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@code{(require 'byte-number)}
@ftindex byte-number
@noindent
The multi-byte sequences produced and used by numeric conversion
routines are always big-endian. Endianness can be changed during
reading and writing bytes using @code{read-bytes} and
@code{write-bytes} @xref{Byte, read-bytes}.
@noindent
The sign of the length argument to bytes/integer conversion
procedures determines the signedness of the number.
@defun bytes->integer bytes n
Converts the first @code{(abs @var{n})} bytes of big-endian @var{bytes} array
to an integer. If @var{n} is negative then the integer coded by the
bytes are treated as two's-complement (can be negative).
@example
(bytes->integer (bytes 0 0 0 15) -4) @result{} 15
(bytes->integer (bytes 0 0 0 15) 4) @result{} 15
(bytes->integer (bytes 255 255 255 255) -4) @result{} -1
(bytes->integer (bytes 255 255 255 255) 4) @result{} 4294967295
(bytes->integer (bytes 128 0 0 0) -4) @result{} -2147483648
(bytes->integer (bytes 128 0 0 0) 4) @result{} 2147483648
@end example
@end defun
@defun integer->bytes n len
Converts the integer @var{n} to a byte-array of @code{(abs @var{n})}
bytes. If @var{n} and @var{len} are both negative, then the bytes in the
returned array are coded two's-complement.
@example
(bytes->list (integer->bytes 15 -4)) @result{} (0 0 0 15)
(bytes->list (integer->bytes 15 4)) @result{} (0 0 0 15)
(bytes->list (integer->bytes -1 -4)) @result{} (255 255 255 255)
(bytes->list (integer->bytes 4294967295 4)) @result{} (255 255 255 255)
(bytes->list (integer->bytes -2147483648 -4)) @result{} (128 0 0 0)
(bytes->list (integer->bytes 2147483648 4)) @result{} (128 0 0 0)
@end example
@end defun
@defun bytes->ieee-float bytes
@var{bytes} must be a 4-element byte-array. @code{bytes->ieee-float} calculates and returns the
value of @var{bytes} interpreted as a big-endian IEEE 4-byte (32-bit) number.
@end defun
@example
(bytes->ieee-float (bytes 0 0 0 0)) @result{} 0.0
(bytes->ieee-float (bytes #x80 0 0 0)) @result{} -0.0
(bytes->ieee-float (bytes #x40 0 0 0)) @result{} 2.0
(bytes->ieee-float (bytes #x40 #xd0 0 0)) @result{} 6.5
(bytes->ieee-float (bytes #xc0 #xd0 0 0)) @result{} -6.5
(bytes->ieee-float (bytes 0 #x80 0 0)) @result{} 11.754943508222875e-39
(bytes->ieee-float (bytes 0 #x40 0 0)) @result{} 5.877471754111437e-39
(bytes->ieee-float (bytes 0 0 0 1)) @result{} 1.401298464324817e-45
(bytes->ieee-float (bytes #xff #x80 0 0)) @result{} -inf.0
(bytes->ieee-float (bytes #x7f #x80 0 0)) @result{} +inf.0
(bytes->ieee-float (bytes #x7f #x80 0 1)) @result{} 0/0
(bytes->ieee-float (bytes #x7f #xc0 0 0)) @result{} 0/0
@end example
@defun bytes->ieee-double bytes
@var{bytes} must be a 8-element byte-array. @code{bytes->ieee-double} calculates and returns the
value of @var{bytes} interpreted as a big-endian IEEE 8-byte (64-bit) number.
@end defun
@example
(bytes->ieee-double (bytes 0 0 0 0 0 0 0 0)) @result{} 0.0
(bytes->ieee-double (bytes #x80 0 0 0 0 0 0 0)) @result{} -0.0
(bytes->ieee-double (bytes #x40 0 0 0 0 0 0 0)) @result{} 2.0
(bytes->ieee-double (bytes #x40 #x1A 0 0 0 0 0 0)) @result{} 6.5
(bytes->ieee-double (bytes #xC0 #x1A 0 0 0 0 0 0)) @result{} -6.5
(bytes->ieee-double (bytes 0 8 0 0 0 0 0 0)) @result{} 11.125369292536006e-309
(bytes->ieee-double (bytes 0 4 0 0 0 0 0 0)) @result{} 5.562684646268003e-309
(bytes->ieee-double (bytes 0 0 0 0 0 0 0 1)) @result{} 4.0e-324
(bytes->ieee-double (list->bytes '(127 239 255 255 255 255 255 255))) 179.76931348623157e306
(bytes->ieee-double (bytes #xFF #xF0 0 0 0 0 0 0)) @result{} -inf.0
(bytes->ieee-double (bytes #x7F #xF0 0 0 0 0 0 0)) @result{} +inf.0
(bytes->ieee-double (bytes #x7F #xF8 0 0 0 0 0 0)) @result{} 0/0
@end example
@defun ieee-float->bytes x
Returns a 4-element byte-array encoding the IEEE single-precision
floating-point of @var{x}.
