fixed.c (16679B)
1 /* libFLAC - Free Lossless Audio Codec library 2 * Copyright (C) 2000,2001,2002,2003,2004,2005 Josh Coalson 3 * 4 * Redistribution and use in source and binary forms, with or without 5 * modification, are permitted provided that the following conditions 6 * are met: 7 * 8 * - Redistributions of source code must retain the above copyright 9 * notice, this list of conditions and the following disclaimer. 10 * 11 * - Redistributions in binary form must reproduce the above copyright 12 * notice, this list of conditions and the following disclaimer in the 13 * documentation and/or other materials provided with the distribution. 14 * 15 * - Neither the name of the Xiph.org Foundation nor the names of its 16 * contributors may be used to endorse or promote products derived from 17 * this software without specific prior written permission. 18 * 19 * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS 20 * ``AS IS'' AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT 21 * LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR 22 * A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE FOUNDATION OR 23 * CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, 24 * EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, 25 * PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR 26 * PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF 27 * LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING 28 * NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS 29 * SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. 30 */ 31 32 #include <math.h> 33 #include "private/bitmath.h" 34 #include "private/fixed.h" 35 #include "FLAC/assert.h" 36 37 #ifndef M_LN2 38 /* math.h in VC++ doesn't seem to have this (how Microsoft is that?) */ 39 #define M_LN2 0.69314718055994530942 40 #endif 41 42 #ifdef min 43 #undef min 44 #endif 45 #define min(x,y) ((x) < (y)? (x) : (y)) 46 47 #ifdef local_abs 48 #undef local_abs 49 #endif 50 #define local_abs(x) ((unsigned)((x)<0? -(x) : (x))) 51 52 #ifdef FLAC__INTEGER_ONLY_LIBRARY 53 /* rbps stands for residual bits per sample 54 * 55 * (ln(2) * err) 56 * rbps = log (-----------) 57 * 2 ( n ) 58 */ 59 static FLAC__fixedpoint local__compute_rbps_integerized(FLAC__uint32 err, FLAC__uint32 n) 60 { 61 FLAC__uint32 rbps; 62 unsigned bits; /* the number of bits required to represent a number */ 63 int fracbits; /* the number of bits of rbps that comprise the fractional part */ 64 65 FLAC__ASSERT(sizeof(rbps) == sizeof(FLAC__fixedpoint)); 66 FLAC__ASSERT(err > 0); 67 FLAC__ASSERT(n > 0); 68 69 FLAC__ASSERT(n <= FLAC__MAX_BLOCK_SIZE); 70 if(err <= n) 71 return 0; 72 /* 73 * The above two things tell us 1) n fits in 16 bits; 2) err/n > 1. 74 * These allow us later to know we won't lose too much precision in the 75 * fixed-point division (err<<fracbits)/n. 76 */ 77 78 fracbits = (8*sizeof(err)) - (FLAC__bitmath_ilog2(err)+1); 79 80 err <<= fracbits; 81 err /= n; 82 /* err now holds err/n with fracbits fractional bits */ 83 84 /* 85 * Whittle err down to 16 bits max. 16 significant bits is enough for 86 * our purposes. 