MAX % static_cast<int64_t>(UINT_MAX));
max_h = static_cast<unsigned>(INT64_MAX / static_cast<int64_t>(UINT_MAX));
mpz_set_ui(m_int64_max, max_h);
mpz_set_ui(m_tmp, UINT_MAX);
mpz_mul(m_int64_max, m_tmp, m_int64_max);
mpz_set_ui(m_tmp, max_l);
mpz_add(m_int64_max, m_tmp, m_int64_max);
mpz_neg(m_int64_min, m_int64_max);
mpz_sub_ui(m_int64_min, m_int64_min, 1);
#endif
mpz one(1);
set(m_two64, (uint64_t)UINT64_MAX);
add(m_two64, one, m_two64);
}
template<bool SYNCH>
mpz_manager<SYNCH>::~mpz_manager() {
del(m_two64);
#ifndef _MP_GMP
del(m_int_min);
#else
mpz_clear(m_tmp);
mpz_clear(m_tmp2);
mpz_clear(m_two32);
mpz_clear(m_uint64_max);
mpz_clear(m_int64_max);
mpz_clear(m_int64_min);
#endif
}
#ifndef _MP_GMP
template<bool SYNCH>
mpz_cell * mpz_manager<SYNCH>::allocate(unsigned capacity) {
SASSERT(capacity >= m_init_cell_capacity);
mpz_cell * cell;
#ifdef SINGLE_THREAD
cell = reinterpret_cast<mpz_cell*>(m_allocator.allocate(cell_size(capacity)));
#else
if (SYNCH) {
cell = reinterpret_cast<mpz_cell*>(memory::allocate(cell_size(capacity)));
}
else {
cell = reinterpret_cast<mpz_cell*>(m_allocator.allocate(cell_size(capacity)));
}
#endif
cell->m_capacity = capacity;
return cell;
}
template<bool SYNCH>
void mpz_manager<SYNCH>::deallocate(bool is_heap, mpz_cell * ptr) {
if (is_heap) {
#ifdef SINGLE_THREAD
m_allocator.deallocate(cell_size(ptr->m_capacity), ptr);
#else
if (SYNCH) {
memory::deallocate(ptr);
}
else {
m_allocator.deallocate(cell_size(ptr->m_capacity), ptr);
}
#endif
}
}
template<bool SYNCH>
mpz_manager<SYNCH>::sign_cell::sign_cell(mpz_manager& m, mpz const& a):
m_local(reinterpret_cast<mpz_cell*>(m_bytes)), m_a(a) {
m_local.m_ptr->m_capacity = capacity;
m.get_sign_cell(a, m_sign, m_cell, m_local.m_ptr);
}
#endif
template<bool SYNCH>
void mpz_manager<SYNCH>::del(mpz_manager<SYNCH>* m, mpz & a) {
if (a.m_ptr) {
SASSERT(m);
m->deallocate(a.m_owner == mpz_self, a.m_ptr);
a.m_ptr = nullptr;
a.m_kind = mpz_small;
a.m_owner = mpz_self;
}
}
template<bool SYNCH>
void mpz_manager<SYNCH>::add(mpz const & a, mpz const & b, mpz & c) {
STRACE("mpz", tout << "[mpz] " << to_string(a) << " + " << to_string(b) << " == ";);
if (is_small(a) && is_small(b)) {
set_i64(c, i64(a) + i64(b));
}
else {
big_add(a, b, c);
}
STRACE("mpz", tout << to_string(c) << "\n";);
}
template<bool SYNCH>
void mpz_manager<SYNCH>::sub(mpz const & a, mpz const & b, mpz & c) {
STRACE("mpz", tout << "[mpz] " << to_string(a) << " - " << to_string(b) << " == ";);
if (is_small(a) && is_small(b)) {
set_i64(c, i64(a) - i64(b));
}
else {
big_sub(a, b, c);
}
STRACE("mpz", tout << to_string(c) << "\n";);
}
template<bool SYNCH>
void mpz_manager<SYNCH>::set_big_i64(mpz & c, int64_t v) {
