z3-z3-4.13.0.src.util.mpf.h Maven / Gradle / Ivy
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/*++
Copyright (c) 2011 Microsoft Corporation
Module Name:
mpf.h
Abstract:
Multi Precision Floating Point Numbers
Author:
Christoph Wintersteiger (cwinter) 2011-12-01.
Revision History:
--*/
#pragma once
#include
#include "util/mpz.h"
#include "util/mpq.h"
#include "util/map.h"
#include "util/scoped_numeral.h"
#include "util/scoped_numeral_vector.h"
#include "util/hash.h"
typedef enum {
MPF_ROUND_NEAREST_TEVEN,
MPF_ROUND_NEAREST_TAWAY,
MPF_ROUND_TOWARD_POSITIVE,
MPF_ROUND_TOWARD_NEGATIVE,
MPF_ROUND_TOWARD_ZERO
} mpf_rounding_mode;
typedef int64_t mpf_exp_t;
class mpf {
friend class mpf_manager;
friend class scoped_mpf;
unsigned ebits:15;
unsigned sbits:16;
unsigned sign:1; // counts as one sbit.
mpz significand;
mpf_exp_t exponent;
void set(unsigned _ebits, unsigned _sbits);
public:
mpf();
mpf(unsigned ebits, unsigned sbits);
mpf(mpf &&) = default;
mpf & operator=(mpf const & other) = delete;
unsigned get_ebits() const { return ebits; }
unsigned get_sbits() const { return sbits; }
void swap(mpf & other) noexcept;
};
class mpf_manager {
unsynch_mpq_manager m_mpq_manager;
unsynch_mpz_manager & m_mpz_manager; // A mpq_manager is a mpz_manager, reusing it.
public:
typedef mpf numeral;
mpf_manager();
void reset(mpf & o, unsigned ebits, unsigned sbits) { set(o, ebits, sbits, 0); }
void set(mpf & o, unsigned ebits, unsigned sbits, int value);
void set(mpf & o, unsigned ebits, unsigned sbits, mpf_rounding_mode rm, int n, int d);
void set(mpf & o, unsigned ebits, unsigned sbits, float value);
void set(mpf & o, unsigned ebits, unsigned sbits, double value);
void set(mpf & o, unsigned ebits, unsigned sbits, mpf_rounding_mode rm, mpq const & value);
void set(mpf & o, unsigned ebits, unsigned sbits, mpf_rounding_mode rm, char const * value);
void set(mpf & o, unsigned ebits, unsigned sbits, mpf_rounding_mode rm, mpz const & exponent, mpq const & significand);
void set(mpf & o, unsigned ebits, unsigned sbits, bool sign, mpf_exp_t exponent, uint64_t significand);
void set(mpf & o, unsigned ebits, unsigned sbits, bool sign, mpf_exp_t exponent, mpz const & significand);
void set(mpf & o, mpf const & x);
void set(mpf & o, unsigned ebits, unsigned sbits, mpf_rounding_mode rm, mpf const & x);
void del(mpf & x) {
m_mpz_manager.del(x.significand);
}
void abs(mpf & o);
void abs(mpf const & x, mpf & o);
void neg(mpf & o);
void neg(mpf const & x, mpf & o);
void swap(mpf& a, mpf& b) noexcept { a.swap(b); }
bool is_zero(mpf const & x);
bool is_neg(mpf const & x);
bool is_pos(mpf const & x);
bool is_one(mpf const & x);
bool is_nzero(mpf const & x);
bool is_pzero(mpf const & x);
// structural eq
bool eq_core(mpf const & x, mpf const & y) {
return
x.ebits == y.ebits &&
x.sbits == y.sbits &&
x.sign == y.sign &&
m_mpz_manager.eq(x.significand, y.significand) &&
x.exponent == y.exponent;
}
bool eq(mpf const & x, mpf const & y);
bool lt(mpf const & x, mpf const & y);
bool lte(mpf const & x, mpf const & y);
bool le(mpf const & x, mpf const & y) { return lte(x, y); }
bool gt(mpf const & x, mpf const & y);
bool gte(mpf const & x, mpf const & y);
bool ge(mpf const & x, mpf const & y) { return gte(x, y); }
void add(mpf_rounding_mode rm, mpf const & x, mpf const & y, mpf & o);
void sub(mpf_rounding_mode rm, mpf const & x, mpf const & y, mpf & o);
void mul(mpf_rounding_mode rm, mpf const & x, mpf const & y, mpf & o);
void div(mpf_rounding_mode rm, mpf const & x, mpf const & y, mpf & o);
void fma(mpf_rounding_mode rm, mpf const & x, mpf const & y, mpf const &z, mpf & o);
void sqrt(mpf_rounding_mode rm, mpf const & x, mpf & o);
void round_to_integral(mpf_rounding_mode rm, mpf const & x, mpf & o);
void rem(mpf const & x, mpf const & y, mpf & o);
void maximum(mpf const & x, mpf const & y, mpf & o);
void minimum(mpf const & x, mpf const & y, mpf & o);
std::string to_string(mpf const & a);
std::string to_rational_string(mpf const & a);
void display_decimal(std::ostream & out, mpf const & a, unsigned k);
void display_smt2(std::ostream & out, mpf const & a, bool decimal);
// Convert x into a mpq numeral. zm is the manager that owns o.
