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• Tlb-key

!tlb-key->r-w-x

Update the |X86ISA|::|R-W-X| field of a tlb-key bit structure.

Signature

(!tlb-key->r-w-x r-w-x x) → new-x

Arguments

r-w-x — Guard (2bits-p r-w-x).

x — Guard (tlb-key-p x).

Returns

new-x — Type (tlb-key-p new-x).

Definitions and Theorems

Function: !tlb-key->r-w-x$inline

(defun !tlb-key->r-w-x$inline (r-w-x x)
  (declare (xargs :guard (and (2bits-p r-w-x) (tlb-key-p x))))
  (mbe :logic
       (b* ((r-w-x (mbe :logic (2bits-fix r-w-x)
                        :exec r-w-x))
            (x (tlb-key-fix x)))
         (part-install r-w-x x :width 2 :low 6))
       :exec (the (unsigned-byte 46)
                  (logior (the (unsigned-byte 46)
                               (logand (the (unsigned-byte 46) x)
                                       (the (signed-byte 9) -193)))
                          (the (unsigned-byte 8)
                               (ash (the (unsigned-byte 2) r-w-x)
                                    6))))))

Theorem: tlb-key-p-of-!tlb-key->r-w-x

(defthm tlb-key-p-of-!tlb-key->r-w-x
  (b* ((new-x (!tlb-key->r-w-x$inline r-w-x x)))
    (tlb-key-p new-x))
  :rule-classes :rewrite)

Theorem: !tlb-key->r-w-x$inline-of-2bits-fix-r-w-x

(defthm !tlb-key->r-w-x$inline-of-2bits-fix-r-w-x
  (equal (!tlb-key->r-w-x$inline (2bits-fix r-w-x)
                                 x)
         (!tlb-key->r-w-x$inline r-w-x x)))

Theorem: !tlb-key->r-w-x$inline-2bits-equiv-congruence-on-r-w-x

(defthm !tlb-key->r-w-x$inline-2bits-equiv-congruence-on-r-w-x
  (implies (2bits-equiv r-w-x r-w-x-equiv)
           (equal (!tlb-key->r-w-x$inline r-w-x x)
                  (!tlb-key->r-w-x$inline r-w-x-equiv x)))
  :rule-classes :congruence)

Theorem: !tlb-key->r-w-x$inline-of-tlb-key-fix-x

(defthm !tlb-key->r-w-x$inline-of-tlb-key-fix-x
  (equal (!tlb-key->r-w-x$inline r-w-x (tlb-key-fix x))
         (!tlb-key->r-w-x$inline r-w-x x)))

Theorem: !tlb-key->r-w-x$inline-tlb-key-equiv-congruence-on-x

(defthm !tlb-key->r-w-x$inline-tlb-key-equiv-congruence-on-x
  (implies (tlb-key-equiv x x-equiv)
           (equal (!tlb-key->r-w-x$inline r-w-x x)
                  (!tlb-key->r-w-x$inline r-w-x x-equiv)))
  :rule-classes :congruence)

Theorem: !tlb-key->r-w-x-is-tlb-key

(defthm !tlb-key->r-w-x-is-tlb-key
  (equal (!tlb-key->r-w-x r-w-x x)
         (change-tlb-key x :r-w-x r-w-x)))

Theorem: tlb-key->r-w-x-of-!tlb-key->r-w-x

(defthm tlb-key->r-w-x-of-!tlb-key->r-w-x
  (b* ((?new-x (!tlb-key->r-w-x$inline r-w-x x)))
    (equal (tlb-key->r-w-x new-x)
           (2bits-fix r-w-x))))

Theorem: !tlb-key->r-w-x-equiv-under-mask

(defthm !tlb-key->r-w-x-equiv-under-mask
  (b* ((?new-x (!tlb-key->r-w-x$inline r-w-x x)))
    (tlb-key-equiv-under-mask new-x x -193)))