#ifndef _MP_GMP
if (c.m_ptr == nullptr) {
c.m_ptr = allocate(m_init_cell_capacity);
c.m_owner = mpz_self;
}
c.m_kind = mpz_large;
SASSERT(capacity(c) >= m_init_cell_capacity);
uint64_t _v;
if (v == std::numeric_limits<int64_t>::min()) {
// min-int is even
_v = -(v/2);
c.m_val = -1;
}
else if (v < 0) {
_v = -v;
c.m_val = -1;
}
else {
_v = v;
c.m_val = 1;
}
if (sizeof(digit_t) == sizeof(uint64_t)) {
// 64-bit machine
digits(c)[0] = static_cast<digit_t>(_v);
c.m_ptr->m_size = 1;
}
else {
// 32-bit machine
digits(c)[0] = static_cast<unsigned>(_v);
digits(c)[1] = static_cast<unsigned>(_v >> 32);
c.m_ptr->m_size = digits(c)[1] == 0 ? 1 : 2;
}
#else
if (c.m_ptr == nullptr) {
c.m_ptr = allocate();
c.m_owner = mpz_self;
}
c.m_kind = mpz_large;
uint64_t _v;
bool sign = v < 0;
if (v == std::numeric_limits<int64_t>::min()) {
_v = -(v/2);
}
else if (v < 0) {
_v = -v;
}
else {
_v = v;
}
mpz_set_ui(*c.m_ptr, static_cast<unsigned>(_v));
MPZ_BEGIN_CRITICAL();
mpz_set_ui(m_tmp, static_cast<unsigned>(_v >> 32));
mpz_mul(m_tmp, m_tmp, m_two32);
mpz_add(*c.m_ptr, *c.m_ptr, m_tmp);
MPZ_END_CRITICAL();
if (sign)
mpz_neg(*c.m_ptr, *c.m_ptr);
#endif
if (v == std::numeric_limits<int64_t>::min()) {
big_add(c, c, c);
}
}
template<bool SYNCH>
void mpz_manager<SYNCH>::set_big_ui64(mpz & c, uint64_t v) {
#ifndef _MP_GMP
if (c.m_ptr == nullptr) {
c.m_ptr = allocate(m_init_cell_capacity);
c.m_owner = mpz_self;
}
c.m_kind = mpz_large;
SASSERT(capacity(c) >= m_init_cell_capacity);
c.m_val = 1;
if (sizeof(digit_t) == sizeof(uint64_t)) {
// 64-bit machine
digits(c)[0] = static_cast<digit_t>(v);
c.m_ptr->m_size = 1;
}
else {
// 32-bit machine
digits(c)[0] = static_cast<unsigned>(v);
digits(c)[1] = static_cast<unsigned>(v >> 32);
c.m_ptr->m_size = digits(c)[1] == 0 ? 1 : 2;
}
#else
if (c.m_ptr == nullptr) {
c.m_ptr = allocate();
c.m_owner = mpz_self;
}
c.m_kind = mpz_large;
mpz_set_ui(*c.m_ptr, static_cast<unsigned>(v));
MPZ_BEGIN_CRITICAL();
mpz_set_ui(m_tmp, static_cast<unsigned>(v >> 32));
mpz_mul(m_tmp, m_tmp, m_two32);
mpz_add(*c.m_ptr, *c.m_ptr, m_tmp);
MPZ_END_CRITICAL();
#endif
}
#ifdef _MP_GMP
template<bool SYNCH>
mpz_manager<SYNCH>::ensure_mpz_t::ensure_mpz_t(mpz const& a) {
if (is_small(a)) {
m_result = &m_local;
mpz_init(m_local);
mpz_set_si(m_local, a.m_val);
}
else {
m_result = a.m_ptr;
}
}
template<bool SYNCH>
mpz_manager<SYNCH>::ensure_mpz_t::~ensure_mpz_t() {
if (m_result == &m_local) {
mpz_clear(m_local);
}
}
#endif
#ifndef _MP_GMP
template<bool SYNCH>
void mpz_manager<SYNCH>::set(mpz_cell& src, mpz & a, int sign, unsigned sz) {
unsigned i = sz;
for (; i > 0 && src.m_digits[i-1] == 0; --i) ;
if (i == 0) {
