Current section
Files
Jump to
Current section
Files
test/rationals_SUITE.erl
%% Copyright (c) 2013-2014 Peter Morgan <peter.james.morgan@gmail.com>
%%
%% 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.
-module(rationals_SUITE).
-include_lib("common_test/include/ct.hrl").
-export([
all/0,
groups/0,
adding_quarters_to_thirds_test/1,
adding_three_quarters_to_five_twelves_test/1,
multiply_two_thirds_by_three_quarters_test/1,
simplify_test/1,
is_greater_than_test/1,
is_equal_to_test/1,
is_less_than_test/1,
subtraction_test/1,
mixed_numbers_test/1,
reciprocal_test/1,
divide_test/1,
six_from_float_test/1,
point_seven_five_from_float_test/1,
point_five_from_float_test/1,
greatest_common_divisor_test/1,
compare_test/1,
gt_lt_eq_test/1,
gte_lte_test/1,
reduce_test/1,
ratio_test/1,
to_float_test/1,
normalize_test/1,
normalize_zero_denominator_test/1,
reduce_canonical_sign_test/1,
compare_sign_robust_test/1,
constants_test/1,
denominator_contract_boundary_test/1,
negate_test/1,
abs_test/1,
sign_test/1,
predicates_test/1,
min_max_test/1,
clamp_between_test/1,
dist_test/1,
pow_test/1,
sum_product_test/1,
floor_test/1,
ceil_test/1,
truncate_test/1,
round_test/1,
to_mixed_test/1,
from_mixed_test/1,
is_integer_test/1,
is_proper_test/1,
parse_test/1,
parse_error_test/1,
format_test/1,
from_integer_test/1,
round_trip_test/1,
mediant_test/1,
is_reduced_test/1,
is_unit_fraction_test/1,
lcm_test/1,
continued_fraction_test/1,
from_continued_fraction_test/1,
convergents_test/1,
rationalize_test/1,
decimal_expansion_test/1,
egyptian_test/1,
farey_test/1
]).
all() ->
common:all().
groups() ->
common:groups(?MODULE).
adding_quarters_to_thirds_test(_Config) ->
Quarter = rationals:new(1, 4),
Third = rationals:new(1, 3),
Sum = rationals:add(Quarter, Third),
7 = rationals:numerator(Sum),
12 = rationals:denominator(Sum).
adding_three_quarters_to_five_twelves_test(_Config) ->
A = rationals:new(3, 4),
B = rationals:new(5, 12),
Sum = rationals:add(A, B),
56 = rationals:numerator(Sum),
48 = rationals:denominator(Sum).
multiply_two_thirds_by_three_quarters_test(_Config) ->
A = rationals:new(2, 3),
B = rationals:new(3, 4),
Product = rationals:multiply(A, B),
6 = rationals:numerator(Product),
12 = rationals:denominator(Product).
simplify_test(_Config) ->
A = rationals:new(63, 462),
Simplified = rationals:simplify(A),
3 = rationals:numerator(Simplified),
22 = rationals:denominator(Simplified).
is_greater_than_test(_Config) ->
A = rationals:new(3, 4),
B = rationals:new(2, 4),
true = rationals:is_greater_than(A, B),
true = rationals:is_greater_or_equal(A, B),
false = rationals:is_greater_than(B, A),
false = rationals:is_greater_than(A, A),
true = rationals:is_greater_or_equal(A, A).
is_equal_to_test(_Config) ->
A = rationals:new(3, 4),
B = rationals:new(2, 4),
C = rationals:new(1, 2),
false = rationals:is_equal_to(A, B),
false = rationals:is_equal_to(B, A),
true = rationals:is_equal_to(A, A),
true = rationals:is_equal_to(B, B),
true = rationals:is_equal_to(B, C),
true = rationals:is_equal_to(C, B).
is_less_than_test(_Config) ->
A = rationals:new(3, 4),
B = rationals:new(2, 4),
false = rationals:is_less_than(A, B),
true = rationals:is_less_or_equal(B, A),
true = rationals:is_less_than(B, A).
subtraction_test(_Config) ->
A = rationals:new(2, 3),
B = rationals:new(1, 2),
Difference = rationals:subtract(A, B),
1 = rationals:numerator(Difference),
6 = rationals:denominator(Difference).
mixed_numbers_test(_Config) ->
A = rationals:new(6),
B = rationals:new(3, 4),
Product = rationals:multiply(A, B),
18 = rationals:numerator(Product),
4 = rationals:denominator(Product).
