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(Bitwise Operations): Note negatives are treated as

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infinite precision twos complement.  Revise `ash' to emphasise this
for right shifts of negatives.  Describe integer-length behaviour on
negatives.  Add `...' to logand, logior, logxor since they take
multiple parameters.
This commit is contained in:
Kevin Ryde 2003-05-10 01:11:58 +00:00
parent 6cced6fea8
commit 7f5efb18b8
1 changed files with 33 additions and 18 deletions
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51
doc/ref/scheme-data.texi
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@ -1055,7 +1055,13 @@ Naturally, these C functions expect and return @code{double} arguments.
@node Bitwise Operations
@subsection Bitwise Operations
@deffn {Scheme Procedure} logand n1 n2
For the following bitwise functions, negative numbers are treated as
infinite precision twos-complements. For instance @math{-6} is bits
@math{@dots{}111010}, with infinitely many ones on the left. It can
be seen that adding 6 (binary 110) to such a bit pattern gives all
zeros.
@deffn {Scheme Procedure} logand n1 n2 @dots{}
Return the bitwise @sc{and} of the integer arguments.
@lisp
@ -1065,7 +1071,7 @@ Return the bitwise @sc{and} of the integer arguments.
@end lisp
@end deffn
@deffn {Scheme Procedure} logior n1 n2
@deffn {Scheme Procedure} logior n1 n2 @dots{}
Return the bitwise @sc{or} of the integer arguments.
@lisp
@ -1075,9 +1081,10 @@ Return the bitwise @sc{or} of the integer arguments.
@end lisp
@end deffn
@deffn {Scheme Procedure} logxor n1 n2
@deffn {Scheme Procedure} logxor n1 n2 @dots{}
Return the bitwise @sc{xor} of the integer arguments. A bit is
set in the result if it is set in an odd number of arguments.
@lisp
(logxor) @result{} 0
(logxor 7) @result{} 7
@ -1124,20 +1131,24 @@ argument, ie.@: each 0 bit is changed to 1 and each 1 bit to 0.
@deffn {Scheme Procedure} ash n cnt
@deffnx {C Function} scm_ash (n, cnt)
The function @code{ash} performs an arithmetic shift left by @var{cnt}
bits (or shift right, if @var{cnt} is negative). `Arithmetic'
means that the function does not guarantee to keep the bit
structure of @var{n}, but rather guarantees that the result
will always be rounded towards minus infinity. Therefore, the
results of @code{ash} and a corresponding bitwise shift will differ if
@var{n} is negative.
Return @var{n} shifted left by @var{cnt} bits, or shifted right if
@var{cnt} is negative. This is an ``arithmetic'' shift.
Formally, the function returns an integer equivalent to
@code{(inexact->exact (floor (* @var{n} (expt 2 @var{cnt}))))}.
This is effectively a multiplication by @m{2^{cnt}, 2^@var{cnt}}, and
when @var{cnt} is negative it's a division, rounded towards negative
infinity. (Note that this is not the same rounding as @code{quotient}
does.)
With @var{n} viewed as an infinite precision twos complement,
@code{ash} means a left shift introducing zero bits, or a right shift
dropping bits.
@lisp
(number->string (ash #b1 3) 2) @result{} "1000"
(number->string (ash #b1010 -1) 2) @result{} "101"
;; -23 is bits ...11101001, -6 is bits ...111010
(ash -23 -2) @result{} -6
@end lisp
@end deffn
@ -1162,13 +1173,17 @@ representation are counted. If 0, 0 is returned.
@deffnx {C Function} scm_integer_length (n)
Return the number of bits necessary to represent @var{n}.
For positive @var{n} this is how many bits to the most significant one
bit. For negative @var{n} it's how many bits to the most significant
zero bit in twos complement form.
@lisp
(integer-length #b10101010)
@result{} 8
(integer-length 0)
@result{} 0
(integer-length #b1111)
@result{} 4
(integer-length #b10101010) @result{} 8
(integer-length #b1111) @result{} 4
(integer-length 0) @result{} 0
(integer-length -1) @result{} 0
(integer-length -256) @result{} 8
(integer-length -257) @result{} 9
@end lisp
@end deffn