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Modr/m

Modr/m->mod

Access the |COMMON-LISP|::|MOD| field of a modr/m bit structure.

Signature
(modr/m->mod x) → mod
Arguments: x — Guard (modr/m-p x).
Returns: mod — Type (2bits-p mod).

Definitions and Theorems

Function: modr/m->mod$inline

(defun modr/m->mod$inline (x)
 (declare (xargs :guard (modr/m-p x)))
 (mbe
     :logic
     (let ((x (modr/m-fix x)))
       (part-select x :low 6 :width 2))
     :exec (the (unsigned-byte 2)
                (logand (the (unsigned-byte 2) 3)
                        (the (unsigned-byte 2)
                             (ash (the (unsigned-byte 8) x) -6))))))

Theorem: 2bits-p-of-modr/m->mod

(defthm 2bits-p-of-modr/m->mod
  (b* ((mod (modr/m->mod$inline x)))
    (2bits-p mod))
  :rule-classes :rewrite)

Theorem: modr/m->mod$inline-of-modr/m-fix-x

(defthm modr/m->mod$inline-of-modr/m-fix-x
  (equal (modr/m->mod$inline (modr/m-fix x))
         (modr/m->mod$inline x)))

Theorem: modr/m->mod$inline-modr/m-equiv-congruence-on-x

(defthm modr/m->mod$inline-modr/m-equiv-congruence-on-x
  (implies (modr/m-equiv x x-equiv)
           (equal (modr/m->mod$inline x)
                  (modr/m->mod$inline x-equiv)))
  :rule-classes :congruence)

Theorem: modr/m->mod-of-modr/m

(defthm modr/m->mod-of-modr/m
  (equal (modr/m->mod (modr/m r/m reg mod))
         (2bits-fix mod)))

Theorem: modr/m->mod-of-write-with-mask

(defthm modr/m->mod-of-write-with-mask
 (implies
  (and
     (fty::bitstruct-read-over-write-hyps x modr/m-equiv-under-mask)
     (modr/m-equiv-under-mask x y fty::mask)
     (equal (logand (lognot fty::mask) 192)
            0))
  (equal (modr/m->mod x)
         (modr/m->mod y))))