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Boost-Commit : |
Subject: [Boost-commit] svn:boost r78014 - in sandbox/big_number: boost/multiprecision boost/multiprecision/depricated libs/multiprecision/example/generic_numerics_examples
From: john_at_[hidden]
Date: 2012-04-16 12:28:57
Author: johnmaddock
Date: 2012-04-16 12:28:57 EDT (Mon, 16 Apr 2012)
New Revision: 78014
URL: http://svn.boost.org/trac/boost/changeset/78014
Log:
Deleted some dead files, moved some others around.
Added:
sandbox/big_number/boost/multiprecision/depricated/
sandbox/big_number/boost/multiprecision/depricated/arithmetic_backend.hpp
- copied unchanged from r77995, /sandbox/big_number/boost/multiprecision/arithmetic_backend.hpp
sandbox/big_number/boost/multiprecision/depricated/fixed_int.hpp
- copied unchanged from r77995, /sandbox/big_number/boost/multiprecision/fixed_int.hpp
Removed:
sandbox/big_number/boost/multiprecision/arithmetic_backend.hpp
sandbox/big_number/boost/multiprecision/fixed_int.hpp
sandbox/big_number/libs/multiprecision/example/generic_numerics_examples/
Deleted: sandbox/big_number/boost/multiprecision/arithmetic_backend.hpp
==============================================================================
--- sandbox/big_number/boost/multiprecision/arithmetic_backend.hpp 2012-04-16 12:28:57 EDT (Mon, 16 Apr 2012)
+++ (empty file)
@@ -1,149 +0,0 @@
-///////////////////////////////////////////////////////////////
-// Copyright 2011 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_MATH_ARITH_BACKEND_HPP
-#define BOOST_MATH_ARITH_BACKEND_HPP
-
-#include <iostream>
-#include <iomanip>
-#include <sstream>
-#include <boost/cstdint.hpp>
-#include <boost/lexical_cast.hpp>
-#include <boost/multiprecision/mp_number.hpp>
-
-namespace boost{
-namespace multiprecision{
-namespace backends{
-
-template <class Arithmetic>
-struct arithmetic_backend
-{
- typedef mpl::list<long long> signed_types;
- typedef mpl::list<unsigned long long> unsigned_types;
- typedef mpl::list<long double> float_types;
- typedef int exponent_type;
-
- arithmetic_backend(){}
- arithmetic_backend(const arithmetic_backend& o)
- {
- m_value = o.m_value;
- }
- arithmetic_backend(const Arithmetic& o) : m_value(o) {}
-#ifndef BOOST_NO_RVALUE_REFERENCES
- arithmetic_backend(arithmetic_backend&& o) : m_value(o.m_value) {}
- arithmetic_backend(Arithmetic&& o) : m_value(o) {}
-#endif
- arithmetic_backend& operator = (const arithmetic_backend& o)
- {
- m_value = o.m_value;
- return *this;
- }
- arithmetic_backend& operator = (unsigned long long i)
- {
- m_value = i;
- return *this;
- }
- arithmetic_backend& operator = (long long i)
- {
- m_value = i;
- return *this;
- }
- arithmetic_backend& operator = (long double d)
- {
- m_value = d;
- return *this;
- }
- arithmetic_backend& operator = (const char* s)
- {
- m_value = boost::lexical_cast<double>(s);
- return *this;
- }
- void swap(arithmetic_backend& o)
- {
- std::swap(m_value, o.m_value);
- }
- std::string str(std::streamsize digits, std::ios_base::fmtflags f)const
- {
- std::stringstream ss;
- ss.flags(f);
- ss << std::setprecision(digits) << m_data;
- return ss.str();
- }
- void negate()
- {
- m_value = -m_value;
- }
- int compare(const arithmetic_backend& o)const
- {
- return m_value > o.m_value ? 1 : (m_value < o.m_value ? -1 : 0);
- }
- int compare(long long i)const
- {
- return m_value > i ? 1 : (m_value < i ? -1 : 0);
- }
- int compare(unsigned long long i)const
- {
- return m_value > i ? 1 : (m_value < i ? -1 : 0);
- }
- int compare(long double d)const
- {
- return m_value > d ? 1 : (m_value < d ? -1 : 0);
- }
- Arithmetic& data() { return m_value; }
- const Arithmetic& data()const { return m_value; }
-private:
- Arithmetic m_value;
-};
-
-template <class Arithmetic>
-inline void eval_add(arithmetic_backend<Arithmetic>& result, const arithmetic_backend<Arithmetic>& o)
-{
- result.data() += o.data();
-}
-template <class Arithmetic>
-inline void eval_subtract(arithmetic_backend<Arithmetic>& result, const arithmetic_backend<Arithmetic>& o)
-{
- result.data() -= o.data();
-}
-template <class Arithmetic>
-inline void eval_multiply(arithmetic_backend<Arithmetic>& result, const arithmetic_backend<Arithmetic>& o)
-{
- result.data() *= o.data();
-}
-template <class Arithmetic>
-inline void eval_divide(arithmetic_backend<Arithmetic>& result, const arithmetic_backend<Arithmetic>& o)
-{
- result.data() /= o.data();
-}
-
-} // namespace backends
-
-using boost::multiprecision::backends::arithmetic_backend;
-
-}} // namespaces
-
-
-namespace std{
-
-template <class Arithmetic, bool ExpressionTemplates>
-class numeric_limits<boost::multiprecision::mp_number<boost::multiprecision::arithmetic_backend<Arithmetic>, ExpressionTemplates > > : public std::numeric_limits<Arithmetic>
-{
- typedef std::numeric_limits<Arithmetic> base_type;
- typedef boost::multiprecision::mp_number<boost::multiprecision::arithmetic_backend<Arithmetic>, ExpressionTemplates> number_type;
-public:
- BOOST_STATIC_CONSTEXPR number_type (min)() BOOST_MP_NOEXCEPT { return (base_type::min)(); }
- BOOST_STATIC_CONSTEXPR number_type (max)() BOOST_MP_NOEXCEPT { return (base_type::max)(); }
- BOOST_STATIC_CONSTEXPR number_type lowest() BOOST_MP_NOEXCEPT { return -(max)(); }
- BOOST_STATIC_CONSTEXPR number_type epsilon() BOOST_MP_NOEXCEPT { return base_type::epsilon(); }
- BOOST_STATIC_CONSTEXPR number_type round_error() BOOST_MP_NOEXCEPT { return epsilon() / 2; }
- BOOST_STATIC_CONSTEXPR number_type infinity() BOOST_MP_NOEXCEPT { return base_type::infinity(); }
- BOOST_STATIC_CONSTEXPR number_type quiet_NaN() BOOST_MP_NOEXCEPT { return base_type::quiet_NaN(); }
- BOOST_STATIC_CONSTEXPR number_type signaling_NaN() BOOST_MP_NOEXCEPT { return base_type::signaling_NaN(); }
- BOOST_STATIC_CONSTEXPR number_type denorm_min() BOOST_MP_NOEXCEPT { return base_type::denorm_min(); }
-};
-
-}
-
-#endif
Deleted: sandbox/big_number/boost/multiprecision/fixed_int.hpp
==============================================================================
--- sandbox/big_number/boost/multiprecision/fixed_int.hpp 2012-04-16 12:28:57 EDT (Mon, 16 Apr 2012)
+++ (empty file)
@@ -1,1599 +0,0 @@
-///////////////////////////////////////////////////////////////
-// Copyright 2011 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_PACKED_INT_HPP
-#define BOOST_MP_PACKED_INT_HPP
-
-#include <iostream>
-#include <iomanip>
-#include <boost/cstdint.hpp>
-#include <boost/multiprecision/mp_number.hpp>
-#include <boost/multiprecision/detail/cpp_int_core.hpp>
-#include <boost/array.hpp>
-#include <boost/type_traits/is_integral.hpp>
