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

      From cppreference.com
      < cpp‎ | numeric‎ | math
       
      C++
       
      Numerics library
       
      Common mathematical functions
      Nearest integer floating point operations
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      Macro constants
       
      Defined in header <cmath>
      (1)
      float       fmod (float x, float y );

      double      fmod (double x, double y );

      longdouble fmod (longdouble x, longdouble y );
      		(until C++23)
      constexpr/*floating-point-type*/

                  fmod (/*floating-point-type*/ x,

                         /*floating-point-type*/ y );
      		(since C++23)
      float       fmodf(float x, float y );
      		 (2)(since C++11)
      (constexpr since C++23)
      longdouble fmodl(longdouble x, longdouble y );
      		 (3)(since C++11)
      (constexpr since C++23)
      SIMD overload(since C++26)
      Defined in header <simd>
      template<class V0, class V1 >

      constexpr/*math-common-simd-t*/<V0, V1>

                  fmod (const V0& v_x, const V1& v_y );
      		 (S) (since C++26)
      Defined in header <cmath>
      template<class Integer >
      double      fmod ( Integer x, Integer y );
      		 (A)(constexpr since C++23)
      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)
      S) The SIMD overload performs an element-wise std::fmod on v_xand v_y.
      (See math-common-simd-t for its definition.)
      		(since C++26)
      A) Additional overloads are provided for all integer types, which are treated as double.
      		(since C++11)

      The floating-point remainder of the division operation x / y calculated by this function is exactly the value x - iquot * y, where iquot is x / y with its fractional part truncated.

      The returned value has the same sign as x and is less than y in magnitude.

      Contents

      [edit]Parameters

      x, y - floating-point or integer values

      [edit]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.

      [edit]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.

      [edit]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 unsignedshort, but std::remainder(std::rint(x), 65536.0 is in the range [-32767.0, +32768.0], which is outside of the range of signedshort.

      The double version of std::fmod behaves as if implemented as follows: 

      double fmod(double x, double y){#pragma STDC FENV_ACCESS ONdouble result =std::remainder(std::fabs(x), y =std::fabs(y));if(std::signbit(result)) result += y;returnstd::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 longdouble, then std::fmod(num1, num2) has the same effect as std::fmod(static_cast<longdouble>(num1),
                  static_cast<longdouble>(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))        .
      		(until C++23)

      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.

      		(since C++23)

      [edit]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 valuesstd::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 handlingstd::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

      [edit]See also

      (C++11)
      		 computes quotient and remainder of integer division
      (function)[edit]
      (C++11)(C++11)(C++11)
      		 signed remainder of the division operation
      (function)[edit]
      (C++11)(C++11)(C++11)
      		 signed remainder as well as the three last bits of the division operation
      (function)[edit]
      C documentation for fmod
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