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• Ia32e-paging

Ia32e-la-to-pa-without-tlb

Signature

(ia32e-la-to-pa-without-tlb lin-addr r-w-x x86) → (mv * * x86)

Arguments

lin-addr — Canonical linear address to be mapped to a physical address.

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

x86 — x86 state.

Definitions and Theorems

Function: ia32e-la-to-pa-without-tlb

(defun ia32e-la-to-pa-without-tlb (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 (and (not (app-view x86))
                             (canonical-address-p lin-addr))))
 (let ((__function__ 'ia32e-la-to-pa-without-tlb))
   (declare (ignorable __function__))
   (if
    (mbt (not (app-view x86)))
    (b*
      ((lin-addr (mbe :logic (logext 48 (loghead 48 lin-addr))
                      :exec lin-addr))
       (r-w-x (mbe :logic (if (member r-w-x '(:r :w :x)) r-w-x :r)
                   :exec r-w-x))
       (implicit-supervisor-access (implicit-supervisor-access x86))
       (cr0 (n32 (ctri *cr0* x86)))
       (cr4 (n22 (ctri *cr4* x86)))
       (cpl (the (unsigned-byte 2)
                 (if implicit-supervisor-access 0
                   (cpl x86))))
       (implicit-supervisor-access
            (the (unsigned-byte 1)
                 (if implicit-supervisor-access 1 0)))
       (ia32-efer (n12 (msri *ia32_efer-idx* x86)))
       (wp (cr0bits->wp cr0))
       (smep (cr4bits->smep cr4))
       (smap (cr4bits->smap cr4))
       (ac (rflagsbits->ac (rflags x86)))
       (nxe (ia32_eferbits->nxe ia32-efer)))
      (ia32e-la-to-pa-without-tlb-internal
           lin-addr wp smep
           smap ac nxe implicit-supervisor-access
           r-w-x cpl x86))
    (mv t 0 x86))))

Theorem: ia32e-la-to-pa-without-tlb-in-non-app-view

(defthm ia32e-la-to-pa-without-tlb-in-non-app-view
  (implies (xr :app-view nil x86)
           (equal (ia32e-la-to-pa-without-tlb lin-addr r-w-x x86)
                  (mv t 0 x86))))

Theorem: n52p-mv-nth-1-ia32e-la-to-pa-without-tlb

(defthm n52p-mv-nth-1-ia32e-la-to-pa-without-tlb
 (unsigned-byte-p
      *physical-address-size*
      (mv-nth 1
              (ia32e-la-to-pa-without-tlb lin-addr r-w-x x86)))
 :rule-classes
 (:rewrite
  (:type-prescription
     :corollary
     (natp (mv-nth 1
                   (ia32e-la-to-pa-without-tlb lin-addr r-w-x x86)))
     :hints
     (("Goal" :in-theory '(unsigned-byte-p integer-range-p natp))))
  (:linear
   :corollary
   (and
       (<= 0
           (mv-nth 1
                   (ia32e-la-to-pa-without-tlb lin-addr r-w-x x86)))
       (< (mv-nth 1
                  (ia32e-la-to-pa-without-tlb lin-addr r-w-x x86))
          (expt 2 *physical-address-size*)))
   :hints
   (("Goal"
        :in-theory '(unsigned-byte-p integer-range-p (:e expt)))))))

Theorem: x86p-mv-nth-2-ia32e-la-to-pa-without-tlb

(defthm x86p-mv-nth-2-ia32e-la-to-pa-without-tlb
 (implies
   (x86p x86)
   (x86p (mv-nth 2
                 (ia32e-la-to-pa-without-tlb lin-addr r-w-x x86)))))

Theorem: xr-ia32e-la-to-pa-without-tlb

(defthm xr-ia32e-la-to-pa-without-tlb
 (implies
  (and (not (equal fld :mem))
       (not (equal fld :fault)))
  (equal
       (xr fld index
           (mv-nth 2
                   (ia32e-la-to-pa-without-tlb lin-addr r-w-x x86)))
       (xr fld index x86))))