-#include <boost/type_traits/is_floating_point.hpp>
-
-namespace boost{
-namespace multiprecision{
-
-template <unsigned Bits, bool Signed>
-struct fixed_int
-{
- typedef mpl::list<signed_limb_type, signed_double_limb_type> signed_types;
- typedef mpl::list<limb_type, double_limb_type> unsigned_types;
- typedef mpl::list<long double> float_types;
-
- BOOST_STATIC_CONSTANT(unsigned, limb_bits = sizeof(limb_type) * CHAR_BIT);
- BOOST_STATIC_CONSTANT(unsigned, limb_count = Bits / limb_bits + (Bits % limb_bits ? 1 : 0));
- BOOST_STATIC_CONSTANT(limb_type, max_limb_value = ~static_cast<limb_type>(0u));
- BOOST_STATIC_CONSTANT(limb_type, upper_limb_mask = (Bits % limb_bits ? (1 << (Bits % limb_bits)) - 1 : max_limb_value));
- BOOST_STATIC_CONSTANT(limb_type, upper_limb_not_mask = ~upper_limb_mask);
- BOOST_STATIC_CONSTANT(limb_type, sign_bit_mask = limb_type(1u) << ((Bits % limb_bits ? Bits % limb_bits : limb_bits) - 1));
- typedef boost::array<limb_type, limb_count> data_type;
-
- fixed_int(){}
- fixed_int(const fixed_int& o)
- {
- m_value = o.m_value;
- }
-#ifndef BOOST_NO_RVALUE_REFERENCES
- fixed_int(fixed_int&& o) : m_value(o.m_value) {}
-#endif
- fixed_int& operator = (const fixed_int& o)
- {
- m_value = o.m_value;
- return *this;
- }
- fixed_int& operator = (limb_type i)
- {
- m_value[limb_count - 1] = i;
- for(int j = static_cast<int>(limb_count) - 2; j >= 0; --j)
- m_value[j] = 0;
- m_value[0] &= fixed_int<Bits, Signed>::upper_limb_mask;
- return *this;
- }
- fixed_int& operator = (signed_limb_type i)
- {
- m_value[limb_count - 1] = i;
- // sign extend:
- for(int j = static_cast<int>(limb_count) - 2; j >= 0; --j)
- m_value[j] = i < 0 ? max_limb_value : 0;
- m_value[0] &= fixed_int<Bits, Signed>::upper_limb_mask;
- return *this;
- }
- fixed_int& operator = (double_limb_type i)
- {
- BOOST_STATIC_ASSERT(sizeof(i) % sizeof(limb_type) == 0);
- double_limb_type mask = max_limb_value;
- unsigned shift = 0;
- for(int j = limb_count - 1; j >= static_cast<int>(limb_count) - static_cast<int>(sizeof(signed_double_limb_type) / sizeof(limb_type)); --j)
- {
- m_value[j] = static_cast<limb_type>((i & mask) >> shift);
- mask <<= limb_bits;
- shift += limb_bits;
- }
- for(int j = static_cast<int>(limb_count) - static_cast<int>(sizeof(signed_double_limb_type) / sizeof(limb_type)) - 1; j >= 0; --j)
- m_value[j] = 0;
- m_value[0] &= fixed_int<Bits, Signed>::upper_limb_mask;
- return *this;
- }
- fixed_int& operator = (signed_double_limb_type i)
- {
- BOOST_STATIC_ASSERT(sizeof(i) % sizeof(limb_type) == 0);
- double_limb_type mask = max_limb_value;
- unsigned shift = 0;
- for(int j = limb_count - 1; j >= static_cast<int>(limb_count) - static_cast<int>(sizeof(signed_double_limb_type) / sizeof(limb_type)); --j)
- {
- m_value[j] = static_cast<limb_type>((i & mask) >> shift);
- mask <<= limb_bits;
- shift += limb_bits;
- }
- for(int j = static_cast<int>(limb_count) - static_cast<int>(sizeof(signed_double_limb_type) / sizeof(limb_type)) - 1; j >= 0; --j)
- m_value[j] = i < 0 ? max_limb_value : 0;
- m_value[0] &= fixed_int<Bits, Signed>::upper_limb_mask;
- return *this;
- }
- fixed_int& operator = (long double a)
- {
- BOOST_STATIC_ASSERT(Bits >= (unsigned)std::numeric_limits<long double>::digits);
- using std::frexp;
- using std::ldexp;
- using std::floor;
-
- if (a == 0) {
- return *this = static_cast<limb_type>(0u);
- }
-
- if (a == 1) {
- return *this = static_cast<limb_type>(1u);
- }
-
- BOOST_ASSERT(!(boost::math::isinf)(a));
- BOOST_ASSERT(!(boost::math::isnan)(a));
-
- int e;
- long double f, term;
- *this = static_cast<limb_type>(0u);
-
- f = frexp(a, &e);
-
- static const limb_type shift = std::numeric_limits<limb_type>::digits;
-
- while(f)
- {
- // extract int sized bits from f:
- f = ldexp(f, shift);
- term = floor(f);
- e -= shift;
- eval_left_shift(*this, shift);
- if(term > 0)
- eval_add(*this, static_cast<limb_type>(term));
- else
- eval_subtract(*this, static_cast<limb_type>(-term));
- f -= term;
- }
- if(e > 0)
- eval_left_shift(*this, e);
- else if(e < 0)
- eval_right_shift(*this, -e);
- data()[0] &= fixed_int<Bits, Signed>::upper_limb_mask;
- return *this;
- }
- fixed_int& operator = (const char* s)
- {
- std::size_t n = s ? std::strlen(s) : 0;
- *this = static_cast<limb_type>(0u);
- unsigned radix = 10;
- bool isneg = false;
- if(n && (*s == '-'))
- {
- --n;
- ++s;
- isneg = true;
- }
- if(n && (*s == '0'))
- {
- if((n > 1) && ((s[1] == 'x') || (s[1] == 'X')))
- {
- radix = 16;
- s +=2;
- n -= 2;
- }
- else
- {
- radix = 8;
- n -= 1;
- }
- }
- if(n)
- {
- if(radix == 8 || radix == 16)
- {
- unsigned shift = radix == 8 ? 3 : 4;
- unsigned block_count = limb_bits / shift;
- unsigned block_shift = shift * block_count;
- limb_type val, block;
- while(*s)
- {
- block = 0;
- for(unsigned i = 0; (i < block_count); ++i)
- {
- if(*s >= '0' && *s <= '9')
- val = *s - '0';
- else if(*s >= 'a' && *s <= 'f')
- val = 10 + *s - 'a';
- else if(*s >= 'A' && *s <= 'F')
- val = 10 + *s - 'A';
- else
- val = max_limb_value;
- if(val > radix)
- {
- m_value[0] &= fixed_int<Bits, Signed>::upper_limb_mask;
- BOOST_THROW_EXCEPTION(std::runtime_error("Unexpected content found while parsing character string."));
- }
- block <<= shift;
- block |= val;
- if(!*++s)
- {
- // final shift is different:
- block_shift = (i + 1) * shift;
- break;
- }
- }
- eval_left_shift(*this, block_shift);
- m_value[limb_count - 1] |= block;
- }
- }
- else
- {
- // Base 10, we extract blocks of size 10^9 at a time, that way
- // the number of multiplications is kept to a minimum:
- limb_type block_mult = max_block_10;
- while(*s)
- {
- limb_type block = 0;
- for(unsigned i = 0; i < digits_per_block_10; ++i)
- {
- limb_type val;
- if(*s >= '0' && *s <= '9')
- val = *s - '0';
- else
- BOOST_THROW_EXCEPTION(std::runtime_error("Unexpected character encountered in input."));
- block *= 10;
- block += val;
- if(!*++s)
- {
- block_mult = block_multiplier(i);
- break;
- }
- }
- eval_multiply(*this, block_mult);
- eval_add(*this, block);
- }
- }
- }
- m_value[0] &= fixed_int<Bits, Signed>::upper_limb_mask;
- if(isneg)
- negate();
- return *this;
- }
- void swap(fixed_int& o)
- {
- std::swap(m_value, o.m_value);
- }
- std::string str(std::streamsize digits, std::ios_base::fmtflags f)const
- {
- int base = 10;
- if((f & std::ios_base::oct) == std::ios_base::oct)
- base = 8;
- else if((f & std::ios_base::hex) == std::ios_base::hex)
- base = 16;
- std::string result;
-
- if(base == 8 || base == 16)
- {
- limb_type shift = base == 8 ? 3 : 4;
- limb_type mask = static_cast<limb_type>((1u << shift) - 1);
- fixed_int t(*this);
