# Float Sum

Accurate floating point summation. Like Python's fsum. Below is listings of fsum.lua:

For an even faster version, see FloatSumFast

For 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
> 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 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 = y - (hi - x)
x = hi
if lo ~= 0 then p[i] = lo; i = i + 1 end
end
if x - x ~= 0 then i = 2 end    -- Inf or NaN
p[1] = i
p[i] = x
end
local function ftotal(clear)
local p, x = p, 0
if clear then p[1] = 1 end      -- ftotal(0) "clear" calculator
for i = p[1], 2, -1 do          -- sum in reverse
local y = p[i]
local hi = x + y
local lo = y - (hi - x)
x = hi
if lo ~= 0 and i ~= 2 then  -- check half way case
if (lo < 0) == (p[i-1] < 0) then
lo = lo * 2         -- |lo| = 1/2 ULP
hi = x + lo         -- -> x off 1 ULP
if lo == hi - x then x = hi end
end
return x
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