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quadmath.hh
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// -*- tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 2 -*-
// vi: set et ts=4 sw=2 sts=2:
// SPDX-FileCopyrightInfo: Copyright © DUNE Project contributors, see file LICENSE.md in module root
// SPDX-License-Identifier: LicenseRef-GPL-2.0-only-with-DUNE-exception
#ifndef DUNE_QUADMATH_HH
#define DUNE_QUADMATH_HH
#if HAVE_QUADMATH
#include <quadmath.h>
#include <cmath>
#include <cstddef>
#include <cstdint>
#include <cstdlib> // abs
#include <istream>
#include <ostream>
#include <type_traits>
#include <utility>
#include <dune/common/exceptions.hh>
#include <dune/common/typetraits.hh>
namespace Dune
{
namespace Impl
{
// forward declaration
class Float128;
} // end namespace Impl
using Impl::Float128;
// The purpose of this namespace is to move the `<cmath>` function overloads
// out of namespace `Dune`, see AlignedNumber in debugalign.hh.
namespace Impl
{
using float128_t = __float128;
class Float128
{
float128_t value_ = 0.0q;
public:
constexpr Float128() = default;
constexpr Float128(const float128_t& value) noexcept
: value_(value)
{}
// constructor from any floating-point or integer type
template <class T,
std::enable_if_t<std::is_arithmetic<T>::value, int> = 0>
constexpr Float128(const T& value) noexcept
: value_(value)
{}
// constructor from pointer to null-terminated byte string
explicit Float128(const char* str) noexcept
: value_(strtoflt128(str, NULL))
{}
// accessors
constexpr operator float128_t() const noexcept { return value_; }
constexpr float128_t const& value() const noexcept { return value_; }
constexpr float128_t& value() noexcept { return value_; }
// I/O
template<class CharT, class Traits>
friend std::basic_istream<CharT, Traits>&
operator>>(std::basic_istream<CharT, Traits>& in, Float128& x)
{
std::string buf;
buf.reserve(128);
in >> buf;
x.value() = strtoflt128(buf.c_str(), NULL);
return in;
}
template<class CharT, class Traits>
friend std::basic_ostream<CharT, Traits>&
operator<<(std::basic_ostream<CharT, Traits>& out, const Float128& x)
{
const std::size_t bufSize = 128;
CharT buf[128];
std::string format = "%." + std::to_string(out.precision()) + "Q" +
((out.flags() | std::ios_base::scientific) ? "e" : "f");
const int numChars = quadmath_snprintf(buf, bufSize, format.c_str(), x.value());
if (std::size_t(numChars) >= bufSize) {
DUNE_THROW(Dune::RangeError, "Failed to print Float128 value: buffer overflow");
}
out << buf;
return out;
}
// Increment, decrement
constexpr Float128& operator++() noexcept { ++value_; return *this; }
constexpr Float128& operator--() noexcept { --value_; return *this; }
constexpr Float128 operator++(int) noexcept { Float128 tmp{*this}; ++value_; return tmp; }
constexpr Float128 operator--(int) noexcept { Float128 tmp{*this}; --value_; return tmp; }
// unary operators
constexpr Float128 operator+() const noexcept { return Float128{+value_}; }
constexpr Float128 operator-() const noexcept { return Float128{-value_}; }
// assignment operators
#define DUNE_ASSIGN_OP(OP) \
constexpr Float128& operator OP(const Float128& u) noexcept \
{ \
value_ OP float128_t(u); \
return *this; \
} \
static_assert(true, "Require semicolon to unconfuse editors")
DUNE_ASSIGN_OP(+=);
DUNE_ASSIGN_OP(-=);
DUNE_ASSIGN_OP(*=);
DUNE_ASSIGN_OP(/=);
#undef DUNE_ASSIGN_OP
}; // end class Float128
// binary operators:
// For symmetry provide overloads with arithmetic types
// in the first or second argument.
