diff options
Diffstat (limited to 'fdk-aac/libFDK/src/fixpoint_math.cpp')
| -rw-r--r-- | fdk-aac/libFDK/src/fixpoint_math.cpp | 900 |
1 files changed, 900 insertions, 0 deletions
diff --git a/fdk-aac/libFDK/src/fixpoint_math.cpp b/fdk-aac/libFDK/src/fixpoint_math.cpp new file mode 100644 index 0000000..6c656fa --- /dev/null +++ b/fdk-aac/libFDK/src/fixpoint_math.cpp @@ -0,0 +1,900 @@ +/* ----------------------------------------------------------------------------- +Software License for The Fraunhofer FDK AAC Codec Library for Android + +© Copyright 1995 - 2018 Fraunhofer-Gesellschaft zur Förderung der angewandten +Forschung e.V. All rights reserved. + + 1. INTRODUCTION +The Fraunhofer FDK AAC Codec Library for Android ("FDK AAC Codec") is software +that implements the MPEG Advanced Audio Coding ("AAC") encoding and decoding +scheme for digital audio. This FDK AAC Codec software is intended to be used on +a wide variety of Android devices. + +AAC's HE-AAC and HE-AAC v2 versions are regarded as today's most efficient +general perceptual audio codecs. AAC-ELD is considered the best-performing +full-bandwidth communications codec by independent studies and is widely +deployed. AAC has been standardized by ISO and IEC as part of the MPEG +specifications. + +Patent licenses for necessary patent claims for the FDK AAC Codec (including +those of Fraunhofer) may be obtained through Via Licensing +(www.vialicensing.com) or through the respective patent owners individually for +the purpose of encoding or decoding bit streams in products that are compliant +with the ISO/IEC MPEG audio standards. Please note that most manufacturers of +Android devices already license these patent claims through Via Licensing or +directly from the patent owners, and therefore FDK AAC Codec software may +already be covered under those patent licenses when it is used for those +licensed purposes only. + +Commercially-licensed AAC software libraries, including floating-point versions +with enhanced sound quality, are also available from Fraunhofer. Users are +encouraged to check the Fraunhofer website for additional applications +information and documentation. + +2. COPYRIGHT LICENSE + +Redistribution and use in source and binary forms, with or without modification, +are permitted without payment of copyright license fees provided that you +satisfy the following conditions: + +You must retain the complete text of this software license in redistributions of +the FDK AAC Codec or your modifications thereto in source code form. + +You must retain the complete text of this software license in the documentation +and/or other materials provided with redistributions of the FDK AAC Codec or +your modifications thereto in binary form. You must make available free of +charge copies of the complete source code of the FDK AAC Codec and your +modifications thereto to recipients of copies in binary form. + +The name of Fraunhofer may not be used to endorse or promote products derived +from this library without prior written permission. + +You may not charge copyright license fees for anyone to use, copy or distribute +the FDK AAC Codec software or your modifications thereto. + +Your modified versions of the FDK AAC Codec must carry prominent notices stating +that you changed the software and the date of any change. For modified versions +of the FDK AAC Codec, the term "Fraunhofer FDK AAC Codec Library for Android" +must be replaced by the term "Third-Party Modified Version of the Fraunhofer FDK +AAC Codec Library for Android." + +3. NO PATENT LICENSE + +NO EXPRESS OR IMPLIED LICENSES TO ANY PATENT CLAIMS, including without +limitation the patents of Fraunhofer, ARE GRANTED BY THIS SOFTWARE LICENSE. +Fraunhofer provides no warranty of patent non-infringement with respect to this +software. + +You may use this FDK AAC Codec software or modifications thereto only for +purposes that are authorized by appropriate patent licenses. + +4. DISCLAIMER + +This FDK AAC Codec software is provided by Fraunhofer on behalf of the copyright +holders and contributors "AS IS" and WITHOUT ANY EXPRESS OR IMPLIED WARRANTIES, +including but not limited to the implied warranties of merchantability and +fitness for a particular purpose. