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873 lines
20 KiB
873 lines
20 KiB
// Copyright John Maddock 2007. |
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// Use, modification and distribution are subject to the |
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// Boost Software License, Version 1.0. (See accompanying file |
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// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) |
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#ifndef BOOST_MATH_NTL_RR_HPP |
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#define BOOST_MATH_NTL_RR_HPP |
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#include <boost/config.hpp> |
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#include <boost/limits.hpp> |
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#include <boost/math/tools/real_cast.hpp> |
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#include <boost/math/tools/precision.hpp> |
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#include <boost/math/constants/constants.hpp> |
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#include <boost/math/tools/roots.hpp> |
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#include <boost/math/special_functions/fpclassify.hpp> |
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#include <boost/math/bindings/detail/big_digamma.hpp> |
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#include <boost/math/bindings/detail/big_lanczos.hpp> |
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#include <ostream> |
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#include <istream> |
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#include <boost/config/no_tr1/cmath.hpp> |
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#include <NTL/RR.h> |
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namespace boost{ namespace math{ |
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namespace ntl |
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{ |
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class RR; |
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RR ldexp(RR r, int exp); |
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RR frexp(RR r, int* exp); |
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class RR |
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{ |
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public: |
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// Constructors: |
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RR() {} |
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RR(const ::NTL::RR& c) : m_value(c){} |
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RR(char c) |
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{ |
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m_value = c; |
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} |
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#ifndef BOOST_NO_INTRINSIC_WCHAR_T |
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RR(wchar_t c) |
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{ |
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m_value = c; |
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} |
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#endif |
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RR(unsigned char c) |
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{ |
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m_value = c; |
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} |
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RR(signed char c) |
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{ |
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m_value = c; |
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} |
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RR(unsigned short c) |
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{ |
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m_value = c; |
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} |
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RR(short c) |
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{ |
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m_value = c; |
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} |
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RR(unsigned int c) |
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{ |
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assign_large_int(c); |
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} |
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RR(int c) |
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{ |
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assign_large_int(c); |
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} |
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RR(unsigned long c) |
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{ |
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assign_large_int(c); |
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} |
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RR(long c) |
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{ |
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assign_large_int(c); |
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} |
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#ifdef BOOST_HAS_LONG_LONG |
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RR(boost::ulong_long_type c) |
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{ |
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assign_large_int(c); |
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} |
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RR(boost::long_long_type c) |
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{ |
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assign_large_int(c); |
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} |
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#endif |
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RR(float c) |
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{ |
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m_value = c; |
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} |
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RR(double c) |
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{ |
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m_value = c; |
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} |
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RR(long double c) |
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{ |
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assign_large_real(c); |
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} |
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// Assignment: |
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RR& operator=(char c) { m_value = c; return *this; } |
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RR& operator=(unsigned char c) { m_value = c; return *this; } |
