diff options
Diffstat (limited to 'libFDK/src/fixpoint_math.cpp')
| -rw-r--r-- | libFDK/src/fixpoint_math.cpp | 895 |
1 files changed, 0 insertions, 895 deletions
diff --git a/libFDK/src/fixpoint_math.cpp b/libFDK/src/fixpoint_math.cpp deleted file mode 100644 index 30283ff..0000000 --- a/libFDK/src/fixpoint_math.cpp +++ /dev/null @@ -1,895 +0,0 @@ - -/* ----------------------------------------------------------------------------------------------------------- -Software License for The Fraunhofer FDK AAC Codec Library for Android - -© Copyright 1995 - 2013 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 ------------------------------------------------------------------------------------------------------------ */ - -/*************************** Fraunhofer IIS FDK Tools ********************** - - Author(s): M. Gayer - Description: Fixed point specific mathematical functions - -******************************************************************************/ - -#include "fixpoint_math.h" - - -#define MAX_LD_PRECISION 10 -#define LD_PRECISION 10 - -/* Taylor series coeffcients for ln(1-x), centered at 0 (MacLaurin polinomial). */ -#ifndef LDCOEFF_16BIT -LNK_SECTION_CONSTDATA_L1 -static const FIXP_DBL ldCoeff[MAX_LD_PRECISION] = { - FL2FXCONST_DBL(-1.0), - FL2FXCONST_DBL(-1.0/2.0), - FL2FXCONST_DBL(-1.0/3.0), - FL2FXCONST_DBL(-1.0/4.0), - FL2FXCONST_DBL(-1.0/5.0), - FL2FXCONST_DBL(-1.0/6.0), - FL2FXCONST_DBL(-1.0/7.0), - FL2FXCONST_DBL(-1.0/8.0), - FL2FXCONST_DBL(-1.0/9.0), - FL2FXCONST_DBL(-1.0/10.0) -}; -#else -LNK_SECTION_CONSTDATA_L1 -static const FIXP_SGL ldCoeff[MAX_LD_PRECISION] = { - FL2FXCONST_SGL(-1.0), - FL2FXCONST_SGL(-1.0/2.0), - FL2FXCONST_SGL(-1.0/3.0), - FL2FXCONST_SGL(-1.0/4.0), - FL2FXCONST_SGL(-1.0/5.0), - FL2FXCONST_SGL(-1.0/6.0), - FL2FXCONST_SGL(-1.0/7.0), - FL2FXCONST_SGL(-1.0/8.0), - FL2FXCONST_SGL(-1.0/9.0), - FL2FXCONST_SGL(-1.0/10.0) -}; -#endif - -/***************************************************************************** - - functionname: CalcLdData - description: Delivers the Logarithm Dualis ld(op)/LD_DATA_SCALING with polynomial approximation. - input: Input op is assumed to be double precision fractional 0 < op < 1.0 - This function does not accept negative values. - output: For op == 0, the result is saturated to -1.0 - This function does not return positive values since input values are treated as fractional values. - It does not make sense to input an integer value into this function (and expect a positive output value) - since input values are treated as fractional values. - -*****************************************************************************/ - -LNK_SECTION_CODE_L1 -FIXP_DBL CalcLdData(FIXP_DBL op) -{ - return fLog2(op, 0); -} - - -/***************************************************************************** - 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] = CalcLdData(srcVector[i]); - } -} - - - -#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 -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 -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: mul_dbl_sgl_rnd - description: Multiply with round. -*****************************************************************************/ - -/* for rounding a dfract to fract */ -#define ACCU_R (LONG) 0x00008000 - -LNK_SECTION_CODE_L1 -FIXP_DBL mul_dbl_sgl_rnd (const FIXP_DBL op1, const FIXP_SGL op2) -{ - FIXP_DBL prod; - LONG v = (LONG)(op1); - SHORT u = (SHORT)(op2); - - LONG low = u*(v&SGL_MASK); - low = (low+(ACCU_R>>1)) >> (FRACT_BITS-1); /* round */ - LONG high = u * ((v>>FRACT_BITS)<<1); - - prod = (LONG)(high+low); - - return((FIXP_DBL)prod); -} - - -/***************************************************************************** - - 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. - -*****************************************************************************/ -LNK_SECTION_CODE_L1 -/* This table is used for lookup 2^x with */ -/* x in range [0...1.0[ in steps of 1/32 */ -LNK_SECTION_DATA_L1 static 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 static 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 static 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 -}; - -LNK_SECTION_CODE_L1 FIXP_DBL CalcInvLdData(FIXP_DBL x) -{ - int set_zero = (x < FL2FXCONST_DBL(-31.0/64.0))? 0 : 1; - int set_max = (x >= FL2FXCONST_DBL( 31.0/64.0)) | (x == FL2FXCONST_DBL(0.0)); - - FIXP_SGL frac = (FIXP_SGL)(LONG)(x & 0x3FF); - UINT index3 = (UINT)(LONG)(x >> 10) & 0x1F; - UINT index2 = (UINT)(LONG)(x >> 15) & 0x1F; - UINT index1 = (UINT)(LONG)(x >> 20) & 0x1F; - int exp = (x > FL2FXCONST_DBL(0.0f)) ? (31 - (int)(x>>25)) : (int)(-(x>>25)); - - UINT lookup1 = exp2_tab_long[index1]*set_zero; - UINT lookup2 = exp2w_tab_long[index2]; - UINT lookup3 = exp2x_tab_long[index3]; - UINT lookup3f = lookup3 + (UINT)(LONG)fMultDiv2((FIXP_DBL)(0x0016302F),(FIXP_SGL)frac); - - UINT lookup12 = (UINT)(LONG)fMult((FIXP_DBL)lookup1, (FIXP_DBL) lookup2); - UINT lookup = (UINT)(LONG)fMult((FIXP_DBL)lookup12, (FIXP_DBL) lookup3f); - - FIXP_DBL retVal = (lookup<<3) >> exp; - - if (set_max) - retVal=FL2FXCONST_DBL(1.0f); - - return retVal; -} - - - - - -/***************************************************************************** - functionname: InitLdInt and CalcLdInt - description: Create and access table with integer LdData (0 to 193) -*****************************************************************************/ - - - LNK_SECTION_CONSTDATA_L1 - static const FIXP_DBL ldIntCoeff[] = { - 0x80000001, 0x00000000, 0x02000000, 0x032b8034, 0x04000000, 0x04a4d3c2, 0x052b8034, 0x059d5da0, - 0x06000000, 0x06570069, 0x06a4d3c2, 0x06eb3a9f, 0x072b8034, 0x0766a009, 0x079d5da0, 0x07d053f7, - 0x08000000, 0x082cc7ee, 0x08570069, 0x087ef05b, 0x08a4d3c2, 0x08c8ddd4, 0x08eb3a9f, 0x090c1050, - 0x092b8034, 0x0949a785, 0x0966a009, 0x0982809d, 0x099d5da0, 0x09b74949, 0x09d053f7, 0x09e88c6b, - 0x0a000000, 0x0a16bad3, 0x0a2cc7ee, 0x0a423162, 0x0a570069, 