• Top
  • Documentation
  • Books
  • Boolean-reasoning
  • Projects
  • Debugging
  • Std
  • Community
  • Proof-automation
  • ACL2
    • Theories
    • Rule-classes
    • Proof-builder
    • Recursion-and-induction
    • Hons-and-memoization
    • Events
    • Parallelism
    • History
    • Programming
    • Operational-semantics
    • Real
    • Start-here
    • Debugging
    • Miscellaneous
    • Output-controls
    • Macros
    • Mailing-lists
    • Interfacing-tools
      • Io
      • Defttag
      • Sys-call
      • Save-exec
      • Quicklisp
      • Std/io
        • Open-channel-lemmas
        • Std/io/read-char$
        • Std/io/read-object
        • Std/io/open-output-channel
        • Unsound-read
        • Read-string
        • Read-bytes$
          • Read-64ule
          • Read-64ube
          • Read-64sle
          • Read-64sbe
          • Read-32ule
          • Read-32sle
          • Read-32sbe
          • Read-32ube
          • Read-16sle
          • Read-16sbe
          • Read-16ule
          • Read-16ube
          • Read-8s
          • Combine-functions
            • Combine64u
            • Combine64s
            • Combine32u
            • Combine32s
            • Combine16u
            • Combine16s
        • File-measure
        • Read-bytes$-n
        • Std/io/read-byte$
        • Std/io/open-input-channel
        • Read-file-lines-no-newlines
        • Print-compressed
        • Nthcdr-bytes
        • Read-file-lines
        • Std/io/close-output-channel
        • Read-file-characters
        • Read-file-bytes
        • Print-legibly
        • Std/io/close-input-channel
        • Read-file-objects
        • Logical-story-of-io
        • Take-bytes
        • Std/io/peek-char$
        • Read-file-characters-rev
        • Read-file-as-string
        • Std/io/write-byte$
        • Std/io/set-serialize-character
        • Std/io/print-object$
        • Std/io/princ$
        • Std/io/read-file-into-string
        • *file-types*
      • Oslib
      • Bridge
      • Clex
      • Tshell
      • Unsound-eval
      • Hacker
      • ACL2s-interface
      • Startup-banner
      • Command-line
  • Macro-libraries
  • Interfacing-tools
    • Io
    • Defttag
    • Sys-call
    • Save-exec
    • Quicklisp
    • Std/io
      • Open-channel-lemmas
      • Std/io/read-char$
      • Std/io/read-object
      • Std/io/open-output-channel
      • Unsound-read
      • Read-string
      • Read-bytes$
        • Read-64ule
        • Read-64ube
        • Read-64sle
        • Read-64sbe
        • Read-32ule
        • Read-32sle
        • Read-32sbe
        • Read-32ube
        • Read-16sle
        • Read-16sbe
        • Read-16ule
        • Read-16ube
        • Read-8s
        • Combine-functions
          • Combine64u
          • Combine64s
          • Combine32u
          • Combine32s
          • Combine16u
          • Combine16s
      • File-measure
      • Read-bytes$-n
      • Std/io/read-byte$
      • Std/io/open-input-channel
      • Read-file-lines-no-newlines
      • Print-compressed
      • Nthcdr-bytes
      • Read-file-lines
      • Std/io/close-output-channel
      • Read-file-characters
      • Read-file-bytes
      • Print-legibly
      • Std/io/close-input-channel
      • Read-file-objects
      • Logical-story-of-io
      • Take-bytes
      • Std/io/peek-char$
      • Read-file-characters-rev
      • Read-file-as-string
      • Std/io/write-byte$
      • Std/io/set-serialize-character
      • Std/io/print-object$
      • Std/io/princ$
      • Std/io/read-file-into-string
      • *file-types*
    • Oslib
    • Bridge
    • Clex
    • Tshell
    • Unsound-eval
    • Hacker
    • ACL2s-interface
    • Startup-banner
    • Command-line
  • Hardware-verification
  • Software-verification
  • Math
  • Testing-utilities

• Combine-functions

Combine32u

(combine32u a3 a2 a1 a0) merges unsigned bytes, producing the 32-bit unsigned interpretation of (a3 << 24) | (a2 << 16) | (a1 << 8) | a0.

Definitions and Theorems

Function: combine32u$inline

(defun combine32u$inline (a3 a2 a1 a0)
  (declare (type (unsigned-byte 8) a3 a2 a1 a0))
  (mbe :logic
       (logior (ash (nfix a3) 24)
               (ash (nfix a2) 16)
               (ash (nfix a1) 8)
               (nfix a0))
       :exec
       (b* ((a3 (the (unsigned-byte 32) (ash a3 24)))
            (a2 (the (unsigned-byte 24) (ash a2 16)))
            (a1 (the (unsigned-byte 16) (ash a1 8)))
            (ans (the (unsigned-byte 16)
                      (logior (the (unsigned-byte 16) a1)
                              (the (unsigned-byte 8) a0))))
            (ans (the (unsigned-byte 24)
                      (logior (the (unsigned-byte 24) a2)
                              (the (unsigned-byte 16) ans)))))
         (the (unsigned-byte 32)
              (logior (the (unsigned-byte 32) a3)
                      (the (unsigned-byte 24) ans))))))

Theorem: combine32u-unsigned-byte

(defthm combine32u-unsigned-byte
  (implies (and (force (unsigned-byte-p 8 a3))
                (force (unsigned-byte-p 8 a2))
                (force (unsigned-byte-p 8 a1))
                (force (unsigned-byte-p 8 a0)))
           (unsigned-byte-p 32 (combine32u a3 a2 a1 a0))))

Theorem: combine32u-loghead-logtail

(defthm combine32u-loghead-logtail
  (implies (natp i)
           (equal (combine32u (logtail 24 i)
                              (loghead 8 (logtail 16 i))
                              (loghead 8 (logtail 8 i))
                              (loghead 8 i))
                  i)))