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
|
##
# Math Test
assert('Math.sin 0') do
check_float(Math.sin(0), 0)
end
assert('Math.sin PI/2') do
check_float(Math.sin(Math::PI / 2), 1)
end
assert('Fundamental trig identities') do
result = true
N = 15
N.times do |i|
a = Math::PI / N * i
ca = Math::PI / 2 - a
s = Math.sin(a)
c = Math.cos(a)
t = Math.tan(a)
result &= check_float(s, Math.cos(ca))
result &= check_float(t, 1 / Math.tan(ca))
result &= check_float(s ** 2 + c ** 2, 1)
result &= check_float(t ** 2 + 1, (1/c) ** 2)
result &= check_float((1/t) ** 2 + 1, (1/s) ** 2)
end
result
end
assert('Math.erf 0') do
check_float(Math.erf(0), 0)
end
assert('Math.exp 0') do
check_float(Math.exp(0), 1.0)
end
assert('Math.exp 1') do
check_float(Math.exp(1), 2.718281828459045)
end
assert('Math.exp 1.5') do
check_float(Math.exp(1.5), 4.4816890703380645)
end
assert('Math.log 1') do
check_float(Math.log(1), 0)
end
assert('Math.log E') do
check_float(Math.log(Math::E), 1.0)
end
assert('Math.log E**3') do
check_float(Math.log(Math::E**3), 3.0)
end
assert('Math.log2 1') do
check_float(Math.log2(1), 0.0)
end
assert('Math.log2 2') do
check_float(Math.log2(2), 1.0)
end
assert('Math.log10 1') do
check_float(Math.log10(1), 0.0)
end
assert('Math.log10 10') do
check_float(Math.log10(10), 1.0)
end
assert('Math.log10 10**100') do
check_float(Math.log10(10**100), 100.0)
end
assert('Math.cbrt') do
num = [-2.0, -1.0, 0.0, 1.0, 2.0]
cub = [-8, -1, 0, 1, 8]
result = true
cub.each_with_index do |v,i|
result &= check_float(Math.cbrt(v), num[i])
end
result
end
assert('Math.hypot') do
check_float(Math.hypot(3, 4), 5.0)
end
assert('Math.frexp 1234') do
n = 1234
fraction, exponent = Math.frexp(n)
check_float(Math.ldexp(fraction, exponent), n)
end
assert('Math.erf 1') do
check_float(Math.erf(1), 0.842700792949715)
end
assert('Math.erfc 1') do
check_float(Math.erfc(1), 0.157299207050285)
end
|
