-- fraction library
-- f1/lua is the usage example

local num=require("num")
local gcd=num.gcd

local Fr = {}
local mt =  {}

local function setmt(t,mt)
	-- set meta-table
	if mt then
		t.mt = mt
		setmetatable(t,mt)
	else
		if t.mt then
			setmetatable(t,t.mt)
		end
	end
end

local function dup(t)
	-- create new table from t
	local tn
	tn = {}
	for k,v in pairs(t) do
		if type(v)=="table" then
			tn[k] = dup(v)
			setmt(tn[k])
		else
			tn[k] = v
		end
	end
	return tn
end

function Fr.tostring(x) -- function in Fr
	if x[1]==0 then
		return "0"
	end
	if x[2] < 0 then
		x[1],x[2] = -x[1], -x[2]
	end
	if x[2]==1 then
		return fmt("%d",x[1])
	end
	return fmt("%d/%d",x[1],x[2])
end
mt.__tostring = Fr.tostring


function Fr.new(a,b) -- function in Fr
	if b==nil then b=1 end
	local f={a,b}
	setmt(f,mt)
	return f
end

local function fix(x)
	if type(x)=="number" then
		return {x,1}
	end
	return x
end

local function fr_add(x,y)
	if type(x)=="number" then
		x = {x,1}
	end
	if type(y)=="number" then
		y = {y,1}
	end
	local a,b,z
	a = x[1]*y[2] + x[2]*y[1]
	b = x[2]*y[2]
	c = gcd(a,b)
	z = {a//c,b//c}
	setmt(z,mt)
	return z
end
mt.__add = fr_add

local function fr_neg(x)
	local z={}
	if type(x)=="number" then
		z[1] = -x
		z[2] = 1
	else
		z[1] = -x[1]
		z[2] = x[2]
	end
	setmt(z,mt)
	return z
end
mt.__unm = fr_neg

local function fr_sub(x,y)
	local z = fr_neg(y)
	setmt(z,mt)
	return fr_add(x,z)
end
mt.__sub = fr_sub

local function fr_mul(x,y)
	if type(x)=="number" then
		x = {x,1}
	end
	if type(y)=="number" then
		y = {y,1}
	end
	local a,b,z
	a = x[1]*y[1]
	b = x[2]*y[2]
	c = gcd(a,b)
	z = {a//c,b//c}
	setmt(z,mt)
	return z
end
mt.__mul = fr_mul

local function fr_inv(x)
	if type(x)=="number" then
		return {1,x}
	end
	return {x[2],x[1]}
end

local function fr_div(x,y)
	return fr_mul(x, fr_inv(y))
end
mt.__div = fr_div -- Lua has no __inv

local function fr_abs(x)
	local t = {abs(x[1]),abs(x[2])}
	setmt(t,mt)
	return t
end

local function fr_eq(x,y)
	if type(x)=="number" then
		x = {x,1}
	end
	if type(y)=="number" then
		y = {y,1}
	end
	return x[1]*y[2]==x[2]*y[1]
end
mt.__eq = fr_eq

local function fr_lt(x,y)
	if x == 0 then
		return y[1]*y[2] > 0
	end
	if y == 0 then
		return x[1]*x[2] < 0
	end
	if type(x)=="number" then
		x = {x,1}
	end
	if type(y)=="number" then
		y = {y,1}
	end
	return x[1]*y[2]-x[2]*y[1] < 0
end
mt.__lt = fr_lt

local function fr_le(x,y)
	if x == 0 then
		return y[1]*y[2] >= 0
	end
	if y == 0 then
		return x[1]*x[2] <= 0
	end
	if type(x)=="number" then
		x = {x,1}
	end
	if type(y)=="number" then
		y = {y,1}
	end
	return x[1]*y[2]-x[2]*y[1] <= 0
end
mt.__le = fr_le

return {
Fr=Fr,
mt=mt,
setmt=setmt,
dup=dup,
fr_abs=fr_abs,
}