浮動小数点数のIEEE754形式への変換

倍精度浮動小数点数をIEEE754形式のビット表現(整数値)にエンコードする方法。

(defun encode-double-float (float)
  (declare (double-float float))
  (multiple-value-bind (fraction exponent sign) 
                       (integer-decode-float float)
    (let ((code 0))
      (setf (ldb (byte  1 63) code) (if (plusp sign) 0 1)
            (ldb (byte 11 52) code) (+ exponent 52 1023)
            (ldb (byte 52  0) code) fraction)
      code)))

デコード。

(defun decode-double-float (code)
  (let ((sign     (ldb (byte  1 63) code))
        (exponent (ldb (byte 11 52) code))
        (fraction (ldb (byte 52  0) code)))
    (assert (not (and (= exponent #b11111111111) (= fraction 0)))) ; infinity
    (assert (not (and (= exponent #b11111111111) (/= fraction 0)))); NaN
    (* (if (zerop sign) 1 -1)
       (scale-float (+ 1.0d0 (* fraction (expt 2 -52)))
                    (- exponent 1023)))))

実行例。

(encode-double-float 1234.5678d0)
--> 4653144502051863213

(format t "~b" *)
100000010010011010010100100010101101101010111001111101010101101
--> NIL

(decode-double-float 4653144502051863213)
--> 1234.5678d0