1 /* 2 * Copyright (C) 2008 The Android Open Source Project 3 * 4 * Licensed under the Apache License, Version 2.0 (the "License"); 5 * you may not use this file except in compliance with the License. 6 * You may obtain a copy of the License at 7 * 8 * http://www.apache.org/licenses/LICENSE-2.0 9 * 10 * Unless required by applicable law or agreed to in writing, software 11 * distributed under the License is distributed on an "AS IS" BASIS, 12 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. 13 * See the License for the specific language governing permissions and 14 * limitations under the License. 15 */ 16 17 #ifndef ANDROID_EFFECTSMATH_H_ 18 #define ANDROID_EFFECTSMATH_H_ 19 20 #include <stdint.h> 21 22 #if __cplusplus 23 extern "C" { 24 #endif 25 26 /** coefs for pan, generates sin, cos */ 27 #define COEFF_PAN_G2 -27146 /* -0.82842712474619 = 2 - 4/sqrt(2) */ 28 #define COEFF_PAN_G0 23170 /* 0.707106781186547 = 1/sqrt(2) */ 29 30 /* 31 coefficients for approximating 32 2^x = gn2toX0 + gn2toX1*x + gn2toX2*x^2 + gn2toX3*x^3 33 where x is a int.frac number representing number of octaves. 34 Actually, we approximate only the 2^(frac) using the power series 35 and implement the 2^(int) as a shift, so that 36 2^x == 2^(int.frac) == 2^(int) * 2^(fract) 37 == (gn2toX0 + gn2toX1*x + gn2toX2*x^2 + gn2toX3*x^3) << (int) 38 39 The gn2toX.. were generated using a best fit for a 3rd 40 order polynomial, instead of taking the coefficients from 41 a truncated Taylor (or Maclaurin?) series. 42 */ 43 44 #define GN2_TO_X0 32768 /* 1 */ 45 #define GN2_TO_X1 22833 /* 0.696807861328125 */ 46 #define GN2_TO_X2 7344 /* 0.22412109375 */ 47 #define GN2_TO_X3 2588 /* 0.0789794921875 */ 48 49 /*---------------------------------------------------------------------------- 50 * Fixed Point Math 51 *---------------------------------------------------------------------------- 52 * These macros are used for fixed point multiplies. If the processor 53 * supports fixed point multiplies, replace these macros with inline 54 * assembly code to improve performance. 55 *---------------------------------------------------------------------------- 56 */ 57 58 /* Fixed point multiply 0.15 x 0.15 = 0.15 returned as 32-bits */ 59 #define FMUL_15x15(a,b) \ 60 /*lint -e(704) <avoid multiply for performance>*/ \ 61 (((int32_t)(a) * (int32_t)(b)) >> 15) 62 63 /* Fixed point multiply 0.7 x 0.7 = 0.15 returned as 32-bits */ 64 #define FMUL_7x7(a,b) \ 65 /*lint -e(704) <avoid multiply for performance>*/ \ 66 (((int32_t)(a) * (int32_t)(b) ) << 1) 67 68 /* Fixed point multiply 0.8 x 0.8 = 0.15 returned as 32-bits */ 69 #define FMUL_8x8(a,b) \ 70 /*lint -e(704) <avoid multiply for performance>*/ \ 71 (((int32_t)(a) * (int32_t)(b) ) >> 1) 72 73 /* Fixed point multiply 0.8 x 1.15 = 0.15 returned as 32-bits */ 74 #define FMUL_8x15(a,b) \ 75 /*lint -e(704) <avoid divide for performance>*/ \ 76 (((int32_t)((a) << 7) * (int32_t)(b)) >> 15) 77 78 /* macros for fractional phase accumulator */ 79 /* 80 Note: changed the _U32 to _I32 on 03/14/02. This should not 81 affect the phase calculations, and should allow us to reuse these 82 macros for other audio sample related math. 83 */ 84 #define HARDWARE_BIT_WIDTH 32 85 86 #define NUM_PHASE_INT_BITS 1 87 #define NUM_PHASE_FRAC_BITS 15 88 89 #define PHASE_FRAC_MASK (uint32_t) ((0x1L << NUM_PHASE_FRAC_BITS) -1) 90 91 #define GET_PHASE_INT_PART(x) (uint32_t)((uint32_t)(x) >> NUM_PHASE_FRAC_BITS) 92 #define GET_PHASE_FRAC_PART(x) (uint32_t)((uint32_t)(x) & PHASE_FRAC_MASK) 93 94 #define DEFAULT_PHASE_FRAC 0 95 #define DEFAULT_PHASE_INT 0 96 97 /* 98 Linear interpolation calculates: 99 output = (1-frac) * sample[n] + (frac) * sample[n+1] 100 101 where conceptually 0 <= frac < 1 102 103 For a fixed point implementation, frac is actually an integer value 104 with an implied binary point one position to the left. The value of 105 one (unity) is given by PHASE_ONE 106 one half and one quarter are useful for 4-point linear interp. 