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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)