| 1 | //! FFT and RDFT implementation. |
| 2 | use std::f32::{self, consts}; |
| 3 | use std::ops::{Not, Neg, Add, AddAssign, Sub, SubAssign, Mul, MulAssign, Div}; |
| 4 | use std::fmt; |
| 5 | |
| 6 | /// Complex number. |
| 7 | #[repr(C)] |
| 8 | #[derive(Debug,Clone,Copy,PartialEq)] |
| 9 | pub struct FFTComplex { |
| 10 | /// Real part of the numner. |
| 11 | pub re: f32, |
| 12 | /// Complex part of the number. |
| 13 | pub im: f32, |
| 14 | } |
| 15 | |
| 16 | impl FFTComplex { |
| 17 | /// Calculates `exp(i * val)`. |
| 18 | pub fn exp(val: f32) -> Self { |
| 19 | FFTComplex { re: val.cos(), im: val.sin() } |
| 20 | } |
| 21 | /// Returns `-Im + i * Re`. |
| 22 | pub fn rotate(self) -> Self { |
| 23 | FFTComplex { re: -self.im, im: self.re } |
| 24 | } |
| 25 | /// Multiplies complex number by scalar. |
| 26 | pub fn scale(self, scale: f32) -> Self { |
| 27 | FFTComplex { re: self.re * scale, im: self.im * scale } |
| 28 | } |
| 29 | /// Returns squared modulus value of the complex number. |
| 30 | pub fn sq_modulus(self) -> f32 { |
| 31 | self.re * self.re + self.im * self.im |
| 32 | } |
| 33 | /// Returns reciprocal of the complex number. |
| 34 | pub fn reciprocal(self) -> Self { |
| 35 | !self.scale(self.sq_modulus()) |
| 36 | } |
| 37 | } |
| 38 | |
| 39 | impl Neg for FFTComplex { |
| 40 | type Output = FFTComplex; |
| 41 | fn neg(self) -> Self::Output { |
| 42 | FFTComplex { re: -self.re, im: -self.im } |
| 43 | } |
| 44 | } |
| 45 | |
| 46 | impl Not for FFTComplex { |
| 47 | type Output = FFTComplex; |
| 48 | fn not(self) -> Self::Output { |
| 49 | FFTComplex { re: self.re, im: -self.im } |
| 50 | } |
| 51 | } |
| 52 | |
| 53 | impl Add for FFTComplex { |
| 54 | type Output = FFTComplex; |
| 55 | fn add(self, other: Self) -> Self::Output { |
| 56 | FFTComplex { re: self.re + other.re, im: self.im + other.im } |
| 57 | } |
| 58 | } |
| 59 | |
| 60 | impl AddAssign for FFTComplex { |
| 61 | fn add_assign(&mut self, other: Self) { |
| 62 | self.re += other.re; |
| 63 | self.im += other.im; |
| 64 | } |
| 65 | } |
| 66 | |
| 67 | impl Sub for FFTComplex { |
| 68 | type Output = FFTComplex; |
| 69 | fn sub(self, other: Self) -> Self::Output { |
| 70 | FFTComplex { re: self.re - other.re, im: self.im - other.im } |
| 71 | } |
| 72 | } |
| 73 | |
| 74 | impl SubAssign for FFTComplex { |
| 75 | fn sub_assign(&mut self, other: Self) { |
| 76 | self.re -= other.re; |
| 77 | self.im -= other.im; |
| 78 | } |
| 79 | } |
| 80 | |
| 81 | impl Mul for FFTComplex { |
| 82 | type Output = FFTComplex; |
| 83 | fn mul(self, other: Self) -> Self::Output { |
| 84 | FFTComplex { re: self.re * other.re - self.im * other.im, |
| 85 | im: self.im * other.re + self.re * other.im } |
| 86 | } |
| 87 | } |
| 88 | |
| 89 | impl MulAssign for FFTComplex { |
| 90 | fn mul_assign(&mut self, other: Self) { |
| 91 | let re = self.re * other.re - self.im * other.im; |
| 92 | let im = self.im * other.re + self.re * other.im; |
| 93 | self.re = re; |
| 94 | self.im = im; |
| 95 | } |
| 96 | } |
| 97 | |
| 98 | impl Div for FFTComplex { |
| 99 | type Output = FFTComplex; |
| 100 | fn div(self, other: Self) -> Self::Output { |
| 101 | self * other.reciprocal() |
| 102 | } |
| 103 | } |
| 104 | |
| 105 | impl fmt::Display for FFTComplex { |
| 106 | fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result { |
| 107 | write!(f, "({}, {})", self.re, self.im) |
| 108 | } |
| 109 | } |
| 110 | |
| 111 | /// Complex number with zero value. |
| 112 | pub const FFTC_ZERO: FFTComplex = FFTComplex { re: 0.0, im: 0.0 }; |
| 113 | |
| 114 | /// Calculates forward or inverse FFT in the straightforward way. |
| 115 | pub fn generic_fft(data: &mut [FFTComplex], forward: bool) { |
| 116 | let mut tmp = Vec::with_capacity(data.len()); |
| 117 | tmp.resize(data.len(), FFTC_ZERO); |
| 118 | let base = if forward { -consts::PI * 2.0 / (data.len() as f32) } |
| 119 | else { consts::PI * 2.0 / (data.len() as f32) }; |
| 120 | for k in 0..data.len() { |
| 121 | let mut sum = FFTC_ZERO; |
| 122 | for n in 0..data.len() { |
| 123 | let w = FFTComplex::exp(base * ((n * k) as f32)); |
| 124 | sum += data[n] * w; |
| 125 | } |
