;;; Procedure:
;;;   remainder
;;; Parameters:
;;;   dividend, an integer [verified]
;;;   divisor, an integer [verified]
;;; Purpose:
;;;   Compute the whole remainder of dividing dividend by divisor.
;;; Produces:
;;;   rem, an integer
;;; Preconditions:
;;;   divisor != 0 [verified]
;;; Postconditions:
;;;   Exists integer, quotient, such that
;;;     quotient*divisor + remainder = dividend
;;;     abs(quotient*divisor) <= abs(dividend)
;;;     abs(dividend) < abs((quotient+1)* divisor)
;;;   Informally: "The quotient is the biggest number such that
;;;     when you multiply it by divisor, the result is less than
;;;     dividend."

;;; Procedure:
;;;   modulo
;;; Parameters:
;;;   val, an integer [verified]
;;;   base, an integer [verified]
;;; Purpose:
;;;   Computes val mod base.
;;; Produces:
;;;   result, an integer
;;; Preconditions:
;;;   base is non 0.
;;; Postconditions:
;;;   If base > 0, 0 <= result < base.
;;;   If base < 0, base < result <= 0.
;;;   Exists integer, quotient, such that
;;;     quotient*base + result = val