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
|
const isLittleEndian = new Uint8Array(new Uint16Array([1]).buffer)[0] === 1;
function fromRawBits(s) {
let bits = s.split(" ").map(n => parseInt(n, 16));
assertEq(bits.length, 8);
if (isLittleEndian) {
bits.reverse();
}
return new Float64Array(new Uint8Array(bits).buffer)[0];
}
function toRawBits(d) {
let bits = [...new Uint8Array(new Float64Array([d]).buffer)];
if (isLittleEndian) {
bits.reverse();
}
return bits.map(n => n.toString(16).padStart(2, "0")).join(" ");
}
assertEq(fromRawBits("7f ef ff ff ff ff ff ff"), Number.MAX_VALUE);
assertEq(toRawBits(Number.MAX_VALUE), "7f ef ff ff ff ff ff ff");
assertEq(fromRawBits("00 00 00 00 00 00 00 01"), Number.MIN_VALUE);
assertEq(toRawBits(Number.MIN_VALUE), "00 00 00 00 00 00 00 01");
let values = [
0, 0.000001, 0.1, 0.125, 1/6, 0.25, 0.3, 1/3, 0.5, 2/3, 0.8, 0.9,
1, 2, 3, 4, 5, 10, 14, 15, 16,
100.1, 100.2,
Number.MAX_SAFE_INTEGER + 4,
Number.MAX_SAFE_INTEGER + 3,
Number.MAX_SAFE_INTEGER + 2,
Number.MAX_SAFE_INTEGER + 1,
Number.MAX_SAFE_INTEGER,
Number.MAX_SAFE_INTEGER - 1,
Number.MAX_SAFE_INTEGER - 2,
Number.MAX_SAFE_INTEGER - 3,
Number.MAX_SAFE_INTEGER - 4,
// Largest normal (Number.MAX_VALUE)
fromRawBits("7f ef ff ff ff ff ff ff"),
fromRawBits("7f ef ff ff ff ff ff fe"),
fromRawBits("7f ef ff ff ff ff ff fd"),
fromRawBits("7f ef ff ff ff ff ff fc"),
fromRawBits("7f ef ff ff ff ff ff fb"),
fromRawBits("7f ef ff ff ff ff ff fa"),
fromRawBits("7f ef ff ff ff ff ff f9"),
fromRawBits("7f ef ff ff ff ff ff f8"),
fromRawBits("7f ef ff ff ff ff ff f7"),
fromRawBits("7f ef ff ff ff ff ff f6"),
fromRawBits("7f ef ff ff ff ff ff f5"),
fromRawBits("7f ef ff ff ff ff ff f4"),
fromRawBits("7f ef ff ff ff ff ff f3"),
fromRawBits("7f ef ff ff ff ff ff f2"),
fromRawBits("7f ef ff ff ff ff ff f1"),
fromRawBits("7f ef ff ff ff ff ff f0"),
// Smallest subnormal (Number.MIN_VALUE)
fromRawBits("00 00 00 00 00 00 00 01"),
fromRawBits("00 00 00 00 00 00 00 02"),
fromRawBits("00 00 00 00 00 00 00 03"),
fromRawBits("00 00 00 00 00 00 00 04"),
fromRawBits("00 00 00 00 00 00 00 05"),
fromRawBits("00 00 00 00 00 00 00 06"),
fromRawBits("00 00 00 00 00 00 00 07"),
fromRawBits("00 00 00 00 00 00 00 08"),
fromRawBits("00 00 00 00 00 00 00 09"),
fromRawBits("00 00 00 00 00 00 00 0a"),
fromRawBits("00 00 00 00 00 00 00 0b"),
fromRawBits("00 00 00 00 00 00 00 0c"),
fromRawBits("00 00 00 00 00 00 00 0d"),
fromRawBits("00 00 00 00 00 00 00 0e"),
fromRawBits("00 00 00 00 00 00 00 0f"),
// Largest subnormal
fromRawBits("00 0f ff ff ff ff ff ff"),
fromRawBits("00 0f ff ff ff ff ff fe"),
fromRawBits("00 0f ff ff ff ff ff fd"),
fromRawBits("00 0f ff ff ff ff ff fc"),
fromRawBits("00 0f ff ff ff ff ff fb"),
fromRawBits("00 0f ff ff ff ff ff fa"),
fromRawBits("00 0f ff ff ff ff ff f9"),
fromRawBits("00 0f ff ff ff ff ff f8"),
fromRawBits("00 0f ff ff ff ff ff f7"),
fromRawBits("00 0f ff ff ff ff ff f6"),
fromRawBits("00 0f ff ff ff ff ff f5"),
fromRawBits("00 0f ff ff ff ff ff f4"),
fromRawBits("00 0f ff ff ff ff ff f3"),
fromRawBits("00 0f ff ff ff ff ff f2"),
fromRawBits("00 0f ff ff ff ff ff f1"),
fromRawBits("00 0f ff ff ff ff ff f0"),
// Least positive normal
fromRawBits("00 10 00 00 00 00 00 00"),
fromRawBits("00 10 00 00 00 00 00 01"),
fromRawBits("00 10 00 00 00 00 00 02"),
fromRawBits("00 10 00 00 00 00 00 03"),
fromRawBits("00 10 00 00 00 00 00 04"),
fromRawBits("00 10 00 00 00 00 00 05"),
fromRawBits("00 10 00 00 00 00 00 06"),
fromRawBits("00 10 00 00 00 00 00 07"),
fromRawBits("00 10 00 00 00 00 00 08"),
fromRawBits("00 10 00 00 00 00 00 09"),
fromRawBits("00 10 00 00 00 00 00 0a"),
fromRawBits("00 10 00 00 00 00 00 0b"),
fromRawBits("00 10 00 00 00 00 00 0c"),
fromRawBits("00 10 00 00 00 00 00 0d"),
fromRawBits("00 10 00 00 00 00 00 0e"),
fromRawBits("00 10 00 00 00 00 00 0f"),
Infinity,
NaN,
Math.E, Math.LN10, Math.LN2, Math.LOG10E, Math.LOG2E,
Math.PI, Math.SQRT1_2, Math.SQRT2,
];
// Also test with sign bit set.
values = values.concat(values.map(x => -x));
function mod(n, d) {
with ({}); // disable Ion
return n % d;
}
function makeTest(divisor) {
function test() {
let expected = values.map(x => mod(x, divisor));
for (let i = 0; i < 2000; ++i) {
let j = i % values.length;
assertEq(values[j] % divisor, expected[j]);
}
}
// Create a new function for each divisor to ensure we have proper compile-time constants.
return Function(`return ${test.toString().replaceAll("divisor", divisor)}`)();
}
// The optimisation is used for power of two values up to 2^31.
for (let i = 0; i <= 31; ++i) {
let divisor = 2 ** i;
let f = makeTest(divisor);
f();
}
// Also cover some cases which don't trigger the optimisation
for (let divisor of [-3, -2, -1, -0.5, 0, 0.5, 3, 5, 10]) {
let f = makeTest(divisor);
f();
}
|
