[PEP] number accuracy

[Luke Kenneth Casson Leighton]

number accuracy, by Luke Kenneth Casson Leighton <lkcl@samba-tng.org>

abstract
--------

python classes that support number types have an automatic
cast mechanism (hierarchical).  unfortunately, the existing
mechanism can only really cope with builtin types.
any user-defined number types cannot be type-cast to or from
any other user-defined number types because every single
other class, including the builtin number types, need to know
about every single other number type.

the proposal is therefore to provide a means by which the
accuracy of numbers may be determined independently.

number ranking
--------------

The Plan is to provide a function that returns a tuple or a
list of tuples indicating the accuracy of the numerical class's
resolution.

then, type-casting may occur by first checking the length
of the list and further by checking the tuples in the lists.

the tuple consists of:

- 0 if the representation can do positive numbers, 1 if it can
  do positive and negative
- the number of binary digits (ln2 of the max range) in the mantissa
- optionally the number of digits in the exponent

example:

class UserLong:

	def __accuracy__(self):
		
		return (1, 1000000000000000L) # presumed infinite!

class UserIEEEFloat:

	def __accuracy__(self):
		
		return (1, 32, 12) # does up to 32-bit mantissa, 12-bit exponent

when complex numbers are involved, you want to do this:

class UserComples:

	def __accuracy__(self):

		return [(1, 32, 12), (1, 32, 12)]

which indicates that both the real and imaginary components of
the 2-dimensional number space are capable of supporting floating
point e.g. "0.95829-32.59j"

usage
-----

a simple test determines whether numbers can be typecast:


	if num1.__accuracy__() > num2.__accuracy():
		return num1
	else:
		return num2


type-casting
------------

*thinks*...

i believe... also... that... the same principle may be
applied to actually performing a typecast...

def __mantissa__(self, dimension=0):

def __exponent__(self, dimension=0):

as long as these two functions return numbers of built-in
types (int and long, basically) then it will be possible
to type-cast between any user-defined numerical types.
	

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