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z3-z3-4.12.6.src.util.mpz.h Maven / Gradle / Ivy
/*++
Copyright (c) 2006 Microsoft Corporation
Module Name:
mpz.h
Abstract:
Author:
Leonardo de Moura (leonardo) 2010-06-17.
Revision History:
--*/
#pragma once
#include
#include "util/mutex.h"
#include "util/util.h"
#include "util/small_object_allocator.h"
#include "util/trace.h"
#include "util/scoped_numeral.h"
#include "util/scoped_numeral_vector.h"
#include "util/mpn.h"
unsigned u_gcd(unsigned u, unsigned v);
uint64_t u64_gcd(uint64_t u, uint64_t v);
unsigned trailing_zeros(uint64_t);
unsigned trailing_zeros(uint32_t);
#ifdef _MP_GMP
typedef unsigned digit_t;
#endif
#ifdef _MSC_VER
#pragma warning(disable : 4200)
#endif
template class mpz_manager;
template class mpq_manager;
#if !defined(_MP_GMP) && !defined(_MP_INTERNAL)
#ifdef _WINDOWS
#define _MP_INTERNAL
#else
#define _MP_GMP
#endif
#endif
#ifndef _MP_GMP
typedef unsigned int digit_t;
class mpz_cell {
unsigned m_size;
unsigned m_capacity;
digit_t m_digits[0];
friend class mpz_manager;
friend class mpz_manager;
friend class mpz_stack;
};
#else
#include
#endif
/**
\brief Multi-precision integer.
If m_kind == mpz_small, it is a small number and the value is stored in m_val.
If m_kind == mpz_large, the value is stored in m_ptr and m_ptr != nullptr.
m_val contains the sign (-1 negative, 1 positive)
under winodws, m_ptr points to a mpz_cell that store the value.
*/
enum mpz_kind { mpz_small = 0, mpz_large = 1};
enum mpz_owner { mpz_self = 0, mpz_ext = 1};
class mpz {
#ifndef _MP_GMP
typedef mpz_cell mpz_type;
#else
typedef mpz_t mpz_type;
#endif
protected:
int m_val;
unsigned m_kind:1;
unsigned m_owner:1;
mpz_type * m_ptr;
friend class mpz_manager;
friend class mpz_manager;
friend class mpq_manager;
friend class mpq_manager;
friend class mpq;
friend class mpbq;
friend class mpbq_manager;
friend class mpz_stack;
public:
mpz(int v):m_val(v), m_kind(mpz_small), m_owner(mpz_self), m_ptr(nullptr) {}
mpz():m_val(0), m_kind(mpz_small), m_owner(mpz_self), m_ptr(nullptr) {}
mpz(mpz_type* ptr): m_val(0), m_kind(mpz_small), m_owner(mpz_ext), m_ptr(ptr) { SASSERT(ptr);}
mpz(mpz && other) noexcept : m_val(other.m_val), m_kind(other.m_kind), m_owner(other.m_owner), m_ptr(nullptr) {
std::swap(m_ptr, other.m_ptr);
}
mpz& operator=(mpz const& other) = delete;
mpz& operator=(mpz &&other) noexcept {
swap(other);
return *this;
}
void swap(mpz & other) noexcept {
std::swap(m_val, other.m_val);
std::swap(m_ptr, other.m_ptr);
unsigned o = m_owner; m_owner = other.m_owner; other.m_owner = o;
unsigned k = m_kind; m_kind = other.m_kind; other.m_kind = k;
}
void set(int v) {
m_val = v;
m_kind = mpz_small;
}
inline bool is_small() const { return m_kind == mpz_small; }
inline int value() const { SASSERT(is_small()); return m_val; }
inline int sign() const { SASSERT(!is_small()); return m_val; }
};
#ifndef _MP_GMP
class mpz_stack : public mpz {
static const unsigned capacity = 8;
unsigned char m_bytes[sizeof(mpz_cell) + sizeof(digit_t) * capacity];
public:
mpz_stack():mpz(reinterpret_cast(m_bytes)) {
m_ptr->m_capacity = capacity;
}
};
#else
class mpz_stack : public mpz {};
#endif
inline void swap(mpz & m1, mpz & m2) noexcept { m1.swap(m2); }
template
class mpz_manager {
mutable small_object_allocator m_allocator;
#ifndef SINGLE_THREAD
mutable std::recursive_mutex m_lock;
#define MPZ_BEGIN_CRITICAL() if (SYNCH) m_lock.lock()
#define MPZ_END_CRITICAL() if (SYNCH) m_lock.unlock()
#else
#define MPZ_BEGIN_CRITICAL() {}
#define MPZ_END_CRITICAL() {}
#endif
mutable mpn_manager m_mpn_manager;
#ifndef _MP_GMP
unsigned m_init_cell_capacity;
mpz m_int_min;
static unsigned cell_size(unsigned capacity) {
return sizeof(mpz_cell) + sizeof(digit_t) * capacity;
}
mpz_cell * allocate(unsigned capacity);
// make sure that n is a big number and has capacity equal to at least c.