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RR& operator=(signed char c) { m_value = c; return *this; } |
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#ifndef BOOST_NO_INTRINSIC_WCHAR_T |
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RR& operator=(wchar_t c) { m_value = c; return *this; } |
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#endif |
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RR& operator=(short c) { m_value = c; return *this; } |
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RR& operator=(unsigned short c) { m_value = c; return *this; } |
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RR& operator=(int c) { assign_large_int(c); return *this; } |
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RR& operator=(unsigned int c) { assign_large_int(c); return *this; } |
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RR& operator=(long c) { assign_large_int(c); return *this; } |
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RR& operator=(unsigned long c) { assign_large_int(c); return *this; } |
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#ifdef BOOST_HAS_LONG_LONG |
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RR& operator=(boost::long_long_type c) { assign_large_int(c); return *this; } |
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RR& operator=(boost::ulong_long_type c) { assign_large_int(c); return *this; } |
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#endif |
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RR& operator=(float c) { m_value = c; return *this; } |
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RR& operator=(double c) { m_value = c; return *this; } |
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RR& operator=(long double c) { assign_large_real(c); return *this; } |
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// Access: |
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NTL::RR& value(){ return m_value; } |
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NTL::RR const& value()const{ return m_value; } |
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// Member arithmetic: |
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RR& operator+=(const RR& other) |
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{ m_value += other.value(); return *this; } |
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RR& operator-=(const RR& other) |
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{ m_value -= other.value(); return *this; } |
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RR& operator*=(const RR& other) |
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{ m_value *= other.value(); return *this; } |
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RR& operator/=(const RR& other) |
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{ m_value /= other.value(); return *this; } |
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RR operator-()const |
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{ return -m_value; } |
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RR const& operator+()const |
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{ return *this; } |
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// RR compatibity: |
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const ::NTL::ZZ& mantissa() const |
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{ return m_value.mantissa(); } |
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long exponent() const |
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{ return m_value.exponent(); } |
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static void SetPrecision(long p) |
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{ ::NTL::RR::SetPrecision(p); } |
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static long precision() |
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{ return ::NTL::RR::precision(); } |
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static void SetOutputPrecision(long p) |
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{ ::NTL::RR::SetOutputPrecision(p); } |
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static long OutputPrecision() |
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{ return ::NTL::RR::OutputPrecision(); } |
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private: |
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::NTL::RR m_value; |
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template <class V> |
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void assign_large_real(const V& a) |
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{ |
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using std::frexp; |
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using std::ldexp; |
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using std::floor; |
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if (a == 0) { |
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clear(m_value); |
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return; |
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} |
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if (a == 1) { |
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NTL::set(m_value); |
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return; |
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} |
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if (!(boost::math::isfinite)(a)) |
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{ |
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throw std::overflow_error("Cannot construct an instance of NTL::RR with an infinite value."); |
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} |
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int e; |
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long double f, term; |
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::NTL::RR t; |
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clear(m_value); |
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f = frexp(a, &e); |
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while(f) |
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{ |
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// extract 30 bits from f: |
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f = ldexp(f, 30); |
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term = floor(f); |
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e -= 30; |
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conv(t.x, (int)term); |
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t.e = e; |
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m_value += t; |
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f -= term; |
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} |
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} |
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template <class V> |
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void assign_large_int(V a) |
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{ |
