# Integer nth-root (Re: [erlang-questions] Integer square root)

Kenji Rikitake < >
Tue Jan 26 06:16:48 CET 2010

```%% This is a quick hack of code for Integer nth-root in Erlang.

%% Power function (X ^ Y) and root function (X ^ (1/Y)) for
%% integers in Erlang
%% by Kenji Rikitake < > 26-JAN-2010

-module(bignum_root).

-export([power/2, root/2]).

%% significand digits for float estimation
-define(DIGITS, 10).

%% computing N ^ E

power(N, E) when (is_integer(N) and (is_integer(E) and (E >= 0))) ->
power(N, E, 1, N).

power(_, 0, Acc, _) ->
Acc;
power(N, E, Acc, Nsq) when (E rem 2 =:= 1) ->
power(N, E - 1, Acc * Nsq, Nsq);
power(N, E, Acc, Nsq) ->
power(N, E div 2, Acc, Nsq * Nsq).

%% computing N ^ (1/E)
%% with Newton-Raphson method

root(N, E) when ((is_integer(N) and (N > 0)) and
(is_integer(E) and (E >= 2))) ->
% estimation of the root by the float calc
L = integer_to_list(N),
Len = length(L),
case Len > ?DIGITS of
true ->
Exp = Len - ?DIGITS,
M = list_to_integer(lists:sublist(L, ?DIGITS)),
XM = math:exp(math:log(M) / E) * math:pow(10, (Exp rem E) / E),
XE = list_to_integer([\$1] ++ lists:duplicate(Exp div E, \$0)),
X = trunc(XM) * XE;
false ->
X = trunc(math:exp(math:log(N) / E))
end,
root(N, E, X).

root(N, E, X) ->
% Newton-Raphson method of solving (E)th-root
X2 = ((N div (power(X, E - 1))) + (X * (E - 1))) div E,
case X2 =/= X of
true ->
root(N, E, X2);
false ->
X
end.

%%  Copyright (c) 2010 by Kenji Rikitake.
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```