Lua has only floats? *wince* Okay, maybe it's not such a good language for our integer-only processor...
I did something like that ages ago. At the time perl had a bignum module, but it didn't support bitwise operations (mainly because its representation was decimal strings). Be warned: I kept getting bitten by special cases. I can't remember what they were, but I think they had to do with signedness.
Question: Arthur Norman, in his lecture on multiplication of really large numbers, gave a (very short) proof that division does not need to be more expensive than multiplication. Can you remember what it was?
It occurred to me recently that for floats, you can have fast division by writing a float class which has one exponent but two mantissas. The value of the object is a/b, where a is (exp,mant1) and b is (0,mant2). Division has the same cost as multiplication, but unfortunately so do addition and subtraction, so this scheme is unlikely to be very useful. But I don't know if I invented that or heard it in ACN's lecture.
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Date: 2008-05-06 20:59 (UTC)I did something like that ages ago. At the time perl had a bignum module, but it didn't support bitwise operations (mainly because its representation was decimal strings). Be warned: I kept getting bitten by special cases. I can't remember what they were, but I think they had to do with signedness.
Question: Arthur Norman, in his lecture on multiplication of really large numbers, gave a (very short) proof that division does not need to be more expensive than multiplication. Can you remember what it was?
It occurred to me recently that for floats, you can have fast division by writing a float class which has
one exponent but two mantissas. The value of the object is a/b, where a is (exp,mant1) and b is (0,mant2).
Division has the same cost as multiplication, but unfortunately so do addition and subtraction, so this scheme is unlikely to be very useful. But I don't know if I invented that or heard it in ACN's lecture.