The floating-point Reference Manual

Table of Contents

The floating-point Reference Manual

This is the floating-point Reference Manual, version 0.1.0, generated automatically by Declt version 3.0 "Montgomery Scott" on Wed Mar 25 18:05:17 2020 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

A.2 Functions

A.3 Variables

A.4 Data types