Трюки с float: быстрое вычисление логарифмов. (комментарии)

union ADVFLOAT
{
  float x;
  struct
  {
    unsigned int mant : 23; /* Mantissa without leading one */ 
    unsigned int exp  : 8;  /* Exponential part */
    unsigned int sign : 1;  /* Indicator of the negative number */
  };
};

#define LOG2E 1.44269504088896340736f

float fastLog2( float x )
{
  ADVFLOAT ax;

  ax.x = x;

  int exp = ax.exp - 127;
  ax.sign = 0;
  ax.exp = 127;

  return (ax.x - 1.0f) * LOG2E + exp;
}

float fastSqrt( float x )
{
  ADVFLOAT ax;
  int exp;

  ax.x = x;
  exp = ax.exp - 127;
  ax.sign = 0;
  ax.exp = 127;

  return (ax.x - 1.0f) * LOG2E + exp;
}

double GetTime()
{
  LARGE_INTEGER c,f;
  QueryPerformanceCounter(&c);
  QueryPerformanceFrequency(&f);
  long long ipart = c.QuadPart / f.QuadPart;
  long long fpart = c.QuadPart % f.QuadPart;
  return (double)ipart + (double)fpart / (double)f.QuadPart;
}

int _tmain(int argc, _TCHAR* argv[])
{
  setlocale(LC_ALL, "Russian");

  double time;
  const size_t arrlen = 10000000;
  __declspec(align(16)) float* src = new float[arrlen];
  __declspec(align(16)) float* dst = new float[arrlen];

  for(size_t i = 0; i < arrlen; i++) src[i] = (float)rand() / (float)RAND_MAX + (float)rand();
  
  for(size_t xxx = 0; xxx < 4; xxx++)
  {

    time = GetTime();
    for(size_t i = 0; i < arrlen; i++) dst[i] = fastLog2(src[i]);
    time = GetTime() - time;
    printf("Эксперимент 1: %.3fмс\n", time * 1000.0);

    __declspec(align(16)) float* _src = src;
    __declspec(align(16)) float* _dst = dst;
    time = GetTime();
    for(size_t i = 0; i < arrlen; i++) *_dst++ = fastLog2(*_src++);
    time = GetTime() - time;
    printf("Эксперимент 2: %.3fмс\n", time * 1000.0);

    time = GetTime();
    for(size_t i = 0; i < arrlen; i++) dst[i] = logf(src[i]);
    time = GetTime() - time;
    printf("Эксперимент 3: %.3fмс\n", time * 1000.0);

    _src = src;
    _dst = dst;
    time = GetTime();
    for(size_t i = 0; i < arrlen; i++) *_dst++ = logf(*_src++);
    time = GetTime() - time;
    printf("Эксперимент 4: %.3fмс\n", time * 1000.0);


    _src = src;
    _dst = dst;
    time = GetTime();
    for(size_t i = 0; i < arrlen; i++) *_dst++ = sqrtf(*_src++);
    time = GetTime() - time;
    printf("Эксперимент 5: %.3fмс\n", time * 1000.0);

    __declspec(align(16)) struct mms_rec { float r0, r1, r2, r3; };
    size_t arrlen2 = arrlen / 4;
    mms_rec* _src2 = (mms_rec*)src;
    mms_rec* _dst2 = (mms_rec*)dst;
    time = GetTime();
    for(size_t i = 0; i < arrlen2; i++)
      _mm_store_ps(&(_dst2++)->r0, _mm_sqrt_ps(_mm_load1_ps(&(_src2++)->r0)));
    time = GetTime() - time;
    printf("Эксперимент 6: %.3fмс\n", time * 1000.0);
  }

  return 0;
}