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Arithmetic Operations ===================== Emacs Lisp provides the traditional four arithmetic operations: addition, subtraction, multiplication, and division. Remainder and modulus functions supplement the division functions. The functions to add or subtract 1 are provided because they are traditional in Lisp and commonly used. All of these functions except `%' return a floating point value if any argument is floating. It is important to note that in GNU Emacs Lisp, arithmetic functions do not check for overflow. Thus `(1+ 8388607)' may equal -8388608, depending on your hardware. - Function: 1+ NUMBER-OR-MARKER This function returns NUMBER-OR-MARKER plus 1. For example, (setq foo 4) => 4 (1+ foo) => 5 This function is not analogous to the C operator `++'--it does not increment a variable. It just computes a sum. Thus, foo => 4 If you want to increment the variable, you must use `setq', like this: (setq foo (1+ foo)) => 5 - Function: 1- NUMBER-OR-MARKER This function returns NUMBER-OR-MARKER minus 1. - Function: abs NUMBER This returns the absolute value of NUMBER. - Function: + &rest NUMBERS-OR-MARKERS This function adds its arguments together. When given no arguments, `+' returns 0. It does not check for overflow. (+) => 0 (+ 1) => 1 (+ 1 2 3 4) => 10 - Function: - &optional NUMBER-OR-MARKER &rest OTHER-NUMBERS-OR-MARKERS The `-' function serves two purposes: negation and subtraction. When `-' has a single argument, the value is the negative of the argument. When there are multiple arguments, each of the OTHER-NUMBERS-OR-MARKERS is subtracted from NUMBER-OR-MARKER, cumulatively. If there are no arguments, the result is 0. This function does not check for overflow. (- 10 1 2 3 4) => 0 (- 10) => -10 (-) => 0 - Function: * &rest NUMBERS-OR-MARKERS This function multiplies its arguments together, and returns the product. When given no arguments, `*' returns 1. It does not check for overflow. (*) => 1 (* 1) => 1 (* 1 2 3 4) => 24 - Function: / DIVIDEND DIVISOR &rest DIVISORS This function divides DIVIDEND by DIVISORS and returns the quotient. If there are additional arguments DIVISORS, then DIVIDEND is divided by each divisor in turn. Each argument may be a number or a marker. If all the arguments are integers, then the result is an integer too. This means the result has to be rounded. On most machines, the result is rounded towards zero after each division, but some machines may round differently with negative arguments. This is because the Lisp function `/' is implemented using the C division operator, which has the same possibility for machine-dependent rounding. As a practical matter, all known machines round in the standard fashion. If you divide by 0, an `arith-error' error is signaled. (*Note Errors::.) (/ 6 2) => 3 (/ 5 2) => 2 (/ 25 3 2) => 4 (/ -17 6) => -2 Since the division operator in Emacs Lisp is implemented using the division operator in C, the result of dividing negative numbers may in principle vary from machine to machine, depending on how they round the result. Thus, the result of `(/ -17 6)' could be -3 on some machines. In practice, all known machines round the quotient towards 0. - Function: % DIVIDEND DIVISOR This function returns the integer remainder after division of DIVIDEND by DIVISOR. The arguments must be integers or markers. For negative arguments, the value is in principle machine-dependent since the quotient is; but in practice, all known machines behave alike. An `arith-error' results if DIVISOR is 0. (% 9 4) => 1 (% -9 4) => -1 (% 9 -4) => 1 (% -9 -4) => -1 For any two integers DIVIDEND and DIVISOR, (+ (% DIVIDEND DIVISOR) (* (/ DIVIDEND DIVISOR) DIVISOR)) always equals DIVIDEND. - Function: mod DIVIDEND DIVISOR This function returns the value of DIVIDEND modulo DIVISOR; in other words, the remainder after division of DIVIDEND by DIVISOR, but with the same sign as DIVISOR. The arguments must be numbers or markers. Unlike `%', the result is well-defined for negative arguments. Also, floating point arguments are permitted. An `arith-error' results if DIVISOR is 0. (mod 9 4) => 1 (mod -9 4) => 3 (mod 9 -4) => -3 (mod -9 -4) => -1 For any two numbers DIVIDEND and DIVISOR, (+ (mod DIVIDEND DIVISOR) (* (floor DIVIDEND DIVISOR) DIVISOR)) always equals DIVIDEND, subject to rounding error if either argument is floating point.