- result.assign(Bits / shift + (Bits % shift ? 1 : 0), '0');
- int pos = result.size() - 1;
- for(unsigned i = 0; i < Bits / shift; ++i)
- {
- char c = '0' + (t.data()[limb_count-1] & mask);
- if(c > '9')
- c += 'A' - '9' - 1;
- result[pos--] = c;
- eval_right_shift(t, shift);
- }
- if(Bits % shift)
- {
- mask = static_cast<limb_type>((1u << (Bits % shift)) - 1);
- char c = '0' + (t.data()[limb_count-1] & mask);
- if(c > '9')
- c += 'A' - '9';
- result[pos] = c;
- }
- //
- // Get rid of leading zeros:
- //
- std::string::size_type n = result.find_first_not_of('0');
- if(!result.empty() && (n == std::string::npos))
- n = result.size() - 1;
- result.erase(0, n);
- if(f & std::ios_base::showbase)
- {
- const char* pp = base == 8 ? "0" : "0x";
- result.insert(0, pp);
- }
- }
- else
- {
- result.assign(Bits / 3 + 1, '0');
- int pos = result.size() - 1;
- fixed_int t(*this);
- fixed_int r;
- bool neg = false;
- if(Signed && (t.data()[0] & sign_bit_mask))
- {
- t.negate();
- neg = true;
- }
- if(limb_count == 1)
- {
- result = boost::lexical_cast<std::string>(t.data()[0]);
- }
- else
- {
- while(eval_get_sign(t) != 0)
- {
- fixed_int t2;
- divide_unsigned_helper(t2, t, max_block_10, r);
- t = t2;
- limb_type v = r.data()[limb_count - 1];
- for(unsigned i = 0; i < digits_per_block_10; ++i)
- {
- char c = '0' + v % 10;
- v /= 10;
- result[pos] = c;
- if(pos-- == 0)
- break;
- }
- }
- }
- unsigned n = result.find_first_not_of('0');
- result.erase(0, n);
- if(result.empty())
- result = "0";
- if(neg)
- result.insert(0, 1, '-');
- else if(f & std::ios_base::showpos)
- result.insert(0, 1, '+');
- }
- return result;
- }
- void negate()
- {
- double_limb_type carry = 1;
- for(int i = fixed_int<Bits, Signed>::limb_count - 1; i >= 0; --i)
- {
- carry += static_cast<double_limb_type>(~m_value[i]);
- m_value[i] = static_cast<limb_type>(carry);
- carry >>= limb_bits;
- }
- m_value[0] &= fixed_int<Bits, Signed>::upper_limb_mask;
- }
- int compare(const fixed_int& o)const
- {
- int result = 0;
- if(Signed && ((m_value[0] & sign_bit_mask) != (o.data()[0] & sign_bit_mask)))
- {
- return m_value[0] & sign_bit_mask ? -1 : 1;
- }
- for(typename data_type::size_type i = 0; i < limb_count; ++i)
- {
- if(m_value[i] != o.data()[i])
- {
- result = (m_value[i] < o.data()[i]) ? -1 : 1;
- break;
- }
- }
- return Signed && (m_value[0] & sign_bit_mask) ? -result : result ;
- }
- template <class Arithmatic>
- typename enable_if<is_arithmetic<Arithmatic>, int>::type compare(Arithmatic i)const
- {
- // braindead version:
- fixed_int<Bits, Signed> t;
- t = i;
- return compare(t);
- }
- data_type& data() { return m_value; }
- const data_type& data()const { return m_value; }
-private:
- data_type m_value;
-};
-
-template <unsigned Bits, bool Signed>
-inline void eval_add(fixed_int<Bits, Signed>& result, const fixed_int<Bits, Signed>& o)
-{
- eval_add(result, result, o);
-}
-template <unsigned Bits, bool Signed>
-inline void eval_add(fixed_int<Bits, Signed>& result, const fixed_int<Bits, Signed>& a, const fixed_int<Bits, Signed>& b)
-{
- // Addition using modular arithmatic.
- // Nothing fancy, just let uintmax_t take the strain:
- double_limb_type carry = 0;
- for(int i = fixed_int<Bits, Signed>::limb_count - 1; i >= 0; --i)
- {
- carry += static_cast<double_limb_type>(a.data()[i]) + static_cast<double_limb_type>(b.data()[i]);
- result.data()[i] = static_cast<limb_type>(carry);
- carry >>= fixed_int<Bits, Signed>::limb_bits;
- }
- result.data()[0] &= fixed_int<Bits, Signed>::upper_limb_mask;
-}
-template <unsigned Bits, bool Signed>
-inline void eval_add(fixed_int<Bits, Signed>& result, const limb_type& o)
-{
- // Addition using modular arithmatic.
- // Nothing fancy, just let uintmax_t take the strain:
- double_limb_type carry = o;
- for(int i = fixed_int<Bits, Signed>::limb_count - 1; carry && i >= 0; --i)
- {
- carry += static_cast<double_limb_type>(result.data()[i]);
- result.data()[i] = static_cast<limb_type>(carry);
- carry >>= fixed_int<Bits, Signed>::limb_bits;
- }
- result.data()[0] &= fixed_int<Bits, Signed>::upper_limb_mask;
-}
-template <unsigned Bits, bool Signed>
-inline void eval_add(fixed_int<Bits, Signed>& result, const signed_limb_type& o)
-{
- if(o < 0)
- eval_subtract(result, static_cast<limb_type>(-o));
- else if(o > 0)
- eval_add(result, static_cast<limb_type>(o));
-}
-template <unsigned Bits, bool Signed>
-inline void eval_subtract(fixed_int<Bits, Signed>& result, const limb_type& o)
-{
- // Subtract using modular arithmatic.
- // This is the same code as for addition, with the twist that we negate o "on the fly":
- double_limb_type carry = static_cast<double_limb_type>(result.data()[fixed_int<Bits, Signed>::limb_count - 1])
- + 1uLL + static_cast<double_limb_type>(~o);
- result.data()[fixed_int<Bits, Signed>::limb_count - 1] = static_cast<limb_type>(carry);
- carry >>= fixed_int<Bits, Signed>::limb_bits;
- for(int i = static_cast<int>(fixed_int<Bits, Signed>::limb_count) - 2; (carry != 1) && (i >= 0); --i)
- {
- carry += static_cast<double_limb_type>(result.data()[i]) + fixed_int<Bits, Signed>::max_limb_value;
- result.data()[i] = static_cast<limb_type>(carry);
- carry >>= fixed_int<Bits, Signed>::limb_bits;
- }
- result.data()[0] &= fixed_int<Bits, Signed>::upper_limb_mask;
-}
-template <unsigned Bits, bool Signed>
-inline void eval_subtract(fixed_int<Bits, Signed>& result, const signed_limb_type& o)
-{
- if(o)
- {
- if(o < 0)
- eval_add(result, static_cast<limb_type>(-o));
- else
- eval_subtract(result, static_cast<limb_type>(o));
- }
-}
-template <unsigned Bits, bool Signed>
-inline void eval_increment(fixed_int<Bits, Signed>& result)
-{
- static const limb_type one = 1;
- if(result.data().elems[fixed_int<Bits, Signed>::limb_count - 1] < fixed_int<Bits, Signed>::max_limb_value)
- ++result.data().elems[fixed_int<Bits, Signed>::limb_count - 1];
- else
- eval_add(result, one);
-}
-template <unsigned Bits, bool Signed>
-inline void eval_decrement(fixed_int<Bits, Signed>& result)
-{
- static const limb_type one = 1;
- if(result.data().elems[fixed_int<Bits, Signed>::limb_count - 1])
- --result.data().elems[fixed_int<Bits, Signed>::limb_count - 1];
- else
- eval_subtract(result, one);
-}
-template <unsigned Bits, bool Signed>
-inline void eval_subtract(fixed_int<Bits, Signed>& result, const fixed_int<Bits, Signed>& o)
-{
- eval_subtract(result, result, o);
-}
-template <unsigned Bits, bool Signed>
-inline void eval_subtract(fixed_int<Bits, Signed>& result, const fixed_int<Bits, Signed>& a, const fixed_int<Bits, Signed>& b)
-{
- // Subtract using modular arithmatic.
