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Merge git://projects.elasticdog.com/git/factor

db4
Doug Coleman 2008-01-14 10:12:05 -10:00
parent e78aa37c77 76558babf4
commit 04b4832454
10 changed files with 127 additions and 55 deletions
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3
extra/editors/vim/vim-docs.factor
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@ -1,5 +1,4 @@
USING: definitions help help.markup help.syntax io io.files
editors words ;
USING: definitions help help.markup help.syntax io io.files editors words ;
IN: editors.vim
ARTICLE: { "vim" "vim" } "Vim support"

6
extra/math/miller-rabin/miller-rabin.factor
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@ -26,10 +26,8 @@ TUPLE: positive-even-expected n ;
dup even? [ -1 shift >r 1+ r> (factor-2s) ] when ;
: factor-2s ( n -- r s )
#! factor an even number into s * 2 ^ r
dup even? over 0 > and [
positive-even-expected construct-boa throw
] unless 0 swap (factor-2s) ;
#! factor an integer into s * 2^r
0 swap (factor-2s) ;
:: (miller-rabin) | n prime?! |
n 1- factor-2s s set r set

25
extra/math/primes/factors/factors-docs.factor
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@ -1,20 +1,23 @@
USING: help.markup help.syntax ;
USING: help.markup help.syntax math sequences ;
IN: math.primes.factors
{ factors count-factors unique-factors } related-words
{ factors group-factors unique-factors } related-words
HELP: factors
{ $values { "n" "a positive integer" } { "seq" "a sequence" } }
{ $description { "Factorize an integer and return an ordered list of factors, possibly repeated." } } ;
{ $values { "n" "a positive integer" } { "seq" sequence } }
{ $description { "Return an ordered list of a number's prime factors, possibly repeated." } }
{ $examples { $example "300 factors ." "{ 2 2 3 5 5 }" } } ;
HELP: count-factors
{ $values { "n" "a positive integer" } { "seq" "a sequence" } }
{ $description { "Return a sequence of pairs representing each factor in the number and its corresponding power." } } ;
HELP: group-factors
{ $values { "n" "a positive integer" } { "seq" sequence } }
{ $description { "Return a sequence of pairs representing each prime factor in the number and its corresponding power (multiplicity)." } }
{ $examples { $example "300 group-factors ." "{ { 2 2 } { 3 1 } { 5 2 } }" } } ;
HELP: unique-factors
{ $values { "n" "a positive integer" } { "seq" "a sequence" } }
{ $description { "Return an ordered list of unique prime factors." } } ;
{ $values { "n" "a positive integer" } { "seq" sequence } }
{ $description { "Return an ordered list of a number's unique prime factors." } }
{ $examples { $example "300 unique-factors ." "{ 2 3 5 }" } } ;
HELP: totient
{ $values { "n" "a positive integer" } { "t" "an integer" } }
{ $description { "Return the number of integers between 1 and " { $snippet "n-1" } " relatively prime to " { $snippet "n" } "." } } ;
{ $values { "n" "a positive integer" } { "t" integer } }
{ $description { "Return the number of integers between 1 and " { $snippet "n-1" } " that are relatively prime to " { $snippet "n" } "." } } ;

2
extra/math/primes/factors/factors-tests.factor
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@ -1,6 +1,6 @@
USING: math.primes.factors tools.test ;
{ { 999983 999983 1000003 } } [ 999969000187000867 factors ] unit-test
{ { { 999983 2 } { 1000003 1 } } } [ 999969000187000867 count-factors ] unit-test
{ { { 999983 2 } { 1000003 1 } } } [ 999969000187000867 group-factors ] unit-test
{ { 999983 1000003 } } [ 999969000187000867 unique-factors ] unit-test
{ 999967000236000612 } [ 999969000187000867 totient ] unit-test

32
extra/math/primes/factors/factors.factor
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@ -6,36 +6,36 @@ IN: math.primes.factors
<PRIVATE
: (factor) ( n d -- n' )
2dup mod zero? [ [ / ] keep dup , (factor) ] [ drop ] if ;
2dup mod zero? [ [ / ] keep dup , (factor) ] [ drop ] if ;
: (count) ( n d -- n' )
[ (factor) ] { } make
dup empty? [ drop ] [ [ first ] keep length 2array , ] if ;
[ (factor) ] { } make
dup empty? [ drop ] [ [ first ] keep length 2array , ] if ;
: (unique) ( n d -- n' )
[ (factor) ] { } make
dup empty? [ drop ] [ first , ] if ;
[ (factor) ] { } make
dup empty? [ drop ] [ first , ] if ;
: (factors) ( quot list n -- )
dup 1 > [ swap uncons >r pick call r> swap (factors) ] [ 3drop ] if ;
dup 1 > [ swap uncons >r pick call r> swap (factors) ] [ 3drop ] if ;
: (decompose) ( n quot -- seq )
[ lprimes rot (factors) ] { } make ;
[ lprimes rot (factors) ] { } make ;
PRIVATE>
: factors ( n -- seq )
[ (factor) ] (decompose) ; foldable
[ (factor) ] (decompose) ; foldable
: count-factors ( n -- seq )
[ (count) ] (decompose) ; foldable
: group-factors ( n -- seq )
[ (count) ] (decompose) ; foldable
: unique-factors ( n -- seq )
[ (unique) ] (decompose) ; foldable
[ (unique) ] (decompose) ; foldable
: totient ( n -- t )
dup 2 < [
drop 0
] [
[ unique-factors dup 1 [ 1- * ] reduce swap product / ] keep *
] if ; foldable
dup 2 < [
drop 0
] [
dup unique-factors dup 1 [ 1- * ] reduce swap product / *
] if ; foldable

