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

DataFormats/Math/test/testApproxMath.cpp
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11 июн 2019, 11:29
11 июн 2019, 11:29146bc98
#include "DataFormats/Math/interface/approx_exp.h"
#include "DataFormats/Math/interface/approx_log.h"
#include "DataFormats/Math/interface/approx_erf.h"
#include <cstdio>
#include <cstdlib>
#include <iostream>

void printEXP(float x) {
  printf("x= %a val= %a %a %a\n", x, std::exp(double(x)), unsafe_expf<6>(x), unsafe_expf<4>(x));
  printf("x= %f val= %f %f %f\n", x, std::exp(double(x)), unsafe_expf<6>(x), unsafe_expf<4>(x));
  printf("x= %f val= %f %f %f\n\n", x, std::exp(x), approx_expf<6>(x), approx_expf<4>(x));
}

void printLOG(float x) {
  printf("x= %a val= %a %a %a\n", x, std::log(double(x)), unsafe_logf<8>(x), unsafe_logf<4>(x));
  printf("x= %f val= %f %f %f\n", x, std::log(double(x)), unsafe_logf<8>(x), unsafe_logf<4>(x));
  printf("x= %f val= %f %f %f\n\n", x, std::log(x), approx_logf<6>(x), approx_logf<4>(x));
}

template <typename PRINT>
void printLim(PRINT printit) {
  constexpr float zero_threshold_ftz = -float(0x5.75628p4);
  constexpr float inf_threshold = float(0x5.8b90cp4);
  std::cout << "\nexp valid for " << zero_threshold_ftz << " < x < " << inf_threshold << std::endl;
  printit(zero_threshold_ftz);
  printit(zero_threshold_ftz - 1);
  printit(zero_threshold_ftz + 1);
  printit(4 * zero_threshold_ftz);
  printit(0);
  printit(1.);
  printit(-1.);
  printit(inf_threshold);
  printit(inf_threshold + 1);
  printit(inf_threshold - 1);
  printit(4 * inf_threshold);
  printit(std::sqrt(-1));
  printit(std::numeric_limits<float>::infinity());
  printit(-std::numeric_limits<float>::infinity());

  std::cout << "\n" << std::endl;
}

namespace justcomp {
  constexpr int NN = 1024 * 1024;
  float a[NN], b[NN];
  template <int DEGREE>
  void bar() {
    for (int i = 0; i != NN; ++i)
      b[i] = approx_expf<DEGREE>(a[i]);
  }
  template <int DEGREE>
  void foo() {
    for (int i = 0; i != NN; ++i)
      b[i] = unsafe_expf<DEGREE>(a[i]);
  }
  template <int DEGREE>
  void lar() {
    for (int i = 0; i != NN; ++i)
      b[i] = approx_logf<DEGREE>(a[i]);
  }
  template <int DEGREE>
  void loo() {
    for (int i = 0; i != NN; ++i)
      b[i] = unsafe_logf<DEGREE>(a[i]);
  }

}  // namespace justcomp

template <typename STD, typename APPROX>
void accTest(STD stdf, APPROX approx, int degree) {
  using namespace approx_math;
  std::cout << std::endl << "launching  exhaustive test for degree " << degree << std::endl;
  binary32 x, r, ref;
  int maxdiff = 0;
  int n127 = 0;
  int n16393 = 0;
  x.ui32 = 0;  // should be 0 but
  while (x.ui32 < 0xffffffff) {
    x.ui32++;
    // remove nans..
    if ((x.ui32 & 0x7f80000) && x.ui32 & 0x7FFFFF)
      continue;
    r.f = approx(x.f);
    ref.f = stdf(double(x.f));  // double-prec one  (no hope with -fno-math-errno)
    int d = abs(r.i32 - ref.i32);
    if (d > maxdiff) {
      // std::cout << "new maxdiff for x=" << x.f << " : " << d << std::endl;
      maxdiff = d;
    }
    if (d > 127)
      ++n127;
    if (d > 16393)
      ++n16393;
  }
  std::cout << "maxdiff / diff >127 / diff >16393 " << maxdiff << " / " << n127 << " / " << n16393 << std::endl;
}

