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bignum_root.erl
Erlang
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%% Power function (X ^ Y) and root function (X ^ (1/Y)) for
%% integers in Erlang
%% by Kenji Rikitake <kenji.rikitake@acm.org> 26-JAN-2010
%% Distributed under MIT license at the end of the source code.
 
-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.
 
%% MIT License:
%% Copyright (c) 2010 by Kenji Rikitake.
%%
%% Permission is hereby granted, free of charge, to any person
%% obtaining a copy of this software and associated documentation
%% files (the "Software"), to deal in the Software without
%% restriction, including without limitation the rights to use,
%% copy, modify, merge, publish, distribute, sublicense, and/or sell
%% copies of the Software, and to permit persons to whom the
%% Software is furnished to do so, subject to the following
%% conditions:
%%
%% The above copyright notice and this permission notice shall be
%% included in all copies or substantial portions of the Software.
%%
%% THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
%% EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES
%% OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
%% NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT
%% HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY,
%% WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
%% FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
%% OTHER DEALINGS IN THE SOFTWARE.

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