Data commit

Task/Modular-inverse/Ruby/modular-inverse-1.rb

@@ -0,0 +1,20 @@
+#based on pseudo code from http://en.wikipedia.org/wiki/Extended_Euclidean_algorithm#Iterative_method_2 and from translating the python implementation.
+def extended_gcd(a, b)
+  last_remainder, remainder = a.abs, b.abs
+  x, last_x, y, last_y = 0, 1, 1, 0
+  while remainder != 0
+    last_remainder, (quotient, remainder) = remainder, last_remainder.divmod(remainder)
+    x, last_x = last_x - quotient*x, x
+    y, last_y = last_y - quotient*y, y
+  end
+
+  return last_remainder, last_x * (a < 0 ? -1 : 1)
+end
+
+def invmod(e, et)
+  g, x = extended_gcd(e, et)
+  if g != 1
+    raise 'The maths are broken!'
+  end
+  x % et
+end

Task/Modular-inverse/Ruby/modular-inverse-2.rb

@@ -0,0 +1,12 @@
+def modinv(a, m) # compute a^-1 mod m if possible
+  raise "NO INVERSE - #{a} and #{m} not coprime" unless a.gcd(m) == 1
+  return m if m == 1
+  m0, inv, x0 = m, 1, 0
+  while a > 1
+    inv -= (a / m) * x0
+    a, m = m, a % m
+    inv, x0 = x0, inv
+  end
+  inv += m0 if inv < 0
+  inv
+end

Task/Modular-inverse/Ruby/modular-inverse-3.rb

@@ -0,0 +1,2 @@
+require 'openssl'
+p OpenSSL::BN.new(42).mod_inverse(2017).to_i