Theorem: xr-fault-ia32e-la-to-pa-without-tlb

(defthm xr-fault-ia32e-la-to-pa-without-tlb
 (implies
  (not (mv-nth 0
               (ia32e-la-to-pa-without-tlb lin-addr r-w-x x86)))
  (equal
       (xr :fault index
           (mv-nth 2
                   (ia32e-la-to-pa-without-tlb lin-addr r-w-x x86)))
       (xr :fault index x86))))

Theorem: xr-and-ia32e-la-to-pa-without-tlb-in-non-marking-view

(defthm xr-and-ia32e-la-to-pa-without-tlb-in-non-marking-view
 (implies
  (and (not (marking-view x86))
       (not (equal fld :fault)))
  (equal
       (xr fld index
           (mv-nth 2
                   (ia32e-la-to-pa-without-tlb lin-addr r-w-x x86)))
       (xr fld index x86))))

Theorem: ia32e-la-to-pa-without-tlb-xw-values

(defthm ia32e-la-to-pa-without-tlb-xw-values
 (implies
  (and (not (equal fld :mem))
       (not (equal fld :rflags))
       (not (equal fld :ctr))
       (not (equal fld :msr))
       (not (equal fld :seg-visible))
       (not (equal fld :app-view))
       (not (equal fld :implicit-supervisor-access)))
  (and
   (equal
    (mv-nth
        0
        (ia32e-la-to-pa-without-tlb lin-addr
                                    r-w-x (xw fld index value x86)))
    (mv-nth 0
            (ia32e-la-to-pa-without-tlb lin-addr r-w-x x86)))
   (equal
    (mv-nth
        1
        (ia32e-la-to-pa-without-tlb lin-addr
                                    r-w-x (xw fld index value x86)))
    (mv-nth 1
            (ia32e-la-to-pa-without-tlb lin-addr r-w-x x86))))))

Theorem: ia32e-la-to-pa-without-tlb-xw-rflags-not-ac

(defthm ia32e-la-to-pa-without-tlb-xw-rflags-not-ac
 (implies
  (equal (rflagsbits->ac value)
         (rflagsbits->ac (rflags x86)))
  (and
   (equal
    (mv-nth
      0
      (ia32e-la-to-pa-without-tlb lin-addr
                                  r-w-x (xw :rflags nil value x86)))
    (mv-nth 0
            (ia32e-la-to-pa-without-tlb lin-addr r-w-x x86)))
   (equal
    (mv-nth
      1
      (ia32e-la-to-pa-without-tlb lin-addr
                                  r-w-x (xw :rflags nil value x86)))
    (mv-nth 1
            (ia32e-la-to-pa-without-tlb lin-addr r-w-x x86))))))

Theorem: ia32e-la-to-pa-without-tlb-xw-state

(defthm ia32e-la-to-pa-without-tlb-xw-state
 (implies
  (and (not (equal fld :mem))
       (not (equal fld :rflags))
       (not (equal fld :fault))
       (not (equal fld :ctr))
       (not (equal fld :msr))
       (not (equal fld :seg-visible))
       (not (equal fld :app-view))
       (not (equal fld :marking-view))
       (not (equal fld :implicit-supervisor-access)))
  (equal
   (mv-nth
        2
        (ia32e-la-to-pa-without-tlb lin-addr
                                    r-w-x (xw fld index value x86)))
   (xw fld index value
       (mv-nth 2
               (ia32e-la-to-pa-without-tlb lin-addr r-w-x x86))))))

