std::remainder, std::remainderf, std::remainderl

Defined in header <cmath>
float       remainder ( float x, float y );
float       remainderf( float x, float y );
(1) (since C++11)
double      remainder ( double x, double y );
(2) (since C++11)
long double remainder ( long double x, long double y );
long double remainderl( long double x, long double y );
(3) (since C++11)
Promoted    remainder ( Arithmetic1 x, Arithmetic2 y );
(4) (since C++11)
1-3) Computes the IEEE remainder of the floating point division operation x/y.
4) A set of overloads or a function template for all combinations of arguments of arithmetic type not covered by (1-3). If any argument has integral type, it is cast to double. If any other argument is long double, then the return type is long double, otherwise it is double.

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 std::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 - values of floating-point or integral types

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.

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


#include <iostream>
#include <cmath>
#include <cfenv>
int main()
    std::cout << "remainder(+5.1, +3.0) = " << std::remainder(5.1,3) << '\n'
              << "remainder(-5.1, +3.0) = " << std::remainder(-5.1,3) << '\n'
              << "remainder(+5.1, -3.0) = " << std::remainder(5.1,-3) << '\n'
              << "remainder(-5.1, -3.0) = " << std::remainder(-5.1,-3) << '\n';
    // special values
    std::cout << "remainder(-0.0, 1.0) = " << std::remainder(-0.0, 1) << '\n'
              << "remainder(5.1, Inf) = " << std::remainder(5.1, INFINITY) << '\n';
    // error handling
    std::cout << "remainder(+5.1, 0) = " << std::remainder(5.1, 0) << '\n';
        std::cout << "    FE_INVALID raised\n";

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

See also

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

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