>I believe you missed the part where it rounds the error away.
I've been down this argument with other HN commenters some time back and explicitly demonstrated that it fails when you do it this way. It's not worth chasing down all the details again.
The short answer is it will fail, and in unexpected places. The only correct answer when doing this to is do the numerical analysis completely and correctly. This half-assed "it rounds the error away" is completely insufficient (and wrong).
The problem with letting such error slop around in code is that someone will take your code and use it to aggregate 1m loans, then your 25 bits of safety just became real money. Then someone will leverage that routine and add more problems.
When you build the lowest pieces so sloppily, it quickly contaminates the whole system. Make each piece as numerically solid as possible, otherwise you will get bitten.
If you have not proven your algorithm correct using numerical analysis for this stuff, it is not correct. End of story.
>but repeating multiplication doesn’t appear in finance naturally
Yes it does - compound interest if you need periods and tables.
And we're in agreement - floating point, not fixed point, is how to do financial calculations. I'm amazed how many people on HN want to argue that fixed point works when it's easy to demonstrate it fails in terrible ways and is significantly more error prone than simply using doubles (or double- or quad- doubles when needed).
Maybe it will, I’m only halfway there. I’ll take the risk, cause your solution (hiring theorem provers) simply costs much more than the risk itself upfront.
Yes it does - compound interest if you need periods and tables.
Only if you don’t round to fixed before capitalizing. But when you don’t, numerically less savvy investors (99.9% of people) would just ask to fix it and stop being so smart. They want deterministic output for any particular end of period.
I see you’re coming from academic side, but real world doesn’t work like that. Nobody’s going to take our algorithms and shove 2^(>20) records of sums greater than $100M into them.
I've been down this argument with other HN commenters some time back and explicitly demonstrated that it fails when you do it this way. It's not worth chasing down all the details again.
The short answer is it will fail, and in unexpected places. The only correct answer when doing this to is do the numerical analysis completely and correctly. This half-assed "it rounds the error away" is completely insufficient (and wrong).
The problem with letting such error slop around in code is that someone will take your code and use it to aggregate 1m loans, then your 25 bits of safety just became real money. Then someone will leverage that routine and add more problems.
When you build the lowest pieces so sloppily, it quickly contaminates the whole system. Make each piece as numerically solid as possible, otherwise you will get bitten.
If you have not proven your algorithm correct using numerical analysis for this stuff, it is not correct. End of story.
>but repeating multiplication doesn’t appear in finance naturally
Yes it does - compound interest if you need periods and tables.
And we're in agreement - floating point, not fixed point, is how to do financial calculations. I'm amazed how many people on HN want to argue that fixed point works when it's easy to demonstrate it fails in terrible ways and is significantly more error prone than simply using doubles (or double- or quad- doubles when needed).