void to_rational(mpf const & x, unsynch_mpq_manager & qm, mpq & o);
void to_rational(mpf const & x, scoped_mpq & o) { to_rational(x, o.m(), o); }
double to_double(mpf const & x);
float to_float(mpf const & x);
bool sgn(mpf const & x) const { return x.sign; }
const mpz & sig(mpf const & x) const { return x.significand; }
void sig_normalized(mpf const & x, mpz & res) {
mpf t;
set(t, x);
unpack(t, true);
mpz_manager().set(res, t.significand);
del(t);
}
const mpf_exp_t & exp(mpf const & x) const { return x.exponent; }
mpf_exp_t exp_normalized(mpf const & x) {
if (is_zero(x))
return 0;
else {
mpf t;
set(t, x);
unpack(t, true);
mpf_exp_t r = t.exponent;
del(t);
return r;
}
}
bool is_nan(mpf const & x);
bool is_inf(mpf const & x);
bool is_pinf(mpf const & x);
bool is_ninf(mpf const & x);
bool is_normal(mpf const & x);
bool is_denormal(mpf const & x);
bool is_regular(mpf const & x) { return x.sbits == 0 || is_normal(x) || is_denormal(x); }
bool is_int(mpf const & x);
void mk_zero(unsigned ebits, unsigned sbits, bool sign, mpf & o);
void mk_nzero(unsigned ebits, unsigned sbits, mpf & o);
void mk_pzero(unsigned ebits, unsigned sbits, mpf & o);
void mk_nan(unsigned ebits, unsigned sbits, mpf & o);
void mk_inf(unsigned ebits, unsigned sbits, bool sign, mpf & o);
void mk_pinf(unsigned ebits, unsigned sbits, mpf & o);
void mk_ninf(unsigned ebits, unsigned sbits, mpf & o);
unsynch_mpz_manager & mpz_manager() { return m_mpz_manager; }
unsynch_mpq_manager & mpq_manager() { return m_mpq_manager; }
unsigned hash(mpf const & a) {
return hash_u_u(m_mpz_manager.hash(a.significand),
m_mpz_manager.hash(hash_ull(a.exponent)));
}
void mk_max_value(unsigned ebits, unsigned sbits, bool sign, mpf & o);
mpf_exp_t mk_bot_exp(unsigned ebits);
mpf_exp_t mk_top_exp(unsigned ebits);
mpf_exp_t mk_max_exp(unsigned ebits);
mpf_exp_t mk_min_exp(unsigned ebits);
mpf_exp_t bias_exp(unsigned ebits, mpf_exp_t unbiased_exponent);
mpf_exp_t unbias_exp(unsigned ebits, mpf_exp_t biased_exponent);
/**
\brief Return the biggest k s.t. 2^k <= a.
\remark Return 0 if a is not positive.
