-! Copyright (C) 2015 Alexander Ilin, John Benediktsson.
+! Copyright (C) 2015 Alexander Ilin, Doug Coleman, John Benediktsson.
! See http://factorcode.org/license.txt for BSD license.
-USING: kernel random sequences assocs locals sorting prettyprint
- math math.functions math.statistics math.vectors math.ranges ;
+USING: assocs fry kernel locals math math.ranges math.statistics
+math.vectors prettyprint random sequences sorting ;
IN: rosetta-code.dice7
! http://rosettacode.org/wiki/Seven-sided_dice_from_five-sided_dice
! Output a random integer 1..5.
: dice5 ( -- x )
- 5 [1,b] random
-;
+ 5 [1,b] random ;
! Output a random integer 1..7 using dice5 as randomness source.
: dice7 ( -- x )
- 0 [ dup 21 < ] [ drop dice5 5 * dice5 + 6 - ] do until
- 7 rem 1 +
-;
-
-! Roll the die by calling the quotation the given number of times and return
-! an array with roll results.
-! Sample call: 1000 [ dice7 ] roll
-: roll ( times quot: ( -- x ) -- array )
- [ call( -- x ) ] curry replicate
-;
-
-! Input array contains outcomes of a number of die throws. Each die result is
-! an integer in the range 1..X. Calculate and return the number of each
-! of the results in the array so that in the first position of the result
-! there is the number of ones in the input array, in the second position
-! of the result there is the number of twos in the input array, etc.
-: count-dice-outcomes ( X array -- array )
+ 0 [ dup 21 < ] [
+ drop dice5 5 * dice5 + 6 -
+ ] do until 7 rem 1 + ;
+
+! Count the number of rolls for each side of the dice,
+! inserting zeros for die rolls that never occur.
+: count-outcomes ( #sides rolls -- counts )
histogram
swap [1,b] [ over [ 0 or ] change-at ] each
- sort-keys values
-;
-
-! Verify distribution uniformity/Naive. Delta is the acceptable deviation
-! from the ideal number of items in each bucket, expressed as a fraction of
-! the total count. Sides is the number of die sides. Die-func is a word that
-! produces a random number on stack in the range [1..sides], times is the
-! number of times to call it.
-! Sample call: 0.02 7 [ dice7 ] 100000 verify
-:: verify ( delta sides die-func: ( -- random ) times -- )
- sides
- times die-func roll
- count-dice-outcomes
- dup .
- times sides / :> ideal-count
- ideal-count v-n vabs
- times v/n
- delta [ < ] curry all?
- [ "Random enough" . ] [ "Not random enough" . ] if
-;
-
-
-! Call verify with 1, 10, 100, ... 1000000 rolls of 7-sided die.
+ sort-keys values ;
+
+! Assumes a fair die [1..n] thrown for sum(counts),
+! where n is length(counts).
+: fair-counts? ( counts error -- ? )
+ [
+ [ ] [ sum ] [ length ] tri
+ [ / v-n vabs ]
+ [ drop v/n ] 2bi
+ ] dip '[ _ < ] all? ;
+
+! Verify distribution uniformity/naive. Error is the acceptable
+! deviation from the ideal number of items in each bucket,
+! expressed as a fraction of the total count.
+:: test-distribution ( #sides #trials quot error -- )
+ #sides #trials quot replicate count-outcomes :> outcomes
+ outcomes .
+ outcomes error fair-counts?
+ "Random enough" "Not random enough" ? . ; inline
+
+CONSTANT: trial-counts { 1 10 100 1000 10000 100000 1000000 }
+CONSTANT: #sides 7
+CONSTANT: error-delta 0.02
+
: verify-all ( -- )
- { 1 10 100 1000 10000 100000 1000000 }
- [| times | 0.02 7 [ dice7 ] times verify ] each
-;
+ #sides trial-counts [
+ [ dice7 ] error-delta test-distribution
+ ] with each ;