531 lines
17 KiB
Plaintext
531 lines
17 KiB
Plaintext
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///////////////////////////////////////////////////////////////////////////////
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// Copyright 2011 John Maddock. Distributed under the Boost
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// 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_MP_GENERIC_INTERCONVERT_HPP
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#define BOOST_MP_GENERIC_INTERCONVERT_HPP
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#include <boost/multiprecision/detail/default_ops.hpp>
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#ifdef BOOST_MSVC
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#pragma warning(push)
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#pragma warning(disable:4127 6326)
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#endif
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namespace boost{ namespace multiprecision{ namespace detail{
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template <class To, class From>
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inline To do_cast(const From & from)
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{
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return static_cast<To>(from);
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}
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template <class To, class B, ::boost::multiprecision::expression_template_option et>
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inline To do_cast(const number<B, et>& from)
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{
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return from.template convert_to<To>();
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}
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template <class To, class From>
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void generic_interconvert(To& to, const From& from, const mpl::int_<number_kind_floating_point>& /*to_type*/, const mpl::int_<number_kind_integer>& /*from_type*/)
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{
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using default_ops::eval_get_sign;
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using default_ops::eval_bitwise_and;
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using default_ops::eval_convert_to;
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using default_ops::eval_right_shift;
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using default_ops::eval_ldexp;
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using default_ops::eval_add;
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using default_ops::eval_is_zero;
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// smallest unsigned type handled natively by "From" is likely to be it's limb_type:
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typedef typename canonical<unsigned char, From>::type l_limb_type;
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// get the corresponding type that we can assign to "To":
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typedef typename canonical<l_limb_type, To>::type to_type;
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From t(from);
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bool is_neg = eval_get_sign(t) < 0;
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if(is_neg)
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t.negate();
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// Pick off the first limb:
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l_limb_type limb;
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l_limb_type mask = static_cast<l_limb_type>(~static_cast<l_limb_type>(0));
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From fl;
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eval_bitwise_and(fl, t, mask);
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eval_convert_to(&limb, fl);
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to = static_cast<to_type>(limb);
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eval_right_shift(t, std::numeric_limits<l_limb_type>::digits);
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//
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// Then keep picking off more limbs until "t" is zero:
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//
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To l;
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unsigned shift = std::numeric_limits<l_limb_type>::digits;
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while(!eval_is_zero(t))
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{
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eval_bitwise_and(fl, t, mask);
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eval_convert_to(&limb, fl);
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l = static_cast<to_type>(limb);
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eval_right_shift(t, std::numeric_limits<l_limb_type>::digits);
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eval_ldexp(l, l, shift);
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eval_add(to, l);
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shift += std::numeric_limits<l_limb_type>::digits;
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}
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//
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// Finish off by setting the sign:
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//
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if(is_neg)
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to.negate();
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}
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template <class To, class From>
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void generic_interconvert(To& to, const From& from, const mpl::int_<number_kind_integer>& /*to_type*/, const mpl::int_<number_kind_integer>& /*from_type*/)
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{
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using default_ops::eval_get_sign;
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using default_ops::eval_bitwise_and;
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using default_ops::eval_convert_to;
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using default_ops::eval_right_shift;
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using default_ops::eval_left_shift;
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using default_ops::eval_bitwise_or;
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using default_ops::eval_is_zero;
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// smallest unsigned type handled natively by "From" is likely to be it's limb_type:
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typedef typename canonical<unsigned char, From>::type limb_type;
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// get the corresponding type that we can assign to "To":
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typedef typename canonical<limb_type, To>::type to_type;
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From t(from);
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bool is_neg = eval_get_sign(t) < 0;
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if(is_neg)
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t.negate();
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// Pick off the first limb:
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limb_type limb;
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limb_type mask = static_cast<limb_type>(~static_cast<limb_type>(0));
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From fl;
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eval_bitwise_and(fl, t, mask);
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eval_convert_to(&limb, fl);
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to = static_cast<to_type>(limb);
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eval_right_shift(t, std::numeric_limits<limb_type>::digits);
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//
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// Then keep picking off more limbs until "t" is zero:
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//
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To l;
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unsigned shift = std::numeric_limits<limb_type>::digits;
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while(!eval_is_zero(t))
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{
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eval_bitwise_and(fl, t, mask);
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eval_convert_to(&limb, fl);
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l = static_cast<to_type>(limb);
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eval_right_shift(t, std::numeric_limits<limb_type>::digits);
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eval_left_shift(l, shift);
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eval_bitwise_or(to, l);
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shift += std::numeric_limits<limb_type>::digits;
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}
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//
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// Finish off by setting the sign:
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//
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if(is_neg)
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to.negate();
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}
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template <class To, class From>
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void generic_interconvert(To& to, const From& from, const mpl::int_<number_kind_floating_point>& /*to_type*/, const mpl::int_<number_kind_floating_point>& /*from_type*/)
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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:4127)
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#endif
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//
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// The code here only works when the radix of "From" is 2, we could try shifting by other
