Data commit

Task/Arithmetic-Rational/Lingo/arithmetic-rational-1.lingo

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+-- parent script "Frac"
+property num
+property denom
+
+----------------------------------------
+-- @constructor
+-- @param {integer} numerator
+-- @param {integer} [denominator=1]
+----------------------------------------
+on new (me, numerator, denominator)
+  if voidP(denominator) then denominator = 1
+  if denominator=0 then return VOID -- rule out division by zero
+  g = me._gcd(numerator, denominator)
+  if g<>0 then
+    numerator = numerator/g
+    denominator = denominator/g
+  else
+    numerator = 0
+    denominator = 1
+  end if
+  if denominator<0 then
+    numerator = -numerator
+    denominator = -denominator
+  end if
+  me.num = numerator
+  me.denom = denominator
+  return me
+end
+
+----------------------------------------
+-- Returns string representation "<num>/<denom>"
+-- @return {string}
+----------------------------------------
+on toString (me)
+  return me.num&"/"&me.denom
+end
+
+----------------------------------------
+--
+----------------------------------------
+on _gcd (me, a, b)
+  if a = 0 then return b
+  if b = 0 then return a
+  if a > b then return me._gcd(b, a mod b)
+  return me._gcd(a, b mod a)
+end

Task/Arithmetic-Rational/Lingo/arithmetic-rational-2.lingo

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+-- Frac library (movie script)
+
+----------------------------------------
+-- Shortcut for creating 'frac' values
+-- @param {integer} numerator
+-- @param {integer} denominator
+-- @return {instance}
+----------------------------------------
+on frac (numerator, denominator)
+  return script("Frac").new(numerator, denominator)
+end
+
+----------------------------------------
+-- All functions below this comment only support 'fracs', i.e. instances
+-- of the Frac Class, as arguments. An integer n is casted to frac via frac(n).
+----------------------------------------
+
+-- Optionally supports more than 2 arguments
+on fAdd (a, b) -- ...
+  res = a
+  repeat with i = 2 to the paramCount
+    p = param(i)
+    num = res.num * p.denom + res.denom * p.num
+    denom = res.denom * p.denom
+    res = frac(num, denom)
+  end repeat
+  return res
+end
+
+on fSub (a, b)
+  return frac(a.num * b.den - a.den * b.num, a.den * b.den)
+end
+
+-- Optionally supports more than 2 arguments
+on fMul (a, b) -- ...
+  res = a
+  repeat with i = 2 to the paramCount
+    p = param(i)
+    res = frac(res.num * p.num, res.denom * p.denom)
+  end repeat
+  return res
+end
+
+on fDiv (a, b)
+  return frac(a.num * b.denom, a.denom * b.num)
+end
+
+on fAbs (f)
+  return frac(abs(f.num), f.denom)
+end
+
+on fNeg (f)
+  return frac(-f.num, f.denom)
+end
+
+on fEQ (a, b)
+  diff = fSub(a, b)
+  return diff.num=0
+end
+
+on fNE (a, b)
+  return not fEQ (a, b)
+end
+
+on fGT (a, b)
+  diff = fSub(a, b)
+  return diff.num>0
+end
+
+on fLT (a, b)
+  diff = fSub(a, b)
+  return diff.num<0
+end
+
+on fGE (a, b)
+  diff = fSub(a, b)
+  return diff.num>=0
+end
+
+on fLE (a, b)
+  diff = fSub(a, b)
+  return diff.num<=0
+end

Task/Arithmetic-Rational/Lingo/arithmetic-rational-3.lingo

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+f = frac(2,3)
+put f.toString()
+-- "2/3"
+
+-- fractions are normalized on the fly
+f = frac(4,6)
+put f.toString()
+-- "2/3"
+
+-- casting integer to frac
+f = frac(23)
+put f.toString()
+-- "23/1"

Task/Arithmetic-Rational/Lingo/arithmetic-rational-4.lingo

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+-- in some movie script
+----------------------------------------
+-- Prints all perfect numbers up to n
+-- @param {integer|float} n
+----------------------------------------
+on findPerfects (n)
+  repeat with i = 2 to n
+    sum = frac(1, i)
+    cnt = sqrt(i)
+    repeat with fac = 2 to cnt
+      if i mod fac = 0 then sum = fAdd(sum, frac(1, fac), frac(fac, i))
+    end repeat
+    if sum.denom = sum.num then put i
+  end repeat
+end

Task/Arithmetic-Rational/Lingo/arithmetic-rational-5.lingo

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+findPerfects(power(2, 19))
+-- 6
+-- 28
+-- 496
+-- 8128