810 lines
26 KiB
Plaintext
810 lines
26 KiB
Plaintext
// Copyright John Maddock 2008.
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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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//
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// Wrapper that works with mpfr_class defined in gmpfrxx.h
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// See http://math.berkeley.edu/~wilken/code/gmpfrxx/
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// Also requires the gmp and mpfr libraries.
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//
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#ifndef BOOST_MATH_E_FLOAT_BINDINGS_HPP
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#define BOOST_MATH_E_FLOAT_BINDINGS_HPP
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#include <boost/config.hpp>
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#include <e_float/e_float.h>
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#include <functions/functions.h>
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#include <boost/math/tools/precision.hpp>
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#include <boost/math/tools/real_cast.hpp>
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#include <boost/math/policies/policy.hpp>
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#include <boost/math/distributions/fwd.hpp>
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#include <boost/math/special_functions/math_fwd.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 <boost/lexical_cast.hpp>
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namespace boost{ namespace math{ namespace ef{
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class e_float
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{
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public:
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// Constructors:
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e_float() {}
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e_float(const ::e_float& c) : m_value(c){}
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e_float(char c)
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{
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m_value = ::e_float(c);
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}
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#ifndef BOOST_NO_INTRINSIC_WCHAR_T
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e_float(wchar_t c)
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{
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m_value = ::e_float(c);
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}
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#endif
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e_float(unsigned char c)
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{
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m_value = ::e_float(c);
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}
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e_float(signed char c)
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{
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m_value = ::e_float(c);
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}
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e_float(unsigned short c)
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{
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m_value = ::e_float(c);
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}
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e_float(short c)
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{
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m_value = ::e_float(c);
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}
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e_float(unsigned int c)
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{
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m_value = ::e_float(c);
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}
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e_float(int c)
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{
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m_value = ::e_float(c);
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}
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e_float(unsigned long c)
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{
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m_value = ::e_float((UINT64)c);
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}
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e_float(long c)
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{
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m_value = ::e_float((INT64)c);
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}
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#ifdef BOOST_HAS_LONG_LONG
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e_float(boost::ulong_long_type c)
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{
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m_value = ::e_float(c);
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}
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e_float(boost::long_long_type c)
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{
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m_value = ::e_float(c);
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}
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#endif
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e_float(float c)
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{
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assign_large_real(c);
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}
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e_float(double c)
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{
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assign_large_real(c);
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}
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e_float(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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e_float& operator=(char c) { m_value = ::e_float(c); return *this; }
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e_float& operator=(unsigned char c) { m_value = ::e_float(c); return *this; }
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e_float& operator=(signed char c) { m_value = ::e_float(c); return *this; }
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#ifndef BOOST_NO_INTRINSIC_WCHAR_T
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e_float& operator=(wchar_t c) { m_value = ::e_float(c); return *this; }
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#endif
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e_float& operator=(short c) { m_value = ::e_float(c); return *this; }
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e_float& operator=(unsigned short c) { m_value = ::e_float(c); return *this; }
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e_float& operator=(int c) { m_value = ::e_float(c); return *this; }
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e_float& operator=(unsigned int c) { m_value = ::e_float(c); return *this; }
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e_float& operator=(long c) { m_value = ::e_float((INT64)c); return *this; }
