NAME¶

std::numeric_limits::tinyness_before - std::numeric_limits::tinyness_before

Synopsis¶

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 (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

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¶

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