[HN Gopher] Taming Floating-Point Sums
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       Taming Floating-Point Sums
        
       Author : todsacerdoti
       Score  : 17 points
       Date   : 2024-05-25 20:28 UTC (2 hours ago)
        
 (HTM) web link (orlp.net)
 (TXT) w3m dump (orlp.net)
        
       | nsajko wrote:
       | I recommend the "Handbook of Floating-point Arithmetic" if this
       | piques interest. I think it's freely available on HAL.
        
         | greenyoda wrote:
         | I found the link to it on HAL, but clicking "Consult the full
         | text" only seems download the table of contents and preface:
         | https://hal.science/hal-01766584
         | 
         | A new copy costs $112 on Amazon:
         | https://www.amazon.com/Handbook-Floating-Point-Arithmetic-Je...
        
       | Infinity315 wrote:
       | A method which this article doesn't mention is stochastic
       | rounding or probabilistic rounding.
       | 
       | Rather than striving for exact values for every computation, we
       | make it so that the expected value is exact. For example, suppose
       | our number system was restricted to the integers and we have
       | incoming value 1.1, with stochastic rounding we'd round down to 1
       | 90% of the time and 2 10% of the time giving an expected value of
       | 1.1!
       | 
       | Further reading:
       | 
       | https://nhigham.com/2020/07/07/what-is-stochastic-rounding/
        
         | orlp wrote:
         | Interesting, I haven't seen that before in the context of
         | numerics.
         | 
         | It is used all the time however in audio and image processing,
         | where it is called dithering.
        
       | caturopath wrote:
       | The motivating example is a mess. 15_000_000 would have been a
       | less distracting example, as this one has more-visible problems
       | unrelated to the problem they're trying to solve. (Further, with
       | default options, the opening example won't have the result shown:
       | it will crash your program.)
        
         | orlp wrote:
         | I don't follow. Why is 15_000_000 less distracting? What
         | problems unrelated to what we're trying to solve? And what
         | 'default options' are you referring to?
        
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       (page generated 2024-05-25 23:00 UTC)