std::numeric_limits<T>::tinyness_before
From cppreference.com
< cpp | types | numeric limits
| 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 | 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 |
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 (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 than std::numeric_limits<T>::min(). Such implementation detects tinyness before rounding (e.g. UltraSparc, 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 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.
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<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) |