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(cl)Numerical Functions

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Numerical Functions
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These functions perform various arithmetic operations on numbers.

 - Function: gcd &rest integers
     This function returns the Greatest Common Divisor of the arguments.
     For one argument, it returns the absolute value of that argument.
     For zero arguments, it returns zero.

 - Function: lcm &rest integers
     This function returns the Least Common Multiple of the arguments.
     For one argument, it returns the absolute value of that argument.
     For zero arguments, it returns one.

 - Function: isqrt integer
     This function computes the "integer square root" of its integer
     argument, i.e., the greatest integer less than or equal to the true
     square root of the argument.

 - Function: floor* number &optional divisor
     This function implements the Common Lisp `floor' function.  It is
     called `floor*' to avoid name conflicts with the simpler `floor'
     function built-in to Emacs.

     With one argument, `floor*' returns a list of two numbers: The
     argument rounded down (toward minus infinity) to an integer, and
     the "remainder" which would have to be added back to the first
     return value to yield the argument again.  If the argument is an
     integer X, the result is always the list `(X 0)'.  If the argument
     is a floating-point number, the first result is a Lisp integer and
     the second is a Lisp float between 0 (inclusive) and 1 (exclusive).

     With two arguments, `floor*' divides NUMBER by DIVISOR, and
     returns the floor of the quotient and the corresponding remainder
     as a list of two numbers.  If `(floor* X Y)' returns `(Q R)', then
     `Q*Y + R = X', with R between 0 (inclusive) and R (exclusive).
     Also, note that `(floor* X)' is exactly equivalent to `(floor* X
     1)'.

     This function is entirely compatible with Common Lisp's `floor'
     function, except that it returns the two results in a list since
     Emacs Lisp does not support multiple-valued functions.

 - Function: ceiling* number &optional divisor
     This function implements the Common Lisp `ceiling' function, which
     is analogous to `floor' except that it rounds the argument or
     quotient of the arguments up toward plus infinity.  The remainder
     will be between 0 and minus R.

 - Function: truncate* number &optional divisor
     This function implements the Common Lisp `truncate' function,
     which is analogous to `floor' except that it rounds the argument
     or quotient of the arguments toward zero.  Thus it is equivalent
     to `floor*' if the argument or quotient is positive, or to
     `ceiling*' otherwise.  The remainder has the same sign as NUMBER.

 - Function: round* number &optional divisor
     This function implements the Common Lisp `round' function, which
     is analogous to `floor' except that it rounds the argument or
     quotient of the arguments to the nearest integer.  In the case of
     a tie (the argument or quotient is exactly halfway between two
     integers), it rounds to the even integer.

 - Function: mod* number divisor
     This function returns the same value as the second return value of
     `floor'.

 - Function: rem* number divisor
     This function returns the same value as the second return value of
     `truncate'.

   These definitions are compatible with those in the Quiroz `cl.el'
package, except that this package appends `*' to certain function names
to avoid conflicts with existing Emacs functions, and that the
mechanism for returning multiple values is different.