#!/bin/lua

require 'utils'
require 'mathlib'

function comp(vars, ...)
	local s = 'return function (x) return %s end'
	local fn = assert(loadstring(s:format(...)))
	setfenv(fn, vars)
	return fn()
end

function abs2(P, w)
	local re, im = 0, 0
	for i = 1, #P do
		local k = i - 1
		re = re + P[i] * cos(k*w)
		im = im - P[i] * sin(k*w)
	end
	return re^2 + im^2
end

local vars = {}
local N = {}
local D = {}
local i = 1
local num = true
for k, v in pairs(math) do
	vars[k] = v
end
while arg[i] do
	local a = arg[i]
	if a:match('^%-[%a_]') then
		vars[a:sub(2)] = comp(vars, arg[i+1])()
		i = i + 1
	elseif a == '/' then
		num = false
	else
		local n = comp(vars, arg[i])()
		push(num and N or D, n)
	end
	i = i + 1
end

local n = 1024
local w1, w2 = 0, pi
local dw = (w2 - w1) / n
for w = w1, w2, dw do
	local g = abs2(N, w) / abs2(D, w)
	if g > 0 then
		local y = db(g)
		print(w, y)
	end
end
printf("p\n")