fmod, fmodf, fmodl

Defined in header <math.h>
float       fmodf( float x, float y );
(1) (since C99)
double      fmod( double x, double y );
long double fmodl( long double x, long double y );
(3) (since C99)
Defined in header <tgmath.h>
#define fmod( x, y )
(4) (since C99)
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.


x, y - floating point values

Return value

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.

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),

  • 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)
    double result = remainder(fabs(x), (y = fabs(y)));
    if (signbit(result)) result += y;
    return copysign(result, x);


#include <stdio.h>
#include <math.h>
#include <fenv.h>
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
    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


  • C11 standard (ISO/IEC 9899:2011):
    • 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):
    • 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):
    • The fmod function

See also

computes quotient and remainder of integer division
computes signed remainder of the floating-point division operation
computes signed remainder as well as the three last bits of the division operation

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