lean2/src/util/numerics/mpq.cpp

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/*
Copyright (c) 2013 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Leonardo de Moura
*/
#include "util/sstream.h"
#include "util/thread.h"
#include "util/numerics/mpq.h"
#include "util/numerics/mpbq.h"
namespace lean {
const mpq numeric_traits<mpq>::pi_l((3373259426.0 + 273688.0 / (1<<21)) / (1<<30));
const mpq numeric_traits<mpq>::pi_n((3373259426.0 + 273688.0 / (1<<21)) / (1<<30));
const mpq numeric_traits<mpq>::pi_u((3373259426.0 + 273688.0 / (1<<21)) / (1<<30));
mpq & mpq::operator=(mpbq const & b) {
*this = 2;
power(*this, *this, b.get_k());
inv();
*this *= b.get_numerator();
return *this;
}
int cmp(mpq const & a, mpz const & b) {
if (a.is_integer()) {
return mpz_cmp(mpq_numref(a.m_val), mpq::zval(b));
} else {
static LEAN_THREAD_LOCAL mpz tmp;
mpz_mul(mpq::zval(tmp), mpq_denref(a.m_val), mpq::zval(b));
return mpz_cmp(mpq_numref(a.m_val), mpq::zval(tmp));
}
}
void mpq::floor() {
if (is_integer())
return;
bool neg = is_neg();
mpz_tdiv_q(mpq_numref(m_val), mpq_numref(m_val), mpq_denref(m_val));
mpz_set_ui(mpq_denref(m_val), 1);
if (neg)
mpz_sub_ui(mpq_numref(m_val), mpq_numref(m_val), 1);
}
void mpq::ceil() {
if (is_integer())
return;
bool pos = is_pos();
mpz_tdiv_q(mpq_numref(m_val), mpq_numref(m_val), mpq_denref(m_val));
mpz_set_ui(mpq_denref(m_val), 1);
if (pos)
mpz_add_ui(mpq_numref(m_val), mpq_numref(m_val), 1);
}
mpz floor(mpq const & a) {
if (a.is_integer())
return a.get_numerator();
mpz r;
mpz_tdiv_q(mpq::zval(r), mpq_numref(a.m_val), mpq_denref(a.m_val));
if (a.is_neg())
--r;
return r;
}
mpz ceil(mpq const & a) {
if (a.is_integer())
return a.get_numerator();
mpz r;
mpz_tdiv_q(mpq::zval(r), mpq_numref(a.m_val), mpq_denref(a.m_val));
if (a.is_pos())
++r;
return r;
}
void power(mpq & a, mpq const & b, unsigned k) {
mpz_pow_ui(mpq_numref(a.m_val), mpq_numref(b.m_val), k);
mpz_pow_ui(mpq_denref(a.m_val), mpq_denref(b.m_val), k);
mpq_canonicalize(a.m_val);
}
extern void display(std::ostream & out, __mpz_struct const * v);
std::ostream & operator<<(std::ostream & out, mpq const & v) {
if (v.is_integer()) {
display(out, mpq_numref(v.m_val));
} else {
display(out, mpq_numref(v.m_val));
out << "/";
display(out, mpq_denref(v.m_val));
}
return out;
}
void display_decimal(std::ostream & out, mpq const & a, unsigned prec) {
mpz n1, d1, v1;
numerator(n1, a);
denominator(d1, a);
if (a.is_neg()) {
out << "-";
n1.neg();
}
v1 = n1 / d1;
out << v1;
n1 = rem(n1, d1);
if (n1.is_zero())
return;
out << ".";
for (unsigned i = 0; i < prec; i++) {
n1 *= 10;
v1 = n1 / d1;
lean_assert(v1 < 10);
out << v1;
n1 = rem(n1, d1);
if (n1.is_zero())
return;
}
out << "?";
}
static mpq g_zero;
mpq const & numeric_traits<mpq>::zero() {
lean_assert(is_zero(g_zero));
return g_zero;
}
serializer & operator<<(serializer & s, mpq const & n) {
std::ostringstream out;
out << n;
s << out.str();
return s;
}
mpq read_mpq(deserializer & d) {
