The cl-factoring Reference Manual

This is the cl-factoring Reference Manual, generated automatically by Declt version 3.0 "Montgomery Scott" on Mon Apr 19 14:45:10 2021 GMT+0.

1 Introduction


* CL-Factoring

This library presents a set of algorithms for computing integer factorizations.
An interface is provided that takes an integer and will return a list of prime
numbers such that, when multiplied together, will result in the original number.

There is no magic sauce here or mathematical breakthroughs; the time
complexities of each algorithm is exponential.

** Interface

The library provides the function =factor=.

Specific factoring methods can be accessed from the package
=cl-factoring-algorithms=.

** General Purpose Factoring Algorithms

 1. Trial Division
 2. Pollard's Rho
 3. Brent's Cycle
 4. Hypercubic Polynomial Quadratic Sieve

** License

This library is licensed under the LLGPL where possible.

Certain algorithms may be developed by others and be licensed under more
permissive licenses.  If development is performed on these, the license will
remain as is (the LLGPL won't infect them).

2 Systems

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

2.1 `cl-factoring`

Author

Zach Kost-Smith <zachkostsmith@gmail.com>

License

LLGPL (http://opensource.franz.com/preamble.html) except for the file "ulimyhmpqs-1.0.lisp" which is 3 Clause BSD

Description

Integer Factoring

Dependencies

iterate
cl-primality

Source

cl-factoring.asd (file)

Components

ulimyhmpqs-1.0.lisp (file)
cl-factoring.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 `cl-factoring.asd`

Location: cl-factoring.asd
Systems: cl-factoring (system)

3.1.2 `cl-factoring/ulimyhmpqs-1.0.lisp`

Parent

cl-factoring (system)

Location

ulimyhmpqs-1.0.lisp

Packages

ulimy-hmpqs

Exported Definitions

hmpqs (function)

Internal Definitions

*count-x* (special variable)
*how-to-handle-new-relations* (special variable)
*max-divide-out* (special variable)
*max-stored-prime* (special variable)
*nr-of-stored-primes* (special variable)
*qr256* (special variable)
*qs-line* (special variable)
*qs-line-width* (special variable)
*stored-primes* (special variable)
2* (macro)
2^i (macro)
? (macro)
a-generator (function)
a_ideal (function)
b-generator (function)
b-opt (function)
binoc (function)
centered-report2 (function)
centered-title (function)
concat (macro)
copy-factor (function)
define-relation-handling (macro)
dfloat (macro)
div (macro)
div2 (macro)
divide-out-mod-2 (function)
divmod (function)
efactors (function)
even-down (macro)
even-up (macro)
expt2 (macro)
exptmod (function)
factor (structure)
factor-1/amodp (function)
(setf factor-1/amodp) (function)
factor-base-size (function)
factor-dp (function)
(setf factor-dp) (function)
factor-ep (function)
(setf factor-ep) (function)
factor-log10p (function)
(setf factor-log10p) (function)
factor-log2p (function)
(setf factor-log2p) (function)
factor-p (function)
factor-prime (function)
(setf factor-prime) (function)
factor-sqrtnmodp (function)
(setf factor-sqrtnmodp) (function)
factors-of-n-report2 (function)
fb-log-sum (function)
fb-log10 (macro)
fb-p (macro)
fb-picture (function)
got-them-all (function)
h1 (macro)
hard (function)
ilog2 (macro)
ilog2h1y (macro)
init-sieve (function)
init-subsieve (macro)
initial-report2 (function)
invmod (function)
invmod! (function)
jacobisymbol (function)
let-qs (macro)
m-opt (function)
make-cubes (function)
make-cublets (function)
make-factor (function)
make-factor-base (function)
make-primes (function)
make-topoff-n-cubes (macro)
merge-cubes (function)
minutes (function)
minutes-per-internal-time-unit (constant)
multiple-append (function)
multiple-cons (function)
new-factor (function)
nextpprime (function)
nice-time (function)
odd-down (macro)
odd-up (macro)
pi_ (function)
power-breaker (function)
pprime? (function)
prime (function)
prime? (function)
put-into-its-bucket (function)
qs (function)
quadratic-residue? (function)
report2 (function)
report2? (function)
report2?sieving-time (function)
report2?total-time (function)
sieve-for-ab (function)
sqrtmodprime (function)
square? (function)
str$ (macro)
topoff-bucket (macro)
topoff-index (macro)
try-to-solve (function)
with-all-primes (macro)
with-all-stored-primes (macro)
xor-merge (function)
yofh (macro)

3.1.3 `cl-factoring/cl-factoring.lisp`

Dependency

ulimyhmpqs-1.0.lisp (file)

Parent

cl-factoring (system)

Location

cl-factoring.lisp

Packages

cl-factoring
cl-factoring-algorithms

Exported Definitions

factor (function)

Internal Definitions

brents-cycle (function)
brents-cycle-attempt (function)
brents-cycle-find-factor (function)
factor-attempt-failed (condition)
pollards-rho (function)
pollards-rho-attempt (function)
pollards-rho-find-factor (function)
squarep (function)
trial-division (function)

4 Packages

Packages are listed by definition order.

