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Representation-of-integer-operations

Mul-sint-sint

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

Definitions and Theorems

Function: mul-sint-sint

(defun mul-sint-sint (x y)
  (declare (xargs :guard (and (sintp x)
                              (sintp y)
                              (mul-sint-sint-okp x y))))
  (sint-from-integer (* (integer-from-sint x)
                        (integer-from-sint y))))

Theorem: sintp-of-mul-sint-sint

(defthm sintp-of-mul-sint-sint
  (sintp (mul-sint-sint x y)))

Theorem: mul-sint-sint-of-sint-fix-x

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

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

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

Theorem: mul-sint-sint-of-sint-fix-y

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

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

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