1 2 /* ----------------------------------------------------------------------------------------------------------- 3 Software License for The Fraunhofer FDK AAC Codec Library for Android 4 5 Copyright 1995 - 2013 Fraunhofer-Gesellschaft zur Frderung der angewandten Forschung e.V. 6 All rights reserved. 7 8 1. INTRODUCTION 9 The Fraunhofer FDK AAC Codec Library for Android ("FDK AAC Codec") is software that implements 10 the MPEG Advanced Audio Coding ("AAC") encoding and decoding scheme for digital audio. 11 This FDK AAC Codec software is intended to be used on a wide variety of Android devices. 12 13 AAC's HE-AAC and HE-AAC v2 versions are regarded as today's most efficient general perceptual 14 audio codecs. AAC-ELD is considered the best-performing full-bandwidth communications codec by 15 independent studies and is widely deployed. AAC has been standardized by ISO and IEC as part 16 of the MPEG specifications. 17 18 Patent licenses for necessary patent claims for the FDK AAC Codec (including those of Fraunhofer) 19 may be obtained through Via Licensing (www.vialicensing.com) or through the respective patent owners 20 individually for the purpose of encoding or decoding bit streams in products that are compliant with 21 the ISO/IEC MPEG audio standards. Please note that most manufacturers of Android devices already license 22 these patent claims through Via Licensing or directly from the patent owners, and therefore FDK AAC Codec 23 software may already be covered under those patent licenses when it is used for those licensed purposes only. 24 25 Commercially-licensed AAC software libraries, including floating-point versions with enhanced sound quality, 26 are also available from Fraunhofer. Users are encouraged to check the Fraunhofer website for additional 27 applications information and documentation. 28 29 2. COPYRIGHT LICENSE 30 31 Redistribution and use in source and binary forms, with or without modification, are permitted without 32 payment of copyright license fees provided that you satisfy the following conditions: 33 34 You must retain the complete text of this software license in redistributions of the FDK AAC Codec or 35 your modifications thereto in source code form. 36 37 You must retain the complete text of this software license in the documentation and/or other materials 38 provided with redistributions of the FDK AAC Codec or your modifications thereto in binary form. 39 You must make available free of charge copies of the complete source code of the FDK AAC Codec and your 40 modifications thereto to recipients of copies in binary form. 41 42 The name of Fraunhofer may not be used to endorse or promote products derived from this library without 43 prior written permission. 44 45 You may not charge copyright license fees for anyone to use, copy or distribute the FDK AAC Codec 46 software or your modifications thereto. 47 48 Your modified versions of the FDK AAC Codec must carry prominent notices stating that you changed the software 49 and the date of any change. For modified versions of the FDK AAC Codec, the term 50 "Fraunhofer FDK AAC Codec Library for Android" must be replaced by the term 51 "Third-Party Modified Version of the Fraunhofer FDK AAC Codec Library for Android." 52 53 3. NO PATENT LICENSE 54 55 NO EXPRESS OR IMPLIED LICENSES TO ANY PATENT CLAIMS, including without limitation the patents of Fraunhofer, 56 ARE GRANTED BY THIS SOFTWARE LICENSE. Fraunhofer provides no warranty of patent non-infringement with 57 respect to this software. 58 59 You may use this FDK AAC Codec software or modifications thereto only for purposes that are authorized 60 by appropriate patent licenses. 61 62 4. DISCLAIMER 63 64 This FDK AAC Codec software is provided by Fraunhofer on behalf of the copyright holders and contributors 65 "AS IS" and WITHOUT ANY EXPRESS OR IMPLIED WARRANTIES, including but not limited to the implied warranties 66 of merchantability and fitness for a particular purpose. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR 67 CONTRIBUTORS BE LIABLE for any direct, indirect, incidental, special, exemplary, or consequential damages, 68 including but not limited to procurement of substitute goods or services; loss of use, data, or profits, 69 or business interruption, however caused and on any theory of liability, whether in contract, strict 70 liability, or tort (including negligence), arising in any way out of the use of this software, even if 71 advised of the possibility of such damage. 72 73 5. CONTACT INFORMATION 74 75 Fraunhofer Institute for Integrated Circuits IIS 76 Attention: Audio and Multimedia Departments - FDK AAC LL 77 Am Wolfsmantel 33 78 91058 Erlangen, Germany 79 80 www.iis.fraunhofer.de/amm 81 amm-info (at) iis.fraunhofer.de 82 ----------------------------------------------------------------------------------------------------------- */ 83 84 /*************************** Fraunhofer IIS FDK Tools ********************** 85 86 Author(s): M. Gayer 87 Description: Fixed point specific mathematical functions 88 89 ******************************************************************************/ 90 91 #include "fixpoint_math.h" 92 93 94 #define MAX_LD_PRECISION 10 95 #define LD_PRECISION 10 96 97 /* Taylor series coeffcients for ln(1-x), centered at 0 (MacLaurin polinomial). */ 98 #ifndef LDCOEFF_16BIT 99 LNK_SECTION_CONSTDATA_L1 100 static const FIXP_DBL ldCoeff[MAX_LD_PRECISION] = { 101 FL2FXCONST_DBL(-1.0), 102 FL2FXCONST_DBL(-1.0/2.0), 103 FL2FXCONST_DBL(-1.0/3.0), 104 FL2FXCONST_DBL(-1.0/4.0), 105 FL2FXCONST_DBL(-1.0/5.0), 106 FL2FXCONST_DBL(-1.0/6.0), 107 FL2FXCONST_DBL(-1.0/7.0), 108 FL2FXCONST_DBL(-1.0/8.0), 109 FL2FXCONST_DBL(-1.0/9.0), 110 FL2FXCONST_DBL(-1.0/10.0) 111 }; 112 #else 113 LNK_SECTION_CONSTDATA_L1 114 static const FIXP_SGL ldCoeff[MAX_LD_PRECISION] = { 115 FL2FXCONST_SGL(-1.0), 116 FL2FXCONST_SGL(-1.0/2.0), 117 FL2FXCONST_SGL(-1.0/3.0), 118 FL2FXCONST_SGL(-1.0/4.0), 119 FL2FXCONST_SGL(-1.0/5.0), 120 FL2FXCONST_SGL(-1.0/6.0), 121 FL2FXCONST_SGL(-1.0/7.0), 122 FL2FXCONST_SGL(-1.0/8.0), 123 FL2FXCONST_SGL(-1.0/9.0), 124 FL2FXCONST_SGL(-1.0/10.0) 125 }; 126 #endif 127 128 /***************************************************************************** 129 130 functionname: CalcLdData 131 description: Delivers the Logarithm Dualis ld(op)/LD_DATA_SCALING with polynomial approximation. 132 input: Input op is assumed to be double precision fractional 0 < op < 1.0 133 This function does not accept negative values. 134 output: For op == 0, the result is saturated to -1.0 135 This function does not return positive values since input values are treated as fractional values. 136 It does not make sense to input an integer value into this function (and expect a positive output value) 137 since input values are treated as fractional values. 138 139 *****************************************************************************/ 140 141 LNK_SECTION_CODE_L1 142 FIXP_DBL CalcLdData(FIXP_DBL op) 143 { 144 return fLog2(op, 0); 145 } 146 147 148 /***************************************************************************** 149 functionname: LdDataVector 150 *****************************************************************************/ 151 LNK_SECTION_CODE_L1 152 void LdDataVector( FIXP_DBL *srcVector, 153 FIXP_DBL *destVector, 154 INT n) 155 { 156 INT i; 157 for ( i=0; i<n; i++) { 158 destVector[i] = CalcLdData(srcVector[i]); 159 } 160 } 161 162 163 164 #define MAX_POW2_PRECISION 8 165 #ifndef SINETABLE_16BIT 166 #define POW2_PRECISION MAX_POW2_PRECISION 167 #else 168 #define POW2_PRECISION 5 169 #endif 170 171 /* 172 Taylor series coefficients of the function x^2. The first coefficient is 173 ommited (equal to 1.0). 