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Sparseint$-unary-bittest-offset

Signature

(sparseint$-unary-bittest-offset op offset x) → test

Arguments

op — Guard (integerp op).

offset — Guard (natp offset).

x — Guard (sparseint$-p x).

Returns

test — Type (booleanp test).

Definitions and Theorems

Function: sparseint$-unary-bittest-offset

(defun sparseint$-unary-bittest-offset (op offset x)
  (declare (type (unsigned-byte 2) op))
  (declare (xargs :guard (and (integerp op)
                              (natp offset)
                              (sparseint$-p x))))
  (let ((__function__ 'sparseint$-unary-bittest-offset))
    (declare (ignorable __function__))
    (b* ((op (mbe :logic (loghead 2 op) :exec op)))
      (case op
        (0 nil)
        (1 (not (sparseint$-equal-int offset x -1)))
        (2 (not (sparseint$-equal-int offset x 0)))
        (t t)))))

Theorem: booleanp-of-sparseint$-unary-bittest-offset

(defthm booleanp-of-sparseint$-unary-bittest-offset
  (b* ((test (sparseint$-unary-bittest-offset op offset x)))
    (booleanp test))
  :rule-classes :type-prescription)

Theorem: sparseint$-unary-bittest-offset-correct

(defthm sparseint$-unary-bittest-offset-correct
 (b* ((?test (sparseint$-unary-bittest-offset op offset x)))
  (equal
    test
    (not (equal (unary-bitop op (logtail offset (sparseint$-val x)))
                0)))))

Theorem: sparseint$-unary-bittest-offset-of-ifix-op

(defthm sparseint$-unary-bittest-offset-of-ifix-op
  (equal (sparseint$-unary-bittest-offset (ifix op)
                                          offset x)
         (sparseint$-unary-bittest-offset op offset x)))

Theorem: sparseint$-unary-bittest-offset-int-equiv-congruence-on-op

(defthm sparseint$-unary-bittest-offset-int-equiv-congruence-on-op
  (implies
       (int-equiv op op-equiv)
       (equal (sparseint$-unary-bittest-offset op offset x)
              (sparseint$-unary-bittest-offset op-equiv offset x)))
  :rule-classes :congruence)

Theorem: sparseint$-unary-bittest-offset-of-nfix-offset

(defthm sparseint$-unary-bittest-offset-of-nfix-offset
  (equal (sparseint$-unary-bittest-offset op (nfix offset)
                                          x)
         (sparseint$-unary-bittest-offset op offset x)))

Theorem: sparseint$-unary-bittest-offset-nat-equiv-congruence-on-offset

(defthm
     sparseint$-unary-bittest-offset-nat-equiv-congruence-on-offset
  (implies
       (nat-equiv offset offset-equiv)
       (equal (sparseint$-unary-bittest-offset op offset x)
              (sparseint$-unary-bittest-offset op offset-equiv x)))
  :rule-classes :congruence)

Theorem: sparseint$-unary-bittest-offset-of-sparseint$-fix-x

(defthm sparseint$-unary-bittest-offset-of-sparseint$-fix-x
 (equal
      (sparseint$-unary-bittest-offset op offset (sparseint$-fix x))
      (sparseint$-unary-bittest-offset op offset x)))

Theorem: sparseint$-unary-bittest-offset-sparseint$-equiv-congruence-on-x

(defthm
   sparseint$-unary-bittest-offset-sparseint$-equiv-congruence-on-x
  (implies
       (sparseint$-equiv x x-equiv)
       (equal (sparseint$-unary-bittest-offset op offset x)
              (sparseint$-unary-bittest-offset op offset x-equiv)))
  :rule-classes :congruence)