The value ofstd::numeric_limits<T>::tinyness_before istrue for all floating-point typesT that test results of floating-point expressions for underflow before rounding.

[edit]Standard specializations

[edit]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 (andFE_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 thanstd::numeric_limits<T>::min(). Such implementation detects tinyness before rounding (e.g. UltraSparc, POWER).
2. Underflow occurs (andFE_UNDERFLOW may be raised) if after the rounding of the result to the target floating-point type (that is, rounding tostd::numeric_limits<T>::digits bits), the result's absolute value is smaller thanstd::numeric_limits<T>::min(). Formally, the absolute value of a nonzero result computed as though the exponent range were unbounded is smaller thanstd::numeric_limits<T>::min(). Such implementation detects tinyness after rounding (e.g. SuperSparc).

[edit]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: trueUnderflow detected0xf.ffffffffffffp-1030 x 0x1.0000000000001p+0 = 0x1p-1022

[edit]See also

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