This version collect partial sums in reverse order, with each entry (except last) used up all 53 bits.
With less partials to sum, it's speed is 2X of my old version (see FloatSum)
To see my C/C++ versions (see https://github.com/achan001/fsum)
--[[ > fsum = require 'fsum' > = fsum(0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1) - 1 0 > fadd, ftotal = fsum() > for i = 1, 10 do fadd(0.1) end > = ftotal() - 1 0 > ftotal(0) -- clear calculator > for i = 1, 10 do fadd(0.1) end > = ftotal() - 1 0 --]] local function fsum(...) local p, abs = {1}, math.abs -- p[1] == #p local function fadd(x) local p, i = p, 2 for j = 2, p[1] do local y = p[j] if abs(x) > abs(y) then x, y = y, x end local hi = x + y local lo = x - (hi - y) x = hi if lo ~= 0 then p[i] = x; x = lo; i = i + 1 end end if x ~= x then p[1] = 2 return end -- Inf or NaN p[1] = i p[i] = x end local function ftotal(clear) if clear then p[1] = 1 end -- clear all partials repeat local n, overlap = p[1], false local prev = {unpack(p, 1, n)} fadd(0) -- remove partials overlap if n <= 3 then return p[2] end for i = 1, n do if p[i] ~= prev[i] then overlap = true; break end end until not overlap local x, lo, err = unpack(p, 2, 4) if (lo < 0) == (err < 0) then lo = lo * 2 -- |lo| = 1/2 ULP local hi = x + lo -- -> x off 1 ULP if lo == hi - x then x = hi end end return x end if select('#', ...) == 0 then return fadd, ftotal end for i = 1, select('#', ...) do fadd(select(i, ...)) end return ftotal() end if select(1, ...) ~= 'fsum' then -- test code local read, fadd, ftotal = io.read, fsum() io.input(select(1, ...)) -- read from file pcall(function() while true do fadd(read('*n')) end end) print(ftotal()) end return fsum