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4vec-operations

4vec-bit-extract

Like logbit for 4vecs; the bit position may be a 4vec.

Signature
(4vec-bit-extract n x) → res
Arguments: n — The bit position to extract.
Guard (4vec-p n).; x — The 4vec to extract it from.
Guard (4vec-p x).
Returns: res — Type (4vec-p res).

We extract the nth bit of x as a new 4vec.

Here n itself can also be a 4vec. This flexibility is often not necessary. When possible, it is generally better (more efficient) to use 4vec-bit-index, which requires n to be a natp. When n happens to be a natural, i.e., a 2vec, both functions compute the same result.

When n is negative or isn't two-valued, i.e., it has some X or Z bit somewhere, then we simply return a one-bit X value. This agrees to the Verilog semantics for foo[n] in cases where n is unknown.

Definitions and Theorems

Function: 4vec-bit-extract

(defun 4vec-bit-extract (n x)
  (declare (xargs :guard (and (4vec-p n) (4vec-p x))))
  (let ((__function__ '4vec-bit-extract))
    (declare (ignorable __function__))
    (if (and (2vec-p n) (<= 0 (2vec->val n)))
        (4vec-bit-index (2vec->val n) x)
      (4vec-1x))))

Theorem: 4vec-p-of-4vec-bit-extract

(defthm 4vec-p-of-4vec-bit-extract
  (b* ((res (4vec-bit-extract n x)))
    (4vec-p res))
  :rule-classes :rewrite)

Theorem: 4vec-bit-extract-of-4vec-fix-n

(defthm 4vec-bit-extract-of-4vec-fix-n
  (equal (4vec-bit-extract (4vec-fix n) x)
         (4vec-bit-extract n x)))

Theorem: 4vec-bit-extract-4vec-equiv-congruence-on-n

(defthm 4vec-bit-extract-4vec-equiv-congruence-on-n
  (implies (4vec-equiv n n-equiv)
           (equal (4vec-bit-extract n x)
                  (4vec-bit-extract n-equiv x)))
  :rule-classes :congruence)

Theorem: 4vec-bit-extract-of-4vec-fix-x

(defthm 4vec-bit-extract-of-4vec-fix-x
  (equal (4vec-bit-extract n (4vec-fix x))
         (4vec-bit-extract n x)))

Theorem: 4vec-bit-extract-4vec-equiv-congruence-on-x

(defthm 4vec-bit-extract-4vec-equiv-congruence-on-x
  (implies (4vec-equiv x x-equiv)
           (equal (4vec-bit-extract n x)
                  (4vec-bit-extract n x-equiv)))
  :rule-classes :congruence)