/usr/share/racket/pkgs/unstable-flonum-doc/unstable-flonum.scrbl is in racket-common 6.1-4.
This file is owned by root:root, with mode 0o644.
The actual contents of the file can be viewed below.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 | #lang scribble/manual
@(require scribble/eval
unstable/scribblings/utils
(for-label racket unstable/flonum racket/flonum))
@(define the-eval (make-base-eval))
@(the-eval '(require unstable/flonum
(rename-in (except-in plot plot plot3d)
[plot-bitmap plot]
[plot3d-bitmap plot3d])))
@unstable-title[#:tag "flonum"]{Flonums}
@unstable[@author+email["Neil Toronto" "ntoronto@racket-lang.org"]]
@defmodule[unstable/flonum]
@defproc[(flonum->bit-field [x flonum?]) (integer-in 0 (- (expt 2 64) 1))]{
Returns the bits comprising @racket[x] as an integer.
A convenient shortcut for composing @racket[integer-bytes->integer] with @racket[real->floating-point-bytes].
@examples[#:eval the-eval
(number->string (flonum->bit-field -inf.0) 16)
(number->string (flonum->bit-field +inf.0) 16)
(number->string (flonum->bit-field -0.0) 16)
(number->string (flonum->bit-field 0.0) 16)
(number->string (flonum->bit-field -1.0) 16)
(number->string (flonum->bit-field 1.0) 16)
(number->string (flonum->bit-field +nan.0) 16)]
}
@defproc[(bit-field->flonum [i (integer-in 0 (- (expt 2 64) 1))]) flonum?]{
The inverse of @racket[flonum->bit-field].
}
@defproc[(flonum->ordinal [x flonum?]) (integer-in (- (- (expt 2 63) 1)) (- (expt 2 63) 1))]{
Returns the signed ordinal index of @racket[x] in a total order over flonums.
When inputs are not @racket[+nan.0], this function is monotone and symmetric;
i.e. if @racket[(fl<= x y)] then @racket[(<= (flonum->ordinal x) (flonum->ordinal y))],
and @racket[(= (flonum->ordinal (- x)) (- (flonum->ordinal x)))].
@examples[#:eval the-eval
(flonum->ordinal -inf.0)
(flonum->ordinal +inf.0)
(flonum->ordinal -0.0)
(flonum->ordinal 0.0)
(flonum->ordinal -1.0)
(flonum->ordinal 1.0)
(flonum->ordinal +nan.0)]
These properties mean that @racket[flonum->ordinal] does not distinguish @racket[-0.0] and @racket[0.0].
The following plot demonstrates how the density of floating-point numbers decreases with magnitude:
@examples[#:eval the-eval
(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))))]
}
@defproc[(ordinal->flonum [i (integer-in (- (- (expt 2 63) 1)) (- (expt 2 63) 1))]) flonum?]{
The inverse of @racket[flonum->ordinal].
}
@defproc[(flonums-between [x flonum?] [y flonum?]) exact-integer?]{
Returns the number of flonums between @racket[x] and @racket[y], excluding one endpoint.
Equivalent to @racket[(- (flonum->ordinal y) (flonum->ordinal x))].
@examples[#:eval the-eval
(flonums-between 0.0 1.0)
(flonums-between 1.0 2.0)
(flonums-between 2.0 3.0)
(flonums-between 1.0 +inf.0)]
}
@defproc[(flstep [x flonum?] [n exact-integer?]) flonum?]{
Returns the flonum @racket[n] flonums away from @racket[x], according to @racket[flonum->ordinal]. If @racket[x] is @racket[+nan.0], returns @racket[+nan.0].
@examples[#:eval the-eval
(flstep 0.0 1)
(flstep (flstep 0.0 1) -1)
(flstep 0.0 -1)
(flstep +inf.0 1)
(flstep +inf.0 -1)
(flstep -inf.0 -1)
(flstep -inf.0 1)
(flstep +nan.0 1000)]
}
@defproc[(flnext [x flonum?]) flonum?]{
Equivalent to @racket[(flstep x 1)].
}
@defproc[(flprev [x flonum?]) flonum?]{
Equivalent to @racket[(flstep x -1)].
}
@deftogether[(@defthing[-max.0 flonum?]
@defthing[-min.0 flonum?]
@defthing[+min.0 flonum?]
@defthing[+max.0 flonum?])]{
The rational flonums with maximum and minimum magnitude.
@examples[#:eval the-eval
(list -max.0 +max.0 -min.0 +min.0)
(plot (function sqrt 0 (* 20 +min.0)))]
}
@(close-eval the-eval)
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