87 */ 88 FLAC__ASSERT(err > 0); 89 bits = FLAC__bitmath_ilog2(err)+1; 90 if(bits > 16) { 91 err >>= (bits-16); 92 fracbits -= (bits-16); 93 } 94 rbps = (FLAC__uint32)err; 95 96 /* Multiply by fixed-point version of ln(2), with 16 fractional bits */ 97 rbps *= FLAC__FP_LN2; 98 fracbits += 16; 99 FLAC__ASSERT(fracbits >= 0); 100 101 /* FLAC__fixedpoint_log2 requires fracbits%4 to be 0 */ 102 { 103 const int f = fracbits & 3; 104 if(f) { 105 rbps >>= f; 106 fracbits -= f; 107 } 108 } 109 110 rbps = FLAC__fixedpoint_log2(rbps, fracbits, (unsigned)(-1)); 111 112 if(rbps == 0) 113 return 0; 114 115 /* 116 * The return value must have 16 fractional bits. Since the whole part 117 * of the base-2 log of a 32 bit number must fit in 5 bits, and fracbits 118 * must be >= -3, these assertion allows us to be able to shift rbps 119 * left if necessary to get 16 fracbits without losing any bits of the 120 * whole part of rbps. 121 * 122 * There is a slight chance due to accumulated error that the whole part 123 * will require 6 bits, so we use 6 in the assertion. Really though as 124 * long as it fits in 13 bits (32 - (16 - (-3))) we are fine. 125 */ 126 FLAC__ASSERT((int)FLAC__bitmath_ilog2(rbps)+1 <= fracbits + 6); 127 FLAC__ASSERT(fracbits >= -3); 128 129 /* now shift the decimal point into place */ 130 if(fracbits < 16) 131 return rbps << (16-fracbits); 132 else if(fracbits > 16) 133 return rbps >> (fracbits-16); 134 else 135 return rbps; 136 } 137 138 static FLAC__fixedpoint local__compute_rbps_wide_integerized(FLAC__uint64 err, FLAC__uint32 n) 139 { 140 FLAC__uint32 rbps; 141 unsigned bits; /* the number of bits required to represent a number */ 142 int fracbits; /* the number of bits of rbps that comprise the fractional part */ 143 144 FLAC__ASSERT(sizeof(rbps) == sizeof(FLAC__fixedpoint)); 145 FLAC__ASSERT(err > 0); 146 FLAC__ASSERT(n > 0); 147 148 FLAC__ASSERT(n <= FLAC__MAX_BLOCK_SIZE); 149 if(err <= n) 150 return 0; 151 /* 152 * The above two things tell us 1) n fits in 16 bits; 2) err/n > 1. 153 * These allow us later to know we won't lose too much precision in the 154 * fixed-point division (err<<fracbits)/n. 155 */ 156 157 fracbits = (8*sizeof(err)) - (FLAC__bitmath_ilog2_wide(err)+1); 158 159 err <<= fracbits; 160 err /= n; 161 /* err now holds err/n with fracbits fractional bits */ 162 163 /* 164 * Whittle err down to 16 bits max. 16 significant bits is enough for 165 * our purposes. 166 */ 167 FLAC__ASSERT(err > 0); 168 bits = FLAC__bitmath_ilog2_wide(err)+1; 169 if(bits > 16) { 170 err >>= (bits-16); 171 fracbits -= (bits-16); 172 } 173 rbps = (FLAC__uint32)err; 174 175 /* Multiply by fixed-point version of ln(2), with 16 fractional bits */ 176 rbps *= FLAC__FP_LN2; 177 fracbits += 16; 178 FLAC__ASSERT(fracbits >= 0); 179 180 /* FLAC__fixedpoint_log2 requires fracbits%4 to be 0 */ 181 { 182 const int f = fracbits & 3; 183 if(f) { 184 rbps >>= f; 185 fracbits -= f; 186 } 187 } 188 189 rbps = FLAC__fixedpoint_log2(rbps, fracbits, (unsigned)(-1)); 190 191 if(rbps == 0) 192 return 0; 193 194 /* 195 * The return value must have 16 fractional bits. Since the whole part 196 * of the base-2 log of a 32 bit number must fit in 5 bits, and fracbits 197 * must be >= -3, these assertion allows us to be able to shift rbps 198 * left if necessary to get 16 fracbits without losing any bits of the 199 * whole part of rbps. 200 * 201 * There is a slight chance due to accumulated error that the whole part 202 * will require 6 bits, so we use 6 in the assertion. Really though as 203 * long as it fits in 13 bits (32 - (16 - (-3))) we are fine. 204 */ 205 FLAC__ASSERT((int)FLAC__bitmath_ilog2(rbps)+1 <= fracbits + 6); 206 FLAC__ASSERT(fracbits >= -3); 207 208 /* now shift the decimal point into place */ 209 if(fracbits < 16) 210 return rbps << (16-fracbits); 211 else if(fracbits > 16) 212 return rbps >> (fracbits-16); 213 else 214 return