107 */ 108 #define PHASE_ONE (int32_t) (0x1L << NUM_PHASE_FRAC_BITS) 109 110 /* 111 Multiply the signed audio sample by the unsigned fraction. 112 - a is the signed audio sample 113 - b is the unsigned fraction (cast to signed int as long as coef 114 uses (n-1) or less bits, where n == hardware bit width) 115 */ 116 #define MULT_AUDIO_COEF(audio,coef) /*lint -e704 <avoid divide for performance>*/ \ 117 (int32_t)( \ 118 ( \ 119 ((int32_t)(audio)) * ((int32_t)(coef)) \ 120 ) \ 121 >> NUM_PHASE_FRAC_BITS \ 122 ) \ 123 /* lint +704 <restore checking>*/ 124 125 /* wet / dry calculation macros */ 126 #define NUM_WET_DRY_FRAC_BITS 7 // 15 127 #define NUM_WET_DRY_INT_BITS 9 // 1 128 129 /* define a 1.0 */ 130 #define WET_DRY_ONE (int32_t) ((0x1L << NUM_WET_DRY_FRAC_BITS)) 131 #define WET_DRY_MINUS_ONE (int32_t) (~WET_DRY_ONE) 132 #define WET_DRY_FULL_SCALE (int32_t) (WET_DRY_ONE - 1) 133 134 #define MULT_AUDIO_WET_DRY_COEF(audio,coef) /*lint -e(702) <avoid divide for performance>*/ \ 135 (int32_t)( \ 136 ( \ 137 ((int32_t)(audio)) * ((int32_t)(coef)) \ 138 ) \ 139 >> NUM_WET_DRY_FRAC_BITS \ 140 ) 141 142 /* Envelope 1 (EG1) calculation macros */ 143 #define NUM_EG1_INT_BITS 1 144 #define NUM_EG1_FRAC_BITS 15 145 146 /* the max positive gain used in the synth for EG1 */ 147 /* SYNTH_FULL_SCALE_EG1_GAIN must match the value in the dls2eas 148 converter, otherwise, the values we read from the .eas file are bogus. */ 149 #define SYNTH_FULL_SCALE_EG1_GAIN (int32_t) ((0x1L << NUM_EG1_FRAC_BITS) -1) 150 151 /* define a 1.0 */ 152 #define EG1_ONE (int32_t) ((0x1L << NUM_EG1_FRAC_BITS)) 153 #define EG1_MINUS_ONE (int32_t) (~SYNTH_FULL_SCALE_EG1_GAIN) 154 155 #define EG1_HALF (int32_t) (EG1_ONE/2) 156 #define EG1_MINUS_HALF (int32_t) (EG1_MINUS_ONE/2) 157 158 /* 159 We implement the EG1 using a linear gain value, which means that the 160 attack segment is handled by incrementing (adding) the linear gain. 161 However, EG1 treats the Decay, Sustain, and Release differently than 162 the Attack portion. For Decay, Sustain, and Release, the gain is 163 linear on dB scale, which is equivalent to exponential damping on 164 a linear scale. Because we use a linear gain for EG1, we implement 165 the Decay and Release as multiplication (instead of incrementing 166 as we did for the attack segment). 167 Therefore, we need the following macro to implement the multiplication 168 (i.e., exponential damping) during the Decay and Release segments of 169 the EG1 170 */ 171 #define MULT_EG1_EG1(gain,damping) /*lint -e(704) <avoid divide for performance>*/ \ 172 (int32_t)( \ 173 ( \ 174 ((int32_t)(gain)) * ((int32_t)(damping)) \ 175 ) \ 176 >> NUM_EG1_FRAC_BITS \ 177 ) 178 179 // Use the following macro specifically for the filter, when multiplying 180 // the b1 coefficient. The 0 <= |b1| < 2, which therefore might overflow 181 // in certain conditions because we store b1 as a 1.15 value. 