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• Ia32e-paging

Ia32e-la-to-pa

Signature

(ia32e-la-to-pa 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

(defun ia32e-la-to-pa (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))
  (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))
     (vpn (logtail 12 (loghead 48 lin-addr)))
     (tlb (tlb x86))
     (tlb-key
         (make-tlb-key-fast
              :vpn vpn
              :r-w-x (case r-w-x (:r 0) (:w 1) (:x 2))
              :wp wp
              :smep smep
              :smap smap
              :ac ac
              :nxe nxe
              :implicit-supervisor-access implicit-supervisor-access
              :cpl cpl))
     (tlb-entry (cdr (hons-get tlb-key tlb)))
     ((when tlb-entry)
      (mv
       nil
       (mbe
           :logic (logapp 12 lin-addr tlb-entry)
           :exec
           (the (unsigned-byte 52)
                (logapp-inline 12 lin-addr
                               (the (unsigned-byte 40) tlb-entry))))
       x86))
     ((mv flg phys-addr x86)
      (mbe :exec (ia32e-la-to-pa-without-tlb-internal
                      lin-addr wp smep
                      smap ac nxe implicit-supervisor-access
                      r-w-x cpl x86)
           :logic (ia32e-la-to-pa-without-tlb lin-addr r-w-x x86)))
     ((when flg) (mv flg phys-addr x86))
     (ppn (logtail 12 phys-addr))
     (x86 (!tlb (hons-acons tlb-key ppn tlb)
                x86)))
    (mv flg phys-addr x86))
   (mv t 0 x86))))

Theorem: n52p-mv-nth-1-ia32e-la-to-pa

(defthm n52p-mv-nth-1-ia32e-la-to-pa
 (unsigned-byte-p *physical-address-size*
                  (mv-nth 1 (ia32e-la-to-pa lin-addr r-w-x x86)))
 :rule-classes
 (:rewrite
  (:type-prescription
    :corollary (natp (mv-nth 1 (ia32e-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 (ia32e-la-to-pa lin-addr r-w-x x86)))
        (< (mv-nth 1 (ia32e-la-to-pa 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

(defthm x86p-mv-nth-2-ia32e-la-to-pa
  (implies (x86p x86)
           (x86p (mv-nth 2
                         (ia32e-la-to-pa lin-addr r-w-x x86)))))

Theorem: xr-ia32e-la-to-pa

(defthm xr-ia32e-la-to-pa
 (implies (and (not (equal fld :mem))
               (not (equal fld :fault))
               (not (equal fld :tlb)))
          (equal (xr fld index
                     (mv-nth 2 (ia32e-la-to-pa lin-addr r-w-x x86)))
                 (xr fld index x86))))

Theorem: xr-fault-ia32e-la-to-pa

(defthm xr-fault-ia32e-la-to-pa
 (implies (not (mv-nth 0 (ia32e-la-to-pa lin-addr r-w-x x86)))
          (equal (xr :fault index
                     (mv-nth 2 (ia32e-la-to-pa lin-addr r-w-x x86)))
                 (xr :fault index x86))))

Theorem: xr-and-ia32e-la-to-pa-in-non-marking-view

(defthm xr-and-ia32e-la-to-pa-in-non-marking-view
 (implies (and (not (marking-view x86))
               (not (equal fld :fault))
               (not (equal fld :tlb)))
          (equal (xr fld index
                     (mv-nth 2 (ia32e-la-to-pa lin-addr r-w-x x86)))
                 (xr fld index x86))))

Theorem: ia32e-la-to-pa-xw-values

(defthm ia32e-la-to-pa-xw-values
 (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 :tlb))
       (not (equal fld :implicit-supervisor-access)))
  (and
     (equal (mv-nth 0
                    (ia32e-la-to-pa lin-addr
                                    r-w-x (xw fld index value x86)))
            (mv-nth 0 (ia32e-la-to-pa lin-addr r-w-x x86)))
     (equal (mv-nth 1
                    (ia32e-la-to-pa lin-addr
                                    r-w-x (xw fld index value x86)))
            (mv-nth 1
                    (ia32e-la-to-pa lin-addr r-w-x x86))))))

