std:: nextafter, std:: nextafterf, std:: nextafterl, std:: nexttoward, std:: nexttowardf, std:: nexttowardl

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nextafter nexttoward
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Defined in header <cmath>
(1)
float nextafter ( float from, float to ) ;

double nextafter ( double from, double to ) ;

long double nextafter ( long double from, long double to ) ;
(since C++11)
(until C++23)
constexpr /* floating-point-type */

nextafter ( /* floating-point-type */ from,

/* floating-point-type */ to ) ;
(since C++23)
float nextafterf ( float from, float to ) ;
(2) (since C++11)
(constexpr since C++23)
long double nextafterl ( long double from, long double to ) ;
(3) (since C++11)
(constexpr since C++23)
(4)
float nexttoward ( float from, long double to ) ;

double nexttoward ( double from, long double to ) ;

long double nexttoward ( long double from, long double to ) ;
(since C++11)
(until C++23)
constexpr /* floating-point-type */

nexttoward ( /* floating-point-type */ from,

long double to ) ;
(since C++23)
float nexttowardf ( float from, long double to ) ;
(5) (since C++11)
(constexpr since C++23)
long double nexttowardl ( long double from, long double to ) ;
(6) (since C++11)
(constexpr since C++23)
Defined in header <cmath>
template < class Arithmetic1, class Arithmetic2 >

/* common-floating-point-type */

nextafter ( Arithmetic1 from, Arithmetic2 to ) ;
(A) (since C++11)
(constexpr since C++23)
template < class Integer >
double nexttoward ( Integer from, long double to ) ;
(B) (since C++11)
(constexpr since C++23)

Returns the next representable value of from in the direction of to .

1-3) If from equals to , to is returned. The library provides overloads of std::nextafter for all cv-unqualified floating-point types as the type of the parameters from and to . (since C++23)
4-6) If from equals to , to is returned, converted from long double to the return type of the function without loss of range or precision.

The library provides overloads of std::nexttoward for all cv-unqualified floating-point types as the type of the parameter from . However, an invocation of std::nexttoward is ill-formed if the argument corresponding to from has extended floating-point type , because the next representable value (or to ) is not guaranteed to be representable as long double .

(since C++23)
A) Additional std::nextafter overloads are provided for all other combinations of arithmetic types.
B) Additional std::nexttoward overloads are provided for all integer types, which are treated as double .

Parameters

from, to - floating-point or integer values

Return value

If no errors occur, the next representable value of from in the direction of to . is returned. If from equals to , then to is returned.

If a range error due to overflow occurs, ±HUGE_VAL , ±HUGE_VALF , or ±HUGE_VALL is returned (with the same sign as from ).

If a range error occurs due to underflow, the correct result is returned.

Error handling

Errors are reported as specified in math_errhandling .

If the implementation supports IEEE floating-point arithmetic (IEC 60559),

  • if from is finite, but the expected result is an infinity, raises FE_INEXACT and FE_OVERFLOW .
  • if from does not equal to and the result is subnormal or zero, raises FE_INEXACT and FE_UNDERFLOW .
  • in any case, the returned value is independent of the current rounding mode.
  • if either from or to is NaN, NaN is returned.

Notes

POSIX specifies that the overflow and the underflow conditions are range errors ( errno may be set).

IEC 60559 recommends that from is returned whenever from == to . These functions return to instead, which makes the behavior around zero consistent: std :: nextafter ( - 0.0 , + 0.0 ) returns + 0.0 and std :: nextafter ( + 0.0 , - 0.0 ) returns - 0.0 .

std::nextafter is typically implemented by manipulation of IEEE representation ( glibc , musl ).

The additional std::nextafter 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 :: nextafter ( num1, num2 ) has the same effect as std :: nextafter ( 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 :: nextafter ( num1, num2 ) has the same effect as std :: nextafter ( static_cast < double > ( num1 ) ,
    static_cast < double > ( num2 ) )     .
  • Otherwise, if num1 or num2 has type float , then std :: nextafter ( num1, num2 ) has the same effect as std :: nextafter ( static_cast < float > ( num1 ) ,
    static_cast < float > ( num2 ) )     .
(until C++23)

If num1 and num2 have arithmetic types, then std :: nextafter ( num1, num2 ) has the same effect as std :: nextafter ( 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)

The additional std::nexttoward overloads are not required to be provided exactly as (B) . They only need to be sufficient to ensure that for their argument num of integer type, std :: nexttoward ( num ) has the same effect as std :: nexttoward ( static_cast < double > ( num ) ) .

