Difference between revisions of "cpp/numeric/math/remainder"

Latest revision as of 09:12, 15 October 2023

Defined in header `<cmath>`
	(1)
float remainder ( float x, float y ); double remainder ( double x, double y ); long double remainder ( long double x, long double y );			(until C++23)
constexpr /* floating-point-type / remainder ( / floating-point-type / x, / floating-point-type */ y );			(since C++23)
float remainderf( float x, float y );		(2)	(since C++11) (constexpr since C++23)
long double remainderl( 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 > double remainder ( Integer x, Integer y );		(A)	(constexpr since C++23)

1-3) Computes the IEEE remainder of the floating point division operation x / y. The library provides overloads of std::remainder 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 treated as double.

(since C++11)

The IEEE floating-point remainder of the division operation x / y calculated by this function is exactly the value x - quo * y, where the value quo is the integral value nearest the exact value x / y. When $|quo - x / y| = ½$ , the value quo is chosen to be even.

In contrast to std::fmod, the returned value is not guaranteed to have the same sign as x.

If the returned value is zero, it will have the same sign as x.

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 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::remainder(num1, num2) has the same effect as std::remainder(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::remainder(num1, num2) has the same effect as std::remainder(static_cast<double>(num1),
static_cast<double>(num2)).
Otherwise, if num1 or num2 has type float, then std::remainder(num1, num2) has the same effect as std::remainder(static_cast<float>(num1),
static_cast<float>(num2)).

(until C++23)

If num1 and num2 have arithmetic types, then std::remainder(num1, num2) has the same effect as std::remainder(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 << "remainder(+5.1, +3.0) = " << std::remainder(5.1, 3) << '\n'
              << "remainder(-5.1, +3.0) = " << std::remainder(-5.1, 3) << '\n'
              << "remainder(+5.1, -3.0) = " << std::remainder(5.1, -3) << '\n'
              << "remainder(-5.1, -3.0) = " << std::remainder(-5.1, -3) << '\n';
 
    // special values
    std::cout << "remainder(-0.0, 1.0) = " << std::remainder(-0.0, 1) << '\n'
              << "remainder(5.1, Inf) = " << std::remainder(5.1, INFINITY) << '\n';
 
    // error handling
    std::feclearexcept(FE_ALL_EXCEPT);
    std::cout << "remainder(+5.1, 0) = " << std::remainder(5.1, 0) << '\n';
    if (fetestexcept(FE_INVALID))
        std::cout << "    FE_INVALID raised\n";
}

Possible output:

remainder(+5.1, +3.0) = -0.9
remainder(-5.1, +3.0) = 0.9
remainder(+5.1, -3.0) = -0.9
remainder(-5.1, -3.0) = 0.9
remainder(-0.0, 1.0) = -0
remainder(5.1, Inf) = 5.1
remainder(+5.1, 0) = -nan
    FE_INVALID raised

[edit] See also

div(int)ldivlldiv (C++11)	computes quotient and remainder of integer division (function) [edit]
fmodfmodffmodl (C++11)(C++11)	remainder of the floating point division operation (function) [edit]
remquoremquofremquol (C++11)(C++11)(C++11)	signed remainder as well as the three last bits of the division operation (function) [edit]
C documentation for remainder