- // This is the same code as for addition, with the twist that we negate b "on the fly":
- double_limb_type carry = 1;
- for(int i = fixed_int<Bits, Signed>::limb_count - 1; i >= 0; --i)
- {
- carry += static_cast<double_limb_type>(a.data()[i]) + static_cast<double_limb_type>(~b.data()[i]);
- result.data()[i] = static_cast<limb_type>(carry);
- carry >>= fixed_int<Bits, Signed>::limb_bits;
- }
- result.data()[0] &= fixed_int<Bits, Signed>::upper_limb_mask;
-}
-template <unsigned Bits, bool Signed>
-inline void eval_multiply(fixed_int<Bits, Signed>& result, const fixed_int<Bits, Signed>& a, const fixed_int<Bits, Signed>& b)
-{
- // Very simple long multiplication, only usable for small numbers of limb_type's
- // but that's the typical use case for this type anyway:
- if(&result == &a)
- {
- fixed_int<Bits, Signed> t(a);
- eval_multiply(result, t, b);
- return;
- }
- if(&result == &b)
- {
- fixed_int<Bits, Signed> t(b);
- eval_multiply(result, a, t);
- return;
- }
- double_limb_type carry = 0;
- for(unsigned i = 0; i < fixed_int<Bits, Signed>::limb_count; ++i)
- result.data()[i] = 0;
- for(int i = fixed_int<Bits, Signed>::limb_count - 1; i >= 0; --i)
- {
- for(int j = fixed_int<Bits, Signed>::limb_count - 1; j >= static_cast<int>(fixed_int<Bits, Signed>::limb_count) - i - 1; --j)
- {
- carry += static_cast<double_limb_type>(a.data()[i]) * static_cast<double_limb_type>(b.data()[j]);
- carry += result.data()[i + j + 1 - fixed_int<Bits, Signed>::limb_count];
- result.data()[i + j + 1 - fixed_int<Bits, Signed>::limb_count] = static_cast<limb_type>(carry);
- carry >>= fixed_int<Bits, Signed>::limb_bits;
- }
- carry = 0;
- }
- result.data()[0] &= fixed_int<Bits, Signed>::upper_limb_mask;
-}
-template <unsigned Bits, bool Signed>
-inline void eval_multiply(fixed_int<Bits, Signed>& result, const fixed_int<Bits, Signed>& a)
-{
- // There is no in-place multiply:
- fixed_int<Bits, Signed> b(result);
- eval_multiply(result, b, a);
-}
-template <unsigned Bits, bool Signed>
-inline void eval_multiply(fixed_int<Bits, Signed>& result, const limb_type& a)
-{
- double_limb_type carry = 0;
- for(int i = fixed_int<Bits, Signed>::limb_count - 1; i >= 0; --i)
- {
- carry += static_cast<double_limb_type>(result.data()[i]) * static_cast<double_limb_type>(a);
- result.data()[i] = static_cast<limb_type>(carry);
- carry >>= fixed_int<Bits, Signed>::limb_bits;
- }
- result.data()[0] &= fixed_int<Bits, Signed>::upper_limb_mask;
-}
-template <unsigned Bits, bool Signed>
-inline void eval_multiply(fixed_int<Bits, Signed>& result, const signed_limb_type& a)
-{
- if(a > 0)
- eval_multiply(result, static_cast<limb_type>(a));
- else
- {
- eval_multiply(result, static_cast<limb_type>(-a));
- result.negate();
- }
-}
-
-/*
-template <unsigned Bits, bool Signed>
-limb_type bitcount(const fixed_int<Bits, Signed>& a)
-{
- // returns the location of the MSB in a:
- limb_type i = 0;
- for(; (i < fixed_int<Bits, Signed>::limb_count) && (a.data()[i] == 0); ++i){}
- limb_type count = (fixed_int<Bits, Signed>::limb_count - i) * fixed_int<Bits, Signed>::limb_bits;
- if(!count)
- return count; // no bits are set, value is zero
- limb_type mask = static_cast<limb_type>(1u) << (fixed_int<Bits, Signed>::limb_bits - 1);
- while((a.data()[i] & mask) == 0)
- {
- --count;
- mask >>= 1;
- }
- return count;
-}
-template <unsigned Bits, bool Signed>
-void divide_unsigned_helper(fixed_int<Bits, Signed>& result, const fixed_int<Bits, Signed>& x, const fixed_int<Bits, Signed>& y, fixed_int<Bits, Signed>& r)
-{
- if((&result == &x) || (&r == &x))
- {
- fixed_int<Bits, Signed> t(x);
- divide_unsigned_helper(result, t, y, r);
- return;
- }
- if((&result == &y) || (&r == &y))
- {
- fixed_int<Bits, Signed> t(y);
- divide_unsigned_helper(result, x, t, r);
- return;
- }
-
-
- using default_ops::eval_subtract;
-
-
- if (eval_is_zero(y))
- {
- volatile int i = 0;
- i /= i;
- return;
- }
-
- if (eval_is_zero(x))
- {
- r = y;
- result = x;
- return;
- }
-
- if(&result == &r)
- {
- fixed_int<Bits, Signed> rem;
- divide_unsigned_helper(result, x, y, rem);
- r = rem;
- return;
- }
-
- r = x;
- result = static_cast<limb_type>(0u);
- if(x.compare(y) < 0)
- {
- return; // We already have the answer: zero.
- }
-
- limb_type n = bitcount(x) - bitcount(y);
-
- if(n == 0)
- {
- // result is exactly 1:
- result = static_cast<limb_type>(1u);
- eval_subtract(r, y);
- return;
- }
-
- // Together mask_index and mask give us the bit we may be about to set in the result:
- limb_type mask_index = fixed_int<Bits, Signed>::limb_count - 1 - n / fixed_int<Bits, Signed>::limb_bits;
- limb_type mask = static_cast<limb_type>(1u) << n % fixed_int<Bits, Signed>::limb_bits;
- fixed_int<Bits, Signed> t(y);
- eval_left_shift(t, n);
- while(mask_index < fixed_int<Bits, Signed>::limb_count)
- {
- int comp = r.compare(t);
- if(comp >= 0)
- {
- result.data()[mask_index] |= mask;
- eval_subtract(r, t);
- if(comp == 0)
- break; // no remainder left - we have an exact result!
- }
- eval_right_shift(t, 1u);
- if(0 == (mask >>= 1))
- {
- ++mask_index;
- mask = static_cast<limb_type>(1u) << (fixed_int<Bits, Signed>::limb_bits - 1);
- }
- }
- BOOST_ASSERT(r.compare(y) < 0); // remainder must be less than the divisor or our code has failed
-}
-*/
-template <unsigned Bits, bool Signed>
-void divide_unsigned_helper(fixed_int<Bits, Signed>& result, const fixed_int<Bits, Signed>& x, const fixed_int<Bits, Signed>& y, fixed_int<Bits, Signed>& r)
-{
- if((&result == &x) || (&r == &x))
- {
- fixed_int<Bits, Signed> t(x);
- divide_unsigned_helper(result, t, y, r);
- return;
- }
- if((&result == &y) || (&r == &y))
- {
- fixed_int<Bits, Signed> t(y);
- divide_unsigned_helper(result, x, t, r);
- return;
- }
-
- /*
- Very simple, fairly braindead long division.
- Start by setting the remainder equal to x, and the
- result equal to 0. Then in each loop we calculate our
- "best guess" for how many times y divides into r,
- add our guess to the result, and subtract guess*y
- from the remainder r. One wrinkle is that the remainder
- may go negative, in which case we subtract the current guess
- from the result rather than adding. The value of the guess
- is determined by dividing the most-significant-limb of the
- current remainder by the most-significant-limb of y.
-
- Note that there are more efficient algorithms than this
- available, in particular see Knuth Vol 2. However for small
- numbers of limbs this generally outperforms the alternatives
- and avoids the normalisation step which would require extra storage.
- */
-
-
- using default_ops::eval_subtract;
-
- if(&result == &r)
- {
- fixed_int<Bits, Signed> rem;
- divide_unsigned_helper(result, x, y, rem);
- r = rem;
- return;
- }
-
- //
- // Find the most significant words of numerator and denominator.
- //
- limb_type y_order = 0;
- while((y.data()[y_order] == 0) && (y_order < fixed_int<Bits, Signed>::limb_count))
- ++y_order;
-
- if(y_order >= fixed_int<Bits, Signed>::limb_count - 1)
- {
- //
- // Only a single non-zero limb in the denominator, in this case
- // we can use a specialized divide-by-single-limb routine which is
- // much faster. This also handles division by zero:
- //
- divide_unsigned_helper(result, x, y.data()[y_order], r);
- return;
- }
-
- limb_type r_order = 0;
- while((x.data()[r_order] == 0) && (r_order < fixed_int<Bits, Signed>::limb_count))
- ++r_order;
- if(r_order == fixed_int<Bits, Signed>::limb_count)
- {
- // x is zero, so is the result:
- r = y;
- result = x;
- return;
- }
-
- r = x;
- result = static_cast<limb_type>(0u);
- //
- // Check if the remainder is already less than the divisor, if so
- // we already have the result. Note we try and avoid a full compare
- // if we can:
- //
- if(r_order >= y_order)
- {
- if((r_order > y_order) || (r.compare(y) < 0))
- {
- return;
- }
- }
-
- fixed_int<Bits, Signed> t;
- bool r_neg = false;
-
- //
- // See if we can short-circuit long division, and use basic arithmetic instead:
- //
- if(r_order == fixed_int<Bits, Signed>::limb_count - 1)
- {
- result = r.data()[fixed_int<Bits, Signed>::limb_count - 1] / y.data()[fixed_int<Bits, Signed>::limb_count - 1];
- r = x.data()[fixed_int<Bits, Signed>::limb_count - 1] % y.data()[fixed_int<Bits, Signed>::limb_count - 1];
- return;
- }
- else if(r_order == static_cast<unsigned>(fixed_int<Bits, Signed>::limb_count) - 2)
- {
- double_limb_type a, b;
- a = (static_cast<double_limb_type>(r.data()[r_order]) << fixed_int<Bits, Signed>::limb_bits) | r.data()[r_order + 1];
- b = y_order < fixed_int<Bits, Signed>::limb_count - 1 ?
