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Vl-bitlist-from-nat

Turn a natural number into a vl-bitlist-p of the given width.

Signature

(vl-bitlist-from-nat x width) → bits

Arguments

x — Guard (natp x).

width — Guard (natp width).

Returns

bits — Type (vl-bitlist-p bits).

Definitions and Theorems

Function: vl-bitlist-from-nat

(defun vl-bitlist-from-nat (x width)
  (declare (xargs :guard (and (natp x) (natp width))))
  (let ((__function__ 'vl-bitlist-from-nat))
    (declare (ignorable __function__))
    (b* (((when (zp width)) nil)
         (width (1- width))
         (bit (if (logbitp width (lnfix x))
                  :vl-1val
                :vl-0val)))
      (cons bit (vl-bitlist-from-nat x width)))))

Theorem: vl-bitlist-p-of-vl-bitlist-from-nat

(defthm vl-bitlist-p-of-vl-bitlist-from-nat
  (b* ((bits (vl-bitlist-from-nat x width)))
    (vl-bitlist-p bits))
  :rule-classes :rewrite)

Theorem: len-of-vl-bitlist-from-nat

(defthm len-of-vl-bitlist-from-nat
  (equal (len (vl-bitlist-from-nat x width))
         (nfix width)))

Theorem: vl-bitlist-from-nat-of-nfix-x

(defthm vl-bitlist-from-nat-of-nfix-x
  (equal (vl-bitlist-from-nat (nfix x) width)
         (vl-bitlist-from-nat x width)))

Theorem: vl-bitlist-from-nat-nat-equiv-congruence-on-x

(defthm vl-bitlist-from-nat-nat-equiv-congruence-on-x
  (implies (acl2::nat-equiv x x-equiv)
           (equal (vl-bitlist-from-nat x width)
                  (vl-bitlist-from-nat x-equiv width)))
  :rule-classes :congruence)

Theorem: vl-bitlist-from-nat-of-nfix-width

(defthm vl-bitlist-from-nat-of-nfix-width
  (equal (vl-bitlist-from-nat x (nfix width))
         (vl-bitlist-from-nat x width)))

Theorem: vl-bitlist-from-nat-nat-equiv-congruence-on-width

(defthm vl-bitlist-from-nat-nat-equiv-congruence-on-width
  (implies (acl2::nat-equiv width width-equiv)
           (equal (vl-bitlist-from-nat x width)
                  (vl-bitlist-from-nat x width-equiv)))
  :rule-classes :congruence)