1 /*---------------------------------------------------------------------------- 2 * 3 * File: 4 * eas_math.h 5 * 6 * Contents and purpose: 7 * Contains common math routines for the various audio engines. 8 * 9 * 10 * Copyright Sonic Network Inc. 2005 11 12 * Licensed under the Apache License, Version 2.0 (the "License"); 13 * you may not use this file except in compliance with the License. 14 * You may obtain a copy of the License at 15 * 16 * http://www.apache.org/licenses/LICENSE-2.0 17 * 18 * Unless required by applicable law or agreed to in writing, software 19 * distributed under the License is distributed on an "AS IS" BASIS, 20 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. 21 * See the License for the specific language governing permissions and 22 * limitations under the License. 23 * 24 *---------------------------------------------------------------------------- 25 * Revision Control: 26 * $Revision: 584 $ 27 * $Date: 2007-03-08 09:49:24 -0800 (Thu, 08 Mar 2007) $ 28 *---------------------------------------------------------------------------- 29 */ 30 31 #ifndef _EAS_MATH_H 32 #define _EAS_MATH_H 33 34 35 /** coefs for pan, generates sin, cos */ 36 #define COEFF_PAN_G2 -27146 /* -0.82842712474619 = 2 - 4/sqrt(2) */ 37 #define COEFF_PAN_G0 23170 /* 0.707106781186547 = 1/sqrt(2) */ 38 39 /* 40 coefficients for approximating 41 2^x = gn2toX0 + gn2toX1*x + gn2toX2*x^2 + gn2toX3*x^3 42 where x is a int.frac number representing number of octaves. 43 Actually, we approximate only the 2^(frac) using the power series 44 and implement the 2^(int) as a shift, so that 45 2^x == 2^(int.frac) == 2^(int) * 2^(fract) 46 == (gn2toX0 + gn2toX1*x + gn2toX2*x^2 + gn2toX3*x^3) << (int) 47 48 The gn2toX.. were generated using a best fit for a 3rd 49 order polynomial, instead of taking the coefficients from 50 a truncated Taylor (or Maclaurin?) series. 51 */ 52 53 #define GN2_TO_X0 32768 /* 1 */ 54 #define GN2_TO_X1 22833 /* 0.696807861328125 */ 55 #define GN2_TO_X2 7344 /* 0.22412109375 */ 56 #define GN2_TO_X3 2588 /* 0.0789794921875 */ 57 58 /*---------------------------------------------------------------------------- 59 * Fixed Point Math 60 *---------------------------------------------------------------------------- 61 * These macros are used for fixed point multiplies. If the processor 62 * supports fixed point multiplies, replace these macros with inline 63 * assembly code to improve performance. 64 *---------------------------------------------------------------------------- 65 */ 66 67 /* Fixed point multiply 0.15 x 0.15 = 0.15 returned as 32-bits */ 68 #define FMUL_15x15(a,b) \ 69 /*lint -e(704) <avoid multiply for performance>*/ \ 70 (((EAS_I32)(a) * (EAS_I32)(b)) >> 15) 71 72 /* Fixed point multiply 0.7 x 0.7 = 0.15 returned as 32-bits */ 73 #define FMUL_7x7(a,b) \ 74 /*lint -e(704) <avoid multiply for performance>*/ \ 75 (((EAS_I32)(a) * (EAS_I32)(b) ) << 1) 76 77 /* Fixed point multiply 0.8 x 0.8 = 0.15 returned as 32-bits */ 78 #define FMUL_8x8(a,b) \ 79 /*lint -e(704) <avoid multiply for performance>*/ \ 80 (((EAS_I32)(a) * (EAS_I32)(b) ) >> 1) 81 82 /* Fixed point multiply 0.8 x 1.15 = 0.15 returned as 32-bits */ 83 #define FMUL_8x15(a,b) \ 84 /*lint -e(704) <avoid divide for performance>*/ \ 85 (((EAS_I32)((a) << 7) * (EAS_I32)(b)) >> 15) 86 87 /* macros for fractional phase accumulator */ 88 /* 89 Note: changed the _U32 to _I32 on 03/14/02. This should not 90 affect the phase calculations, and should allow us to reuse these 91 macros for other audio sample related math. 92 */ 93 #define HARDWARE_BIT_WIDTH 32 94 95 #define NUM_PHASE_INT_BITS 1 96 #define NUM_PHASE_FRAC_BITS 15 97 98 #define PHASE_FRAC_MASK (EAS_U32) ((0x1L << NUM_PHASE_FRAC_BITS) -1) 99 100 #define