/C

# 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`.

### Parameters

 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`.

### Example

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

#pragma STDC FENV_ACCESS ON
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
feclearexcept(FE_ALL_EXCEPT);
printf("remainder(+5.1, 0) = %.1f\n", remainder(5.1, 0));
if(fetestexcept(FE_INVALID)) puts("    FE_INVALID raised");
}```

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) = 0.0
remainder(-0.0, 1.0) = -0.0
remainder(+5.1, Inf) = 5.1
remainder(+5.1, 0) = -nan
FE_INVALID raised```
• C11 standard (ISO/IEC 9899:2011):
• 7.12.10.2 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):
• 7.12.10.2 The remainder functions (p: 235)
• 7.22 Type-generic math <tgmath.h> (p: 335-337)
• F.9.7.2 The remainder functions (p: 465)