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Bassem Girgis
2023-11-24 12:56:13 -06:00
parent cfc99971af
commit 19d727037a
9260 changed files with 849256 additions and 299957 deletions
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276
linx64/include/boost/multiprecision/integer.hpp
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@@ -1,95 +1,95 @@
///////////////////////////////////////////////////////////////
// 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 http://www.boost.org/LICENSE_1_
// 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{
namespace boost {
namespace multiprecision {
template <class Integer, class I2>
typename enable_if_c<is_integral<Integer>::value && is_integral<I2>::value, Integer&>::type
multiply(Integer& result, const I2& a, const I2& b)
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>
typename enable_if_c<is_integral<Integer>::value && is_integral<I2>::value, Integer&>::type
add(Integer& result, const I2& a, const I2& b)
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>
typename enable_if_c<is_integral<Integer>::value && is_integral<I2>::value, Integer&>::type
subtract(Integer& result, const I2& a, const I2& b)
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>
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>
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);
}
namespace detail{
namespace detail {
//
// 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<
2 * sizeof(I) <= sizeof(double_limb_type),
typename mpl::if_c<
is_signed<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;
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 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, (boost::multiprecision::detail::is_signed<I>::value ? signed_magnitude : unsigned_magnitude), unchecked, void> > >::type>::type;
};
}
} // namespace detail
template <class I1, class I2, class I3>
typename enable_if_c<is_integral<I1>::value && is_unsigned<I2>::value && is_integral<I3>::value, I1>::type
powm(const I1& a, I2 b, I3 c)
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;
I1 x(1), y(a);
double_type result(0);
while(b > 0)
while (b > 0)
{
if(b & 1)
if (b & 1)
{
multiply(result, x, y);
x = integer_modulus(result, c);
@@ -102,99 +102,184 @@ typename enable_if_c<is_integral<I1>::value && is_unsigned<I2>::value && is_inte
}
template <class I1, class I2, class I3>
inline typename enable_if_c<is_integral<I1>::value && is_signed<I2>::value && is_integral<I3>::value, I1>::type
powm(const I1& a, I2 b, I3 c)
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)
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>
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)
{
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>
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)
{
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>
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)
if (index >= sizeof(Integer) * CHAR_BIT)
return 0;
if(index)
if (index)
mask <<= index;
return val & mask ? true : false;
}
template <class Integer>
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)
if (index >= sizeof(Integer) * CHAR_BIT)
return val;
if(index)
if (index)
mask <<= index;
val |= mask;
return val;
}
template <class Integer>
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)
if (index >= sizeof(Integer) * CHAR_BIT)
return val;
if(index)
if (index)
mask <<= index;
val &= ~mask;
return val;
}
template <class Integer>
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)
if (index >= sizeof(Integer) * CHAR_BIT)
return val;
if(index)
if (index)
mask <<= index;
val ^= mask;
return val;
}
namespace detail {
template <class Integer>
typename enable_if_c<is_integral<Integer>::value, Integer>::type sqrt(const Integer& x, Integer& r)
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 Integer bitwise_sqrt(const Integer& x, Integer& r)
{
//
// This is slow bit-by-bit integer square root, see for example
@@ -204,18 +289,26 @@ typename enable_if_c<is_integral<Integer>::value, Integer>::type sqrt(const Inte
// at some point.
//
Integer s = 0;
if(x == 0)
switch (x)
{
case 0:
r = 0;
return s;
}
int g = msb(x);
if(g == 0)
{
case 1:
r = 0;
return 1;
case 2:
r = 1;
return s;
return 1;
case 3:
r = 2;
return 1;
default:
break;
// fall through:
}
std::ptrdiff_t g = msb(x);
Integer t = 0;
r = x;
g /= 2;
@@ -228,24 +321,43 @@ typename enable_if_c<is_integral<Integer>::value, Integer>::type sqrt(const Inte
t = s;
t <<= g + 1;
bit_set(t, 2 * g);
if(t <= r)
if (t <= r)
{
bit_set(s, g);
r -= t;
}
--g;
}
while(g >= 0);
} while (g >= 0);
return s;
}
} // namespace detail
template <class Integer>
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)
{
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 std::enable_if<boost::multiprecision::detail::is_integral<Integer>::value, Integer>::type sqrt(const Integer& x)
{
Integer r(0);
return sqrt(x, r);
}
}} // namespaces
}} // namespace boost::multiprecision
#endif