///////////////////////////////////////////////////////////////
-// Copyright 2012 John Maddock. Distributed under the Boost
+// Copyright 2012-21 John Maddock.
+// Copyright 2021 Iskandarov Lev. Distributed under the Boost
// Software License, Version 1.0. (See accompanying file
// LICENSE_1_0.txt or copy at https://www.boost.org/LICENSE_1_0.txt
#ifndef BOOST_MP_INTEGER_HPP
#define BOOST_MP_INTEGER_HPP
+#include <type_traits>
#include <boost/multiprecision/cpp_int.hpp>
#include <boost/multiprecision/detail/bitscan.hpp>
+#include <boost/multiprecision/detail/no_exceptions_support.hpp>
+#include <boost/multiprecision/detail/standalone_config.hpp>
namespace boost {
namespace multiprecision {
template <class Integer, class I2>
-inline BOOST_MP_CXX14_CONSTEXPR typename enable_if_c<is_integral<Integer>::value && is_integral<I2>::value, Integer&>::type
+inline BOOST_MP_CXX14_CONSTEXPR typename std::enable_if<boost::multiprecision::detail::is_integral<Integer>::value && boost::multiprecision::detail::is_integral<I2>::value, Integer&>::type
multiply(Integer& result, const I2& a, const I2& b)
{
return result = static_cast<Integer>(a) * static_cast<Integer>(b);
}
template <class Integer, class I2>
-inline BOOST_MP_CXX14_CONSTEXPR typename enable_if_c<is_integral<Integer>::value && is_integral<I2>::value, Integer&>::type
+inline BOOST_MP_CXX14_CONSTEXPR typename std::enable_if<boost::multiprecision::detail::is_integral<Integer>::value && boost::multiprecision::detail::is_integral<I2>::value, Integer&>::type
add(Integer& result, const I2& a, const I2& b)
{
return result = static_cast<Integer>(a) + static_cast<Integer>(b);
}
template <class Integer, class I2>
-inline BOOST_MP_CXX14_CONSTEXPR typename enable_if_c<is_integral<Integer>::value && is_integral<I2>::value, Integer&>::type
+inline BOOST_MP_CXX14_CONSTEXPR typename std::enable_if<boost::multiprecision::detail::is_integral<Integer>::value && boost::multiprecision::detail::is_integral<I2>::value, Integer&>::type
subtract(Integer& result, const I2& a, const I2& b)
{
return result = static_cast<Integer>(a) - static_cast<Integer>(b);
}
template <class Integer>
-inline BOOST_MP_CXX14_CONSTEXPR typename enable_if_c<is_integral<Integer>::value>::type divide_qr(const Integer& x, const Integer& y, Integer& q, Integer& r)
+inline BOOST_MP_CXX14_CONSTEXPR typename std::enable_if<boost::multiprecision::detail::is_integral<Integer>::value>::type divide_qr(const Integer& x, const Integer& y, Integer& q, Integer& r)
{
q = x / y;
r = x % y;
}
template <class I1, class I2>
-inline BOOST_MP_CXX14_CONSTEXPR typename enable_if_c<is_integral<I1>::value && is_integral<I2>::value, I2>::type integer_modulus(const I1& x, I2 val)
+inline BOOST_MP_CXX14_CONSTEXPR typename std::enable_if<boost::multiprecision::detail::is_integral<I1>::value && boost::multiprecision::detail::is_integral<I2>::value, I2>::type integer_modulus(const I1& x, I2 val)
{
return static_cast<I2>(x % val);
}
//
// Figure out the kind of integer that has twice as many bits as some builtin
// integer type I. Use a native type if we can (including types which may not
-// be recognised by boost::int_t because they're larger than boost::long_long_type),
+// be recognised by boost::int_t because they're larger than long long),
// otherwise synthesize a cpp_int to do the job.
