FE_DOWNWARD, FE_TONEAREST, FE_TOWARDZERO, FE_UPWARD
<cfenv>
Each of these macro constants expands to a nonnegative integer constant expression, which can be used with std::fesetround and std::fegetround to indicate one of the supported floating-point rounding modes. The implementation may define additional rounding mode constants in <cfenv>, which should all begin with FE_ followed by at least one uppercase letter. Each macro is only defined if it is supported.
FE_DOWNWARD
rounding towards negative infinity
FE_TONEAREST
rounding towards nearest representable value
FE_TOWARDZERO
rounding towards zero
FE_UPWARD
rounding towards positive infinity
Additional rounding modes may be supported by an implementation.
The current rounding mode affects the following:
- results of floating-point arithmetic operators outside of constant expressions
double x = 1; x / 10; // 0.09999999999999999167332731531132594682276248931884765625 // or 0.1000000000000000055511151231257827021181583404541015625
- results of standard library mathematical functions
std::sqrt (2); // 1.41421356237309492343001693370752036571502685546875 // or 1.4142135623730951454746218587388284504413604736328125
- floating-point to floating-point implicit conversion and casts
double d = 1 + std::numeric_limits <double>::epsilon(); float f = d; // 1.00000000000000000000000 // or 1.00000011920928955078125
- string conversions such as std::strtod or std::printf
std::stof ("0.1"); // 0.0999999940395355224609375 // or 0.100000001490116119384765625
- the library rounding functions std::nearbyint , std::rint , std::lrint
std::lrint (2.1); // 2 or 3
The current rounding mode does NOT affect the following:
- floating-point to integer implicit conversion and casts (always towards zero),
- results of floating-point arithmetic operators in expressions executed at compile time (always to nearest),
- the library functions std::round , std::lround , std::llround , std::ceil , std::floor , std::trunc .
As with any floating-point environment functionality, rounding is only guaranteed if #pragma STDC FENV_ACCESS ON is set.
Compilers that do not support the pragma may offer their own ways to support current rounding mode. For example Clang and GCC have the option -frounding-math intended to disable optimizations that would change the meaning of rounding-sensitive code.
[edit] Example
#include <cfenv> #include <cmath> #include <iomanip> #include <iostream> #include <string> // #pragma STDC FENV_ACCESS ON int main() { std::fesetround (FE_DOWNWARD); std::cout << "rounding down: \n" << std::setprecision (50) << " pi = " << std::acos (-1.f) << '\n' << "stof(\"1.1\") = " << std::stof ("1.1") << '\n' << " rint(2.1) = " << std::rint (2.1) << "\n\n"; std::fesetround (FE_UPWARD); std::cout << "rounding up: \n" << " pi = " << std::acos (-1.f) << '\n' << "stof(\"1.1\") = " << std::stof ("1.1") << '\n' << " rint(2.1) = " << std::rint (2.1) << '\n'; }
Output:
rounding down:
pi = 3.141592502593994140625
stof("1.1") = 1.099999904632568359375
rint(2.1) = 2
rounding up:
pi = 3.1415927410125732421875
stof("1.1") = 1.10000002384185791015625
rint(2.1) = 3