mirror of
https://github.com/ecency/ecency-mobile.git
synced 2024-12-21 04:11:50 +03:00
496 lines
16 KiB
C++
496 lines
16 KiB
C++
///////////////////////////////////////////////////////////////
|
|
// Copyright 2012 John Maddock. 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_
|
|
|
|
#ifndef BOOST_MP_INT_FUNC_HPP
|
|
#define BOOST_MP_INT_FUNC_HPP
|
|
|
|
#include <boost/multiprecision/number.hpp>
|
|
|
|
namespace boost{ namespace multiprecision{
|
|
|
|
namespace default_ops
|
|
{
|
|
|
|
template <class Backend>
|
|
inline void eval_qr(const Backend& x, const Backend& y, Backend& q, Backend& r)
|
|
{
|
|
eval_divide(q, x, y);
|
|
eval_modulus(r, x, y);
|
|
}
|
|
|
|
template <class Backend, class Integer>
|
|
inline Integer eval_integer_modulus(const Backend& x, Integer val)
|
|
{
|
|
BOOST_MP_USING_ABS
|
|
using default_ops::eval_modulus;
|
|
using default_ops::eval_convert_to;
|
|
typedef typename boost::multiprecision::detail::canonical<Integer, Backend>::type int_type;
|
|
Backend t;
|
|
eval_modulus(t, x, static_cast<int_type>(val));
|
|
Integer result;
|
|
eval_convert_to(&result, t);
|
|
return abs(result);
|
|
}
|
|
|
|
#ifdef BOOST_MSVC
|
|
#pragma warning(push)
|
|
#pragma warning(disable:4127)
|
|
#endif
|
|
|
|
template <class B>
|
|
inline void eval_gcd(B& result, const B& a, const B& b)
|
|
{
|
|
using default_ops::eval_lsb;
|
|
using default_ops::eval_is_zero;
|
|
using default_ops::eval_get_sign;
|
|
|
|
int shift;
|
|
|
|
B u(a), v(b);
|
|
|
|
int s = eval_get_sign(u);
|
|
|
|
/* GCD(0,x) := x */
|
|
if(s < 0)
|
|
{
|
|
u.negate();
|
|
}
|
|
else if(s == 0)
|
|
{
|
|
result = v;
|
|
return;
|
|
}
|
|
s = eval_get_sign(v);
|
|
if(s < 0)
|
|
{
|
|
v.negate();
|
|
}
|
|
else if(s == 0)
|
|
{
|
|
result = u;
|
|
return;
|
|
}
|
|
|
|
/* Let shift := lg K, where K is the greatest power of 2
|
|
dividing both u and v. */
|
|
|
|
unsigned us = eval_lsb(u);
|
|
unsigned vs = eval_lsb(v);
|
|
shift = (std::min)(us, vs);
|
|
eval_right_shift(u, us);
|
|
eval_right_shift(v, vs);
|
|
|
|
do
|
|
{
|
|
/* Now u and v are both odd, so diff(u, v) is even.
|
|
Let u = min(u, v), v = diff(u, v)/2. */
|
|
s = u.compare(v);
|
|
if(s > 0)
|
|
u.swap(v);
|
|
if(s == 0)
|
|
break;
|
|
eval_subtract(v, u);
|
|
vs = eval_lsb(v);
|
|
eval_right_shift(v, vs);
|
|
}
|
|
while(true);
|
|
|
|
result = u;
|
|
eval_left_shift(result, shift);
|
|
}
|
|
|
|
#ifdef BOOST_MSVC
|
|
#pragma warning(pop)
|
|
#endif
|
|
|
|
template <class B>
|
|
inline void eval_lcm(B& result, const B& a, const B& b)
|
|
{
|
|
typedef typename mpl::front<typename B::unsigned_types>::type ui_type;
|
|
B t;
|
|
eval_gcd(t, a, b);
|
|
|
|
if(eval_is_zero(t))
|
|
{
|
|
result = static_cast<ui_type>(0);
|
|
}
|
|
else
|
|
{
|
|
eval_divide(result, a, t);
|
|
eval_multiply(result, b);
|
|
}
|
|
if(eval_get_sign(result) < 0)
|
|
result.negate();
|
|
}
|
|
|
|
}
|
|
|
|
template <class Backend, expression_template_option ExpressionTemplates>
|
|
inline typename enable_if_c<number_category<Backend>::value == number_kind_integer>::type
|
|
divide_qr(const number<Backend, ExpressionTemplates>& x, const number<Backend, ExpressionTemplates>& y,
|
|
number<Backend, ExpressionTemplates>& q, number<Backend, ExpressionTemplates>& r)
|
|
{
|
|
using default_ops::eval_qr;
|
|
eval_qr(x.backend(), y.backend(), q.backend(), r.backend());