| 126 | tmp[k] = sum; |
| 127 | } |
| 128 | for k in 0..data.len() { |
| 129 | data[k] = tmp[k]; |
| 130 | } |
| 131 | } |
| 132 | |
| 133 | struct FFTData { |
| 134 | table: Vec<FFTComplex>, |
| 135 | tmp: Vec<FFTComplex>, |
| 136 | twiddle: Vec<FFTComplex>, |
| 137 | size: usize, |
| 138 | step: usize, |
| 139 | div: usize, |
| 140 | } |
| 141 | |
| 142 | struct FFTGeneric {} |
| 143 | |
| 144 | const FFT3_CONST: f32 = 0.86602540378443864677; |
| 145 | const FFT5_CONST1: FFTComplex = FFTComplex { re: 0.80901699437494742410, im: 0.58778525229247312915 }; |
| 146 | const FFT5_CONST2: FFTComplex = FFTComplex { re: 0.30901699437494742411, im: 0.95105651629515357211 }; |
| 147 | |
| 148 | fn twiddle5(a: FFTComplex, b: FFTComplex, c: FFTComplex) -> (FFTComplex, FFTComplex) { |
| 149 | let re = a.re * c.re; |
| 150 | let im = a.im * c.re; |
| 151 | let diffre = b.im * c.im; |
| 152 | let diffim = b.re * c.im; |
| 153 | |
| 154 | (FFTComplex { re: re - diffre, im: im + diffim }, FFTComplex { re: re + diffre, im: im - diffim }) |
| 155 | } |
| 156 | |
| 157 | impl FFTGeneric { |
| 158 | fn new_data(size: usize, forward: bool) -> FFTData { |
| 159 | let mut table: Vec<FFTComplex> = Vec::with_capacity(size * size); |
| 160 | table.resize(size * size, FFTC_ZERO); |
| 161 | let base = consts::PI * 2.0 / (size as f32); |
| 162 | if forward { |
| 163 | for n in 0..size { |
| 164 | for k in 0..size { |
| 165 | table[n * size + k] = FFTComplex::exp(-base * ((n * k) as f32)); |
| 166 | } |
| 167 | } |
| 168 | } else { |
| 169 | for n in 0..size { |
| 170 | for k in 0..size { |
| 171 | table[n * size + k] = FFTComplex::exp( base * ((n * k) as f32)); |
| 172 | } |
| 173 | } |
| 174 | } |
| 175 | let mut tmp = Vec::with_capacity(size); |
| 176 | tmp.resize(size, FFTC_ZERO); |
| 177 | FFTData { table, tmp, twiddle: Vec::new(), size, step: 0, div: 0 } |
| 178 | } |
| 179 | fn fft(tbl: &mut FFTData, size: usize, data: &mut [FFTComplex], step: usize) { |
| 180 | if size == 3 { |
| 181 | let s0 = data[step * 0]; |
| 182 | let s1 = data[step * 1]; |
| 183 | let s2 = data[step * 2]; |
| 184 | let t0 = s1 + s2; |
| 185 | data[step * 0] += t0; |
| 186 | let t1 = s0 - t0.scale(0.5); |
| 187 | let t2 = (s2 - s1).rotate().scale(FFT3_CONST); |
| 188 | data[step * 1] = t1 + t2; |
| 189 | data[step * 2] = t1 - t2; |
| 190 | return; |
| 191 | } |
| 192 | if size == 5 { |
| 193 | let s0 = data[step * 0]; |
| 194 | let s1 = data[step * 1]; |
| 195 | let s2 = data[step * 2]; |
| 196 | let s3 = data[step * 3]; |
| 197 | let s4 = data[step * 4]; |
| 198 | |
| 199 | let t0 = s1 + s4; |
| 200 | let t1 = s1 - s4; |
| 201 | let t2 = s2 + s3; |
| 202 | let t3 = s2 - s3; |
| 203 | let (t4, t5) = twiddle5(t0, t1, FFT5_CONST2); |
| 204 | let (t6, t7) = twiddle5(t2, t3, FFT5_CONST1); |
| 205 | let (t8, t9) = twiddle5(t0, t1, FFT5_CONST1); |
| 206 | let (ta, tb) = twiddle5(t2, t3, FFT5_CONST2); |
| 207 | |
| 208 | data[step * 0] = s0 + t0 + t2; |
| 209 | data[step * 1] = s0 + t5 - t6; |
| 210 | data[step * 2] = s0 - t8 + ta; |
| 211 | data[step * 3] = s0 - t9 + tb; |
| 212 | data[step * 4] = s0 + t4 - t7; |
| 213 | return; |
| 214 | } |
| 215 | for k in 0..tbl.size { |
| 216 | tbl.tmp[k] = FFTC_ZERO; |
| 217 | for n in 0..tbl.size { |
| 218 | tbl.tmp[k] += data[n * step] * tbl.table[k * tbl.size + n]; |
| 219 | } |
| 220 | } |
| 221 | for n in 0..tbl.size { |
| 222 | data[n * step] = tbl.tmp[n]; |
| 223 | } |
| 224 | } |
| 225 | fn ifft(tbl: &mut FFTData, size: usize, data: &mut [FFTComplex], step: usize) { |
| 226 | if size == 3 { |
| 227 | let s0 = data[step * 0]; |
| 228 | let s1 = data[step * 1]; |
| 229 | let s2 = data[step * 2]; |
| 230 | let t0 = s1 + s2; |
| 231 | data[step * 0] += t0; |
| 232 | let t1 = s0 - t0.scale(0.5); |
| 233 | let t2 = (s2 - s1).rotate().scale(FFT3_CONST); |
| 234 | data[step * 1] = t1 - t2; |
| 235 | data[step * 2] = t1 + t2; |
| 236 | return; |
| 237 | } |
| 238 | if size == 5 { |
| 239 | let s0 = data[step * 0]; |
| 240 | let s1 = data[step * 1]; |
| 241 | let s2 = data[step * 2]; |
| 242 | let s3 = data[step * 3]; |
| 243 | let s4 = data[step * 4]; |
| 244 | |
| 245 | let t0 = s1 + s4; |