- (static_cast<double_limb_type>(y.data()[y_order]) << fixed_int<Bits, Signed>::limb_bits) | y.data()[y_order + 1]
- : y.data()[y_order];
- result = a / b;
- r = a % b;
- return;
- }
-
- do
- {
- //
- // Update r_order, this can't run past the end as r must be non-zero at this point:
- //
- while(r.data()[r_order] == 0)
- ++r_order;
- //
- // Calculate our best guess for how many times y divides into r:
- //
- limb_type guess;
- if((r.data()[r_order] <= y.data()[y_order]) && (r_order < fixed_int<Bits, Signed>::limb_count - 1))
- {
- double_limb_type a, b, v;
- a = (static_cast<double_limb_type>(r.data()[r_order]) << fixed_int<Bits, Signed>::limb_bits) | r.data()[r_order + 1];
- b = y.data()[y_order];
- v = a / b;
- if(v > fixed_int<Bits, Signed>::max_limb_value)
- guess = 1;
- else
- {
- guess = static_cast<limb_type>(v);
- ++r_order;
- }
- }
- else if(r_order == fixed_int<Bits, Signed>::limb_count - 1)
- {
- guess = r.data()[r_order] / y.data()[y_order];
- }
- else
- {
- double_limb_type a, b, v;
- a = (static_cast<double_limb_type>(r.data()[r_order]) << fixed_int<Bits, Signed>::limb_bits) | r.data()[r_order + 1];
- b = (y_order < fixed_int<Bits, Signed>::limb_count - 1) ? (static_cast<double_limb_type>(y.data()[y_order]) << fixed_int<Bits, Signed>::limb_bits) | y.data()[y_order + 1] : (static_cast<double_limb_type>(y.data()[y_order]) << fixed_int<Bits, Signed>::limb_bits);
- v = a / b;
- guess = static_cast<limb_type>(v);
- }
- BOOST_ASSERT(guess); // If the guess ever gets to zero we go on forever....
- //
- // Update result:
- //
- limb_type shift = y_order - r_order;
- //t = limb_type(0);
- //t.data()[fixed_int<Bits, Signed>::limb_count - 1 - shift] = guess;
- if(r_neg)
- {
- if(result.data()[fixed_int<Bits, Signed>::limb_count - 1 - shift] > guess)
- result.data()[fixed_int<Bits, Signed>::limb_count - 1 - shift] -= guess;
- else
- {
- t = limb_type(0);
- t.data()[fixed_int<Bits, Signed>::limb_count - 1 - shift] = guess;
- eval_subtract(result, t);
- }
- }
- else if(fixed_int<Bits, Signed>::max_limb_value - result.data()[fixed_int<Bits, Signed>::limb_count - 1 - shift] > guess)
- result.data()[fixed_int<Bits, Signed>::limb_count - 1 - shift] += guess;
- else
- {
- t = limb_type(0);
- t.data()[fixed_int<Bits, Signed>::limb_count - 1 - shift] = guess;
- eval_add(result, t);
- }
- //
- // Calculate guess * y, we use a fused mutiply-shift O(N) for this
- // rather than a full O(N^2) multiply:
- //
- double_limb_type carry = 0;
- for(unsigned i = fixed_int<Bits, Signed>::limb_count - 1; i > fixed_int<Bits, Signed>::limb_count - shift - 1; --i)
- t.data()[i] = 0;
- for(int i = fixed_int<Bits, Signed>::limb_count - 1; i >= static_cast<int>(shift); --i)
- {
- carry += static_cast<double_limb_type>(y.data()[i]) * static_cast<double_limb_type>(guess);
- t.data()[i - shift] = static_cast<limb_type>(carry);
- carry >>= fixed_int<Bits, Signed>::limb_bits;
- }
- t.data()[0] &= fixed_int<Bits, Signed>::upper_limb_mask;
- //
- // Update r:
- //
- eval_subtract(r, t);
- if(r.data()[0] & fixed_int<Bits, Signed>::sign_bit_mask)
- {
- r.negate();
- r_neg = !r_neg;
- }
- }
- // Termination condition is really just a check that r > y, but with two common
- // short-circuit cases handled first:
- while((r_order < y_order) || (r.data()[r_order] > y.data()[y_order]) || (r.compare(y) > 0));
-
- //
- // We now just have to normalise the result:
- //
- if(r_neg)
- {
- // We have one too many in the result:
- eval_decrement(result);
- r.negate();
- eval_add(r, y);
- }
-
- BOOST_ASSERT(r.compare(y) < 0); // remainder must be less than the divisor or our code has failed
-}
-
-template <unsigned Bits, bool Signed>
-void divide_unsigned_helper(fixed_int<Bits, Signed>& result, const fixed_int<Bits, Signed>& x, limb_type y, fixed_int<Bits, Signed>& r)
-{
- if((&result == &x) || (&r == &x))
- {
- fixed_int<Bits, Signed> t(x);
- divide_unsigned_helper(result, t, y, r);
- return;
- }
-
- if(&result == &r)
- {
- fixed_int<Bits, Signed> rem;
- divide_unsigned_helper(result, x, y, rem);
- r = rem;
- return;
- }
-
- // As above, but simplified for integer divisor:
-
- using default_ops::eval_subtract;
-
- if(y == 0)
- {
- BOOST_THROW_EXCEPTION(std::runtime_error("Integer Division by zero."));
- }
- //
- // Find the most significant word of numerator.
