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• Integer-operations

Long-rem

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

Signature

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

Arguments

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

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

Returns

result — Type (long-valuep result).

Definitions and Theorems

Function: long-rem

(defun long-rem (operand-left operand-right)
  (declare (xargs :guard (and (long-valuep operand-left)
                              (long-valuep operand-right))))
  (declare (xargs :guard (not (equal (long-value->int operand-right)
                                     0))))
  (b* ((x (long-value->int operand-left))
       (y (long-value->int operand-right)))
    (long-value (logext 64 (rem x y)))))

Theorem: long-valuep-of-long-rem

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

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

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

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

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

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

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

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

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