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#ifdef BOOST_MSVC |
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#pragma warning(push) |
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#pragma warning(disable:4146) |
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#endif |
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clear(m_value); |
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int exp = 0; |
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NTL::RR t; |
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bool neg = a < V(0) ? true : false; |
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if(neg) |
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a = -a; |
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while(a) |
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{ |
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t = static_cast<double>(a & 0xffff); |
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m_value += ldexp(RR(t), exp).value(); |
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a >>= 16; |
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exp += 16; |
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} |
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if(neg) |
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m_value = -m_value; |
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#ifdef BOOST_MSVC |
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#pragma warning(pop) |
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#endif |
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} |
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}; |
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// Non-member arithmetic: |
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inline RR operator+(const RR& a, const RR& b) |
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{ |
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RR result(a); |
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result += b; |
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return result; |
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} |
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inline RR operator-(const RR& a, const RR& b) |
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{ |
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RR result(a); |
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result -= b; |
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return result; |
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} |
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inline RR operator*(const RR& a, const RR& b) |
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{ |
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RR result(a); |
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result *= b; |
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return result; |
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} |
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inline RR operator/(const RR& a, const RR& b) |
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{ |
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RR result(a); |
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result /= b; |
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return result; |
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} |
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// Comparison: |
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inline bool operator == (const RR& a, const RR& b) |
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{ return a.value() == b.value() ? true : false; } |
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inline bool operator != (const RR& a, const RR& b) |
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{ return a.value() != b.value() ? true : false;} |
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inline bool operator < (const RR& a, const RR& b) |
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{ return a.value() < b.value() ? true : false; } |
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inline bool operator <= (const RR& a, const RR& b) |
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{ return a.value() <= b.value() ? true : false; } |
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inline bool operator > (const RR& a, const RR& b) |
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{ return a.value() > b.value() ? true : false; } |
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inline bool operator >= (const RR& a, const RR& b) |
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{ return a.value() >= b.value() ? true : false; } |
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#if 0 |
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// Non-member mixed compare: |
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template <class T> |
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inline bool operator == (const T& a, const RR& b) |
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{ |
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return a == b.value(); |
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} |
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template <class T> |
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inline bool operator != (const T& a, const RR& b) |
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{ |
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return a != b.value(); |
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} |
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template <class T> |
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inline bool operator < (const T& a, const RR& b) |
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{ |
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return a < b.value(); |
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} |
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template <class T> |
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inline bool operator > (const T& a, const RR& b) |
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{ |
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return a > b.value(); |
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} |
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template <class T> |
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inline bool operator <= (const T& a, const RR& b) |
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{ |
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return a <= b.value(); |
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} |
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template <class T> |
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inline bool operator >= (const T& a, const RR& b) |
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{ |
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return a >= b.value(); |
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} |
