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
My father owned a copy of it which I still have to this day. It had a lot of different formulas than the ones we were taught in school, and I liked the range of topics that it covered.
> 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
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.