std::numeric_limits<T>::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>::tinyness_before
is true
for all floating-point types T
that test results of floating-point expressions for underflow before rounding.
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 |
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 required to detect the floating-point underflow, and have two alternative situations where this can be done.
- 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 thanstd::numeric_limits<T>::min()
. Such implementation detects tinyness before rounding (e.g. UltraSparc, POWER). - Underflow occurs (and
FE_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)
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 (IBM Power7) detects tinyness before rounding.
#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'; }
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) |
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