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#endif // Non-member mixed compare: |
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// Non-member functions: |
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/* |
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inline RR acos(RR a) |
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{ return ::NTL::acos(a.value()); } |
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*/ |
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inline RR cos(RR a) |
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{ return ::NTL::cos(a.value()); } |
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/* |
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inline RR asin(RR a) |
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{ return ::NTL::asin(a.value()); } |
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inline RR atan(RR a) |
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{ return ::NTL::atan(a.value()); } |
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inline RR atan2(RR a, RR b) |
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{ return ::NTL::atan2(a.value(), b.value()); } |
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*/ |
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inline RR ceil(RR a) |
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{ return ::NTL::ceil(a.value()); } |
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/* |
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inline RR fmod(RR a, RR b) |
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{ return ::NTL::fmod(a.value(), b.value()); } |
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inline RR cosh(RR a) |
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{ return ::NTL::cosh(a.value()); } |
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*/ |
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inline RR exp(RR a) |
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{ return ::NTL::exp(a.value()); } |
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inline RR fabs(RR a) |
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{ return ::NTL::fabs(a.value()); } |
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inline RR abs(RR a) |
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{ return ::NTL::abs(a.value()); } |
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inline RR floor(RR a) |
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{ return ::NTL::floor(a.value()); } |
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/* |
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inline RR modf(RR a, RR* ipart) |
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{ |
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::NTL::RR ip; |
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RR result = modf(a.value(), &ip); |
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*ipart = ip; |
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return result; |
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} |
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inline RR frexp(RR a, int* expon) |
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{ return ::NTL::frexp(a.value(), expon); } |
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inline RR ldexp(RR a, int expon) |
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{ return ::NTL::ldexp(a.value(), expon); } |
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*/ |
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inline RR log(RR a) |
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{ return ::NTL::log(a.value()); } |
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inline RR log10(RR a) |
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{ return ::NTL::log10(a.value()); } |
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/* |
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inline RR tan(RR a) |
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{ return ::NTL::tan(a.value()); } |
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*/ |
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inline RR pow(RR a, RR b) |
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{ return ::NTL::pow(a.value(), b.value()); } |
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inline RR pow(RR a, int b) |
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{ return ::NTL::power(a.value(), b); } |
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inline RR sin(RR a) |
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{ return ::NTL::sin(a.value()); } |
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/* |
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inline RR sinh(RR a) |
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{ return ::NTL::sinh(a.value()); } |
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*/ |
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inline RR sqrt(RR a) |
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{ return ::NTL::sqrt(a.value()); } |
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/* |
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inline RR tanh(RR a) |
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{ return ::NTL::tanh(a.value()); } |
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*/ |
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inline RR pow(const RR& r, long l) |
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{ |
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return ::NTL::power(r.value(), l); |
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} |
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inline RR tan(const RR& a) |
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{ |
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return sin(a)/cos(a); |
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} |
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inline RR frexp(RR r, int* exp) |
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{ |
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*exp = r.value().e; |
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r.value().e = 0; |
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while(r >= 1) |
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{ |
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*exp += 1; |
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r.value().e -= 1; |
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} |
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while(r < 0.5) |
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{ |
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*exp -= 1; |
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r.value().e += 1; |
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} |
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BOOST_ASSERT(r < 1); |
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BOOST_ASSERT(r >= 0.5); |
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return r; |
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} |
