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4vec-operations

4vec-rev-blocks

Similar to a streaming concatenation operation in SystemVerilog.

Signature
(4vec-rev-blocks nbits blocksz x) → res
Arguments: nbits — Guard (4vec-p nbits).; blocksz — Guard (4vec-p blocksz).; x — Guard (4vec-p x).
Returns: res — Type (4vec-p res).

BOZO document me.

Definitions and Theorems

Function: 4vec-rev-blocks

(defun 4vec-rev-blocks (nbits blocksz x)
  (declare (xargs :guard (and (4vec-p nbits)
                              (4vec-p blocksz)
                              (4vec-p x))))
  (let ((__function__ '4vec-rev-blocks))
    (declare (ignorable __function__))
    (if (and (2vec-p nbits)
             (<= 0 (2vec->val nbits))
             (2vec-p blocksz)
             (< 0 (2vec->val blocksz)))
        (b* (((4vec x)))
          (4vec (rev-blocks (2vec->val nbits)
                            (2vec->val blocksz)
                            x.upper)
                (rev-blocks (2vec->val nbits)
                            (2vec->val blocksz)
                            x.lower)))
      (4vec-x))))

Theorem: 4vec-p-of-4vec-rev-blocks

(defthm 4vec-p-of-4vec-rev-blocks
  (b* ((res (4vec-rev-blocks nbits blocksz x)))
    (4vec-p res))
  :rule-classes :rewrite)

Theorem: 4vec-rev-blocks-of-4vec-fix-nbits

(defthm 4vec-rev-blocks-of-4vec-fix-nbits
  (equal (4vec-rev-blocks (4vec-fix nbits)
                          blocksz x)
         (4vec-rev-blocks nbits blocksz x)))

Theorem: 4vec-rev-blocks-4vec-equiv-congruence-on-nbits

(defthm 4vec-rev-blocks-4vec-equiv-congruence-on-nbits
  (implies (4vec-equiv nbits nbits-equiv)
           (equal (4vec-rev-blocks nbits blocksz x)
                  (4vec-rev-blocks nbits-equiv blocksz x)))
  :rule-classes :congruence)

Theorem: 4vec-rev-blocks-of-4vec-fix-blocksz

(defthm 4vec-rev-blocks-of-4vec-fix-blocksz
  (equal (4vec-rev-blocks nbits (4vec-fix blocksz)
                          x)
         (4vec-rev-blocks nbits blocksz x)))

Theorem: 4vec-rev-blocks-4vec-equiv-congruence-on-blocksz

(defthm 4vec-rev-blocks-4vec-equiv-congruence-on-blocksz
  (implies (4vec-equiv blocksz blocksz-equiv)
           (equal (4vec-rev-blocks nbits blocksz x)
                  (4vec-rev-blocks nbits blocksz-equiv x)))
  :rule-classes :congruence)

Theorem: 4vec-rev-blocks-of-4vec-fix-x

(defthm 4vec-rev-blocks-of-4vec-fix-x
  (equal (4vec-rev-blocks nbits blocksz (4vec-fix x))
         (4vec-rev-blocks nbits blocksz x)))

Theorem: 4vec-rev-blocks-4vec-equiv-congruence-on-x

(defthm 4vec-rev-blocks-4vec-equiv-congruence-on-x
  (implies (4vec-equiv x x-equiv)
           (equal (4vec-rev-blocks nbits blocksz x)
                  (4vec-rev-blocks nbits blocksz x-equiv)))
  :rule-classes :congruence)

Subtopics

Rev-blocks: Reverses blocks, like the streaming concatenation operator in SystemVerilog.
Rev-block-index: For reasoning about rev-blocks, computes the offset into x corresponding to an offset into (rev-blocks nbits blocksz x).