--- /dev/null
+//! FFT and RDFT implementation.
+use std::f32::{self, consts};
+use std::ops::{Not, Neg, Add, AddAssign, Sub, SubAssign, Mul, MulAssign};
+use std::fmt;
+
+/// Complex number.
+#[repr(C)]
+#[derive(Debug,Clone,Copy,PartialEq)]
+pub struct FFTComplex {
+ /// Real part of the numner.
+ pub re: f32,
+ /// Complex part of the number.
+ pub im: f32,
+}
+
+impl FFTComplex {
+ /// Calculates `exp(i * val)`.
+ pub fn exp(val: f32) -> Self {
+ FFTComplex { re: val.cos(), im: val.sin() }
+ }
+ /// Returns `-Im + i * Re`.
+ pub fn rotate(self) -> Self {
+ FFTComplex { re: -self.im, im: self.re }
+ }
+ /// Multiplies complex number by scalar.
+ pub fn scale(self, scale: f32) -> Self {
+ FFTComplex { re: self.re * scale, im: self.im * scale }
+ }
+}
+
+impl Neg for FFTComplex {
+ type Output = FFTComplex;
+ fn neg(self) -> Self::Output {
+ FFTComplex { re: -self.re, im: -self.im }
+ }
+}
+
+impl Not for FFTComplex {
+ type Output = FFTComplex;
+ fn not(self) -> Self::Output {
+ FFTComplex { re: self.re, im: -self.im }
+ }
+}
+
+impl Add for FFTComplex {
+ type Output = FFTComplex;
+ fn add(self, other: Self) -> Self::Output {
+ FFTComplex { re: self.re + other.re, im: self.im + other.im }
+ }
+}
+
+impl AddAssign for FFTComplex {
+ fn add_assign(&mut self, other: Self) {
+ self.re += other.re;
+ self.im += other.im;
+ }
+}
+
+impl Sub for FFTComplex {
+ type Output = FFTComplex;
+ fn sub(self, other: Self) -> Self::Output {
+ FFTComplex { re: self.re - other.re, im: self.im - other.im }
+ }
+}
+
+impl SubAssign for FFTComplex {
+ fn sub_assign(&mut self, other: Self) {
+ self.re -= other.re;
+ self.im -= other.im;
+ }
+}
+
+impl Mul for FFTComplex {
+ type Output = FFTComplex;
+ fn mul(self, other: Self) -> Self::Output {
+ FFTComplex { re: self.re * other.re - self.im * other.im,
+ im: self.im * other.re + self.re * other.im }
+ }
+}
+
+impl MulAssign for FFTComplex {
+ fn mul_assign(&mut self, other: Self) {
+ let re = self.re * other.re - self.im * other.im;
+ let im = self.im * other.re + self.re * other.im;
+ self.re = re;
+ self.im = im;
+ }
+}
+
+impl fmt::Display for FFTComplex {
+ fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result {
+ write!(f, "({}, {})", self.re, self.im)
+ }
+}
+
+/// Complex number with zero value.
+pub const FFTC_ZERO: FFTComplex = FFTComplex { re: 0.0, im: 0.0 };
+
+/// Calculates forward or inverse FFT in the straightforward way.
+pub fn generic_fft(data: &mut [FFTComplex], forward: bool) {
+ let mut tmp = Vec::with_capacity(data.len());
+ tmp.resize(data.len(), FFTC_ZERO);
+ let base = if forward { -consts::PI * 2.0 / (data.len() as f32) }
+ else { consts::PI * 2.0 / (data.len() as f32) };
+ for k in 0..data.len() {
+ let mut sum = FFTC_ZERO;
+ for n in 0..data.len() {
+ let w = FFTComplex::exp(base * ((n * k) as f32));
+ sum += data[n] * w;
+ }
+ tmp[k] = sum;
+ }
+ for k in 0..data.len() {
+ data[k] = tmp[k];
+ }
+}
+
+struct FFTData {
+ table: Vec<FFTComplex>,
+ tmp: Vec<FFTComplex>,
+ twiddle: Vec<FFTComplex>,
+ size: usize,
+ step: usize,
+ div: usize,
+}
+
+struct FFTGeneric {}
+
+const FFT3_CONST: f32 = 0.86602540378443864677;
