Fibonacci sequence: Difference between revisions
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===Iterative=== |
===Iterative=== |
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≪ 0 1 |
≪ 0 1 |
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0 4 ROLL START |
0 4 ROLL '''START''' |
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OVER + SWAP |
OVER + SWAP |
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NEXT |
'''NEXT''' SWAP DROP |
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≫ '<span style="color:blue">→FIB</span>' STO |
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SWAP DROP |
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´→FIB´ STO |
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≪ { } 0 20 FOR j j →FIB + NEXT ≫ EVAL |
≪ { } 0 20 FOR j j →FIB + NEXT ≫ EVAL |
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===Recursive=== |
===Recursive=== |
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≪ '''IF''' DUP 2 > '''THEN''' |
≪ '''IF''' DUP 2 > '''THEN''' |
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DUP 1 - →FIB |
DUP 1 - <span style="color:blue">→FIB</span> |
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SWAP 2 - →FIB + |
SWAP 2 - <span style="color:blue">→FIB</span> + |
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'''ELSE''' |
'''ELSE''' SIGN '''END''' |
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≫ '<span style="color:blue">→FIB</span>' STO |
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SIGN |
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'''END''' |
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≫ |
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´→FIB´ STO |
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≪ { } 0 20 FOR j j →FIB + NEXT ≫ EVAL |
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{{out}} |
{{out}} |
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<pre> |
<pre> |
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</pre> |
</pre> |
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===Fast recursive=== |
===Fast recursive=== |
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A much better recursive approach, based on the formulas: F(2k) = |
A much better recursive approach, based on the formulas: <code>F(2k) = [2*F(k-1) + F(k)]*F(k)</code> and <code>F(2k+1) = F(k)² + F(k+1)²</code> |
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≪ '''IF''' DUP 2 ≤ |
≪ '''IF''' DUP 2 ≤ '''THEN''' SIGN '''ELSE''' |
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'''THEN''' SIGN |
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'''ELSE''' |
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'''IF''' DUP 2 MOD |
'''IF''' DUP 2 MOD |
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'''THEN''' 1 - 2 / DUP →FIB SQ SWAP 1 + →FIB SQ + |
'''THEN''' 1 - 2 / DUP <span style="color:blue">→FIB</span> SQ SWAP 1 + <span style="color:blue">→FIB</span> SQ + |
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'''ELSE''' 2 / DUP →FIB DUP ROT 1 - →FIB 2 * + * |
'''ELSE''' 2 / DUP <span style="color:blue">→FIB</span> DUP ROT 1 - <span style="color:blue">→FIB</span> 2 * + * |
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'''END''' |
'''END END''' |
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≫ '<span style="color:blue">→FIB</span>' STO |
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≫ |
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'→FIB' STO |
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=={{header|Ruby}}== |
=={{header|Ruby}}== |
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