353 lines
8.2 KiB
C++
353 lines
8.2 KiB
C++
/*
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Copyright (c) 2013 Microsoft Corporation. All rights reserved.
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Released under Apache 2.0 license as described in the file LICENSE.
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Author: Leonardo de Moura
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*/
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#include <limits.h>
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#include "util/numerics/mpbq.h"
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namespace lean {
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bool set(mpbq & a, mpq const & b) {
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if (b.is_integer()) {
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numerator(a.m_num, b);
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a.m_k = 0;
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return true;
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} else {
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static thread_local mpz d;
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denominator(d, b);
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unsigned shift;
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if (d.is_power_of_two(shift)) {
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numerator(a.m_num, b);
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a.m_k = shift;
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lean_assert(a == b);
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return true;
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} else {
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numerator(a.m_num, b);
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a.m_k = d.log2() + 1;
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return false;
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}
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}
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}
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void mpbq::normalize() {
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if (m_k == 0)
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return;
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if (is_zero()) {
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m_k = 0;
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return;
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}
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unsigned k = m_num.power_of_two_multiple();
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if (k > m_k)
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k = m_k;
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div2k(m_num, m_num, k);
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m_k -= k;
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}
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int cmp(mpbq const & a, mpbq const & b) {
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static thread_local mpz tmp;
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if (a.m_k == b.m_k) {
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return cmp(a.m_num, b.m_num);
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} else if (a.m_k < b.m_k) {
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mul2k(tmp, a.m_num, b.m_k - a.m_k);
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return cmp(tmp, b.m_num);
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} else {
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lean_assert(a.m_k > b.m_k);
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mul2k(tmp, b.m_num, a.m_k - b.m_k);
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return cmp(a.m_num, tmp);
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}
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}
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int cmp(mpbq const & a, mpz const & b) {
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static thread_local mpz tmp;
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if (a.m_k == 0) {
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return cmp(a.m_num, b);
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} else {
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mul2k(tmp, b, a.m_k);
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return cmp(a.m_num, tmp);
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}
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}
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int cmp(mpbq const & a, mpq const & b) {
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if (a.is_integer() && b.is_integer()) {
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return -cmp(b, a.m_num);
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} else {
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static thread_local mpz tmp1;
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static thread_local mpz tmp2;
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// tmp1 <- numerator(a)*denominator(b)
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denominator(tmp1, b); tmp1 *= a.m_num;
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// tmp2 <- numerator(b)*denominator(a)
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numerator(tmp2, b); mul2k(tmp2, tmp2, a.m_k);
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return cmp(tmp1, tmp2);
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}
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}
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mpbq & mpbq::operator+=(mpbq const & a) {
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if (m_k == a.m_k) {
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m_num += a.m_num;
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} else if (m_k < a.m_k) {
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mul2k(m_num, m_num, a.m_k - m_k);
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m_k = a.m_k;
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m_num += a.m_num;
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} else {
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lean_assert(m_k > a.m_k);
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static thread_local mpz tmp;
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mul2k(tmp, a.m_num, m_k - a.m_k);
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m_num += tmp;
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}
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normalize();
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return *this;
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}
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template<typename T>
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mpbq & mpbq::add_int(T const & a) {
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if (m_k == 0) {
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m_num += a;
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} else {
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lean_assert(m_k > 0);
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static thread_local mpz tmp;
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tmp = a;
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mul2k(tmp, tmp, m_k);
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m_num += tmp;
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}
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normalize();
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return *this;
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}
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mpbq & mpbq::operator+=(unsigned a) { return add_int<unsigned>(a); }
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mpbq & mpbq::operator+=(int a) { return add_int<int>(a); }
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mpbq & mpbq::operator-=(mpbq const & a) {
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if (m_k == a.m_k) {
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m_num -= a.m_num;
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} else if (m_k < a.m_k) {
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mul2k(m_num, m_num, a.m_k - m_k);
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m_k = a.m_k;
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m_num -= a.m_num;
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} else {
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lean_assert(m_k > a.m_k);
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static thread_local mpz tmp;
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mul2k(tmp, a.m_num, m_k - a.m_k);
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m_num -= tmp;
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}
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normalize();
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return *this;
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}
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template<typename T>
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mpbq & mpbq::sub_int(T const & a) {
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if (m_k == 0) {
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m_num -= a;
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} else {
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lean_assert(m_k > 0);
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static thread_local mpz tmp;
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tmp = a;
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mul2k(tmp, tmp, m_k);
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m_num -= tmp;
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}
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normalize();
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return *this;
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}
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mpbq & mpbq::operator-=(unsigned a) { return sub_int<unsigned>(a); }
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mpbq & mpbq::operator-=(int a) { return sub_int<int>(a); }
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mpbq & mpbq::operator*=(mpbq const & a) {
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m_num *= a.m_num;
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if (m_k == 0 || a.m_k == 0) {
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m_k += a.m_k;
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normalize();
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} else {
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m_k += a.m_k;
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}
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return *this;
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}
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template<typename T>
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mpbq & mpbq::mul_int(T const & a) {
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m_num *= a;
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normalize();
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return *this;
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}
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mpbq & mpbq::operator*=(unsigned a) { return mul_int<unsigned>(a); }
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mpbq & mpbq::operator*=(int a) { return mul_int<int>(a); }
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void power(mpbq & a, mpbq const & b, unsigned k) {
