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

use std::ops;
use std::cmp;
use std::fmt;

#[derive(Debug, Clone, Copy, PartialEq, Eq, Hash)]
pub struct FixFloat(i64);

impl FixFloat {
    pub const FRACTION_BITS: i64 = 10;
    pub const SQR_FRACTION_BITS: i64 = 20;
    pub const CUBE_FRACTION_BITS: i64 = 30;
    pub const TETRA_FRACTION_BITS: i64 = 40;
    pub const PENTA_FRACTION_BITS: i64 = 50;
    pub const MAX_BITS: i64 = (64 >> 1) - 1;
    pub const MAX_FIX: i64 = (1 << Self::MAX_BITS) - 1;
    pub const MIN_FIX: i64 = -Self::MAX_FIX;
    pub const ZERO: FixFloat = FixFloat(0);
    pub const UNIT: i64 = 1 << Self::FRACTION_BITS;
    pub const SQR_UNIT: i64 = 1 << Self::SQR_FRACTION_BITS;
    pub const CUBE_UNIT: i64 = 1 << Self::CUBE_FRACTION_BITS;
    pub const HALF: i64 = 1 << (Self::FRACTION_BITS - 1);
    pub const PI: i64 = 3217;

    pub fn value(&self) -> i64 {
        self.0
    }

    pub fn new_number(value: i64) -> Self {
        FixFloat(value << Self::FRACTION_BITS)
    }

    pub fn new_f64(value: f64) -> Self {
        FixFloat((value * 1024.0 + 0.001) as i64)
    }

    pub fn new_f32(value: f32) -> Self {
        FixFloat((value * 1024.0 + 0.001) as i64)
    }

    pub fn new_i64(value: i64) -> Self {
        FixFloat(value)
    }

    pub fn div(self, value: FixFloat) -> FixFloat {
        FixFloat((self.0 << Self::FRACTION_BITS) / value.0)
    }

    pub fn mul(self, value: FixFloat) -> FixFloat {
        FixFloat((self.0 * value.0) / Self::UNIT)
    }

    pub fn sqr(self) -> FixFloat {
        FixFloat((self.0 * self.0) >> Self::FRACTION_BITS)
    }

    pub fn sqrt(self) -> FixFloat {
        FixFloat(fast_square_root(self.0 << Self::FRACTION_BITS))
    }

    pub fn double(self) -> f64 {
        self.0 as f64 / Self::UNIT as f64
    }

    pub fn float(self) -> f32 {
        self.0 as f32 / Self::UNIT as f32
    }

    pub fn int(self) -> FixFloat {
        FixFloat(self.0 >> Self::FRACTION_BITS)
    }

    pub fn clamp(self, min: FixFloat, max: FixFloat) -> FixFloat {
        FixFloat(std::cmp::min(max.0, std::cmp::max(min.0, self.0)))
    }
    pub fn invert(self) -> FixFloat {
        FixFloat(Self::SQR_UNIT / self.0)
    }
}

pub fn normalize(value: i64) -> FixFloat {
    FixFloat(value / FixFloat::UNIT)
}
pub fn fast_normalize(value: i64) -> FixFloat {
    FixFloat(value >> FixFloat::FRACTION_BITS)
}
pub fn sqr_normalize(value: i64) -> FixFloat {
    FixFloat(value / FixFloat::SQR_UNIT)
}

pub fn fix(value: f64) -> FixFloat {
    FixFloat((value * FixFloat::UNIT as f64) as i64)
}

pub fn fast_square_root(value: i64) -> i64 {
    let a = (value as f64).sqrt() as i64;
    let b = a + 1;

    if b * b > value { a } else { b }
}

impl ops::Neg for FixFloat {
    type Output = Self;

    fn neg(self) -> Self::Output {
        FixFloat(-self.0)
    }
}

impl ops::Add for FixFloat {
    type Output = Self;

    fn add(self, other: Self) -> Self {
        FixFloat(self.0 + other.0)
    }
}

impl ops::Sub for FixFloat {
    type Output = Self;

    fn sub(self, other: Self) -> Self {
        FixFloat(self.0 - other.0)
    }
}

impl ops::Mul for FixFloat {

    type Output = Self;

    fn mul(self, rhs: Self) -> Self::Output {
        normalize(self.0 * rhs.0)
    }
}

impl ops::Div for FixFloat {

    type Output = Self;

    fn div(self, rhs: Self) -> Self::Output {
        normalize(self.0 * rhs.0)
    }
}

impl cmp::PartialOrd for FixFloat {
    fn partial_cmp(&self, other: &Self) -> Option<cmp::Ordering> {
        Some(self.cmp(other))
    }
}

impl Ord for FixFloat {
    fn cmp(&self, other: &Self) -> cmp::Ordering {
        self.0.cmp(&other.0)
    }
}

impl fmt::Display for FixFloat {
    fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result {
        write!(f, "{}", self.0)
    }
}