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b/src/fft.rs @@ -1,16 +1,66 @@ -pub mod mixed_radix; -pub mod radix2; pub mod dft; +pub mod mixed_radix; pub mod rader; +pub mod radix2; -use crate::complex::Complex32; +use crate::{ + complex::Complex32, + fft::{dft::NaiveDFT, mixed_radix::MixedRadixFFT, rader::RaderFFT, radix2::Radix2FFT}, +}; pub trait DFT { fn create(size: usize) -> Self - where Self: Sized; + where + Self: Sized; fn get_input(&mut self) -> &mut [Complex32]; fn get_output(&self) -> &[Complex32]; fn execute(&mut self); } + +pub fn create_fft(size: usize) -> Box { + if size == 1 { + return Box::new(NaiveDFT::create(size)); + } + if size.count_ones() == 1 { + // TODO: Return hardcoded fft for small sized + return Box::new(Radix2FFT::create(size)); + } + + // Get factors + if is_prime(size) { + return Box::new(RaderFFT::create(size)); + } + + return Box::new(MixedRadixFFT::create(size)); +} + +// Utilities +fn prime_factors(n: usize) -> Vec { + let mut factors = vec![]; + + let mut num = n; + // Divide num successively + while num != 1 { + // Try divisors from 2 up to n (included) + for i in 2..n + 1 { + // if i divides num, it is a prime factor (if it wasn't, then i would have prime + // factors that would divide into num before i) + if num % i == 0 { + factors.push(i); + num /= i; + } + } + } + + // If n = 1 then it does not have any prime factors + // The prime factor decomposition theorem states that any integer + // greater than TWO has a unique decomposition + + factors +} + +pub fn is_prime(n: usize) -> bool { + prime_factors(n).len() == 1 +} diff --git a/src/fft/mixed_radix.rs b/src/fft/mixed_radix.rs index 9a17ce5..c9f2991 100644 --- a/src/fft/mixed_radix.rs +++ b/src/fft/mixed_radix.rs @@ -2,7 +2,10 @@ use std::f32::consts::PI; -use crate::{complex::Complex32, fft::{dft::NaiveDFT, DFT}}; +use crate::{ + complex::Complex32, + fft::{DFT, create_fft, dft::NaiveDFT, prime_factors}, +}; pub struct MixedRadixFFT { input_buffer: Box<[Complex32]>, @@ -16,23 +19,23 @@ pub struct MixedRadixFFT { qfft: Box, pfft: Box, - staging_buffer: Box<[Complex32]> + staging_buffer: Box<[Complex32]>, } impl DFT for MixedRadixFFT { fn create(size: usize) -> Self { let q = decide_radix_factor(size); let p = size / q; - let qfft = NaiveDFT::create(q); - let pfft = NaiveDFT::create(p); + let qfft = create_fft(q); + let pfft = create_fft(p); MixedRadixFFT { input_buffer: vec![Complex32::zero(); size].into_boxed_slice(), output_buffer: vec![Complex32::zero(); size].into_boxed_slice(), size, twiddle_factors: compute_twiddle_factors(q, p), - qfft: Box::new(qfft), - pfft: Box::new(pfft), + qfft, + pfft, staging_buffer: vec![Complex32::zero(); size].into_boxed_slice(), p, @@ -40,43 +43,36 @@ impl DFT for MixedRadixFFT { } } - fn execute(&mut self) - { + fn execute(&mut self) { // Perform p ffts of size q - for k0 in 0..self.p - { + for k0 in 0..self.p { // Copy samples into input buffer - for k1 in 0..self.q - { + for k1 in 0..self.q { self.qfft.get_input()[k1] = self.input_buffer[k1 * self.p + k0]; } self.qfft.execute(); - for j0 in 0..self.q - { + for j0 in 0..self.q { // "Store j0'th of k0'th fft into staging buffer" - self.staging_buffer[k0 * self.q + j0] = self.qfft.get_output()[j0] * self.twiddle_factors[k0 * self.q + j0]; + self.staging_buffer[k0 * self.q + j0] = + self.qfft.get_output()[j0] * self.twiddle_factors[k0 * self.q + j0]; } } // Perform q ffts of size p - for j0 in 0..self.q - { + for j0 in 0..self.q { // Copy input - for k0 in 0..self.p - { + for k0 in 0..self.p { self.pfft.get_input()[k0] = self.staging_buffer[k0 * self.q + j0]; } self.pfft.execute(); - for j1 in 0..self.p - { + for j1 in 0..self.p { self.output_buffer[j1 * self.q + j0] = self.pfft.get_output()[j1]; } } - } fn get_input(&mut self) -> &mut [Complex32] { @@ -88,15 +84,12 @@ impl DFT for MixedRadixFFT { } } -fn compute_twiddle_factors(q: usize, p: usize) -> Box<[Complex32]> -{ +fn compute_twiddle_factors(q: usize, p: usize) -> Box<[Complex32]> { let mut factors = vec![Complex32::zero(); q * p].into_boxed_slice(); let n = p * q; - for i in 0..q - { - for j in 0..p - { + for i in 0..q { + for j in 0..p { factors[i * p + j] = Complex32::cexp(2. * PI / (n as f32)); } } @@ -116,32 +109,3 @@ fn decide_radix_factor(n: usize) -> usize { // Otherwise take next big prime return *factors.iter().skip(two_count).next().unwrap(); } - -// Utilities -fn prime_factors(n: usize) -> Vec { - let mut factors = vec![]; - - let mut num = n; - // Divide num successively - while num != 1 { - // Try divisors from 2 up to n (included) - for i in 2..n + 1 { - // if i divides num, it is a prime factor (if it wasn't, then i would have prime - // factors that would divide into num before i) - if num % i == 0 { - factors.push(i); - num /= i; - } - } - } - - // If n = 1 then it does not have any prime factors - // The prime factor decomposition theorem states that any integer - // greater than TWO has a unique decomposition - - factors -} - -pub fn is_prime(n: usize) -> bool { - prime_factors(n).len() == 1 -} diff --git a/src/fft/rader.rs b/src/fft/rader.rs index b26be7f..10afe00 100644 --- a/src/fft/rader.rs +++ b/src/fft/rader.rs @@ -1,78 +1,74 @@ // Implementation of raders's fft for prime sized ffts -use std::f32::consts::PI; +use std::{f32::consts::PI, ops::Deref}; -use crate::{complex::Complex32, fft::{dft::NaiveDFT, mixed_radix::is_prime, DFT}}; use super::mixed_radix; +use crate::{ + complex::Complex32, + fft::{DFT, create_fft, dft::NaiveDFT, is_prime}, +}; + +pub struct RaderFFT { + input_buffer: Box<[Complex32]>, + output_buffer: Box<[Complex32]>, -pub struct RaderFFT -{ - input_buffer: Box<[Complex32]>, - output_buffer: Box<[Complex32]>, - size: usize, g: usize, // Fourrier transform of the exponential terms convolution_operand: Box<[Complex32]>, - convolution_fft: NaiveDFT, // TODO: Use fft + convolution_fft: Box, // TODO: Use fft + permutation: Box<[usize]>, } -impl DFT for RaderFFT -{ +impl DFT for RaderFFT { fn create(size: usize) -> Self - where Self: Sized { - let g = compute_prime_primitive_root(size); - RaderFFT - { - input_buffer: vec![Complex32::zero(); size].into_boxed_slice(), - output_buffer: vec![Complex32::zero(); size].into_boxed_slice(), + where + Self: Sized, + { + let g = compute_prime_primitive_root(size); + let permutation: Box<[usize]> = (0..(size - 1)).map(|i| exp_mod(g, i + 1, size)).collect(); + RaderFFT { + input_buffer: vec![Complex32::zero(); size].into_boxed_slice(), + output_buffer: vec![Complex32::zero(); size].into_boxed_slice(), - size, - g, - - convolution_operand: compute_convolution_operand(size, g), - convolution_fft: NaiveDFT::create(size - 1), - } + size, + g, + + convolution_operand: compute_convolution_operand(size, &permutation), + convolution_fft: Box::new(NaiveDFT::create(size - 1)), + permutation, + } } fn execute(&mut self) { - - // Copy to convolution fft with permutation - for i in 0..(self.size - 1) - { - self.convolution_fft.get_input()[i] = self.input_buffer[exp_mod(self.g, self.size - 1 - i - 1, self.size)]; + for i in 0..(self.size - 1) { + self.convolution_fft.get_input()[i] = + self.input_buffer[self.permutation[self.size - 1 - i - 1]] } self.convolution_fft.execute(); - // Convolve (use output buffer as staging buffer) - self.output_buffer - .iter_mut() - .skip(1) - .zip(self.convolution_operand.iter()) - .zip(self.convolution_fft.get_output().iter()) - .for_each(|((dest, a), b)| *dest = *a * *b); - - // Add first sample as DC-offset - //self.output_buffer[1] = self.output_buffer[1] + self.input_buffer[0]; - - // Copy to input - self - .convolution_fft - .get_input() - .iter_mut() - .zip(self.output_buffer.iter().skip(1)) - .for_each(|(dest, x)| *dest = - *x); - - self.convolution_fft.execute(); // Inverse fft - - // Copy to output buffer : n - 1 terms to copy - for i in 1..(self.size) - { - self.output_buffer[i] = - self.convolution_fft.get_output()[exp_mod(self.g, i, self.size) - 1] / (self.size as f32 - 1.) + self.input_buffer[0]; + // Use output buffer as staging buffer + for i in 0..(self.size - 1) { + self.output_buffer[i] = + self.convolution_fft.get_output()[i] * self.convolution_operand[i]; } + + for i in 0..(self.size - 1) { + self.convolution_fft.get_input()[i] = self.output_buffer[self.size - 1 - i - 1]; + } + self.convolution_fft.get_input()[0] = + self.convolution_fft.get_input()[0] + self.input_buffer[0]; + + // Compute ifft to obtain convolution + self.convolution_fft.execute(); + + for i in 0..