diff options
| -rw-r--r-- | README.txt | 1 | ||||
| -rw-r--r-- | beanpole.lua | 4 | ||||
| -rw-r--r-- | init.lua | 385 | ||||
| -rw-r--r-- | init.lua_orig | 192 | ||||
| -rw-r--r-- | statistics.lua | 150 |
5 files changed, 696 insertions, 36 deletions
@@ -13,6 +13,7 @@ This mod works by adding your new plant to the {growing=1} group and numbering t Changelog: +1.20 - NEW growing routine added that allows crops to grow while player is away doing other things (thanks prestidigitator) 1.14 - Added Green Beans from Crops mod (thanks sofar), little bushels in the wild but need to be grown using beanpoles crafted with 4 sticks (2 either side) 1.13 - Fixed seed double-placement glitch. Mapgen now uses 0.4.12+ for plant generation 1.12 - Player cannot place seeds in protected area, also growing speeds changed to match defaults diff --git a/beanpole.lua b/beanpole.lua index 0387fa0..895b6fa 100644 --- a/beanpole.lua +++ b/beanpole.lua @@ -65,7 +65,7 @@ minetest.register_craft({ } }) --- Define Corn growth stages +-- Define Green Bean growth stages minetest.register_node("farming:beanpole_1", { drawtype = "plantlike", @@ -140,7 +140,7 @@ minetest.register_node("farming:beanpole_4", { sounds = default.node_sound_leaves_defaults(), }) --- Last stage of Corn growth doesnnot have growing=1 so abm never has to check these +-- Last stage of Green Bean growth does not have growing=1 so abm never has to check these minetest.register_node("farming:beanpole_5", { drawtype = "plantlike", @@ -1,6 +1,7 @@ --[[ - Minetest Farming Redo Mod 1.14 (11th May 2015) + Minetest Farming Redo Mod 1.20 (20th May 2015) by TenPlus1 + NEW growing routine by prestidigitator ]] farming = {} @@ -8,6 +9,39 @@ farming.mod = "redo" farming.path = minetest.get_modpath("farming") farming.hoe_on_use = default.hoe_on_use +farming.DEBUG = false +-- farming.DEBUG = {} -- Uncomment to turn on profiling code/functions + +local DEBUG_abm_runs = 0 +local DEBUG_abm_time = 0 +local DEBUG_timer_runs = 0 +local DEBUG_timer_time = 0 +if farming.DEBUG then + function farming.DEBUG.reset_times() + DEBUG_abm_runs = 0 + DEBUG_abm_time = 0 + DEBUG_timer_runs = 0 + DEBUG_timer_time = 0 + end + + function farming.DEBUG.report_times() + local abm_n = DEBUG_abm_runs + local abm_dt = DEBUG_abm_time + local abm_avg = (abm_n > 0 and abm_dt / abm_n) or 0 + local timer_n = DEBUG_timer_runs + local timer_dt = DEBUG_timer_time + local timer_avg = (timer_n > 0 and timer_dt / timer_n) or 0 + local dt = abm_dt + timer_dt + print("ABM ran for "..abm_dt.."µs over "..abm_n.." runs: ".. + abm_avg.."µs/run") + print("Timer ran for "..timer_dt.."µs over "..timer_n.." runs: ".. + timer_avg.."µs/run") + print("Total farming time: "..dt.."µs") + end +else +end + +local statistics = dofile(farming.path.."/statistics.lua") dofile(farming.path.."/soil.lua") dofile(farming.path.."/hoes.lua") dofile(farming.path.."/grass.lua") @@ -31,6 +65,319 @@ dofile(farming.path.."/donut.lua") dofile(farming.path.."/mapgen.lua") dofile(farming.path.."/compatibility.lua") -- Farming Plus compatibility +-- Utility Functions + +local time_speed = tonumber(minetest.setting_get("time_speed")) or 72 +local SECS_PER_CYCLE = (time_speed > 0 and 24 * 60 * 60/time_speed) or nil + +local function clamp(x, min, max) + return (x < min and min) or (x > max and max) or x +end + +local function in_range(x, min, max) + return min <= x and x <= max +end + +--- Tests the amount of day or night time between two times. + -- + -- @param t_game + -- The current time, as reported by mintest.get_gametime(). + -- @param t_day + -- The current time, as reported by mintest.get_timeofday(). + -- @param dt + -- The amount of elapsed time. + -- @param count_day + -- If true, count elapsed day time. Otherwise, count elapsed night time. + -- @return + -- The amount of day or night time that has