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4vec-operations

4vec-quotient

Integer division as in truncate for 4vecs.

Signature
(4vec-quotient x y) → quotient
Arguments: x — Guard (4vec-p x).; y — Guard (4vec-p y).
Returns: quotient — Type (4vec-p quotient).

This is a fairly conservative definition in the style of the Verilog semantics: if either input has X or Z bits, or if you try to divide by zero, then the result is all X bits. Otherwise, we produce the integer division of \frac{x}{y}, rounding toward zero as in truncate.

Definitions and Theorems

Function: 4vec-quotient

(defun 4vec-quotient (x y)
  (declare (xargs :guard (and (4vec-p x) (4vec-p y))))
  (let ((__function__ '4vec-quotient))
    (declare (ignorable __function__))
    (if (and (2vec-p x)
             (2vec-p y)
             (not (eql (2vec->val y) 0)))
        (2vec (truncate (the integer (2vec->val x))
                        (the integer (2vec->val y))))
      (4vec-x))))

Theorem: 4vec-p-of-4vec-quotient

(defthm 4vec-p-of-4vec-quotient
  (b* ((quotient (4vec-quotient x y)))
    (4vec-p quotient))
  :rule-classes :rewrite)

Theorem: 4vec-quotient-of-2vecx-fix-x

(defthm 4vec-quotient-of-2vecx-fix-x
  (equal (4vec-quotient (2vecx-fix x) y)
         (4vec-quotient x y)))

Theorem: 4vec-quotient-2vecx-equiv-congruence-on-x

(defthm 4vec-quotient-2vecx-equiv-congruence-on-x
  (implies (2vecx-equiv x x-equiv)
           (equal (4vec-quotient x y)
                  (4vec-quotient x-equiv y)))
  :rule-classes :congruence)

Theorem: 4vec-quotient-of-2vecx-fix-y

(defthm 4vec-quotient-of-2vecx-fix-y
  (equal (4vec-quotient x (2vecx-fix y))
         (4vec-quotient x y)))

Theorem: 4vec-quotient-2vecx-equiv-congruence-on-y

(defthm 4vec-quotient-2vecx-equiv-congruence-on-y
  (implies (2vecx-equiv y y-equiv)
           (equal (4vec-quotient x y)
                  (4vec-quotient x y-equiv)))
  :rule-classes :congruence)