NB. Some models of floating point representations and operations
NB. These models handle infinities and nan's

NB. Some helping definitions
floor =: <.
log2 =: 2&^.
copy =: #

fs2bin =: monad define 
NB. check for infinities and nan's
if. _ = y
   do. 0 1 1 1 1 1 1 1 1 , 23 copy 0
       return.
  elseif. __ = y
   do. 1 1 1 1 1 1 1 1 1 , 23 copy 0
       return.
NB. this case is tricky since (for some reason)
NB. _. = _. is false.  Perhaps this is because
NB. IEEE 754 specifies _1 + 2 ^ 23 different 
NB. representations for nan.
  elseif. 0 not_equal y - y
   do. 0 1 1 1 1 1 1 1 1 , 23 copy 1
       return.
end.
NB. compute the characteristic
e =. 1 + floor log2 | y + y = 0
NB. now the mantissa
f =. 1 drop (24 copy 2) rep floor (2 ^ 24 - e) * | y
NB. finally get the sign and exponent (binary form)
se =. (9 copy 2) rep (y not_equal 0) * (256 * y < 0) + e + 126
se , f
)

traced_fs2bin =: monad define 
NB. check for infinities and nan's
if. _ = y
   do. 0 1 1 1 1 1 1 1 1 , 23 copy 0
       return.
  elseif. __ = y
   do. 1 1 1 1 1 1 1 1 1 , 23 copy 0
       return.
NB. this case is tricky since (for some reason)
NB. _. = _. is false.
  elseif. 0 not_equal y - y
   do. 0 1 1 1 1 1 1 1 1 , 23 copy 1
       return.
end.
NB. compute the characteristic
display'exponent'; e =. 1 + floor log2 | y + y = 0
if. _ = e
  do. _
  return.
end.
NB. now the mantissa
display'mantissa'; f=.1 drop (24 copy 2) rep floor (2 ^ 24 - e) * | y
NB. finally get the sign and exponent (binary form)
display'sign-exp'; se =. (9 copy 2) rep (y not_equal 0) * (256 * y < 0) + e + 126
se , f
)

bin2fs =: monad define 
s =. 0 from y
e =. base 1 2 3 4 5 6 7 8 from y
f =. base 9 drop y
if. (0 = e) and 0 = f
  do. 0
elseif. (255 = e) and 0 = f
  do. _ * _1 ^ s
elseif. (255 = e) and 0 not_equal f
  do. _.
elseif. (0 = e) and 0 not_equal f
  do. (_1 ^ s) * f * 2 ^ e - 126
elseif. 1
  do. (_1 ^ s) * (2 ^ e - 127) * (base 1 , 9 drop y) % 2 ^ 23
end.
)


traced_bin2fs =: monad define 
display's';s =. 0 from y
display'e';e =. base 1 2 3 4 5 6 7 8 from y
display'f';f =. base 9 drop y
if. (0 = e) and 0 = f
  do. 0
elseif. (255 = e) and 0 = f
  do. _ * _1 ^ s
elseif. (255 = e) and 0 not_equal f
  do. _.
elseif. (0 = e) and 0 not_equal f
  do. (_1 ^ s) * f * 2 ^ e - 126
elseif. 1
  do. (_1 ^ s) * (2 ^ e - 127) * (base 1 , 9 drop y) % 2 ^ 23
end.
)