Theorem: ia32e-la-to-pa-xw-rflags-not-ac

(defthm ia32e-la-to-pa-xw-rflags-not-ac
 (implies
  (equal (rflagsbits->ac value)
         (rflagsbits->ac (rflags x86)))
  (and
   (equal (mv-nth 0
                  (ia32e-la-to-pa lin-addr
                                  r-w-x (xw :rflags nil value x86)))
          (mv-nth 0 (ia32e-la-to-pa lin-addr r-w-x x86)))
   (equal (mv-nth 1
                  (ia32e-la-to-pa lin-addr
                                  r-w-x (xw :rflags nil value x86)))
          (mv-nth 1
                  (ia32e-la-to-pa lin-addr r-w-x x86))))))

Theorem: ia32e-la-to-pa-xw-state

(defthm ia32e-la-to-pa-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 :tlb))
          (not (equal fld :implicit-supervisor-access)))
     (equal (mv-nth 2
                    (ia32e-la-to-pa lin-addr
                                    r-w-x (xw fld index value x86)))
            (xw fld index value
                (mv-nth 2
                        (ia32e-la-to-pa lin-addr r-w-x x86))))))

Theorem: ia32e-la-to-pa-xw-rflags-state-not-ac

(defthm ia32e-la-to-pa-xw-rflags-state-not-ac
 (implies
   (equal (rflagsbits->ac value)
          (rflagsbits->ac (rflags x86)))
   (equal (mv-nth 2
                  (ia32e-la-to-pa lin-addr
                                  r-w-x (xw :rflags nil value x86)))
          (xw :rflags nil value
              (mv-nth 2
                      (ia32e-la-to-pa lin-addr r-w-x x86))))))

Theorem: 64-bit-modep-of-ia32e-la-to-pa

(defthm 64-bit-modep-of-ia32e-la-to-pa
  (equal
       (64-bit-modep (mv-nth 2 (ia32e-la-to-pa lin-addr r-w-x x86)))
       (64-bit-modep x86)))

Theorem: x86-operation-mode-of-ia32e-la-to-pa

(defthm x86-operation-mode-of-ia32e-la-to-pa
  (equal (x86-operation-mode
              (mv-nth 2 (ia32e-la-to-pa lin-addr r-w-x x86)))
         (x86-operation-mode x86)))

Theorem: ia32e-la-to-pa-flg-same-if-virt-addr-same-page

(defthm ia32e-la-to-pa-flg-same-if-virt-addr-same-page
  (implies (same-page lin-addr lin-addr-2)
           (equal (mv-nth 0 (ia32e-la-to-pa lin-addr r-w-x x86))
                  (mv-nth 0
                          (ia32e-la-to-pa lin-addr-2 r-w-x x86))))
  :rule-classes :congruence)

Theorem: ia32e-la-to-pa-phys-addr-same-if-virt-addr-same-page

(defthm ia32e-la-to-pa-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 lin-addr r-w-x x86))
                  (mv-nth 1
                          (ia32e-la-to-pa lin-addr-2 r-w-x x86))))
  :rule-classes :congruence)

Theorem: ia32e-la-to-pa-fixes-address

(defthm ia32e-la-to-pa-fixes-address
  (implies (not (canonical-address-p lin-addr))
           (equal (ia32e-la-to-pa lin-addr r-w-x x86)
                  (ia32e-la-to-pa (logext 48 lin-addr)
                                  r-w-x x86))))

Theorem: ia32e-la-to-pa-fixes-perm

(defthm ia32e-la-to-pa-fixes-perm
  (implies (not (member-p r-w-x '(:r :w :x)))
           (equal (ia32e-la-to-pa lin-addr r-w-x x86)
                  (ia32e-la-to-pa lin-addr :r x86))))