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Please don’t spread FUD about floating point arithmetic. IEEE754 is an extremely carefully worked out standard which provides a good trade off between speed and

Please don’t spread FUD about floating point arithmetic. IEEE754 is an extremely carefully worked out standard which provides a good trade off between speed and accuracy. The problem of representing a continuum of real numbers in a fixed amount of memory is highly nontrivial. The error incurred by each operation is bounded and predictable—not exact, but as good as you’re going to get given the constraints. Also, results are replicable. Speaking as someone working in numerical analysis and scientific computing, so I work with floats all day long.

defrost 3y ago
> Please don’t spread FUD about floating point arithmetic. I'm sorry, my apologies. Are you saying that IEEE754 does exactly represent 14.7 ? > Speaking as someone working in numerical analysis and scientific computing You're hardly the only Scot in Glasgow. I feel certain a few here abouts have arc'd through PDP-11's, Cyber 205's, and landed in modern centres such as Pawsey.
- sfpotter 3y ago
  No, I’m not. In the applications IEEE754 was developed to support through standardization, being able to represent 14.7 exactly is simply unimportant.
  - shadowgovt 3y ago
    ... unless I have $14.70 in my bank account, and some naif was handed the job of writing the code to track that and didn't know about the non-intuitive consequences of relying on the IEEE floating point standard. Then its limitations suddenly become very meaningful to me or my financial institution.
    - sfpotter 3y ago
      I guess you're right. We should throw the baby out with the bathwater because a bank hired a crappy engineer. There is no other solution to this problem.
      - shadowgovt 3y ago
        I don't think anyone's calling for that. I think they are commenting on the fact that floating-point is an excellent tool for a special case of computing (a tool which has some significant drawbacks if the representation is treated as equivalent to another representation) and most languages we use make it frighteningly easy to slip-slide from one representation to the other without noticing when they are, in fact, extremely different representations of numbers and numerical computation.
        sfpotter 3y ago
        It isn't frightening if you've been properly trained and understand how your tools work. The onus is on the bank to train its employees to use the proper number type for money. I have no problem with languages having first-class support for big integers, arbitrary precision floating point numbers, arbitrary precision rationals, etc. The more representations the merrier, provided they have an efficient implementation. Having programming languages where floating point types are first class, unboxed types is extremely important for anyone who writes software which crunches numbers. I would say this is more important than providing training wheels for inexperienced programmers.
        shadowgovt 3y ago
        It's not so much that floating point needs to be boxed as that all-too-many languages allow smooth (read "sloppy") casting from float to int and back, often with semantics that are unclear to the developer and require esoteric memorization. In 5 seconds or less, can you say whether 1.0/4 will be 0.25 or 0 for every language you use regularly? Most developers can't, and most languages make statements like that trivial (and worse, it far more often shows up as "x/y" for x and y of types that need to be looked up to know what the evaluated type will be). There's a reason C++, for example, has the MISRA rules about avoiding implicit coercions (because even though what happens is [generally] well-defined, enough code in the wild has been broken for developers mis-remembering or mis-applying the rules that explicit casts are highly recommended for high-reliability code).
- josefx 3y ago
  > Are you saying that IEEE754 does exactly represent 14.7 ? Pedantic: You are aware that 754 also specifies a decimal model?

defrost 3y ago

> Please don’t spread FUD about floating point arithmetic. I'm sorry, my apologies. Are you saying that IEEE754 does exactly represent 14.7 ? > Speaking as someone working in numerical analysis and scientific computing You're hardly the only Scot in Glasgow. I feel certain a few here abouts have arc'd through PDP-11's, Cyber 205's, and landed in modern centres such as Pawsey.

sfpotter 3y ago
No, I’m not. In the applications IEEE754 was developed to support through standardization, being able to represent 14.7 exactly is simply unimportant.
- shadowgovt 3y ago
  ... unless I have $14.70 in my bank account, and some naif was handed the job of writing the code to track that and didn't know about the non-intuitive consequences of relying on the IEEE floating point standard. Then its limitations suddenly become very meaningful to me or my financial institution.
  - sfpotter 3y ago
    I guess you're right. We should throw the baby out with the bathwater because a bank hired a crappy engineer. There is no other solution to this problem.
    - shadowgovt 3y ago
      I don't think anyone's calling for that. I think they are commenting on the fact that floating-point is an excellent tool for a special case of computing (a tool which has some significant drawbacks if the representation is treated as equivalent to another representation) and most languages we use make it frighteningly easy to slip-slide from one representation to the other without noticing when they are, in fact, extremely different representations of numbers and numerical computation.
      - sfpotter 3y ago
        It isn't frightening if you've been properly trained and understand how your tools work. The onus is on the bank to train its employees to use the proper number type for money. I have no problem with languages having first-class support for big integers, arbitrary precision floating point numbers, arbitrary precision rationals, etc. The more representations the merrier, provided they have an efficient implementation. Having programming languages where floating point types are first class, unboxed types is extremely important for anyone who writes software which crunches numbers. I would say this is more important than providing training wheels for inexperienced programmers.
        shadowgovt 3y ago
        It's not so much that floating point needs to be boxed as that all-too-many languages allow smooth (read "sloppy") casting from float to int and back, often with semantics that are unclear to the developer and require esoteric memorization. In 5 seconds or less, can you say whether 1.0/4 will be 0.25 or 0 for every language you use regularly? Most developers can't, and most languages make statements like that trivial (and worse, it far more often shows up as "x/y" for x and y of types that need to be looked up to know what the evaluated type will be). There's a reason C++, for example, has the MISRA rules about avoiding implicit coercions (because even though what happens is [generally] well-defined, enough code in the wild has been broken for developers mis-remembering or mis-applying the rules that explicit casts are highly recommended for high-reliability code).
josefx 3y ago
> Are you saying that IEEE754 does exactly represent 14.7 ? Pedantic: You are aware that 754 also specifies a decimal model?