+const FFT5_CONST1: FFTComplex = FFTComplex { re: 0.80901699437494742410, im: 0.58778525229247312915 };
+const FFT5_CONST2: FFTComplex = FFTComplex { re: 0.30901699437494742411, im: 0.95105651629515357211 };
+
+fn twiddle5(a: FFTComplex, b: FFTComplex, c: FFTComplex) -> (FFTComplex, FFTComplex) {
+ let re = a.re * c.re;
+ let im = a.im * c.re;
+ let diffre = b.im * c.im;
+ let diffim = b.re * c.im;
+
+ (FFTComplex { re: re - diffre, im: im + diffim }, FFTComplex { re: re + diffre, im: im - diffim })
+}
+
+impl FFTGeneric {
+ fn new_data(size: usize, forward: bool) -> FFTData {
+ let mut table: Vec<FFTComplex> = Vec::with_capacity(size * size);
+ table.resize(size * size, FFTC_ZERO);
+ let base = consts::PI * 2.0 / (size as f32);
+ if forward {
+ for n in 0..size {
+ for k in 0..size {
+ table[n * size + k] = FFTComplex::exp(-base * ((n * k) as f32));
+ }
+ }
+ } else {
+ for n in 0..size {
+ for k in 0..size {
+ table[n * size + k] = FFTComplex::exp( base * ((n * k) as f32));
+ }
+ }
+ }
+ let mut tmp = Vec::with_capacity(size);
+ tmp.resize(size, FFTC_ZERO);
+ FFTData { table, tmp, twiddle: Vec::new(), size, step: 0, div: 0 }
+ }
+ fn fft(tbl: &mut FFTData, size: usize, data: &mut [FFTComplex], step: usize) {
+ if size == 3 {
+ let s0 = data[step * 0];
+ let s1 = data[step * 1];
+ let s2 = data[step * 2];
+ let t0 = s1 + s2;
+ data[step * 0] += t0;
+ let t1 = s0 - t0.scale(0.5);
+ let t2 = (s2 - s1).rotate().scale(FFT3_CONST);
+ data[step * 1] = t1 + t2;
+ data[step * 2] = t1 - t2;
+ return;
+ }
+ if size == 5 {
+ let s0 = data[step * 0];
+ let s1 = data[step * 1];
+ let s2 = data[step * 2];
+ let s3 = data[step * 3];
+ let s4 = data[step * 4];
+
+ let t0 = s1 + s4;
+ let t1 = s1 - s4;
+ let t2 = s2 + s3;
+ let t3 = s2 - s3;
+ let (t4, t5) = twiddle5(t0, t1, FFT5_CONST2);
+ let (t6, t7) = twiddle5(t2, t3, FFT5_CONST1);
+ let (t8, t9) = twiddle5(t0, t1, FFT5_CONST1);
+ let (ta, tb) = twiddle5(t2, t3, FFT5_CONST2);
+
+ data[step * 0] = s0 + t0 + t2;
+ data[step * 1] = s0 + t5 - t6;
+ data[step * 2] = s0 - t8 + ta;
+ data[step * 3] = s0 - t9 + tb;
+ data[step * 4] = s0 + t4 - t7;
+ return;
+ }
+ for k in 0..tbl.size {
+ tbl.tmp[k] = FFTC_ZERO;
+ for n in 0..tbl.size {
+ tbl.tmp[k] += data[n * step] * tbl.table[k * tbl.size + n];
+ }
+ }
+ for n in 0..tbl.size {
+ data[n * step] = tbl.tmp[n];
+ }
+ }
+ fn ifft(tbl: &mut FFTData, size: usize, data: &mut [FFTComplex], step: usize) {
+ if size == 3 {
+ let s0 = data[step * 0];
+ let s1 = data[step * 1];
+ let s2 = data[step * 2];
+ let t0 = s1 + s2;
+ data[step * 0] += t0;
+ let t1 = s0 - t0.scale(0.5);
+ let t2 = (s2 - s1).rotate().scale(FFT3_CONST);
+ data[step * 1] = t1 - t2;
+ data[step * 2] = t1 + t2;
+ return;
+ }
+ if size == 5 {
+ let s0 = data[step * 0];
+ let s1 = data[step * 1];
+ let s2 = data[step * 2];
+ let s3 = data[step * 3];
+ let s4 = data[step * 4];
+
+ let t0 = s1 + s4;
+ let t1 = s1 - s4;
+ let t2 = s2 + s3;
+ let t3 = s2 - s3;
+ let (t4, t5) = twiddle5(t0, t1, FFT5_CONST2);
+ let (t6, t7) = twiddle5(t2, t3, FFT5_CONST1);
+ let (t8, t9) = twiddle5(t0, t1, FFT5_CONST1);
+ let (ta, tb) = twiddle5(t2, t3, FFT5_CONST2);
+
+ data[step * 0] = s0 + t0 + t2;