//
template <class I>
struct double_integer
{
- static const unsigned int_t_digits =
- 2 * sizeof(I) <= sizeof(boost::long_long_type) ? std::numeric_limits<I>::digits * 2 : 1;
+ static constexpr const unsigned int_t_digits =
+ 2 * sizeof(I) <= sizeof(long long) ? std::numeric_limits<I>::digits * 2 : 1;
- typedef typename mpl::if_c<
- 2 * sizeof(I) <= sizeof(boost::long_long_type),
- typename mpl::if_c<
- is_signed<I>::value,
- typename boost::int_t<int_t_digits>::least,
- typename boost::uint_t<int_t_digits>::least>::type,
- typename mpl::if_c<
+ using type = typename std::conditional<
+ 2 * sizeof(I) <= sizeof(long long),
+ typename std::conditional<
+ boost::multiprecision::detail::is_signed<I>::value && boost::multiprecision::detail::is_integral<I>::value,
+ typename boost::multiprecision::detail::int_t<int_t_digits>::least,
+ typename boost::multiprecision::detail::uint_t<int_t_digits>::least>::type,
+ typename std::conditional<
2 * sizeof(I) <= sizeof(double_limb_type),
- typename mpl::if_c<
- is_signed<I>::value,
+ typename std::conditional<
+ boost::multiprecision::detail::is_signed<I>::value && boost::multiprecision::detail::is_integral<I>::value,
signed_double_limb_type,
double_limb_type>::type,
- number<cpp_int_backend<sizeof(I) * CHAR_BIT * 2, sizeof(I) * CHAR_BIT * 2, (is_signed<I>::value ? signed_magnitude : unsigned_magnitude), unchecked, void> > >::type>::type type;
+ number<cpp_int_backend<sizeof(I) * CHAR_BIT * 2, sizeof(I) * CHAR_BIT * 2, (boost::multiprecision::detail::is_signed<I>::value ? signed_magnitude : unsigned_magnitude), unchecked, void> > >::type>::type;
};
} // namespace detail
template <class I1, class I2, class I3>
-BOOST_MP_CXX14_CONSTEXPR typename enable_if_c<is_integral<I1>::value && is_unsigned<I2>::value && is_integral<I3>::value, I1>::type
+BOOST_MP_CXX14_CONSTEXPR typename std::enable_if<boost::multiprecision::detail::is_integral<I1>::value && boost::multiprecision::detail::is_unsigned<I2>::value && boost::multiprecision::detail::is_integral<I3>::value, I1>::type
powm(const I1& a, I2 b, I3 c)
{
- typedef typename detail::double_integer<I1>::type double_type;
+ using double_type = typename detail::double_integer<I1>::type;
I1 x(1), y(a);
double_type result(0);
}
template <class I1, class I2, class I3>
-inline BOOST_MP_CXX14_CONSTEXPR typename enable_if_c<is_integral<I1>::value && is_signed<I2>::value && is_integral<I3>::value, I1>::type
+inline BOOST_MP_CXX14_CONSTEXPR typename std::enable_if<boost::multiprecision::detail::is_integral<I1>::value && boost::multiprecision::detail::is_signed<I2>::value && boost::multiprecision::detail::is_integral<I2>::value && boost::multiprecision::detail::is_integral<I3>::value, I1>::type
powm(const I1& a, I2 b, I3 c)
{
if (b < 0)
{
- BOOST_THROW_EXCEPTION(std::runtime_error("powm requires a positive exponent."));
+ BOOST_MP_THROW_EXCEPTION(std::runtime_error("powm requires a positive exponent."));
}
- return powm(a, static_cast<typename make_unsigned<I2>::type>(b), c);
+ return powm(a, static_cast<typename boost::multiprecision::detail::make_unsigned<I2>::type>(b), c);
}
template <class Integer>
-BOOST_MP_CXX14_CONSTEXPR typename enable_if_c<is_integral<Integer>::value, unsigned>::type lsb(const Integer& val)
+BOOST_MP_CXX14_CONSTEXPR typename std::enable_if<boost::multiprecision::detail::is_integral<Integer>::value, std::size_t>::type lsb(const Integer& val)
{
if (val <= 0)
{
if (val == 0)
{
