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// Copyright (c) 2022 Weird Constructor <weirdconstructor@gmail.com>
// This file is a part of synfx-dsp. Released under GPL-3.0-or-later.
// See README.md and COPYING for details.
//
// This file contains the VA filter code of Fredemus' aka Frederik Halkjær aka RocketPhysician
// VA filter implementation.
// Copied under GPL-3.0-or-later from https://github.com/Fredemus/va-filter
use crate::{fh_va::DKSolver, fh_va::FilterParams};
// use packed_simd::f32x4;
// use core_simd::*;
// use std_float::*;
use std::sync::Arc;
use std::simd::f32x4;
//const N_P: usize = 2;
//const N_N: usize = 4;
//const P_LEN: usize = 8;
const N_OUTS: usize = 1;
const N_STATES: usize = 2;
const TOL: f64 = 1e-5;
/// This is a 2-pole lowpass filter.
///
/// This is a 2-pole lowpass filter loosely based on the one found in the
/// second revision of the Korg MS20 synthesizer. It distorts really nicely and
/// gets especially gnarly when resonance is high. My personal favorite.
///
/// It's able to self-oscillate and starts doing so when its resonance is above
/// 0.8.
///
/// OTA core, nonlinear op-amp buffers. Resonance is limited by a diode
/// clipper, but it disappears quite quickly at high drives.
///
/// Its convergence is generally good, but it does get a bit slower at high
/// drives. The parameter vector for the nonlinear contributions is just 2
/// entries long, meaning that it might be reasonable to create a lookup table
/// to guarantee stable, fast runtime. <- not as reasonable as I thought, also
/// needs entries for g and res
///
/// Circuit solved by Holters & Zölzer's generalization of the DK-method.
///
/// The fast version is optimized by removing unnecessary operations and
/// replacing the general solver with an analytic solution of the specific
/// model. At some point I'll look into how a simd-optimized version would
/// compare, since most of the operations are dot products anyway, but the
/// current fast version is definitely fast enough for real-time use in DAW
/// projects. pub struct SallenKey { filters: [SallenKeyCoreFast; 2], }
#[derive(Debug, Clone)]
pub struct SallenKey {
filters: [SallenKeyCoreFast; 2],
}
impl SallenKey {
pub fn new(params: Arc<FilterParams>) -> Self {
Self { filters: [SallenKeyCoreFast::new(params.clone()), SallenKeyCoreFast::new(params)] }
}
/// Process a stereo sample.
pub fn process(&mut self, input: f32x4) -> f32x4 {
f32x4::from_array([
self.filters[0].tick_dk(input[0]),
self.filters[1].tick_dk(input[1]),
0.,
0.,
])
}
/// Call this whenver the resonance or cutoff frequency of the [FilterParams] change.
pub fn update(&mut self) {
self.filters[0].update_matrices();
self.filters[1].update_matrices();
}
/// Reset the filter.
pub fn reset(&mut self) {
self.filters[0].reset();
self.filters[1].reset();
}
}
//pub struct SallenKeyCore {
// pub params: Arc<FilterParams>,
// pub vout: [f32; N_OUTS],
// pub s: [f32; N_STATES],
//
// // used to find the nonlinear contributions
// dq: [[f32; N_STATES]; N_P],
// eq: [f32; N_P],
// pub fq: [[f64; N_N]; P_LEN],
// // dq, eq are actually much larger, pexps are used to reduce them
// pexps: [[f64; N_P]; P_LEN],
//
// // used to update the capacitor states
// a: [[f32; N_STATES]; N_STATES],
// b: [f32; N_STATES],
// c: [[f32; N_N]; N_STATES],
//
// // used to find the output values
// // dy: [[f32; 2]; 2],
// dy: [[f32; N_STATES]; N_OUTS],
