...... LispWorks ......

CL-USER 2 > (let ((x (* most-positive-double-float most-positive-double-float)))
             (- x x))
1D+-0 #| 1D+-0 is double-float not-a-number |#

CL-USER 3 > 1D+-0
1D+-0 #| 1D+-0 is double-float not-a-number |#

CL-USER 4 >

...... Allegro CL ......

CL-USER(1): (let ((x (* most-positive-double-float most-positive-double-float)))
             (- x x))
#.*NAN-DOUBLE*
CL-USER(2): *NAN-DOUBLE*
#.*NAN-DOUBLE*
CL-USER(3):

...... CCL ......

? (set-fpu-mode :overflow nil :division-by-zero nil :invalid nil)
8064
? (let ((x (* most-positive-double-float most-positive-double-float)))
    (- x x))
1D+-0 #| not-a-number |#
? 1D+-0
1D+-0 #| not-a-number |#
?

...... SBCL ......

* (sb-int:set-floating-point-modes :traps nil)
* (let ((x (* most-positive-double-float most-positive-double-float)))
    (- x x))
#<DOUBLE-FLOAT quiet NaN>
*

...... CMUCL ......

* (set-floating-point-modes :traps nil)

* (let ((x (* most-positive-double-float most-positive-double-float)))
    (- x x))

#<DOUBLE-FLOAT Quiet NaN>
*