test/examples/complex/complex.lua

   1 -- complex.lua
   2 -- complex arithmetic package for lua
   3 -- Luiz Henrique de Figueiredo (lhf@csg.uwaterloo.ca)
   4 -- 24 Oct 95
   5 $debug
   6
   7 Complex={type="package"}
   8
   9 function complex(x,y)
  10  return { re=x, im=y, type="complex" }
  11 end
  12
  13 function Complex.conj(x,y)
  14  return complex(x.re,-x.im)
  15 end
  16
  17 function Complex.norm2(x)
  18  local n=Complex.mul(x,Complex.conj(x))
  19  return n.re
  20 end
  21
  22 function Complex.abs(x)
  23  return sqrt(Complex.norm2(x))
  24 end
  25
  26 function Complex.add(x,y)
  27  return complex(x.re+y.re,x.im+y.im)
  28 end
  29
  30 function Complex.sub(x,y)
  31  return complex(x.re-y.re,x.im-y.im)
  32 end
  33
  34 function Complex.mul(x,y)
  35  return complex(x.re*y.re-x.im*y.im,x.re*y.im+x.im*y.re)
  36 end
  37
  38 function Complex.div(x,y)
  39  local z=x*Complex.conj(y)
  40  local t=Complex.norm2(y)
  41  z.re=z.re/t
  42  z.im=z.im/t
  43  return z
  44 end
  45
  46 function Complex.fallback(x,y,op)
  47  if type(x)=="number" then x=complex(x,0) end
  48  if type(y)=="number" then y=complex(y,0) end
  49  if type(x)=="complex" and type(y)=="complex" then
  50   return Complex[op](x,y)
  51  else
  52   return Complex.oldfallback(x,y)
  53  end
  54 end
  55
  56 function Complex.newtype(x)
  57  local t=Complex.oldtype(x)
  58  if t=="table" and x.type then return x.type else return t end
  59 end
  60
  61 function Complex.print(x)
  62  if type(x)~="complex" then
  63   Complex.oldprint(x)
  64  else
  65   local s
  66   if x.im>=0 then s="+" else s="" end
  67   Complex.oldprint(x.re..s..x.im.."I")
  68  end
  69 end
  70
  71 function Complex.newabs(x)
  72  if type(x)~="complex" then
  73   return Complex.oldabs(x)
  74  else
  75   return Complex.abs(x)
  76  end
  77 end
  78
  79 Complex.oldfallback=setfallback("arith",Complex.fallback)
  80 Complex.oldtype=type    type=Complex.newtype
  81 Complex.oldprint=print  print=Complex.print
  82 Complex.oldabs=abs      abs=Complex.abs