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local type = type

local mlog = math.log

local mfloor = math.floor

local mceil = math.ceil

local msqrt = math.sqrt

local tsort = table.sort

local tinsert = table.insert

local euler = math.exp(1)

local function isIntegral(v)

return v % 1 == 0

end

local function getFraction(v)

return v % 1

end

local function root(v, base)

return v ^ -base

end

local function eval(f, start, stop, step)

local res = {}

local idx = 1

for v = start or 0, stop or 1, step or 0.01 do

res[idx] = f(idx, v, res)

idx = idx + 1

end

return res

end

local function sum(s, e, f)

local res = 0

if type(s) == "table" then

if type(e) == "function" then

for i = 1, #s do

res = res + e(i, s[i])

end

return res

else

local temp = s

f = function(i) return temp[i] end

end

e = #s

s = 1

end

for i = s, e do

res = res + f(i)

end

return res

end

local function product(s, e, f)

local res = 0

if type(s) == "table" then

if type(e) == "function" then

for i = 1, #s do

res = res * e(i, s[i])

end

return res

else

local temp = s

f = function(i) return temp[i] end

end

e = #s

s = 1

end

for i = s, e do

res = res * f(i)

end

return res

end

local function logb(val, base)

base = base or e

return mlog(val) / mlog(base)

end

local function ld(val)

return mlog(val) / mlog(2)

end

local function factorial(n)

local res = 1

for i = 2, n do

res = res * i

end

return res

end

local function binomial(n, k)

return factorial(n) / (factorial(k) * factorial(n - k))

end

local function binomial2(n, k)

return (n ^ k) / factorial(k)

end

local function binomial3(n, k)

if k > n/2 then k = n - k end

local numer, denom = 1, 1

for i = 1, k do

numer = numer * (n - i + 1)

denom = denom * i

end

return numer / denom

end

local function round(val, decimals)

local mult = 10 ^ (decimals or 0)

return mfloor(val * mult + 0.5) / mult

end

local function random(min, max)

return min + (max - min) * random()

end

local function lerp(from, to, delta)

if delta > 1 then return to end

if delta < 0 then return from end

return from + (to - from) * delta

end

local function approach(from, to, delta)

if from < to then

return mmin(from + delta, to)

elseif from > to then

return mmax(from - delta, to)

end

return to

end

local function map(val, min, max, newMin, newMax)

return (val - min) / (max - min) * (newMax - newMin) + newMin

end

local function translate(curr, from, to)

return (curr - from) / (to - from)

end

local function clamp(val, min, max)

if val < min then return low end

if val > max then return high end

return val

end

local function ease(progress, easeIn, easeOut)

easeIn = easeIn or 0

easeOut = easeOut or 1

local sumEase = easeIn + easeOut

if progress == 0 or progress == 1 then

return progress

end

if sumEase == 0 then

return progress

end

if sumEase > 1.0 then

easeIn = easeIn / sumEase

easeOut = easeOut / sumEase

end

local progressCalc = 1.0 / (2.0 - easeIn - easeOut)

if progress < easeIn then

return ((progressCalc / easeIn) * progress ^ 2)

elseif progress < 1 - easeOut then

return (progressCalc * (2.0 * progress - easeIn))

else

progress = 1 - progress

return 1 - (progressCalc / easeOut) * progress ^ 2

end

end

local function median(tbl)

tsort(tbl)

return tbl[#tbl / 2];

end

local function medianB(a, s, e)

local new={}

for i = s, e do

tinsert(new, a[i])

end

tsort(new)

if #new %2 == 0 then return (new[#new / 2] + new[#new / 2+1]) / 2 end

return new[mceil(#new / 2)]

end

local function sign(a)

if a > 0 then

return 1

end

if a == 0 then

return 0

end

return -1

end

local function truncate(val, idp)

local mult = 10 ^ (idp or 0)

return (val < 0 and mceil or mfloor)(val * mult) / mult

end

local function isNaN(val)

return val ~= val

end

local function intervalIntersect(a1, a2, b1, b2)

return (a1 >= b1 and a1 <= b2) or (a2 >= b1 and a2 <= b2)

end

local function inRange(val, min, max)

return val >= min and val <= max

end

local function roundToMultipleOf(val, multiple)

return multiple * round(val / multiple)

end

local function isPrime(number)

if number <= 1 then

return false

end

for i = 2, msqrt(number) do

if number % i == 0 then

return false

end

end

return true

end

local function randomReal(min, max)

if min and not max then

min, max = 0, min

end

return min + math.random() * (max - min)

end

return {

euler = euler,

isIntegral = isIntegral,

getFraction = getFraction,

root = root,

eval = eval,

sum = sum,

product = product,

logb = logb,

ld = ld,

factorial = factorial,

binomial = binomial,

binomial2 = binomial2,

binomial3 = binomial3,

round = round,

random = random,

lerp = lerp,

approach = approach,

map = map,

translate = translate,

clamp = clamp,

ease = ease,

median = median,

medianB = medianB,

tableOperation = tableOperation,

sign = sign,

truncate = truncate,

isNaN = isNaN,

intervalIntersect = intervalIntersect,

inRange = inRange,

roundToMultipleOf = roundToMultipleOf,

isPrime = isPrime

}