%% This file is part of erl_sim.

%% erl_sim is free software: you can redistribute it and/or modify
%% it under the terms of the GNU Lesser General Public License as published by
%% the Free Software Foundation, either version 3 of the License, or
%% (at your option) any later version.
%%
%% erl_sim is distributed in the hope that it will be useful,
%% but WITHOUT ANY WARRANTY; without even the implied warranty of
%% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
%% GNU Lesser General Public License for more details.
%%
%% You should have received a copy of the GNU Lesser General Public License
%% along with QuickConnectiPhoneHybrid. If not, see http://www.gnu.org/licenses/.
%% Description: This file contains functions for doing division with very large numbers as well as some other
%% useful functions
-module(sim_math).

%%
%% Include files
%%

%%
%% Exported Functions
%%
-export([big_divide/2, big_div_with_rem/2, big_rem/2, floor/1,
factorial/1, m_choose_n/2]).

%%
%% API Functions
%%

%%
%% TODO: Add description of div_with_rem/function_arity
%%
big_div_with_rem(Dividend, Divisor) ->
if
Divisor /= 0 ->
{ok,New_divisor,Cnt} = count_div_shifts(abs(Dividend), abs(Divisor), 0),
case big_div_with_rem_helper(abs(Dividend), abs(New_divisor),Cnt,0) of
{ok, Quotient, Remainder} when (Dividend < 0) xor (Divisor
{ok,-Quotient,-Remainder};
{ok, Quotient, Remainder} ->
{ok, Quotient, Remainder};
{error,Why} ->
{error,Why};
true ->
{error,"Unknown error"}
end;
true ->
{error,"Division by Zero error"}
end.

%%
%% TODO: Add description of big_divide/function_arity
%%
big_divide(Dividend, Divisor)->
%double limit. Erlang uses underlying system algorithms for floating point mathematics
Limit = math:pow(2,1023),
case big_div_with_rem(Dividend, Divisor) of
{ok,Quotient,Remainder} ->
if
Remainder == 0 ->
{ok, Quotient};

%the quotient must be less than the limit or else and error will happen
%when the result floating point value is added to it
%the remainder and the divisor must be less than the limit or else the
%division will fail.

Remainder < Limit andalso Divisor < Limit andalso Quotient
Result = Remainder/abs(Divisor),
io:format("Remainder/Divisor:~p Quotient:~p~n",[Result,Quotient]),
{ok, Quotient+Result};
true ->
{ok, Quotient,Remainder}
end;
{error,Why} ->
{error,Why}
end.

%%
%% TODO: Add description of big_rem/function_arity
%%
big_rem(A, B) ->
if
B /= 0 ->
{ok,New_divisor,Cnt} = count_div_shifts(abs(A), abs(B), 0),
case big_div_with_rem_helper(abs(A), abs(New_divisor),Cnt,0) of
{ok, Quotient, Remainder} when (A < 0) xor (B
{ok,-Remainder};
{ok, Quotient, Remainder} ->
{ok, Remainder};
{error,Why} ->
{error,Why};
true ->
{error,"Unknown error"}
end;
true ->
{error,"Division by Zero error"}
end.

%%
%% TODO: Add description of floor/function_arity
%%
floor(X) ->
T = trunc(X),
case X - T T - 1;
false -> T
end.

%factorial of N

factorial(N) ->
fact_helper(N, 1).

fact_helper(0, Product) ->
Product;
fact_helper(1, Product) ->
Product;
fact_helper(N, Product) ->
%io:format("N: ~p Product: ~p~n",[N, Product]),
fact_helper(N - 1, Product * N).

m_choose_n(M,N) ->
if
N > M orelse N < 0 orelse M 0;
true ->
factorial(M)/(factorial(N)*factorial(M-N))
end.

%%
%% Local Functions
%%
big_div_with_rem_helper(Dividend, Divisor, Count, Quotient) ->
%io:format("Dividend:~p Divisor:~p Count:~p~n",[Dividend, Divisor, Count, Quotient]),
if
Count
{ok, Quotient, Dividend};
true ->
if
Divisor =
big_div_with_rem_helper(Dividend-Divisor, Divisor bsr 1, Count-1, (Quotient bsl 1) +1);
true ->
big_div_with_rem_helper(Dividend, Divisor bsr 1, Count -1, Quotient bsl 1)
end
end.