4.1 `ulimy-hmpqs`

Source

ulimyhmpqs-1.0.lisp (file)

Use List

common-lisp

Exported Definitions

hmpqs (function)

Internal Definitions

*count-x* (special variable)
*how-to-handle-new-relations* (special variable)
*max-divide-out* (special variable)
*max-stored-prime* (special variable)
*nr-of-stored-primes* (special variable)
*qr256* (special variable)
*qs-line* (special variable)
*qs-line-width* (special variable)
*stored-primes* (special variable)
2* (macro)
2^i (macro)
? (macro)
a-generator (function)
a_ideal (function)
b-generator (function)
b-opt (function)
binoc (function)
centered-report2 (function)
centered-title (function)
concat (macro)
copy-factor (function)
define-relation-handling (macro)
dfloat (macro)
div (macro)
div2 (macro)
divide-out-mod-2 (function)
divmod (function)
efactors (function)
even-down (macro)
even-up (macro)
expt2 (macro)
exptmod (function)
factor (structure)
factor-1/amodp (function)
(setf factor-1/amodp) (function)
factor-base-size (function)
factor-dp (function)
(setf factor-dp) (function)
factor-ep (function)
(setf factor-ep) (function)
factor-log10p (function)
(setf factor-log10p) (function)
factor-log2p (function)
(setf factor-log2p) (function)
factor-p (function)
factor-prime (function)
(setf factor-prime) (function)
factor-sqrtnmodp (function)
(setf factor-sqrtnmodp) (function)
factors-of-n-report2 (function)
fb-log-sum (function)
fb-log10 (macro)
fb-p (macro)
fb-picture (function)
got-them-all (function)
h1 (macro)
hard (function)
ilog2 (macro)
ilog2h1y (macro)
init-sieve (function)
init-subsieve (macro)
initial-report2 (function)
invmod (function)
invmod! (function)
jacobisymbol (function)
let-qs (macro)
m-opt (function)
make-cubes (function)
make-cublets (function)
make-factor (function)
make-factor-base (function)
make-primes (function)
make-topoff-n-cubes (macro)
merge-cubes (function)
minutes (function)
minutes-per-internal-time-unit (constant)
multiple-append (function)
multiple-cons (function)
new-factor (function)
nextpprime (function)
nice-time (function)
odd-down (macro)
odd-up (macro)
pi_ (function)
power-breaker (function)
pprime? (function)
prime (function)
prime? (function)
put-into-its-bucket (function)
qs (function)
quadratic-residue? (function)
report2 (function)
report2? (function)
report2?sieving-time (function)
report2?total-time (function)
sieve-for-ab (function)
sqrtmodprime (function)
square? (function)
str$ (macro)
topoff-bucket (macro)
topoff-index (macro)
try-to-solve (function)
with-all-primes (macro)
with-all-stored-primes (macro)
xor-merge (function)
yofh (macro)

4.2 `cl-factoring`

Source

cl-factoring.lisp (file)

Use List

cl-primality
iterate
common-lisp

Exported Definitions

factor (function)

Internal Definitions

brents-cycle (function)
brents-cycle-attempt (function)
brents-cycle-find-factor (function)
factor-attempt-failed (condition)
pollards-rho (function)
pollards-rho-attempt (function)
pollards-rho-find-factor (function)
squarep (function)
trial-division (function)

4.3 `cl-factoring-algorithms`

Source: cl-factoring.lisp (file)

5 Definitions

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

5.1 Exported definitions

5.1.1 Functions

Function: factor N

Return the prime factorization of N as a sorted (smallest to largest) list. Factors that appear more than once are present mulitiple times in the output.

(reduce ’* (factor n)) = n

Package: cl-factoring
Source: cl-factoring.lisp (file)

Function: hmpqs N &key REPORT2

Package: ulimy-hmpqs
Source: ulimyhmpqs-1.0.lisp (file)

5.2 Internal definitions

5.2.1 Constants

Constant: minutes-per-internal-time-unit

Package: ulimy-hmpqs
Source: ulimyhmpqs-1.0.lisp (file)

5.2.2 Special variables

Special Variable: *count-x*

Package: ulimy-hmpqs
Source: ulimyhmpqs-1.0.lisp (file)

Special Variable: *how-to-handle-new-relations*

Package: ulimy-hmpqs
Source: ulimyhmpqs-1.0.lisp (file)

Special Variable: *max-divide-out*

Package: ulimy-hmpqs
Source: ulimyhmpqs-1.0.lisp (file)

Special Variable: *max-stored-prime*

Package: ulimy-hmpqs
Source: ulimyhmpqs-1.0.lisp (file)

Special Variable: *nr-of-stored-primes*

Package: ulimy-hmpqs
Source: ulimyhmpqs-1.0.lisp (file)

Special Variable: *qr256*

Package: ulimy-hmpqs
Source: ulimyhmpqs-1.0.lisp (file)

Special Variable: *qs-line*

Package: ulimy-hmpqs
Source: ulimyhmpqs-1.0.lisp (file)

