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< title > Algorithms_in_C: math/fibonacci_formula.c File Reference< / title >
2022-09-30 16:55:00 +08:00
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< div class = "headertitle" > < div class = "title" > fibonacci_formula.c File Reference< / div > < / div >
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< p > Finding Fibonacci number of any < code > n< / code > number using [Binet's closed form formula](< a href = "https://en.wikipedia.org/wiki/Fibonacci_number#Binet's_formula" > https://en.wikipedia.org/wiki/Fibonacci_number#Binet's_formula< / a > ) compute \(f_{nth}\) Fibonacci number using the binet's formula: Fn = 1√5 * (1+√5 / 2)^n+1 − −
< a href = "#details" > More...< / a > < / p >
< div class = "textblock" > < code > #include < math.h> < / code > < br / >
< code > #include < stdio.h> < / code > < br / >
< code > #include < assert.h> < / code > < br / >
< / div > < div class = "textblock" > < div class = "dynheader" >
Include dependency graph for fibonacci_formula.c:< / div >
< div class = "dyncontent" >
< div class = "center" > < iframe scrolling = "no" frameborder = "0" src = "../../d3/da6/fibonacci__formula_8c__incl.svg" width = "254" height = "110" > < p > < b > This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.< / b > < / p > < / iframe >
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Functions< / h2 > < / td > < / tr >
< tr class = "memitem:a4d369ae048e0ccc7f515a243533cd946" > < td class = "memItemLeft" align = "right" valign = "top" > int  < / td > < td class = "memItemRight" valign = "bottom" > < a class = "el" href = "../../d8/d75/fibonacci__formula_8c.html#a4d369ae048e0ccc7f515a243533cd946" > fib< / a > (unsigned int n)< / td > < / tr >
< tr class = "memdesc:a4d369ae048e0ccc7f515a243533cd946" > < td class = "mdescLeft" >   < / td > < td class = "mdescRight" > for pow and sqrt for printf for assert < a href = "../../d8/d75/fibonacci__formula_8c.html#a4d369ae048e0ccc7f515a243533cd946" > More...< / a > < br / > < / td > < / tr >
< tr class = "separator:a4d369ae048e0ccc7f515a243533cd946" > < td class = "memSeparator" colspan = "2" >   < / td > < / tr >
< tr class = "memitem:aa8dca7b867074164d5f45b0f3851269d" > < td class = "memItemLeft" align = "right" valign = "top" > static void  < / td > < td class = "memItemRight" valign = "bottom" > < a class = "el" href = "../../d8/d75/fibonacci__formula_8c.html#aa8dca7b867074164d5f45b0f3851269d" > test< / a > ()< / td > < / tr >
< tr class = "memdesc:aa8dca7b867074164d5f45b0f3851269d" > < td class = "mdescLeft" >   < / td > < td class = "mdescRight" > Self-test implementations. < a href = "../../d8/d75/fibonacci__formula_8c.html#aa8dca7b867074164d5f45b0f3851269d" > More...< / a > < br / > < / td > < / tr >
< tr class = "separator:aa8dca7b867074164d5f45b0f3851269d" > < td class = "memSeparator" colspan = "2" >   < / td > < / tr >
< tr class = "memitem:ae66f6b31b5ad750f1fe042a706a4e3d4" > < td class = "memItemLeft" align = "right" valign = "top" > int  < / td > < td class = "memItemRight" valign = "bottom" > < a class = "el" href = "../../d8/d75/fibonacci__formula_8c.html#ae66f6b31b5ad750f1fe042a706a4e3d4" > main< / a > ()< / td > < / tr >
< tr class = "memdesc:ae66f6b31b5ad750f1fe042a706a4e3d4" > < td class = "mdescLeft" >   < / td > < td class = "mdescRight" > Main function. < a href = "../../d8/d75/fibonacci__formula_8c.html#ae66f6b31b5ad750f1fe042a706a4e3d4" > More...< / a > < br / > < / td > < / tr >
< tr class = "separator:ae66f6b31b5ad750f1fe042a706a4e3d4" > < td class = "memSeparator" colspan = "2" >   < / td > < / tr >
< / table >
< a name = "details" id = "details" > < / a > < h2 class = "groupheader" > Detailed Description< / h2 >
< div class = "textblock" > < p > Finding Fibonacci number of any < code > n< / code > number using [Binet's closed form formula](< a href = "https://en.wikipedia.org/wiki/Fibonacci_number#Binet's_formula" > https://en.wikipedia.org/wiki/Fibonacci_number#Binet's_formula< / a > ) compute \(f_{nth}\) Fibonacci number using the binet's formula: Fn = 1√5 * (1+√5 / 2)^n+1 − − < / p >
< dl class = "section author" > < dt > Author< / dt > < dd > < a href = "https://github.com/GrandSir/" target = "_blank" > GrandSir< / a > < / dd > < / dl >
< / div > < h2 class = "groupheader" > Function Documentation< / h2 >
