Unstable Flonums: May Change Without Warning

6.2.1

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Unstable Flonums: May Change Without Warning

This library is unstable; compatibility will not be maintained. See Unstable: May Change Without Warning for more information.

(require unstable/flonum)

package: unstable-flonum-lib

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

procedure
(flonum->bit-field x) → (integer-in 0 (- (expt 2 64) 1))
x : flonum?

Returns the bits comprising x as an integer. A convenient shortcut for composing integer-bytes->integer with real->floating-point-bytes.

Examples:

> (number->string (flonum->bit-field -inf.0) 16)
"fff0000000000000"
> (number->string (flonum->bit-field +inf.0) 16)
"7ff0000000000000"
> (number->string (flonum->bit-field -0.0) 16)
"8000000000000000"
> (number->string (flonum->bit-field 0.0) 16)
"0"
> (number->string (flonum->bit-field -1.0) 16)
"bff0000000000000"
> (number->string (flonum->bit-field 1.0) 16)
"3ff0000000000000"
> (number->string (flonum->bit-field +nan.0) 16)
"7ff8000000000000"

procedure
(bit-field->flonum i) → flonum?
i : (integer-in 0 (- (expt 2 64) 1))

The inverse of flonum->bit-field.

procedure
(flonum->ordinal x)
→ (integer-in (- (- (expt 2 63) 1)) (- (expt 2 63) 1))
x : flonum?

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:

> (parameterize ([y-axis-ticks? #f])
(plot (list (function (compose flonum->ordinal exact->inexact) 1/4 8)
(y-axis 1/2) (y-axis 1) (y-axis 2) (y-axis 4))))

procedure
(ordinal->flonum i) → flonum?
i : (integer-in (- (- (expt 2 63) 1)) (- (expt 2 63) 1))

The inverse of flonum->ordinal.

procedure
(flonums-between x y) → exact-integer?
x : flonum?
y : flonum?

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

procedure
(flstep x n) → flonum?
x : flonum?
n : exact-integer?

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)
4.9406564584125e-324
> (flstep (flstep 0.0 1) -1)
0.0
> (flstep 0.0 -1)
-4.9406564584125e-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

procedure
(flnext x) → flonum?
x : flonum?

Equivalent to (flstep x 1).

procedure
(flprev x) → flonum?
x : flonum?

Equivalent to (flstep x -1).

value
-max.0 : flonum?
value
-min.0 : flonum?
value
+min.0 : flonum?
value
+max.0 : flonum?

The rational flonums with maximum and minimum magnitude.

Examples:

> (list -max.0 +max.0 -min.0 +min.0)
'(-1.7976931348623157e+308
  1.7976931348623157e+308
  -4.9406564584125e-324
  4.9406564584125e-324)
> (plot (function sqrt 0 (* 20 +min.0)))

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