174 175 pow2Coeff[i-1] = (1/i!) d^i(2^x)/dx^i, i=1..MAX_POW2_PRECISION 176 To evaluate the taylor series around x = 0, the coefficients are: 1/!i * ln(2)^i 177 */ 178 #ifndef POW2COEFF_16BIT 179 LNK_SECTION_CONSTDATA_L1 180 static const FIXP_DBL pow2Coeff[MAX_POW2_PRECISION] = { 181 FL2FXCONST_DBL(0.693147180559945309417232121458177), /* ln(2)^1 /1! */ 182 FL2FXCONST_DBL(0.240226506959100712333551263163332), /* ln(2)^2 /2! */ 183 FL2FXCONST_DBL(0.0555041086648215799531422637686218), /* ln(2)^3 /3! */ 184 FL2FXCONST_DBL(0.00961812910762847716197907157365887), /* ln(2)^4 /4! */ 185 FL2FXCONST_DBL(0.00133335581464284434234122219879962), /* ln(2)^5 /5! */ 186 FL2FXCONST_DBL(1.54035303933816099544370973327423e-4), /* ln(2)^6 /6! */ 187 FL2FXCONST_DBL(1.52527338040598402800254390120096e-5), /* ln(2)^7 /7! */ 188 FL2FXCONST_DBL(1.32154867901443094884037582282884e-6) /* ln(2)^8 /8! */ 189 }; 190 #else 191 LNK_SECTION_CONSTDATA_L1 192 static const FIXP_SGL pow2Coeff[MAX_POW2_PRECISION] = { 193 FL2FXCONST_SGL(0.693147180559945309417232121458177), /* ln(2)^1 /1! */ 194 FL2FXCONST_SGL(0.240226506959100712333551263163332), /* ln(2)^2 /2! */ 195 FL2FXCONST_SGL(0.0555041086648215799531422637686218), /* ln(2)^3 /3! */ 196 FL2FXCONST_SGL(0.00961812910762847716197907157365887), /* ln(2)^4 /4! */ 197 FL2FXCONST_SGL(0.00133335581464284434234122219879962), /* ln(2)^5 /5! */ 198 FL2FXCONST_SGL(1.54035303933816099544370973327423e-4), /* ln(2)^6 /6! */ 199 FL2FXCONST_SGL(1.52527338040598402800254390120096e-5), /* ln(2)^7 /7! */ 200 FL2FXCONST_SGL(1.32154867901443094884037582282884e-6) /* ln(2)^8 /8! */ 201 }; 202 #endif 203 204 205 206 /***************************************************************************** 207 208 functionname: mul_dbl_sgl_rnd 209 description: Multiply with round. 210 *****************************************************************************/ 211 212 /* for rounding a dfract to fract */ 213 #define ACCU_R (LONG) 0x00008000 214 215 LNK_SECTION_CODE_L1 216 FIXP_DBL mul_dbl_sgl_rnd (const FIXP_DBL op1, const FIXP_SGL op2) 217 { 218 FIXP_DBL prod; 219 LONG v = (LONG)(op1); 220 SHORT u = (SHORT)(op2); 221 222 LONG low = u*(v&SGL_MASK); 223 low = (low+(ACCU_R>>1)) >> (FRACT_BITS-1); /* round */ 224 LONG high = u * ((v>>FRACT_BITS)<<1); 225 226 prod = (LONG)(high+low); 227 228 return((FIXP_DBL)prod); 229 } 230 231 232 /***************************************************************************** 233 234 functionname: CalcInvLdData 235 description: Delivers the inverse of function CalcLdData(). 236 Delivers 2^(op*LD_DATA_SCALING) 237 input: Input op is assumed to be fractional -1.0 < op < 1.0 238 output: For op == 0, the result is MAXVAL_DBL (almost 1.0). 239 For negative input values the output should be treated as a positive fractional value. 240 For positive input values the output should be treated as a positive integer value. 241 This function does not output negative values. 242 243 *****************************************************************************/ 244 LNK_SECTION_CODE_L1 245 /* This table is used for lookup 2^x with */ 246 /* x in range [0...1.0[ in steps of 1/32 */ 247 LNK_SECTION_DATA_L1 static const UINT exp2_tab_long[32]={ 248 0x40000000,0x4166C34C,0x42D561B4,0x444C0740, 249 0x45CAE0F2,0x47521CC6,0x48E1E9BA,0x4A7A77D4, 250 0x4C1BF829,0x4DC69CDD,0x4F7A9930,0x51382182, 251 0x52FF6B55,0x54D0AD5A,0x56AC1F75,0x5891FAC1, 252 0x5A82799A,0x5C7DD7A4,0x5E8451D0,0x60962665, 253 0x62B39509,0x64DCDEC3,0x6712460B,0x69540EC9, 254 0x6BA27E65,0x6DFDDBCC,0x70666F76,0x72DC8374, 255 0x75606374,0x77F25CCE,0x7A92BE8B,0x7D41D96E 256 // 0x80000000 257 }; 258 259 /* This table is used for lookup 2^x with */ 260 /* x in range [0...1/32[ in steps of 1/1024 */ 261 LNK_SECTION_DATA_L1 static const UINT exp2w_tab_long[32]={ 262 0x40000000,0x400B1818,0x4016321B,0x40214E0C, 