[HN Gopher] How much precision can you squeeze out of a table?
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       How much precision can you squeeze out of a table?
        
       Author : nomemory
       Score  : 31 points
       Date   : 2026-03-26 19:47 UTC (3 hours ago)
        
 (HTM) web link (www.johndcook.com)
 (TXT) w3m dump (www.johndcook.com)
        
       | PaulHoule wrote:
       | When I was in high school I thought book this was so much fun
       | 
       | http://182.160.97.198:8080/xmlui/bitstream/handle/123456789/...
       | 
       | which is all about the kind of numerical analysis you would do by
       | hand and introduces a lot of really cool math like the calculus
       | of differences
       | 
       | https://en.wikipedia.org/wiki/Finite_difference
        
       | gus_massa wrote:
       | Nitpicking:
       | 
       | > _You're never going to get error less than 10E-15 since that's
       | the error in the tabulated values,_
       | 
       | If you have like 100 (or 400) values in the table, you can
       | squeeze one more digit.
       | 
       | In the simple case, imagine you have the constant pi, with 15
       | digits, repeated 100 times. If the rounding was done in a random
       | direction like                 floor(pi * 1E15 + random() - 1/2 )
       | / 1E15
       | 
       | then you can use statistic to get an average with an error that
       | is like K/sqrt(N) where K is a constant and N is the number of
       | samples. If you were paying attention in you statistic clases,
       | you probably know the value of K, but it's not my case. Anyway,
       | just pick N=100 or N=400 or something like that and you get
       | another digit for "free".
       | 
       | Nobody builds a table for a constant and uses a uniform offset
       | for rounding. Anyway, with some smooth function that has no
       | special values in the points where it's sample, the exact value
       | of the cut decimal is quite "random" and you get a similar
       | randomization.
        
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