On Sat, Dec 31, 2016 at 1:47 AM, Steve D'Aprano <steve+pyt...@pearwood.info> wrote: > How about *signed* integers? > > 7 + 1 => -8 > 7 + 2 => -7 > 7 + 7 => -2 > > 7 * 2 => -2 > 7 * 3 => 5 > 7 * 4 => -4 > > > Again, assume both operands are in range for an N-bit signed integer. What's > a good way to efficiently, or at least not too inefficiently, do the > calculations in Python?
One way would be to work with the integers as unsigned numbers, and then render them signed for display only. The neat thing about two's complement (as opposed to two's compliment, which is a really sweet thing to say to someone) is that a lot of operations work exactly the same way. You add 7+2 and get 9, and then display 9 as -7. You take that 9 (really -7) and add 5 to it, and you get 14, which you display as -2. Add another 4 and you get 18, mask that off and you get 2. You may have to handle multiplication and division differently, I think, and you might need a sign-extend right shift operator (as opposed to a zero-fill right shift), but they should be able to be defined in terms of the other operations. 7 * 2 => 14, displayed as -2 7 * 3 => 21, mask to 5 7 * 4 => 28, mask to 12, display as -4 7 * 9 => 63, mask to 15, display as -1. Conceptually 7*-7 => -49. Actually you might be able to get away with multiplication perfectly. I'm thinking of the Intel 80x86 opcodes, where MUL and IMUL are unsigned and signed multiplication, respectively, but they differ because the result is twice as wide as the operands (eg if you multiply two 16-bit numbers, you get a 32-bit result). The Intel chips do the same with division (eg you divide a 32-bit number by a 16-bit and get back a 16-bit quotient and 16-bit remainder). You may be able to take the exact same short-cut. > Signed arithmetic also has some gotchas. For example, -x is not necessarily > defined, nor is abs(x). AIUI -x is always defined, but might be equal to x in two circumstances (zero and MAXINT+1). Not sure about abs(x), but probably would be the same. ChrisA -- https://mail.python.org/mailman/listinfo/python-list
