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# Why the nonsense number appears?

 P: n/a Hi, Pls take a look at this code: ---------- t1 = "1130748744" t2 = "461" t3 = "1130748744" t4 = "500" time1 = t1+"."+t2 time2 = t3+"."+t4 print time1, time2 1130748744.461 1130748744.500 float(time2) - float(time1) 0.039000034332275391 Why are there so many nonsense tails? thanks for your help. Regards, Johnny Oct 31 '05 #1
9 Replies

 P: n/a Johnny Lee enlightened us with: Why are there so many nonsense tails? thanks for your help. Because if the same reason you can't write 1/3 in decimal: http://docs.python.org/tut/node16.html Sybren -- The problem with the world is stupidity. Not saying there should be a capital punishment for stupidity, but why don't we just take the safety labels off of everything and let the problem solve itself? Frank Zappa Oct 31 '05 #2

 P: n/a Johnny Lee wrote: Why are there so many nonsense tails? thanks for your help. I guess you were expecting 0.039? You first need to understand floating point numbers: http://docs.python.org/tut/node16.html What you see are the effects of representation errors. The solution is presented here: http://www.python.org/peps/pep-0327.html But briefly, it means your code should read: from decimal import * t1 = "1130748744" t2 = "461" t3 = "1130748744" t4 = "500" time1 = t1+"."+t2 time2 = t3+"."+t4 print time1, time2 Decimal(time2) - Decimal(time1) Oct 31 '05 #3

 P: n/a Johnny Lee wrote:print time1, time2 1130748744.461 1130748744.500float(time2) - float(time1) 0.039000034332275391 Why are there so many nonsense tails? thanks for your help. http://en.wikipedia.org/wiki/Floatin...floating-point, especially 'Rounding'. Or google for "gloating point precision" if you need more details. Daniel Oct 31 '05 #4

 P: n/a On Mon, October 31, 2005 9:39, Sybren Stuvel said: Johnny Lee enlightened us with: Why are there so many nonsense tails? thanks for your help. Because if the same reason you can't write 1/3 in decimal: http://docs.python.org/tut/node16.html Sybren -- The problem with the world is stupidity. Not saying there should be a capital punishment for stupidity, but why don't we just take the safety labels off of everything and let the problem solve itself? Frank Zappa -- http://mail.python.org/mailman/listinfo/python-list I think that the previous poster was asking something different. I think he was asking something like this: If t1 = 0.500 t2 = 0.461 print t1-t2 0.039 Then why: t1 += 12345678910 t2 += 12345678910 # Note, both t1 and t2 have been incremented by the same amount. print t1-t2 0.0389995574951 It appears Yu-Xi Lim beat me to the punch. Using decimal as opposed to float sorts out this error as floats are not built to handle the size of number used here. Ben Oct 31 '05 #5

 P: n/a Ben O'Steen enlightened us with: I think that the previous poster was asking something different. It all boils down to floating point inprecision. If t1 = 0.500 t2 = 0.461 print t1-t2 0.039 Then why: t1 += 12345678910 t2 += 12345678910 # Note, both t1 and t2 have been incremented by the same amount. print t1-t2 0.0389995574951 It's easier to explain in decimals. Just assume you only have memory to keep three decimals. 12345678910.500 is internally stored as something like 1.23456789105e10. Strip that to three decimals, and you have 1.234e10. In that case, t1 - t2 = 1.234e10 - 1.234e10 = 0. Using decimal as opposed to float sorts out this error as floats are not built to handle the size of number used here. They can handle the size just fine. What they can't handle is 1/1000th precision when using numbers in the order of 1e10. Sybren -- The problem with the world is stupidity. Not saying there should be a capital punishment for stupidity, but why don't we just take the safety labels off of everything and let the problem solve itself? Frank Zappa Oct 31 '05 #6

 P: n/a On Mon, October 31, 2005 10:23, Sybren Stuvel said: Ben O'Steen enlightened us with: Using decimal as opposed to float sorts out this error as floats are not built to handle the size of number used here. They can handle the size just fine. What they can't handle is 1/1000th precision when using numbers in the order of 1e10. I used the word 'size' here incorrectly, I intended to mean 'length' rather than numerical value. Sorry for the confusion :) Sybren -- The problem with the world is stupidity. Not saying there should be a capital punishment for stupidity, but why don't we just take the safety labels off of everything and let the problem solve itself? Frank Zappa -- http://mail.python.org/mailman/listinfo/python-list Oct 31 '05 #7

 P: n/a Ben O'Steen wrote: On Mon, October 31, 2005 10:23, Sybren Stuvel said: Ben O'Steen enlightened us with: Using decimal as opposed to float sorts out this error as floats are not built to handle the size of number used here. They can handle the size just fine. What they can't handle is 1/1000th precision when using numbers in the order of 1e10. I used the word 'size' here incorrectly, I intended to mean 'length' rather than numerical value. Sorry for the confusion :) Sybren is right. The problem is not the length or the size, it's the fact that 0.039 cannot be represented exactly in binary, in just the same way that 1/3 cannot be represented exactly in decimal. They both give recurring numbers. If you truncate those recurring numbers to a finite number of digits, you lose precision. And this shows up when you convert the inaccurate number from binary into decimal representation where an exact representation IS possible. Steve Oct 31 '05 #8

 P: n/a Steve Horsley wrote: Ben O'Steen wrote: On Mon, October 31, 2005 10:23, Sybren Stuvel said: Ben O'Steen enlightened us with: Using decimal as opposed to float sorts out this error as floats are not built to handle the size of number used here. They can handle the size just fine. What they can't handle is 1/1000th precision when using numbers in the order of 1e10. I used the word 'size' here incorrectly, I intended to mean 'length' rather than numerical value. Sorry for the confusion :) Sybren is right. The problem is not the length or the size, it's the fact that 0.039 cannot be represented exactly in binary, in just the same way that 1/3 cannot be represented exactly in decimal. They both give recurring numbers. If you truncate those recurring numbers to a finite number of digits, you lose precision. And this shows up when you convert the inaccurate number from binary into decimal representation where an exact representation IS possible. That's A source of error, but it's only part of the story. The double-precision binary representation of 0.039 is 5620492334958379 * 2**(-57), which is in error by 1/18014398509481984000. By contrast, Johnny Lee's answer is in error by 9/262144000, which is more than 618 billion times the error of simply representing 0.039 in floating point -- a loss of 39 bits. The problem here is catastrophic cancellation. 1130748744.500 ~= 4742703982051328 * 2**(-22) 1130748744.461 ~= 4742703981887750 * 2**(-22) Subtracting gives 163578 * 2**(-22), which has only 18 significant bits. Nov 1 '05 #9

 P: n/a Dan Bishop wrote: That's A source of error, but it's only part of the story. The double-precision binary representation of 0.039 is 5620492334958379 * 2**(-57), which is in error by 1/18014398509481984000. By contrast, Johnny Lee's answer is in error by 9/262144000, which is more than 618 billion times the error of simply representing 0.039 in floating point -- a loss of 39 bits. The problem here is catastrophic cancellation. 1130748744.500 ~= 4742703982051328 * 2**(-22) 1130748744.461 ~= 4742703981887750 * 2**(-22) Subtracting gives 163578 * 2**(-22), which has only 18 significant bits. Hmm. Good point. Nov 1 '05 #10

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