Added comparison functions for floats and doubles… (#2321)

* Added comparison functions for floats and doubles, providing a safer way to do things like `double value; if( value == 0.0 ){}`.

* Added approxEqualRelative() functions and removed the custom epsilon in favor of FLT_EPSILON and DBL_EPSILON.

authored-by: paulhoux <paulhoux@users.noreply.github.com>

Author: paulhoux

include/cinder/CinderMath.h

@@ -123,9 +123,75 @@ struct CI_API math<float>
 #define M_PI           3.14159265358979323846
 #endif
 
-const double EPSILON_VALUE = 4.37114e-05;
+constexpr double EPSILON_VALUE = 4.37114e-05;
 #define EPSILON EPSILON_VALUE
 
+CI_API inline bool approxZero( float n, float epsilon = float(EPSILON_VALUE) )
+{
+	return std::abs( n ) < epsilon;
+}
+
+CI_API inline bool approxZero( double n, double epsilon = EPSILON_VALUE )
+{
+	return std::abs( n ) < epsilon;
+}
+
+CI_API inline float roundToZero( float n, float epsilon = float(EPSILON_VALUE) )
+{
+	return approxZero( n, epsilon ) ? 0.0f : n;
+}
+
+CI_API inline double roundToZero( double n, double epsilon = EPSILON_VALUE )
+{
+	return approxZero( n, epsilon ) ? 0.0 : n;
+}
+
+CI_API inline bool approxEqual( float a, float b, float epsilon = float(EPSILON_VALUE) )
+{
+	return std::abs( b - a ) < epsilon;
+}
+
+CI_API inline bool approxEqual( double a, double b, double epsilon = EPSILON_VALUE )
+{
+	return std::abs( b - a ) < epsilon;
+}
+
+CI_API inline bool approxEqualRelative( float a, float b, float maxRelDiff = float(EPSILON_VALUE) )
+{
+	// See: https://randomascii.wordpress.com/2012/02/25/comparing-floating-point-numbers-2012-edition/
+
+	// Calculate the difference.
+	const float diff = std::abs( a - b );
+
+	// Find the largest.
+	a = std::abs( a );
+	b = std::abs( b );
+	const float largest = ( b > a ) ? b : a;
+
+	if( diff <= largest * maxRelDiff )
+		return true;
+
+	return false;
+}
+
+CI_API inline bool approxEqualRelative( double a, double b, double maxRelDiff = EPSILON_VALUE )
+{
+	// See: https://randomascii.wordpress.com/2012/02/25/comparing-floating-point-numbers-2012-edition/
+
+	// Calculate the difference.
+	const double diff = std::abs( a - b );
+
+	// Find the largest.
+	a = std::abs( a );
+	b = std::abs( b );
+	const double largest = ( b > a ) ? b : a;
+
+	if( diff <= largest * maxRelDiff )
+		return true;
+
+	return false;
+}
+
 inline float toRadians( float x )
 {
 	return x * 0.017453292519943295769f; // ( x * PI / 180 )