fmod, fmodf, fmodl

< c‎ | numeric‎ | math
Common mathematical functions
Basic operations
Exponential functions
Power functions
Trigonometric and hyperbolic functions
Error and gamma functions
Nearest integer floating point operations
Floating point manipulation functions
Macro constants
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