+ data[step * 1] = s0 + t4 - t7;
+ data[step * 2] = s0 - t9 + tb;
+ data[step * 3] = s0 - t8 + ta;
+ data[step * 4] = s0 + t5 - t6;
+ return;
+ }
+ Self::fft(tbl, size, data, step);
+ }
+}
+
+struct FFTSplitRadix {}
+
+impl FFTSplitRadix {
+ fn new_data(bits: u8, _forward: bool) -> FFTData {
+ let size = 1 << bits;
+ let mut table = Vec::with_capacity(size);
+ for _ in 0..4 { table.push(FFTC_ZERO); }
+ for b in 3..=bits {
+ let qsize = (1 << (b - 2)) as usize;
+ let base = -consts::PI / ((qsize * 2) as f32);
+ for k in 0..qsize {
+ table.push(FFTComplex::exp(base * ((k * 1) as f32)));
+ table.push(FFTComplex::exp(base * ((k * 3) as f32)));
+ }
+ }
+ FFTData { table, tmp: Vec::new(), twiddle: Vec::new(), size, step: 0, div: 0 }
+ }
+ fn fft(fftdata: &mut FFTData, bits: u8, data: &mut [FFTComplex]) {
+ if bits == 0 { return; }
+ if bits == 1 {
+ let sum01 = data[0] + data[1];
+ let dif01 = data[0] - data[1];
+ data[0] = sum01;
+ data[1] = dif01;
+ return;
+ }
+ if bits == 2 {
+ let sum01 = data[0] + data[2];
+ let dif01 = data[0] - data[2];
+ let sum23 = data[1] + data[3];
+ let dif23 = data[1] - data[3];
+ data[0] = sum01 + sum23;
+ data[1] = dif01 - dif23.rotate();
+ data[2] = sum01 - sum23;
+ data[3] = dif01 + dif23.rotate();
+ return;
+ }
+ let qsize = (1 << (bits - 2)) as usize;
+ let hsize = (1 << (bits - 1)) as usize;
+ let q3size = qsize + hsize;
+
+ Self::fft(fftdata, bits - 1, &mut data[0 ..hsize]);
+ Self::fft(fftdata, bits - 2, &mut data[hsize ..q3size]);
+ Self::fft(fftdata, bits - 2, &mut data[q3size..]);
+ let off = hsize;
+ {
+ let t3 = data[0 + hsize] + data[0 + q3size];
+ let t4 = (data[0 + hsize] - data[0 + q3size]).rotate();
+ let e1 = data[0];
+ let e2 = data[0 + qsize];
+ data[0] = e1 + t3;
+ data[0 + qsize] = e2 - t4;
+ data[0 + hsize] = e1 - t3;
+ data[0 + q3size] = e2 + t4;
+ }
+ for k in 1..qsize {
+ let t1 = fftdata.table[off + k * 2 + 0] * data[k + hsize];
+ let t2 = fftdata.table[off + k * 2 + 1] * data[k + q3size];
+ let t3 = t1 + t2;
+ let t4 = (t1 - t2).rotate();
+ let e1 = data[k];
+ let e2 = data[k + qsize];
+ data[k] = e1 + t3;
+ data[k + qsize] = e2 - t4;
+ data[k + hsize] = e1 - t3;
+ data[k + qsize * 3] = e2 + t4;
+ }
+ }
+ fn ifft(fftdata: &mut FFTData, bits: u8, data: &mut [FFTComplex]) {
+ if bits == 0 { return; }
+ if bits == 1 {
+ let sum01 = data[0] + data[1];
+ let dif01 = data[0] - data[1];
+ data[0] = sum01;
+ data[1] = dif01;
+ return;
+ }
+ if bits == 2 {
+ let sum01 = data[0] + data[2];
+ let dif01 = data[0] - data[2];
+ let sum23 = data[1] + data[3];
+ let dif23 = data[1] - data[3];
+ data[0] = sum01 + sum23;
+ data[1] = dif01 + dif23.rotate();
+ data[2] = sum01 - sum23;
+ data[3] = dif01 - dif23.rotate();
+ return;
+ }
+ let qsize = (1 << (bits - 2)) as usize;
+ let hsize = (1 << (bits - 1)) as usize;
+ let q3size = qsize + hsize;
+
+ Self::ifft(fftdata, bits - 1, &mut data[0 ..hsize]);
+ Self::ifft(fftdata, bits - 2, &mut data[hsize ..q3size]);
+ Self::ifft(fftdata, bits - 2, &mut data[q3size..]);
+ let off = hsize;
+ {
+ let t3 = data[0 + hsize] + data[0 + q3size];
+ let t4 = (data[0 + hsize] - data[0 + q3size]).rotate();