GET_PHASE_INT_PART(x) (EAS_U32)((EAS_U32)(x) >> NUM_PHASE_FRAC_BITS) 101 #define GET_PHASE_FRAC_PART(x) (EAS_U32)((EAS_U32)(x) & PHASE_FRAC_MASK) 102 103 #define DEFAULT_PHASE_FRAC 0 104 #define DEFAULT_PHASE_INT 0 105 106 /* 107 Linear interpolation calculates: 108 output = (1-frac) * sample[n] + (frac) * sample[n+1] 109 110 where conceptually 0 <= frac < 1 111 112 For a fixed point implementation, frac is actually an integer value 113 with an implied binary point one position to the left. The value of 114 one (unity) is given by PHASE_ONE 115 one half and one quarter are useful for 4-point linear interp. 116 */ 117 #define PHASE_ONE (EAS_I32) (0x1L << NUM_PHASE_FRAC_BITS) 118 119 /* 120 Multiply the signed audio sample by the unsigned fraction. 121 - a is the signed audio sample 122 - b is the unsigned fraction (cast to signed int as long as coef 123 uses (n-1) or less bits, where n == hardware bit width) 124 */ 125 #define MULT_AUDIO_COEF(audio,coef) /*lint -e704 <avoid divide for performance>*/ \ 126 (EAS_I32)( \ 127 ( \ 128 ((EAS_I32)(audio)) * ((EAS_I32)(coef)) \ 129 ) \ 130 >> NUM_PHASE_FRAC_BITS \ 131 ) \ 132 /* lint +704 <restore checking>*/ 133 134 /* wet / dry calculation macros */ 135 #define NUM_WET_DRY_FRAC_BITS 7 // 15 136 #define NUM_WET_DRY_INT_BITS 9 // 1 137 138 /* define a 1.0 */ 139 #define WET_DRY_ONE (EAS_I32) ((0x1L << NUM_WET_DRY_FRAC_BITS)) 140 #define WET_DRY_MINUS_ONE (EAS_I32) (~WET_DRY_ONE) 141 #define WET_DRY_FULL_SCALE (EAS_I32) (WET_DRY_ONE - 1) 142 143 #define MULT_AUDIO_WET_DRY_COEF(audio,coef) /*lint -e(702) <avoid divide for performance>*/ \ 144 (EAS_I32)( \ 145 ( \ 146 ((EAS_I32)(audio)) * ((EAS_I32)(coef)) \ 147 ) \ 148 >> NUM_WET_DRY_FRAC_BITS \ 149 ) 150 151 /* Envelope 1 (EG1) calculation macros */ 152 #define NUM_EG1_INT_BITS 1 153 #define NUM_EG1_FRAC_BITS 15 154 155 /* the max positive gain used in the synth for EG1 */ 156 /* SYNTH_FULL_SCALE_EG1_GAIN must match the value in the dls2eas 157 converter, otherwise, the values we read from the .eas file are bogus. */ 158 #define SYNTH_FULL_SCALE_EG1_GAIN (EAS_I32) ((0x1L << NUM_EG1_FRAC_BITS) -1) 159 160 /* define a 1.0 */ 161 #define EG1_ONE (EAS_I32) ((0x1L << NUM_EG1_FRAC_BITS)) 162 #define EG1_MINUS_ONE (EAS_I32) (~SYNTH_FULL_SCALE_EG1_GAIN) 163 164 #define EG1_HALF (EAS_I32) (EG1_ONE/2) 165 #define EG1_MINUS_HALF (EAS_I32) (EG1_MINUS_ONE/2) 166 167 /* 168 We implement the EG1 using a linear gain value, which means that the 169 attack segment is handled by incrementing (adding) the linear gain. 170 However, EG1 treats the Decay, Sustain, and Release differently than 171 the Attack portion. For Decay, Sustain, and Release, the gain is 172 linear on dB scale, which is equivalent to exponential damping on 173 a linear scale. Because we use a linear gain for EG1, we implement 174 the Decay and Release as multiplication (instead of incrementing 175 as we did for the attack segment). 176 Therefore, we need the following macro to implement the multiplication 177 (i.e., exponential damping) during the Decay and Release segments of 178 the EG1 179 */ 180 #define MULT_EG1_EG1(gain,damping) /*lint -e(704) <avoid divide for performance>*/ \ 181 (EAS_I32)( \ 182 ( \ 183 ((EAS_I32)(gain)) * ((EAS_I32)(damping)) \ 184 ) \ 185 >> NUM_EG1_FRAC_BITS \ 186 ) 187 188 // Use the following macro specifically for the filter, when multiplying 189 // the b1 coefficient. The 0 <= |b1| < 2, which therefore might overflow 190 // in certain conditions because we store b1 as a 1.15 value. 