parallel 512-bit full adder in avx512. pseudocode. probably works

avx512-full-adder

// we want to compute r,c := x + y + i
// c carry-out
// r sum
// x y addends
// i carry-in
// carry in/out is zmm with most significant qword -1/0

t := vpaddq(x, y)
ct := vmovm2q(ctm := vpcmpeqq(t, -1))			// carry-through
c# := vmovm2q(c#m := vpcmpnltuq(t, vpmaxuq(x,y)))	// approximate carry (inverted)

// now, to element t_i, we want to add 1-c#_i-1, unless ct_i-1, in which case we take c#_i-2, etc.
// (that means t_0 + 1-c#_-1, which we can arrange to be the carry-in with perm2q)
// so for each element, we want to count the number of ct immediately preceding it

// preceding mask
pm := vperm2b(c#, -1 0 0 0 0 0 0 0,	64 64 64 64 64 64 64 64
					64 64 64 64 64 64 64  0
					64 64 64 64 64 64  0  8
					64 64 64 64 64  0  8 16
					64 64 64 64  0  8 16 24
					64 64 64  0  8 16 24 32
					64 64  0  8 16 24 32 40
					64  0  8 16 24 32 40 48)
// pm could probably also be built by moving c#m to a gpr, broadcast to zmm, shift each lane

// preceding count
pc := vpshrq(vplzcntq(pm), 3)
r := vpsubq(vpaddq(t, 1), vperm2q(c#, i, vpsubq(-1 0 1 2 3 4 5 6, pc)))
// carry-out needs masked to handle the case x[7]=y[7]=-1 and carry-in
// we only care about the most significant qword but this is the easiest way to get it
// using c#m as dst is just convenient because it's dead here; we just need something with a 0 in the msb
// i think this is right w/e
c := vmovm2q(vpcmpnltuq{c#m}(c#m, r, vpmaxuq(x,y)))

// is there a way to skip >>3 in pc?