boost/multiprecision/detail/generic_interconvert.hpp
///////////////////////////////////////////////////////////////////////////////
// Copyright 2011 John Maddock. Distributed under the Boost
// Software License, Version 1.0. (See accompanying file
// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
#ifndef BOOST_MP_GENERIC_INTERCONVERT_HPP
#define BOOST_MP_GENERIC_INTERCONVERT_HPP
#include <cmath>
#include <limits>
#include <boost/multiprecision/detail/standalone_config.hpp>
#include <boost/multiprecision/detail/default_ops.hpp>
#include <boost/multiprecision/detail/no_exceptions_support.hpp>
#include <boost/multiprecision/detail/assert.hpp>
#include <boost/multiprecision/detail/functions/trunc.hpp>
#ifdef BOOST_MSVC
#pragma warning(push)
#pragma warning(disable : 4127 6326)
#endif
namespace boost { namespace multiprecision { namespace detail {
template <class To, class From>
inline To do_cast(const From& from)
{
return static_cast<To>(from);
}
template <class To, class B, ::boost::multiprecision::expression_template_option et>
inline To do_cast(const number<B, et>& from)
{
return from.template convert_to<To>();
}
template <class To, class From>
void generic_interconvert(To& to, const From& from, const std::integral_constant<int, number_kind_floating_point>& /*to_type*/, const std::integral_constant<int, number_kind_integer>& /*from_type*/)
{
using default_ops::eval_add;
using default_ops::eval_bitwise_and;
using default_ops::eval_convert_to;
using default_ops::eval_get_sign;
using default_ops::eval_is_zero;
using default_ops::eval_ldexp;
using default_ops::eval_right_shift;
// smallest unsigned type handled natively by "From" is likely to be it's limb_type:
using l_limb_type = typename canonical<unsigned char, From>::type;
// get the corresponding type that we can assign to "To":
using to_type = typename canonical<l_limb_type, To>::type;
From t(from);
bool is_neg = eval_get_sign(t) < 0;
if (is_neg)
t.negate();
// Pick off the first limb:
l_limb_type limb;
l_limb_type mask = static_cast<l_limb_type>(~static_cast<l_limb_type>(0));
From fl;
eval_bitwise_and(fl, t, mask);
eval_convert_to(&limb, fl);
to = static_cast<to_type>(limb);
eval_right_shift(t, std::numeric_limits<l_limb_type>::digits);
//
// Then keep picking off more limbs until "t" is zero:
//
To l;
unsigned shift = std::numeric_limits<l_limb_type>::digits;
while (!eval_is_zero(t))
{
eval_bitwise_and(fl, t, mask);
eval_convert_to(&limb, fl);
l = static_cast<to_type>(limb);
eval_right_shift(t, std::numeric_limits<l_limb_type>::digits);
eval_ldexp(l, l, shift);
eval_add(to, l);
shift += std::numeric_limits<l_limb_type>::digits;
}
//
// Finish off by setting the sign:
//
if (is_neg)
to.negate();
}
template <class To, class From>
void generic_interconvert(To& to, const From& from, const std::integral_constant<int, number_kind_integer>& /*to_type*/, const std::integral_constant<int, number_kind_integer>& /*from_type*/)
{
using default_ops::eval_bitwise_and;
using default_ops::eval_bitwise_or;
using default_ops::eval_convert_to;
using default_ops::eval_get_sign;
using default_ops::eval_is_zero;
using default_ops::eval_left_shift;
using default_ops::eval_right_shift;
// smallest unsigned type handled natively by "From" is likely to be it's limb_type:
using limb_type = typename canonical<unsigned char, From>::type;
// get the corresponding type that we can assign to "To":
using to_type = typename canonical<limb_type, To>::type;
From t(from);
bool is_neg = eval_get_sign(t) < 0;
if (is_neg)
t.negate();
// Pick off the first limb:
limb_type limb;
limb_type mask = static_cast<limb_type>(~static_cast<limb_type>(0));
From fl;
eval_bitwise_and(fl, t, mask);
eval_convert_to(&limb, fl);
to = static_cast<to_type>(limb);
eval_right_shift(t, std::numeric_limits<limb_type>::digits);
//
// Then keep picking off more limbs until "t" is zero:
//
To l;
