Unstable Flonums: May Change Without Warning (original) (raw)

8.15

You should almost certainly use math/flonum instead of this module, which is more complete and can be used in Typed Racket code.

The inverse of flonum->bit-field.

Returns the signed ordinal index of x in a total order over flonums.

When inputs are not +nan.0, this function is monotone and symmetric; i.e. if (fl<= x y) then (<= (flonum->ordinal x) (flonum->ordinal y)), and (= (flonum->ordinal (- x)) (- (flonum->ordinal x))).

Examples:

> (flonum->ordinal -inf.0)
-9218868437227405312
> (flonum->ordinal +inf.0)
9218868437227405312
> (flonum->ordinal -0.0)
0
> (flonum->ordinal 0.0)
0
> (flonum->ordinal -1.0)
-4607182418800017408
> (flonum->ordinal 1.0)
4607182418800017408
> (flonum->ordinal +nan.0)
9221120237041090560

These properties mean that flonum->ordinal does not distinguish -0.0 and 0.0.

The following plot demonstrates how the density of floating-point numbers decreases with magnitude:

Example:

The inverse of flonum->ordinal.

Returns the number of flonums between x and y, excluding one endpoint. Equivalent to (- (flonum->ordinal y) (flonum->ordinal x)).

Examples:

> (flonums-between 0.0 1.0)
4607182418800017408
> (flonums-between 1.0 2.0)
4503599627370496
> (flonums-between 2.0 3.0)
2251799813685248
> (flonums-between 1.0 +inf.0)
4611686018427387904

Returns the flonum n flonums away from x, according to flonum->ordinal. If x is +nan.0, returns +nan.0.

Examples:

> (flstep 0.0 1)
5e-324
> (flstep (flstep 0.0 1) -1)
0.0
> (flstep 0.0 -1)
-5e-324
> (flstep +inf.0 1)
+inf.0
> (flstep +inf.0 -1)
1.7976931348623157e+308
> (flstep -inf.0 -1)
-inf.0
> (flstep -inf.0 1)
-1.7976931348623157e+308
> (flstep +nan.0 1000)
+nan.0

Equivalent to (flstep x 1).

Equivalent to (flstep x -1).

The rational flonums with maximum and minimum magnitude.

Examples:

> (list -max.0 +max.0 -min.0 +min.0)
'(-1.7976931348623157e+308 1.7976931348623157e+308 -5e-324 5e-324)
> (plot (function sqrt 0 (* 20 +min.0)))