std::numeric_limits<T>:: tinyness_before

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

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

#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';
}

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

See also