std::remain...:remainderl(3)

okay bestie, welcome to the std::remain...:remainderl(3) page from the C++ Standard Libary manual 💅 yes, it's that IEEE remainder trio, and no cap, the math is giving main character energy.

💖 NAME 💖

std::remainder,std::remainderf,std::remainderl — the whole squad: std::remainder, std::remainderf, and std::remainderl. We're getting into IEEE remainder of floating-point division, and it's lowkey iconic. 🦋

✨ Synopsis ✨

Defined in header <cmath> — here are the overloads, exactly as the page serves them:

float       remainder ( float x, float y );

double      remainder ( double x, double y );                (until C++23)

long double remainder ( long double x, long double y );
constexpr /* floating-point-type */
            remainder ( /* floating-point-type */ x,          (since C++23)
                                                             (1)
                        /* floating-point-type */ y );

float       remainderf( float x, float y );                   (2) (since C++11)
                                                              (constexpr since C++23)

long double remainderl( long double x, long double y );       (3) (since C++11)
                                                              (constexpr since C++23)

Additional overloads (since C++11) — also defined in header <cmath>:

template< class Integer >                                (A)
                                                         (constexpr since C++23)
double      remainder ( Integer x, Integer y );

• 1-3) Computes the IEEE remainder of the floating point division operation x / y.
• The library provides overloads of std::remainder for all cv-unqualified floating-point types as the type of the parameters. (since C++23)
• A) Additional overloads are provided for all integer types, which are (since C++11) treated as double.

The IEEE floating-point remainder of the division operation x / y calculated by this function is exactly the value x - quo * y, where the value quo is the integral value nearest the exact value x / y. When |quo - x / y| = ½, the value quo is chosen to be even.

In contrast to std::fmod, the returned value is not guaranteed to have the same sign as x.

If the returned value is zero, it will have the same sign as x.

🎀 Parameters 🎀

• x, y — floating-point or integer values. That's it, bestie. ✨

🌈 Return value 🌈

If successful, returns the IEEE floating-point remainder of the division x / y as defined above.

If a domain error occurs, an implementation-defined value is returned (NaN where supported).

If a range error occurs due to underflow, the correct result is returned.

If y is zero, but the domain error does not occur, zero is returned.

💀 Error handling 💀

Errors are reported as specified in math_errhandling.

Domain error may occur if y is zero.

If the implementation supports IEEE floating-point arithmetic (IEC 60559),

• The current rounding mode has no effect.
• FE_INEXACT is never raised, the result is always exact.
• If x is ±∞ and y is not NaN, NaN is returned and FE_INVALID is raised.
• If y is ±0 and x is not NaN, NaN is returned and FE_INVALID is raised.
• If either argument is NaN, NaN is returned.

🧚 Notes 🧚

POSIX requires that a domain error occurs if x is infinite or y is zero.

std::fmod, but not std::remainder is useful for doing silent wrapping of floating-point types to unsigned integer types: (0.0 <= (y = std::fmod(std::rint(x), 65536.0)) ? y : 65536.0 + y) is in the range [-0.0, 65535.0], which corresponds to unsigned short, but std::remainder(std::rint(x), 65536.0) is in the range [-32767.0, +32768.0], which is outside of the range of signed short.

The additional overloads are not required to be provided exactly as (A). They only need to be sufficient to ensure that for their first argument num1 and second argument num2:

• If num1 or num2 has type long double, then std::remainder(num1, num2) has the same effect as std::remainder(static_cast<long double>(num1), static_cast<long double>(num2)).
• Otherwise, if num1 and/or num2 has type double or an integer type, then std::remainder(num1, num2) has the same effect as (until C++23) std::remainder(static_cast<double>(num1), static_cast<double>(num2)).
• Otherwise, if num1 or num2 has type float, then std::remainder(num1, num2) has the same effect as std::remainder(static_cast<float>(num1), static_cast<float>(num2)).

If num1 and num2 have arithmetic types, then std::remainder(num1, num2) has the same effect as std::remainder(static_cast</* common-floating-point-type */>(num1), static_cast</* common-floating-point-type */>(num2)), where /* common-floating-point-type */ is the floating-point type with the greatest floating-point conversion rank and greatest floating-point conversion subrank between the types of num1 and num2, (since C++23) arguments of integer type are considered to have the same floating-point conversion rank as double.

If no such floating-point type with the greatest rank and subrank exists, then overload resolution does not result in a usable candidate from the overloads provided.

🌸 Example 🌸

// Run this code

#include <cfenv>
#include <cmath>
#include <iostream>
// #pragma STDC FENV_ACCESS ON

int main()
{
    std::cout << "remainder(+5.1, +3.0) = " << std::remainder(5.1, 3) << '\n'
              << "remainder(-5.1, +3.0) = " << std::remainder(-5.1, 3) << '\n'
              << "remainder(+5.1, -3.0) = " << std::remainder(5.1, -3) << '\n'
              << "remainder(-5.1, -3.0) = " << std::remainder(-5.1, -3) << '\n';

    // special values
    std::cout << "remainder(-0.0, 1.0) = " << std::remainder(-0.0, 1) << '\n'
              << "remainder(5.1, Inf) = " << std::remainder(5.1, INFINITY) << '\n';

    // error handling
    std::feclearexcept(FE_ALL_EXCEPT);
    std::cout << "remainder(+5.1, 0) = " << std::remainder(5.1, 0) << '\n';
    if (fetestexcept(FE_INVALID))
        std::cout << "    FE_INVALID raised\n";
}

🍓 Possible output 🍓

remainder(+5.1, +3.0) = -0.9
remainder(-5.1, +3.0) = 0.9
remainder(+5.1, -3.0) = -0.9
remainder(-5.1, -3.0) = 0.9
remainder(-0.0, 1.0) = -0
remainder(5.1, Inf) = 5.1
remainder(+5.1, 0) = -nan
    FE_INVALID raised

👑 See also 👑

• div(int), ldiv, lldiv — computes quotient and remainder of integer division (function). (C++11) for lldiv.
• fmod, fmodf, fmodl — remainder of the floating point division operation (function). (C++11) for fmodf and fmodl.
• remquo, remquof, remquol — signed remainder as well as the three last bits of the division operation (function). (C++11) for remquo, remquof, and remquol.
• C documentation for remainder.

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mwah 💋 — this came from http://cppreference.com, dated 2024.06.10, page std::remain...:remainderl(3). That's the whole page, bestie, and it ate. 🫶