0x0a6b3d79, 0x0a7ef05b, 0x0a92203d, - 0x0aa4d3c2, 0x0ab7110e, 0x0ac8ddd4, 0x0ada3f60, 0x0aeb3a9f, 0x0afbd42b, 0x0b0c1050, 0x0b1bf312, - 0x0b2b8034, 0x0b3abb40, 0x0b49a785, 0x0b584822, 0x0b66a009, 0x0b74b1fd, 0x0b82809d, 0x0b900e61, - 0x0b9d5da0, 0x0baa708f, 0x0bb74949, 0x0bc3e9ca, 0x0bd053f7, 0x0bdc899b, 0x0be88c6b, 0x0bf45e09, - 0x0c000000, 0x0c0b73cb, 0x0c16bad3, 0x0c21d671, 0x0c2cc7ee, 0x0c379085, 0x0c423162, 0x0c4caba8, - 0x0c570069, 0x0c6130af, 0x0c6b3d79, 0x0c7527b9, 0x0c7ef05b, 0x0c88983f, 0x0c92203d, 0x0c9b8926, - 0x0ca4d3c2, 0x0cae00d2, 0x0cb7110e, 0x0cc0052b, 0x0cc8ddd4, 0x0cd19bb0, 0x0cda3f60, 0x0ce2c97d, - 0x0ceb3a9f, 0x0cf39355, 0x0cfbd42b, 0x0d03fda9, 0x0d0c1050, 0x0d140ca0, 0x0d1bf312, 0x0d23c41d, - 0x0d2b8034, 0x0d3327c7, 0x0d3abb40, 0x0d423b08, 0x0d49a785, 0x0d510118, 0x0d584822, 0x0d5f7cff, - 0x0d66a009, 0x0d6db197, 0x0d74b1fd, 0x0d7ba190, 0x0d82809d, 0x0d894f75, 0x0d900e61, 0x0d96bdad, - 0x0d9d5da0, 0x0da3ee7f, 0x0daa708f, 0x0db0e412, 0x0db74949, 0x0dbda072, 0x0dc3e9ca, 0x0dca258e, - 0x0dd053f7, 0x0dd6753e, 0x0ddc899b, 0x0de29143, 0x0de88c6b, 0x0dee7b47, 0x0df45e09, 0x0dfa34e1, - 0x0e000000, 0x0e05bf94, 0x0e0b73cb, 0x0e111cd2, 0x0e16bad3, 0x0e1c4dfb, 0x0e21d671, 0x0e275460, - 0x0e2cc7ee, 0x0e323143, 0x0e379085, 0x0e3ce5d8, 0x0e423162, 0x0e477346, 0x0e4caba8, 0x0e51daa8, - 0x0e570069, 0x0e5c1d0b, 0x0e6130af, 0x0e663b74, 0x0e6b3d79, 0x0e7036db, 0x0e7527b9, 0x0e7a1030, - 0x0e7ef05b, 0x0e83c857, 0x0e88983f, 0x0e8d602e, 0x0e92203d, 0x0e96d888, 0x0e9b8926, 0x0ea03232, - 0x0ea4d3c2, 0x0ea96df0, 0x0eae00d2, 0x0eb28c7f, 0x0eb7110e, 0x0ebb8e96, 0x0ec0052b, 0x0ec474e4, - 0x0ec8ddd4, 0x0ecd4012, 0x0ed19bb0, 0x0ed5f0c4, 0x0eda3f60, 0x0ede8797, 0x0ee2c97d, 0x0ee70525, - 0x0eeb3a9f, 0x0eef69ff, 0x0ef39355, 0x0ef7b6b4, 0x0efbd42b, 0x0effebcd, 0x0f03fda9, 0x0f0809cf, - 0x0f0c1050, 0x0f10113b, 0x0f140ca0, 0x0f18028d, 0x0f1bf312, 0x0f1fde3d, 0x0f23c41d, 0x0f27a4c0, - 0x0f2b8034 - }; - - - LNK_SECTION_INITCODE - void InitLdInt() - { - /* nothing to do! Use preinitialized logarithm table */ - } - - - -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 193 */ - - FDK_ASSERT((193>0) && ((FIXP_DBL)ldIntCoeff[0]==(FIXP_DBL)0x80000001)); /* tab has to be initialized */ - - if ((i>0)&&(i<193)) - return ldIntCoeff[i]; - else - { - return (0); - } -} - - -/***************************************************************************** - - functionname: invSqrtNorm2 - description: delivers 1/sqrt(op) normalized to .5...1 and the shift value of the OUTPUT - -*****************************************************************************/ -#define SQRT_BITS 7 -#define SQRT_VALUES 128 -#define SQRT_BITS_MASK 0x7f - -LNK_SECTION_CONSTDATA_L1 -static const FIXP_DBL invSqrtTab[SQRT_VALUES] = { - 0x5a827999, 0x5a287e03, 0x59cf8cbb, 0x5977a0ab, 0x5920b4de, 0x58cac480, 0x5875cade, 0x5821c364, - 0x57cea99c, 0x577c792f, 0x572b2ddf, 0x56dac38d, 0x568b3631, 0x563c81df, 0x55eea2c3, 0x55a19521, - 0x55555555, 0x5509dfd0, 0x54bf311a, 0x547545d0, 