Re: [Numpy-discussion] Importance of order when summing values in anarray
On my two systems with Intel Core2 DUO, finfo(float128) gives me the nameerro, NameError: name 'float128' is not defined. Why? Thanks Frank Date: Tue, 9 Dec 2008 21:10:32 -0600 From: [EMAIL PROTECTED] To: numpy-discussion@scipy.org Subject: Re: [Numpy-discussion] Importance of order when summing values in anarray On Tue, Dec 9, 2008 at 21:01, Charles R Harris [EMAIL PROTECTED] wrote:On Tue, Dec 9, 2008 at 1:40 PM, Robert Kern [EMAIL PROTECTED] wrote: On Tue, Dec 9, 2008 at 09:51, Nadav Horesh [EMAIL PROTECTED] wrote: As much as I know float128 are in fact 80 bits (64 mantissa + 16 exponent) so the precision is 18-19 digits (not 34) float128 should be 128 bits wide. If it's not on your platform, please let us know as that is a bug in your build. I think he means the actual precision is the ieee extended precision, the number just happens to be stored into larger chunks of memory for alignment purposes. Ah, that's good to know. Yes, float128 on my Intel Mac behaves this way. In [12]: f = finfo(float128) In [13]: f.nmant Out[13]: 63 In [14]: f.nexp Out[14]: 15 -- Robert Kern I have come to believe that the whole world is an enigma, a harmless enigma that is made terrible by our own mad attempt to interpret it as though it had an underlying truth. -- Umberto Eco ___ Numpy-discussion mailing list Numpy-discussion@scipy.org http://projects.scipy.org/mailman/listinfo/numpy-discussion _ You live life online. So we put Windows on the web. http://clk.atdmt.com/MRT/go/127032869/direct/01/___ Numpy-discussion mailing list Numpy-discussion@scipy.org http://projects.scipy.org/mailman/listinfo/numpy-discussion
Re: [Numpy-discussion] Importance of order when summing values in anarray
On Wed, Dec 10, 2008 at 11:00 AM, frank wang [EMAIL PROTECTED] wrote: On my two systems with Intel Core2 DUO, finfo(float128) gives me the nameerro, NameError: name 'float128' is not defined. Why? You probably run a 32 bit OS. IEEE extended precision is 80 bits. On 32 bit systems it fits in three 32 bit words and shows up as float96. On 64 bit systems it fits in two 64 bit words and shows up as float128. Chuck ___ Numpy-discussion mailing list Numpy-discussion@scipy.org http://projects.scipy.org/mailman/listinfo/numpy-discussion
Re: [Numpy-discussion] Importance of order when summing values in anarray
On Wed, Dec 10, 2008 at 12:07, Charles R Harris [EMAIL PROTECTED] wrote: On Wed, Dec 10, 2008 at 11:00 AM, frank wang [EMAIL PROTECTED] wrote: On my two systems with Intel Core2 DUO, finfo(float128) gives me the nameerro, NameError: name 'float128' is not defined. Why? You probably run a 32 bit OS. IEEE extended precision is 80 bits. On 32 bit systems it fits in three 32 bit words and shows up as float96. On 64 bit systems it fits in two 64 bit words and shows up as float128. I'm running a 32-bit OS (well, a 32-bit build of Python on OS X) on an Intel Core2 Duo, and I get a float128. -- Robert Kern I have come to believe that the whole world is an enigma, a harmless enigma that is made terrible by our own mad attempt to interpret it as though it had an underlying truth. -- Umberto Eco ___ Numpy-discussion mailing list Numpy-discussion@scipy.org http://projects.scipy.org/mailman/listinfo/numpy-discussion
Re: [Numpy-discussion] Importance of order when summing values in anarray
On Wed, Dec 10, 2008 at 11:58 AM, Robert Kern [EMAIL PROTECTED] wrote: On Wed, Dec 10, 2008 at 12:07, Charles R Harris [EMAIL PROTECTED] wrote: On Wed, Dec 10, 2008 at 11:00 AM, frank wang [EMAIL PROTECTED] wrote: On my two systems with Intel Core2 DUO, finfo(float128) gives me the nameerro, NameError: name 'float128' is not defined. Why? You probably run a 32 bit OS. IEEE extended precision is 80 bits. On 32 bit systems it fits in three 32 bit words and shows up as float96. On 64 bit systems it fits in two 64 bit words and shows up as float128. I'm running a 32-bit OS (well, a 32-bit build of Python on OS X) on an Intel Core2 Duo, and I get a float128. -- Robert Kern I have come to believe that the whole world is an enigma, a harmless enigma that is made terrible by our own mad attempt to interpret it as though it had an underlying truth. -- Umberto Eco ___ Numpy-discussion mailing list Numpy-discussion@scipy.org http://projects.scipy.org/mailman/listinfo/numpy-discussion ___ Numpy-discussion mailing list Numpy-discussion@scipy.org http://projects.scipy.org/mailman/listinfo/numpy-discussion
