chickadee » library » flonum-print-precision

flonum-print-precision #!optional PRECISIONprocedure

Gets and sets the number of significant digits printed for a floating-point number. PRECISION must be a positive fixnum. Returns the setting that was previously in effect.

The default print precision is 15 on nearly all systems, and 7 on the rare system on which the double type is only single-precision.

Note: To ensure read/write invariance for all floating-point numbers, you must increase print precision from 15 to 17 (or from 7 to 9). For example:

> (define a (expt 2 -53))
> (define b (+ a (* 2 (expt 10 -32))))
> (eqv? a b)
> (flonum-print-precision 15)
> (cons a b)
(1.11022302462516e-16 .
 1.11022302462516e-16)            ;; same printed representation
> (flonum-print-precision 17)
> (cons a b)
(1.1102230246251565e-16 .
 1.1102230246251568e-16)          ;; differs in last place

On the downside, this will result in unnecessarily precise representations of many numbers:

> (flonum-print-precision 17)
> 0.1

The maximum number of decimal digits required to uniquely represent all floating-point numbers of a certain precision is given by the formula ceil(1+N*log10(2)), where N is the number of bits of precision; for double-precision, N=53.