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• Ia32e-paging

La-to-pa

Top-level page translation function

Signature

(la-to-pa lin-addr r-w-x x86) → (mv flg p-addr x86)

Arguments

r-w-x — Indicates whether this translation is on the behalf of a read, write, or instruction fetch.

x86 — x86 state.

Returns

p-addr — Type (physical-address-p p-addr).

x86 — Type (x86p x86), given (x86p x86).

Definitions and Theorems

Function: la-to-pa$inline

(defun la-to-pa$inline (lin-addr r-w-x x86)
 (declare (xargs :stobjs (x86)))
 (declare (type (signed-byte 48) lin-addr)
          (type (member :r :w :x) r-w-x))
 (declare (xargs :guard (not (app-view x86))))
 (if (mbt (and (canonical-address-p lin-addr)
               (not (app-view x86))))
     (ia32e-la-to-pa lin-addr r-w-x x86)
   (mv (list :ia32e-paging-invalid-linear-address-or-not-in-sys-view
             lin-addr)
       0 x86)))

Theorem: physical-address-p-of-la-to-pa.p-addr

(defthm physical-address-p-of-la-to-pa.p-addr
  (b* (((mv ?flg ?p-addr ?x86)
        (la-to-pa$inline lin-addr r-w-x x86)))
    (physical-address-p p-addr))
  :rule-classes :rewrite)

Theorem: x86p-of-la-to-pa.x86

(defthm x86p-of-la-to-pa.x86
  (implies (x86p x86)
           (b* (((mv ?flg ?p-addr ?x86)
                 (la-to-pa$inline lin-addr r-w-x x86)))
             (x86p x86)))
  :rule-classes :rewrite)

Theorem: n52p-mv-nth-1-la-to-pa

(defthm n52p-mv-nth-1-la-to-pa
 (unsigned-byte-p 52
                  (mv-nth 1 (la-to-pa lin-addr r-w-x x86)))
 :rule-classes
 (:rewrite
  (:type-prescription
      :corollary (natp (mv-nth 1 (la-to-pa lin-addr r-w-x x86)))
      :hints
      (("Goal" :in-theory '(unsigned-byte-p integer-range-p natp))))
  (:linear
   :corollary (and (<= 0
                       (mv-nth 1 (la-to-pa lin-addr r-w-x x86)))
                   (< (mv-nth 1 (la-to-pa lin-addr r-w-x x86))
                      4503599627370496))
   :hints
   (("Goal"
        :in-theory '(unsigned-byte-p integer-range-p (:e expt)))))))

Theorem: xr-and-la-to-pa

(defthm xr-and-la-to-pa
  (implies (and (not (equal fld :tlb))
                (not (equal fld :mem))
                (not (equal fld :fault)))
           (equal (xr fld index
                      (mv-nth 2 (la-to-pa lin-addr r-w-x x86)))
                  (xr fld index x86))))