Re: [Numpy-discussion] Importance of order when summing values in anarray
On Wed, Dec 10, 2008 at 11:58 AM, Robert Kern [EMAIL PROTECTED] wrote: On Wed, Dec 10, 2008 at 12:07, Charles R Harris [EMAIL PROTECTED] wrote: On Wed, Dec 10, 2008 at 11:00 AM, frank wang [EMAIL PROTECTED] wrote: On my two systems with Intel Core2 DUO, finfo(float128) gives me the nameerro, NameError: name 'float128' is not defined. Why? You probably run a 32 bit OS. IEEE extended precision is 80 bits. On 32 bit systems it fits in three 32 bit words and shows up as float96. On 64 bit systems it fits in two 64 bit words and shows up as float128. I'm running a 32-bit OS (well, a 32-bit build of Python on OS X) on an Intel Core2 Duo, and I get a float128. Curious. It probably has something to do with the way the FPU is set up when running on a 64 bit system that is independent of how python is compiled. Chuck ___ Numpy-discussion mailing list Numpy-discussion@scipy.org http://projects.scipy.org/mailman/listinfo/numpy-discussion
Re: [Numpy-discussion] Importance of order when summing values in anarray
The highest accuracy is obtained when you sum an acceding ordered series, and the lowest accuracy with descending ordered. In between you might get a variety of rounding errors. Nadav. -הודעה מקורית- מאת: [EMAIL PROTECTED] בשם Hanni Ali נשלח: ג 09-דצמבר-08 16:07 אל: Discussion of Numerical Python נושא: [Numpy-discussion] Importance of order when summing values in anarray Hi All, I have encountered a puzzling issue and I am not certain if this is a mistake of my own doing or not. Would someone kindly just look over this issue to make sure I'm not doing something very silly. So, why would the sum of an array have a different value depending on the order I select the indices of the array? vector[[39, 46, 49, 50, 6, 9, 12, 14, 15, 17, 21]].sum() 8933281.8757099733 vector[[6, 9, 12, 14, 15, 17, 21, 39, 46, 49, 50]].sum() 8933281.8757099714 sum(vector[[39, 46, 49, 50, 6, 9, 12, 14, 15, 17, 21]]) 8933281.8757099733 sum(vector[[6, 9, 12, 14, 15, 17, 21, 39, 46, 49, 50]]) 8933281.8757099714 Any thoughts? Cheers, Hanni winmail.dat___ Numpy-discussion mailing list Numpy-discussion@scipy.org http://projects.scipy.org/mailman/listinfo/numpy-discussion
Re: [Numpy-discussion] Importance of order when summing values in anarray
Thank you Nadav. 2008/12/9 Nadav Horesh [EMAIL PROTECTED] The highest accuracy is obtained when you sum an acceding ordered series, and the lowest accuracy with descending ordered. In between you might get a variety of rounding errors. Nadav. -הודעה מקורית- מאת: [EMAIL PROTECTED] בשם Hanni Ali נשלח: ג 09-דצמבר-08 16:07 אל: Discussion of Numerical Python נושא: [Numpy-discussion] Importance of order when summing values in anarray Hi All, I have encountered a puzzling issue and I am not certain if this is a mistake of my own doing or not. Would someone kindly just look over this issue to make sure I'm not doing something very silly. So, why would the sum of an array have a different value depending on the order I select the indices of the array? vector[[39, 46, 49, 50, 6, 9, 12, 14, 15, 17, 21]].sum() 8933281.8757099733 vector[[6, 9, 12, 14, 15, 17, 21, 39, 46, 49, 50]].sum() 8933281.8757099714 sum(vector[[39, 46, 49, 50, 6, 9, 12, 14, 15, 17, 21]]) 8933281.8757099733 sum(vector[[6, 9, 12, 14, 15, 17, 21, 39, 46, 49, 50]]) 8933281.8757099714 Any thoughts? Cheers, Hanni ___ Numpy-discussion mailing list Numpy-discussion@scipy.org http://projects.scipy.org/mailman/listinfo/numpy-discussion ___ Numpy-discussion mailing list Numpy-discussion@scipy.org http://projects.scipy.org/mailman/listinfo/numpy-discussion
Re: [Numpy-discussion] Importance of order when summing values in anarray