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inline RR ldexp(RR r, int exp) |
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{ |
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r.value().e += exp; |
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return r; |
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} |
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// Streaming: |
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template <class charT, class traits> |
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inline std::basic_ostream<charT, traits>& operator<<(std::basic_ostream<charT, traits>& os, const RR& a) |
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{ |
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return os << a.value(); |
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} |
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template <class charT, class traits> |
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inline std::basic_istream<charT, traits>& operator>>(std::basic_istream<charT, traits>& is, RR& a) |
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{ |
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::NTL::RR v; |
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is >> v; |
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a = v; |
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return is; |
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} |
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} // namespace ntl |
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namespace lanczos{ |
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struct ntl_lanczos |
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{ |
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static ntl::RR lanczos_sum(const ntl::RR& z) |
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{ |
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unsigned long p = ntl::RR::precision(); |
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if(p <= 72) |
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return lanczos13UDT::lanczos_sum(z); |
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else if(p <= 120) |
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return lanczos22UDT::lanczos_sum(z); |
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else if(p <= 170) |
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return lanczos31UDT::lanczos_sum(z); |
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else //if(p <= 370) approx 100 digit precision: |
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return lanczos61UDT::lanczos_sum(z); |
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} |
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static ntl::RR lanczos_sum_expG_scaled(const ntl::RR& z) |
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{ |
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unsigned long p = ntl::RR::precision(); |
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if(p <= 72) |
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return lanczos13UDT::lanczos_sum_expG_scaled(z); |
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else if(p <= 120) |
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return lanczos22UDT::lanczos_sum_expG_scaled(z); |
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else if(p <= 170) |
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return lanczos31UDT::lanczos_sum_expG_scaled(z); |
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else //if(p <= 370) approx 100 digit precision: |
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return lanczos61UDT::lanczos_sum_expG_scaled(z); |
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} |
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static ntl::RR lanczos_sum_near_1(const ntl::RR& z) |
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{ |
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unsigned long p = ntl::RR::precision(); |
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if(p <= 72) |
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return lanczos13UDT::lanczos_sum_near_1(z); |
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else if(p <= 120) |
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return lanczos22UDT::lanczos_sum_near_1(z); |
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else if(p <= 170) |
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return lanczos31UDT::lanczos_sum_near_1(z); |
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else //if(p <= 370) approx 100 digit precision: |
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return lanczos61UDT::lanczos_sum_near_1(z); |
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} |
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static ntl::RR lanczos_sum_near_2(const ntl::RR& z) |
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{ |
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unsigned long p = ntl::RR::precision(); |
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if(p <= 72) |
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return lanczos13UDT::lanczos_sum_near_2(z); |
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else if(p <= 120) |
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return lanczos22UDT::lanczos_sum_near_2(z); |
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else if(p <= 170) |
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return lanczos31UDT::lanczos_sum_near_2(z); |
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else //if(p <= 370) approx 100 digit precision: |
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return lanczos61UDT::lanczos_sum_near_2(z); |
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} |
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static ntl::RR g() |
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{ |
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unsigned long p = ntl::RR::precision(); |
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if(p <= 72) |
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return lanczos13UDT::g(); |
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else if(p <= 120) |
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return lanczos22UDT::g(); |
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else if(p <= 170) |
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return lanczos31UDT::g(); |
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else //if(p <= 370) approx 100 digit precision: |
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return lanczos61UDT::g(); |
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} |
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}; |
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template<class Policy> |
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struct lanczos<ntl::RR, Policy> |
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{ |
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typedef ntl_lanczos type; |
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}; |
