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
|
func main()
# Basic arithmetic
n := 1.5
assert n == 1.5
assert n + n == 3.0
assert n * 2. == 3.0
assert n - n == 0.0
assert n / 2. == 0.75
# Exact rational arithmetic
third := 1. / 3.
assert third * 3. == 1.
assert (third + third + third) == 1.
# Decimal representation
assert 0.1 + 0.2 == 0.3
assert Text(0.1 + 0.2) == "0.3"
# Fraction representation
assert Text(1. / 3.) == "1/3"
assert Text(5. / 7.) == "5/7"
# Terminating decimals
assert Text(3. / 4.) == "0.75"
assert Text(1. / 8.) == "0.125"
# Square root
assert (4.).sqrt() == 2.
assert (9.).sqrt() == 3.
assert (1. / 4.).sqrt() == 1. / 2.
# Symbolic sqrt simplification
sqrt2 := (2.).sqrt()
assert (sqrt2 * sqrt2) == 2.
# Rounding
assert sqrt2.rounded_to(0.01) == 1.41
assert sqrt2.rounded_to(0.001) == 1.414
assert (1234.).rounded_to(100.) == 1200.
assert (1250.).rounded_to(100.) == 1300.
# Trigonometric functions
assert (0.).sin() == 0.
assert (0.).cos() == 1.
assert (0.).tan() == 0.
# Exponential and logarithm
assert (0.).exp() == 1.
# Absolute value
assert (-5.).abs() == 5.
assert (5.).abs() == 5.
assert (-3. / 4.).abs() == 3. / 4.
# Floor and ceiling
assert (2.7).floor() == 2.
assert (2.3).floor() == 2.
assert (-2.3).floor() == -3.
assert (2.3).ceil() == 3.
assert (2.7).ceil() == 3.
assert (-2.3).ceil() == -2.
# Floor/ceil on rationals
assert (7. / 3.).floor() == 2.
assert (7. / 3.).ceil() == 3.
assert (-7. / 3.).floor() == -3.
assert (-7. / 3.).ceil() == -2.
# Modulo
assert 7. mod 3. == 1.
assert -7. mod 3. == 2. # Euclidean division
assert 7. mod -3. == 1.
assert 2.5 mod 1.0 == 0.5
# Mod1
assert 3.7 mod1 2. == 1.7
# Mix (linear interpolation)
assert (0.25).mix(10., 20.) == 12.5
assert (0.0).mix(10., 20.) == 10.
assert (1.0).mix(10., 20.) == 20.
assert (0.5).mix(10., 20.) == 15.
# Is between
assert (5.).is_between(1., 10.)
assert (1.).is_between(1., 10.)
assert (10.).is_between(1., 10.)
assert (0.).is_between(1., 10.) == no
assert (11.).is_between(1., 10.) == no
# Clamped
assert (5.).clamped(1., 10.) == 5.
assert (0.).clamped(1., 10.) == 1.
assert (15.).clamped(1., 10.) == 10.
assert (1.).clamped(1., 10.) == 1.
assert (10.).clamped(1., 10.) == 10.
# Comparison
assert 3. > 2.
assert 2. < 3.
assert 3. >= 3.
assert 3. <= 3.
assert (1. / 3.) < (1. / 2.)
# Negation
assert -(5.) == -5.
assert -(1. / 3.) == -1. / 3.
# Power
assert (2.).power(3.) == 8.
assert (2.).power(0.) == 1.
# Parsing
assert Real.parse("123") == 123.
assert Real.parse("1.5") == 1.5
assert Real.parse("0.3333333333333333") == 0.3333333333333333
assert Real.parse("-5") == -5.
assert Real.parse("-2.5") == -2.5
# None handling
none_real : Real? = none
assert none_real == none
assert Real.parse("not_a_number") == none
assert Real.parse("") == none
# Large integers
big := (99999999999999999999999999999999.)
assert big + 1. == (100000000000000000000000000000000.)
# >> bigger := 1e999999999999999999999999999999999999999999
# assert bigger + bigger == 2.*bigger
# Mixed operations preserve exactness
result := 1. / 3. + 2. / 3.
assert result == 1.
# Symbolic expressions maintain structure
expr := sqrt2 + 1.
assert Text(expr) == "(sqrt(2) + 1)"
print("All Real tests passed!")
|