return mpq(d.read_string().c_str());
}
DECL_UDATA(mpq)
template<int idx>
static mpq const & to_mpq(lua_State * L) {
static LEAN_THREAD_LOCAL mpq arg;
switch (lua_type(L, idx)) {
case LUA_TNUMBER: arg = lua_tonumber(L, idx); return arg;
case LUA_TSTRING: arg = mpq(lua_tostring(L, idx)); return arg;
case LUA_TUSERDATA:
if (is_mpz(L, idx)) {
arg = mpq(to_mpz(L, idx));
return arg;
} else {
return *static_cast<mpq*>(luaL_checkudata(L, idx, mpq_mt));
}
default: throw exception(sstream() << "arg #" << idx << " must be a number, string, mpz or mpq");
}
}
mpq to_mpq_ext(lua_State * L, int idx) {
switch (lua_type(L, idx)) {
case LUA_TNUMBER: return mpq(lua_tonumber(L, idx));
case LUA_TSTRING: return mpq(lua_tostring(L, idx));
case LUA_TUSERDATA:
if (is_mpz(L, idx)) {
return mpq(to_mpz(L, idx));
} else {
return *static_cast<mpq*>(luaL_checkudata(L, idx, mpq_mt));
}
default: throw exception(sstream() << "arg #" << idx << " must be a number, string, mpz or mpq");
}
}
static int mpq_tostring(lua_State * L) {
mpq * n = static_cast<mpq*>(luaL_checkudata(L, 1, mpq_mt));
std::ostringstream out;
out << *n;
return pushstring(L, out.str().c_str());
}
static int mpq_eq(lua_State * L) {
return pushboolean(L, to_mpq<1>(L) == to_mpq<2>(L));
}
static int mpq_lt(lua_State * L) {
return pushboolean(L, to_mpq<1>(L) < to_mpq<2>(L));
}
static int mpq_add(lua_State * L) {
return push_mpq(L, to_mpq<1>(L) + to_mpq<2>(L));
}
static int mpq_sub(lua_State * L) {
return push_mpq(L, to_mpq<1>(L) - to_mpq<2>(L));
}
static int mpq_mul(lua_State * L) {
return push_mpq(L, to_mpq<1>(L) * to_mpq<2>(L));
}
static int mpq_div(lua_State * L) {
mpq const & arg2 = to_mpq<2>(L);
if (arg2 == 0) throw exception("division by zero");
return push_mpq(L, to_mpq<1>(L) / arg2);
}
static int mpq_umn(lua_State * L) {
return push_mpq(L, 0 - to_mpq<1>(L));
}
static int mpq_power(lua_State * L) {
int k = luaL_checkinteger(L, 2);
if (k < 0) throw exception("argument #2 must be positive");
return push_mpq(L, pow(to_mpq<1>(L), k));
}
static int mk_mpq(lua_State * L) {
mpq const & arg = to_mpq<1>(L);
return push_mpq(L, arg);
}
static const struct luaL_Reg mpq_m[] = {
{"__gc", mpq_gc}, // never throws
{"__tostring", safe_function<mpq_tostring>},
{"__eq", safe_function<mpq_eq>},
{"__lt", safe_function<mpq_lt>},
{"__add", safe_function<mpq_add>},
{"__sub", safe_function<mpq_sub>},
{"__mul", safe_function<mpq_mul>},
{"__div", safe_function<mpq_div>},
{"__pow", safe_function<mpq_power>},
{"__unm", safe_function<mpq_umn>},
{0, 0}
};
static void mpq_migrate(lua_State * src, int i, lua_State * tgt) {
push_mpq(tgt, to_mpq(src, i));
}
void open_mpq(lua_State * L) {
luaL_newmetatable(L, mpq_mt);
set_migrate_fn_field(L, -1, mpq_migrate);
lua_pushvalue(L, -1);
lua_setfield(L, -2, "__index");
setfuncs(L, mpq_m, 0);
SET_GLOBAL_FUN(mk_mpq, "mpq");
SET_GLOBAL_FUN(mpq_pred, "is_mpq");
}
}
void print(lean::mpq const & v) { std::cout << v << std::endl; }