< a id = "a4d369ae048e0ccc7f515a243533cd946" name = "a4d369ae048e0ccc7f515a243533cd946" > < / a >
< h2 class = "memtitle" > < span class = "permalink" > < a href = "#a4d369ae048e0ccc7f515a243533cd946" > ◆   < / a > < / span > fib()< / h2 >
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< td class = "memname" > int fib < / td >
< td > (< / td >
< td class = "paramtype" > unsigned int  < / td >
< td class = "paramname" > < em > n< / em > < / td > < td > )< / td >
< td > < / td >
< / tr >
< / table >
< / div > < div class = "memdoc" >
< p > for pow and sqrt for printf for assert < / p >
< dl class = "params" > < dt > Parameters< / dt > < dd >
< table class = "params" >
< tr > < td class = "paramname" > n< / td > < td > index of number in Fibonacci sequence < / td > < / tr >
< / table >
< / dd >
< / dl >
< dl class = "section return" > < dt > Returns< / dt > < dd > nth value of fibonacci sequence for all n > = 0 < / dd > < / dl >
< div class = "fragment" > < div class = "line" > < span class = "lineno" > 17< / span > {< / div >
< div class = "line" > < span class = "lineno" > 18< / span > < span class = "keywordtype" > float< / span > seq = (1 / sqrt(5) * pow(((1 + sqrt(5)) / 2), n + 1)) - (1 / sqrt(5) * pow(((1 - sqrt(5)) / 2), n + 1));< / div >
< div class = "line" > < span class = "lineno" > 19< / span > < / div >
< div class = "line" > < span class = "lineno" > 20< / span > < span class = "comment" > // removing unnecessary fractional part by implicitly converting float to int< / span > < / div >
< div class = "line" > < span class = "lineno" > 21< / span > < span class = "keywordflow" > return< / span > seq;< / div >
< div class = "line" > < span class = "lineno" > 22< / span > }< / div >
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< a id = "ae66f6b31b5ad750f1fe042a706a4e3d4" name = "ae66f6b31b5ad750f1fe042a706a4e3d4" > < / a >
< h2 class = "memtitle" > < span class = "permalink" > < a href = "#ae66f6b31b5ad750f1fe042a706a4e3d4" > ◆   < / a > < / span > main()< / h2 >
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< td class = "memname" > int main < / td >
< td > (< / td >
< td class = "paramtype" > void  < / td >
< td class = "paramname" > < / td > < td > )< / td >
< td > < / td >
< / tr >
< / table >
< / div > < div class = "memdoc" >
< p > Main function. < / p >
< dl class = "section return" > < dt > Returns< / dt > < dd > 0 on exit < / dd > < / dl >
< div class = "fragment" > < div class = "line" > < span class = "lineno" > 52< / span > {< / div >
< div class = "line" > < span class = "lineno" > 53< / span > < a class = "code hl_function" href = "../../d8/d75/fibonacci__formula_8c.html#aa8dca7b867074164d5f45b0f3851269d" > test< / a > (); < span class = "comment" > // run self-test implementations< / span > < / div >
< div class = "line" > < span class = "lineno" > 54< / span > < / div >
< div class = "line" > < span class = "lineno" > 55< / span > < span class = "keywordflow" > for< / span > (< span class = "keywordtype" > int< / span > i = 0; i < = 10; i++){< / div >
< div class = "line" > < span class = "lineno" > 56< / span > printf(< span class = "stringliteral" > " %d. fibonacci number is: %d\n" < / span > , i, < a class = "code hl_function" href = "../../d8/d75/fibonacci__formula_8c.html#a4d369ae048e0ccc7f515a243533cd946" > fib< / a > (i));< / div >
< div class = "line" > < span class = "lineno" > 57< / span > }< / div >
< div class = "line" > < span class = "lineno" > 58< / span > < span class = "keywordflow" > return< / span > 0;< / div >
< div class = "line" > < span class = "lineno" > 59< / span > }< / div >
< div class = "ttc" id = "afibonacci__formula_8c_html_a4d369ae048e0ccc7f515a243533cd946" > < div class = "ttname" > < a href = "../../d8/d75/fibonacci__formula_8c.html#a4d369ae048e0ccc7f515a243533cd946" > fib< / a > < / div > < div class = "ttdeci" > int fib(unsigned int n)< / div > < div class = "ttdoc" > for pow and sqrt for printf for assert< / div > < div class = "ttdef" > < b > Definition:< / b > fibonacci_formula.c:17< / div > < / div >
< div class = "ttc" id = "afibonacci__formula_8c_html_aa8dca7b867074164d5f45b0f3851269d" > < div class = "ttname" > < a href = "../../d8/d75/fibonacci__formula_8c.html#aa8dca7b867074164d5f45b0f3851269d" > test< / a > < / div > < div class = "ttdeci" > static void test()< / div > < div class = "ttdoc" > Self-test implementations.< / div > < div class = "ttdef" > < b > Definition:< / b > fibonacci_formula.c:28< / div > < / div >