| 246 | let t1 = s1 - s4; |
| 247 | let t2 = s2 + s3; |
| 248 | let t3 = s2 - s3; |
| 249 | let (t4, t5) = twiddle5(t0, t1, FFT5_CONST2); |
| 250 | let (t6, t7) = twiddle5(t2, t3, FFT5_CONST1); |
| 251 | let (t8, t9) = twiddle5(t0, t1, FFT5_CONST1); |
| 252 | let (ta, tb) = twiddle5(t2, t3, FFT5_CONST2); |
| 253 | |
| 254 | data[step * 0] = s0 + t0 + t2; |
| 255 | data[step * 1] = s0 + t4 - t7; |
| 256 | data[step * 2] = s0 - t9 + tb; |
| 257 | data[step * 3] = s0 - t8 + ta; |
| 258 | data[step * 4] = s0 + t5 - t6; |
| 259 | return; |
| 260 | } |
| 261 | Self::fft(tbl, size, data, step); |
| 262 | } |
| 263 | } |
| 264 | |
| 265 | struct FFTSplitRadix {} |
| 266 | |
| 267 | impl FFTSplitRadix { |
| 268 | fn new_data(bits: u8, _forward: bool) -> FFTData { |
| 269 | let size = 1 << bits; |
| 270 | let mut table = Vec::with_capacity(size); |
| 271 | for _ in 0..4 { table.push(FFTC_ZERO); } |
| 272 | for b in 3..=bits { |
| 273 | let qsize = (1 << (b - 2)) as usize; |
| 274 | let base = -consts::PI / ((qsize * 2) as f32); |
| 275 | for k in 0..qsize { |
| 276 | table.push(FFTComplex::exp(base * ((k * 1) as f32))); |
| 277 | table.push(FFTComplex::exp(base * ((k * 3) as f32))); |
| 278 | } |
| 279 | } |
| 280 | FFTData { table, tmp: Vec::new(), twiddle: Vec::new(), size, step: 0, div: 0 } |
| 281 | } |
| 282 | fn fft(fftdata: &mut FFTData, bits: u8, data: &mut [FFTComplex]) { |
| 283 | if bits == 0 { return; } |
| 284 | if bits == 1 { |
| 285 | let sum01 = data[0] + data[1]; |
| 286 | let dif01 = data[0] - data[1]; |
| 287 | data[0] = sum01; |
| 288 | data[1] = dif01; |
| 289 | return; |
| 290 | } |
| 291 | if bits == 2 { |
| 292 | let sum01 = data[0] + data[2]; |
| 293 | let dif01 = data[0] - data[2]; |
| 294 | let sum23 = data[1] + data[3]; |
| 295 | let dif23 = data[1] - data[3]; |
| 296 | data[0] = sum01 + sum23; |
| 297 | data[1] = dif01 - dif23.rotate(); |
| 298 | data[2] = sum01 - sum23; |
| 299 | data[3] = dif01 + dif23.rotate(); |
| 300 | return; |
| 301 | } |
| 302 | let qsize = (1 << (bits - 2)) as usize; |
| 303 | let hsize = (1 << (bits - 1)) as usize; |
| 304 | let q3size = qsize + hsize; |
| 305 | |
| 306 | Self::fft(fftdata, bits - 1, &mut data[0 ..hsize]); |
| 307 | Self::fft(fftdata, bits - 2, &mut data[hsize ..q3size]); |
| 308 | Self::fft(fftdata, bits - 2, &mut data[q3size..]); |
| 309 | let off = hsize; |
| 310 | { |
| 311 | let t3 = data[0 + hsize] + data[0 + q3size]; |
| 312 | let t4 = (data[0 + hsize] - data[0 + q3size]).rotate(); |
| 313 | let e1 = data[0]; |
| 314 | let e2 = data[0 + qsize]; |
| 315 | data[0] = e1 + t3; |
| 316 | data[0 + qsize] = e2 - t4; |
| 317 | data[0 + hsize] = e1 - t3; |
| 318 | data[0 + q3size] = e2 + t4; |
| 319 | } |
| 320 | for k in 1..qsize { |
| 321 | let t1 = fftdata.table[off + k * 2 + 0] * data[k + hsize]; |
| 322 | let t2 = fftdata.table[off + k * 2 + 1] * data[k + q3size]; |
| 323 | let t3 = t1 + t2; |
| 324 | let t4 = (t1 - t2).rotate(); |
| 325 | let e1 = data[k]; |
| 326 | let e2 = data[k + qsize]; |
| 327 | data[k] = e1 + t3; |
| 328 | data[k + qsize] = e2 - t4; |
| 329 | data[k + hsize] = e1 - t3; |
| 330 | data[k + qsize * 3] = e2 + t4; |
| 331 | } |
| 332 | } |
| 333 | fn ifft(fftdata: &mut FFTData, bits: u8, data: &mut [FFTComplex]) { |
| 334 | if bits == 0 { return; } |
| 335 | if bits == 1 { |
| 336 | let sum01 = data[0] + data[1]; |
| 337 | let dif01 = data[0] - data[1]; |
| 338 | data[0] = sum01; |
| 339 | data[1] = dif01; |
| 340 | return; |
| 341 | } |
| 342 | if bits == 2 { |
| 343 | let sum01 = data[0] + data[2]; |
| 344 | let dif01 = data[0] - data[2]; |
| 345 | let sum23 = data[1] + data[3]; |
| 346 | let dif23 = data[1] - data[3]; |
| 347 | data[0] = sum01 + sum23; |
| 348 | data[1] = dif01 + dif23.rotate(); |
| 349 | data[2] = sum01 - sum23; |
| 350 | data[3] = dif01 - dif23.rotate(); |
| 351 | return; |
| 352 | } |
| 353 | let qsize = (1 << (bits - 2)) as usize; |
| 354 | let hsize = (1 << (bits - 1)) as usize; |
| 355 | let q3size = qsize + hsize; |
| 356 | |
| 357 | Self::ifft(fftdata, bits - 1, &mut data[0 ..hsize]); |
| 358 | Self::ifft(fftdata, bits - 2, &mut data[hsize ..q3size]); |