20
extra/math/statistics/statistics-docs.factor
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@ -1,50 +1,50 @@
USING: help.markup help.syntax debugger ;
IN: math.statistics
IN: math.statistics
HELP: geometric-mean
{ $values { "seq" "a sequence of numbers" } { "n" "a non-negative real number"} }
{ $description "Computes the geometric mean of all elements in " { $snippet "seq" } ". The geometric mean measures the central tendency of a data set that minimizes the effects of extreme values." }
{ $examples { $example "USE: math.statistics" "{ 1 2 3 } geometric-mean ." "1.81712059283214" } }
{ $examples { $example "USE: math.statistics" "{ 1 2 3 } geometric-mean ." "1.81712059283214" } }
{ $errors "Throws a " { $link signal-error. } " (square-root of 0) if the sequence is empty." } ;
HELP: harmonic-mean
{ $values { "seq" "a sequence of numbers" } { "n" "a non-negative real number"} }
{ $description "Computes the harmonic mean of the elements in " { $snippet "seq" } ". The harmonic mean is appropriate when the average of rates is desired." }
{ $examples { $example "USE: math.statistics" "{ 1 2 3 } harmonic-mean ." "6/11" } }
{ $examples { $example "USE: math.statistics" "{ 1 2 3 } harmonic-mean ." "6/11" } }
{ $errors "Throws a " { $link signal-error. } " (divide by zero) if the sequence is empty." } ;
HELP: mean
{ $values { "seq" "a sequence of numbers" } { "n" "a non-negative real number"} }
{ $description "Computes the arithmetic mean of all elements in " { $snippet "seq" } "." }
{ $examples { $example "USE: math.statistics" "{ 1 2 3 } mean ." "2" } }
{ $examples { $example "USE: math.statistics" "{ 1 2 3 } mean ." "2" } }
{ $errors "Throws a " { $link signal-error. } " (divide by zero) if the sequence is empty." } ;
HELP: median
{ $values { "seq" "a sequence of numbers" } { "n" "a non-negative real number"} }
{ $description "Computes the median of " { $snippet "seq" } " by sorting the sequence from lowest value to highest and outputting the middle one. If there is an even number of elements in the sequence, the median is not unique, so the mean of the two middle values is outputted." }
{ $examples
{ $examples
{ $example "USE: math.statistics" "{ 1 2 3 } median ." "2" }
{ $example "USE: math.statistics" "{ 1 2 3 4 } median ." "5/2" } }
{ $example "USE: math.statistics" "{ 1 2 3 4 } median ." "5/2" } }
{ $errors "Throws a " { $link signal-error. } " (divide by zero) if the sequence is empty." } ;
HELP: range
{ $values { "seq" "a sequence of numbers" } { "n" "a non-negative real number"} }
{ $description "Computes the distance of the maximum and minimum values in " { $snippet "seq" } "." }
{ $examples
{ $examples
{ $example "USE: math.statistics" "{ 1 2 3 } range ." "2" }
{ $example "USE: math.statistics" "{ 1 2 3 4 } range ." "3" } } ;
HELP: std
{ $values { "seq" "a sequence of numbers" } { "x" "a non-negative real number"} }
{ $description "Computes the standard deviation of " { $snippet "seq" } " by squaring the variance of the sequence. It measures how widely spread the values in a sequence are about the mean." }
{ $examples
{ $examples
{ $example "USE: math.statistics" "{ 1 2 3 } std ." "1.0" }
{ $example "USE: math.statistics" "{ 1 2 3 4 } std ." "1.290994448735806" } } ;
HELP: ste
{ $values { "seq" "a sequence of numbers" } { "x" "a non-negative real number"} }
{ $description "Computes the standard error of the mean for " { $snippet "seq" } ". It's defined as the standard deviation divided by the square root of the length of the sequence, and measures uncertainty associated with the estimate of the mean." }
{ $examples
{ $examples
{ $example "USE: math.statistics" "{ -2 2 } ste ." "2.0" }
{ $example "USE: math.statistics" "{ -2 2 2 } ste ." "1.333333333333333" } } ;
@ -52,7 +52,7 @@ HELP: var
{ $values { "seq" "a sequence of numbers" } { "x" "a non-negative real number"} }
{ $description "Computes the variance of " { $snippet "seq" } ". It's a measurement of the spread of values in a sequence. The larger the variance, the larger the distance of values from the mean." }
{ $notes "If the number of elements in " { $snippet "seq" } " is 1 or less, it outputs 0." }
{ $examples
{ $examples
{ $example "USE: math.statistics" "{ 1 } var ." "0" }
{ $example "USE: math.statistics" "{ 1 2 3 } var ." "1" }
{ $example "USE: math.statistics" "{ 1 2 3 4 } var ." "5/3" } } ;

