DataFormats/Math/test/testApproximations.cpp - master - githubmirror/cmssw

DataFormats/Math/test/testApproximations.cpp
234 строки7 KB
Cms Build
Clang-Format
11 июн 2019, 11:29
11 июн 2019, 11:29146bc98
#include <iostream>
#include <sstream>
#include <fstream>
#include <string>
#include <vector>
#include <cstdlib>
#include <cstdio>
#include <cmath>

#include "DataFormats/Math/interface/approx_exp.h"
#include "DataFormats/Math/interface/approx_log.h"

inline int diff(float a, float b) {
  approx_math::binary32 ba(a);
  approx_math::binary32 bb(b);
  return ba.i32 - bb.i32;
}

inline int bits(int a) {
  unsigned int aa = abs(a);
  int b = 0;
  if (a == 0)
    return 0;
  while ((aa /= 2) > 0)
    ++b;
  return (a > 0) ? b : -b;
}

void testIt() {
  float y[10];
  int a[10]{0}, h[10]{0}, l[10]{9999999};
  const int N = 1000000;
  for (int i = 0; i != N; ++i) {
    float x = 1.e-9 + 1.e9 * drand48();
    y[0] = logf(x);
    y[2] = unsafe_logf<2>(x);
    y[3] = unsafe_logf<3>(x);
    y[4] = unsafe_logf<4>(x);
    y[5] = unsafe_logf<5>(x);
    y[6] = unsafe_logf<6>(x);
    y[7] = unsafe_logf<7>(x);
    y[8] = unsafe_logf<8>(x);
    for (int k = 2; k != 9; k++) {
      a[k] += diff(y[0], y[k]);
      h[k] = std::max(h[k], diff(y[0], y[k]));
      l[k] = std::min(l[k], diff(y[0], y[k]));
    }
  }
  for (int k = 2; k != 9; k++) {
    std::cout << k << ": ave/min/max " << double(a[k]) / double(N) << " " << l[k] << " " << h[k] << std::endl;
  }
}

inline float ms(float radLen, float m2, float p2) {
  constexpr float amscon = 1.8496e-4;  // (13.6MeV)**2
  float e2 = p2 + m2;

  float fact = 1.f + 0.038f * log(radLen);
  fact /= p2;
  fact *= fact;
  float a = e2 * fact;
  return amscon * radLen * a;
}

inline float msf(float radLen, float m2, float p2) {
  constexpr float amscon = 1.8496e-4;  // (13.6MeV)**2
  float e2 = p2 + m2;

  float fact = 1.f + 0.038f * unsafe_logf<2>(radLen);
  fact /= p2;
  fact *= fact;
  float a = e2 * fact;
  return amscon * radLen * a;
}

inline float ms2(float radLen, float m2, float p2) {
  constexpr float amscon = 1.8496e-4;  // (13.6MeV)**2
  float e2 = p2 + m2;
  float beta2 = p2 / e2;
  float fact = 1.f + 0.038f * log(radLen);
  fact *= fact;
  float a = fact / (beta2 * p2);
  return amscon * radLen * a;
}

template <typename T>
inline float bb2(float xi, float m2, float p2) {
  const T emass = 0.511e-3;
  const T poti = 16.e-9 * 10.75;                     // = 16 eV * Z**0.9, for Si Z=14
  const T eplasma = 28.816e-9 * sqrt(2.33 * 0.498);  // 28.816 eV * sqrt(rho*(Z/A)) for Si
  const T delta0 = 2 * log(eplasma / poti) - 1.;

  // calculate general physics things
  T p = sqrt(p2);
  T m = sqrt(m2);
  T e = sqrt(p2 + m2);
  T beta = p / e;
  T gamma = e / m;
  T eta2 = beta * gamma;
  eta2 *= eta2;
  T ratio = emass / m;
  T emax = 2. * emass * eta2 / (1. + 2. * ratio * gamma + ratio * ratio);

  xi /= (beta * beta);

  return xi * (log(2. * emass * emax / (poti * poti)) - 2. * (beta * beta) - delta0);
}

template <typename T>
inline float bb(float xi, float m2, float p2) {
  const T emass = 0.511e-3;
  const T poti = 16.e-9 * 10.75;                     // = 16 eV * Z**0.9, for Si Z=14
  const T eplasma = 28.816e-9 * sqrt(2.33 * 0.498);  // 28.816 eV * sqrt(rho*(Z/A)) for Si
  const T delta0 = 2 * log(eplasma / poti) - 1.;