| 359 | Self::ifft(fftdata, bits - 2, &mut data[q3size..]); |
| 360 | let off = hsize; |
| 361 | { |
| 362 | let t3 = data[0 + hsize] + data[0 + q3size]; |
| 363 | let t4 = (data[0 + hsize] - data[0 + q3size]).rotate(); |
| 364 | let e1 = data[0]; |
| 365 | let e2 = data[0 + qsize]; |
| 366 | data[0] = e1 + t3; |
| 367 | data[0 + qsize] = e2 + t4; |
| 368 | data[0 + hsize] = e1 - t3; |
| 369 | data[0 + q3size] = e2 - t4; |
| 370 | } |
| 371 | for k in 1..qsize { |
| 372 | let t1 = !fftdata.table[off + k * 2 + 0] * data[k + hsize]; |
| 373 | let t2 = !fftdata.table[off + k * 2 + 1] * data[k + q3size]; |
| 374 | let t3 = t1 + t2; |
| 375 | let t4 = (t1 - t2).rotate(); |
| 376 | let e1 = data[k]; |
| 377 | let e2 = data[k + qsize]; |
| 378 | data[k] = e1 + t3; |
| 379 | data[k + qsize] = e2 + t4; |
| 380 | data[k + hsize] = e1 - t3; |
| 381 | data[k + qsize * 3] = e2 - t4; |
| 382 | } |
| 383 | } |
| 384 | } |
| 385 | |
| 386 | struct FFT15 {} |
| 387 | |
| 388 | 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 ]; |
| 389 | 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 ]; |
| 390 | |
| 391 | impl FFT15 { |
| 392 | fn new_data(size: usize, _forward: bool) -> FFTData { |
| 393 | FFTData { table: Vec::new(), tmp: Vec::new(), twiddle: Vec::new(), size, step: 0, div: 0 } |
| 394 | } |
| 395 | fn fft3(dst: &mut [FFTComplex], src: &[FFTComplex], step: usize, n: usize) { |
| 396 | let s0 = src[0]; |
| 397 | let s1 = src[1]; |
| 398 | let s2 = src[2]; |
| 399 | |
| 400 | let t0 = s1 + s2; |
| 401 | let t1 = s0 - t0.scale(0.5); |
| 402 | let t2 = (s2 - s1).rotate().scale(FFT3_CONST); |
| 403 | |
| 404 | dst[FFT15_OUTSWAP[n * 4 + 0] * step] = s0 + t0; |
| 405 | dst[FFT15_OUTSWAP[n * 4 + 1] * step] = t1 + t2; |
| 406 | dst[FFT15_OUTSWAP[n * 4 + 2] * step] = t1 - t2; |
| 407 | } |
| 408 | fn ifft3(dst: &mut [FFTComplex], src: &[FFTComplex], step: usize, n: usize) { |
| 409 | let s0 = src[0]; |
| 410 | let s1 = src[1]; |
| 411 | let s2 = src[2]; |
| 412 | |
| 413 | let t0 = s1 + s2; |
| 414 | let t1 = s0 - t0.scale(0.5); |
| 415 | let t2 = (s2 - s1).rotate().scale(FFT3_CONST); |
| 416 | |
| 417 | dst[FFT15_OUTSWAP[n * 4 + 0] * step] = s0 + t0; |
| 418 | dst[FFT15_OUTSWAP[n * 4 + 1] * step] = t1 - t2; |
| 419 | dst[FFT15_OUTSWAP[n * 4 + 2] * step] = t1 + t2; |
| 420 | } |
| 421 | fn fft5(dst: &mut [FFTComplex], src: &[FFTComplex], step: usize, n: usize) { |
| 422 | let s0 = src[FFT15_INSWAP[n + 0 * 4] * step]; |
| 423 | let s1 = src[FFT15_INSWAP[n + 1 * 4] * step]; |
| 424 | let s2 = src[FFT15_INSWAP[n + 2 * 4] * step]; |
| 425 | let s3 = src[FFT15_INSWAP[n + 3 * 4] * step]; |
| 426 | let s4 = src[FFT15_INSWAP[n + 4 * 4] * step]; |
| 427 | |
| 428 | let t0 = s1 + s4; |
| 429 | let t1 = s1 - s4; |
| 430 | let t2 = s2 + s3; |
| 431 | let t3 = s2 - s3; |
| 432 | let (t4, t5) = twiddle5(t0, t1, FFT5_CONST2); |
| 433 | let (t6, t7) = twiddle5(t2, t3, FFT5_CONST1); |
| 434 | let (t8, t9) = twiddle5(t0, t1, FFT5_CONST1); |
| 435 | let (ta, tb) = twiddle5(t2, t3, FFT5_CONST2); |
| 436 | |
| 437 | dst[0 * 3] = s0 + t0 + t2; |
| 438 | dst[1 * 3] = s0 + t5 - t6; |
| 439 | dst[2 * 3] = s0 - t8 + ta; |
| 440 | dst[3 * 3] = s0 - t9 + tb; |
| 441 | dst[4 * 3] = s0 + t4 - t7; |
| 442 | } |
| 443 | fn ifft5(dst: &mut [FFTComplex], src: &[FFTComplex], step: usize, n: usize) { |
| 444 | let s0 = src[FFT15_INSWAP[n + 0 * 4] * step]; |
| 445 | let s1 = src[FFT15_INSWAP[n + 1 * 4] * step]; |
| 446 | let s2 = src[FFT15_INSWAP[n + 2 * 4] * step]; |
| 447 | let s3 = src[FFT15_INSWAP[n + 3 * 4] * step]; |
| 448 | let s4 = src[FFT15_INSWAP[n + 4 * 4] * step]; |
| 449 | |
| 450 | let t0 = s1 + s4; |
| 451 | let t1 = s1 - s4; |
| 452 | let t2 = s2 + s3; |
| 453 | let t3 = s2 - s3; |
| 454 | let (t4, t5) = twiddle5(t0, t1, FFT5_CONST2); |
| 455 | let (t6, t7) = twiddle5(t2, t3, FFT5_CONST1); |
| 456 | let (t8, t9) = twiddle5(t0, t1, FFT5_CONST1); |
| 457 | let (ta, tb) = twiddle5(t2, t3, FFT5_CONST2); |
| 458 | |
| 459 | dst[0 * 3] = s0 + t0 + t2; |
| 460 | dst[1 * 3] = s0 + t4 - t7; |
| 461 | dst[2 * 3] = s0 - t9 + tb; |
| 462 | dst[3 * 3] = s0 - t8 + ta; |
| 463 | dst[4 * 3] = s0 + t5 - t6; |
| 464 | } |
