Fibonacci is a Ruby gem written as a C-extension for exploring the Fibonacci series.

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Installation:

gem install fibonacci

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Usage:

irb(main):001:0> require 'fibonacci'
#=> true

irb(main):002:0> fib = Fibonacci.new
#=> #<Fibonacci:0x000000025cf218>

fib.print(n) will print the first n terms of the series

irb(main):003:0> fib.print(5)
#=> 0
    1
    1
    2
    3

fib[n] will return the nth term of the series, the nth term is computed iteratively

irb(main):004:0> fib[1000]
#=> 43466557686937456435688527675040625802564660517371780402481729089536555417949051890403879840079255169295922593080322634775209689623239873322471161642996440906533187938298969649928516003704476137795166849228875

fib.matrix(n) will return the nth power of matrix(http://en.wikipedia.org/wiki/Fibonacci_number#Matrix_form)

irb(main):013:0> fib.matrix(100)
#=> [[573147844013817084101, 354224848179261915075], [354224848179261915075, 218922995834555169026]]

fib.terms(n) will return an array of first n terms of the series

irb(main):005:0> fib.terms(5)
#=> [0, 1, 1, 2, 3]

fib.num_digits(n) will return the number of digits in the nth term of series (http://en.wikipedia.org/wiki/Fibonacci_number#Computation_by_rounding)

irb(main):007:0> fib.num_digits(1000)
#=> 209

irb(main):006:0> fib[1000].to_s.length
#=> 209

fib.fast_val(n) will return the nth term of the series, the nth term is computed as the product of the Lucas numbers,

ref: Daisuke Takahashi, A fast algorithm for computing large Fibonacci numbers, Information Processing Letters, Volume 75, Issue 6, 30 November 2000, Pages 243-246, ISSN 0020-0190, 10.1016/S0020-0190(00)00112-5.

irb(main):004:0> fib.fast_val(10000)
#=> 33644764876431783266621612005107543310302148460680063906564769974680081442166662368155595513633734025582065332680836159373734790483865268263040892463056431887354544369559827491606602099884183933864652731300088830269235673613135117579297437854413752130520504347701602264758318906527890855154366159582987279682987510631200575428783453215515103870818298969791613127856265033195487140214287532698187962046936097879900350962302291026368131493195275630227837628441540360584402572114334961180023091208287046088923962328835461505776583271252546093591128203925285393434620904245248929403901706233888991085841065183173360437470737908552631764325733993712871937587746897479926305837065742830161637408969178426378624212835258112820516370298089332099905707920064367426202389783111470054074998459250360633560933883831923386783056136435351892133279732908133732642652633989763922723407882928177953580570993691049175470808931841056146322338217465637321248226383092103297701648054726243842374862411453093812206564914032751086643394517512161526545361333111314042436854805106765843493523836959653428071768775328348234345557366719731392746273629108210679280784718035329131176778924659089938635459327894523777674406192240337638674004021330343297496902028328145933418826817683893072003634795623117103101291953169794607632737589253530772552375943788434504067715555779056450443016640119462580972216729758615026968443146952034614932291105970676243268515992834709891284706740862008587135016260312071903172086094081298321581077282076353186624611278245537208532365305775956430072517744315051539600905168603220349163222640885248852433158051534849622434848299380905070483482449327453732624567755879089187190803662058009594743150052402532709746995318770724376825907419939632265984147498193609285223945039707165443156421328157688908058783183404917434556270520223564846495196112460268313970975069382648706613264507665074611512677522748621598642530711298441182622661057163515069260029861704945425047491378115154139941550671256271197133252763631939606902895650288268608362241082050562430701794976171121233066073310059947366875