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PHP: The BC Math module provides arbitrary precision mathematics. PicoLisp: supports arbitrary precision integers. Pike: the built-in int type will silently change from machine-native integer to arbitrary precision as soon as the value exceeds the former's capacity. Prolog: ISO standard compatible Prolog systems can check the Prolog flag ...
A floating-point number is a rational number, because it can be represented as one integer divided by another; for example 1.45 × 10 3 is (145/100)×1000 or 145,000 /100. The base determines the fractions that can be represented; for instance, 1/5 cannot be represented exactly as a floating-point number using a binary base, but 1/5 can be ...
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 ...
One method, more obscure than most, is to alternate direction when rounding a number with 0.5 fractional part. All others are rounded to the closest integer. Whenever the fractional part is 0.5, alternate rounding up or down: for the first occurrence of a 0.5 fractional part, round up, for the second occurrence, round down, and so on.
Mac OS calculator: Proprietary: macOS: Double (64 bit) Yes Yes Yes GNOME Calculator: GPL-3.0-or-later: Linux, BSDs, macOS: Arbitrary decimal Yes Yes Yes KCalc: GPL-2.0-or-later: Linux, BSDs, macOS: Arbitrary decimal Yes Yes Yes Windows Calculator: MIT: Windows: ≥32 decimal Yes Yes Yes WRPN Calculator: Public domain: Windows, Linux, macOS ...
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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.
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