| 465 | fn fft(_fftdata: &mut FFTData, data: &mut [FFTComplex], step: usize) { |
| 466 | let mut tmp = [FFTC_ZERO; 15]; |
| 467 | for n in 0..3 { |
| 468 | Self::fft5(&mut tmp[n..], data, step, n); |
| 469 | } |
| 470 | for n in 0..5 { |
| 471 | Self::fft3(data, &tmp[n * 3..][..3], step, n); |
| 472 | } |
| 473 | } |
| 474 | fn ifft(_fftdata: &mut FFTData, data: &mut [FFTComplex], step: usize) { |
| 475 | let mut tmp = [FFTC_ZERO; 15]; |
| 476 | for n in 0..3 { |
| 477 | Self::ifft5(&mut tmp[n..], data, step, n); |
| 478 | } |
| 479 | for n in 0..5 { |
| 480 | Self::ifft3(data, &tmp[n * 3..][..3], step, n); |
| 481 | } |
| 482 | } |
| 483 | } |
| 484 | |
| 485 | |
| 486 | enum FFTMode { |
| 487 | Generic(usize), |
| 488 | SplitRadix(u8), |
| 489 | Prime15, |
| 490 | } |
| 491 | |
| 492 | impl FFTMode { |
| 493 | fn permute(&self, perms: &mut [usize]) { |
| 494 | match *self { |
| 495 | FFTMode::Generic(_) => {}, |
| 496 | FFTMode::SplitRadix(bits) => { |
| 497 | let div = perms.len() >> bits; |
| 498 | gen_sr_perms(perms, 1 << bits); |
| 499 | if div > 1 { |
| 500 | for i in 0..(1 << bits) { |
| 501 | perms[i] *= div; |
| 502 | } |
| 503 | for i in 1..div { |
| 504 | for j in 0..(1 << bits) { |
| 505 | perms[(i << bits) + j] = perms[j] + i; |
| 506 | } |
| 507 | } |
| 508 | } |
| 509 | }, |
| 510 | FFTMode::Prime15 => {}, |
| 511 | }; |
| 512 | } |
| 513 | fn do_fft(&self, fftdata: &mut FFTData, data: &mut [FFTComplex]) { |
| 514 | match *self { |
| 515 | FFTMode::Generic(size) => FFTGeneric::fft(fftdata, size, data, 1), |
| 516 | FFTMode::SplitRadix(bits) => FFTSplitRadix::fft(fftdata, bits, data), |
| 517 | FFTMode::Prime15 => FFT15::fft(fftdata, data, 1), |
| 518 | }; |
| 519 | } |
| 520 | fn do_fft2(&self, fftdata: &mut FFTData, data: &mut [FFTComplex], step: usize) { |
| 521 | match *self { |
| 522 | FFTMode::Generic(size) => FFTGeneric::fft(fftdata, size, data, step), |
| 523 | FFTMode::SplitRadix(_) => unreachable!(), |
| 524 | FFTMode::Prime15 => FFT15::fft(fftdata, data, step), |
| 525 | }; |
| 526 | } |
| 527 | fn do_ifft(&self, fftdata: &mut FFTData, data: &mut [FFTComplex]) { |
| 528 | match *self { |
| 529 | FFTMode::Generic(size) => FFTGeneric::ifft(fftdata, size, data, 1), |
| 530 | FFTMode::SplitRadix(bits) => FFTSplitRadix::ifft(fftdata, bits, data), |
| 531 | FFTMode::Prime15 => FFT15::ifft(fftdata, data, 1), |
| 532 | }; |
| 533 | } |
| 534 | fn do_ifft2(&self, fftdata: &mut FFTData, data: &mut [FFTComplex], step: usize) { |
| 535 | match *self { |
| 536 | FFTMode::Generic(size) => FFTGeneric::ifft(fftdata, size, data, step), |
| 537 | FFTMode::SplitRadix(_) => unreachable!(), |
| 538 | FFTMode::Prime15 => FFT15::ifft(fftdata, data, step), |
| 539 | }; |
| 540 | } |
| 541 | fn get_size(&self) -> usize { |
| 542 | match *self { |
| 543 | FFTMode::Generic(size) => size, |
| 544 | FFTMode::SplitRadix(bits) => 1 << bits, |
| 545 | FFTMode::Prime15 => 15, |
| 546 | } |
| 547 | } |
| 548 | } |
| 549 | |
| 550 | /// FFT working context. |
| 551 | pub struct FFT { |
| 552 | perms: Vec<usize>, |
| 553 | swaps: Vec<usize>, |
| 554 | ffts: Vec<(FFTMode, FFTData)>, |
| 555 | } |
| 556 | |
| 557 | impl FFT { |
| 558 | /// Calculates Fourier transform. |
| 559 | pub fn do_fft(&mut self, src: &[FFTComplex], dst: &mut [FFTComplex]) { |
| 560 | for k in 0..src.len() { dst[k] = src[self.perms[k]]; } |
| 561 | self.do_fft_core(dst); |
| 562 | } |
| 563 | /// Calculates inverse Fourier transform. |
| 564 | pub fn do_ifft(&mut self, src: &[FFTComplex], dst: &mut [FFTComplex]) { |
| 565 | for k in 0..src.len() { dst[k] = src[self.perms[k]]; } |
| 566 | self.do_ifft_core(dst); |
| 567 | } |
| 568 | /// Performs inplace FFT. |
| 569 | pub fn do_fft_inplace(&mut self, data: &mut [FFTComplex]) { |
| 570 | for idx in 0..self.swaps.len() { |
| 571 | let nidx = self.swaps[idx]; |
| 572 | if idx != nidx { |
| 573 | data.swap(nidx, idx); |
| 574 | } |
| 575 | } |
| 576 | self.do_fft_core(data); |
| 577 | } |
| 578 | /// Performs inplace inverse FFT. |
| 579 | pub fn do_ifft_inplace(&mut self, data: &mut [FFTComplex]) { |
| 580 | for idx in 0..self.swaps.len() { |
| 581 | let nidx = self.swaps[idx]; |
| 582 | if idx != nidx { |
