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Adjusted a literal scribble tabular to use 2d

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Robby Findler 2013-02-23 20:12:23 -06:00
parent a00bcfd16e
commit 8adbd7e836
1 changed files with 58 additions and 29 deletions
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87
collects/math/scribblings/math-flonum.scrbl
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@ -1,9 +1,10 @@
#lang scribble/manual
#lang unstable/2d scribble/manual
@(require scribble/eval
scribble/core
scribble/html-properties
racket/sandbox
unstable/2d/tabular
(for-label racket/base racket/vector racket/list
math plot
(only-in typed/racket/base
@ -199,34 +200,62 @@ these identities for @racket[b > 0.0]:
Unlike with @racket[flexpt], there is no standard for @racket[fllogb]'s behavior at limit values.
Fortunately, deriving the following rules (applied in order) is not prohibitively difficult.
@centered{
@tabular[#:style
(style 'plain
(list (table-columns (list (style 'plain (list 'left))
(style 'plain (list 'center))
(style 'plain (list 'right))))
(attributes '((width . "90%")))))
(list (list @bold{Case} @bold{Condition} @bold{Value})
(list @racket[(fllogb b 1.0)] "" @racket[0.0])
(list @racket[(fllogb 1.0 x)] "" @racket[+nan.0])
(list @racket[(fllogb b x)]
@nested{@racket[b < 0.0] or @racket[x < 0.0]}
@racket[+nan.0])
(list @italic{Double limits} 'cont 'cont)
(list @racket[(fllogb 0.0 0.0)] "" @racket[+inf.0])
(list @racket[(fllogb 0.0 +inf.0)] "" @racket[-inf.0])
(list @racket[(fllogb +inf.0 0.0)] "" @racket[-inf.0])
(list @racket[(fllogb +inf.0 +inf.0)] "" @racket[+inf.0])
(list @italic{Limits with respect to @racket[b]} 'cont 'cont)
(list @racket[(fllogb 0.0 x)] @nested{@racket[x < 1.0]} @racket[0.0])
(list @racket[(fllogb 0.0 x)] @nested{@racket[x > 1.0]} @racket[-0.0])
(list @racket[(fllogb +inf.0 x)] @nested{@racket[x > 1.0]} @racket[0.0])
(list @racket[(fllogb +inf.0 x)] @nested{@racket[x < 1.0]} @racket[-0.0])
(list @italic{Limits with respect to @racket[x]} 'cont 'cont)
(list @racket[(fllogb b 0.0)] @nested{@racket[b < 1.0]} @racket[+inf.0])
(list @racket[(fllogb b 0.0)] @nested{@racket[b > 1.0]} @racket[-inf.0])
(list @racket[(fllogb b +inf.0)] @nested{@racket[b > 1.0]} @racket[+inf.0])
(list @racket[(fllogb b +inf.0)] @nested{@racket[b < 1.0]} @racket[-inf.0]))]}
@centered[
#2dtabular
╔═════════════════════════════════╦══════════════════╦═════════════════╗
║ @bold{Case} ║@bold{Condition} ║ @bold{Value} ║
╠═════════════════════════════════╬══════════════════╬═════════════════╣
║ @racket[(fllogb b 1.0)] ║ ║ @racket[0.0] ║
╠═════════════════════════════════╬══════════════════╬═════════════════╣
║ @racket[(fllogb 1.0 x)] ║ ║ @racket[+nan.0] ║
╠═════════════════════════════════╬══════════════════╬═════════════════╣
║ @racket[(fllogb b x)] ║ @racket[b < 0.0] ║ @racket[+nan.0] ║
║ ║ "or" ║ ║
║ ║ @racket[x < 0.0] ║ ║
╠═════════════════════════════════╩══════════════════╩═════════════════╣
║ ║
║ @italic{Double limits} ║
║ ║
╠═════════════════════════════════╦══════════════════╦═════════════════╣
║ @racket[(fllogb 0.0 0.0)] ║ ║ @racket[+inf.0] ║
╠═════════════════════════════════╬══════════════════╬═════════════════╣
║ @racket[(fllogb 0.0 +inf.0)] ║ ║ @racket[-inf.0] ║
╠═════════════════════════════════╬══════════════════╬═════════════════╣
║ @racket[(fllogb +inf.0 0.0)] ║ ║ @racket[-inf.0] ║
╠═════════════════════════════════╬══════════════════╬═════════════════╣
║ @racket[(fllogb +inf.0 +inf.0)] ║ ║ @racket[+inf.0] ║
╠═════════════════════════════════╩══════════════════╩═════════════════╣
║ ║
║ @italic{Limits with respect to @racket[b]} ║
║ ║
╠═════════════════════════════════╦══════════════════╦═════════════════╣
║ @racket[(fllogb 0.0 x)] ║ @racket[x < 1.0] ║ @racket[0.0] ║
╠═════════════════════════════════╬══════════════════╬═════════════════╣
║ @racket[(fllogb 0.0 x)] ║ @racket[x > 1.0] ║ @racket[-0.0] ║
╠═════════════════════════════════╬══════════════════╬═════════════════╣
║ @racket[(fllogb +inf.0 x)] ║ @racket[x > 1.0] ║ @racket[0.0] ║
╠═════════════════════════════════╬══════════════════╬═════════════════╣
║ @racket[(fllogb +inf.0 x)] ║ @racket[x < 1.0] ║ @racket[-0.0] ║
╠═════════════════════════════════╩══════════════════╩═════════════════╣
║ ║
║ @italic{Limits with respect to @racket[x]} ║
║ ║
╠═════════════════════════════════╦══════════════════╦═════════════════╣
║ @racket[(fllogb b 0.0)] ║ @racket[b < 1.0] ║ @racket[+inf.0] ║
╠═════════════════════════════════╬══════════════════╬═════════════════╣
║ @racket[(fllogb b 0.0)] ║ @racket[b > 1.0] ║ @racket[-inf.0] ║
╠═════════════════════════════════╬══════════════════╬═════════════════╣
║ @racket[(fllogb b +inf.0)] ║ @racket[b > 1.0] ║ @racket[+inf.0] ║
╠═════════════════════════════════╬══════════════════╬═════════════════╣
║ @racket[(fllogb b +inf.0)] ║ @racket[b < 1.0] ║ @racket[-inf.0] ║
╠═════════════════════════════════╩══════════════════╩═════════════════╣
║ #:style ║
║ (style 'plain ║
║ (list (table-columns (list (style 'plain (list 'left)) ║
║ (style 'plain (list 'center)) ║
║ (style 'plain (list 'right)))) ║
║ (attributes '((width . "90%"))))) ║
╚══════════════════════════════════════════════════════════════════════╝]
Most of these rules are derived by taking limits of the mathematical base-@racket[b] log function.
Except for @racket[(fllogb 1.0 x)], when doing so gives rise to ambiguities, they are resolved using
@racket[flexpt]'s behavior, which follows the IEEE 754 and C99 standards for @tt{pow}.