g_math 0.4.2

Multi-domain fixed-point arithmetic with geometric extension: Lie groups, manifolds, ODE solvers, tensors, fiber bundles — zero-float, 0 ULP transcendentals
Documentation 
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

// mpmath-validated reference values for Q16.16 realtime profile
// Generated with mpmath at 50-digit precision
// IMPORTANT: expected values computed from quantized Q16.16 input through Q64.64 native
// This matches the actual g_math computation path: parse → Q16.16 → Q64.64 → compute → Q16.16

pub const Q16_REFS: &[(&str, i32, i32, &str)] = &[
    ("0.5", 32768_i32, 108051_i32, "exp"),
    ("1.0", 65536_i32, 178145_i32, "exp"),
    ("-0.5", -32768_i32, 39750_i32, "exp"),
    ("2.0", 131072_i32, 484249_i32, "exp"),
    ("-1.0", -65536_i32, 24109_i32, "exp"),
    ("0.1", 6554_i32, 72428_i32, "exp"),
    ("0.5", 32768_i32, -45426_i32, "ln"),
    ("1.0", 65536_i32, 0_i32, "ln"),
    ("2.0", 131072_i32, 45426_i32, "ln"),
    ("3.0", 196608_i32, 71999_i32, "ln"),
    ("0.1", 6554_i32, -150902_i32, "ln"),
    ("10.0", 655360_i32, 150902_i32, "ln"),
    ("0.25", 16384_i32, 32768_i32, "sqrt"),
    ("1.0", 65536_i32, 65536_i32, "sqrt"),
    ("2.0", 131072_i32, 92682_i32, "sqrt"),
    ("4.0", 262144_i32, 131072_i32, "sqrt"),
    ("9.0", 589824_i32, 196608_i32, "sqrt"),
    ("0.5", 32768_i32, 46341_i32, "sqrt"),
    ("0.0", 0_i32, 0_i32, "sin"),
    ("0.5", 32768_i32, 31420_i32, "sin"),
    ("1.0", 65536_i32, 55147_i32, "sin"),
    ("-1.0", -65536_i32, -55147_i32, "sin"),
    ("1.5", 98304_i32, 65372_i32, "sin"),
    ("3.0", 196608_i32, 9248_i32, "sin"),
    ("0.0", 0_i32, 65536_i32, "cos"),
    ("0.5", 32768_i32, 57513_i32, "cos"),
    ("1.0", 65536_i32, 35409_i32, "cos"),
    ("-1.0", -65536_i32, 35409_i32, "cos"),
    ("1.5", 98304_i32, 4636_i32, "cos"),
    ("2.0", 131072_i32, -27273_i32, "cos"),
    ("0.0", 0_i32, 0_i32, "tan"),
    ("0.5", 32768_i32, 35802_i32, "tan"),
    ("1.0", 65536_i32, 102066_i32, "tan"),
    ("-0.5", -32768_i32, -35802_i32, "tan"),
    ("0.75", 49152_i32, 61053_i32, "tan"),
    ("-0.75", -49152_i32, -61053_i32, "tan"),
    ("0.0", 0_i32, 0_i32, "atan"),
    ("0.5", 32768_i32, 30386_i32, "atan"),
    ("1.0", 65536_i32, 51472_i32, "atan"),
    ("-1.0", -65536_i32, -51472_i32, "atan"),
    ("0.1", 6554_i32, 6532_i32, "atan"),
    ("100.0", 6553600_i32, 102288_i32, "atan"),
    ("0.0", 0_i32, 0_i32, "asin"),
    ("0.5", 32768_i32, 34315_i32, "asin"),
    ("-0.5", -32768_i32, -34315_i32, "asin"),
    ("0.9", 58982_i32, 73385_i32, "asin"),
    ("-0.9", -58982_i32, -73385_i32, "asin"),
    ("0.1", 6554_i32, 6565_i32, "asin"),
    ("0.0", 0_i32, 102944_i32, "acos"),
    ("0.5", 32768_i32, 68629_i32, "acos"),
    ("-0.5", -32768_i32, 137258_i32, "acos"),
    ("0.9", 58982_i32, 29558_i32, "acos"),
    ("-0.9", -58982_i32, 176329_i32, "acos"),
    ("0.1", 6554_i32, 96379_i32, "acos"),
    ("0.0", 0_i32, 0_i32, "sinh"),
    ("0.5", 32768_i32, 34151_i32, "sinh"),
    ("1.0", 65536_i32, 77018_i32, "sinh"),
    ("-1.0", -65536_i32, -77018_i32, "sinh"),
    ("2.0", 131072_i32, 237690_i32, "sinh"),
    ("-0.5", -32768_i32, -34151_i32, "sinh"),
    ("0.0", 0_i32, 65536_i32, "cosh"),
    ("0.5", 32768_i32, 73900_i32, "cosh"),
    ("1.0", 65536_i32, 101127_i32, "cosh"),
    ("-1.0", -65536_i32, 101127_i32, "cosh"),
    ("2.0", 131072_i32, 246559_i32, "cosh"),
    ("-0.5", -32768_i32, 73900_i32, "cosh"),
    ("0.0", 0_i32, 0_i32, "tanh"),
    ("0.5", 32768_i32, 30285_i32, "tanh"),
    ("1.0", 65536_i32, 49912_i32, "tanh"),
    ("-1.0", -65536_i32, -49912_i32, "tanh"),
    ("2.0", 131072_i32, 63179_i32, "tanh"),
    ("-0.5", -32768_i32, -30285_i32, "tanh"),
    ("0.0", 0_i32, 0_i32, "asinh"),
    ("0.5", 32768_i32, 31537_i32, "asinh"),
    ("1.0", 65536_i32, 57762_i32, "asinh"),
    ("-1.0", -65536_i32, -57762_i32, "asinh"),
    ("2.0", 131072_i32, 94610_i32, "asinh"),
    ("10.0", 655360_i32, 196492_i32, "asinh"),
    ("1.0", 65536_i32, 0_i32, "acosh"),
    ("1.5", 98304_i32, 63073_i32, "acosh"),
    ("2.0", 131072_i32, 86308_i32, "acosh"),
    ("3.0", 196608_i32, 115523_i32, "acosh"),
    ("10.0", 655360_i32, 196164_i32, "acosh"),
    ("1.1", 72090_i32, 29070_i32, "acosh"),
    ("0.0", 0_i32, 0_i32, "atanh"),
    ("0.5", 32768_i32, 35999_i32, "atanh"),
    ("-0.5", -32768_i32, -35999_i32, "atanh"),
    ("0.9", 58982_i32, 96483_i32, "atanh"),
    ("-0.9", -58982_i32, -96483_i32, "atanh"),
    ("0.1", 6554_i32, 6576_i32, "atanh"),
];