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// radixes but it would complicate things.... use a string conversion when the radix is other
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// than 2:
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//
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if(std::numeric_limits<number<From> >::radix != 2)
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{
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to = from.str(0, std::ios_base::fmtflags()).c_str();
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return;
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}
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typedef typename canonical<unsigned char, To>::type ui_type;
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using default_ops::eval_fpclassify;
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using default_ops::eval_add;
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using default_ops::eval_subtract;
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using default_ops::eval_convert_to;
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using default_ops::eval_get_sign;
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using default_ops::eval_is_zero;
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//
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// First classify the input, then handle the special cases:
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//
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int c = eval_fpclassify(from);
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if(c == (int)FP_ZERO)
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{
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to = ui_type(0);
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return;
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}
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else if(c == (int)FP_NAN)
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{
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to = static_cast<const char*>("nan");
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return;
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}
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else if(c == (int)FP_INFINITE)
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{
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to = static_cast<const char*>("inf");
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if(eval_get_sign(from) < 0)
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to.negate();
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return;
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}
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typename From::exponent_type e;
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From f, term;
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to = ui_type(0);
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eval_frexp(f, from, &e);
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static const int shift = std::numeric_limits<boost::intmax_t>::digits - 1;
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while(!eval_is_zero(f))
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{
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// extract int sized bits from f:
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eval_ldexp(f, f, shift);
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eval_floor(term, f);
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e -= shift;
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eval_ldexp(to, to, shift);
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typename boost::multiprecision::detail::canonical<boost::intmax_t, To>::type ll;
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eval_convert_to(&ll, term);
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eval_add(to, ll);
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eval_subtract(f, term);
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}
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typedef typename To::exponent_type to_exponent;
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if((e > (std::numeric_limits<to_exponent>::max)()) || (e < (std::numeric_limits<to_exponent>::min)()))
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{
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to = static_cast<const char*>("inf");
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if(eval_get_sign(from) < 0)
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to.negate();
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return;
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}
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eval_ldexp(to, to, static_cast<to_exponent>(e));
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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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template <class To, class From>
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void generic_interconvert(To& to, const From& from, const mpl::int_<number_kind_rational>& /*to_type*/, const mpl::int_<number_kind_rational>& /*from_type*/)
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{
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typedef typename component_type<number<To> >::type to_component_type;
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number<From> t(from);
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to_component_type n(numerator(t)), d(denominator(t));
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using default_ops::assign_components;
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assign_components(to, n.backend(), d.backend());
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}
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template <class To, class From>
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void generic_interconvert(To& to, const From& from, const mpl::int_<number_kind_rational>& /*to_type*/, const mpl::int_<number_kind_integer>& /*from_type*/)
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{
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typedef typename component_type<number<To> >::type to_component_type;
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number<From> t(from);
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to_component_type n(t), d(1);
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using default_ops::assign_components;
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assign_components(to, n.backend(), d.backend());
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}
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template <class R, class LargeInteger>
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R safe_convert_to_float(const LargeInteger& i)
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{
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using std::ldexp;
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if(!i)
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return R(0);
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if(std::numeric_limits<R>::is_specialized && std::numeric_limits<R>::max_exponent)
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{
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LargeInteger val(i);
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if(val.sign() < 0)
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val = -val;
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unsigned mb = msb(val);
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if(mb >= std::numeric_limits<R>::max_exponent)
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{
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int scale_factor = (int)mb + 1 - std::numeric_limits<R>::max_exponent;
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BOOST_ASSERT(scale_factor >= 1);
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val >>= scale_factor;
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R result = val.template convert_to<R>();
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if(std::numeric_limits<R>::digits == 0 || std::numeric_limits<R>::digits >= std::numeric_limits<R>::max_exponent)
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{
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//
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// Calculate and add on the remainder, only if there are more
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// digits in the mantissa that the size of the exponent, in
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// other words if we are dropping digits in the conversion
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// otherwise:
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//
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LargeInteger remainder(i);
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remainder &= (LargeInteger(1) << scale_factor) - 1;
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result += ldexp(safe_convert_to_float<R>(remainder), -scale_factor);
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}
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return i.sign() < 0 ? static_cast<R>(-result) : result;
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}
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}
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return i.template convert_to<R>();
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}
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template <class To, class Integer>
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inline typename disable_if_c<is_number<To>::value || is_floating_point<To>::value>::type
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generic_convert_rational_to_float_imp(To& result, const Integer& n, const Integer& d, const mpl::true_&)
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{
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//
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// If we get here, then there's something about one type or the other
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// that prevents an exactly rounded result from being calculated
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// (or at least it's not clear how to implement such a thing).