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e_float& operator=(unsigned long c) { m_value = ::e_float((UINT64)c); return *this; }
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#ifdef BOOST_HAS_LONG_LONG
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e_float& operator=(boost::long_long_type c) { m_value = ::e_float(c); return *this; }
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e_float& operator=(boost::ulong_long_type c) { m_value = ::e_float(c); return *this; }
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#endif
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e_float& operator=(float c) { assign_large_real(c); return *this; }
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e_float& operator=(double c) { assign_large_real(c); return *this; }
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e_float& operator=(long double c) { assign_large_real(c); return *this; }
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// Access:
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::e_float& value(){ return m_value; }
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::e_float const& value()const{ return m_value; }
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// Member arithmetic:
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e_float& operator+=(const e_float& other)
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{ m_value += other.value(); return *this; }
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e_float& operator-=(const e_float& other)
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{ m_value -= other.value(); return *this; }
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e_float& operator*=(const e_float& other)
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{ m_value *= other.value(); return *this; }
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e_float& operator/=(const e_float& other)
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{ m_value /= other.value(); return *this; }
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e_float operator-()const
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{ return -m_value; }
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e_float const& operator+()const
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{ return *this; }
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private:
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::e_float 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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m_value = ::ef::zero();
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return;
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}
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if (a == 1) {
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m_value = ::ef::one();
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return;
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}
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if ((boost::math::isinf)(a))
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{
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m_value = a > 0 ? m_value.my_value_inf() : -m_value.my_value_inf();
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return;
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}
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if((boost::math::isnan)(a))
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{
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m_value = m_value.my_value_nan();
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return;
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}
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int e;
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long double f, term;
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::e_float t;
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m_value = ::ef::zero();
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f = frexp(a, &e);
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::e_float shift = ::ef::pow2(30);
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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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m_value *= shift;
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m_value += ::e_float(static_cast<INT64>(term));
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f -= term;
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}
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m_value *= ::ef::pow2(e);
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}
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};
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// Non-member arithmetic:
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inline e_float operator+(const e_float& a, const e_float& b)
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{
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e_float result(a);
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result += b;
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return result;
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}
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inline e_float operator-(const e_float& a, const e_float& b)
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{
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e_float result(a);
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result -= b;
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return result;
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}
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inline e_float operator*(const e_float& a, const e_float& b)
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{
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e_float result(a);
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result *= b;
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return result;
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}
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inline e_float operator/(const e_float& a, const e_float& b)
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{
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e_float 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 e_float& a, const e_float& b)
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{ return a.value() == b.value() ? true : false; }
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inline bool operator != (const e_float& a, const e_float& b)
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{ return a.value() != b.value() ? true : false;}
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inline bool operator < (const e_float& a, const e_float& b)
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{ return a.value() < b.value() ? true : false; }
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inline bool operator <= (const e_float& a, const e_float& b)
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{ return a.value() <= b.value() ? true : false; }
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inline bool operator > (const e_float& a, const e_float& b)
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{ return a.value() > b.value() ? true : false; }
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inline bool operator >= (const e_float& a, const e_float& b)