unsigned shift = std::numeric_limits<limb_type>::digits;
while (!eval_is_zero(t))
{
eval_bitwise_and(fl, t, mask);
eval_convert_to(&limb, fl);
l = static_cast<to_type>(limb);
eval_right_shift(t, std::numeric_limits<limb_type>::digits);
eval_left_shift(l, shift);
eval_bitwise_or(to, l);
shift += std::numeric_limits<limb_type>::digits;
}
//
// Finish off by setting the sign:
//
if (is_neg)
to.negate();
}
template <class To, class From>
void generic_interconvert(To& to, const From& from, const std::integral_constant<int, number_kind_floating_point>& /*to_type*/, const std::integral_constant<int, number_kind_floating_point>& /*from_type*/)
{
#ifdef BOOST_MSVC
#pragma warning(push)
//#pragma warning(disable : 4127)
#endif
//
// The code here only works when the radix of "From" is 2, we could try shifting by other
// radixes but it would complicate things.... use a string conversion when the radix is other
// than 2:
//
BOOST_IF_CONSTEXPR(std::numeric_limits<number<From> >::radix != 2)
{
to = from.str(0, std::ios_base::fmtflags()).c_str();
return;
}
else
{
using ui_type = typename canonical<unsigned char, To>::type;
using default_ops::eval_add;
using default_ops::eval_convert_to;
using default_ops::eval_fpclassify;
using default_ops::eval_get_sign;
using default_ops::eval_is_zero;
using default_ops::eval_subtract;
//
// First classify the input, then handle the special cases:
//
int c = eval_fpclassify(from);
if (c == static_cast<int>(FP_ZERO))
{
to = ui_type(0);
return;
}
else if (c == static_cast<int>(FP_NAN))
{
to = static_cast<const char*>("nan");
return;
}
else if (c == static_cast<int>(FP_INFINITE))
{
to = static_cast<const char*>("inf");
if (eval_get_sign(from) < 0)
to.negate();
return;
}
typename From::exponent_type e;
From f, term;
to = ui_type(0);
eval_frexp(f, from, &e);
constexpr int shift = std::numeric_limits<std::intmax_t>::digits - 1;
while (!eval_is_zero(f))
{
// extract int sized bits from f:
eval_ldexp(f, f, shift);
eval_floor(term, f);
e -= shift;
eval_ldexp(to, to, shift);
typename boost::multiprecision::detail::canonical<std::intmax_t, To>::type ll;
eval_convert_to(&ll, term);
eval_add(to, ll);
eval_subtract(f, term);
}
using to_exponent = typename To::exponent_type;
if (e > (std::numeric_limits<to_exponent>::max)())
{
to = static_cast<const char*>("inf");
if (eval_get_sign(from) < 0)
to.negate();
return;
}
if (e < (std::numeric_limits<to_exponent>::min)())
{
to = ui_type(0);
if (eval_get_sign(from) < 0)
to.negate();
return;
}
eval_ldexp(to, to, static_cast<to_exponent>(e));
}
#ifdef BOOST_MSVC
#pragma warning(pop)
#endif
}
template <class To, class From>
void generic_interconvert(To& to, const From& from, const std::integral_constant<int, number_kind_rational>& /*to_type*/, const std::integral_constant<int, number_kind_rational>& /*from_type*/)
{
using to_component_type = typename component_type<number<To> >::type;
number<From> t(from);
to_component_type n(numerator(t)), d(denominator(t));
using default_ops::assign_components;
assign_components(to, n.backend(), d.backend());
}
template <class To, class From>
void generic_interconvert(To& to, const From& from, const std::integral_constant<int, number_kind_rational>& /*to_type*/, const std::integral_constant<int, number_kind_integer>& /*from_type*/)
{
using to_component_type = typename component_type<number<To> >::type;
number<From> t(from);
to_component_type n(t), d(1);
using default_ops::assign_components;
assign_components(to, n.backend(), d.backend());
}
template <class LargeInteger>
inline typename std::enable_if<is_signed_number<LargeInteger>::value>::type make_positive(LargeInteger& val)
{
if (val.sign() < 0)
val = -val;
}
template <class LargeInteger>
inline typename std::enable_if<!is_signed_number<LargeInteger>::value>::type make_positive(LargeInteger&){}
template <class R, class LargeInteger>
R safe_convert_to_float(const LargeInteger& i)
