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
 

include/internal/catch_matchers_floating.h

@@ -35,6 +35,20 @@ namespace Matchers {
             FloatingPointKind m_type;
         };
 
+        // Given IEEE-754 format for floats and doubles, we can assume
+        // that float -> double promotion is lossless. Given this, we can
+        // assume that if we do the standard relative comparison of
+        // |lhs - rhs| <= epsilon * max(fabs(lhs), fabs(rhs)), then we get
+        // the same result if we do this for floats, as if we do this for
+        // doubles that were promoted from floats.
+        struct WithinRelMatcher : MatcherBase<double> {
+            WithinRelMatcher(double target, double epsilon);
+            bool match(double const& matchee) const override;
+            std::string describe() const override;
+        private:
+            double m_target;
+            double m_epsilon;
+        };
 
     } // namespace Floating
 
@@ -43,6 +57,12 @@ namespace Matchers {
     Floating::WithinUlpsMatcher WithinULP(double target, uint64_t maxUlpDiff);
     Floating::WithinUlpsMatcher WithinULP(float target, uint64_t maxUlpDiff);
     Floating::WithinAbsMatcher WithinAbs(double target, double margin);
+    Floating::WithinRelMatcher WithinRel(double target, double eps);
+    // defaults epsilon to 100*numeric_limits<double>::epsilon()
+    Floating::WithinRelMatcher WithinRel(double target);
+    Floating::WithinRelMatcher WithinRel(float target, float eps);
+    // defaults epsilon to 100*numeric_limits<float>::epsilon()
+    Floating::WithinRelMatcher WithinRel(float target);
 
 } // namespace Matchers
 } // namespace Catch