1 /* ----------------------------------------------------------------------------- 2 Software License for The Fraunhofer FDK AAC Codec Library for Android 3 4 Copyright 1995 - 2018 Fraunhofer-Gesellschaft zur Frderung der angewandten 5 Forschung e.V. All rights reserved. 6 7 1. INTRODUCTION 8 The Fraunhofer FDK AAC Codec Library for Android ("FDK AAC Codec") is software 9 that implements the MPEG Advanced Audio Coding ("AAC") encoding and decoding 10 scheme for digital audio. This FDK AAC Codec software is intended to be used on 11 a wide variety of Android devices. 12 13 AAC's HE-AAC and HE-AAC v2 versions are regarded as today's most efficient 14 general perceptual audio codecs. AAC-ELD is considered the best-performing 15 full-bandwidth communications codec by independent studies and is widely 16 deployed. AAC has been standardized by ISO and IEC as part of the MPEG 17 specifications. 18 19 Patent licenses for necessary patent claims for the FDK AAC Codec (including 20 those of Fraunhofer) may be obtained through Via Licensing 21 (www.vialicensing.com) or through the respective patent owners individually for 22 the purpose of encoding or decoding bit streams in products that are compliant 23 with the ISO/IEC MPEG audio standards. Please note that most manufacturers of 24 Android devices already license these patent claims through Via Licensing or 25 directly from the patent owners, and therefore FDK AAC Codec software may 26 already be covered under those patent licenses when it is used for those 27 licensed purposes only. 28 29 Commercially-licensed AAC software libraries, including floating-point versions 30 with enhanced sound quality, are also available from Fraunhofer. Users are 31 encouraged to check the Fraunhofer website for additional applications 32 information and documentation. 33 34 2. COPYRIGHT LICENSE 35 36 Redistribution and use in source and binary forms, with or without modification, 37 are permitted without payment of copyright license fees provided that you 38 satisfy the following conditions: 39 40 You must retain the complete text of this software license in redistributions of 41 the FDK AAC Codec or your modifications thereto in source code form. 42 43 You must retain the complete text of this software license in the documentation 44 and/or other materials provided with redistributions of the FDK AAC Codec or 45 your modifications thereto in binary form. You must make available free of 46 charge copies of the complete source code of the FDK AAC Codec and your 47 modifications thereto to recipients of copies in binary form. 48 49 The name of Fraunhofer may not be used to endorse or promote products derived 50 from this library without prior written permission. 51 52 You may not charge copyright license fees for anyone to use, copy or distribute 53 the FDK AAC Codec software or your modifications thereto. 54 55 Your modified versions of the FDK AAC Codec must carry prominent notices stating 56 that you changed the software and the date of any change. For modified versions 57 of the FDK AAC Codec, the term "Fraunhofer FDK AAC Codec Library for Android" 58 must be replaced by the term "Third-Party Modified Version of the Fraunhofer FDK 59 AAC Codec Library for Android." 