Hi all -
While doing a little piece on computing Fibonacci numbers and the
Golden ratio, I came across this behaviour of recursive functions
which I do not yet understand:
(A)
Defining a simple range as
r:=. 2 + i.7
2 3 4 5 6 7 8
I have been able to print e.g. a small table of sines
> r,. sin r
2 0.909297427
3 0.141120008
4 _0.756802495
5 _0.958924275
6 _0.279415498
7 0.656986599
8 0.989358247
(B)
Playing around with the factorial I found that
(B1) using this definition (from: Burke/Reiter, Brief Reference)
fac=: 3 : 'if. y <: 1 do. 1 else. y * fac y - 1 end.'
I will get
fac 5
120
alright, but
> r,. fac r
2 2
3 3
4 4
5 5
6 6
7 7
8 8
which seems strange (at least to me).
(B2) using this slightly more elaborate definition
fac=: 3 : 0
n=. y
select. n
case. 0 do. f=. 1
case. 1 do. f=. 1
case. do. f=. n * fac (n-1)
end.
f
)
I will get
fac 5
120
as above, but
> r,. fac r
|stack error: fac
| f=.n* fac(n-1)
(C)
Something similar happens with ((sorry for probable too may parentheses))
fib=: 3 : 0
n=. y
select. n
case. 0 do. f=. 0
case. 1 do. f=. 1
case. do. f=. (fib (n-1)) + (fib (n-2))
end.
f
)
fib 13
233
computes alright, but this throws an error
> r,. fib r
|stack error: fib
| f=.(fib(n-1))+( fib(n-2))
Could anybody shed some light on this..? Thanks, M.
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