• Top
  • Documentation
  • Books
  • Boolean-reasoning
  • Projects
  • Debugging
  • Std
    • Std/lists
    • Std/alists
    • Obags
    • Std/util
    • Std/strings
    • Std/osets
    • 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*
    • Std/basic
    • Std/system
    • Std/typed-lists
    • Std/bitsets
    • Std/testing
    • Std/typed-alists
    • Std/stobjs
  • Proof-automation
  • Macro-libraries
  • ACL2
  • Interfacing-tools
  • Hardware-verification
  • Software-verification
  • Math
  • Testing-utilities

• Combine-functions

Combine16u

(combine16u a1 a0) merges unsigned bytes, producing the 16-bit unsigned interpretation of (a1 << 8) | a0.

Definitions and Theorems

Function: combine16u$inline

(defun combine16u$inline (a1 a0)
  (declare (type (unsigned-byte 8) a1 a0))
  (mbe :logic (logior (ash (nfix a1) 8) (nfix a0))
       :exec (the (unsigned-byte 16)
                  (logior (ash a1 8) a0))))

Theorem: combine16u-unsigned-byte

(defthm combine16u-unsigned-byte
  (implies (and (force (unsigned-byte-p 8 a1))
                (force (unsigned-byte-p 8 a0)))
           (unsigned-byte-p 16 (combine16u a1 a0))))

Theorem: combine16u-loghead-logtail

(defthm combine16u-loghead-logtail
  (implies (natp i)
           (equal (combine16u (logtail 8 i) (loghead 8 i))
                  i)))