diff --git a/extra/editors/vim/vim-docs.factor b/extra/editors/vim/vim-docs.factor index 2e2583cc7f..020117564d 100644 --- a/extra/editors/vim/vim-docs.factor +++ b/extra/editors/vim/vim-docs.factor @@ -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" diff --git a/extra/math/miller-rabin/miller-rabin.factor b/extra/math/miller-rabin/miller-rabin.factor index de5a262268..e2d012ec0a 100644 --- a/extra/math/miller-rabin/miller-rabin.factor +++ b/extra/math/miller-rabin/miller-rabin.factor @@ -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 diff --git a/extra/math/primes/factors/factors-docs.factor b/extra/math/primes/factors/factors-docs.factor index 2238420d32..f5b14b5a5a 100644 --- a/extra/math/primes/factors/factors-docs.factor +++ b/extra/math/primes/factors/factors-docs.factor @@ -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" } "." } } ; diff --git a/extra/math/primes/factors/factors-tests.factor b/extra/math/primes/factors/factors-tests.factor index 71bdd56a81..70b905f4ab 100644 --- a/extra/math/primes/factors/factors-tests.factor +++ b/extra/math/primes/factors/factors-tests.factor @@ -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 diff --git a/extra/math/primes/factors/factors.factor b/extra/math/primes/factors/factors.factor index b841d49f7d..2f70ab24b4 100644 --- a/extra/math/primes/factors/factors.factor +++ b/extra/math/primes/factors/factors.factor @@ -6,36 +6,36 @@ IN: math.primes.factors [ 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 diff --git a/extra/math/statistics/statistics-docs.factor b/extra/math/statistics/statistics-docs.factor index 620501c16e..4787a85aed 100644 --- a/extra/math/statistics/statistics-docs.factor +++ b/extra/math/statistics/statistics-docs.factor @@ -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" } } ; diff --git a/extra/project-euler/006/006.factor b/extra/project-euler/006/006.factor index 2f09912412..fb4fb954fa 100644 --- a/extra/project-euler/006/006.factor +++ b/extra/project-euler/006/006.factor @@ -24,14 +24,18 @@ IN: project-euler.006 ! SOLUTION ! -------- + : 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 diff --git a/extra/project-euler/026/026.factor b/extra/project-euler/026/026.factor new file mode 100644 index 0000000000..d79effed02 --- /dev/null +++ b/extra/project-euler/026/026.factor @@ -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 +! -------- + + + +: 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 ; + + + +: euler026 ( -- answer ) + source-026 max-period drop denominator ; + +! [ euler026 ] 100 ave-time +! 724 ms run / 7 ms GC ave time - 100 trials + +MAIN: euler026 diff --git a/extra/project-euler/common/common.factor b/extra/project-euler/common/common.factor index 6279606481..2bd2b7ec0b 100644 --- a/extra/project-euler/common/common.factor +++ b/extra/project-euler/common/common.factor @@ -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 * ; diff --git a/extra/project-euler/project-euler.factor b/extra/project-euler/project-euler.factor index 038ae3c5b8..6abb056d28 100644 --- a/extra/project-euler/project-euler.factor +++ b/extra/project-euler/project-euler.factor @@ -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