*/
unsigned prev_power_of_two(mpf const & a);
void to_sbv_mpq(mpf_rounding_mode rm, const mpf & x, scoped_mpq & o);
void to_ieee_bv_mpz(const mpf & x, scoped_mpz & o);
protected:
void mk_one(unsigned ebits, unsigned sbits, bool sign, mpf & o) const;
bool has_bot_exp(mpf const & x);
bool has_top_exp(mpf const & x);
void unpack(mpf & o, bool normalize);
void add_sub(mpf_rounding_mode rm, mpf const & x, mpf const & y, mpf & o, bool sub);
void round(mpf_rounding_mode rm, mpf & o);
void round_sqrt(mpf_rounding_mode rm, mpf & o);
void renormalize(unsigned ebits, unsigned sbits, mpf_exp_t & exp, mpz & sig);
void partial_remainder(mpf & x, mpf const & y, mpf_exp_t const & exp_diff, bool partial);
void mk_round_inf(mpf_rounding_mode rm, mpf & o);
// Convert x into a mpz numeral. zm is the manager that owns o.
void to_mpz(mpf const & x, unsynch_mpz_manager & zm, mpz & o);
void to_mpz(mpf const & x, scoped_mpz & o) { to_mpz(x, o.m(), o); }
class powers2 {
unsynch_mpz_manager & m;
u_map m_p;
u_map m_pn;
u_map m_pm1;
u_map m_pm1n;
public:
powers2(unsynch_mpz_manager & m) : m(m) {}
~powers2() {
dispose(m_p);
dispose(m_pn);
dispose(m_pm1);
dispose(m_pm1n);
}
void dispose(u_map & map) {
for (u_map::iterator it = map.begin(); it != map.end(); it++) {
m.del(*it->m_value);
dealloc(it->m_value);
}
}
const mpz & operator()(unsigned n, bool negated = false) {
u_map & map = (negated) ? m_pn : m_p;
u_map::iterator it = map.find_iterator(n);
if (it != map.end())
return *it->m_value;
else {
mpz * new_obj = alloc(mpz);
map.insert(n, new_obj);
m.power(unsynch_mpz_manager::mk_z(2), n, *new_obj);
if (negated) m.neg(*new_obj);
return *new_obj;
}
}
const mpz & m1(unsigned n, bool negated=false) { // (2 ^ n) - 1
u_map & map = (negated) ? m_pm1n : m_pm1;
u_map::iterator it = map.find_iterator(n);
if (it != map.end())
return *it->m_value;
else {
mpz * new_obj = alloc(mpz);
map.insert(n, new_obj);
m.power(unsynch_mpz_manager::mk_z(2), n, *new_obj);
m.dec(*new_obj);
if (negated) m.neg(*new_obj);
return *new_obj;
}
}
};
std::string to_string_raw(mpf const & a);
std::string to_string_hexfloat(mpf const & a);
std::string to_string_hexfloat(bool sgn, mpf_exp_t exp, scoped_mpz const & sig, unsigned ebits, unsigned sbits, unsigned rbits);
std::string to_string_binary(mpf const & x, unsigned upper_extra, unsigned lower_extra);
public:
powers2 m_powers2;
};
class scoped_mpf : public _scoped_numeral {
friend class mpf_manager;
mpz & significand() { return get().significand; }
const mpz & significand() const { return get().significand; }
bool sign() const { return get().sign; }
mpf_exp_t exponent() const { return get().exponent; }
unsigned sbits() const { return get().sbits; }
void set(unsigned ebits, unsigned sbits) { get().set(ebits, sbits); }
void set(unsigned ebits, unsigned sbits, bool sign, mpf_exp_t exp, mpz & significand) {
get().set(ebits, sbits);
get().exponent = exp;
get().sign = sign;
if (&get().significand != &significand)
m().mpz_manager().set(get().significand, significand);
}
void set(unsigned ebits, unsigned sbits, bool sign, mpf_exp_t exp) {
get().set(ebits, sbits);
get().exponent = exp;
get().sign = sign;
m().mpz_manager().set(get().significand, 0);
}
public:
scoped_mpf(mpf_manager & m):_scoped_numeral(m) {}
scoped_mpf(scoped_mpf const & n):_scoped_numeral(n) {}
scoped_mpf(mpf_manager & m, unsigned ebits, unsigned sbits):_scoped_numeral(m) { set(ebits, sbits); }
};
typedef _scoped_numeral_vector scoped_mpf_vector;