|
|
}
|
|
|
|
template <class Backend, expression_template_option ExpressionTemplates, class tag, class A1, class A2, class A3, class A4>
|
|
inline typename enable_if_c<number_category<Backend>::value == number_kind_integer>::type
|
|
divide_qr(const number<Backend, ExpressionTemplates>& x, const multiprecision::detail::expression<tag, A1, A2, A3, A4>& y,
|
|
number<Backend, ExpressionTemplates>& q, number<Backend, ExpressionTemplates>& r)
|
|
{
|
|
divide_qr(x, number<Backend, ExpressionTemplates>(y), q, r);
|
|
}
|
|
|
|
template <class tag, class A1, class A2, class A3, class A4, class Backend, expression_template_option ExpressionTemplates>
|
|
inline typename enable_if_c<number_category<Backend>::value == number_kind_integer>::type
|
|
divide_qr(const multiprecision::detail::expression<tag, A1, A2, A3, A4>& x, const number<Backend, ExpressionTemplates>& y,
|
|
number<Backend, ExpressionTemplates>& q, number<Backend, ExpressionTemplates>& r)
|
|
{
|
|
divide_qr(number<Backend, ExpressionTemplates>(x), y, q, r);
|
|
}
|
|
|
|
template <class tag, class A1, class A2, class A3, class A4, class tagb, class A1b, class A2b, class A3b, class A4b, class Backend, expression_template_option ExpressionTemplates>
|
|
inline typename enable_if_c<number_category<Backend>::value == number_kind_integer>::type
|
|
divide_qr(const multiprecision::detail::expression<tag, A1, A2, A3, A4>& x, const multiprecision::detail::expression<tagb, A1b, A2b, A3b, A4b>& y,
|
|
number<Backend, ExpressionTemplates>& q, number<Backend, ExpressionTemplates>& r)
|
|
{
|
|
divide_qr(number<Backend, ExpressionTemplates>(x), number<Backend, ExpressionTemplates>(y), q, r);
|
|
}
|
|
|
|
template <class Backend, expression_template_option ExpressionTemplates, class Integer>
|
|
inline typename enable_if<mpl::and_<is_integral<Integer>, mpl::bool_<number_category<Backend>::value == number_kind_integer> >, Integer>::type
|
|
integer_modulus(const number<Backend, ExpressionTemplates>& x, Integer val)
|
|
{
|
|
using default_ops::eval_integer_modulus;
|
|
return eval_integer_modulus(x.backend(), val);
|
|
}
|
|
|
|
template <class tag, class A1, class A2, class A3, class A4, class Integer>
|
|
inline typename enable_if<mpl::and_<is_integral<Integer>, mpl::bool_<number_category<typename multiprecision::detail::expression<tag, A1, A2, A3, A4>::result_type>::value == number_kind_integer> >, Integer>::type
|
|
integer_modulus(const multiprecision::detail::expression<tag, A1, A2, A3, A4>& x, Integer val)
|
|
{
|
|
typedef typename multiprecision::detail::expression<tag, A1, A2, A3, A4>::result_type result_type;
|
|
return integer_modulus(result_type(x), val);
|
|
}
|
|
|
|
template <class Backend, expression_template_option ExpressionTemplates>
|
|
inline typename enable_if_c<number_category<Backend>::value == number_kind_integer, unsigned>::type
|
|
lsb(const number<Backend, ExpressionTemplates>& x)
|
|
{
|
|
using default_ops::eval_lsb;
|
|
return eval_lsb(x.backend());
|
|
}
|
|
|
|
template <class tag, class A1, class A2, class A3, class A4>
|
|
inline typename enable_if_c<number_category<typename multiprecision::detail::expression<tag, A1, A2, A3, A4>::result_type>::value == number_kind_integer, unsigned>::type
|
|
lsb(const multiprecision::detail::expression<tag, A1, A2, A3, A4>& x)
|
|
{
|
|
