embedded-dsp 0.5.1

A no_std Rust digital signal processing library for microcontrollers, embedded systems, and real-time signals.
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
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
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189

//! CORDIC (Coordinate Rotation Digital Computer) pure-integer arithmetic engine.
//!
//! Computes trigonometric functions (`sin`, `cos`, `atan2`), polar/Cartesian vector
//! rotations, and square roots using only additions, subtractions, and bit shifts.
//! Ideal for ultra-low-power microcontrollers without hardware multipliers or FPU.

use crate::types::{q15, q31};

/// CORDIC gain compensation factor in Q15 format: `0.607252935 * 32768 ≈ 19898`.
pub const CORDIC_K_Q15: q15 = q15::from_bits(19898);

/// CORDIC gain compensation factor in Q31 format: `0.607252935 * 2^31 ≈ 1304065792`.
pub const CORDIC_K_Q31: q31 = q31::from_bits(1304065792);

/// Number of CORDIC iterations.
pub const CORDIC_ITERATIONS: usize = 16;

/// Precomputed arctangent lookup table in Q15 radians (`atan(2^-i) * 32768`).
pub const ATAN_TABLE_Q15: [q15; 16] = [
    q15::from_bits(25736), // atan(1.0) = pi/4 ≈ 0.785398
    q15::from_bits(15193), // atan(0.5) ≈ 0.463648
    q15::from_bits(8027),  // atan(0.25) ≈ 0.244979
    q15::from_bits(4075),  // atan(0.125) ≈ 0.124355
    q15::from_bits(2045),  // atan(0.0625) ≈ 0.062419
    q15::from_bits(1024),  // atan(0.03125) ≈ 0.031240
    q15::from_bits(512),   // atan(0.015625) ≈ 0.015624
    q15::from_bits(256),   // atan(0.0078125) ≈ 0.007812
    q15::from_bits(128),   // atan(0.00390625)
    q15::from_bits(64),    // atan(0.001953125)
    q15::from_bits(32),    // atan(0.0009765625)
    q15::from_bits(16),    // atan(0.00048828125)
    q15::from_bits(8),     // atan(0.000244140625)
    q15::from_bits(4),     // atan(0.0001220703125)
    q15::from_bits(2),     // atan(0.00006103515625)
    q15::from_bits(1),     // atan(0.000030517578125)
];

/// Precomputed arctangent lookup table in Q31 radians (`atan(2^-i) * 2^31`).
pub const ATAN_TABLE_Q31: [q31; 16] = [
    q31::from_bits(1686629713), // atan(1.0)
    q31::from_bits(995716174),  // atan(0.5)
    q31::from_bits(526057390),  // atan(0.25)
    q31::from_bits(267073177),  // atan(0.125)
    q31::from_bits(134079828),  // atan(0.0625)
    q31::from_bits(67098489),   // atan(0.03125)
    q31::from_bits(33556754),   // atan(0.015625)
    q31::from_bits(16779316),   // atan(0.0078125)
    q31::from_bits(8389776),    // atan(0.00390625)
    q31::from_bits(4194903),    // atan(0.001953125)
    q31::from_bits(2097453),    // atan(0.0009765625)
    q31::from_bits(1048727),    // atan(0.00048828125)
    q31::from_bits(524363),     // atan(0.000244140625)
    q31::from_bits(262182),     // atan(0.0001220703125)
    q31::from_bits(131091),     // atan(0.00006103515625)
    q31::from_bits(65545),      // atan(0.000030517578125)
];

/// Computes `(sin(θ), cos(θ))` for an angle in Q15 radians (`[-π/2, π/2]`).
///
/// Returns `(sin, cos)` as Q15 format.
pub fn cordic_sin_cos_q15(angle_rad: q15) -> (q15, q15) {
    // Normal rotation mode: initialize x = K, y = 0
    let mut x: i32 = CORDIC_K_Q15.to_bits() as i32;
    let mut y: i32 = 0;
    let mut z: i32 = angle_rad.to_bits() as i32;

    for i in 0..CORDIC_ITERATIONS {
        let (x_new, y_new, z_new) = if z >= 0 {
            (
                x - (y >> i),
                y + (x >> i),
                z - (ATAN_TABLE_Q15[i].to_bits() as i32),
            )
        } else {
            (
                x + (y >> i),
                y - (x >> i),
                z + (ATAN_TABLE_Q15[i].to_bits() as i32),
            )
        };
        x = x_new;
        y = y_new;
        z = z_new;
    }

    let sin = q15::from_bits(y.clamp(i16::MIN as i32, i16::MAX as i32) as i16);
    let cos = q15::from_bits(x.clamp(i16::MIN as i32, i16::MAX as i32) as i16);
    (sin, cos)
}

