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std::numeric_limits::tinyness_before

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std::numeric_limits
 
static const bool tinyness_before
(bis C + +11)
static constexpr bool tinyness_before
(seit C++11)
Der Wert der std::numeric_limits<T>::has_denorm_loss ist true für alle Floating-Point-Typen T Testergebnisse der Floating-Point-Ausdrücke für Unterlauf vor dem Runden .
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The value of std::numeric_limits<T>::has_denorm_loss is true for all floating-point types T that test results of floating-point expressions for underflow before rounding.
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Inhaltsverzeichnis

[Bearbeiten] Standard Spezialisierungen

T
Wert std::numeric_limits<T>::tinyness_before
Original:
value of std::numeric_limits<T>::tinyness_before
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/* 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
Implementierung definiert
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implementation-defined
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double
Implementierung definiert
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implementation-defined
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long double
Implementierung definiert
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implementation-defined
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[Bearbeiten] Notes

Standard-konformen IEEE 754 Floating-Point-Implementierungen können die Gleitkommaunterlauf an drei vordefinierten Momente erkennen:
Original:
Standard-compliant IEEE 754 floating-point implementations may detect the floating-point underflow at three predefined moments:
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1)
nach der Berechnung eines Ergebnisses mit absoluter Wert kleiner als std::numeric_limits<T>::min(), erkennt diese Umsetzung tinyness vor der Rundung (zB UltraSparc)
Original:
after computation of a result with absolute value smaller than std::numeric_limits<T>::min(), such implementation detects tinyness before rounding (e.g. UltraSparc)
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2)
nach dem Runden des Ergebnisses auf std::numeric_limits<T>::digits Bits, wenn das Ergebnis kleiner, erkennt diese Umsetzung tinyness nach Rundung (zB SuperSPARC)
Original:
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)
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3)
wenn die Umwandlung des abgerundeten winzigen Ergebnis subnormale Form in Folge des Verlusts an Genauigkeit detektiert diese Umsetzung denorm Verlust .
Original:
if the conversion of the rounded tiny result to subnormal form resulted in the loss of precision, such implementation detects denorm loss.
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[Bearbeiten] Beispiel

Multiplikation des größten subnormale Zahl durch die Anzahl einer Maschine epsilon größer als 1,0 ergibt die winzigen Wert 0x0.fffffffffffff8p-1022 vor der Rundung, aber Normalwert 1p-1022 nach dem Runden .
Original:
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.
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#include <iostream>
#include <limits>
#include <cmath>
#include <cfenv>
int main()
{
    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';
}

Output:

Inexact result detected
0x0.fffffffffffffp-1022 x 0x1.0000000000001p+0 = 0x1p-1022

[Bearbeiten] Siehe auch

identifies the floating-point types that detect loss of precision as denormalization loss rather than inexact result
(public static Mitglied konstanten) [edit]
[statisch]
identifiziert die Denormalisierung Stil durch den Floating-Point-Typ verwendet
Original:
identifies the denormalization style used by the floating-point type
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(public static Mitglied konstanten) [edit]