/usr/include/dune/common/float_cmp.cc is in libdune-common-dev 2.5.1-1.
This file is owned by root:root, with mode 0o644.
The actual contents of the file can be viewed below.
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// vi: set et ts=4 sw=2 sts=2:
#include "float_cmp.hh"
#include <vector>
#include <limits>
#include <algorithm>
#include <cstdlib>
#include <dune/common/fvector.hh>
namespace Dune {
namespace FloatCmp {
// traits
//! Mapping of value type to epsilon type
/**
* @ingroup FloatCmp
* @tparam T The value type
*/
template<class T> struct EpsilonType {
//! The epsilon type corresponding to value type T
typedef T Type;
};
//! Specialization of EpsilonType for std::vector
/**
* @ingroup FloatCmp
* @tparam T The value_type of the std::vector
* @tparam A The Allocator of the std::vector
*/
template<class T, typename A>
struct EpsilonType<std::vector<T, A> > {
//! The epsilon type corresponding to value type std::vector<T, A>
typedef EpsilonType<T> Type;
};
//! Specialization of EpsilonType for Dune::FieldVector
/**
* @ingroup FloatCmp
* @tparam T The field_type of the Dune::FieldVector
* @tparam n The size of the Dune::FieldVector
*/
template<class T, int n>
struct EpsilonType<FieldVector<T, n> > {
//! The epsilon type corresponding to value type Dune::FieldVector<T, n>
typedef EpsilonType<T> Type;
};
// default epsilon
template<class T>
struct DefaultEpsilon<T, relativeWeak> {
static typename EpsilonType<T>::Type value()
{ return std::numeric_limits<typename EpsilonType<T>::Type>::epsilon()*8; }
};
template<class T>
struct DefaultEpsilon<T, relativeStrong> {
static typename EpsilonType<T>::Type value()
{ return std::numeric_limits<typename EpsilonType<T>::Type>::epsilon()*8; }
};
template<class T>
struct DefaultEpsilon<T, absolute> {
static typename EpsilonType<T>::Type value()
{ return std::max(std::numeric_limits<typename EpsilonType<T>::Type>::epsilon(), 1e-6); }
};
namespace Detail {
// basic comparison
template<class T, CmpStyle style = defaultCmpStyle>
struct eq_t;
template<class T>
struct eq_t<T, relativeWeak> {
static bool eq(const T &first,
const T &second,
typename EpsilonType<T>::Type epsilon = DefaultEpsilon<T>::value())
{ return std::abs(first - second) <= epsilon*std::max(std::abs(first), std::abs(second)); }
};
template<class T>
struct eq_t<T, relativeStrong> {
static bool eq(const T &first,
const T &second,
typename EpsilonType<T>::Type epsilon = DefaultEpsilon<T>::value())
{ return std::abs(first - second) <= epsilon*std::min(std::abs(first), std::abs(second)); }
};
template<class T>
struct eq_t<T, absolute> {
static bool eq(const T &first,
const T &second,
typename EpsilonType<T>::Type epsilon = DefaultEpsilon<T>::value())
{ return std::abs(first-second) <= epsilon; }
};
template<class T, CmpStyle cstyle>
struct eq_t<std::vector<T>, cstyle> {
static bool eq(const std::vector<T> &first,
const std::vector<T> &second,
typename EpsilonType<T>::Type epsilon = DefaultEpsilon<T>::value()) {
unsigned int size = first.size();
if(size != second.size()) return false;
for(unsigned int i = 0; i < size; ++i)
if(!eq_t<T, cstyle>(first[i], second[i], epsilon))
return false;
return true;