void allocate_if_needed(mpz & n, unsigned c) {
if (m_init_cell_capacity > c) c = m_init_cell_capacity;
if (n.m_ptr == nullptr || capacity(n) < c) {
deallocate(n);
n.m_val = 1;
n.m_kind = mpz_large;
n.m_owner = mpz_self;
n.m_ptr = allocate(c);
}
else {
n.m_kind = mpz_large;
}
}
void deallocate(bool is_heap, mpz_cell * ptr);
// Expand capacity of a while preserving its content.
void ensure_capacity(mpz & a, unsigned sz);
void normalize(mpz & a);
void clear(mpz& n) { reset(n); }
/**
\brief Set \c a with the value stored at src, and the given sign.
\c sz is an overapproximation of the size of the number stored at \c src.
*/
void set(mpz_cell& src, mpz & a, int sign, unsigned sz);
#else
// GMP code
mutable mpz_t m_tmp, m_tmp2;
mutable mpz_t m_two32;
mpz_t * m_arg[2];
mutable mpz_t m_uint64_max;
mutable mpz_t m_int64_max;
mutable mpz_t m_int64_min;
mpz_t * allocate() {
mpz_t * cell;
#ifdef SINGLE_THREAD
cell = reinterpret_cast(m_allocator.allocate(sizeof(mpz_t)));
#else
if (SYNCH) {
cell = reinterpret_cast(memory::allocate(sizeof(mpz_t)));
}
else {
cell = reinterpret_cast(m_allocator.allocate(sizeof(mpz_t)));
}
#endif
mpz_init(*cell);
return cell;
}
void deallocate(bool is_heap, mpz_t * ptr) {
mpz_clear(*ptr);
if (is_heap) {
#ifdef SINGLE_THREAD
m_allocator.deallocate(sizeof(mpz_t), ptr);
#else
if (SYNCH) {
memory::deallocate(ptr);
}
else {
m_allocator.deallocate(sizeof(mpz_t), ptr);
}
#endif
}
}
void clear(mpz& n) { if (n.m_ptr) { mpz_clear(*n.m_ptr); }}
#endif
void deallocate(mpz& n) {
if (n.m_ptr) {
deallocate(n.m_owner == mpz_self, n.m_ptr);
n.m_ptr = nullptr;
n.m_kind = mpz_small;
}
}
mpz m_two64;
static int64_t i64(mpz const & a) { return static_cast(a.value()); }
void set_big_i64(mpz & c, int64_t v);
void set_i64(mpz & c, int64_t v) {
if (v >= INT_MIN && v <= INT_MAX) {
c.set(static_cast(v));
}
else {
set_big_i64(c, v);
}
}
void set_big_ui64(mpz & c, uint64_t v);
#ifndef _MP_GMP
static unsigned capacity(mpz const & c) { return c.m_ptr->m_capacity; }
static unsigned size(mpz const & c) { return c.m_ptr->m_size; }
static digit_t * digits(mpz const & c) { return c.m_ptr->m_digits; }
// Return true if the absolute value fits in a UINT64
static bool is_abs_uint64(mpz const & a) {
if (is_small(a))
return true;
if (sizeof(digit_t) == sizeof(uint64_t))
return size(a) <= 1;
else
return size(a) <= 2;
}
// CAST the absolute value into a UINT64
static uint64_t big_abs_to_uint64(mpz const & a) {
SASSERT(is_abs_uint64(a));
SASSERT(!is_small(a));
if (a.m_ptr->m_size == 1)
return digits(a)[0];
if (sizeof(digit_t) == sizeof(uint64_t))
// 64-bit machine
return digits(a)[0];
else
// 32-bit machine
return ((static_cast(digits(a)[1]) << 32) | (static_cast(digits(a)[0])));
}
class sign_cell {
static const unsigned capacity = 2;
unsigned char m_bytes[sizeof(mpz_cell) + sizeof(digit_t) * capacity];
mpz m_local;
mpz const& m_a;
int m_sign;
mpz_cell* m_cell;
public:
