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Linear-memory

Rml16

Signature
(rml16 lin-addr r-x x86) → (mv * * x86)

Definitions and Theorems

Theorem: rb-and-rvm16

(defthm rb-and-rvm16
  (implies (and (app-view x86)
                (canonical-address-p lin-addr)
                (canonical-address-p (1+ lin-addr))
                (x86p x86))
           (equal (rvm16 lin-addr x86)
                  (rb 2 lin-addr r-x x86))))

Function: rml16

(defun rml16 (lin-addr r-x x86)
 (declare (xargs :stobjs (x86)))
 (declare (type (signed-byte 48) lin-addr)
          (type (member :r :x) r-x))
 (declare (xargs :guard (canonical-address-p lin-addr)))
 (let ((__function__ 'rml16))
  (declare (ignorable __function__))
  (let* ((1+lin-addr (the (signed-byte 49)
                          (1+ (the (signed-byte 48) lin-addr)))))
   (if
    (mbe :logic (canonical-address-p 1+lin-addr)
         :exec (< (the (signed-byte 49) 1+lin-addr)
                  140737488355328))
    (mbe
     :logic (rb 2 lin-addr r-x x86)
     :exec
     (if (app-view x86)
         (rvm16 lin-addr x86)
      (b* (((mv flag (the (unsigned-byte 52) p-addr0)
                x86)
            (la-to-pa lin-addr r-x x86))
           ((when flag) (mv flag 0 x86))
           (1+lin-addr (the (signed-byte 49)
                            (1+ (the (signed-byte 48) lin-addr))))
           ((mv flag (the (unsigned-byte 52) ?p-addr1)
                x86)
            (la-to-pa 1+lin-addr r-x x86))
           ((when flag) (mv flag 0 x86))
           (byte0 (the (unsigned-byte 8)
                       (memi p-addr0 x86)))
           (byte1 (the (unsigned-byte 8)
                       (memi p-addr1 x86)))
           (word (the (unsigned-byte 16)
                      (logior (the (unsigned-byte 16) (ash byte1 8))
                              byte0))))
        (mv nil word x86))))
    (mv 'rml16 0 x86)))))

Theorem: n16p-mv-nth-1-rml16

(defthm n16p-mv-nth-1-rml16
 (unsigned-byte-p 16 (mv-nth 1 (rml16 lin-addr r-x x86)))
 :rule-classes
 (:rewrite
  (:type-prescription
      :corollary (natp (mv-nth 1 (rml16 lin-addr r-x x86)))
      :hints
      (("Goal" :in-theory '(unsigned-byte-p integer-range-p natp))))
  (:linear
   :corollary (and (<= 0 (mv-nth 1 (rml16 lin-addr r-x x86)))
                   (< (mv-nth 1 (rml16 lin-addr r-x x86))
                      65536))
   :hints
   (("Goal"
        :in-theory '(unsigned-byte-p integer-range-p (:e expt)))))))

Theorem: x86p-rml16

(defthm x86p-rml16
  (implies (force (x86p x86))
           (x86p (mv-nth 2 (rml16 lin-addr r-x x86))))
  :rule-classes (:rewrite :type-prescription))

Theorem: rml16-value-when-error

(defthm rml16-value-when-error
  (implies (mv-nth 0 (rml16 lin-addr r-x x86))
           (equal (mv-nth 1 (rml16 lin-addr r-x x86))
                  0)))

Theorem: rml16-x86-unmodified-in-app-view

(defthm rml16-x86-unmodified-in-app-view
  (implies (app-view x86)
           (equal (mv-nth 2 (rml16 lin-addr r-x x86))
                  x86)))

Theorem: xr-rml16-state-sys-view

(defthm xr-rml16-state-sys-view
  (implies (and (not (app-view x86))
                (not (equal fld :mem))
                (not (equal fld :fault))
                (not (equal fld :tlb))
                (member-equal fld *x86-field-names-as-keywords*))
           (equal (xr fld index
                      (mv-nth 2 (rml16 lin-addr r-x x86)))
                  (xr fld index x86))))

Theorem: rml16-xw-app-view

(defthm rml16-xw-app-view
 (implies
  (and (app-view x86)
       (not (equal fld :mem))
       (not (equal fld :app-view)))
  (and (equal (mv-nth 0
                      (rml16 lin-addr r-x (xw fld index value x86)))
              (mv-nth 0 (rml16 lin-addr r-x x86)))
       (equal (mv-nth 1
                      (rml16 lin-addr r-x (xw fld index value x86)))
              (mv-nth 1 (rml16 lin-addr r-x x86))))))

Theorem: rml16-xw-sys-view

(defthm rml16-xw-sys-view
 (implies
  (and (not (app-view x86))
       (not (equal fld :fault))
       (not (equal fld :seg-visible))
       (not (equal fld :seg-hidden-base))
       (not (equal fld :seg-hidden-limit))
       (not (equal fld :seg-hidden-attr))
       (not (equal fld :mem))
       (not (equal fld :ctr))
       (not (equal fld :msr))
       (not (equal fld :rflags))
       (not (equal fld :app-view))
       (not (equal fld :marking-view))
       (not (equal fld :tlb))
       (not (equal fld :implicit-supervisor-access))
       (member-equal fld *x86-field-names-as-keywords*))
  (and (equal (mv-nth 0
                      (rml16 lin-addr r-x (xw fld index value x86)))
              (mv-nth 0 (rml16 lin-addr r-x x86)))
       (equal (mv-nth 1
                      (rml16 lin-addr r-x (xw fld index value x86)))
              (mv-nth 1 (rml16 lin-addr r-x x86)))
       (equal (mv-nth 2
                      (rml16 lin-addr r-x (xw fld index value x86)))
              (xw fld index value
                  (mv-nth 2 (rml16 lin-addr r-x x86)))))))

Theorem: rml16-xw-sys-view-rflags-not-ac

(defthm rml16-xw-sys-view-rflags-not-ac
  (implies
       (and (not (app-view x86))
            (equal (rflagsbits->ac value)
                   (rflagsbits->ac (rflags x86))))
       (and (equal (mv-nth 0
                           (rml16 lin-addr
                                  r-x (xw :rflags nil value x86)))
                   (mv-nth 0 (rml16 lin-addr r-x x86)))
            (equal (mv-nth 1
                           (rml16 lin-addr
                                  r-x (xw :rflags nil value x86)))
                   (mv-nth 1 (rml16 lin-addr r-x x86)))
            (equal (mv-nth 2
                           (rml16 lin-addr
                                  r-x (xw :rflags nil value x86)))
                   (xw :rflags nil value
                       (mv-nth 2 (rml16 lin-addr r-x x86)))))))