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{ return a.value() >= b.value() ? true : false; }
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std::istream& operator >> (std::istream& is, e_float& f)
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{
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return is >> f.value();
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}
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std::ostream& operator << (std::ostream& os, const e_float& f)
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{
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return os << f.value();
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}
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inline e_float fabs(const e_float& v)
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{
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return ::ef::fabs(v.value());
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}
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inline e_float abs(const e_float& v)
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{
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return ::ef::fabs(v.value());
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}
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inline e_float floor(const e_float& v)
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{
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return ::ef::floor(v.value());
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}
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inline e_float ceil(const e_float& v)
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{
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return ::ef::ceil(v.value());
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}
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inline e_float pow(const e_float& v, const e_float& w)
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{
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return ::ef::pow(v.value(), w.value());
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}
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inline e_float pow(const e_float& v, int i)
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{
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return ::ef::pow(v.value(), ::e_float(i));
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}
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inline e_float exp(const e_float& v)
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{
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return ::ef::exp(v.value());
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}
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inline e_float log(const e_float& v)
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{
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return ::ef::log(v.value());
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}
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inline e_float sqrt(const e_float& v)
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{
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return ::ef::sqrt(v.value());
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}
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inline e_float sin(const e_float& v)
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{
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return ::ef::sin(v.value());
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}
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inline e_float cos(const e_float& v)
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{
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return ::ef::cos(v.value());
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}
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inline e_float tan(const e_float& v)
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{
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return ::ef::tan(v.value());
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}
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inline e_float acos(const e_float& v)
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{
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return ::ef::acos(v.value());
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}
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inline e_float asin(const e_float& v)
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{
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return ::ef::asin(v.value());
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}
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inline e_float atan(const e_float& v)
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{
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return ::ef::atan(v.value());
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}
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inline e_float atan2(const e_float& v, const e_float& u)
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{
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return ::ef::atan2(v.value(), u.value());
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}
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inline e_float ldexp(const e_float& v, int e)
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{
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return v.value() * ::ef::pow2(e);
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}
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inline e_float frexp(const e_float& v, int* expon)
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{
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double d;
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INT64 i;
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v.value().extract_parts(d, i);
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*expon = static_cast<int>(i);
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return v.value() * ::ef::pow2(-i);
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}
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inline e_float sinh (const e_float& x)
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{
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return ::ef::sinh(x.value());
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}
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inline e_float cosh (const e_float& x)
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{
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return ::ef::cosh(x.value());
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}
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inline e_float tanh (const e_float& x)
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{
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return ::ef::tanh(x.value());
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}
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inline e_float asinh (const e_float& x)
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{
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return ::ef::asinh(x.value());
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}
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inline e_float acosh (const e_float& x)
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{
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return ::ef::acosh(x.value());