typedef typename multiprecision::detail::expression<tag, A1, A2, A3, A4>::result_type number_type;
|
|
number_type n(x);
|
|
using default_ops::eval_lsb;
|
|
return eval_lsb(n.backend());
|
|
}
|
|
|
|
template <class Backend, expression_template_option ExpressionTemplates>
|
|
inline typename enable_if_c<number_category<Backend>::value == number_kind_integer, unsigned>::type
|
|
msb(const number<Backend, ExpressionTemplates>& x)
|
|
{
|
|
using default_ops::eval_msb;
|
|
return eval_msb(x.backend());
|
|
}
|
|
|
|
template <class tag, class A1, class A2, class A3, class A4>
|
|
inline typename enable_if_c<number_category<typename multiprecision::detail::expression<tag, A1, A2, A3, A4>::result_type>::value == number_kind_integer, unsigned>::type
|
|
msb(const multiprecision::detail::expression<tag, A1, A2, A3, A4>& x)
|
|
{
|
|
typedef typename multiprecision::detail::expression<tag, A1, A2, A3, A4>::result_type number_type;
|
|
number_type n(x);
|
|
using default_ops::eval_msb;
|
|
return eval_msb(n.backend());
|
|
}
|
|
|
|
template <class Backend, expression_template_option ExpressionTemplates>
|
|
inline typename enable_if_c<number_category<Backend>::value == number_kind_integer, bool>::type
|
|
bit_test(const number<Backend, ExpressionTemplates>& x, unsigned index)
|
|
{
|
|
using default_ops::eval_bit_test;
|
|
return eval_bit_test(x.backend(), index);
|
|
}
|
|
|
|
template <class tag, class A1, class A2, class A3, class A4>
|
|
inline typename enable_if_c<number_category<typename multiprecision::detail::expression<tag, A1, A2, A3, A4>::result_type>::value == number_kind_integer, bool>::type
|
|
bit_test(const multiprecision::detail::expression<tag, A1, A2, A3, A4>& x, unsigned index)
|
|
{
|
|
typedef typename multiprecision::detail::expression<tag, A1, A2, A3, A4>::result_type number_type;
|
|
number_type n(x);
|
|
using default_ops::eval_bit_test;
|
|
return eval_bit_test(n.backend(), index);
|
|
}
|
|
|
|
template <class Backend, expression_template_option ExpressionTemplates>
|
|
inline typename enable_if_c<number_category<Backend>::value == number_kind_integer, number<Backend, ExpressionTemplates>&>::type
|
|
bit_set(number<Backend, ExpressionTemplates>& x, unsigned index)
|
|
{
|
|
using default_ops::eval_bit_set;
|
|
eval_bit_set(x.backend(), index);
|
|
return x;
|
|
}
|
|
|
|
template <class Backend, expression_template_option ExpressionTemplates>
|
|
inline typename enable_if_c<number_category<Backend>::value == number_kind_integer, number<Backend, ExpressionTemplates>&>::type
|
|
bit_unset(number<Backend, ExpressionTemplates>& x, unsigned index)
|
|
{
|
|
using default_ops::eval_bit_unset;
|
|
eval_bit_unset(x.backend(), index);
|
|
return x;
|
|
}
|
|
|
|
template <class Backend, expression_template_option ExpressionTemplates>
|
|
inline typename enable_if_c<number_category<Backend>::value == number_kind_integer, number<Backend, ExpressionTemplates>&>::type
|
|
bit_flip(number<Backend, ExpressionTemplates>& x, unsigned index)
|
|
{
|
|
using default_ops::eval_bit_flip;
|
|
eval_bit_flip(x.backend(), index);
|
|
return x;
|
|
}
|
|
|
|
namespace default_ops{
|
|
|
|
//
|
|
// Within powm, we need a type with twice as many digits as the argument type, define
|
|
// a traits class to obtain that type:
|
|
//
|
|
template <class Backend>
|
|
struct double_precision_type
|
|
{
|
|
