The Special Functions Reference Manual

Table of Contents

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The Special Functions Reference Manual

This is the Special Functions Reference Manual, version 1.1.


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1 Systems

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


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1.1 special-functions

Author

Steve Nunez <steve@symbolics.tech>

License

MS-PL

Description

Special functions in Common Lisp

Version

1.1

Dependencies
Source

special-functions.asd (file)

Directory

s:/src/special-functions/

Components

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2 Files

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


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2.1 Lisp


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2.1.1 special-functions.asd

Location

/src/special-functions/special-functions.asd

Systems

special-functions (system)


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2.1.2 special-functions/pkgdcl.lisp

Parent

special-functions (system)

Location

pkgdcl.lisp

Packages

special-functions


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2.1.3 special-functions/utils.lisp

Dependency

pkgdcl.lisp (file)

Parent

special-functions (system)

Location

utils.lisp

Internal Definitions

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2.1.4 special-functions/erf.lisp

Dependency

utils.lisp (file)

Parent

special-functions (system)

Location

erf.lisp

Exported Definitions
Internal Definitions

inverse-error (function)


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2.1.5 special-functions/gamma.lisp

Dependency

erf.lisp (file)

Parent

special-functions (system)

Location

gamma.lisp

Exported Definitions

gamma (function)

Internal Definitions

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2.1.6 special-functions/log-gamma.lisp

Dependency

gamma.lisp (file)

Parent

special-functions (system)

Location

log-gamma.lisp

Exported Definitions

log-gamma (function)


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2.1.7 special-functions/factorial.lisp

Dependency

log-gamma.lisp (file)

Parent

special-functions (system)

Location

factorial.lisp

Exported Definitions

factorial (function)

Internal Definitions

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3 Packages

Packages are listed by definition order.


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3.1 special-functions

Source

pkgdcl.lisp (file)

Nicknames
Use List
Exported Definitions
Internal Definitions

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4 Definitions

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


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4.1 Exported definitions


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4.1.1 Functions

Function: erf N

Returns the error function of n

Package

special-functions

Source

erf.lisp (file)

Function: erfc X

Returns the complementary error function of x

Package

special-functions

Source

erf.lisp (file)

Function: factorial X

Return the factorial value X! for X <= MAX-FACTORIAL; DOUBLE-FLOAT-POSITIVE-INFINITY if x < 0. X must be an INTEGER.

Package

special-functions

Source

factorial.lisp (file)

Function: gamma X

Return gamma(x), x <= MAXGAMD; NAN/RTE if x is a non-positive integer

Package

special-functions

Source

gamma.lisp (file)

Function: inverse-erf X

Return the inverse function of erf: (erf (inverse-erf x)) = x, -1 < x < 1

Package

special-functions

Source

erf.lisp (file)

Function: inverse-erfc X

Return the inverse function of erfc: (erfc (inverse-erfc x)) = x, 0 < x < 2

Package

special-functions

Source

erf.lisp (file)

Function: log-gamma N

Return the logarithm of gamma(x)

Package

special-functions

Source

log-gamma.lisp (file)


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4.2 Internal definitions


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4.2.1 Constants

Constant: +square-root-2-pi+
Package

special-functions

Source

utils.lisp (file)

Constant: maxgamd

Maximum argument for gamma

Package

special-functions

Source

gamma.lisp (file)

Constant: tiny
Package

special-functions

Source

gamma.lisp (file)


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4.2.2 Special variables

Special Variable: factorial-table

Table of factorials for integer values up to 100

Package

special-functions

Source

factorial.lisp (file)


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4.2.3 Functions

Function: decode-float64 X

Convert the (unsigned-byte 64) bit representation into a native double-float

Package

special-functions

Source

utils.lisp (file)

Function: encode-float64 X

Returns the bit representation of the double-float X as an (unsigned-byte 64)

Package

special-functions

Source

utils.lisp (file)

Function: gamma-inverse-small X

Return 1/gamma(x) for |x| < 0.03125

Package

special-functions

Source

gamma.lisp (file)

Function: gamma-medium X

Return gamma(x), |x| <= 13, x negative integer produces div by 0

Package

special-functions

Source

gamma.lisp (file)

Function: inverse-error P Q

Return value of inverse error function: erf_inv(p) if p <= 0.5, erfc_inv(q) otherwise

Package

special-functions

Source

erf.lisp (file)

Function: ramanujan X

Ramanujan’s original approximation of n!