{
if (!i)
return R(0);
BOOST_IF_CONSTEXPR(std::numeric_limits<R>::is_specialized && std::numeric_limits<R>::max_exponent)
{
using std::ldexp;
LargeInteger val(i);
make_positive(val);
std::size_t mb = msb(val);
if (mb >= std::numeric_limits<R>::max_exponent)
{
int scale_factor = static_cast<int>(mb) + 1 - std::numeric_limits<R>::max_exponent;
BOOST_MP_ASSERT(scale_factor >= 1);
val >>= scale_factor;
R result = val.template convert_to<R>();
BOOST_IF_CONSTEXPR(std::numeric_limits<R>::digits == 0 || std::numeric_limits<R>::digits >= std::numeric_limits<R>::max_exponent)
{
//
// Calculate and add on the remainder, only if there are more
// digits in the mantissa that the size of the exponent, in
// other words if we are dropping digits in the conversion
// otherwise:
//
LargeInteger remainder(i);
remainder &= (LargeInteger(1) << scale_factor) - 1;
result += ldexp(safe_convert_to_float<R>(remainder), -scale_factor);
}
return i.sign() < 0 ? static_cast<R>(-result) : result;
}
}
return i.template convert_to<R>();
}
template <class To, class Integer>
inline typename std::enable_if<!(is_number<To>::value || std::is_floating_point<To>::value)>::type
generic_convert_rational_to_float_imp(To& result, const Integer& n, const Integer& d, const std::integral_constant<bool, true>&)
{
//
// If we get here, then there's something about one type or the other
// that prevents an exactly rounded result from being calculated
// (or at least it's not clear how to implement such a thing).
//
using default_ops::eval_divide;
number<To> fn(safe_convert_to_float<number<To> >(n)), fd(safe_convert_to_float<number<To> >(d));
eval_divide(result, fn.backend(), fd.backend());
}
template <class To, class Integer>
inline typename std::enable_if<is_number<To>::value || std::is_floating_point<To>::value>::type
generic_convert_rational_to_float_imp(To& result, const Integer& n, const Integer& d, const std::integral_constant<bool, true>&)
{
//
// If we get here, then there's something about one type or the other
// that prevents an exactly rounded result from being calculated
// (or at least it's not clear how to implement such a thing).
//
To fd(safe_convert_to_float<To>(d));
result = safe_convert_to_float<To>(n);
result /= fd;
}
template <class To, class Integer>
typename std::enable_if<is_number<To>::value || std::is_floating_point<To>::value>::type
generic_convert_rational_to_float_imp(To& result, Integer& num, Integer& denom, const std::integral_constant<bool, false>&)
{
//
// If we get here, then the precision of type To is known, and the integer type is unbounded
// so we can use integer division plus manipulation of the remainder to get an exactly
// rounded result.
//
if (num == 0)
{
result = 0;
return;
}
bool s = false;
if (num < 0)
{
s = true;
num = -num;
}
std::ptrdiff_t denom_bits = msb(denom);
std::ptrdiff_t shift = std::numeric_limits<To>::digits + denom_bits - msb(num);
if (shift > 0)
num <<= shift;
else if (shift < 0)
denom <<= boost::multiprecision::detail::unsigned_abs(shift);
Integer q, r;
divide_qr(num, denom, q, r);
std::ptrdiff_t q_bits = msb(q);
if (q_bits == std::numeric_limits<To>::digits - 1)
{
//
// Round up if 2 * r > denom:
//
r <<= 1;
int c = r.compare(denom);
if (c > 0)
++q;
else if ((c == 0) && (q & 1u))
{
++q;
}
}
else
{
BOOST_MP_ASSERT(q_bits == std::numeric_limits<To>::digits);
//
// We basically already have the rounding info:
//
if (q & 1u)
{
if (r || (q & 2u))
++q;
}
}
using std::ldexp;
result = do_cast<To>(q);
result = ldexp(result, static_cast<int>(-shift));
if (s)
result = -result;
}
template <class To, class Integer>
inline typename std::enable_if<!(is_number<To>::value || std::is_floating_point<To>::value)>::type
generic_convert_rational_to_float_imp(To& result, Integer& num, Integer& denom, const std::integral_constant<bool, 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.
