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• Decoding-and-spec-utils

Effective-address-computations

Computing effective address using ModR/M, SIB bytes, and displacement bytes present in the instruction

Definitions and Theorems

Function: x86-effective-addr-from-sib

(defun x86-effective-addr-from-sib
       (proc-mode temp-rip rex-byte mod sib x86)
 (declare (xargs :stobjs (x86)))
 (declare (type (integer 0 4) proc-mode)
          (type (signed-byte 48) temp-rip)
          (type (unsigned-byte 8) rex-byte)
          (type (unsigned-byte 2) mod)
          (type (unsigned-byte 8) sib))
 (declare (xargs :guard (sib-p sib)))
 (let ((__function__ 'x86-effective-addr-from-sib))
  (declare (ignorable __function__))
  (b*
   (((the (unsigned-byte 3) b)
     (sib->base sib))
    (check-alignment? nil)
    ((mv flg base displacement nrip-bytes x86)
     (case mod
      (0
       (if (equal b 5)
           (b* (((mv ?flg0 dword x86)
                 (rime-size-opt proc-mode
                                4 temp-rip 1 :x check-alignment? x86
                                :mem-ptr? nil))
                ((when flg0)
                 (mv (cons flg0 'rime-size-opt-error)
                     0 0 0 x86)))
             (mv nil 0 dword 4 x86))
         (mv nil
             (if (equal proc-mode 0)
                 (rgfi (reg-index b rex-byte 0) x86)
               (rr32 b x86))
             0 0 x86)))
      (1 (b* (((mv ?flg1 byte x86)
               (rime-size-opt proc-mode
                              1 temp-rip 1 :x check-alignment? x86
                              :mem-ptr? nil))
              ((when flg1)
               (mv (cons flg1 'rime-size-opt-error)
                   0 0 0 x86)))
           (mv nil
               (if (equal proc-mode 0)
                   (rgfi (reg-index b rex-byte 0) x86)
                 (rr32 b x86))
               byte 1 x86)))
      (2 (b* (((mv ?flg2 dword x86)
               (rime-size-opt proc-mode
                              4 temp-rip 1 :x check-alignment? x86
                              :mem-ptr? nil))
              ((when flg2)
               (mv (cons flg2 'rime-size-opt-error)
                   0 0 0 x86)))
           (mv nil
               (if (equal proc-mode 0)
                   (rgfi (reg-index b rex-byte 0) x86)
                 (rr32 b x86))
               dword 4 x86)))
      (otherwise (mv 'mod-can-not-be-anything-other-than-0-1-or-2
                     0 0 0 x86))))
    (ix (reg-index (sib->index sib) rex-byte 1))
    (index (case ix
             (4 0)
             (otherwise (if (equal proc-mode 0)
                            (rgfi ix x86)
                          (i32 (rgfi ix x86))))))
    (scale (the (unsigned-byte 2)
                (sib->scale sib)))
    (scaled-index (ash index scale))
    (effective-addr (+ base scaled-index)))
   (mv flg effective-addr
       displacement nrip-bytes x86))))

Theorem: integerp-of-x86-effective-addr-from-sib.non-truncated-memory-address

(defthm
 integerp-of-x86-effective-addr-from-sib.non-truncated-memory-address
 (implies
   (and (force (x86p x86))
        (integerp temp-rip))
   (b*
     (((mv ?flg ?non-truncated-memory-address
           ?disp ?increment-rip-by ?x86)
       (x86-effective-addr-from-sib proc-mode
                                    temp-rip rex-byte mod sib x86)))
     (integerp non-truncated-memory-address)))
 :rule-classes :type-prescription)

Theorem: natp-of-x86-effective-addr-from-sib.increment-rip-by

(defthm natp-of-x86-effective-addr-from-sib.increment-rip-by
 (b* (((mv ?flg ?non-truncated-memory-address
           ?disp ?increment-rip-by ?x86)
       (x86-effective-addr-from-sib proc-mode
                                    temp-rip rex-byte mod sib x86)))
   (natp increment-rip-by))
 :rule-classes :type-prescription)

