3 ms·

That’s not too surprising to me, I imagine that many number types are used, and it depends entirely on the task at hand? If you have deeper knowledge of what ge

by dahart 1y ago

That’s not too surprising to me, I imagine that many number types are used, and it depends entirely on the task at hand? If you have deeper knowledge of what gets done in practice, I’m still curious what criteria and types and how many decimal points might get used in the most restrictive cases. What do people use in practice for, say, interest compounding on a trillion dollars? I can calculate how many decimal places I need at a minimum for any given transaction to guarantee the correct pennies value, but I don’t have first-hand experience with banks and I don’t know what the rules of thumb, or formal standards might be for safe & careful calculation on large sums of money. I would imagine they avoid doing floating point analysis in every case, since that’s expensive engineering?

PaulKeeble 1y ago
Floats all the way. Its floats compounding errors so they estimate the error along the way and then adjust the results. Its floats all the way down!
- dahart 1y ago
  Oh now that is somewhat surprising! Is this 64 bit or 128 bit floats? 32 bit floats aren’t accurate enough to represent $1B to the penny. Do error values get stored as deltas and passed around with the float values? Would love to hear more about this, do you know of any good summaries of the engineering workflow online?
jcranmer 1y ago
My electricity and gas bills both charge me $0.xxxxxx per unit price, or 10,000ths of a ¢, although the last digit is invariably a zero. I've also seen 4-5 digits on currency exchange places. I'd have to break out a calculator to be certain, but my guess is that most of these transactions amount to sum( round_to_nearest_cent(multiply(a * b))), where a is a value in thousandths of a cent--which is to say, there isn't a single "this is the fixed-point unit to use for all your calculations." For financial modeling, the answer is definitely "just use floats," because any rounding-induced error is going to be much smaller than the inherent uncertainty of your model values anyways. It's not like companies report their income to the nearest cent, after all.
- dahart 1y ago
  Right, the number of digits you need for any given calculation depends on the magnitudes of the numbers involved, and the acceptable precision of the result. BTW round to nearest might be unsafe, I’m certain that there are many situations where people will specifically avoid rounding to nearest, I would not assume that companies use that scheme. It seems like a decent assumption that financial companies are not spending engineering time (money) on a floating point analysis of every single computation. They must generally have a desired accuracy, some default numeric types, and workflows that use more bits than necessary for most calculations in exchange for not having to spend time thinking hard about every math op, right? That’s how it works everywhere else. The accuracy used for reporting doesn’t seem relevant to the accuracy used for internal calculations. It’s fine for large companies to report incomes to rounded millions, while it’s absolutely unacceptable to round compound interest calculations in a bank account to millions, regardless of the balance.

by dahart 1y ago

PaulKeeble 1y ago

Floats all the way. Its floats compounding errors so they estimate the error along the way and then adjust the results. Its floats all the way down!

dahart 1y ago
Oh now that is somewhat surprising! Is this 64 bit or 128 bit floats? 32 bit floats aren’t accurate enough to represent $1B to the penny. Do error values get stored as deltas and passed around with the float values? Would love to hear more about this, do you know of any good summaries of the engineering workflow online?

jcranmer 1y ago

My electricity and gas bills both charge me $0.xxxxxx per unit price, or 10,000ths of a ¢, although the last digit is invariably a zero. I've also seen 4-5 digits on currency exchange places. I'd have to break out a calculator to be certain, but my guess is that most of these transactions amount to sum( round_to_nearest_cent(multiply(a * b))), where a is a value in thousandths of a cent--which is to say, there isn't a single "this is the fixed-point unit to use for all your calculations." For financial modeling, the answer is definitely "just use floats," because any rounding-induced error is going to be much smaller than the inherent uncertainty of your model values anyways. It's not like companies report their income to the nearest cent, after all.

dahart 1y ago
Right, the number of digits you need for any given calculation depends on the magnitudes of the numbers involved, and the acceptable precision of the result. BTW round to nearest might be unsafe, I’m certain that there are many situations where people will specifically avoid rounding to nearest, I would not assume that companies use that scheme. It seems like a decent assumption that financial companies are not spending engineering time (money) on a floating point analysis of every single computation. They must generally have a desired accuracy, some default numeric types, and workflows that use more bits than necessary for most calculations in exchange for not having to spend time thinking hard about every math op, right? That’s how it works everywhere else. The accuracy used for reporting doesn’t seem relevant to the accuracy used for internal calculations. It’s fine for large companies to report incomes to rounded millions, while it’s absolutely unacceptable to round compound interest calculations in a bank account to millions, regardless of the balance.