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• Combine-functions

Combine64s

(combine64s a7 a6 a5 a4 a3 a2 a1 a0) merges unsigned bytes, producing the 64-bit unsigned interpretation of {a7, a6, a5, a4, a3, a2, a1, a0}.

Definitions and Theorems

Function: combine64s$inline

(defun combine64s$inline (a7 a6 a5 a4 a3 a2 a1 a0)
  (declare (type (unsigned-byte 8)
                 a7 a6 a5 a4 a3 a2 a1 a0))
  (mbe :logic
       (logior (ash (fast-logext 8 (nfix a7)) 56)
               (ash (nfix a6) 48)
               (ash (nfix a5) 40)
               (ash (nfix a4) 32)
               (ash (nfix a3) 24)
               (ash (nfix a2) 16)
               (ash (nfix a1) 8)
               (nfix a0))
       :exec
       (b* ((a1 (the (unsigned-byte 16) (ash a1 8)))
            (ans (the (unsigned-byte 16)
                      (logior (the (unsigned-byte 16) a1)
                              (the (unsigned-byte 16) a0))))
            (a2 (the (unsigned-byte 24) (ash a2 16)))
            (ans (the (unsigned-byte 24)
                      (logior (the (unsigned-byte 24) a2)
                              (the (unsigned-byte 24) ans))))
            (a3 (the (unsigned-byte 32) (ash a3 24)))
            (ans (the (unsigned-byte 32)
                      (logior (the (unsigned-byte 32) a3)
                              (the (unsigned-byte 32) ans))))
            (a4 (the (unsigned-byte 40) (ash a4 32)))
            (ans (the (unsigned-byte 40)
                      (logior (the (unsigned-byte 40) a4)
                              (the (unsigned-byte 40) ans))))
            (a5 (the (unsigned-byte 48) (ash a5 40)))
            (ans (the (unsigned-byte 48)
                      (logior (the (unsigned-byte 48) a5)
                              (the (unsigned-byte 48) ans))))
            (a6 (the (unsigned-byte 56) (ash a6 48)))
            (ans (the (unsigned-byte 56)
                      (logior (the (unsigned-byte 56) a6)
                              (the (unsigned-byte 56) ans))))
            (a7 (the (signed-byte 64)
                     (ash (the (signed-byte 8) (fast-logext 8 a7))
                          56))))
         (the (signed-byte 64)
              (logior (the (signed-byte 64) a7)
                      (the (unsigned-byte 56) ans))))))

Theorem: combine64s-unsigned-byte

(defthm combine64s-unsigned-byte
  (implies (and (force (unsigned-byte-p 8 a7))
                (force (unsigned-byte-p 8 a6))
                (force (unsigned-byte-p 8 a5))
                (force (unsigned-byte-p 8 a4))
                (force (unsigned-byte-p 8 a3))
                (force (unsigned-byte-p 8 a2))
                (force (unsigned-byte-p 8 a1))
                (force (unsigned-byte-p 8 a0)))
           (signed-byte-p 64
                          (combine64s a7 a6 a5 a4 a3 a2 a1 a0))))