+ let e1 = data[0];
+ let e2 = data[0 + qsize];
+ data[0] = e1 + t3;
+ data[0 + qsize] = e2 + t4;
+ data[0 + hsize] = e1 - t3;
+ data[0 + q3size] = e2 - t4;
+ }
+ for k in 1..qsize {
+ let t1 = !fftdata.table[off + k * 2 + 0] * data[k + hsize];
+ let t2 = !fftdata.table[off + k * 2 + 1] * data[k + q3size];
+ let t3 = t1 + t2;
+ let t4 = (t1 - t2).rotate();
+ let e1 = data[k];
+ let e2 = data[k + qsize];
+ data[k] = e1 + t3;
+ data[k + qsize] = e2 + t4;
+ data[k + hsize] = e1 - t3;
+ data[k + qsize * 3] = e2 - t4;
+ }
+ }
+}
+
+struct FFT15 {}
+
+const FFT15_INSWAP: [usize; 20] = [ 0, 5, 10, 42, 3, 8, 13, 42, 6, 11, 1, 42, 9, 14, 4, 42, 12, 2, 7, 42 ];
+const FFT15_OUTSWAP: [usize; 20] = [ 0, 10, 5, 42, 6, 1, 11, 42, 12, 7, 2, 42, 3, 13, 8, 42, 9, 4, 14, 42 ];
+
+impl FFT15 {
+ fn new_data(size: usize, _forward: bool) -> FFTData {
+ FFTData { table: Vec::new(), tmp: Vec::new(), twiddle: Vec::new(), size, step: 0, div: 0 }
+ }
+ fn fft3(dst: &mut [FFTComplex], src: &[FFTComplex], step: usize, n: usize) {
+ let s0 = src[0];
+ let s1 = src[1];
+ let s2 = src[2];
+
+ let t0 = s1 + s2;
+ let t1 = s0 - t0.scale(0.5);
+ let t2 = (s2 - s1).rotate().scale(FFT3_CONST);
+
+ dst[FFT15_OUTSWAP[n * 4 + 0] * step] = s0 + t0;
+ dst[FFT15_OUTSWAP[n * 4 + 1] * step] = t1 + t2;
+ dst[FFT15_OUTSWAP[n * 4 + 2] * step] = t1 - t2;
+ }
+ fn ifft3(dst: &mut [FFTComplex], src: &[FFTComplex], step: usize, n: usize) {
+ let s0 = src[0];
+ let s1 = src[1];
+ let s2 = src[2];
+
+ let t0 = s1 + s2;
+ let t1 = s0 - t0.scale(0.5);
+ let t2 = (s2 - s1).rotate().scale(FFT3_CONST);
+
+ dst[FFT15_OUTSWAP[n * 4 + 0] * step] = s0 + t0;
+ dst[FFT15_OUTSWAP[n * 4 + 1] * step] = t1 - t2;
+ dst[FFT15_OUTSWAP[n * 4 + 2] * step] = t1 + t2;
+ }
+ fn fft5(dst: &mut [FFTComplex], src: &[FFTComplex], step: usize, n: usize) {
+ let s0 = src[FFT15_INSWAP[n + 0 * 4] * step];
+ let s1 = src[FFT15_INSWAP[n + 1 * 4] * step];
+ let s2 = src[FFT15_INSWAP[n + 2 * 4] * step];
+ let s3 = src[FFT15_INSWAP[n + 3 * 4] * step];
+ let s4 = src[FFT15_INSWAP[n + 4 * 4] * step];
+
+ let t0 = s1 + s4;
+ let t1 = s1 - s4;
+ let t2 = s2 + s3;
+ let t3 = s2 - s3;
+ let (t4, t5) = twiddle5(t0, t1, FFT5_CONST2);
+ let (t6, t7) = twiddle5(t2, t3, FFT5_CONST1);
+ let (t8, t9) = twiddle5(t0, t1, FFT5_CONST1);
+ let (ta, tb) = twiddle5(t2, t3, FFT5_CONST2);
+
+ dst[0 * 3] = s0 + t0 + t2;
+ dst[1 * 3] = s0 + t5 - t6;
+ dst[2 * 3] = s0 - t8 + ta;
+ dst[3 * 3] = s0 - t9 + tb;
+ dst[4 * 3] = s0 + t4 - t7;
+ }
+ fn ifft5(dst: &mut [FFTComplex], src: &[FFTComplex], step: usize, n: usize) {
+ let s0 = src[FFT15_INSWAP[n + 0 * 4] * step];
+ let s1 = src[FFT15_INSWAP[n + 1 * 4] * step];
+ let s2 = src[FFT15_INSWAP[n + 2 * 4] * step];
+ let s3 = src[FFT15_INSWAP[n + 3 * 4] * step];
+ let s4 = src[FFT15_INSWAP[n + 4 * 4] * step];
+
+ let t0 = s1 + s4;
+ let t1 = s1 - s4;
+ let t2 = s2 + s3;
+ let t3 = s2 - s3;
+ let (t4, t5) = twiddle5(t0, t1, FFT5_CONST2);
+ let (t6, t7) = twiddle5(t2, t3, FFT5_CONST1);
+ let (t8, t9) = twiddle5(t0, t1, FFT5_CONST1);
+ let (ta, tb) = twiddle5(t2, t3, FFT5_CONST2);
+
+ dst[0 * 3] = s0 + t0 + t2;
+ dst[1 * 3] = s0 + t4 - t7;
+ dst[2 * 3] = s0 - t9 + tb;
