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std::numeri...ness_before(3) C++ Standard Libary std::numeri...ness_before(3) NAME std::numeric_limits::tinyness_before - std::numeric_limits::tiny- ness_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 under- flow before rounding. Standard specializations T value of std::numeric_limits<T>::tiny- ness_before /* non-specialized */ false bool false char false signed char false unsigned char false wchar_t false char8_t (C++20) false char16_t (C++11) false char32_t (C++11) false short false unsigned short false int false unsigned int false long false unsigned long false long long (C++11) false unsigned long long (C++11) false float implementation-defined double implementation-defined long double implementation-defined Notes Standard-compliant IEEE 754 floating-point implementations are re- quired 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 computa- tion produces a result whose absolute value, computed as though both the expo- nent range and the precision were unbounded, is smaller than std::numeric_lim- its<T>::min(). Such implementation detects tinyness before rounding (e.g. Ultra- Sparc, 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 tiny- ness after rounding (e.g. SuperSparc) Example Multiplication of the largest subnormal number by the number one ma- chine epsilon greater than 1.0 gives the tiny value 0x0.fffffffffffff8p-1022 be- fore rounding, but normal value 1p-1022 after rounding. The implementation used to exe- cute 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<dou- ble>::min(), 0); double multiplier = 1 + std::numeric_limits<double>::epsilon(); std::feclearexcept(FE_ALL_EXCEPT); double result = denorm_max*multiplier; // Underflow only if tiny- ness_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 See also has_denorm_loss identifies the floating-point types that detect loss of precision as [static] denormalization loss rather than inexact result (public static member constant) has_denorm identifies the denormalization style used by the floating-point type [static] (public static member constant) http://cppreference.com 2022.07.31 std::numeri...ness_before(3)
NAME | Synopsis | Standard specializations | Notes | Example | Possible output: | See also
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