Theorem: ia32e-la-to-pa-without-tlb-xw-rflags-state-not-ac

(defthm ia32e-la-to-pa-without-tlb-xw-rflags-state-not-ac
 (implies
  (equal (rflagsbits->ac value)
         (rflagsbits->ac (rflags x86)))
  (equal
   (mv-nth
      2
      (ia32e-la-to-pa-without-tlb lin-addr
                                  r-w-x (xw :rflags nil value x86)))
   (xw :rflags nil value
       (mv-nth 2
               (ia32e-la-to-pa-without-tlb lin-addr r-w-x x86))))))

Theorem: ia32e-la-to-pa-without-tlb-same-page-offset

(defthm ia32e-la-to-pa-without-tlb-same-page-offset
 (implies
      (not (mv-nth 0
                   (ia32e-la-to-pa-without-tlb lin-addr r-w-x x86)))
      (same-page-offset
           (mv-nth 1
                   (ia32e-la-to-pa-without-tlb lin-addr r-w-x x86))
           lin-addr)))

Theorem: ia32e-la-to-pa-without-tlb-flg-same-if-virt-addr-same-page

(defthm ia32e-la-to-pa-without-tlb-flg-same-if-virt-addr-same-page
 (implies
   (same-page lin-addr lin-addr-2)
   (equal
        (mv-nth 0
                (ia32e-la-to-pa-without-tlb lin-addr r-w-x x86))
        (mv-nth 0
                (ia32e-la-to-pa-without-tlb lin-addr-2 r-w-x x86))))
 :rule-classes :congruence)

Theorem: ia32e-la-to-pa-without-tlb-phys-addr-same-if-virt-addr-same-page

(defthm
   ia32e-la-to-pa-without-tlb-phys-addr-same-if-virt-addr-same-page
 (implies
   (same-page lin-addr lin-addr-2)
   (same-page
        (mv-nth 1
                (ia32e-la-to-pa-without-tlb lin-addr r-w-x x86))
        (mv-nth 1
                (ia32e-la-to-pa-without-tlb lin-addr-2 r-w-x x86))))
 :rule-classes :congruence)

Theorem: mv-nth-2-ia32e-la-to-pa-without-tlb-system-level-non-marking-view

(defthm
  mv-nth-2-ia32e-la-to-pa-without-tlb-system-level-non-marking-view
 (implies
  (and
     (not (marking-view x86))
     (not (mv-nth 0
                  (ia32e-la-to-pa-without-tlb lin-addr r-w-x x86))))
  (equal (mv-nth 2
                 (ia32e-la-to-pa-without-tlb lin-addr r-w-x x86))
         x86)))

Theorem: 64-bit-modep-of-ia32e-la-to-pa-without-tlb

(defthm 64-bit-modep-of-ia32e-la-to-pa-without-tlb
 (equal
      (64-bit-modep
           (mv-nth 2
                   (ia32e-la-to-pa-without-tlb lin-addr r-w-x x86)))
      (64-bit-modep x86)))

Theorem: x86-operation-mode-of-ia32e-la-to-pa-without-tlb

(defthm x86-operation-mode-of-ia32e-la-to-pa-without-tlb
 (equal
      (x86-operation-mode
           (mv-nth 2
                   (ia32e-la-to-pa-without-tlb lin-addr r-w-x x86)))
      (x86-operation-mode x86)))

Theorem: ia32e-la-to-pa-without-tlb-fixes-address

(defthm ia32e-la-to-pa-without-tlb-fixes-address
  (equal (ia32e-la-to-pa-without-tlb (logext 48 lin-addr)
                                     r-w-x x86)
         (ia32e-la-to-pa-without-tlb lin-addr r-w-x x86)))

Theorem: ia32e-la-to-pa-without-tlb-fixes-perm

(defthm ia32e-la-to-pa-without-tlb-fixes-perm
  (implies (not (member-p r-w-x '(:r :w :x)))
           (equal (ia32e-la-to-pa-without-tlb lin-addr r-w-x x86)
                  (ia32e-la-to-pa-without-tlb lin-addr
                                              :r x86))))