| 583 | data.swap(nidx, idx); |
| 584 | } |
| 585 | } |
| 586 | self.do_ifft_core(data); |
| 587 | } |
| 588 | fn do_fft_core(&mut self, data: &mut [FFTComplex]) { |
| 589 | for el in self.ffts.iter_mut() { |
| 590 | let (mode, ref mut fftdata) = el; |
| 591 | let bsize = mode.get_size(); |
| 592 | let div = fftdata.div; |
| 593 | let step = fftdata.step; |
| 594 | if step == 1 { |
| 595 | mode.do_fft(fftdata, data); |
| 596 | for i in 1..div { |
| 597 | mode.do_fft(fftdata, &mut data[i * bsize..]); |
| 598 | } |
| 599 | } else { |
| 600 | mode.do_fft2(fftdata, data, div); |
| 601 | let mut toff = bsize; |
| 602 | for i in 1..div { |
| 603 | for j in 1..bsize { |
| 604 | data[i + j * div] *= fftdata.twiddle[toff + j]; |
| 605 | } |
| 606 | mode.do_fft2(fftdata, &mut data[i..], div); |
| 607 | toff += bsize; |
| 608 | } |
| 609 | } |
| 610 | } |
| 611 | } |
| 612 | fn do_ifft_core(&mut self, data: &mut [FFTComplex]) { |
| 613 | for el in self.ffts.iter_mut() { |
| 614 | let (mode, ref mut fftdata) = el; |
| 615 | let bsize = mode.get_size(); |
| 616 | let div = fftdata.div; |
| 617 | let step = fftdata.step; |
| 618 | if step == 1 { |
| 619 | mode.do_ifft(fftdata, data); |
| 620 | for i in 1..div { |
| 621 | mode.do_ifft(fftdata, &mut data[i * bsize..]); |
| 622 | } |
| 623 | } else { |
| 624 | mode.do_ifft2(fftdata, data, div); |
| 625 | let mut toff = bsize; |
| 626 | for i in 1..div { |
| 627 | for j in 1..bsize { |
| 628 | data[i + j * div] *= fftdata.twiddle[toff + j]; |
| 629 | } |
| 630 | mode.do_ifft2(fftdata, &mut data[i..], div); |
| 631 | toff += bsize; |
| 632 | } |
| 633 | } |
| 634 | } |
| 635 | } |
| 636 | } |
| 637 | |
| 638 | /// [`FFT`] context creator. |
| 639 | /// |
| 640 | /// [`FFT`]: ./struct.FFT.html |
| 641 | pub struct FFTBuilder { |
| 642 | } |
| 643 | |
| 644 | /*fn reverse_bits(inval: u32) -> u32 { |
| 645 | const REV_TAB: [u8; 16] = [ |
| 646 | 0b0000, 0b1000, 0b0100, 0b1100, 0b0010, 0b1010, 0b0110, 0b1110, |
| 647 | 0b0001, 0b1001, 0b0101, 0b1101, 0b0011, 0b1011, 0b0111, 0b1111, |
| 648 | ]; |
| 649 | |
| 650 | let mut ret = 0; |
| 651 | let mut val = inval; |
| 652 | for _ in 0..8 { |
| 653 | ret = (ret << 4) | (REV_TAB[(val & 0xF) as usize] as u32); |
| 654 | val = val >> 4; |
| 655 | } |
| 656 | ret |
| 657 | } |
| 658 | |
| 659 | fn swp_idx(idx: usize, bits: u32) -> usize { |
| 660 | let s = reverse_bits(idx as u32) as usize; |
| 661 | s >> (32 - bits) |
| 662 | }*/ |
| 663 | |
| 664 | fn gen_sr_perms(swaps: &mut [usize], size: usize) { |
| 665 | if size <= 4 { return; } |
| 666 | let mut evec: Vec<usize> = Vec::with_capacity(size / 2); |
| 667 | let mut ovec1: Vec<usize> = Vec::with_capacity(size / 4); |
| 668 | let mut ovec2: Vec<usize> = Vec::with_capacity(size / 4); |
| 669 | for k in 0..size/4 { |
| 670 | evec.push (swaps[k * 4 + 0]); |
| 671 | ovec1.push(swaps[k * 4 + 1]); |
| 672 | evec.push (swaps[k * 4 + 2]); |
| 673 | ovec2.push(swaps[k * 4 + 3]); |
| 674 | } |
| 675 | for k in 0..size/2 { swaps[k] = evec[k]; } |
| 676 | for k in 0..size/4 { swaps[k + size/2] = ovec1[k]; } |
| 677 | for k in 0..size/4 { swaps[k + 3*size/4] = ovec2[k]; } |
| 678 | gen_sr_perms(&mut swaps[0..size/2], size/2); |
| 679 | gen_sr_perms(&mut swaps[size/2..3*size/4], size/4); |
| 680 | gen_sr_perms(&mut swaps[3*size/4..], size/4); |
| 681 | } |
| 682 | |
| 683 | fn gen_swaps_for_perm(swaps: &mut Vec<usize>, perms: &[usize]) { |
| 684 | let mut idx_arr: Vec<usize> = Vec::with_capacity(perms.len()); |
| 685 | for i in 0..perms.len() { idx_arr.push(i); } |
| 686 | let mut run_size = 0; |
| 687 | let mut run_pos = 0; |
| 688 | for idx in 0..perms.len() { |
| 689 | if perms[idx] == idx_arr[idx] { |
| 690 | if run_size == 0 { run_pos = idx; } |
| 691 | run_size += 1; |
| 692 | } else { |
| 693 | for i in 0..run_size { |
| 694 | swaps.push(run_pos + i); |
| 695 | } |
| 696 | run_size = 0; |
| 697 | let mut spos = idx + 1; |
| 698 | while idx_arr[spos] != perms[idx] { spos += 1; } |
| 699 | idx_arr[spos] = idx_arr[idx]; |
| 700 | idx_arr[idx] = perms[idx]; |
| 701 | swaps.push(spos); |
| 702 | } |
| 703 | } |
| 704 | } |
| 705 | |
| 706 | impl FFTBuilder { |
