[triangle-zpug] rounding errors with floating point operations

[Chris Calloway]

On Jul 19, 2008, at 10:21 AM, Joseph Mack NA3T wrote:
> This is about floating point ops, and not specific to python. It  
> just came up when I was writing python code.
>
> If you do the following floating point ops
>
> x=0.1
> y=x/n	#n some floating point number
> z=y*n
>
> I would expect due to the finite precision of floating point  
> representation, that some digits would fall off the end when doing  
> y=x/n and that the z you get would give z!=x. However I find that  
> z==x. Here's an example where n is a power of 2.
>
>>>> n_128=2**128
>>>> print n_128
> 340282366920938463463374607431768211456
>>>> x=0.1
>>>> y=x/n_128
>>>> z=y*n_128
>>>> print "%30.30g, %30.30g, %30.30g" %(x,y,z)
> 0.100000000000000005551115123126,  
> 2.93873587705571893305445304302e-40, 0.100000000000000005551115123126
>
> I'm happy with this one. Dividing by a power of 2 just changes the  
> exponent and not the mantissa in the floating point prepresentation  
> of a number. So I wouldn't expect the precision of the mantissa to  
> change.
>
> Here's an example when the divisor should affect the mantisssa, but  
> still I don't see any sign of digits falling off the right side of  
> the mantissa due to the division
>
>>>> n_prime=149.0
>>>> y=x/n_prime
>>>> z=y*n_prime
>>>> print "%30.30g, %30.30g, %30.30g" %(x,y,z)
> 0.100000000000000005551115123126,  
> 0.000671140939597315508424735241988, 0.100000000000000005551115123126
>
> Why doesn't division of reals loose precision?
>
> Thanks Joe
> -- 
> Joseph Mack NA3T EME(B,D), FM05lw North Carolina
> jmack (at) wm7d (dot) net - azimuthal equidistant map
> generator at http://www.wm7d.net/azproj.shtml
> Homepage http://www.austintek.com/ It's GNU/Linux!
>
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It's all in all the print spec. It's not giving you an accurate  
representation of the precision when you specify more precision in the  
print spec than there is in a C double. It's all still  
0.10000000000000001.

-- 
Sincerely,

Chris Calloway
http://www.secoora.org
office: 332 Chapman Hall   phone: (919) 599-3530
mail: Campus Box #3300, UNC-CH, Chapel Hill, NC 27599