(self.size - 1) { + self.output_buffer[self.permutation[i]] = + self.convolution_fft.get_output()[i] / (self.size - 1) as f32; + } + self.output_buffer[0] = self.input_buffer.iter().copied().sum(); } @@ -83,46 +79,39 @@ impl DFT for RaderFFT fn get_output(&self) -> &[Complex32] { &self.output_buffer } - } -pub fn compute_convolution_operand(n: usize, g: usize) -> Box<[Complex32]> -{ - println!("TODO: Change to better fft"); - let mut fft = NaiveDFT::create(n - 1); //TODO: Use fft +pub fn compute_convolution_operand(n: usize, permutation: &[usize]) -> Box<[Complex32]> { + //let mut fft = create_fft(n - 1); + let mut fft = NaiveDFT::create(n - 1); - fft.get_input().iter_mut().enumerate() - .for_each(|(i, x)| *x = Complex32::cexp(- 2. * PI * (exp_mod(g, i + 1, n) as f32) / (n as f32))); + fft.get_input() + .iter_mut() + .enumerate() + .for_each(|(i, x)| *x = Complex32::cexp(-2. * PI * (permutation[i] as f32) / (n as f32))); fft.execute(); - fft.get_output().iter().map(|x| *x).collect::>().into_boxed_slice() + fft.get_output().iter().copied().collect() } - - -pub fn compute_prime_primitive_root(n: usize) -> usize -{ +pub fn compute_prime_primitive_root(n: usize) -> usize { assert!(is_prime(n)); let phi = n - 1; // Euler's totient for n prime // Test all candidates - for i in 1..(n + 1) - { - // Find multiplicative order of i + for i in 1..(n + 1) { + // Find multiplicative order of i let mut val = i; let mut order = 1; - for j in 0..n - { - if val == 1 - { + for j in 0..n { + if val == 1 { break; } val = (val * i) % n; order += 1; } - - if order == phi - { + + if order == phi { return i; } } @@ -130,31 +119,21 @@ pub fn compute_prime_primitive_root(n: usize) -> usize unreachable!("Prime must have primitive root"); } -pub fn exp_mod(n: usize, exp: usize, m: usize) -> usize -{ - let mut num = n % m; - let mut acc = 1; - let mut exp = exp; - if exp == 0 - { - return 1; +pub fn exp_mod(mut n: usize, mut exp: usize, m: usize) -> usize { + if m == 1 { + return 0; } - while exp != 1 - { - if exp % 2 == 0 - { - num = (num * num) % m; - exp /= 2; - } - else - { - acc = (acc * n) % m; - exp -= 1; - num = num * num % m; - exp /= 2; + n %= m; + let mut r = 1; + while exp > 0 { + if exp % 2 == 1 { + r = (r * n) % m; } + + n = (n * n) % m; + exp >>= 1; } - (num * acc) % m + r } diff --git a/src/main.rs b/src/main.rs index 43c1be4..3ac6981 100644 --- a/src/main.rs +++ b/src/main.rs @@ -12,11 +12,17 @@ mod nco; use bfsk::BFSKMod; use complex::Complex; -use fft::rader; use complex::Complex32; +use fft::rader; use nco::Nco; -use crate::fft::{dft::NaiveDFT, mixed_radix::MixedRadixFFT, rader::{compute_prime_primitive_root, RaderFFT}, radix2::Radix2FFT, DFT}; +use crate::fft::{ + DFT, create_fft, + dft::NaiveDFT, + mixed_radix::MixedRadixFFT, + rader::{RaderFFT, compute_prime_primitive_root, exp_mod}, + radix2::Radix2FFT, +}; // Utilities fn map(input: T, in_min: T, in_max: T, out_min: T, out_max: T) -> T @@ -38,16 +44,18 @@ fn test() { let freq1 = 2. * PI / 4.0; let freq2 = 2. * PI / 8.0; + let sample_count = 4799; + let mut o1 = Nco::new(freq1); let mut o2 = Nco::new(freq2); - let mut fft = RaderFFT::create(4799); - let mut dft = NaiveDFT::create(4799); + let mut fft = RaderFFT::create(sample_count); + //let mut dft = NaiveDFT::create(sample_count); let vals = fft.get_input(); - let vals_dft = dft.get_input(); - for (x, y) in vals.iter_mut().zip(vals_dft.iter_mut()) { + //let vals_dft = dft.get_input(); + for x in vals.iter_mut() { *x = o1.cexp() + o2.cexp(); - *y = *x; + //*y = *x; //*x = o2.cexp(); //+ o2.cexp(); //*x = *x * (1. / x.mag()); o1.step(); @@ -55,14 +63,20 @@ fn test() { } fft.execute(); + //dft.execute(); let output = fft.get_output(); let mut f = File::create("out.csv").unwrap(); - for (i, (v, v2)) in output.iter().zip(dft.get_output()).enumerate() { + for (i, v) in output.iter().enumerate() { f.write_all( - format!("{},{},{},\n", i as f32 / 8192., v.mag(), v2.mag()) - .to_string() - .as_bytes(), + format!( + "{},{},\n", + i as f32 / sample_count as f32, + v.mag(), + //v2.mag() + ) + .to_string() + .as_bytes(), ) .unwrap(); }