@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 (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

