std::numeric_limits::tinyness_before - cppreference.com (original) (raw)
| 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.
[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 |
| char8_t (since C++20) | false |
| char16_t (since C++11) | false |
| char32_t (since C++11) | false |
| short | false |
| unsigned short | false |
| int | false |
| unsigned int | false |
| long | false |
| unsigned long | false |
| long long (since C++11) | false |
| unsigned long long (since C++11) | false |
| float | implementation-defined |
| double | implementation-defined |
| long double | implementation-defined |
[edit] 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 than std::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 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).
[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. The implementation used to execute this test (IBM Power7) detects tinyness before rounding.
Possible output:
Tinyness before: true Underflow detected 0xf.ffffffffffffp-1030 x 0x1.0000000000001p+0 = 0x1p-1022
[edit] See also
| | identifies the floating-point types that detect loss of precision as denormalization loss rather than inexact result (public static member constant) [edit] | | ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | | | identifies the denormalization style used by the floating-point type (public static member constant) [edit] |