123 lines
3.7 KiB
C++
123 lines
3.7 KiB
C++
/* boost random/detail/large_arithmetic.hpp header file
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*
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* Copyright Steven Watanabe 2011
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* Distributed under the Boost Software License, Version 1.0. (See
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* accompanying file LICENSE_1_0.txt or copy at
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* http://www.boost.org/LICENSE_1_0.txt)
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*
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* See http://www.boost.org for most recent version including documentation.
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*
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* $Id: large_arithmetic.hpp 71018 2011-04-05 21:27:52Z steven_watanabe $
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*/
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#ifndef BOOST_RANDOM_DETAIL_LARGE_ARITHMETIC_HPP
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#define BOOST_RANDOM_DETAIL_LARGE_ARITHMETIC_HPP
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#include <boost/cstdint.hpp>
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#include <boost/integer.hpp>
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#include <boost/limits.hpp>
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#include <boost/random/detail/integer_log2.hpp>
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#include <boost/random/detail/disable_warnings.hpp>
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namespace boost {
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namespace random {
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namespace detail {
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struct div_t {
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boost::uintmax_t quotient;
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boost::uintmax_t remainder;
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};
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inline div_t muldivmod(boost::uintmax_t a, boost::uintmax_t b, boost::uintmax_t m)
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{
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static const int bits =
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::std::numeric_limits< ::boost::uintmax_t>::digits / 2;
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static const ::boost::uintmax_t mask = (::boost::uintmax_t(1) << bits) - 1;
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typedef ::boost::uint_t<bits>::fast digit_t;
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int shift = std::numeric_limits< ::boost::uintmax_t>::digits - 1
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- detail::integer_log2(m);
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a <<= shift;
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m <<= shift;
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digit_t product[4] = { 0, 0, 0, 0 };
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digit_t a_[2] = { digit_t(a & mask), digit_t((a >> bits) & mask) };
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digit_t b_[2] = { digit_t(b & mask), digit_t((b >> bits) & mask) };
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digit_t m_[2] = { digit_t(m & mask), digit_t((m >> bits) & mask) };
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// multiply a * b
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for(int i = 0; i < 2; ++i) {
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digit_t carry = 0;
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for(int j = 0; j < 2; ++j) {
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::boost::uint64_t temp = ::boost::uintmax_t(a_[i]) * b_[j] +
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carry + product[i + j];
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product[i + j] = digit_t(temp & mask);
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carry = digit_t(temp >> bits);
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}
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if(carry != 0) {
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product[i + 2] += carry;
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}
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}
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digit_t quotient[2];
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if(m == 0) {
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div_t result = {
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((::boost::uintmax_t(product[3]) << bits) | product[2]),
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((::boost::uintmax_t(product[1]) << bits) | product[0]) >> shift,
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};
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return result;
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}
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// divide product / m
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for(int i = 3; i >= 2; --i) {
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::boost::uintmax_t temp =
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::boost::uintmax_t(product[i]) << bits | product[i - 1];
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digit_t q = digit_t((product[i] == m_[1]) ? mask : temp / m_[1]);
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::boost::uintmax_t rem =
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((temp - ::boost::uintmax_t(q) * m_[1]) << bits) + product[i - 2];
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::boost::uintmax_t diff = m_[0] * ::boost::uintmax_t(q);
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int error = 0;
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if(diff > rem) {
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if(diff - rem > m) {
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error = 2;
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} else {
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error = 1;
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}
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}
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q -= error;
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rem = rem + error * m - diff;
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quotient[i - 2] = q;
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product[i] = 0;
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product[i-1] = (rem >> bits) & mask;
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product[i-2] = rem & mask;
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}
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div_t result = {
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((::boost::uintmax_t(quotient[1]) << bits) | quotient[0]),
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((::boost::uintmax_t(product[1]) << bits) | product[0]) >> shift,
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};
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return result;
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}
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inline boost::uintmax_t muldiv(boost::uintmax_t a, boost::uintmax_t b, boost::uintmax_t m)
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{ return detail::muldivmod(a, b, m).quotient; }
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inline boost::uintmax_t mulmod(boost::uintmax_t a, boost::uintmax_t b, boost::uintmax_t m)
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{ return detail::muldivmod(a, b, m).remainder; }
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} // namespace detail
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} // namespace random
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} // namespace boost
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#include <boost/random/detail/enable_warnings.hpp>
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#endif // BOOST_RANDOM_DETAIL_LARGE_ARITHMETIC_HPP
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