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Showing content from https://en.cppreference.com/w/cpp/algorithm/../algorithm/../../cpp/../c/numeric/math/remainder.html below:

remainder, remainderf, remainderl - cppreference.com

float       remainderf( float x, float y );

double      remainder( double x, double y );

long double remainderl( long double x, long double y );

#define remainder( x, y )

1-3) Computes the IEEE remainder of the floating-point division operation x/y.

4) Type-generic macro: If any argument has type long double, remainderl is called. Otherwise, if any argument has integer type or has type double, remainder is called. Otherwise, remainderf is called.

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

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

If the returned value is ​0​, it will have the same sign as x.

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.

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.

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

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

#include <fenv.h>
#include <math.h>
#include <stdio.h>
// #pragma STDC FENV_ACCESS ON
 
int main(void)
{
    printf("remainder(+5.1, +3.0) = %.1f\n", remainder(5.1, 3));
    printf("remainder(-5.1, +3.0) = %.1f\n", remainder(-5.1, 3));
    printf("remainder(+5.1, -3.0) = %.1f\n", remainder(5.1, -3));
    printf("remainder(-5.1, -3.0) = %.1f\n", remainder(-5.1, -3));
 
    // special values
    printf("remainder(-0.0, 1.0) = %.1f\n", remainder(-0.0, 1));
    printf("remainder(+5.1, Inf) = %.1f\n", remainder(5.1, INFINITY));
 
    // error handling
    feclearexcept(FE_ALL_EXCEPT);
    printf("remainder(+5.1, 0) = %.1f\n", remainder(5.1, 0));
    if (fetestexcept(FE_INVALID))
        puts("    FE_INVALID raised");
}

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

• C23 standard (ISO/IEC 9899:2024):

• 7.12.10.2 The remainder functions (p: TBD)

• 7.25 Type-generic math <tgmath.h> (p: TBD)

• F.10.7.2 The remainder functions (p: TBD)

• C17 standard (ISO/IEC 9899:2018):

• 7.12.10.2 The remainder functions (p: 185-186)

• 7.25 Type-generic math <tgmath.h> (p: 272-273)

• F.10.7.2 The remainder functions (p: 385)

• C11 standard (ISO/IEC 9899:2011):

• 7.12.10.2 The remainder functions (p: 254-255)

• 7.25 Type-generic math <tgmath.h> (p: 373-375)

• F.10.7.2 The remainder functions (p: 529)

• C99 standard (ISO/IEC 9899:1999):

• 7.12.10.2 The remainder functions (p: 235)

• 7.22 Type-generic math <tgmath.h> (p: 335-337)

• F.9.7.2 The remainder functions (p: 465)

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