From cppreference.com
staticconstbooltinyness_before;(until C++11)staticconstexprbooltinyness_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
Tvalue of std::numeric_limits<T>::tinyness_before/* non-specialized */falseboolfalsecharfalsesignedcharfalseunsignedcharfalsewchar_tfalsechar8_t(since C++20)falsechar16_t(since C++11)falsechar32_t(since C++11)falseshortfalseunsignedshortfalseintfalseunsignedintfalselongfalseunsignedlongfalselonglong(since C++11)falseunsignedlonglong(since C++11)falsefloatimplementation-defined doubleimplementation-defined longdoubleimplementation-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
Underflow occurs (and
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).
Underflow occurs (and
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 (
) detects tinyness before rounding.
Run this code
#include<iostream>#include<limits>#include<cmath>#include<cfenv>intmain(){std::cout<<"Tinyness before: "<<std::boolalpha<<std::numeric_limits<double>::tinyness_before<<'\n';doubledenorm_max=std::nextafter(std::numeric_limits<double>::min(),0);doublemultiplier=1+std::numeric_limits<double>::epsilon();std::feclearexcept(FE_ALL_EXCEPT);doubleresult=denorm_max*multiplier;// Underflow only if tinyness_beforeif(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 See also
[static]
identifies the floating-point types that detect loss of precision as denormalization loss rather than inexact result
(public static member constant)
[static]
identifies the denormalization style used by the floating-point type
(public static member constant)