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math_pos_SUITE.erl
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% @copyright 2011 Zuse Institute Berlin
% Licensed under the Apache License, Version 2.0 (the "License");
% you may not use this file except in compliance with the License.
% You may obtain a copy of the License at
%
% http://www.apache.org/licenses/LICENSE-2.0
%
% Unless required by applicable law or agreed to in writing, software
% distributed under the License is distributed on an "AS IS" BASIS,
% WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
% See the License for the specific language governing permissions and
% limitations under the License.
%% @author Nico Kruber <kruber@zib.de>
%% @doc Test suite for the math_pos module.
%% @end
%% @version $Id$
-module(math_pos_SUITE).
-author('kruber@zib.de').
-vsn('$Id$').
-compile(export_all).
-include("unittest.hrl").
-include("scalaris.hrl").
all() ->
[plus, minus, multiply, divide,
tester_make_same_length,
tester_plus_symm, tester_plus_valid,
tester_minus, tester_minus_valid,
tester_divide_valid, tester_divide_decimals,
tester_multiply_valid, tester_multiply_decimals].
suite() ->
[
{timetrap, {seconds, 20}}
].
init_per_suite(Config) ->
Config.
end_per_suite(_Config) ->
ok.
-spec plus(Config::[tuple()]) -> true.
plus(_Config) ->
?equals(math_pos:plus( [1], [1], 10), [2]),
?equals(math_pos:plus( [1], [2], 10), [3]),
?equals(math_pos:plus( [1], [9], 10), [0]),
?equals(math_pos:plus([0,1], [0,9], 10), [1,0]),
?equals(math_pos:plus( [2], [1], 10), [3]),
?equals(math_pos:plus( [9], [1], 10), [0]),
?equals(math_pos:plus([0,9], [0,1], 10), [1,0]).
-spec minus(Config::[tuple()]) -> true.
minus(_Config) ->
?equals(math_pos:minus( [1], [1], 10), [0]),
?equals(math_pos:minus( [1], [2], 10), [9]),
?equals(math_pos:minus( [1], [9], 10), [2]),
?equals(math_pos:minus([0,1], [0,9], 10), [9,2]),
?equals(math_pos:minus( [2], [1], 10), [1]),
?equals(math_pos:minus( [9], [1], 10), [8]),
?equals(math_pos:minus([0,9], [0,1], 10), [0,8]).
-spec multiply(Config::[tuple()]) -> true.
multiply(_Config) ->
?equals(math_pos:multiply( [1], 2, 10), [2]),
?equals(math_pos:multiply( [2], 2, 10), [4]),
?equals(math_pos:multiply( [3], 2, 10), [6]),
?equals(math_pos:multiply( [4], 2, 10), [8]),
?equals(math_pos:multiply( [5], 2, 10), [0]),
?equals(math_pos:multiply( [6], 2, 10), [2]),
?equals(math_pos:multiply( [7], 2, 10), [4]),
?equals(math_pos:multiply([0,1], 2, 10), [0,2]),
?equals(math_pos:multiply([0,2], 2, 10), [0,4]),
?equals(math_pos:multiply([0,3], 2, 10), [0,6]),
?equals(math_pos:multiply([0,4], 2, 10), [0,8]),
?equals(math_pos:multiply([0,5], 2, 10), [1,0]),
?equals(math_pos:multiply([0,6], 2, 10), [1,2]),
?equals(math_pos:multiply([0,7], 2, 10), [1,4]),
?equals(math_pos:multiply( [1], 3, 10), [3]),
?equals(math_pos:multiply( [2], 3, 10), [6]),
?equals(math_pos:multiply( [3], 3, 10), [9]),
?equals(math_pos:multiply( [4], 3, 10), [2]),
?equals(math_pos:multiply( [5], 3, 10), [5]),
?equals(math_pos:multiply( [6], 3, 10), [8]),
?equals(math_pos:multiply( [7], 3, 10), [1]),
?equals(math_pos:multiply([0,1], 3, 10), [0,3]),
?equals(math_pos:multiply([0,2], 3, 10), [0,6]),
?equals(math_pos:multiply([0,3], 3, 10), [0,9]),
?equals(math_pos:multiply([0,4], 3, 10), [1,2]),