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR +CONTRIBUTORS BE LIABLE for any direct, indirect, incidental, special, exemplary, +or consequential damages, including but not limited to procurement of substitute +goods or services; loss of use, data, or profits, or business interruption, +however caused and on any theory of liability, whether in contract, strict +liability, or tort (including negligence), arising in any way out of the use of +this software, even if advised of the possibility of such damage. + +5. CONTACT INFORMATION + +Fraunhofer Institute for Integrated Circuits IIS +Attention: Audio and Multimedia Departments - FDK AAC LL +Am Wolfsmantel 33 +91058 Erlangen, Germany + +www.iis.fraunhofer.de/amm +amm-info@iis.fraunhofer.de +----------------------------------------------------------------------------- */ + +/******************* Library for basic calculation routines ******************** + + Author(s): M. Gayer + + Description: Fixed point specific mathematical functions + +*******************************************************************************/ + +#include "fixpoint_math.h" + +/* + * Hardware specific implementations + */ + +/* + * Fallback implementations + */ + +/***************************************************************************** + functionname: LdDataVector +*****************************************************************************/ +LNK_SECTION_CODE_L1 +void LdDataVector(FIXP_DBL *srcVector, FIXP_DBL *destVector, INT n) { + INT i; + for (i = 0; i < n; i++) { + destVector[i] = fLog2(srcVector[i], 0); + } +} + +#define MAX_POW2_PRECISION 8 +#ifndef SINETABLE_16BIT +#define POW2_PRECISION MAX_POW2_PRECISION +#else +#define POW2_PRECISION 5 +#endif + +/* + Taylor series coefficients of the function x^2. The first coefficient is + ommited (equal to 1.0). + + pow2Coeff[i-1] = (1/i!) d^i(2^x)/dx^i, i=1..MAX_POW2_PRECISION + To evaluate the taylor series around x = 0, the coefficients are: 1/!i * + ln(2)^i + */ +#ifndef POW2COEFF_16BIT +RAM_ALIGN +LNK_SECTION_CONSTDATA_L1 +static const FIXP_DBL pow2Coeff[MAX_POW2_PRECISION] = { + FL2FXCONST_DBL(0.693147180559945309417232121458177), /* ln(2)^1 /1! */ + FL2FXCONST_DBL(0.240226506959100712333551263163332), /* ln(2)^2 /2! */ + FL2FXCONST_DBL(0.0555041086648215799531422637686218), /* ln(2)^3 /3! */ + FL2FXCONST_DBL(0.00961812910762847716197907157365887), /* ln(2)^4 /4! */ + FL2FXCONST_DBL(0.00133335581464284434234122219879962), /* ln(2)^5 /5! */ + FL2FXCONST_DBL(1.54035303933816099544370973327423e-4), /* ln(2)^6 /6! */ + FL2FXCONST_DBL(1.52527338040598402800254390120096e-5), /* ln(2)^7 /7! */ + FL2FXCONST_DBL(1.32154867901443094884037582282884e-6) /* ln(2)^8 /8! */ +}; +#else +RAM_ALIGN +LNK_SECTION_CONSTDATA_L1 +static const FIXP_SGL pow2Coeff[MAX_POW2_PRECISION] = { + FL2FXCONST_SGL(0.693147180559945309417232121458177), /* ln(2)^1 /1! */ + FL2FXCONST_SGL(0.240226506959100712333551263163332), /* ln(2)^2 /2! */ + FL2FXCONST_SGL(0.0555041086648215799531422637686218), /* ln(2)^3 /3! */ + FL2FXCONST_SGL(0.00961812910762847716197907157365887), /* ln(2)^4 /4! */ + FL2FXCONST_SGL(0.00133335581464284434234122219879962), /* ln(2)^5 /5! */ + FL2FXCONST_SGL(1.54035303933816099544370973327423e-4), /* ln(2)^6 /6! */ + FL2FXCONST_SGL(1.52527338040598402800254390120096e-5), /* ln(2)^7 /7! */ + FL2FXCONST_SGL(1.32154867901443094884037582282884e-6) /* ln(2)^8 /8! */ +}; +#endif + +/***************************************************************************** + + functionname: CalcInvLdData + description: Delivers the inverse of function CalcLdData(). + Delivers 2^(op*LD_DATA_SCALING) + input: Input op is assumed to be fractional -1.0 < op < 1.0 + output: For op == 0, the result is MAXVAL_DBL (almost 1.0). + For