std::numeric_limits::tinyness_before
static const bool tinyness_before |
(until C++11) | |
static constexpr bool tinyness_before |
(since C++11) | |
The value of std::numeric_limits<T>::has_denorm_loss is true for all floating-point types T that test results of floating-point expressions for underflow before rounding.
Contents |
[edit] 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 |
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 |
[edit] Notes
Standard-compliant IEEE 754 floating-point implementations may detect the floating-point underflow at three predefined moments:
1) after computation of a result with absolute value smaller than std::numeric_limits<T>::min(), such implementation detects tinyness before rounding (e.g. UltraSparc)
2) after rounding of the result to std::numeric_limits<T>::digits bits, if the result is tiny, such implementation detects tinyness after rounding (e.g. SuperSparc)
3) if the conversion of the rounded tiny result to subnormal form resulted in the loss of precision, such implementation detects denorm loss.
[edit] 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.
#include <iostream> #include <limits> #include <cmath> #include <cfenv> int main() { 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"; else if (std::fetestexcept(FE_INEXACT)) std::cout << "Inexact result detected\n"; std::cout << std::hexfloat << denorm_max << " x " << multiplier << " = " << result << '\n'; }
Output:
Inexact result detected 0x0.fffffffffffffp-1022 x 0x1.0000000000001p+0 = 0x1p-1022
[edit] 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) |