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floating-pointprecisionnumerical-methods
Elizabeth Welz
Elizabeth Welz

Reputation: 41

Is the computation precise in 64-bit floating point

Let's say I have probabilities between 0.1 and 0.2(10,000 of them), and I want to store the result, which is the multiplication of all these probabilities in the 64-bit floating point? Is it a reliable computation?

Upvotes: 0

Views: 85

Answers (1)

Nate Eldredge
Nate Eldredge

Reputation: 57922

This will not work. If you multiply together 10000 numbers, all less than 0.2, the result will be less than 0.2^10000 which is about 1e-7000. The smallest positive number that can be represented in 64-bit double precision floating point is about 2.2e-308 so you will underflow by several thousand orders of magnitude. If you try this you'll just get the result 0.0.

You may want to add their logs instead.

Upvotes: 5

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