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Representation-of-integer-operations

Mul-uint-slong

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

Definitions and Theorems

Function: mul-uint-slong

(defun mul-uint-slong (x y)
  (declare (xargs :guard (and (uintp x)
                              (slongp y)
                              (mul-uint-slong-okp x y))))
  (mul-slong-slong (slong-from-uint x) y))

Theorem: slongp-of-mul-uint-slong

(defthm slongp-of-mul-uint-slong
  (slongp (mul-uint-slong x y)))

Theorem: mul-uint-slong-of-uint-fix-x

(defthm mul-uint-slong-of-uint-fix-x
  (equal (mul-uint-slong (uint-fix x) y)
         (mul-uint-slong x y)))

Theorem: mul-uint-slong-uint-equiv-congruence-on-x

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

Theorem: mul-uint-slong-of-slong-fix-y

(defthm mul-uint-slong-of-slong-fix-y
  (equal (mul-uint-slong x (slong-fix y))
         (mul-uint-slong x y)))

Theorem: mul-uint-slong-slong-equiv-congruence-on-y

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