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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.
One may also round half away from zero (or round half toward infinity), a tie-breaking rule that is commonly taught and used, namely: If the fractional part of x is exactly 0.5, then y = x + 0.5 if x is positive, and y = x − 0.5 if x is negative.
For tie-breaking, Python 3 uses round to even: round(1.5) and round(2.5) both produce 2. [119] Versions before 3 used round-away-from-zero: round(0.5) is 1.0, round(-0.5) is −1.0. [120] Python allows Boolean expressions with multiple equality relations in a manner that is consistent with general use in mathematics.
Unicode was designed to provide code-point-by-code-point round-trip format conversion to and from any preexisting character encodings, so that text files in older character sets can be converted to Unicode and then back and get back the same file, without employing context-dependent interpretation.
By default, 1/3 rounds up, instead of down like double precision, because of the even number of bits in the significand. The bits of 1/3 beyond the rounding point are 1010... which is more than 1/2 of a unit in the last place. Encodings of qNaN and sNaN are not specified in IEEE 754 and implemented differently on different processors.
For example, a Q15.1 format number requires 15+1 = 16 bits, has resolution 2 −1 = 0.5, and the representable values range from −2 14 = −16384.0 to +2 14 − 2 −1 = +16383.5. In hexadecimal, the negative values range from 0x8000 to 0xFFFF followed by the non-negative ones from 0x0000 to 0x7FFF.
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.
ASCII (/ ˈ æ s k iː / ⓘ ASS-kee), [3]: 6 an acronym for American Standard Code for Information Interchange, is a character encoding standard for electronic communication. . ASCII codes represent text in computers, telecommunications equipment, and other devic