Fast rounding code?

Jobbo · 29 October 2021, 04:34

Hi

I'm working on something where I need to efficiently round down to the nearest multiple for different rounding values.

This is on 68000 and the rounding values are 2 through 16.

Obviously for the like of 2, 4, 8, 16 it's easy enough to mask the lowest bits.

But for the other values I'm not aware of any tricks I can pull.

The best I've come up with is to use a table, which should be fine because the range of numbers I'm rounding is only 0...319.

Using a table the code ends up as:

Code:

add.w d0,d0
move.w (a0,d0.w),d0

Not terrible, but I was curious if anyone knows of any alternatives?

hooverphonique · 29 October 2021, 10:06

If you by "efficiently" mean "as fast as possible", a table is the best you can do (for any number between 2 and 16).

Thomas Richter · 29 October 2021, 10:42

There are a couple of cases (2^n-1) where simple algorithms exist, but in general, it is either a table or a division and a multiplication.

Photon · 13 December 2021, 23:05

Late reply, but the scholarly answer is that in binary arithmetic, to preserve precision you work in at least 5 bits higher resolution. Only at the end of the calculation do you round.

Rounding is done by a half-add (minus 1) and a shift down.

In the example of 32x precision, you add 15 and shift down by 5.

29 October 2021, 04:34	#1
Jobbo Registered User Join Date: Jun 2020 Location: Druidia Posts: 387	Fast rounding code? Hi I'm working on something where I need to efficiently round down to the nearest multiple for different rounding values. This is on 68000 and the rounding values are 2 through 16. Obviously for the like of 2, 4, 8, 16 it's easy enough to mask the lowest bits. But for the other values I'm not aware of any tricks I can pull. The best I've come up with is to use a table, which should be fine because the range of numbers I'm rounding is only 0...319. Using a table the code ends up as: Code: add.w d0,d0 move.w (a0,d0.w),d0 Not terrible, but I was curious if anyone knows of any alternatives?

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29 October 2021, 10:06	#2
hooverphonique ex. demoscener "Bigmama" Join Date: Jun 2012 Location: Fyn / Denmark Posts: 1,624	If you by "efficiently" mean "as fast as possible", a table is the best you can do (for any number between 2 and 16).

29 October 2021, 10:42	#3
Thomas Richter Registered User Join Date: Jan 2019 Location: Germany Posts: 3,215	There are a couple of cases (2^n-1) where simple algorithms exist, but in general, it is either a table or a division and a multiplication.

13 December 2021, 23:05	#4
Photon Moderator Join Date: Nov 2004 Location: Eksjö / Sweden Posts: 5,602	Late reply, but the scholarly answer is that in binary arithmetic, to preserve precision you work in at least 5 bits higher resolution. Only at the end of the calculation do you round. Rounding is done by a half-add (minus 1) and a shift down. In the example of 32x precision, you add 15 and shift down by 5.

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