std::numeric_limits<T>::tinyness_before (3) - Linux Manuals

std::numeric_limits<T>::tinyness_before: std::numeric_limits<T>::tinyness_before

NAME

std::numeric_limits<T>::tinyness_before - std::numeric_limits<T>::tinyness_before

Synopsis

static const bool tinyness_before; (until C++11)
static constexpr bool tinyness_before; (since C++11)

The value of std::numeric_limits<T>::tinyness_before is true for all floating-point types T that test results of floating-point expressions for underflow before rounding.

Standard specializations

T value of std::numeric_limits<T>::tinyness_before
/* non-specialized */ false
bool false
char false
signed char false
unsigned char false
wchar_t false
char8_t false
char16_t false
char32_t false
short false
unsigned short false
int false
unsigned int false
long false
unsigned long false
long long false
unsigned long long false
float implementation-defined
double implementation-defined
long double implementation-defined

Notes

Standard-compliant IEEE 754 floating-point implementations are required to detect the floating-point underflow, and have two alternative situations where this can be done
1) Underflow occurs (and FE_UNDERFLOW may be raised) if a computation produces a result whose absolute value, computed as though both the exponent range and the precision were unbounded, is smaller than std::numeric_limits<T>::min(). Such implementation detects tinyness before rounding (e.g. UltraSparc, POWER).
2) Underflow occurs (and FE_UNDERFLOW may be raised) if after the rounding of the result to the target floating-point type (that is, rounding to std::numeric_limits<T>::digits bits), the result's absolute value is smaller than std::numeric_limits<T>::min(). Formally, the absolute value of a nonzero result computed as though the exponent range were unbounded is smaller than std::numeric_limits<T>::min(). Such implementation detects tinyness after rounding (e.g. SuperSparc)

Example

Multiplication of the largest subnormal number by the number one machine epsilon greater than 1.0 gives the tiny value 0x0.fffffffffffff8p-1022 before rounding, but normal value 1p-1022 after rounding. The implementation used to execute this test (IBM Power7) detects tinyness before rounding.
// Run this code

  #include <iostream>
  #include <limits>
  #include <cmath>
  #include <cfenv>
  int main()
  {
      std::cout << "Tinyness before: " << std::boolalpha
                << std::numeric_limits<double>::tinyness_before << '\n';

      double denorm_max = std::nextafter(std::numeric_limits<double>::min(), 0);
      double multiplier = 1 + std::numeric_limits<double>::epsilon();

      std::feclearexcept(FE_ALL_EXCEPT);

      double result = denorm_max*multiplier; // Underflow only if tinyness_before

      if(std::fetestexcept(FE_UNDERFLOW))
          std::cout << "Underflow detected\n";

      std::cout << std::hexfloat << denorm_max << " x " << multiplier << " = "
                << result << '\n';
  }

Possible output:

  Tinyness before: true
  Underflow detected
  0xf.ffffffffffffp-1030 x 0x1.0000000000001p+0 = 0x1p-1022