#define DUNE_BINARY_OP(OP) \
constexpr Float128 operator OP(const Float128& t, \
const Float128& u) noexcept \
{ \
return Float128{float128_t(t) OP float128_t(u)}; \
} \
constexpr Float128 operator OP(const float128_t& t, \
const Float128& u) noexcept \
{ \
return Float128{t OP float128_t(u)}; \
} \
constexpr Float128 operator OP(const Float128& t, \
const float128_t& u) noexcept \
{ \
return Float128{float128_t(t) OP u}; \
} \
template <class T, \
std::enable_if_t<std::is_arithmetic<T>::value, int> = 0> \
constexpr Float128 operator OP(const T& t, \
const Float128& u) noexcept \
{ \
return Float128{float128_t(t) OP float128_t(u)}; \
} \
template <class U, \
std::enable_if_t<std::is_arithmetic<U>::value, int> = 0> \
constexpr Float128 operator OP(const Float128& t, \
const U& u) noexcept \
{ \
return Float128{float128_t(t) OP float128_t(u)}; \
} \
static_assert(true, "Require semicolon to unconfuse editors")
DUNE_BINARY_OP(+);
DUNE_BINARY_OP(-);
DUNE_BINARY_OP(*);
DUNE_BINARY_OP(/);
#undef DUNE_BINARY_OP
// logical operators:
// For symmetry provide overloads with arithmetic types
// in the first or second argument.
#define DUNE_BINARY_BOOL_OP(OP) \
constexpr bool operator OP(const Float128& t, \
const Float128& u) noexcept \
{ \
return float128_t(t) OP float128_t(u); \
} \
template <class T, \
std::enable_if_t<std::is_arithmetic<T>::value, int> = 0> \
constexpr bool operator OP(const T& t, \
const Float128& u) noexcept \
{ \
return float128_t(t) OP float128_t(u); \
} \
template <class U, \
std::enable_if_t<std::is_arithmetic<U>::value, int> = 0> \
constexpr bool operator OP(const Float128& t, \
const U& u) noexcept \
{ \
return float128_t(t) OP float128_t(u); \
} \
static_assert(true, "Require semicolon to unconfuse editors")
DUNE_BINARY_BOOL_OP(==);
DUNE_BINARY_BOOL_OP(!=);
DUNE_BINARY_BOOL_OP(<);
DUNE_BINARY_BOOL_OP(>);
DUNE_BINARY_BOOL_OP(<=);
DUNE_BINARY_BOOL_OP(>=);
#undef DUNE_BINARY_BOOL_OP
// Overloads for the cmath functions
// function with name `name` redirects to quadmath function `func`
#define DUNE_UNARY_FUNC(name,func) \
inline Float128 name(const Float128& u) noexcept \
{ \
return Float128{func (float128_t(u))}; \
} \
static_assert(true, "Require semicolon to unconfuse editors")
// like DUNE_UNARY_FUNC but with custom return type
