approx_log.h File Reference

#include <cstdint>
#include <cmath>
#include <limits>
#include <algorithm>

Go to the source code of this file.

Classes
union	approx_math::binary32

Namespaces
	approx_math

Macros
#define	APPROX_MATH_N

Functions
template<int DEGREE>
float	approx_logf (float x)
template<int DEGREE>
float	approx_logf_P (float p)
template<>
float	approx_logf_P< 2 > (float y)
template<>
float	approx_logf_P< 3 > (float y)
template<>
float	approx_logf_P< 4 > (float y)
template<>
float	approx_logf_P< 5 > (float y)
template<>
float	approx_logf_P< 6 > (float y)
template<>
float	approx_logf_P< 7 > (float y)
template<>
float	approx_logf_P< 8 > (float y)
template<int DEGREE>
float	unsafe_logf (float x)
template<int DEGREE>
float	unsafe_logf_impl (float x)

Macro Definition Documentation

#define APPROX_MATH_N

Definition at line 36 of file approx_log.h.

Function Documentation

template<int DEGREE>

float approx_logf ( float  x )

inline

Definition at line 137 of file approx_log.h.

References constexpr, infinity, and x.

                                  {
  using namespace approx_math;


  constexpr float MAXNUMF = 3.4028234663852885981170418348451692544e38f;

  //x = std::max(std::min(x,MAXNUMF),0.f);
  float  res = unsafe_logf<DEGREE>(x);
  res =  (x<MAXNUMF) ? res : std::numeric_limits<float>::infinity();
  return (x>0) ? res :std::numeric_limits<float>::quiet_NaN();
}

template<int DEGREE>

float approx_logf_P ( float  p )

inline

template<>

float approx_logf_P< 2 > ( float  y )

inline

Definition at line 60 of file approx_log.h.

References detailsBasic3DVector::y.

                                       {
  return  y * ( float(0x1.0671c4p0) + y * ( float(-0x7.27744p-4) )) ;
}

template<>

float approx_logf_P< 3 > ( float  y )

inline

Definition at line 66 of file approx_log.h.

References detailsBasic3DVector::y.

                                       {
  return  y * (float(0x1.013354p0) + y * (-float(0x8.33006p-4) + y * float(0x4.0d16cp-4))) ;
}                 

template<>

float approx_logf_P< 4 > ( float  y )

inline

Definition at line 72 of file approx_log.h.

References detailsBasic3DVector::y.

                                       {
  return  y * (float(0xf.ff5bap-4) + y * (-float(0x8.13e5ep-4) + y * (float(0x5.826ep-4) + y * (-float(0x2.e87fb8p-4))))) ;
}

template<>

float approx_logf_P< 5 > ( float  y )

inline

Definition at line 78 of file approx_log.h.

References detailsBasic3DVector::y.

                                       {
  return  y * (float(0xf.ff652p-4) + y * (-float(0x8.0048ap-4) + y * (float(0x5.72782p-4) + y * (-float(0x4.20904p-4) + y * float(0x2.1d7fd8p-4))))) ;
}

template<>

float approx_logf_P< 6 > ( float  y )

inline

Definition at line 84 of file approx_log.h.

References detailsBasic3DVector::y.

                                       {
  return  y * (float(0xf.fff14p-4) + y * (-float(0x7.ff4bfp-4) + y * (float(0x5.582f6p-4) + y * (-float(0x4.1dcf2p-4) + y * (float(0x3.3863f8p-4) + y * (-float(0x1.9288d4p-4))))))) ;
}

template<>

float approx_logf_P< 7 > ( float  y )

inline

Definition at line 90 of file approx_log.h.

References detailsBasic3DVector::y.

                                       {
  return  y * (float(0x1.000034p0) + y * (-float(0x7.ffe57p-4) + y * (float(0x5.5422ep-4) + y * (-float(0x4.037a6p-4) + y * (float(0x3.541c88p-4) + y * (-float(0x2.af842p-4) + y * float(0x1.48b3d8p-4))))))) ;
}

template<>

float approx_logf_P< 8 > ( float  y )

inline

Definition at line 96 of file approx_log.h.

References detailsBasic3DVector::y.

                                       {
   return  y * ( float(0x1.00000cp0) + y * (float(-0x8.0003p-4) + y * (float(0x5.55087p-4) + y * ( float(-0x3.fedcep-4) + y * (float(0x3.3a1dap-4) + y * (float(-0x2.cb55fp-4) + y * (float(0x2.38831p-4) + y * (float(-0xf.e87cap-8) )))))))) ;
}

template<int DEGREE>

float unsafe_logf ( float  x )

inline

Definition at line 132 of file approx_log.h.

References x.

                                  {
  return unsafe_logf_impl<DEGREE>(x);
}

template<int DEGREE>

float unsafe_logf_impl ( float  x )

inline

Definition at line 103 of file approx_log.h.

References constexpr, alignCSCRings::e, m, AlCaHLTBitMon_ParallelJobs::p, x, and detailsBasic3DVector::y.

                                       {
  using namespace approx_math;

  binary32 xx,m;
  xx.f = x;
  
  // as many integer computations as possible, most are 1-cycle only, and lots of ILP.
  int e= (((xx.i32) >> 23) & 0xFF) -127; // extract exponent
  m.i32 = (xx.i32 & 0x007FFFFF) | 0x3F800000; // extract mantissa as an FP number
  
  int adjust = (xx.i32>>22)&1; // first bit of the mantissa, tells us if 1.m > 1.5
  m.i32 -= adjust << 23; // if so, divide 1.m by 2 (exact operation, no rounding)
  e += adjust;           // and update exponent so we still have x=2^E*y
  
  // now back to floating-point
  float y = m.f -1.0f; // Sterbenz-exact; cancels but we don't care about output relative error
  // all the computations so far were free of rounding errors...

  // the following is based on Sollya output
  float p = approx_logf_P<DEGREE>(y);
  

  constexpr float Log2=0xb.17218p-4; // 0.693147182464599609375 
  return float(e)*Log2+p;

}