priv/stdlib/Frac.aes

@@ -7,6 +7,7 @@ namespace Frac =
 
   datatype frac = Pos(int, int) | Zero | Neg(int, int)
 
+  // Checks if internal representation is correct. Numerator and denominator must be positive.
   function is_sane(f : frac) : bool = switch(f)
     Pos(n, d) => n > 0 && d > 0
     Zero => true
@@ -37,6 +38,7 @@ namespace Frac =
     Neg(n, d) => String.concat("-", to_str(Pos(n, d)))
     Zero      => "0"
 
+  // Reduce fraction to normal form
   function simplify(f : frac) : frac =
     switch(f)
       Neg(n, d) =>
@@ -47,7 +49,7 @@ namespace Frac =
         let cd = gcd(n, d)
         Pos(n / cd, d / cd)
 
-  function make_frac(n : int, d : int): frac =
+  function make_frac(n : int, d : int) : frac =
     if (d == 0) abort("Division by zero")
     elif (n == 0) Zero
     elif ((n < 0) == (d < 0)) simplify(Pos(abs_int(n), abs_int(d)))
@@ -109,6 +111,7 @@ namespace Frac =
     Zero      => 0
     Neg(n, d) => -(n + d - 1) / d
 
+  // Round towards nearest integer. If two integers are in the same distance, choose the even one.
   function round(f : frac) : int =
     let fl = floor(f)
     let cl = ceil(f)
@@ -153,4 +156,16 @@ namespace Frac =
       else
         let half = int_exp_(b, e / 2)
         if (e mod 2 == 1) mul(mul(half, half), b)
-        else mul(half, half)
+        else mul(half, half)
+
+  // Reduces the fraction's in-memory size by dividing its components by two until the
+  // the error is bigger than `loss` value
+  function optimize(f : frac, loss : frac) : frac =
+    require(geq(loss, Zero), "negative loss optimize")
+    let s = sign(f)
+    mul(from_int(s), run_optimize(abs(f), loss))
+  private function run_optimize(f : frac, loss : frac) : frac =
+    let t = make_frac((num(f) + 1) / 2, (den(f) + 1)/2)
+    if(gt(abs(sub(t, f)), loss)) f
+    elif (eq(t, f)) f
+    else run_optimize(t, loss)