0x542c1aa3, 0x53e3ac5a, 0x539bf7cc, 0x5354f9e6, - 0x530eafa4, 0x52c91617, 0x52842a5e, 0x523fe9ab, 0x51fc513f, 0x51b95e6b, 0x51770e8e, 0x51355f19, - 0x50f44d88, 0x50b3d768, 0x5073fa4f, 0x5034b3e6, 0x4ff601df, 0x4fb7e1f9, 0x4f7a5201, 0x4f3d4fce, - 0x4f00d943, 0x4ec4ec4e, 0x4e8986e9, 0x4e4ea718, 0x4e144ae8, 0x4dda7072, 0x4da115d9, 0x4d683948, - 0x4d2fd8f4, 0x4cf7f31b, 0x4cc08604, 0x4c898fff, 0x4c530f64, 0x4c1d0293, 0x4be767f5, 0x4bb23df9, - 0x4b7d8317, 0x4b4935ce, 0x4b1554a6, 0x4ae1de2a, 0x4aaed0f0, 0x4a7c2b92, 0x4a49ecb3, 0x4a1812fa, - 0x49e69d16, 0x49b589bb, 0x4984d7a4, 0x49548591, 0x49249249, 0x48f4fc96, 0x48c5c34a, 0x4896e53c, - 0x48686147, 0x483a364c, 0x480c6331, 0x47dee6e0, 0x47b1c049, 0x4784ee5f, 0x4758701c, 0x472c447c, - 0x47006a80, 0x46d4e130, 0x46a9a793, 0x467ebcb9, 0x46541fb3, 0x4629cf98, 0x45ffcb80, 0x45d61289, - 0x45aca3d5, 0x45837e88, 0x455aa1ca, 0x45320cc8, 0x4509beb0, 0x44e1b6b4, 0x44b9f40b, 0x449275ec, - 0x446b3b95, 0x44444444, 0x441d8f3b, 0x43f71bbe, 0x43d0e917, 0x43aaf68e, 0x43854373, 0x435fcf14, - 0x433a98c5, 0x43159fdb, 0x42f0e3ae, 0x42cc6397, 0x42a81ef5, 0x42841527, 0x4260458d, 0x423caf8c, - 0x4219528b, 0x41f62df1, 0x41d3412a, 0x41b08ba1, 0x418e0cc7, 0x416bc40d, 0x4149b0e4, 0x4127d2c3, - 0x41062920, 0x40e4b374, 0x40c3713a, 0x40a261ef, 0x40818511, 0x4060da21, 0x404060a1, 0x40201814 -}; - -LNK_SECTION_INITCODE -void InitInvSqrtTab() -{ - /* nothing to do ! - use preinitialized square root table - */ -} - - - -#if !defined(FUNCTION_invSqrtNorm2) -/***************************************************************************** - delivers 1/sqrt(op) normalized to .5...1 and the shift value of the OUTPUT, - i.e. the denormalized result is 1/sqrt(op) = invSqrtNorm(op) * 2^(shift) - uses Newton-iteration for approximation - Q(n+1) = Q(n) + Q(n) * (0.5 - 2 * V * Q(n)^2) - with Q = 0.5* V ^-0.5; 0.5 <= V < 1.0 -*****************************************************************************/ -FIXP_DBL invSqrtNorm2(FIXP_DBL op, INT *shift) -{ - - FIXP_DBL val = op ; - FIXP_DBL reg1, reg2, regtmp ; - - if (val == FL2FXCONST_DBL(0.0)) { - *shift = 1 ; - return((LONG)1); /* minimum positive value */ - } - - - /* normalize input, calculate shift value */ - FDK_ASSERT(val > FL2FXCONST_DBL(0.0)); - *shift = fNormz(val) - 1; /* CountLeadingBits() is not necessary here since test value is always > 0 */ - val <<=*shift ; /* normalized input V */ - *shift+=2 ; /* bias for exponent */ - - /* Newton iteration of 1/sqrt(V) */ - reg1 = invSqrtTab[ (INT)(val>>(DFRACT_BITS-1-(SQRT_BITS+1))) & SQRT_BITS_MASK ]; - reg2 = FL2FXCONST_DBL(0.0625f); /* 0.5 >> 3 */ - - regtmp= fPow2Div2(reg1); /* a = Q^2 */ - regtmp= reg2 - fMultDiv2(regtmp, val); /* b = 0.5 - 2 * V * Q^2 */ - reg1 += (fMultDiv2(regtmp, reg1)<<4); /* Q = Q + Q*b */ - - /* calculate the output exponent = input exp/2 */ - if (*shift & 0x00000001) { /* odd shift values ? */ - reg2 = FL2FXCONST_DBL(0.707106781186547524400844362104849f); /* 1/sqrt(2); */ - reg1 = fMultDiv2(reg1, reg2) << 2; - } - - *shift = *shift>>1; - - return(reg1); -} -#endif /* !defined(FUNCTION_invSqrtNorm2) */ - -/***************************************************************************** - - functionname: sqrtFixp - description: delivers sqrt(op) - -*****************************************************************************/ -FIXP_DBL sqrtFixp(FIXP_DBL op) -{ - INT tmp_exp = 0; - FIXP_DBL tmp_inv = invSqrtNorm2(op, &tmp_exp); - - FDK_ASSERT(tmp_exp > 0) ; - return( (FIXP_DBL) ( fMultDiv2( (op<<(tmp_exp-1)), tmp_inv ) << 2 )); -} - - -#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; - - 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_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 */ - - - -FIXP_DBL CalcLog2(FIXP_DBL base_m, INT base_e, INT *result_e) -{ - return fLog2(base_m, base_e, result_e); -} - -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); - } - - /* 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); - } - } - - /* "+ 1" compensates fMultAddDiv2() of the polynomial evaluation above. */ - *result_e = int_part + 1; - - 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; -} - -FIXP_DBL fLog2(FIXP_DBL x_m, INT x_e, INT *result_e) -{ - FIXP_DBL result_m; - - /* Short cut for zero and negative numbers. */ - if ( x_m <= FL2FXCONST_DBL(0.0f) ) { - *result_e = DFRACT_BITS-1; - return FL2FXCONST_DBL(-1.0f); - } - - /* Calculate log2() */ - { - FIXP_DBL px2_m, x2_m; - - /* Move input value x_m * 2^x_e toward 1.0, where the taylor approximation - of the function log(1-x) centered at 0 is most accurate. */ - { - INT b_norm; - - b_norm = fNormz(x_m)-1; - x2_m = x_m << b_norm; - x_e = x_e - b_norm; - } - - /* map x from log(x) domain to log(1-x) domain. */ - x2_m = - (x2_m + FL2FXCONST_DBL(-1.0) ); - - /* Taylor polinomial approximation of ln(1-x) */ - result_m = FL2FXCONST_DBL(0.0); - px2_m = x2_m; - for (int i=0; i<LD_PRECISION; i++) { - result_m = fMultAddDiv2(result_m, ldCoeff[i], px2_m); - px2_m = fMult(px2_m, x2_m); - } - /* Multiply result with 1/ln(2) = 1.0 + 0.442695040888 (get log2(x) from ln(x) result). */ - result_m = fMultAddDiv2(result_m, result_m, FL2FXCONST_DBL(2.0*0.4426950408889634073599246810019)); - - /* Add exponent part. log2(x_m * 2^x_e) = log2(x_m) + x_e */ - if (x_e != 0) - { - int enorm; - - enorm = DFRACT_BITS - fNorm((FIXP_DBL)x_e); - /* The -1 in the right shift of result_m compensates the fMultDiv2() above in the taylor polinomial evaluation loop.*/ - result_m = (result_m >> (enorm-1)) + ((FIXP_DBL)x_e << (DFRACT_BITS-1-enorm)); - - *result_e = enorm; - } else { - /* 1 compensates the fMultDiv2() above in the taylor polinomial evaluation loop.*/ - *result_e = 1; - } - } - - return result_m; -} - -FIXP_DBL fLog2(FIXP_DBL x_m, INT x_e) -{ - if ( x_m <= FL2FXCONST_DBL(0.0f) ) { - x_m = FL2FXCONST_DBL(-1.0f); - } - else { - INT result_e; - x_m = fLog2(x_m, x_e, &result_e); - x_m = scaleValue(x_m, result_e-LD_DATA_SHIFT); - } - return x_m; -} - - - - |