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< a id = "aa8dca7b867074164d5f45b0f3851269d" name = "aa8dca7b867074164d5f45b0f3851269d" > < / a >
< h2 class = "memtitle" > < span class = "permalink" > < a href = "#aa8dca7b867074164d5f45b0f3851269d" > ◆   < / a > < / span > test()< / h2 >
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< td class = "memname" > static void test < / td >
< td > (< / td >
< td class = "paramtype" > void  < / td >
< td class = "paramname" > < / td > < td > )< / td >
< td > < / td >
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< p > Self-test implementations. < / p >
< dl class = "section return" > < dt > Returns< / dt > < dd > void < / dd > < / dl >
< div class = "fragment" > < div class = "line" > < span class = "lineno" > 28< / span > {< / div >
< div class = "line" > < span class = "lineno" > 29< / span > < span class = "comment" > /* this ensures that the first 10 number of fibonacci sequence< / span > < / div >
< div class = "line" > < span class = "lineno" > 30< / span > < span class = "comment" > * (1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89)< / span > < / div >
< div class = "line" > < span class = "lineno" > 31< / span > < span class = "comment" > * matches with algorithm< / span > < / div >
< div class = "line" > < span class = "lineno" > 32< / span > < span class = "comment" > */< / span > < / div >
< div class = "line" > < span class = "lineno" > 33< / span > assert(< a class = "code hl_function" href = "../../d8/d75/fibonacci__formula_8c.html#a4d369ae048e0ccc7f515a243533cd946" > fib< / a > (0) == 1);< / div >
< div class = "line" > < span class = "lineno" > 34< / span > assert(< a class = "code hl_function" href = "../../d8/d75/fibonacci__formula_8c.html#a4d369ae048e0ccc7f515a243533cd946" > fib< / a > (1) == 1);< / div >
< div class = "line" > < span class = "lineno" > 35< / span > assert(< a class = "code hl_function" href = "../../d8/d75/fibonacci__formula_8c.html#a4d369ae048e0ccc7f515a243533cd946" > fib< / a > (2) == 2);< / div >
< div class = "line" > < span class = "lineno" > 36< / span > assert(< a class = "code hl_function" href = "../../d8/d75/fibonacci__formula_8c.html#a4d369ae048e0ccc7f515a243533cd946" > fib< / a > (3) == 3);< / div >
< div class = "line" > < span class = "lineno" > 37< / span > assert(< a class = "code hl_function" href = "../../d8/d75/fibonacci__formula_8c.html#a4d369ae048e0ccc7f515a243533cd946" > fib< / a > (4) == 5);< / div >
< div class = "line" > < span class = "lineno" > 38< / span > assert(< a class = "code hl_function" href = "../../d8/d75/fibonacci__formula_8c.html#a4d369ae048e0ccc7f515a243533cd946" > fib< / a > (5) == 8);< / div >
< div class = "line" > < span class = "lineno" > 39< / span > assert(< a class = "code hl_function" href = "../../d8/d75/fibonacci__formula_8c.html#a4d369ae048e0ccc7f515a243533cd946" > fib< / a > (6) == 13);< / div >
< div class = "line" > < span class = "lineno" > 40< / span > assert(< a class = "code hl_function" href = "../../d8/d75/fibonacci__formula_8c.html#a4d369ae048e0ccc7f515a243533cd946" > fib< / a > (7) == 21);< / div >
< div class = "line" > < span class = "lineno" > 41< / span > assert(< a class = "code hl_function" href = "../../d8/d75/fibonacci__formula_8c.html#a4d369ae048e0ccc7f515a243533cd946" > fib< / a > (8) == 34);< / div >
< div class = "line" > < span class = "lineno" > 42< / span > assert(< a class = "code hl_function" href = "../../d8/d75/fibonacci__formula_8c.html#a4d369ae048e0ccc7f515a243533cd946" > fib< / a > (9) == 55);< / div >
< div class = "line" > < span class = "lineno" > 43< / span > assert(< a class = "code hl_function" href = "../../d8/d75/fibonacci__formula_8c.html#a4d369ae048e0ccc7f515a243533cd946" > fib< / a > (10) == 89);< / div >
< div class = "line" > < span class = "lineno" > 44< / span > < / div >
< div class = "line" > < span class = "lineno" > 45< / span > printf(< span class = "stringliteral" > " All tests have successfully passed!\n" < / span > );< / div >
< div class = "line" > < span class = "lineno" > 46< / span > }< / div >
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