1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
|
require File.expand_path('../../../spec_helper', __FILE__)
describe :rational_exponent, shared: true do
describe "when passed Rational" do
conflicts_with :Prime do
it "returns Rational(1) if the exponent is Rational(0)" do
(Rational(0) ** Rational(0)).should eql(Rational(1))
(Rational(1) ** Rational(0)).should eql(Rational(1))
(Rational(3, 4) ** Rational(0)).should eql(Rational(1))
(Rational(-1) ** Rational(0)).should eql(Rational(1))
(Rational(-3, 4) ** Rational(0)).should eql(Rational(1))
(Rational(bignum_value) ** Rational(0)).should eql(Rational(1))
(Rational(-bignum_value) ** Rational(0)).should eql(Rational(1))
end
it "returns self raised to the argument as a Rational if the exponent's denominator is 1" do
(Rational(3, 4) ** Rational(1, 1)).should eql(Rational(3, 4))
(Rational(3, 4) ** Rational(2, 1)).should eql(Rational(9, 16))
(Rational(3, 4) ** Rational(-1, 1)).should eql(Rational(4, 3))
(Rational(3, 4) ** Rational(-2, 1)).should eql(Rational(16, 9))
end
it "returns self raised to the argument as a Float if the exponent's denominator is not 1" do
(Rational(3, 4) ** Rational(4, 3)).should be_close(0.681420222312052, TOLERANCE)
(Rational(3, 4) ** Rational(-4, 3)).should be_close(1.46752322173095, TOLERANCE)
(Rational(3, 4) ** Rational(4, -3)).should be_close(1.46752322173095, TOLERANCE)
end
it "returns a complex number when self is negative and the passed argument is not 0" do
(Rational(-3, 4) ** Rational(-4, 3)).should be_close(Complex(-0.7337616108654732, 1.2709123906625817), TOLERANCE)
end
end
end
describe "when passed Integer" do
it "returns the Rational value of self raised to the passed argument" do
(Rational(3, 4) ** 4).should == Rational(81, 256)
(Rational(3, 4) ** -4).should == Rational(256, 81)
(Rational(-3, 4) ** -4).should == Rational(256, 81)
(Rational(3, -4) ** -4).should == Rational(256, 81)
(Rational(bignum_value, 4) ** 4).should == Rational(28269553036454149273332760011886696253239742350009903329945699220681916416, 1)
(Rational(3, bignum_value) ** -4).should == Rational(7237005577332262213973186563042994240829374041602535252466099000494570602496, 81)
(Rational(-bignum_value, 4) ** -4).should == Rational(1, 28269553036454149273332760011886696253239742350009903329945699220681916416)
(Rational(3, -bignum_value) ** -4).should == Rational(7237005577332262213973186563042994240829374041602535252466099000494570602496, 81)
end
conflicts_with :Prime do
it "returns Rational(1, 1) when the passed argument is 0" do
(Rational(3, 4) ** 0).should eql(Rational(1, 1))
(Rational(-3, 4) ** 0).should eql(Rational(1, 1))
(Rational(3, -4) ** 0).should eql(Rational(1, 1))
(Rational(bignum_value, 4) ** 0).should eql(Rational(1, 1))
(Rational(3, -bignum_value) ** 0).should eql(Rational(1, 1))
end
end
end
describe "when passed Bignum" do
# #5713
it "returns Rational(0) when self is Rational(0) and the exponent is positive" do
(Rational(0) ** bignum_value).should eql(Rational(0))
end
it "raises ZeroDivisionError when self is Rational(0) and the exponent is negative" do
lambda { Rational(0) ** -bignum_value }.should raise_error(ZeroDivisionError)
end
it "returns Rational(1) when self is Rational(1)" do
(Rational(1) ** bignum_value).should eql(Rational(1))
(Rational(1) ** -bignum_value).should eql(Rational(1))
end
it "returns Rational(1) when self is Rational(-1) and the exponent is positive and even" do
(Rational(-1) ** bignum_value(0)).should eql(Rational(1))