263 0x402C6BE9,0x40378BB4,0x4042AD6D,0x404DD113, 264 0x4058F6A8,0x40641E2B,0x406F479E,0x407A7300, 265 0x4085A051,0x4090CF92,0x409C00C4,0x40A733E6, 266 0x40B268FA,0x40BD9FFF,0x40C8D8F5,0x40D413DD, 267 0x40DF50B8,0x40EA8F86,0x40F5D046,0x410112FA, 268 0x410C57A2,0x41179E3D,0x4122E6CD,0x412E3152, 269 0x41397DCC,0x4144CC3B,0x41501CA0,0x415B6EFB, 270 // 0x4166C34C, 271 }; 272 /* This table is used for lookup 2^x with */ 273 /* x in range [0...1/1024[ in steps of 1/32768 */ 274 LNK_SECTION_DATA_L1 static const UINT exp2x_tab_long[32]={ 275 0x40000000,0x400058B9,0x4000B173,0x40010A2D, 276 0x400162E8,0x4001BBA3,0x4002145F,0x40026D1B, 277 0x4002C5D8,0x40031E95,0x40037752,0x4003D011, 278 0x400428CF,0x4004818E,0x4004DA4E,0x4005330E, 279 0x40058BCE,0x4005E48F,0x40063D51,0x40069613, 280 0x4006EED5,0x40074798,0x4007A05B,0x4007F91F, 281 0x400851E4,0x4008AAA8,0x4009036E,0x40095C33, 282 0x4009B4FA,0x400A0DC0,0x400A6688,0x400ABF4F, 283 //0x400B1818 284 }; 285 286 LNK_SECTION_CODE_L1 FIXP_DBL CalcInvLdData(FIXP_DBL x) 287 { 288 int set_zero = (x < FL2FXCONST_DBL(-31.0/64.0))? 0 : 1; 289 int set_max = (x >= FL2FXCONST_DBL( 31.0/64.0)) | (x == FL2FXCONST_DBL(0.0)); 290 291 FIXP_SGL frac = (FIXP_SGL)(LONG)(x & 0x3FF); 292 UINT index3 = (UINT)(LONG)(x >> 10) & 0x1F; 293 UINT index2 = (UINT)(LONG)(x >> 15) & 0x1F; 294 UINT index1 = (UINT)(LONG)(x >> 20) & 0x1F; 295 int exp = (x > FL2FXCONST_DBL(0.0f)) ? (31 - (int)(x>>25)) : (int)(-(x>>25)); 296 297 UINT lookup1 = exp2_tab_long[index1]*set_zero; 298 UINT lookup2 = exp2w_tab_long[index2]; 299 UINT lookup3 = exp2x_tab_long[index3]; 300 UINT lookup3f = lookup3 + (UINT)(LONG)fMultDiv2((FIXP_DBL)(0x0016302F),(FIXP_SGL)frac); 301 302 UINT lookup12 = (UINT)(LONG)fMult((FIXP_DBL)lookup1, (FIXP_DBL) lookup2); 303 UINT lookup = (UINT)(LONG)fMult((FIXP_DBL)lookup12, (FIXP_DBL) lookup3f); 304 305 FIXP_DBL retVal = (lookup<<3) >> exp; 306 307 if (set_max) 308 retVal=FL2FXCONST_DBL(1.0f); 309 310 return retVal; 311 } 312 313 314 315 316 317 /***************************************************************************** 318 functionname: InitLdInt and CalcLdInt 319 description: Create and access table with integer LdData (0 to 193) 320 *****************************************************************************/ 321 322 323 LNK_SECTION_CONSTDATA_L1 324 static const FIXP_DBL ldIntCoeff[] = { 325 0x80000001, 0x00000000, 0x02000000, 0x032b8034, 0x04000000, 0x04a4d3c2, 0x052b8034, 0x059d5da0, 326 0x06000000, 0x06570069, 0x06a4d3c2, 0x06eb3a9f, 0x072b8034, 0x0766a009, 0x079d5da0, 0x07d053f7, 327 0x08000000, 0x082cc7ee, 0x08570069, 0x087ef05b, 0x08a4d3c2, 0x08c8ddd4, 0x08eb3a9f, 0x090c1050, 328 0x092b8034, 0x0949a785, 0x0966a009, 0x0982809d, 0x099d5da0, 0x09b74949, 0x09d053f7, 0x09e88c6b, 329 0x0a000000, 0x0a16bad3, 0x0a2cc7ee, 0x0a423162, 0x0a570069, 0x0a6b3d79, 0x0a7ef05b, 0x0a92203d, 330 0x0aa4d3c2, 0x0ab7110e, 0x0ac8ddd4, 0x0ada3f60, 0x0aeb3a9f, 0x0afbd42b, 0x0b0c1050, 0x0b1bf312, 331 0x0b2b8034, 0x0b3abb40, 0x0b49a785, 0x0b584822, 0x0b66a009, 0x0b74b1fd, 0x0b82809d, 0x0b900e61, 332 0x0b9d5da0, 0x0baa708f, 0x0bb74949, 0x0bc3e9ca, 0x0bd053f7, 0x0bdc899b, 0x0be88c6b, 0x0bf45e09, 333 0x0c000000, 0x0c0b73cb, 0x0c16bad3, 0x0c21d671, 0x0c2cc7ee, 0x0c379085, 0x0c423162, 0x0c4caba8, 334 0x0c570069, 0x0c6130af, 0x0c6b3d79, 0x0c7527b9, 0x0c7ef05b, 0x0c88983f, 0x0c92203d, 0x0c9b8926, 335 0x0ca4d3c2, 0x0cae00d2, 0x0cb7110e, 0x0cc0052b, 0x0cc8ddd4, 0x0cd19bb0, 0x0cda3f60, 0x0ce2c97d, 336 0x0ceb3a9f, 0x0cf39355, 0x0cfbd42b, 0x0d03fda9, 0x0d0c1050, 0x0d140ca0, 0x0d1bf312, 0x0d23c41d, 337 0x0d2b8034, 0x0d3327c7, 0x0d3abb40, 0x0d423b08, 0x0d49a785, 0x0d510118, 0x0d584822, 0x0d5f7cff, 338 0x0d66a009, 0x0d6db197, 0x0d74b1fd, 0x0d7ba190, 0x0d82809d, 0x0d894f75, 0x0d900e61, 0x0d96bdad, 339 0x0d9d5da0, 0x0da3ee7f, 0x0daa708f, 0x0db0e412, 0x0db74949, 0x0dbda072, 0x0dc3e9ca, 