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} // namespace lanczos |
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namespace tools |
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{ |
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template<> |
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inline int digits<boost::math::ntl::RR>(BOOST_MATH_EXPLICIT_TEMPLATE_TYPE_SPEC(boost::math::ntl::RR)) |
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{ |
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return ::NTL::RR::precision(); |
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} |
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template <> |
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inline float real_cast<float, boost::math::ntl::RR>(boost::math::ntl::RR t) |
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{ |
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double r; |
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conv(r, t.value()); |
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return static_cast<float>(r); |
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} |
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template <> |
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inline double real_cast<double, boost::math::ntl::RR>(boost::math::ntl::RR t) |
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{ |
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double r; |
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conv(r, t.value()); |
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return r; |
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} |
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namespace detail{ |
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template<class I> |
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void convert_to_long_result(NTL::RR const& r, I& result) |
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{ |
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result = 0; |
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I last_result(0); |
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NTL::RR t(r); |
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double term; |
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do |
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{ |
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conv(term, t); |
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last_result = result; |
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result += static_cast<I>(term); |
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t -= term; |
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}while(result != last_result); |
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} |
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} |
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template <> |
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inline long double real_cast<long double, boost::math::ntl::RR>(boost::math::ntl::RR t) |
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{ |
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long double result(0); |
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detail::convert_to_long_result(t.value(), result); |
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return result; |
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} |
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template <> |
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inline boost::math::ntl::RR real_cast<boost::math::ntl::RR, boost::math::ntl::RR>(boost::math::ntl::RR t) |
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{ |
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return t; |
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} |
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template <> |
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inline unsigned real_cast<unsigned, boost::math::ntl::RR>(boost::math::ntl::RR t) |
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{ |
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unsigned result; |
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detail::convert_to_long_result(t.value(), result); |
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return result; |
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} |
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template <> |
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inline int real_cast<int, boost::math::ntl::RR>(boost::math::ntl::RR t) |
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{ |
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int result; |
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detail::convert_to_long_result(t.value(), result); |
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return result; |
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} |
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template <> |
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inline long real_cast<long, boost::math::ntl::RR>(boost::math::ntl::RR t) |
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{ |
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long result; |
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detail::convert_to_long_result(t.value(), result); |
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return result; |
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} |
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template <> |
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inline long long real_cast<long long, boost::math::ntl::RR>(boost::math::ntl::RR t) |
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{ |
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long long result; |
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detail::convert_to_long_result(t.value(), result); |
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return result; |
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} |
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template <> |
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inline boost::math::ntl::RR max_value<boost::math::ntl::RR>(BOOST_MATH_EXPLICIT_TEMPLATE_TYPE_SPEC(boost::math::ntl::RR)) |
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{ |
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static bool has_init = false; |
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static NTL::RR val; |
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if(!has_init) |
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{ |
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val = 1; |
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val.e = NTL_OVFBND-20; |
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has_init = true; |
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} |
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return val; |
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} |
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template <> |