negative input values the output should be treated as a +positive fractional value. For positive input values the output should be +treated as a positive integer value. This function does not output negative +values. + +*****************************************************************************/ +/* Date: 06-JULY-2012 Arthur Tritthart, IIS Fraunhofer Erlangen */ +/* Version with 3 table lookup and 1 linear interpolations */ +/* Algorithm: compute power of 2, argument x is in Q7.25 format */ +/* result = 2^(x/64) */ +/* We split exponent (x/64) into 5 components: */ +/* integer part: represented by b31..b25 (exp) */ +/* fractional part 1: represented by b24..b20 (lookup1) */ +/* fractional part 2: represented by b19..b15 (lookup2) */ +/* fractional part 3: represented by b14..b10 (lookup3) */ +/* fractional part 4: represented by b09..b00 (frac) */ +/* => result = (lookup1*lookup2*(lookup3+C1*frac)<<3)>>exp */ +/* Due to the fact, that all lookup values contain a factor 0.5 */ +/* the result has to be shifted by 3 to the right also. */ +/* Table exp2_tab_long contains the log2 for 0 to 1.0 in steps */ +/* of 1/32, table exp2w_tab_long the log2 for 0 to 1/32 in steps*/ +/* of 1/1024, table exp2x_tab_long the log2 for 0 to 1/1024 in */ +/* steps of 1/32768. Since the 2-logarithm of very very small */ +/* negative value is rather linear, we can use interpolation. */ +/* Limitations: */ +/* For x <= 0, the result is fractional positive */ +/* For x > 0, the result is integer in range 1...7FFF.FFFF */ +/* For x < -31/64, we have to clear the result */ +/* For x = 0, the result is ~1.0 (0x7FFF.FFFF) */ +/* For x >= 31/64, the result is 0x7FFF.FFFF */ + +/* This table is used for lookup 2^x with */ +/* x in range [0...1.0[ in steps of 1/32 */ +LNK_SECTION_DATA_L1 +const UINT exp2_tab_long[32] = { + 0x40000000, 0x4166C34C, 0x42D561B4, 0x444C0740, 0x45CAE0F2, 0x47521CC6, + 0x48E1E9BA, 0x4A7A77D4, 0x4C1BF829, 0x4DC69CDD, 0x4F7A9930, 0x51382182, + 0x52FF6B55, 0x54D0AD5A, 0x56AC1F75, 0x5891FAC1, 0x5A82799A, 0x5C7DD7A4, + 0x5E8451D0, 0x60962665, 0x62B39509, 0x64DCDEC3, 0x6712460B, 0x69540EC9, + 0x6BA27E65, 0x6DFDDBCC, 0x70666F76, 0x72DC8374, 0x75606374, 0x77F25CCE, + 0x7A92BE8B, 0x7D41D96E + // 0x80000000 +}; + +/* This table is used for lookup 2^x with */ +/* x in range [0...1/32[ in steps of 1/1024 */ +LNK_SECTION_DATA_L1 +const UINT exp2w_tab_long[32] = { + 0x40000000, 0x400B1818, 0x4016321B, 0x40214E0C, 0x402C6BE9, 0x40378BB4, + 0x4042AD6D, 0x404DD113, 0x4058F6A8, 0x40641E2B, 0x406F479E, 0x407A7300, + 0x4085A051, 0x4090CF92, 0x409C00C4, 0x40A733E6, 0x40B268FA, 0x40BD9FFF, + 0x40C8D8F5, 0x40D413DD, 0x40DF50B8, 0x40EA8F86, 0x40F5D046, 0x410112FA, + 0x410C57A2, 0x41179E3D, 0x4122E6CD, 0x412E3152, 0x41397DCC, 0x4144CC3B, + 0x41501CA0, 0x415B6EFB, + // 0x4166C34C, +}; +/* This table is used for lookup 2^x with */ +/* x in range [0...1/1024[ in steps of 1/32768 */ +LNK_SECTION_DATA_L1 +const UINT exp2x_tab_long[32] = { + 0x40000000, 0x400058B9, 0x4000B173, 0x40010A2D, 0x400162E8, 0x4001BBA3, + 0x4002145F, 0x40026D1B, 0x4002C5D8, 0x40031E95, 0x40037752, 0x4003D011, + 0x400428CF, 0x4004818E, 0x4004DA4E, 0x4005330E, 0x40058BCE, 0x4005E48F, + 0x40063D51, 0x40069613, 0x4006EED5, 0x40074798, 0x4007A05B, 0x4007F91F, + 0x400851E4, 0x4008AAA8, 0x4009036E, 0x40095C33, 0x4009B4FA, 0x400A0DC0, + 0x400A6688, 0x400ABF4F, + // 0x400B1818 +}; + +/***************************************************************************** + functionname: InitLdInt and CalcLdInt + description: Create and access table with integer LdData (0 to +LD_INT_TAB_LEN) +*****************************************************************************/ +#ifndef LD_INT_TAB_LEN +#define LD_INT_TAB_LEN \ + 193 /* Default tab length. Lower value should be set in fix.h */ +#endif + +#if (LD_INT_TAB_LEN <= 120) +LNK_SECTION_CONSTDATA_L1 +static const FIXP_DBL