4.2.5 Extflonums

package: base

An extflonum is an extended-precision (80-bit) floating-point number. extflonum arithmetic is supported on platforms with extended-precision hardware and where the extflonum implementation does not conflict with normal double-precision arithmetic (i.e., on x86 and x86_64 platforms when Racket is compiled to use SSE instructions for floating-point operations, and on Windows when "longdouble.dll" is available).

A extflonum is not a number in the sense of number?. Only extflonum-specific operations such as extfl+ perform extflonum arithmetic.

A literal extflonum is written like an inexact number, but using an explicit t or T exponent marker (see Reading Extflonums). For example, 3.5t0 is an extflonum. The extflonum infinities and non-a-number values are +inf.t, -inf.t, and +nan.t.

If (extflonum-available?) produces #f, then all operations exported by racket/extflonum raise exn:fail:unsupported, except for extflonum?, extflonum-available?, and extflvector? (which always work). The reader (see The Reader) always accepts extflonum input; when extflonum operations are not supported, printing an extflonum from the reader uses its source notation (as opposed to normalizing the format).

Two extflonums are equal? if extfl= produces #t for the extflonums. If extflonums are not supported in a platform, extflonums are equal? only if they are eq?.

procedure
(extflonum? v) → boolean?
v : any/c

Returns #t if v is an extflonum, #f otherwise.

procedure
(extflonum-available?) → boolean?

Returns #t if extflonum operations are supported on the current platform, #f otherwise.

4.2.5.1 Extflonum Arithmetic

procedure
(extfl+ a b) → extflonum?
  a : extflonum?
  b : extflonum?
procedure
(extfl- a b) → extflonum?
  a : extflonum?
  b : extflonum?
procedure
(extfl* a b) → extflonum?
  a : extflonum?
  b : extflonum?
procedure
(extfl/ a b) → extflonum?
  a : extflonum?
  b : extflonum?
procedure
(extflabs a) → extflonum?
  a : extflonum?

Like fl+, fl-, fl*, fl/, and flabs, but for extflonums.

procedure
(extfl= a b) → boolean?
  a : extflonum?
  b : extflonum?
procedure
(extfl< a b) → boolean?
  a : extflonum?
  b : extflonum?
procedure
(extfl> a b) → boolean?
  a : extflonum?
  b : extflonum?
procedure
(extfl<= a b) → boolean?
  a : extflonum?
  b : extflonum?
procedure
(extfl>= a b) → boolean?
  a : extflonum?
  b : extflonum?
procedure
(extflmin a b) → extflonum?
  a : extflonum?
  b : extflonum?
procedure
(extflmax a b) → extflonum?
  a : extflonum?
  b : extflonum?

Like fl=, fl<, fl>, fl<=, fl>=, flmin, and flmax, but for extflonums.

procedure
(extflround a) → extflonum?
  a : extflonum?
procedure
(extflfloor a) → extflonum?
  a : extflonum?
procedure
(extflceiling a) → extflonum?
  a : extflonum?
procedure
(extfltruncate a) → extflonum?
  a : extflonum?

Like flround, flfloor, flceiling, and fltruncate, but for extflonums.

procedure
(extflsin a) → extflonum?
  a : extflonum?
procedure
(extflcos a) → extflonum?
  a : extflonum?
procedure
(extfltan a) → extflonum?
  a : extflonum?
procedure
(extflasin a) → extflonum?
  a : extflonum?
procedure
(extflacos a) → extflonum?
  a : extflonum?
procedure
(extflatan a) → extflonum?
  a : extflonum?
procedure
(extfllog a) → extflonum?
  a : extflonum?
procedure
(extflexp a) → extflonum?
  a : extflonum?
procedure
(extflsqrt a) → extflonum?
  a : extflonum?
procedure
(extflexpt a b) → extflonum?
  a : extflonum?
  b : extflonum?

Like flsin, flcos, fltan, flasin, flacos, flatan, fllog, flexp, and flsqrt, and flexpt, but for extflonums.

procedure
(->extfl a) → extflonum?
  a : exact-integer?
procedure
(extfl->exact-integer a) → exact-integer?
  a : extflonum?
procedure
(real->extfl a) → extflonum?
  a : real?
procedure
(extfl->exact a) → (and/c real? exact?)
  a : real?
procedure
(extfl->inexact a) → flonum?
  a : real?

The first four are like ->fl, fl->exact, fl->real, inexact->exact, but for extflonums. The extfl->inexact function converts a extflonum to its closest "flonum" approximation.