60 61 3. NO PATENT LICENSE 62 63 NO EXPRESS OR IMPLIED LICENSES TO ANY PATENT CLAIMS, including without 64 limitation the patents of Fraunhofer, ARE GRANTED BY THIS SOFTWARE LICENSE. 65 Fraunhofer provides no warranty of patent non-infringement with respect to this 66 software. 67 68 You may use this FDK AAC Codec software or modifications thereto only for 69 purposes that are authorized by appropriate patent licenses. 70 71 4. DISCLAIMER 72 73 This FDK AAC Codec software is provided by Fraunhofer on behalf of the copyright 74 holders and contributors "AS IS" and WITHOUT ANY EXPRESS OR IMPLIED WARRANTIES, 75 including but not limited to the implied warranties of merchantability and 76 fitness for a particular purpose. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR 77 CONTRIBUTORS BE LIABLE for any direct, indirect, incidental, special, exemplary, 78 or consequential damages, including but not limited to procurement of substitute 79 goods or services; loss of use, data, or profits, or business interruption, 80 however caused and on any theory of liability, whether in contract, strict 81 liability, or tort (including negligence), arising in any way out of the use of 82 this software, even if advised of the possibility of such damage. 83 84 5. CONTACT INFORMATION 85 86 Fraunhofer Institute for Integrated Circuits IIS 87 Attention: Audio and Multimedia Departments - FDK AAC LL 88 Am Wolfsmantel 33 89 91058 Erlangen, Germany 90 91 www.iis.fraunhofer.de/amm 92 amm-info (at) iis.fraunhofer.de 93 ----------------------------------------------------------------------------- */ 94 95 /******************* Library for basic calculation routines ******************** 96 97 Author(s): Haricharan Lakshman, Manuel Jander 98 99 Description: Trigonometric functions fixed point fractional implementation. 100 101 *******************************************************************************/ 102 103 #include "FDK_trigFcts.h" 104 105 #include "fixpoint_math.h" 106 107 #define IMPROVE_ATAN2_ACCURACY 1 /* 0 --> 59 dB SNR 1 --> 65 dB SNR */ 108 #define MINSFTAB 7 109 #define MAXSFTAB 25 110 111 #if IMPROVE_ATAN2_ACCURACY 112 static const FIXP_DBL f_atan_expand_range[MAXSFTAB - (MINSFTAB - 1)] = { 113 /***************************************************************************** 114 * 115 * Table holds fixp_atan() output values which are outside of input range 116 * of fixp_atan() to improve SNR of fixp_atan2(). 117 * 118 * This Table might also be used in fixp_atan() so there a wider input 119 * range can be covered, too. 120 * 121 *****************************************************************************/ 122 FL2FXCONST_DBL(7.775862990872099e-001), 123 FL2FXCONST_DBL(7.814919928673978e-001), 124 FL2FXCONST_DBL(7.834450483314648e-001), 125 FL2FXCONST_DBL(7.844216021392089e-001), 126 FL2FXCONST_DBL(7.849098823026687e-001), 127 FL2FXCONST_DBL(7.851540227918509e-001), 128 FL2FXCONST_DBL(7.852760930873737e-001), 129 FL2FXCONST_DBL(7.853371282415015e-001), 130 FL2FXCONST_DBL(7.853676458193612e-001), 131 FL2FXCONST_DBL(7.853829046083906e-001), 132 FL2FXCONST_DBL(7.853905340029177e-001), 133 FL2FXCONST_DBL(7.853943487001828e-001), 134 FL2FXCONST_DBL(7.853962560488155e-001), 135 FL2FXCONST_DBL(7.853972097231319e-001), 