+ dst[3 * 3] = s0 - t8 + ta;
+ dst[4 * 3] = s0 + t5 - t6;
+ }
+ fn fft(_fftdata: &mut FFTData, data: &mut [FFTComplex], step: usize) {
+ let mut tmp = [FFTC_ZERO; 15];
+ for n in 0..3 {
+ Self::fft5(&mut tmp[n..], data, step, n);
+ }
+ for n in 0..5 {
+ Self::fft3(data, &tmp[n * 3..][..3], step, n);
+ }
+ }
+ fn ifft(_fftdata: &mut FFTData, data: &mut [FFTComplex], step: usize) {
+ let mut tmp = [FFTC_ZERO; 15];
+ for n in 0..3 {
+ Self::ifft5(&mut tmp[n..], data, step, n);
+ }
+ for n in 0..5 {
+ Self::ifft3(data, &tmp[n * 3..][..3], step, n);
+ }
+ }
+}
+
+
+enum FFTMode {
+ Generic(usize),
+ SplitRadix(u8),
+ Prime15,
+}
+
+impl FFTMode {
+ fn permute(&self, perms: &mut [usize]) {
+ match *self {
+ FFTMode::Generic(_) => {},
+ FFTMode::SplitRadix(bits) => {
+ let div = perms.len() >> bits;
+ gen_sr_perms(perms, 1 << bits);
+ if div > 1 {
+ for i in 0..(1 << bits) {
+ perms[i] *= div;
+ }
+ for i in 1..div {
+ for j in 0..(1 << bits) {
+ perms[(i << bits) + j] = perms[j] + i;
+ }
+ }
+ }
+ },
+ FFTMode::Prime15 => {},
+ };
+ }
+ fn do_fft(&self, fftdata: &mut FFTData, data: &mut [FFTComplex]) {
+ match *self {
+ FFTMode::Generic(size) => FFTGeneric::fft(fftdata, size, data, 1),
+ FFTMode::SplitRadix(bits) => FFTSplitRadix::fft(fftdata, bits, data),
+ FFTMode::Prime15 => FFT15::fft(fftdata, data, 1),
+ };
+ }
+ fn do_fft2(&self, fftdata: &mut FFTData, data: &mut [FFTComplex], step: usize) {
+ match *self {
+ FFTMode::Generic(size) => FFTGeneric::fft(fftdata, size, data, step),
+ FFTMode::SplitRadix(_) => unreachable!(),
+ FFTMode::Prime15 => FFT15::fft(fftdata, data, step),
+ };
+ }
+ fn do_ifft(&self, fftdata: &mut FFTData, data: &mut [FFTComplex]) {
+ match *self {
+ FFTMode::Generic(size) => FFTGeneric::ifft(fftdata, size, data, 1),
+ FFTMode::SplitRadix(bits) => FFTSplitRadix::ifft(fftdata, bits, data),
+ FFTMode::Prime15 => FFT15::ifft(fftdata, data, 1),
+ };
+ }
+ fn do_ifft2(&self, fftdata: &mut FFTData, data: &mut [FFTComplex], step: usize) {
+ match *self {
+ FFTMode::Generic(size) => FFTGeneric::ifft(fftdata, size, data, step),
+ FFTMode::SplitRadix(_) => unreachable!(),
+ FFTMode::Prime15 => FFT15::ifft(fftdata, data, step),
+ };
+ }
+ fn get_size(&self) -> usize {
+ match *self {
+ FFTMode::Generic(size) => size,
+ FFTMode::SplitRadix(bits) => 1 << bits,
+ FFTMode::Prime15 => 15,
+ }
+ }
+}
+
+/// FFT working context.
+pub struct FFT {
+ perms: Vec<usize>,
+ swaps: Vec<usize>,
+ ffts: Vec<(FFTMode, FFTData)>,
+}
+
+impl FFT {
+ /// Calculates Fourier transform.
+ pub fn do_fft(&mut self, src: &[FFTComplex], dst: &mut [FFTComplex]) {
+ for k in 0..src.len() { dst[k] = src[self.perms[k]]; }
+ self.do_fft_core(dst);
+ }
+ /// Calculates inverse Fourier transform.
+ pub fn do_ifft(&mut self, src: &[FFTComplex], dst: &mut [FFTComplex]) {
+ for k in 0..src.len() { dst[k] = src[self.perms[k]]; }
+ self.do_ifft_core(dst);
+ }
+ /// Performs inplace FFT.
+ pub fn do_fft_inplace(&mut self, data: &mut [FFTComplex]) {
+ for idx in 0..self.swaps.len() {
+ let nidx = self.swaps[idx];
+ if idx != nidx {
+ data.swap(nidx, idx);
+ }
+ }
+ self.do_fft_core(data);
+ }
+ /// Performs inplace inverse FFT.
