diff options
Diffstat (limited to 'bytenumb.txi')
| -rw-r--r-- | bytenumb.txi | 181 |
1 files changed, 181 insertions, 0 deletions
diff --git a/bytenumb.txi b/bytenumb.txi new file mode 100644 index 0000000..67c340b --- /dev/null +++ b/bytenumb.txi @@ -0,0 +1,181 @@ +@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 #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{} -1/0 +(bytes->ieee-float (bytes #x7f #x80 0 0)) @result{} 1/0 +(bytes->ieee-float (bytes #x7f #x80 0 1)) @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 #x40 0 0 0 0 0 0 0)) @result{} 2 +(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 (bytes #xFF #xF0 0 0 0 0 0 0)) @result{} -1/0 +(bytes->ieee-double (bytes #x7F #xF0 0 0 0 0 0 0)) @result{} 1/0 +(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 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 -1/0)) @result{} (255 128 0 0) +(bytes->list (ieee-float->bytes 1/0)) @result{} (127 128 0 0) +(bytes->list (ieee-float->bytes 0/0)) @result{} (127 128 0 1) +@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 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 -1/0)) @result{} (255 240 0 0 0 0 0 0) +(bytes->list (ieee-double->bytes 1/0)) @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 |