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 #include <stdint.h> 35 36 /** coefs for pan, generates sin, cos */ 37 #define COEFF_PAN_G2 -27146 /* -0.82842712474619 = 2 - 4/sqrt(2) */ 38 #define COEFF_PAN_G0 23170 /* 0.707106781186547 = 1/sqrt(2) */ 39 40 /* 41 coefficients for approximating 42 2^x = gn2toX0 + gn2toX1*x + gn2toX2*x^2 + gn2toX3*x^3 43 where x is a int.frac number representing number of octaves. 44 Actually, we approximate only the 2^(frac) using the power series 45 and implement the 2^(int) as a shift, so that 46 2^x == 2^(int.frac) == 2^(int) * 2^(fract) 47 == (gn2toX0 + gn2toX1*x + gn2toX2*x^2 + gn2toX3*x^3) << (int) 48 49 The gn2toX.. were generated using a best fit for a 3rd 50 order polynomial, instead of taking the coefficients from 51 a truncated Taylor (or Maclaurin?) series. 52 */ 53 54 #define GN2_TO_X0 32768 /* 1 */ 55 #define GN2_TO_X1 22833 /* 0.696807861328125 */ 56 #define GN2_TO_X2 7344 /* 0.22412109375 */ 57 #define GN2_TO_X3 2588 /* 0.0789794921875 */ 58 59 /*---------------------------------------------------------------------------- 60 * Fixed Point Math 61 *---------------------------------------------------------------------------- 62 * These macros are used for fixed point multiplies. If the processor 63 * supports fixed point multiplies, replace these macros with inline 64 * assembly code to improve performance. 65 *---------------------------------------------------------------------------- 66 */ 67 68 /* Fixed point multiply 0.15 x 0.15 = 0.15 returned as 32-bits */ 69 #define FMUL_15x15(a,b) \ 70 /*lint -e(704) <avoid multiply for performance>*/ \ 71 (((int32_t)(a) * (int32_t)(b)) >> 15) 72 73 /* Fixed point multiply 0.7 x 0.7 = 0.15 returned as 32-bits */ 74 #define FMUL_7x7(a,b) \ 75 /*lint -e(704) <avoid multiply for performance>*/ \ 76 (((int32_t)(a) * (int32_t)(b) ) << 1) 77 78 /* Fixed point multiply 0.8 x 0.8 = 0.15 returned as 32-bits */ 79 #define FMUL_8x8(a,b) \ 80 /*lint -e(704) <avoid multiply for performance>*/ \ 81 (((int32_t)(a) * (int32_t)(b) ) >> 1) 82 83 /* Fixed point multiply 0.8 x 1.15 = 0.15 returned as 32-bits */ 84 #define FMUL_8x15(a,b) \ 85 /*lint -e(704) <avoid divide for performance>*/ \ 86 (((int32_t)((a) << 7) * (int32_t)(b)) >> 15) 87 88 /* macros for fractional phase accumulator */ 89 /* 90 Note: changed the _U32 to _I32 on 03/14/02. This should not 91 affect the phase calculations, and should allow us to reuse these 92 macros for other audio sample related math. 93 */ 94 #define HARDWARE_BIT_WIDTH 32 95 96 #define NUM_PHASE_INT_BITS 1 97 #define NUM_PHASE_FRAC_BITS 15 98 99 #define PHASE_FRAC_MASK (uint32_t) ((0x1L << NUM_PHASE_FRAC_BITS) -1) 100 101 #define GET_PHASE_INT_PART(x) (uint32_t)((uint32_t)(x) >> NUM_PHASE_FRAC_BITS) 102 #define GET_PHASE_FRAC_PART(x) (uint32_t)((uint32_t)(x) & PHASE_FRAC_MASK) 103 104 #define DEFAULT_PHASE_FRAC 0 105 #define DEFAULT_PHASE_INT 0 106 107 /* 108 Linear interpolation calculates: 109 output = (1-frac) * sample[n] + (frac) * sample[n+1] 110 111 where conceptually 0 <= frac < 1 112 113 For a fixed point implementation, frac is actually an integer value 114 with an implied binary point one position to the left. The value of 115 one (unity) is given by PHASE_ONE 116 one half and one quarter are useful for 4-point linear interp. 117 */ 118 #define PHASE_ONE (int32_t) (0x1L << NUM_PHASE_FRAC_BITS) 119 120 /* 121 Multiply the signed audio sample by the unsigned fraction. 