Remquo

Defined in header <cmath>.

Description

Computes the floating-point remainder of the division operation x / y as the std::remainder function does. Additionally, the sign and at least the three of the last bits of x / y will be stored in quo, sufficient to determine the octant of the result within a period.

Declarations

C++23

// 1)
constexpr /* floating-point-type */
            remquo ( /* floating-point-type */ x,
                     /* floating-point-type */ y, int* quo );
// 2)
constexpr float remquof( float x, float y, int* quo );
// 3)
constexpr long double remquol( long double x, long double y, int* quo );

Additional Overloads

// 4)
template< class Arithmetic1, class Arithmetic2 >
/* common-floating-point-type */
    constexpr remquo( Arithmetic1 x, Arithmetic2 y, int* quo );

C++11

// 1)
float remquo ( float x, float y, int* quo );
// 2)
double remquo ( double x, double y, int* quo );
// 3)
long double remquo ( long double x, long double y, int* quo );
// 4)
float remquof( float x, float y, int* quo );
// 5)
long double remquol( long double x, long double y, int* quo );

Additional Overloads

// 6)
template< class Arithmetic1, class Arithmetic2 >
/* common-floating-point-type */
    remquo( Arithmetic1 x, Arithmetic2 y, int* quo );

Parameters

x,y - floating-point or integer values quo - pointer to int to store the sign and some bits of x / y

Return Value

If successful, returns the floating-point remainder of the division x / y as defined in std::remainder, and stores, in *quo, the sign and at least three of the least significant bits of x / y (formally, stores a value whose sign is the sign of x / y and whose magnitude is congruent modulo 2n to the magnitude of the integral quotient of x / y, where n is an implementation-defined integer greater than or equal to 3).

If y is zero, the value stored in *quo is unspecified.

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 subnormals are supported.

If y is zero, but the domain error does not occur, zero is returned.

Error handling

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

• 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 x or y is NaN, NaN is returned

Examples

#include <cfenv>
#include <cmath>
#include <iostream>
 
#ifndef __GNUC__
#pragma STDC FENV_ACCESS ON
#endif
 
const double pi = std::acos(-1);
// or std::numbers::pi since C++20
 
double cos_pi_x_naive(double x)
{
    return std::cos(pi * x);
}
 
// the period is 2, values are (0;0.5) positive,
// (0.5;1.5) negative, (1.5,2) positive
double cos_pi_x_smart(double x)
{
    int quadrant;
    double rem = std::remquo(x, 1, &quadrant);
    quadrant = static_cast<unsigned>(quadrant) % 2; 
    // The period is 2.
    return quadrant == 0 ?  std::cos(pi * rem)
                         : -std::cos(pi * rem);
}
 
int main()
{
    std::cout << std::showpos
        << "naive:\n"
        << "  cos(pi * 0.25) = " 
        << cos_pi_x_naive(0.25) << '\n'
        << "  cos(pi * 1.25) = " 
        << cos_pi_x_naive(1.25) << '\n'
        << "  cos(pi * 2.25) = " 
        << cos_pi_x_naive(2.25) << '\n'
        << "smart:\n"
        << "  cos(pi * 0.25) = " 
        << cos_pi_x_smart(0.25) << '\n'
        << "  cos(pi * 1.25) = " 
        << cos_pi_x_smart(1.25) << '\n'
        << "  cos(pi * 2.25) = " 
        << cos_pi_x_smart(2.25) << '\n'
        << "naive:\n"
        << "  cos(pi * 1000000000000.25) = "
        << cos_pi_x_naive(1000000000000.25) << '\n'
        << "  cos(pi * 1000000000001.25) = "
        << cos_pi_x_naive(1000000000001.25) << '\n'
        << "smart:\n"
        << "  cos(pi * 1000000000000.25) = "
        << cos_pi_x_smart(1000000000000.25) << '\n'
        << "  cos(pi * 1000000000001.25) = "
        << cos_pi_x_smart(1000000000001.25) << '\n';
 
    // error handling
    std::feclearexcept(FE_ALL_EXCEPT);
 
    int quo;
    std::cout << "remquo(+Inf, 1) = " 
    << std::remquo(INFINITY, 1, &quo) << '\n';
    if (fetestexcept(FE_INVALID))
        std::cout << "  FE_INVALID raised\n";
}

Possible Result

naive:
  cos(pi * 0.25) = +0.707107
  cos(pi * 1.25) = -0.707107
  cos(pi * 2.25) = +0.707107
smart:
  cos(pi * 0.25) = +0.707107
  cos(pi * 1.25) = -0.707107
  cos(pi * 2.25) = +0.707107
naive:
  cos(pi * 1000000000000.25) = +0.707123
  cos(pi * 1000000000001.25) = -0.707117
smart:
  cos(pi * 1000000000000.25) = +0.707107
  cos(pi * 1000000000001.25) = -0.707107
remquo(+Inf, 1) = -nan
  FE_INVALID raised