Special Variable: *qs-line-width*

Package: ulimy-hmpqs
Source: ulimyhmpqs-1.0.lisp (file)

Special Variable: *stored-primes*

Package: ulimy-hmpqs
Source: ulimyhmpqs-1.0.lisp (file)

5.2.3 Macros

Macro: 2* I

Package: ulimy-hmpqs
Source: ulimyhmpqs-1.0.lisp (file)

Macro: 2^i I

Package: ulimy-hmpqs
Source: ulimyhmpqs-1.0.lisp (file)

Macro: ? &rest XXX

Package: ulimy-hmpqs
Source: ulimyhmpqs-1.0.lisp (file)

Macro: concat &rest STRNGS

Package: ulimy-hmpqs
Source: ulimyhmpqs-1.0.lisp (file)

Macro: define-relation-handling MODE

Package: ulimy-hmpqs
Source: ulimyhmpqs-1.0.lisp (file)

Macro: dfloat X

Package: ulimy-hmpqs
Source: ulimyhmpqs-1.0.lisp (file)

Macro: div A B

Package: ulimy-hmpqs
Source: ulimyhmpqs-1.0.lisp (file)

Macro: div2 X

Package: ulimy-hmpqs
Source: ulimyhmpqs-1.0.lisp (file)

Macro: even-down I

Package: ulimy-hmpqs
Source: ulimyhmpqs-1.0.lisp (file)

Macro: even-up I

Package: ulimy-hmpqs
Source: ulimyhmpqs-1.0.lisp (file)

Macro: expt2 I

Package: ulimy-hmpqs
Source: ulimyhmpqs-1.0.lisp (file)

Macro: fb-log10 Q

Package: ulimy-hmpqs
Source: ulimyhmpqs-1.0.lisp (file)

Macro: fb-p Q

Package: ulimy-hmpqs
Source: ulimyhmpqs-1.0.lisp (file)

Macro: h1 Y

Package: ulimy-hmpqs
Source: ulimyhmpqs-1.0.lisp (file)

Macro: ilog2 X

Package: ulimy-hmpqs
Source: ulimyhmpqs-1.0.lisp (file)

Macro: ilog2h1y Y

Package: ulimy-hmpqs
Source: ulimyhmpqs-1.0.lisp (file)

Macro: init-subsieve Y YSTOP QUADRANT

Package: ulimy-hmpqs
Source: ulimyhmpqs-1.0.lisp (file)

Macro: let-qs RETURN-IDS N &rest STUFF

Package: ulimy-hmpqs
Source: ulimyhmpqs-1.0.lisp (file)

Macro: make-topoff-n-cubes DIMENSION

Package: ulimy-hmpqs
Source: ulimyhmpqs-1.0.lisp (file)

Macro: odd-down I

Package: ulimy-hmpqs
Source: ulimyhmpqs-1.0.lisp (file)

Macro: odd-up I

Package: ulimy-hmpqs
Source: ulimyhmpqs-1.0.lisp (file)

Macro: str$ X

Package: ulimy-hmpqs
Source: ulimyhmpqs-1.0.lisp (file)

Macro: topoff-bucket LOG-SUM

Package: ulimy-hmpqs
Source: ulimyhmpqs-1.0.lisp (file)

Macro: topoff-index LOG-SUM

Package: ulimy-hmpqs
Source: ulimyhmpqs-1.0.lisp (file)

Macro: with-all-primes P &rest BODY

Package: ulimy-hmpqs
Source: ulimyhmpqs-1.0.lisp (file)

Macro: with-all-stored-primes P &rest BODY

Package: ulimy-hmpqs
Source: ulimyhmpqs-1.0.lisp (file)

Macro: yofh H QUADRANT

Package: ulimy-hmpqs
Source: ulimyhmpqs-1.0.lisp (file)

5.2.4 Functions

Function: a-generator ()

Package: ulimy-hmpqs
Source: ulimyhmpqs-1.0.lisp (file)

Function: a_ideal N M

Package: ulimy-hmpqs
Source: ulimyhmpqs-1.0.lisp (file)

Function: b-generator A A-FACTORS D

Package: ulimy-hmpqs
Source: ulimyhmpqs-1.0.lisp (file)

Function: b-opt N

Package: ulimy-hmpqs
Source: ulimyhmpqs-1.0.lisp (file)

Function: binoc N K

Package: ulimy-hmpqs
Source: ulimyhmpqs-1.0.lisp (file)

Function: brents-cycle N

Find the prime factorization of N.