ldIntCoeff[] = { + (FIXP_DBL)0x80000001, (FIXP_DBL)0x00000000, (FIXP_DBL)0x02000000, + (FIXP_DBL)0x032b8034, (FIXP_DBL)0x04000000, (FIXP_DBL)0x04a4d3c2, + (FIXP_DBL)0x052b8034, (FIXP_DBL)0x059d5da0, (FIXP_DBL)0x06000000, + (FIXP_DBL)0x06570069, (FIXP_DBL)0x06a4d3c2, (FIXP_DBL)0x06eb3a9f, + (FIXP_DBL)0x072b8034, (FIXP_DBL)0x0766a009, (FIXP_DBL)0x079d5da0, + (FIXP_DBL)0x07d053f7, (FIXP_DBL)0x08000000, (FIXP_DBL)0x082cc7ee, + (FIXP_DBL)0x08570069, (FIXP_DBL)0x087ef05b, (FIXP_DBL)0x08a4d3c2, + (FIXP_DBL)0x08c8ddd4, (FIXP_DBL)0x08eb3a9f, (FIXP_DBL)0x090c1050, + (FIXP_DBL)0x092b8034, (FIXP_DBL)0x0949a785, (FIXP_DBL)0x0966a009, + (FIXP_DBL)0x0982809d, (FIXP_DBL)0x099d5da0, (FIXP_DBL)0x09b74949, + (FIXP_DBL)0x09d053f7, (FIXP_DBL)0x09e88c6b, (FIXP_DBL)0x0a000000, + (FIXP_DBL)0x0a16bad3, (FIXP_DBL)0x0a2cc7ee, (FIXP_DBL)0x0a423162, + (FIXP_DBL)0x0a570069, (FIXP_DBL)0x0a6b3d79, (FIXP_DBL)0x0a7ef05b, + (FIXP_DBL)0x0a92203d, (FIXP_DBL)0x0aa4d3c2, (FIXP_DBL)0x0ab7110e, + (FIXP_DBL)0x0ac8ddd4, (FIXP_DBL)0x0ada3f60, (FIXP_DBL)0x0aeb3a9f, + (FIXP_DBL)0x0afbd42b, (FIXP_DBL)0x0b0c1050, (FIXP_DBL)0x0b1bf312, + (FIXP_DBL)0x0b2b8034, (FIXP_DBL)0x0b3abb40, (FIXP_DBL)0x0b49a785, + (FIXP_DBL)0x0b584822, (FIXP_DBL)0x0b66a009, (FIXP_DBL)0x0b74b1fd, + (FIXP_DBL)0x0b82809d, (FIXP_DBL)0x0b900e61, (FIXP_DBL)0x0b9d5da0, + (FIXP_DBL)0x0baa708f, (FIXP_DBL)0x0bb74949, (FIXP_DBL)0x0bc3e9ca, + (FIXP_DBL)0x0bd053f7, (FIXP_DBL)0x0bdc899b, (FIXP_DBL)0x0be88c6b, + (FIXP_DBL)0x0bf45e09, (FIXP_DBL)0x0c000000, (FIXP_DBL)0x0c0b73cb, + (FIXP_DBL)0x0c16bad3, (FIXP_DBL)0x0c21d671, (FIXP_DBL)0x0c2cc7ee, + (FIXP_DBL)0x0c379085, (FIXP_DBL)0x0c423162, (FIXP_DBL)0x0c4caba8, + (FIXP_DBL)0x0c570069, (FIXP_DBL)0x0c6130af, (FIXP_DBL)0x0c6b3d79, + (FIXP_DBL)0x0c7527b9, (FIXP_DBL)0x0c7ef05b, (FIXP_DBL)0x0c88983f, + (FIXP_DBL)0x0c92203d, (FIXP_DBL)0x0c9b8926, (FIXP_DBL)0x0ca4d3c2, + (FIXP_DBL)0x0cae00d2, (FIXP_DBL)0x0cb7110e, (FIXP_DBL)0x0cc0052b, + (FIXP_DBL)0x0cc8ddd4, (FIXP_DBL)0x0cd19bb0, (FIXP_DBL)0x0cda3f60, + (FIXP_DBL)0x0ce2c97d, (FIXP_DBL)0x0ceb3a9f, (FIXP_DBL)0x0cf39355, + (FIXP_DBL)0x0cfbd42b, (FIXP_DBL)0x0d03fda9, (FIXP_DBL)0x0d0c1050, + (FIXP_DBL)0x0d140ca0, (FIXP_DBL)0x0d1bf312, (FIXP_DBL)0x0d23c41d, + (FIXP_DBL)0x0d2b8034, (FIXP_DBL)0x0d3327c7, (FIXP_DBL)0x0d3abb40, + (FIXP_DBL)0x0d423b08, (FIXP_DBL)0x0d49a785, (FIXP_DBL)0x0d510118, + (FIXP_DBL)0x0d584822, (FIXP_DBL)0x0d5f7cff, (FIXP_DBL)0x0d66a009, + (FIXP_DBL)0x0d6db197, (FIXP_DBL)0x0d74b1fd, (FIXP_DBL)0x0d7ba190, + (FIXP_DBL)0x0d82809d, (FIXP_DBL)0x0d894f75, (FIXP_DBL)0x0d900e61, + (FIXP_DBL)0x0d96bdad, (FIXP_DBL)0x0d9d5da0, (FIXP_DBL)0x0da3ee7f, + (FIXP_DBL)0x0daa708f, (FIXP_DBL)0x0db0e412, (FIXP_DBL)0x0db74949, + (FIXP_DBL)0x0dbda072, (FIXP_DBL)0x0dc3e9ca, (FIXP_DBL)0x0dca258e}; + +#elif (LD_INT_TAB_LEN <= 193) +LNK_SECTION_CONSTDATA_L1 +static const FIXP_DBL ldIntCoeff[] = { + (FIXP_DBL)0x80000001, (FIXP_DBL)0x00000000, (FIXP_DBL)0x02000000, + (FIXP_DBL)0x032b8034, (FIXP_DBL)0x04000000, (FIXP_DBL)0x04a4d3c2, + (FIXP_DBL)0x052b8034, (FIXP_DBL)0x059d5da0, (FIXP_DBL)0x06000000, + (FIXP_DBL)0x06570069, (FIXP_DBL)0x06a4d3c2, (FIXP_DBL)0x06eb3a9f, + (FIXP_DBL)0x072b8034, (FIXP_DBL)0x0766a009, (FIXP_DBL)0x079d5da0, + (FIXP_DBL)0x07d053f7, (FIXP_DBL)0x08000000, (FIXP_DBL)0x082cc7ee, + (FIXP_DBL)0x08570069, (FIXP_DBL)0x087ef05b, (FIXP_DBL)0x08a4d3c2, + (FIXP_DBL)0x08c8ddd4, (FIXP_DBL)0x08eb3a9f, (FIXP_DBL)0x090c1050, + (FIXP_DBL)0x092b8034, (FIXP_DBL)0x0949a785, (FIXP_DBL)0x0966a009, + (FIXP_DBL)0x0982809d, (FIXP_DBL)0x099d5da0, (FIXP_DBL)0x09b74949, + (FIXP_DBL)0x09d053f7, (FIXP_DBL)0x09e88c6b, (FIXP_DBL)0x0a000000, + (FIXP_DBL)0x0a16bad3, (FIXP_DBL)0x0a2cc7ee, (FIXP_DBL)0x0a423162, + (FIXP_DBL)0x0a570069, (FIXP_DBL)0x0a6b3d79, (FIXP_DBL)0x0a7ef05b, + (FIXP_DBL)0x0a92203d, (FIXP_DBL)0x0aa4d3c2, (FIXP_DBL)0x0ab7110e, + (FIXP_DBL)0x0ac8ddd4, (FIXP_DBL)0x0ada3f60, (FIXP_DBL)0x0aeb3a9f, + (FIXP_DBL)0x0afbd42b, (FIXP_DBL)0x0b0c1050, (FIXP_DBL)0x0b1bf312, + (FIXP_DBL)0x0b2b8034, (FIXP_DBL)0x0b3abb40, (FIXP_DBL)0x0b49a785, + (FIXP_DBL)0x0b584822, (FIXP_DBL)0x0b66a009, (FIXP_DBL)0x0b74b1fd, + (FIXP_DBL)0x0b82809d, (FIXP_DBL)0x0b900e61, (FIXP_DBL)0x0