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}
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inline e_float atanh (const e_float& x)
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{
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return ::ef::atanh(x.value());
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}
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e_float fmod(const e_float& v1, const e_float& v2)
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{
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e_float n;
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if(v1 < 0)
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n = ceil(v1 / v2);
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else
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n = floor(v1 / v2);
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return v1 - n * v2;
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}
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} namespace detail{
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template <>
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inline int fpclassify_imp< boost::math::ef::e_float> BOOST_NO_MACRO_EXPAND(boost::math::ef::e_float x, const generic_tag<true>&)
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{
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if(x.value().isnan())
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return FP_NAN;
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if(x.value().isinf())
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return FP_INFINITE;
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if(x == 0)
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return FP_ZERO;
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return FP_NORMAL;
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}
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} namespace ef{
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template <class Policy>
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inline int itrunc(const e_float& v, const Policy& pol)
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{
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BOOST_MATH_STD_USING
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e_float r = boost::math::trunc(v, pol);
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if(fabs(r) > (std::numeric_limits<int>::max)())
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return static_cast<int>(policies::raise_rounding_error("boost::math::itrunc<%1%>(%1%)", 0, 0, v, pol));
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return static_cast<int>(r.value().extract_int64());
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}
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template <class Policy>
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inline long ltrunc(const e_float& v, const Policy& pol)
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{
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BOOST_MATH_STD_USING
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e_float r = boost::math::trunc(v, pol);
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if(fabs(r) > (std::numeric_limits<long>::max)())
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return static_cast<long>(policies::raise_rounding_error("boost::math::ltrunc<%1%>(%1%)", 0, 0L, v, pol));
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return static_cast<long>(r.value().extract_int64());
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}
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#ifdef BOOST_HAS_LONG_LONG
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template <class Policy>
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inline boost::long_long_type lltrunc(const e_float& v, const Policy& pol)
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{
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BOOST_MATH_STD_USING
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e_float r = boost::math::trunc(v, pol);
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if(fabs(r) > (std::numeric_limits<boost::long_long_type>::max)())
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return static_cast<boost::long_long_type>(policies::raise_rounding_error("boost::math::lltrunc<%1%>(%1%)", 0, v, 0LL, pol).value().extract_int64());
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return static_cast<boost::long_long_type>(r.value().extract_int64());
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}
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#endif
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template <class Policy>
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inline int iround(const e_float& v, const Policy& pol)
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{
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BOOST_MATH_STD_USING
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e_float r = boost::math::round(v, pol);
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if(fabs(r) > (std::numeric_limits<int>::max)())
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return static_cast<int>(policies::raise_rounding_error("boost::math::iround<%1%>(%1%)", 0, v, 0, pol).value().extract_int64());
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return static_cast<int>(r.value().extract_int64());
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}
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template <class Policy>
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inline long lround(const e_float& v, const Policy& pol)
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{
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BOOST_MATH_STD_USING
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e_float r = boost::math::round(v, pol);
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if(fabs(r) > (std::numeric_limits<long>::max)())
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return static_cast<long int>(policies::raise_rounding_error("boost::math::lround<%1%>(%1%)", 0, v, 0L, pol).value().extract_int64());
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return static_cast<long int>(r.value().extract_int64());
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}
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#ifdef BOOST_HAS_LONG_LONG
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template <class Policy>
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inline boost::long_long_type llround(const e_float& v, const Policy& pol)
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{
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BOOST_MATH_STD_USING
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e_float r = boost::math::round(v, pol);
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if(fabs(r) > (std::numeric_limits<boost::long_long_type>::max)())
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return static_cast<boost::long_long_type>(policies::raise_rounding_error("boost::math::llround<%1%>(%1%)", 0, v, 0LL, pol).value().extract_int64());
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return static_cast<boost::long_long_type>(r.value().extract_int64());
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}
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#endif
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}}}