reciprocal_test(_Config) ->
A = rationals:new(3, 4),
Reciprocal = rationals:reciprocal(A),
4 = rationals:numerator(Reciprocal),
3 = rationals:denominator(Reciprocal).
divide_test(_Config) ->
A = rationals:new(1, 2),
B = rationals:new(3, 4),
R = rationals:divide(A, B),
4 = rationals:numerator(R),
6 = rationals:denominator(R).
six_from_float_test(_Config) ->
A = rationals:from_float(6.0),
6 = rationals:numerator(A),
1 = rationals:denominator(A).
point_seven_five_from_float_test(_Config) ->
A = rationals:from_float(0.75),
3 = rationals:numerator(A),
4 = rationals:denominator(A).
point_five_from_float_test(_Config) ->
A = rationals:from_float(0.5),
1 = rationals:numerator(A),
2 = rationals:denominator(A).
greatest_common_divisor_test(_Config) ->
6 = rationals:gcd(48, 18).
compare_test(_Config) ->
A = rationals:new(3, 4),
B = rationals:new(2, 4),
C = rationals:new(1, 2),
gt = rationals:compare(A, B),
lt = rationals:compare(B, A),
eq = rationals:compare(B, C),
eq = rationals:compare(A, A).
gt_lt_eq_test(_Config) ->
A = rationals:new(3, 4),
B = rationals:new(2, 4),
true = rationals:gt(A, B),
false = rationals:gt(B, A),
false = rationals:gt(A, A),
true = rationals:lt(B, A),
false = rationals:lt(A, B),
false = rationals:lt(A, A),
true = rationals:eq(A, A),
true = rationals:eq(rationals:new(2, 4), rationals:new(1, 2)),
false = rationals:eq(A, B).
gte_lte_test(_Config) ->
A = rationals:new(3, 4),
B = rationals:new(2, 4),
true = rationals:gte(A, B),
true = rationals:gte(A, A),
false = rationals:gte(B, A),
true = rationals:lte(B, A),
true = rationals:lte(A, A),
false = rationals:lte(A, B).
reduce_test(_Config) ->
A = rationals:new(63, 462),
R = rationals:reduce(A),
3 = rationals:numerator(R),
22 = rationals:denominator(R),
Half = rationals:new(1, 2),
1 = rationals:numerator(rationals:reduce(Half)),
2 = rationals:denominator(rationals:reduce(Half)).
ratio_test(_Config) ->
A = rationals:new(3, 4),
{3, 4} = rationals:ratio(A).
to_float_test(_Config) ->
A = rationals:new(1, 4),
0.25 = rationals:to_float(A).
normalize_test(_Config) ->
{-1, 2} = rationals:ratio(rationals:normalize(rationals:new(1, -2))),
{3, 4} = rationals:ratio(rationals:normalize(rationals:new(-3, -4))),
{-1, 2} = rationals:ratio(rationals:normalize(rationals:new(2, -4))),
{-3, 4} = rationals:ratio(rationals:normalize(rationals:new(-6, 8))),
{0, 1} = rationals:ratio(rationals:normalize(rationals:new(0, -5))),
{2, 1} = rationals:ratio(rationals:normalize(rationals:new(6, 3))),
{3, 4} = rationals:ratio(rationals:normalize(rationals:new(3, 4))).
normalize_zero_denominator_test(_Config) ->
try rationals:normalize(rationals:new(1, 0)) of
_ -> error(should_have_crashed)
catch
error:function_clause -> ok
end.
reduce_canonical_sign_test(_Config) ->
{-1, 2} = rationals:ratio(rationals:reduce(rationals:new(1, -2))).
compare_sign_robust_test(_Config) ->
lt = rationals:compare(rationals:new(1, -2), rationals:new(1, 3)),
eq = rationals:compare(rationals:new(1, -2), rationals:new(-1, 2)).
constants_test(_Config) ->
{0, 1} = rationals:ratio(rationals:zero()),
{1, 1} = rationals:ratio(rationals:one()),
F = rationals:new(3, 4),
eq = rationals:compare(rationals:add(F, rationals:zero()), F),
eq = rationals:compare(rationals:multiply(F, rationals:one()), F).
denominator_contract_boundary_test(_Config) ->
Lazy = rationals:new(1, -2),
Normalized = rationals:normalize(Lazy),
{1, -2} = rationals:ratio(Lazy),
{-1, 2} = rationals:ratio(Normalized).
negate_test(_Config) ->
{-3, 4} = rationals:ratio(rationals:negate(rationals:new(3, 4))),
{3, 4} = rationals:ratio(rationals:negate(rationals:new(-3, 4))).