Package: cl-factoring
Source: cl-factoring.lisp (file)

Function: brents-cycle-attempt ()

Package: cl-factoring
Source: cl-factoring.lisp (file)

Function: brents-cycle-find-factor N

Package: cl-factoring
Source: cl-factoring.lisp (file)

Function: centered-report2 X

Package: ulimy-hmpqs
Source: ulimyhmpqs-1.0.lisp (file)

Function: centered-title X

Package: ulimy-hmpqs
Source: ulimyhmpqs-1.0.lisp (file)

Function: copy-factor INSTANCE

Package: ulimy-hmpqs
Source: ulimyhmpqs-1.0.lisp (file)

Function: divide-out-mod-2 X HX A-FACTORS

Package: ulimy-hmpqs
Source: ulimyhmpqs-1.0.lisp (file)

Function: divmod A B MODULO

Package: ulimy-hmpqs
Source: ulimyhmpqs-1.0.lisp (file)

Function: efactors N &key REPORT2

Package: ulimy-hmpqs
Source: ulimyhmpqs-1.0.lisp (file)

Function: exptmod BASE POWER MODULO

Package: ulimy-hmpqs
Source: ulimyhmpqs-1.0.lisp (file)

Function: factor-1/amodp INSTANCE

Function: (setf factor-1/amodp) VALUE INSTANCE

Package: ulimy-hmpqs
Source: ulimyhmpqs-1.0.lisp (file)

Function: factor-base-size N

Package: ulimy-hmpqs
Source: ulimyhmpqs-1.0.lisp (file)

Function: factor-dp INSTANCE

Function: (setf factor-dp) VALUE INSTANCE

Package: ulimy-hmpqs
Source: ulimyhmpqs-1.0.lisp (file)

Function: factor-ep INSTANCE

Function: (setf factor-ep) VALUE INSTANCE

Package: ulimy-hmpqs
Source: ulimyhmpqs-1.0.lisp (file)

Function: factor-log10p INSTANCE

Function: (setf factor-log10p) VALUE INSTANCE

Package: ulimy-hmpqs
Source: ulimyhmpqs-1.0.lisp (file)

Function: factor-log2p INSTANCE

Function: (setf factor-log2p) VALUE INSTANCE

Package: ulimy-hmpqs
Source: ulimyhmpqs-1.0.lisp (file)

Function: factor-p OBJECT

Package: ulimy-hmpqs
Source: ulimyhmpqs-1.0.lisp (file)

Function: factor-prime INSTANCE

Function: (setf factor-prime) VALUE INSTANCE

Package: ulimy-hmpqs
Source: ulimyhmpqs-1.0.lisp (file)

Function: factor-sqrtnmodp INSTANCE

Function: (setf factor-sqrtnmodp) VALUE INSTANCE

Package: ulimy-hmpqs
Source: ulimyhmpqs-1.0.lisp (file)

Function: factors-of-n-report2 ()

Package: ulimy-hmpqs
Source: ulimyhmpqs-1.0.lisp (file)

Function: fb-log-sum I0 I1

Package: ulimy-hmpqs
Source: ulimyhmpqs-1.0.lisp (file)

Function: fb-picture WID

Package: ulimy-hmpqs
Source: ulimyhmpqs-1.0.lisp (file)

Function: got-them-all ()

Package: ulimy-hmpqs
Source: ulimyhmpqs-1.0.lisp (file)

Function: hard D

Package: ulimy-hmpqs
Source: ulimyhmpqs-1.0.lisp (file)

Function: init-sieve A BETA GAMMA

Package: ulimy-hmpqs
Source: ulimyhmpqs-1.0.lisp (file)

Function: initial-report2 ()

Package: ulimy-hmpqs
Source: ulimyhmpqs-1.0.lisp (file)

Function: invmod X M

Package: ulimy-hmpqs
Source: ulimyhmpqs-1.0.lisp (file)

Function: invmod! X M

Package: ulimy-hmpqs
Source: ulimyhmpqs-1.0.lisp (file)

Function: jacobisymbol P Q

Package: ulimy-hmpqs
Source: ulimyhmpqs-1.0.lisp (file)

Function: m-opt LOG10N

Package: ulimy-hmpqs
Source: ulimyhmpqs-1.0.lisp (file)

Function: make-cubes A-LIST LOG-REST Q QMAX D

Package: ulimy-hmpqs
Source: ulimyhmpqs-1.0.lisp (file)

Function: make-cublets A-LIST LOG-REST Q QMAX D

Package: ulimy-hmpqs
Source: ulimyhmpqs-1.0.lisp (file)

Function: make-factor &key (PRIME PRIME) (SQRTNMODP SQRTNMODP) (LOG2P LOG2P) (LOG10P LOG10P) (1/AMODP 1/AMODP) (DP DP) (EP EP)

Package: ulimy-hmpqs
Source: ulimyhmpqs-1.0.lisp (file)

Function: make-factor-base N FB-SIZE

Package: ulimy-hmpqs
Source: ulimyhmpqs-1.0.lisp (file)

Function: make-primes N

Package: ulimy-hmpqs
Source: ulimyhmpqs-1.0.lisp (file)

Function: merge-cubes A1 A2

Package: ulimy-hmpqs
Source: ulimyhmpqs-1.0.lisp (file)

Function: minutes ()

Package: ulimy-hmpqs
Source: ulimyhmpqs-1.0.lisp (file)

Function: multiple-append X NROFCOPIES XCOPIES

Package: ulimy-hmpqs
Source: ulimyhmpqs-1.0.lisp (file)

Function: multiple-cons X NROFCOPIES XCOPIES

Package: ulimy-hmpqs
Source: ulimyhmpqs-1.0.lisp (file)

Function: new-factor F

Package: ulimy-hmpqs
Source: ulimyhmpqs-1.0.lisp (file)

Function: nextpprime P

Package: ulimy-hmpqs
Source: ulimyhmpqs-1.0.lisp (file)

Function: nice-time MINS

Package: ulimy-hmpqs
Source: ulimyhmpqs-1.0.lisp (file)

Function: pi_ N

approx #{p | p<=n & p prime}

Package: ulimy-hmpqs
Source: ulimyhmpqs-1.0.lisp (file)

Function: pollards-rho N

Find the prime factorization of N.