- BOOST_THROW_EXCEPTION(std::range_error("No bits were set in the operand."));
+ BOOST_MP_THROW_EXCEPTION(std::domain_error("No bits were set in the operand."));
}
else
{
- BOOST_THROW_EXCEPTION(std::range_error("Testing individual bits in negative values is not supported - results are undefined."));
+ BOOST_MP_THROW_EXCEPTION(std::domain_error("Testing individual bits in negative values is not supported - results are undefined."));
}
}
return detail::find_lsb(val);
}
template <class Integer>
-BOOST_MP_CXX14_CONSTEXPR typename enable_if_c<is_integral<Integer>::value, unsigned>::type msb(Integer val)
+BOOST_MP_CXX14_CONSTEXPR typename std::enable_if<boost::multiprecision::detail::is_integral<Integer>::value, std::size_t>::type msb(Integer val)
{
if (val <= 0)
{
if (val == 0)
{
- BOOST_THROW_EXCEPTION(std::range_error("No bits were set in the operand."));
+ BOOST_MP_THROW_EXCEPTION(std::domain_error("No bits were set in the operand."));
}
else
{
- BOOST_THROW_EXCEPTION(std::range_error("Testing individual bits in negative values is not supported - results are undefined."));
+ BOOST_MP_THROW_EXCEPTION(std::domain_error("Testing individual bits in negative values is not supported - results are undefined."));
}
}
return detail::find_msb(val);
}
template <class Integer>
-BOOST_MP_CXX14_CONSTEXPR typename enable_if_c<is_integral<Integer>::value, bool>::type bit_test(const Integer& val, unsigned index)
+BOOST_MP_CXX14_CONSTEXPR typename std::enable_if<boost::multiprecision::detail::is_integral<Integer>::value, bool>::type bit_test(const Integer& val, std::size_t index)
{
Integer mask = 1;
if (index >= sizeof(Integer) * CHAR_BIT)
}
template <class Integer>
-BOOST_MP_CXX14_CONSTEXPR typename enable_if_c<is_integral<Integer>::value, Integer&>::type bit_set(Integer& val, unsigned index)
+BOOST_MP_CXX14_CONSTEXPR typename std::enable_if<boost::multiprecision::detail::is_integral<Integer>::value, Integer&>::type bit_set(Integer& val, std::size_t index)
{
Integer mask = 1;
if (index >= sizeof(Integer) * CHAR_BIT)
}
template <class Integer>
-BOOST_MP_CXX14_CONSTEXPR typename enable_if_c<is_integral<Integer>::value, Integer&>::type bit_unset(Integer& val, unsigned index)
+BOOST_MP_CXX14_CONSTEXPR typename std::enable_if<boost::multiprecision::detail::is_integral<Integer>::value, Integer&>::type bit_unset(Integer& val, std::size_t index)
{
Integer mask = 1;
if (index >= sizeof(Integer) * CHAR_BIT)
}
template <class Integer>
-BOOST_MP_CXX14_CONSTEXPR typename enable_if_c<is_integral<Integer>::value, Integer&>::type bit_flip(Integer& val, unsigned index)
+BOOST_MP_CXX14_CONSTEXPR typename std::enable_if<boost::multiprecision::detail::is_integral<Integer>::value, Integer&>::type bit_flip(Integer& val, std::size_t index)
{
Integer mask = 1;
if (index >= sizeof(Integer) * CHAR_BIT)
return val;
}
+namespace detail {
+
+template <class Integer>
+BOOST_MP_CXX14_CONSTEXPR Integer karatsuba_sqrt(const Integer& x, Integer& r, size_t bits)
+{
+ //
+ // Define the floating point type used for std::sqrt, in our tests, sqrt(double) and sqrt(long double) take
+ // about the same amount of time as long as long double is not an emulated 128-bit type (ie the same type
+ // as __float128 from libquadmath). So only use long double if it's an 80-bit type:
+ //
+#ifndef __clang__
+ typedef typename std::conditional<(std::numeric_limits<long double>::digits == 64), long double, double>::type real_cast_type;
