Questions tagged [machine-precision]

My math-book states that when a real number $x$ is replaced by a floating-point number $F(x)$ then the error between the two is: $|error|=|x-F(x)|\le\epsilon |x|$ Now the book asks: Consider two different, but mathematically equivalent…

A, B, C, have finite precisions with machine epsilon of $10^{-16}$. When will the associative law A + (B+C) = (A+B) + C fail in this finite precision system? I have difficulty to find A, B and C. but I am thinking A can be a big number, B and C…

I try to compute a function of type $e^x$. Since its natural fast-growing behaviour, the most natural behaviour is to decompose the resulting number into its mantissa and exponent components. However, due limited computational precision, one may not…

1 AU is 149597870700 meters. This is much more information than typically needed, so 150 million kilometers would be precise enough in most situations. Does spreadsheets have a function to handle this? (I use Google Spreadsheet, LibraOffice and…