//
using actual_from_type = typename std::conditional<is_number<From>::value, From, number<From> >::type ;
using actual_to_type = typename std::conditional<is_number<To>::value || std::is_floating_point<To>::value, To, number<To> >::type ;
using integer_type = typename component_type<actual_from_type>::type ;
using dispatch_tag = std::integral_constant<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)>;
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 std::integral_constant<int, number_kind_floating_point>& /*to_type*/, const std::integral_constant<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 std::integral_constant<int, 2>& /*radix*/)
{
using std::ldexp;
using std::frexp;
using ui_type = typename std::tuple_element<0, typename To::unsigned_types>::type;
constexpr int shift = std::numeric_limits<long long>::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;
long long ll = boost::multiprecision::detail::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 std::integral_constant<int, Radix>& /*radix*/)
{
using std::ilogb;
using std::scalbn;
using std::pow;
using std::abs;
//
// 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!
//
using ui_type = typename std::tuple_element<0, typename To::unsigned_types>::type;
typename From::exponent_type e;
typename component_type<number<To>>::type num, denom;
number<From> val(from);
if (!val)
{
to = ui_type(0u);
return;
}
e = ilogb(val);
val = scalbn(val, -e);
while (val)
{
long long ll = boost::multiprecision::detail::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 std::integral_constant<int, number_kind_rational>& /*to_type*/, const std::integral_constant<int, number_kind_floating_point>& /*from_type*/)
{
generic_interconvert_float2rational(to, from, std::integral_constant<int, std::numeric_limits<number<From> >::is_specialized ? std::numeric_limits<number<From> >::radix : 2>());
}
template <class To, class From>
void generic_interconvert(To& to, const From& from, const std::integral_constant<int, number_kind_integer>& /*to_type*/, const std::integral_constant<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 std::integral_constant<int, 2>& /*radix*/)
{
using std::frexp;
using std::ldexp;
using exponent_type = typename From::exponent_type;
constexpr exponent_type shift = std::numeric_limits<long long>::digits;
exponent_type e;
number<To> num(0u);
number<From> val(from);
val = frexp(val, &e);
bool neg = false;
if (val.sign() < 0)
{
val.backend().negate();
neg = true;
}
while (e > 0)
{
exponent_type s = (std::min)(e, shift);
val = ldexp(val, s);
e -= s;
long long ll = boost::multiprecision::detail::lltrunc(val);
val -= ll;
num <<= s;
num += ll;
}
to = num.backend();
if (neg)
to.negate();
}
template <class To, class From, int Radix>
void generic_interconvert_float2int(To& to, const From& from, const std::integral_constant<int, Radix>& /*radix*/)
{
using std::ilogb;
using std::scalbn;
//
// 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)
{
long long ll = boost::multiprecision::detail::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 std::integral_constant<int, number_kind_integer>& /*to_type*/, const std::integral_constant<int, number_kind_floating_point>& /*from_type*/)
{
generic_interconvert_float2int(to, from, std::integral_constant<int, (std::numeric_limits<number<From> >::is_specialized ? std::numeric_limits<number<From> >::radix : 2)>());
}
template <class To, class From, class tag>
void generic_interconvert_complex_to_scalar(To& to, const From& from, const std::integral_constant<bool, true>&, const tag&)
{
// We just want the real part, and "to" is the correct type already:
eval_real(to, from);
To im;
eval_imag(im, from);
if (!eval_is_zero(im))
BOOST_MP_THROW_EXCEPTION(std::runtime_error("Could not convert imaginary number to scalar."));
}
template <class To, class From>
void generic_interconvert_complex_to_scalar(To& to, const From& from, const std::integral_constant<bool, false>&, const std::integral_constant<bool, true>&)
{
using component_number = typename component_type<number<From> >::type;
using component_backend = typename component_number::backend_type ;
//
// Get the real part and copy-construct the result from it:
//
scoped_precision_options<component_number> scope(from);
component_backend r;
generic_interconvert_complex_to_scalar(r, from, std::integral_constant<bool, true>(), std::integral_constant<bool, true>());
to = r;
}
template <class To, class From>
void generic_interconvert_complex_to_scalar(To& to, const From& from, const std::integral_constant<bool, false>&, const std::integral_constant<bool, false>&)
{
using component_number = typename component_type<number<From> >::type;
