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So don't use floating points? You can use arbitrary precision math libraries. If you devote enough memory, you can be much more precise with continuous values
by jonfw 8y ago
So don't use floating points? You can use arbitrary precision math libraries.
If you devote enough memory, you can be much more precise with continuous values than an analog computer could ever hope to be. Frankly it wouldn't take much memory at all by modern standards though.
- jhayward 8y agoArbitrary precision doesn't help with irrational numbers. You may be thinking of the "just use enough bits so you're sure the accumulated error isn't significant" approach, which is essentially what modern floating-point attempts to do. There are still some pitfalls though, around doing an analysis that proves the bounds of said error in a given algorithm and data set. You might be interested in the concepts used in interval arithmetic [1] and specifically the work of Gustafson in designing some models for using those in scientific computing hardware. [1] https://en.wikipedia.org/wiki/Interval_arithmetic https://en.wikipedia.org/wiki/Interval_arithmetic