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Qalculate! supports common mathematical functions and operations, multiple bases, autocompletion, complex numbers, infinite numbers, arrays and matrices, variables, mathematical and physical constants, user-defined functions, symbolic derivation and integration, solving of equations involving unknowns, uncertainty propagation using interval arithmetic, plotting using Gnuplot, unit and currency ...
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. Round-to-nearest: () is set to the nearest floating-point number to . When there ...
The main objective of interval arithmetic is to provide a simple way of calculating upper and lower bounds of a function's range in one or more variables. These endpoints are not necessarily the true supremum or infimum of a range since the precise calculation of those values can be difficult or impossible; the bounds only need to contain the function's range as a subset.
returns the nearest integer not greater in magnitude than the given value round lround llround: returns the nearest integer, rounding away from zero in halfway cases nearbyint: returns the nearest integer using current rounding mode rint lrint llrint: returns the nearest integer using current rounding mode with exception if the result differs ...
The nearest floating-point number with only five digits is 12.346. And 1/3 = 0.3333… is not a floating-point number in base ten with any finite number of digits. In practice, most floating-point systems use base two, though base ten (decimal floating point) is also common.
Rounding to a specified power is very different from rounding to a specified multiple; for example, it is common in computing to need to round a number to a whole power of 2. The steps, in general, to round a positive number x to a power of some positive number b other than 1, are:
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.
Here we start with 0 in single precision (binary32) and repeatedly add 1 until the operation does not change the value. Since the significand for a single-precision number contains 24 bits, the first integer that is not exactly representable is 2 24 +1, and this value rounds to 2 24 in round to nearest, ties to even.