#define DUNE_CUSTOM_UNARY_FUNC(type,name,func) \
inline type name(const Float128& u) noexcept \
{ \
return (type)(func (float128_t(u))); \
} \
static_assert(true, "Require semicolon to unconfuse editors")
// redirects to quadmath function with two arguments
#define DUNE_BINARY_FUNC(name,func) \
inline Float128 name(const Float128& t, \
const Float128& u) noexcept \
{ \
return Float128{func (float128_t(t), float128_t(u))}; \
} \
static_assert(true, "Require semicolon to unconfuse editors")
DUNE_UNARY_FUNC(abs, fabsq);
DUNE_UNARY_FUNC(acos, acosq);
DUNE_UNARY_FUNC(acosh, acoshq);
DUNE_UNARY_FUNC(asin, asinq);
DUNE_UNARY_FUNC(asinh, asinhq);
DUNE_UNARY_FUNC(atan, atanq);
DUNE_UNARY_FUNC(atanh, atanhq);
DUNE_UNARY_FUNC(cbrt, cbrtq);
DUNE_UNARY_FUNC(ceil, ceilq);
DUNE_UNARY_FUNC(cos, cosq);
DUNE_UNARY_FUNC(cosh, coshq);
DUNE_UNARY_FUNC(erf, erfq);
DUNE_UNARY_FUNC(erfc, erfcq);
DUNE_UNARY_FUNC(exp, expq);
DUNE_UNARY_FUNC(expm1, expm1q);
DUNE_UNARY_FUNC(fabs, fabsq);
DUNE_UNARY_FUNC(floor, floorq);
DUNE_CUSTOM_UNARY_FUNC(int, ilogb, ilogbq);
DUNE_UNARY_FUNC(lgamma, lgammaq);
DUNE_CUSTOM_UNARY_FUNC(long long int, llrint, llrintq);
DUNE_CUSTOM_UNARY_FUNC(long long int, llround, llroundq);
DUNE_UNARY_FUNC(log, logq);
DUNE_UNARY_FUNC(log10, log10q);
DUNE_UNARY_FUNC(log1p, log1pq);
DUNE_UNARY_FUNC(log2, log2q);
// DUNE_UNARY_FUNC(logb, logbq); // not available in gcc5
DUNE_CUSTOM_UNARY_FUNC(long int, lrint, lrintq);
DUNE_CUSTOM_UNARY_FUNC(long int, lround, lroundq);
DUNE_UNARY_FUNC(nearbyint, nearbyintq);
DUNE_BINARY_FUNC(nextafter, nextafterq);
DUNE_BINARY_FUNC(pow, powq); // overload for integer argument see below
DUNE_UNARY_FUNC(rint, rintq);
DUNE_UNARY_FUNC(round, roundq);
DUNE_UNARY_FUNC(sin, sinq);
DUNE_UNARY_FUNC(sinh, sinhq);
DUNE_UNARY_FUNC(sqrt, sqrtq);
DUNE_UNARY_FUNC(tan, tanq);
DUNE_UNARY_FUNC(tanh, tanhq);
DUNE_UNARY_FUNC(tgamma, tgammaq);
DUNE_UNARY_FUNC(trunc, truncq);
DUNE_CUSTOM_UNARY_FUNC(bool, isfinite, finiteq);
DUNE_CUSTOM_UNARY_FUNC(bool, isinf, isinfq);
DUNE_CUSTOM_UNARY_FUNC(bool, isnan, isnanq);
DUNE_CUSTOM_UNARY_FUNC(bool, signbit, signbitq);
#undef DUNE_UNARY_FUNC
#undef DUNE_CUSTOM_UNARY_FUNC
#undef DUNE_BINARY_FUNC
// like DUNE_BINARY_FUNC but provide overloads with arithmetic
// types in the first or second argument.