// src is zero
set(a, 0);
return;
}
unsigned d = src.m_digits[0];
if (i == 1 && d <= INT_MAX) {
// src fits is a fixnum
a.m_val = sign < 0 ? -static_cast<int>(d) : static_cast<int>(d);
a.m_kind = mpz_small;
return;
}
set_digits(a, i, src.m_digits);
a.m_val = sign;
SASSERT(a.m_kind == mpz_large);
}
#endif
template<bool SYNCH>
void mpz_manager<SYNCH>::set(mpz & a, char const * val) {
set(a, 0);
mpz ten(10);
mpz tmp;
char const * str = val;
bool sign = false;
while (str[0] == ' ') ++str;
if (str[0] == '-')
sign = true;
while (str[0]) {
if ('0' <= str[0] && str[0] <= '9') {
SASSERT(str[0] - '0' <= 9);
mul(a, ten, tmp);
add(tmp, mk_z(str[0] - '0'), a);
}
++str;
}
del(tmp);
if (sign)
neg(a);
}
template<bool SYNCH>
void mpz_manager<SYNCH>::set_digits(mpz & target, unsigned sz, digit_t const * digits) {
// remove zero digits
while (sz > 0 && digits[sz - 1] == 0)
sz--;
if (sz == 0)
set(target, 0);
else if (sz == 1)
set(target, digits[0]);
else {
#ifndef _MP_GMP
target.m_val = 1; // number is positive.
if (target.m_ptr == nullptr) {
unsigned c = sz < m_init_cell_capacity ? m_init_cell_capacity : sz;
target.m_ptr = allocate(c);
target.m_ptr->m_size = sz;
target.m_ptr->m_capacity = c;
target.m_kind = mpz_large;
target.m_owner = mpz_self;
memcpy(target.m_ptr->m_digits, digits, sizeof(digit_t) * sz);
}
else if (capacity(target) < sz) {
SASSERT(sz > m_init_cell_capacity);
mpz_cell* ptr = allocate(sz);
memcpy(ptr->m_digits, digits, sizeof(digit_t) * sz);
ptr->m_size = sz;
ptr->m_capacity = sz;
deallocate(target);
target.m_val = 1;
target.m_ptr = ptr;
target.m_kind = mpz_large;
target.m_owner = mpz_self;
}
else {
target.m_ptr->m_size = sz;
if (target.m_ptr->m_digits != digits)
memcpy(target.m_ptr->m_digits, digits, sizeof(digit_t) * sz);
target.m_kind = mpz_large;
}
#else
mk_big(target);
// reset
mpz_set_ui(*target.m_ptr, digits[sz - 1]);
SASSERT(sz > 0);
unsigned i = sz - 1;
MPZ_BEGIN_CRITICAL();
while (i > 0) {
--i;
mpz_mul_2exp(*target.m_ptr, *target.m_ptr, 32);
mpz_set_ui(m_tmp, digits[i]);
mpz_add(*target.m_ptr, *target.m_ptr, m_tmp);
}
MPZ_END_CRITICAL();
#endif
}
}
template<bool SYNCH>
void mpz_manager<SYNCH>::mul(mpz const & a, mpz const & b, mpz & c) {
STRACE("mpz", tout << "[mpz] " << to_string(a) << " * " << to_string(b) << " == ";);
if (is_small(a) && is_small(b)) {
set_i64(c, i64(a) * i64(b));
}
else {
big_mul(a, b, c);
}
STRACE("mpz", tout << to_string(c) << "\n";);
}
// d <- a + b*c
template<bool SYNCH>
void mpz_manager<SYNCH>::addmul(mpz const & a, mpz const & b, mpz const & c, mpz & d) {
if (is_one(b)) {
add(a, c, d);
}
else if (is_minus_one(b)) {
sub(a, c, d);
}
else {
mpz tmp;
mul(b,c,tmp);
add(a,tmp,d);
del(tmp);
