# 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 Wed May 15 05:15:07 2024 GMT+0.

## 2 Systems

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

### 2.1 `floating-point-contractions`

Numerically stable contractions of floating-point operations.

Author

Paul M. Rodriguez <>

MIT

Source
Child Components

## 3 Files

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

### 3.1 Lisp

Source
Parent Component
ASDF Systems

Source
Parent Component
Packages

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

Dependency

`package.lisp` (file).

Source
Parent Component
Public Interface
Internals

`sq` (function).

## 4 Packages

Packages are listed by definition order.

### 4.1 `floating-point-contractions`

Source
Use List

`common-lisp`.

Public Interface
Internals

`sq` (function).

## 5 Definitions

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

### 5.1 Public Interface

#### 5.1.1 Ordinary functions

Function: exp-1 (x)

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

Package
Source
Function: exp-1/x (x)

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

Package
Source
Function: expt-1 (a z)

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

Package
Source
Function: hypot (x y)

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

Package
Source
Function: lb (n)

Binary logarithm.

Package
Source
Function: lg (n)

Decimal logarithm.

Package
Source
Function: ln (n)

Natural logarithm.

Package
Source
Function: log1+ (x)

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

Package
Source
Function: log1+/x (x)

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

Package
Source
Function: log1+exp (a)

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

Package
Source
Function: log1- (x)

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

Package
Source
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
Source
Function: log2-exp (x)

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

Package
Source
Function: logexp-1 (a)

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

Package
Source

Function: sq (x)
Package
Source