1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358
use numbers::*; use multicore_support::*; use simd_extensions::*; use super::super::{Vector, MetaData, DspVec, ToSliceMut, Domain, RealNumberSpace}; /// Operations on real types. /// /// # Failures /// /// If one of the methods is called on complex data then `self.len()` will be set to `0`. /// To avoid this it's recommended to use the `to_real_time_vec`, `to_real_freq_vec` /// `to_complex_time_vec` and `to_complex_freq_vec` constructor methods since /// the resulting types will already check at compile time (using the type system) /// that the data is real. pub trait RealOps { /// Gets the absolute value of all vector elements. /// # Example /// /// ``` /// use basic_dsp_vector::*; /// let mut vector = vec!(1.0, -2.0).to_real_time_vec(); /// vector.abs(); /// assert_eq!([1.0, 2.0], vector[..]); /// ``` fn abs(&mut self); } /// Operations on real types. /// /// # Failures /// /// If one of the methods is called on complex data then `self.len()` will be set to `0`. /// To avoid this it's recommended to use the `to_real_time_vec`, `to_real_freq_vec` /// `to_complex_time_vec` and `to_complex_freq_vec` constructor methods since /// the resulting types will already check at compile time (using the type system) /// that the data is real. pub trait ModuloOps<T> where T: RealNumber { /// Each value in the vector is dividable by the divisor and the remainder /// is stored in the resulting /// vector. This the same a modulo operation or to phase wrapping. /// /// # Example /// /// ``` /// use basic_dsp_vector::*; /// let mut vector = vec!(1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0).to_real_time_vec(); /// vector.wrap(4.0); /// assert_eq!([1.0, 2.0, 3.0, 0.0, 1.0, 2.0, 3.0, 0.0], vector[..]); /// ``` fn wrap(&mut self, divisor: T); /// This function corrects the jumps in the given vector which occur due /// to wrap or modulo operations. /// This will undo a wrap operation only if the deltas are smaller than half the divisor. /// /// # Example /// /// ``` /// use basic_dsp_vector::*; /// let mut vector = vec!(1.0, 2.0, 3.0, 0.0, 1.0, 2.0, 3.0, 0.).to_real_time_vec(); /// vector.unwrap(4.0); /// assert_eq!([1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0], vector[..]); /// ``` fn unwrap(&mut self, divisor: T); } /// Recommended to be only used with feature flags `use_sse` or `use_avx`. /// /// This trait provides alternative implementations for some standard functions which /// are less accurate but perform faster. Those approximations are written for SSE2 /// (feature flag `use_sse`) or AVX2 (feature flag `use_avx`) processors. Without any of those /// feature flags the standard library functions will be used instead. /// /// Information on the error of the approximation and their performance are rough numbers. /// A detailed table can be obtained by running the `approx_accuracy` example. /// /// # Failures /// /// If one of the methods is called on complex data then `self.len()` will be set to `0`. /// To avoid this it's recommended to use the `to_real_time_vec`, `to_real_freq_vec` /// `to_complex_time_vec` and `to_complex_freq_vec` constructor methods since /// the resulting types will already check at compile time (using the type system) /// that the data is real. pub trait ApproximatedOps<T> where T: RealNumber { /// Computes the principal value approximation of natural logarithm of every element in the vector. /// /// Error should be below `1%` as long as the values in the vector are larger than `1`. /// Single core performance should be about `5x` as fast. /// /// # Example /// /// ``` /// # use std::f64; /// use basic_dsp_vector::*; /// let mut vector = vec!(2.718281828459045, 7.389056, 20.085537).to_real_time_vec(); /// vector.ln_approx(); /// let actual = &vector[0..]; /// let expected = &[1.0, 2.0, 3.0]; /// assert_eq!(actual.len(), expected.len()); /// for i in 0..actual.len() { /// assert!(f64::abs(actual[i] - expected[i]) < 1e-2); /// } /// ``` fn ln_approx(&mut self); /// Calculates the natural exponential approximation for every vector element. /// /// Error should be less than `1%`` as long as the values in the vector are small /// (e.g. in the range between -10 and 10). /// Single core performance should be about `50%` faster. /// /// # Example /// /// ``` /// # use std::f64; /// use basic_dsp_vector::*; /// let mut vector = vec!(1.0, 2.0, 3.0).to_real_time_vec(); /// vector.exp_approx(); /// let actual = &vector[0..]; /// let expected = &[2.718281828459045, 7.389056, 20.085537]; /// assert_eq!(actual.len(), expected.len()); /// for i in 0..actual.len() { /// assert!(f64::abs(actual[i] - expected[i]) < 1e-4); /// } /// ``` fn exp_approx(&mut self); /// Calculates the sine approximation of each element in radians. /// /// Error should be below `1E-6`. /// Single core performance should be about `2x` as fast. /// /// # Example /// /// ``` /// use std::f32; /// use basic_dsp_vector::*; /// let mut vector = vec!(f32::consts::PI/2.0, -f32::consts::PI/2.0).to_real_time_vec(); /// vector.sin_approx(); /// assert_eq!