using component_backend = typename component_number::backend_type;
//
// Get the real part and use a generic_interconvert to type To:
//
scoped_precision_options<component_number> scope(from);
component_backend r;
generic_interconvert_complex_to_scalar(r, from, std::integral_constant<bool, true>(), std::integral_constant<bool, true>());
generic_interconvert(to, r, std::integral_constant<int, number_category<To>::value>(), std::integral_constant<int, number_category<component_backend>::value>());
}
template <class To, class From>
void generic_interconvert(To& to, const From& from, const std::integral_constant<int, number_kind_floating_point>& /*to_type*/, const std::integral_constant<int, number_kind_complex>& /*from_type*/)
{
using component_number = typename component_type<number<From> >::type;
using component_backend = typename component_number::backend_type ;
generic_interconvert_complex_to_scalar(to, from, std::integral_constant<bool, std::is_same<component_backend, To>::value>(), std::integral_constant<bool, std::is_constructible<To, const component_backend&>::value>());
}
template <class To, class From>
void generic_interconvert(To& to, const From& from, const std::integral_constant<int, number_kind_integer>& /*to_type*/, const std::integral_constant<int, number_kind_complex>& /*from_type*/)
{
using component_number = typename component_type<number<From> >::type;
using component_backend = typename component_number::backend_type ;
generic_interconvert_complex_to_scalar(to, from, std::integral_constant<bool, std::is_same<component_backend, To>::value>(), std::integral_constant<bool, std::is_constructible<To, const component_backend&>::value>());
}
template <class To, class From>
void generic_interconvert(To& to, const From& from, const std::integral_constant<int, number_kind_rational>& /*to_type*/, const std::integral_constant<int, number_kind_complex>& /*from_type*/)
{
using component_number = typename component_type<number<From> >::type;
using component_backend = typename component_number::backend_type ;
generic_interconvert_complex_to_scalar(to, from, std::integral_constant<bool, std::is_same<component_backend, To>::value>(), std::integral_constant<bool, std::is_constructible<To, const component_backend&>::value>());
}
template <class To, class From>
void generic_interconvert(To& to, const From& from, const std::integral_constant<int, number_kind_complex>& /*to_type*/, const std::integral_constant<int, number_kind_integer>& /*from_type*/)
{
using component_number = typename component_type<number<To> >::type;
scoped_source_precision<number<From> > scope1;
scoped_precision_options<component_number> scope2(number<To>::thread_default_precision(), number<To>::thread_default_variable_precision_options());
(void)scope1;
(void)scope2;
number<From> f(from);
component_number scalar(f);
number<To> result(scalar);
to = result.backend();
}
template <class To, class From>
void generic_interconvert(To& to, const From& from, const std::integral_constant<int, number_kind_complex>& /*to_type*/, const std::integral_constant<int, number_kind_rational>& /*from_type*/)
{
using component_number = typename component_type<number<To> >::type;
scoped_source_precision<number<From> > scope1;
scoped_precision_options<component_number> scope2(number<To>::thread_default_precision(), number<To>::thread_default_variable_precision_options());
(void)scope1;
(void)scope2;
number<From> f(from);
component_number scalar(f);
number<To> result(scalar);
to = result.backend();
}
template <class To, class From>
void generic_interconvert(To& to, const From& from, const std::integral_constant<int, number_kind_complex>& /*to_type*/, const std::integral_constant<int, number_kind_floating_point>& /*from_type*/)
{
using component_number = typename component_type<number<To> >::type;
scoped_source_precision<number<From> > scope1;
scoped_precision_options<component_number> scope2(number<To>::thread_default_precision(), number<To>::thread_default_variable_precision_options());
(void)scope1;
(void)scope2;
number<From> f(from);
component_number scalar(f);
number<To> result(scalar);
to = result.backend();
}
template <class To, class From, int Tag1, int Tag2>
void generic_interconvert(To& /*to*/, const From& /*from*/, const std::integral_constant<int, Tag1>& /*to_type*/, const std::integral_constant<int, Tag2>& /*from_type*/)
{
static_assert(sizeof(To) == 0, "Sorry, you asked for a conversion bewteen types that hasn't been implemented yet!!");
}
}
}
} // namespace boost::multiprecision::detail
#ifdef BOOST_MSVC
#pragma warning(pop)
#endif
#endif // BOOST_MP_GENERIC_INTERCONVERT_HPP