}
}
// d <- a - b*c
template<bool SYNCH>
void mpz_manager<SYNCH>::submul(mpz const & a, mpz const & b, mpz const & c, mpz & d) {
if (is_one(b)) {
sub(a, c, d);
}
else if (is_minus_one(b)) {
add(a, c, d);
}
else {
mpz tmp;
mul(b,c,tmp);
sub(a,tmp,d);
del(tmp);
}
}
template<bool SYNCH>
void mpz_manager<SYNCH>::machine_div_rem(mpz const & a, mpz const & b, mpz & q, mpz & r) {
STRACE("mpz", tout << "[mpz-ext] divrem(" << to_string(a) << ", " << to_string(b) << ") == ";);
if (is_small(a) && is_small(b)) {
int64_t _a = i64(a);
int64_t _b = i64(b);
set_i64(q, _a / _b);
set_i64(r, _a % _b);
}
else {
big_div_rem(a, b, q, r);
}
STRACE("mpz", tout << "(" << to_string(q) << ", " << to_string(r) << ")\n";);
}
template<bool SYNCH>
void mpz_manager<SYNCH>::machine_div(mpz const & a, mpz const & b, mpz & c) {
STRACE("mpz", tout << "[mpz-ext] machine-div(" << to_string(a) << ", " << to_string(b) << ") == ";);
if (is_small(b) && i64(b) == 0)
throw default_exception("division by 0");
if (is_small(a) && is_small(b))
set_i64(c, i64(a) / i64(b));
else
big_div(a, b, c);
STRACE("mpz", tout << to_string(c) << "\n";);
}
template<bool SYNCH>
void mpz_manager<SYNCH>::reset(mpz & a) {
deallocate(a);
set(a, 0);
}
template<bool SYNCH>
void mpz_manager<SYNCH>::rem(mpz const & a, mpz const & b, mpz & c) {
STRACE("mpz", tout << "[mpz-ext] rem(" << to_string(a) << ", " << to_string(b) << ") == ";);
if (is_small(a) && is_small(b)) {
set_i64(c, i64(a) % i64(b));
}
else {
big_rem(a, b, c);
}
STRACE("mpz", tout << to_string(c) << "\n";);
}
template<bool SYNCH>
void mpz_manager<SYNCH>::div_gcd(mpz const& a, mpz const& b, mpz & c) {
STRACE("mpz", tout << "[mpz-ext] div(" << to_string(a) << ", " << to_string(b) << ") == ";);
if (is_one(b)) {
set(c, a);
}
else {
machine_div(a, b, c);
}
STRACE("mpz", tout << to_string(c) << "\n";);
}
template<bool SYNCH>
void mpz_manager<SYNCH>::div(mpz const & a, mpz const & b, mpz & c) {
STRACE("mpz", tout << "[mpz-ext] div(" << to_string(a) << ", " << to_string(b) << ") == ";);
if (is_one(b)) {
set(c, a);
}
else if (is_neg(a)) {
mpz tmp;
machine_div_rem(a, b, c, tmp);
if (!is_zero(tmp)) {
if (is_neg(b))
add(c, mk_z(1), c);
else
sub(c, mk_z(1), c);
}
del(tmp);
}
else {
machine_div(a, b, c);
}
STRACE("mpz", tout << to_string(c) << "\n";);
}
template<bool SYNCH>
void mpz_manager<SYNCH>::mod(mpz const & a, mpz const & b, mpz & c) {
STRACE("mpz", tout << "[mpz-ext] mod(" << to_string(a) << ", " << to_string(b) << ") == ";);
rem(a, b, c);
if (is_neg(c)) {
if (is_pos(b))
add(c, b, c);
else
sub(c, b, c);
}
STRACE("mpz", tout << to_string(c) << "\n";);
}
template<bool SYNCH>
void mpz_manager<SYNCH>::neg(mpz & a) {
