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Double-add

Addition + on doubles [JLS14:4.2.4] [JLS14:15.18.2].

Signature

(double-add operand-left operand-right) → result

Arguments

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

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

Returns

result — Type (double-valuep result).

Definitions and Theorems

Function: double-add

(defun double-add (operand-left operand-right)
  (declare (xargs :guard (and (double-valuep operand-left)
                              (double-valuep operand-right))))
  (b* ((x (double-value->double operand-left))
       (y (double-value->double operand-right)))
    (double-value (double-add-abs x y))))

Theorem: double-valuep-of-double-add

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

Theorem: double-add-of-double-value-fix-operand-left

(defthm double-add-of-double-value-fix-operand-left
  (equal (double-add (double-value-fix operand-left)
                     operand-right)
         (double-add operand-left operand-right)))

Theorem: double-add-double-value-equiv-congruence-on-operand-left

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

Theorem: double-add-of-double-value-fix-operand-right

(defthm double-add-of-double-value-fix-operand-right
  (equal (double-add operand-left
                     (double-value-fix operand-right))
         (double-add operand-left operand-right)))

Theorem: double-add-double-value-equiv-congruence-on-operand-right

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