182 // Instead, we could store b1 as b1p (b1' == b1 "prime") where 183 // b1p == b1/2, thus ensuring no potential overflow for b1p because 184 // 0 <= |b1p| < 1 185 // However, during the filter calculation, we must account for the fact 186 // that we are using b1p instead of b1, and thereby multiply by 187 // an extra factor of 2. Rather than multiply by an extra factor of 2, 188 // we can instead shift the result right by one less, hence the 189 // modified shift right value of (NUM_EG1_FRAC_BITS -1) 190 #define MULT_EG1_EG1_X2(gain,damping) /*lint -e(702) <avoid divide for performance>*/ \ 191 (int32_t)( \ 192 ( \ 193 ((int32_t)(gain)) * ((int32_t)(damping)) \ 194 ) \ 195 >> (NUM_EG1_FRAC_BITS -1) \ 196 ) 197 198 #define SATURATE_EG1(x) /*lint -e{734} saturation operation */ \ 199 ((int32_t)(x) > SYNTH_FULL_SCALE_EG1_GAIN) ? (SYNTH_FULL_SCALE_EG1_GAIN) : \ 200 ((int32_t)(x) < EG1_MINUS_ONE) ? (EG1_MINUS_ONE) : (x); 201 202 203 /* use "digital cents" == "dents" instead of cents */ 204 /* we coudl re-use the phase frac macros, but if we do, 205 we must change the phase macros to cast to _I32 instead of _U32, 206 because using a _U32 cast causes problems when shifting the exponent 207 for the 2^x calculation, because right shift a negative values MUST 208 be sign extended, or else the 2^x calculation is wrong */ 209 210 /* use "digital cents" == "dents" instead of cents */ 211 #define NUM_DENTS_FRAC_BITS 12 212 #define NUM_DENTS_INT_BITS (HARDWARE_BIT_WIDTH - NUM_DENTS_FRAC_BITS) 213 214 #define DENTS_FRAC_MASK (int32_t) ((0x1L << NUM_DENTS_FRAC_BITS) -1) 215 216 #define GET_DENTS_INT_PART(x) /*lint -e(704) <avoid divide for performance>*/ \ 217 (int32_t)((int32_t)(x) >> NUM_DENTS_FRAC_BITS) 218 219 #define GET_DENTS_FRAC_PART(x) (int32_t)((int32_t)(x) & DENTS_FRAC_MASK) 220 221 #define DENTS_ONE (int32_t) (0x1L << NUM_DENTS_FRAC_BITS) 222 223 /* use CENTS_TO_DENTS to convert a value in cents to dents */ 224 #define CENTS_TO_DENTS (int32_t) (DENTS_ONE * (0x1L << NUM_EG1_FRAC_BITS) / 1200L) \ 225 226 227 /* 228 For gain, the LFO generates a value that modulates in terms 229 of dB. However, we use a linear gain value, so we must convert 230 the LFO value in dB to a linear gain. Normally, we would use 231 linear gain = 10^x, where x = LFO value in dB / 20. 232 Instead, we implement 10^x using our 2^x approximation. 233 because 234 235 10^x = 2^(log2(10^x)) = 2^(x * log2(10)) 236 237 so we need to multiply by log2(10) which is just a constant. 238 Ah, but just wait -- our 2^x actually doesn't exactly implement 239 2^x, but it actually assumes that the input is in cents, and within 240 the 2^x approximation converts its input from cents to octaves 241 by dividing its input by 1200. 242 243 So, in order to convert the LFO gain value in dB to something 244 that our existing 2^x approximation can use, multiply the LFO gain 245 by log2(10) * 1200 / 20 246 247 The divide by 20 helps convert dB to linear gain, and we might 248 as well incorporate that operation into this conversion. 249 Of course, we need to keep some fractional bits, so multiply 250 the constant by NUM_EG1_FRAC_BITS 251 */ 252 253 /* use LFO_GAIN_TO_CENTS to convert the LFO gain value to cents */ 254 255 #define LFO_GAIN_TO_CENTS (int32_t) (1671981156L >> (23 - NUM_EG1_FRAC_BITS)) 256 257 258 #define MULT_DENTS_COEF(dents,coef) /*lint -e704 <avoid divide for performance>*/ \ 259 (int32_t)( \ 260 ( \ 261 ((int32_t)(dents)) * ((int32_t)(coef)) \ 262 ) \ 263 >> NUM_DENTS_FRAC_BITS \ 264 ) \ 265 /* lint +e704 <restore checking>*/ 266 267 268 /* we use 16-bits in the PC per audio sample */ 269 #define BITS_PER_AUDIO_SAMPLE 16 270 271 /* we define 1 as 1.0 - 1 LSbit */ 272 #define DISTORTION_ONE (int32_t)((0x1L << (BITS_PER_AUDIO_SAMPLE-1)) -1) 273 #define DISTORTION_MINUS_ONE (int32_t)(~DISTORTION_ONE) 274 275 /* drive coef is given as int.frac */ 276 #define NUM_DRIVE_COEF_INT_BITS 1 277 #define NUM_DRIVE_COEF_FRAC_BITS 4 278 279 #define MULT_AUDIO_DRIVE(audio,drive) /*lint -e(702) <avoid divide for performance>*/ \ 280 (int32_t) ( \ 281 ( \ 282 ((int32_t)(audio)) * ((int32_t)(drive)) \ 283 ) \ 284 >> NUM_DRIVE_COEF_FRAC_BITS \ 285 ) 286 287 #define MULT_AUDIO_AUDIO(audio1,audio2) /*lint -e(702) <avoid divide for performance>*/ \ 288 (int32_t) ( \ 289 ( \ 290 ((int32_t)(audio1)) * ((int32_t)(audio2)) \ 291 ) \ 292 >> (BITS_PER_AUDIO_SAMPLE-1) \ 293 ) 294 295 #define SATURATE(x) \ 296 ((((int32_t)(x)) > DISTORTION_ONE) ? (DISTORTION_ONE) : \ 297 (((int32_t)(x)) < DISTORTION_MINUS_ONE) ? (DISTORTION_MINUS_ONE) : ((int32_t)(x))); 298 299 300 /*---------------------------------------------------------------------------- 301 * Effects_log2() 302 *---------------------------------------------------------------------------- 303 * Purpose: 304 * Fixed-point log2 function. 