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Representation-of-integer-operations

Mul-ulong-ulong

Multiplication of a value of type unsigned long and a value of type unsigned long [C:6.5.5].

Definitions and Theorems

Function: mul-ulong-ulong

(defun mul-ulong-ulong (x y)
  (declare (xargs :guard (and (ulongp x) (ulongp y))))
  (ulong-from-integer-mod (* (integer-from-ulong x)
                             (integer-from-ulong y))))

Theorem: ulongp-of-mul-ulong-ulong

(defthm ulongp-of-mul-ulong-ulong
  (ulongp (mul-ulong-ulong x y)))

Theorem: mul-ulong-ulong-of-ulong-fix-x

(defthm mul-ulong-ulong-of-ulong-fix-x
  (equal (mul-ulong-ulong (ulong-fix x) y)
         (mul-ulong-ulong x y)))

Theorem: mul-ulong-ulong-ulong-equiv-congruence-on-x

(defthm mul-ulong-ulong-ulong-equiv-congruence-on-x
  (implies (ulong-equiv x x-equiv)
           (equal (mul-ulong-ulong x y)
                  (mul-ulong-ulong x-equiv y)))
  :rule-classes :congruence)

Theorem: mul-ulong-ulong-of-ulong-fix-y

(defthm mul-ulong-ulong-of-ulong-fix-y
  (equal (mul-ulong-ulong x (ulong-fix y))
         (mul-ulong-ulong x y)))

Theorem: mul-ulong-ulong-ulong-equiv-congruence-on-y

(defthm mul-ulong-ulong-ulong-equiv-congruence-on-y
  (implies (ulong-equiv y y-equiv)
           (equal (mul-ulong-ulong x y)
                  (mul-ulong-ulong x y-equiv)))
  :rule-classes :congruence)