sign_cell(mpz_manager& m, mpz const& a);
int sign() { return m_sign; }
mpz_cell const* cell() { return m_cell; }
};
void get_sign_cell(mpz const & a, int & sign, mpz_cell * & cell, mpz_cell* reserve) {
if (is_small(a)) {
if (a.value() == INT_MIN) {
sign = -1;
cell = m_int_min.m_ptr;
}
else {
cell = reserve;
cell->m_size = 1;
if (a.value() < 0) {
sign = -1;
cell->m_digits[0] = -a.value();
}
else {
sign = 1;
cell->m_digits[0] = a.value();
}
}
}
else {
sign = a.sign();
cell = a.m_ptr;
}
}
#else
// GMP code
class ensure_mpz_t {
mpz_t m_local;
mpz_t* m_result;
public:
ensure_mpz_t(mpz const& a);
~ensure_mpz_t();
mpz_t& operator()() { return *m_result; }
};
void mk_big(mpz & a) {
if (a.m_ptr == nullptr) {
a.m_val = 0;
a.m_ptr = allocate();
a.m_owner = mpz_self;
}
a.m_kind = mpz_large;
}
#endif
#ifndef _MP_GMP
template
void big_add_sub(mpz const & a, mpz const & b, mpz & c);
#endif
void big_add(mpz const & a, mpz const & b, mpz & c);
void big_sub(mpz const & a, mpz const & b, mpz & c);
void big_mul(mpz const & a, mpz const & b, mpz & c);
void big_set(mpz & target, mpz const & source);
#ifndef _MP_GMP
#define QUOT_ONLY 0
#define REM_ONLY 1
#define QUOT_AND_REM 2
#define qr_mode int
template
void quot_rem_core(mpz const & a, mpz const & b, mpz & q, mpz & r);
#endif
void big_div_rem(mpz const & a, mpz const & b, mpz & q, mpz & r);
void big_div(mpz const & a, mpz const & b, mpz & c);
void big_rem(mpz const & a, mpz const & b, mpz & c);
int big_compare(mpz const & a, mpz const & b);
public:
unsigned size_info(mpz const & a);
struct sz_lt;
static bool precise() { return true; }
static bool field() { return false; }
typedef mpz numeral;
mpz_manager();
~mpz_manager();
static bool is_small(mpz const & a) { return a.is_small(); }
static mpz mk_z(int val) { return mpz(val); }
void del(mpz & a) { del(this, a); }
static void del(mpz_manager* m, mpz & a);
void add(mpz const & a, mpz const & b, mpz & c);
void sub(mpz const & a, mpz const & b, mpz & c);
void inc(mpz & a) { add(a, mpz(1), a); }
void dec(mpz & a) { add(a, mpz(-1), a); }
void mul(mpz const & a, mpz const & b, mpz & c);
// d <- a + b*c
void addmul(mpz const & a, mpz const & b, mpz const & c, mpz & d);
// d <- a - b*c
void submul(mpz const & a, mpz const & b, mpz const & c, mpz & d);
void machine_div_rem(mpz const & a, mpz const & b, mpz & q, mpz & r);
void machine_div(mpz const & a, mpz const & b, mpz & c);
void rem(mpz const & a, mpz const & b, mpz & c);
void div_gcd(mpz const & a, mpz const & b, mpz & c);
void div(mpz const & a, mpz const & b, mpz & c);
void mod(mpz const & a, mpz const & b, mpz & c);
void neg(mpz & a);
void abs(mpz & a);
static bool is_pos(mpz const & a) { return sign(a) > 0; }
static bool is_neg(mpz const & a) { return sign(a) < 0; }
static bool is_zero(mpz const & a) { return sign(a) == 0; }
static int sign(mpz const & a) {
#ifndef _MP_GMP
return a.m_val;
#else
if (is_small(a))
return a.m_val;
