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The floating-point-contractions Reference Manual

This is the floating-point-contractions Reference Manual, generated automatically by Declt version 4.0 beta 2 "William Riker" on Tue Jul 15 05:07:55 2025 GMT+0.

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1 Introduction

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2 Systems

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

floating-point-contractions

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2.1 `floating-point-contractions`

Numerically stable contractions of floating-point operations.

Author

Paul M. Rodriguez <pmr@ruricolist.com>

License

MIT

Source

floating-point-contractions.asd.

Child Components

package.lisp (file).
floating-point-contractions.lisp (file).

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3 Files

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

Lisp

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3.1.3 `floating-point-contractions/floating-point-contractions.lisp`

Dependency

package.lisp (file).

Source

floating-point-contractions.asd.

Parent Component

floating-point-contractions (system).

Public Interface

exp-1 (function).
exp-1/x (function).
expt-1 (function).
hypot (function).
lb (function).
lg (function).
ln (function).
log1+ (function).
log1+/x (function).
log1+exp (function).
log1- (function).
log1-exp (function).
log2-exp (function).
logexp-1 (function).

Internals

sq (function).

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4 Packages

Packages are listed by definition order.

floating-point-contractions

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4.1 `floating-point-contractions`

Source

package.lisp.

Use List

common-lisp.

Public Interface

exp-1 (function).
exp-1/x (function).
expt-1 (function).
hypot (function).
lb (function).
lg (function).
ln (function).
log1+ (function).
log1+/x (function).
log1+exp (function).
log1- (function).
log1-exp (function).
log2-exp (function).
logexp-1 (function).

Internals

sq (function).

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5 Definitions

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

Public Interface
Internals

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5.1 Public Interface

Ordinary functions

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5.1.1 Ordinary functions

Function: exp-1 (x) ¶

Compute (- (exp x) 1) stably even when X is near zero.

Package: floating-point-contractions.
Source: floating-point-contractions.lisp.

Function: exp-1/x (x) ¶

Compute (/ (- (exp x) 1) x) stably even when X is near zero.

Package: floating-point-contractions.
Source: floating-point-contractions.lisp.

Function: expt-1 (a z) ¶

Compute (a^z)-1 stably even when A is close to 1 or Z is close to zero.

Package: floating-point-contractions.
Source: floating-point-contractions.lisp.

Function: hypot (x y) ¶

Compute the hypotenuse of X and Y without danger of floating-point overflow or underflow.

Package: floating-point-contractions.
Source: floating-point-contractions.lisp.

Function: lb (n) ¶

Binary logarithm.

Package: floating-point-contractions.
Source: floating-point-contractions.lisp.

Function: lg (n) ¶

Decimal logarithm.

Package: floating-point-contractions.
Source: floating-point-contractions.lisp.

Function: ln (n) ¶

Natural logarithm.

Package: floating-point-contractions.
Source: floating-point-contractions.lisp.

Function: log1+ (x) ¶

Compute (log (+ 1 x)) stably even when X is near zero.

Package: floating-point-contractions.
Source: floating-point-contractions.lisp.

Function: log1+/x (x) ¶

Compute (/ (log (+ 1 x)) x) stably even when X is near zero.

Package: floating-point-contractions.
Source: floating-point-contractions.lisp.

Function: log1+exp (a) ¶

Accurately compute log(1+exp(x)) even when A is near zero.

Package: floating-point-contractions.
Source: floating-point-contractions.lisp.

Function: log1- (x) ¶

Compute (log (- 1 x)) stably even when X is near zero.

Package: floating-point-contractions.
Source: floating-point-contractions.lisp.

Function: log1-exp (a) ¶

Compute log(1-exp(x)) stably even when A is near zero.

This is sometimes known as the E_3, the third Einstein function.

See Mächler 2008 for notes on accurate calculation.

https://cran.r-project.org/web/packages/Rmpfr/vignettes/log1mexp-note.pdf

Package: floating-point-contractions.
Source: floating-point-contractions.lisp.

Function: log2-exp (x) ¶

Compute log(2-exp(x)) stably even when X is near zero.

Package: floating-point-contractions.
Source: floating-point-contractions.lisp.

Function: logexp-1 (a) ¶

Compute log(exp(a)-1) stably even when A is small.

Package: floating-point-contractions.
Source: floating-point-contractions.lisp.

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5.2 Internals

Ordinary functions

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5.2.1 Ordinary functions

Function: sq (x) ¶

Package: floating-point-contractions.
Source: floating-point-contractions.lisp.

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Next: Functions, Previous: Indexes, Up: Indexes [Contents][Index]

A.1 Concepts

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A.2 Functions

Jump to:	E F H L S

	Index Entry	Section

E
	`exp-1`:	Public ordinary functions
	`exp-1/x`:	Public ordinary functions
	`expt-1`:	Public ordinary functions

F
	`Function, exp-1`:	Public ordinary functions
	`Function, exp-1/x`:	Public ordinary functions
	`Function, expt-1`:	Public ordinary functions
	`Function, hypot`:	Public ordinary functions
	`Function, lb`:	Public ordinary functions
	`Function, lg`:	Public ordinary functions
	`Function, ln`:	Public ordinary functions
	`Function, log1+`:	Public ordinary functions
	`Function, log1+/x`:	Public ordinary functions
	`Function, log1+exp`:	Public ordinary functions
	`Function, log1-`:	Public ordinary functions
	`Function, log1-exp`:	Public ordinary functions
	`Function, log2-exp`:	Public ordinary functions
	`Function, logexp-1`:	Public ordinary functions
	`Function, sq`:	Private ordinary functions

H
	`hypot`:	Public ordinary functions

L
	`lb`:	Public ordinary functions
	`lg`:	Public ordinary functions
	`ln`:	Public ordinary functions
	`log1+`:	Public ordinary functions
	`log1+/x`:	Public ordinary functions
	`log1+exp`:	Public ordinary functions
	`log1-`:	Public ordinary functions
	`log1-exp`:	Public ordinary functions
	`log2-exp`:	Public ordinary functions
	`logexp-1`:	Public ordinary functions

S
	`sq`:	Private ordinary functions

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A.3 Variables

Previous: Variables, Up: Indexes [Contents][Index]

A.4 Data types

Jump to:	F P S

	Index Entry	Section

F
	`File, floating-point-contractions.asd`:	The floating-point-contractions/floating-point-contractions․asd file
	`File, floating-point-contractions.lisp`:	The floating-point-contractions/floating-point-contractions․lisp file
	`File, package.lisp`:	The floating-point-contractions/package․lisp file
	`floating-point-contractions`:	The floating-point-contractions system
	`floating-point-contractions`:	The floating-point-contractions package
	`floating-point-contractions.asd`:	The floating-point-contractions/floating-point-contractions․asd file
	`floating-point-contractions.lisp`:	The floating-point-contractions/floating-point-contractions․lisp file

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

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

The floating-point-contractions Reference Manual

Table of Contents

1 Introduction

2 Systems

2.1 floating-point-contractions

3 Files

3.1 Lisp

3.1.1 floating-point-contractions/floating-point-contractions.asd

3.1.2 floating-point-contractions/package.lisp

3.1.3 floating-point-contractions/floating-point-contractions.lisp

4 Packages

4.1 floating-point-contractions

5 Definitions

5.1 Public Interface

5.1.1 Ordinary 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-contractions`

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

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

3.1.3 `floating-point-contractions/floating-point-contractions.lisp`

4.1 `floating-point-contractions`