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Modr/m

!modr/m->r/m

Update the |X86ISA|::|R/M| field of a modr/m bit structure.

Signature
(!modr/m->r/m r/m x) → new-x
Arguments: r/m — Guard (3bits-p r/m).; x — Guard (modr/m-p x).
Returns: new-x — Type (modr/m-p new-x).

Definitions and Theorems

Function: !modr/m->r/m$inline

(defun !modr/m->r/m$inline (r/m x)
  (declare (xargs :guard (and (3bits-p r/m) (modr/m-p x))))
  (mbe :logic
       (b* ((r/m (mbe :logic (3bits-fix r/m) :exec r/m))
            (x (modr/m-fix x)))
         (part-install r/m x :width 3 :low 0))
       :exec (the (unsigned-byte 8)
                  (logior (the (unsigned-byte 8)
                               (logand (the (unsigned-byte 8) x)
                                       (the (signed-byte 4) -8)))
                          (the (unsigned-byte 3) r/m)))))

Theorem: modr/m-p-of-!modr/m->r/m

(defthm modr/m-p-of-!modr/m->r/m
  (b* ((new-x (!modr/m->r/m$inline r/m x)))
    (modr/m-p new-x))
  :rule-classes :rewrite)

Theorem: !modr/m->r/m$inline-of-3bits-fix-r/m

(defthm !modr/m->r/m$inline-of-3bits-fix-r/m
  (equal (!modr/m->r/m$inline (3bits-fix r/m) x)
         (!modr/m->r/m$inline r/m x)))

Theorem: !modr/m->r/m$inline-3bits-equiv-congruence-on-r/m

(defthm !modr/m->r/m$inline-3bits-equiv-congruence-on-r/m
  (implies (3bits-equiv r/m r/m-equiv)
           (equal (!modr/m->r/m$inline r/m x)
                  (!modr/m->r/m$inline r/m-equiv x)))
  :rule-classes :congruence)

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

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

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

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

Theorem: !modr/m->r/m-is-modr/m

(defthm !modr/m->r/m-is-modr/m
  (equal (!modr/m->r/m r/m x)
         (change-modr/m x :r/m r/m)))

Theorem: modr/m->r/m-of-!modr/m->r/m

(defthm modr/m->r/m-of-!modr/m->r/m
  (b* ((?new-x (!modr/m->r/m$inline r/m x)))
    (equal (modr/m->r/m new-x)
           (3bits-fix r/m))))

Theorem: !modr/m->r/m-equiv-under-mask

(defthm !modr/m->r/m-equiv-under-mask
  (b* ((?new-x (!modr/m->r/m$inline r/m x)))
    (modr/m-equiv-under-mask new-x x -8)))