On Tue, 6 Jul 2021 at 13:15, David Rowley <dgrowle...@gmail.com> wrote: > > Can you give an example where calling half_rounded too many times will > give the wrong value? Keeping in mind we call half_rounded the number > of times that the passed in value would need to be left-shifted by to > get the equivalent truncated value. >
./half_rounded 10241 10 1. half_round(10241) == 5121 :: 10241 >> 1 = 5120 2. half_round(5121) == 2561 :: 5120 >> 1 = 2560 3. half_round(2561) == 1281 :: 2560 >> 1 = 1280 4. half_round(1281) == 641 :: 1280 >> 1 = 640 5. half_round(641) == 321 :: 640 >> 1 = 320 6. half_round(321) == 161 :: 320 >> 1 = 160 7. half_round(161) == 81 :: 160 >> 1 = 80 8. half_round(81) == 41 :: 80 >> 1 = 40 9. half_round(41) == 21 :: 40 >> 1 = 20 10. half_round(21) == 11 :: 20 >> 1 = 10 The correct result should be 10 (it would be very odd to claim that 10241 bytes should be displayed as 11kb), but the half-rounding keeps rounding up at each stage. That's a general property of rounding -- you need to be very careful when rounding more than once, since otherwise errors will propagate. C.f. 4083f445c0, which removed a double-round in numeric sqrt(). To be clear, I'm not saying that the current code half-rounds more than once, just that it reads as if it does. Regards, Dean
