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  2. Rounding - Wikipedia

    en.wikipedia.org/wiki/Rounding

    In the example from "Double rounding" section, rounding 9.46 to one decimal gives 9.4, which rounding to integer in turn gives 9. With binary arithmetic, this rounding is also called "round to odd" (not to be confused with "round half to odd"). For example, when rounding to 1/4 (0.01 in binary), x = 2.0 ⇒ result is 2 (10.00 in binary)

  3. Decimal data type - Wikipedia

    en.wikipedia.org/wiki/Decimal_data_type

    Some programming languages (or compilers for them) provide a built-in (primitive) or library decimal data type to represent non-repeating decimal fractions like 0.3 and −1.17 without rounding, and to do arithmetic on them. Examples are the decimal.Decimal or num7.Num type of Python, and analogous types provided by other languages.

  4. Round-off error - Wikipedia

    en.wikipedia.org/wiki/Round-off_error

    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 is a tie, the floating-point number whose last stored digit is even (also, the last digit, in binary form, is equal ...

  5. 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.

  6. Floating-point arithmetic - Wikipedia

    en.wikipedia.org/wiki/Floating-point_arithmetic

    The "decimal" data type of the C# and Python programming languages, and the decimal formats of the IEEE 754-2008 standard, are designed to avoid the problems of binary floating-point representations when applied to human-entered exact decimal values, and make the arithmetic always behave as expected when numbers are printed in decimal.

  7. Python (programming language) - Wikipedia

    en.wikipedia.org/wiki/Python_(programming_language)

    Python provides a round function for rounding a float to the nearest integer. For tie-breaking, Python 3 uses round to even: round(1.5) and round(2.5) both produce 2. [123] Versions before 3 used round-away-from-zero: round(0.5) is 1.0, round(-0.5) is −1.0. [124] Python allows Boolean expressions with multiple equality relations in a manner ...

  8. List of arbitrary-precision arithmetic software - Wikipedia

    en.wikipedia.org/wiki/List_of_arbitrary...

    SmartXML big numbers can have up to 100,000,000 decimal digits and up to 100,000,000 whole digits. Standard ML: The optional built-in IntInf structure implements the INTEGER signature and supports arbitrary-precision integers. Tcl: As of version 8.5 (2007), integers are arbitrary-precision by default. (Behind the scenes, the language switches ...

  9. IEEE 754-2008 revision - Wikipedia

    en.wikipedia.org/wiki/IEEE_754-2008_revision

    Decimal arithmetic, compatible with that used in Java, C#, PL/I, COBOL, Python, REXX, etc., is also defined in this section. In general, decimal arithmetic follows the same rules as binary arithmetic (results are correctly rounded, and so on), with additional rules that define the exponent of a result (more than one is possible in many cases).