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Documented unstable/flonum

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Neil Toronto 2012-01-27 17:35:00 -07:00
parent 47fcdd4916
commit ec96e37e09
5 changed files with 119 additions and 20 deletions
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5
collects/plot/plot3d/isosurface.rkt
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@ -178,13 +178,16 @@
(define 2pi (* 2 pi))
(define (flmodulo x y)
(fl- x (fl* y (flfloor (fl/ x y)))))
(define ((2d-polar->3d-function f) x y z)
(let ([x (exact->inexact x)]
[y (exact->inexact y)]
[z (exact->inexact z)])
(define-values (θ ρ)
(cond [(and (fl= x 0.0) (fl= y 0.0)) (values 0.0 0.0)]
[else (values (flmodulo (flatan2 y x) 2pi)
[else (values (flmodulo (atan y x) 2pi)
(flatan (fl/ z (fldistance x y))))]))
(fl- (exact->inexact (f θ ρ)) (fldistance x y z))))

2
collects/plot/plot3d/plot-area.rkt
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@ -711,7 +711,7 @@
[else 1.0]))
;; Specular highlighting: Blinn-Phong model
(define spec
(cond [specular-light? (fl* 32.0 (flexpt (flabs (vdot normal half-dir)) 20.0))]
(cond [specular-light? (fl* 32.0 (expt (flabs (vdot normal half-dir)) 20.0))]
[else 0.0]))
;; Blend ambient light with diffuse light, return specular as it is
;; As ambient-light -> 1.0, contribution of diffuse -> 0.0

26
collects/unstable/flonum.rkt
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@ -2,26 +2,11 @@
(require racket/unsafe/ops)
(provide flatan2 flmodulo flexpt
flonum->bit-field bit-field->flonum
(provide flonum->bit-field bit-field->flonum
flonum->ordinal ordinal->flonum
flstep flnext flprev
-max.0 -min.0 +min.0 +max.0)
(define (flatan2 y x)
(cond [(not (flonum? y)) (raise-type-error 'flatan2 "flonum" 0 y x)]
[(not (flonum? x)) (raise-type-error 'flatan2 "flonum" 1 y x)]
[else (exact->inexact (atan y x))]))
(define (flmodulo x y)
(cond [(not (flonum? x)) (raise-type-error 'flmodulo "flonum" 0 x y)]
[(not (flonum? y)) (raise-type-error 'flmodulo "flonum" 1 x y)]
[else (unsafe-fl- x (unsafe-fl* y (unsafe-flfloor (unsafe-fl/ x y))))]))
(define (flexpt b x)
(cond [(not (flonum? b)) (raise-type-error 'flexpt "flonum" 0 b x)]
[(not (flonum? x)) (raise-type-error 'flexpt "flonum" 1 b x)]
[else (unsafe-flexp (unsafe-fl* x (unsafe-fllog b)))]))
-max.0 -min.0 +min.0 +max.0
flonums-between)
(define (flonum->bit-field x)
(cond [(flonum? x) (integer-bytes->integer (real->floating-point-bytes x 8) #f)]
@ -67,3 +52,8 @@
(define -min.0 (flprev 0.0))
(define +min.0 (flnext 0.0))
(define +max.0 (flprev +inf.0))
(define (flonums-between x y)
(cond [(not (flonum? x)) (raise-type-error 'flonums-between "flonum" 0 x y)]
[(not (flonum? y)) (raise-type-error 'flonums-between "flonum" 1 x y)]
[else (- (flonum->ordinal y) (flonum->ordinal x))]))

105
collects/unstable/scribblings/flonum.scrbl Normal file
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@ -0,0 +1,105 @@
#lang scribble/manual
@(require scribble/eval
"utils.rkt"
(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])))
@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)

1
collects/unstable/scribblings/unstable.scrbl
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@ -82,6 +82,7 @@ Keep documentation and tests up to date.
@include-section["define.scrbl"]
@include-section["file.scrbl"]
@include-section["find.scrbl"]
@include-section["flonum.scrbl"]
@include-section["future.scrbl"]
@include-section["function.scrbl"]
@include-section["generics.scrbl"]