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All models are wrong. Some (wrong) models are useful. Computers can't represent 0.1 (in floating point), yet that hasn't stopped anyone from doing finances on

All models are wrong. Some (wrong) models are useful. Computers can't represent 0.1 (in floating point), yet that hasn't stopped anyone from doing finances on their computer. I don't think this is big news OR a parlor trick. It's just some obscure thing computers can't do that nobody has noticed for 70 years because nobody needed it.

lisper 2y ago
> Computers can't represent 0.1 (in floating point) Of course they can. They just can't do it in binary [EDIT: base 2]. But they can certainly do it in (say) BCD [EDIT: base 10].
- brewmarche 2y ago
  .NET’s decimal datatype for example represents a decimal floating point number
- pvg 2y ago
  Just as a total pedantipoint, they also do that in binary (hence the B in BCD, in that specific case).
  - lisper 2y ago
    I've updated my comment with appropriate pedantedits.
    - BraveNewCurency 2y ago
      But BCD is not floating point (generally shorthand for the IEEE 754 Floating Point standard, which nearly every CPU and GPU have hardware support for). And I don't know much about BCD, but it is probably missing niceties like NaN and Inf for capturing edge cases that happen deep inside your equations. These matter if your system is to be reliable.
      - lisper 2y ago
        > generally shorthand for the IEEE 754 Floating Point standard Yes, generally, but that is just a social convention. There is nothing stopping you from doing floating point in base 10 rather than base 2, and if you do, 0.1 becomes representable exactly. It's just a quirk that 1/10 happens to be a repeating decimal in base 2. It is in no way a reflection of a limitation on computation.
      - brewmarche 2y ago
        IEEE 754 defines decimal floating point in single (32 bit), double (64) and quadruple (128) precision since the 754-2008 revision. (However .NET’s type I mentioned above even though it’s 128-bit is its own thing and does not adhere to it).
deleted 2y ago
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TacticalCoder 2y ago
> Computers can't represent 0.1 (in floating point), yet that hasn't stopped anyone from doing finances on their computer. floating point for financial data may have made sense back when my 386 DX CPU has a FP coprocessor and computation were dog slow. In this day and age though you'll typically be not just a bit but much better using an abstraction that can represent numbers with decimals precisely, which frees you from a great many rounding error, epsilon computation, error propagation, etc.

lisper 2y ago

> Computers can't represent 0.1 (in floating point) Of course they can. They just can't do it in binary [EDIT: base 2]. But they can certainly do it in (say) BCD [EDIT: base 10].

brewmarche 2y ago
.NET’s decimal datatype for example represents a decimal floating point number
pvg 2y ago
Just as a total pedantipoint, they also do that in binary (hence the B in BCD, in that specific case).
- lisper 2y ago
  I've updated my comment with appropriate pedantedits.
  - BraveNewCurency 2y ago
    But BCD is not floating point (generally shorthand for the IEEE 754 Floating Point standard, which nearly every CPU and GPU have hardware support for). And I don't know much about BCD, but it is probably missing niceties like NaN and Inf for capturing edge cases that happen deep inside your equations. These matter if your system is to be reliable.
    - lisper 2y ago
      > generally shorthand for the IEEE 754 Floating Point standard Yes, generally, but that is just a social convention. There is nothing stopping you from doing floating point in base 10 rather than base 2, and if you do, 0.1 becomes representable exactly. It's just a quirk that 1/10 happens to be a repeating decimal in base 2. It is in no way a reflection of a limitation on computation.
    - brewmarche 2y ago
      IEEE 754 defines decimal floating point in single (32 bit), double (64) and quadruple (128) precision since the 754-2008 revision. (However .NET’s type I mentioned above even though it’s 128-bit is its own thing and does not adhere to it).

deleted 2y ago

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TacticalCoder 2y ago

> Computers can't represent 0.1 (in floating point), yet that hasn't stopped anyone from doing finances on their computer. floating point for financial data may have made sense back when my 386 DX CPU has a FP coprocessor and computation were dog slow. In this day and age though you'll typically be not just a bit but much better using an abstraction that can represent numbers with decimals precisely, which frees you from a great many rounding error, epsilon computation, error propagation, etc.