#!/bin/lua

function note(...)
	io.stderr:write(string.format(...))
end

require 'utils'
require 'mathlib'

function testsum(T, f, H)
	local s = 0
	for t = 0, T-1 do
		for h = 1, H do
			local w = 2*pi*t*f/T
			s = s + cos(w*h)
		end
	end
	return s/H
end

function intsum(T, f, H)
	local s = 0
	local intu = 0
	local intt = 0
	local du = 1/T
	local dt = 1/T
	for t = 0, 1, du do
		local s = 0
		local w = 2*pi*t*f
		for h = 1, H do
			s = s + cos(w*h)
		end
		print(t, s)
		intu = intu + s * du
		intt = intt + intu * du
	end
	note("%f %f\n", intu, intt)
end

function testdfs(T, f, H, off)
	local s = 0
	off = off or 0
	for t = 0, T-1 do
		local w = f*(t/T + off)
		if fmod(w, 1) < 0.000001 or fmod(w, 1) > 0.999999 then
			s = s + (2*H+1)*cos((2*H+1)*pi*w)/cos(pi*w) - 1
		else
			s = s + sin((2*H+1)*pi*w)/sin(pi*w) - 1
		end
	end
	return s/2/H
end

function intdfs(T, f, H)
	local s = 0
	local intu = 0
	local intt = 0
	local du = 1/T
	local dt = 1/T
	for t = 0, 1, du do
		local s = 0
		local w = t*f
		if fmod(w, 1) < 0.000001 or fmod(w, 1) > 0.999999 then
			s = s + (2*H+1)*cos((2*H+1)*pi*w)/cos(pi*w)
		else
			s = s + sin((2*H+1)*pi*w)/sin(pi*w)
		end
		s = (s - 1)/2
		intu = intu + s * du
		intt = intt + intu * du
		print(t, intt)
	end
	note("%f %f\n", intu, intt)
end

local T = 44100			-- sampling interval
local f = tonumber(arg[1])	-- base frequency
local H = tonumber(arg[2]) or floor(T/2/f)	-- number of harmonics

--s2 = testdfs(T, f, H)
--print(s2)
--s1 = testsum(T, f, H)
--print(s1, s2)
intdfs(T, f, H)
print('"dfs"')
--intsum(T, f, H)
--print('"sum"')