+ pub fn do_ifft_inplace(&mut self, data: &mut [FFTComplex]) {
+ for idx in 0..self.swaps.len() {
+ let nidx = self.swaps[idx];
+ if idx != nidx {
+ data.swap(nidx, idx);
+ }
+ }
+ self.do_ifft_core(data);
+ }
+ fn do_fft_core(&mut self, data: &mut [FFTComplex]) {
+ for el in self.ffts.iter_mut() {
+ let (mode, ref mut fftdata) = el;
+ let bsize = mode.get_size();
+ let div = fftdata.div;
+ let step = fftdata.step;
+ if step == 1 {
+ mode.do_fft(fftdata, data);
+ for i in 1..div {
+ mode.do_fft(fftdata, &mut data[i * bsize..]);
+ }
+ } else {
+ mode.do_fft2(fftdata, data, div);
+ let mut toff = bsize;
+ for i in 1..div {
+ for j in 1..bsize {
+ data[i + j * div] *= fftdata.twiddle[toff + j];
+ }
+ mode.do_fft2(fftdata, &mut data[i..], div);
+ toff += bsize;
+ }
+ }
+ }
+ }
+ fn do_ifft_core(&mut self, data: &mut [FFTComplex]) {
+ for el in self.ffts.iter_mut() {
+ let (mode, ref mut fftdata) = el;
+ let bsize = mode.get_size();
+ let div = fftdata.div;
+ let step = fftdata.step;
+ if step == 1 {
+ mode.do_ifft(fftdata, data);
+ for i in 1..div {
+ mode.do_ifft(fftdata, &mut data[i * bsize..]);
+ }
+ } else {
+ mode.do_ifft2(fftdata, data, div);
+ let mut toff = bsize;
+ for i in 1..div {
+ for j in 1..bsize {
+ data[i + j * div] *= fftdata.twiddle[toff + j];
+ }
+ mode.do_ifft2(fftdata, &mut data[i..], div);
+ toff += bsize;
+ }
+ }
+ }
+ }
+}
+
+/// [`FFT`] context creator.
+///
+/// [`FFT`]: ./struct.FFT.html
+pub struct FFTBuilder {
+}
+
+/*fn reverse_bits(inval: u32) -> u32 {
+ const REV_TAB: [u8; 16] = [
+ 0b0000, 0b1000, 0b0100, 0b1100, 0b0010, 0b1010, 0b0110, 0b1110,
+ 0b0001, 0b1001, 0b0101, 0b1101, 0b0011, 0b1011, 0b0111, 0b1111,
+ ];
+
+ let mut ret = 0;
+ let mut val = inval;
+ for _ in 0..8 {
+ ret = (ret << 4) | (REV_TAB[(val & 0xF) as usize] as u32);
+ val = val >> 4;
+ }
+ ret
+}
+
+fn swp_idx(idx: usize, bits: u32) -> usize {
+ let s = reverse_bits(idx as u32) as usize;
+ s >> (32 - bits)
+}*/
+
+fn gen_sr_perms(swaps: &mut [usize], size: usize) {
+ if size <= 4 { return; }
+ let mut evec: Vec<usize> = Vec::with_capacity(size / 2);
+ let mut ovec1: Vec<usize> = Vec::with_capacity(size / 4);
+ let mut ovec2: Vec<usize> = Vec::with_capacity(size / 4);
+ for k in 0..size/4 {
+ evec.push (swaps[k * 4 + 0]);
+ ovec1.push(swaps[k * 4 + 1]);
+ evec.push (swaps[k * 4 + 2]);
+ ovec2.push(swaps[k * 4 + 3]);
+ }
+ for k in 0..size/2 { swaps[k] = evec[k]; }
+ for k in 0..size/4 { swaps[k + size/2] = ovec1[k]; }
+ for k in 0..size/4 { swaps[k + 3*size/4] = ovec2[k]; }
+ gen_sr_perms(&mut swaps[0..size/2], size/2);
+ gen_sr_perms(&mut swaps[size/2..3*size/4], size/4);
+ gen_sr_perms(&mut swaps[3*size/4..], size/4);
+}
+
+fn gen_swaps_for_perm(swaps: &mut Vec<usize>, perms: &[usize]) {
+ let mut idx_arr: Vec<usize> = Vec::with_capacity(perms.len());
+ for i in 0..perms.len() { idx_arr.push(i); }
+ let mut run_size = 0;
+ let mut run_pos = 0;
+ for idx in 0..perms.len() {
+ if perms[idx] == idx_arr[idx] {
+ if run_size == 0 { run_pos = idx; }
+ run_size += 1;
+ } else {
+ for i in 0..run_size {
+ swaps.push(run_pos + i);
+ }
+ run_size = 0;
+ let mut spos = idx + 1;
+ while idx_arr[spos] != perms[idx] { spos += 1; }
+ idx_arr[spos] = idx_arr[idx];
+ idx_arr[idx] = perms[idx];
+ swaps.push(spos);
+ }
+ }
+}
+
+impl FFTBuilder {
+ fn generate_twiddle(data: &mut FFTData, size: usize, cur_size: usize, forward: bool) {
+ if size == cur_size { return; }
+ data.twiddle = Vec::with_capacity(size);
+ let div = size / cur_size;
+ let base = if forward { -2.0 * consts::PI / (size as f32) } else { 2.0 * consts::PI / (size as f32) };
+ for n in 0..div {
+ for k in 0..cur_size {
+ data.twiddle.push(FFTComplex::exp(base * ((k * n) as f32)));
+ }
+ }
+ }
+ /// Constructs a new `FFT` context.
