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

fmod, fmodf, fmodl - cppreference.com

float       fmodf( float x, float y );

double      fmod( double x, double y );

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

#define fmod( x, y )

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

4) Type-generic macro: If any argument has type long double, fmodl is called. Otherwise, if any argument has integer type or has type double, fmod is called. Otherwise, fmodf is called.

The floating-point remainder of the division operation x / y calculated by this function is exactly the value x - n * y, where n is x / y with its fractional part truncated.

The returned value has the same sign as x and is less or equal to y in magnitude.

If successful, returns the 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 (after rounding) 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):

• If x is ±0 and y is not zero, ±0 is returned.
• 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 y is ±∞ and x is finite, x is returned.
• 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.

The double version of fmod behaves as if implemented as follows:

double fmod(double x, double y)
{
#pragma STDC FENV_ACCESS ON
    double result = remainder(fabs(x), (y = fabs(y)));
    if (signbit(result))
        result += y;
    return copysign(result, x);
}

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

Possible output:

fmod(+5.1, +3.0) = 2.1
fmod(-5.1, +3.0) = -2.1
fmod(+5.1, -3.0) = 2.1
fmod(-5.1, -3.0) = -2.1
fmod(+0.0, 1.0) = 0.0
fmod(-0.0, 1.0) = -0.0
fmod(+5.1, Inf) = 5.1
fmod(+5.1, 0) = nan
    FE_INVALID raised

• C23 standard (ISO/IEC 9899:2024):

• 7.12.10.1 The fmod functions (p: TBD)

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

• F.10.7.1 The fmod functions (p: TBD)

• C17 standard (ISO/IEC 9899:2018):

• 7.12.10.1 The fmod functions (p: 185)

• 7.25 Type-generic math <tgmath.h> (p: 274-275)

• F.10.7.1 The fmod functions (p: 385)

• C11 standard (ISO/IEC 9899:2011):

• 7.12.10.1 The fmod functions (p: 254)

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

• F.10.7.1 The fmod functions (p: 528)

• C99 standard (ISO/IEC 9899:1999):

• 7.12.10.1 The fmod functions (p: 235)

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

• F.9.7.1 The fmod functions (p: 465)

• C89/C90 standard (ISO/IEC 9899:1990):

• 4.5.6.4 The fmod function

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