0x0dca258e, 340 0x0dd053f7, 0x0dd6753e, 0x0ddc899b, 0x0de29143, 0x0de88c6b, 0x0dee7b47, 0x0df45e09, 0x0dfa34e1, 341 0x0e000000, 0x0e05bf94, 0x0e0b73cb, 0x0e111cd2, 0x0e16bad3, 0x0e1c4dfb, 0x0e21d671, 0x0e275460, 342 0x0e2cc7ee, 0x0e323143, 0x0e379085, 0x0e3ce5d8, 0x0e423162, 0x0e477346, 0x0e4caba8, 0x0e51daa8, 343 0x0e570069, 0x0e5c1d0b, 0x0e6130af, 0x0e663b74, 0x0e6b3d79, 0x0e7036db, 0x0e7527b9, 0x0e7a1030, 344 0x0e7ef05b, 0x0e83c857, 0x0e88983f, 0x0e8d602e, 0x0e92203d, 0x0e96d888, 0x0e9b8926, 0x0ea03232, 345 0x0ea4d3c2, 0x0ea96df0, 0x0eae00d2, 0x0eb28c7f, 0x0eb7110e, 0x0ebb8e96, 0x0ec0052b, 0x0ec474e4, 346 0x0ec8ddd4, 0x0ecd4012, 0x0ed19bb0, 0x0ed5f0c4, 0x0eda3f60, 0x0ede8797, 0x0ee2c97d, 0x0ee70525, 347 0x0eeb3a9f, 0x0eef69ff, 0x0ef39355, 0x0ef7b6b4, 0x0efbd42b, 0x0effebcd, 0x0f03fda9, 0x0f0809cf, 348 0x0f0c1050, 0x0f10113b, 0x0f140ca0, 0x0f18028d, 0x0f1bf312, 0x0f1fde3d, 0x0f23c41d, 0x0f27a4c0, 349 0x0f2b8034 350 }; 351 352 353 LNK_SECTION_INITCODE 354 void InitLdInt() 355 { 356 /* nothing to do! Use preinitialized logarithm table */ 357 } 358 359 360 361 LNK_SECTION_CODE_L1 362 FIXP_DBL CalcLdInt(INT i) 363 { 364 /* calculates ld(op)/LD_DATA_SCALING */ 365 /* op is assumed to be an integer value between 1 and 193 */ 366 367 FDK_ASSERT((193>0) && ((FIXP_DBL)ldIntCoeff[0]==(FIXP_DBL)0x80000001)); /* tab has to be initialized */ 368 369 if ((i>0)&&(i<193)) 370 return ldIntCoeff[i]; 371 else 372 { 373 return (0); 374 } 375 } 376 377 378 /***************************************************************************** 379 380 functionname: invSqrtNorm2 381 description: delivers 1/sqrt(op) normalized to .5...1 and the shift value of the OUTPUT 382 383 *****************************************************************************/ 384 #define SQRT_BITS 7 385 #define SQRT_VALUES 128 386 #define SQRT_BITS_MASK 0x7f 387 388 LNK_SECTION_CONSTDATA_L1 389 static const FIXP_DBL invSqrtTab[SQRT_VALUES] = { 390 0x5a827999, 0x5a287e03, 0x59cf8cbb, 0x5977a0ab, 0x5920b4de, 0x58cac480, 0x5875cade, 0x5821c364, 391 0x57cea99c, 0x577c792f, 0x572b2ddf, 0x56dac38d, 0x568b3631, 0x563c81df, 0x55eea2c3, 0x55a19521, 392 0x55555555, 0x5509dfd0, 0x54bf311a, 0x547545d0, 0x542c1aa3, 0x53e3ac5a, 0x539bf7cc, 0x5354f9e6, 393 0x530eafa4, 0x52c91617, 0x52842a5e, 0x523fe9ab, 0x51fc513f, 0x51b95e6b, 0x51770e8e, 0x51355f19, 394 0x50f44d88, 0x50b3d768, 0x5073fa4f, 0x5034b3e6, 0x4ff601df, 0x4fb7e1f9, 0x4f7a5201, 0x4f3d4fce, 395 0x4f00d943, 0x4ec4ec4e, 0x4e8986e9, 0x4e4ea718, 0x4e144ae8, 0x4dda7072, 0x4da115d9, 0x4d683948, 396 0x4d2fd8f4, 0x4cf7f31b, 0x4cc08604, 0x4c898fff, 0x4c530f64, 0x4c1d0293, 0x4be767f5, 0x4bb23df9, 397 0x4b7d8317, 0x4b4935ce, 0x4b1554a6, 0x4ae1de2a, 0x4aaed0f0, 0x4a7c2b92, 0x4a49ecb3, 0x4a1812fa, 398 0x49e69d16, 0x49b589bb, 0x4984d7a4, 0x49548591, 0x49249249, 0x48f4fc96, 0x48c5c34a, 0x4896e53c, 399 0x48686147, 0x483a364c, 0x480c6331, 0x47dee6e0, 0x47b1c049, 0x4784ee5f, 0x4758701c, 0x472c447c, 400 0x47006a80, 0x46d4e130, 0x46a9a793, 0x467ebcb9, 0x46541fb3, 0x4629cf98, 0x45ffcb80, 0x45d61289, 401 0x45aca3d5, 0x45837e88, 0x455aa1ca, 0x45320cc8, 0x4509beb0, 0x44e1b6b4, 0x44b9f40b, 0x449275ec, 402 0x446b3b95, 0x44444444, 0x441d8f3b, 0x43f71bbe, 0x43d0e917, 0x43aaf68e, 0x43854373, 0x435fcf14, 403 0x433a98c5, 0x43159fdb, 0x42f0e3ae, 0x42cc6397, 0x42a81ef5, 0x42841527, 0x4260458d, 0x423caf8c, 404 0x4219528b, 0x41f62df1, 0x41d3412a, 0x41b08ba1, 0x418e0cc7, 0x416bc40d, 0x4149b0e4, 0x4127d2c3, 405 0x41062920, 0x40e4b374, 0x40c3713a, 0x40a261ef, 0x40818511, 0x4060da21, 0x404060a1, 0x40201814 406 }; 407 408 LNK_SECTION_INITCODE 409 void InitInvSqrtTab() 410 { 411 /* nothing to do ! 