(fl+ x)
(fl* x)

should be (fl+ x ...) and (fl* x ...) respectively.

Regarding flabsdiff, you refer to C99 fdim, but unlike every other useful suggestion offered, fdim does not appear to be useful here (ie. fdim(-10.0,10.0) => 0).      Also, it's unclear why overflow would be of concern here - unless there's some representation of flonums where there is not a 1<->1 relationship between positive and negative (non-nan) values.    For IEEE representations, if an overflow occurs on the subtraction, there's no finite result that is the correct value.

flsgn refers to "flcopy-sign", which was previously spelled "flcopysign".

fllog1+ , "Equivalent to (fllog (fl+ 1 x)), but ..."    fl+ requires flonum arguments, but 1 is an exact integer.   Change to 1.0, or (flonum 1).

<trigonometric functions>

"These are the usual trigonometric functions. The flatan function, when passed two arguments, returns (flatan (/ y x)) without requiring the use of complex numbers (C99 atan2)."

..except that atan2 does not return the same thing as atan(y/x).    Also, the spec suggests that y is the second argument to flatan, but "y" is conventionally the first argument to atan2.