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Prefixes

Prefixes->num

Access the |X86ISA|::|NUM| field of a prefixes bit structure.

Signature
(prefixes->num x) → num
Arguments: x — Guard (prefixes-p x).
Returns: num — Type (4bits-p num).

Definitions and Theorems

Function: prefixes->num$inline

(defun prefixes->num$inline (x)
  (declare (xargs :guard (prefixes-p x)))
  (mbe :logic
       (let ((x (prefixes-fix x)))
         (part-select x :low 0 :width 4))
       :exec (the (unsigned-byte 4)
                  (logand (the (unsigned-byte 4) 15)
                          (the (unsigned-byte 52) x)))))

Theorem: 4bits-p-of-prefixes->num

(defthm 4bits-p-of-prefixes->num
  (b* ((num (prefixes->num$inline x)))
    (4bits-p num))
  :rule-classes :rewrite)

Theorem: prefixes->num$inline-of-prefixes-fix-x

(defthm prefixes->num$inline-of-prefixes-fix-x
  (equal (prefixes->num$inline (prefixes-fix x))
         (prefixes->num$inline x)))

Theorem: prefixes->num$inline-prefixes-equiv-congruence-on-x

(defthm prefixes->num$inline-prefixes-equiv-congruence-on-x
  (implies (prefixes-equiv x x-equiv)
           (equal (prefixes->num$inline x)
                  (prefixes->num$inline x-equiv)))
  :rule-classes :congruence)

Theorem: prefixes->num-of-prefixes

(defthm prefixes->num-of-prefixes
  (equal (prefixes->num (prefixes num lck rep seg opr adr nxt))
         (4bits-fix num)))

Theorem: prefixes->num-of-write-with-mask

(defthm prefixes->num-of-write-with-mask
 (implies
  (and
   (fty::bitstruct-read-over-write-hyps x prefixes-equiv-under-mask)
   (prefixes-equiv-under-mask x y fty::mask)
   (equal (logand (lognot fty::mask) 15)
          0))
  (equal (prefixes->num x)
         (prefixes->num y))))