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 Mon Aug 15 04:33:47 2022 GMT+0.

1 Introduction

floating-point

floating-point is a Common Lisp library with functions for calculating
the error between and predicates for determining the equality of 2
floating point numbers. The routines were originally developed for
lisp-unit, but are generally useful and warranted a separate package.

2 Systems

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

floating-point

2.1 `floating-point`

Floating point functions.

Author

Thomas M. Hermann <thomas.m.hermann@odonata-research.com>

License

MIT

Version

0.1.0

Source

floating-point.asd.

Child Components

floating-point.lisp (file).
constants.lisp (file).
error-analysis.lisp (file).
predicates.lisp (file).

3 Files

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

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

default-epsilon (generic function).
relative-error (generic function).

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

*epsilon* (special variable).
*significant-figures* (special variable).
float-equal (generic function).
sigfig-equal (generic function).

Internals

%float-equal (function).
%normalize-float (function).

4 Packages

Packages are listed by definition order.

floating-point

4.1 `floating-point`

Source

floating-point.lisp.

Nickname

fp

Use List

common-lisp.

Public Interface

*epsilon* (special variable).
*significant-figures* (special variable).
default-epsilon (generic function).
float-equal (generic function).
pi/2 (constant).
relative-error (generic function).
sigfig-equal (generic function).

Internals

%float-equal (function).
%normalize-float (function).
%relative-error (function).

5 Definitions

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

Public Interface
Internals

5.1 Public Interface

Constants
Special variables
Generic functions

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

Ordinary functions

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

Concepts
Functions
Variables
Data types

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

Jump to:	% D F G M R S

A.3 Variables

Jump to:	* C P S

	Index Entry	Section

*
	`epsilon`:	Public special variables
	`significant-figures`:	Public special variables

C
	`Constant, pi/2`:	Public constants

P
	`pi/2`:	Public constants

S
	`Special Variable, epsilon`:	Public special variables
	`Special Variable, significant-figures`:	Public special variables

Jump to:	* C P S

A.4 Data types

Jump to:	C E F P S

	Index Entry	Section

C
	`constants.lisp`:	The floating-point/constants․lisp file

E
	`error-analysis.lisp`:	The floating-point/error-analysis․lisp file

F
	`File, constants.lisp`:	The floating-point/constants․lisp file
	`File, error-analysis.lisp`:	The floating-point/error-analysis․lisp file
	`File, floating-point.asd`:	The floating-point/floating-point․asd file
	`File, floating-point.lisp`:	The floating-point/floating-point․lisp file
	`File, predicates.lisp`:	The floating-point/predicates․lisp file
	`floating-point`:	The floating-point system
	`floating-point`:	The floating-point package
	`floating-point.asd`:	The floating-point/floating-point․asd file
	`floating-point.lisp`:	The floating-point/floating-point․lisp file

P
	`Package, floating-point`:	The floating-point package
	`predicates.lisp`:	The floating-point/predicates․lisp file

S
	`System, floating-point`:	The floating-point system

Jump to:	C E F P S

The floating-point Reference Manual

The floating-point Reference Manual

Table of Contents

1 Introduction

2 Systems

2.1 floating-point

3 Files

3.1 Lisp

3.1.1 floating-point/floating-point.asd

3.1.2 floating-point/floating-point.lisp

3.1.3 floating-point/constants.lisp

3.1.4 floating-point/error-analysis.lisp

3.1.5 floating-point/predicates.lisp

4 Packages

4.1 floating-point

5 Definitions

5.1 Public Interface

5.1.1 Constants

5.1.2 Special variables

5.1.3 Generic functions

5.2 Internals

5.2.1 Ordinary functions

Appendix A Indexes

A.1 Concepts

A.2 Functions

A.3 Variables

A.4 Data types

2.1 `floating-point`

3.1.1 `floating-point/floating-point.asd`

3.1.2 `floating-point/floating-point.lisp`

3.1.3 `floating-point/constants.lisp`

3.1.4 `floating-point/error-analysis.lisp`

3.1.5 `floating-point/predicates.lisp`

4.1 `floating-point`