abs_test(_Config) ->
eq = rationals:compare(rationals:abs(rationals:new(-3, 4)), rationals:new(3, 4)),
eq = rationals:compare(rationals:abs(rationals:new(3, -4)), rationals:new(3, 4)),
true = rationals:is_zero(rationals:abs(rationals:zero())).
sign_test(_Config) ->
Neg = -1,
1 = rationals:sign(rationals:new(3, 4)),
Neg = rationals:sign(rationals:new(-3, 4)),
0 = rationals:sign(rationals:zero()),
Neg = rationals:sign(rationals:new(3, -4)),
1 = rationals:sign(rationals:new(-3, -4)).
predicates_test(_Config) ->
true = rationals:is_zero(rationals:zero()),
false = rationals:is_zero(rationals:one()),
true = rationals:is_positive(rationals:new(3, 4)),
false = rationals:is_positive(rationals:zero()),
true = rationals:is_negative(rationals:new(-3, 4)),
true = rationals:is_negative(rationals:new(1, -2)),
false = rationals:is_negative(rationals:zero()).
min_max_test(_Config) ->
Half = rationals:new(1, 2),
ThreeQuarters = rationals:new(3, 4),
eq = rationals:compare(rationals:min(Half, ThreeQuarters), Half),
eq = rationals:compare(rationals:max(Half, ThreeQuarters), ThreeQuarters),
eq = rationals:compare(rationals:min(Half, Half), Half),
eq = rationals:compare(rationals:max(Half, Half), Half).
clamp_between_test(_Config) ->
Lo = rationals:zero(),
Hi = rationals:new(3, 1),
Below = rationals:new(-1, 1),
Within = rationals:new(1, 1),
Above = rationals:new(5, 1),
eq = rationals:compare(rationals:clamp(Below, Lo, Hi), Lo),
eq = rationals:compare(rationals:clamp(Within, Lo, Hi), Within),
eq = rationals:compare(rationals:clamp(Above, Lo, Hi), Hi),
true = rationals:between(Lo, Lo, Hi),
true = rationals:between(Hi, Lo, Hi),
true = rationals:between(Within, Lo, Hi),
false = rationals:between(Below, Lo, Hi),
false = rationals:between(Above, Lo, Hi).
dist_test(_Config) ->
eq = rationals:compare(
rationals:dist(rationals:new(1, 2), rationals:new(3, 4)),
rationals:new(1, 4)
),
eq = rationals:compare(
rationals:dist(rationals:new(3, 4), rationals:new(1, 2)),
rationals:new(1, 4)
).
pow_test(_Config) ->
F = rationals:new(2, 3),
{1, 1} = rationals:ratio(rationals:pow(F, 0)),
eq = rationals:compare(rationals:pow(F, 1), F),
eq = rationals:compare(rationals:pow(F, 2), rationals:new(4, 9)),
eq = rationals:compare(rationals:pow(F, -1), rationals:new(3, 2)),
eq = rationals:compare(rationals:pow(F, -2), rationals:new(9, 4)),
{1, 1} = rationals:ratio(rationals:pow(rationals:zero(), 0)).
sum_product_test(_Config) ->
Half = rationals:new(1, 2),
Third = rationals:new(1, 3),
Sixth = rationals:new(1, 6),
eq = rationals:compare(rationals:sum([Half, Third, Sixth]), rationals:one()),
{0, 1} = rationals:ratio(rationals:sum([])),
TwoThirds = rationals:new(2, 3),
ThreeQuarters = rationals:new(3, 4),
eq = rationals:compare(rationals:product([TwoThirds, ThreeQuarters]), Half),
{1, 1} = rationals:ratio(rationals:product([])).
floor_test(_Config) ->
3 = rationals:floor(rationals:new(7, 2)),
Neg4 = -4,
Neg4 = rationals:floor(rationals:new(-7, 2)),
2 = rationals:floor(rationals:new(6, 3)),
0 = rationals:floor(rationals:new(3, 4)),
Neg1 = -1,
Neg1 = rationals:floor(rationals:new(-3, 4)).
ceil_test(_Config) ->
4 = rationals:ceil(rationals:new(7, 2)),
Neg3 = -3,
Neg3 = rationals:ceil(rationals:new(-7, 2)),
2 = rationals:ceil(rationals:new(6, 3)),
1 = rationals:ceil(rationals:new(3, 4)),
0 = rationals:ceil(rationals:new(-3, 4)).