305 * 306 * Inputs: 307 * Input is interpreted as an integer (should not be 0). 308 * 309 * Outputs: 310 * Output is in 15-bit precision. 311 * 312 * Side Effects: 313 * 314 *---------------------------------------------------------------------------- 315 */ 316 int32_t Effects_log2(uint32_t x); 317 318 /*---------------------------------------------------------------------------- 319 * Effects_exp2() 320 *---------------------------------------------------------------------------- 321 * Purpose: 322 * Fixed-point radix-2 exponent. 323 * 324 * Inputs: 325 * Input is in 15-bit precision. Must be non-negative and less than 32. 326 * 327 * Outputs: 328 * Output is an integer. 329 * 330 * Side Effects: 331 * 332 *---------------------------------------------------------------------------- 333 */ 334 uint32_t Effects_exp2(int32_t x); 335 336 /*---------------------------------------------------------------------------- 337 * Effects_MillibelsToLinear16() 338 *---------------------------------------------------------------------------- 339 * Purpose: 340 * Transform gain in millibels to linear gain multiplier: 341 * 342 * mB = 2000*log(lin/32767) 343 * => lin = 2^((mB+2000*log(32767))/2000*log(2)) 344 * => lin = Effects_exp2(((mB + K1) << 15) / K2) 345 * with: 346 * K1 = 2000*log(32767) and K2 = 2000*log(2) 347 * 348 * Inputs: 349 * nGain - log scale value in millibels. 350 * 351 * Outputs: 352 * Returns a 16-bit linear value approximately equal to 2^(nGain/1024) 353 * 354 * Side Effects: 355 * 356 *---------------------------------------------------------------------------- 357 */ 358 #define MB_TO_LIN_K1 9031 359 #define MB_TO_LIN_K2 602 360 int16_t Effects_MillibelsToLinear16 (int32_t nGain); 361 362 /*---------------------------------------------------------------------------- 363 * Effects_Linear16ToMillibels() 364 *---------------------------------------------------------------------------- 365 * Purpose: 366 * Transform linear gain multiplier to millibels 367 * mB = 2000*log(lin/32767) 368 * = 2000*log(2)*log2(lin)-2000*log(32767) 369 * => mB = K1*Effects_log2(lin) + K2 370 * with: 371 * K1 = 2000*log(2) and K2 = -2000*log(32767) 372 * 373 * Inputs: 374 * nGain - linear multiplier ranging form 0 to 32767 (corresponding to [0 1] gain range). 375 * 376 * Outputs: 377 * Returns a 16-bit log value expressed in milllibels. 378 * 379 * Side Effects: 380 * 381 *---------------------------------------------------------------------------- 382 */ 383 int16_t Effects_Linear16ToMillibels (int32_t nGain); 384 385 /*---------------------------------------------------------------------------- 386 * Effects_Sqrt() 387 *---------------------------------------------------------------------------- 388 * Purpose: 389 * Returns the square root of the argument given. 390 * 391 * Inputs: 392 * in - positive number in the range 0 - 2^28 393 * 394 * Outputs: 395 * Returned value: square root of in. 396 * 397 * Side Effects: 398 * 399 *---------------------------------------------------------------------------- 400 */ 401 int32_t Effects_Sqrt(int32_t in); 402 403 #if __cplusplus 404 } // extern "C" 405 #endif 406 407 #endif /*ANDROID_EFFECTSMATH_H_*/ 408 409