Package

special-functions

Source

factorial.lisp (file)

Function: sam-ramanujan X

Modification of Ramanujan’s approximation of n! by Sidney A. Morris

Package

special-functions

Source

factorial.lisp (file)

Function: sign-gamma X

Return sign(gamma(x)), invalid for 0 or negative integer

Package

special-functions

Source

gamma.lisp (file)

Function: sin-pi X

Returns (sin (* pi x))

Package

special-functions

Source

utils.lisp (file)

Function: stirling X

Return (gamma x) for x > 13

Package

special-functions

Source

gamma.lisp (file)


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Appendix A Indexes


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A.1 Concepts

Jump to:   F   L   S  
Index Entry  Section

F
File, Lisp, special-functions.asd: The special-functions․asd file
File, Lisp, special-functions/erf.lisp: The special-functions/erf․lisp file
File, Lisp, special-functions/factorial.lisp: The special-functions/factorial․lisp file
File, Lisp, special-functions/gamma.lisp: The special-functions/gamma․lisp file
File, Lisp, special-functions/log-gamma.lisp: The special-functions/log-gamma․lisp file
File, Lisp, special-functions/pkgdcl.lisp: The special-functions/pkgdcl․lisp file
File, Lisp, special-functions/utils.lisp: The special-functions/utils․lisp file

L
Lisp File, special-functions.asd: The special-functions․asd file
Lisp File, special-functions/erf.lisp: The special-functions/erf․lisp file
Lisp File, special-functions/factorial.lisp: The special-functions/factorial․lisp file
Lisp File, special-functions/gamma.lisp: The special-functions/gamma․lisp file
Lisp File, special-functions/log-gamma.lisp: The special-functions/log-gamma․lisp file
Lisp File, special-functions/pkgdcl.lisp: The special-functions/pkgdcl․lisp file
Lisp File, special-functions/utils.lisp: The special-functions/utils․lisp file

S
special-functions.asd: The special-functions․asd file
special-functions/erf.lisp: The special-functions/erf․lisp file
special-functions/factorial.lisp: The special-functions/factorial․lisp file
special-functions/gamma.lisp: The special-functions/gamma․lisp file
special-functions/log-gamma.lisp: The special-functions/log-gamma․lisp file
special-functions/pkgdcl.lisp: The special-functions/pkgdcl․lisp file
special-functions/utils.lisp: The special-functions/utils․lisp file

Jump to:   F   L   S  

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A.2 Functions

Jump to:   D   E   F   G   I   L   R   S  
Index Entry  Section

D
decode-float64: Internal functions

E
encode-float64: Internal functions
erf: Exported functions
erfc: Exported functions

F
factorial: Exported functions
Function, decode-float64: Internal functions
Function, encode-float64: Internal functions
Function, erf: Exported functions
Function, erfc: Exported functions
Function, factorial: Exported functions
Function, gamma: Exported functions
Function, gamma-inverse-small: Internal functions
Function, gamma-medium: Internal functions
Function, inverse-erf: Exported functions
Function, inverse-erfc: Exported functions
Function, inverse-error: Internal functions
Function, log-gamma: Exported functions
Function, ramanujan: Internal functions
Function, sam-ramanujan: Internal functions
Function, sign-gamma: Internal functions
Function, sin-pi: Internal functions
Function, stirling: Internal functions

G
gamma: Exported functions
gamma-inverse-small: Internal functions
gamma-medium: Internal functions

I
inverse-erf: Exported functions
inverse-erfc: Exported functions
inverse-error: Internal functions

L
log-gamma: Exported functions

R
ramanujan: Internal functions

S
sam-ramanujan: Internal functions
sign-gamma: Internal functions
sin-pi: Internal functions
stirling: Internal functions

Jump to:   D   E   F   G   I   L   R   S  

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A.3 Variables

Jump to:   +  
C   F   M   S   T  
Index Entry  Section

+
+square-root-2-pi+: Internal constants

C
Constant, +square-root-2-pi+: Internal constants
Constant, maxgamd: Internal constants
Constant, tiny: Internal constants

F
factorial-table: Internal special variables

M
maxgamd: Internal constants

S
Special Variable, factorial-table: Internal special variables

T
tiny: Internal constants

Jump to:   +  
C   F   M   S   T  

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A.4 Data types

Jump to:   P   S  
Index Entry  Section

P
Package, special-functions: The special-functions package

S
special-functions: The special-functions system
special-functions: The special-functions package
System, special-functions: The special-functions system

Jump to:   P   S