std::numeri...ness_before(3)

💖 std::numeric_limits::tinyness_before(3) 💖

okay so the page header is std::numeri...ness_before(3) and the manual is C++ Standard Libary (yes, with the typo, iconic 💅). this whole page is about std::numeric_limits::tinyness_before, and bestie, it's giving "niche floating-point lore" in the best way.

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✨ NAME ✨

std::numeric_limits::tinyness_before — std::numeric_limits::tinyness_before

like yes, the name is the name twice. it's that kind of page. 🎀

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🌀 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.

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🎀 Standard specializations

the two columns are T and value of std::numeric_limits<T>::tinyness_before, and the vibe check goes like this:

• /* 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

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🧠 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).

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💻 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.

the page literally says // Run this code, so here it is, bestie:

#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';
}

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🌈 Possible output

Tinyness before: true
Underflow detected
0xf.ffffffffffffp-1030 x 0x1.0000000000001p+0 = 0x1p-1022

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👀 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)
• has_denorm [static] — identifies the denormalization style used by the floating-point type (public static member constant)

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okay that's the whole page, bestie 🫶 source/version: http://cppreference.com; date: 2024.06.10; footer tag: std::numeri...ness_before(3). slay, go detect some tinyness 💅✨