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Sparseint

Sparseint-binary-bittest

Test whether a binary bitwise operation (represented as a 4-bit truth table) on two sparseints yields a nonzero value.

Signature
(sparseint-binary-bittest op x y) → test
Arguments: op — Guard (integerp op).; x — Guard (sparseint-p x).; y — Guard (sparseint-p y).
Returns: test — Type (booleanp test).

Definitions and Theorems

Function: sparseint-binary-bittest$inline

(defun sparseint-binary-bittest$inline (op x y)
  (declare (type (unsigned-byte 4) op))
  (declare (xargs :guard (and (integerp op)
                              (sparseint-p x)
                              (sparseint-p y))))
  (let ((__function__ 'sparseint-binary-bittest))
    (declare (ignorable __function__))
    (sparseint$-binary-bittest op (sparseint-fix x)
                               (sparseint-fix y))))

Theorem: booleanp-of-sparseint-binary-bittest

(defthm booleanp-of-sparseint-binary-bittest
  (b* ((test (sparseint-binary-bittest$inline op x y)))
    (booleanp test))
  :rule-classes :type-prescription)

Theorem: sparseint-val-of-sparseint-binary-bittest

(defthm sparseint-val-of-sparseint-binary-bittest
  (b* ((?test (sparseint-binary-bittest$inline op x y)))
    (equal test
           (binary-bittest op (sparseint-val x)
                           (sparseint-val y)))))

Theorem: sparseint-binary-bittest$inline-of-ifix-op

(defthm sparseint-binary-bittest$inline-of-ifix-op
  (equal (sparseint-binary-bittest$inline (ifix op)
                                          x y)
         (sparseint-binary-bittest$inline op x y)))

Theorem: sparseint-binary-bittest$inline-int-equiv-congruence-on-op

(defthm sparseint-binary-bittest$inline-int-equiv-congruence-on-op
  (implies (int-equiv op op-equiv)
           (equal (sparseint-binary-bittest$inline op x y)
                  (sparseint-binary-bittest$inline op-equiv x y)))
  :rule-classes :congruence)

Theorem: sparseint-binary-bittest$inline-of-sparseint-fix-x

(defthm sparseint-binary-bittest$inline-of-sparseint-fix-x
  (equal (sparseint-binary-bittest$inline op (sparseint-fix x)
                                          y)
         (sparseint-binary-bittest$inline op x y)))

Theorem: sparseint-binary-bittest$inline-sparseint-equiv-congruence-on-x

(defthm
    sparseint-binary-bittest$inline-sparseint-equiv-congruence-on-x
  (implies (sparseint-equiv x x-equiv)
           (equal (sparseint-binary-bittest$inline op x y)
                  (sparseint-binary-bittest$inline op x-equiv y)))
  :rule-classes :congruence)

Theorem: sparseint-binary-bittest$inline-of-sparseint-fix-y

(defthm sparseint-binary-bittest$inline-of-sparseint-fix-y
  (equal (sparseint-binary-bittest$inline op x (sparseint-fix y))
         (sparseint-binary-bittest$inline op x y)))

Theorem: sparseint-binary-bittest$inline-sparseint-equiv-congruence-on-y

(defthm
    sparseint-binary-bittest$inline-sparseint-equiv-congruence-on-y
  (implies (sparseint-equiv y y-equiv)
           (equal (sparseint-binary-bittest$inline op x y)
                  (sparseint-binary-bittest$inline op x y-equiv)))
  :rule-classes :congruence)