Introduce normalised value in fraction class

Bit of a cheat but it would allow us to do some interesting graphical
stuff later.

src/numerics.cpp

@@ -19,13 +19,17 @@
 #include <sstream>
 
 Fraction::Fraction(word_t numerator, word_t denominator)
-    : numerator{numerator}, denominator{denominator}
+    : numerator{numerator}, denominator{denominator},
+      norm{numerator / ((long double)denominator)}
 {
   word_t hcf = gcd(MIN(numerator, denominator), MAX(numerator, denominator));
   numerator /= hcf;
   denominator /= hcf;
 }
 
+// floating point arithmetic inaccuracies blah blah blah better to use
+// simplified fractions here
+
 bool Fraction::operator<(const Fraction other)
 {
   if (other.denominator == denominator)

src/numerics.hpp

@@ -30,6 +30,7 @@ typedef uint64_t word_t;
 struct Fraction
 {
   word_t numerator, denominator;
+  long double norm;
 
   Fraction(word_t numerator = 0, word_t denominator = 1);
   bool operator<(const Fraction other);