// ey: [f32; N_OUTS],
// fy: [[f32; N_N]; N_OUTS],
//
// pub solver: DKSolver<N_N, N_P, P_LEN>,
//}
//// here we flatten a bunch of stuff to hopefully make it faster
//impl SallenKeyCore {
// pub fn new(params: Arc<FilterParams>) -> Self {
// // TODO: pass in proper params
// let fs = params.sample_rate;
// let g = (std::f32::consts::PI * 1000. / (fs as f32)).tan();
// let res = 0.1;
// let g_f64 = g as f64;
// let res_f64 = res as f64;
//
// let pexps =
// [[0., 0.], [0., 0.], [1., 0.], [0., 0.], [0., -1.], [0., 1.], [0., 1.], [0., 0.]];
// let fq = [
// [0., 1., 0., 0.],
// [0., 0., 1., 0.],
// [
// -4. * g_f64 * ((res_f64 - 1.) / (4. * res_f64) - 0.25) * (1. / (4. * g_f64) + 0.5),
// 0.,
// 4. * g_f64 * (1. / (4. * g_f64) + 0.5) - 1.,
// 0.,
// ],
// [(res_f64 - 1.) / (4. * res_f64) - 0.25, 0., 0., 0.],
// [-0.25, -1., -(2. * g_f64 + 1.), 0.],
// [1.25, 1., 2. * g_f64 + 1., 1.],
// [0.25, 1., 2. * g_f64 + 1., 0.],
// [0., 0., 0., 1.],
// ];
// let mut a = Self {
// params,
// vout: [0.; 1],
// s: [0.; 2],
//
// dq: [[0., 1.], [-1., 0.]],
// eq: [0., -2. * g],
// fq,
// pexps,
//
// a: [[1., 0.], [0., 1.]],
// b: [4. * g, 0.],
// c: [
// [0., 0., -4. * g, 0.],
// [-4. * g * ((res - 1.) / (4. * res) - 0.25), 0., 4. * g, 0.],
// ],
//
// dy: [[0., 0.]],
// ey: [0.],
// fy: [[(res - 1.) / (4. * res) - 0.25, 0., 0., 0.]],
//
// solver: DKSolver::new(),
// };
// a.reset();
//
// a
// }
// pub fn update_matrices(&mut self) {
// let g = self.params.g;
// // the model starts to self-oscillate at 0.8
// let res = (self.params.res * 0.79).clamp(0.01, 0.99);
// let g_f64 = g as f64;
// let res_f64 = res as f64;
//
// self.fq = [
// [0., 1., 0., 0.],
// [0., 0., 1., 0.],
// [
// -4. * g_f64 * ((res_f64 - 1.) / (4. * res_f64) - 0.25) * (1. / (4. * g_f64) + 0.5),
// 0.,
// 4. * g_f64 * (1. / (4. * g_f64) + 0.5) - 1.,
// 0.,
// ],
// [(res_f64 - 1.) / (4. * res_f64) - 0.25, 0., 0., 0.],
// [-0.25, -1., -(2. * g_f64 + 1.), 0.],
// [1.25, 1., 2. * g_f64 + 1., 1.],
// [0.25, 1., 2. * g_f64 + 1., 0.],
// [0., 0., 0., 1.],
// ];
//
// self.b[0] = 4. * g;
//
// self.c[0][2] = -4. * g;
// self.c[1][0] = g / res;
// self.c[1][2] = 4. * g;
//
// self.eq[1] = 2. * g;
//
// self.fy[0][0] = -0.25 / res;
// }
//
// pub fn tick_dk(&mut self, input: f32) -> f32 {
// let input = input * self.params.drive;
//
// let mut p = [0f64; 2];
//
// p[0] = (self.dq[0][0] * self.s[0] + self.dq[0][1] * self.s[1] + self.eq[0] * input) as f64;
// p[1] = (self.dq[1][0] * self.s[0] + self.dq[1][1] * self.s[1] + self.eq[1] * input) as f64;
//
// //
// // find nonlinear contributions (solver.z), applying homotopy if it fails to converge
// // self.nonlinear_contribs(p);
// self.homotopy_solver(p);
// self.vout[0] = self.dy[0][0] * self.s[0] + self.dy[0][1] * self.s[1] + self.ey[0] * input;
//
// for i in 0..N_OUTS {
// for j in 0..N_N {
// self.vout[i] += self.solver.z[j] as f32 * self.fy[i][j];
// }
// }
// let s1_update = self.a[1][0] * self.s[0] + self.a[1][1] * self.s[1];
// self.s[0] = self.a[0][0] * self.s[0] + self.a[0][1] * self.s[1] + self.b[0] * input;
// self.s[1] = s1_update + self.b[1] * input;
// for i in 0..N_STATES {
// for j in 0..N_N {
// self.s[i] += self.solver.z[j] as f32 * self.c[i][j];
// }
// }
// self.vout[0]
// }
//
// pub fn homotopy_solver(&mut self, p: [f64; N_P]) {
// self.nonlinear_contribs(p);
// // if the newton solver failed to converge, apply homotopy