+ pub fn new_fft(size: usize, forward: bool) -> FFT {
+ let mut ffts: Vec<(FFTMode, FFTData)> = Vec::with_capacity(1);
+ let mut perms: Vec<usize> = Vec::with_capacity(size);
+ let mut swaps: Vec<usize> = Vec::with_capacity(size);
+ let mut rem_size = size;
+ if rem_size.trailing_zeros() > 0 {
+ let bits = rem_size.trailing_zeros() as u8;
+ let mut data = FFTSplitRadix::new_data(bits, forward);
+ Self::generate_twiddle(&mut data, size, 1 << bits, forward);
+ data.step = 1;
+ data.div = rem_size >> bits;
+ ffts.push((FFTMode::SplitRadix(bits), data));
+ rem_size >>= bits;
+ }
+ if (rem_size % 15) == 0 {
+ let mut data = FFT15::new_data(size, forward);
+ Self::generate_twiddle(&mut data, size, 15, forward);
+ data.step = size / rem_size;
+ data.div = size / rem_size;
+ ffts.push((FFTMode::Prime15, data));
+ rem_size /= 15;
+ }
+ if rem_size > 1 {
+ let mut data = FFTGeneric::new_data(rem_size, forward);
+ Self::generate_twiddle(&mut data, size, rem_size, forward);
+ data.step = size / rem_size;
+ data.div = size / rem_size;
+ ffts.push((FFTMode::Generic(rem_size), data));
+ }
+
+ for i in 0..size {
+ perms.push(i);
+ }
+ for (mode, _) in ffts.iter().rev() {
+ mode.permute(&mut perms);
+ }
+ gen_swaps_for_perm(&mut swaps, perms.as_slice());
+
+ FFT { perms, swaps, ffts }
+ }
+}
+
+/// RDFT working context.
+pub struct RDFT {
+ table: Vec<FFTComplex>,
+ fft: FFT,
+ fwd: bool,
+ size: usize,
+ fwd_fft: bool,
+}
+
+fn crossadd(a: FFTComplex, b: FFTComplex) -> FFTComplex {
+ FFTComplex { re: a.re + b.re, im: a.im - b.im }
+}
+
+impl RDFT {
+ /// Calculates RDFT.
+ pub fn do_rdft(&mut self, src: &[FFTComplex], dst: &mut [FFTComplex]) {
+ dst.copy_from_slice(src);
+ self.do_rdft_inplace(dst);
+ }
+ /// Calculates inplace RDFT.
+ pub fn do_rdft_inplace(&mut self, buf: &mut [FFTComplex]) {
+ if !self.fwd {
+ for n in 0..self.size/2 {
+ let in0 = buf[n + 1];
+ let in1 = buf[self.size - n - 1];
+
+ let t0 = crossadd(in0, in1);
+ let t1 = FFTComplex { re: in1.im + in0.im, im: in1.re - in0.re };
+ let tab = self.table[n];
+ let t2 = FFTComplex { re: t1.im * tab.im + t1.re * tab.re, im: t1.im * tab.re - t1.re * tab.im };
+
+ buf[n + 1] = FFTComplex { re: t0.im - t2.im, im: t0.re - t2.re }; // (t0 - t2).conj().rotate()
+ buf[self.size - n - 1] = (t0 + t2).rotate();
+ }
+ let a = buf[0].re;
+ let b = buf[0].im;
+ buf[0].re = a - b;
+ buf[0].im = a + b;
+ }
+ if self.fwd_fft {
+ self.fft.do_fft_inplace(buf);
+ } else {
+ self.fft.do_ifft_inplace(buf);
+ }
+ if self.fwd {
+ for n in 0..self.size/2 {
+ let in0 = buf[n + 1];
+ let in1 = buf[self.size - n - 1];
+
+ let t0 = crossadd(in0, in1).scale(0.5);
+ let t1 = FFTComplex { re: in0.im + in1.im, im: in0.re - in1.re };
+ let t2 = t1 * self.table[n];
+
+ buf[n + 1] = crossadd(t0, t2);
+ buf[self.size - n - 1] = FFTComplex { re: t0.re - t2.re, im: -(t0.im + t2.im) };
+ }
+ let a = buf[0].re;
+ let b = buf[0].im;
+ buf[0].re = a + b;
+ buf[0].im = a - b;
+ } else {
+ for n in 0..self.size {
+ buf[n] = FFTComplex{ re: buf[n].im, im: buf[n].re };
+ }
+ }
+ }
+}
+
+/// [`RDFT`] context creator.
