approx_exp.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_expf (float x)
template<int DEGREE>
constexpr float	approx_expf_P (float p)
template<>
constexpr float	approx_expf_P< 2 > (float y)
template<>
constexpr float	approx_expf_P< 3 > (float y)
template<>
constexpr float	approx_expf_P< 4 > (float y)
template<>
constexpr float	approx_expf_P< 5 > (float y)
template<>
constexpr float	approx_expf_P< 6 > (float y)
template<>
constexpr float	approx_expf_P< 7 > (float y)
template<int DEGREE>
constexpr float	unsafe_expf (float x)
template<int DEGREE>
constexpr float	unsafe_expf_impl (float x)

Function Documentation

template<int DEGREE>

constexpr float approx_expf

(

float

x

)

Definition at line 176 of file approx_exp.h.

References SiStripPI::max, min(), alignCSCRings::r, and gpuClustering::x.

                                     {
  constexpr float inf_threshold = float(0x5.8b90cp4);
  // log of the smallest normal
  constexpr float zero_threshold_ftz = -float(0x5.75628p4);  // sollya: single(log(1b-126));
  // flush to zero on the output
  // manage infty output:
  // faster than directly on output!
  x = std::min(std::max(x, zero_threshold_ftz), inf_threshold);
  float r = unsafe_expf<DEGREE>(x);

  return r;
}

template<int DEGREE>

constexpr float approx_expf_P

(

float

p

)

template<>

constexpr float approx_expf_P< 2 >

(

float

y

)

Definition at line 43 of file approx_exp.h.

References detailsBasic3DVector::y.

                                          {
  return float(0x2.p0) + y * (float(0x2.07b99p0) + y * float(0x1.025b84p0));
}

template<>

constexpr float approx_expf_P< 3 >

(

float

y

)

Definition at line 48 of file approx_exp.h.

References detailsBasic3DVector::y.

                                          {
#ifdef HORNER  // HORNER
  return float(0x2.p0) + y * (float(0x1.fff798p0) + y * (float(0x1.02249p0) + y * float(0x5.62042p-4)));
#else  // ESTRIN
  float p23 = (float(0x1.02249p0) + y * float(0x5.62042p-4));
  float p01 = float(0x2.p0) + y * float(0x1.fff798p0);
  return p01 + y * y * p23;
#endif
}

template<>

constexpr float approx_expf_P< 4 >

(

float

y

)

Definition at line 59 of file approx_exp.h.

References detailsBasic3DVector::y.

                                          {
  return float(0x2.p0) +
         y * (float(0x1.fffb1p0) + y * (float(0xf.ffe84p-4) + y * (float(0x5.5f9c1p-4) + y * float(0x1.57755p-4))));
}

template<>

constexpr float approx_expf_P< 5 >

(

float

y

)

Definition at line 65 of file approx_exp.h.

References detailsBasic3DVector::y.

                                          {
  return float(0x2.p0) +
         y * (float(0x2.p0) + y * (float(0xf.ffed8p-4) +
                                   y * (float(0x5.5551cp-4) + y * (float(0x1.5740d8p-4) + y * float(0x4.49368p-8)))));
}

template<>

constexpr float approx_expf_P< 6 >

(

float

y

)

Definition at line 72 of file approx_exp.h.

References AlCaHLTBitMon_ParallelJobs::p, and detailsBasic3DVector::y.

                                          {
#ifdef HORNER  // HORNER
  float p =
      float(0x2.p0) +
      y * (float(0x2.p0) +
           y * (float(0x1.p0) + y * (float(0x5.55523p-4) + y * (float(0x1.5554dcp-4) +
                                                                y * (float(0x4.48f41p-8) + y * float(0xb.6ad4p-12))))));
#else  // ESTRIN does seem to save a cycle or two
  float p56 = float(0x4.48f41p-8) + y * float(0xb.6ad4p-12);
  float p34 = float(0x5.55523p-4) + y * float(0x1.5554dcp-4);
  float y2 = y * y;
  float p12 = float(0x2.p0) + y;  // By chance we save one operation here! Funny.
  float p36 = p34 + y2 * p56;
  float p16 = p12 + y2 * p36;
  float p = float(0x2.p0) + y * p16;
#endif
  return p;
}

template<>

constexpr float approx_expf_P< 7 >

(

float

y

)

Definition at line 93 of file approx_exp.h.

References detailsBasic3DVector::y.

                                          {
  return float(0x2.p0) +
         y * (float(0x2.p0) +
              y * (float(0x1.p0) +
                   y * (float(0x5.55555p-4) +
                        y * (float(0x1.5554e4p-4) +
                             y * (float(0x4.444adp-8) + y * (float(0xb.6a8a6p-12) + y * float(0x1.9ec814p-12)))))));
}

template<int DEGREE>

constexpr float unsafe_expf

(

float

x

)

Definition at line 171 of file approx_exp.h.

References gpuClustering::x.

                                     {
  return unsafe_expf_impl<DEGREE>(x);
}

template<int DEGREE>

constexpr float unsafe_expf_impl

(

float

x

)

Definition at line 125 of file approx_exp.h.

References alignCSCRings::e, validate-o2o-wbm::f, approx_math::fpfloor(), and AlCaHLTBitMon_ParallelJobs::p.

                                          {
  using namespace approx_math;
  /* Sollya for the following constants:
     display=hexadecimal;
     1b23+1b22;
     single(1/log(2));
     log2H=round(log(2), 16, RN);
     log2L = single(log(2)-log2H);
     log2H; log2L;
     
  */
  // constexpr float rnd_cst = float(0xc.p20);
  constexpr float inv_log2f = float(0x1.715476p0);
  constexpr float log2H = float(0xb.172p-4);
  constexpr float log2L = float(0x1.7f7d1cp-20);

  float y = x;
  // This is doing round(x*inv_log2f) to the nearest integer
  float z = fpfloor((x * inv_log2f) + 0.5f);
  // Cody-and-Waite accurate range reduction. FMA-safe.
  y -= z * log2H;
  y -= z * log2L;
  // exponent
  int32_t e = z;

  // we want RN above because it centers the interval around zero
  // but then we could have 2^e = below being infinity when it shouldn't
  // (when e=128 but p<1)
  // so we avoid this case by reducing e and evaluating a polynomial for 2*exp
  e -= 1;

  // NaN inputs will propagate to the output as expected

  float p = approx_expf_P<DEGREE>(y);

  // cout << "x=" << x << "  e=" << e << "  y=" << y << "  p=" << p <<"\n";
  binary32 ef;
  uint32_t biased_exponent = e + 127;
  ef.ui32 = (biased_exponent << 23);

  return p * ef.f;
}