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The horner Reference Manual

This is the horner Reference Manual, generated automatically by Declt version 4.0 beta 2 "William Riker" on Tue Jul 15 05:17:39 2025 GMT+0.

Table of Contents

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1 Introduction

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2 Systems

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

horner

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2.1 `horner`

Inline polynomial evaluation using Horner’s rule.

Author

Paul M. Rodriguez <pmr@ruricolist.com>

License

MIT

Dependencies

alexandria (system).
serapeum (system).
infix-math (system).

Source

Child Components

package.lisp (file).
horner.lisp (file).
goertzel.lisp (file).
evalpoly.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 Lisp

horner/horner.asd
horner/package.lisp
horner/horner.lisp
horner/goertzel.lisp
horner/evalpoly.lisp

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3.1.1 `horner/horner.asd`

Source: horner.asd.
Parent Component: horner (system).
ASDF Systems: horner.

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3.1.2 `horner/package.lisp`

Source: horner.asd.
Parent Component: horner (system).
Packages: horner.

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3.1.3 `horner/horner.lisp`

Dependency

package.lisp (file).

Source

Parent Component

horner (system).

Public Interface

eval-horner (function).
horner (macro).
horner/even (macro).
horner/odd (macro).

Internals

horner/coeffs (macro).
horner/monic (macro).
horner/precond (macro).
horner/simple (macro).
monic (function).
quartic (macro).
quintic (macro).
sextic (macro).

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3.1.4 `horner/goertzel.lisp`

Dependency: package.lisp (file).
Source: horner.asd.
Parent Component: horner (system).
Public Interface: goertzel (macro).

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3.1.5 `horner/evalpoly.lisp`

Dependency: package.lisp (file).
Source: horner.asd.
Parent Component: horner (system).
Public Interface: evalpoly (macro).

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4 Packages

Packages are listed by definition order.

horner

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4.1 `horner`

Source

package.lisp.

Use List

alexandria.
common-lisp.
infix-math/infix-math.
serapeum.

Public Interface

eval-horner (function).
evalpoly (macro).
goertzel (macro).
horner (macro).
horner/even (macro).
horner/odd (macro).

Internals

horner/coeffs (macro).
horner/monic (macro).
horner/precond (macro).
horner/simple (macro).
monic (function).
quartic (macro).
quintic (macro).
sextic (macro).

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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

Macros
Ordinary functions

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5.1.1 Macros

Macro: evalpoly (z &body p) ¶

Package: horner.
Source: evalpoly.lisp.

Macro: goertzel (z &body p) ¶

Package: horner.
Source: goertzel.lisp.

Macro: horner (x &body coeffs) ¶

Compute a polynomial using Horner’s rule.
Note that the coefficients COEFFS are provided in ascending order of powers: p0 + p1*x + p2*x^2...

Package: horner.
Source: horner.lisp.

Macro: horner/even (x &body coeffs) ¶

Evaluate polynomial with even powers only: p0 + p1*x^2 + p2*x^4...

Package: horner.
Source: horner.lisp.

Macro: horner/odd (x &body coeffs) ¶

Evaluate polynomial with odd powers only: p0*x + p1*x^3 + p2*x^5...

Package: horner.
Source: horner.lisp.

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5.1.2 Ordinary functions

Function: eval-horner (x coeffs) ¶

Eval COEFFS at run time, for testing.

Package: horner.
Source: horner.lisp.

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5.2 Internals

Macros
Ordinary functions

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5.2.1 Macros

Macro: horner/coeffs (x &body coeffs) ¶

Package: horner.
Source: horner.lisp.

Macro: horner/monic (x &body coeffs) ¶

Like ‘horner’ when the last coefficient is 1 (and omitted). Cf. p1evl in Cephes.

Package: horner.
Source: horner.lisp.

Macro: horner/precond (x &body coeffs) ¶

Package: horner.
Source: horner.lisp.

Macro: horner/simple (x &body coeffs) ¶

Package: horner.
Source: horner.lisp.

Macro: quartic (x u0 u1 u2 u3 u4) ¶

Better-than-Horner computation of the quartic. See Higham 2002, Knuth v.2.

Package: horner.
Source: horner.lisp.

Macro: quintic (x u0 u1 u2 u3 u4 u5) ¶

Package: horner.
Source: horner.lisp.

Macro: sextic (x u0 u1 u2 u3 u4 u5 u6) ¶

Optimized sextic using Pan’s method.

Package: horner.
Source: horner.lisp.

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5.2.2 Ordinary functions

Function: monic (&rest coefficients) ¶

Convert coefficients u_0, u_1... u_n to monic form and return them as multiple values.

Package: horner.
Source: horner.lisp.

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Appendix A Indexes

Concepts
Functions
Variables
Data types

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A.1 Concepts

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A.2 Functions

Jump to:	E F G H M Q S

	Index Entry		Section

E
	`eval-horner`:		Public ordinary functions
	`evalpoly`:		Public macros

F
	`Function, eval-horner`:		Public ordinary functions
	`Function, monic`:		Private ordinary functions

G
	`goertzel`:		Public macros

H
	`horner`:		Public macros
	`horner/coeffs`:		Private macros
	`horner/even`:		Public macros
	`horner/monic`:		Private macros
	`horner/odd`:		Public macros
	`horner/precond`:		Private macros
	`horner/simple`:		Private macros

M
	`Macro, evalpoly`:		Public macros
	`Macro, goertzel`:		Public macros
	`Macro, horner`:		Public macros
	`Macro, horner/coeffs`:		Private macros
	`Macro, horner/even`:		Public macros
	`Macro, horner/monic`:		Private macros
	`Macro, horner/odd`:		Public macros
	`Macro, horner/precond`:		Private macros
	`Macro, horner/simple`:		Private macros
	`Macro, quartic`:		Private macros
	`Macro, quintic`:		Private macros
	`Macro, sextic`:		Private macros
	`monic`:		Private ordinary functions

Q
	`quartic`:		Private macros
	`quintic`:		Private macros

S
	`sextic`:		Private macros

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A.3 Variables

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A.4 Data types

Jump to:	E F G H P S

	Index Entry		Section

E
	`evalpoly.lisp`:		The horner/evalpoly․lisp file

F
	`File, evalpoly.lisp`:		The horner/evalpoly․lisp file
	`File, goertzel.lisp`:		The horner/goertzel․lisp file
	`File, horner.asd`:		The horner/horner․asd file
	`File, horner.lisp`:		The horner/horner․lisp file
	`File, package.lisp`:		The horner/package․lisp file

G
	`goertzel.lisp`:		The horner/goertzel․lisp file

H
	`horner`:		The horner system
	`horner`:		The horner package
	`horner.asd`:		The horner/horner․asd file
	`horner.lisp`:		The horner/horner․lisp file

P
	`Package, horner`:		The horner package
	`package.lisp`:		The horner/package․lisp file

S
	`System, horner`:		The horner system