Where to find algorithms for standard math functions? [closed]

Question

I'm looking to submit a patch to the D programming language standard library that will allow much of std.math to be evaluated at compile time using the compile-time function evaluation facilities of the language. Compile-time function evaluation has several limitations, the most important ones being:

1. You can't use assembly language.
2. You can't call C code or code for which the source is otherwise unavailable.

Several std.math functions violate these and compile-time versions need to be written. Where can I get information on good algorithms for computing things such as logarithms, exponents, powers, and trig functions? I prefer just high level descriptions of algorithms to actual code, for two reasons:

1. To avoid legal ambiguity and the need to make my code look "different enough" from the source to make sure I own the copyright.

2. I want simple, portable algorithms. I don't care about micro-optimization as long as they're at least asymptotically efficient.

Edit: D's compile time function evaluation model allows floating point results computed at compile time to differ from those computed at runtime anyhow, so I don't care if my compile-time algorithms don't give exactly the same result as the runtime version as long as they aren't less accurate to a practically significant extent.

Answer 1

John Hart Computer Approximations 1968 by John Wiley & Sons.

The calculations ideally should match precisely what they would if done at runtime. That can be tricky. For many functions, no series converges quickly over the full domain, so algoritms paste together various methods.

Also, there are various floating point formats. Most platforms (I think) now use IEEE 754. When I wrote a compiler ca. 1985, I had to deal with cross-platform floating point formats. It was very tedious to get it right, because you have to piece the numbers together bit by bit, being sure that you get precisely the value that would be calculated on the target machine. I don't know if you have to deal with that.