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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 may detect the floating-point underflow at three predefined moments:

1) after computation of a result with absolute value smaller than std::numeric_limits<T>::min(), such implementation detects tinyness before rounding (e.g. UltraSparc)

2) after rounding of the result to std::numeric_limits<T>::digits bits, if the result is tiny, such implementation detects tinyness after rounding (e.g. SuperSparc)

3) if the conversion of the rounded tiny result to subnormal form resulted in the loss of precision, such implementation detects denorm loss.

### [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";
        else if (std::fetestexcept(FE_INEXACT))
            std::cout << "Inexact result 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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