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Diffstat (limited to 'lispref/numbers.texi')
| -rw-r--r-- | lispref/numbers.texi | 111 |
1 files changed, 51 insertions, 60 deletions
diff --git a/lispref/numbers.texi b/lispref/numbers.texi index 0c331545e1d..e7db42f727b 100644 --- a/lispref/numbers.texi +++ b/lispref/numbers.texi @@ -249,9 +249,10 @@ Here's a function to do this: @example (defvar fuzz-factor 1.0e-6) (defun approx-equal (x y) - (< (/ (abs (- x y)) - (max (abs x) (abs y))) - fuzz-factor)) + (or (and (= x 0) (= y 0)) + (< (/ (abs (- x y)) + (max (abs x) (abs y))) + fuzz-factor))) @end example @cindex CL note---integers vrs @code{eq} @@ -356,7 +357,9 @@ This returns @var{number}, converted to an integer by rounding upward @defun round number This returns @var{number}, converted to an integer by rounding towards the -nearest integer. +nearest integer. Rounding a value equidistant between two integers +may choose the integer closer to zero, or it may prefer an even integer, +depending on your machine. @end defun @node Arithmetic Operations @@ -386,8 +389,8 @@ For example, @result{} 5 @end example -This function is not analogous to the C operator @code{++}---it does -not increment a variable. It just computes a sum. Thus, +This function is not analogous to the C operator @code{++}---it does not +increment a variable. It just computes a sum. Thus, if we continue, @example foo @@ -413,7 +416,7 @@ This returns the absolute value of @var{number}. @defun + &rest numbers-or-markers This function adds its arguments together. When given no arguments, -@code{+} returns 0. It does not check for overflow. +@code{+} returns 0. @example (+) @@ -430,8 +433,7 @@ The @code{-} function serves two purposes: negation and subtraction. When @code{-} has a single argument, the value is the negative of the argument. When there are multiple arguments, @code{-} subtracts each of the @var{other-numbers-or-markers} from @var{number-or-marker}, -cumulatively. If there are no arguments, the result is 0. This -function does not check for overflow. +cumulatively. If there are no arguments, the result is 0. @example (- 10 1 2 3 4) @@ -445,8 +447,7 @@ function does not check for overflow. @defun * &rest numbers-or-markers This function multiplies its arguments together, and returns the -product. When given no arguments, @code{*} returns 1. It does -not check for overflow. +product. When given no arguments, @code{*} returns 1. @example (*) @@ -562,8 +563,9 @@ For any two numbers @var{dividend} and @var{divisor}, @end example @noindent -always equals @var{dividend}, subject to rounding error if -either argument is floating point. +always equals @var{dividend}, subject to rounding error if either +argument is floating point. For @code{floor}, see @ref{Numeric +Conversions}. @end defun @node Rounding Operations @@ -640,36 +642,7 @@ As the examples illustrate, shifting the pattern of bits one place to the left produces a number that is twice the value of the previous number. -The function @code{lsh}, like all Emacs Lisp arithmetic functions, does -not check for overflow, so shifting left can discard significant bits -and change the sign of the number. For example, left shifting -134,217,727 produces @minus{}2 on a 28-bit machine: - -@example -(lsh 134217727 1) ; @r{left shift} - @result{} -2 -@end example - -In binary, in the 28-bit implementation, the argument looks like this: - -@example -@group -;; @r{Decimal 134.217,727} -0111 1111 1111 1111 1111 1111 1111 -@end group -@end example - -@noindent -which becomes the following when left shifted: - -@example -@group -;; @r{Decimal @minus{}2} -1111 1111 1111 1111 1111 1111 1110 -@end group -@end example - -Shifting the pattern of bits two places to the left produces results +Shifting a pattern of bits two places to the left produces results like this (with 8-bit binary numbers): @example @@ -681,8 +654,7 @@ like this (with 8-bit binary numbers): @end group @end example -On the other hand, shifting the pattern of bits one place to the right -looks like this: +On the other hand, shifting one place to the right looks like this: @example @group @@ -701,8 +673,37 @@ looks like this: @end example @noindent -As the example illustrates, shifting the pattern of bits one place to -the right divides the value of the binary number by two, rounding downward. +As the example illustrates, shifting one place to the right divides the +value of a positive integer by two, rounding downward. + +The function @code{lsh}, like all Emacs Lisp arithmetic functions, does +not check for overflow, so shifting left can discard significant bits +and change the sign of the number. For example, left shifting +134,217,727 produces @minus{}2 on a 28-bit machine: + +@example +(lsh 134217727 1) ; @r{left shift} + @result{} -2 +@end example + +In binary, in the 28-bit implementation, the argument looks like this: + +@example +@group +;; @r{Decimal 134.217,727} +0111 1111 1111 1111 1111 1111 1111 +@end group +@end example + +@noindent +which becomes the following when left shifted: + +@example +@group +;; @r{Decimal @minus{}2} +1111 1111 1111 1111 1111 1111 1110 +@end group +@end example @end defun @defun ash integer1 count @@ -713,8 +714,8 @@ is negative. @code{ash} gives the same results as @code{lsh} except when @var{integer1} and @var{count} are both negative. In that case, -@code{ash} puts a one in the leftmost position, while @code{lsh} puts -a zero in the leftmost position. +@code{ash} puts ones in the empty bit positions on the left, while +@code{lsh} puts zeros in those bit positions. Thus, with @code{ash}, shifting the pattern of bits one place to the right looks like this: @@ -1008,18 +1009,8 @@ Emacs's process @sc{id} number. This function returns a pseudo-random integer. Repeated calls return a series of pseudo-random integers. -If @var{limit} is @code{nil}, then the value may in principle be any -integer. However, on machines where integers have more than 32 bits, -the possible values may be limited to the interval -@tex -$[0,2^{32})$. -@end tex -@ifinfo -[0,2**32). -@end ifinfo - If @var{limit} is a positive integer, the value is chosen to be -nonnegative and less than @var{limit} (only in Emacs 19). +nonnegative and less than @var{limit}. If @var{limit} is @code{t}, it means to choose a new seed based on the current time of day and on Emacs's process @sc{id} number. |