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lean_assert(static_cast<unsigned long long>(k) * static_cast<unsigned long long>(b.m_k) <= static_cast<unsigned long long>(UINT_MAX));
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// We don't need to normalize because:
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// If b.m_k == 0, then b is an integer, and the result be an integer
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// If b.m_k > 0, then b.m_num must be odd, and the (b.m_num)^k will also be odd
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a.m_k = b.m_k * k;
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power(a.m_num, b.m_num, k);
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}
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int mpbq::magnitude_lb() const {
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int s = m_num.sgn();
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if (s < 0) {
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return m_num.mlog2() - m_k + 1;
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} else if (s == 0) {
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return 0;
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} else {
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lean_assert(s > 0);
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return m_num.log2() - m_k;
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}
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}
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int mpbq::magnitude_ub() const {
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int s = m_num.sgn();
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if (s < 0) {
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return m_num.mlog2() - m_k;
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} else if (s == 0) {
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return 0;
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} else {
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lean_assert(s > 0);
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return m_num.log2() - m_k + 1;
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}
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}
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void mul2(mpbq & a) {
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if (a.m_k == 0) {
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mul2k(a.m_num, a.m_num, 1);
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} else {
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a.m_k--;
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}
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}
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void mul2k(mpbq & a, unsigned k) {
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if (k == 0)
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return;
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if (a.m_k < k) {
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mul2k(a.m_num, a.m_num, k - a.m_k);
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a.m_k = 0;
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} else {
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lean_assert(a.m_k >= k);
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a.m_k -= k;
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}
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}
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bool root_lower(mpbq & a, mpbq const & b, unsigned n) {
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bool r = root(a.m_num, b.m_num, n);
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if (!r)
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--a.m_num;
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if (b.m_k % n == 0) {
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a.m_k = b.m_k / n;
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a.normalize();
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return r;
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} else if (a.m_num.is_neg()) {
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a.m_k = b.m_k / n;
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a.normalize();
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return false;
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} else {
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a.m_k = b.m_k / n;
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a.m_k++;
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a.normalize();
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return false;
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}
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}
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bool root_upper(mpbq & a, mpbq const & b, unsigned n) {
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bool r = root(a.m_num, b.m_num, n);
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if (b.m_k % n == 0) {
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a.m_k = b.m_k / n;
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a.normalize();
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return r;
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} else if (a.m_num.is_neg()) {
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a.m_k = b.m_k / n;
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a.m_k++;
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a.normalize();
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return false;
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} else {
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a.m_k = b.m_k / n;
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a.normalize();
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return false;
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}
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}
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void refine_upper(mpq const & q, mpbq & l, mpbq & u) {
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lean_assert(l < q && q < u);
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lean_assert(!q.get_denominator().is_power_of_two());
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mpbq mid;
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while (true) {
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mid = l + u;
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div2(mid);
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if (mid > q) {
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swap(u, mid);
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lean_assert(l < q && q < u);
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return;
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}
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swap(l, mid);
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}
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}
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void refine_lower(mpq const & q, mpbq & l, mpbq & u) {
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lean_assert(l < q && q < u);
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lean_assert(!q.get_denominator().is_power_of_two());
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mpbq mid;
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while (true) {
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mid = l + u;
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div2(mid);
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if (mid < q) {
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swap(l, mid);
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lean_assert(l < q && q < u);
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return;
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}
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swap(u, mid);
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}
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}
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bool lt_1div2k(mpbq const & a, unsigned k) {
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if (a.m_num.is_nonpos())
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return true;
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if (a.m_k <= k) {
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// since a.m_num >= 1
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return false;
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} else {
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lean_assert(a.m_k > k);
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static thread_local mpz tmp;
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tmp = 1;
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mul2k(tmp, tmp, a.m_k - k);
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return a.m_num < tmp;
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}
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}
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std::ostream & operator<<(std::ostream & out, mpbq const & v) {
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if (v.m_k == 0) {
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out << v.m_num;
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} else if (v.m_k == 1) {
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out << v.m_num << "/2";
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} else {
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out << v.m_num << "/2^" << v.m_k;
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}
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return out;
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}
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void display_decimal(std::ostream & out, mpbq const & a, unsigned prec) {
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if (a.is_integer()) {
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out << a.m_num;
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return;
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} else {
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mpz two_k;
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mpz n1, v1;
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if (a.is_neg())
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out << "-";
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v1 = abs(a.m_num);
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power(two_k, mpz(2), a.m_k);
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n1 = rem(v1, two_k);
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v1 = v1/two_k;
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lean_assert(!n1.is_zero());
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out << v1;
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out << ".";
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for (unsigned i = 0; i < prec; i++) {
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n1 *= 10;
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v1 = n1/two_k;
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n1 = rem(n1, two_k);
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out << v1;
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if (n1.is_zero())
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return;
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}
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out << "?";
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}
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}
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}
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void print(lean::mpbq const & n) { std::cout << n << std::endl; }
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