Theorem: x86p-of-x86-effective-addr-from-sib.x86

(defthm x86p-of-x86-effective-addr-from-sib.x86
 (implies
   (force (x86p x86))
   (b*
     (((mv ?flg ?non-truncated-memory-address
           ?disp ?increment-rip-by ?x86)
       (x86-effective-addr-from-sib proc-mode
                                    temp-rip rex-byte mod sib x86)))
     (x86p x86)))
 :rule-classes :rewrite)

Theorem: x86-effective-addr-from-sib-returns-integerp-displacement

(defthm x86-effective-addr-from-sib-returns-integerp-displacement
 (implies
  (x86p x86)
  (integerp
   (mv-nth
      2
      (x86-effective-addr-from-sib proc-mode
                                   temp-rip rex-byte mod sib x86))))
 :rule-classes (:rewrite :type-prescription))

Theorem: x86-effective-addr-from-sib-returns-<=-increment-rip-bytes

(defthm x86-effective-addr-from-sib-returns-<=-increment-rip-bytes
 (<=
   (mv-nth
        3
        (x86-effective-addr-from-sib proc-mode
                                     temp-rip rex-byte mod sib x86))
   4)
 :rule-classes :linear)

Theorem: logext-loghead-identity

(defthm logext-loghead-identity
  (implies (signed-byte-p n x)
           (equal (logext n (loghead n x)) x)))

Function: x86-effective-addr-16-disp

(defun x86-effective-addr-16-disp (proc-mode temp-rip mod x86)
  (declare (xargs :stobjs (x86)))
  (declare (type (integer 0 4) proc-mode)
           (type (signed-byte 48) temp-rip)
           (type (unsigned-byte 2) mod))
  (declare (xargs :guard (2bits-p mod)))
  (let ((__function__ 'x86-effective-addr-16-disp))
    (declare (ignorable __function__))
    (case mod
      (0 (mv nil 0 0 x86))
      (1 (b* (((mv flg byte x86)
               (rime-size-opt proc-mode 1 temp-rip 1 :x nil x86
                              :mem-ptr? nil))
              ((when flg) (mv flg 0 0 x86)))
           (mv nil byte 1 x86)))
      (2 (b* (((mv flg word x86)
               (rime-size-opt proc-mode 2 temp-rip 1 :x nil x86
                              :mem-ptr? nil))
              ((when flg) (mv flg 0 0 x86)))
           (mv nil word 2 x86)))
      (otherwise (mv 'mod-value-wrong 0 0 x86)))))

Theorem: i16p-of-x86-effective-addr-16-disp.disp

(defthm i16p-of-x86-effective-addr-16-disp.disp
 (implies
     (x86p x86)
     (b* (((mv ?flg ?disp ?increment-rip-by ?x86)
           (x86-effective-addr-16-disp proc-mode temp-rip mod x86)))
       (i16p disp)))
 :rule-classes :rewrite)

Theorem: natp-of-x86-effective-addr-16-disp.increment-rip-by

(defthm natp-of-x86-effective-addr-16-disp.increment-rip-by
  (b* (((mv ?flg ?disp ?increment-rip-by ?x86)
        (x86-effective-addr-16-disp proc-mode temp-rip mod x86)))
    (natp increment-rip-by))
  :rule-classes :rewrite)

Theorem: x86p-of-x86-effective-addr-16-disp.x86

(defthm x86p-of-x86-effective-addr-16-disp.x86
 (implies
     (x86p x86)
     (b* (((mv ?flg ?disp ?increment-rip-by ?x86)
           (x86-effective-addr-16-disp proc-mode temp-rip mod x86)))
       (x86p x86)))
 :rule-classes :rewrite)

Theorem: integerp-of-x86-effective-addr-16-disp.disp

(defthm integerp-of-x86-effective-addr-16-disp.disp
 (implies
     (x86p x86)
     (b* (((mv ?flg ?disp ?increment-rip-by ?x86)
           (x86-effective-addr-16-disp proc-mode temp-rip mod x86)))
       (integerp disp)))
 :rule-classes :type-prescription)