@end defun
@example
(bytes->list (ieee-float->bytes 0.0)) @result{} (0 0 0 0)
(bytes->list (ieee-float->bytes -0.0)) @result{} (128 0 0 0)
(bytes->list (ieee-float->bytes 2.0)) @result{} (64 0 0 0)
(bytes->list (ieee-float->bytes 6.5)) @result{} (64 208 0 0)
(bytes->list (ieee-float->bytes -6.5)) @result{} (192 208 0 0)
(bytes->list (ieee-float->bytes 11.754943508222875e-39)) @result{} ( 0 128 0 0)
(bytes->list (ieee-float->bytes 5.877471754111438e-39)) @result{} ( 0 64 0 0)
(bytes->list (ieee-float->bytes 1.401298464324817e-45)) @result{} ( 0 0 0 1)
(bytes->list (ieee-float->bytes -inf.0)) @result{} (255 128 0 0)
(bytes->list (ieee-float->bytes +inf.0)) @result{} (127 128 0 0)
(bytes->list (ieee-float->bytes 0/0)) @result{} (127 192 0 0)
@end example
@defun ieee-double->bytes x
Returns a 8-element byte-array encoding the IEEE double-precision
floating-point of @var{x}.
@end defun
@example
(bytes->list (ieee-double->bytes 0.0)) @result{} (0 0 0 0 0 0 0 0)
(bytes->list (ieee-double->bytes -0.0)) @result{} (128 0 0 0 0 0 0 0)
(bytes->list (ieee-double->bytes 2.0)) @result{} (64 0 0 0 0 0 0 0)
(bytes->list (ieee-double->bytes 6.5)) @result{} (64 26 0 0 0 0 0 0)
(bytes->list (ieee-double->bytes -6.5)) @result{} (192 26 0 0 0 0 0 0)
(bytes->list (ieee-double->bytes 11.125369292536006e-309))
@result{} ( 0 8 0 0 0 0 0 0)
(bytes->list (ieee-double->bytes 5.562684646268003e-309))
@result{} ( 0 4 0 0 0 0 0 0)
(bytes->list (ieee-double->bytes 4.0e-324))
@result{} ( 0 0 0 0 0 0 0 1)
(bytes->list (ieee-double->bytes -inf.0)) @result{} (255 240 0 0 0 0 0 0)
(bytes->list (ieee-double->bytes +inf.0)) @result{} (127 240 0 0 0 0 0 0)
(bytes->list (ieee-double->bytes 0/0)) @result{} (127 248 0 0 0 0 0 0)
@end example
@subsubheading Byte Collation Order
@noindent
The @code{string<?} ordering of big-endian byte-array
representations of fixed and IEEE floating-point numbers agrees with
the numerical ordering only when those numbers are non-negative.
@noindent
Straighforward modification of these formats can extend the
byte-collating order to work for their entire ranges. This
agreement enables the full range of numbers as keys in
@dfn{indexed-sequential-access-method} databases.
@cindex indexed-sequential-access-method
@deffn {Procedure} integer-byte-collate! byte-vector
Modifies sign bit of @var{byte-vector} so that @code{string<?} ordering of
two's-complement byte-vectors matches numerical order. @code{integer-byte-collate!} returns
@var{byte-vector} and is its own functional inverse.
@end deffn
@defun integer-byte-collate byte-vector
Returns copy of @var{byte-vector} with sign bit modified so that @code{string<?}
ordering of two's-complement byte-vectors matches numerical order.
@code{integer-byte-collate} is its own functional inverse.
@end defun
@deffn {Procedure} ieee-byte-collate! byte-vector
Modifies @var{byte-vector} so that @code{string<?} ordering of IEEE floating-point
byte-vectors matches numerical order. @code{ieee-byte-collate!} returns @var{byte-vector}.
@end deffn
@deffn {Procedure} ieee-byte-decollate! byte-vector
Given @var{byte-vector} modified by @code{ieee-byte-collate!}, reverses the @var{byte-vector}
modifications.
@end deffn
@defun ieee-byte-collate byte-vector
Returns copy of @var{byte-vector} encoded so that @code{string<?} ordering of IEEE
floating-point byte-vectors matches numerical order.
@end defun
@defun ieee-byte-decollate byte-vector
Given @var{byte-vector} returned by @code{ieee-byte-collate}, reverses the @var{byte-vector}
modifications.
@end defun
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