# What is the most elegant way to specifiy a start case for recursion?

When writing recursive code that computes the least value at which a condition is true and various other scenarios it is often necessary to specify a base case. What I have done to supply this is create a function parameter that must always have the specified base case passed into it:

least2nbigger[x_, n_] := If[2^n >= x, 2^n, least2nbigger[x, 1 + n]]

This is used with a structure like

least2nbigger[4097, 1]

Where the 1 is the start value for the recursion. x is the only parameter of interest to someone using the function; n is always to be passed as 1.

In SML I would do something like this:

fun least2nbigger x = least2nbigger (x, 1)
|   least2nbigger (x, n) =
let
p = pow (2, n)
in
if p > x then p
else least2nbigger (x, n+1)
end;


(My SML is a bit rusty, that might not be entirely valid but the idea is clear).

There is an alternative definition provided for the recursive case; the function can be called without the tuple.

The only way I see to do this in Mathematica would be to make two functions, the recursive case and a dummy function that calls the recursive case with is base parameter. Is there a better way to accomplish this?

• least2nbigger[x_, n_:1] :=... ? – Rojo Feb 4 '14 at 3:20

As Rojo notes in a comment you can make n an Optional parameter with a default value:

f[x_, n_: 1] := If[2^n >= x, 2^n, f[x, 1 + n]]

f

8192


More manually you could use a definition for the single parameter case:

g[x_] := g[x, 1];
g[x_, n_] := If[2^n >= x, 2^n, g[x, 1 + n]]

g

8192


You can also convert the If statement into a Condition, e.g.:

h[x_] := h[x, 1];
h[x_, n_] /; 2^n >= x := 2^n
h[x_, n_] := h[x, 1 + n]

h

8192


You may find that this syntax is somewhat more efficient than If, Switch, etc.