412 use preinitialized square root table 413 */ 414 } 415 416 417 418 #if !defined(FUNCTION_invSqrtNorm2) 419 /***************************************************************************** 420 delivers 1/sqrt(op) normalized to .5...1 and the shift value of the OUTPUT, 421 i.e. the denormalized result is 1/sqrt(op) = invSqrtNorm(op) * 2^(shift) 422 uses Newton-iteration for approximation 423 Q(n+1) = Q(n) + Q(n) * (0.5 - 2 * V * Q(n)^2) 424 with Q = 0.5* V ^-0.5; 0.5 <= V < 1.0 425 *****************************************************************************/ 426 FIXP_DBL invSqrtNorm2(FIXP_DBL op, INT *shift) 427 { 428 429 FIXP_DBL val = op ; 430 FIXP_DBL reg1, reg2, regtmp ; 431 432 if (val == FL2FXCONST_DBL(0.0)) { 433 *shift = 1 ; 434 return((LONG)1); /* minimum positive value */ 435 } 436 437 438 /* normalize input, calculate shift value */ 439 FDK_ASSERT(val > FL2FXCONST_DBL(0.0)); 440 *shift = fNormz(val) - 1; /* CountLeadingBits() is not necessary here since test value is always > 0 */ 441 val <<=*shift ; /* normalized input V */ 442 *shift+=2 ; /* bias for exponent */ 443 444 /* Newton iteration of 1/sqrt(V) */ 445 reg1 = invSqrtTab[ (INT)(val>>(DFRACT_BITS-1-(SQRT_BITS+1))) & SQRT_BITS_MASK ]; 446 reg2 = FL2FXCONST_DBL(0.0625f); /* 0.5 >> 3 */ 447 448 regtmp= fPow2Div2(reg1); /* a = Q^2 */ 449 regtmp= reg2 - fMultDiv2(regtmp, val); /* b = 0.5 - 2 * V * Q^2 */ 450 reg1 += (fMultDiv2(regtmp, reg1)<<4); /* Q = Q + Q*b */ 451 452 /* calculate the output exponent = input exp/2 */ 453 if (*shift & 0x00000001) { /* odd shift values ? */ 454 reg2 = FL2FXCONST_DBL(0.707106781186547524400844362104849f); /* 1/sqrt(2); */ 455 reg1 = fMultDiv2(reg1, reg2) << 2; 456 } 457 458 *shift = *shift>>1; 459 460 return(reg1); 461 } 462 #endif /* !defined(FUNCTION_invSqrtNorm2) */ 463 464 /***************************************************************************** 465 466 functionname: sqrtFixp 467 description: delivers sqrt(op) 468 469 *****************************************************************************/ 470 FIXP_DBL sqrtFixp(FIXP_DBL op) 471 { 472 INT tmp_exp = 0; 473 FIXP_DBL tmp_inv = invSqrtNorm2(op, &tmp_exp); 474 475 FDK_ASSERT(tmp_exp > 0) ; 476 return( (FIXP_DBL) ( fMultDiv2( (op<<(tmp_exp-1)), tmp_inv ) << 2 )); 477 } 478 479 480 #if !defined(FUNCTION_schur_div) 481 /***************************************************************************** 482 483 functionname: schur_div 484 description: delivers op1/op2 with op3-bit accuracy 485 486 *****************************************************************************/ 487 488 489 FIXP_DBL schur_div(FIXP_DBL num, FIXP_DBL denum, INT count) 490 { 491 INT L_num = (LONG)num>>1; 492 INT L_denum = (LONG)denum>>1; 493 INT div = 0; 494 INT k = count; 495 496 FDK_ASSERT (num>=(FIXP_DBL)0); 497 FDK_ASSERT (denum>(FIXP_DBL)0); 498 FDK_ASSERT (num <= denum); 499 500 if (L_num != 0) 501 while (--k) 502 { 503 div <<= 1; 504 L_num <<= 1; 505 if (L_num >= L_denum) 506 { 507 L_num -= L_denum; 508 div++; 509 } 510 } 511 return (FIXP_DBL)(div << (DFRACT_BITS - count)); 512 } 513 514 515 #endif /* !defined(FUNCTION_schur_div) */ 516 517 518 #ifndef FUNCTION_fMultNorm 519 FIXP_DBL fMultNorm(FIXP_DBL f1, FIXP_DBL f2, INT *result_e) 520 { 521 INT product = 0; 522 INT norm_f1, norm_f2; 523 524 if ( (f1 == (FIXP_DBL)0) || (f2 == (FIXP_DBL)0) ) { 525 *result_e = 0; 526 return (FIXP_DBL)0; 527 } 528 norm_f1 = CountLeadingBits(f1); 529 f1 = f1 << norm_f1; 530 norm_f2 = CountLeadingBits(f2); 531 f2 = f2 << norm_f2; 532 533 product = fMult(f1, f2); 534 *result_e = - (norm_f1 + norm_f2); 535 536 return (FIXP_DBL)product; 537 } 538 #endif 539 540 #ifndef FUNCTION_fDivNorm 541 FIXP_DBL fDivNorm(FIXP_DBL L_num, FIXP_DBL L_denum, INT *result_e) 542 { 543 FIXP_DBL div; 544 INT norm_num, norm_den; 545 546 FDK_ASSERT (L_num >= (FIXP_DBL)0); 547 FDK_ASSERT (L_denum > (FIXP_DBL)0); 548 549 if(L_num == (FIXP_DBL)0) 550 { 551 *result_e = 0; 552 return ((FIXP_DBL)0); 553 } 554 555 norm_num = CountLeadingBits(L_num); 556 L_num = L_num << norm_num; 557 L_num = L_num >> 1; 558 *result_e = - norm_num + 1; 559 560 norm_den = CountLeadingBits(L_denum); 561 L_denum = L_denum << norm_den; 562 *result_e -= - norm_den; 563 564 div = schur_div(L_num, L_denum, FRACT_BITS); 565 566 return div; 567 } 568 #endif /* !FUNCTION_fDivNorm */ 569 570 #ifndef FUNCTION_fDivNorm 571 FIXP_DBL fDivNorm(FIXP_DBL num, FIXP_DBL denom) 572 { 573 INT e; 574 FIXP_DBL res; 575 576 FDK_ASSERT (denom >= num); 577 578 res = fDivNorm(num, denom, &e); 579 580 /* Avoid overflow since we must output a value with exponent 0 581 there is no other choice than saturating to almost 1.0f */ 582 if(res == (FIXP_DBL)(1<<(DFRACT_BITS-2)) && e == 1) 583 { 584 res = (FIXP_DBL)MAXVAL_DBL; 585 } 586 else 587 { 588 res = scaleValue(res, e); 589 } 590 591 return res; 592 } 593 #endif /* !FUNCTION_fDivNorm */ 594 595 #ifndef FUNCTION_fDivNormHighPrec 596 FIXP_DBL fDivNormHighPrec(FIXP_DBL num, FIXP_DBL denom, INT *result_e) 597 { 598 FIXP_DBL div; 599 INT norm_num, norm_den; 600 601 FDK_ASSERT (num >= (FIXP_DBL)0); 602 FDK_ASSERT (denom > (FIXP_DBL)0); 603 604 if(num == (FIXP_DBL)0) 605 { 606 *result_e = 0; 607 return ((FIXP_DBL)0); 608 } 609 610 norm_num = CountLeadingBits(num); 611 num = num << norm_num; 612 num = num >> 1; 613 *result_e = - norm_num + 1; 614 615 norm_den = CountLeadingBits(denom); 616 denom = denom << norm_den; 617 *result_e -= - norm_den; 618 619 div = schur_div(num, denom, 31); 620 return div; 621 } 622 #endif /* !FUNCTION_fDivNormHighPrec */ 623 624 625 626 FIXP_DBL CalcLog2(FIXP_DBL base_m, INT base_e, INT *result_e) 627 { 628 return fLog2(base_m, base_e, result_e); 629 } 630 631 FIXP_DBL f2Pow( 632 const FIXP_DBL exp_m, const INT exp_e, 633 INT *result_e 634 ) 635 { 636 FIXP_DBL frac_part, result_m; 637 INT int_part; 638 639 if (exp_e > 0) 640 { 641 INT exp_bits = DFRACT_BITS-1 - exp_e; 642 int_part = exp_m >> exp_bits; 643 frac_part = exp_m - (FIXP_DBL)(int_part << exp_bits); 644 frac_part = frac_part << exp_e; 645 } 646 else 647 { 648 int_part = 0; 649 frac_part = exp_m >> -exp_e; 650 } 651 652 /* Best accuracy is around 0, so try to get there with the fractional part. */ 653 if( frac_part > FL2FXCONST_DBL(0.5f) ) 654 { 655 int_part = int_part + 1; 656 frac_part = frac_part + FL2FXCONST_DBL(-1.0f); 657 } 658 if( frac_part < FL2FXCONST_DBL(-0.5f) ) 659 { 660 int_part = int_part - 1; 661 frac_part = -(FL2FXCONST_DBL(-1.0f) - frac_part); 662 } 663 664 /* Evaluate taylor polynomial which approximates 2^x */ 665 { 666 FIXP_DBL p; 667 668 /* result_m ~= 2^frac_part */ 669 p = frac_part; 670 /* First taylor series coefficient a_0 = 1.0, scaled by 0.5 due to fMultDiv2(). */ 671 result_m = FL2FXCONST_DBL(1.0f/2.0f); 672 for (INT i = 0; i < POW2_PRECISION; i++) { 673 /* next taylor series term: a_i * x^i, x=0 */ 674 result_m = fMultAddDiv2(result_m, pow2Coeff[i], p); 675 p = fMult(p, frac_part); 676 } 677 } 678 679 /* "+ 1" compensates fMultAddDiv2() of the polynomial evaluation above. */ 680 *result_e = int_part + 1; 681 682 return result_m; 683 } 684 685 FIXP_DBL f2Pow( 686 const FIXP_DBL exp_m, const INT exp_e 687 ) 688 { 689 FIXP_DBL result_m; 690 INT result_e; 691 692 result_m = f2Pow(exp_m, exp_e, &result_e); 693 result_e = fixMin(DFRACT_BITS-1,fixMax(-(DFRACT_BITS-1),result_e)); 694 695 return scaleValue(result_m, result_e); 696 } 697 698 FIXP_DBL fPow( 699 FIXP_DBL base_m, INT base_e, 700 FIXP_DBL exp_m, INT exp_e, 701 INT *result_e 702 ) 703 { 704 INT ans_lg2_e, baselg2_e; 705 FIXP_DBL base_lg2, ans_lg2, result; 706 707 /* Calc log2 of base */ 708 base_lg2 = fLog2(base_m, base_e, &baselg2_e); 709 710 /* Prepare exp */ 711 { 712 INT leadingBits; 713 714 leadingBits = CountLeadingBits(fAbs(exp_m)); 715 exp_m = exp_m << leadingBits; 716 exp_e -= leadingBits; 717 } 718 719 /* Calc base pow exp */ 720 ans_lg2 = fMult(base_lg2, exp_m); 721 ans_lg2_e = exp_e + baselg2_e; 722 723 /* Calc antilog */ 724 result = f2Pow(ans_lg2, ans_lg2_e, result_e); 725 726 return result; 727 } 728 729 FIXP_DBL fLdPow( 730 FIXP_DBL baseLd_m, 731 INT baseLd_e, 732 FIXP_DBL exp_m, INT exp_e, 733 INT *result_e 734 ) 735 { 736 INT ans_lg2_e; 737 FIXP_DBL ans_lg2, result; 738 739 /* Prepare exp */ 740 { 741 INT leadingBits; 742 743 leadingBits = CountLeadingBits(fAbs(exp_m)); 744 exp_m = exp_m << leadingBits; 745 exp_e -= leadingBits; 746 } 747 748 /* Calc base pow exp */ 749 ans_lg2 = fMult(baseLd_m, exp_m); 750 ans_lg2_e = exp_e + baseLd_e; 751 752 /* Calc antilog */ 753 result = f2Pow(ans_lg2, ans_lg2_e, result_e); 754 755 return result; 756 } 757 758 FIXP_DBL fLdPow( 759 FIXP_DBL baseLd_m, INT baseLd_e, 760 FIXP_DBL exp_m, INT exp_e 761 ) 762 { 763 FIXP_DBL result_m; 764 int result_e; 765 766 result_m = fLdPow(baseLd_m, baseLd_e, exp_m, exp_e, &result_e); 767 768 return SATURATE_SHIFT(result_m, -result_e, DFRACT_BITS); 769 } 770 771 FIXP_DBL fPowInt( 772 FIXP_DBL base_m, INT base_e, 773 INT exp, 774 INT *pResult_e 775 ) 776 { 777 FIXP_DBL result; 778 779 if (exp != 0) { 780 INT result_e = 0; 781 782 if (base_m != (FIXP_DBL)0) { 783 { 784 INT leadingBits; 785 leadingBits = CountLeadingBits( base_m ); 786 base_m <<= leadingBits; 787 base_e -= leadingBits; 788 } 789 790 result = base_m; 791 792 { 793 int i; 794 for (i = 1; i < fAbs(exp); i++) { 795 result = fMult(result, base_m); 796 } 797 } 798 799 if (exp < 0) { 800 /* 1.0 / ans */ 801 result = fDivNorm( FL2FXCONST_DBL(0.5f), result, &result_e ); 802 result_e++; 803 } else { 804 int ansScale = CountLeadingBits( result ); 805 result <<= ansScale; 806 result_e -= ansScale; 807 } 808 809 result_e += exp * base_e; 810 811 } else { 812 result = (FIXP_DBL)0; 813 } 814 *pResult_e = result_e; 815 } 816 else { 817 result = FL2FXCONST_DBL(0.5f); 818 *pResult_e = 1; 819 } 820 821 return result; 822 } 823 824 FIXP_DBL fLog2(FIXP_DBL x_m, INT x_e, INT *result_e) 825 { 826 FIXP_DBL result_m; 827 828 /* Short cut for zero and negative numbers. */ 829 if ( x_m <= FL2FXCONST_DBL(0.0f) ) { 830 *result_e = DFRACT_BITS-1; 831 return FL2FXCONST_DBL(-1.0f); 832 } 833 834 /* Calculate log2() */ 835 { 836 FIXP_DBL px2_m, x2_m; 837 838 /* Move input value x_m * 2^x_e toward 1.0, where the taylor approximation 839 of the function log(1-x) centered at 0 is most accurate. */ 840 { 841 INT b_norm; 842 843 b_norm = fNormz(x_m)-1; 844 x2_m = x_m << b_norm; 845 x_e = x_e - b_norm; 846 } 847 848 /* map x from log(x) domain to log(1-x) domain. */ 849 x2_m = - (x2_m + FL2FXCONST_DBL(-1.0) ); 850 851 /* Taylor polinomial approximation of ln(1-x) */ 852 result_m = FL2FXCONST_DBL(0.0); 853 px2_m = x2_m; 854 for (int i=0; i<LD_PRECISION; i++) { 855 result_m = fMultAddDiv2(result_m, ldCoeff[i], px2_m); 856 px2_m = fMult(px2_m, x2_m); 857 } 858 /* Multiply result with 1/ln(2) = 1.0 + 0.442695040888 (get log2(x) from ln(x) result). */ 859 result_m = fMultAddDiv2(result_m, result_m, FL2FXCONST_DBL(2.0*0.4426950408889634073599246810019)); 860 861 /* Add exponent part. log2(x_m * 2^x_e) = log2(x_m) + x_e */ 862 if (x_e != 0) 863 { 864 int enorm; 865 866 enorm = DFRACT_BITS - fNorm((FIXP_DBL)x_e); 867 /* The -1 in the right shift of result_m compensates the fMultDiv2() above in the taylor polinomial evaluation loop.*/ 868 result_m = (result_m >> (enorm-1)) + ((FIXP_DBL)x_e << (DFRACT_BITS-1-enorm)); 869 870 *result_e = enorm; 871 } else { 872 /* 1 compensates the fMultDiv2() above in the taylor polinomial evaluation loop.*/ 873 *result_e = 1; 874 } 875 } 876 877 return result_m; 878 } 879 880 FIXP_DBL fLog2(FIXP_DBL x_m, INT x_e) 881 { 882 if ( x_m <= FL2FXCONST_DBL(0.0f) ) { 883 x_m = FL2FXCONST_DBL(-1.0f); 884 } 885 else { 886 INT result_e; 887 x_m = fLog2(x_m, x_e, &result_e); 888 x_m = scaleValue(x_m, result_e-LD_DATA_SHIFT); 889 } 890 return x_m; 891 } 892 893 894 895 896