}
};
template<class T, int n, CmpStyle cstyle>
struct eq_t<Dune::FieldVector<T, n>, cstyle> {
static bool eq(const Dune::FieldVector<T, n> &first,
const Dune::FieldVector<T, n> &second,
typename EpsilonType<T>::Type epsilon = DefaultEpsilon<T>::value()) {
for(int i = 0; i < n; ++i)
if(!eq_t<T, cstyle>(first[i], second[i], epsilon))
return false;
return true;
}
};
} // namespace Detail
// operations in functional style
template <class T, CmpStyle style>
bool eq(const T &first,
const T &second,
typename EpsilonType<T>::Type epsilon)
{
return Detail::eq_t<T, style>::eq(first, second, epsilon);
}
template <class T, CmpStyle style>
bool ne(const T &first,
const T &second,
typename EpsilonType<T>::Type epsilon)
{
return !eq<T, style>(first, second, epsilon);
}
template <class T, CmpStyle style>
bool gt(const T &first,
const T &second,
typename EpsilonType<T>::Type epsilon)
{
return first > second && ne<T, style>(first, second, epsilon);
}
template <class T, CmpStyle style>
bool lt(const T &first,
const T &second,
typename EpsilonType<T>::Type epsilon)
{
return first < second && ne<T, style>(first, second, epsilon);
}
template <class T, CmpStyle style>
bool ge(const T &first,
const T &second,
typename EpsilonType<T>::Type epsilon)
{
return first > second || eq<T, style>(first, second, epsilon);
}
template <class T, CmpStyle style>
bool le(const T &first,
const T &second,
typename EpsilonType<T>::Type epsilon)
{
return first < second || eq<T, style>(first, second, epsilon);
}
// default template arguments
template <class T>
bool eq(const T &first,
const T &second,
typename EpsilonType<T>::Type epsilon = DefaultEpsilon<T, defaultCmpStyle>::value())
{
return eq<T, defaultCmpStyle>(first, second, epsilon);
}
template <class T>
bool ne(const T &first,
const T &second,
typename EpsilonType<T>::Type epsilon = DefaultEpsilon<T, defaultCmpStyle>::value())
{
return ne<T, defaultCmpStyle>(first, second, epsilon);
}
template <class T>
bool gt(const T &first,
const T &second,
typename EpsilonType<T>::Type epsilon = DefaultEpsilon<T, defaultCmpStyle>::value())
{
return gt<T, defaultCmpStyle>(first, second, epsilon);
}
template <class T>
bool lt(const T &first,
const T &second,
typename EpsilonType<T>::Type epsilon = DefaultEpsilon<T, defaultCmpStyle>::value())
{
return lt<T, defaultCmpStyle>(first, second, epsilon);
}
template <class T>
bool ge(const T &first,
const T &second,
typename EpsilonType<T>::Type epsilon = DefaultEpsilon<T, defaultCmpStyle>::value())
{
return ge<T, defaultCmpStyle>(first, second, epsilon);
}
template <class T>
bool le(const T &first,
const T &second,
typename EpsilonType<T>::Type epsilon = DefaultEpsilon<T, defaultCmpStyle>::value())
{
return le<T, defaultCmpStyle>(first, second, epsilon);
}
// rounding operations
namespace Detail {
template<class I, class T, CmpStyle cstyle = defaultCmpStyle, RoundingStyle rstyle = defaultRoundingStyle>
struct round_t;
template<class I, class T, CmpStyle cstyle>
struct round_t<I, T, cstyle, downward> {
static I
round(const T &val,
typename EpsilonType<T>::Type epsilon = (DefaultEpsilon<T, cstyle>::value())) {
// first get an approximation
I lower = I(val);
