On 11/08/2012 12:05 PM, Debashish Saha wrote: > (1500000000+1.00067968)-(1500000000+1.00067961) > Out[102]: 2.384185791015625e-07 > > 1.00067968-(1.00067961) > Out[103]: 7.000000001866624e-08 > > above i am showing the two different results,though the two outputs > should be same if we do it in copy(the lass one is acceptable value). > so my question is how to increase the accuracy(windows7(32bit) > ,python2.7.2)
To improve accuracy, do some algebra before coding brute force. If you know you'll be subtracting two values that are nearly equal, see if you can factor out the large part, and only subtract the small parts. If you have a processor with 16 digits of float accuracy, and you calculate an 18 digit sum, you're going to lose 3 digts at a minimum. Each sum has the same problem. So now you have lopped off all the digits that are different. So subtracting them is meaningless. Picture needing to know how thick a leaf is. So measure the distance from one side of it to the sun. Then measure the distance from the other side to the sun. Now just subtract the answers. Silly, isn't it? You have (a+b) - (a+c), where a is much larger than either b or c. So simplify it to b-c before programming it. Oh, yeah, that's your second approach. More generally, if you have a sum of 3 or more values (which you can get by just stating the problem as a + b + -a + -c), you can usually minimize error by reordering the arithmetic, based on the sizes of the items. Fortunately Python has a library function that knows how to do that: http://docs.python.org/2/library/math.html#math.fsum If you want to postpone the problem so instead of hitting at 15 digits or so, it hits at a few hundred digits, you could use decimal.Decimal, which is a standard library in Python. It permits you to specify your own precision, instead of being what Intel (professor Kahn) decided on in about 1985. They constrained themselves to what could be encoded in 8 bytes. Naturally, if you ask for much higher precision with Decimal, you'll pay for it with space and/or time. But apparently in 3.3, they did a very good job minimizing the time it takes, for reasonable precision. Interestingly, I got a similar question in about 1977, concerning a trig package I had microcoded. A man was measuring the flatness of a hypothetical level table (which must be curved, of course). And he did it with trig, and effectively by subtracting two measurements to the center of the earth. I was able to simplify his problem using some geometry (similar triangles) to get all the accuracy he needed. And strangely enough, the trig canceled out and was unnecessary. -- DaveA -- http://mail.python.org/mailman/listinfo/python-list
