approx_log.h File Reference

#include "DataFormats/Math/interface/approx_math.h"

Go to the source code of this file.

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

Function Documentation

template<int DEGREE>

constexpr float approx_logf

(

float

x

)

Definition at line 127 of file approx_log.h.

References infinity.

                                     {
  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>

constexpr float approx_logf_P

(

float

p

)

template<>

constexpr float approx_logf_P< 2 >

(

float

y

)

Definition at line 38 of file approx_log.h.

References detailsBasic3DVector::y.

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

template<>

constexpr float approx_logf_P< 3 >

(

float

y

)

Definition at line 44 of file approx_log.h.

References detailsBasic3DVector::y.

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

template<>

constexpr float approx_logf_P< 4 >

(

float

y

)

Definition at line 50 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<>

constexpr float approx_logf_P< 5 >

(

float

y

)

Definition at line 57 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<>

constexpr float approx_logf_P< 6 >

(

float

y

)

Definition at line 65 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<>

constexpr float approx_logf_P< 7 >

(

float

y

)

Definition at line 74 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<>

constexpr float approx_logf_P< 8 >

(

float

y

)

Definition at line 84 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>

constexpr float unsafe_logf

(

float

x

)

Definition at line 122 of file approx_log.h.

References gpuClustering::x.

                                     {
  return unsafe_logf_impl<DEGREE>(x);
}

template<int DEGREE>

constexpr float unsafe_logf_impl

(

float

x

)

Definition at line 95 of file approx_log.h.

References alignCSCRings::e, visualization-live-secondInstance_cfg::m, and AlCaHLTBitMon_ParallelJobs::p.

                                          {
  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;
}