Machine Floats

Axiom provides two kinds of floating point numbers. The domain Float (abbreviation FLOAT) implements a model of arbitrary precisions floating point numbers. The domain DoubleFloat (abbreviation DFLOAT) is intended to make available hardware floating point arithmetic in Axiom. The actual model of floating point DoubleFloat that Axiom provides is system dependent. For example, on the IBM System 370, Axiom uses IBM double precision which has fourteen hexadecimal digits of precision or roughly sixteen decimal digits. Arbitrary precision floats allow the user to specify the precision at which arithmetic operations are computed. Although this is an attractive facility, it comes at a cost. Arbitrary precision floating point arithmetic typically takes twenty to two hundred times more time than hardware floating point. By default, floating point numbers that you enter into Axiom are of type Float.

You must therefore tell Axiom that you want to use DoubleFloat values and operations. The following are some conservative guidelines for getting Axiom to use DoubleFloat. To get a value of type DoubleFloat., use a target with "@", ...

a conversion,...

or an assignment to a declared variable. It is more efficient if you use a target rather than an explicit or implicit conversion.

You also need to declare functions that work with DoubleFloat.

Use package calling for operations from DoubleFloat unless the arguments themselves are already of type DoubleFloat.

By far, the most common usage of DoubleFloat is for functions to be graphied. For more information about Axiom's numerical and graphical facilities, see Graphics in section 7, Numeric Functions in section 8.1, and Float The usual arithmetic and elementary functions are available for DoubleFloat. Use

to get a list of operations.