- //
- limb_type r_order = 0;
- while((x.data()[r_order] == 0) && (r_order < fixed_int<Bits, Signed>::limb_count))
- ++r_order;
-
- //
- // Set remainder and result to their initial values:
- //
- r = x;
- result = static_cast<limb_type>(0u);
-
- if(r_order == fixed_int<Bits, Signed>::limb_count)
- {
- // All the limbs in x are zero, so is the result:
- return;
- }
- //
- // check for x < y, try to do this without actually having to
- // do a full comparison:
- //
- if((r_order == fixed_int<Bits, Signed>::limb_count - 1) && (r.data()[r_order] < y))
- {
- return;
- }
-
- //
- // See if we can short-circuit long division, and use basic arithmetic instead:
- //
- if(r_order == fixed_int<Bits, Signed>::limb_count - 1)
- {
- result = r.data()[fixed_int<Bits, Signed>::limb_count - 1] / y;
- r = x.data()[fixed_int<Bits, Signed>::limb_count - 1] % y;
- return;
- }
- else if(r_order == static_cast<limb_type>(fixed_int<Bits, Signed>::limb_count) - 2)
- {
- double_limb_type a;
- a = (static_cast<double_limb_type>(r.data()[r_order]) << fixed_int<Bits, Signed>::limb_bits) | r.data()[r_order + 1];
- result = a / y;
- r = a % y;
- return;
- }
-
- do
- {
- //
- // Update r_order, this can't run past the end as r must be non-zero at this point:
- //
- while(r.data()[r_order] == 0)
- ++r_order;
- //
- // Calculate our best guess for how many times y divides into r:
- //
- if((r.data()[r_order] < y) && (r_order < fixed_int<Bits, Signed>::limb_count - 1))
- {
- double_limb_type a, b;
- a = (static_cast<double_limb_type>(r.data()[r_order]) << fixed_int<Bits, Signed>::limb_bits) | r.data()[r_order + 1];
- b = a % y;
- r.data()[r_order] = 0;
- ++r_order;
- r.data()[r_order] = static_cast<limb_type>(b);
- result.data()[r_order] = static_cast<limb_type>(a / y);
- }
- else
- {
- result.data()[r_order] = r.data()[r_order] / y;
- r.data()[r_order] %= y;
- }
- }
- // Termination condition is really just a check that r > y, but with two common
- // short-circuit cases handled first:
- while((r_order < fixed_int<Bits, Signed>::limb_count - 1) || (r.data()[r_order] > y));
-
- BOOST_ASSERT(r.compare(y) < 0); // remainder must be less than the divisor or our code has failed
-}
-
-template <unsigned Bits, bool Signed>
-inline void eval_divide(fixed_int<Bits, Signed>& result, const fixed_int<Bits, Signed>& a, const fixed_int<Bits, Signed>& b)
-{
- fixed_int<Bits, Signed> r;
- if(Signed && (a.data()[0] & fixed_int<Bits, Signed>::sign_bit_mask))
- {
- if(Signed && (b.data()[0] & fixed_int<Bits, Signed>::sign_bit_mask))
- {
- fixed_int<Bits, Signed> t1(a), t2(b);
- t1.negate();
- t2.negate();
- divide_unsigned_helper(result, t1, t2, r);
- }
- else
- {
- fixed_int<Bits, Signed> t(a);
- t.negate();
- divide_unsigned_helper(result, t, b, r);
- result.negate();
- }
- }
- else if(Signed && (b.data()[0] & fixed_int<Bits, Signed>::sign_bit_mask))
- {
- fixed_int<Bits, Signed> t(b);
- t.negate();
- divide_unsigned_helper(result, a, t, r);
- result.negate();
- }
- else
- {
- divide_unsigned_helper(result, a, b, r);
- }
-}
-template <unsigned Bits, bool Signed>
-inline void eval_divide(fixed_int<Bits, Signed>& result, const fixed_int<Bits, Signed>& a, limb_type& b)
-{
- fixed_int<Bits, Signed> r;
- if(Signed && (a.data()[0] & fixed_int<Bits, Signed>::sign_bit_mask))
- {
- fixed_int<Bits, Signed> t(a);
- t.negate();
- divide_unsigned_helper(result, t, b, r);
- result.negate();
- }
- else
- {
- divide_unsigned_helper(result, a, b, r);
- }
-}
-template <unsigned Bits, bool Signed>
-inline void eval_divide(fixed_int<Bits, Signed>& result, const fixed_int<Bits, Signed>& a, signed_limb_type& b)
-{
- fixed_int<Bits, Signed> r;
- if(Signed && (a.data()[0] & fixed_int<Bits, Signed>::sign_bit_mask))
- {
- if(b < 0)
- {
- fixed_int<Bits, Signed> t(a);
- t.negate();
- divide_unsigned_helper(result, t, static_cast<limb_type>(-b), r);
- }
- else
- {
- fixed_int<Bits, Signed> t(a);
- t.negate();
- divide_unsigned_helper(result, t, b, r);
- result.negate();
- }
- }
- else if(b < 0)
- {
- divide_unsigned_helper(result, a, static_cast<limb_type>(-b), r);
- result.negate();
- }
- else
- {
- divide_unsigned_helper(result, a, static_cast<limb_type>(b), r);
- }
-}
-template <unsigned Bits, bool Signed>
-inline void eval_divide(fixed_int<Bits, Signed>& result, const fixed_int<Bits, Signed>& b)
-{
- // There is no in place divide:
- fixed_int<Bits, Signed> a(result);
- eval_divide(result, a, b);
-}
-template <unsigned Bits, bool Signed>
-inline void eval_divide(fixed_int<Bits, Signed>& result, limb_type b)
-{
- // There is no in place divide:
- fixed_int<Bits, Signed> a(result);
- eval_divide(result, a, b);
-}
-template <unsigned Bits, bool Signed>
-inline void eval_divide(fixed_int<Bits, Signed>& result, signed_limb_type b)
-{
- // There is no in place divide:
- fixed_int<Bits, Signed> a(result);
- eval_divide(result, a, b);
-}
-template <unsigned Bits, bool Signed>
-inline void eval_modulus(fixed_int<Bits, Signed>& result, const fixed_int<Bits, Signed>& a, const fixed_int<Bits, Signed>& b)
-{
- fixed_int<Bits, Signed> r;
- if(Signed && (a.data()[0] & fixed_int<Bits, Signed>::sign_bit_mask))
- {
- if(Signed && (b.data()[0] & fixed_int<Bits, Signed>::sign_bit_mask))
- {
- fixed_int<Bits, Signed> t1(a), t2(b);
- t1.negate();
- t2.negate();
- divide_unsigned_helper(r, t1, t2, result);
- result.negate();
- }
- else
- {
- fixed_int<Bits, Signed> t(a);
- t.negate();
- divide_unsigned_helper(r, t, b, result);
- result.negate();
- }
- }
- else if(Signed && (b.data()[0] & fixed_int<Bits, Signed>::sign_bit_mask))
- {
- fixed_int<Bits, Signed> t(b);
- t.negate();
- divide_unsigned_helper(r, a, t, result);
- }
- else
- {
- divide_unsigned_helper(r, a, b, result);
- }
-}
-template <unsigned Bits, bool Signed>
-inline void eval_modulus(fixed_int<Bits, Signed>& result, const fixed_int<Bits, Signed>& a, limb_type b)
-{
- fixed_int<Bits, Signed> r;
- if(Signed && (a.data()[0] & fixed_int<Bits, Signed>::sign_bit_mask))
- {
- fixed_int<Bits, Signed> t(a);
- t.negate();
- divide_unsigned_helper(r, t, b, result);
- result.negate();
- }
- else
- {
- divide_unsigned_helper(r, a, b, result);
- }
-}
-template <unsigned Bits, bool Signed>
-inline void eval_modulus(fixed_int<Bits, Signed>& result, const fixed_int<Bits, Signed>& a, signed_limb_type b)
-{
- fixed_int<Bits, Signed> r;
- if(Signed && (a.data()[0] & fixed_int<Bits, Signed>::sign_bit_mask))
- {
- if(b < 0)
- {
- fixed_int<Bits, Signed> t1(a);
- t1.negate();
- divide_unsigned_helper(r, t1, static_cast<limb_type>(-b), result);
- result.negate();
- }
- else
- {
- fixed_int<Bits, Signed> t(a);
- t.negate();
- divide_unsigned_helper(r, t, b, result);
- result.negate();
- }
- }
- else if(b < 0)
- {
- divide_unsigned_helper(r, a, static_cast<limb_type>(-b), result);
- }
- else
- {
- divide_unsigned_helper(r, a, static_cast<limb_type>(b), result);
- }
-}
-template <unsigned Bits, bool Signed>
-inline void eval_modulus(fixed_int<Bits, Signed>& result, const fixed_int<Bits, Signed>& b)
-{
- // There is no in place divide:
- fixed_int<Bits, Signed> a(result);
- eval_modulus(result, a, b);
-}
-template <unsigned Bits, bool Signed>
-inline void eval_modulus(fixed_int<Bits, Signed>& result, limb_type b)
-{
- // There is no in place divide:
- fixed_int<Bits, Signed> a(result);
- eval_modulus(result, a, b);
-}
-template <unsigned Bits, bool Signed>