+///
+/// [`RDFT`]: ./struct.FFT.html
+pub struct RDFTBuilder {
+}
+
+impl RDFTBuilder {
+ /// Constructs a new `RDFT` context.
+ pub fn new_rdft(size: usize, forward: bool, forward_fft: bool) -> RDFT {
+ let mut table: Vec<FFTComplex> = Vec::with_capacity(size / 4);
+ let (base, scale) = if forward { (consts::PI / (size as f32), 0.5) } else { (-consts::PI / (size as f32), 1.0) };
+ for i in 0..size/2 {
+ table.push(FFTComplex::exp(base * ((i + 1) as f32)).scale(scale));
+ }
+ let fft = FFTBuilder::new_fft(size, forward_fft);
+ RDFT { table, fft, size, fwd: forward, fwd_fft: forward_fft }
+ }
+}
+
+
+#[cfg(test)]
+mod test {
+ use super::*;
+
+ fn test_fft(size: usize) {
+ println!("testing FFT {}", size);
+ let mut fin: Vec<FFTComplex> = Vec::with_capacity(size);
+ let mut fout1: Vec<FFTComplex> = Vec::with_capacity(size);
+ let mut fout2: Vec<FFTComplex> = Vec::with_capacity(size);
+ fin.resize(size, FFTC_ZERO);
+ fout1.resize(size, FFTC_ZERO);
+ fout2.resize(size, FFTC_ZERO);
+ let mut fft = FFTBuilder::new_fft(size, true);
+ let mut seed: u32 = 42;
+ for i in 0..fin.len() {
+ seed = seed.wrapping_mul(1664525).wrapping_add(1013904223);
+ let val = (seed >> 16) as i16;
+ fin[i].re = (val as f32) / 256.0;
+ seed = seed.wrapping_mul(1664525).wrapping_add(1013904223);
+ let val = (seed >> 16) as i16;
+ fin[i].im = (val as f32) / 256.0;
+ }
+ fft.do_fft(&fin, &mut fout1);
+ fout2.copy_from_slice(&fin);
+ generic_fft(&mut fout2, true);
+
+ for i in 0..fin.len() {
+ assert!((fout1[i].re - fout2[i].re).abs() < 1.0);
+ assert!((fout1[i].im - fout2[i].im).abs() < 1.0);
+ }
+ let mut ifft = FFTBuilder::new_fft(size, false);
+ ifft.do_ifft_inplace(&mut fout1);
+ generic_fft(&mut fout2, false);
+
+ let sc = 1.0 / (size as f32);
+ for i in 0..fin.len() {
+ assert!((fin[i].re - fout1[i].re * sc).abs() < 1.0);
+ assert!((fin[i].im - fout1[i].im * sc).abs() < 1.0);
+ assert!((fout1[i].re - fout2[i].re).abs() * sc < 1.0);
+ assert!((fout1[i].im - fout2[i].im).abs() * sc < 1.0);
+ }
+ }
+
+ #[test]
+ fn test_ffts() {
+ test_fft(3);
+ test_fft(5);
+ test_fft(16);
+ test_fft(15);
+ test_fft(60);
+ test_fft(256);
+ test_fft(240);
+ }
+
+ #[test]
+ fn test_rdft() {
+ let mut fin: [FFTComplex; 128] = [FFTC_ZERO; 128];
+ let mut fout1: [FFTComplex; 128] = [FFTC_ZERO; 128];
+ let mut rdft = RDFTBuilder::new_rdft(fin.len(), true, true);
+ let mut seed: u32 = 42;
+ for i in 0..fin.len() {
+ seed = seed.wrapping_mul(1664525).wrapping_add(1013904223);
+ let val = (seed >> 16) as i16;
+ fin[i].re = (val as f32) / 256.0;
+ seed = seed.wrapping_mul(1664525).wrapping_add(1013904223);
+ let val = (seed >> 16) as i16;
+ fin[i].im = (val as f32) / 256.0;
+ }
+ rdft.do_rdft(&fin, &mut fout1);
+ let mut irdft = RDFTBuilder::new_rdft(fin.len(), false, true);
+ irdft.do_rdft_inplace(&mut fout1);
+
+ for i in 0..fin.len() {
+ let tst = fout1[i].scale(0.5/(fout1.len() as f32));
+ assert!((tst.re - fin[i].re).abs() < 1.0);
+ assert!((tst.im - fin[i].im).abs() < 1.0);
+ }
+ }
+}
projects / nihav.git / blobdiff