Claymer Documentation
1 Fibonacci Sequence Function
NoteOUT
sut/fib
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1.0.1 fib
[n]
Takes a non-negative integer n and returns the nth number in the Fibonacci sequence.
1.1 Rich comments from example.core
(
;; this is an example comment
(fib 10)
;; recursive
(fib (fib 10))
;; functional
(map fib (range 10)))
1.2 Examples:
Produces nth number in the fibonacci sequence:
(deftest fib-test
(testing
(is (= (sut/fib 0) 0)))
(testing
(is (= (sut/fib 12) 144)))
(testing
(is (= (sut/fib 69) 117669030460994))))PASS: (= 0 0)PASS: (= 144 144)PASS: (= 117669030460994 117669030460994)
Negitive numbers are out of bounds.
(deftest fib-neg-n-out-of-range-test
(is
(try (sut/fib -1)
(catch Exception e
(= (type e) java.lang.IndexOutOfBoundsException)))))PASS: true1.3 Properties
1.3.1 Parity Invarient
Every third Fibonacci number is even. This is because an odd + even = odd so we get the cycle:
0+1=1 -> 1+1=2 -> 1+2=3 -> ...
E+O=O -> O+O=E -> O+E=O -> ...(def parity-invariant
(prop/for-all
[v gen/pos-int]
(let [fib-number (sut/fib v)]
(if (zero? (rem v 3))
(even? fib-number)
(odd? fib-number)))))(tc/quick-check 10000 parity-invariant){:result true,
:pass? true,
:num-tests 10000,
:time-elapsed-ms 60,
:seed 1772375518663}1.4 Performance Comparison
Below we compare the efficient iterative fib against a naive recursive fib-naive implementation across a range of input sizes. The naive version has exponential time complexity, so its execution time grows dramatically.