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[8.5.2] 1000.0e171 does NOT equal 1.0e174

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Richard Sargent

[8.5.2] 1000.0e171 does NOT equal 1.0e174

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The subject pretty well says it all.
One would expect the following expression to answer 'true'. It doesn't.

1000.0e171 = 1.0e174

(There is a discrepancy in the least significant bit.)

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Seth Berman

Re: [8.5.2] 1000.0e171 does NOT equal 1.0e174

Hi Richard,

We will take a look at this and report back. Thanks.

-- Seth

On Wednesday, February 26, 2014 2:12:39 PM UTC-5, Richard Sargent wrote:

The subject pretty well says it all.
One would expect the following expression to answer 'true'. It doesn't.

1000.0e171 = 1.0e174

(There is a discrepancy in the least significant bit.)

John O'Keefe-3

Re: [8.5.2] 1000.0e171 does NOT equal 1.0e174

In reply to this post by Richard Sargent

Richards -

While I agree that it appears that this expression should answer true when evaluated, you should not count on it doing so. Floating point values are inherently inaccurate because they are approximations.

Looking at EsScanner>>#readNumber, I see that the exponent is turned into an Integer (or, in this case, a LargeInteger) by sending it #powerOfTen. So what we really have is:

1.0 * (174 powerOfTen asFloat) = 1000.0 * (171 powerOfTen asFloat)

Since there are floating point operations involved in this comparison, you can get lucky (the values are exactly representable as Floats) or unlucky (the values are not exactly representable as Floats) -- you got unlucky.

Also notice that:

1.0e171 * 1000.0 = 1000.0e171

answers true. In this case there is no uncertainty associated with the exponent since both sides use the same exponent.

So, the message is: "Don't use = with Floats" because you will get unexpected results.

On Wednesday, February 26, 2014 2:12:39 PM UTC-5, Richard Sargent wrote:

The subject pretty well says it all.
One would expect the following expression to answer 'true'. It doesn't.

1000.0e171 = 1.0e174

(There is a discrepancy in the least significant bit.)

John O'Keefe-3

Re: [8.5.2] 1000.0e171 does NOT equal 1.0e174

Richard -

Of course, EsScanner>>#readNumber could normalize the number before applying the exponent and the problem would be corrected, but it doesn't.

Just for a point of comparison, VW 7.9.1 answers false for 1.0d174 = 1000.0d171, and Pharo 2 answers true for 1.0e174 = 1000.0e171 (probably because it uses a different internal representation for Floats), so there is no consistency among the 3.

John

On Monday, March 3, 2014 3:38:17 PM UTC-5, John O'Keefe wrote:

Richards -

While I agree that it appears that this expression should answer true when evaluated, you should not count on it doing so. Floating point values are inherently inaccurate because they are approximations.

Looking at EsScanner>>#readNumber, I see that the exponent is turned into an Integer (or, in this case, a LargeInteger) by sending it #powerOfTen. So what we really have is:

1.0 * (174 powerOfTen asFloat) = 1000.0 * (171 powerOfTen asFloat)

Since there are floating point operations involved in this comparison, you can get lucky (the values are exactly representable as Floats) or unlucky (the values are not exactly representable as Floats) -- you got unlucky.

Also notice that:

1.0e171 * 1000.0 = 1000.0e171

answers true. In this case there is no uncertainty associated with the exponent since both sides use the same exponent.

So, the message is: "Don't use = with Floats" because you will get unexpected results.

On Wednesday, February 26, 2014 2:12:39 PM UTC-5, Richard Sargent wrote:
The subject pretty well says it all.
One would expect the following expression to answer 'true'. It doesn't.

1000.0e171 = 1.0e174

(There is a discrepancy in the least significant bit.)