-inline void eval_modulus(fixed_int<Bits, Signed>& result, signed_limb_type b)
-{
- // There is no in place divide:
- fixed_int<Bits, Signed> a(result);
- eval_modulus(result, a, b);
-}
-
-template <unsigned Bits, bool Signed>
-inline void eval_bitwise_and(fixed_int<Bits, Signed>& result, const fixed_int<Bits, Signed>& o)
-{
- for(typename fixed_int<Bits, Signed>::data_type::size_type i = 0; i < fixed_int<Bits, Signed>::limb_count; ++i)
- result.data()[i] &= o.data()[i];
-}
-template <unsigned Bits, bool Signed>
-inline void eval_bitwise_and(fixed_int<Bits, Signed>& result, limb_type o)
-{
- result.data()[fixed_int<Bits, Signed>::limb_count - 1] &= o;
- for(typename fixed_int<Bits, Signed>::data_type::size_type i = 0; i < fixed_int<Bits, Signed>::limb_count - 1; ++i)
- result.data()[i] = 0;
-}
-template <unsigned Bits, bool Signed>
-inline void eval_bitwise_and(fixed_int<Bits, Signed>& result, signed_limb_type o)
-{
- result.data()[fixed_int<Bits, Signed>::limb_count - 1] &= o;
- limb_type mask = o < 0 ? fixed_int<Bits, Signed>::max_limb_value : 0;
- for(typename fixed_int<Bits, Signed>::data_type::size_type i = 0; i < fixed_int<Bits, Signed>::limb_count - 1; ++i)
- result.data()[i] &= mask;
-}
-template <unsigned Bits, bool Signed>
-inline void eval_bitwise_or(fixed_int<Bits, Signed>& result, const fixed_int<Bits, Signed>& o)
-{
- for(typename fixed_int<Bits, Signed>::data_type::size_type i = 0; i < fixed_int<Bits, Signed>::limb_count; ++i)
- result.data()[i] |= o.data()[i];
-}
-template <unsigned Bits, bool Signed>
-inline void eval_bitwise_or(fixed_int<Bits, Signed>& result, limb_type o)
-{
- result.data()[fixed_int<Bits, Signed>::limb_count - 1] |= o;
-}
-template <unsigned Bits, bool Signed>
-inline void eval_bitwise_or(fixed_int<Bits, Signed>& result, signed_limb_type o)
-{
- result.data()[fixed_int<Bits, Signed>::limb_count - 1] |= o;
- limb_type mask = o < 0 ? fixed_int<Bits, Signed>::max_limb_value : 0;
- for(typename fixed_int<Bits, Signed>::data_type::size_type i = 0; i < fixed_int<Bits, Signed>::limb_count - 1; ++i)
- result.data()[i] |= mask;
-}
-template <unsigned Bits, bool Signed>
-inline void eval_bitwise_xor(fixed_int<Bits, Signed>& result, const fixed_int<Bits, Signed>& o)
-{
- for(typename fixed_int<Bits, Signed>::data_type::size_type i = 0; i < fixed_int<Bits, Signed>::limb_count; ++i)
- result.data()[i] ^= o.data()[i];
- result.data()[0] &= fixed_int<Bits, Signed>::upper_limb_mask;
-}
-template <unsigned Bits, bool Signed>
-inline void eval_bitwise_xor(fixed_int<Bits, Signed>& result, limb_type o)
-{
- result.data()[fixed_int<Bits, Signed>::limb_count - 1] ^= o;
-}
-template <unsigned Bits, bool Signed>
-inline void eval_bitwise_xor(fixed_int<Bits, Signed>& result, signed_limb_type o)
-{
- result.data()[fixed_int<Bits, Signed>::limb_count - 1] ^= o;
- limb_type mask = o < 0 ? fixed_int<Bits, Signed>::max_limb_value : 0;
- for(typename fixed_int<Bits, Signed>::data_type::size_type i = 0; i < fixed_int<Bits, Signed>::limb_count - 1; ++i)
- result.data()[i] ^= mask;
-}
-template <unsigned Bits, bool Signed>
-inline void eval_complement(fixed_int<Bits, Signed>& result, const fixed_int<Bits, Signed>& o)
-{
- for(typename fixed_int<Bits, Signed>::data_type::size_type i = 0; i < fixed_int<Bits, Signed>::limb_count; ++i)
- result.data()[i] = ~o.data()[i];
- result.data()[0] &= fixed_int<Bits, Signed>::upper_limb_mask;
-}
-template <unsigned Bits, bool Signed>
-inline void eval_left_shift(fixed_int<Bits, Signed>& result, double_limb_type s)
-{
- if(!s)
- return;
- if(s >= Bits)
- {
- result = static_cast<limb_type>(0);
- return;
- }
- limb_type offset = static_cast<limb_type>(s / fixed_int<Bits, Signed>::limb_bits);
- limb_type shift = static_cast<limb_type>(s % fixed_int<Bits, Signed>::limb_bits);
- unsigned i = 0;
- if(shift)
- {
- // This code only works when shift is non-zero, otherwise we invoke undefined behaviour!
- for(; i + offset + 1 < fixed_int<Bits, Signed>::limb_count; ++i)
- {
- result.data()[i] = result.data()[i+offset] << shift;
- result.data()[i] |= result.data()[i+offset+1] >> (fixed_int<Bits, Signed>::limb_bits - shift);
- }
- result.data()[i] = result.data()[i+offset] << shift;
- ++i;
- for(; i < fixed_int<Bits, Signed>::limb_count; ++i)
- result.data()[i] = 0;
- }
- else
- {
- for(; i + offset < fixed_int<Bits, Signed>::limb_count; ++i)
- result.data()[i] = result.data()[i+offset];
- for(; i < fixed_int<Bits, Signed>::limb_count; ++i)
- result.data()[i] = 0;
- }
- result.data()[0] &= fixed_int<Bits, Signed>::upper_limb_mask;
-}
-template <unsigned Bits, bool Signed>
-inline void eval_right_shift(fixed_int<Bits, Signed>& result, double_limb_type s)
-{
- if(!s)
- return;
- limb_type fill = (Signed && (result.data()[0] & fixed_int<Bits, Signed>::sign_bit_mask)) ? fixed_int<Bits, Signed>::max_limb_value : 0u;
- if(s >= Bits)
- {
- for(unsigned i = 0; i < fixed_int<Bits, Signed>::limb_count; ++i)
- result.data()[i] = fill;
- return;
- }
- limb_type offset = static_cast<limb_type>(s / fixed_int<Bits, Signed>::limb_bits);
- limb_type shift = static_cast<limb_type>(s % fixed_int<Bits, Signed>::limb_bits);
- int i = fixed_int<Bits, Signed>::limb_count - 1;
- if(shift)
- {
- // This code only works for non-zero shift, otherwise we invoke undefined behaviour!
- if(fill && (Bits % fixed_int<Bits, Signed>::limb_bits))
- {
- // We need to sign extend the leftmost bits, otherwise we may shift zeros into the result:
- result.data()[0] |= fill << (Bits % fixed_int<Bits, Signed>::limb_bits);
- }
- for(; i - offset > 0; --i)
- {
- result.data()[i] = result.data()[i-offset] >> shift;
- result.data()[i] |= result.data()[i-offset-1] << (fixed_int<Bits, Signed>::limb_bits - shift);
- }
- result.data()[i] = result.data()[i+offset] >> shift;
- result.data()[i] |= fill << (fixed_int<Bits, Signed>::limb_bits - shift);
- --i;
- for(; i >= 0; --i)
- result.data()[i] = fill;
- }
- else
- {
- for(; i - offset > 0; --i)
- result.data()[i] = result.data()[i - offset];
- for(; i >= 0; --i)
- result.data()[i] = fill;
- }
- result.data()[0] &= fixed_int<Bits, Signed>::upper_limb_mask;
-}
-
-template <class R, unsigned Bits, bool Signed>
-inline typename enable_if<is_integral<R>, void>::type eval_convert_to(R* result, const fixed_int<Bits, Signed>& backend, const mpl::true_&)
-{
- if(backend.data()[0] & fixed_int<Bits, Signed>::sign_bit_mask)
- {
- fixed_int<Bits, Signed> t(backend);
- t.negate();
- eval_convert_to(result, t, mpl::false_());
- *result = -*result;
- return;
- }
- else
- eval_convert_to(result, backend, mpl::false_());
-}
-
-template <class R, unsigned Bits, bool Signed>
-inline typename enable_if<is_integral<R>, void>::type eval_convert_to(R* result, const fixed_int<Bits, Signed>& backend, const mpl::false_&)
-{
- unsigned shift = (fixed_int<Bits, Signed>::limb_count - 1) * fixed_int<Bits, Signed>::limb_bits;
- *result = static_cast<limb_type>(0);
- for(unsigned i = 0; i < fixed_int<Bits, Signed>::limb_count; ++i)
- {
- *result += static_cast<R>(backend.data()[i]) << shift;
- shift -= fixed_int<Bits, Signed>::limb_bits;
- }
-}
-
-template <class R, unsigned Bits, bool Signed>
-inline typename enable_if<is_integral<R>, void>::type eval_convert_to(R* result, const fixed_int<Bits, Signed>& backend)
-{
- typedef mpl::bool_<Signed && std::numeric_limits<R>::is_signed> tag_type;