#define DUNE_BINARY_ARITHMETIC_FUNC(name,func) \
inline Float128 name(const Float128& t, \
const Float128& u) noexcept \
{ \
return Float128{func (float128_t(t), float128_t(u))}; \
} \
template <class T, \
std::enable_if_t<std::is_arithmetic<T>::value, int> = 0> \
inline Float128 name(const T& t, \
const Float128& u) noexcept \
{ \
return Float128{func (float128_t(t), float128_t(u))}; \
} \
template <class U, \
std::enable_if_t<std::is_arithmetic<U>::value, int> = 0> \
inline Float128 name(const Float128& t, \
const U& u) noexcept \
{ \
return Float128{func (float128_t(t), float128_t(u))}; \
} \
static_assert(true, "Require semicolon to unconfuse editors")
DUNE_BINARY_ARITHMETIC_FUNC(atan2,atan2q);
DUNE_BINARY_ARITHMETIC_FUNC(copysign,copysignq);
DUNE_BINARY_ARITHMETIC_FUNC(fdim,fdimq);
DUNE_BINARY_ARITHMETIC_FUNC(fmax,fmaxq);
DUNE_BINARY_ARITHMETIC_FUNC(fmin,fminq);
DUNE_BINARY_ARITHMETIC_FUNC(fmod,fmodq);
DUNE_BINARY_ARITHMETIC_FUNC(hypot,hypotq);
DUNE_BINARY_ARITHMETIC_FUNC(remainder,remainderq);
#undef DUNE_BINARY_ARITHMETIC_FUNC
// some more cmath functions with special signature
inline Float128 fma(const Float128& t, const Float128& u, const Float128& v)
{
return Float128{fmaq(float128_t(t),float128_t(u),float128_t(v))};
}
inline Float128 frexp(const Float128& u, int* p)
{
return Float128{frexpq(float128_t(u), p)};
}
inline Float128 ldexp(const Float128& u, int p)
{
return Float128{ldexpq(float128_t(u), p)};
}
inline Float128 remquo(const Float128& t, const Float128& u, int* quo)
{
return Float128{remquoq(float128_t(t), float128_t(u), quo)};
}
inline Float128 scalbln(const Float128& u, long int e)
{
return Float128{scalblnq(float128_t(u), e)};
}
inline Float128 scalbn(const Float128& u, int e)
{
return Float128{scalbnq(float128_t(u), e)};
}
// NOTE: This is much faster than a pow(x, Float128(p)) call
// NOTE: This is a modified version of boost::math::cstdfloat::detail::pown
// (adapted to the type Float128) that is part of the Boost 1.65 Math toolkit 2.8.0
// and is implemented by Christopher Kormanyos, John Maddock, and Paul A. Bristow,
// distributed under the Boost Software License, Version 1.0
// (See http://www.boost.org/LICENSE_1_0.txt)
template <class Int,
std::enable_if_t<std::is_integral<Int>::value, int> = 0>
inline Float128 pow(const Float128& x, const Int p)
{
static const Float128 max_value = FLT128_MAX;
static const Float128 min_value = FLT128_MIN;
static const Float128 inf_value = float128_t{1} / float128_t{0};
const bool isneg = (x < 0);
const bool isnan = (x != x);
const bool isinf = (isneg ? bool(-x > max_value) : bool(+x > max_value));
if (isnan) { return x; }
if (isinf) { return Float128{nanq("")}; }
const Float128 abs_x = (isneg ? -x : x);
if (p < Int(0)) {
if (abs_x < min_value)
return (isneg ? -inf_value : +inf_value);
else
return Float128(1) / pow(x, Int(-p));
}
if (p == Int(0)) { return Float128(1); }
if (p == Int(1)) { return x; }
if (abs_x > max_value)
return (isneg ? -inf_value : +inf_value);
if (p == Int(2)) { return (x * x); }
if (p == Int(3)) { return ((x * x) * x); }
if (p == Int(4)) { const Float128 x2 = (x * x); return (x2 * x2); }
Float128 result = ((p % Int(2)) != Int(0)) ? x : Float128(1);
Float128 xn = x; // binary powers of x
Int p2 = p;
while (Int(p2 /= 2) != Int(0)) {
xn *= xn; // Square xn for each binary power
const bool has_binary_power = (Int(p2 % Int(2)) != Int(0));
if (has_binary_power)
result *= xn;
}
return result;
}
} // end namespace Impl
template <>
struct IsNumber<Impl::Float128>
: public std::true_type {};
} // end namespace Dune
namespace std
{
#ifndef NO_STD_NUMERIC_LIMITS_SPECIALIZATION
template <>
class numeric_limits<Dune::Impl::Float128>