Example

Run this code 
#include <cfenv>
#include <cfloat>
#include <cmath>
#include <concepts>
#include <iomanip>
#include <iostream>
 
int main()
{
    float from1 = 0, to1 = std::nextafter(from1, 1.f);
    std::cout << "The next representable float after " << std::setprecision(20) << from1
              << " is " << to1
              << std::hexfloat << " (" << to1 << ")\n" << std::defaultfloat;
 
    float from2 = 1, to2 = std::nextafter(from2, 2.f);
    std::cout << "The next representable float after " << from2 << " is " << to2
              << std::hexfloat << " (" << to2 << ")\n" << std::defaultfloat;
 
    double from3 = std::nextafter(0.1, 0), to3 = 0.1;
    std::cout << "The number 0.1 lies between two valid doubles:\n"
              << std::setprecision(56) << "    " << from3
              << std::hexfloat << " (" << from3 << ')' << std::defaultfloat
              << "\nand " << to3 << std::hexfloat << "  (" << to3 << ")\n"
              << std::defaultfloat << std::setprecision(20);
 
    std::cout << "\nDifference between nextafter and nexttoward:\n";
    long double dir = std::nextafter(from1, 1.0L); // first subnormal long double
    float x = std::nextafter(from1, dir); // first converts dir to float, giving 0
    std::cout << "With nextafter, next float after " << from1 << " is " << x << '\n';
    x = std::nexttoward(from1, dir);
    std::cout << "With nexttoward, next float after " << from1 << " is " << x << '\n';
 
    std::cout << "\nSpecial values:\n";
    {
        // #pragma STDC FENV_ACCESS ON
        std::feclearexcept(FE_ALL_EXCEPT);
        double from4 = DBL_MAX, to4 = std::nextafter(from4, INFINITY);
        std::cout << "The next representable double after " << std::setprecision(6)
                  << from4 << std::hexfloat << " (" << from4 << ')'
                  << std::defaultfloat << " is " << to4
                  << std::hexfloat << " (" << to4 << ")\n" << std::defaultfloat;
 
        if (std::fetestexcept(FE_OVERFLOW))
            std::cout << "   raised FE_OVERFLOW\n";
        if (std::fetestexcept(FE_INEXACT))
            std::cout << "   raised FE_INEXACT\n";
    } // end FENV_ACCESS block
 
    float from5 = 0.0, to5 = std::nextafter(from5, -0.0);
    std::cout << "std::nextafter(+0.0, -0.0) gives " << std::fixed << to5 << '\n';
 
    auto precision_loss_demo = []<std::floating_point Fp>(const auto rem, const Fp start)
    {
        std::cout << rem;
        for (Fp from = start, to, Δ;
            (Δ = (to = std::nextafter(from, +INFINITY)) - from) < Fp(10.0);
            from *= Fp(10.0))
            std::cout << "nextafter(" << std::scientific << std::setprecision(0) << from 
                      << ", INF) gives " << std::fixed << std::setprecision(6) << to
                      << "; Δ = " << Δ << '\n';
    };
 
    precision_loss_demo("\nPrecision loss demo for float:\n", 10.0f);
    precision_loss_demo("\nPrecision loss demo for double:\n", 10.0e9);
    precision_loss_demo("\nPrecision loss demo for long double:\n", 10.0e17L);
}

Output: 

The next representable float after 0 is 1.4012984643248170709e-45 (0x1p-149)
The next representable float after 1 is 1.0000001192092895508 (0x1.000002p+0)
The number 0.1 lies between two valid doubles:
    0.09999999999999999167332731531132594682276248931884765625 (0x1.9999999999999p-4)
and 0.1000000000000000055511151231257827021181583404541015625  (0x1.999999999999ap-4)
 
Difference between nextafter and nexttoward:
With nextafter, next float after 0 is 0
With nexttoward, next float after 0 is 1.4012984643248170709e-45
 
Special values:
The next representable double after 1.79769e+308 (0x1.fffffffffffffp+1023) is inf (inf)
   raised FE_OVERFLOW
   raised FE_INEXACT
std::nextafter(+0.0, -0.0) gives -0.000000
 
Precision loss demo for float:
nextafter(1e+01, INF) gives 10.000001; Δ = 0.000001
nextafter(1e+02, INF) gives 100.000008; Δ = 0.000008
nextafter(1e+03, INF) gives 1000.000061; Δ = 0.000061
nextafter(1e+04, INF) gives 10000.000977; Δ = 0.000977
nextafter(1e+05, INF) gives 100000.007812; Δ = 0.007812
nextafter(1e+06, INF) gives 1000000.062500; Δ = 0.062500
nextafter(1e+07, INF) gives 10000001.000000; Δ = 1.000000
nextafter(1e+08, INF) gives 100000008.000000; Δ = 8.000000
 
Precision loss demo for double:
nextafter(1e+10, INF) gives 10000000000.000002; Δ = 0.000002
nextafter(1e+11, INF) gives 100000000000.000015; Δ = 0.000015
nextafter(1e+12, INF) gives 1000000000000.000122; Δ = 0.000122
nextafter(1e+13, INF) gives 10000000000000.001953; Δ = 0.001953
nextafter(1e+14, INF) gives 100000000000000.015625; Δ = 0.015625
nextafter(1e+15, INF) gives 1000000000000000.125000; Δ = 0.125000
nextafter(1e+16, INF) gives 10000000000000002.000000; Δ = 2.000000
 
Precision loss demo for long double:
nextafter(1e+18, INF) gives 1000000000000000000.062500; Δ = 0.062500
nextafter(1e+19, INF) gives 10000000000000000001.000000; Δ = 1.000000
nextafter(1e+20, INF) gives 100000000000000000008.000000; Δ = 8.000000

See also

C documentation for nextafter
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