General Arithmetic Functions

Properties

odd?   integer   =>  boolean	[Generic Function]
even?   integer  =>  boolean	[Generic Function]
zero?   number  =>  boolean	[Generic Function]
positive?   real  =>  boolean	[Generic Function]
negative?   real  =>  boolean	[Generic Function]
integral?   number  =>  boolean	[Generic Function]

These functions test a number for the given property and return a Boolean result.

Arithmetic Operations

+   number1 number2  =>  number	[Generic Function]
*  number1 number2  =>  number	[Generic Function]
-   number1 number2  =>  number	[Generic Function]
/   number1 number2  =>  number	[Generic Function]

These functions return the sum, product, difference, and quotient of their arguments, respectively. Division by zero signals an error.

Use the name of the function (+, *, -, or /) when you use the function in an infix expression:

5 + 6 * 4

Use the name of the function preceded by a backslash (\+, \*, \-, or \/) when you are using the function in any other way, such as adding new methods to it or passing it as a functional argument:

define class <my-number> (<number>) end class;

define method \+ (a :: <my-number>, b :: <my-number>)
  my-personal-addition-method(a, b);
end method;

negative  number  =>  number	[Generic Function]

This function returns the additive inverse of its argument. The unary minus operator is defined to call negative.

floor   real  =>  integer real	[Generic Function]
ceiling   real =>  integer real	[Generic Function]
round   real =>  integer real	[Generic Function]
truncate   real =>  integer real	[Generic Function]

These functions are equivalent to the one-argument forms of the like-named Common Lisp (X3J13) functions.

floor/   real1 real2 =>  integer real	[Generic Function]
ceiling/   real1 real2 =>  integer real	[Generic Function]
round/   real1 real2 =>  integer real	[Generic Function]
truncate/   real1 real2 =>  integer real	[Generic Function]

These functions are equivalent to the two-argument forms of floor, ceiling, round, and truncate in Common Lisp (X3J13). Division by zero signals an error.

modulo   real1 real2  =>  real	[Generic Function]

modulo returns the second value of floor/ ( real1 , real2).

remainder   real1 real2  =>  real	[Generic Function]

remainder returns the second value of truncate/ ( real1 , real2).

number1  ^ integer2 =>  number	[Generic Function]

Returns number1 raised to the power integer2.

abs   number =>  number	[Generic Function]
logior   #rest integers =>  integer	[Generic Function]
logxor   #rest integers =>  integer	[Generic Function]
logand   #rest integers =>  integer	[Generic Function]
lognot   integer =>  integer	[Generic Function]
logbit?   index integer =>  boolean	[Generic Function]
ash   integer count =>  integer	[Generic Function]

The generic functions abs, logior, logxor, logand, lognot, ash are as defined in Common Lisp. logbit? is equivalent to Common Lisp's logbitp.

rationalize   number =>  number	[Generic Function]
numerator   number =>  number	[Generic Function]
denominator   number =>  number	[Generic Function]

The generic functions rationalize, numerator, and denominator are as defined in Revised[4] Report on Scheme.

lcm   integer1 integer2  =>  integer	[Generic Function]
gcd   integer1 integer2  =>  integer	[Generic Function]

These functions return the least common multiple and greatest common divisor of integer1 and integer2, respectively

min   real #rest more-reals  =>  real	[Function]
max   real #rest more-reals  =>  real	[Function]

min returns the argument that is least (closest to negative infinity). max returns the argument that is greatest (closest to positive infinity). The methods operate by calling <.