10
extra/project-euler/006/006.factor
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@ -24,14 +24,18 @@ IN: project-euler.006
! SOLUTION
! --------
<PRIVATE
: sum-of-squares ( seq -- n )
0 [ sq + ] reduce ;
: square-of-sums ( seq -- n )
0 [ + ] reduce sq ;
: square-of-sum ( seq -- n )
sum sq ;
PRIVATE>
: euler006 ( -- answer )
1 100 [a,b] dup sum-of-squares swap square-of-sums - abs ;
1 100 [a,b] dup sum-of-squares swap square-of-sum - abs ;
! [ euler006 ] 100 ave-time
! 0 ms run / 0 ms GC ave time - 100 trials

71
extra/project-euler/026/026.factor Normal file
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@ -0,0 +1,71 @@
! Copyright (c) 2007 Aaron Schaefer.
! See http://factorcode.org/license.txt for BSD license.
USING: kernel math math.functions math.primes math.ranges sequences ;
IN: project-euler.026
! http://projecteuler.net/index.php?section=problems&id=26
! DESCRIPTION
! -----------
! A unit fraction contains 1 in the numerator. The decimal representation of
! the unit fractions with denominators 2 to 10 are given:
! 1/2 = 0.5
! 1/3 = 0.(3)
! 1/4 = 0.25
! 1/5 = 0.2
! 1/6 = 0.1(6)
! 1/7 = 0.(142857)
! 1/8 = 0.125
! 1/9 = 0.(1)
! 1/10 = 0.1
! Where 0.1(6) means 0.166666..., and has a 1-digit recurring cycle. It can be
! seen that 1/7 has a 6-digit recurring cycle.
! Find the value of d < 1000 for which 1/d contains the longest recurring cycle
! in its decimal fraction part.
! SOLUTION
! --------
<PRIVATE
: source-026 ( -- seq )
1 1000 (a,b) [ prime? ] subset [ 1 swap / ] map ;
: (mult-order) ( n a m -- k )
3dup ^ swap mod 1 = [ 2nip ] [ 1+ (mult-order) ] if ;
PRIVATE>
: coprime? ( m n -- ? )
gcd 1 = nip ;
: recurring-period? ( a/b -- ? )
denominator 10 coprime? ;
! Multiplicative order a.k.a. modulo order
: mult-order ( a n -- k )
swap 1 (mult-order) ;
: period-length ( a/b -- n )
dup recurring-period? [ denominator 10 swap mult-order ] [ drop 0 ] if ;
<PRIVATE
: max-period ( seq -- elt n )
dup [ period-length ] map dup supremum
over index [ swap nth ] curry 2apply ;
PRIVATE>
: euler026 ( -- answer )
source-026 max-period drop denominator ;
! [ euler026 ] 100 ave-time
! 724 ms run / 7 ms GC ave time - 100 trials
MAIN: euler026

9
extra/project-euler/common/common.factor
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@ -34,9 +34,6 @@ IN: project-euler.common
: propagate ( bottom top -- newtop )
[ over 1 tail rot first2 max rot + ] map nip ;
: reduce-2s ( n -- r s )
dup even? [ factor-2s >r 1+ r> ] [ 1 swap ] if ;
: shift-3rd ( seq obj obj -- seq obj obj )
rot 1 tail -rot ;
@ -88,11 +85,11 @@ PRIVATE>
! The divisor function, counts the number of divisors
: tau ( m -- n )
count-factors flip second 1 [ 1+ * ] reduce ;
group-factors flip second 1 [ 1+ * ] reduce ;
! Optimized brute-force, is often faster than prime factorization
: tau* ( m -- n )
reduce-2s [ perfect-square? -1 0 ? ] keep
factor-2s [ 1+ ] dip [ perfect-square? -1 0 ? ] keep
dup sqrt >fixnum [1,b] [
dupd mod zero? [ >r 2 + r> ] when
dupd mod zero? [ [ 2 + ] dip ] when
] each drop * ;

4
extra/project-euler/project-euler.factor
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@ -8,8 +8,8 @@ USING: definitions io io.files kernel math.parser sequences vocabs
project-euler.013 project-euler.014 project-euler.015 project-euler.016
project-euler.017 project-euler.018 project-euler.019 project-euler.020
project-euler.021 project-euler.022 project-euler.023 project-euler.024
project-euler.025 project-euler.067 project-euler.134 project-euler.169
project-euler.173 project-euler.175 ;
project-euler.025 project-euler.026 project-euler.067 project-euler.134
project-euler.169 project-euler.173 project-euler.175 ;
IN: project-euler
<PRIVATE