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Bitops/extra-defs

Nth-slice32

Extract the nth 32-bit slice of the integer x.

Signature
(nth-slice32 n x) → slice
Arguments: n — Guard (natp n).; x — Guard (integerp x).
Returns: slice — Type (natp slice).

We leave this enabled; we would usually not expect to try to reason about it.

Definitions and Theorems

Function: nth-slice32$inline

(defun acl2::nth-slice32$inline (n x)
  (declare (xargs :guard (and (natp n) (integerp x))))
  (let ((__function__ 'nth-slice32))
    (declare (ignorable __function__))
    (mbe :logic (logand (ash (ifix x) (* (nfix n) -32))
                        (1- (expt 2 32)))
         :exec (the (unsigned-byte 32)
                    (logand (ash x (the (integer * 0) (* n -32)))
                            4294967295)))))

Theorem: natp-of-nth-slice32

(defthm acl2::natp-of-nth-slice32
  (b* ((slice (acl2::nth-slice32$inline n x)))
    (natp slice))
  :rule-classes :type-prescription)

Theorem: nat-equiv-implies-equal-nth-slice32-1

(defthm nat-equiv-implies-equal-nth-slice32-1
  (implies (nat-equiv n n-equiv)
           (equal (nth-slice32 n x)
                  (nth-slice32 n-equiv x)))
  :rule-classes (:congruence))

Theorem: int-equiv-implies-equal-nth-slice32-2

(defthm int-equiv-implies-equal-nth-slice32-2
  (implies (int-equiv x x-equiv)
           (equal (nth-slice32 n x)
                  (nth-slice32 n x-equiv)))
  :rule-classes (:congruence))

Theorem: unsigned-byte-p-32-of-nth-slice32

(defthm unsigned-byte-p-32-of-nth-slice32
  (unsigned-byte-p 32 (nth-slice32 n x)))

Theorem: nth-slice32-is-nth-slice

(defthm nth-slice32-is-nth-slice
  (equal (nth-slice32 n x)
         (nth-slice 32 n x)))