([1.0, -1.0], vector[..]); /// ``` fn sin_approx(&mut self); /// Calculates the cosine approximation of each element in radians /// /// Error should be below `1E-6`. /// Single core performance should be about `2x` as fast. /// /// # Example /// /// ``` /// use std::f32; /// use basic_dsp_vector::*; /// let mut vector = vec!(2.0 * f32::consts::PI, f32::consts::PI).to_real_time_vec(); /// vector.cos_approx(); /// assert_eq!([1.0, -1.0], vector[..]); /// ``` fn cos_approx(&mut self); /// Calculates the approximated logarithm to the given base for every vector element. /// /// Error should be below `1%` as long as the values in the vector are larger than `1`. /// Single core performance should be about `5x` as fast. /// /// # Example /// /// ``` /// # use std::f64; /// use basic_dsp_vector::*; /// let mut vector = vec!(10.0, 100.0, 1000.0).to_real_time_vec(); /// vector.log_approx(10.0); /// let actual = &vector[0..]; /// let expected = &[1.0, 2.0, 3.0]; /// assert_eq!(actual.len(), expected.len()); /// for i in 0..actual.len() { /// assert!(f64::abs(actual[i] - expected[i]) < 1e-4); /// } /// ``` fn log_approx(&mut self, base: T); /// Calculates the approximated exponential to the given base for every vector element. /// /// Error should be less than `1%`` as long as the values in the vector are small /// (e.g. in the range between -10 and 10). /// Single core performance should be about `5x` as fast. /// /// # Example /// /// ``` /// use basic_dsp_vector::*; /// use std::f32; /// let vector: Vec<f32> = vec!(1.0, 2.0, 3.0); /// let mut vector = vector.to_real_time_vec(); /// vector.expf_approx(10.0); /// assert!((vector[0] - 10.0).abs() < 1e-3); /// assert!((vector[1] - 100.0).abs() < 1e-3); /// assert!((vector[2] - 1000.0).abs() < 1e-3); /// ``` fn expf_approx(&mut self, base: T); /// Raises every vector element to approximately a floating point power. /// /// Error should be less than `1%`` as long as the values in the vector are really small /// (e.g. in the range between -0.1 and 0.1). /// Single core performance should be about `5x` as fast. /// /// # Example /// /// ``` /// use basic_dsp_vector::*; /// use std::f32; /// let vector: Vec<f32> = vec!(1.0, 2.0, 3.0); /// let mut vector = vector.to_real_time_vec(); /// vector.powf_approx(3.0); /// assert!((vector[0] - 1.0).abs() < 1e-3); /// assert!((vector[1] - 8.0).abs() < 1e-3); /// assert!((vector[2] - 27.0).abs() < 1e-3); /// ``` fn powf_approx(&mut self, exponent: T); } macro_rules! assert_real { ($self_: ident) => { if $self_.is_complex() { $self_.valid_len = 0; return; } } } impl<S, T, N, D> RealOps for DspVec<S, T, N, D> where S: ToSliceMut<T>, T: RealNumber, N: RealNumberSpace, D: Domain { fn abs(&mut self) { assert_real!(self); self.simd_real_operation(|x, _arg| (x * x).sqrt(), |x, _arg| x.abs(), (), Complexity::Small); } } impl<S, T, N, D> ModuloOps<T> for DspVec<S, T, N, D> where S: ToSliceMut<T>, T: RealNumber, N: RealNumberSpace, D: Domain { fn wrap(&mut self, divisor: T) { assert_real!(self); self.pure_real_operation(|x, y| x % y, divisor, Complexity::Small); } fn unwrap(&mut self, divisor: T) { assert_real!(self); let data_length = self.len(); let mut data = self.data.to_slice_mut(); let mut i = 0; let mut j = 1; let half = divisor / T::from(2.0).unwrap(); while j < data_length { let mut diff = data[j] - data[i]; if diff > half { diff = diff % divisor; diff = diff - divisor; data[j] = data[i] + diff; } else if diff < -half { diff = diff % divisor; diff = diff + divisor; data[j] = data[i] + diff; } i += 1; j += 1; } } } /// Complexity of all approximation functions. Medium, because even if the approximations are faster /// than the standard version, it seems to be benificial to spawn threads early. const APPROX_COMPLEXITY: Complexity = Complexity::Medium; impl<S, T, N, D> ApproximatedOps<T> for DspVec<S, T, N, D> where S: ToSliceMut<T>, T: RealNumber, N: RealNumberSpace, D: Domain { fn ln_approx(&mut self) { assert_real!(self); self.simd_real_operation(|x, _arg| x.ln_approx(), |x, _arg| x.ln(), (), APPROX_COMPLEXITY); } fn exp_approx(&mut self) { assert_real!(self); self.simd_real_operation(|x, _arg| x.exp_approx(), |x, _arg| x.exp(), (), APPROX_COMPLEXITY); } fn sin_approx(&mut self) { assert_real!(self); self.simd_real_operation(|x, _arg| x.sin_approx(), |x, _arg| x.sin(), (), APPROX_COMPLEXITY); } fn cos_approx(&mut self) { assert_real!(self); self.simd_real_operation(|x, _arg| x.cos_approx(), |x, _arg| x.cos(), (), APPROX_COMPLEXITY); } fn log_approx(&mut self, base: T) { assert_real!(self); let base_ln = T::Reg::splat(base.ln()); self.simd_real_operation(|x, b| x.ln_approx() / b, |x, b| x.ln() / b.extract(0), (base_ln), APPROX_COMPLEXITY); } fn expf_approx(&mut self, base: T) { assert_real!(self); // Transform base with: // x^y = e^(ln(x)*y) let base_ln = T::Reg::splat(base.ln()); self.simd_real_operation(|y, x| (x * y).exp_approx(), |y, x| (x.extract(0) * y).exp(), (base_ln), APPROX_COMPLEXITY); } fn powf_approx(&mut self, exponent: T) { assert_real!(self); // Transform base with the same equation as for `expf_approx` let exponent = T::Reg::splat(exponent); self.simd_real_operation(|x, y| (x.ln_approx() * y).exp_approx(), |x, y| (x.ln() * y.extract(0)).exp(), (exponent), APPROX_COMPLEXITY); } }