fdk-aac/libFDK/include/fixpoint_math.h

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

<EFBFBD> Copyright  1995 - 2015 Fraunhofer-Gesellschaft zur F<EFBFBD>rderung 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
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You must retain the complete text of this software license in redistributions of the FDK AAC Codec or
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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
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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

******************************************************************************/

#ifndef __fixpoint_math_H
#define __fixpoint_math_H


#include "common_fix.h"

#if !defined(FUNCTION_fIsLessThan)
/**
 * \brief Compares two fixpoint values incl. scaling.
 * \param a_m mantissa of the first input value.
 * \param a_e exponent of the first input value.
 * \param b_m mantissa of the second input value.
 * \param b_e exponent of the second input value.
 * \return non-zero if (a_m*2^a_e) < (b_m*2^b_e), 0 otherwise
 */
FDK_INLINE INT fIsLessThan(FIXP_DBL a_m, INT a_e, FIXP_DBL b_m, INT b_e)
{
  if (a_e > b_e) {
    return (b_m >> fMin(a_e-b_e, DFRACT_BITS-1) > a_m);
  } else {
    return (a_m >> fMin(b_e-a_e, DFRACT_BITS-1) < b_m);
  }
}

FDK_INLINE INT fIsLessThan(FIXP_SGL a_m, INT a_e, FIXP_SGL b_m, INT b_e)
{
  if (a_e > b_e) {
    return (b_m >> fMin(a_e-b_e, FRACT_BITS-1) > a_m);
  } else {
    return (a_m >> fMin(b_e-a_e, FRACT_BITS-1) < b_m);
  }
}
#endif



#define LD_DATA_SCALING (64.0f)
#define LD_DATA_SHIFT   6   /* pow(2, LD_DATA_SHIFT) = LD_DATA_SCALING */

/**
 * \brief deprecated. Use fLog2() instead.
 */
FIXP_DBL CalcLdData(FIXP_DBL op);

void LdDataVector(FIXP_DBL *srcVector, FIXP_DBL *destVector, INT number);

FIXP_DBL CalcInvLdData(FIXP_DBL op);


void     InitLdInt();
FIXP_DBL CalcLdInt(INT i);

extern const USHORT sqrt_tab[49];

inline FIXP_DBL sqrtFixp_lookup(FIXP_DBL x)
{
  UINT y = (INT)x;
  UCHAR is_zero=(y==0);
  INT zeros=fixnormz_D(y) & 0x1e;
  y<<=zeros;
  UINT idx=(y>>26)-16;
  USHORT frac=(y>>10)&0xffff;
  USHORT nfrac=0xffff^frac;
  UINT t=nfrac*sqrt_tab[idx]+frac*sqrt_tab[idx+1];
  t=t>>(zeros>>1);
  return(is_zero ? 0 : t);
}

inline FIXP_DBL sqrtFixp_lookup(FIXP_DBL x, INT *x_e)
{
  UINT y = (INT)x;
  INT e;

  if (x == (FIXP_DBL)0) {
    return x;
  }

  /* Normalize */
  e=fixnormz_D(y);
  y<<=e;
  e  = *x_e - e + 2;

  /* Correct odd exponent. */
  if (e & 1) {
    y >>= 1;
    e ++;
  }
  /* Get square root */
  UINT idx=(y>>26)-16;
  USHORT frac=(y>>10)&0xffff;
  USHORT nfrac=0xffff^frac;
  UINT t=nfrac*sqrt_tab[idx]+frac*sqrt_tab[idx+1];

  /* Write back exponent */
  *x_e = e >> 1;
  return (FIXP_DBL)(LONG)(t>>1);
}



FIXP_DBL sqrtFixp(FIXP_DBL op);

void InitInvSqrtTab();

FIXP_DBL invSqrtNorm2(FIXP_DBL op, INT *shift);

/*****************************************************************************

    functionname: invFixp
    description:  delivers 1/(op)

*****************************************************************************/
inline FIXP_DBL invFixp(FIXP_DBL op)
{
    INT tmp_exp ;
    FIXP_DBL tmp_inv = invSqrtNorm2(op, &tmp_exp) ;
    FDK_ASSERT((31-(2*tmp_exp+1))>=0) ;
    return ( fPow2Div2( (FIXP_DBL)tmp_inv ) >> (31-(2*tmp_exp+1)) ) ;
}



#if defined(__mips__) && (__GNUC__==2)

#define FUNCTION_schur_div
inline FIXP_DBL schur_div(FIXP_DBL num,FIXP_DBL denum, INT count)
{
  INT result, tmp ;
   __asm__ ("srl %1, %2, 15\n"
            "div %3, %1\n" : "=lo" (result)
                           : "%d" (tmp), "d" (denum) ,  "d" (num)
                           : "hi" ) ;
  return result<<16 ;
}

