Initial data commit

Task/Modular-inverse/ObjectIcon/modular-inverse.oi

@@ -0,0 +1,55 @@
+# -*- ObjectIcon -*-
+
+import exception
+import io
+
+procedure main ()
+  test_euclid_div ()
+  io.write (inverse (42, 2017))
+end
+
+procedure inverse (a, n)        # FAILS if there is no inverse.
+  local t, newt, r, newr, quotient, tmp
+
+  if n <= 0 then throw ("non-positive modulus")
+  t := 0;  newt := 1
+  r := n;  newr := a
+  while newr ~= 0 do
+  {
+    quotient := euclid_div (r, newr)
+    tmp := newt;  newt := t - (quotient * newt);  t := tmp
+    tmp := newr;  newr := r - (quotient * newr);  r := tmp
+  }
+  r <= 1 | fail
+  return (if t < 0 then t + n else t)
+end
+
+procedure euclid_div (x, y)
+  # This kind of integer division always gives a remainder between 0
+  # and abs(y)-1, inclusive. Thus the remainder is always a LEAST
+  # RESIDUE modulo abs(y). (If y is a positive modulus, then only the
+  # floor division branch is used.)
+  return \
+    if 0 <= y then              # Do floor division.
+      (if 0 <= x then x / y
+      else if (-x) % y = 0 then -((-x) / y)
+      else -((-x) / y) - 1)
+    else                        # Do ceiling division.
+      (if 0 <= x then -(x / (-y))
+      else if (-x) % (-y) = 0 then ((-x) / (-y))
+      else ((-x) / (-y)) + 1)
+end
+
+procedure test_euclid_div ()
+  local x, y, q, r
+
+  every x := -100 to 100 do
+    every y := -100 to 100 & y ~= 0 do
+    {
+      q := euclid_div (x, y)
+      r := x - (q * y)
+      if r < 0 | abs (y) <= r then
+        # A remainder was outside the expected range.
+        throw ("Test of euclid_div failed.")
+    }
+end