885 lines
21 KiB
Plaintext
885 lines
21 KiB
Plaintext
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// 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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|
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r.value().e -= 1;
|
||
|
|
}
|
||
|
|
while(r < 0.5)
|
||
|
|
{
|
||
|
|
*exp -= 1;
|
||
|
|
r.value().e += 1;
|
||
|
|
}
|
||
|
|
BOOST_ASSERT(r < 1);
|
||
|
|
BOOST_ASSERT(r >= 0.5);
|
||
|
|
return r;
|
||
|
|
}
|
||
|
|
inline RR ldexp(RR r, int exp)
|
||
|
|
{
|
||
|
|
r.value().e += exp;
|
||
|
|
return r;
|
||
|
|
}
|
||
|
|
|
||
|
|
// Streaming:
|
||
|
|
template <class charT, class traits>
|
||
|
|
inline std::basic_ostream<charT, traits>& operator<<(std::basic_ostream<charT, traits>& os, const RR& a)
|
||
|
|
{
|
||
|
|
return os << a.value();
|
||
|
|
}
|
||
|
|
template <class charT, class traits>
|
||
|
|
inline std::basic_istream<charT, traits>& operator>>(std::basic_istream<charT, traits>& is, RR& a)
|
||
|
|
{
|
||
|
|
::NTL::RR v;
|
||
|
|
is >> v;
|
||
|
|
a = v;
|
||
|
|
return is;
|
||
|
|
}
|
||
|
|
|
||
|
|
} // namespace ntl
|
||
|
|
|
||
|
|
namespace lanczos{
|
||
|
|
|
||
|
|
struct ntl_lanczos
|
||
|
|
{
|
||
|
|
static ntl::RR lanczos_sum(const ntl::RR& z)
|
||
|
|
{
|
||
|
|
unsigned long p = ntl::RR::precision();
|
||
|
|
if(p <= 72)
|
||
|
|
return lanczos13UDT::lanczos_sum(z);
|
||
|
|
else if(p <= 120)
|
||
|
|
return lanczos22UDT::lanczos_sum(z);
|
||
|
|
else if(p <= 170)
|
||
|
|
return lanczos31UDT::lanczos_sum(z);
|
||
|
|
else //if(p <= 370) approx 100 digit precision:
|
||
|
|
return lanczos61UDT::lanczos_sum(z);
|
||
|
|
}
|
||
|
|
static ntl::RR lanczos_sum_expG_scaled(const ntl::RR& z)
|
||
|
|
{
|
||
|
|
unsigned long p = ntl::RR::precision();
|
||
|
|
if(p <= 72)
|
||
|
|
return lanczos13UDT::lanczos_sum_expG_scaled(z);
|
||
|
|
else if(p <= 120)
|
||
|
|
return lanczos22UDT::lanczos_sum_expG_scaled(z);
|
||
|
|
else if(p <= 170)
|
||
|
|
return lanczos31UDT::lanczos_sum_expG_scaled(z);
|
||
|
|
else //if(p <= 370) approx 100 digit precision:
|
||
|
|
return lanczos61UDT::lanczos_sum_expG_scaled(z);
|
||
|
|
}
|
||
|
|
static ntl::RR lanczos_sum_near_1(const ntl::RR& z)
|
||
|
|
{
|
||
|
|
unsigned long p = ntl::RR::precision();
|
||
|
|
if(p <= 72)
|
||
|
|
return lanczos13UDT::lanczos_sum_near_1(z);
|
||
|
|
else if(p <= 120)
|
||
|
|
return lanczos22UDT::lanczos_sum_near_1(z);
|
||
|
|
else if(p <= 170)
|
||
|
|
return lanczos31UDT::lanczos_sum_near_1(z);
|
||
|
|
else //if(p <= 370) approx 100 digit precision:
|
||
|
|
return lanczos61UDT::lanczos_sum_near_1(z);
|
||
|
|
}
|
||
|
|
static ntl::RR lanczos_sum_near_2(const ntl::RR& z)
|
||
|
|
{
|
||
|
|
unsigned long p = ntl::RR::precision();
|
||
|
|
if(p <= 72)
|
||
|
|
return lanczos13UDT::lanczos_sum_near_2(z);
|
||
|
|
else if(p <= 120)
|
||
|
|
return lanczos22UDT::lanczos_sum_near_2(z);
|
||
|
|
else if(p <= 170)
|
||
|
|
return lanczos31UDT::lanczos_sum_near_2(z);
|
||
|
|
else //if(p <= 370) approx 100 digit precision:
|
||
|
|
return lanczos61UDT::lanczos_sum_near_2(z);
|
||
|
|
}
|
||
|
|
static ntl::RR g()
|
||
|
|
{
|
||
|
|
unsigned long p = ntl::RR::precision();
|
||
|
|
if(p <= 72)
|
||
|
|
return lanczos13UDT::g();
|
||
|
|
else if(p <= 120)
|
||
|
|
return lanczos22UDT::g();
|
||
|
|
else if(p <= 170)
|
||
|
|
return lanczos31UDT::g();
|
||
|
|
else //if(p <= 370) approx 100 digit precision:
|
||
|
|
return lanczos61UDT::g();
|
||
|
|
}
|
||
|
|
};
|
||
|
|
|
||
|
|
template<class Policy>
|
||
|
|