b9d5da0, + (FIXP_DBL)0x0baa708f, (FIXP_DBL)0x0bb74949, (FIXP_DBL)0x0bc3e9ca, + (FIXP_DBL)0x0bd053f7, (FIXP_DBL)0x0bdc899b, (FIXP_DBL)0x0be88c6b, + (FIXP_DBL)0x0bf45e09, (FIXP_DBL)0x0c000000, (FIXP_DBL)0x0c0b73cb, + (FIXP_DBL)0x0c16bad3, (FIXP_DBL)0x0c21d671, (FIXP_DBL)0x0c2cc7ee, + (FIXP_DBL)0x0c379085, (FIXP_DBL)0x0c423162, (FIXP_DBL)0x0c4caba8, + (FIXP_DBL)0x0c570069, (FIXP_DBL)0x0c6130af, (FIXP_DBL)0x0c6b3d79, + (FIXP_DBL)0x0c7527b9, (FIXP_DBL)0x0c7ef05b, (FIXP_DBL)0x0c88983f, + (FIXP_DBL)0x0c92203d, (FIXP_DBL)0x0c9b8926, (FIXP_DBL)0x0ca4d3c2, + (FIXP_DBL)0x0cae00d2, (FIXP_DBL)0x0cb7110e, (FIXP_DBL)0x0cc0052b, + (FIXP_DBL)0x0cc8ddd4, (FIXP_DBL)0x0cd19bb0, (FIXP_DBL)0x0cda3f60, + (FIXP_DBL)0x0ce2c97d, (FIXP_DBL)0x0ceb3a9f, (FIXP_DBL)0x0cf39355, + (FIXP_DBL)0x0cfbd42b, (FIXP_DBL)0x0d03fda9, (FIXP_DBL)0x0d0c1050, + (FIXP_DBL)0x0d140ca0, (FIXP_DBL)0x0d1bf312, (FIXP_DBL)0x0d23c41d, + (FIXP_DBL)0x0d2b8034, (FIXP_DBL)0x0d3327c7, (FIXP_DBL)0x0d3abb40, + (FIXP_DBL)0x0d423b08, (FIXP_DBL)0x0d49a785, (FIXP_DBL)0x0d510118, + (FIXP_DBL)0x0d584822, (FIXP_DBL)0x0d5f7cff, (FIXP_DBL)0x0d66a009, + (FIXP_DBL)0x0d6db197, (FIXP_DBL)0x0d74b1fd, (FIXP_DBL)0x0d7ba190, + (FIXP_DBL)0x0d82809d, (FIXP_DBL)0x0d894f75, (FIXP_DBL)0x0d900e61, + (FIXP_DBL)0x0d96bdad, (FIXP_DBL)0x0d9d5da0, (FIXP_DBL)0x0da3ee7f, + (FIXP_DBL)0x0daa708f, (FIXP_DBL)0x0db0e412, (FIXP_DBL)0x0db74949, + (FIXP_DBL)0x0dbda072, (FIXP_DBL)0x0dc3e9ca, (FIXP_DBL)0x0dca258e, + (FIXP_DBL)0x0dd053f7, (FIXP_DBL)0x0dd6753e, (FIXP_DBL)0x0ddc899b, + (FIXP_DBL)0x0de29143, (FIXP_DBL)0x0de88c6b, (FIXP_DBL)0x0dee7b47, + (FIXP_DBL)0x0df45e09, (FIXP_DBL)0x0dfa34e1, (FIXP_DBL)0x0e000000, + (FIXP_DBL)0x0e05bf94, (FIXP_DBL)0x0e0b73cb, (FIXP_DBL)0x0e111cd2, + (FIXP_DBL)0x0e16bad3, (FIXP_DBL)0x0e1c4dfb, (FIXP_DBL)0x0e21d671, + (FIXP_DBL)0x0e275460, (FIXP_DBL)0x0e2cc7ee, (FIXP_DBL)0x0e323143, + (FIXP_DBL)0x0e379085, (FIXP_DBL)0x0e3ce5d8, (FIXP_DBL)0x0e423162, + (FIXP_DBL)0x0e477346, (FIXP_DBL)0x0e4caba8, (FIXP_DBL)0x0e51daa8, + (FIXP_DBL)0x0e570069, (FIXP_DBL)0x0e5c1d0b, (FIXP_DBL)0x0e6130af, + (FIXP_DBL)0x0e663b74, (FIXP_DBL)0x0e6b3d79, (FIXP_DBL)0x0e7036db, + (FIXP_DBL)0x0e7527b9, (FIXP_DBL)0x0e7a1030, (FIXP_DBL)0x0e7ef05b, + (FIXP_DBL)0x0e83c857, (FIXP_DBL)0x0e88983f, (FIXP_DBL)0x0e8d602e, + (FIXP_DBL)0x0e92203d, (FIXP_DBL)0x0e96d888, (FIXP_DBL)0x0e9b8926, + (FIXP_DBL)0x0ea03232, (FIXP_DBL)0x0ea4d3c2, (FIXP_DBL)0x0ea96df0, + (FIXP_DBL)0x0eae00d2, (FIXP_DBL)0x0eb28c7f, (FIXP_DBL)0x0eb7110e, + (FIXP_DBL)0x0ebb8e96, (FIXP_DBL)0x0ec0052b, (FIXP_DBL)0x0ec474e4, + (FIXP_DBL)0x0ec8ddd4, (FIXP_DBL)0x0ecd4012, (FIXP_DBL)0x0ed19bb0, + (FIXP_DBL)0x0ed5f0c4, (FIXP_DBL)0x0eda3f60, (FIXP_DBL)0x0ede8797, + (FIXP_DBL)0x0ee2c97d, (FIXP_DBL)0x0ee70525, (FIXP_DBL)0x0eeb3a9f, + (FIXP_DBL)0x0eef69ff, (FIXP_DBL)0x0ef39355, (FIXP_DBL)0x0ef7b6b4, + (FIXP_DBL)0x0efbd42b, (FIXP_DBL)0x0effebcd, (FIXP_DBL)0x0f03fda9, + (FIXP_DBL)0x0f0809cf, (FIXP_DBL)0x0f0c1050, (FIXP_DBL)0x0f10113b, + (FIXP_DBL)0x0f140ca0, (FIXP_DBL)0x0f18028d, (FIXP_DBL)0x0f1bf312, + (FIXP_DBL)0x0f1fde3d, (FIXP_DBL)0x0f23c41d, (FIXP_DBL)0x0f27a4c0, + (FIXP_DBL)0x0f2b8034}; + +#else +#error "ldInt table size too small" + +#endif + +LNK_SECTION_INITCODE +void InitLdInt() { /* nothing to do! Use preinitialized logarithm table */ +} + +#if (LD_INT_TAB_LEN != 0) + +LNK_SECTION_CODE_L1 +FIXP_DBL CalcLdInt(INT i) { + /* calculates ld(op)/LD_DATA_SCALING */ + /* op is assumed to be an integer value between 1 and LD_INT_TAB_LEN */ + + FDK_ASSERT((LD_INT_TAB_LEN > 0) && + ((FIXP_DBL)ldIntCoeff[0] == + (FIXP_DBL)0x80000001)); /* tab has to be initialized */ + + if ((i > 0) && (i < LD_INT_TAB_LEN)) + return ldIntCoeff[i]; + else { + return (0); + } +} +#endif /* (LD_INT_TAB_LEN!