4 ms·

Floating point numbers are almost always a mistake. Classic howlers: "Well, we can represent almost all the values we care about." Until the day you can't. "W

by kabdib 11y ago

Floating point numbers are almost always a mistake. Classic howlers: "Well, we can represent almost all the values we care about." Until the day you can't. "We'll represent time with a double, with the fractional part being part of a day, and the day being an integer day number from when Somebody Famous Did Something." Until you realize that the 10AM meeting you want to put in your scheduler can't be exactly represented. "We'll put our account balances in there as floats because unlike everyone else who has done this, we know what we're doing." But you don't. And that noise you heard was a million accountants crying out in pain. You wouldn't represent a pointer as "some fraction of the amount of memory the machine has, from 0.0 to 0.9999", which is my usual retort when someone wants to smuggle a scalar or structural value in a float.

roel_v 11y ago
"Floating point numbers are almost always a mistake." This. The problem is that it's almost impossible to internalize this without having first-hand experience - experience which usually takes years to accumulate. By coincidence, over the last month I had to explain the problems with floating point numbers to non-technical people on two disjoint occasions, and failed miserably each time, because the technical details are too complicated and the examples too obscure. The 'store account balance in double, let's put the remainder on our own account' parable is the only example that sort of works but then they look at you blank-faced and say 'we're not a bank'. Just venting I guess. It's the simple things in mapping real-world things to bits that trip me up the most - why is it so hard to represent 'numbers' in computers? Why is it so hard to represent 'date' in computers? Why is it so hard to represent 'locations' in computers?
- jbb555 11y ago
  I find it interesting that people don't realize that decimal notation has exactly the same issues as floating point. You can't store 1/10 of a £ in a binary floating point number exactly so don't use it for money. Well, you can't store 1/3 of a £ in a decimal number exactly either. The only difference is that people have got so used to decimal that we don't even notice the issue any more, and choose prices and have systems to work around the issue. It's so ingrained we don't even know we are doing it. So don't think that decimals are any better at storing money amounts than binary floating point, they are not. however all of the history and workarounds that we've been using for many years before computers for this issue also work if you store them in computers the same way. That's why you use decimals, it's because they replicate the representation issues we are used to already so we don't even notice they are there, it's not that they are fundementally better in any way.
  - roel_v 11y ago
    I think I disagree (depending on what you mean exactly). You say "That's why you use decimals, it's because they replicate the representation issues we are used to already so we don't even notice they are there, it's not that they are fundamentally better in any way." So decimals are better, because they allow us to represent money amounts in the exact same way we do in real life, which is what we're modeling in software. 1/10 = 0.1, an amount you want to be able to represent in a computer. 1/3 = 0.33..., an amount (when talking about money) you don't want to represent (when we're talking about maintaining balances). Unless you're saying "decimal as a concept is not philosophically or morally better than floating point", which is a position to which I suspect pretty much everybody subscribes.
    - emiliobumachar 11y ago
      I think gp's point is that 0.33... is "an amount (when talking about money) you don't want to represent (when we're talking about maintaining balances)" precisely because you, and everybody else, is so used to decimal that it disappears. There's nothing intrinsic about 1/10 that makes it "rounder" than 1/3, except as an artifact of the numbering system. Aliens with three hands with three fingers each, whose societies got used to base 9, would think 1/3 looks much "rounder", and 1/10 is the one you'd never want to represent.
      - roel_v 11y ago
        No. It's not that a gum costs 5 cents because it's the only fraction of a dollar that can be represented in cents, it's because pricing is inherently done in one-cent increments. If there was a need to price single items at a lower-than-a-cent cost, or at prices between one-cent increments, and if the need for that outweighed the disadvantages, there would be a way to do it. Other example: an apple doesn't cost 1/3 of a dollar, it costs 33 cents. The need for pricing things as a fraction is simply not there. I doubt most people would see 20 cents as '1/5 of a dollar' in the first place. This might be a difference between people thinking in metric and thinking in imperial, too. (I'm metric, fwiw). (before someone says 'I buy resistors that cost less than a cent', please show me a place that sells them individually)
im3w1l 11y ago
My understanding was that they used doubles as int52's, and the troubles they had came when that int52 overflowed and corrupted the exponent of the double. As opposed to the usual double problems.

by kabdib 11y ago

roel_v 11y ago

"Floating point numbers are almost always a mistake." This. The problem is that it's almost impossible to internalize this without having first-hand experience - experience which usually takes years to accumulate. By coincidence, over the last month I had to explain the problems with floating point numbers to non-technical people on two disjoint occasions, and failed miserably each time, because the technical details are too complicated and the examples too obscure. The 'store account balance in double, let's put the remainder on our own account' parable is the only example that sort of works but then they look at you blank-faced and say 'we're not a bank'. Just venting I guess. It's the simple things in mapping real-world things to bits that trip me up the most - why is it so hard to represent 'numbers' in computers? Why is it so hard to represent 'date' in computers? Why is it so hard to represent 'locations' in computers?

jbb555 11y ago
I find it interesting that people don't realize that decimal notation has exactly the same issues as floating point. You can't store 1/10 of a £ in a binary floating point number exactly so don't use it for money. Well, you can't store 1/3 of a £ in a decimal number exactly either. The only difference is that people have got so used to decimal that we don't even notice the issue any more, and choose prices and have systems to work around the issue. It's so ingrained we don't even know we are doing it. So don't think that decimals are any better at storing money amounts than binary floating point, they are not. however all of the history and workarounds that we've been using for many years before computers for this issue also work if you store them in computers the same way. That's why you use decimals, it's because they replicate the representation issues we are used to already so we don't even notice they are there, it's not that they are fundementally better in any way.
- roel_v 11y ago
  I think I disagree (depending on what you mean exactly). You say "That's why you use decimals, it's because they replicate the representation issues we are used to already so we don't even notice they are there, it's not that they are fundamentally better in any way." So decimals are better, because they allow us to represent money amounts in the exact same way we do in real life, which is what we're modeling in software. 1/10 = 0.1, an amount you want to be able to represent in a computer. 1/3 = 0.33..., an amount (when talking about money) you don't want to represent (when we're talking about maintaining balances). Unless you're saying "decimal as a concept is not philosophically or morally better than floating point", which is a position to which I suspect pretty much everybody subscribes.
  - emiliobumachar 11y ago
    I think gp's point is that 0.33... is "an amount (when talking about money) you don't want to represent (when we're talking about maintaining balances)" precisely because you, and everybody else, is so used to decimal that it disappears. There's nothing intrinsic about 1/10 that makes it "rounder" than 1/3, except as an artifact of the numbering system. Aliens with three hands with three fingers each, whose societies got used to base 9, would think 1/3 looks much "rounder", and 1/10 is the one you'd never want to represent.
    - roel_v 11y ago
      No. It's not that a gum costs 5 cents because it's the only fraction of a dollar that can be represented in cents, it's because pricing is inherently done in one-cent increments. If there was a need to price single items at a lower-than-a-cent cost, or at prices between one-cent increments, and if the need for that outweighed the disadvantages, there would be a way to do it. Other example: an apple doesn't cost 1/3 of a dollar, it costs 33 cents. The need for pricing things as a fraction is simply not there. I doubt most people would see 20 cents as '1/5 of a dollar' in the first place. This might be a difference between people thinking in metric and thinking in imperial, too. (I'm metric, fwiw). (before someone says 'I buy resistors that cost less than a cent', please show me a place that sells them individually)

im3w1l 11y ago

My understanding was that they used doubles as int52's, and the troubles they had came when that int52 overflowed and corrupted the exponent of the double. As opposed to the usual double problems.