std::nextafter, std::nexttoward
From cppreference.com
| Defined in header
<cmath>
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| float nextafter( float from, float to );
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(1) | (since C++11) |
| double nextafter( double from, double to );
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(2) | (since C++11) |
| long double nextafter( long double from, long double to );
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(3) | (since C++11) |
| Promoted nextafter( Arithmetic from, Arithmetic to );
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(4) | (since C++11) |
| float nexttoward( float from, long double to );
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(5) | (since C++11) |
| double nexttoward( double from, long double to );
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(6) | (since C++11) |
| long double nexttoward( long double from, long double to );
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(7) | (since C++11) |
| double nexttoward( Integral from, long double to );
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(8) | (since C++11) |
Returns the next representable value of from in the direction of to.
1-3) If
from equals to to, to is returned.
5-7) If
from equals to to, to is returned, converted from long double to the return type of the function without loss of range or precision.
4) A set of overloads or a function template for all combinations of arguments of arithmetic type not covered by (1-3). If any argument has integral type, it is cast to double. If any argument is long double, then the return type
Promoted is also long double, otherwise the return type is always double.
8) A set of overloads or a function template accepting the
from argument of any integral type. Equivalent to (6) (the argument is cast to double).
Contents |
[edit] Parameters
| from, to | - | floating point values |
[edit] 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.
[edit] Error handling
Errors are reported as specified in math_errhandling
If the implementation supports IEEE floating-point arithmetic (IEC 60559),
- if
fromis finite, but the expected result is an infinity, raises FE_INEXACT and FE_OVERFLOW - if
fromdoes not equaltoand 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
fromortois NaN, NaN is returned
[edit] 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.
[edit] Example
Run this code
#include <cmath> #include <iomanip> #include <iostream> #include <cfloat> #include <cfenv> 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); // difference between nextafter and nexttoward: long double dir = std::nextafter(from1, 1.0L); // first subnormal long double float x = 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'; // special values { #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'; }
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)
With nextafter, next float after 0 is 0
With nexttoward, next float after 0 is 1.4012984643248170709e-45
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[edit] See also
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C documentation for nextafter
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