// if self.solver.resmaxabs >= TOL {
// // println!("needs homotopy. p: {:?}", p);
// let mut a = 0.5;
// let mut best_a = 0.;
// while best_a < 1. {
// let mut pa = self.solver.last_p;
//
// for i in 0..pa.len() {
// pa[i] = pa[i] * (1. - a);
// pa[i] = pa[i] + a * p[i];
// }
// self.nonlinear_contribs(pa);
// if self.solver.resmaxabs < TOL {
// best_a = a;
// a = 1.0;
// } else {
// let new_a = (a + best_a) / 2.;
// if !(best_a < new_a && new_a < a) {
// // no values between a and best_a. This could probably be simplified
// break;
// }
// a = new_a;
// }
// }
// // if self.solver.resmaxabs >= TOL {
// // println!("failed to converge. residue: {:?}", self.solver.residue);
//
// // for x in &self.solver.z {
// // if !x.is_finite() {
// // panic!("solution contains infinite value");
// // }
// // }
// // }
// }
// }
//
// // uses newton's method to find the nonlinear contributions in the circuit. Not guaranteed to converge
// fn nonlinear_contribs(&mut self, p: [f64; N_P]) -> [f64; N_N] {
// self.solver.set_p(p, &self.pexps);
//
// let mut tmp_np = [0.; N_P];
// tmp_np[0] = p[0] - self.solver.last_p[0];
// tmp_np[1] = p[1] - self.solver.last_p[1];
//
// let mut tmp_nn = [0.; N_N];
// for i in 0..N_N {
// for j in 0..N_P {
// tmp_nn[i] += self.solver.jp[i][j] * tmp_np[j];
// }
// }
//
// tmp_nn = self.solver.solve_linear_equations(tmp_nn);
//
// for i in 0..self.solver.z.len() {
// self.solver.z[i] = self.solver.last_z[i] - tmp_nn[i];
// }
//
// for _plsconverge in 0..500 {
// self.evaluate_nonlinearities(self.solver.z, self.fq);
//
// self.solver.resmaxabs = 0.;
// for x in &self.solver.residue {
// if x.is_finite() {
// if x.abs() > self.solver.resmaxabs {
// self.solver.resmaxabs = x.abs();
// }
// } else {
// // if any of the residue have become NaN/inf, stop early with big residue
// self.solver.resmaxabs = 1000.;
// return self.solver.z;
// }
// }
//
// self.solver.set_lin_solver(self.solver.j);
// if self.solver.resmaxabs < TOL {
// // dbg!(_plsconverge);
// break;
// }
//
// // update z with the linsolver according to the residue
// tmp_nn = self.solver.solve_linear_equations(self.solver.residue);
//
// for i in 0..self.solver.z.len() {
// self.solver.z[i] -= tmp_nn[i];
// }
// }
// if self.solver.resmaxabs < TOL {
// self.solver.set_jp(&self.pexps);
// self.solver.set_extrapolation_origin(p, self.solver.z);
// } else {
// // println!("failed to converge. residue: {:?}", self.solver.residue);
// }
// self.solver.z
// }
//
// fn evaluate_nonlinearities(&mut self, z: [f64; N_N], fq: [[f64; N_N]; P_LEN]) {
// let mut dot_p = [0.; P_LEN];
// let mut q = self.solver.p_full;
// for i in 0..P_LEN {
// for j in 0..N_N {
// dot_p[i] += z[j] * fq[i][j];
// }
// q[i] += dot_p[i];
// }
//
// let (res1, jq1) = self.solver.eval_opamp(q[0], q[1]);
// let (res2, jq2) = self.solver.eval_opamp(q[2], q[3]);
//
// let (res3, jq3) = self.solver.eval_diode(&q[4..6], 1e-15, 1.5);
// let (res4, jq4) = self.solver.eval_diode(&q[6..8], 1e-15, 1.5);
//
// self.solver.jq[0][0] = jq1[0];
// self.solver.jq[0][1] = jq1[1];
// self.solver.jq[1][2] = jq2[0];
// self.solver.jq[1][3] = jq2[1];
//
// self.solver.jq[2][4] = jq3[0];
// self.solver.jq[2][5] = jq3[1];
// self.solver.jq[3][6] = jq4[0];
// self.solver.jq[3][7] = jq4[1];
//
// // update j to the matrix product fq * jq
// for i in 0..self.solver.jq.len() {
// for j in 0..N_N {
// self.solver.j[i][j] = 0.;
// for k in 0..P_LEN {
