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This variant of the round-to-nearest method is also called convergent rounding, statistician's rounding, Dutch rounding, Gaussian rounding, odd–even rounding, [6] or bankers' rounding. [ 7 ] This is the default rounding mode used in IEEE 754 operations for results in binary floating-point formats.
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 ...
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.
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.
Python 3.12 dropped some outdated modules, and more will be dropped in the future, deprecated as of 3.13; already deprecated array 'u' format code will emit DeprecationWarning since 3.13 and will be removed in Python 3.16. The 'w' format code should be used instead.
round up (toward +∞; negative results thus round toward zero) round down (toward −∞; negative results thus round away from zero) round toward zero (truncation; it is similar to the common behavior of float-to-integer conversions, which convert −3.9 to −3 and 3.9 to 3)
The leading digit is between 0 and 9 (3 or 4 binary bits), and the rest of the significand uses the densely packed decimal (DPD) encoding. The leading 2 bits of the exponent and the leading digit (3 or 4 bits) of the significand are combined into the five bits that follow the sign bit. This is followed by a fixed-offset exponent continuation field.
Rounds (parameter 1) by (parameter 2) decimal places, and formats. Scientific notation is used for numbers greater than 1×10^9, or less than 1×10^−4. Template parameters [Edit template data] Parameter Description Type Status number 1 The number to be rounded Number required decimal places 2 The number of decimal places, if negative the number is rounded so the last (parameter 2) digits are ...