Stephen Tetley wrote:
Hello Mike
A pitch class set represents Z12 numbers so I'd define a Z12 number
type then store it in a list (if you have need a multiset -
duplicates) or Data.Set (if you need uniqueness).
If you want an efficient implementation for *sets* of Z12 numbers I'd
recommend using bit arithmetic. Pick some Word type with at least 12
bits and use bit0 to represent including 0 in the set, bit1 to represent
including 1, bit2 for 2, etc. This can be generalized for any Zn
provided n is a suitably small number. Z16 may be a good place to start
if you want wider applicability, though you'd want to wrap that with
error checking code in order to exclude 12..15.
import Data.Word
import Data.Bits
newtype Z16 = Z16 Word16
z16_0 = 1 `shiftL` 0
z16_1 = 1 `shiftL` 1
z16_2 = 1 `shiftL` 2
...
union = (.|.)
intersection = (.&.)
...
But I don't know whether you need to deal more with sets or with the
elements therein, so that might reduce the efficiency of this approach.
--
Live well,
~wren
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