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Showing content from https://en.cppreference.com/w/cpp/language/../types/numeric_limits/tinyness_before.html below:

std::numeric_limits<T>::tinyness_before - cppreference.com

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

  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).
[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]

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