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namespace std{
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template<>
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class numeric_limits< ::boost::math::ef::e_float> : public numeric_limits< ::e_float>
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{
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public:
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static const ::boost::math::ef::e_float (min) (void)
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{
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return (numeric_limits< ::e_float>::min)();
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}
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static const ::boost::math::ef::e_float (max) (void)
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{
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return (numeric_limits< ::e_float>::max)();
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}
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static const ::boost::math::ef::e_float epsilon (void)
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{
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return (numeric_limits< ::e_float>::epsilon)();
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}
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static const ::boost::math::ef::e_float round_error(void)
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{
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return (numeric_limits< ::e_float>::round_error)();
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}
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static const ::boost::math::ef::e_float infinity (void)
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{
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return (numeric_limits< ::e_float>::infinity)();
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}
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static const ::boost::math::ef::e_float quiet_NaN (void)
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{
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return (numeric_limits< ::e_float>::quiet_NaN)();
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}
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//
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// e_float's supplied digits member is wrong
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// - it should be same the same as digits 10
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// - given that radix is 10.
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//
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static const int digits = digits10;
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};
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} // namespace std
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namespace boost{ namespace math{
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namespace policies{
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template <class Policy>
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struct precision< ::boost::math::ef::e_float, Policy>
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{
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typedef typename Policy::precision_type precision_type;
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typedef digits2<((::std::numeric_limits< ::boost::math::ef::e_float>::digits10 + 1) * 1000L) / 301L> digits_2;
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typedef typename mpl::if_c<
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((digits_2::value <= precision_type::value)
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|| (Policy::precision_type::value <= 0)),
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// Default case, full precision for RealType:
|
|
digits_2,
|
|
// User customised precision:
|
|
precision_type
|
|
>::type type;
|
|
};
|
|
|
|
}
|
|
|
|
namespace tools{
|
|
|
|
template <>
|
|
inline int digits< ::boost::math::ef::e_float>(BOOST_MATH_EXPLICIT_TEMPLATE_TYPE_SPEC( ::boost::math::ef::e_float))
|
|
{
|
|
return ((::std::numeric_limits< ::boost::math::ef::e_float>::digits10 + 1) * 1000L) / 301L;
|
|
}
|
|
|
|
template <>
|
|
inline ::boost::math::ef::e_float root_epsilon< ::boost::math::ef::e_float>()
|
|
{
|
|
return detail::root_epsilon_imp(static_cast< ::boost::math::ef::e_float const*>(0), mpl::int_<0>());
|
|
}
|
|
|
|
template <>
|
|
inline ::boost::math::ef::e_float forth_root_epsilon< ::boost::math::ef::e_float>()
|
|
{
|
|
return detail::forth_root_epsilon_imp(static_cast< ::boost::math::ef::e_float const*>(0), mpl::int_<0>());
|
|
}
|
|
|
|
}
|
|
|
|
namespace lanczos{
|
|
|
|
template<class Policy>
|
|
struct lanczos<boost::math::ef::e_float, Policy>
|
|
{
|
|
typedef typename mpl::if_c<
|
|
std::numeric_limits< ::e_float>::digits10 < 22,
|
|
lanczos13UDT,
|
|
typename mpl::if_c<
|
|
std::numeric_limits< ::e_float>::digits10 < 36,
|
|
lanczos22UDT,
|
|
typename mpl::if_c<
|
|
std::numeric_limits< ::e_float>::digits10 < 50,
|
|
lanczos31UDT,
|
|
typename mpl::if_c<
|
|
std::numeric_limits< ::e_float>::digits10 < 110,
|
|
lanczos61UDT,
|
|
undefined_lanczos
|
|
>::type
|
|
>::type
|
|
>::type
|
|
>::type type;
|
|
};
|
|
|
|
} // namespace lanczos
|
|
|
|
template <class Policy>
|
|
inline boost::math::ef::e_float skewness(const extreme_value_distribution<boost::math::ef::e_float, Policy>& /*dist*/)
|
|
{
|
|
//
|
|
// This is 12 * sqrt(6) * zeta(3) / pi^3:
|
|
// See http://mathworld.wolfram.com/ExtremeValueDistribution.html
|
|
//
|
|
return boost::lexical_cast<boost::math::ef::e_float>("1.1395470994046486574927930193898461120875997958366");
|
|
}
|
|
|
|
template <class Policy>
|
|
inline boost::math::ef::e_float skewness(const rayleigh_distribution<boost::math::ef::e_float, Policy>& /*dist*/)
|
|
{
|
|
// using namespace boost::math::constants;
|
|
return boost::lexical_cast<boost::math::ef::e_float>("0.63111065781893713819189935154422777984404221106391");
|
|
// Computed using NTL at 150 bit, about 50 decimal digits.
|
|
// return 2 * root_pi<RealType>() * pi_minus_three<RealType>() / pow23_four_minus_pi<RealType>();
|
|
}
|
|
|
|
template <class Policy>
|
|
inline boost::math::ef::e_float kurtosis(const rayleigh_distribution<boost::math::ef::e_float, Policy>& /*dist*/)
|
|
{
|
|
// using namespace boost::math::constants;
|
|
return boost::lexical_cast<boost::math::ef::e_float>("3.2450893006876380628486604106197544154170667057995");
|
|
// Computed using NTL at 150 bit, about 50 decimal digits.
|
|
// return 3 - (6 * pi<RealType>() * pi<RealType>() - 24 * pi<RealType>() + 16) /
|
|
// (four_minus_pi<RealType>() * four_minus_pi<RealType>());
|
|
}
|
|
|
|
template <class Policy>
|
|
inline boost::math::ef::e_float kurtosis_excess(const rayleigh_distribution<boost::math::ef::e_float, Policy>& /*dist*/)
|
|
{
|
|
//using namespace boost::math::constants;
|
|
// Computed using NTL at 150 bit, about 50 decimal digits.
|
|
return boost::lexical_cast<boost::math::ef::e_float>("0.2450893006876380628486604106197544154170667057995");
|
|
// return -(6 * pi<RealType>() * pi<RealType>() - 24 * pi<RealType>() + 16) /
|
|
// (four_minus_pi<RealType>() * four_minus_pi<RealType>());
|
|
} // kurtosis
|
|
|
|
namespace detail{
|
|
|
|
//
|
|
// Version of Digamma accurate to ~100 decimal digits.
