fixpoint_math.cpp - Android社区 - https://www.androidos.net.cn/

/* -----------------------------------------------------------------------------------------------------------
Software License for The Fraunhofer FDK AAC Codec Library for Android

1.    INTRODUCTION
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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.

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Patent licenses for necessary patent claims for the FDK AAC Codec (including those of Fraunhofer)
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Commercially-licensed AAC software libraries, including floating-point versions with enhanced sound quality,
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This FDK AAC Codec software is provided by Fraunhofer on behalf of the copyright holders and contributors
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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
FIXP_DBL CalcInvLdData(FIXP_DBL op)
{
  FIXP_DBL result_m;

if ( op == FL2FXCONST_DBL(0.0f) ) {
    result_m = (FIXP_DBL)MAXVAL_DBL;
  }
  else if ( op < FL2FXCONST_DBL(0.0f) ) {
    result_m = f2Pow(op, LD_DATA_SHIFT);
  }
  else {
    int result_e;

result_m = f2Pow(op, LD_DATA_SHIFT, &result_e);
    result_e = fixMin(fixMax(result_e+1-(DFRACT_BITS-1), -(DFRACT_BITS-1)), (DFRACT_BITS-1)); /* rounding and saturation */

if ( (result_e>0) && ( result_m > (((FIXP_DBL)MAXVAL_DBL)>>result_e) ) ) {
      result_m = (FIXP_DBL)MAXVAL_DBL; /* saturate to max representable value */
    }
    else {
      result_m = (scaleValue(result_m, result_e)+(FIXP_DBL)1)>>1; /* descale result + rounding */
    }
  }
  return result_m;
}

/*****************************************************************************
    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;
}

C++程序 | 854行 | 27.3 KB

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