Package: cl-factoring
Source: cl-factoring.lisp (file)

Function: pollards-rho-attempt N

Package: cl-factoring
Source: cl-factoring.lisp (file)

Function: pollards-rho-find-factor N

Package: cl-factoring
Source: cl-factoring.lisp (file)

Function: power-breaker X &optional MAX-FACTOR

Package: ulimy-hmpqs
Source: ulimyhmpqs-1.0.lisp (file)

Function: pprime? P &optional TRIALS

Package: ulimy-hmpqs
Source: ulimyhmpqs-1.0.lisp (file)

Function: prime I

Package: ulimy-hmpqs
Source: ulimyhmpqs-1.0.lisp (file)

Function: prime? X

Package: ulimy-hmpqs
Source: ulimyhmpqs-1.0.lisp (file)

Function: put-into-its-bucket R

Package: ulimy-hmpqs
Source: ulimyhmpqs-1.0.lisp (file)

Function: qs N &key M B DELTA-T OMIT-BELOW SLP-LOG2 ALFA REPORT2 RETURN2

Package: ulimy-hmpqs
Source: ulimyhmpqs-1.0.lisp (file)

Function: quadratic-residue? N P

Package: ulimy-hmpqs
Source: ulimyhmpqs-1.0.lisp (file)

Function: report2 ()

Package: ulimy-hmpqs
Source: ulimyhmpqs-1.0.lisp (file)

Function: report2? ()

Package: ulimy-hmpqs
Source: ulimyhmpqs-1.0.lisp (file)

Function: report2?sieving-time ()

Package: ulimy-hmpqs
Source: ulimyhmpqs-1.0.lisp (file)

Function: report2?total-time ()

Package: ulimy-hmpqs
Source: ulimyhmpqs-1.0.lisp (file)

Function: sieve-for-ab A B A-FACTORS

Package: ulimy-hmpqs
Source: ulimyhmpqs-1.0.lisp (file)

Function: sqrtmodprime N P

Package: ulimy-hmpqs
Source: ulimyhmpqs-1.0.lisp (file)

Function: square? X

Package: ulimy-hmpqs
Source: ulimyhmpqs-1.0.lisp (file)

Function: squarep N

Package: cl-factoring
Source: cl-factoring.lisp (file)

Function: trial-division N

Package: cl-factoring
Source: cl-factoring.lisp (file)

Function: try-to-solve IX-LIST

Package: ulimy-hmpqs
Source: ulimyhmpqs-1.0.lisp (file)

Function: xor-merge U V

Package: ulimy-hmpqs
Source: ulimyhmpqs-1.0.lisp (file)

5.2.5 Conditions

Condition: factor-attempt-failed ()

Package: cl-factoring
Source: cl-factoring.lisp (file)
Direct superclasses: condition (condition)

5.2.6 Structures

Structure: factor ()

Package

ulimy-hmpqs

Source

ulimyhmpqs-1.0.lisp (file)

Direct superclasses

structure-object (structure)

Direct slots

Slot: prime

Type: fixnum
Initform: 0
Readers: factor-prime (function)
Writers: (setf factor-prime) (function)

Slot: sqrtnmodp

Type: fixnum
Initform: 0
Readers: factor-sqrtnmodp (function)
Writers: (setf factor-sqrtnmodp) (function)

Slot: log2p

Type: fixnum
Initform: 0
Readers: factor-log2p (function)
Writers: (setf factor-log2p) (function)

Slot: log10p

Type: float
Initform: 0.0
Readers: factor-log10p (function)
Writers: (setf factor-log10p) (function)

Slot: 1/amodp

Type: fixnum
Initform: 0
Readers: factor-1/amodp (function)
Writers: (setf factor-1/amodp) (function)

Slot: dp

Type: fixnum
Initform: 0
Readers: factor-dp (function)
Writers: (setf factor-dp) (function)

Slot: ep

Type: fixnum
Initform: 0
Readers: factor-ep (function)
Writers: (setf factor-ep) (function)

Appendix A Indexes

A.1 Concepts

Jump to:	C F L

	Index Entry	Section

C
	`cl-factoring.asd`:	The cl-factoring․asd file
	`cl-factoring/cl-factoring.lisp`:	The cl-factoring/cl-factoring․lisp file
	`cl-factoring/ulimyhmpqs-1.0.lisp`:	The cl-factoring/ulimyhmpqs-1․0․lisp file

