▼ |  | Unstable: May Change Without Warning

1 | Guidelines for Developing unstable Libraries
2 | Automata: Compiling State Machines
3 | Bytes
4 | Contracts
5 | Converting Values to Strings
6 | Contracts for Macro Subexpressions
7 | Debugging
8 | Definitions
9 | Filesystem
10 | Find
11 | Flonums
12 | Futures
13 | Functions
14 | Hash Tables
15 | Interface-Oriented Programming for Classes
16 | Lazy Require
17 | Lists
18 | Logging
19 | Mark Parameters
20 | Match
21 | Parameter Groups
22 | Pretty-Printing
23 | Sequences
24 | Strings
25 | Structs
26 | Syntax
27 | Temporal Contracts: Explicit Contract Monitors
28 | GUI Libraries

On this page:

flonum->bit-field
bit-field->flonum
flonum->ordinal
ordinal->flonum
flonums-between
flstep
flnext
flprev
-max.0
-min.0
+ min.0
+ max.0

Version: 5.3
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### 11`` Flonums

Neil Toronto <ntoronto@racket-lang.org>

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

(require unstable/flonum)

> > 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)
> "fff8000000000000"

> > 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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