From 00af677577973758b3b35e1c94ab4142c45c3f67 Mon Sep 17 00:00:00 2001
From: Pfiffikus <2845742+Pfiffikus@users.noreply.github.com>
Date: Thu, 26 Oct 2017 09:19:57 +0200
Subject: [PATCH] Approx rework: default scale == 0, epsilon applies to
 Approx::value

Also adds check to Approx::epsilon that the new epsilon has a valid
(ie one between 0 and 1)

Based on
http://realtimecollisiondetection.net/blog/?p=89
https://randomascii.wordpress.com/2012/02/25/comparing-floating-point-numbers-2012-edition/
https://docs.oracle.com/cd/E19957-01/806-3568/ncg_goldberg.html
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)
is true.
The default scale should be invisible, thus,
e.g. 101.01 == Approx(100).epsilon(0.01) gets false.
Finally even 101.000001 == Approx(100).epsilon(0.01) is false
---
 include/internal/catch_approx.cpp |  2 +-
 include/internal/catch_approx.h   | 11 ++++++++---
 2 files changed, 9 insertions(+), 4 deletions(-)

diff --git a/include/internal/catch_approx.cpp b/include/internal/catch_approx.cpp
index ca3ac94a..826a1049 100644
--- a/include/internal/catch_approx.cpp
+++ b/include/internal/catch_approx.cpp
@@ -23,7 +23,7 @@ namespace Detail {
     Approx::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 )
     {}
 
diff --git a/include/internal/catch_approx.h b/include/internal/catch_approx.h
index 69428c8a..8ca7f315 100644
--- a/include/internal/catch_approx.h
+++ b/include/internal/catch_approx.h
@@ -44,8 +44,9 @@ namespace Detail {
         friend bool operator == ( const T& lhs, Approx const& rhs ) {
             // Thanks to Richard Harris for his help refining this formula
             auto lhs_v = static_cast<double>(lhs);
-            bool relativeOK = std::fabs(lhs_v - rhs.m_value) < rhs.m_epsilon * (rhs.m_scale +
-                    dmax(std::fabs(lhs_v), std::fabs(rhs.m_value)));
+
+            bool relativeOK = std::fabs( lhs_v - rhs.m_value ) < rhs.m_epsilon * (rhs.m_scale + std::fabs(rhs.m_value) );
+
             if (relativeOK) {
                 return true;
             }
@@ -89,7 +90,11 @@ namespace Detail {
 
         template <typename T, typename = typename std::enable_if<std::is_constructible<double, T>::value>::type>
         Approx& epsilon( T const& newEpsilon ) {
-            m_epsilon = static_cast<double>(newEpsilon);
+            double asDouble = static_cast<double>(newEpsilon);
+            CATCH_ENFORCE(asDouble >= 0 && asDouble <= 1.0,
+                          "Invalid Approx::epsilon: " << m_epsilon <<
+                          ", Approx::epsilon has to be between 0 and 1");
+            m_epsilon = asDouble;
             return *this;
         }