F
	File, Lisp, `cl-factoring.asd`:	The cl-factoring․asd file
	File, Lisp, `cl-factoring/cl-factoring.lisp`:	The cl-factoring/cl-factoring․lisp file
	File, Lisp, `cl-factoring/ulimyhmpqs-1.0.lisp`:	The cl-factoring/ulimyhmpqs-1․0․lisp file

L
	Lisp File, `cl-factoring.asd`:	The cl-factoring․asd file
	Lisp File, `cl-factoring/cl-factoring.lisp`:	The cl-factoring/cl-factoring․lisp file
	Lisp File, `cl-factoring/ulimyhmpqs-1.0.lisp`:	The cl-factoring/ulimyhmpqs-1․0․lisp file

Jump to:	C F L

A.2 Functions

Jump to:	( 2 ? A B C D E F G H I J L M N O P Q R S T W X Y

	Index Entry	Section

(
	`(setf factor-1/amodp)`:	Internal functions
	`(setf factor-dp)`:	Internal functions
	`(setf factor-ep)`:	Internal functions
	`(setf factor-log10p)`:	Internal functions
	`(setf factor-log2p)`:	Internal functions
	`(setf factor-prime)`:	Internal functions
	`(setf factor-sqrtnmodp)`:	Internal functions

2
	`2*`:	Internal macros
	`2^i`:	Internal macros

?
	`?`:	Internal macros

A
	`a-generator`:	Internal functions
	`a_ideal`:	Internal functions

B
	`b-generator`:	Internal functions
	`b-opt`:	Internal functions
	`binoc`:	Internal functions
	`brents-cycle`:	Internal functions
	`brents-cycle-attempt`:	Internal functions
	`brents-cycle-find-factor`:	Internal functions

C
	`centered-report2`:	Internal functions
	`centered-title`:	Internal functions
	`concat`:	Internal macros
	`copy-factor`:	Internal functions

D
	`define-relation-handling`:	Internal macros
	`dfloat`:	Internal macros
	`div`:	Internal macros
	`div2`:	Internal macros
	`divide-out-mod-2`:	Internal functions
	`divmod`:	Internal functions

E
	`efactors`:	Internal functions
	`even-down`:	Internal macros
	`even-up`:	Internal macros
	`expt2`:	Internal macros
	`exptmod`:	Internal functions

F
	`factor`:	Exported functions
	`factor-1/amodp`:	Internal functions
	`factor-base-size`:	Internal functions
	`factor-dp`:	Internal functions
	`factor-ep`:	Internal functions
	`factor-log10p`:	Internal functions
	`factor-log2p`:	Internal functions
	`factor-p`:	Internal functions
	`factor-prime`:	Internal functions
	`factor-sqrtnmodp`:	Internal functions
	`factors-of-n-report2`:	Internal functions
	`fb-log-sum`:	Internal functions
	`fb-log10`:	Internal macros
	`fb-p`:	Internal macros
	`fb-picture`:	Internal functions
	`Function, (setf factor-1/amodp)`:	Internal functions
	`Function, (setf factor-dp)`:	Internal functions
	`Function, (setf factor-ep)`:	Internal functions
	`Function, (setf factor-log10p)`:	Internal functions
	`Function, (setf factor-log2p)`:	Internal functions
	`Function, (setf factor-prime)`:	Internal functions
	`Function, (setf factor-sqrtnmodp)`:	Internal functions
	`Function, a-generator`:	Internal functions
	`Function, a_ideal`:	Internal functions
	`Function, b-generator`:	Internal functions
	`Function, b-opt`:	Internal functions
	`Function, binoc`:	Internal functions
	`Function, brents-cycle`:	Internal functions
	`Function, brents-cycle-attempt`:	Internal functions
	`Function, brents-cycle-find-factor`:	Internal functions
	`Function, centered-report2`:	Internal functions
	`Function, centered-title`:	Internal functions
	`Function, copy-factor`:	Internal functions
	`Function, divide-out-mod-2`:	Internal functions
	`Function, divmod`:	Internal functions
	`Function, efactors`:	Internal functions
	`Function, exptmod`:	Internal functions
	`Function, factor`:	Exported functions
	`Function, factor-1/amodp`:	Internal functions
	`Function, factor-base-size`:	Internal functions
	`Function, factor-dp`:	Internal functions
	`Function, factor-ep`:	Internal functions
	`Function, factor-log10p`:	Internal functions
	`Function, factor-log2p`:	Internal functions
	`Function, factor-p`:	Internal functions
	`Function, factor-prime`:	Internal functions
	`Function, factor-sqrtnmodp`:	Internal functions
	`Function, factors-of-n-report2`:	Internal functions
	`Function, fb-log-sum`:	Internal functions
	`Function, fb-picture`:	Internal functions
	`Function, got-them-all`:	Internal functions
	`Function, hard`:	Internal functions
	`Function, hmpqs`:	Exported functions
	`Function, init-sieve`:	Internal functions
	`Function, initial-report2`:	Internal functions
	`Function, invmod`:	Internal functions
	`Function, invmod!`:	Internal functions
	`Function, jacobisymbol`:	Internal functions
	`Function, m-opt`:	Internal functions
	`Function, make-cubes`:	Internal functions
	`Function, make-cublets`:	Internal functions
	`Function, make-factor`:	Internal functions
	`Function, make-factor-base`:	Internal functions
	`Function, make-primes`:	Internal functions
	`Function, merge-cubes`:	Internal functions
	`Function, minutes`:	Internal functions
	`Function, multiple-append`:	Internal functions
	`Function, multiple-cons`:	Internal functions
	`Function, new-factor`:	Internal functions
	`Function, nextpprime`:	Internal functions
	`Function, nice-time`:	Internal functions
	`Function, pi_`:	Internal functions
	`Function, pollards-rho`:	Internal functions
	`Function, pollards-rho-attempt`:	Internal functions
	`Function, pollards-rho-find-factor`:	Internal functions
	`Function, power-breaker`:	Internal functions
	`Function, pprime?`:	Internal functions
	`Function, prime`:	Internal functions
	`Function, prime?`:	Internal functions
	`Function, put-into-its-bucket`:	Internal functions
	`Function, qs`:	Internal functions
	`Function, quadratic-residue?`:	Internal functions
	`Function, report2`:	Internal functions
	`Function, report2?`:	Internal functions
	`Function, report2?sieving-time`:	Internal functions
	`Function, report2?total-time`:	Internal functions
	`Function, sieve-for-ab`:	Internal functions
	`Function, sqrtmodprime`:	Internal functions
	`Function, square?`:	Internal functions
	`Function, squarep`:	Internal functions
	`Function, trial-division`:	Internal functions
	`Function, try-to-solve`:	Internal functions
	`Function, xor-merge`:	Internal functions

