R2=: | R1=: (] - [ * [: <.!.0 ] % [)"0 R0=: (|&x:)"0
(14^2) R1 5729082486784839 147 (14^2) R2 5729082486784839 0 X=: (0.1-0.1)+i.1000 Y=: 5729082486784839+i:1000 datatype X floating +/,X (R0/ ~: R2/) Y 1845046 +/,X (R0/ ~: R1/) Y 0 Good question. Thanks, -- Raul On Tue, Sep 12, 2017 at 4:26 AM, Erling Hellenäs <erl...@erlinghellenas.se> wrote: > Residue1=: ] - [ * [: <.!.0 ] % [ > > Residue2=: | > > (14^2) Residue1 5729082486784839 > > 147 > > (14^2) Residue2 5729082486784839 > > 0 > > Why is Residue2 losing precision when Residue1 is not? > > /Erling > > > > Den 2017-09-12 kl. 02:04, skrev Don Kelly: >> >> I believe that Raul has hit it on the head. 14^2 will be floating as will >> generally be the case with % so it is possible that errors add or subtract >> to give an erroneous result. Note that >> >> (14^2) (] - [ * [: <. ] % [)5729082486784839x >> >> 147 >> >> >> (14^2x) (] - [ * [: <. ] % [)5729082486784839 >> >> 147 >> >> and >> >> (14^2x)|5729082486784839 >> >> 147 >> >> >> does it more simply >> >> >> Don >> >> On 2017-09-11 6:50 AM, Erling Hellenäs wrote: >>> >>> (14^2x) (] - [ * [: <. ] % [)5729082486784839x >>> >>> 147 >>> >>> (14^2) (] - [ * [: <. ] % [)5729082486784839 >>> >>> _49 >>> >>> (14^2) (] - [ * _1 + [: <. ] % [)5729082486784839 >>> >>> 147 >>> >>> /Erling >>> >>> >>> Den 2017-09-11 kl. 15:40, skrev Erling Hellenäs: >>>> >>>> From what I see, floor gives an incorrect result which I correct with >>>> the " _1 + " There is not other problem. No loss of precision. /Erling >>>> >>>> >>>> Den 2017-09-11 kl. 15:27, skrev Raul Miller: >>>>> >>>>> I do not know what you are thinking, and you have not illustrated your >>>>> thoughts sufficiently for me to grasp them. >>>>> >>>>> So, I thought I'd work through this: >>>>> >>>>> (14^2) (] - [ * _1 + [: <. ] % [)5729082486784839 >>>>> 147 >>>>> (14^2x) (] - [ * _1 + [: <. ] % [)5729082486784839x >>>>> 343 >>>>> >>>>> Clearly, the exact answer is different from the quick answer. >>>>> >>>>> If we compare >>>>> load'debug/dissect' >>>>> dissect '(14^2) (] - [ * _1 + [: <. ] % [)5729082486784839' >>>>> dissect '(14^2x) (] - [ * _1 + [: <. ] % [)5729082486784839x' >>>>> >>>>> We can see the initial off-by-one errors, but the big difference shows >>>>> up at the end (where we subtract from 5729082486784839) >>>>> >>>>> The value we are subtracting is: >>>>> >>>>> (14^2x) ([ * _1 + [: <. ] % [)5729082486784839x >>>>> 5729082486784496 >>>>> (14^2) ([ * _1 + [: <. ] % [)5729082486784839 >>>>> 5.72908e15 >>>>> >>>>> Looking at the bits needed to represent that as an integer: >>>>> >>>>> 2^.(14^2) ([ * _1 + [: <. ] % [)5729082486784839 >>>>> 52.3472 >>>>> >>>>> we can see that that's right on the edge of being the number of >>>>> representable digits in a 64 bit float. >>>>> >>>>> But, also, it's the result of multiplying >>>>> >>>>> 14^2 >>>>> 196 >>>>> >>>>> by an off-by-one amount. And... >>>>> >>>>> 343-196 >>>>> 147 >>>>> >>>>> ... >>>>> >>>>> Anyways, I'm not sure what you were thinking, but I guess we can take >>>>> this as a good example of the idea that errors can actually >>>>> accumulate. >>>>> >>>>> Thanks, >>>>> >>>> >>>> ---------------------------------------------------------------------- >>>> For information about J forums see http://www.jsoftware.com/forums.htm >>> >>> >>> ---------------------------------------------------------------------- >>> For information about J forums see http://www.jsoftware.com/forums.htm >> >> >> ---------------------------------------------------------------------- >> For information about J forums see http://www.jsoftware.com/forums.htm > > > ---------------------------------------------------------------------- > For information about J forums see http://www.jsoftware.com/forums.htm ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