|
|
//
|
|
template <class Policy>
|
|
boost::math::ef::e_float digamma_imp(boost::math::ef::e_float x, const mpl::int_<0>* , const Policy& pol)
|
|
{
|
|
//
|
|
// This handles reflection of negative arguments, and all our
|
|
// eboost::math::ef::e_floator handling, then forwards to the T-specific approximation.
|
|
//
|
|
BOOST_MATH_STD_USING // ADL of std functions.
|
|
|
|
boost::math::ef::e_float result = 0;
|
|
//
|
|
// Check for negative arguments and use reflection:
|
|
//
|
|
if(x < 0)
|
|
{
|
|
// Reflect:
|
|
x = 1 - x;
|
|
// Argument reduction for tan:
|
|
boost::math::ef::e_float 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<boost::math::ef::e_float>("boost::math::digamma<%1%>(%1%)", 0, (1-x), pol);
|
|
}
|
|
result = constants::pi<boost::math::ef::e_float>() / tan(constants::pi<boost::math::ef::e_float>() * remainder);
|
|
}
|
|
result += big_digamma(x);
|
|
return result;
|
|
}
|
|
boost::math::ef::e_float bessel_i0(boost::math::ef::e_float x)
|
|
{
|
|
static const boost::math::ef::e_float P1[] = {
|
|
boost::lexical_cast<boost::math::ef::e_float>("-2.2335582639474375249e+15"),
|
|
boost::lexical_cast<boost::math::ef::e_float>("-5.5050369673018427753e+14"),
|
|
boost::lexical_cast<boost::math::ef::e_float>("-3.2940087627407749166e+13"),
|
|
boost::lexical_cast<boost::math::ef::e_float>("-8.4925101247114157499e+11"),
|
|
boost::lexical_cast<boost::math::ef::e_float>("-1.1912746104985237192e+10"),
|
|
boost::lexical_cast<boost::math::ef::e_float>("-1.0313066708737980747e+08"),
|
|
boost::lexical_cast<boost::math::ef::e_float>("-5.9545626019847898221e+05"),
|
|
boost::lexical_cast<boost::math::ef::e_float>("-2.4125195876041896775e+03"),
|
|
boost::lexical_cast<boost::math::ef::e_float>("-7.0935347449210549190e+00"),
|
|
boost::lexical_cast<boost::math::ef::e_float>("-1.5453977791786851041e-02"),
|
|
boost::lexical_cast<boost::math::ef::e_float>("-2.5172644670688975051e-05"),
|
|
boost::lexical_cast<boost::math::ef::e_float>("-3.0517226450451067446e-08"),
|
|
boost::lexical_cast<boost::math::ef::e_float>("-2.6843448573468483278e-11"),
|
|
boost::lexical_cast<boost::math::ef::e_float>("-1.5982226675653184646e-14"),
|
|
boost::lexical_cast<boost::math::ef::e_float>("-5.2487866627945699800e-18"),
|
|
};
|
|
static const boost::math::ef::e_float Q1[] = {
|
|
boost::lexical_cast<boost::math::ef::e_float>("-2.2335582639474375245e+15"),
|
|
boost::lexical_cast<boost::math::ef::e_float>("7.8858692566751002988e+12"),
|
|
boost::lexical_cast<boost::math::ef::e_float>("-1.2207067397808979846e+10"),
|
|
boost::lexical_cast<boost::math::ef::e_float>("1.0377081058062166144e+07"),
|
|
boost::lexical_cast<boost::math::ef::e_float>("-4.8527560179962773045e+03"),
|
|
boost::lexical_cast<boost::math::ef::e_float>("1.0"),
|
|
};
|
|
static const boost::math::ef::e_float P2[] = {
|
|
