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Modr/m

!modr/m->reg

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

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

Definitions and Theorems

Function: !modr/m->reg$inline

(defun !modr/m->reg$inline (reg x)
 (declare (xargs :guard (and (3bits-p reg) (modr/m-p x))))
 (mbe
    :logic
    (b* ((reg (mbe :logic (3bits-fix reg) :exec reg))
         (x (modr/m-fix x)))
      (part-install reg x :width 3 :low 3))
    :exec (the (unsigned-byte 8)
               (logior (the (unsigned-byte 8)
                            (logand (the (unsigned-byte 8) x)
                                    (the (signed-byte 7) -57)))
                       (the (unsigned-byte 6)
                            (ash (the (unsigned-byte 3) reg) 3))))))

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

(defthm !modr/m->reg-equiv-under-mask
  (b* ((?new-x (!modr/m->reg$inline reg x)))
    (modr/m-equiv-under-mask new-x x -57)))