Chapter 11

The Built-In Classes

Numbers

Dylan provides a variety of numeric classes. Classes under <complex> are sealed, so that numeric operations on them can be highly optimized. User defined numeric classes will be subclasses of <number>.

Figure 11-3 shows the built-in number classes and some of their characteristics.

Figure 11-3 The Number Classes

S	– Sealed	P	– Primary	C	– Concrete	I	– Instantiable
O	– Open	F	– Free	A	– Abstract	U	– Uninstantiable

Errata: In the published book, <complex> is incorrectly identified as <complex-number> in Figure 11-3.

General Numbers

`<number>` [Open Abstract Class]

The class of all numbers.

Superclasses:

<object>

Init-keywords:

None.

Operations:

None.

Description:

The class of all numbers.

The class <number> is open, to allow programmers to create additional numeric classes. The built-in numeric operations do not provide default implementations for <number>, but for <complex>, a sealed subclass of <number>.

Complex Numbers

`<complex>` [Sealed Abstract Class]

The class of complex numbers.

Superclasses:

<number>

Init-keywords:

None.

Description:

The sealed superclass of all built-in numbers, including real numbers. There are no non-real subclasses of <complex> defined by the language, but implementations may define such subclasses. Because <complex> and all its defined subclasses are sealed, implementation-defined subclasses may be added efficiently.

Many built-in functions are defined to have methods on <complex>. This means that the function is defined on all built-in subclasses of <complex>. It does not imply that there is a single method specialized on the <complex> class.

Operations:

The class <complex> provides implementations for the following functions:

**Table 11-10** Methods on <complex>
Function	Description	Page
`=`	Compares two objects for equality.	269
`zero?`	Tests for the property of being equal to zero.	275
`+`	Returns the sum of its arguments.	277
`*`	Returns the product of its arguments.	277
`-`	Returns the difference of its arguments.	278
`/`	Returns the quotient of its arguments.	278
`^`	Raises an object to a specified power.	283

Reals

`<real>` [Sealed Abstract Class]

The class of real numbers.

Superclasses:

<complex>

Init-keywords:

None.

Description:

The class of real numbers.

Operations:

The class <real> provides implementations for the following functions:

**Table 11-11** Functions on <real>
Function	Description	Page
`floor`	Truncates a real number toward negative infinity.	279
`ceiling`	Truncates a real number toward positive infinity.	280
`round`	Rounds a real number toward the nearest mathematical integer.	280
`truncate`	Truncates a real number toward zero.	280
`floor/`	Returns the floor of the quotient of two numbers.	281
`ceiling/`	Returns the ceiling of the quotient of two numbers.	281
`round/`	Rounds off the quotient of two numbers.	282
`truncate/`	Returns the truncated quotient of two numbers.	282
`modulo`	Returns the second value of `floor/`.	282
`remainder`	Returns the second value of `truncate/`.	283

**Table 11-12** Methods on <real>
Function	Description	Page
`<`	Returns true if its first operand is less than its second operand.	271
`abs`	Returns the absolute value of its argument.	284
`positive?`	Tests for the property of being positive.	276
`negative?`	Tests for the property of being negative.	276
`integral?`	Tests for the property of being integral.	276
`negative`	Returns the negation of an object.	279

Floats

The classes <single-float> and <double-float> are intended but not required to be the corresponding IEEE types. The class <extended-float> is intended but not required to have more range and/or precision than <double-float>.

If an implementation has fewer than three floating point classes, the names <single-float>, <double-float> and <extended-float> may all refer to the same object.

`<float>` [Sealed Abstract Class]

The class of floating-point numbers.

Superclasses:: <real>
Init-keywords:: None.
Description:: The class of all floating-point numbers. This class is abstract. All floating point numbers will be instances of some concrete subclass of this class.
Operations:: None.

`<single-float>` [Sealed Class]

The class of single-precision floating-point numbers.

Superclasses:: <float>
Init-keywords:: None.
Description:: The class of single-precision floating-point numbers. This class is intended but not required to correspond to IEEE single-precision.
Operations:: None.

`<double-float>` [Sealed Class]

The class of double-precision floating-point numbers.

Superclasses:: <float>
Init-keywords:: None.
Description:: The class of double-precision floating-point numbers. This class is intended but not required to correspond to IEEE double-precision.
Operations:: None.

`<extended-float>` [Sealed Class]

The class of extended-precision floating-point numbers.

Superclasses:: <float>
Init-keywords:: None.
Description:: The class of extended-precision floating-point numbers. This class is intended but not required to provide more precision than <double-float>.
Operations:: None.

Rationals

`<rational>` [Sealed Abstract Class]

The class of rational numbers.

Superclasses:: <real>
Init-keywords:: None.
Description:: The class of rational numbers.
Operations:: None.

Integers

`<integer>` [Sealed Class]

The class of integers.

Superclasses:

<rational>

Init-keywords:

None.

Description:

The class of integers.

Implementations are required to support integers with at least 28 bits of precision. The overflow and underflow behavior is implementation-defined. (Some implementations may choose to have integers of unlimited size, but this is not required.)

The result of dividing two integers with / is implementation defined. Portable programs should use floor/, ceiling/, round/, or truncate/ to divide two integers.

Operations:

The class <integer> provides the following operations:

**Table 11-13** Functions on <integer>
Function	Description	Page
`odd?`	Tests for the property of being an odd number.	275
`even?`	Tests for the property of being an even number.	275
`logior`	Returns the bitwise inclusive or of its integer arguments.	284
`logxor`	Returns the bitwise exclusive or of its integer arguments.	284
`logand`	Returns the bitwise and of its integer arguments.	285
`lognot`	Returns the bitwise not of its integer argument.	285
`logbit?`	Tests the value of a particular bit in its integer argument.	285
`ash`	Performs an arithmetic shift on its first argument.	286

**Table 11-14** Methods on <integer>
Function	Description	Page
`lcm`	Returns the least common multiple of its two arguments.	286
`gcd`	Returns the greatest common divisor of its two arguments.	287

**Table 11-15** Methods on singleton(<integer>)
Function	Description	Page
`limited`	Returns a limited subtype of a class.	263

Numbers

General Numbers

<number> [Open Abstract Class]

Complex Numbers

<complex> [Sealed Abstract Class]

Reals

<real> [Sealed Abstract Class]

Floats

<float> [Sealed Abstract Class]

<single-float> [Sealed Class]

<double-float> [Sealed Class]

<extended-float> [Sealed Class]

Rationals

<rational> [Sealed Abstract Class]

Integers

<integer> [Sealed Class]

`<number>` [Open Abstract Class]

`<complex>` [Sealed Abstract Class]

`<real>` [Sealed Abstract Class]

`<float>` [Sealed Abstract Class]

`<single-float>` [Sealed Class]

`<double-float>` [Sealed Class]

`<extended-float>` [Sealed Class]

`<rational>` [Sealed Abstract Class]

`<integer>` [Sealed Class]