4.2.5.2 Extflonum Constants

value
pi.t : extflonum?

Like pi, but with 80 bits precision.

4.2.5.3 Extflonum Vectors

An extflvector is like an flvector, but it holds only extflonums. See also Unsafe Extflonum Operations.

Two extflvectors are equal? if they have the same length, and if the values in corresponding slots of the extflvectors are equal?.

procedure
(extflvector? v) → boolean?
  v : any/c
procedure
(extflvector x ...) → extflvector?
  x : extflonum?
procedure
(make-extflvector size [x]) → extflvector?
  size : exact-nonnegative-integer?
  x : extflonum? = 0.0
procedure
(extflvector-length vec) → exact-nonnegative-integer?
  vec : extflvector?
procedure
(extflvector-ref vec pos) → extflonum?
  vec : extflvector?
  pos : exact-nonnegative-integer?
procedure
(extflvector-set! vec pos x) → extflonum?
  vec : extflvector?
  pos : exact-nonnegative-integer?
  x : extflonum?
procedure
(extflvector-copy vec [start end]) → extflvector?
  vec : extflvector?
  start : exact-nonnegative-integer? = 0
  end : exact-nonnegative-integer? = (vector-length v)

Like flvector?, flvector, make-flvector, flvector-length, flvector-ref, flvector-set, and flvector-copy, but for extflvectors.

procedure
(in-extflvector vec [start stop step]) → sequence?
  vec : extflvector?
  start : exact-nonnegative-integer? = 0
  stop : (or/c exact-integer? #f) = #f
  step : (and/c exact-integer? (not/c zero?)) = 1
syntax
(for/extflvector maybe-length (for-clause ...) body ...)
syntax
(for*/extflvector maybe-length (for-clause ...) body ...)

maybe-length =
| #:length length-expr
| #:length length-expr #:fill fill-expr

   length-expr : exact-nonnegative-integer?
   fill-expr : extflonum?

Like in-flvector, for/flvector, and for*/flvector, but for extflvectors.

procedure
(make-shared-extflvector size [x]) → extflvector?
size : exact-nonnegative-integer?
x : extflonum? = 0.0

Like make-shared-flvector, but for extflvectors.

4.2.5.4 Extflonum Byte Strings

procedure
(floating-point-bytes->extfl bstr
[ big-endian?
start
end]) → extflonum?
  bstr : bytes?
  big-endian? : any/c = (system-big-endian?)
  start : exact-nonnegative-integer? = 0
  end : exact-nonnegative-integer? = (bytes-length bstr)

Like floating-point-bytes->real, but for extflonums: Converts the extended-precision floating-point number encoded in bstr from position start (inclusive) to end (exclusive) to an extflonum. The difference between start an end must be 10 bytes.

procedure
(extfl->floating-point-bytes x
[ big-endian?
dest-bstr
start]) → bytes?
  x : extflonum?
  big-endian? : any/c = (system-big-endian?)
   dest-bstr : (and/c bytes? (not/c immutable?))
= (make-bytes 10)
  start : exact-nonnegative-integer? = 0

Like real->floating-point-bytes, but for extflonums: Converts x to its representation in a byte string of length 10.

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2	Notation for Documentation
3	Syntactic Forms
4	Datatypes
5	Structures
6	Classes and Objects
7	Units
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9	Pattern Matching
10	Control Flow
11	Concurrency and Parallelism
12	Macros
13	Input and Output
14	Reflection and Security
15	Operating System
16	Memory Management
17	Unsafe Operations
18	Running Racket
	Bibliography
	Index

4.1	Booleans and Equality
4.2	Numbers
4.3	Strings
4.4	Byte Strings
4.5	Characters
4.6	Symbols
4.7	Regular Expressions
4.8	Keywords
4.9	Pairs and Lists
4.10	Mutable Pairs and Lists
4.11	Vectors
4.12	Boxes
4.13	Hash Tables
4.14	Sequences and Streams
4.15	Dictionaries
4.16	Sets
4.17	Procedures
4.18	Void
4.19	Undefined

4.2.1	Number Types
4.2.2	Generic Numerics
4.2.3	Flonums
4.2.4	Fixnums
4.2.5	Extflonums

4.2.5.1	Extflonum Arithmetic
4.2.5.2	Extflonum Constants
4.2.5.3	Extflonum Vectors
4.2.5.4	Extflonum Byte Strings