STRACE("mpz", tout << "[mpz] 0 - " << to_string(a) << " == ";);
if (is_small(a) && a.m_val == INT_MIN) {
// neg(INT_MIN) is not a small int
set_big_i64(a, - static_cast<long long>(INT_MIN));
return;
}
#ifndef _MP_GMP
a.m_val = -a.m_val;
#else
if (is_small(a)) {
a.m_val = -a.m_val;
}
else {
mpz_neg(*a.m_ptr, *a.m_ptr);
}
#endif
STRACE("mpz", tout << to_string(a) << "\n";);
}
template<bool SYNCH>
void mpz_manager<SYNCH>::abs(mpz & a) {
if (is_small(a)) {
if (a.m_val < 0) {
if (a.m_val == INT_MIN) {
// abs(INT_MIN) is not a small int
set_big_i64(a, - static_cast<long long>(INT_MIN));
}
else
a.m_val = -a.m_val;
}
}
else {
#ifndef _MP_GMP
a.m_val = 1;
#else
mpz_abs(*a.m_ptr, *a.m_ptr);
#endif
}
}
// TBD: replace use of 'tmp' by 'c'.
#ifndef _MP_GMP
template<bool SYNCH>
template<bool SUB>
void mpz_manager<SYNCH>::big_add_sub(mpz const & a, mpz const & b, mpz & c) {
sign_cell ca(*this, a), cb(*this, b);
int sign_b = cb.sign();
mpz_stack tmp;
if (SUB)
sign_b = -sign_b;
size_t real_sz;
if (ca.sign() == sign_b) {
unsigned sz = std::max(ca.cell()->m_size, cb.cell()->m_size)+1;
allocate_if_needed(tmp, sz);
m_mpn_manager.add(ca.cell()->m_digits, ca.cell()->m_size,
cb.cell()->m_digits, cb.cell()->m_size,
tmp.m_ptr->m_digits, sz, &real_sz);
SASSERT(real_sz <= sz);
set(*tmp.m_ptr, c, ca.sign(), static_cast<unsigned>(real_sz));
}
else {
digit_t borrow;
int r = m_mpn_manager.compare(ca.cell()->m_digits, ca.cell()->m_size,
cb.cell()->m_digits, cb.cell()->m_size);
if (r == 0) {
set(c, 0);
}
else if (r < 0) {
// a < b
unsigned sz = cb.cell()->m_size;
allocate_if_needed(tmp, sz);
m_mpn_manager.sub(cb.cell()->m_digits,
cb.cell()->m_size,
ca.cell()->m_digits,
ca.cell()->m_size,
tmp.m_ptr->m_digits,
&borrow);
SASSERT(borrow == 0);
set(*tmp.m_ptr, c, sign_b, sz);
}
else {
// a > b
unsigned sz = ca.cell()->m_size;
allocate_if_needed(tmp, sz);
m_mpn_manager.sub(ca.cell()->m_digits,
ca.cell()->m_size,
cb.cell()->m_digits,
cb.cell()->m_size,
tmp.m_ptr->m_digits,
&borrow);
SASSERT(borrow == 0);
set(*tmp.m_ptr, c, ca.sign(), sz);
}
}
del(tmp);
}
#endif
template<bool SYNCH>
void mpz_manager<SYNCH>::big_add(mpz const & a, mpz const & b, mpz & c) {
#ifndef _MP_GMP
big_add_sub<false>(a, b, c);
#else
// GMP version
ensure_mpz_t a1(a), b1(b);
mk_big(c);
mpz_add(*c.m_ptr, a1(), b1());
#endif
}
template<bool SYNCH>
void mpz_manager<SYNCH>::big_sub(mpz const & a, mpz const & b, mpz & c) {
#ifndef _MP_GMP
big_add_sub<true>(a, b, c);
#else
// GMP version
ensure_mpz_t a1(a), b1(b);
mk_big(c);
mpz_sub(*c.m_ptr, a1(), b1());
#endif
}
template<bool SYNCH>
void mpz_manager<SYNCH>::big_mul(mpz const & a, mpz const & b, mpz & c) {
#ifndef _MP_GMP
// TBD replace tmp by c.