typedef Backend type;
|
|
};
|
|
|
|
//
|
|
// If the exponent is a signed integer type, then we need to
|
|
// check the value is positive:
|
|
//
|
|
template <class Backend>
|
|
inline void check_sign_of_backend(const Backend& v, const mpl::true_)
|
|
{
|
|
if(eval_get_sign(v) < 0)
|
|
{
|
|
BOOST_THROW_EXCEPTION(std::runtime_error("powm requires a positive exponent."));
|
|
}
|
|
}
|
|
template <class Backend>
|
|
inline void check_sign_of_backend(const Backend&, const mpl::false_){}
|
|
//
|
|
// Calculate (a^p)%c:
|
|
//
|
|
template <class Backend>
|
|
void eval_powm(Backend& result, const Backend& a, const Backend& p, const Backend& c)
|
|
{
|
|
using default_ops::eval_bit_test;
|
|
using default_ops::eval_get_sign;
|
|
using default_ops::eval_multiply;
|
|
using default_ops::eval_modulus;
|
|
using default_ops::eval_right_shift;
|
|
|
|
typedef typename double_precision_type<Backend>::type double_type;
|
|
typedef typename boost::multiprecision::detail::canonical<unsigned char, double_type>::type ui_type;
|
|
|
|
check_sign_of_backend(p, mpl::bool_<std::numeric_limits<number<Backend> >::is_signed>());
|
|
|
|
double_type x, y(a), b(p), t;
|
|
x = ui_type(1u);
|
|
|
|
while(eval_get_sign(b) > 0)
|
|
{
|
|
if(eval_bit_test(b, 0))
|
|
{
|
|
eval_multiply(t, x, y);
|
|
eval_modulus(x, t, c);
|
|
}
|
|
eval_multiply(t, y, y);
|
|
eval_modulus(y, t, c);
|
|
eval_right_shift(b, ui_type(1));
|
|
}
|
|
Backend x2(x);
|
|
eval_modulus(result, x2, c);
|
|
}
|
|
|
|
template <class Backend, class Integer>
|
|
void eval_powm(Backend& result, const Backend& a, const Backend& p, Integer c)
|
|
{
|
|
typedef typename double_precision_type<Backend>::type double_type;
|
|
typedef typename boost::multiprecision::detail::canonical<unsigned char, double_type>::type ui_type;
|
|
typedef typename boost::multiprecision::detail::canonical<Integer, double_type>::type i1_type;
|
|
typedef typename boost::multiprecision::detail::canonical<Integer, Backend>::type i2_type;
|
|
|
|
using default_ops::eval_bit_test;
|
|
using default_ops::eval_get_sign;
|
|
using default_ops::eval_multiply;
|
|
using default_ops::eval_modulus;
|
|
using default_ops::eval_right_shift;
|
|
|
|
check_sign_of_backend(p, mpl::bool_<std::numeric_limits<number<Backend> >::is_signed>());
|
|
|
|
if(eval_get_sign(p) < 0)
|
|
{
|
|
BOOST_THROW_EXCEPTION(std::runtime_error("powm requires a positive exponent."));
|
|
}
|
|
|
|
double_type x, y(a), b(p), t;
|
|
x = ui_type(1u);
|
|
|
|
while(eval_get_sign(b) > 0)
|
|
{
|
|
if(eval_bit_test(b, 0))
|
|
{
|
|
eval_multiply(t, x, y);
|
|
eval_modulus(x, t, static_cast<i1_type>(c));
|
|
}
|
|
eval_multiply(t, y, y);
|
|
eval_modulus(y, t, static_cast<i1_type>(c));
|
|
eval_right_shift(b, ui_type(1));
|
|
}
|
|
Backend x2(x);
|
|
eval_modulus(result, x2, static_cast<i2_type>(c));
|
|
}
|
|
|
|
template <class Backend, class Integer>
|
|
typename enable_if<is_unsigned<Integer> >::type eval_powm(Backend& result, const Backend& a, Integer b, const Backend& c)
|
|
{
|
|
typedef typename double_precision_type<Backend>::type double_type;
|
|
typedef typename boost::multiprecision::detail::canonical<unsigned char, double_type>::type ui_type;
|
|
|
|
using default_ops::eval_bit_test;
|
|
using default_ops::eval_get_sign;
|
|
using default_ops::eval_multiply;
|
|
using default_ops::eval_modulus;
|
|