122 - a is the signed audio sample 123 - b is the unsigned fraction (cast to signed int as long as coef 124 uses (n-1) or less bits, where n == hardware bit width) 125 */ 126 #define MULT_AUDIO_COEF(audio,coef) /*lint -e704 <avoid divide for performance>*/ \ 127 (int32_t)( \ 128 ( \ 129 ((int32_t)(audio)) * ((int32_t)(coef)) \ 130 ) \ 131 >> NUM_PHASE_FRAC_BITS \ 132 ) \ 133 /* lint +704 <restore checking>*/ 134 135 /* wet / dry calculation macros */ 136 #define NUM_WET_DRY_FRAC_BITS 7 // 15 137 #define NUM_WET_DRY_INT_BITS 9 // 1 138 139 /* define a 1.0 */ 140 #define WET_DRY_ONE (int32_t) ((0x1L << NUM_WET_DRY_FRAC_BITS)) 141 #define WET_DRY_MINUS_ONE (int32_t) (~WET_DRY_ONE) 142 #define WET_DRY_FULL_SCALE (int32_t) (WET_DRY_ONE - 1) 143 144 #define MULT_AUDIO_WET_DRY_COEF(audio,coef) /*lint -e(702) <avoid divide for performance>*/ \ 145 (int32_t)( \ 146 ( \ 147 ((int32_t)(audio)) * ((int32_t)(coef)) \ 148 ) \ 149 >> NUM_WET_DRY_FRAC_BITS \ 150 ) 151 152 /* Envelope 1 (EG1) calculation macros */ 153 #define NUM_EG1_INT_BITS 1 154 #define NUM_EG1_FRAC_BITS 15 155 156 /* the max positive gain used in the synth for EG1 */ 157 /* SYNTH_FULL_SCALE_EG1_GAIN must match the value in the dls2eas 158 converter, otherwise, the values we read from the .eas file are bogus. */ 159 #define SYNTH_FULL_SCALE_EG1_GAIN (int32_t) ((0x1L << NUM_EG1_FRAC_BITS) -1) 160 161 /* define a 1.0 */ 162 #define EG1_ONE (int32_t) ((0x1L << NUM_EG1_FRAC_BITS)) 163 #define EG1_MINUS_ONE (int32_t) (~SYNTH_FULL_SCALE_EG1_GAIN) 164 165 #define EG1_HALF (int32_t) (EG1_ONE/2) 166 #define EG1_MINUS_HALF (int32_t) (EG1_MINUS_ONE/2) 167 168 /* 169 We implement the EG1 using a linear gain value, which means that the 170 attack segment is handled by incrementing (adding) the linear gain. 171 However, EG1 treats the Decay, Sustain, and Release differently than 172 the Attack portion. For Decay, Sustain, and Release, the gain is 173 linear on dB scale, which is equivalent to exponential damping on 174 a linear scale. Because we use a linear gain for EG1, we implement 175 the Decay and Release as multiplication (instead of incrementing 176 as we did for the attack segment). 177 Therefore, we need the following macro to implement the multiplication 178 (i.e., exponential damping) during the Decay and Release segments of 179 the EG1 180 */ 181 #define MULT_EG1_EG1(gain,damping) /*lint -e(704) <avoid divide for performance>*/ \ 182 (int32_t)( \ 183 ( \ 184 ((int32_t)(gain)) * ((int32_t)(damping)) \ 185 ) \ 186 >> NUM_EG1_FRAC_BITS \ 187 ) 188 189 // Use the following macro specifically for the filter, when multiplying 190 // the b1 coefficient. The 0 <= |b1| < 2, which therefore might overflow 191 // in certain conditions because we store b1 as a 1.15 value. 192 // Instead, we could store b1 as b1p (b1' == b1 "prime") where 193 // b1p == b1/2, thus ensuring no potential overflow for b1p because 194 // 0 <= |b1p| < 1 195 // However, during the filter calculation, we must account for the fact 196 // that we are using b1p instead of b1, and thereby multiply by 197 // an extra factor of 2. Rather than multiply by an extra factor of 2, 198 // we can instead shift the result right by one less, hence the 199 // modified shift right value of (NUM_EG1_FRAC_BITS -1) 200 #define MULT_EG1_EG1_X2(gain,damping) /*lint -e(702) <avoid divide for performance>*/ \ 201 (int32_t)( \ 202 ( \ 203 ((int32_t)(gain)) * ((int32_t)(damping)) \ 204 ) \ 205 >> (NUM_EG1_FRAC_BITS -1) \ 206 ) 207 208 #define SATURATE_EG1(x) /*lint -e{734} saturation operation */ \ 209 ((int32_t)(x) > SYNTH_FULL_SCALE_EG1_GAIN) ? (SYNTH_FULL_SCALE_EG1_GAIN) : \ 210 ((int32_t)(x) < EG1_MINUS_ONE) ? (EG1_MINUS_ONE) : (x); 211 212 213 /* use "digital cents" == "dents" instead of cents */ 214 /* we coudl re-use the phase frac macros, but if we do, 215 we must change the phase macros to cast to _I32 instead of _U32, 216 because using a _U32 cast causes problems when shifting the exponent 217 for the 2^x calculation, because right shift a negative values MUST 218 be sign extended, or else the 2^x calculation is wrong */ 219 220 /* use "digital cents" == "dents" instead of cents */ 221 #define NUM_DENTS_FRAC_BITS 12 222 #define NUM_DENTS_INT_BITS (HARDWARE_BIT_WIDTH - NUM_DENTS_FRAC_BITS) 223 224 #define DENTS_FRAC_MASK (int32_t) ((0x1L << NUM_DENTS_FRAC_BITS) -1) 225 226 #define GET_DENTS_INT_PART(x) /*lint -e(704) <avoid divide for performance>*/ \ 227 (int32_t)((int32_t)(x) >> NUM_DENTS_FRAC_BITS) 228 229 #define GET_DENTS_FRAC_PART(x) (int32_t)((int32_t)(x) & DENTS_FRAC_MASK) 230 231 #define DENTS_ONE (int32_t) (0x1L << NUM_DENTS_FRAC_BITS) 232 233 /* use CENTS_TO_DENTS to convert a value in cents to dents */ 234 #define CENTS_TO_DENTS (int32_t) (DENTS_ONE * (0x1L << NUM_EG1_FRAC_BITS) / 1200L) \ 235 236 237 /* 238 For gain, the LFO generates a value that modulates in terms 239 of dB. However, we use a linear gain value, so we must convert 240 the LFO value in dB to a linear gain. Normally, we would use 241 linear gain = 10^x, where x = LFO value in dB / 20. 242 Instead, we implement 10^x using our 2^x approximation. 243 because 244 245 10^x = 2^(log2(10^x)) = 2^(x * log2(10)) 246 247 so we need to multiply by log2(10) which is just a constant. 248 Ah, but just wait -- our 2^x actually doesn't exactly implement 249 2^x, but it actually assumes that the input is in cents, and within 250 the 2^x approximation converts its input from cents to octaves 251 by dividing its input by 1200. 252 253 So, in order to convert the LFO gain value in dB to something 254 that our existing 2^x approximation can use, multiply the LFO gain 255 by log2(10) * 1200 / 20 256 257 The divide by 20 helps convert dB to linear gain, and we might 258 as well incorporate that operation into this conversion. 259 Of course, we need to keep some fractional bits, so multiply 260 the constant by NUM_EG1_FRAC_BITS 261 */ 262 263 /* use LFO_GAIN_TO_CENTS to convert the LFO gain value to cents */ 264 #if 0 265 #define DOUBLE_LOG2_10 (double) (3.32192809488736) /* log2(10) */ 266 267 #define DOUBLE_LFO_GAIN_TO_CENTS (double) \ 268 ( \ 269 (DOUBLE_LOG2_10) * \ 270 1200.0 / \ 271 20.0 \ 272 ) 273 274 #define LFO_GAIN_TO_CENTS (int32_t) \ 275 ( \ 276 DOUBLE_LFO_GAIN_TO_CENTS * \ 277 (0x1L << NUM_EG1_FRAC_BITS) \ 278 ) 279 #endif 280 281 #define LFO_GAIN_TO_CENTS (int32_t) (1671981156L >> (23 - NUM_EG1_FRAC_BITS)) 282 283 284 #define MULT_DENTS_COEF(dents,coef) /*lint -e704 <avoid divide for performance>*/ \ 285 (int32_t)( \ 286 ( \ 287 ((int32_t)(dents)) * ((int32_t)(coef)) \ 288 ) \ 289 >> NUM_DENTS_FRAC_BITS \ 290 ) \ 291 /* lint +e704 <restore checking>*/ 292 293 /* we use 16-bits in the PC per audio sample */ 294 #define BITS_PER_AUDIO_SAMPLE 16 295 296 /* we define 1 as 1.0 - 1 LSbit */ 297 #define DISTORTION_ONE (int32_t)((0x1L << (BITS_PER_AUDIO_SAMPLE-1)) -1) 298 #define DISTORTION_MINUS_ONE (int32_t)(~DISTORTION_ONE) 299 300 /* drive coef is given as int.frac */ 301 #define NUM_DRIVE_COEF_INT_BITS 1 302 #define NUM_DRIVE_COEF_FRAC_BITS 4 303 304 #define