I upper;
if(eq<T, cstyle>(T(lower), val, epsilon)) return lower;
if(T(lower) > val) { upper = lower; lower--; }
else upper = lower+1;
if(le<T, cstyle>(val - T(lower), T(upper) - val, epsilon))
return lower;
else return upper;
}
};
template<class I, class T, CmpStyle cstyle>
struct round_t<I, T, cstyle, upward> {
static I
round(const T &val,
typename EpsilonType<T>::Type epsilon = (DefaultEpsilon<T, cstyle>::value())) {
// first get an approximation
I lower = I(val);
I upper;
if(eq<T, cstyle>(T(lower), val, epsilon)) return lower;
if(T(lower) > val) { upper = lower; lower--; }
else upper = lower+1;
if(lt<T, cstyle>(val - T(lower), T(upper) - val, epsilon))
return lower;
else return upper;
}
};
template<class I, class T, CmpStyle cstyle>
struct round_t<I, T, cstyle, towardZero> {
static I
round(const T &val,
typename EpsilonType<T>::Type epsilon = (DefaultEpsilon<T, cstyle>::value())) {
if(val > T(0))
return round_t<I, T, cstyle, downward>::round(val, epsilon);
else return round_t<I, T, cstyle, upward>::round(val, epsilon);
}
};
template<class I, class T, CmpStyle cstyle>
struct round_t<I, T, cstyle, towardInf> {
static I
round(const T &val,
typename EpsilonType<T>::Type epsilon = (DefaultEpsilon<T, cstyle>::value())) {
if(val > T(0))
return round_t<I, T, cstyle, upward>::round(val, epsilon);
else return round_t<I, T, cstyle, downward>::round(val, epsilon);
}
};
template<class I, class T, CmpStyle cstyle, RoundingStyle rstyle>
struct round_t<std::vector<I>, std::vector<T>, cstyle, rstyle> {
static std::vector<I>
round(const T &val,
typename EpsilonType<T>::Type epsilon = (DefaultEpsilon<T, cstyle>::value())) {
unsigned int size = val.size();
std::vector<I> res(size);
for(unsigned int i = 0; i < size; ++i)
res[i] = round_t<I, T, cstyle, rstyle>::round(val[i], epsilon);
return res;
}
};
template<class I, class T, int n, CmpStyle cstyle, RoundingStyle rstyle>
struct round_t<Dune::FieldVector<I, n>, Dune::FieldVector<T, n>, cstyle, rstyle> {
static Dune::FieldVector<I, n>
round(const T &val,
typename EpsilonType<T>::Type epsilon = (DefaultEpsilon<T, cstyle>::value())) {
Dune::FieldVector<I, n> res;
for(int i = 0; i < n; ++i)
res[i] = round_t<I, T, cstyle, rstyle>::round(val[i], epsilon);
return res;
}
};
} // namespace Detail
template<class I, class T, CmpStyle cstyle, RoundingStyle rstyle>
I round(const T &val, typename EpsilonType<T>::Type epsilon /*= DefaultEpsilon<T, cstyle>::value()*/)
{
return Detail::round_t<I, T, cstyle, rstyle>::round(val, epsilon);
}
template<class I, class T, CmpStyle cstyle>
I round(const T &val, typename EpsilonType<T>::Type epsilon = DefaultEpsilon<T, cstyle>::value())
{
return round<I, T, cstyle, defaultRoundingStyle>(val, epsilon);
}
template<class I, class T, RoundingStyle rstyle>
I round(const T &val, typename EpsilonType<T>::Type epsilon = DefaultEpsilon<T, defaultCmpStyle>::value())
{
return round<I, T, defaultCmpStyle, rstyle>(val, epsilon);
}
template<class I, class T>
I round(const T &val, typename EpsilonType<T>::Type epsilon = DefaultEpsilon<T, defaultCmpStyle>::value())
{
return round<I, T, defaultCmpStyle>(val, epsilon);
}
// truncation
namespace Detail {
