Tag: Math

Because the Fibonacci sequence is simply defined by recursion, it makes for an elegant programming exercise. Here is one way to do it in SAS, and another way to do it in R. I’ve also included unit testing code to check that it works.

Fibonacci sequence in SAS using a recursive macro:

%macro fib(n);
%if &n = 1 %then 1; * first seed value;
%else %if &n = 2 %then 1; * second seed value;
%else %eval(%fib(%eval(&n-1))+%fib(%eval(&n-2))); * use recursion;
%mend;

* show values 1-5;
%put %fib(1);
%put %fib(2);
%put %fib(3);
%put %fib(4);
%put %fib(5);

* check values 1-10;
%macro check_fib;
%if %fib(1) ne 1 %then %abort;
%if %fib(2) ne 1 %then %abort;
%if %fib(3) ne 2 %then %abort;
%if %fib(4) ne 3 %then %abort;
%if %fib(5) ne 5 %then %abort;
%if %fib(6) ne 8 %then %abort;
%if %fib(7) ne 13 %then %abort;
%if %fib(8) ne 21 %then %abort;
%if %fib(9) ne 34 %then %abort;
%if %fib(10) ne 55 %then %abort;
%put NOTE: OK!;
%mend;
%check_fib;

Fibonacci sequence in R using a recursive function that supports either single integers or a vector of integers:

fib  {
    if (length(n) > 1) return(sapply(n, fib)) # accept a numeric vector
    if (n == 1) return(1) # first seed value
    if (n == 2) return(1) # second seed value
    return(fib(n-1)+fib(n-2)) # use recursion
}

# print first five Fibonacci numbers
fib(1)
fib(2)
fib(3)
fib(4)
fib(5)

# verify the Fibonacci sequence 1 through 10
(actual (expected all.equal(actual,expected)

For alternative implements, see SAS and R: Example 7.1: Create a Fibonacci sequence. In SAS, Nick Horton calculates the Fibonacci sequence using a DATA STEP, and in R he uses a FOR loop.

Adam Rich responded with his post Fibonacci Sequence in R with Memoization which gives a performance boost by caching the results.

In the comments below, Rick Wicklin referred to his SAS/IML solution that generates the Fibonacci sequence iteratively and Matrices, eigenvalues, Fibonacci, and the golden ratio.

This post first appeared on Heuristic Andrew.

Read more →