Initial data commit

Task/Modular-inverse/Fortran/modular-inverse.f

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+program modular_inverse_task
+
+  implicit none
+
+  write (*,*) inverse (42, 2017)
+
+contains
+
+  ! Returns -1 if there is no inverse. I assume n > 0. The algorithm
+  ! is described at
+  ! https://en.wikipedia.org/w/index.php?title=Extended_Euclidean_algorithm&oldid=1135569411#Modular_integers
+  function inverse (a, n) result (inverse_value)
+    integer, intent(in) :: a, n
+    integer :: inverse_value
+
+    integer :: t, newt
+    integer :: r, newr
+    integer :: quotient, remainder, tmp
+
+    if (n <= 0) error stop
+    t = 0;  newt = 1
+    r = n;  newr = a
+    do while (newr /= 0)
+       remainder = modulo (r, newr) ! Floor division.
+       quotient = (r - remainder) / newr
+       tmp = newt;  newt = t - (quotient * newt);  t = tmp
+       r   = newr;  newr = remainder
+    end do
+    if (r > 1) then
+       inverse_value = -1
+    else if (t < 0) then
+       inverse_value = t + n
+    else
+       inverse_value = t
+    end if
+  end function inverse
+
+end program modular_inverse_task