Theorem: mv-nth-2-x86-effective-addr-16-disp-<=-4

(defthm mv-nth-2-x86-effective-addr-16-disp-<=-4
 (<=
    (mv-nth 2
            (x86-effective-addr-16-disp proc-mode temp-rip mod x86))
    4)
 :rule-classes :linear)

Function: x86-effective-addr-16

(defun x86-effective-addr-16 (proc-mode temp-rip r/m mod x86)
 (declare (xargs :stobjs (x86)))
 (declare (type (integer 0 4) proc-mode)
          (type (signed-byte 48) temp-rip)
          (type (unsigned-byte 3) r/m)
          (type (unsigned-byte 2) mod))
 (declare (xargs :guard (and (2bits-p mod) (3bits-p r/m))))
 (let ((__function__ 'x86-effective-addr-16))
  (declare (ignorable __function__))
  (case r/m
   (0 (b* ((bx (rr16 3 x86))
           (si (rr16 6 x86))
           ((mv flg disp increment-rip-by x86)
            (x86-effective-addr-16-disp proc-mode temp-rip mod x86))
           ((when flg) (mv flg 0 0 x86)))
        (mv nil (n16 (+ bx si disp))
            increment-rip-by x86)))
   (1 (b* ((bx (rr16 3 x86))
           (di (rr16 7 x86))
           ((mv flg disp increment-rip-by x86)
            (x86-effective-addr-16-disp proc-mode temp-rip mod x86))
           ((when flg) (mv flg 0 0 x86)))
        (mv nil (n16 (+ bx di disp))
            increment-rip-by x86)))
   (2 (b* ((bp (rr16 5 x86))
           (si (rr16 6 x86))
           ((mv flg disp increment-rip-by x86)
            (x86-effective-addr-16-disp proc-mode temp-rip mod x86))
           ((when flg) (mv flg 0 0 x86)))
        (mv nil (n16 (+ bp si disp))
            increment-rip-by x86)))
   (3 (b* ((bp (rr16 5 x86))
           (di (rr16 7 x86))
           ((mv flg disp increment-rip-by x86)
            (x86-effective-addr-16-disp proc-mode temp-rip mod x86))
           ((when flg) (mv flg 0 0 x86)))
        (mv nil (n16 (+ bp di disp))
            increment-rip-by x86)))
   (4 (b* ((si (rr16 6 x86))
           ((mv flg disp increment-rip-by x86)
            (x86-effective-addr-16-disp proc-mode temp-rip mod x86))
           ((when flg) (mv flg 0 0 x86)))
        (mv nil (n16 (+ si disp))
            increment-rip-by x86)))
   (5 (b* ((di (rr16 7 x86))
           ((mv flg disp increment-rip-by x86)
            (x86-effective-addr-16-disp proc-mode temp-rip mod x86))
           ((when flg) (mv flg 0 0 x86)))
        (mv nil (n16 (+ di disp))
            increment-rip-by x86)))
   (6
    (case mod
     (0 (b* (((mv flg disp x86)
              (rime-size-opt proc-mode 2 temp-rip 1 :x nil x86
                             :mem-ptr? nil))
             ((when flg) (mv flg 0 0 x86)))
          (mv nil (n16 disp) 2 x86)))
     (otherwise
      (b* ((bp (rr16 5 x86))
           ((mv flg disp increment-rip-by x86)
            (x86-effective-addr-16-disp proc-mode temp-rip mod x86))
           ((when flg) (mv flg 0 0 x86)))
        (mv nil (n16 (+ bp disp))
            increment-rip-by x86)))))
   (7 (b* ((bx (rr16 3 x86))
           ((mv flg disp increment-rip-by x86)
            (x86-effective-addr-16-disp proc-mode temp-rip mod x86))
           ((when flg) (mv flg 0 0 x86)))
        (mv nil (n16 (+ bx disp))
            increment-rip-by x86)))
   (otherwise (mv :r/m-out-of-range 0 0 x86)))))

Theorem: n16p-of-x86-effective-addr-16.address

(defthm n16p-of-x86-effective-addr-16.address
  (b* (((mv ?flg ?address ?increment-rip-by ?x86)
        (x86-effective-addr-16 proc-mode temp-rip r/m mod x86)))
    (n16p address))
  :rule-classes :rewrite)