MULT_AUDIO_DRIVE(audio,drive) /*lint -e(702) <avoid divide for performance>*/ \ 305 (int32_t) ( \ 306 ( \ 307 ((int32_t)(audio)) * ((int32_t)(drive)) \ 308 ) \ 309 >> NUM_DRIVE_COEF_FRAC_BITS \ 310 ) 311 312 #define MULT_AUDIO_AUDIO(audio1,audio2) /*lint -e(702) <avoid divide for performance>*/ \ 313 (int32_t) ( \ 314 ( \ 315 ((int32_t)(audio1)) * ((int32_t)(audio2)) \ 316 ) \ 317 >> (BITS_PER_AUDIO_SAMPLE-1) \ 318 ) 319 320 #define SATURATE(x) \ 321 ((((int32_t)(x)) > DISTORTION_ONE) ? (DISTORTION_ONE) : \ 322 (((int32_t)(x)) < DISTORTION_MINUS_ONE) ? (DISTORTION_MINUS_ONE) : ((int32_t)(x))); 323 324 325 326 /*---------------------------------------------------------------------------- 327 * EAS_Calculate2toX() 328 *---------------------------------------------------------------------------- 329 * Purpose: 330 * Calculate 2^x 331 * 332 * Inputs: 333 * nCents - measured in cents 334 * 335 * Outputs: 336 * nResult - int.frac result (where frac has NUM_DENTS_FRAC_BITS) 337 * 338 * Side Effects: 339 * 340 *---------------------------------------------------------------------------- 341 */ 342 EAS_I32 EAS_Calculate2toX (EAS_I32 nCents); 343 344 /*---------------------------------------------------------------------------- 345 * EAS_LogToLinear16() 346 *---------------------------------------------------------------------------- 347 * Purpose: 348 * Transform log value to linear gain multiplier using piece-wise linear 349 * approximation 350 * 351 * Inputs: 352 * nGain - log scale value in 20.10 format. Even though gain is normally 353 * stored in 6.10 (16-bit) format we use 32-bit numbers here to eliminate 354 * the need for saturation checking when combining gain values. 355 * 356 * Outputs: 357 * Returns a 16-bit linear value approximately equal to 2^(nGain/1024) 358 * 359 * Side Effects: 360 * 361 *---------------------------------------------------------------------------- 362 */ 363 EAS_U16 EAS_LogToLinear16 (EAS_I32 nGain); 364 365 /*---------------------------------------------------------------------------- 366 * EAS_VolumeToGain() 367 *---------------------------------------------------------------------------- 368 * Purpose: 369 * Transform volume control in 1dB increments to gain multiplier 370 * 371 * Inputs: 372 * volume - 100 = 0dB, 99 = -1dB, 0 = -inf 373 * 374 * Outputs: 375 * Returns a 16-bit linear value 376 *---------------------------------------------------------------------------- 377 */ 378 EAS_I16 EAS_VolumeToGain (EAS_INT volume); 379 380 /*---------------------------------------------------------------------------- 381 * EAS_fsqrt() 382 *---------------------------------------------------------------------------- 383 * Purpose: 384 * Calculates the square root of a 32-bit fixed point value 385 * 386 * Inputs: 387 * n = value of interest 388 * 389 * Outputs: 390 * returns the square root of n 391 * 392 *---------------------------------------------------------------------------- 393 */ 394 EAS_U16 EAS_fsqrt (EAS_U32 n); 395 396 /*---------------------------------------------------------------------------- 397 * EAS_flog2() 398 *---------------------------------------------------------------------------- 399 * Purpose: 400 * Calculates the log2 of a 32-bit fixed point value 401 * 402 * Inputs: 403 * n = value of interest 404 * 405 * Outputs: 406 * returns the log2 of n 407 * 408 *---------------------------------------------------------------------------- 409 */ 410 EAS_I32 EAS_flog2 (EAS_U32 n); 411 412 #endif 413 414