rbps; 215 } 216 #endif 217 218 #ifndef FLAC__INTEGER_ONLY_LIBRARY 219 unsigned FLAC__fixed_compute_best_predictor(const FLAC__int32 data[], unsigned data_len, FLAC__float residual_bits_per_sample[FLAC__MAX_FIXED_ORDER+1]) 220 #else 221 unsigned FLAC__fixed_compute_best_predictor(const FLAC__int32 data[], unsigned data_len, FLAC__fixedpoint residual_bits_per_sample[FLAC__MAX_FIXED_ORDER+1]) 222 #endif 223 { 224 FLAC__int32 last_error_0 = data[-1]; 225 FLAC__int32 last_error_1 = data[-1] - data[-2]; 226 FLAC__int32 last_error_2 = last_error_1 - (data[-2] - data[-3]); 227 FLAC__int32 last_error_3 = last_error_2 - (data[-2] - 2*data[-3] + data[-4]); 228 FLAC__int32 error, save; 229 FLAC__uint32 total_error_0 = 0, total_error_1 = 0, total_error_2 = 0, total_error_3 = 0, total_error_4 = 0; 230 unsigned i, order; 231 232 for(i = 0; i < data_len; i++) { 233 error = data[i] ; total_error_0 += local_abs(error); save = error; 234 error -= last_error_0; total_error_1 += local_abs(error); last_error_0 = save; save = error; 235 error -= last_error_1; total_error_2 += local_abs(error); last_error_1 = save; save = error; 236 error -= last_error_2; total_error_3 += local_abs(error); last_error_2 = save; save = error; 237 error -= last_error_3; total_error_4 += local_abs(error); last_error_3 = save; 238 } 239 240 if(total_error_0 < min(min(min(total_error_1, total_error_2), total_error_3), total_error_4)) 241 order = 0; 242 else if(total_error_1 < min(min(total_error_2, total_error_3), total_error_4)) 243 order = 1; 244 else if(total_error_2 < min(total_error_3, total_error_4)) 245 order = 2; 246 else if(total_error_3 < total_error_4) 247 order = 3; 248 else 249 order = 4; 250 251 /* Estimate the expected number of bits per residual signal sample. */ 252 /* 'total_error*' is linearly related to the variance of the residual */ 253 /* signal, so we use it directly to compute E(|x|) */ 254 FLAC__ASSERT(data_len > 0 || total_error_0 == 0); 255 FLAC__ASSERT(data_len > 0 || total_error_1 == 0); 256 FLAC__ASSERT(data_len > 0 || total_error_2 == 0); 257 FLAC__ASSERT(data_len > 0 || total_error_3 == 0); 258 FLAC__ASSERT(data_len > 0 || total_error_4 == 0); 259 #ifndef FLAC__INTEGER_ONLY_LIBRARY 260 residual_bits_per_sample[0] = (FLAC__float)((total_error_0 > 0) ? log(M_LN2 * (FLAC__double)total_error_0 / (FLAC__double)data_len) / M_LN2 : 0.0); 261 residual_bits_per_sample[1] = (FLAC__float)((total_error_1 > 0) ? log(M_LN2 * (FLAC__double)total_error_1 / (FLAC__double)data_len) / M_LN2 : 0.0); 262 residual_bits_per_sample[2] = (FLAC__float)((total_error_2 > 0) ? log(M_LN2 * (FLAC__double)total_error_2 / (FLAC__double)data_len) / M_LN2 : 0.0); 263 residual_bits_per_sample[3] = (FLAC__float)((total_error_3 > 0) ? log(M_LN2 * (FLAC__double)total_error_3 / (FLAC__double)data_len) / M_LN2 : 0.0); 264 residual_bits_per_sample[4] = (FLAC__float)((total_error_4 > 0) ? log(M_LN2 * (FLAC__double)total_error_4 / (FLAC__double)data_len) / M_LN2 : 0.0); 265 #else 266 residual_bits_per_sample[0] = (total_error_0 > 0) ? local__compute_rbps_integerized(total_error_0, data_len) : 0; 267 residual_bits_per_sample[1] = (total_error_1 > 0) ? local__compute_rbps_integerized(total_error_1, data_len) : 0; 268 residual_bits_per_sample[2] = (total_error_2 > 0) ? local__compute_rbps_integerized(total_error_2, data_len) : 0; 269 residual_bits_per_sample[3] = (total_error_3 > 0) ? local__compute_rbps_integerized(total_error_3, data_len) : 0; 270 residual_bits_per_sample[4] = (total_error_4 > 0) ? local__compute_rbps_integerized(total_error_4, data_len) : 0; 271 #endif 272 273 return order; 274 } 275 276 #ifndef FLAC__INTEGER_ONLY_LIBRARY 277 unsigned FLAC__fixed_compute_best_predictor_wide(const FLAC__int32 data[], unsigned data_len, FLAC__float residual_bits_per_sample[FLAC__MAX_FIXED_ORDER+1]) 278 #else 279 unsigned FLAC__fixed_compute_best_predictor_wide(const FLAC__int32 data[], unsigned data_len, FLAC__fixedpoint residual_bits_per_sample[FLAC__MAX_FIXED_ORDER+1]) 280 #endif 281 { 282 FLAC__int32 last_error_0 = data[-1]; 283 FLAC__int32 last_error_1 = data[-1] - data[-2]; 284 FLAC__int32 last_error_2 = last_error_1 - (data[-2] - data[-3]); 285 FLAC__int32 last_error_3 = last_error_2 - (data[-2] - 2*data[-3] + data[-4]); 286 FLAC__int32 error, save; 287 /* total_error_* are 64-bits to avoid overflow when encoding 288 * erratic signals when the bits-per-sample and blocksize are 289 * large. 290 */ 291 FLAC__uint64 total_error_0 = 0, total_error_1 = 0, total_error_2 = 0, total_error_3 = 0, total_error_4 = 0; 292 unsigned i, order; 293 294 for(i = 0; i < data_len; i++) { 295 error = data[i] ; total_error_0 += local_abs(error); save = error; 296 error -= last_error_0; total_error_1 += local_abs(error); last_error_0 = save; save = error; 297 error -= last_error_1; total_error_2 += local_abs(error); last_error_1 = save; save = error; 298 error -= last_error_2; total_error_3 += local_abs(error); last_error_2 = save; save = error; 299 error -= last_error_3; total_error_4 += local_abs(error); last_error_3 = save; 300 } 301 302 if(total_error_0 < min(min(min(total_error_1, total_error_2), total_error_3), total_error_4)) 303 order = 0; 304 else if(total_error_1 < min(min(total_error_2, total_error_3), total_error_4)) 305 order = 1; 306 else if(total_error_2 < min(total_error_3, total_error_4)) 307 order = 2; 308 else if(total_error_3 < total_error_4) 309 order = 3; 310 else 311 order = 4; 312 313 /* Estimate the expected number of bits per residual signal sample. */ 314 /* 'total_error*' is linearly related to the variance of the residual */ 315 /* signal, so we use it directly to compute E(|x|) */ 316 FLAC__ASSERT(data_len > 0 || total_error_0 == 0); 317 FLAC__ASSERT(data_len > 0 || total_error_1 == 0); 318 FLAC__ASSERT(data_len > 0 || total_error_2 == 0); 319 FLAC__ASSERT(data_len > 0 || total_error_3 == 0); 320 FLAC__ASSERT(data_len > 0 || total_error_4 == 0); 321 #ifndef FLAC__INTEGER_ONLY_LIBRARY 322 #if defined _MSC_VER || defined __MINGW32__ 323 /* with MSVC you have to spoon feed it the casting */ 324 residual_bits_per_sample[0] = (FLAC__float)((total_error_0 > 0) ? log(M_LN2 * (FLAC__double)(FLAC__int64)total_error_0 / (FLAC__double)data_len) / M_LN2 : 0.0); 325 residual_bits_per_sample[1] = (FLAC__float)((total_error_1 > 0) ? log(M_LN2 * (FLAC__double)(FLAC__int64)total_error_1 / (FLAC__double)data_len) / M_LN2 : 0.0); 326 residual_bits_per_sample[2] = (FLAC__float)((total_error_2 > 0) ? log(M_LN2 * (FLAC__double)(FLAC__int64)total_error_2 / (FLAC__double)data_len) / M_LN2 : 0.0); 327 residual_bits_per_sample[3] = (FLAC__float)((total_error_3 > 0) ? log(M_LN2 * (FLAC__double)(FLAC__int64)total_error_3 / (FLAC__double)data_len) / M_LN2 : 0.0); 328 residual_bits_per_sample[4] = (FLAC__float)((total_error_4 > 0) ? log(M_LN2 * (FLAC__double)(FLAC__int64)total_error_4 / (FLAC__double)data_len) / M_LN2 : 0.0); 329 #else 330 residual_bits_per_sample[0] = (FLAC__float)((total_error_0 > 0) ? log(M_LN2 * (FLAC__double)total_error_0 / (FLAC__double)data_len) / M_LN2 : 0.0); 331 residual_bits_per_sample[1] = (FLAC__float)((total_error_1 > 0) ? log(M_LN2 * (FLAC__double)total_error_1 / (FLAC__double)data_len) / M_LN2 : 0.0); 332 residual_bits_per_sample[2] = (FLAC__float)((total_error_2 > 0) ? log(M_LN2 * (FLAC__double)total_error_2 / (FLAC__double)data_len) / M_LN2 : 0.0); 333 residual_bits_per_sample[3] = (FLAC__float)((total_error_3 > 0) ? log(M_LN2 * (FLAC__double)total_error_3 / (FLAC__double)data_len) / M_LN2 : 0.0); 334 residual_bits_per_sample[4] = (FLAC__float)((total_error_4 > 0) ? log(M_LN2 * (FLAC__double)total_error_4 / (FLAC__double)data_len) / M_LN2 : 0.0); 335 #endif 336 #else 337 residual_bits_per_sample[0] = (total_error_0 > 0) ? local__compute_rbps_wide_integerized(total_error_0, data_len) : 0; 338 residual_bits_per_sample[1] = (total_error_1 > 0) ? local__compute_rbps_wide_integerized(total_error_1, data_len) : 0; 339 residual_bits_per_sample[2] = (total_error_2 > 0) ? local__compute_rbps_wide_integerized(total_error_2, data_len) : 0; 340 residual_bits_per_sample[3] = (total_error_3 > 0) ? local__compute_rbps_wide_integerized(total_error_3, data_len) : 0; 341 residual_bits_per_sample[4] = (total_error_4 > 0) ? local__compute_rbps_wide_integerized(total_error_4, data_len) : 0; 342 #endif 343 344 return order; 345 } 346 347 void FLAC__fixed_compute_residual(const FLAC__int32 data[], unsigned data_len, unsigned order, FLAC__int32 residual[]) 348 { 349 const int idata_len = (int)data_len; 350 int i; 351 352 switch(order) { 353 case 0: 354 for(i = 0; i < idata_len; i++) { 355 residual[i] = data[i]; 356 } 357 break; 358 case 1: 359 for(i = 0; i < idata_len; i++) { 360 residual[i] = data[i] - data[i-1]; 361 } 362 break; 363 case 2: 364 for(i = 0; i < idata_len; i++) { 365 /* == data[i] - 2*data[i-1] + data[i-2] */ 366 residual[i] = data[i] - (data[i-1] << 1) + data[i-2]; 367 } 368 break; 369 case 3: 370 for(i = 0; i < idata_len; i++) { 371 /* == data[i] - 3*data[i-1] + 3*data[i-2] - data[i-3] */ 372 residual[i] = data[i] - (((data[i-1]-data[i-2])<<1) + (data[i-1]-data[i-2])) - data[i-3]; 373 } 374 break; 375 case 4: 376 for(i = 0; i < idata_len; i++) { 377 /* == data[i] - 4*data[i-1] + 6*data[i-2] - 4*data[i-3] + data[i-4] */ 378 residual[i] = data[i] - ((data[i-1]+data[i-3])<<2) + ((data[i-2]<<2) + (data[i-2]<<1)) + data[i-4]; 379 } 380 break; 381 default: 382 FLAC__ASSERT(0); 383 } 384 } 385 386 void FLAC__fixed_restore_signal(const FLAC__int32 residual[], unsigned data_len, unsigned order, FLAC__int32 data[]) 387 { 388 int i, idata_len = (int)data_len; 389 390 switch(order) { 391 case 0: 392 for(i = 0; i < idata_len; i++) { 393 data[i] = residual[i]; 394 } 395 break; 396 case 1: 397 for(i = 0; i < idata_len; i++) { 398 data[i] = residual[i] + data[i-1]; 399 } 400 break; 401 case 2: 402 for(i = 0; i < idata_len; i++) { 403 /* == residual[i] + 2*data[i-1] - data[i-2] */ 404 data[i] = residual[i] + (data[i-1]<<1) - data[i-2]; 405 } 406 break; 407 case 3: 408 for(i = 0; i < idata_len; i++) { 409 /* residual[i] + 3*data[i-1] - 3*data[i-2]) + data[i-3] */ 410 data[i] = residual[i] + (((data[i-1]-data[i-2])<<1) + (data[i-1]-data[i-2])) + data[i-3]; 411 } 412 break; 413 case 4: 414 for(i = 0; i < idata_len; i++) { 415 /* == residual[i] + 4*data[i-1] - 6*data[i-2] + 4*data[i-3] - data[i-4] */ 416 data[i] = residual[i] + ((data[i-1]+data[i-3])<<2) - ((data[i-2]<<2) + (data[i-2]<<1)) - data[i-4]; 417 } 418 break; 419 default: 420 FLAC__ASSERT(0); 421 } 422 }