#!/bin/lua

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

require 'utils'
require 'mathlib'

function sinc(t, H2)
	local ph = fmod(t, 1)
	local eps = 0.000001
	
	if ph < eps or ph > (1 - eps) then
		return H2*cos(H2*pi*t)/cos(pi*t)
	else
		return sin(H2*pi*t)/sin(pi*t)
	end
end

function evf(t1, t2, n, fn, c)
	local dt = (t2 - t1) / n
	local u = 0
	local c = c or 0
	for t = t1, t2, dt do
		u = fn(t)
		print(t, u+c)
	end
end

function int(t1, t2, n, fn, c)
	local dt = (t2 - t1) / n
	local u = 0
	local c = c or 0
	for t = t1, t2, dt do
		print(t, u+c)
		u = u + (fn(t) + fn(t+dt)) * dt / 2
	end
	return u
end

-- dvojny integral pres ten samy interval
function intint(t1, t2, n, fn, c)
	local dt = (t2 - t1) / n
	local dx = dt
	local u = 0
	local y = 0
	local u1 = 0
	local c = c or 0
	for t = t1, t2, dt do
		print(t, y+c)
		u1 = u
		u = u + (fn(t) + fn(t+dt)) * dt / 2
		y = y + (u1 + u) * dt / 2
--[[
		y = y 
		u = u + (fn(t) + 2*fn(t+dt) + fn(t+2*dt)) * dt / 2
]]
	end
	return y
end

function impulse(N)
	return function(t)
		return sinc(t, 2*N+1)
	end
end

function square(N, pwm)
	pwm = pwm or 0.5
	return function(t)
		return sinc(t, 2*N+1) - sinc(t+pwm, 2*N+1)
	end
end

function morph(N, swsq)
	swsq = swsq or 0.5
	return function(t)
		return sinc(t, 2*N+1) - swsq * sinc(t+0.5, 2*N+1) - 1 + swsq
	end
end

function saw(N)
	return function(t)
		return sinc(t, 2*N+1) - 1
	end
end

function supersaw(N, pwm)
	return function(t)
		return sinc(t+pwm, 2*N+1) - 1
		--return sinc(t, 2*N+1) - 1 + sinc(t+pwm, 2*N+1) - 1
	end
end

--intint(0, 4, 1024, square(32));
--int(0, 4, 4096, saw(64), 0)
int(0, 2, 4096, supersaw(64, 0.5), 0)