template<class I, class T, CmpStyle cstyle = defaultCmpStyle, RoundingStyle rstyle = defaultRoundingStyle>
struct trunc_t;
template<class I, class T, CmpStyle cstyle>
struct trunc_t<I, T, cstyle, downward> {
static I
trunc(const T &val,
typename EpsilonType<T>::Type epsilon = (DefaultEpsilon<T, cstyle>::value())) {
// this should be optimized away unless needed
if(!std::numeric_limits<I>::is_signed)
// make sure this works for all useful cases even if I is an unsigned type
if(eq<T, cstyle>(val, T(0), epsilon)) return I(0);
// first get an approximation
I lower = I(val); // now |val-lower| < 1
// make sure we're really lower in case the cast truncated to an unexpected direction
if(T(lower) > val) lower--; // now val-lower < 1
// check whether lower + 1 is approximately val
if(eq<T, cstyle>(T(lower+1), val, epsilon))
return lower+1;
else return lower;
}
};
template<class I, class T, CmpStyle cstyle>
struct trunc_t<I, T, cstyle, upward> {
static I
trunc(const T &val,
typename EpsilonType<T>::Type epsilon = (DefaultEpsilon<T, cstyle>::value())) {
I upper = trunc_t<I, T, cstyle, downward>::trunc(val, epsilon);
if(ne<T, cstyle>(T(upper), val, epsilon)) ++upper;
return upper;
}
};
template<class I, class T, CmpStyle cstyle>
struct trunc_t<I, T, cstyle, towardZero> {
static I
trunc(const T &val,
typename EpsilonType<T>::Type epsilon = (DefaultEpsilon<T, cstyle>::value())) {
if(val > T(0)) return trunc_t<I, T, cstyle, downward>::trunc(val, epsilon);
else return trunc_t<I, T, cstyle, upward>::trunc(val, epsilon);
}
};
template<class I, class T, CmpStyle cstyle>
struct trunc_t<I, T, cstyle, towardInf> {
static I
trunc(const T &val,
typename EpsilonType<T>::Type epsilon = (DefaultEpsilon<T, cstyle>::value())) {
if(val > T(0)) return trunc_t<I, T, cstyle, upward>::trunc(val, epsilon);
else return trunc_t<I, T, cstyle, downward>::trunc(val, epsilon);
}
};
template<class I, class T, CmpStyle cstyle, RoundingStyle rstyle>
struct trunc_t<std::vector<I>, std::vector<T>, cstyle, rstyle> {
static std::vector<I>
trunc(const std::vector<T> &val,
typename EpsilonType<T>::Type epsilon = (DefaultEpsilon<T, cstyle>::value())) {
unsigned int size = val.size();
std::vector<I> res(size);
for(unsigned int i = 0; i < size; ++i)
res[i] = trunc_t<I, T, cstyle, rstyle>::trunc(val[i], epsilon);
return res;
}
};
template<class I, class T, int n, CmpStyle cstyle, RoundingStyle rstyle>
struct trunc_t<Dune::FieldVector<I, n>, Dune::FieldVector<T, n>, cstyle, rstyle> {
static Dune::FieldVector<I, n>
trunc(const Dune::FieldVector<T, n> &val,
typename EpsilonType<T>::Type epsilon = (DefaultEpsilon<T, cstyle>::value())) {
Dune::FieldVector<I, n> res;
for(int i = 0; i < n; ++i)
res[i] = trunc_t<I, T, cstyle, rstyle>::trunc(val[i], epsilon);
return res;
}
};
} // namespace Detail
template<class I, class T, CmpStyle cstyle, RoundingStyle rstyle>
I trunc(const T &val, typename EpsilonType<T>::Type epsilon /*= DefaultEpsilon<T, cstyle>::value()*/)
{
return Detail::trunc_t<I, T, cstyle, rstyle>::trunc(val, epsilon);
}
template<class I, class T, CmpStyle cstyle>
I trunc(const T &val, typename EpsilonType<T>::Type epsilon = DefaultEpsilon<T, cstyle>::value())
