std::fmod,std::fmodf,std::fmodl(3)

NAME
std::fmod,std::fmodf,std::fmodl - std::fmod,std::fmodf,std::fmodl

Synopsis
   Defined in header <cmath>
   float fmod ( float x, float y );
   double fmod ( double x, double y ); (until C++23)
   long double fmod ( long double x, long double y );
   constexpr /* floating-point-type */
               fmod ( /* floating-point-type */ x, (since C++23)
                        (1)
                      /* floating-point-type */ y );
   float fmodf( float x, float y ); (2) (since C++11)
                        (constexpr since C++23)
   long double fmodl( long double x, long double y ); (3) (since C++11)
                        (constexpr since C++23)
   Additional overloads (since C++11)
   Defined in header <cmath>
   template< class Integer > (A) (constexpr since C++23)
   double fmod ( Integer x, Integer y );
   1-3) Computes the floating-point remainder of the division operation x / y.
   The library provides overloads of std::fmod for all cv-unqualified floating-point
   types as the type of the parameters.
   (since C++23)
   A) Additional overloads are provided for all integer types, which are (since C++11)
   treated as double.
   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.

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
   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 - 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 (until C++23)
       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 (since C++23)
   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.

Example
// Run this code
 #include <cfenv>
 #include <cmath>
 #include <iostream>
 // #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

See also
   div(int)
   ldiv computes quotient and remainder of integer division
   lldiv (function)
   (C++11)
   remainder
   remainderf
   remainderl signed remainder of the division operation
   (C++11) (function)
   (C++11)
   (C++11)
   remquo
   remquof
   remquol signed remainder as well as the three last bits of the division operation
   (C++11) (function)
   (C++11)
   (C++11)
   C documentation for
   fmod