+#else
+ // clang has buggy __int128 -> long double conversion:
+ typedef double real_cast_type;
+#endif
+ //
+ // As per the Karatsuba sqrt algorithm, the low order bits/4 bits pay no part in the result, only in the remainder,
+ // so define the number of bits our argument must have before passing to std::sqrt is safe, even if doing so
+ // looses a few bits:
+ //
+ constexpr std::size_t cutoff = (std::numeric_limits<real_cast_type>::digits * 4) / 3;
+ //
+ // Type which can hold at least "cutoff" bits:
+ //
+#ifdef BOOST_HAS_INT128
+ using cutoff_t = typename std::conditional<(cutoff > 64), uint128_type, std::uint64_t>::type;
+#else
+ using cutoff_t = std::uint64_t;
+#endif
+ //
+ // See if we can take the fast path:
+ //
+ if (bits <= cutoff)
+ {
+ constexpr cutoff_t half_bits = (cutoff_t(1u) << ((sizeof(cutoff_t) * CHAR_BIT) / 2)) - 1;
+ cutoff_t val = static_cast<cutoff_t>(x);
+ real_cast_type real_val = static_cast<real_cast_type>(val);
+ cutoff_t s64 = static_cast<cutoff_t>(std::sqrt(real_val));
+ // converting to long double can loose some precision, and `sqrt` can give eps error, so we'll fix this
+ // this is needed
+ while ((s64 > half_bits) || (s64 * s64 > val))
+ s64--;
+ // in my tests this never fired, but theoretically this might be needed
+ while ((s64 < half_bits) && ((s64 + 1) * (s64 + 1) <= val))
+ s64++;
+ r = static_cast<Integer>(val - s64 * s64);
+ return static_cast<Integer>(s64);
+ }
+ // https://hal.inria.fr/file/index/docid/72854/filename/RR-3805.pdf
+ std::size_t b = bits / 4;
+ Integer q = x;
+ q >>= b * 2;
+ Integer s = karatsuba_sqrt(q, r, bits - b * 2);
+ Integer t = 0u;
+ bit_set(t, static_cast<unsigned>(b * 2));
+ r <<= b;
+ t--;
+ t &= x;
+ t >>= b;
+ t += r;
+ s <<= 1;
+ divide_qr(t, s, q, r);
+ r <<= b;
+ t = 0u;
+ bit_set(t, static_cast<unsigned>(b));
+ t--;
+ t &= x;
+ r += t;
+ s <<= (b - 1); // we already <<1 it before
+ s += q;
+ q *= q;
+ // we substract after, so it works for unsigned integers too
+ if (r < q)
+ {
+ t = s;
+ t <<= 1;
+ t--;
+ r += t;
+ s--;
+ }
+ r -= q;
+ return s;
+}
+
template <class Integer>
-BOOST_MP_CXX14_CONSTEXPR typename enable_if_c<is_integral<Integer>::value, Integer>::type sqrt(const Integer& x, Integer& r)
+BOOST_MP_CXX14_CONSTEXPR Integer bitwise_sqrt(const Integer& x, Integer& r)
{
//
// This is slow bit-by-bit integer square root, see for example
r = 0;
return s;
}
- int g = msb(x);
+ std::ptrdiff_t g = msb(x);
if (g == 0)
{
r = 1;
}
Integer t = 0;
- r = x;
+ r = x;
g /= 2;
bit_set(s, g);
bit_set(t, 2 * g);
return s;
}
+} // namespace detail
+
+template <class Integer>
+BOOST_MP_CXX14_CONSTEXPR typename std::enable_if<boost::multiprecision::detail::is_integral<Integer>::value, Integer>::type sqrt(const Integer& x, Integer& r)
+{
+#ifndef BOOST_MP_NO_CONSTEXPR_DETECTION
+ // recursive Karatsuba sqrt can cause issues in constexpr context:
+ if (BOOST_MP_IS_CONST_EVALUATED(x))
+ return detail::bitwise_sqrt(x, r);
+#endif
+ if (x == 0u) {
+ r = 0u;
+ return 0u;
+ }
+
+ return detail::karatsuba_sqrt(x, r, msb(x) + 1);
+}
+
template <class Integer>
-BOOST_MP_CXX14_CONSTEXPR typename enable_if_c<is_integral<Integer>::value, Integer>::type sqrt(const Integer& x)
+BOOST_MP_CXX14_CONSTEXPR typename std::enable_if<boost::multiprecision::detail::is_integral<Integer>::value, Integer>::type sqrt(const Integer& x)
{
Integer r(0);
return sqrt(x, r);
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