--[[ Test Complex Number Rectangular Coordinates Module
     H. Conrad Cunningham, Professor
     Computer and Information Science
     University of Mississippi

Developed for CSci 658, Software Language Engineering, Fall 2013

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2013-09-20: Translated SICP Scheme code to Lua draft
2013-09-21: Prototyped complex number modules
2013-09-22: Added require of utilities module

--]]

-- INITIALIZATION

-- Load complex number utilities module
local util = require "complexUtilities"

-- local definitions for convenience
local square    = util.square
local show_data = util.show_data

-- Load complex number module
local cn = require "complexRectangular"

-- local definitions for convenience
local make_from_real_imag = cn.make_from_real_imag
local make_from_mag_ang   = cn.make_from_mag_ang 
local real_part           = cn.real_part
local imag_part           = cn.imag_part
local magnitude           = cn.magnitude
local angle               = cn.angle
local add_complex         = cn.add_complex
local sub_complex         = cn.sub_complex
local mul_complex         = cn.mul_complex
local div_complex         = cn.div_complex
local to_string           = cn.to_string


-- TESTING

print("\nTest error output function show_data")
print("string --    " .. show_data("error string test"))
print("number 13 -- " .. show_data(13))
print("nil --       " .. show_data(nil))
print("boolean  --  " .. show_data(false))
print("function --  " .. show_data(function() return 1 end))
print("function --  " .. show_data({tag = "Triangular", stuff="stuff",
                          contents = {"only in index 1"}} ) )

print("\nTest representation")
local z  = {real = 1, imag = 2}
print("check raw of rep {real = 1, imag = 2}:   " .. 
       to_string({real = 1, imag = 2}))
z = make_from_real_imag(1,2)
print("check using make_from_real_imag(1,2):    " .. to_string(z))

print("real_part(z)               => " .. real_part(z))
print("imag_part(z)               => " .. imag_part(z))
print("magnitude(z)               => " .. magnitude(z))
print("angle(z)                   => " .. angle(z))

print("]nTest functions")
print("\n0+0i")
local zero    = make_from_real_imag(0,0)
print("make_from_real_imag(0,0)   => " 
       .. to_string(zero) .. " zero" )

local zerop   = make_from_mag_ang(0,0)
print("make_from_mag_ang(0,0)     => " 
       .. to_string(zerop) .. " zerop" )

print("\n1+0i")
local one    = make_from_real_imag(1,0)
print("make_from_real_imag(1,0)   => " 
       .. to_string(one) .. " one" )

local onep   = make_from_mag_ang(1,0)
print("make_from_mag_ang(1,0)     => " 
       .. to_string(onep) .. " onep" )

print("\n0+1i")
local ione   = make_from_real_imag(0,1)
print("make_from_real_imag(0,1)   => " 
      .. to_string(ione) .. " ione" )

local ionep  = make_from_mag_ang(1,math.pi/2)
print("make_from_mag_ang(1,math.pi/2)   => " 
      .. to_string(ionep) .. " ionep" )

print("\n1+1i")
local oneone = make_from_real_imag(1,1)
print("make_from_real_imag(1,1)   => " 
      .. to_string(oneone) .. " oneone" )

local oneonep = make_from_mag_ang(math.sqrt(2),math.pi/4)
print("make_from__mag_ang(math.sqrt(2),math.pi/4)  => " 
      .. to_string(oneonep) .. " oneonep")

print("\npi+0i")
local rpi    = make_from_real_imag(math.pi,0)
print("make_from_real_imag(math.pi,0) => " 
      .. to_string(rpi) .. " rpi")

local rpip    = make_from_mag_ang(math.pi,0)
print("make_from_mag_ang(math.pi,0) => " 
      .. to_string(rpip) .. " rpip")

print("\n-1+0i")
local neg1    = make_from_real_imag(-1,0)
print("make_from_real_imag(-1,0) => " 
      .. to_string(neg1) .. " neg1")

local neg1p    = make_from_mag_ang(1,math.pi)
print("make_from_mag_ang(1,math.pi) => " 
      .. to_string(neg1p) .. " neg1p")

print("")
print("magnitude(zero)            => " .. tostring(magnitude(zero)))
print("angle(zero)                => " .. tostring(angle(zero)))
print("magnitude(zerop)           => " .. tostring(magnitude(zerop)))
print("angle(zerop)               => " .. tostring(angle(zerop)))
print("magnitude(one)             => " .. tostring(magnitude(one)))
print("angle(one)                 => " .. tostring(angle(one)))
print("magnitude(onep)            => " .. tostring(magnitude(onep)))
print("angle(onep)                => " .. tostring(angle(onep)))
print("magnitude(oneone)          => " .. tostring(magnitude(oneone)))
print("angle(oneone)              => " .. tostring(angle(oneone)))
print("magnitude(oneonep)         => " ..tostring(magnitude(oneonep)))
print("angle(oneonep)             => " .. tostring(angle(oneonep)))
print("magnitude(rpi)             => " .. tostring(magnitude(rpi)))
print("angle(rpi)                 => " .. tostring(angle(rpi)))
print("magnitude(rpip)            => " .. tostring(magnitude(rpip)))
print("angle(rpip)                => " .. tostring(angle(rpip)))
print("magnitude(neg1)             => " .. tostring(magnitude(neg1)))
print("angle(neg1)                 => " .. tostring(angle(neg1)))
print("magnitude(neg1p)            => " .. tostring(magnitude(neg1p)))
print("angle(neg1p)                => " .. tostring(angle(neg1p)))

local z1 = add_complex(one,ione)
print("add_complex(one,ione)      => " .. to_string(z1) .. " z1")

local z2 = add_complex(oneone,rpi)
print("add_complex(oneone,rpi)    => " .. to_string(z2) .. " z2")

local z3 = sub_complex(z1,ione)
print("sub_complex(z1,ione)       => " .. to_string(z3) .. " z3")

local z4 = sub_complex(z2,oneone)
print("sub_complex(z2,oneone)     => " .. to_string(z4) .. " z4")

local z5 = mul_complex(one,one)
print("mul_complex(one,one)       => " .. to_string(z5) .. " z5")

local z6 = mul_complex(rpi,one)
print("mul_complex(rpi,one)       => " .. to_string(z6) .. " z6")

local z7 = mul_complex(oneone,one)
print("mul_complex(oneone,one)    => " .. to_string(z7) .. " z7")

local z8 = div_complex(one,one)
print("div_complex(one,one)       => " .. to_string(z8) .. " z8")

local z9 = div_complex(one,ione)
print("div_complex(one,ione)      => " .. to_string(z9) .. " z9")

local z10 = make_from_mag_ang(0,0)
print("make_from_mag_ang(0,0)     => " ..to_string(z10) .. " z10")

local z11 = make_from_mag_ang(1,math.pi/2)
print("make_from_mag_ang(1,PI/2)  => " ..to_string(z11) .. " z11")

local z12 = make_from_mag_ang(10,math.pi)
print("make_from_mag_ang(10,PI)   => " ..to_string(z12) .. " z12")