154 lines
4.9 KiB
Rust
154 lines
4.9 KiB
Rust
use core::f64::consts::PI;
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include!(concat!(env!("OUT_DIR"), "/cossin_table.rs"));
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/// Compute the cosine and sine of an angle.
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/// This is ported from the MiSoC cossin core.
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/// (https://github.com/m-labs/misoc/blob/master/misoc/cores/cossin.py)
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///
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/// # Arguments
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/// * `phase` - 32-bit phase.
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///
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/// # Returns
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/// The cos and sin values of the provided phase as a `(i32, i32)`
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/// tuple. With a 7-bit deep LUT there is 9e-6 max and 4e-6 RMS error
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/// in each quadrature over 20 bit phase.
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pub fn cossin(phase: i32) -> (i32, i32) {
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// Phase bits excluding the three highest MSB
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const OCTANT_BITS: usize = 32 - 3;
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// This is a slightly more compact way to compute the four flags for
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// octant mapping/unmapping used below.
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let mut octant = (phase as u32) >> OCTANT_BITS;
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octant ^= octant << 1;
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let mut phase = phase;
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if octant & 1 != 0 {
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// phase = pi/4 - phase
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phase = !phase;
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}
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// Mask off octant bits. This leaves the angle in the range [0, pi/4).
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phase &= (1 << OCTANT_BITS) - 1;
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// 16 + 1 bits for cos/sin and 15 for dphi to saturate the i32 range.
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const ALIGN_MSB: usize = 32 - 16 - 1;
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phase >>= OCTANT_BITS - COSSIN_DEPTH - ALIGN_MSB;
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let lookup = COSSIN[(phase >> ALIGN_MSB) as usize];
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phase &= (1 << ALIGN_MSB) - 1;
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// The phase values used for the LUT are at midpoint for the truncated phase.
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// Interpolate relative to the LUT entry midpoint.
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phase -= 1 << (ALIGN_MSB - 1);
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// Cancel the -1 bias that was conditionally introduced above.
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// This lowers the DC spur from 2e-8 to 2e-10 magnitude.
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// phase += (octant & 1) as i32;
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// Fixed point pi/4.
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const PI4: i32 = (PI / 4. * (1 << 16) as f64) as _;
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// No rounding bias necessary here since we keep enough low bits.
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let dphi = (phase * PI4) >> 16;
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// 1/2 < cos(0 <= x <= pi/4) <= 1: Shift the cos
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// values and scale the sine values as encoded in the LUT.
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let mut cos = (lookup & 0xffff) as i32 + (1 << 16);
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let mut sin = (lookup >> 16) as i32;
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let dcos = (sin * dphi) >> COSSIN_DEPTH;
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let dsin = (cos * dphi) >> (COSSIN_DEPTH + 1);
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cos = (cos << (ALIGN_MSB - 1)) - dcos;
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sin = (sin << ALIGN_MSB) + dsin;
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// Unmap using octant bits.
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if octant & 2 != 0 {
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core::mem::swap(&mut sin, &mut cos);
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}
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if octant & 4 != 0 {
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cos = -cos;
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}
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if octant & 8 != 0 {
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sin = -sin;
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}
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(cos, sin)
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}
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#[cfg(test)]
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mod tests {
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use super::*;
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use core::f64::consts::PI;
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#[test]
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fn cossin_error_max_rms_all_phase() {
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// Constant amplitude error due to LUT data range.
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const AMPLITUDE: f64 = (1i64 << 31) as f64 - 0.85 * (1i64 << 15) as f64;
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const MAX_PHASE: f64 = (1i64 << 32) as _;
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let mut rms_err = (0f64, 0f64);
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let mut sum_err = (0f64, 0f64);
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let mut max_err = (0f64, 0f64);
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let mut sum = (0f64, 0f64);
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let mut demod = (0f64, 0f64);
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// use std::{fs::File, io::{BufWriter, prelude::*}, path::Path};
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// let mut file = BufWriter::new(File::create(Path::new("data.bin")).unwrap());
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// log2 of the number of phase values to check
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const PHASE_DEPTH: usize = 20;
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for phase in 0..(1 << PHASE_DEPTH) {
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let phase = (phase << (32 - PHASE_DEPTH)) as i32;
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let have = cossin(phase);
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// file.write(&have.0.to_le_bytes()).unwrap();
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// file.write(&have.1.to_le_bytes()).unwrap();
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let have = (have.0 as f64 / AMPLITUDE, have.1 as f64 / AMPLITUDE);
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let radian_phase = 2. * PI * phase as f64 / MAX_PHASE;
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let want = (radian_phase.cos(), radian_phase.sin());
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sum.0 += have.0;
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sum.1 += have.1;
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demod.0 += have.0 * want.0 - have.1 * want.1;
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demod.1 += have.1 * want.0 + have.0 * want.1;
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let err = (have.0 - want.0, have.1 - want.1);
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sum_err.0 += err.0;
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sum_err.1 += err.1;
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rms_err.0 += err.0 * err.0;
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rms_err.1 += err.1 * err.1;
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max_err.0 = max_err.0.max(err.0.abs());
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max_err.1 = max_err.1.max(err.1.abs());
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}
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rms_err.0 /= (1 << PHASE_DEPTH) as f64;
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rms_err.1 /= (1 << PHASE_DEPTH) as f64;
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println!("sum: {:.2e} {:.2e}", sum.0, sum.1);
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println!("demod: {:.2e} {:.2e}", demod.0, demod.1);
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println!("sum_err: {:.2e} {:.2e}", sum_err.0, sum_err.1);
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println!("rms: {:.2e} {:.2e}", rms_err.0.sqrt(), rms_err.1.sqrt());
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println!("max: {:.2e} {:.2e}", max_err.0, max_err.1);
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assert!(sum.0.abs() < 4e-10);
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assert!(sum.1.abs() < 3e-8);
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assert!(demod.0.abs() < 4e-10);
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assert!(demod.1.abs() < 1e-8);
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assert!(sum_err.0.abs() < 4e-10);
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assert!(sum_err.1.abs() < 4e-10);
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assert!(rms_err.0.sqrt() < 4e-6);
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assert!(rms_err.1.sqrt() < 4e-6);
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assert!(max_err.0 < 1e-5);
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assert!(max_err.1 < 1e-5);
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}
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}
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