Theorem: natp-of-x86-effective-addr-16.increment-rip-by

(defthm natp-of-x86-effective-addr-16.increment-rip-by
  (b* (((mv ?flg ?address ?increment-rip-by ?x86)
        (x86-effective-addr-16 proc-mode temp-rip r/m mod x86)))
    (natp increment-rip-by))
  :rule-classes :rewrite)

Theorem: x86p-of-x86-effective-addr-16.x86

(defthm x86p-of-x86-effective-addr-16.x86
 (implies
      (x86p x86)
      (b* (((mv ?flg ?address ?increment-rip-by ?x86)
            (x86-effective-addr-16 proc-mode temp-rip r/m mod x86)))
        (x86p x86)))
 :rule-classes :rewrite)

Theorem: i64p-mv-nth-1-x86-effective-addr-16

(defthm i64p-mv-nth-1-x86-effective-addr-16
 (signed-byte-p
    64
    (mv-nth 1
            (x86-effective-addr-16 proc-mode temp-rip r/m mod x86)))
 :rule-classes
 (:rewrite
  (:type-prescription
   :corollary
   (integerp
    (mv-nth 1
            (x86-effective-addr-16 proc-mode temp-rip r/m mod x86)))
   :hints (("Goal" :in-theory '(signed-byte-p integer-range-p))))
  (:linear
   :corollary
   (and
    (<=
       -9223372036854775808
       (mv-nth
            1
            (x86-effective-addr-16 proc-mode temp-rip r/m mod x86)))
    (<
     (mv-nth 1
             (x86-effective-addr-16 proc-mode temp-rip r/m mod x86))
     9223372036854775808))
   :hints
   (("Goal"
         :in-theory '(signed-byte-p integer-range-p (:e expt)))))))

Theorem: natp-mv-nth-2-x86-effective-addr-16

(defthm natp-mv-nth-2-x86-effective-addr-16
 (natp
    (mv-nth 2
            (x86-effective-addr-16 proc-mode temp-rip r/m mod x86)))
 :rule-classes :type-prescription)

Theorem: mv-nth-2-x86-effective-addr-16-<=-4

(defthm mv-nth-2-x86-effective-addr-16-<=-4
 (<= (mv-nth 2
             (x86-effective-addr-16 proc-mode temp-rip r/m mod x86))
     4)
 :rule-classes :linear)

Function: x86-effective-addr-32/64

(defun x86-effective-addr-32/64
       (proc-mode p4 temp-rip
                  rex-byte r/m mod sib num-imm-bytes x86)
 (declare (xargs :stobjs (x86)))
 (declare (type (integer 0 4) proc-mode)
          (type (signed-byte 48) temp-rip)
          (type (unsigned-byte 8) rex-byte)
          (type (unsigned-byte 3) r/m)
          (type (unsigned-byte 2) mod)
          (type (unsigned-byte 8) sib)
          (type (unsigned-byte 3) num-imm-bytes))
 (declare (xargs :guard (and (2bits-p mod)
                             (3bits-p r/m)
                             (sib-p sib))))
 (let ((__function__ 'x86-effective-addr-32/64))
  (declare (ignorable __function__))
  (b*
   (((mv flg
         addr displacement increment-rip-by x86)
     (case mod
      (0
       (case r/m
         (4 (x86-effective-addr-from-sib
                 proc-mode
                 temp-rip rex-byte mod sib x86))
         (5 (if (equal proc-mode 0)
                (b* (((mv ?flg0 dword x86)
                      (rime-size-opt 0 4 temp-rip 1 :x nil x86
                                     :mem-ptr? nil))
                     ((mv flg next-rip)
                      (add-to-*ip 0 temp-rip (+ 4 num-imm-bytes)
                                  x86))
                     ((when flg) (mv flg 0 0 0 x86)))
                  (mv flg0 next-rip dword 4 x86))
              (b* (((mv flg dword x86)
                    (rime-size-opt proc-mode 4 temp-rip 1 :x nil x86
                                   :mem-ptr? nil))
                   ((when flg) (mv flg 0 0 0 x86)))
                (mv nil 0 dword 4 x86))))
         (otherwise (mv nil
                        (if (equal proc-mode 0)
                            (rgfi (reg-index r/m rex-byte 0) x86)
                          (rr32 r/m x86))
                        0 0 x86))))
      (1
       (case r/m
         (4 (x86-effective-addr-from-sib
                 proc-mode
                 temp-rip rex-byte mod sib x86))
         (otherwise
              (b* (((mv ?flg2 byte2 x86)
                    (rime-size-opt proc-mode 1 temp-rip 1 :x nil x86
                                   :mem-ptr? nil))
                   (reg (if (equal proc-mode 0)
                            (rgfi (reg-index r/m rex-byte 0) x86)
                          (rr32 r/m x86))))
                (mv flg2 reg byte2 1 x86)))))
      (2
       (case r/m
         (4 (x86-effective-addr-from-sib
                 proc-mode
                 temp-rip rex-byte mod sib x86))
         (otherwise
              (b* (((mv ?flg1 dword x86)
                    (rime-size-opt proc-mode 4 temp-rip 1 :x nil x86
                                   :mem-ptr? nil))
                   (reg (if (equal proc-mode 0)
                            (rgfi (reg-index r/m rex-byte 0) x86)
                          (rr32 r/m x86))))
                (mv flg1 reg dword 4 x86)))))
      (otherwise (mv 'mod-value-wrong 0 0 0 x86))))
    (dst-base (+ addr displacement))
    (dst-base (if (equal proc-mode 0)
                  (if p4 (n32 dst-base)
                    (n64-to-i64 (n64 dst-base)))
                (n32 dst-base))))
   (mv flg dst-base increment-rip-by x86))))

