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 23extern "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/* 31coefficients for approximating 322^x = gn2toX0 + gn2toX1*x + gn2toX2*x^2 + gn2toX3*x^3 33where x is a int.frac number representing number of octaves. 34Actually, we approximate only the 2^(frac) using the power series 35and implement the 2^(int) as a shift, so that 362^x == 2^(int.frac) == 2^(int) * 2^(fract) 37 == (gn2toX0 + gn2toX1*x + gn2toX2*x^2 + gn2toX3*x^3) << (int) 38 39The gn2toX.. were generated using a best fit for a 3rd 40order polynomial, instead of taking the coefficients from 41a 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/* 80Note: changed the _U32 to _I32 on 03/14/02. This should not 81affect the phase calculations, and should allow us to reuse these 82macros 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/* 98Linear interpolation calculates: 99output = (1-frac) * sample[n] + (frac) * sample[n+1] 100 101where conceptually 0 <= frac < 1 102 103For a fixed point implementation, frac is actually an integer value 104with an implied binary point one position to the left. The value of 105one (unity) is given by PHASE_ONE 106one 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 148converter, 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/* 159We implement the EG1 using a linear gain value, which means that the 160attack segment is handled by incrementing (adding) the linear gain. 161However, EG1 treats the Decay, Sustain, and Release differently than 162the Attack portion. For Decay, Sustain, and Release, the gain is 163linear on dB scale, which is equivalent to exponential damping on 164a linear scale. Because we use a linear gain for EG1, we implement 165the Decay and Release as multiplication (instead of incrementing 166as we did for the attack segment). 167Therefore, we need the following macro to implement the multiplication 168(i.e., exponential damping) during the Decay and Release segments of 169the 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, 205we must change the phase macros to cast to _I32 instead of _U32, 206because using a _U32 cast causes problems when shifting the exponent 207for the 2^x calculation, because right shift a negative values MUST 208be 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/* 228For gain, the LFO generates a value that modulates in terms 229of dB. However, we use a linear gain value, so we must convert 230the LFO value in dB to a linear gain. Normally, we would use 231linear gain = 10^x, where x = LFO value in dB / 20. 232Instead, we implement 10^x using our 2^x approximation. 233because 234 235 10^x = 2^(log2(10^x)) = 2^(x * log2(10)) 236 237so we need to multiply by log2(10) which is just a constant. 238Ah, but just wait -- our 2^x actually doesn't exactly implement 2392^x, but it actually assumes that the input is in cents, and within 240the 2^x approximation converts its input from cents to octaves 241by dividing its input by 1200. 242 243So, in order to convert the LFO gain value in dB to something 244that our existing 2^x approximation can use, multiply the LFO gain 245by log2(10) * 1200 / 20 246 247The divide by 20 helps convert dB to linear gain, and we might 248as well incorporate that operation into this conversion. 249Of course, we need to keep some fractional bits, so multiply 250the constant by NUM_EG1_FRAC_BITS 251*/ 252 253/* use LFO_GAIN_TO_CENTS to convert the LFO gain value to cents */ 254#if 0 255#define DOUBLE_LOG2_10 (double) (3.32192809488736) /* log2(10) */ 256 257#define DOUBLE_LFO_GAIN_TO_CENTS (double) \ 258 ( \ 259 (DOUBLE_LOG2_10) * \ 260 1200.0 / \ 261 20.0 \ 262 ) 263 264#define LFO_GAIN_TO_CENTS (int32_t) \ 265 ( \ 266 DOUBLE_LFO_GAIN_TO_CENTS * \ 267 (0x1L << NUM_EG1_FRAC_BITS) \ 268 ) 269#endif 270 271#define LFO_GAIN_TO_CENTS (int32_t) (1671981156L >> (23 - NUM_EG1_FRAC_BITS)) 272 273 274#define MULT_DENTS_COEF(dents,coef) /*lint -e704 <avoid divide for performance>*/ \ 275 (int32_t)( \ 276 ( \ 277 ((int32_t)(dents)) * ((int32_t)(coef)) \ 278 ) \ 279 >> NUM_DENTS_FRAC_BITS \ 280 ) \ 281 /* lint +e704 <restore checking>*/ 282 283 284/* we use 16-bits in the PC per audio sample */ 285#define BITS_PER_AUDIO_SAMPLE 16 286 287/* we define 1 as 1.0 - 1 LSbit */ 