The floating-point Reference Manual

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The floating-point Reference Manual

This is the floating-point Reference Manual, version 0.1.0, generated automatically by Declt version 2.3 "Robert April" on Wed Mar 14 03:54:03 2018 GMT+0.


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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.


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2 Systems

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


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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

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3 Files

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


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3.1 Lisp


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3.1.1 floating-point.asd

Location

floating-point.asd

Systems

floating-point (system)


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3.1.2 floating-point/floating-point.lisp

Parent

floating-point (system)

Location

floating-point.lisp

Packages

floating-point


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3.1.3 floating-point/constants.lisp

Dependency

floating-point.lisp (file)

Parent

floating-point (system)

Location

constants.lisp

Exported Definitions

pi/2 (constant)


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3.1.4 floating-point/error-analysis.lisp

Dependency

floating-point.lisp (file)

Parent

floating-point (system)

Location

error-analysis.lisp

Exported Definitions
Internal Definitions

%relative-error (function)


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3.1.5 floating-point/predicates.lisp

Dependency

error-analysis.lisp (file)

Parent

floating-point (system)

Location

predicates.lisp

Exported Definitions
Internal Definitions

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4 Packages

Packages are listed by definition order.


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4.1 floating-point

Source

floating-point.lisp (file)

Nickname

fp

Use List

common-lisp

Exported Definitions
Internal Definitions

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5 Definitions

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


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5.1 Exported definitions


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5.1.1 Constants

Constant: pi/2

PI/2 or 90-degrees.

Package

floating-point

Source

constants.lisp (file)


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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)


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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.


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5.2 Internal definitions


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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)


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Appendix A Indexes


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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  

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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  

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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  

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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