Theorem: x86p-of-x86-effective-addr-32/64.x86

(defthm x86p-of-x86-effective-addr-32/64.x86
 (implies
    (force (x86p x86))
    (b* (((mv ?flg ?i64p-memory-address
              ?increment-rip-by ?x86)
          (x86-effective-addr-32/64 proc-mode p4 temp-rip rex-byte
                                    r/m mod sib num-imm-bytes x86)))
      (x86p x86)))
 :rule-classes :rewrite)

Theorem: i64p-mv-nth-1-x86-effective-addr-32/64

(defthm i64p-mv-nth-1-x86-effective-addr-32/64
 (signed-byte-p
  64
  (mv-nth 1
          (x86-effective-addr-32/64 proc-mode p4 temp-rip rex-byte
                                    r/m mod sib num-imm-bytes x86)))
 :rule-classes
 (:rewrite
  (:type-prescription
   :corollary
   (integerp
     (mv-nth
          1
          (x86-effective-addr-32/64 proc-mode p4 temp-rip rex-byte
                                    r/m mod sib num-imm-bytes x86)))
   :hints (("Goal" :in-theory '(signed-byte-p integer-range-p))))
  (:linear
   :corollary
   (and
    (<=
     -9223372036854775808
     (mv-nth
          1
          (x86-effective-addr-32/64 proc-mode p4 temp-rip rex-byte
                                    r/m mod sib num-imm-bytes x86)))
    (< (mv-nth 1
               (x86-effective-addr-32/64
                    proc-mode p4 temp-rip
                    rex-byte r/m mod sib num-imm-bytes x86))
       9223372036854775808))
   :hints
   (("Goal"
         :in-theory '(signed-byte-p integer-range-p (:e expt)))))))

Theorem: natp-mv-nth-2-x86-effective-addr-32/64

(defthm natp-mv-nth-2-x86-effective-addr-32/64
 (natp
  (mv-nth 2
          (x86-effective-addr-32/64 proc-mode p4 temp-rip rex-byte
                                    r/m mod sib num-imm-bytes x86)))
 :rule-classes :type-prescription)

Theorem: mv-nth-2-x86-effective-addr-32/64-<=-4

(defthm mv-nth-2-x86-effective-addr-32/64-<=-4
  (<= (mv-nth 2
              (x86-effective-addr-32/64
                   proc-mode p4 temp-rip
                   rex-byte r/m mod sib num-imm-bytes x86))
      4)
  :rule-classes :linear)