truncate_test(_Config) ->
3 = rationals:truncate(rationals:new(7, 2)),
Neg3 = -3,
Neg3 = rationals:truncate(rationals:new(-7, 2)),
0 = rationals:truncate(rationals:new(-3, 4)).
round_test(_Config) ->
Neg1 = -1,
1 = rationals:round(rationals:new(1, 2)),
Neg1 = rationals:round(rationals:new(-1, 2)),
2 = rationals:round(rationals:new(3, 2)),
3 = rationals:round(rationals:new(5, 2)),
1 = rationals:round(rationals:new(2, 3)),
0 = rationals:round(rationals:new(1, 3)),
Neg1 = rationals:round(rationals:new(-2, 3)).
to_mixed_test(_Config) ->
{2, Frac1} = rationals:to_mixed(rationals:new(7, 3)),
eq = rationals:compare(Frac1, rationals:new(1, 3)),
{Neg2, Frac2} = rationals:to_mixed(rationals:new(-7, 3)),
Neg2 = -2,
eq = rationals:compare(Frac2, rationals:new(-1, 3)),
{2, Frac3} = rationals:to_mixed(rationals:new(6, 3)),
true = rationals:is_zero(Frac3),
{1, Frac4} = rationals:to_mixed(rationals:new(8, 6)),
eq = rationals:compare(Frac4, rationals:new(1, 3)).
from_mixed_test(_Config) ->
eq = rationals:compare(rationals:from_mixed(2, 1, 3), rationals:new(7, 3)),
eq = rationals:compare(rationals:from_mixed(-2, -1, 3), rationals:new(-7, 3)).
is_integer_test(_Config) ->
true = rationals:is_integer(rationals:new(4, 2)),
false = rationals:is_integer(rationals:new(3, 4)),
true = rationals:is_integer(rationals:new(0, 5)),
true = rationals:is_integer(rationals:new(6, 3)).
is_proper_test(_Config) ->
true = rationals:is_proper(rationals:new(3, 4)),
false = rationals:is_proper(rationals:new(4, 3)),
false = rationals:is_proper(rationals:new(6, 4)),
true = rationals:is_proper(rationals:new(-3, 4)),
false = rationals:is_proper(rationals:new(5, 5)),
true = rationals:is_proper(rationals:new(0, 5)).
parse_test(_Config) ->
{ok, F1} = rationals:parse("3/4"),
eq = rationals:compare(F1, rationals:new(3, 4)),
{ok, F2} = rationals:parse("3"),
eq = rationals:compare(F2, rationals:new(3, 1)),
{ok, F3} = rationals:parse("-3/4"),
eq = rationals:compare(F3, rationals:new(-3, 4)),
{ok, F4} = rationals:parse(<<"3/4">>),
eq = rationals:compare(F4, rationals:new(3, 4)),
{ok, F5} = rationals:parse(" 3 / 4 "),
eq = rationals:compare(F5, rationals:new(3, 4)).
parse_error_test(_Config) ->
{error, zero_denominator} = rationals:parse("3/0"),
{error, invalid} = rationals:parse("x"),
{error, invalid} = rationals:parse("3/"),
{error, invalid} = rationals:parse("/4"),
{error, invalid} = rationals:parse("3/4/5"),
{error, invalid} = rationals:parse("").
format_test(_Config) ->
<<"3/4">> = rationals:format(rationals:new(3, 4)),
<<"3">> = rationals:format(rationals:new(3, 1)),
<<"-3/4">> = rationals:format(rationals:new(-3, 4)),
<<"0">> = rationals:format(rationals:zero()).
from_integer_test(_Config) ->
{5, 1} = rationals:ratio(rationals:from_integer(5)),
true = rationals:is_integer(rationals:from_integer(5)).
round_trip_test(_Config) ->
{ok, G} = rationals:parse(rationals:format(rationals:new(7, 12))),
eq = rationals:compare(G, rationals:new(7, 12)).
mediant_test(_Config) ->
{2, 5} = rationals:ratio(rationals:mediant(rationals:new(1, 2), rationals:new(1, 3))),
eq = rationals:compare(
rationals:mediant(rationals:new(2, 4), rationals:new(1, 3)),
rationals:new(2, 5)
),
M = rationals:mediant(rationals:new(1, 3), rationals:new(1, 2)),
lt = rationals:compare(rationals:new(1, 3), M),
lt = rationals:compare(M, rationals:new(1, 2)).