  // calculate general physics things
  T im2 = T(1.) / m2;
  T e2 = p2 + m2;
  T e = sqrt(e2);
  T beta2 = p2 / e2;
  T eta2 = p2 * im2;
  T ratio2 = (emass * emass) * im2;
  T emax = T(2.) * emass * eta2 / (T(1.) + T(2.) * emass * e * im2 + ratio2);

  xi /= beta2;

  return xi * (log(T(2.) * emass * emax / (poti * poti)) - T(2.) * (beta2)-delta0);
}

template <typename T>
inline float bbf(float xi, float m2, float p2) {
  const T emass = 0.511e-3;
  const T poti = 16.e-9 * 10.75;                     // = 16 eV * Z**0.9, for Si Z=14
  const T eplasma = 28.816e-9 * sqrt(2.33 * 0.498);  // 28.816 eV * sqrt(rho*(Z/A)) for Si
  const T delta0 = 2 * log(eplasma / poti) - 1.;

  // calculate general physics things
  T im2 = T(1.) / m2;
  T e2 = p2 + m2;
  T e = sqrt(e2);
  T beta2 = p2 / e2;
  T eta2 = p2 * im2;
  T ratio2 = (emass * emass) * im2;
  T emax = T(2.) * emass * eta2 / (T(1.) + T(2.) * emass * e * im2 + ratio2);

  xi /= beta2;

  return xi * (unsafe_logf<2>(T(2.) * emass * emax / (poti * poti)) - T(2.) * (beta2)-delta0);
}

template <typename T>
inline float bbf2(float xi, float m2, float p2) {
  const T emass = 0.511e-3;
  const T poti = 16.e-9 * 10.75;                     // = 16 eV * Z**0.9, for Si Z=14
  const T eplasma = 28.816e-9 * sqrt(2.33 * 0.498);  // 28.816 eV * sqrt(rho*(Z/A)) for Si
  const T delta0 = 2 * log(eplasma / poti) - 1.;

  // calculate general physics things
  T im2 = T(1.) / m2;
  T e2 = p2;  //  + m2;
  T e = sqrt(e2);
  T beta2 = T(1);  //  p2/e2;
  T eta2 = p2 * im2;
  T ratio2 = (emass * emass) * im2;
  T emax = T(2.) * emass * eta2 / (T(1.) + T(2.) * emass * e * im2 + ratio2);

  xi /= beta2;

  return xi * (unsafe_logf<2>(T(2.) * emass * emax / (poti * poti)) - T(2.) * (beta2)-delta0);
}

template <typename Fun>
void compare(Fun F, Fun F2, Fun Fapx) {
  std::cout << std::endl;

  float m2 = 0.138;
  m2 *= m2;

  int d1 = 0, d2 = 0, d3 = 0;
  int c1 = 99999999, c2 = c1, c3 = c1;
  int dm = 99999999;

  float p2 = 0.01;
  for (int i = 0; i != 6; ++i) {
    p2 *= 10;
    float rl = 0.001;
    for (int j = 0; j != 4; ++j) {
      rl *= 10;
      float ref = F(rl, m2, p2);
      float rp = F(rl * 1.001, m2, p2);
      float rm = F(rl * 0.999, m2, p2);
      float apx = Fapx(rl, m2, p2);

      int dd = std::min(abs(diff(rm, ref)), abs(diff(rp, ref)));
      dd -= abs(diff(apx, ref));  // negative if apx-ref is bigger than the uncer-interval
      dm = std::min(dm, dd);

      d1 = std::max(d1, abs(diff(F2(rl, m2, p2), ref)));
      d2 = std::max(d2, abs(diff(apx, ref)));
      d3 = std::max(d3, abs(diff(rp, ref)));
      d3 = std::max(d3, abs(diff(rm, ref)));

      c1 = std::min(c1, abs(diff(F2(rl, m2, p2), ref)));
      c2 = std::min(c2, abs(diff(apx, ref)));
      c3 = std::min(c3, abs(diff(rp, ref)));
      c3 = std::min(c3, abs(diff(rm, ref)));

      // std::cout << diff(ms2(rl,m2,p2),ref) << std::endl;
      // std::cout << diff(msf(rl,m2,p2),ref) << std::endl;
      // std::cout << diff(ms(1.001*rl,m2,p2),ref) << std::endl;
      // std::cout << diff(ms(0.999*rl,m2,p2),ref) << std::endl;
    }
  }

  std::cout << dm << "," << bits(dm) << std::endl;

  std::cout << d1 << "," << bits(d1) << " " << d2 << "," << bits(d2) << " " << d3 << "," << bits(d3) << " "
            << std::endl;

  std::cout << c1 << "," << bits(c1) << " " << c2 << "," << bits(c2) << " " << c3 << "," << bits(c3) << " "
            << std::endl;
}

int main() {
  std::cout << bits(0) << " " << bits(1) << " " << bits(2) << " " << bits(-31) << " " << bits(32) << std::endl;

  testIt();
  compare(ms, ms2, msf);
  compare(bb<float>, bb2<float>, bbf<float>);
  compare(bb<float>, bb2<float>, bbf2<float>);
  compare(bb<double>, bb2<double>, bbf<double>);

  return 0;
}