Add a Relative Comparison matcher for floating point numbers

It checks Knuth's _close enough with tolerance_ relationship, that
is `|lhs - rhs| <= epsilon * max(|lhs|, |rhs|)`, rather then the
_very close with tolerance_ relationship that can be written down as
`|lhs - rhs| <= epsilon * min(|lhs|, |rhs|)`.

This is because it is the more common model around the internet, and
as such is likely to be less surprising to the users. In the future
we might want to provide the other model as well.

Closes #1746

include/internal/catch_matchers_floating.cpp

@@ -11,6 +11,7 @@
 #include "catch_to_string.hpp"
 #include "catch_tostring.h"
 
+#include <algorithm>
 #include <cmath>
 #include <cstdlib>
 #include <cstdint>
@@ -57,7 +58,8 @@ namespace {
         auto ulpDiff = std::abs(lc - rc);
         return static_cast<uint64_t>(ulpDiff) <= maxUlpDiff;
     }
-}
+
+} //end anonymous namespace
 
 #if defined(CATCH_CONFIG_GLOBAL_NEXTAFTER)
 
@@ -98,6 +100,17 @@ FP step(FP start, FP direction, uint64_t steps) {
     }
     return start;
 }
+
+namespace {
+
+    // Performs equivalent check of std::fabs(lhs - rhs) <= margin
+    // But without the subtraction to allow for INFINITY in comparison
+    bool marginComparison(double lhs, double rhs, double margin) {
+        return (lhs + margin >= rhs) && (rhs + margin >= lhs);
+    }
+
+}
+
 } // end anonymous namespace
 
 namespace Matchers {
@@ -180,6 +193,25 @@ namespace Floating {
         //return "is within " + Catch::to_string(m_ulps) + " ULPs of " + ::Catch::Detail::stringify(m_target) + ((m_type == FloatingPointKind::Float)? "f" : "");
     }
 
+    WithinRelMatcher::WithinRelMatcher(double target, double epsilon):
+        m_target(target),
+        m_epsilon(epsilon){
+        CATCH_ENFORCE(m_epsilon >= 0., "Relative comparison with epsilon <  0 does not make sense.");
+        CATCH_ENFORCE(m_epsilon  < 1., "Relative comparison with epsilon >= 1 does not make sense.");
+    }
+
+    bool WithinRelMatcher::match(double const& matchee) const {
+        const auto relMargin = m_epsilon * std::max(std::fabs(matchee), std::fabs(m_target));
+        return marginComparison(matchee, m_target,
+                                std::isinf(relMargin)? 0 : relMargin);
+    }
+
+    std::string WithinRelMatcher::describe() const {
+        Catch::ReusableStringStream sstr;
+        sstr << "and " << m_target << " are within " << m_epsilon * 100. << "% of each other";
+        return sstr.str();
+    }
+
 }// namespace Floating
 
 
@@ -196,6 +228,23 @@ Floating::WithinAbsMatcher WithinAbs(double target, double margin) {
     return Floating::WithinAbsMatcher(target, margin);
 }
 
+Floating::WithinRelMatcher WithinRel(double target, double eps) {
+    return Floating::WithinRelMatcher(target, eps);
+}
+
+Floating::WithinRelMatcher WithinRel(double target) {
+    return Floating::WithinRelMatcher(target, std::numeric_limits<double>::epsilon() * 100);
+}
+
+Floating::WithinRelMatcher WithinRel(float target, float eps) {
+    return Floating::WithinRelMatcher(target, eps);
+}
+
+Floating::WithinRelMatcher WithinRel(float target) {
+    return Floating::WithinRelMatcher(target, std::numeric_limits<float>::epsilon() * 100);
+}
+
+
 } // namespace Matchers
 } // namespace Catch