191 // Instead, we could store b1 as b1p (b1' == b1 "prime") where 192 // b1p == b1/2, thus ensuring no potential overflow for b1p because 193 // 0 <= |b1p| < 1 194 // However, during the filter calculation, we must account for the fact 195 // that we are using b1p instead of b1, and thereby multiply by 196 // an extra factor of 2. Rather than multiply by an extra factor of 2, 197 // we can instead shift the result right by one less, hence the 198 // modified shift right value of (NUM_EG1_FRAC_BITS -1) 199 #define MULT_EG1_EG1_X2(gain,damping) /*lint -e(702) <avoid divide for performance>*/ \ 200 (EAS_I32)( \ 201 ( \ 202 ((EAS_I32)(gain)) * ((EAS_I32)(damping)) \ 203 ) \ 204 >> (NUM_EG1_FRAC_BITS -1) \ 205 ) 206 207 #define SATURATE_EG1(x) /*lint -e{734} saturation operation */ \ 208 ((EAS_I32)(x) > SYNTH_FULL_SCALE_EG1_GAIN) ? (SYNTH_FULL_SCALE_EG1_GAIN) : \ 209 ((EAS_I32)(x) < EG1_MINUS_ONE) ? (EG1_MINUS_ONE) : (x); 210 211 212 /* use "digital cents" == "dents" instead of cents */ 213 /* we coudl re-use the phase frac macros, but if we do, 214 we must change the phase macros to cast to _I32 instead of _U32, 215 because using a _U32 cast causes problems when shifting the exponent 216 for the 2^x calculation, because right shift a negative values MUST 217 be sign extended, or else the 2^x calculation is wrong */ 218 219 /* use "digital cents" == "dents" instead of cents */ 220 #define NUM_DENTS_FRAC_BITS 12 221 #define NUM_DENTS_INT_BITS (HARDWARE_BIT_WIDTH - NUM_DENTS_FRAC_BITS) 222 223 #define DENTS_FRAC_MASK (EAS_I32) ((0x1L << NUM_DENTS_FRAC_BITS) -1) 224 225 #define GET_DENTS_INT_PART(x) /*lint -e(704) <avoid divide for performance>*/ \ 226 (EAS_I32)((EAS_I32)(x) >> NUM_DENTS_FRAC_BITS) 227 228 #define GET_DENTS_FRAC_PART(x) (EAS_I32)((EAS_I32)(x) & DENTS_FRAC_MASK) 229 230 #define DENTS_ONE (EAS_I32) (0x1L << NUM_DENTS_FRAC_BITS) 231 232 /* use CENTS_TO_DENTS to convert a value in cents to dents */ 233 #define CENTS_TO_DENTS (EAS_I32) (DENTS_ONE * (0x1L << NUM_EG1_FRAC_BITS) / 1200L) \ 234 235 236 /* 237 For gain, the LFO generates a value that modulates in terms 238 of dB. However, we use a linear gain value, so we must convert 239 the LFO value in dB to a linear gain. Normally, we would use 240 linear gain = 10^x, where x = LFO value in dB / 20. 241 Instead, we implement 10^x using our 2^x approximation. 242 because 243 244 10^x = 2^(log2(10^x)) = 2^(x * log2(10)) 245 246 so we need to multiply by log2(10) which is just a constant. 247 Ah, but just wait -- our 2^x actually doesn't exactly implement 248 2^x, but it actually assumes that the input is in cents, and within 249 the 2^x approximation converts its input from cents to octaves 250 by dividing its input by 1200. 251 252 So, in order to convert the LFO gain value in dB to something 253 that our existing 2^x approximation can use, multiply the LFO gain 254 by log2(10) * 1200 / 20 255 256 The divide by 20 helps convert dB to linear gain, and we might 257 as well incorporate that operation into this conversion. 258 Of course, we need to keep some fractional bits, so multiply 259 the constant by NUM_EG1_FRAC_BITS 260 */ 261 262 /* use LFO_GAIN_TO_CENTS to convert the LFO gain value to cents */ 263 #if 0 264 #define DOUBLE_LOG2_10 (double) (3.32192809488736) /* log2(10) */ 265 266 #define DOUBLE_LFO_GAIN_TO_CENTS (double) \ 267 ( \ 268 (DOUBLE_LOG2_10) * \ 269 1200.0 / \ 270 20.0 \ 271 ) 272 273 #define LFO_GAIN_TO_CENTS (EAS_I32) \ 274 ( \ 275 DOUBLE_LFO_GAIN_TO_CENTS * \ 276 (0x1L << NUM_EG1_FRAC_BITS) \ 277 ) 278 #endif 279 280 #define LFO_GAIN_TO_CENTS (EAS_I32) (1671981156L >> (23 - NUM_EG1_FRAC_BITS)) 281 282 283 #define MULT_DENTS_COEF(dents,coef) /*lint -e704 <avoid divide for performance>*/ \ 284 (EAS_I32)( \ 285 ( \ 286 ((EAS_I32)(dents)) * ((EAS_I32)(coef)) \ 287 ) \ 288 >> NUM_DENTS_FRAC_BITS \ 289 ) \ 290 /* lint +e704 <restore checking>*/ 291 292 /* we use 16-bits in the PC per audio sample */ 293 #define BITS_PER_AUDIO_SAMPLE 16 294 295 /* we define 1 as 1.0 - 1 LSbit */ 296 #define