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# std::numeric_limits::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.

### [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 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.

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

### [edit] See also

has_denorm_loss [static] | identifies the floating-point types that detect loss of precision as denormalization loss rather than inexact result (public static member constant) [edit]
has_denorm [static] | identifies the denormalization style used by the floating-point type (public static member constant) [edit]

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