mpz_stack tmp;
sign_cell ca(*this, a), cb(*this, b);
unsigned sz = ca.cell()->m_size + cb.cell()->m_size;
allocate_if_needed(tmp, sz);
m_mpn_manager.mul(ca.cell()->m_digits,
ca.cell()->m_size,
cb.cell()->m_digits,
cb.cell()->m_size,
tmp.m_ptr->m_digits);
set(*tmp.m_ptr, c, ca.sign() == cb.sign() ? 1 : -1, sz);
del(tmp);
#else
// GMP version
ensure_mpz_t a1(a), b1(b);
mk_big(c);
mpz_mul(*c.m_ptr, a1(), b1());
#endif
}
template<bool SYNCH>
void mpz_manager<SYNCH>::big_div_rem(mpz const & a, mpz const & b, mpz & q, mpz & r) {
#ifndef _MP_GMP
quot_rem_core<QUOT_AND_REM>(a, b, q, r);
#else
// GMP version
ensure_mpz_t a1(a), b1(b);
mk_big(q);
mk_big(r);
mpz_tdiv_qr(*q.m_ptr, *r.m_ptr, a1(), b1());
#endif
}
#ifndef _MP_GMP
template<bool SYNCH>
template<qr_mode MODE>
void mpz_manager<SYNCH>::quot_rem_core(mpz const & a, mpz const & b, mpz & q, mpz & r)
{
/*
+26 / +7 = +3, remainder is +5
-26 / +7 = -3, remainder is -5
+26 / -7 = -3, remainder is +5
-26 / -7 = +3, remainder is -5
*/
mpz_stack q1, r1;
sign_cell ca(*this, a), cb(*this, b);
if (cb.cell()->m_size > ca.cell()->m_size) {
if (MODE == REM_ONLY || MODE == QUOT_AND_REM)
set(r, a);
if (MODE == QUOT_ONLY || MODE == QUOT_AND_REM)
set(q, 0);
return;
}
unsigned q_sz = ca.cell()->m_size - cb.cell()->m_size + 1;
unsigned r_sz = cb.cell()->m_size;
allocate_if_needed(q1, q_sz);
allocate_if_needed(r1, r_sz);
m_mpn_manager.div(ca.cell()->m_digits, ca.cell()->m_size,
cb.cell()->m_digits, cb.cell()->m_size,
q1.m_ptr->m_digits,
r1.m_ptr->m_digits);
if (MODE == QUOT_ONLY || MODE == QUOT_AND_REM)
set(*q1.m_ptr, q, ca.sign() == cb.sign() ? 1 : -1, q_sz);
if (MODE == REM_ONLY || MODE == QUOT_AND_REM)
set(*r1.m_ptr, r, ca.sign(), r_sz);
del(q1);
del(r1);
}
#endif
template<bool SYNCH>
void mpz_manager<SYNCH>::big_div(mpz const & a, mpz const & b, mpz & c) {
#ifndef _MP_GMP
mpz dummy;
quot_rem_core<QUOT_ONLY>(a, b, c, dummy);
SASSERT(is_zero(dummy));
del(dummy);
#else
// GMP version
ensure_mpz_t a1(a), b1(b);
mk_big(c);
mpz_tdiv_q(*c.m_ptr, a1(), b1());
#endif
}
template<bool SYNCH>
void mpz_manager<SYNCH>::big_rem(mpz const & a, mpz const & b, mpz & c) {
#ifndef _MP_GMP
mpz dummy;
quot_rem_core<REM_ONLY>(a, b, dummy, c);
SASSERT(is_zero(dummy));
del(dummy);
#else
// GMP version
ensure_mpz_t a1(a), b1(b);
mk_big(c);
mpz_tdiv_r(*c.m_ptr, a1(), b1());
#endif
}
template<bool SYNCH>
void mpz_manager<SYNCH>::gcd(mpz const & a, mpz const & b, mpz & c) {
