252 lines
6.9 KiB
Plaintext
252 lines
6.9 KiB
Plaintext
///////////////////////////////////////////////////////////////
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// Copyright 2012 John Maddock. Distributed under the Boost
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// Software License, Version 1.0. (See accompanying file
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// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_
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#ifndef BOOST_MP_INTEGER_HPP
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#define BOOST_MP_INTEGER_HPP
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#include <boost/multiprecision/cpp_int.hpp>
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#include <boost/multiprecision/detail/bitscan.hpp>
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namespace boost{
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namespace multiprecision{
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template <class Integer, class I2>
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typename enable_if_c<is_integral<Integer>::value && is_integral<I2>::value, Integer&>::type
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multiply(Integer& result, const I2& a, const I2& b)
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{
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return result = static_cast<Integer>(a) * static_cast<Integer>(b);
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}
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template <class Integer, class I2>
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typename enable_if_c<is_integral<Integer>::value && is_integral<I2>::value, Integer&>::type
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add(Integer& result, const I2& a, const I2& b)
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{
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return result = static_cast<Integer>(a) + static_cast<Integer>(b);
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}
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template <class Integer, class I2>
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typename enable_if_c<is_integral<Integer>::value && is_integral<I2>::value, Integer&>::type
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subtract(Integer& result, const I2& a, const I2& b)
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{
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return result = static_cast<Integer>(a) - static_cast<Integer>(b);
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}
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template <class Integer>
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typename enable_if_c<is_integral<Integer>::value>::type divide_qr(const Integer& x, const Integer& y, Integer& q, Integer& r)
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{
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q = x / y;
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r = x % y;
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}
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template <class I1, class I2>
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typename enable_if_c<is_integral<I1>::value && is_integral<I2>::value, I2>::type integer_modulus(const I1& x, I2 val)
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{
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return static_cast<I2>(x % val);
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}
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namespace detail{
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//
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// Figure out the kind of integer that has twice as many bits as some builtin
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// integer type I. Use a native type if we can (including types which may not
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// be recognised by boost::int_t because they're larger than boost::long_long_type),
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// otherwise synthesize a cpp_int to do the job.
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//
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template <class I>
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struct double_integer
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{
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static const unsigned int_t_digits =
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2 * sizeof(I) <= sizeof(boost::long_long_type) ? std::numeric_limits<I>::digits * 2 : 1;
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typedef typename mpl::if_c<
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2 * sizeof(I) <= sizeof(boost::long_long_type),
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typename mpl::if_c<
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is_signed<I>::value,
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typename boost::int_t<int_t_digits>::least,
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typename boost::uint_t<int_t_digits>::least
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>::type,
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typename mpl::if_c<
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2 * sizeof(I) <= sizeof(double_limb_type),
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typename mpl::if_c<
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is_signed<I>::value,
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signed_double_limb_type,
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double_limb_type
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>::type,
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number<cpp_int_backend<sizeof(I)*CHAR_BIT*2, sizeof(I)*CHAR_BIT*2, (is_signed<I>::value ? signed_magnitude : unsigned_magnitude), unchecked, void> >
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>::type
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>::type type;
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};
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}
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template <class I1, class I2, class I3>
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typename enable_if_c<is_integral<I1>::value && is_unsigned<I2>::value && is_integral<I3>::value, I1>::type
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powm(const I1& a, I2 b, I3 c)
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{
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typedef typename detail::double_integer<I1>::type double_type;
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I1 x(1), y(a);
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double_type result;
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while(b > 0)
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{
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if(b & 1)
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{
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multiply(result, x, y);
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x = integer_modulus(result, c);
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}
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multiply(result, y, y);
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y = integer_modulus(result, c);
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b >>= 1;
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}
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return x % c;
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}
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template <class I1, class I2, class I3>
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inline typename enable_if_c<is_integral<I1>::value && is_signed<I2>::value && is_integral<I3>::value, I1>::type
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powm(const I1& a, I2 b, I3 c)
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{
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if(b < 0)
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{
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BOOST_THROW_EXCEPTION(std::runtime_error("powm requires a positive exponent."));
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}
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return powm(a, static_cast<typename make_unsigned<I2>::type>(b), c);
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}
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template <class Integer>
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typename enable_if_c<is_integral<Integer>::value, unsigned>::type lsb(const Integer& val)
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{
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if(val <= 0)
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{
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if(val == 0)
