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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 to 0) is used. For IEEE standard where the base is , this means when there is a tie it is rounded so that the last digit is equal to .
If x is negative, round-down is the same as round-away-from-zero, and round-up is the same as round-toward-zero. In any case, if x is an integer, y is just x . Where many calculations are done in sequence, the choice of rounding method can have a very significant effect on the result.
Prices are generally rounded to the nearest 10 won (though generally to the nearest 50 or 100 won in many stores apart from supermarkets), and cash payments are rounded to the same. In Ukraine , from 1 October 2019, the 1-, 2- and 5- kopiyka coins were demonetized and withdrawn from circulation, with the 25-kopiyok coin softly withdrawn.
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) round up (toward +∞; negative results thus round toward zero)
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dc: "Desktop Calculator" arbitrary-precision RPN calculator that comes standard on most Unix-like systems. KCalc, Linux based scientific calculator; Maxima: a computer algebra system which bignum integers are directly inherited from its implementation language Common Lisp. In addition, it supports arbitrary-precision floating-point numbers ...
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.
Commons: reusable Java libraries and utilities too small to merit their own project BCEL: Bytecode Engineering Library; Daemon: Commons Daemon; Jelly: Jelly is a Java and XML based scripting engine. Jelly combines the best ideas from JSTL, Velocity, DVSL, Ant and Cocoon all together in a simple yet powerful scripting engine