• Top
  • Documentation
  • Books
  • Boolean-reasoning
  • Projects
  • Debugging
  • Std
  • Community
  • Proof-automation
  • Macro-libraries
  • ACL2
  • Interfacing-tools
  • Hardware-verification
  • Software-verification
    • Kestrel-books
    • X86isa
      • Program-execution
      • Sdm-instruction-set-summary
      • Tlb
      • Running-linux
      • Introduction
      • Asmtest
      • X86isa-build-instructions
      • Publications
      • Contributors
      • Machine
        • X86isa-state
        • Syscalls
        • Cpuid
        • Linear-memory
        • Rflag-specifications
        • Characterizing-undefined-behavior
        • Top-level-memory
        • App-view
        • X86-decoder
        • Physical-memory
        • Decoding-and-spec-utils
        • Instructions
        • Register-readers-and-writers
          • Zmms-reads-and-writes
          • Gprs-reads-and-writes
          • Mmx-registers-reads-and-writes
          • Xmms-reads-and-writes
          • Rflags-reads-and-writes
          • Gpr-indices
            • Reg-index
            • Reg-indexp
          • Vex-vvvv-reg-index
          • Msr-reads-and-writes
          • Ctr-reads-and-writes
        • X86-modes
        • Segmentation
        • Other-non-deterministic-computations
        • Environment
        • Paging
      • Implemented-opcodes
      • To-do
      • Proof-utilities
      • Peripherals
      • Model-validation
      • Modelcalls
      • Concrete-simulation-examples
      • Utils
      • Debugging-code-proofs
    • Axe
    • Execloader
  • Math
  • Testing-utilities

• Register-readers-and-writers

Gpr-indices

Functions that enable the use of extended GPRs using the rex byte

Definitions and Theorems

Function: reg-indexp

(defun reg-indexp (reg rex-byte)
  (declare (type (unsigned-byte 8) rex-byte))
  (let ((__function__ 'reg-indexp))
    (declare (ignorable __function__))
    (if (eql rex-byte 0)
        (n03p reg)
      (n04p reg))))

Theorem: reg-indexp-for-3-bits

(defthm reg-indexp-for-3-bits
  (implies (and (syntaxp (quotep reg)) (n03p reg))
           (reg-indexp reg rex)))

Theorem: reg-indexp-logand-7

(defthm reg-indexp-logand-7
  (implies (n08p rex-byte)
           (reg-indexp (loghead 3 modr/m)
                       rex-byte)))

Function: reg-index$inline

(defun reg-index$inline (reg rex-byte index)
  (declare (type (unsigned-byte 3) reg)
           (type (unsigned-byte 8) rex-byte)
           (type (unsigned-byte 2) index))
  (if (logbitp index rex-byte)
      (logior 8 (mbe :logic (n03 reg) :exec reg))
    (mbe :logic (n03 reg) :exec reg)))

Theorem: reg-indexp-reg-index

(defthm reg-indexp-reg-index
  (reg-indexp (reg-index reg rex-byte name)
              rex-byte))

Theorem: n04p-reg-index

(defthm n04p-reg-index
 (unsigned-byte-p 4 (reg-index reg rex-byte name))
 :rule-classes
 (:rewrite
  (:type-prescription
      :corollary (natp (reg-index reg rex-byte name))
      :hints
      (("Goal" :in-theory '(unsigned-byte-p integer-range-p natp))))
  (:linear
   :corollary (and (<= 0 (reg-index reg rex-byte name))
                   (< (reg-index reg rex-byte name) 16))
   :hints
   (("Goal"
        :in-theory '(unsigned-byte-p integer-range-p (:e expt)))))))

Theorem: reg-indexp-forward

(defthm reg-indexp-forward
  (implies (reg-indexp reg rex-byte)
           (unsigned-byte-p 4 reg))
  :rule-classes :forward-chaining)

Subtopics

Reg-index

Using the REX prefix to access general-purpose registers

Reg-indexp

Valid GPR index recognizer