{
return trunc<I, T, cstyle, defaultRoundingStyle>(val, epsilon);
}
template<class I, class T, RoundingStyle rstyle>
I trunc(const T &val, typename EpsilonType<T>::Type epsilon = DefaultEpsilon<T, defaultCmpStyle>::value())
{
return trunc<I, T, defaultCmpStyle, rstyle>(val, epsilon);
}
template<class I, class T>
I trunc(const T &val, typename EpsilonType<T>::Type epsilon = DefaultEpsilon<T, defaultCmpStyle>::value())
{
return trunc<I, T, defaultCmpStyle>(val, epsilon);
}
} //namespace Dune
// oo interface
template<class T, FloatCmp::CmpStyle cstyle_, FloatCmp::RoundingStyle rstyle_>
FloatCmpOps<T, cstyle_, rstyle_>::
FloatCmpOps(EpsilonType epsilon) : epsilon_(epsilon) {}
template<class T, FloatCmp::CmpStyle cstyle_, FloatCmp::RoundingStyle rstyle_>
typename FloatCmpOps<T, cstyle_, rstyle_>::EpsilonType
FloatCmpOps<T, cstyle_, rstyle_>::epsilon() const
{
return epsilon_;
}
template<class T, FloatCmp::CmpStyle cstyle_, FloatCmp::RoundingStyle rstyle_>
void
FloatCmpOps<T, cstyle_, rstyle_>::epsilon(EpsilonType epsilon__)
{
epsilon_ = epsilon__;
}
template<class T, FloatCmp::CmpStyle cstyle_, FloatCmp::RoundingStyle rstyle_>
bool FloatCmpOps<T, cstyle_, rstyle_>::
eq(const ValueType &first, const ValueType &second) const
{
return Dune::FloatCmp::eq<ValueType, cstyle>(first, second, epsilon_);
}
template<class T, FloatCmp::CmpStyle cstyle_, FloatCmp::RoundingStyle rstyle_>
bool FloatCmpOps<T, cstyle_, rstyle_>::
ne(const ValueType &first, const ValueType &second) const
{
return Dune::FloatCmp::ne<ValueType, cstyle>(first, second, epsilon_);
}
template<class T, FloatCmp::CmpStyle cstyle_, FloatCmp::RoundingStyle rstyle_>
bool FloatCmpOps<T, cstyle_, rstyle_>::
gt(const ValueType &first, const ValueType &second) const
{
return Dune::FloatCmp::gt<ValueType, cstyle>(first, second, epsilon_);
}
template<class T, FloatCmp::CmpStyle cstyle_, FloatCmp::RoundingStyle rstyle_>
bool FloatCmpOps<T, cstyle_, rstyle_>::
lt(const ValueType &first, const ValueType &second) const
{
return Dune::FloatCmp::lt<ValueType, cstyle>(first, second, epsilon_);
}
template<class T, FloatCmp::CmpStyle cstyle_, FloatCmp::RoundingStyle rstyle_>
bool FloatCmpOps<T, cstyle_, rstyle_>::
ge(const ValueType &first, const ValueType &second) const
{
return Dune::FloatCmp::ge<ValueType, cstyle>(first, second, epsilon_);
}
template<class T, FloatCmp::CmpStyle cstyle_, FloatCmp::RoundingStyle rstyle_>
bool FloatCmpOps<T, cstyle_, rstyle_>::
le(const ValueType &first, const ValueType &second) const
{
return Dune::FloatCmp::le<ValueType, cstyle>(first, second, epsilon_);
}
template<class T, FloatCmp::CmpStyle cstyle_, FloatCmp::RoundingStyle rstyle_>
template<class I>
I FloatCmpOps<T, cstyle_, rstyle_>::
round(const ValueType &val) const
{
return Dune::FloatCmp::round<I, ValueType, cstyle, rstyle_>(val, epsilon_);
}
template<class T, FloatCmp::CmpStyle cstyle_, FloatCmp::RoundingStyle rstyle_>
template<class I>
I FloatCmpOps<T, cstyle_, rstyle_>::
trunc(const ValueType &val) const
{
return Dune::FloatCmp::trunc<I, ValueType, cstyle, rstyle_>(val, epsilon_);
}
} //namespace Dune
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