136 FL2FXCONST_DBL(7.853976865602901e-001), 137 FL2FXCONST_DBL(7.853979249788692e-001), 138 FL2FXCONST_DBL(7.853980441881587e-001), 139 FL2FXCONST_DBL(7.853981037928035e-001), 140 FL2FXCONST_DBL(7.853981335951259e-001) 141 /* pi/4 = 0.785398163397448 = pi/2/ATO_SCALE */ 142 }; 143 #endif 144 145 FIXP_DBL fixp_atan2(FIXP_DBL y, FIXP_DBL x) { 146 FIXP_DBL q; 147 FIXP_DBL at; /* atan out */ 148 FIXP_DBL at2; /* atan2 out */ 149 FIXP_DBL ret = FL2FXCONST_DBL(-1.0f); 150 INT sf, sfo, stf; 151 152 /* --- division */ 153 154 if (y > FL2FXCONST_DBL(0.0f)) { 155 if (x > FL2FXCONST_DBL(0.0f)) { 156 q = fDivNormHighPrec(y, x, &sf); /* both pos. */ 157 } else if (x < FL2FXCONST_DBL(0.0f)) { 158 q = -fDivNormHighPrec(y, -x, &sf); /* x neg. */ 159 } else { /* (x == FL2FXCONST_DBL(0.0f)) */ 160 q = FL2FXCONST_DBL(+1.0f); /* y/x = pos/zero = +Inf */ 161 sf = 0; 162 } 163 } else if (y < FL2FXCONST_DBL(0.0f)) { 164 if (x > FL2FXCONST_DBL(0.0f)) { 165 q = -fDivNormHighPrec(-y, x, &sf); /* y neg. */ 166 } else if (x < FL2FXCONST_DBL(0.0f)) { 167 q = fDivNormHighPrec(-y, -x, &sf); /* both neg. */ 168 } else { /* (x == FL2FXCONST_DBL(0.0f)) */ 169 q = FL2FXCONST_DBL(-1.0f); /* y/x = neg/zero = -Inf */ 170 sf = 0; 171 } 172 } else { /* (y == FL2FXCONST_DBL(0.0f)) */ 173 q = FL2FXCONST_DBL(0.0f); 174 sf = 0; 175 } 176 sfo = sf; 177 178 /* --- atan() */ 179 180 if (sfo > ATI_SF) { 181 /* --- could not calc fixp_atan() here bec of input data out of range */ 182 /* ==> therefore give back boundary values */ 183 184 #if IMPROVE_ATAN2_ACCURACY 185 if (sfo > MAXSFTAB) sfo = MAXSFTAB; 186 #endif 187 188 if (q > FL2FXCONST_DBL(0.0f)) { 189 #if IMPROVE_ATAN2_ACCURACY 190 at = +f_atan_expand_range[sfo - ATI_SF - 1]; 191 #else 192 at = FL2FXCONST_DBL(+M_PI / 2 / ATO_SCALE); 193 #endif 194 } else if (q < FL2FXCONST_DBL(0.0f)) { 195 #if IMPROVE_ATAN2_ACCURACY 196 at = -f_atan_expand_range[sfo - ATI_SF - 1]; 197 #else 198 at = FL2FXCONST_DBL(-M_PI / 2 / ATO_SCALE); 199 #endif 200 } else { /* q == FL2FXCONST_DBL(0.0f) */ 201 at = FL2FXCONST_DBL(0.0f); 202 } 203 } else { 204 /* --- calc of fixp_atan() is possible; input data within range */ 205 /* ==> set q on fixed scale level as desired from fixp_atan() */ 206 stf = sfo - ATI_SF; 207 if (stf > 0) 208 q = q << (INT)fMin(stf, DFRACT_BITS - 1); 209 else 210 q = q >> (INT)fMin(-stf, DFRACT_BITS - 1); 211 at = fixp_atan(q); /* ATO_SF */ 212 } 213 214 // --- atan2() 215 216 at2 = at >> (AT2O_SF - ATO_SF); // now AT2O_SF for atan2 217 if (x > FL2FXCONST_DBL(0.0f)) { 218 ret = at2; 219 } else if (x < FL2FXCONST_DBL(0.0f)) { 220 if (y >= FL2FXCONST_DBL(0.0f)) { 221 ret = at2 + FL2FXCONST_DBL(M_PI / AT2O_SCALE); 222 } else { 223 ret = at2 - FL2FXCONST_DBL(M_PI / AT2O_SCALE); 224 } 225 } else { 226 // x == 0 227 if (y > FL2FXCONST_DBL(0.0f)) { 228 ret = FL2FXCONST_DBL(+M_PI / 2 / AT2O_SCALE); 229 } else if (y < FL2FXCONST_DBL(0.0f)) { 230 ret = FL2FXCONST_DBL(-M_PI / 2 / AT2O_SCALE); 231 } else if (y == FL2FXCONST_DBL(0.0f)) { 232 ret = FL2FXCONST_DBL(0.0f); 233 } 234 } 235 return ret; 236 } 237 238 FIXP_DBL fixp_atan(FIXP_DBL x) { 239 INT sign; 240 FIXP_DBL result, temp; 241 242 /* SNR of fixp_atan() = 56 dB */ 243 FIXP_DBL P281 = (FIXP_DBL)0x00013000; // 0.281 in q18 244 