// self.solver.j[i][j] += self.solver.jq[i][k] * fq[k][j];
// }
// }
// }
// self.solver.residue = [res1, res2, res3, res4];
// }
// pub fn reset(&mut self) {
// self.s = [0.; 2];
// self.solver.set_p([0.; N_P], &self.pexps);
// self.evaluate_nonlinearities([0.; N_N], self.fq);
// self.solver.set_lin_solver(self.solver.j);
// self.solver.set_jp(&self.pexps);
// self.solver.set_extrapolation_origin([0.; N_P], [0.; N_N]);
// }
//}
const N_P2: usize = 2;
const N_N2: usize = 3;
const P_LEN2: usize = 6;
/// this does the same as `SallenKeyCore`, but with most equations simplified to make it faster
#[derive(Debug, Clone)]
struct SallenKeyCoreFast {
pub params: Arc<FilterParams>,
pub vout: [f32; N_OUTS],
pub s: [f32; N_STATES],
// used to find the nonlinear contributions
eq: [f32; N_P2],
// pub fq: [[f64; N_N2]; P_LEN2],
fq20: f64,
fq22: f64,
fq30: f64,
fq40: f64,
fq42: f64,
fq50: f64,
fq52: f64,
// used to update the capacitor states
b: [f32; N_STATES],
c: [[f32; N_N2]; N_STATES],
// used to find the output values
fy: [[f32; N_N2]; N_OUTS],
jq: [f64; 6],
solver: DKSolver<N_N2, N_P2, P_LEN2>,
}
// here we flatten a bunch of stuff to hopefully make it faster
impl SallenKeyCoreFast {
pub fn new(params: Arc<FilterParams>) -> Self {
let fs = params.sample_rate;
let g = (std::f32::consts::PI * 1000. / (fs as f32)).tan();
let res = 0.1;
let g_f64 = g as f64;
let res_f64 = res as f64;
let mut a = Self {
params,
vout: [0.; 1],
s: [0.; 2],
eq: [0., 2. * g],
fq20: (0.25 + 0.5 * g_f64) / res_f64,
fq22: 2. * g_f64,
fq30: -0.25 / res_f64,
fq40: 0.25,
fq42: (2. * g_f64 + 1.),
fq50: -1.25,
fq52: -(2. * g_f64 + 1.),
b: [4. * g, 0.],
c: [[0., 0., -4. * g], [g / res, 0., 4. * g]],
fy: [[-0.25 / res, 0., 0.]],
jq: [0., -1., 0., -1., 0., 1.],
solver: DKSolver::new(),
};
a.reset();
a
}
pub fn update_matrices(&mut self) {
let g = self.params.g;
let res = (self.params.res * 0.79).clamp(0.01, 0.99);
let g_f64 = g as f64;
let res_f64 = res as f64;
self.fq30 = -0.25 / res_f64;
self.fq22 = 2. * g_f64;
self.fq20 = (0.25 + 0.5 * g_f64) / res_f64;
self.fq42 = 2. * g_f64 + 1.;
self.fq52 = -(2. * g_f64 + 1.);
self.b[0] = 4. * g;
self.c[0][2] = -4. * g;
self.c[1][0] = g / res;
self.c[1][2] = 4. * g;
self.eq[1] = 2. * g;
self.fy[0][0] = -0.25 / res;
}
pub fn tick_dk(&mut self, input: f32) -> f32 {
let input = input * self.params.drive;
// let p = dot(dq, s) + dot(eq, input);
let mut p = [0f64; 2];
p[0] = self.s[1] as f64;
p[1] = (self.s[0] + self.eq[1] * input) as f64;
// self.nonlinear_contribs(p);
// find nonlinear contributions (values for solver.z that falls in the null-space described by fq), applying homotopy if it fails to converge
self.homotopy_solver(p);
// find output voltage(s)
self.vout[0] = self.fy[0][0] * self.solver.z[0] as f32;
// update states
self.s[0] = self.s[0] + self.b[0] * input + self.solver.z[2] as f32 * self.c[0][2];
self.s[1] = self.s[1]
+ self.solver.z[0] as f32 * self.c[1][0]
+ self.solver.z[2] as f32 * self.c[1][2];
self.vout[0]
}
pub fn homotopy_solver(&mut self, p: [f64; N_P2]) {
self.nonlinear_contribs(p);
// if the newton solver failed to converge, apply homotopy
if self.solver.resmaxabs >= TOL {
// println!("needs homotopy. p: {:?}", p);
let mut a = 0.5;
let mut best_a = 0.;
while best_a < 1. {
let mut pa = self.solver.last_p;
for i in 0..pa.len() {
pa[i] = pa[i] * (1. - a);
pa[i] = pa[i] + a * p[i];
}
self.nonlinear_contribs(pa);
if self.solver.resmaxabs < TOL {
