Python solution Mike 29th July, 2008 12:05 (UTC)
fibonacci = lambda n,m: (n+m,n)
iccanobif = lambda n,m: (m,n-m)
def sequence(next,n,m):
while True:
n,m = next(n,m)
yield n
def fib(k):
n,m = 0,1
next = k > 1 and fibonacci or iccanobif
for i in range(0,abs(k)):
n,m = next(n,m)
return n
Python solution Mike 29th July, 2008 12:08 (UTC)
# a smaller solution:
def fib(k):
n,m,p,q = 0,1,0,1
if k>0: p,q = q,p
for i in range(0,abs(k)):
n,m = m+p*n,n-q*m
return n
# i removed the square brackets
fib(n) for n in range(-10,10)
-55, 34, -21, 13, -8, 5, -3, 2, -1, 1, 0, 1, 1, 2, 3, 5, 8, 13, 21, 34
Python solution Mike 29th July, 2008 12:22 (UTC)
sorry, the first fib definition should have had k>0
Python solution Mike 30th July, 2008 11:14 (UTC)
1. faster solution (adapted to solve the problem from http://en.literateprograms.org/Fibonacci_numbers_(Python))
def fib_positive(n):
def powLF(n):
if n == 1:     return (1, 1)
L, F = powLF(n//2)
L, F = (L**2 + 5*F**2) >> 1, L*F
if n & 1:
return ((L + 5*F)>>1, (L + F) >>1)
else:
return (L, F)
L,F = powLF(n)
return F

def fib(n):
return n and (n > 0 and fib_positive(n) or (fib_positive(-n)*(n%2*2-1))) or 0

>>> fib(n) for n in range(-10,10)
-55, 34, -21, 13, -8, 5, -3, 2, -1, 1, 0, 1, 1, 2, 3, 5, 8, 13, 21, 34
>>> fib(10000)
33644764876431783266621612005107543310302148460680063906564769974680081442166662368155595513633734025582065332680836159373734790483865268263040892463056431887354544369559827491606602099884183933864652731300088830269235673613135117579297437854413752130520504347701602264758318906527890855154366159582987279682987510631200575428783453215515103870818298969791613127856265033195487140214287532698187962046936097879900350962302291026368131493195275630227837628441540360584402572114334961180023091208287046088923962328835461505776583271252546093591128203925285393434620904245248929403901706233888991085841065183173360437470737908552631764325733993712871937587746897479926305837065742830161637408969178426378624212835258112820516370298089332099905707920064367426202389783111470054074998459250360633560933883831923386783056136435351892133279732908133732642652633989763922723407882928177953580570993691049175470808931841056146322338217465637321248226383092103297701648054726243842374862411453093812206564914032751086643394517512161526545361333111314042436854805106765843493523836959653428071768775328348234345557366719731392746273629108210679280784718035329131176778924659089938635459327894523777674406192240337638674004021330343297496902028328145933418826817683893072003634795623117103101291953169794607632737589253530772552375943788434504067715555779056450443016640119462580972216729758615026968443146952034614932291105970676243268515992834709891284706740862008587135016260312071903172086094081298321581077282076353186624611278245537208532365305775956430072517744315051539600905168603220349163222640885248852433158051534849622434848299380905070483482449327453732624567755879089187190803662058009594743150052402532709746995318770724376825907419939632265984147498193609285223945039707165443156421328157688908058783183404917434556270520223564846495196112460268313970975069382648706613264507665074611512677522748621598642530711298441182622661057163515069260029861704945425047491378115154139941550671256271197133252763631939606902895650288268608362241082050562430701794976171121233066073310059947366875L