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Floating-point-operations

Double-rem

Remainder % on doubles [JLS14:4.2.4] [JLS14:15.17.3].

Signature
(double-rem 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-rem

(defun double-rem (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-rem-abs x y))))

Theorem: double-valuep-of-double-rem

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

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

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

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

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

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

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

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

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