288#define DISTORTION_ONE (int32_t)((0x1L << (BITS_PER_AUDIO_SAMPLE-1)) -1) 289#define DISTORTION_MINUS_ONE (int32_t)(~DISTORTION_ONE) 290 291/* drive coef is given as int.frac */ 292#define NUM_DRIVE_COEF_INT_BITS 1 293#define NUM_DRIVE_COEF_FRAC_BITS 4 294 295#define MULT_AUDIO_DRIVE(audio,drive) /*lint -e(702) <avoid divide for performance>*/ \ 296 (int32_t) ( \ 297 ( \ 298 ((int32_t)(audio)) * ((int32_t)(drive)) \ 299 ) \ 300 >> NUM_DRIVE_COEF_FRAC_BITS \ 301 ) 302 303#define MULT_AUDIO_AUDIO(audio1,audio2) /*lint -e(702) <avoid divide for performance>*/ \ 304 (int32_t) ( \ 305 ( \ 306 ((int32_t)(audio1)) * ((int32_t)(audio2)) \ 307 ) \ 308 >> (BITS_PER_AUDIO_SAMPLE-1) \ 309 ) 310 311#define SATURATE(x) \ 312 ((((int32_t)(x)) > DISTORTION_ONE) ? (DISTORTION_ONE) : \ 313 (((int32_t)(x)) < DISTORTION_MINUS_ONE) ? (DISTORTION_MINUS_ONE) : ((int32_t)(x))); 314 315 316/*---------------------------------------------------------------------------- 317 * Effects_log2() 318 *---------------------------------------------------------------------------- 319 * Purpose: 320 * Fixed-point log2 function. 321 * 322 * Inputs: 323 * Input is interpreted as an integer (should not be 0). 324 * 325 * Outputs: 326 * Output is in 15-bit precision. 327 * 328 * Side Effects: 329 * 330 *---------------------------------------------------------------------------- 331*/ 332int32_t Effects_log2(uint32_t x); 333 334/*---------------------------------------------------------------------------- 335 * Effects_exp2() 336 *---------------------------------------------------------------------------- 337 * Purpose: 338 * Fixed-point radix-2 exponent. 339 * 340 * Inputs: 341 * Input is in 15-bit precision. Must be non-negative and less than 32. 342 * 343 * Outputs: 344 * Output is an integer. 345 * 346 * Side Effects: 347 * 348 *---------------------------------------------------------------------------- 349*/ 350uint32_t Effects_exp2(int32_t x); 351 352/*---------------------------------------------------------------------------- 353 * Effects_MillibelsToLinear16() 354 *---------------------------------------------------------------------------- 355 * Purpose: 356 * Transform gain in millibels to linear gain multiplier: 357 * 358 * mB = 2000*log(lin/32767) 359 * => lin = 2^((mB+2000*log(32767))/2000*log(2)) 360 * => lin = Effects_exp2(((mB + K1) << 15) / K2) 361 * with: 362 * K1 = 2000*log(32767) and K2 = 2000*log(2) 363 * 364 * Inputs: 365 * nGain - log scale value in millibels. 366 * 367 * Outputs: 368 * Returns a 16-bit linear value approximately equal to 2^(nGain/1024) 369 * 370 * Side Effects: 371 * 372 *---------------------------------------------------------------------------- 373*/ 374#define MB_TO_LIN_K1 9031 375#define MB_TO_LIN_K2 602 376int16_t Effects_MillibelsToLinear16 (int32_t nGain); 377 378/*---------------------------------------------------------------------------- 379 * Effects_Linear16ToMillibels() 380 *---------------------------------------------------------------------------- 381 * Purpose: 382 * Transform linear gain multiplier to millibels 383 * mB = 2000*log(lin/32767) 384 * = 2000*log(2)*log2(lin)-2000*log(32767) 385 * => mB = K1*Effects_log2(lin) + K2 386 * with: 387 * K1 = 2000*log(2) and K2 = -2000*log(32767) 388 * 389 * Inputs: 390 * nGain - linear multiplier ranging form 0 to 32767 (corresponding to [0 1] gain range). 391 * 392 * Outputs: 393 * Returns a 16-bit log value expressed in milllibels. 394 * 395 * Side Effects: 396 * 397 *---------------------------------------------------------------------------- 398*/ 399int16_t Effects_Linear16ToMillibels (int32_t nGain); 400 401/*---------------------------------------------------------------------------- 402 * Effects_Sqrt() 403 *---------------------------------------------------------------------------- 404 * Purpose: 405 * Returns the square root of the argument given. 406 * 407 * Inputs: 408 * in - positive number in the range 0 - 2^28 409 * 410 * Outputs: 411 * Returned value: square root of in. 412 * 413 * Side Effects: 414 * 415 *---------------------------------------------------------------------------- 416*/ 417int32_t Effects_Sqrt(int32_t in); 418 419#if __cplusplus 420} // extern "C" 421#endif 422 423#endif /*ANDROID_EFFECTSMATH_H_*/ 424 425