# Science computation approach & errors

After reading one interesting science paper last week, I'd like to hear opinion of someone experienced or who is "in the theme":

Modern processors have some finite level of precision, so what processors are used in nuclear physics or genetics, for example? What's their level of precison when we talk about numbers like 10e-19 (unit charge) or 10e-34 (Planck constant)?

Take a look at Gravitational constant definition @Wired.com, difference is about "240 x 10e-6". I am confused a bit, what kind of processors did they use?

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Arbitrary precision is possible in scientific computing. You just pay for it in additional processing.

It is the responsibility of the the scientist to be aware of computational limitations in their calculations and to test for them. For example, small changes in input parameters should produce correspondingly small changes in the output.

Arbitrary precision is achieved by using an arbitrary number or words to encode a number. Arithmetic operations become more complicated as rounding and remainders must be tracked and re-included to the computation:

http://en.wikipedia.org/wiki/Arbitrary-precision_arithmetic

Support for high-precision numbers exists in almost all programming languages. Some high-level tools like Mathematica try to do the handling for you (it estimates the precision you need).

Generally, these tools are completely agnostic to the processor used, as long as that processor doesn't make errors:

http://engineeringfailures.org/?p=466

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"small changes in input parameters should produce correspondingly small changes in the output"—except for chaotic systems. ☺ – Paul A. Clayton Jun 19 '14 at 18:58
Even for chaotic systems, there is typically a scaling such that smaller changes in inputs produce smaller changes in outputs. Rounding errors generally appear different. Nevertheless, the expert needs to be aware of potential rounding errors, test for them, and compensate where needed. – sudoodus Jun 19 '14 at 19:24