using default_ops::eval_right_shift;
|
|
|
|
double_type x, y(a), t;
|
|
x = ui_type(1u);
|
|
|
|
while(b > 0)
|
|
{
|
|
if(b & 1)
|
|
{
|
|
eval_multiply(t, x, y);
|
|
eval_modulus(x, t, c);
|
|
}
|
|
eval_multiply(t, y, y);
|
|
eval_modulus(y, t, c);
|
|
b >>= 1;
|
|
}
|
|
Backend x2(x);
|
|
eval_modulus(result, x2, c);
|
|
}
|
|
|
|
template <class Backend, class Integer>
|
|
typename enable_if<is_signed<Integer> >::type eval_powm(Backend& result, const Backend& a, Integer b, const Backend& c)
|
|
{
|
|
if(b < 0)
|
|
{
|
|
BOOST_THROW_EXCEPTION(std::runtime_error("powm requires a positive exponent."));
|
|
}
|
|
eval_powm(result, a, static_cast<typename make_unsigned<Integer>::type>(b), c);
|
|
}
|
|
|
|
template <class Backend, class Integer1, class Integer2>
|
|
typename enable_if<is_unsigned<Integer1> >::type eval_powm(Backend& result, const Backend& a, Integer1 b, Integer2 c)
|
|
{
|
|
typedef typename double_precision_type<Backend>::type double_type;
|
|
typedef typename boost::multiprecision::detail::canonical<unsigned char, double_type>::type ui_type;
|
|
typedef typename boost::multiprecision::detail::canonical<Integer1, double_type>::type i1_type;
|
|
typedef typename boost::multiprecision::detail::canonical<Integer2, Backend>::type i2_type;
|
|
|
|
using default_ops::eval_bit_test;
|
|
using default_ops::eval_get_sign;
|
|
using default_ops::eval_multiply;
|
|
using default_ops::eval_modulus;
|
|
using default_ops::eval_right_shift;
|
|
|
|
double_type x, y(a), t;
|
|
x = ui_type(1u);
|
|
|
|
while(b > 0)
|
|
{
|
|
if(b & 1)
|
|
{
|
|
eval_multiply(t, x, y);
|
|
eval_modulus(x, t, static_cast<i1_type>(c));
|
|
}
|
|
eval_multiply(t, y, y);
|
|
eval_modulus(y, t, static_cast<i1_type>(c));
|
|
b >>= 1;
|
|
}
|
|
Backend x2(x);
|
|
eval_modulus(result, x2, static_cast<i2_type>(c));
|
|
}
|
|
|
|
template <class Backend, class Integer1, class Integer2>
|
|
typename enable_if<is_signed<Integer1> >::type eval_powm(Backend& result, const Backend& a, Integer1 b, Integer2 c)
|
|
{
|
|
if(b < 0)
|
|
{
|
|
BOOST_THROW_EXCEPTION(std::runtime_error("powm requires a positive exponent."));
|
|
}
|
|
eval_powm(result, a, static_cast<typename make_unsigned<Integer1>::type>(b), c);
|
|
}
|
|
|
|
struct powm_func
|
|
{
|
|
template <class T, class U, class V>
|
|
void operator()(T& result, const T& b, const U& p, const V& m)const
|
|
{
|
|
eval_powm(result, b, p, m);
|
|
}
|
|
};
|
|
|
|
}
|
|
|
|
template <class T, class U, class V>
|
|
inline typename enable_if<
|
|
mpl::and_<
|
|
mpl::bool_<number_category<T>::value == number_kind_integer>,
|
|
mpl::or_<
|
|
is_number<T>,
|
|
is_number_expression<T>
|
|
>,
|
|
mpl::or_<
|
|
is_number<U>,
|
|
is_number_expression<U>,
|
|
is_integral<U>
|
|
>,
|
|
mpl::or_<
|
|
is_number<V>,
|
|
is_number_expression<V>,
|
|
is_integral<V>
|
|
>
|
|
>,
|
|
typename mpl::if_<
|
|
is_no_et_number<T>,
|
|
T,
|
|
typename mpl::if_<
|
|
is_no_et_number<U>,
|
|
U,
|
|
typename mpl::if_<
|
|
is_no_et_number<V>,
|
|
V,
|
|
detail::expression<detail::function, default_ops::powm_func, T, U, V> >::type
|
|
>::type
|
|
>::type
|
|
>::type
|
|
powm(const T& b, const U& p, const V& mod)
|
|
{
|
|
return detail::expression<detail::function, default_ops::powm_func, T, U, V>(
|
|
default_ops::powm_func(), b, p, mod);
|
|
}
|
|
|
|
}} //namespaces
|
|
|
|
#endif
|
|
|
|
|