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I wonder if it makes sense to treat floating points not as single points on the number line but as a range. This way when you subtract two similar numbers the r
by ema 6y ago
I wonder if it makes sense to treat floating points not as single points on the number line but as a range. This way when you subtract two similar numbers the result is a range that is wide in relation to the distance from 0, explicitly encoding the bigger relative rounding error.
- atq2119 6y agoThat exists and is called interval arithmetic.
- ritter2a 6y agoThere are even more improvements (in some regard) to this, e.g. Affine Arithmetic[0, 1]. Here, error terms from different operations are accumulated symbolically so that in the case where they would cancel out (as could be useful for numerical algorithms), tighter bounds can be obtained. There are several research groups working on improving such analyses. -- [0] - https://en.wikipedia.org/wiki/Affine_arithmetic https://en.wikipedia.org/wiki/Affine_arithmetic [1] - http://users.ece.cmu.edu/~rutenbar/pdf/rutenbar-intervalicassp03.pdf http://users.ece.cmu.edu/~rutenbar/pdf/rutenbar-intervalicas... edit: formatting
- nestorD 6y agoAnd the problem with it is that it can lead to [-inf;+inf] intervals on sane computation such as Newton's method (refinements have been introduced but nothing that fully solves the problem).