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• Utilities

60bits-0-59

Partially unrolled version of bits-between that collects the bits from a 60-bit unsigned x and adds offset to each.

Signature

(60bits-0-59 offset x acc) → *

In CCL, 60-bit unsigned numbers are fixnums and, according to the following loops, this is about 3.6x faster than bits-between.

(progn
 (gc$)
 ;; 21.540 seconds
 (time (loop for x fixnum from 1 to 30000000 do
             (bits-between 0 60 x)))
 ;; 6.013 seconds
 (gc$)
 (time (loop for x fixnum from 1 to 30000000 do
             (60bits-0-59 0 x nil))))

Definitions and Theorems

Function: 60bits-0-59

(defun 60bits-0-59 (offset x acc)
  (declare (type unsigned-byte offset)
           (type (unsigned-byte 60) x))
  (let ((__function__ '60bits-0-59))
    (declare (ignorable __function__))
    (b* ((acc (60bits-0-3 (+ offset 56)
                          (the (unsigned-byte 60) (ash x -56))
                          acc))
         (acc (60bits-0-7 (+ offset 48)
                          (the (unsigned-byte 60) (ash x -48))
                          acc))
         (acc (60bits-0-7 (+ offset 40)
                          (the (unsigned-byte 60) (ash x -40))
                          acc))
         (acc (60bits-0-7 (+ offset 32)
                          (the (unsigned-byte 60) (ash x -32))
                          acc))
         (acc (60bits-0-7 (+ offset 24)
                          (the (unsigned-byte 60) (ash x -24))
                          acc))
         (acc (60bits-0-7 (+ offset 16)
                          (the (unsigned-byte 60) (ash x -16))
                          acc))
         (acc (60bits-0-7 (+ offset 8)
                          (the (unsigned-byte 60) (ash x -8))
                          acc)))
      (60bits-0-7 offset x acc))))

Theorem: 60bits-0-59-redef

(defthm 60bits-0-59-redef
  (implies (natp offset)
           (equal (60bits-0-59 offset x acc)
                  (append (add-to-each offset (bits-between 0 60 x))
                          acc))))