I'm starting a project where I need better precision. I think the limits of 64-bit pecision will be a big limitation if I'm careless. Is there a good book that people like for this topic? Ideally the book will be good at explaining similar techniques, and also provide context of when they're helpful/hurtful.

Also, there are two techniques that I can't remember their name. Does either of these sound familar to anyone:

Technique 1) When adding a long sequence of numbers, this technique keeps track of (a) the typical sum and (b) a remainder-like tally, that represents the info that was truncated from the finite precision additions. At the end of the sequences these two values are summed.

Technique 2) An equation like " a + b*z + c*z*z + d*z*z*z ", is reexpressed something like " a+z*(b + z*(c + d*z)) ".

(Edit: the first one is 'Kahan summation' and the second seems to be commonly called 'nested multiplication'.)