data

#!/usr/bin/env lua

local multicore_times = {
  { cores =  1, time = 136.0, half_sigma = 0.228, n_runs = 5 },
  { cores =  2, time = 83.0,  half_sigma = 0.099, n_runs = 5 },
  { cores =  4, time = 46.8,  half_sigma = 0.208, n_runs = 5 },
  { cores =  8, time =  26.9, half_sigma = 0.216, n_runs = 5 },
  { cores = 12, time =  22.5, half_sigma = 0.327, n_runs = 5 },
  { cores = 16, time =  21.0, half_sigma = 0.301, n_runs = 5 },
  { cores = 24, time =  21.9, half_sigma = 0.512, n_runs = 5 },
  { cores = 48, time =  77.5, half_sigma = 8.574, n_runs = 5 },
}

for _, t in ipairs(multicore_times) do
  t.sigma = t.sigma or 2 * t.half_sigma
end

local function ratio_variance(x, y, varx, vary)
  return varx / (y * y) + (x * x) * vary / (y * y * y * y)
    -- assume zero covariance
end



local sequential_time = 134.20
local sequential_sigma = 4.32
local sequential_n     = 5

local template = [[
newgraph
  xaxis label fontsize 10 font Times-Roman
  yaxis label fontsize 10 font Times-Roman
  xaxis no_auto_hash_labels size 3.7 $log min $xmin max $xmax label : Cores used
  yaxis size 2.1 min 0 max $ymax label : $ylabel
  newcurve $curve pts $pts
  $labels
    (* $lines *)
]]

local function fill(s, fields)
  return (s:gsub('%$(%w+)', fields))
end

local function labels()
  local l = { 'xaxis no_auto_hash_marks' }
  for _, pt in ipairs(multicore_times) do
    table.insert(l, string.format('  xaxis hash_label at %d : %d',
                                  pt.cores, pt.cores))
    table.insert(l, string.format('  xaxis hash_at %d', pt.cores))
  end
  return table.concat(l, '\n')
end

local function eff(x)
  return  1 - math.log(x)/4.5
end

local function spd(x) return x * eff(x) end

local function newline(f, lo, hi)
  local points = { 'newline pts' }
  for x=lo, hi, (hi-lo)/1000 do
    table.insert(points, string.format("%.4f %.4f", x, f(x)))
  end
  return table.concat(points, ' ')
end    


local function speedup()
  local fields = { ylabel = "Speedup", ymax = '7 hash 1 mhash 1', xmax = 50, xmin = 0,
                   labels = 'xaxis auto_hash_labels', log = '',
                   lines = newline(spd, 1.05, 50),
                   curve = '  marktype circle marksize 0.36 0.10'  }
  -- y_eps x y y-minus y_plus

  local points = "y_epts"
  local seqvar = sequential_sigma * sequential_sigma
  for _, pt in ipairs(multicore_times) do
    local ptvar = pt.sigma * pt.sigma
    local svar = ratio_variance(sequential_time, pt.time, seqvar, ptvar)
    local error = math.sqrt(svar) / math.sqrt(math.min(sequential_n, pt.n_runs)-1)
--    points = string.format("%s %d %.2f", points, pt.cores, sequential_time / pt.time)
    local ratio = sequential_time / pt.time
    points = string.format("%s %d %.2f %.2f %.2f", points, pt.cores, ratio,
                           ratio - error, ratio + error)
                  
  end
  fields.pts = points
  return fill(template, fields)
end


  
local function efficiency()
  local fields = { ylabel = "Parallel efficiency", ymax = 1.0, xmax = 48, xmin = 1,
                   log = 'log', labels = labels(),  curve = '',
                   lines = newline(eff, 1.2, 48),
                 }
  local points = ""
  for _, pt in ipairs(multicore_times) do
    points = string.format("%s %d %.2f", points, pt.cores,
                           sequential_time / (pt.time * pt.cores))
  end
  fields.pts = points
  return fill(template, fields)
end

local function set(filename, s)
  local f = io.open(filename, 'w')
  f:write(s, '\n')
  f:close()
end

set('speedup.j', speedup())
set('efficiency.j', efficiency())