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• Integer-operations

Int-rem

Remainder & on ints [JLS14:4.2.2] [JLS14:15.17.3].

Signature

(int-rem operand-left operand-right) → result

Arguments

operand-left — Guard (int-valuep operand-left).

operand-right — Guard (int-valuep operand-right).

Returns

result — Type (int-valuep result).

Definitions and Theorems

Function: int-rem

(defun int-rem (operand-left operand-right)
  (declare (xargs :guard (and (int-valuep operand-left)
                              (int-valuep operand-right))))
  (declare (xargs :guard (not (equal (int-value->int operand-right)
                                     0))))
  (b* ((x (int-value->int operand-left))
       (y (int-value->int operand-right)))
    (int-value (logext 32 (rem x y)))))

Theorem: int-valuep-of-int-rem

(defthm int-valuep-of-int-rem
  (b* ((result (int-rem operand-left operand-right)))
    (int-valuep result))
  :rule-classes :rewrite)

Theorem: int-rem-of-int-value-fix-operand-left

(defthm int-rem-of-int-value-fix-operand-left
  (equal (int-rem (int-value-fix operand-left)
                  operand-right)
         (int-rem operand-left operand-right)))

Theorem: int-rem-int-value-equiv-congruence-on-operand-left

(defthm int-rem-int-value-equiv-congruence-on-operand-left
  (implies (int-value-equiv operand-left operand-left-equiv)
           (equal (int-rem operand-left operand-right)
                  (int-rem operand-left-equiv operand-right)))
  :rule-classes :congruence)

Theorem: int-rem-of-int-value-fix-operand-right

(defthm int-rem-of-int-value-fix-operand-right
  (equal (int-rem operand-left
                  (int-value-fix operand-right))
         (int-rem operand-left operand-right)))

Theorem: int-rem-int-value-equiv-congruence-on-operand-right

(defthm int-rem-int-value-equiv-congruence-on-operand-right
  (implies (int-value-equiv operand-right operand-right-equiv)
           (equal (int-rem operand-left operand-right)
                  (int-rem operand-left operand-right-equiv)))
  :rule-classes :congruence)