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//
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using default_ops::eval_divide;
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number<To> fn(safe_convert_to_float<number<To> >(n)), fd(safe_convert_to_float<number<To> >(d));
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eval_divide(result, fn.backend(), fd.backend());
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}
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template <class To, class Integer>
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inline typename enable_if_c<is_number<To>::value || is_floating_point<To>::value>::type
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generic_convert_rational_to_float_imp(To& result, const Integer& n, const Integer& d, const mpl::true_&)
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{
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//
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// If we get here, then there's something about one type or the other
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// that prevents an exactly rounded result from being calculated
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// (or at least it's not clear how to implement such a thing).
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//
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To fd(safe_convert_to_float<To>(d));
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result = safe_convert_to_float<To>(n);
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result /= fd;
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}
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template <class To, class Integer>
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typename enable_if_c<is_number<To>::value || is_floating_point<To>::value>::type
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generic_convert_rational_to_float_imp(To& result, Integer& num, Integer& denom, const mpl::false_&)
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{
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//
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// If we get here, then the precision of type To is known, and the integer type is unbounded
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// so we can use integer division plus manipulation of the remainder to get an exactly
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// rounded result.
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//
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if(num == 0)
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{
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result = 0;
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return;
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}
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bool s = false;
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if(num < 0)
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{
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s = true;
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num = -num;
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}
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int denom_bits = msb(denom);
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int shift = std::numeric_limits<To>::digits + denom_bits - msb(num);
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if(shift > 0)
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num <<= shift;
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else if(shift < 0)
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denom <<= boost::multiprecision::detail::unsigned_abs(shift);
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Integer q, r;
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divide_qr(num, denom, q, r);
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int q_bits = msb(q);
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if(q_bits == std::numeric_limits<To>::digits - 1)
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{
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//
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// Round up if 2 * r > denom:
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//
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r <<= 1;
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int c = r.compare(denom);
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if(c > 0)
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++q;
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else if((c == 0) && (q & 1u))
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{
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++q;
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}
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}
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else
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{
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BOOST_ASSERT(q_bits == std::numeric_limits<To>::digits);
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//
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// We basically already have the rounding info:
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//
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if(q & 1u)
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{
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if(r || (q & 2u))
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++q;
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}
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}
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using std::ldexp;
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result = do_cast<To>(q);
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result = ldexp(result, -shift);
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if(s)
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result = -result;
|
||
|
|
}
|
||
|
|
template <class To, class Integer>
|
||
|
|
inline typename disable_if_c<is_number<To>::value || is_floating_point<To>::value>::type
|
||
|
|
generic_convert_rational_to_float_imp(To& result, Integer& num, Integer& denom, const mpl::false_& tag)
|
||
|
|
{
|
||
|
|
number<To> t;
|
||
|
|
generic_convert_rational_to_float_imp(t, num, denom, tag);
|
||
|
|
result = t.backend();
|
||
|
|
}
|
||
|
|
|
||
|
|
template <class To, class From>
|
||
|
|
inline void generic_convert_rational_to_float(To& result, const From& f)
|
||
|
|
{
|
||
|
|
//
|
||
|
|
// Type From is always a Backend to number<>, or an
|
||
|
|
// instance of number<>, but we allow
|
||
|
|
// To to be either a Backend type, or a real number type,
|
||
|
|
// that way we can call this from generic conversions, and
|
||
|
|
// from specific conversions to built in types.
