Fmod
Defined in header <cmath>
.
Description
The floating-point remainder of the division operation x / y
calculated by this function is exactly the value x - rem * y
, where rem is x / y
with its fractional part truncated.
The returned value has the same sign as x
and is less than y
in magnitude.
Declarations
- C++23
- C++11
// 1)
constexpr /* floating-point-type */
fmod ( /* floating-point-type */ x,
/* floating-point-type */ y );
// 2)
constexpr float fmodf( float x, float y );
// 3)
constexpr long double fmodl( long double x, long double y );
// 4)
template< class Arithmetic1, class Arithmetic2 >
/* common-floating-point-type */ fmod( Arithmetic1 x, Arithmetic2 y );
// 1)
float fmod ( float x, float y );
double fmod ( double x, double y );
long double fmod ( long double x, long double y );
// 2)
float fmodf( float x, float y );
// 3)
long double fmodl( long double x, long double y );
// 4)
template< class Arithmetic1, class Arithmetic2 >
/* common-floating-point-type */ fmod( Arithmetic1 x, Arithmetic2 y );
Parameters
x
, y
- floating-point or integer 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
Domain error may occur if y
is zero.
If the implementation supports IEEE floating-point arithmetic (IEC 60559),
- If
x
is ±0 andy
is not zero, ±0 is returned - If
x
is ±∞ andy
is not NaN, NaN is returned and FE_INVALID is raised - If
y
is ±0 andx
is not NaN, NaN is returned and FE_INVALID is raised - If
y
is ±∞ andx
is finite,x
is returned. - If either argument is NaN, NaN is returned
Notes
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.
The double version of std::fmod
behaves as if implemented as follows:
double fmod(double x, double y)
{
#pragma STDC FENV_ACCESS ON
double result = std::remainder(std::fabs(x), y = std::fabs(y));
if (std::signbit(result))
result += y;
return std::copysign(result, x);
}
The expression x - std::trunc(x / y) * y
may not equal std::fmod(x, y)
, when the rounding of x / y
to initialize the argument of std::trunc
loses too much precision (example: x = 30.508474576271183309
, y = 6.1016949152542370172
).
The additional overloads are not required to be provided exactly as (A). They only need to be sufficient to ensure that for their first argument num1
and second argument num2
:
If num1
or num2
has type long double, then
std::fmod(num1, num2)
has the same effect as
std::fmod(static_cast<long double>(num1), static_cast<long double>(num2))
.
Otherwise, if num1
and/or num2
has type double or an integer type, then
std::fmod(num1, num2)
has the same effect as
std::fmod(static_cast<double>(num1), static_cast<double>(num2))
.
Otherwise, if num1
or num2
has type float, then
std::fmod(num1, num2)
has the same effect as
std::fmod(static_cast<float>(num1), static_cast<float>(num2))
.
If num1
and num2
have arithmetic types, then
std::fmod(num1, num2)
has the same effect as
std::fmod(static_cast</* common-floating-point-type */>(num1), static_cast</* common-floating-point-type */>(num2))
where /* common-floating-point-type */ is the floating-point type with the greatest floating-point conversion rank and greatest floating-point conversion subrank between the types of num1
and num2
, arguments of integer type are considered to have the same floating-point conversion rank as double.
If no such floating-point type with the greatest rank and subrank exists, then overload resolution does not result in a usable candidate from the overloads provided.
Examples
#include <iostream>
#include <cmath>
#include <cfenv>
// #pragma STDC FENV_ACCESS ON
int main()
{
std::cout
<< "fmod(+5.1, +3.0) = "
<< std::fmod(5.1,3) << '\n'
<< "fmod(-5.1, +3.0) = "
<< std::fmod(-5.1,3) << '\n'
<< "fmod(+5.1, -3.0) = "
<< std::fmod(5.1,-3) << '\n'
<< "fmod(-5.1, -3.0) = "
<< std::fmod(-5.1,-3) << '\n';
// special values
std::cout
<< "fmod(+0.0, 1.0) = "
<< std::fmod(0, 1) << '\n'
<< "fmod(-0.0, 1.0) = "
<< std::fmod(-0.0, 1) << '\n'
<< "fmod(5.1, Inf) = "
<< std::fmod(5.1, INFINITY) << '\n';
// error handling
std::feclearexcept(FE_ALL_EXCEPT);
std::cout << "fmod(+5.1, 0) = "
<< std::fmod(5.1, 0) << '\n';
if (std::fetestexcept(FE_INVALID))
std::cout << "FE_INVALID raised\n";
}
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
fmod(-0.0, 1.0) = -0
fmod(5.1, Inf) = 5.1
fmod(+5.1, 0) = -nan
FE_INVALID raised