?equals(math_pos:multiply([0,5], 3, 10), [1,5]),
?equals(math_pos:multiply([0,6], 3, 10), [1,8]),
?equals(math_pos:multiply([0,7], 3, 10), [2,1]),
?equals(math_pos:multiply( [1], 15, 10), [5]),
?equals(math_pos:multiply( [2], 15, 10), [0]),
?equals(math_pos:multiply( [3], 15, 10), [5]),
?equals(math_pos:multiply( [4], 15, 10), [0]),
?equals(math_pos:multiply( [5], 15, 10), [5]),
?equals(math_pos:multiply( [6], 15, 10), [0]),
?equals(math_pos:multiply( [7], 15, 10), [5]),
?equals(math_pos:multiply([0,1], 15, 10), [1,5]),
?equals(math_pos:multiply([0,2], 15, 10), [3,0]),
?equals(math_pos:multiply([0,3], 15, 10), [4,5]),
?equals(math_pos:multiply([0,4], 15, 10), [6,0]),
?equals(math_pos:multiply([0,5], 15, 10), [7,5]),
?equals(math_pos:multiply([0,6], 15, 10), [9,0]),
?equals(math_pos:multiply([0,7], 15, 10), [0,5]),
?equals(math_pos:multiply( [1], 15, 10, enlarge), {[1,5],1}),
?equals(math_pos:multiply( [2], 15, 10, enlarge), {[3,0],1}),
?equals(math_pos:multiply( [3], 15, 10, enlarge), {[4,5],1}),
?equals(math_pos:multiply( [4], 15, 10, enlarge), {[6,0],1}),
?equals(math_pos:multiply( [5], 15, 10, enlarge), {[7,5],1}),
?equals(math_pos:multiply( [6], 15, 10, enlarge), {[9,0],1}),
?equals(math_pos:multiply( [7], 15, 10, enlarge), {[1,0,5],2}),
?equals(math_pos:multiply([0,1], 15, 10, enlarge), {[1,5],0}),
?equals(math_pos:multiply([0,2], 15, 10, enlarge), {[3,0],0}),
?equals(math_pos:multiply([0,3], 15, 10, enlarge), {[4,5],0}),
?equals(math_pos:multiply([0,4], 15, 10, enlarge), {[6,0],0}),
?equals(math_pos:multiply([0,5], 15, 10, enlarge), {[7,5],0}),
?equals(math_pos:multiply([0,6], 15, 10, enlarge), {[9,0],0}),
?equals(math_pos:multiply([0,7], 15, 10, enlarge), {[1,0,5],1}).
-spec divide(Config::[tuple()]) -> true.
divide(_Config) ->
?equals(math_pos:divide( [1], 2, 10), [0]),
?equals(math_pos:divide( [2], 2, 10), [1]),
?equals(math_pos:divide( [3], 2, 10), [1]),
?equals(math_pos:divide( [4], 2, 10), [2]),
?equals(math_pos:divide([1,0], 2, 10), [0,5]),
?equals(math_pos:divide([1,1], 2, 10), [0,5]),
?equals(math_pos:divide([1,2], 2, 10), [0,6]),
?equals(math_pos:divide([1,3], 2, 10), [0,6]),
?equals(math_pos:divide([1,4], 2, 10), [0,7]),
?equals(math_pos:divide([2,0], 2, 10), [1,0]),
?equals(math_pos:divide([2,1], 2, 10), [1,0]),
?equals(math_pos:divide([2,2], 2, 10), [1,1]),
?equals(math_pos:divide([2,3], 2, 10), [1,1]),
?equals(math_pos:divide([2,4], 2, 10), [1,2]),
?equals(math_pos:divide( [1], 3, 10), [0]),
?equals(math_pos:divide( [2], 3, 10), [0]),
?equals(math_pos:divide( [3], 3, 10), [1]),
?equals(math_pos:divide( [4], 3, 10), [1]),
?equals(math_pos:divide([1,0], 3, 10), [0,3]),
?equals(math_pos:divide([1,1], 3, 10), [0,3]),
?equals(math_pos:divide([1,2], 3, 10), [0,4]),
?equals(math_pos:divide([1,3], 3, 10), [0,4]),
?equals(math_pos:divide([1,4], 3, 10), [0,4]),
?equals(math_pos:divide([2,0], 3, 10), [0,6]),
?equals(math_pos:divide([2,1], 3, 10), [0,7]),
?equals(math_pos:divide([3,0], 3, 10), [1,0]),
?equals(math_pos:divide([3,1], 3, 10), [1,0]),
?equals(math_pos:divide([3,2], 3, 10), [1,0]),
?equals(math_pos:divide([3,3], 3, 10), [1,1]),
?equals(math_pos:divide([3,4], 3, 10), [1,1]),
?equals(math_pos:divide([3,5], 3, 10), [1,1]),
?equals(math_pos:divide([3,6], 3, 10), [1,2]).
