Merge branch 'QPR-11265' into 'master'

QPR-11265 optimize close_enough (this is ql mr 1494)

Closes QPR-11265

See merge request qs/quantlib!33

Author: pcaspers

ql/math/comparison.hpp

@@ -57,7 +57,18 @@ namespace QuantLib {
     // inline definitions
 
     inline bool close(Real x, Real y) {
-        return close(x,y,42);
+        // Deals with +infinity and -infinity representations etc.
+        if (x == y)
+            return true;
+
+        Real diff = std::fabs(x-y);
+        constexpr Real tolerance = 42 * QL_EPSILON;
+
+        if (x == 0.0 || y == 0.0)
+            return diff < (tolerance * tolerance);
+
+        return diff <= tolerance*std::fabs(x) &&
+               diff <= tolerance*std::fabs(y);
     }
 
     inline bool close(Real x, Real y, Size n) {
@@ -67,15 +78,26 @@ namespace QuantLib {
 
         Real diff = std::fabs(x-y), tolerance = n * QL_EPSILON;
 
-        if (x * y == 0.0) // x or y = 0.0
+        if (x == 0.0 || y == 0.0)
             return diff < (tolerance * tolerance);
 
         return diff <= tolerance*std::fabs(x) &&
                diff <= tolerance*std::fabs(y);
     }
 
     inline bool close_enough(Real x, Real y) {
-        return close_enough(x,y,42);
+        // Deals with +infinity and -infinity representations etc.
+        if (x == y)
+            return true;
+
+        Real diff = std::fabs(x-y);
+        constexpr Real tolerance = 42 * QL_EPSILON;
+
+        if (x == 0.0 || y == 0.0) // x or y = 0.0
+            return diff < (tolerance * tolerance);
+
+        return diff <= tolerance*std::fabs(x) ||
+               diff <= tolerance*std::fabs(y);
     }
 
     inline bool close_enough(Real x, Real y, Size n) {
@@ -85,7 +107,7 @@ namespace QuantLib {
 
         Real diff = std::fabs(x-y), tolerance = n * QL_EPSILON;
 
-        if (x * y == 0.0) // x or y = 0.0
+        if (x == 0.0 || y == 0.0)
             return diff < (tolerance * tolerance);
 
         return diff <= tolerance*std::fabs(x) ||