(Rational(-1) ** bignum_value(2)).should eql(Rational(1))
end
it "returns Rational(-1) when self is Rational(-1) and the exponent is positive and odd" do
(Rational(-1) ** bignum_value(1)).should eql(Rational(-1))
(Rational(-1) ** bignum_value(3)).should eql(Rational(-1))
end
it "returns positive Infinity when self is > 1" do
(Rational(2) ** bignum_value).infinite?.should == 1
(Rational(fixnum_max) ** bignum_value).infinite?.should == 1
end
it "returns 0.0 when self is > 1 and the exponent is negative" do
(Rational(2) ** -bignum_value).should eql(0.0)
(Rational(fixnum_max) ** -bignum_value).should eql(0.0)
end
# Fails on linux due to pow() bugs in glibc: http://sources.redhat.com/bugzilla/show_bug.cgi?id=3866
platform_is_not :linux do
it "returns positive Infinity when self < -1" do
(Rational(-2) ** bignum_value).infinite?.should == 1
(Rational(-2) ** (bignum_value + 1)).infinite?.should == 1
(Rational(fixnum_min) ** bignum_value).infinite?.should == 1
end
it "returns 0.0 when self is < -1 and the exponent is negative" do
(Rational(-2) ** -bignum_value).should eql(0.0)
(Rational(fixnum_min) ** -bignum_value).should eql(0.0)
end
end
end
describe "when passed Float" do
it "returns self converted to Float and raised to the passed argument" do
(Rational(3, 1) ** 3.0).should eql(27.0)
(Rational(3, 1) ** 1.5).should be_close(5.19615242270663, TOLERANCE)
(Rational(3, 1) ** -1.5).should be_close(0.192450089729875, TOLERANCE)
end
it "returns a complex number if self is negative and the passed argument is not 0" do
(Rational(-3, 2) ** 1.5).should be_close(Complex(-3.374618290464398e-16, -1.8371173070873836), TOLERANCE)
(Rational(3, -2) ** 1.5).should be_close(Complex(-3.374618290464398e-16, -1.8371173070873836), TOLERANCE)
(Rational(3, -2) ** -1.5).should be_close(Complex(-9.998869008783402e-17, 0.5443310539518174), TOLERANCE)
end
it "returns Complex(1.0) when the passed argument is 0.0" do
(Rational(3, 4) ** 0.0).should == Complex(1.0)
(Rational(-3, 4) ** 0.0).should == Complex(1.0)
(Rational(-3, 4) ** 0.0).should == Complex(1.0)
end
end
it "calls #coerce on the passed argument with self" do
rational = Rational(3, 4)
obj = mock("Object")
obj.should_receive(:coerce).with(rational).and_return([1, 2])
rational ** obj
end
it "calls #** on the coerced Rational with the coerced Object" do
rational = Rational(3, 4)
coerced_rational = mock("Coerced Rational")
coerced_rational.should_receive(:**).and_return(:result)
coerced_obj = mock("Coerced Object")
obj = mock("Object")
obj.should_receive(:coerce).and_return([coerced_rational, coerced_obj])
(rational ** obj).should == :result
end
it "raises ZeroDivisionError for Rational(0, 1) passed a negative Integer" do
[-1, -4, -9999].each do |exponent|
lambda { Rational(0, 1) ** exponent }.should raise_error(ZeroDivisionError, "divided by 0")
end
end
it "raises ZeroDivisionError for Rational(0, 1) passed a negative Rational with denominator 1" do
[Rational(-1, 1), Rational(-3, 1)].each do |exponent|
lambda { Rational(0, 1) ** exponent }.should raise_error(ZeroDivisionError, "divided by 0")
end
end
# #7513
it "raises ZeroDivisionError for Rational(0, 1) passed a negative Rational" do
lambda { Rational(0, 1) ** Rational(-3, 2) }.should raise_error(ZeroDivisionError, "divided by 0")
end
platform_is_not :solaris do # See https://github.com/ruby/spec/issues/134
it "returns Infinity for Rational(0, 1) passed a negative Float" do
[-1.0, -3.0, -3.14].each do |exponent|
(Rational(0, 1) ** exponent).infinite?.should == 1
end
end
end
end
|