/*###########################################################################################*/
#elif defined(__mips__) && (__GNUC__==3)

#define FUNCTION_schur_div
inline FIXP_DBL schur_div(FIXP_DBL num,FIXP_DBL denum, INT count)
{
  INT result, tmp;

   __asm__ ("srl  %[tmp], %[denum], 15\n"
            "div %[result], %[num], %[tmp]\n"
            : [tmp] "+r" (tmp), [result]"=r"(result)
            : [denum]"r"(denum), [num]"r"(num)
            : "hi", "lo");
  return result << (DFRACT_BITS-16);
}

/*###########################################################################################*/
#elif defined(SIMULATE_MIPS_DIV)

#define FUNCTION_schur_div
inline FIXP_DBL schur_div(FIXP_DBL num, FIXP_DBL denum, INT count)
{
    FDK_ASSERT (count<=DFRACT_BITS-1);
    FDK_ASSERT (num>=(FIXP_DBL)0);
    FDK_ASSERT (denum>(FIXP_DBL)0);
    FDK_ASSERT (num <= denum);

    INT tmp = denum >> (count-1);
    INT result = 0;

    while (num > tmp)
    {
        num -= tmp;
        result++;
    }

    return result << (DFRACT_BITS-count);
}

/*###########################################################################################*/
#endif /* target architecture selector */

#if !defined(FUNCTION_schur_div)
/**
 * \brief Divide two FIXP_DBL values with given precision.
 * \param num dividend
 * \param denum divisor
 * \param count amount of significant bits of the result (starting to the MSB)
 * \return num/divisor
 */
FIXP_DBL schur_div(FIXP_DBL num,FIXP_DBL denum, INT count);
#endif



FIXP_DBL mul_dbl_sgl_rnd (const FIXP_DBL op1,
                          const FIXP_SGL op2);

/**
 * \brief multiply two values with normalization, thus max precision.
 * Author: Robert Weidner
 *
 * \param f1 first factor
 * \param f2 secod factor
 * \param result_e pointer to an INT where the exponent of the result is stored into
 * \return mantissa of the product f1*f2
 */
FIXP_DBL fMultNorm(
        FIXP_DBL f1,
        FIXP_DBL f2,
        INT *result_e
        );

inline FIXP_DBL fMultNorm(FIXP_DBL f1, FIXP_DBL f2)
{
  FIXP_DBL m;
  INT e;

  m = fMultNorm(f1, f2, &e);

  m = scaleValueSaturate(m, e);

  return m;
}

/**
 * \brief Divide 2 FIXP_DBL values with normalization of input values.
 * \param num numerator
 * \param denum denomintator
 * \return num/denum with exponent = 0
 */
FIXP_DBL fDivNorm(FIXP_DBL num, FIXP_DBL denom, INT *result_e);

/**
 * \brief Divide 2 FIXP_DBL values with normalization of input values.
 * \param num numerator
 * \param denum denomintator
 * \param result_e pointer to an INT where the exponent of the result is stored into
 * \return num/denum with exponent = *result_e
 */
FIXP_DBL fDivNorm(FIXP_DBL num, FIXP_DBL denom);

/**
 * \brief Divide 2 FIXP_DBL values with normalization of input values.
 * \param num numerator
 * \param denum denomintator
 * \return num/denum with exponent = 0
 */
FIXP_DBL fDivNormHighPrec(FIXP_DBL L_num, FIXP_DBL L_denum, INT *result_e);

/**
 * \brief Calculate log(argument)/log(2) (logarithm with base 2). deprecated. Use fLog2() instead.
 * \param arg mantissa of the argument
 * \param arg_e exponent of the argument
 * \param result_e pointer to an INT to store the exponent of the result
 * \return the mantissa of the result.
 * \param
 */
FIXP_DBL CalcLog2(FIXP_DBL arg, INT arg_e, INT *result_e);

/**
 * \brief return 2 ^ (exp * 2^exp_e)
 * \param exp_m mantissa of the exponent to 2.0f
 * \param exp_e exponent of the exponent to 2.0f
 * \param result_e pointer to a INT where the exponent of the result will be stored into
 * \return mantissa of the result
 */
FIXP_DBL f2Pow(const FIXP_DBL exp_m, const INT exp_e, INT *result_e);

/**
 * \brief return 2 ^ (exp_m * 2^exp_e). This version returns only the mantissa with implicit exponent of zero.
 * \param exp_m mantissa of the exponent to 2.0f
 * \param exp_e exponent of the exponent to 2.0f
 * \return mantissa of the result
 */
FIXP_DBL f2Pow(const FIXP_DBL exp_m, const INT exp_e);