Function: x86-effective-addr

(defun x86-effective-addr
       (proc-mode p4 temp-rip
                  rex-byte r/m mod sib num-imm-bytes x86)
  (declare (xargs :stobjs (x86)))
  (declare (type (integer 0 4) proc-mode)
           (type (signed-byte 48) temp-rip)
           (type (unsigned-byte 8) rex-byte)
           (type (unsigned-byte 3) r/m)
           (type (unsigned-byte 2) mod)
           (type (unsigned-byte 8) sib)
           (type (unsigned-byte 3) num-imm-bytes))
  (declare (xargs :guard (and (2bits-p mod)
                              (3bits-p r/m)
                              (sib-p sib))))
  (let ((__function__ 'x86-effective-addr))
    (declare (ignorable __function__))
    (if (eql 2
             (select-address-size proc-mode (if p4 t nil)
                                  x86))
        (x86-effective-addr-16 proc-mode temp-rip r/m mod x86)
      (x86-effective-addr-32/64 proc-mode p4 temp-rip rex-byte
                                r/m mod sib num-imm-bytes x86))))

Theorem: x86p-of-x86-effective-addr.x86

(defthm x86p-of-x86-effective-addr.x86
 (implies (force (x86p x86))
          (b* (((mv ?flg ?i64p-memory-address
                    ?increment-rip-by ?x86)
                (x86-effective-addr proc-mode p4 temp-rip rex-byte
                                    r/m mod sib num-imm-bytes x86)))
            (x86p x86)))
 :rule-classes :rewrite)

Theorem: i64p-mv-nth-1-x86-effective-addr

(defthm i64p-mv-nth-1-x86-effective-addr
 (signed-byte-p
      64
      (mv-nth 1
              (x86-effective-addr proc-mode p4 temp-rip rex-byte
                                  r/m mod sib num-imm-bytes x86)))
 :rule-classes
 (:rewrite
  (:type-prescription
   :corollary
   (integerp
        (mv-nth 1
                (x86-effective-addr proc-mode p4 temp-rip rex-byte
                                    r/m mod sib num-imm-bytes x86)))
   :hints (("Goal" :in-theory '(signed-byte-p integer-range-p))))
  (:linear
   :corollary
   (and
    (<= -9223372036854775808
        (mv-nth 1
                (x86-effective-addr proc-mode p4 temp-rip rex-byte
                                    r/m mod sib num-imm-bytes x86)))
    (<
     (mv-nth
        1
        (x86-effective-addr proc-mode p4 temp-rip
                            rex-byte r/m mod sib num-imm-bytes x86))
     9223372036854775808))
   :hints
   (("Goal"
         :in-theory '(signed-byte-p integer-range-p (:e expt)))))))

Theorem: natp-mv-nth-2-x86-effective-addr

(defthm natp-mv-nth-2-x86-effective-addr
  (natp (mv-nth 2
                (x86-effective-addr proc-mode p4 temp-rip rex-byte
                                    r/m mod sib num-imm-bytes x86)))
  :rule-classes :type-prescription)

Theorem: mv-nth-2-x86-effective-addr-<=-4

(defthm mv-nth-2-x86-effective-addr-<=-4
 (<=
   (mv-nth
        2
        (x86-effective-addr proc-mode p4 temp-rip
                            rex-byte r/m mod sib num-imm-bytes x86))
   4)
 :rule-classes :linear)

Theorem: x86-effective-addr-when-64-bit-modep

(defthm x86-effective-addr-when-64-bit-modep
  (equal (x86-effective-addr 0 p4 temp-rip
                             rex-byte r/m mod sib num-imm-bytes x86)
         (x86-effective-addr-32/64 0 p4 temp-rip rex-byte
                                   r/m mod sib num-imm-bytes x86)))

Subtopics

X86-effective-addr-32/64

Effective address calculation with 32-bit and 64-bit addressing.

X86-effective-addr-from-sib

Calculates effective address when SIB is present.

X86-effective-addr-16

Effective address calculation with 16-bit addressing.

X86-effective-addr-16-disp

Calculate the displacement for 16-bit effective address calculation.

X86-effective-addr

Effective address calculation.