@@ Line 1: / Line 1: @@
-{{cpp/title|remainder}}
+{{cpp/title|remainder|remainderf|remainderl}}
 {{cpp/numeric/math/navbar}}
-{{dcl begin}}
+{{cpp/numeric/math/declarations
-{{dcl header | cmath}}
+|family=remainder
-{{dcl | since=c++11 |num=1|
+|param1=x
-float       remainder( float x, float y );
+|param2=y
+|constexpr_since=23
+|desc=Computes the IEEE remainder of the floating point division operation {{c|x / y}}.
 }}
-{{dcl | since=c++11 |num=2|
-double      remainder( double x, double y );
-}}
-{{dcl | since=c++11 |num=3|
-long double remainder( long double x, long double y );
-}}
-{{dcl | since=c++11 |num=4|
-Promoted    remainder( Arithmetic x, Arithmetic y );
-}}
-{{dcl end}}
-Computes the remainder of the floating point division operation {{c|x/y}}.  In difference to {{rlpt|fmod}}, the return type will be negative if {{c|fmod(x, y)>y/2}}.
+The IEEE floating-point remainder of the division operation {{c|x / y}} calculated by this function is exactly the value {{c|x - quo * y}}, where the value {{c|quo}} is the integral value nearest the exact value {{c|x / y}}. When {{math|{{!}}quo - x / y{{!}} {{=}} ½}}, the value {{c|quo}} is chosen to be even.
+In contrast to {{lc|std::fmod}}, the returned value is not guaranteed to have the same sign as {{c|x}}.
+If the returned value is zero, it will have the same sign as {{c|x}}.
-) If any argument has integral type, it is cast to {{c|double}}. If any other argument is {{c|long double}}, then the return type is {{c|long double}}, otherwise it is {{c|double}}
 ===Parameters===
 {{par begin}}
-{{par | x, y | floating point values}}
+{{par|x, y|floating-point or integer values}}
 {{par end}}
 ===Return value===
+If successful, returns the IEEE floating-point remainder of the division {{c|x / y}} as defined above.
-remainder of dividing arguments
+If a domain error occurs, an implementation-defined value is returned (NaN where supported).
-===See also===
+If a range error occurs due to underflow, the correct result is returned.
+If {{c|y}} is zero, but the domain error does not occur, zero is returned.
+===Error handling===
+Errors are reported as specified in {{lc|math_errhandling}}.
+Domain error may occur if {{c|y}} is zero.
+If the implementation supports IEEE floating-point arithmetic (IEC 60559),
+* The current [[cpp/numeric/fenv/FE_round|rounding mode]] has no effect.
+* {{lc|FE_INEXACT}} is never raised, the result is always exact.
+* If {{c|x}} is ±∞ and {{c|y}} is not NaN, NaN is returned and {{lc|FE_INVALID}} is raised.
+* If {{c|y}} is ±0 and {{c|x}} is not NaN, NaN is returned and {{lc|FE_INVALID}} is raised.
+* If either argument is NaN, NaN is returned.
+===Notes===
+[https://pubs.opengroup.org/onlinepubs/9699919799/functions/remainder.html POSIX requires] that a domain error occurs if {{c|x}} is infinite or {{c|y}} is zero.
+{{lc|std::fmod}}, but not {{tt|std::remainder}} is useful for doing silent wrapping of floating-point types to unsigned integer types: {{c|1=(0.0 <= (y = std::fmod(std::rint(x), 65536.0)) ? y : 65536.0 + y)}} is in the range {{closed range|-0.0|65535.0}}, which corresponds to {{c/core|unsigned short}}, but {{c|std::remainder(std::rint(x), 65536.0)}} is in the range {{closed range|-32767.0|+32768.0}}, which is outside of the range of {{c/core|signed short}}.
+{{cpp/numeric/math/additional overload note|remainder}}
+===Example===
+{{example
+|code=
+#include <cfenv>
+#include <cmath>
+#include <iostream>
+// #pragma STDC FENV_ACCESS ON
+int main()
+{
+    std::cout << "remainder(+5.1, +3.0) = " << std::remainder(5.1, 3) << '\n'
+              << "remainder(-5.1, +3.0) = " << std::remainder(-5.1, 3) << '\n'
+              << "remainder(+5.1, -3.0) = " << std::remainder(5.1, -3) << '\n'
+              << "remainder(-5.1, -3.0) = " << std::remainder(-5.1, -3) << '\n';
+    // special values
+    std::cout << "remainder(-0.0, 1.0) = " << std::remainder(-0.0, 1) << '\n'
+              << "remainder(5.1, Inf) = " << std::remainder(5.1, INFINITY) << '\n';
+    // error handling
+    std::feclearexcept(FE_ALL_EXCEPT);
+    std::cout << "remainder(+5.1, 0) = " << std::remainder(5.1, 0) << '\n';
+    if (fetestexcept(FE_INVALID))
+        std::cout << "    FE_INVALID raised\n";
+}
+|p=true
+|output=
+remainder(+5.1, +3.0) = -0.9
+remainder(-5.1, +3.0) = 0.9
+remainder(+5.1, -3.0) = -0.9
+remainder(-5.1, -3.0) = 0.9
+remainder(-0.0, 1.0) = -0
+remainder(5.1, Inf) = 5.1
+remainder(+5.1, 0) = -nan
+    FE_INVALID raised
+}}
+===See also===
 {{dsc begin}}
-{{dsc inc | cpp/numeric/math/dsc fmod}}
+{{dsc inc|cpp/numeric/math/dsc div}}
-{{dsc inc | cpp/numeric/math/dsc div}}
+{{dsc inc|cpp/numeric/math/dsc fmod}}
+{{dsc inc|cpp/numeric/math/dsc remquo}}
+{{dsc see c|c/numeric/math/remainder}}
 {{dsc end}}
-[[de:cpp/numeric/math/remainder]]
+{{langlinks|de|es|fr|it|ja|ko|pt|ru|zh}}
-[[es:cpp/numeric/math/remainder]]
-[[fr:cpp/numeric/math/remainder]]
-[[it:cpp/numeric/math/remainder]]
-[[ja:cpp/numeric/math/remainder]]
-[[pt:cpp/numeric/math/remainder]]
-[[ru:cpp/numeric/math/remainder]]
-[[zh:cpp/numeric/math/remainder]]

Compiler support
Freestanding and hosted
Language
Standard library
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)
Execution support library (C++26)
Technical specifications
Symbols index
External libraries

cppreference.com

Namespaces

Variants

Views

Actions

Difference between revisions of "cpp/numeric/math/remainder"

Latest revision as of 09:12, 15 October 2023

Contents

[edit] Parameters

[edit] Return value

[edit] Error handling

[edit] Notes

[edit] Example

[edit] See also

Navigation

Toolbox