Well... I'm inclined to agree with you that your perl 5.8.6 result is incorrect. The decimal to binary conversion is incorrectly rounded -- so worse than the usual representation error.

On my perl 5.10.0, using IEEE-754 floating point doubles, your 0.99999999976716936 value is converted to the binary floating point value whose bit pattern is 0x3FEF_FFFF_FFDF_FFFF (or +0x1.F_FFFF_FFDF_FFFFp-1, if you prefer). This appears to be the same as your 5.8.6 result.

Looking at that and the next two larger values I see:

  0x3FEF_FFFF_FFDF_FFFF == 0.999999999767169245323827908578 (approx)
  0x3FEF_FFFF_FFE0_0000 == 0.999999999767169356346130371093 (approx)
         original value == 0.99999999976716936
  0x3FEF_FFFF_FFE0_0001 == 0.999999999767169467368432833609 (approx)

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What's odd about this is that the decimal to binary conversion is not 'correctly rounded' (I'm assuming round-to-nearest as the only sensible rounding for the conversion) -- 0x3FEF_FFFF_FFE0_0000 is clearly a lot closer to the original 0.99999999976716936 than the values on either side of it !

I'm damned if I can see a good reason for getting this wrong. I note only that if you truncate the original value to 16 significant digits (ie to 0.9999999997671693) then 0x3FEF_FFFF_FFDF_FFFF is the correctly converted result.

I get the same results on 64-bit Linux machine and 32-bit Winders. So, either two different libraries have the same decimal to binary fault, or something in perl is wrong.

This is bad. IEEE-754 requires the result of a conversion from binary to decimal and back to binary to be the original binary value, provided that at least 17 significant decimal digits are used (for doubles). I find that:

  0x3FEF_FFFF_FFE0_0000 -> 0.99999999976716936 -> 0x3FEF_FFFF_FFDF_FFF
+F

[download]

However, wrong as this is, the general advice -- not to depend on floating point results to be exactly equal to something -- always applies.

In reply to Re: Perl 5.8.x floating point representation error by gone2015
in thread Perl 5.8.x floating point representation error by satish.rpr

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