%% make_same_length
-spec prop_make_same_length(A::string(), B::string(), front | back) -> true.
prop_make_same_length(A, B, Pos) ->
{A1, B1, ALen, BLen, A1Added, B1Added} = math_pos:make_same_length(A, B, Pos),
?equals(ALen, erlang:length(A)),
?equals(BLen, erlang:length(B)),
A1Len = erlang:length(A1),
?equals(A1Len, erlang:length(B1)),
?equals(ALen + A1Added, A1Len),
?equals(math_pos:remove_zeros(A1, Pos, all), math_pos:remove_zeros(A, Pos, all)),
?equals(math_pos:remove_zeros(B1, Pos, all), math_pos:remove_zeros(B, Pos, all)),
?equals(math_pos:remove_zeros(A1, Pos, A1Added), A),
?equals(math_pos:remove_zeros(B1, Pos, B1Added), B).
-spec tester_make_same_length(Config::[tuple()]) -> ok.
tester_make_same_length(_Config) ->
tester:test(?MODULE, prop_make_same_length, 3, 10000, [{threads, 2}]).
%% plus
-spec prop_plus_valid_base(X, X, Pos::front | back, Base::pos_integer()) -> true when is_subtype(X, list(non_neg_integer())).
prop_plus_valid_base(A_, B_, Pos, Base) ->
{A, B, _, _, _, _} = math_pos:make_same_length(A_, B_, Pos),
A_plus_B = math_pos:plus(A, B, Base),
?equals(erlang:length(A_plus_B), erlang:length(A)),
case lists:all(fun(E) -> E >= 0 andalso E < Base end, A_plus_B) of
true -> true;
_ -> ?ct_fail("math_pos:plus(A, B, ~B) evaluated to \"~.0p\" and "
"contains invalid elements~n",
[Base, A_plus_B])
end.
-spec prop_plus_valid1(A::[0..9], B::[0..9]) -> true.
prop_plus_valid1(A_, B_) -> prop_plus_valid_base(A_, B_, front, 10).
-spec prop_plus_valid2(A::string(), B::string()) -> true.
prop_plus_valid2(A_, B_) -> prop_plus_valid_base(A_, B_, back, 16#10ffff + 1).
-spec prop_plus_valid3(A::nonempty_string(), B::nonempty_string()) -> true.
prop_plus_valid3(A_, B_) ->
Base = erlang:max(lists:max(A_), lists:max(B_)) + 1,
prop_plus_valid_base(A_, B_, back, Base).
-spec tester_plus_valid(Config::[tuple()]) -> ok.
tester_plus_valid(_Config) ->
tester:test(?MODULE, prop_plus_valid1, 2, 10000, [{threads, 2}]),
tester:test(?MODULE, prop_plus_valid2, 2, 10000, [{threads, 2}]),
tester:test(?MODULE, prop_plus_valid3, 2, 10000, [{threads, 2}]).
-spec prop_plus_symm_base(X, X, Pos::front | back, Base::pos_integer()) -> true when is_subtype(X, list(non_neg_integer())).
prop_plus_symm_base(A_, B_, Pos, Base) ->
{A, B, _, _, _, _} = math_pos:make_same_length(A_, B_, Pos),
?equals(math_pos:plus(A, B, Base), math_pos:plus(B, A, Base)).
-spec prop_plus_symm1(A::[0..9], B::[0..9]) -> true.
prop_plus_symm1(A_, B_) -> prop_plus_symm_base(A_, B_, front, 10).
-spec prop_plus_symm2(A::string(), B::string()) -> true.
prop_plus_symm2(A_, B_) -> prop_plus_symm_base(A_, B_, back, 16#10ffff + 1).
