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On Sat, Aug 22 2015, Mike Gilbert wrote: |
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> On Sat, Aug 22, 2015 at 1:32 PM, Alan McKinnon <alan.mckinnon@×××××.com> wrote: |
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>> I can tell you that equality comparisons on floats are problematic, and |
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>> always will be due to how they are stored (double-precision floats, |
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>> inhernetly inexact). This is not a "problem" per se, it's a systemic |
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>> side effect of how our computers represent floats i.e. you can't "fix" |
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>> it as there is nothing to fix |
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> |
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> It's not that floats are inherently "inexact"; it really has to do |
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> with trying to represent a base-10 number in a data structure designed |
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> to hold a base-2 number. |
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> |
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> If your number can be represented by some multiple of a power of 2, |
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> equality comparisons will work. If it cannot be, it has to be stored |
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> as an approximation. |
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I am not sure exactly what you mean. Every number is a multiple of a |
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power of 2, in particular a multiple of 2^0=1. |
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Also |
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2^0 + 2^1 + 2^2 + ... 2^100 != 2^100 + 2^99 + ... + 2^1 + 2^0 |
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on a 64-bit machine assuming left to right addition. |
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This example does not use floating point for that use negative exponents |
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2^-0 + 2^-1 + ... + 2^-100 != 2^-100 + ... + 2^-1 + 2^-0 |
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In general for adding many positive floating point numbers, it is better |
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to add the small numbers first. |
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One more example. Assume a DECIMAL floating point machine with two |
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digits of mantissa and say 20 digits of exponent. This machine cannot |
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express 101 since that requires 3 digits of mantissa. Then |
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100 + 1 + 1 + ... + 1 (100 1s) = 100 |
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1 + 1 + ... + 1 + 100 (100 1s) = 200 |
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allan |
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