boost::lexical_cast<boost::math::ef::e_float>("-2.2210262233306573296e-04"),
|
|
boost::lexical_cast<boost::math::ef::e_float>("1.3067392038106924055e-02"),
|
|
boost::lexical_cast<boost::math::ef::e_float>("-4.4700805721174453923e-01"),
|
|
boost::lexical_cast<boost::math::ef::e_float>("5.5674518371240761397e+00"),
|
|
boost::lexical_cast<boost::math::ef::e_float>("-2.3517945679239481621e+01"),
|
|
boost::lexical_cast<boost::math::ef::e_float>("3.1611322818701131207e+01"),
|
|
boost::lexical_cast<boost::math::ef::e_float>("-9.6090021968656180000e+00"),
|
|
};
|
|
static const boost::math::ef::e_float Q2[] = {
|
|
boost::lexical_cast<boost::math::ef::e_float>("-5.5194330231005480228e-04"),
|
|
boost::lexical_cast<boost::math::ef::e_float>("3.2547697594819615062e-02"),
|
|
boost::lexical_cast<boost::math::ef::e_float>("-1.1151759188741312645e+00"),
|
|
boost::lexical_cast<boost::math::ef::e_float>("1.3982595353892851542e+01"),
|
|
boost::lexical_cast<boost::math::ef::e_float>("-6.0228002066743340583e+01"),
|
|
boost::lexical_cast<boost::math::ef::e_float>("8.5539563258012929600e+01"),
|
|
boost::lexical_cast<boost::math::ef::e_float>("-3.1446690275135491500e+01"),
|
|
boost::lexical_cast<boost::math::ef::e_float>("1.0"),
|
|
};
|
|
boost::math::ef::e_float value, factor, r;
|
|
|
|
BOOST_MATH_STD_USING
|
|
using namespace boost::math::tools;
|
|
|
|
if (x < 0)
|
|
{
|
|
x = -x; // even function
|
|
}
|
|
if (x == 0)
|
|
{
|
|
return static_cast<boost::math::ef::e_float>(1);
|
|
}
|
|
if (x <= 15) // x in (0, 15]
|
|
{
|
|
boost::math::ef::e_float y = x * x;
|
|
value = evaluate_polynomial(P1, y) / evaluate_polynomial(Q1, y);
|
|
}
|
|
else // x in (15, \infty)
|
|
{
|
|
boost::math::ef::e_float y = 1 / x - boost::math::ef::e_float(1) / 15;
|
|
r = evaluate_polynomial(P2, y) / evaluate_polynomial(Q2, y);
|
|
factor = exp(x) / sqrt(x);
|
|
value = factor * r;
|
|
}
|
|
|
|
return value;
|
|
}
|
|
|
|
boost::math::ef::e_float bessel_i1(boost::math::ef::e_float x)
|
|
{
|
|
static const boost::math::ef::e_float P1[] = {
|
|
lexical_cast<boost::math::ef::e_float>("-1.4577180278143463643e+15"),
|
|
lexical_cast<boost::math::ef::e_float>("-1.7732037840791591320e+14"),
|
|
lexical_cast<boost::math::ef::e_float>("-6.9876779648010090070e+12"),
|
|
lexical_cast<boost::math::ef::e_float>("-1.3357437682275493024e+11"),
|
|
lexical_cast<boost::math::ef::e_float>("-1.4828267606612366099e+09"),
|
|
lexical_cast<boost::math::ef::e_float>("-1.0588550724769347106e+07"),
|
|
lexical_cast<boost::math::ef::e_float>("-5.1894091982308017540e+04"),
|
|
lexical_cast<boost::math::ef::e_float>("-1.8225946631657315931e+02"),
|
|
lexical_cast<boost::math::ef::e_float>("-4.7207090827310162436e-01"),
|
|
lexical_cast<boost::math::ef::e_float>("-9.1746443287817501309e-04"),
|
|
lexical_cast<boost::math::ef::e_float>("-1.3466829827635152875e-06"),