-spec prop_plus_symm3(A::nonempty_string(), B::nonempty_string()) -> true.
prop_plus_symm3(A_, B_) ->
Base = erlang:max(lists:max(A_), lists:max(B_)) + 1,
prop_plus_symm_base(A_, B_, back, Base).
-spec tester_plus_symm(Config::[tuple()]) -> ok.
tester_plus_symm(_Config) ->
tester:test(?MODULE, prop_plus_symm1, 2, 10000, [{threads, 2}]),
tester:test(?MODULE, prop_plus_symm2, 2, 10000, [{threads, 2}]),
tester:test(?MODULE, prop_plus_symm3, 2, 10000, [{threads, 2}]).
%% minus
-spec prop_minus_valid_base(X, X, Pos::front | back, Base::pos_integer()) -> true when is_subtype(X, list(non_neg_integer())).
prop_minus_valid_base(A_, B_, Pos, Base) ->
{A, B, _, _, _, _} = math_pos:make_same_length(A_, B_, Pos),
A_minus_B = math_pos:minus(A, B, Base),
?equals(erlang:length(A_minus_B), erlang:length(A)),
case lists:all(fun(E) -> E >= 0 andalso E < Base end, A_minus_B) of
true -> true;
_ -> ?ct_fail("math_pos:minus(A, B, ~B) evaluated to \"~.0p\" and "
"contains invalid elements~n",
[Base, A_minus_B])
end.
-spec prop_minus_valid1(A::[0..9], B::[0..9]) -> true.
prop_minus_valid1(A_, B_) -> prop_minus_valid_base(A_, B_, front, 10).
-spec prop_minus_valid2(A::string(), B::string()) -> true.
prop_minus_valid2(A_, B_) -> prop_minus_valid_base(A_, B_, back, 16#10ffff + 1).
-spec prop_minus_valid3(A::nonempty_string(), B::nonempty_string()) -> true.
prop_minus_valid3(A_, B_) ->
Base = erlang:max(lists:max(A_), lists:max(B_)) + 1,
prop_minus_valid_base(A_, B_, back, Base).
-spec tester_minus_valid(Config::[tuple()]) -> ok.
tester_minus_valid(_Config) ->
tester:test(?MODULE, prop_minus_valid1, 2, 10000, [{threads, 2}]),
prop_minus_valid2([557056,0,0,0,0,1], [557055,1114111,1114111,1114111,1114111,1114111]),
tester:test(?MODULE, prop_minus_valid2, 2, 10000, [{threads, 2}]),
tester:test(?MODULE, prop_minus_valid3, 2, 10000, [{threads, 2}]).
-spec prop_minus_base(X, X, Pos::front | back, Base::pos_integer()) -> true when is_subtype(X, list(non_neg_integer())).
prop_minus_base(A_, B_, Pos, Base) ->
{A, B, _, _, _, _} = math_pos:make_same_length(A_, B_, Pos),
A_B = math_pos:minus(A, B, Base),
?equals(math_pos:plus(A_B, B, Base), A).
-spec prop_minus1(A::[0..9], B::[0..9]) -> true.
prop_minus1(A_, B_) -> prop_minus_base(A_, B_, front, 10).
-spec prop_minus2(A::string(), B::string()) -> true.
prop_minus2(A_, B_) -> prop_minus_base(A_, B_, back, 16#10ffff + 1).
-spec prop_minus3(A::nonempty_string(), B::nonempty_string()) -> true.
prop_minus3(A_, B_) ->
Base = erlang:max(lists:max(A_), lists:max(B_)) + 1,
prop_minus_base(A_, B_, back, Base).
-spec tester_minus(Config::[tuple()]) -> ok.
tester_minus(_Config) ->
tester:test(?MODULE, prop_minus1, 2, 10000, [{threads, 2}]),
tester:test(?MODULE, prop_minus2, 2, 10000, [{threads, 2}]),
tester:test(?MODULE, prop_minus3, 2, 10000, [{threads, 2}]).
%% divide
-spec prop_divide_valid_base(X, Div::pos_integer(), Base::pos_integer()) -> true when is_subtype(X, list(non_neg_integer())).
prop_divide_valid_base(A, Div, Base) ->
A_div = math_pos:divide(A, Div, Base),
?equals(erlang:length(A_div), erlang:length(A)),
case lists:all(fun(E) -> E >= 0 andalso E < Base end, A_div) of
true -> true;
_ -> ?ct_fail("math_pos:divide(A, Div, ~B) evaluated to \"~.0p\" and "
"contains invalid elements~n",
[Base, A_div])
end.