template <typename STD, typename APPROX>
void accuTest(STD stdf,
              APPROX approx,
              const char* name,
              float mm = std::numeric_limits<float>::min(),
              float mx = std::numeric_limits<float>::max()) {
  using namespace approx_math;
  std::cout << std::endl << "launching  exhaustive test for " << name << std::endl;
  binary32 x, pend, r, ref;
  int maxdiff = 0;
  int n127 = 0;
  int n16393 = 0;
  float ad = 0., rd = 0;
  x.f = mm;
  x.ui32++;
  pend.f = mx;
  pend.ui32--;
  std::cout << "limits " << x.f << " " << pend.f << " " << pend.ui32 - x.ui32 << std::endl;
  while (x.ui32 < pend.ui32) {
    x.ui32++;
    r.f = approx(x.f);
    ref.f = stdf(x.f);  // double-prec one  (no hope with -fno-math-errno)
    ad = std::max(ad, std::abs(r.f - ref.f));
    rd = std::max(rd, std::abs((r.f / ref.f) - 1.f));
    int d = abs(r.i32 - ref.i32);
    if (d > maxdiff) {
      // std::cout << "new maxdiff for x=" << x.f << " : " << d << std::endl;
      maxdiff = d;
    }
    if (d > 127)
      ++n127;
    if (d > 16393)
      ++n16393;
  }
  std::cout << "absdiff / reldeff/ maxdiff / diff >127 / diff >16393 :  " << ad << " / " << rd << " / " << maxdiff
            << " / " << n127 << " / " << n16393 << std::endl;
}

// performance test
#include "rdtscp.h"

template <int DEGREE, int WHAT>
struct Measure {
  inline void operator()(unsigned long long& t) const;
};

template <int DEGREE>
struct Measure<DEGREE, 0> {
  inline void operator()(unsigned long long& t) const {
    t -= rdtsc();
    justcomp::foo<DEGREE>();
    t += rdtsc();
  }
};

template <int DEGREE>
struct Measure<DEGREE, 1> {
  inline void operator()(unsigned long long& t) const {
    t -= rdtsc();
    justcomp::bar<DEGREE>();
    t += rdtsc();
  }
};

template <int DEGREE>
struct Measure<DEGREE, 2> {
  inline void operator()(unsigned long long& t) const {
    t -= rdtsc();
    justcomp::loo<DEGREE>();
    t += rdtsc();
  }
};

template <int DEGREE>
struct Measure<DEGREE, 3> {
  inline void operator()(unsigned long long& t) const {
    t -= rdtsc();
    justcomp::lar<DEGREE>();
    t += rdtsc();
  }
};

template <int DEGREE, int WHAT = 1>
void perf() {
  if (!has_rdtscp())
    return;
  Measure<DEGREE, WHAT> measure;
  using namespace approx_math;
  unsigned long long t = 0;
  binary32 x;
  float sum = 0;
  long long ntot = 0;
  x.f = 1.0;          // should be 0 but
  while (x.f < 32) {  // this is 5*2^23 tests
    ++ntot;
    int i = 0;
    while (i < justcomp::NN) {
      x.ui32++;
      justcomp::a[i++] = x.f;
      justcomp::a[i++] = (WHAT < 2) ? -x.f : 1.f / x.f;
    }
    measure(t);
    // binary32 r;
    //  r.f=approx_expf<6>(x.f);// time	0m1.180s
    // r.f=expf(x.f);	// time 0m4.372s
    // r.f=exp(x.f);  // time 	0m1.789s
    for (int i = 0; i != justcomp::NN; ++i)
      sum += justcomp::b[i];
  }
  const char* what[] = {"exp unsafe", "exp apporx", "log unsafe", "log approx"};
  std::cout << "time for " << what[WHAT] << " degree " << DEGREE << " is " << double(t) / double(justcomp::NN * ntot)
            << std::endl;
  std::cout << "sum= " << sum << " to prevent compiler optim." << std::endl;
  ;
}

int main() {
  printLim(printEXP);
  printLim(printLOG);

  perf<2, 0>();
  perf<3, 0>();
  perf<3>();
  perf<4>();
  perf<6>();

  perf<2, 2>();
  perf<2, 3>();
  perf<4, 2>();
  perf<4, 3>();
  perf<8, 2>();
  perf<8, 3>();

  accTest(::exp, approx_expf<2>, 2);
  accTest(::exp, approx_expf<3>, 3);
  accTest(::exp, approx_expf<4>, 4);
  accTest(::exp, approx_expf<6>, 6);

  accTest(::log, approx_logf<2>, 2);
  accTest(::log, approx_logf<4>, 4);
  accTest(::log, approx_logf<8>, 8);

  accuTest(::erf, approx_erf, "erf", .01, 8);

  return 0;
}