struct lanczos<ntl::RR, Policy>
|
||
|
|
{
|
||
|
|
typedef ntl_lanczos type;
|
||
|
|
};
|
||
|
|
|
||
|
|
} // namespace lanczos
|
||
|
|
|
||
|
|
namespace tools
|
||
|
|
{
|
||
|
|
|
||
|
|
template<>
|
||
|
|
inline int digits<boost::math::ntl::RR>(BOOST_MATH_EXPLICIT_TEMPLATE_TYPE_SPEC(boost::math::ntl::RR))
|
||
|
|
{
|
||
|
|
return ::NTL::RR::precision();
|
||
|
|
}
|
||
|
|
|
||
|
|
template <>
|
||
|
|
inline float real_cast<float, boost::math::ntl::RR>(boost::math::ntl::RR t)
|
||
|
|
{
|
||
|
|
double r;
|
||
|
|
conv(r, t.value());
|
||
|
|
return static_cast<float>(r);
|
||
|
|
}
|
||
|
|
template <>
|
||
|
|
inline double real_cast<double, boost::math::ntl::RR>(boost::math::ntl::RR t)
|
||
|
|
{
|
||
|
|
double r;
|
||
|
|
conv(r, t.value());
|
||
|
|
return r;
|
||
|
|
}
|
||
|
|
|
||
|
|
namespace detail{
|
||
|
|
|
||
|
|
template<class I>
|
||
|
|
void convert_to_long_result(NTL::RR const& r, I& result)
|
||
|
|
{
|
||
|
|
result = 0;
|
||
|
|
I last_result(0);
|
||
|
|
NTL::RR t(r);
|
||
|
|
double term;
|
||
|
|
do
|
||
|
|
{
|
||
|
|
conv(term, t);
|
||
|
|
last_result = result;
|
||
|
|
result += static_cast<I>(term);
|
||
|
|
t -= term;
|
||
|
|
}while(result != last_result);
|
||
|
|
}
|
||
|
|
|
||
|
|
}
|
||
|
|
|
||
|
|
template <>
|
||
|
|
inline long double real_cast<long double, boost::math::ntl::RR>(boost::math::ntl::RR t)
|
||
|
|
{
|
||
|
|
long double result(0);
|
||
|
|
detail::convert_to_long_result(t.value(), result);
|
||
|
|
return result;
|
||
|
|
}
|
||
|
|
template <>
|
||
|
|
inline boost::math::ntl::RR real_cast<boost::math::ntl::RR, boost::math::ntl::RR>(boost::math::ntl::RR t)
|
||
|
|
{
|
||
|
|
return t;
|
||
|
|
}
|
||
|
|
template <>
|
||
|
|
inline unsigned real_cast<unsigned, boost::math::ntl::RR>(boost::math::ntl::RR t)
|
||
|
|
{
|
||
|
|
unsigned result;
|
||
|
|
detail::convert_to_long_result(t.value(), result);
|
||
|
|
return result;
|
||
|
|
}
|
||
|
|
template <>
|
||
|
|
inline int real_cast<int, boost::math::ntl::RR>(boost::math::ntl::RR t)
|
||
|
|
{
|
||
|
|
int result;
|
||
|
|
detail::convert_to_long_result(t.value(), result);
|
||
|
|
return result;
|
||
|
|
}
|
||
|
|
template <>
|
||
|
|
inline long real_cast<long, boost::math::ntl::RR>(boost::math::ntl::RR t)
|
||
|
|
{
|
||
|
|
long result;
|
||
|
|
detail::convert_to_long_result(t.value(), result);
|
||
|
|
return result;
|
||
|
|
}
|
||
|
|
template <>
|
||
|
|
inline long long real_cast<long long, boost::math::ntl::RR>(boost::math::ntl::RR t)
|
||
|
|
{
|
||
|
|
long long result;
|
||
|
|
detail::convert_to_long_result(t.value(), result);
|
||
|
|
return result;
|
||
|
|
}
|
||
|
|
|
||
|
|
template <>
|
||
|
|
inline boost::math::ntl::RR 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;
|
||
|
|
has_init = true;
|
||
|
|
}
|
||
|
|
return val;
|
||
|
|
}
|
||
|
|
|
||
|
|
template <>
|
||
|
|
inline boost::math::ntl::RR 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;
|
||
|
|
has_init = true;
|
||
|
|
}
|
||
|
|
return val;
|
||
|
|
}
|
||
|
|
|
||
|
|
template <>
|
||
|
|
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 atan2(RR y, RR x)
|
||
|
|
{
|
||
|
|
if(x > 0)
|
||
|
|
return atan(y / x);
|
||
|
|
if(x < 0)
|
||
|
|
{
|
||
|
|
return y < 0 ? atan(y / x) - boost::math::constants::pi<RR>() : atan(y / x) + boost::math::constants::pi<RR>();
|
||
|
|
}
|
||
|
|
return y < 0 ? -boost::math::constants::half_pi<RR>() : boost::math::constants::half_pi<RR>() ;
|
||
|
|
}
|
||
|
|
|
||
|
|
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
|
||
|
|
|
||
|
|
|