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inline boost::math::ntl::RR min_value<boost::math::ntl::RR>(BOOST_MATH_EXPLICIT_TEMPLATE_TYPE_SPEC(boost::math::ntl::RR)) |
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{ |
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static bool has_init = false; |
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static NTL::RR val; |
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if(!has_init) |
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{ |
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val = 1; |
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val.e = -NTL_OVFBND+20; |
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has_init = true; |
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} |
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return val; |
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} |
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template <> |
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inline boost::math::ntl::RR log_max_value<boost::math::ntl::RR>(BOOST_MATH_EXPLICIT_TEMPLATE_TYPE_SPEC(boost::math::ntl::RR)) |
|
{ |
|
static bool has_init = false; |
|
static NTL::RR val; |
|
if(!has_init) |
|
{ |
|
val = 1; |
|
val.e = NTL_OVFBND-20; |
|
val = log(val); |
|
has_init = true; |
|
} |
|
return val; |
|
} |
|
|
|
template <> |
|
inline boost::math::ntl::RR log_min_value<boost::math::ntl::RR>(BOOST_MATH_EXPLICIT_TEMPLATE_TYPE_SPEC(boost::math::ntl::RR)) |
|
{ |
|
static bool has_init = false; |
|
static NTL::RR val; |
|
if(!has_init) |
|
{ |
|
val = 1; |
|
val.e = -NTL_OVFBND+20; |
|
val = log(val); |
|
has_init = true; |
|
} |
|
return val; |
|
} |
|
|
|
template <> |
|
inline boost::math::ntl::RR epsilon<boost::math::ntl::RR>(BOOST_MATH_EXPLICIT_TEMPLATE_TYPE_SPEC(boost::math::ntl::RR)) |
|
{ |
|
return ldexp(boost::math::ntl::RR(1), 1-boost::math::policies::digits<boost::math::ntl::RR, boost::math::policies::policy<> >()); |
|
} |
|
|
|
} // namespace tools |
|
|
|
// |
|
// The number of digits precision in RR can vary with each call |
|
// so we need to recalculate these with each call: |
|
// |
|
namespace constants{ |
|
|
|
template<> inline boost::math::ntl::RR pi<boost::math::ntl::RR>(BOOST_MATH_EXPLICIT_TEMPLATE_TYPE_SPEC(boost::math::ntl::RR)) |
|
{ |
|
NTL::RR result; |
|
ComputePi(result); |
|
return result; |
|
} |
|
template<> inline boost::math::ntl::RR e<boost::math::ntl::RR>(BOOST_MATH_EXPLICIT_TEMPLATE_TYPE_SPEC(boost::math::ntl::RR)) |
|
{ |
|
NTL::RR result; |
|
result = 1; |
|
return exp(result); |
|
} |
|
|
|
} // namespace constants |
|
|
|
namespace ntl{ |
|
// |
|
// These are some fairly brain-dead versions of the math |
|
// functions that NTL fails to provide. |
|
// |
|
|
|
|
|
// |
|
// Inverse trig functions: |
|
// |
|
struct asin_root |
|
{ |
|
asin_root(RR const& target) : t(target){} |
|
|
|
boost::math::tuple<RR, RR, RR> operator()(RR const& p) |
|
{ |
|
RR f0 = sin(p); |
|
RR f1 = cos(p); |
|
RR f2 = -f0; |
|
f0 -= t; |
|
return boost::math::make_tuple(f0, f1, f2); |
|
} |
|
private: |
|
RR t; |
|
}; |
|
|
|
inline RR asin(RR z) |
|
{ |
|
double r; |
|
conv(r, z.value()); |
|
return boost::math::tools::halley_iterate( |
|
asin_root(z), |
|
RR(std::asin(r)), |
|
RR(-boost::math::constants::pi<RR>()/2), |
|
RR(boost::math::constants::pi<RR>()/2), |
|
NTL::RR::precision()); |
|
} |
|
|
|
struct acos_root |
|
{ |
|
acos_root(RR const& target) : t(target){} |
|
|
|
boost::math::tuple<RR, RR, RR> operator()(RR const& p) |
|
{ |
|
RR f0 = cos(p); |
|
RR f1 = -sin(p); |
|
RR f2 = -f0; |
|
f0 -= t; |
|
return boost::math::make_tuple(f0, f1, f2); |
|
} |
|
private: |
|
RR t; |
|
}; |
|
|
|
inline RR acos(RR z) |
|
{ |
|
double r; |
|
conv(r, z.value()); |
|
return boost::math::tools::halley_iterate( |
|
acos_root(z), |
|
RR(std::acos(r)), |
|
RR(-boost::math::constants::pi<RR>()/2), |
|
RR(boost::math::constants::pi<RR>()/2), |
|
NTL::RR::precision()); |
|
} |
|
|
|
struct atan_root |
|
{ |
|
atan_root(RR const& target) : t(target){} |
|
|
|
boost::math::tuple<RR, RR, RR> operator()(RR const& p) |
|
{ |
|
RR c = cos(p); |
|
RR ta = tan(p); |
|
RR f0 = ta - t; |
|
RR f1 = 1 / (c * c); |
|
RR f2 = 2 * ta / (c * c); |
|
return boost::math::make_tuple(f0, f1, f2); |
|
} |
|
private: |
|
RR t; |
|
}; |
|
|
|
inline RR atan(RR z) |
|
{ |
|
double r; |
|
conv(r, z.value()); |
|
return boost::math::tools::halley_iterate( |
|
atan_root(z), |
|
RR(std::atan(r)), |
|
-boost::math::constants::pi<RR>()/2, |
|
boost::math::constants::pi<RR>()/2, |
|
NTL::RR::precision()); |
|
} |
|
|
|
inline RR sinh(RR z) |
|
{ |
|
return (expm1(z.value()) - expm1(-z.value())) / 2; |
|
} |
|
|
|
inline RR cosh(RR z) |
|
{ |
|
return (exp(z) + exp(-z)) / 2; |
|
} |
|
|
|
inline RR tanh(RR z) |
|
{ |
|
return sinh(z) / cosh(z); |
|
} |
|
|
|
inline RR fmod(RR x, RR y) |
|
{ |
|
// This is a really crummy version of fmod, we rely on lots |
|
// of digits to get us out of trouble... |
|
RR factor = floor(x/y); |
|
return x - factor * y; |
|
} |
|
|
|
template <class Policy> |
|
inline int iround(RR const& x, const Policy& pol) |
|
{ |
|
return tools::real_cast<int>(round(x, pol)); |
|
} |
|
|
|
template <class Policy> |
|
inline long lround(RR const& x, const Policy& pol) |
|
{ |
|
return tools::real_cast<long>(round(x, pol)); |
|
} |
|
|
|
template <class Policy> |
|
inline long long llround(RR const& x, const Policy& pol) |
|
{ |
|
return tools::real_cast<long long>(round(x, pol)); |
|
} |
|
|
|
template <class Policy> |
|
inline int itrunc(RR const& x, const Policy& pol) |
|
{ |
|
return tools::real_cast<int>(trunc(x, pol)); |
|
} |
|
|
|
template <class Policy> |
|
inline long ltrunc(RR const& x, const Policy& pol) |
|
{ |
|
return tools::real_cast<long>(trunc(x, pol)); |
|
} |
|
|
|
template <class Policy> |
|
inline long long lltrunc(RR const& x, const Policy& pol) |
|
{ |
|
return tools::real_cast<long long>(trunc(x, pol)); |
|
} |
|
|
|
} // namespace ntl |
|
|
|
namespace detail{ |
|
|
|
template <class Policy> |
|
ntl::RR digamma_imp(ntl::RR x, const mpl::int_<0>* , const Policy& pol) |
|
{ |
|
// |
|
// This handles reflection of negative arguments, and all our |
|
// error handling, then forwards to the T-specific approximation. |
|
// |
|
BOOST_MATH_STD_USING // ADL of std functions. |
|
|
|
ntl::RR result = 0; |
|
// |
|
// Check for negative arguments and use reflection: |
|
// |
|
if(x < 0) |
|
{ |
|
// Reflect: |
|
x = 1 - x; |
|
// Argument reduction for tan: |
|
ntl::RR remainder = x - floor(x); |
|
// Shift to negative if > 0.5: |
|
if(remainder > 0.5) |
|
{ |
|
remainder -= 1; |
|
} |
|
// |
|
// check for evaluation at a negative pole: |
|
// |
|
if(remainder == 0) |
|
{ |
|
return policies::raise_pole_error<ntl::RR>("boost::math::digamma<%1%>(%1%)", 0, (1-x), pol); |
|
} |
|
result = constants::pi<ntl::RR>() / tan(constants::pi<ntl::RR>() * remainder); |
|
} |
|
result += big_digamma(x); |
|
return result; |
|
} |
|
|
|
} // namespace detail |
|
|
|
} // namespace math |
|
} // namespace boost |
|
|
|
#endif // BOOST_MATH_REAL_CONCEPT_HPP |
|
|
|
|
|
|