best_a = a;
a = 1.0;
} else {
let new_a = (a + best_a) / 2.;
if !(best_a < new_a && new_a < a) {
// no values between a and best_a. This means the homotopy failed to find an in-between value for the solution
break;
}
a = new_a;
}
}
// this doesn't seem to ever happen anymore
// if self.solver.resmaxabs >= TOL {
// println!("failed to converge. residue: {:?}", self.solver.residue);
// for x in &self.solver.z {
// if !x.is_finite() {
// panic!("solution contains infinite value");
// }
// }
// }
}
}
// uses newton's method to find the nonlinear contributions in the circuit. Not guaranteed to converge
#[inline]
fn nonlinear_contribs(&mut self, p: [f64; N_P2]) -> [f64; N_N2] {
self.solver.p_full[2] = p[0];
self.solver.p_full[4] = -p[1];
self.solver.p_full[5] = p[1];
let tmp_np = [p[0] - self.solver.last_p[0], p[1] - self.solver.last_p[1]];
let mut tmp_nn = [0., self.jq[2] * tmp_np[0], (-self.jq[4] - 1.0) * tmp_np[1]];
tmp_nn = self.solve_lin_equations(tmp_nn);
for i in 0..N_N2 {
self.solver.z[i] = self.solver.last_z[i] - tmp_nn[i];
}
for _plsconverge in 0..500 {
self.evaluate_nonlinearities(self.solver.z);
self.solver.resmaxabs = 0.;
for x in &self.solver.residue {
if x.is_finite() {
if x.abs() > self.solver.resmaxabs {
self.solver.resmaxabs = x.abs();
}
} else {
// if any of the residues have become NaN/inf, stop early with big residue
self.solver.resmaxabs = 1000.;
return self.solver.z;
}
}
if self.solver.resmaxabs < TOL {
break;
}
// update z with the linsolver according to the residue
tmp_nn = self.solve_lin_equations(self.solver.residue);
for i in 0..N_N2 {
self.solver.z[i] -= tmp_nn[i];
}
}
if self.solver.resmaxabs < TOL {
// only update this when residue's below tolerance, so homotopy solver can try again with the same initial guess if it failed to converge
self.solver.set_extrapolation_origin(p, self.solver.z);
}
self.solver.z
}
// solve for a value of z, that according to the jacobian should hit the nullspace, so it can be subtracted from the current z
#[inline]
fn solve_lin_equations(&mut self, b: [f64; N_N2]) -> [f64; N_N2] {
// let j = self.solver.j;
let mut x = [0.; 3];
let j01 = self.jq[0];
let j10 = self.jq[2] * self.fq20 - self.fq30;
let j12 = self.jq[2] * self.fq22;
let j20 = self.jq[4] * self.fq40 - self.fq50;
let j21 = self.jq[4] + 1.0;
let j22 = self.jq[4] * self.fq42 - self.fq52;
// solved the equation `dot_product(self.solver.j, x) = b` for x analytically to get this
let x0_den = j01 * j10 * j22 - j01 * j12 * j20 + j10 * j21;
x[0] = (b[0] * j12 * j21 + b[1] * j01 * j22 - b[2] * j01 * j12 + b[1] * j21) / x0_den;
x[2] = (-j10 * x[0] + b[1]) / j12;
x[1] = (b[0] + x[2]) / j01;
x
}
#[inline(always)]
pub fn evaluate_nonlinearities(&mut self, z: [f64; N_N2]) {
let q = [
z[1],
z[2],
self.solver.p_full[2] + z[0] * self.fq20 + z[2] * self.fq22,
z[0] * self.fq30,
self.solver.p_full[4] + z[0] * 0.25 + z[1] + z[2] * self.fq42,
self.solver.p_full[5] + z[0] * -1.25 - z[1] + z[2] * self.fq52,
];
let (res1, jq1) = self.solver.eval_opamp(q[0], q[1]);
let (res2, jq2) = self.solver.eval_opamp(q[2], q[3]);
let (res3, jq3) = self.solver.eval_diodepair(q[4], q[5], 1e-15, 1.7);
self.solver.residue = [res1, res2, res3];
self.jq[0] = jq1[0];
self.jq[2] = jq2[0];
self.jq[4] = jq3[0];
}
pub fn reset(&mut self) {
self.s = [0.; 2];
self.solver.p_full = [0.; P_LEN2];
self.evaluate_nonlinearities([0.; N_N2]);
self.solver.set_extrapolation_origin([0.; N_P2], [0.; N_N2]);
}
}