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  2. Rounding - Wikipedia

    en.wikipedia.org/wiki/Rounding

    Rounding to a specified power is very different from rounding to a specified multiple; for example, it is common in computing to need to round a number to a whole power of 2. The steps, in general, to round a positive number x to a power of some positive number b other than 1, are:

  3. Round-off error - Wikipedia

    en.wikipedia.org/wiki/Round-off_error

    There are two common rounding rules, round-by-chop and round-to-nearest. The IEEE standard uses round-to-nearest. Round-by-chop: The base-expansion of is truncated after the ()-th digit. This rounding rule is biased because it always moves the result toward zero. Round-to-nearest: () is set to the nearest floating-point number to . When there ...

  4. IEEE 754 - Wikipedia

    en.wikipedia.org/wiki/IEEE_754

    Round to nearest, ties to even – rounds to the nearest value; if the number falls midway, it is rounded to the nearest value with an even least significant digit. Round to nearest, ties away from zero (or ties to away ) – rounds to the nearest value; if the number falls midway, it is rounded to the nearest value above (for positive numbers ...

  5. Floating-point arithmetic - Wikipedia

    en.wikipedia.org/wiki/Floating-point_arithmetic

    Alternative rounding options are also available. IEEE 754 specifies the following rounding modes: round to nearest, where ties round to the nearest even digit in the required position (the default and by far the most common mode) round to nearest, where ties round away from zero (optional for binary floating-point and commonly used in decimal)

  6. IEEE 754-1985 - Wikipedia

    en.wikipedia.org/wiki/IEEE_754-1985

    Round to Nearest – rounds to the nearest value; if the number falls midway it is rounded to the nearest value with an even (zero) least significant bit, which means it is rounded up 50% of the time (in IEEE 754-2008 this mode is called roundTiesToEven to distinguish it from another round-to-nearest mode)

  7. Unit in the last place - Wikipedia

    en.wikipedia.org/wiki/Unit_in_the_last_place

    Here we start with 0 in single precision (binary32) and repeatedly add 1 until the operation does not change the value. Since the significand for a single-precision number contains 24 bits, the first integer that is not exactly representable is 2 24 +1, and this value rounds to 2 24 in round to nearest, ties to even.

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  9. Machine epsilon - Wikipedia

    en.wikipedia.org/wiki/Machine_epsilon

    This alternative definition is significantly more widespread: machine epsilon is the difference between 1 and the next larger floating point number.This definition is used in language constants in Ada, C, C++, Fortran, MATLAB, Mathematica, Octave, Pascal, Python and Rust etc., and defined in textbooks like «Numerical Recipes» by Press et al.