Euler Identity in Home

[Han]

(04-06-2014 11:31 PM)ColinJDenman Wrote:  Others seem to feel I do not recognise the inevitability of approximation in digital computation. I do, but feel a simple calculation displaying these errors questions the reliability of much more involved calculations. The calculator does not offer an estimate of the size of the error in the result. If you see a 'very' small result and discard it as approximation error, what is the purpose in having a calculator that displays 9E-499?

I think you are confusing the ability to have numbers like 9E-499 with algorithms that are accurate to 499 decimal places. They are two very different concepts. Floating point-precision requires that the calculator be able to handle small numbers, but the ability to handle small numbers does not immediately imply fast and efficient floating point algorithms scale to such high precision in a nice way (esp. in terms of speed). High-precision floating point libraries tend to take up more space and more time for computations, and are usually provided through external libraries when such precision is needed. Most of the "typical" users of calculators will find that 10-12 decimal places provide enough accuracy.