else
return mpz_sgn(*a.m_ptr);
#endif
}
static bool is_nonpos(mpz const & a) { return !is_pos(a); }
static bool is_nonneg(mpz const & a) { return !is_neg(a); }
bool eq(mpz const & a, mpz const & b) {
if (is_small(a) && is_small(b)) {
return a.value() == b.value();
}
else {
return big_compare(a, b) == 0;
}
}
bool lt(mpz const& a, int b) {
if (is_small(a)) {
return a.value() < b;
}
else {
return lt(a, mpz(b));
}
}
bool lt(mpz const & a, mpz const & b) {
if (is_small(a) && is_small(b)) {
return a.value() < b.value();
}
else {
return big_compare(a, b) < 0;
}
}
bool neq(mpz const & a, mpz const & b) { return !eq(a, b); }
bool gt(mpz const & a, mpz const & b) { return lt(b, a); }
bool ge(mpz const & a, mpz const & b) { return !lt(a, b); }
bool le(mpz const & a, mpz const & b) { return !lt(b, a); }
void gcd(mpz const & a, mpz const & b, mpz & c);
void gcd(unsigned sz, mpz const * as, mpz & g);
/**
\brief Extended Euclid:
r1*a + r2*b = g
*/
void gcd(mpz const & r1, mpz const & r2, mpz & a, mpz & b, mpz & g);
void lcm(mpz const & a, mpz const & b, mpz & c);
/**
\brief Return true if a | b
*/
bool divides(mpz const & a, mpz const & b);
// not a field
void inv(mpz & a) {
SASSERT(false);
}
void bitwise_or(mpz const & a, mpz const & b, mpz & c);
void bitwise_and(mpz const & a, mpz const & b, mpz & c);
void bitwise_xor(mpz const & a, mpz const & b, mpz & c);
void bitwise_not(unsigned sz, mpz const & a, mpz & c);
void set(mpz & target, mpz const & source) {
if (is_small(source)) {
target.set(source.value());
}
else {
big_set(target, source);
}
}
void set(mpz & a, int val) {
a.set(val);
}
void set(mpz & a, unsigned val) {
if (val <= INT_MAX)
set(a, static_cast(val));
else
set(a, static_cast(static_cast(val)));
}
void set(mpz & a, char const * val);
void set(mpz & a, int64_t val) {
set_i64(a, val);
}
void set(mpz & a, uint64_t val) {
if (val < INT_MAX) {
a.set(static_cast(val));
}
else {
set_big_ui64(a, val);
}
}
void set_digits(mpz & target, unsigned sz, digit_t const * digits);
mpz dup(const mpz & source) {
mpz temp;
set(temp, source);
return temp;
}
// deallocates any memory.
void reset(mpz & a);
void swap(mpz & a, mpz & b) noexcept {
a.swap(b);
}
bool is_uint64(mpz const & a) const;
bool is_int64(mpz const & a) const;
uint64_t get_uint64(mpz const & a) const;
int64_t get_int64(mpz const & a) const;
bool is_uint(mpz const & a) const { return is_uint64(a) && get_uint64(a) < UINT_MAX; }
unsigned get_uint(mpz const & a) const { SASSERT(is_uint(a)); return static_cast(get_uint64(a)); }
bool is_int(mpz const & a) const { return is_int64(a) && INT_MIN < get_int64(a) && get_int64(a) < INT_MAX; }
int get_int(mpz const & a) const { SASSERT(is_int(a)); return static_cast(get_int64(a)); }
double get_double(mpz const & a) const;
std::string to_string(mpz const & a) const;
void display(std::ostream & out, mpz const & a) const;
/**
\brief Display mpz number in SMT 2.0 format.