| 707 | fn generate_twiddle(data: &mut FFTData, size: usize, cur_size: usize, forward: bool) { |
| 708 | if size == cur_size { return; } |
| 709 | data.twiddle = Vec::with_capacity(size); |
| 710 | let div = size / cur_size; |
| 711 | let base = if forward { -2.0 * consts::PI / (size as f32) } else { 2.0 * consts::PI / (size as f32) }; |
| 712 | for n in 0..div { |
| 713 | for k in 0..cur_size { |
| 714 | data.twiddle.push(FFTComplex::exp(base * ((k * n) as f32))); |
| 715 | } |
| 716 | } |
| 717 | } |
| 718 | /// Constructs a new `FFT` context. |
| 719 | pub fn new_fft(size: usize, forward: bool) -> FFT { |
| 720 | let mut ffts: Vec<(FFTMode, FFTData)> = Vec::with_capacity(1); |
| 721 | let mut perms: Vec<usize> = Vec::with_capacity(size); |
| 722 | let mut swaps: Vec<usize> = Vec::with_capacity(size); |
| 723 | let mut rem_size = size; |
| 724 | if rem_size.trailing_zeros() > 0 { |
| 725 | let bits = rem_size.trailing_zeros() as u8; |
| 726 | let mut data = FFTSplitRadix::new_data(bits, forward); |
| 727 | Self::generate_twiddle(&mut data, size, 1 << bits, forward); |
| 728 | data.step = 1; |
| 729 | data.div = rem_size >> bits; |
| 730 | ffts.push((FFTMode::SplitRadix(bits), data)); |
| 731 | rem_size >>= bits; |
| 732 | } |
| 733 | if (rem_size % 15) == 0 { |
| 734 | let mut data = FFT15::new_data(size, forward); |
| 735 | Self::generate_twiddle(&mut data, size, 15, forward); |
| 736 | data.step = size / rem_size; |
| 737 | data.div = size / rem_size; |
| 738 | ffts.push((FFTMode::Prime15, data)); |
| 739 | rem_size /= 15; |
| 740 | } |
| 741 | if rem_size > 1 { |
| 742 | let mut data = FFTGeneric::new_data(rem_size, forward); |
| 743 | Self::generate_twiddle(&mut data, size, rem_size, forward); |
| 744 | data.step = size / rem_size; |
| 745 | data.div = size / rem_size; |
| 746 | ffts.push((FFTMode::Generic(rem_size), data)); |
| 747 | } |
| 748 | |
| 749 | for i in 0..size { |
| 750 | perms.push(i); |
| 751 | } |
| 752 | for (mode, _) in ffts.iter().rev() { |
| 753 | mode.permute(&mut perms); |
| 754 | } |
| 755 | gen_swaps_for_perm(&mut swaps, perms.as_slice()); |
| 756 | |
| 757 | FFT { perms, swaps, ffts } |
| 758 | } |
| 759 | } |
| 760 | |
| 761 | /// RDFT working context. |
| 762 | pub struct RDFT { |
| 763 | table: Vec<FFTComplex>, |
| 764 | fft: FFT, |
| 765 | fwd: bool, |
| 766 | size: usize, |
| 767 | fwd_fft: bool, |
| 768 | } |
| 769 | |
| 770 | fn crossadd(a: FFTComplex, b: FFTComplex) -> FFTComplex { |
| 771 | FFTComplex { re: a.re + b.re, im: a.im - b.im } |
| 772 | } |
| 773 | |
| 774 | impl RDFT { |
| 775 | /// Calculates RDFT. |
| 776 | pub fn do_rdft(&mut self, src: &[FFTComplex], dst: &mut [FFTComplex]) { |
| 777 | dst.copy_from_slice(src); |
| 778 | self.do_rdft_inplace(dst); |
| 779 | } |
| 780 | /// Calculates inplace RDFT. |
| 781 | pub fn do_rdft_inplace(&mut self, buf: &mut [FFTComplex]) { |
| 782 | if !self.fwd { |
| 783 | for n in 0..self.size/2 { |
| 784 | let in0 = buf[n + 1]; |
| 785 | let in1 = buf[self.size - n - 1]; |
| 786 | |
| 787 | let t0 = crossadd(in0, in1); |
| 788 | let t1 = FFTComplex { re: in1.im + in0.im, im: in1.re - in0.re }; |
| 789 | let tab = self.table[n]; |
| 790 | let t2 = FFTComplex { re: t1.im * tab.im + t1.re * tab.re, im: t1.im * tab.re - t1.re * tab.im }; |
| 791 | |
| 792 | buf[n + 1] = FFTComplex { re: t0.im - t2.im, im: t0.re - t2.re }; // (t0 - t2).conj().rotate() |
| 793 | buf[self.size - n - 1] = (t0 + t2).rotate(); |
| 794 | } |
| 795 | let a = buf[0].re; |
| 796 | let b = buf[0].im; |
| 797 | buf[0].re = a - b; |
| 798 | buf[0].im = a + b; |
| 799 | } |
| 800 | if self.fwd_fft { |
| 801 | self.fft.do_fft_inplace(buf); |
| 802 | } else { |
| 803 | self.fft.do_ifft_inplace(buf); |
| 804 | } |
| 805 | if self.fwd { |
| 806 | for n in 0..self.size/2 { |
| 807 | let in0 = buf[n + 1]; |
| 808 | let in1 = buf[self.size - n - 1]; |
| 809 | |
| 810 | let t0 = crossadd(in0, in1).scale(0.5); |
| 811 | let t1 = FFTComplex { re: in0.im + in1.im, im: in0.re - in1.re }; |
| 812 | let t2 = t1 * self.table[n]; |
| 813 | |
| 814 | buf[n + 1] = crossadd(t0, t2); |
| 815 | buf[self.size - n - 1] = FFTComplex { re: t0.re - t2.re, im: -(t0.im + t2.im) }; |
