remainder, remainderf, remainderl

Defined in header <math.h>
float       remainderf( float x, float y );
(1) (since C99)
double      remainder( double x, double y );
(2) (since C99)
long double remainderl( long double x, long double y );
(3) (since C99)
Defined in header <tgmath.h>
#define remainder( x, y )
(4) (since C99)
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.


x, y - floating point values

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


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 <stdio.h>
#include <math.h>
#include <fenv.h>
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
    printf("remainder(+5.1, 0) = %.1f\n", remainder(5.1, 0));
    if(fetestexcept(FE_INVALID)) puts("    FE_INVALID raised");


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


  • C17 standard (ISO/IEC 9899:2018):
    • 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):
    • 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):
    • The remainder functions (p: 235)
    • 7.22 Type-generic math <tgmath.h> (p: 335-337)
    • F.9.7.2 The remainder functions (p: 465)

See also

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

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