Nadav Horesh wrote: The highest accuracy is obtained when you sum an acceding ordered series, and the lowest accuracy with descending ordered. In between you might get a variety of rounding errors. Nadav. -הודעה מקורית- מאת: [EMAIL PROTECTED] בשם Hanni Ali נשלח: ג 09-דצמבר-08 16:07 אל: Discussion of Numerical Python נושא: [Numpy-discussion] Importance of order when summing values in anarray Hi All, I have encountered a puzzling issue and I am not certain if this is a mistake of my own doing or not. Would someone kindly just look over this issue to make sure I'm not doing something very silly. So, why would the sum of an array have a different value depending on the order I select the indices of the array? vector[[39, 46, 49, 50, 6, 9, 12, 14, 15, 17, 21]].sum() 8933281.8757099733 vector[[6, 9, 12, 14, 15, 17, 21, 39, 46, 49, 50]].sum() 8933281.8757099714 sum(vector[[39, 46, 49, 50, 6, 9, 12, 14, 15, 17, 21]]) 8933281.8757099733 sum(vector[[6, 9, 12, 14, 15, 17, 21, 39, 46, 49, 50]]) 8933281.8757099714 Any thoughts? Cheers, Hanni ___ Numpy-discussion mailing list Numpy-discussion@scipy.org http://projects.scipy.org/mailman/listinfo/numpy-discussion Also, increase the numerical precision as that may depend on your platform especially given the input values above are ints. Numpy has float128 and int64 that will minimize rounding error. Bruce ___ Numpy-discussion mailing list Numpy-discussion@scipy.org http://projects.scipy.org/mailman/listinfo/numpy-discussion
Re: [Numpy-discussion] Importance of order when summing values in anarray
Hi Bruce, Ahh, but I would have thought the precision for the array operation would be the same no matter which values I wish to sum? The array is in float64 in all cases. I would not have thought altering the type of the integer values would make any difference as these indices are all below 5 milllion. Perhaps I have misunderstood your suggestion could you expand. Cheers, Hanni Also, increase the numerical precision as that may depend on your platform especially given the input values above are ints. Numpy has float128 and int64 that will minimize rounding error. Bruce ___ Numpy-discussion mailing list Numpy-discussion@scipy.org http://projects.scipy.org/mailman/listinfo/numpy-discussion ___ Numpy-discussion mailing list Numpy-discussion@scipy.org http://projects.scipy.org/mailman/listinfo/numpy-discussion
Re: [Numpy-discussion] Importance of order when summing values in anarray
Hanni Ali wrote: Hi Bruce, Ahh, but I would have thought the precision for the array operation would be the same no matter which values I wish to sum? The array is in float64 in all cases. I would not have thought altering the type of the integer values would make any difference as these indices are all below 5 milllion. Perhaps I have misunderstood your suggestion could you expand. Cheers, Hanni Also, increase the numerical precision as that may depend on your platform especially given the input values above are ints. Numpy has float128 and int64 that will minimize rounding error. Bruce ___ Numpy-discussion mailing list Numpy-discussion@scipy.org mailto:Numpy-discussion@scipy.org http://projects.scipy.org/mailman/listinfo/numpy-discussion ___ Numpy-discussion mailing list Numpy-discussion@scipy.org http://projects.scipy.org/mailman/listinfo/numpy-discussion Hi, The main issue is the number of significant digits that you have which is not the number of decimals in your case. So while the numerical difference in the results is in the order about 1.86e-09, the actual difference starts at the 15th significant place. This is expected due to the number of significant digits of a 64-bit number (15-16). With higher precision like float128 you should get about 34 significant digits depending accuracy in all steps (i.e., the numbers must be stored as float128 and the summations done in float128 precision). Note there is a secondary issue of converting numbers between different types as well as the binary representation of decimal numbers. Also, rather than just simple summing, there are alternative algorithms like Kahan summation algorithm that can minimize errors. Bruce ___ Numpy-discussion mailing list Numpy-discussion@scipy.org http://projects.scipy.org/mailman/listinfo/numpy-discussion
