251–260 of 422 posts
MS Excel tries to be clever and disguise the most common places this is noticed. Give it =0.1+0.2-0.3 and it will see what you are trying to do and return 0. Give it anything slightly more complicated such as =(0.1+0.2-0.3) and this won't trip, in this example displaying 5.55112E-17 or similar.
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They said floating point decimal types which probably means BCD.
There are different implementations, and BCD is only one of them. Another popular one is a mantissa and exponent, but the exponent is for a 10-based shift rather than the typical floating point.
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I think what that commentator meant is that floating-point math is not an accurate model of rational-number arithmetic, not that there aren't certain computations that are in fact exact. (As you point out, there are: 1.5 + 4.25 is indeed exact)
> is that floating-point math is not an accurate model of rational-number arithmetic Well, this is true. But integer math is also not an accurate model of rational-number arithmetic, yet nobody would claim that integer math is inexact.
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> is that floating-point math is not an accurate model of rational-number arithmetic Well, this is true. But integer math is also not an accurate model of rational-number arithmetic, yet nobody would claim that integer math is inexact.
Unsigned integer math (on typical machines) is an exact model of the ring of integers modulo 2^64. Floating point arithmetic is not an exact model of anything with nice properties that people are used to from algebra.
And even this is only true if you retrict yourself to unsigned integers. For signed integers you have quirks (-0x8000.. = 0x8000..) or minefields (undefined overflow semantics in C, which can yield non-associativity, tests deleted by the compiler, etc.).
And I'd argue that whoever understands the ring of integers modulo 2^64, will also understand the IEEE754 semantics (which are, I agree, sometimes unfortunate. But not inexact).
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For including words in a sale pitch, I'd agree. But this isn't a sales pitch. Some people are just bad at things. The explanation on that page require grade school levels of math. I think math that's taught in grade school can be objectively called simple. Some people suck at math. That's ok. I'm very geeky. I get geeky things. Many times geeky things can be very simple to me. I went to a dance lesson. I'm terribly u…
When faced with criticism about your lack of inclusivity, what's to gain by doubling down in order to intentionally exclude people? The argument you are presenting always feels disingenuous because you imply that there is something lost in the efforts to be more inclusive. The idea that you care about the growth of people you are actively excluding doesn't make a whole lot of sense. In this example we're talking abou…
Yes there is something lost. I included it in my post but I'll repeat it: People who aren't good at math are 'shielded from the truth' (they objectively suck at math because they can't grasp something that is objectively simple in the domain of math). Again, feeling bad about not grasping something simple is the necessary element for a humbling experience. Humbling experiences aren't meant to feel great. For me, I've learned the most with humbling experiences. I honestly believe most people in the first world need more of them.
The suggested language is more inclusive, that's an advantage to sales, but less clear, that's a disadvantage to communication/learning. Personally, I like learning and want to see things optimized for that.
BTW; I loved the sly way of you implying that: A- I took offense (I am not, nor do I see anything in my comment that says I'm offended) and B- That I'm the lowest common denominator because of A. It's a subtle way of attacking me and not my point. It says a lot about both the person doing the attack and the strength of their argument that they have to resort to ad-hominems. Though I will credit you with using a smartly disguised one.
Also, you are speaking to me as if I was the website author. I'm not the OP of the article, which if you read TFA you would see the actual author changed in favor of the suggestion.
I remember in college when we learned about this and I had the thought, "Why don't we just store the numerator and denominator?", and threw together a little C++ class complete with (then novel, to me) operator-overloads, which implemented the concept. I felt very proud of myself. Then years later I learned that it's a thing people actually use: https://en.wikipedia.org/wiki/Rational_data_type
It's actually in use in many places, for things like handling currency and money, and for when you get funny corner cases involving rounding such numbers and pooling the change. Whenever I see someone handling currency in floats, something inside me wither and die a small death.
In trading, it's super common to use floating point arithmetic for decision logic since it's very fast and straightforward to write. The actual trade execution, however, almost always relies on integer arithmetic because then money is actually being used (and hence must be tracked properly).
It's not therefore inherently incorrect to do currency conversions with floats in some situations provided that the actual transaction execution relies on fixed precision or decimal arithmetic.
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Currency handling is almost never done with rationals (numerator and denominator) and is frequently (and correctly so!) done with fixed or floating point decimal types.
This is false. It's not correct to handle currency with floating point types.
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Storing money in floating point is always terrible. If speed is an issue, store it in integer types representing the smallest unit in the currency, e.g. pennies. Unless you’re doing, what, massively parallel GPU algos on batches of independent amounts? But even then you could use the float as an int in that way... Honestly when is float ever actually good for money? Not for speed, not for correctness, ...
I think you mean that storing money in floating point is always terrible for accounting . Not all of finance is accounting. Imagine you work at a hedge fund, and you have a model that predicts the true value of some option. Assume the option is trading for $3.00. You do not really care if your model spits out $3.5 or $3.5000000001, you are going to buy either way. And your model probably involves a bunch of transcend…
There can be two companies with 100M market cap. Corp A has issued 10M shares @ 10 each, Corp B has 10B shares priced at 0.01
A +/-0.001 change in Corp A share price is just 0.01% and moves the market cap by +/-10k, so probably nothing significant. The same nominal change in Corp B amounts to 10%, or +/- 10M in the company value, which is quite a big deal.
Also I think there may be some money to be made in changes at the 7th decimal place with large enough volume of high frequency transactions.