-spec prop_divide_valid1(A::[0..9], Div::pos_integer()) -> true.
prop_divide_valid1(A, Div) -> prop_divide_valid_base(A, Div, 10).
-spec prop_divide_valid2(A::string(), Div::pos_integer()) -> true.
prop_divide_valid2(A, Div) -> prop_divide_valid_base(A, Div, 16#10ffff + 1).
-spec prop_divide_valid3(A::nonempty_string(), Div::pos_integer()) -> true.
prop_divide_valid3(A, Div) ->
Base = lists:max(A) + 1,
prop_divide_valid_base(A, Div, Base).
-spec tester_divide_valid(Config::[tuple()]) -> ok.
tester_divide_valid(_Config) ->
tester:test(?MODULE, prop_divide_valid1, 2, 10000, [{threads, 2}]),
tester:test(?MODULE, prop_divide_valid2, 2, 10000, [{threads, 2}]),
tester:test(?MODULE, prop_divide_valid3, 2, 10000, [{threads, 2}]).
-spec prop_divide_decimals(A::non_neg_integer(), Div::pos_integer()) -> true.
prop_divide_decimals(A, Div) ->
APos = decimal_to_pos(A),
?equals(pos_to_decimal(math_pos:divide(APos, Div, 10)), A div Div).
-spec tester_divide_decimals(Config::[tuple()]) -> ok.
tester_divide_decimals(_Config) ->
tester:test(?MODULE, prop_divide_decimals, 2, 10000, [{threads, 2}]).
%% multiply
-spec prop_multiply_valid_base(A::[non_neg_integer()], Fac::non_neg_integer(), Base::pos_integer()) -> true.
prop_multiply_valid_base(A, Fac, Base) ->
A_prod = math_pos:multiply(A, Fac, Base),
?equals(erlang:length(A_prod), erlang:length(A)),
case lists:all(fun(E) -> E >= 0 andalso E < Base end, A_prod) of
true -> true;
_ -> ?ct_fail("math_pos:multiply(A, Div, ~B) evaluated to \"~.0p\" and "
"contains invalid elements~n",
[Base, A_prod])
end.
-spec prop_multiply_valid1(A::[0..9], Fac::0..9) -> true.
prop_multiply_valid1(A, Fac) -> prop_multiply_valid_base(A, Fac, 10).
-spec prop_multiply_valid2(A::string(), Fac::0..16#10ffff) -> true.
prop_multiply_valid2(A, Fac) -> prop_multiply_valid_base(A, Fac, 16#10ffff + 1).
-spec prop_multiply_valid3(A::nonempty_string(), Fac::non_neg_integer()) -> true.
prop_multiply_valid3(A, Fac) ->
A_max = lists:max(A), Base = A_max + 1,
prop_multiply_valid_base(A, Fac, Base).
-spec tester_multiply_valid(Config::[tuple()]) -> ok.
tester_multiply_valid(_Config) ->
tester:test(?MODULE, prop_multiply_valid1, 2, 10000, [{threads, 2}]),
tester:test(?MODULE, prop_multiply_valid2, 2, 10000, [{threads, 2}]),
tester:test(?MODULE, prop_multiply_valid3, 2, 10000, [{threads, 2}]).
-spec prop_multiply_decimals(A::non_neg_integer(), Fac::0..100000) -> true.
prop_multiply_decimals(A, Fac) ->
APos = decimal_to_pos(A),
{ProdPos, Added} = math_pos:multiply(APos, Fac, 10, enlarge),
?equals(pos_to_decimal(ProdPos), A * Fac),
?equals(Added, length(ProdPos) - length(APos)).
-spec tester_multiply_decimals(Config::[tuple()]) -> ok.
tester_multiply_decimals(_Config) ->
tester:test(?MODULE, prop_multiply_decimals, 2, 10000, [{threads, 2}]).
%% helpers
decimal_to_pos(X) -> [A - 48 || A <- lists:flatten(io_lib:format("~B", [X]))].
pos_to_decimal(X) -> element(2, lists:foldr(fun(A, {Fac, Res}) ->
{Fac * 10, Res + A * Fac}
end, {1, 0}, X)).