/// Computes `(sin(θ), cos(θ))` for an angle in Q31 radians.
pub fn cordic_sin_cos_q31(angle_rad: q31) -> (q31, q31) {
    let mut x: i64 = CORDIC_K_Q31.to_bits() as i64;
    let mut y: i64 = 0;
    let mut z: i64 = angle_rad.to_bits() as i64;

    for i in 0..CORDIC_ITERATIONS {
        let (x_new, y_new, z_new) = if z >= 0 {
            (
                x - (y >> i),
                y + (x >> i),
                z - (ATAN_TABLE_Q31[i].to_bits() as i64),
            )
        } else {
            (
                x + (y >> i),
                y - (x >> i),
                z + (ATAN_TABLE_Q31[i].to_bits() as i64),
            )
        };
        x = x_new;
        y = y_new;
        z = z_new;
    }

    let sin = q31::from_bits(y.clamp(i32::MIN as i64, i32::MAX as i64) as i32);
    let cos = q31::from_bits(x.clamp(i32::MIN as i64, i32::MAX as i64) as i32);
    (sin, cos)
}

/// Converts Cartesian coordinates `(x, y)` to Polar `(magnitude, angle_rad)` using CORDIC vectoring mode.
///
/// Returns `(magnitude, angle_rad)` in Q15 format.
pub fn cordic_cartesian_to_polar_q15(x_in: q15, y_in: q15) -> (q15, q15) {
    if x_in == q15::ZERO && y_in == q15::ZERO {
        return (q15::ZERO, q15::ZERO);
    }

    let mut x = (x_in.to_bits() as i32).abs();
    let mut y = y_in.to_bits() as i32;
    let mut z: i32 = 0;

    for i in 0..CORDIC_ITERATIONS {
        let (x_new, y_new, z_new) = if y < 0 {
            (
                x - (y >> i),
                y + (x >> i),
                z - (ATAN_TABLE_Q15[i].to_bits() as i32),
            )
        } else {
            (
                x + (y >> i),
                y - (x >> i),
                z + (ATAN_TABLE_Q15[i].to_bits() as i32),
            )
        };
        x = x_new;
        y = y_new;
        z = z_new;
    }

    // Compensate gain K: magnitude = x * K
    let mag = q15::from_bits(
        ((x * CORDIC_K_Q15.to_bits() as i32) >> 15).clamp(0, i16::MAX as i32) as i16,
    );
    let mut angle = q15::from_bits(z.clamp(i16::MIN as i32, i16::MAX as i32) as i16);
    if x_in < q15::ZERO {
        angle = if angle >= q15::ZERO {
            q15::from_bits(
                (25736 * 4 - angle.to_bits() as i32).clamp(i16::MIN as i32, i16::MAX as i32)
                    as i16,
            )
        } else {
            q15::from_bits(
                (-25736 * 4 - angle.to_bits() as i32).clamp(i16::MIN as i32, i16::MAX as i32)
                    as i16,
            )
        };
    }

    (mag, angle)
}

/// Four-quadrant inverse tangent `atan2(y, x)` computed via CORDIC vectoring mode.
pub fn cordic_atan2_q15(y: q15, x: q15) -> q15 {
    let (_, angle) = cordic_cartesian_to_polar_q15(x, y);
    angle
}

/// Square root of non-negative number `x` in Q15 format using CORDIC vectoring.
pub fn cordic_sqrt_q15(x: q15) -> q15 {
    if x <= q15::ZERO {
        return q15::ZERO;
    }
    // sqrt(x) = magnitude of (x + 1/4, x - 1/4) in hyperbolic mode or fast root
    let mut out = q15::ZERO;
    let _ = crate::fast_math::sqrt_q15(x, &mut out);
    out
}