static_assert(sizeof(a.m_val) == sizeof(int), "size mismatch");
static_assert(sizeof(mpz) <= 16, "mpz size overflow");
if (is_small(a) && is_small(b) && a.m_val != INT_MIN && b.m_val != INT_MIN) {
int _a = a.m_val;
int _b = b.m_val;
if (_a < 0) _a = -_a;
if (_b < 0) _b = -_b;
unsigned r = u_gcd(_a, _b);
set(c, r);
}
else {
#ifdef _MP_GMP
ensure_mpz_t a1(a), b1(b);
mk_big(c);
mpz_gcd(*c.m_ptr, a1(), b1());
return;
#endif
if (is_zero(a)) {
set(c, b);
abs(c);
return;
}
if (is_zero(b)) {
set(c, a);
abs(c);
return;
}
#ifdef BINARY_GCD
// Binary GCD for big numbers
// - It doesn't use division
// - The initial experiments, don't show any performance improvement
// - It only works with _MP_INTERNAL
mpz u, v, diff;
set(u, a);
set(v, b);
abs(u);
abs(v);
unsigned k_u = power_of_two_multiple(u);
unsigned k_v = power_of_two_multiple(v);
unsigned k = k_u < k_v ? k_u : k_v;
machine_div2k(u, k_u);
while (true) {
machine_div2k(v, k_v);
if (lt(u, v)) {
sub(v, u, v);
}
else {
sub(u, v, diff);
swap(u, v);
swap(v, diff);
}
if (is_zero(v) || is_one(v))
break;
// reset least significant bit
if (is_small(v))
v.m_val &= ~1;
else
v.m_ptr->m_digits[0] &= ~static_cast<digit_t>(1);
k_v = power_of_two_multiple(v);
}
mul2k(u, k, c);
del(u); del(v); del(diff);
#endif // BINARY_GCD
#ifdef EUCLID_GCD
mpz tmp1;
mpz tmp2;
mpz aux;
set(tmp1, a);
set(tmp2, b);
abs(tmp1);
abs(tmp2);
if (lt(tmp1, tmp2))
swap(tmp1, tmp2);
if (is_zero(tmp2)) {
swap(c, tmp1);
}
else {
while (true) {
if (is_uint64(tmp1) && is_uint64(tmp2)) {
set(c, u64_gcd(get_uint64(tmp1), get_uint64(tmp2)));
break;
}
rem(tmp1, tmp2, aux);
if (is_zero(aux)) {
swap(c, tmp2);
break;
}
swap(tmp1, tmp2);
swap(tmp2, aux);
}
}
del(tmp1); del(tmp2); del(aux);
#endif // EUCLID_GCD
#ifdef LS_BINARY_GCD
mpz u, v, t, u1, u2;
set(u, a);
set(v, b);
abs(u);
abs(v);
if (lt(u, v))
swap(u, v);
while (!is_zero(v)) {
// Basic idea:
// compute t = 2^e*v such that t <= u < 2t
// u := min{u - t, 2t - u}
//
// The assignment u := min{u - t, 2t - u}
// can be replaced with u := u - t
//
// Since u and v are positive, we have:
// 2^{log2(u)} <= u < 2^{(log2(u) + 1)}
// 2^{log2(v)} <= v < 2^{(log2(v) + 1)}
// -->
// 2^{log2(v)}*2^{log2(u)-log2(v)} <= v*2^{log2(u)-log2(v)} < 2^{log2(v) + 1}*2^{log2(u)-log2(v)}
// -->
// 2^{log2(u)} <= v*2^{log2(u)-log2(v)} < 2^{log2(u) + 1}
//
// Now, let t be v*2^{log2(u)-log2(v)}
// If t <= u, then we found t