=0) */ + +#if !defined(FUNCTION_schur_div) +/***************************************************************************** + + functionname: schur_div + description: delivers op1/op2 with op3-bit accuracy + +*****************************************************************************/ + +FIXP_DBL schur_div(FIXP_DBL num, FIXP_DBL denum, INT count) { + INT L_num = (LONG)num >> 1; + INT L_denum = (LONG)denum >> 1; + INT div = 0; + INT k = count; + + FDK_ASSERT(num >= (FIXP_DBL)0); + FDK_ASSERT(denum > (FIXP_DBL)0); + FDK_ASSERT(num <= denum); + + if (L_num != 0) + while (--k) { + div <<= 1; + L_num <<= 1; + if (L_num >= L_denum) { + L_num -= L_denum; + div++; + } + } + return (FIXP_DBL)(div << (DFRACT_BITS - count)); +} + +#endif /* !defined(FUNCTION_schur_div) */ + +#ifndef FUNCTION_fMultNorm +FIXP_DBL fMultNorm(FIXP_DBL f1, FIXP_DBL f2, INT *result_e) { + INT product = 0; + INT norm_f1, norm_f2; + + if ((f1 == (FIXP_DBL)0) || (f2 == (FIXP_DBL)0)) { + *result_e = 0; + return (FIXP_DBL)0; + } + norm_f1 = CountLeadingBits(f1); + f1 = f1 << norm_f1; + norm_f2 = CountLeadingBits(f2); + f2 = f2 << norm_f2; + + if ((f1 == (FIXP_DBL)MINVAL_DBL) && (f2 == (FIXP_DBL)MINVAL_DBL)) { + product = -((FIXP_DBL)MINVAL_DBL >> 1); + *result_e = -(norm_f1 + norm_f2 - 1); + } else { + product = fMult(f1, f2); + *result_e = -(norm_f1 + norm_f2); + } + + return (FIXP_DBL)product; +} +#endif + +#ifndef FUNCTION_fDivNorm +FIXP_DBL fDivNorm(FIXP_DBL L_num, FIXP_DBL L_denum, INT *result_e) { + FIXP_DBL div; + INT norm_num, norm_den; + + FDK_ASSERT(L_num >= (FIXP_DBL)0); + FDK_ASSERT(L_denum > (FIXP_DBL)0); + + if (L_num == (FIXP_DBL)0) { + *result_e = 0; + return ((FIXP_DBL)0); + } + + norm_num = CountLeadingBits(L_num); + L_num = L_num << norm_num; + L_num = L_num >> 1; + *result_e = -norm_num + 1; + + norm_den = CountLeadingBits(L_denum); + L_denum = L_denum << norm_den; + *result_e -= -norm_den; + + div = schur_div(L_num, L_denum, FRACT_BITS); + + return div; +} +#endif /* !FUNCTION_fDivNorm */ + +#ifndef FUNCTION_fDivNorm +FIXP_DBL fDivNorm(FIXP_DBL num, FIXP_DBL denom) { + INT e; + FIXP_DBL res; + + FDK_ASSERT(denom >= num); + + res = fDivNorm(num, denom, &e); + + /* Avoid overflow since we must output a value with exponent 0 + there is no other choice than saturating to almost 1.0f */ + if (res == (FIXP_DBL)(1 << (DFRACT_BITS - 2)) && e == 1) { + res = (FIXP_DBL)MAXVAL_DBL; + } else { + res = scaleValue(res, e); + } + + return res; +} +#endif /* !FUNCTION_fDivNorm */ + +#ifndef FUNCTION_fDivNormSigned +FIXP_DBL fDivNormSigned(FIXP_DBL num, FIXP_DBL denom) { + INT e; + FIXP_DBL res; + int sign; + + if (denom == (FIXP_DBL)0) { + return (FIXP_DBL)MAXVAL_DBL; + } + + sign = ((num >= (FIXP_DBL)0) != (denom >= (FIXP_DBL)0)); + res = fDivNormSigned(num, denom, &e); + + /* Saturate since we must output a value with exponent 0 */ + if ((e > 0) && (fAbs(res) >= FL2FXCONST_DBL(0.5))) { + if (sign) { + res = (FIXP_DBL)MINVAL_DBL; + } else { + res = (FIXP_DBL)MAXVAL_DBL; + } + } else { + res = scaleValue(res, e); + } + + return res; +} +FIXP_DBL fDivNormSigned(FIXP_DBL L_num, FIXP_DBL L_denum, INT *result_e) { + FIXP_DBL div; + INT norm_num, norm_den; + int sign; + + sign = ((L_num >= (FIXP_DBL)0) != (L_denum >= (FIXP_DBL)0)); + + if (L_num == (FIXP_DBL)0) { + *result_e = 0; + return ((FIXP_DBL)0); + } + if (L_denum == (FIXP_DBL)0) { + *result_e = 14; + return ((FIXP_DBL)MAXVAL_DBL); + } + + norm_num = CountLeadingBits(L_num); + L_num = L_num << norm_num; + L_num = L_num >> 2; + L_num = fAbs(L_num); + *result_e = -norm_num + 1; + + norm_den = CountLeadingBits(L_denum); + L_denum = L_denum << norm_den; + L_denum = L_denum >> 1; + L_denum = fAbs(L_denum); + *result_e -= -norm_den; + + div = schur_div(L_num, L_denum, FRACT_BITS); + + if (sign) { + div = -div; + } + + return div; +} +#endif /* FUNCTION_fDivNormSigned */ + +#ifndef FUNCTION_fDivNormHighPrec +FIXP_DBL fDivNormHighPrec(FIXP_DBL num, FIXP_DBL denom, INT *result_e) { + FIXP_DBL div; + INT norm_num, norm_den; + + FDK_ASSERT(num >= (FIXP_DBL)0); + FDK_ASSERT(denom > (FIXP_DBL)0); + + if (num == (FIXP_DBL)0) { + *result_e = 0; + return ((FIXP_DBL)0); + } + + norm_num = CountLeadingBits(num); + num = num << norm_num; + num = num >> 1; + *result_e = -norm_num + 1; + + norm_den = CountLeadingBits(denom); + denom = denom << norm_den; + *result_e -= -norm_den; + + div = schur_div(num, denom, 31); + return div; +} +#endif /* !FUNCTION_fDivNormHighPrec */ + +#ifndef FUNCTION_fPow +FIXP_DBL f2Pow(const FIXP_DBL exp_m, const INT exp_e, INT *result_e) { + FIXP_DBL frac_part, result_m; + INT int_part; + + if (exp_e > 0) { + INT exp_bits = DFRACT_BITS - 1 - exp_e; + int_part = exp_m >> exp_bits; + frac_part = exp_m - (FIXP_DBL)(int_part << exp_bits); + frac_part = frac_part << exp_e; + } else { + int_part = 0; + frac_part = exp_m >> -exp_e; + } + + /* Best accuracy is around 0, so try to get there with the fractional part. */ + if (frac_part > FL2FXCONST_DBL(0.5f)) { + int_part = int_part + 1; + frac_part = frac_part + FL2FXCONST_DBL(-1.0f); + } + if (frac_part < FL2FXCONST_DBL(-0.5f)) { + int_part = int_part - 1; + frac_part = -(FL2FXCONST_DBL(-1.0f) - frac_part); + } + + /* "+ 1" compensates fMultAddDiv2() of the polynomial evaluation below. */ + *result_e = int_part + 1; + + /* Evaluate taylor polynomial which approximates 2^x */ + { + FIXP_DBL p; + + /* result_m ~= 2^frac_part */ + p = frac_part; + /* First taylor series coefficient a_0 = 1.0, scaled by 0.5 due to + * fMultDiv2(). */ + result_m = FL2FXCONST_DBL(1.0f / 2.0f); + for (INT i = 0; i < POW2_PRECISION; i++) { + /* next taylor series term: a_i * x^i, x=0 */ + result_m = fMultAddDiv2(result_m, pow2Coeff[i], p); + p = fMult(p, frac_part); + } + } + return result_m; +} + +FIXP_DBL f2Pow(const FIXP_DBL exp_m, const INT exp_e) { + FIXP_DBL result_m; + INT result_e; + + result_m = f2Pow(exp_m, exp_e, &result_e); + result_e = fixMin(DFRACT_BITS - 1, fixMax(-(DFRACT_BITS - 1), result_e)); + + return scaleValue(result_m, result_e); +} + +FIXP_DBL fPow(FIXP_DBL base_m, INT base_e, FIXP_DBL exp_m, INT exp_e, + INT *result_e) { + INT ans_lg2_e, baselg2_e; + FIXP_DBL base_lg2, ans_lg2, result; + + /* Calc log2 of base */ + base_lg2 = fLog2(base_m, base_e, &baselg2_e); + + /* Prepare exp */ + { + INT leadingBits; + + leadingBits = CountLeadingBits(fAbs(exp_m)); + exp_m = exp_m << leadingBits; + exp_e -= leadingBits; + } + + /* Calc base pow exp */ + ans_lg2 = fMult(base_lg2, exp_m); + ans_lg2_e = exp_e + baselg2_e; + + /* Calc antilog */ + result = f2Pow(ans_lg2, ans_lg2_e, result_e); + + return result; +} + +FIXP_DBL fLdPow(FIXP_DBL baseLd_m, INT baseLd_e, FIXP_DBL exp_m, INT exp_e, + INT *result_e) { + INT ans_lg2_e; + FIXP_DBL ans_lg2, result; + + /* Prepare exp */ + { + INT leadingBits; + + leadingBits = CountLeadingBits(fAbs(exp_m)); + exp_m = exp_m << leadingBits; + exp_e -= leadingBits; + } + + /* Calc base pow exp */ + ans_lg2 = fMult(baseLd_m, exp_m); + ans_lg2_e = exp_e + baseLd_e; + + /* Calc antilog */ + result = f2Pow(ans_lg2, ans_lg2_e, result_e); + + return result; +} + +FIXP_DBL fLdPow(FIXP_DBL baseLd_m, INT baseLd_e, FIXP_DBL exp_m, INT exp_e) { + FIXP_DBL result_m; + int result_e; + + result_m = fLdPow(baseLd_m, baseLd_e, exp_m, exp_e, &result_e); + + return SATURATE_SHIFT(result_m, -result_e, DFRACT_BITS); +} + +FIXP_DBL fPowInt(FIXP_DBL base_m, INT base_e, INT exp, INT *pResult_e) { + FIXP_DBL result; + + if (exp != 0) { + INT result_e = 0; + + if (base_m != (FIXP_DBL)0) { + { + INT leadingBits; + leadingBits = CountLeadingBits(base_m); + base_m <<= leadingBits; + base_e -= leadingBits; + } + + result = base_m; + + { + int i; + for (i = 1; i < fAbs(exp); i++) { + result = fMult(result, base_m); + } + } + + if (exp < 0) { + /* 1.0 / ans */ + result = fDivNorm(FL2FXCONST_DBL(0.5f), result, &result_e); + result_e++; + } else { + int ansScale = CountLeadingBits(result); + result <<= ansScale; + result_e -= ansScale; + } + + result_e += exp * base_e; + + } else { + result = (FIXP_DBL)0; + } + *pResult_e = result_e; + } else { + result = FL2FXCONST_DBL(0.5f); + *pResult_e = 1; + } + + return result; +} +#endif /* FUNCTION_fPow */ + +#ifndef FUNCTION_fLog2 +FIXP_DBL CalcLog2(FIXP_DBL base_m, INT base_e, INT *result_e) { + return fLog2(base_m, base_e, result_e); +} +#endif /* FUNCTION_fLog2 */ + +INT fixp_floorToInt(FIXP_DBL f_inp, INT sf) { + FDK_ASSERT(sf >= 0); + INT floorInt = (INT)(f_inp >> ((DFRACT_BITS - 1) - sf)); + return floorInt; +} + +FIXP_DBL fixp_floor(FIXP_DBL f_inp, INT sf) { + FDK_ASSERT(sf >= 0); + INT floorInt = fixp_floorToInt(f_inp, sf); + FIXP_DBL f_floor = (FIXP_DBL)(floorInt << ((DFRACT_BITS - 1) - sf)); + return f_floor; +} + +INT fixp_ceilToInt(FIXP_DBL f_inp, INT sf) // sf mantissaBits left of dot +{ + FDK_ASSERT(sf >= 0); + INT sx = (DFRACT_BITS - 1) - sf; // sx mantissaBits right of dot + INT inpINT = (INT)f_inp; + + INT mask = (0x1 << sx) - 1; + INT ceilInt = (INT)(f_inp >> sx); + + if (inpINT & mask) { + ceilInt++; // increment only, if there is at least one set mantissaBit + // right of dot [in inpINT] + } + + return ceilInt; +} + +FIXP_DBL fixp_ceil(FIXP_DBL f_inp, INT sf) { + FDK_ASSERT(sf >= 0); + INT sx = (DFRACT_BITS - 1) - sf; + INT ceilInt = fixp_ceilToInt(f_inp, sf); + ULONG mask = (ULONG)0x1 << (DFRACT_BITS - 1); // 0x80000000 + ceilInt = ceilInt + << sx; // no fract warn bec. shift into saturation done on int side + + if ((f_inp > FL2FXCONST_DBL(0.0f)) && (ceilInt & mask)) { + --ceilInt; + } + FIXP_DBL f_ceil = (FIXP_DBL)ceilInt; + + return f_ceil; +} + +/***************************************************************************** + fixp_truncateToInt() + Just remove the fractional part which is located right of decimal point + Same as which is done when a float is casted to (INT) : + result_INTtype = (INT)b_floatTypeInput; + + returns INT +*****************************************************************************/ +INT fixp_truncateToInt(FIXP_DBL f_inp, INT sf) // sf mantissaBits left of dot + // (without sign) e.g. at width + // 32 this would be [sign]7. + // supposed sf equals 8. +{ + FDK_ASSERT(sf >= 0); + INT sx = (DFRACT_BITS - 1) - sf; // sx mantissaBits right of dot + // at width 32 this would be .24 + // supposed sf equals 8. + INT fbaccu = (INT)f_inp; + INT mask = (0x1 << sx); + + if ((fbaccu < 0) && (fbaccu & (mask - 1))) { + fbaccu = fbaccu + mask; + } + + fbaccu = fbaccu >> sx; + return fbaccu; +} + +/***************************************************************************** + fixp_truncate() + Just remove the fractional part which is located right of decimal point + + returns FIXP_DBL +*****************************************************************************/ +FIXP_DBL fixp_truncate(FIXP_DBL f_inp, INT sf) { + FDK_ASSERT(sf >= 0); + INT truncateInt = fixp_truncateToInt(f_inp, sf); + FIXP_DBL f_truncate = (FIXP_DBL)(truncateInt << ((DFRACT_BITS - 1) - sf)); + return f_truncate; +} + +/***************************************************************************** + fixp_roundToInt() + round [typical rounding] + + See fct roundRef() [which is the reference] + returns INT +*****************************************************************************/ +INT fixp_roundToInt(FIXP_DBL f_inp, INT sf) { + FDK_ASSERT(sf >= 0); + INT sx = DFRACT_BITS - 1 - sf; + INT inp = (INT)f_inp; + INT mask1 = (0x1 << (sx - 1)); + INT mask2 = (0x1 << (sx)) - 1; + INT mask3 = 0x7FFFFFFF; + INT iam = inp & mask2; + INT rnd; + + if ((inp < 0) && !(iam == mask1)) + rnd = inp + mask1; + else if ((inp > 0) && !(inp == mask3)) + rnd = inp + mask1; + else + rnd = inp; + + rnd = rnd >> sx; + + if (inp == mask3) rnd++; + + return rnd; +} + +/***************************************************************************** + fixp_round() + round [typical rounding] + + See fct roundRef() [which is the reference] + returns FIXP_DBL +*****************************************************************************/ +FIXP_DBL fixp_round(FIXP_DBL f_inp, INT sf) { + FDK_ASSERT(sf >= 0); + INT sx = DFRACT_BITS - 1 - sf; + INT r = fixp_roundToInt(f_inp, sf); + ULONG mask = (ULONG)0x1 << (DFRACT_BITS - 1); // 0x80000000 + r = r << sx; + + if ((f_inp > FL2FXCONST_DBL(0.0f)) && (r & mask)) { + --r; + } + + FIXP_DBL f_round = (FIXP_DBL)r; + return f_round; +} |