- eval_convert_to(result, backend, tag_type());
-}
-
-template <class R, unsigned Bits, bool Signed>
-inline typename enable_if<is_floating_point<R>, void>::type eval_convert_to(R* result, const fixed_int<Bits, Signed>& backend)
-{
- if(Signed && (backend.data()[0] & fixed_int<Bits, Signed>::sign_bit_mask))
- {
- fixed_int<Bits, Signed> t(backend);
- t.negate();
- eval_convert_to(result, t);
- *result = -*result;
- return;
- }
- unsigned shift = (fixed_int<Bits, Signed>::limb_count - 1) * fixed_int<Bits, Signed>::limb_bits;
- *result = static_cast<limb_type>(0);
- for(unsigned i = 0; i < fixed_int<Bits, Signed>::limb_count; ++i)
- {
- *result += static_cast<R>(std::ldexp(static_cast<double>(backend.data()[i]), shift));
- shift -= fixed_int<Bits, Signed>::limb_bits;
- }
-}
-
-template <unsigned Bits, bool Signed>
-inline bool eval_is_zero(const fixed_int<Bits, Signed>& val)
-{
- for(typename fixed_int<Bits, Signed>::data_type::size_type i = 0; i < fixed_int<Bits, Signed>::limb_count; ++i)
- {
- if(val.data()[i])
- return false;
- }
- return true;
-}
-template <unsigned Bits>
-inline int eval_get_sign(const fixed_int<Bits, false>& val)
-{
- return eval_is_zero(val) ? 0 : 1;
-}
-template <unsigned Bits>
-inline int eval_get_sign(const fixed_int<Bits, true>& val)
-{
- return eval_is_zero(val) ? 0 : val.data()[0] & fixed_int<Bits, true>::sign_bit_mask ? -1 : 1;
-}
-
-namespace detail{
-//
-// Get the location of the least-significant-bit:
-//
-template <unsigned Bits, bool Signed>
-inline unsigned get_lsb(const fixed_int<Bits, Signed>& a)
-{
- BOOST_ASSERT(eval_get_sign(a) != 0);
-
- unsigned result = 0;
- //
- // Find the index of the least significant limb that is non-zero:
- //
- int index = fixed_int<Bits, Signed>::limb_count - 1;
- while(!a.data()[index] && index)
- --index;
- //
- // Find the index of the least significant bit within that limb:
- //
- limb_type l = a.data()[index];
- while(!(l & 1u))
- {
- l >>= 1;
- ++result;
- }
-
- return result + (fixed_int<Bits, Signed>::limb_count - 1 - index) * fixed_int<Bits, Signed>::limb_bits;
-}
-
-}
-
-template <unsigned Bits, bool Signed>
-inline void eval_gcd(fixed_int<Bits, Signed>& result, const fixed_int<Bits, Signed>& a, const fixed_int<Bits, Signed>& b)
-{
- int shift;
-
- fixed_int<Bits, Signed> 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 = detail::get_lsb(u);
- unsigned vs = detail::get_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. */
- if(u.compare(v) > 0)
- u.swap(v);
- eval_subtract(v, u);
- // Termination condition tries not to do a full compare if possible:
- if(!v.data()[fixed_int<Bits, Signed>::limb_count - 1] && eval_is_zero(v))
- break;
- vs = detail::get_lsb(v);
- eval_right_shift(v, vs);
- BOOST_ASSERT((v.data()[fixed_int<Bits, Signed>::limb_count - 1] & 1));
- BOOST_ASSERT((u.data()[fixed_int<Bits, Signed>::limb_count - 1] & 1));
- }
- while(true);
-
- result = u;
- eval_left_shift(result, shift);
-}
-
-template <unsigned Bits, bool Signed>
-inline void eval_lcm(fixed_int<Bits, Signed>& result, const fixed_int<Bits, Signed>& a, const fixed_int<Bits, Signed>& b)
-{
- fixed_int<Bits, Signed> t;
- eval_gcd(t, a, b);
-
- if(eval_is_zero(t))
- {
- result = static_cast<limb_type>(0);
- }
- else
- {
- eval_divide(result, a, t);
- eval_multiply(result, b);
- }
- if(eval_get_sign(result) < 0)
- result.negate();
-}
-
-template <unsigned Bits, bool Signed>
-struct number_category<fixed_int<Bits, Signed> > : public mpl::int_<number_kind_integer>{};
-
-typedef mp_number<fixed_int<128, false> > mp_uint128_t;
-typedef mp_number<fixed_int<256, false> > mp_uint256_t;
-typedef mp_number<fixed_int<512, false> > mp_uint512_t;
-
-typedef mp_number<fixed_int<128, true> > mp_int128_t;
-typedef mp_number<fixed_int<256, true> > mp_int256_t;
-typedef mp_number<fixed_int<512, true> > mp_int512_t;
-
-}} // namespaces
-
-
-namespace std{
-
-template <unsigned Bits, bool Signed, bool ExpressionTemplates>
-class numeric_limits<boost::multiprecision::mp_number<boost::multiprecision::fixed_int<Bits, Signed>, ExpressionTemplates> >
-{
- typedef boost::multiprecision::mp_number<boost::multiprecision::fixed_int<Bits, Signed>, ExpressionTemplates> number_type;
-
- struct initializer
- {
- initializer()
- {
- (std::numeric_limits<boost::multiprecision::mp_number<boost::multiprecision::fixed_int<Bits, Signed> > >::min)();
- (std::numeric_limits<boost::multiprecision::mp_number<boost::multiprecision::fixed_int<Bits, Signed> > >::max)();
- }
- void do_nothing()const{}
- };
- static const initializer init;
-public:
- BOOST_STATIC_CONSTEXPR bool is_specialized = true;
- //
- // Largest and smallest numbers are bounded only by available memory, set
- // to zero:
- //
- BOOST_STATIC_CONSTEXPR number_type (min)() BOOST_MP_NOEXCEPT
- {
- static bool init = false;
- static number_type val;
- if(!init)
- {
- init = true;
- val = Signed ? number_type(number_type(1) << (Bits - 1)) : 0;
- }
- return val;
- }
- BOOST_STATIC_CONSTEXPR number_type (max)() BOOST_MP_NOEXCEPT
- {
- static bool init = false;
- static number_type val;
- if(!init)
- {
- init = true;
- val = Signed ? number_type(~(number_type(1) << Bits - 1)) : number_type(~number_type(0));
- }
- return val;
- }
- BOOST_STATIC_CONSTEXPR number_type lowest() BOOST_MP_NOEXCEPT { return (min)(); }
- BOOST_STATIC_CONSTEXPR int digits = Bits;
- BOOST_STATIC_CONSTEXPR int digits10 = (digits * 301L) / 1000;
- BOOST_STATIC_CONSTEXPR int max_digits10 = digits10 + 2;
- BOOST_STATIC_CONSTEXPR bool is_signed = Signed;
- BOOST_STATIC_CONSTEXPR bool is_integer = true;
- BOOST_STATIC_CONSTEXPR bool is_exact = true;
- BOOST_STATIC_CONSTEXPR int radix = 2;
- BOOST_STATIC_CONSTEXPR number_type epsilon() BOOST_MP_NOEXCEPT { return 0; }
- BOOST_STATIC_CONSTEXPR number_type round_error() BOOST_MP_NOEXCEPT { return 0; }
- BOOST_STATIC_CONSTEXPR int min_exponent = 0;
- BOOST_STATIC_CONSTEXPR int min_exponent10 = 0;
- BOOST_STATIC_CONSTEXPR int max_exponent = 0;
- BOOST_STATIC_CONSTEXPR int max_exponent10 = 0;
- BOOST_STATIC_CONSTEXPR bool has_infinity = false;
- BOOST_STATIC_CONSTEXPR bool has_quiet_NaN = false;
- BOOST_STATIC_CONSTEXPR bool has_signaling_NaN = false;
- BOOST_STATIC_CONSTEXPR float_denorm_style has_denorm = denorm_absent;
- BOOST_STATIC_CONSTEXPR bool has_denorm_loss = false;
- BOOST_STATIC_CONSTEXPR number_type infinity() BOOST_MP_NOEXCEPT { return 0; }
- BOOST_STATIC_CONSTEXPR number_type quiet_NaN() BOOST_MP_NOEXCEPT { return 0; }
- BOOST_STATIC_CONSTEXPR number_type signaling_NaN() BOOST_MP_NOEXCEPT { return 0; }
- BOOST_STATIC_CONSTEXPR number_type denorm_min() BOOST_MP_NOEXCEPT { return 0; }
- BOOST_STATIC_CONSTEXPR bool is_iec559 = false;
- BOOST_STATIC_CONSTEXPR bool is_bounded = true;
- BOOST_STATIC_CONSTEXPR bool is_modulo = true;
- BOOST_STATIC_CONSTEXPR bool traps = false;
- BOOST_STATIC_CONSTEXPR bool tinyness_before = false;
- BOOST_STATIC_CONSTEXPR float_round_style round_style = round_toward_zero;
-};
-
-template <unsigned Bits, bool Signed, bool ExpressionTemplates>
-typename numeric_limits<boost::multiprecision::mp_number<boost::multiprecision::fixed_int<Bits, Signed>, ExpressionTemplates> >::initializer const
- numeric_limits<boost::multiprecision::mp_number<boost::multiprecision::fixed_int<Bits, Signed>, ExpressionTemplates> >::init;
-}
-
-#endif
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