|
|
lexical_cast<boost::math::ef::e_float>("-1.4831904935994647675e-09"),
|
|
lexical_cast<boost::math::ef::e_float>("-1.1928788903603238754e-12"),
|
|
lexical_cast<boost::math::ef::e_float>("-6.5245515583151902910e-16"),
|
|
lexical_cast<boost::math::ef::e_float>("-1.9705291802535139930e-19"),
|
|
};
|
|
static const boost::math::ef::e_float Q1[] = {
|
|
lexical_cast<boost::math::ef::e_float>("-2.9154360556286927285e+15"),
|
|
lexical_cast<boost::math::ef::e_float>("9.7887501377547640438e+12"),
|
|
lexical_cast<boost::math::ef::e_float>("-1.4386907088588283434e+10"),
|
|
lexical_cast<boost::math::ef::e_float>("1.1594225856856884006e+07"),
|
|
lexical_cast<boost::math::ef::e_float>("-5.1326864679904189920e+03"),
|
|
lexical_cast<boost::math::ef::e_float>("1.0"),
|
|
};
|
|
static const boost::math::ef::e_float P2[] = {
|
|
lexical_cast<boost::math::ef::e_float>("1.4582087408985668208e-05"),
|
|
lexical_cast<boost::math::ef::e_float>("-8.9359825138577646443e-04"),
|
|
lexical_cast<boost::math::ef::e_float>("2.9204895411257790122e-02"),
|
|
lexical_cast<boost::math::ef::e_float>("-3.4198728018058047439e-01"),
|
|
lexical_cast<boost::math::ef::e_float>("1.3960118277609544334e+00"),
|
|
lexical_cast<boost::math::ef::e_float>("-1.9746376087200685843e+00"),
|
|
lexical_cast<boost::math::ef::e_float>("8.5591872901933459000e-01"),
|
|
lexical_cast<boost::math::ef::e_float>("-6.0437159056137599999e-02"),
|
|
};
|
|
static const boost::math::ef::e_float Q2[] = {
|
|
lexical_cast<boost::math::ef::e_float>("3.7510433111922824643e-05"),
|
|
lexical_cast<boost::math::ef::e_float>("-2.2835624489492512649e-03"),
|
|
lexical_cast<boost::math::ef::e_float>("7.4212010813186530069e-02"),
|
|
lexical_cast<boost::math::ef::e_float>("-8.5017476463217924408e-01"),
|
|
lexical_cast<boost::math::ef::e_float>("3.2593714889036996297e+00"),
|
|
lexical_cast<boost::math::ef::e_float>("-3.8806586721556593450e+00"),
|
|
lexical_cast<boost::math::ef::e_float>("1.0"),
|
|
};
|
|
boost::math::ef::e_float value, factor, r, w;
|
|
|
|
BOOST_MATH_STD_USING
|
|
using namespace boost::math::tools;
|
|
|
|
w = abs(x);
|
|
if (x == 0)
|
|
{
|
|
return static_cast<boost::math::ef::e_float>(0);
|
|
}
|
|
if (w <= 15) // w in (0, 15]
|
|
{
|
|
boost::math::ef::e_float y = x * x;
|
|
r = evaluate_polynomial(P1, y) / evaluate_polynomial(Q1, y);
|
|
factor = w;
|
|
value = factor * r;
|
|
}
|
|
else // w in (15, \infty)
|
|
{
|
|
boost::math::ef::e_float y = 1 / w - boost::math::ef::e_float(1) / 15;
|
|
r = evaluate_polynomial(P2, y) / evaluate_polynomial(Q2, y);
|
|
factor = exp(w) / sqrt(w);
|
|
value = factor * r;
|
|
}
|
|
|
|
if (x < 0)
|
|
{
|
|
value *= -value; // odd function
|
|
}
|
|
return value;
|
|
}
|
|
|
|
} // namespace detail
|
|
|
|
}}
|
|
#endif // BOOST_MATH_E_FLOAT_BINDINGS_HPP
|
|
|