std::fmod, std::fmodf, std::fmodl

Defined in header `<cmath>`
float fmod ( float x, float y );	(1)	(constexpr since C++23)
float fmodf( float x, float y );	(2)	(since C++11) (constexpr since C++23)
double fmod ( double x, double y );	(3)	(constexpr since C++23)
long double fmod ( long double x, long double y );	(4)	(constexpr since C++23)
long double fmodl( long double x, long double y );	(5)	(since C++11) (constexpr since C++23)
Promoted fmod ( Arithmetic1 x, Arithmetic2 y );	(6)	(since C++11) (constexpr since C++23)

1-5) Computes the floating-point remainder of the division operation x/y.

6) A set of overloads or a function template for all combinations of arguments of arithmetic type not covered by (1-5). 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 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 than y in magnitude.

Parameters

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

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 - trunc(x/y)*y may not equal fmod(x,y), when the rounding of x/y to initialize the argument of trunc loses too much precision (example: x = 30.508474576271183309, y = 6.1016949152542370172).

Example

Run this code

#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";
}

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
fmod(-0.0, 1.0) = -0
fmod(5.1, Inf) = 5.1
fmod(+5.1, 0) = -nan
    FE_INVALID raised

Compiler support
Freestanding and hosted
Language
Standard library headers
Named requirements
Feature test macros (C++20)
Language support library
Concepts library (C++20)
Metaprogramming library (C++11)
Diagnostics library
General utilities library
Strings library
Containers library
Iterators library
Ranges library (C++20)
Algorithms library
Numerics library
Localizations library
Input/output library
Filesystem library (C++17)
Regular expressions library (C++11)
Concurrency support library (C++11)
Technical specifications
Symbols index
External libraries

Common mathematical functions
Mathematical special functions (C++17)
Mathematical constants (C++20)
Floating-point environment (C++11)
Complex numbers
Numeric arrays
Pseudo-random number generation
Factor operations
gcd (C++17)
lcm (C++17)
Interpolations
midpoint (C++20)
lerp (C++20)
Generic numeric operations
iota (C++11)
ranges::iota (C++23)
accumulate
inner_product
adjacent_difference
partial_sum
reduce (C++17)
transform_reduce (C++17)
inclusive_scan (C++17)
exclusive_scan (C++17)
transform_inclusive_scan (C++17)
transform_exclusive_scan (C++17)
Bit operations
bit_cast (C++20)
byteswap (C++23)
has_single_bit (C++20)
bit_ceil (C++20)
bit_floor (C++20)
bit_width (C++20)
rotl (C++20)
rotr (C++20)
countl_zero (C++20)
countl_one (C++20)
countr_zero (C++20)
countr_one (C++20)
popcount (C++20)
endian (C++20)

div(int)ldivlldiv (C++11)	computes quotient and remainder of integer division (function)
remainderremainderfremainderl (C++11)(C++11)(C++11)	signed remainder of the division operation (function)
remquoremquofremquol (C++11)(C++11)(C++11)	signed remainder as well as the three last bits of the division operation (function)