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doc clarifications on numbers

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Matthew Flatt 2011-02-01 07:59:49 -07:00
parent 0011b386ba
commit aed0980f1b
1 changed files with 10 additions and 10 deletions
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20
collects/scribblings/reference/numbers.scrbl
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@ -18,9 +18,9 @@
All @deftech{numbers} are @deftech{complex numbers}. Some of them are
@deftech{real numbers}, and all of the real numbers that can be
represented are also @deftech{rational numbers}, except for
@as-index{@racket[+inf.0]} and @as-index{@racket[+inf.f]} (positive @as-index{infinity}),
@as-index{@racket[-inf.0]} an @as-index{@racket[-inf.f]} (negative infinity), and
@as-index{@racket[+nan.0]} and @as-index{@racket[+nan.f]} (@as-index{not-a-number}). Among the
@as-index{@racket[+inf.0]} (positive @as-index{infinity}), @as-index{@racket[+inf.f]} (single-precision variant),
@as-index{@racket[-inf.0]} (negative infinity), @as-index{@racket[-inf.f]} (single-precision variant),
@as-index{@racket[+nan.0]} (@as-index{not-a-number}), and @as-index{@racket[+nan.f]} (single-precision variant). Among the
rational numbers, some are @deftech{integers}, because @racket[round]
applied to the number produces the same number.
@ -54,8 +54,8 @@ numbers). In particular, adding, multiplying, subtracting, and
dividing exact numbers always produces an exact result.
Inexact numbers can be coerced to exact form, except for the inexact
numbers @racket[+inf.0] (double-precision), @racket[+inf.f] (single-precision),
@racket[-inf.0], @racket[-inf.f], @racket[+nan.0], and @racket[+nan.f] which
numbers @racket[+inf.0], @racket[+inf.f],
@racket[-inf.0], @racket[-inf.f], @racket[+nan.0], and @racket[+nan.f], which
have no exact form. @index["division by inexact zero"]{Dividing} a
number by exact zero raises an exception; dividing a non-zero number
other than @racket[+nan.0] or @racket[+nan.f] by an inexact zero returns @racket[+inf.0],
@ -65,14 +65,14 @@ or @racket[-inf.f], depending on the sign and precision of the dividend. The
is @racket[eqv?] to itself, and @racket[+nan.f] is similarly @racket[eqv?] but
not @racket[=] to itself. Conversely, @racket[(= 0.0 -0.0)] is
@racket[#t], but @racket[(eqv? 0.0 -0.0)] is @racket[#f], and the
same for @racket[0.0f0] and @racket[-0.0f0]. The datum
same for @racket[0.0f0] and @racket[-0.0f0] (which are single-precision variants). The datum
@racketvalfont{-nan.0} refers to the same constant as @racket[+nan.0],
and @racketvalfont{-nan.f} is the same as @racket[+nan.f],
and @racketvalfont{-nan.f} is the same as @racket[+nan.f].
Calculations with infinites produce results consistent with IEEE
double-precision floating point where IEEE specifies the result; in
cases where IEEE provides no specification (e.g., @racket[(angle
+inf.0+inf.0i)]), the result corresponds to the limit approaching
double- or single-precision floating point where IEEE specifies the result; in
cases where IEEE provides no specification, such as @racket[(angle
+inf.0+inf.0i)], the result corresponds to the limit approaching
infinity, or @racket[+nan.0] or @racket[+nan.f] if no such limit exists.
A @deftech{fixnum} is an exact integer whose two's complement