/**
 * \brief return x ^ (exp * 2^exp_e), where log2(x) = baseLd_m * 2^(baseLd_e). This saves
 *        the need to compute log2() of constant values (when x is a constant).
 * \param ldx_m mantissa of log2() of x.
 * \param ldx_e exponent of log2() of x.
 * \param exp_m mantissa of the exponent to 2.0f
 * \param exp_e exponent of the exponent to 2.0f
 * \param result_e pointer to a INT where the exponent of the result will be stored into
 * \return mantissa of the result
 */
FIXP_DBL fLdPow(
        FIXP_DBL baseLd_m,
        INT baseLd_e,
        FIXP_DBL exp_m, INT exp_e,
        INT *result_e
        );

/**
 * \brief return x ^ (exp * 2^exp_e), where log2(x) = baseLd_m * 2^(baseLd_e). This saves
 *        the need to compute log2() of constant values (when x is a constant). This version
 *        does not return an exponent, which is implicitly 0.
 * \param ldx_m mantissa of log2() of x.
 * \param ldx_e exponent of log2() of x.
 * \param exp_m mantissa of the exponent to 2.0f
 * \param exp_e exponent of the exponent to 2.0f
 * \return mantissa of the result
 */
FIXP_DBL fLdPow(
        FIXP_DBL baseLd_m, INT baseLd_e,
        FIXP_DBL exp_m, INT exp_e
        );

/**
 * \brief return (base * 2^base_e) ^ (exp * 2^exp_e). Use fLdPow() instead whenever possible.
 * \param base_m mantissa of the base.
 * \param base_e exponent of the base.
 * \param exp_m mantissa of power to be calculated of the base.
 * \param exp_e exponent of power to be calculated of the base.
 * \param result_e pointer to a INT where the exponent of the result will be stored into.
 * \return mantissa of the result.
 */
FIXP_DBL fPow(FIXP_DBL base_m, INT base_e, FIXP_DBL exp_m, INT exp_e, INT *result_e);

/**
 * \brief return (base * 2^base_e) ^ N
 * \param base mantissa of the base
 * \param base_e exponent of the base
 * \param power to be calculated of the base
 * \param result_e pointer to a INT where the exponent of the result will be stored into
 * \return mantissa of the result
 */
FIXP_DBL fPowInt(FIXP_DBL base_m, INT base_e, INT N, INT *result_e);

/**
 * \brief calculate logarithm of base 2 of x_m * 2^(x_e)
 * \param x_m mantissa of the input value.
 * \param x_e exponent of the input value.
 * \param pointer to an INT where the exponent of the result is returned into.
 * \return mantissa of the result.
 */
FIXP_DBL fLog2(FIXP_DBL x_m, INT x_e, INT *result_e);

/**
 * \brief calculate logarithm of base 2 of x_m * 2^(x_e)
 * \param x_m mantissa of the input value.
 * \param x_e exponent of the input value.
 * \return mantissa of the result with implicit exponent of LD_DATA_SHIFT.
 */
FIXP_DBL fLog2(FIXP_DBL x_m, INT x_e);

/**
 * \brief Add with saturation of the result.
 * \param a first summand
 * \param b second summand
 * \return saturated sum of a and b.
 */
inline FIXP_SGL fAddSaturate(const FIXP_SGL a, const FIXP_SGL b)
{
  LONG sum;

  sum = (LONG)(SHORT)a + (LONG)(SHORT)b;
  sum = fMax(fMin((INT)sum, (INT)MAXVAL_SGL), (INT)MINVAL_SGL);
  return (FIXP_SGL)(SHORT)sum;
}

/**
 * \brief Add with saturation of the result.
 * \param a first summand
 * \param b second summand
 * \return saturated sum of a and b.
 */
inline FIXP_DBL fAddSaturate(const FIXP_DBL a, const FIXP_DBL b)
{
  LONG sum;

  sum = (LONG)(a>>1) + (LONG)(b>>1);
  sum = fMax(fMin((INT)sum, (INT)(MAXVAL_DBL>>1)), (INT)(MINVAL_DBL>>1));
  return (FIXP_DBL)(LONG)(sum<<1);
}

//#define TEST_ROUNDING




/*****************************************************************************

 array for 1/n, n=1..80

****************************************************************************/

  extern const FIXP_DBL invCount[80];

  LNK_SECTION_INITCODE
  inline void InitInvInt(void) {}


/**
 * \brief Calculate the value of 1/i where i is a integer value. It supports
 *        input values from 1 upto 80.
 * \param intValue Integer input value.
 * \param FIXP_DBL representation of 1/intValue
 */
inline FIXP_DBL GetInvInt(int intValue)
{
  FDK_ASSERT((intValue > 0) && (intValue < 80));
  FDK_ASSERT(intValue<80);
	return invCount[intValue];
}


#endif