elapsed. + -- +local function day_or_night_time(t_game, t_day, dt, count_day) + local t1_day = t_day - dt / SECS_PER_CYCLE + + local t1_c, t2_c -- t1_c < t2_c and t2_c always in [0, 1) + if count_day then + if t_day < 0.25 then + t1_c = t1_day + 0.75 -- Relative to sunup, yesterday + t2_c = t_day + 0.75 + else + t1_c = t1_day - 0.25 -- Relative to sunup, today + t2_c = t_day - 0.25 + end + else + if t_day < 0.75 then + t1_c = t1_day + 0.25 -- Relative to sundown, yesterday + t2_c = t_day + 0.25 + else + t1_c = t1_day - 0.75 -- Relative to sundown, today + t2_c = t_day - 0.75 + end + end + + local dt_c = clamp(t2_c, 0, 0.5) - clamp(t1_c, 0, 0.5) -- this cycle + if t1_c < -0.5 then + local nc = math.floor(-t1_c) + t1_c = t1_c + nc + dt_c = dt_c + 0.5 * nc + clamp(-t1_c - 0.5, 0, 0.5) + end + + return dt_c * SECS_PER_CYCLE +end + +--- Tests the amount of elapsed day time. + -- + -- @param dt + -- The amount of elapsed time. + -- @return + -- The amount of day time that has elapsed. + -- +local function day_time(dt) + return day_or_night_time(minetest.get_gametime(), minetest.get_timeofday(), dt, true) +end + +--- Tests the amount of elapsed night time. + -- + -- @param dt + -- The amount of elapsed time. + -- @return + -- The amount of night time that has elapsed. + -- +local function night_time(time_game, time_day, dt, count_day) + return day_or_night_time(minetest.get_gametime(), minetest.get_timeofday(), dt, false) +end + + +-- Growth Logic + +local STAGE_LENGTH_AVG = 160.0 +local STAGE_LENGTH_DEV = STAGE_LENGTH_AVG / 6 +local MIN_LIGHT = 13 +local MAX_LIGHT = 1000 + +--- Determines plant name and stage from node. + -- + -- Separates node name on the last underscore (_). + -- + -- @param node + -- Node or position table, or node name. + -- @return + -- List (plant_name, stage), or nothing (nil) if node isn't loaded + -- +local function plant_name_stage(node) + local name + if type(node) == 'table' then + if node.name then + name = node.name + elseif node.x and node.y and node.z then + node = minetest.get_node_or_nil(node) + name = node and node.name + end + else + name = tostring(node) + end + if not name or name == "ignore" then return nil end + + local sep_pos = name:find("_[^_]+$") + if sep_pos and sep_pos > 1 then + local stage = tonumber(name:sub(sep_pos + 1)) + if stage and stage >= 0 then + return name:sub(1, sep_pos - 1), stage + end + end + + return name, 0 +end + +--- Map from node name to + -- { plant_name = ..., name = ..., stage = n, stages_left = { node_name, ... } } +local plant_stages = {} +farming.plant_stages = plant_stages + +--- Registers the stages of growth of a (possible plant) node. + -- + -- @param node + -- Node or position table, or node name. + -- @return + -- The (possibly zero) number of stages of growth the plant will go through + -- before being fully grown, or nil if not a plant. + -- +local register_plant_node +-- Recursive helper +local function reg_plant_stages(plant_name, stage, force_last) + local node_name = plant_name and plant_name .. "_" .. stage + local node_def = node_name and minetest.registered_nodes[node_name] + if not node_def then return nil end + + local stages = plant_stages[node_name] + if stages then return stages end + + if minetest.get_item_group(node_name, "growing") > 0 then + local ns = reg_plant_stages(plant_name, stage + 1, true) + + local stages_left = (ns and { ns.name, unpack(ns.stages_left) }) or {} + stages = { plant_name = plant_name, name = node_name, stage = stage, stages_left = stages_left } + + if #stages_left > 0 then + local old_constr = node_def.on_construct + local old_destr = node_def.on_destruct + minetest.override_item(node_name, + { + on_construct = function(pos) + if old_constr then old_constr(pos) end + farming.handle_growth(pos) + end, + + on_destruct = function(pos) + minetest.get_node_timer(pos):stop() + if old_destr then old_destr(pos) end + end, + + on_timer = function(pos, elapsed) + return farming.plant_growth_timer(pos, elapsed, node_name) + end, + }) + end + elseif force_last then + stages = { plant_name = plant_name, name = node_name, stage = stage, stages_left = {} } + else + return nil + end + + plant_stages[node_name] = stages + return stages +end + +register_plant_node = function(node) + local plant_name, stage = plant_name_stage(node) + if plant_name then + local stages = reg_plant_stages(plant_name, stage, false) + return stages and #stages.stages_left + else + return nil + end +end + +local function set_growing(pos, stages_left) + if not stages_left then return end + + local timer = minetest.get_node_timer(pos) + if stages_left > 0 then + if not timer:is_started() then + local stage_length = statistics.normal(STAGE_LENGTH_AVG, STAGE_LENGTH_DEV) + stage_length = clamp(stage_length, 0.5 * STAGE_LENGTH_AVG, 3.0 * STAGE_LENGTH_AVG) + timer:set(stage_length, -0.5 * math.random() * STAGE_LENGTH_AVG) + end + elseif timer:is_started() then + timer:stop() + end +end + +--- Detects a plant type node at the given position, starting or stopping the plant growth timer as appopriate + -- + -- @param pos + -- The node's position. + -- @param node + -- The cached node table if available, or nil. + -- +function farming.handle_growth(pos, node) + if not pos then return end + local stages_left = register_plant_node(node or pos) + if stages_left then set_growing(pos, stages_left) end +end + +minetest.after(0, + function() + for _, node_def in pairs(minetest.registered_nodes) do + register_plant_node(node_def) + end + end) + +local abm_func = farming.handle_growth +if farming.DEBUG then + local normal_abm_func = abm_func + abm_func = function(...) + local t0 = minetest.get_us_time() + local r = { normal_abm_func(...) } + local t1 = minetest.get_us_time() + DEBUG_abm_runs = DEBUG_abm_runs + 1 + DEBUG_abm_time = DEBUG_abm_time + (t1 - t0) + return unpack(r) + end +end + +-- Just in case a growing type or added node is missed (also catches existing +-- nodes added to map before timers were incorporated). +minetest.register_abm({ + nodenames = { "group:growing" }, + interval = 300, + chance = 1, + action = abm_func}) + +--- Plant timer function. + -- + -- Grows plants under the right conditions. + -- +function farming.plant_growth_timer(pos, elapsed, node_name) + local stages = plant_stages[node_name] + if not stages then return false end + + local max_growth = #stages.stages_left + if max_growth <= 0 then return false end + + if stages.plant_name == "farming:cocoa" then + if not minetest.find_node_near(pos, 1, { "default:jungletree", "moretrees:jungletree_leaves_green" }) then + return true + end + else + local under = minetest.get_node_or_nil({ x = pos.x, y = pos.y - 1, z = pos.z }) + if not under or under.name ~= "farming:soil_wet" then return true end + end + + local growth + + local light_pos = { x = pos.x, y = pos.y + 1, z = pos.z } + local lambda = elapsed / STAGE_LENGTH_AVG + if lambda < 0.1 then return true end + if max_growth == 1 or lambda < 2.0 then + local light = minetest.get_node_light(light_pos) + if not in_range(light, MIN_LIGHT, MAX_LIGHT) then return true end + growth = 1 + else + local night_light = minetest.get_node_light(light_pos, 0) + local day_light = minetest.get_node_light(light_pos, 0.5) + local night_growth = in_range(night_light, MIN_LIGHT, MAX_LIGHT) + local day_growth = in_range(day_light, MIN_LIGHT, MAX_LIGHT) + + if not night_growth then + if not day_growth then return true end + lambda = day_time(elapsed) / STAGE_LENGTH_AVG + elseif not day_growth then + lambda = night_time(elapsed) / STAGE_LENGTH_AVG + end + + growth = statistics.poisson(lambda, max_growth) + if growth < 1 then return true end + end + + minetest.swap_node(pos, { name = stages.stages_left[growth] }) + + return growth ~= max_growth +end + +if farming.DEBUG then + local timer_func = farming.plant_growth_timer; + farming.plant_growth_timer = function(pos, elapsed, node_name) + local t0 = minetest.get_us_time() + + local r = { timer_func(pos, elapsed, node_name) } + + local t1 = minetest.get_us_time() + DEBUG_timer_runs = DEBUG_timer_runs + 1 + DEBUG_timer_time = DEBUG_timer_time + (t1 - t0) + return unpack(r) + end +end + + -- Place Seeds on Soil function farming.place_seed(itemstack, placer, pointed_thing, plantname) @@ -72,38 +419,6 @@ function farming.place_seed(itemstack, placer, pointed_thing, plantname) end end --- Single ABM Handles Growing of All Plants - -minetest.register_abm({ - nodenames = {"group:growing"}, - neighbors = {"farming:soil_wet", "default:jungletree"}, - interval = 80, - chance = 2, - - action = function(pos, node) - - -- split plant name (e.g. farming:wheat_1) - local plant = node.name:split("_")[1].."_" - local numb = node.name:split("_")[2] - - -- fully grown ? - if not minetest.registered_nodes[plant..(numb + 1)] then return end - - -- cocoa pod on jungle tree ? - if plant ~= "farming:cocoa_" then - - -- growing on wet soil ? - if minetest.get_node({x=pos.x,y=pos.y-1,z=pos.z}).name ~= "farming:soil_wet" then return end - end - - -- enough light ? - if minetest.get_node_light(pos) < 13 then return end - - -- grow - minetest.set_node(pos, {name=plant..(numb + 1)}) - - end -}) -- Function to register plants (for compatibility) @@ -163,7 +478,8 @@ farming.register_plant = function(name, def) g = {snappy = 3, flammable = 2, plant = 1, not_in_creative_inventory = 1, attached_node = 1} end - minetest.register_node(mname .. ":" .. pname .. "_" .. i, { + local node_name = mname .. ":" .. pname .. "_" .. i + minetest.register_node(node_name, { drawtype = "plantlike", waving = 1, tiles = {mname .. "_" .. pname .. "_" .. i .. ".png"}, @@ -176,6 +492,7 @@ farming.register_plant = function(name, def) groups = g, sounds = default.node_sound_leaves_defaults(), }) + register_plant_node(node_name) end -- Return info diff --git a/init.lua_orig b/init.lua_orig new file mode 100644 index 0000000..aee9976 --- /dev/null +++ b/init.lua_orig @@ -0,0 +1,192 @@ +--[[ + Minetest Farming Redo Mod 1.14 (11th May 2015) + by TenPlus1 +]] + +farming = {} +farming.mod = "redo" +farming.path = minetest.get_modpath("farming") +farming.hoe_on_use = default.hoe_on_use + +dofile(farming.path.."/soil.lua") +dofile(farming.path.."/hoes.lua") +dofile(farming.path.."/grass.lua") +dofile(farming.path.."/wheat.lua") +dofile(farming.path.."/cotton.lua") +dofile(farming.path.."/carrot.lua") +dofile(farming.path.."/potato.lua") +dofile(farming.path.."/tomato.lua") +dofile(farming.path.."/cucumber.lua") +dofile(farming.path.."/corn.lua") +dofile(farming.path.."/coffee.lua") +dofile(farming.path.."/melon.lua") +dofile(farming.path.."/sugar.lua") +dofile(farming.path.."/pumpkin.lua") +dofile(farming.path.."/cocoa.lua") +dofile(farming.path.."/raspberry.lua") +dofile(farming.path.."/blueberry.lua") +dofile(farming.path.."/rhubarb.lua") +dofile(farming.path.."/beanpole.lua") +dofile(farming.path.."/donut.lua") +dofile(farming.path.."/mapgen.lua") +dofile(farming.path.."