NAME¶

std::remquo,std::remquof,std::remquol - std::remquo,std::remquof,std::remquol

Synopsis¶

Defined in header <cmath>
float remquo ( float x, float y, int* quo );

double remquo ( double x, double y, int* quo ); (since C++11)
(until C++23)
long double remquo ( long double x, long double y,
int* quo );
constexpr /* floating-point-type */

remquo ( /* floating-point-type */ x, (since C++23)

/* floating-point-type */ y,
int* quo ); (1)
float remquof( float x, float y, int* quo ); (2) (since C++11)
(constexpr since C++23)
long double remquol( long double x, long double y, (3) (since C++11)
int* quo ); (constexpr since C++23)
Additional overloads
Defined in header <cmath>
template< class Arithmetic1, class Arithmetic2 >

/* common-floating-point-type */ (A) (since C++11)
(constexpr since C++23)
remquo( Arithmetic1 x, Arithmetic2 y, int* quo
);

1-3) 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.
The library provides overloads of std::remquo for all cv-unqualified floating-point
types as the type of the parameters x and y.
(since C++23)
A) Additional overloads are provided for all other combinations of arithmetic types.

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¶

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),

* 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.

Notes¶

POSIX requires that a domain error occurs if x is infinite or y is zero.

This function is useful when implementing periodic functions with the period exactly
representable as a floating-point value: when calculating sin(πx) for a very large
x, calling std::sin directly may result in a large error, but if the function
argument is first reduced with std::remquo, the low-order bits of the quotient may
be used to determine the sign and the octant of the result within the period, while
the remainder may be used to calculate the value with high precision.

On some platforms this operation is supported by hardware (and, for example, on
Intel CPUs, FPREM1 leaves exactly 3 bits of precision in the quotient when
complete).

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::remquo(num1, num2,
quo) has the same effect as std::remquo(static_cast<long
double>(num1),
static_cast<long double>(num2), quo).
* Otherwise, if num1 and/or num2 has type double or an integer type,
then std::remquo(num1, num2, quo) has the same effect as (until C++23)
std::remquo(static_cast<double>(num1),
static_cast<double>(num2), quo).
* Otherwise, if num1 or num2 has type float, then std::remquo(num1,
num2, quo) has the same effect as
std::remquo(static_cast<float>(num1),
static_cast<float>(num2), quo).
If num1 and num2 have arithmetic types, then std::remquo(num1, num2,
quo) has the same effect as std::remquo(static_cast</*
common-floating-point-type */>(num1),
static_cast</* common-floating-point-type */>(num2), quo),
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, (since C++23)
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.

Example¶

// Run this code

#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 output:¶

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

See also¶

div(int)
ldiv computes quotient and remainder of integer division
lldiv (function)
(C++11)
fmod
fmodf remainder of the floating point division operation
fmodl (function)
(C++11)
(C++11)
remainder
remainderf
remainderl signed remainder of the division operation
(C++11) (function)
(C++11)
(C++11)
C documentation for
remquo