The floating-point Reference Manual

This is the floating-point Reference Manual, version 0.1.0, generated automatically by Declt version 4.0 beta 2 "William Riker" on Sat Dec 03 21:27:52 2022 GMT+0.

Table of Contents


1 Introduction


2 Systems

The main system appears first, followed by any subsystem dependency.


2.1 floating-point

Floating point functions.

Author

Thomas M. Hermann <>

License

MIT

Version

0.1.0

Source

floating-point.asd.

Child Components

3 Files

Files are sorted by type and then listed depth-first from the systems components trees.


3.1 Lisp


3.1.1 floating-point/floating-point.asd

Source

floating-point.asd.

Parent Component

floating-point (system).

ASDF Systems

floating-point.


3.1.2 floating-point/floating-point.lisp

Source

floating-point.asd.

Parent Component

floating-point (system).

Packages

floating-point.


3.1.3 floating-point/constants.lisp

Dependency

floating-point.lisp (file).

Source

floating-point.asd.

Parent Component

floating-point (system).

Public Interface

pi/2 (constant).


3.1.4 floating-point/error-analysis.lisp

Dependency

floating-point.lisp (file).

Source

floating-point.asd.

Parent Component

floating-point (system).

Public Interface
Internals

%relative-error (function).


3.1.5 floating-point/predicates.lisp

Dependency

error-analysis.lisp (file).

Source

floating-point.asd.

Parent Component

floating-point (system).

Public Interface
Internals

4 Packages

Packages are listed by definition order.


4.1 floating-point

Source

floating-point.lisp.

Nickname

fp

Use List

common-lisp.

Public Interface
Internals

5 Definitions

Definitions are sorted by export status, category, package, and then by lexicographic order.


5.1 Public Interface


5.1.1 Constants

Constant: pi/2

PI/2 or 90-degrees.

Package

floating-point.

Source

constants.lisp.


5.1.2 Special variables

Special Variable: *epsilon*

The default error epsilon.

Package

floating-point.

Source

predicates.lisp.

Special Variable: *significant-figures*

The default number of significant figures.

Package

floating-point.

Source

predicates.lisp.


5.1.3 Generic functions

Generic Function: default-epsilon (value)

Return the default epsilon for the value.

Package

floating-point.

Source

error-analysis.lisp.

Methods
Method: default-epsilon ((value complex))

Return a default epsilon value based on the complex type.

Method: default-epsilon ((value float))

Return a default epsilon value based on the floating point type.

Generic Function: float-equal (data1 data2 &optional epsilon)

Return true if the floating point data is equal.

Package

floating-point.

Source

predicates.lisp.

Methods
Method: float-equal ((data1 complex) (data2 complex) &optional epsilon)

Return true if the relative error between data1 and data2 is less than epsilon.

Method: float-equal ((data1 complex) (data2 float) &optional epsilon)

Return true if the relative error between data1 and data2 is less than epsilon.

Method: float-equal ((data1 float) (data2 complex) &optional epsilon)

Return true if the relative error between data1 and data2 is less than epsilon.

Method: float-equal ((data1 rational) (data2 float) &optional epsilon)

Return true if the relative error between data1 and data2 is less than epsilon.

Method: float-equal ((data1 float) (data2 rational) &optional epsilon)

Return true if the relative error between data1 and data2 is less than epsilon.

Method: float-equal ((data1 float) (data2 float) &optional epsilon)

Return true if the relative error between data1 and data2 is less than epsilon.

Generic Function: relative-error (exact approximate)

Return the relative-error between the 2 quantities.

Package

floating-point.

Source

error-analysis.lisp.

Methods
Method: relative-error ((exact complex) (approximate complex))

Return the relative error of the complex numbers.

Method: relative-error ((exact complex) (approximate float))

Return the relative error between the float and complex number.

Method: relative-error ((exact float) (approximate complex))

Return the relative error between the float and complex number.

Method: relative-error ((exact float) (approximate float))

Return the error delta between the exact and approximate floating point value.

Generic Function: sigfig-equal (data1 data2 &optional significant-figures)

Return true if the data have equal significant figures.

Package

floating-point.

Source

predicates.lisp.

Methods
Method: sigfig-equal ((data1 float) (data2 float) &optional significant-figures)

Return true if the floating point numbers have equal significant figures.


5.2 Internals


5.2.1 Ordinary functions

Function: %float-equal (data1 data2 epsilon)

Return true if the relative error between the data is less than epsilon.

Package

floating-point.

Source

predicates.lisp.

Function: %normalize-float (significand &optional exponent)

Return the normalized floating point number and exponent.

Package

floating-point.

Source

predicates.lisp.

Function: %relative-error (exact approximate)

Return the relative error of the numbers.

Package

floating-point.

Source

error-analysis.lisp.


Appendix A Indexes


A.1 Concepts


A.2 Functions

Jump to:   %  
D   F   G   M   R   S  
Index Entry  Section

%
%float-equal: Private ordinary functions
%normalize-float: Private ordinary functions
%relative-error: Private ordinary functions

D
default-epsilon: Public generic functions
default-epsilon: Public generic functions
default-epsilon: Public generic functions

F
float-equal: Public generic functions
float-equal: Public generic functions
float-equal: Public generic functions
float-equal: Public generic functions
float-equal: Public generic functions
float-equal: Public generic functions
float-equal: Public generic functions
Function, %float-equal: Private ordinary functions
Function, %normalize-float: Private ordinary functions
Function, %relative-error: Private ordinary functions

G
Generic Function, default-epsilon: Public generic functions
Generic Function, float-equal: Public generic functions
Generic Function, relative-error: Public generic functions
Generic Function, sigfig-equal: Public generic functions

M
Method, default-epsilon: Public generic functions
Method, default-epsilon: Public generic functions
Method, float-equal: Public generic functions
Method, float-equal: Public generic functions
Method, float-equal: Public generic functions
Method, float-equal: Public generic functions
Method, float-equal: Public generic functions
Method, float-equal: Public generic functions
Method, relative-error: Public generic functions
Method, relative-error: Public generic functions
Method, relative-error: Public generic functions
Method, relative-error: Public generic functions
Method, sigfig-equal: Public generic functions

R
relative-error: Public generic functions
relative-error: Public generic functions
relative-error: Public generic functions
relative-error: Public generic functions
relative-error: Public generic functions

S
sigfig-equal: Public generic functions
sigfig-equal: Public generic functions