/compatibility.lua") -- Farming Plus compatibility + +-- Place Seeds on Soil + +function farming.place_seed(itemstack, placer, pointed_thing, plantname) + local pt = pointed_thing + + -- check if pointing at a node + if not pt and pt.type ~= "node" then + return + end + + local under = minetest.get_node(pt.under) + local above = minetest.get_node(pt.above) + + -- check if pointing at the top of the node + if pt.above.y ~= pt.under.y+1 then + return + end + + -- return if any of the nodes is not registered + if not minetest.registered_nodes[under.name] + or not minetest.registered_nodes[above.name] then + return + end + + -- can I replace above node, and am I pointing at soil + if not minetest.registered_nodes[above.name].buildable_to + or minetest.get_item_group(under.name, "soil") < 2 + or minetest.get_item_group(above.name, "plant") ~= 0 then -- ADDED this line for multiple seed placement bug + return + end + + -- add the node and remove 1 item from the itemstack + if not minetest.is_protected(pt.above, placer:get_player_name()) then + minetest.add_node(pt.above, {name=plantname}) + if not minetest.setting_getbool("creative_mode") then + itemstack:take_item() + end + return itemstack + end +end + +-- Single ABM Handles Growing of All Plants + +minetest.register_abm({ + nodenames = {"group:growing"}, + neighbors = {"farming:soil_wet", "default:jungletree"}, + interval = 80, + chance = 2, + + action = function(pos, node) + + -- split plant name (e.g. farming:wheat_1) + local plant = node.name:split("_")[1].."_" + local numb = node.name:split("_")[2] + + -- fully grown ? + if not minetest.registered_nodes[plant..(numb + 1)] then return end + + -- cocoa pod on jungle tree ? + if plant ~= "farming:cocoa_" then + + -- growing on wet soil ? + if minetest.get_node({x=pos.x,y=pos.y-1,z=pos.z}).name ~= "farming:soil_wet" then return end + end + + -- enough light ? + if minetest.get_node_light(pos) < 13 then return end + + -- grow + minetest.set_node(pos, {name=plant..(numb + 1)}) + + end +}) + +-- Function to register plants (for compatibility) + +farming.register_plant = function(name, def) + local mname = name:split(":")[1] + local pname = name:split(":")[2] + + -- Check def table + if not def.description then + def.description = "Seed" + end + if not def.inventory_image then + def.inventory_image = "unknown_item.png" + end + if not def.steps then + return nil + end + + -- Register seed + minetest.register_node(":" .. mname .. ":seed_" .. pname, { + description = def.description, + tiles = {def.inventory_image}, + inventory_image = def.inventory_image, + wield_image = def.inventory_image, + drawtype = "signlike", + groups = {seed = 1, snappy = 3, attached_node = 1}, + paramtype = "light", + paramtype2 = "wallmounted", + walkable = false, + sunlight_propagates = true, + selection_box = {type = "fixed", fixed = {-0.5, -0.5, -0.5, 0.5, -5/16, 0.5},}, + on_place = function(itemstack, placer, pointed_thing) + return farming.place_seed(itemstack, placer, pointed_thing, mname .. ":"..pname.."_1") + end + }) + + -- Register harvest + minetest.register_craftitem(":" .. mname .. ":" .. pname, { + description = pname:gsub("^%l", string.upper), + inventory_image = mname .. "_" .. pname .. ".png", + }) + + -- Register growing steps + for i=1,def.steps do + local drop = { + items = { + {items = {mname .. ":" .. pname}, rarity = 9 - i}, + {items = {mname .. ":" .. pname}, rarity= 18 - i * 2}, + {items = {mname .. ":seed_" .. pname}, rarity = 9 - i}, + {items = {mname .. ":seed_" .. pname}, rarity = 18 - i * 2}, + } + } + + local g = {snappy = 3, flammable = 2, plant = 1, not_in_creative_inventory = 1, attached_node = 1, growing = 1} + -- Last step doesn't need growing=1 so Abm never has to check these + if i == def.steps then + g = {snappy = 3, flammable = 2, plant = 1, not_in_creative_inventory = 1, attached_node = 1} + end + + minetest.register_node(mname .. ":" .. pname .. "_" .. i, { + drawtype = "plantlike", + waving = 1, + tiles = {mname .. "_" .. pname .. "_" .. i .. ".png"}, + paramtype = "light", + walkable = false, + buildable_to = true, + is_ground_content = true, + drop = drop, + selection_box = {type = "fixed", fixed = {-0.5, -0.5, -0.5, 0.5, -5/16, 0.5},}, + groups = g, + sounds = default.node_sound_leaves_defaults(), + }) + end + + -- Return info + local r = {seed = mname .. ":seed_" .. pname, harvest = mname .. ":" .. pname} + return r +end + +--[[ Cotton (example, is already registered in cotton.lua) +farming.register_plant("farming:cotton", { + description = "Cotton seed", + inventory_image = "farming_cotton_seed.png", + steps = 8, +}) +--]] diff --git a/statistics.lua b/statistics.lua new file mode 100644 index 0000000..aaa4f51 --- /dev/null +++ b/statistics.lua @@ -0,0 +1,150 @@ +local statistics = {} + +local ROOT_2 = math.sqrt(2.0) + +-- Approximations for erf(x) and erfInv(x) from +-- https://en.wikipedia.org/wiki/Error_function +local erf +local erf_inv + +local A = 8 * (math.pi - 3.0)/(3.0 * math.pi * (4.0 - math.pi)) +local B = 4.0 / math.pi +local C = 2.0/(math.pi * A) +local D = 1.0 / A + +erf = function(x) + if x == 0 then return 0; end + local xSq = x * x + local aXSq = A * xSq + local v = math.sqrt(1.0 - math.exp(-xSq * (B + aXSq)/(1.0 + aXSq))) + return (x > 0 and v) or -v +end + +erf_inv = function(x) + if x == 0 then return 0; end + if x <= -1 or x >= 1 then return nil; end + local y = math.log(1 - x * x) + local u = C + 0.5 * y + local v = math.sqrt(math.sqrt(u * u - D * y) - u) + return (x > 0 and v) or -v +end + +local function std_normal(u) + return ROOT_2 * erf_inv(2.0 * u - 1.0) +end + +local poisson +local cdf_table = {} + +local function generate_cdf(lambda_index, lambda) + local max = math.ceil(4 * lambda) + local pdf = math.exp(-lambda) + local cdf = pdf + local t = { [0] = pdf } + + for i = 1, max - 1 do + pdf = pdf * lambda / i + cdf = cdf + pdf + t[i] = cdf + end + + return t +end + +for li = 1, 100 do + cdf_table[li] = generate_cdf(li, 0.25 * li) +end + +poisson = function(lambda, max) + if max < 2 then + return (math.random() < math.exp(-lambda) and 0) or 1 + elseif lambda >= 2 * max then + return max + end + + local u = math.random() + local lambda_index = math.floor(4 * lambda + 0.5) + local cdfs = cdf_table[lambda_index] + + if cdfs then + lambda = 0.25 * lambda_index + + if u < cdfs[0] then return 0; end + if max > #cdfs then max = #cdfs + 1 else max = math.floor(max); end + if u >= cdfs[max - 1] then return max; end + + if max > 4 then -- Binary search + local s = 0 + while s + 1 < max do + local m = math.floor(0.5 * (s + max)) + if u < cdfs[m] then max = m; else s = m; end + end + else + for i = 1, max - 1 do + if u < cdfs[i] then return i; end + end + end + + return max + else + local x = lambda + math.sqrt(lambda) * std_normal(u) + return (x < 0.5 and 0) or (x >= max - 0.5 and max) or math.floor(x + 0.5) + end +end + +-- Error function. +statistics.erf = erf + +-- Inverse error function. +statistics.erf_inv = erf_inv + +--- Standard normal distribution function (mean 0, standard deviation 1). + -- + -- @return + -- Any real number (actually between -3.0 and 3.0). + -- +statistics.std_normal = function() + local u = math.random() + if u < 0.001 then + return -3.0 + elseif u > 0.999 then + return 3.0 + end + return std_normal(u) +end + +--- Standard normal distribution function (mean 0, standard deviation 1). + -- + -- @param mu + -- The distribution mean. + -- @param sigma + -- The distribution standard deviation. + -- @return + -- Any real number (actually between -3*sigma and 3*sigma). + -- +statistics.normal = function(mu, sigma) + local u = math.random() + if u < 0.001 then + return mu - 3.0 * sigma + elseif u > 0.999 then + return mu + 3.0 * sigma + end + return mu + sigma * std_normal(u) +end + +--- Poisson distribution function. + -- + -- @param lambda + -- The distribution mean and variance. + -- @param max + -- The distribution maximum. + -- @return + -- An integer between 0 and max (both inclusive). + -- +statistics.poisson = function(lambda, max) + lambda, max = tonumber(lambda), tonumber(max) + if not lambda or not max or lambda <= 0 or max < 1 then return 0; end + return poisson(lambda, max) +end + +return statistics |