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# FE_DOWNWARD, FE_TONEAREST, FE_TOWARDZERO, FE_UPWARD

From cppreference.com
< c‎ | numeric‎ | fenv

Defined in header `<fenv.h>` |  |
#define FE_DOWNWARD /*implementation defined*/ |  | (since C99)
#define FE_TONEAREST /*implementation defined*/ |  | (since C99)
#define FE_TOWARDZERO /*implementation defined*/ |  | (since C99)
#define FE_UPWARD /*implementation defined*/ |  | (since C99)

Each of these macro constants expands to a nonnegative integer constant expression, which can be used with fesetround and fegetround to indicate one of the supported floating-point rounding modes. The implementation may define additional rounding mode constants in `<fenv.h>`, which should all begin with `FE_` followed by at least one uppercase letter. Each macro is only defined if it is supported.

On most implementations, these macro constants expand to the values equal to the values of FLT_ROUNDS and float_round_style

Constant | Explanation
`FE_DOWNWARD` | rounding towards negative infinity
`FE_TONEAREST` | rounding towards nearest integer
`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

    sqrt(2); // 1.41421356237309492343001693370752036571502685546875
          // or 1.4142135623730951454746218587388284504413604736328125

- floating-point to floating-point implicit conversion and casts

    double d = 1 + DBL_EPSILON;
    float f = d; //  1.00000000000000000000000
               // or 1.00000011920928955078125

- string conversions such as strtod or printf

    strtof("0.1", NULL); // 0.0999999940395355224609375
                      // or 0.100000001490116119384765625

- the library rounding functions nearbyint, rint, lrint

    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 constant expressions (always to nearest)
- the library functions round, lround, ceil, floor, trunc

As with any floating-point environment functionality, rounding is only guaranteed if `#pragma STDC FENV_ACCESS ON` is set.

### [edit] Example

Run this code

    #include <stdio.h>
    #include <stdlib.h>
    #include <fenv.h>
    #include <math.h>
    int main()
    {
    #pragma STDC FENV_ACCESS ON
        fesetround(FE_DOWNWARD);
        puts("rounding down: ");
        printf("           pi = %.22f\n", acosf(-1));
        printf("strtof(\"1.1\") = %.22f\n", strtof("1.1", NULL));
        printf("    rint(2.1) = %.22f\n\n", rintf(2.1));
        fesetround(FE_UPWARD);
        puts("rounding up: ");
        printf("           pi = %.22f\n", acosf(-1));
        printf("strtof(\"1.1\") = %.22f\n", strtof("1.1", NULL));
        printf("    rint(2.1) = %.22f\n", rintf(2.1));
    }

Output:

    rounding down:
               pi = 3.1415925025939941406250
    strtof("1.1") = 1.0999999046325683593750
        rint(2.1) = 2.0000000000000000000000

    rounding up:
               pi = 3.1415927410125732421875
    strtof("1.1") = 1.1000000238418579101563
        rint(2.1) = 3.0000000000000000000000

### [edit] References

- C11 standard (ISO/IEC 9899:2011):

  - 7.6/8 Floating-point environment <fenv.h> (p: 207)

- C99 standard (ISO/IEC 9899:1999):

  - 7.6/7 Floating-point environment <fenv.h> (p: 188)

### [edit] See also

fegetround fesetround (C99)(C99) | gets or sets rounding direction (function) [edit]
C++ documentation for floating point rounding macros

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