G
	`got-them-all`:	Internal functions

H
	`h1`:	Internal macros
	`hard`:	Internal functions
	`hmpqs`:	Exported functions

I
	`ilog2`:	Internal macros
	`ilog2h1y`:	Internal macros
	`init-sieve`:	Internal functions
	`init-subsieve`:	Internal macros
	`initial-report2`:	Internal functions
	`invmod`:	Internal functions
	`invmod!`:	Internal functions

J
	`jacobisymbol`:	Internal functions

L
	`let-qs`:	Internal macros

M
	`m-opt`:	Internal functions
	`Macro, 2*`:	Internal macros
	`Macro, 2^i`:	Internal macros
	`Macro, ?`:	Internal macros
	`Macro, concat`:	Internal macros
	`Macro, define-relation-handling`:	Internal macros
	`Macro, dfloat`:	Internal macros
	`Macro, div`:	Internal macros
	`Macro, div2`:	Internal macros
	`Macro, even-down`:	Internal macros
	`Macro, even-up`:	Internal macros
	`Macro, expt2`:	Internal macros
	`Macro, fb-log10`:	Internal macros
	`Macro, fb-p`:	Internal macros
	`Macro, h1`:	Internal macros
	`Macro, ilog2`:	Internal macros
	`Macro, ilog2h1y`:	Internal macros
	`Macro, init-subsieve`:	Internal macros
	`Macro, let-qs`:	Internal macros
	`Macro, make-topoff-n-cubes`:	Internal macros
	`Macro, odd-down`:	Internal macros
	`Macro, odd-up`:	Internal macros
	`Macro, str$`:	Internal macros
	`Macro, topoff-bucket`:	Internal macros
	`Macro, topoff-index`:	Internal macros
	`Macro, with-all-primes`:	Internal macros
	`Macro, with-all-stored-primes`:	Internal macros
	`Macro, yofh`:	Internal macros
	`make-cubes`:	Internal functions
	`make-cublets`:	Internal functions
	`make-factor`:	Internal functions
	`make-factor-base`:	Internal functions
	`make-primes`:	Internal functions
	`make-topoff-n-cubes`:	Internal macros
	`merge-cubes`:	Internal functions
	`minutes`:	Internal functions
	`multiple-append`:	Internal functions
	`multiple-cons`:	Internal functions

N
	`new-factor`:	Internal functions
	`nextpprime`:	Internal functions
	`nice-time`:	Internal functions

O
	`odd-down`:	Internal macros
	`odd-up`:	Internal macros

P
	`pi_`:	Internal functions
	`pollards-rho`:	Internal functions
	`pollards-rho-attempt`:	Internal functions
	`pollards-rho-find-factor`:	Internal functions
	`power-breaker`:	Internal functions
	`pprime?`:	Internal functions
	`prime`:	Internal functions
	`prime?`:	Internal functions
	`put-into-its-bucket`:	Internal functions

Q
	`qs`:	Internal functions
	`quadratic-residue?`:	Internal functions

R
	`report2`:	Internal functions
	`report2?`:	Internal functions
	`report2?sieving-time`:	Internal functions
	`report2?total-time`:	Internal functions

S
	`sieve-for-ab`:	Internal functions
	`sqrtmodprime`:	Internal functions
	`square?`:	Internal functions
	`squarep`:	Internal functions
	`str$`:	Internal macros

