Alternative reduce with specifiable precision

@@ -49,6 +49,22 @@ impl Continuous {
         inner(&mut v, x, a0, 0, 1, a0);
         Continuous(v)
     }
+
+    pub fn into_prec(&self, prec :usize) -> Fractional {
+        let Continuous(c) = self;
+        let             p = if prec <= c.len() { prec } else { c.len() };
+
+        let to_frac = |acc :Fractional, x :&i64| {
+            let Fractional(an, ad) = acc.noreduce_add((*x).into());
+            Fractional(ad, an)
+        };
+
+        let Fractional(n, d) = c[..p]
+                             . into_iter()
+                             . rev()
+                             . fold(Fractional(0, 1), to_frac);
+        Fractional(d, n)
+    }
 }
 
 impl From<&Fractional> for Continuous {
@@ -57,11 +73,12 @@ impl From<&Fractional> for Continuous {
         fn inner(mut v :Vec<i64>, f :Fractional) -> Vec<i64> {
             let Fractional(n, d)   = f;
             let a                  = n / d;
-            let Fractional(_n, _d) = f - a.into();
+            let Fractional(_n, _d) = f.noreduce_sub(a.into());
 
             v.push(a);
             match _n {
                 1 => { v.push(_d); v },
+                0 => v,
                 _ => inner(v, Fractional(_d, _n)),
             }
         }

@@ -28,6 +28,8 @@ use std::fmt::{Formatter, Display};
 use std::num::TryFromIntError;
 use std::ops::{Add,Sub,Neg,Mul,Div};
 
+use crate::continuous::Continuous;
+
 #[derive(Debug, Eq, Clone, Copy)]
 pub struct Fractional (pub i64, pub i64);
 
@@ -67,9 +69,28 @@ impl Fractional {
                 Self(1, _n / _d)
             }
         } else {
-            Self(n / hcf(n, d), d / hcf(n, d))
+            //Self(n / hcf(n, d), d / hcf(n, d))
+            let regular_reduced = self;
+            let cont :Continuous = (&regular_reduced).into();
+            cont.into_prec(5)
         }
     }
+
+    pub fn noreduce_add(self, other: Self) -> Self {
+        let Fractional(n1, d1) = self;
+        let Fractional(n2, d2) = other;
+        let n = n1 * (self.gcd(other) / d1) + n2 * (self.gcd(other) / d2);
+        Self(n, self.gcd(other))
+    }
+
+    pub fn noreduce_sub(self, other: Self) -> Self {
+        self.noreduce_add(other.noreduce_neg())
+    }
+
+    pub fn noreduce_neg(self) -> Self {
+        let Fractional(n, d) = self;
+        Self(-n, d)
+    }
 }
 
 impl From<i64> for Fractional {