Re: [Numpy-discussion] Importance of order when summing values in anarray
On Tue, Dec 9, 2008 at 09:51, Nadav Horesh [EMAIL PROTECTED] wrote: As much as I know float128 are in fact 80 bits (64 mantissa + 16 exponent) so the precision is 18-19 digits (not 34) float128 should be 128 bits wide. If it's not on your platform, please let us know as that is a bug in your build. -- Robert Kern I have come to believe that the whole world is an enigma, a harmless enigma that is made terrible by our own mad attempt to interpret it as though it had an underlying truth. -- Umberto Eco ___ Numpy-discussion mailing list Numpy-discussion@scipy.org http://projects.scipy.org/mailman/listinfo/numpy-discussion
Re: [Numpy-discussion] Importance of order when summing values in anarray
On Tue, Dec 9, 2008 at 1:40 PM, Robert Kern [EMAIL PROTECTED] wrote: On Tue, Dec 9, 2008 at 09:51, Nadav Horesh [EMAIL PROTECTED] wrote: As much as I know float128 are in fact 80 bits (64 mantissa + 16 exponent) so the precision is 18-19 digits (not 34) float128 should be 128 bits wide. If it's not on your platform, please let us know as that is a bug in your build. I think he means the actual precision is the ieee extended precision, the number just happens to be stored into larger chunks of memory for alignment purposes. Chuck ___ Numpy-discussion mailing list Numpy-discussion@scipy.org http://projects.scipy.org/mailman/listinfo/numpy-discussion
Re: [Numpy-discussion] Importance of order when summing values in anarray
On Tue, Dec 9, 2008 at 21:01, Charles R Harris [EMAIL PROTECTED] wrote: On Tue, Dec 9, 2008 at 1:40 PM, Robert Kern [EMAIL PROTECTED] wrote: On Tue, Dec 9, 2008 at 09:51, Nadav Horesh [EMAIL PROTECTED] wrote: As much as I know float128 are in fact 80 bits (64 mantissa + 16 exponent) so the precision is 18-19 digits (not 34) float128 should be 128 bits wide. If it's not on your platform, please let us know as that is a bug in your build. I think he means the actual precision is the ieee extended precision, the number just happens to be stored into larger chunks of memory for alignment purposes. Ah, that's good to know. Yes, float128 on my Intel Mac behaves this way. In [12]: f = finfo(float128) In [13]: f.nmant Out[13]: 63 In [14]: f.nexp Out[14]: 15 -- Robert Kern I have come to believe that the whole world is an enigma, a harmless enigma that is made terrible by our own mad attempt to interpret it as though it had an underlying truth. -- Umberto Eco ___ Numpy-discussion mailing list Numpy-discussion@scipy.org http://projects.scipy.org/mailman/listinfo/numpy-discussion
Re: [Numpy-discussion] Importance of order when summing values in anarray
On Tue, Dec 9, 2008 at 8:10 PM, Robert Kern [EMAIL PROTECTED] wrote: On Tue, Dec 9, 2008 at 21:01, Charles R Harris [EMAIL PROTECTED] wrote: On Tue, Dec 9, 2008 at 1:40 PM, Robert Kern [EMAIL PROTECTED] wrote: On Tue, Dec 9, 2008 at 09:51, Nadav Horesh [EMAIL PROTECTED] wrote: As much as I know float128 are in fact 80 bits (64 mantissa + 16 exponent) so the precision is 18-19 digits (not 34) float128 should be 128 bits wide. If it's not on your platform, please let us know as that is a bug in your build. I think he means the actual precision is the ieee extended precision, the number just happens to be stored into larger chunks of memory for alignment purposes. Ah, that's good to know. Yes, float128 on my Intel Mac behaves this way. In [12]: f = finfo(float128) In [13]: f.nmant Out[13]: 63 In [14]: f.nexp Out[14]: 15 Yep. That's the reason I worry a bit about what will happen when ieee quad precision comes out; it really is 128 bits wide and the normal identifiers won't account for the difference. I expect c will just call them long doubles and they will get the 'g' letter code just like extended precision does now. Chuck ___ Numpy-discussion mailing list Numpy-discussion@scipy.org http://projects.scipy.org/mailman/listinfo/numpy-discussion
