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          • Tlb-key->vpn
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          • Tlb-key->smap
          • Tlb-key->r-w-x
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• Tlb-key

!tlb-key->vpn

Update the |X86ISA|::|VPN| field of a tlb-key bit structure.

Signature

(!tlb-key->vpn vpn x) → new-x

Arguments

vpn — Guard (36bits-p vpn).

x — Guard (tlb-key-p x).

Returns

new-x — Type (tlb-key-p new-x).

Definitions and Theorems

Function: !tlb-key->vpn$inline

(defun !tlb-key->vpn$inline (vpn x)
 (declare (xargs :guard (and (36bits-p vpn) (tlb-key-p x))))
 (mbe
  :logic
  (b* ((vpn (mbe :logic (36bits-fix vpn) :exec vpn))
       (x (tlb-key-fix x)))
    (part-install vpn x :width 36 :low 10))
  :exec
  (the (unsigned-byte 46)
       (logior (the (unsigned-byte 46)
                    (logand (the (unsigned-byte 46) x)
                            (the (signed-byte 47) -70368744176641)))
               (the (unsigned-byte 46)
                    (ash (the (unsigned-byte 36) vpn)
                         10))))))

Theorem: tlb-key-p-of-!tlb-key->vpn

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

Theorem: !tlb-key->vpn$inline-of-36bits-fix-vpn

(defthm !tlb-key->vpn$inline-of-36bits-fix-vpn
  (equal (!tlb-key->vpn$inline (36bits-fix vpn)
                               x)
         (!tlb-key->vpn$inline vpn x)))

Theorem: !tlb-key->vpn$inline-36bits-equiv-congruence-on-vpn

(defthm !tlb-key->vpn$inline-36bits-equiv-congruence-on-vpn
  (implies (36bits-equiv vpn vpn-equiv)
           (equal (!tlb-key->vpn$inline vpn x)
                  (!tlb-key->vpn$inline vpn-equiv x)))
  :rule-classes :congruence)

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

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

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

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

Theorem: !tlb-key->vpn-is-tlb-key

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

Theorem: tlb-key->vpn-of-!tlb-key->vpn

(defthm tlb-key->vpn-of-!tlb-key->vpn
  (b* ((?new-x (!tlb-key->vpn$inline vpn x)))
    (equal (tlb-key->vpn new-x)
           (36bits-fix vpn))))

Theorem: !tlb-key->vpn-equiv-under-mask

(defthm !tlb-key->vpn-equiv-under-mask
  (b* ((?new-x (!tlb-key->vpn$inline vpn x)))
    (tlb-key-equiv-under-mask new-x x 1023)))