I agree hardware quad is more useful. The big int problem I was talking about would benefit from hardware quad but not hardware 128-bit ALU. The big int problem I have a bit of knowledge of is squaring for the Lucas-Lehmer algorithm to find huge primes (Mersenne primes). The best algorithm in this space is the IBDWT (irrational base discrete weighted transform). You perform an autoconvolution (compute the FFT, square each term in the frequency domain, and then take the IFFT). You want the FFT lengths to be as short as possible, since FFT is an O(N log N) algorithm. Quads would let you use shorter FFTs since you have more bits available for each element.
Even though it is a big int problem, floating point is used. Their are integer FFT algoritms that are usable (NTTs), but they are much slower than floating point FFTs on modern CPUs.
Even though it is a big int problem, floating point is used. Their are integer FFT algoritms that are usable (NTTs), but they are much slower than floating point FFTs on modern CPUs.