If decimal == true, then ".0" is appended.
*/
void display_smt2(std::ostream & out, mpz const & a, bool decimal) const;
/**
\brief Displays the num_bits least significant bits of a mpz number in hexadecimal format.
num_bits must be divisible by 4.
*/
void display_hex(std::ostream & out, mpz const & a, unsigned num_bits) const;
/**
\brief Displays the num_bits least significant bits of a mpz number in binary format.
*/
void display_bin(std::ostream & out, mpz const & a, unsigned num_bits) const;
static unsigned hash(mpz const & a);
static bool is_one(mpz const & a) {
#ifndef _MP_GMP
return is_small(a) && a.value() == 1;
#else
if (is_small(a))
return a.value() == 1;
return mpz_cmp_si(*a.m_ptr, 1) == 0;
#endif
}
static bool is_minus_one(mpz const & a) {
#ifndef _MP_GMP
return is_small(a) && a.value() == -1;
#else
if (is_small(a))
return a.value() == -1;
return mpz_cmp_si(*a.m_ptr, -1) == 0;
#endif
}
void power(mpz const & a, unsigned p, mpz & b);
bool is_power_of_two(mpz const & a);
bool is_power_of_two(mpz const & a, unsigned & shift);
void machine_div2k(mpz & a, unsigned k);
void machine_div2k(mpz const & a, unsigned k, mpz & r) { set(r, a); machine_div2k(r, k); }
void mul2k(mpz & a, unsigned k);
void mul2k(mpz const & a, unsigned k, mpz & r) { set(r, a); mul2k(r, k); }
/**
\brief Return largest k s.t. n is a multiple of 2^k
*/
unsigned power_of_two_multiple(mpz const & n);
/**
\brief Return the position of the most significant bit.
Return 0 if the number is negative
*/
unsigned log2(mpz const & n);
/**
\brief log2(-n)
Return 0 if the number is nonegative
*/
unsigned mlog2(mpz const & n);
/**
\brief Return the bit-size of n. This method is mainly used for collecting statistics.
*/
unsigned bitsize(mpz const & n);
/**
\brief Return true if the number is a perfect square, and
store the square root in 'root'.
If the number n is positive and the result is false, then
root will contain the smallest integer r such that r*r > n.
*/
bool is_perfect_square(mpz const & a, mpz & root);
/**
\brief Return the biggest k s.t. 2^k <= a.
\remark Return 0 if a is not positive.
*/
unsigned prev_power_of_two(mpz const & a) { return log2(a); }
/**
\brief Return the smallest k s.t. a <= 2^k.
\remark Return 0 if a is not positive.
*/
unsigned next_power_of_two(mpz const & a);
/**
\brief Return true if a^{1/n} is an integer, and store the result in a.
Otherwise return false, and update a with the smallest
integer r such that r*r > n.
\remark This method assumes that if n is even, then a is nonegative
*/
bool root(mpz & a, unsigned n);
bool root(mpz const & a, unsigned n, mpz & r) { set(r, a); return root(r, n); }
bool is_even(mpz const & a) {
if (is_small(a))
return !(a.value() & 0x1);
#ifndef _MP_GMP
return !(0x1 & digits(a)[0]);
#else
return mpz_even_p(*a.m_ptr);
#endif
}
bool is_odd(mpz const & n) { return !is_even(n); }
// Store the digits of n into digits, and return the sign.
bool decompose(mpz const & n, svector & digits);
bool get_bit(mpz const& a, unsigned bit);
};
#ifndef SINGLE_THREAD
typedef mpz_manager synch_mpz_manager;
#else
typedef mpz_manager synch_mpz_manager;
#endif
typedef mpz_manager unsynch_mpz_manager;
typedef _scoped_numeral scoped_mpz;
typedef _scoped_numeral scoped_synch_mpz;
typedef _scoped_numeral_vector scoped_mpz_vector;