{
using Float128 = Dune::Impl::Float128;
using float128_t = Dune::Impl::float128_t;
public:
static constexpr bool is_specialized = true;
static constexpr Float128 min() noexcept { return FLT128_MIN; }
static constexpr Float128 max() noexcept { return FLT128_MAX; }
static constexpr Float128 lowest() noexcept { return -FLT128_MAX; }
static constexpr int digits = FLT128_MANT_DIG;
static constexpr int digits10 = 34;
static constexpr int max_digits10 = 36;
static constexpr bool is_signed = true;
static constexpr bool is_integer = false;
static constexpr bool is_exact = false;
static constexpr int radix = 2;
static constexpr Float128 epsilon() noexcept { return FLT128_EPSILON; }
static constexpr Float128 round_error() noexcept { return float128_t{0.5}; }
static constexpr int min_exponent = FLT128_MIN_EXP;
static constexpr int min_exponent10 = FLT128_MIN_10_EXP;
static constexpr int max_exponent = FLT128_MAX_EXP;
static constexpr int max_exponent10 = FLT128_MAX_10_EXP;
static constexpr bool has_infinity = true;
static constexpr bool has_quiet_NaN = true;
static constexpr bool has_signaling_NaN = false;
static constexpr float_denorm_style has_denorm = denorm_present;
static constexpr bool has_denorm_loss = false;
static constexpr Float128 infinity() noexcept { return float128_t{1}/float128_t{0}; }
static Float128 quiet_NaN() noexcept { return nanq(""); }
static constexpr Float128 signaling_NaN() noexcept { return float128_t{}; }
static constexpr Float128 denorm_min() noexcept { return FLT128_DENORM_MIN; }
static constexpr bool is_iec559 = true;
static constexpr bool is_bounded = false;
static constexpr bool is_modulo = false;
static constexpr bool traps = false;
static constexpr bool tinyness_before = false;
static constexpr float_round_style round_style = round_to_nearest;
};
#endif
} // end namespace std
#endif // HAVE_QUADMATH
#endif // DUNE_QUADMATH_HH
DUNE_BINARY_OP
#define DUNE_BINARY_OP(OP)
Definition debugalign.hh:261
DUNE_UNARY_FUNC
#define DUNE_UNARY_FUNC(name)
DUNE_ASSIGN_OP
#define DUNE_ASSIGN_OP(OP)
Definition debugalign.hh:220
typetraits.hh
Traits for type conversions and type information.
exceptions.hh
A few common exception classes.
Dune::operator>>
std::istream & operator>>(std::istream &stream, std::tuple< Ts... > &t)
Read a std::tuple.
Definition streamoperators.hh:43
Dune::Hybrid::max
constexpr auto max
Function object that returns the greater of the given values.
Definition hybridutilities.hh:489
Dune::Hybrid::min
constexpr auto min
Function object that returns the smaller of the given values.
Definition hybridutilities.hh:511
Dune::operator<<
std::ostream & operator<<(std::ostream &s, const bigunsignedint< k > &x)
Definition bigunsignedint.hh:301
Dune::operator-
bigunsignedint< k > operator-(const bigunsignedint< k > &x, std::uintmax_t y)
Definition bigunsignedint.hh:565
Dune::operator+
bigunsignedint< k > operator+(const bigunsignedint< k > &x, std::uintmax_t y)
Definition bigunsignedint.hh:558
DUNE_THROW
#define DUNE_THROW(E,...)
Definition exceptions.hh:314
Dune::operator++
constexpr decltype(auto) operator++()
Preincrement operator.
Definition iteratorfacades.hh:1138
Dune::operator--
constexpr decltype(auto) operator--()
Predecrement operator.
Definition iteratorfacades.hh:1169
std
STL namespace.
Dune
Dune namespace
Definition alignedallocator.hh:13
Dune::max_value
T max_value(const AlignedNumber< T, align > &val)
Definition debugalign.hh:494
Dune::min_value
T min_value(const AlignedNumber< T, align > &val)
Definition debugalign.hh:500
Dune::IsNumber
Whether this type acts as a scalar in the context of (hierarchically blocked) containers.
Definition typetraits.hh:194