DISTORTION_ONE (EAS_I32)((0x1L << (BITS_PER_AUDIO_SAMPLE-1)) -1) 297 #define DISTORTION_MINUS_ONE (EAS_I32)(~DISTORTION_ONE) 298 299 /* drive coef is given as int.frac */ 300 #define NUM_DRIVE_COEF_INT_BITS 1 301 #define NUM_DRIVE_COEF_FRAC_BITS 4 302 303 #define MULT_AUDIO_DRIVE(audio,drive) /*lint -e(702) <avoid divide for performance>*/ \ 304 (EAS_I32) ( \ 305 ( \ 306 ((EAS_I32)(audio)) * ((EAS_I32)(drive)) \ 307 ) \ 308 >> NUM_DRIVE_COEF_FRAC_BITS \ 309 ) 310 311 #define MULT_AUDIO_AUDIO(audio1,audio2) /*lint -e(702) <avoid divide for performance>*/ \ 312 (EAS_I32) ( \ 313 ( \ 314 ((EAS_I32)(audio1)) * ((EAS_I32)(audio2)) \ 315 ) \ 316 >> (BITS_PER_AUDIO_SAMPLE-1) \ 317 ) 318 319 #define SATURATE(x) \ 320 ((((EAS_I32)(x)) > DISTORTION_ONE) ? (DISTORTION_ONE) : \ 321 (((EAS_I32)(x)) < DISTORTION_MINUS_ONE) ? (DISTORTION_MINUS_ONE) : ((EAS_I32)(x))); 322 323 324 325 /*---------------------------------------------------------------------------- 326 * EAS_Calculate2toX() 327 *---------------------------------------------------------------------------- 328 * Purpose: 329 * Calculate 2^x 330 * 331 * Inputs: 332 * nCents - measured in cents 333 * 334 * Outputs: 335 * nResult - int.frac result (where frac has NUM_DENTS_FRAC_BITS) 336 * 337 * Side Effects: 338 * 339 *---------------------------------------------------------------------------- 340 */ 341 EAS_I32 EAS_Calculate2toX (EAS_I32 nCents); 342 343 /*---------------------------------------------------------------------------- 344 * EAS_LogToLinear16() 345 *---------------------------------------------------------------------------- 346 * Purpose: 347 * Transform log value to linear gain multiplier using piece-wise linear 348 * approximation 349 * 350 * Inputs: 351 * nGain - log scale value in 20.10 format. Even though gain is normally 352 * stored in 6.10 (16-bit) format we use 32-bit numbers here to eliminate 353 * the need for saturation checking when combining gain values. 354 * 355 * Outputs: 356 * Returns a 16-bit linear value approximately equal to 2^(nGain/1024) 357 * 358 * Side Effects: 359 * 360 *---------------------------------------------------------------------------- 361 */ 362 EAS_U16 EAS_LogToLinear16 (EAS_I32 nGain); 363 364 /*---------------------------------------------------------------------------- 365 * EAS_VolumeToGain() 366 *---------------------------------------------------------------------------- 367 * Purpose: 368 * Transform volume control in 1dB increments to gain multiplier 369 * 370 * Inputs: 371 * volume - 100 = 0dB, 99 = -1dB, 0 = -inf 372 * 373 * Outputs: 374 * Returns a 16-bit linear value 375 *---------------------------------------------------------------------------- 376 */ 377 EAS_I16 EAS_VolumeToGain (EAS_INT volume); 378 379 /*---------------------------------------------------------------------------- 380 * EAS_fsqrt() 381 *---------------------------------------------------------------------------- 382 * Purpose: 383 * Calculates the square root of a 32-bit fixed point value 384 * 385 * Inputs: 386 * n = value of interest 387 * 388 * Outputs: 389 * returns the square root of n 390 * 391 *---------------------------------------------------------------------------- 392 */ 393 EAS_U16 EAS_fsqrt (EAS_U32 n); 394 395 /*---------------------------------------------------------------------------- 396 * EAS_flog2() 397 *---------------------------------------------------------------------------- 398 * Purpose: 399 * Calculates the log2 of a 32-bit fixed point value 400 * 401 * Inputs: 402 * n = value of interest 403 * 404 * Outputs: 405 * returns the log2 of n 406 * 407 *---------------------------------------------------------------------------- 408 */ 409 EAS_I32 EAS_flog2 (EAS_U32 n); 410 411 #endif 412 413