|
||
|
|
//
|
||
|
|
typedef typename mpl::if_c<is_number<From>::value, From, number<From> >::type actual_from_type;
|
||
|
|
typedef typename mpl::if_c<is_number<To>::value || is_floating_point<To>::value, To, number<To> >::type actual_to_type;
|
||
|
|
typedef typename component_type<actual_from_type>::type integer_type;
|
||
|
|
typedef mpl::bool_<!std::numeric_limits<integer_type>::is_specialized
|
||
|
|
|| std::numeric_limits<integer_type>::is_bounded
|
||
|
|
|| !std::numeric_limits<actual_to_type>::is_specialized
|
||
|
|
|| !std::numeric_limits<actual_to_type>::is_bounded
|
||
|
|
|| (std::numeric_limits<actual_to_type>::radix != 2)> dispatch_tag;
|
||
|
|
|
||
|
|
integer_type n(numerator(static_cast<actual_from_type>(f))), d(denominator(static_cast<actual_from_type>(f)));
|
||
|
|
generic_convert_rational_to_float_imp(result, n, d, dispatch_tag());
|
||
|
|
}
|
||
|
|
|
||
|
|
template <class To, class From>
|
||
|
|
inline void generic_interconvert(To& to, const From& from, const mpl::int_<number_kind_floating_point>& /*to_type*/, const mpl::int_<number_kind_rational>& /*from_type*/)
|
||
|
|
{
|
||
|
|
generic_convert_rational_to_float(to, from);
|
||
|
|
}
|
||
|
|
|
||
|
|
template <class To, class From>
|
||
|
|
void generic_interconvert_float2rational(To& to, const From& from, const mpl::int_<2>& /*radix*/)
|
||
|
|
{
|
||
|
|
typedef typename mpl::front<typename To::unsigned_types>::type ui_type;
|
||
|
|
static const int shift = std::numeric_limits<boost::long_long_type>::digits;
|
||
|
|
typename From::exponent_type e;
|
||
|
|
typename component_type<number<To> >::type num, denom;
|
||
|
|
number<From> val(from);
|
||
|
|
val = frexp(val, &e);
|
||
|
|
while(val)
|
||
|
|
{
|
||
|
|
val = ldexp(val, shift);
|
||
|
|
e -= shift;
|
||
|
|
boost::long_long_type ll = boost::math::lltrunc(val);
|
||
|
|
val -= ll;
|
||
|
|
num <<= shift;
|
||
|
|
num += ll;
|
||
|
|
}
|
||
|
|
denom = ui_type(1u);
|
||
|
|
if(e < 0)
|
||
|
|
denom <<= -e;
|
||
|
|
else if(e > 0)
|
||
|
|
num <<= e;
|
||
|
|
assign_components(to, num.backend(), denom.backend());
|
||
|
|
}
|
||
|
|
|
||
|
|
template <class To, class From, int Radix>
|
||
|
|
void generic_interconvert_float2rational(To& to, const From& from, const mpl::int_<Radix>& /*radix*/)
|
||
|
|
{
|
||
|
|
//
|
||
|
|
// This is almost the same as the binary case above, but we have to use
|
||
|
|
// scalbn and ilogb rather than ldexp and frexp, we also only extract
|
||
|
|
// one Radix digit at a time which is terribly inefficient!
