std::numeric_limits<T>::tinyness_before

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numeric_limits::tinyness_before
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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 (C++20) false
char16_t (C++11) false
char32_t (C++11) false
short false
unsigned short false
int false
unsigned int false
long false
unsigned long false
long long (C++11) false
unsigned long long (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

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