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0 pointsseppel6y ago0 comments

> The real lesson is, no matter what base (radix) you use, floating point math is inexact.

This is just not true. If you add 1.5 + 4.25 with IEEE754, there is nothing inexact or rounded. That you cannot exactly represent 0.1 in base2 FP is a problem of base2, not FP.

You get inexact results with FP math for underflows, overflows, or if you don't have enough precision for the result (or an intermediate result). But the same is true for normal integer types.

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umanwizard6y ago

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)

seppelOP6y ago

> 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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swebs6y ago

A 32 bit floating point number can only have around 4 billion unique values, yet must represent numbers from 10^38, to very small decimals. 99.99999% of numbers in this range cannot be accurately represented in floating point form.

Compare that to a 32 bit integer, which can have 4 billion unique values, and supports numbers from 0 to 4 billion. It's a 1:1 mapping.

bspammer6y ago

To be mathematically pedantic, 100% of numbers in that range cannot be accurately represented in floating point form.

seppelOP6y ago

> yet must represent numbers from 10^38

No, they don't must represent all number in the range. I don't know where you get from that they must. An integer also can't represent all real numbers in its range.

johnday6y ago

There's no such thing as a "problem of base2". Base 2 is an ineffable fact of the universe, and it is neither virtuous nor problematic. All the problems you are describing are problems of floating-point arithmetic.

seppelOP6y ago

> There's no such thing as a "problem of base2".

That you cannot represent 1/3 as a non-periodic decimal number is a problem of base 10.

That you cannot represent 1/10 as a non-periodic binary number is a problem of base 2.

These are just mathematic facts. Maybe you don't like the world "problem", but it does not change that this is where we are.

The problem that you cannot represent 0.1 in base 2 FP, is a problem of base 2. You can represent it exactly in base 10 FP.

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umanwizard6y ago

seppelOP6y ago

> 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.

2 more replies

swebs6y ago

Compare that to a 32 bit integer, which can have 4 billion unique values, and supports numbers from 0 to 4 billion. It's a 1:1 mapping.

bspammer6y ago

To be mathematically pedantic, 100% of numbers in that range cannot be accurately represented in floating point form.

seppelOP6y ago

> yet must represent numbers from 10^38

No, they don't must represent all number in the range. I don't know where you get from that they must. An integer also can't represent all real numbers in its range.

johnday6y ago

seppelOP6y ago

> There's no such thing as a "problem of base2".

That you cannot represent 1/3 as a non-periodic decimal number is a problem of base 10.

That you cannot represent 1/10 as a non-periodic binary number is a problem of base 2.

These are just mathematic facts. Maybe you don't like the world "problem", but it does not change that this is where we are.

The problem that you cannot represent 0.1 in base 2 FP, is a problem of base 2. You can represent it exactly in base 10 FP.

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