Name: Anonymous 2015-11-16 22:11
Let's design a suckless bignum library. (I'm not part of suckless though, just curious about replacing GMP).
I researched a bit into algorithms and the rundown is this:
* long multiplication: O(n^2)
* karatsuba O(n^1.5)
* Toom-Cook, fourier transform based methods - even faster but only used for numbers 10k digits+ long. Much more complex.
So we should probably use karatsuba for all multiplications. Squaring can be done a bit faster than multiplying two different numbers sometimes.
Now I suggest programming it in assembly, that gives you access to the carry bit (C doesn't get you that). Of course we will use libc and the normal C calling conventions so that it's a regular C library.
What to do about memory management? e.g. if you want to add two numbers do we need to allocate a new 'number' as long as the largest to write the result into or do it destructively "x <- x + y"? Maybe the library should support both - then a calculator program would figure out the best primitives to use for a given computation.
It might be nice to also support things like (big modulus) modular arithmetic and polynomials. stuff like exponentiation and modular inverses have interesting algorithms.
What other integer operations would we want? I don't really want to do anything with arb. prec. real numbers - arithmetic with rationals could be done though.
I researched a bit into algorithms and the rundown is this:
* long multiplication: O(n^2)
* karatsuba O(n^1.5)
* Toom-Cook, fourier transform based methods - even faster but only used for numbers 10k digits+ long. Much more complex.
So we should probably use karatsuba for all multiplications. Squaring can be done a bit faster than multiplying two different numbers sometimes.
Now I suggest programming it in assembly, that gives you access to the carry bit (C doesn't get you that). Of course we will use libc and the normal C calling conventions so that it's a regular C library.
What to do about memory management? e.g. if you want to add two numbers do we need to allocate a new 'number' as long as the largest to write the result into or do it destructively "x <- x + y"? Maybe the library should support both - then a calculator program would figure out the best primitives to use for a given computation.
It might be nice to also support things like (big modulus) modular arithmetic and polynomials. stuff like exponentiation and modular inverses have interesting algorithms.
What other integer operations would we want? I don't really want to do anything with arb. prec. real numbers - arithmetic with rationals could be done though.