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{
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BOOST_THROW_EXCEPTION(std::range_error("No bits were set in the operand."));
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}
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else
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{
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BOOST_THROW_EXCEPTION(std::range_error("Testing individual bits in negative values is not supported - results are undefined."));
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}
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}
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return detail::find_lsb(val);
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}
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template <class Integer>
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typename enable_if_c<is_integral<Integer>::value, unsigned>::type msb(Integer val)
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{
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if(val <= 0)
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{
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if(val == 0)
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{
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BOOST_THROW_EXCEPTION(std::range_error("No bits were set in the operand."));
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}
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else
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{
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BOOST_THROW_EXCEPTION(std::range_error("Testing individual bits in negative values is not supported - results are undefined."));
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}
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}
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return detail::find_msb(val);
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}
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template <class Integer>
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typename enable_if_c<is_integral<Integer>::value, bool>::type bit_test(const Integer& val, unsigned index)
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{
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Integer mask = 1;
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if(index >= sizeof(Integer) * CHAR_BIT)
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return 0;
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if(index)
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mask <<= index;
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return val & mask ? true : false;
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}
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template <class Integer>
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typename enable_if_c<is_integral<Integer>::value, Integer&>::type bit_set(Integer& val, unsigned index)
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{
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Integer mask = 1;
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if(index >= sizeof(Integer) * CHAR_BIT)
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return val;
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if(index)
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mask <<= index;
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val |= mask;
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return val;
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}
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template <class Integer>
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typename enable_if_c<is_integral<Integer>::value, Integer&>::type bit_unset(Integer& val, unsigned index)
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{
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Integer mask = 1;
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if(index >= sizeof(Integer) * CHAR_BIT)
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return val;
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if(index)
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mask <<= index;
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val &= ~mask;
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return val;
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}
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template <class Integer>
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typename enable_if_c<is_integral<Integer>::value, Integer&>::type bit_flip(Integer& val, unsigned index)
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{
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Integer mask = 1;
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if(index >= sizeof(Integer) * CHAR_BIT)
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return val;
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if(index)
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mask <<= index;
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val ^= mask;
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return val;
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}
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template <class Integer>
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typename enable_if_c<is_integral<Integer>::value, Integer>::type sqrt(const Integer& x, Integer& r)
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{
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//
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// This is slow bit-by-bit integer square root, see for example
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// http://en.wikipedia.org/wiki/Methods_of_computing_square_roots#Binary_numeral_system_.28base_2.29
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// There are better methods such as http://hal.inria.fr/docs/00/07/28/54/PDF/RR-3805.pdf
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// and http://hal.inria.fr/docs/00/07/21/13/PDF/RR-4475.pdf which should be implemented
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// at some point.
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//
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Integer s = 0;
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if(x == 0)
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{
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r = 0;
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return s;
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}
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int g = msb(x);
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if(g == 0)
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{
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r = 1;
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return s;
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}
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Integer t = 0;
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r = x;
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g /= 2;
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bit_set(s, g);
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bit_set(t, 2 * g);
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r = x - t;
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--g;
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do
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{
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t = s;
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t <<= g + 1;
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bit_set(t, 2 * g);
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if(t <= r)
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{
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bit_set(s, g);
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r -= t;
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}
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--g;
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}
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while(g >= 0);
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return s;
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}
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template <class Integer>
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typename enable_if_c<is_integral<Integer>::value, Integer>::type sqrt(const Integer& x)
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{
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Integer r;
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return sqrt(x, r);
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}
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}} // namespaces
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#endif
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