T
	`topoff-bucket`:	Internal macros
	`topoff-index`:	Internal macros
	`trial-division`:	Internal functions
	`try-to-solve`:	Internal functions

W
	`with-all-primes`:	Internal macros
	`with-all-stored-primes`:	Internal macros

X
	`xor-merge`:	Internal functions

Y
	`yofh`:	Internal macros

Jump to:	( 2 ? A B C D E F G H I J L M N O P Q R S T W X Y

A.3 Variables

Jump to:	* 1 C D E L M P S

	Index Entry	Section

*
	`count-x`:	Internal special variables
	`how-to-handle-new-relations`:	Internal special variables
	`max-divide-out`:	Internal special variables
	`max-stored-prime`:	Internal special variables
	`nr-of-stored-primes`:	Internal special variables
	`qr256`:	Internal special variables
	`qs-line`:	Internal special variables
	`qs-line-width`:	Internal special variables
	`stored-primes`:	Internal special variables

1
	`1/amodp`:	Internal structures

C
	`Constant, minutes-per-internal-time-unit`:	Internal constants

D
	`dp`:	Internal structures

E
	`ep`:	Internal structures

L
	`log10p`:	Internal structures
	`log2p`:	Internal structures

M
	`minutes-per-internal-time-unit`:	Internal constants

P
	`prime`:	Internal structures

S
	`Slot, 1/amodp`:	Internal structures
	`Slot, dp`:	Internal structures
	`Slot, ep`:	Internal structures
	`Slot, log10p`:	Internal structures
	`Slot, log2p`:	Internal structures
	`Slot, prime`:	Internal structures
	`Slot, sqrtnmodp`:	Internal structures
	`Special Variable, count-x`:	Internal special variables
	`Special Variable, how-to-handle-new-relations`:	Internal special variables
	`Special Variable, max-divide-out`:	Internal special variables
	`Special Variable, max-stored-prime`:	Internal special variables
	`Special Variable, nr-of-stored-primes`:	Internal special variables
	`Special Variable, qr256`:	Internal special variables
	`Special Variable, qs-line`:	Internal special variables
	`Special Variable, qs-line-width`:	Internal special variables
	`Special Variable, stored-primes`:	Internal special variables
	`sqrtnmodp`:	Internal structures

Jump to:	* 1 C D E L M P S

A.4 Data types

Jump to:	C F P S U

	Index Entry	Section

C
	`cl-factoring`:	The cl-factoring system
	`cl-factoring`:	The cl-factoring package
	`cl-factoring-algorithms`:	The cl-factoring-algorithms package
	`Condition, factor-attempt-failed`:	Internal conditions

F
	`factor`:	Internal structures
	`factor-attempt-failed`:	Internal conditions

P
	`Package, cl-factoring`:	The cl-factoring package
	`Package, cl-factoring-algorithms`:	The cl-factoring-algorithms package
	`Package, ulimy-hmpqs`:	The ulimy-hmpqs package

S
	`Structure, factor`:	Internal structures
	`System, cl-factoring`:	The cl-factoring system

U
	`ulimy-hmpqs`:	The ulimy-hmpqs package

Jump to:	C F P S U

• Introduction		What cl-factoring is all about
• Systems		The systems documentation
• Files		The files documentation
• Packages		The packages documentation
• Definitions		The symbols documentation
• Indexes		Concepts, functions, variables and data types

• Internal constants
• Internal special variables
• Internal macros
• Internal functions
• Internal conditions
• Internal structures

• Concept index
• Function index
• Variable index
• Data type index

• The cl-factoring.asd file
• The cl-factoring/ulimyhmpqs-1.0.lisp file
• The cl-factoring/cl-factoring.lisp file

• The ulimy-hmpqs package
• The cl-factoring package
• The cl-factoring-algorithms package

The cl-factoring Reference Manual

Table of Contents

The cl-factoring Reference Manual

1 Introduction

2 Systems

2.1 cl-factoring

3 Files

3.1 Lisp

3.1.1 cl-factoring.asd

3.1.2 cl-factoring/ulimyhmpqs-1.0.lisp

3.1.3 cl-factoring/cl-factoring.lisp

4 Packages

4.1 ulimy-hmpqs

4.2 cl-factoring

4.3 cl-factoring-algorithms

5 Definitions

5.1 Exported definitions

5.1.1 Functions

5.2 Internal definitions

5.2.1 Constants

5.2.2 Special variables

5.2.3 Macros

5.2.4 Functions

5.2.5 Conditions

5.2.6 Structures

Appendix A Indexes

A.1 Concepts

A.2 Functions

A.3 Variables

A.4 Data types

2.1 `cl-factoring`

3.1.1 `cl-factoring.asd`

3.1.2 `cl-factoring/ulimyhmpqs-1.0.lisp`

3.1.3 `cl-factoring/cl-factoring.lisp`

4.1 `ulimy-hmpqs`

4.2 `cl-factoring`

4.3 `cl-factoring-algorithms`