The floating-point Reference Manual

This is the floating-point Reference Manual, version 0.1.0, generated automatically by Declt version 2.4 "Will Decker" on Wed Jun 20 11:47:09 2018 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.

2.1 `floating-point`

Author

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

License

MIT

Description

Floating point functions.

Version

0.1.0

Source

floating-point.asd (file)

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.

3.1 Lisp

3.1.1 `floating-point.asd`

Location: floating-point.asd
Systems: floating-point (system)

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

Parent: floating-point (system)
Location: floating-point.lisp
Packages: floating-point

3.1.3 `floating-point/constants.lisp`

Dependency: floating-point.lisp (file)
Parent: floating-point (system)
Location: constants.lisp
Exported Definitions: pi/2 (constant)

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

Dependency

floating-point.lisp (file)

Parent

floating-point (system)

Location

error-analysis.lisp

Exported Definitions

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

Internal Definitions

%relative-error (function)

3.1.5 `floating-point/predicates.lisp`

Dependency

error-analysis.lisp (file)

Parent

floating-point (system)

Location

predicates.lisp

Exported Definitions

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

Internal Definitions

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

4 Packages

Packages are listed by definition order.

4.1 `floating-point`

Source

floating-point.lisp (file)

Nickname

fp

Use List

common-lisp

Exported Definitions

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

Internal Definitions

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

5 Definitions

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

5.1 Exported definitions

5.1.1 Constants

Constant: pi/2

PI/2 or 90-degrees.

Package: floating-point
Source: constants.lisp (file)

5.1.2 Special variables

Special Variable: *epsilon*

The default error epsilon.

Package: floating-point
Source: predicates.lisp (file)

Special Variable: *significant-figures*

The default number of significant figures.

Package: floating-point
Source: predicates.lisp (file)

5.1.3 Generic functions

Generic Function: default-epsilon VALUE

Return the default epsilon for the value.

Package

floating-point

Source

error-analysis.lisp (file)

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 (file)

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 (file)

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 (file)

Methods

Method: sigfig-equal (DATA1 float) (DATA2 float) &optional SIGNIFICANT-FIGURES: Return true if the floating point numbers have equal significant figures.

5.2 Internal definitions

5.2.1 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 (file)

Function: %normalize-float SIGNIFICAND &optional EXPONENT

Return the normalized floating point number and exponent.

Package: floating-point
Source: predicates.lisp (file)

Function: %relative-error EXACT APPROXIMATE

Return the relative error of the numbers.

Package: floating-point
Source: error-analysis.lisp (file)

Appendix A Indexes

A.1 Concepts

Jump to:	F L

	Index Entry	Section

F
	File, Lisp, `floating-point.asd`:	The floating-point<dot>asd file
	File, Lisp, `floating-point/constants.lisp`:	The floating-point/constants<dot>lisp file
	File, Lisp, `floating-point/error-analysis.lisp`:	The floating-point/error-analysis<dot>lisp file
	File, Lisp, `floating-point/floating-point.lisp`:	The floating-point/floating-point<dot>lisp file
	File, Lisp, `floating-point/predicates.lisp`:	The floating-point/predicates<dot>lisp file
	`floating-point.asd`:	The floating-point<dot>asd file
	`floating-point/constants.lisp`:	The floating-point/constants<dot>lisp file
	`floating-point/error-analysis.lisp`:	The floating-point/error-analysis<dot>lisp file
	`floating-point/floating-point.lisp`:	The floating-point/floating-point<dot>lisp file
	`floating-point/predicates.lisp`:	The floating-point/predicates<dot>lisp file

L
	Lisp File, `floating-point.asd`:	The floating-point<dot>asd file
	Lisp File, `floating-point/constants.lisp`:	The floating-point/constants<dot>lisp file
	Lisp File, `floating-point/error-analysis.lisp`:	The floating-point/error-analysis<dot>lisp file
	Lisp File, `floating-point/floating-point.lisp`:	The floating-point/floating-point<dot>lisp file
	Lisp File, `floating-point/predicates.lisp`:	The floating-point/predicates<dot>lisp file

Jump to:	F L

A.2 Functions

Jump to:	% D F G M R S

	Index Entry	Section

%
	`%float-equal`:	Internal functions
	`%normalize-float`:	Internal functions
	`%relative-error`:	Internal functions

D
	`default-epsilon`:	Exported generic functions
	`default-epsilon`:	Exported generic functions
	`default-epsilon`:	Exported generic functions

F
	`float-equal`:	Exported generic functions
	`float-equal`:	Exported generic functions
	`float-equal`:	Exported generic functions
	`float-equal`:	Exported generic functions
	`float-equal`:	Exported generic functions
	`float-equal`:	Exported generic functions
	`float-equal`:	Exported generic functions
	`Function, %float-equal`:	Internal functions
	`Function, %normalize-float`:	Internal functions
	`Function, %relative-error`:	Internal functions

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

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

R
	`relative-error`:	Exported generic functions
	`relative-error`:	Exported generic functions
	`relative-error`:	Exported generic functions
	`relative-error`:	Exported generic functions
	`relative-error`:	Exported generic functions

S
	`sigfig-equal`:	Exported generic functions
	`sigfig-equal`:	Exported generic functions

Jump to:	% D F G M R S

A.3 Variables

Jump to:	* C P S

	Index Entry	Section

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

C
	`Constant, pi/2`:	Exported constants

P
	`pi/2`:	Exported constants

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

Jump to:	* C P S

A.4 Data types

Jump to:	F P S

	Index Entry	Section

F
	`floating-point`:	The floating-point system
	`floating-point`:	The floating-point package

P
	`Package, floating-point`:	The floating-point package

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

Jump to:	F P S

• Introduction:		What floating-point is all about
• Systems:		The systems documentation
• Files:		The files documentation
• Packages:		The packages documentation
• Definitions:		The symbols documentation
• Indexes:		Concepts, functions, variables and data types

• The floating-point.asd file:
• The floating-point/floating-point.lisp file:
• The floating-point/constants.lisp file:
• The floating-point/error-analysis.lisp file:
• The floating-point/predicates.lisp file:

• Concept index:
• Function index:
• Variable index:
• Data type index:

• Exported constants:
• Exported special variables:
• Exported generic functions:

The floating-point Reference Manual

Table of Contents

The floating-point Reference Manual

1 Introduction

2 Systems

2.1 floating-point

3 Files

3.1 Lisp

3.1.1 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 Exported definitions

5.1.1 Constants

5.1.2 Special variables

5.1.3 Generic functions

5.2 Internal definitions

5.2.1 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.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`