|
||
|
|
//
|
||
|
|
typedef typename mpl::front<typename To::unsigned_types>::type ui_type;
|
||
|
|
typename From::exponent_type e;
|
||
|
|
typename component_type<number<To> >::type num, denom;
|
||
|
|
number<From> val(from);
|
||
|
|
e = ilogb(val);
|
||
|
|
val = scalbn(val, -e);
|
||
|
|
while(val)
|
||
|
|
{
|
||
|
|
boost::long_long_type ll = boost::math::lltrunc(val);
|
||
|
|
val -= ll;
|
||
|
|
val = scalbn(val, 1);
|
||
|
|
num *= Radix;
|
||
|
|
num += ll;
|
||
|
|
--e;
|
||
|
|
}
|
||
|
|
++e;
|
||
|
|
denom = ui_type(Radix);
|
||
|
|
denom = pow(denom, abs(e));
|
||
|
|
if(e > 0)
|
||
|
|
{
|
||
|
|
num *= denom;
|
||
|
|
denom = 1;
|
||
|
|
}
|
||
|
|
assign_components(to, num.backend(), denom.backend());
|
||
|
|
}
|
||
|
|
|
||
|
|
template <class To, class From>
|
||
|
|
void generic_interconvert(To& to, const From& from, const mpl::int_<number_kind_rational>& /*to_type*/, const mpl::int_<number_kind_floating_point>& /*from_type*/)
|
||
|
|
{
|
||
|
|
generic_interconvert_float2rational(to, from, mpl::int_<std::numeric_limits<number<From> >::radix>());
|
||
|
|
}
|
||
|
|
|
||
|
|
template <class To, class From>
|
||
|
|
void generic_interconvert(To& to, const From& from, const mpl::int_<number_kind_integer>& /*to_type*/, const mpl::int_<number_kind_rational>& /*from_type*/)
|
||
|
|
{
|
||
|
|
number<From> t(from);
|
||
|
|
number<To> result(numerator(t) / denominator(t));
|
||
|
|
to = result.backend();
|
||
|
|
}
|
||
|
|
|
||
|
|
template <class To, class From>
|
||
|
|
void generic_interconvert_float2int(To& to, const From& from, const mpl::int_<2>& /*radix*/)
|
||
|
|
{
|
||
|
|
typedef typename From::exponent_type exponent_type;
|
||
|
|
static const exponent_type shift = std::numeric_limits<boost::long_long_type>::digits;
|
||
|
|
exponent_type e;
|
||
|
|
number<To> num(0u);
|
||
|
|
number<From> val(from);
|
||
|
|
val = frexp(val, &e);
|
||
|
|
while(e > 0)
|
||
|
|
{
|
||
|
|
int s = (std::min)(e, shift);
|
||
|
|
val = ldexp(val, s);
|
||
|
|
e -= s;
|
||
|
|
boost::long_long_type ll = boost::math::lltrunc(val);
|
||
|
|
val -= ll;
|
||
|
|
num <<= s;
|
||
|
|
num += ll;
|
||
|
|
}
|
||
|
|
to = num.backend();
|
||
|
|
}
|
||
|
|
|
||
|
|
template <class To, class From, int Radix>
|
||
|
|
void generic_interconvert_float2int(To& to, const From& from, const mpl::int_<Radix>& /*radix*/)
|
||
|
|
{
|
||
|
|
//
|
||
|
|
// This is almost the same as the binary case above, but we have to use
|
||
|
|
// scalbn and ilogb rather than ldexp and frexp, we also only extract
|
||
|
|
// one Radix digit at a time which is terribly inefficient!
|
||
|
|
//
|
||
|
|
typename From::exponent_type e;
|
||
|
|
number<To> num(0u);
|
||
|
|
number<From> val(from);
|
||
|
|
e = ilogb(val);
|
||
|
|
val = scalbn(val, -e);
|
||
|
|
while(e >= 0)
|
||
|
|
{
|
||
|
|
boost::long_long_type ll = boost::math::lltrunc(val);
|
||
|
|
val -= ll;
|
||
|
|
val = scalbn(val, 1);
|
||
|
|
num *= Radix;
|
||
|
|
num += ll;
|
||
|
|
--e;
|
||
|
|
}
|
||
|
|
to = num.backend();
|
||
|
|
}
|
||
|
|
|
||
|
|
template <class To, class From>
|
||
|
|
void generic_interconvert(To& to, const From& from, const mpl::int_<number_kind_integer>& /*to_type*/, const mpl::int_<number_kind_floating_point>& /*from_type*/)
|
||
|
|
{
|
||
|
|
generic_interconvert_float2int(to, from, mpl::int_<std::numeric_limits<number<From> >::radix>());
|
||
|
|
}
|
||
|
|
|
||
|
|
}
|
||
|
|
}
|
||
|
|
} // namespaces
|
||
|
|
|
||
|
|
#ifdef BOOST_MSVC
|
||
|
|
#pragma warning(pop)
|
||
|
|
#endif
|
||
|
|
|
||
|
|
#endif // BOOST_MP_GENERIC_INTERCONVERT_HPP
|
||
|
|
|