is_reduced_test(_Config) ->
true = rationals:is_reduced(rationals:new(1, 2)),
true = rationals:is_reduced(rationals:new(1, -2)),
true = rationals:is_reduced(rationals:new(0, 1)),
false = rationals:is_reduced(rationals:new(2, 4)),
false = rationals:is_reduced(rationals:new(0, 5)).
is_unit_fraction_test(_Config) ->
true = rationals:is_unit_fraction(rationals:new(1, 3)),
true = rationals:is_unit_fraction(rationals:new(2, 6)),
false = rationals:is_unit_fraction(rationals:new(2, 3)),
false = rationals:is_unit_fraction(rationals:new(-1, 2)),
false = rationals:is_unit_fraction(rationals:zero()).
lcm_test(_Config) ->
12 = rationals:lcm(4, 6),
12 = rationals:lcm(-4, 6),
0 = rationals:lcm(0, 5),
0 = rationals:lcm(7, 0),
7 = rationals:lcm(7, 1).
continued_fraction_test(_Config) ->
[2, 3] = rationals:continued_fraction(rationals:new(7, 3)),
[0, 2] = rationals:continued_fraction(rationals:new(1, 2)),
[3] = rationals:continued_fraction(rationals:new(3, 1)),
[-3, 1, 2] = rationals:continued_fraction(rationals:new(-7, 3)).
from_continued_fraction_test(_Config) ->
eq = rationals:compare(rationals:from_continued_fraction([2, 3]), rationals:new(7, 3)),
eq = rationals:compare(rationals:from_continued_fraction([3]), rationals:new(3, 1)),
eq = rationals:compare(rationals:from_continued_fraction([-3, 1, 2]), rationals:new(-7, 3)).
convergents_test(_Config) ->
C1 = rationals:convergents(rationals:new(7, 3)),
2 = length(C1),
eq = rationals:compare(lists:last(C1), rationals:new(7, 3)),
eq = rationals:compare(hd(C1), rationals:new(2, 1)),
C2 = rationals:convergents(rationals:new(3, 1)),
1 = length(C2),
eq = rationals:compare(hd(C2), rationals:new(3, 1)).
rationalize_test(_Config) ->
{1, 2} = rationals:ratio(rationals:rationalize(0.5, 0.01)),
{1, 3} = rationals:ratio(rationals:rationalize(0.333333, 0.001)),
{2, 1} = rationals:ratio(rationals:rationalize(2.5, 0.5)),
{0, 1} = rationals:ratio(rationals:rationalize(0.0, 0.5)),
{-1, 2} = rationals:ratio(rationals:rationalize(-0.5, 0.01)).
decimal_expansion_test(_Config) ->
{<<"0.25">>, <<>>} = rationals:decimal_expansion(rationals:new(1, 4)),
{<<"0.5">>, <<>>} = rationals:decimal_expansion(rationals:new(1, 2)),
{<<"0.">>, <<"3">>} = rationals:decimal_expansion(rationals:new(1, 3)),
{<<"0.1">>, <<"6">>} = rationals:decimal_expansion(rationals:new(1, 6)),
{<<"0.">>, <<"285714">>} = rationals:decimal_expansion(rationals:new(2, 7)),
{<<"2.">>, <<"3">>} = rationals:decimal_expansion(rationals:new(7, 3)),
{<<"3">>, <<>>} = rationals:decimal_expansion(rationals:new(3, 1)),
{<<"-0.">>, <<"3">>} = rationals:decimal_expansion(rationals:new(-1, 3)),
{<<"0">>, <<>>} = rationals:decimal_expansion(rationals:zero()).
egyptian_test(_Config) ->
E1 = rationals:egyptian(rationals:new(2, 3)),
2 = length(E1),
eq = rationals:compare(hd(E1), rationals:new(1, 2)),
eq = rationals:compare(lists:last(E1), rationals:new(1, 6)),
E2 = rationals:egyptian(rationals:new(3, 4)),
2 = length(E2),
eq = rationals:compare(hd(E2), rationals:new(1, 2)),
eq = rationals:compare(lists:last(E2), rationals:new(1, 4)),
[] = rationals:egyptian(rationals:zero()).
farey_test(_Config) ->
F1 = rationals:farey(1),
[{0, 1}, {1, 1}] = [rationals:ratio(X) || X <- F1],
F2 = rationals:farey(2),
[{0, 1}, {1, 2}, {1, 1}] = [rationals:ratio(X) || X <- F2],
F3 = rationals:farey(3),
[{0, 1}, {1, 3}, {1, 2}, {2, 3}, {1, 1}] = [rationals:ratio(X) || X <- F3].