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well-defined newEpsilon, target-epsilon, invisible default scale 

What about to check for a well-defined newEpsilon (cf. http://realtimecollisiondetection.net/blog/?p=89)?
Apart from computational sciences view (cf. https://randomascii.wordpress.com/2012/02/25/comparing-floating-point-numbers-2012-edition/ or https://docs.oracle.com/cd/E19957-01/806-3568/ncg_goldberg.html) I would prefer two slight modifications referring to https://en.wikipedia.org/wiki/Approximation_error#Formal_Definition:
The given epsilon should refer to the target value, otherwise the result would be unexpected, e.g. 101.02 == Approx(100).epsilon(0.01) gets true. The default scale should be invisible, thus, e.g. 101.01 == Approx(100).epsilon(0.01) gets false. Finally (both modifications accepted) even 101.000001 == Approx(100).epsilon(0.01) should get false, e.g.

To prevent a misuse of epsilon its setting should be checked.
This commit is contained in:
Pfiffikus 2017-10-26 09:19:57 +02:00 committed by GitHub
parent 93b3d2cb8f
commit 957b98a32a
1 changed files with 5 additions and 3 deletions
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8
include/internal/catch_approx.hpp
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@ -25,7 +25,7 @@ namespace Detail {
explicit Approx ( double value )
: m_epsilon( std::numeric_limits<float>::epsilon()*100 ),
m_margin( 0.0 ),
m_scale( 1.0 ),
m_scale( 0.0 ),
m_value( value )
{}
@ -53,7 +53,7 @@ namespace Detail {
friend bool operator == ( const T& lhs, Approx const& rhs ) {
// Thanks to Richard Harris for his help refining this formula
auto lhs_v = double(lhs);
bool relativeOK = std::fabs(lhs_v - rhs.m_value) < rhs.m_epsilon * (rhs.m_scale + (std::max)(std::fabs(lhs_v), std::fabs(rhs.m_value)));
bool relativeOK = std::fabs( lhs - rhs.m_value ) < rhs.m_epsilon * (rhs.m_scale + std::fabs(rhs.m_value) );
if (relativeOK) {
return true;
}
@ -97,6 +97,7 @@ namespace Detail {
template <typename T, typename = typename std::enable_if<std::is_constructible<double, T>::value>::type>
Approx& epsilon( T newEpsilon ) {
assert(newEpsilon >= 0.0f && newEpsilon < = 1.0f); // i.e. check for well-defined newEpsilon
m_epsilon = double(newEpsilon);
return *this;
}
@ -126,7 +127,7 @@ namespace Detail {
friend bool operator == ( double lhs, Approx const& rhs ) {
// Thanks to Richard Harris for his help refining this formula
bool relativeOK = std::fabs( lhs - rhs.m_value ) < rhs.m_epsilon * (rhs.m_scale + (std::max)( std::fabs(lhs), std::fabs(rhs.m_value) ) );
bool relativeOK = std::fabs( lhs - rhs.m_value ) < rhs.m_epsilon * (rhs.m_scale + std::fabs(rhs.m_value) );
if (relativeOK) {
return true;
}
@ -162,6 +163,7 @@ namespace Detail {
}
Approx& epsilon( double newEpsilon ) {
assert(newEpsilon >= 0.0f && newEpsilon < = 1.0f); // i.e. check for well-defined newEpsilon
m_epsilon = newEpsilon;
return *this;
}