| 816 | } |
| 817 | let a = buf[0].re; |
| 818 | let b = buf[0].im; |
| 819 | buf[0].re = a + b; |
| 820 | buf[0].im = a - b; |
| 821 | } else { |
| 822 | for n in 0..self.size { |
| 823 | buf[n] = FFTComplex{ re: buf[n].im, im: buf[n].re }; |
| 824 | } |
| 825 | } |
| 826 | } |
| 827 | } |
| 828 | |
| 829 | /// [`RDFT`] context creator. |
| 830 | /// |
| 831 | /// [`RDFT`]: ./struct.FFT.html |
| 832 | pub struct RDFTBuilder { |
| 833 | } |
| 834 | |
| 835 | impl RDFTBuilder { |
| 836 | /// Constructs a new `RDFT` context. |
| 837 | pub fn new_rdft(size: usize, forward: bool, forward_fft: bool) -> RDFT { |
| 838 | let mut table: Vec<FFTComplex> = Vec::with_capacity(size / 4); |
| 839 | let (base, scale) = if forward { (consts::PI / (size as f32), 0.5) } else { (-consts::PI / (size as f32), 1.0) }; |
| 840 | for i in 0..size/2 { |
| 841 | table.push(FFTComplex::exp(base * ((i + 1) as f32)).scale(scale)); |
| 842 | } |
| 843 | let fft = FFTBuilder::new_fft(size, forward_fft); |
| 844 | RDFT { table, fft, size, fwd: forward, fwd_fft: forward_fft } |
| 845 | } |
| 846 | } |
| 847 | |
| 848 | |
| 849 | #[cfg(test)] |
| 850 | mod test { |
| 851 | use super::*; |
| 852 | |
| 853 | fn test_fft(size: usize) { |
| 854 | println!("testing FFT {}", size); |
| 855 | let mut fin: Vec<FFTComplex> = Vec::with_capacity(size); |
| 856 | let mut fout1: Vec<FFTComplex> = Vec::with_capacity(size); |
| 857 | let mut fout2: Vec<FFTComplex> = Vec::with_capacity(size); |
| 858 | fin.resize(size, FFTC_ZERO); |
| 859 | fout1.resize(size, FFTC_ZERO); |
| 860 | fout2.resize(size, FFTC_ZERO); |
| 861 | let mut fft = FFTBuilder::new_fft(size, true); |
| 862 | let mut seed: u32 = 42; |
| 863 | for i in 0..fin.len() { |
| 864 | seed = seed.wrapping_mul(1664525).wrapping_add(1013904223); |
| 865 | let val = (seed >> 16) as i16; |
| 866 | fin[i].re = (val as f32) / 256.0; |
| 867 | seed = seed.wrapping_mul(1664525).wrapping_add(1013904223); |
| 868 | let val = (seed >> 16) as i16; |
| 869 | fin[i].im = (val as f32) / 256.0; |
| 870 | } |
| 871 | fft.do_fft(&fin, &mut fout1); |
| 872 | fout2.copy_from_slice(&fin); |
| 873 | generic_fft(&mut fout2, true); |
| 874 | |
| 875 | for i in 0..fin.len() { |
| 876 | assert!((fout1[i].re - fout2[i].re).abs() < 1.0); |
| 877 | assert!((fout1[i].im - fout2[i].im).abs() < 1.0); |
| 878 | } |
| 879 | let mut ifft = FFTBuilder::new_fft(size, false); |
| 880 | ifft.do_ifft_inplace(&mut fout1); |
| 881 | generic_fft(&mut fout2, false); |
| 882 | |
| 883 | let sc = 1.0 / (size as f32); |
| 884 | for i in 0..fin.len() { |
| 885 | assert!((fin[i].re - fout1[i].re * sc).abs() < 1.0); |
| 886 | assert!((fin[i].im - fout1[i].im * sc).abs() < 1.0); |
| 887 | assert!((fout1[i].re - fout2[i].re).abs() * sc < 1.0); |
| 888 | assert!((fout1[i].im - fout2[i].im).abs() * sc < 1.0); |
| 889 | } |
| 890 | } |
| 891 | |
| 892 | #[test] |
| 893 | fn test_ffts() { |
| 894 | test_fft(3); |
| 895 | test_fft(5); |
| 896 | test_fft(16); |
| 897 | test_fft(15); |
| 898 | test_fft(60); |
| 899 | test_fft(256); |
| 900 | test_fft(240); |
| 901 | } |
| 902 | |
| 903 | #[test] |
| 904 | fn test_rdft() { |
| 905 | let mut fin: [FFTComplex; 128] = [FFTC_ZERO; 128]; |
| 906 | let mut fout1: [FFTComplex; 128] = [FFTC_ZERO; 128]; |
| 907 | let mut rdft = RDFTBuilder::new_rdft(fin.len(), true, true); |
| 908 | let mut seed: u32 = 42; |
| 909 | for i in 0..fin.len() { |
| 910 | seed = seed.wrapping_mul(1664525).wrapping_add(1013904223); |
| 911 | let val = (seed >> 16) as i16; |
| 912 | fin[i].re = (val as f32) / 256.0; |
| 913 | seed = seed.wrapping_mul(1664525).wrapping_add(1013904223); |
| 914 | let val = (seed >> 16) as i16; |
| 915 | fin[i].im = (val as f32) / 256.0; |
| 916 | } |
| 917 | rdft.do_rdft(&fin, &mut fout1); |
| 918 | let mut irdft = RDFTBuilder::new_rdft(fin.len(), false, true); |
| 919 | irdft.do_rdft_inplace(&mut fout1); |
| 920 | |
| 921 | for i in 0..fin.len() { |
| 922 | let tst = fout1[i].scale(0.5/(fout1.len() as f32)); |
| 923 | assert!((tst.re - fin[i].re).abs() < 1.0); |
| 924 | assert!((tst.im - fin[i].im).abs() < 1.0); |
| 925 | } |
| 926 | } |
| 927 | } |