FIXP_DBL ONEP571 = (FIXP_DBL)0x6487ef00; // 1.571 in q30 245 246 if (x < FIXP_DBL(0)) { 247 sign = 1; 248 x = -x; 249 } else { 250 sign = 0; 251 } 252 FDK_ASSERT(FL2FXCONST_DBL(1.0 / 64.0) == Q(Q_ATANINP)); 253 /* calc of arctan */ 254 if (x < FL2FXCONST_DBL(1.0 / 64.0)) 255 /* 256 Chebyshev polynomial approximation of atan(x) 257 5th-order approximation: atan(x) = a1*x + a2*x^3 + a3*x^5 = x(a1 + x^2*(a2 + 258 a3*x^2)); a1 = 0.9949493661166540f, a2 = 0.2870606355326520f, a3 = 259 0.0780371764464410f; 7th-order approximation: atan(x) = a1*x + a2*x^3 + 260 a3*x^5 + a3*x^7 = x(a1 + x^2*(a2 + x^2*(a3 + a4*x^2))); a1 = 261 0.9991334482227801, a2 = -0.3205332923816640, a3 = 0.1449824901444650, a4 = 262 -0.0382544649702990; 7th-order approximation in use (the most accurate 263 solution) 264 */ 265 { 266 x <<= ATI_SF; 267 FIXP_DBL x2 = fPow2(x); 268 temp = fMultAddDiv2((FL2FXCONST_DBL(0.1449824901444650f) >> 1), x2, 269 FL2FXCONST_DBL(-0.0382544649702990)); 270 temp = fMultAddDiv2((FL2FXCONST_DBL(-0.3205332923816640f) >> 2), x2, temp); 271 temp = fMultAddDiv2((FL2FXCONST_DBL(0.9991334482227801f) >> 3), x2, temp); 272 result = fMult(x, (temp << 2)); 273 } else if (x < FL2FXCONST_DBL(1.28 / 64.0)) { 274 FIXP_DBL delta_fix; 275 FIXP_DBL PI_BY_4 = FL2FXCONST_DBL(3.1415926 / 4.0) >> 1; /* pi/4 in q30 */ 276 277 delta_fix = (x - FL2FXCONST_DBL(1.0 / 64.0)) << 5; /* q30 */ 278 result = PI_BY_4 + (delta_fix >> 1) - (fPow2Div2(delta_fix)); 279 } else { 280 /* Other approximation for |x| > 1.28 */ 281 INT res_e; 282 283 temp = fPow2Div2(x); /* q25 * q25 - (DFRACT_BITS-1) - 1 = q18 */ 284 temp = temp + P281; /* q18 + q18 = q18 */ 285 result = fDivNorm(x, temp, &res_e); 286 result = scaleValue(result, 287 (Q_ATANOUT - Q_ATANINP + 18 - DFRACT_BITS + 1) + res_e); 288 result = ONEP571 - result; /* q30 + q30 = q30 */ 289 } 290 if (sign) { 291 result = -result; 292 } 293 294 return (result); 295 } 296 297 #include "FDK_tools_rom.h" 298 299 FIXP_DBL fixp_cos(FIXP_DBL x, int scale) { 300 FIXP_DBL residual, error, sine, cosine; 301 302 residual = fixp_sin_cos_residual_inline(x, scale, &sine, &cosine); 303 error = fMult(sine, residual); 304 305 #ifdef SINETABLE_16BIT 306 return cosine - error; 307 #else 308 /* Undo downscaling by 1 which was done at fixp_sin_cos_residual_inline */ 309 return SATURATE_LEFT_SHIFT(cosine - error, 1, DFRACT_BITS); 310 #endif 311 } 312 313 FIXP_DBL fixp_sin(FIXP_DBL x, int scale) { 314 FIXP_DBL residual, error, sine, cosine; 315 316 residual = fixp_sin_cos_residual_inline(x, scale, &sine, &cosine); 317 error = fMult(cosine, residual); 318 319 #ifdef SINETABLE_16BIT 320 return sine + error; 321 #else 322 return SATURATE_LEFT_SHIFT(sine + error, 1, DFRACT_BITS); 323 #endif 324 } 325 326 void fixp_cos_sin(FIXP_DBL x, int scale, FIXP_DBL *cos, FIXP_DBL *sin) { 327 FIXP_DBL residual, error0, error1, sine, cosine; 328 329 residual = fixp_sin_cos_residual_inline(x, scale, &sine, &cosine); 330 error0 = fMult(sine, residual); 331 error1 = fMult(cosine, residual); 332 333 #ifdef SINETABLE_16BIT 334 *cos = cosine - error0; 335 *sin = sine + error1; 336 #else 337 *cos = SATURATE_LEFT_SHIFT(cosine - error0, 1, DFRACT_BITS); 338 *sin = SATURATE_LEFT_SHIFT(sine + error1, 1, DFRACT_BITS); 339 #endif 340 } 341
