How To Deal With Rounding Errors
Hey, Short version of my question: I believe I am having rounding errors because I am working with really, really small values. Would it help if I multiplied these values by a scalar (say, 1,000), did math with them, and then divided them by the scalar? I remember learning how IEEE floating point numbers are stored, but I can't remember enough about it to know if this would have any effect on precision. If not, what is a good way to get better precision? I am already using doubles instead of floats. Long explanation of my question: In my project, I have users clicking and dragging to adjust values. I would like to map values from the left-most of the view being zero, and the right-most of the view to be one. This is fairly simple. However, it feels a little unnatural if the value initially jumps to match where the mouse clicks before dragging. For example, if the initial value is 0.3, and they click in the middle of the view, the value jumps to 0.5. To take care of this I construct a polynomial which maps 0 to 0, the right-most of the view to 1, and the initial click location (middle) to the initial value (0.3). This works very well, and feels natural. However, when any of the values near the edges (the user clicks just off the left of the view), the values go crazy. I believe this is because of a rounding error. The same question still stands, would multiplying (and later dividing) everything by a scalar help me get greater precision? Thank You, Bridger Maxwell ___ Cocoa-dev mailing list (Cocoa-dev@lists.apple.com) Please do not post admin requests or moderator comments to the list. Contact the moderators at cocoa-dev-admins(at)lists.apple.com Help/Unsubscribe/Update your Subscription: http://lists.apple.com/mailman/options/cocoa-dev/archive%40mail-archive.com This email sent to [EMAIL PROTECTED]
Re: How To Deal With Rounding Errors
The way floats work the round will always be to the same number of bits no matter what the order of magnitude (ignoring the extreme values 2^-1023 for doubles). Check that you haven't let any integers into you calculations. On 04/12/2008, at 7:08 PM, Bridger Maxwell wrote: Hey, Short version of my question: I believe I am having rounding errors because I am working with really, really small values. Would it help if I multiplied these values by a scalar (say, 1,000), did math with them, and then divided them by the scalar? I remember learning how IEEE floating point numbers are stored, but I can't remember enough about it to know if this would have any effect on precision. If not, what is a good way to get better precision? I am already using doubles instead of floats. Long explanation of my question: In my project, I have users clicking and dragging to adjust values. I would like to map values from the left-most of the view being zero, and the right-most of the view to be one. This is fairly simple. However, it feels a little unnatural if the value initially jumps to match where the mouse clicks before dragging. For example, if the initial value is 0.3, and they click in the middle of the view, the value jumps to 0.5. To take care of this I construct a polynomial which maps 0 to 0, the right-most of the view to 1, and the initial click location (middle) to the initial value (0.3). This works very well, and feels natural. However, when any of the values near the edges (the user clicks just off the left of the view), the values go crazy. I believe this is because of a rounding error. The same question still stands, would multiplying (and later dividing) everything by a scalar help me get greater precision? Thank You, Bridger Maxwell ___ Cocoa-dev mailing list (Cocoa-dev@lists.apple.com) Please do not post admin requests or moderator comments to the list. Contact the moderators at cocoa-dev-admins(at)lists.apple.com Help/Unsubscribe/Update your Subscription: http://lists.apple.com/mailman/options/cocoa-dev/nathan_day%40mac.com This email sent to [EMAIL PROTECTED] ___ Cocoa-dev mailing list (Cocoa-dev@lists.apple.com) Please do not post admin requests or moderator comments to the list. Contact the moderators at cocoa-dev-admins(at)lists.apple.com Help/Unsubscribe/Update your Subscription: http://lists.apple.com/mailman/options/cocoa-dev/archive%40mail-archive.com This email sent to [EMAIL PROTECTED]
Re: How To Deal With Rounding Errors
On 04 Dec 08, at 00:08, Bridger Maxwell wrote: Short version of my question: I believe I am having rounding errors because I am working with really, really small values. Would it help if I multiplied these values by a scalar (say, 1,000), did math with them, and then divided them by the scalar? I remember learning how IEEE floating point numbers are stored, but I can't remember enough about it to know if this would have any effect on precision. If not, what is a good way to get better precision? I am already using doubles instead of floats. No; if anything, multiplying by a constant will reduce your precision slightly. If you're having precision issues with doubles, you are probably manipulating your intermediate values in such a way as to destroy precision (loss of significance). A common culprit is subtracting two values of nearly equal value. Without knowing what your math looks like, it's hard to guess what might be at fault, but rearranging your float math to avoid this sort of thing may improve your results. Goldberg's What Every Computer Scientist Should Know About Floating Point is a worthwhile read, and covers this issue (as well as many other pitfalls) in great detail: http://www.engr.pitt.edu/hunsaker/3097/floatingpoint.pdf ___ Cocoa-dev mailing list (Cocoa-dev@lists.apple.com) Please do not post admin requests or moderator comments to the list. Contact the moderators at cocoa-dev-admins(at)lists.apple.com Help/Unsubscribe/Update your Subscription: http://lists.apple.com/mailman/options/cocoa-dev/archive%40mail-archive.com This email sent to [EMAIL PROTECTED]
Re: How To Deal With Rounding Errors
On Dec 4, 2008, at 6:37 AM, Andrew Farmer wrote: On 04 Dec 08, at 00:08, Bridger Maxwell wrote: Short version of my question: I believe I am having rounding errors because I am working with really, really small values. Would it help if I multiplied these values by a scalar (say, 1,000), did math with them, and then divided them by the scalar? I remember learning how IEEE floating point numbers are stored, but I can't remember enough about it to know if this would have any effect on precision. If not, what is a good way to get better precision? I am already using doubles instead of floats. No; if anything, multiplying by a constant will reduce your precision slightly. If you're having precision issues with doubles, you are probably manipulating your intermediate values in such a way as to destroy precision (loss of significance). A common culprit is subtracting two values of nearly equal value. Without knowing what your math looks like, it's hard to guess what might be at fault, but rearranging your float math to avoid this sort of thing may improve your results. Goldberg's What Every Computer Scientist Should Know About Floating Point is a worthwhile read, and covers this issue (as well as many other pitfalls) in great detail: http://www.engr.pitt.edu/hunsaker/3097/floatingpoint.pdf One common thing to do when working with very small values (i.e. values close to zero), is to order your operations. For example, if you have a set of values that you want to compute a sum, adding them in smallest to largest order will often be different than largest to smallest. ___ Ricky A. Sharp mailto:[EMAIL PROTECTED] Instant Interactive(tm) http://www.instantinteractive.com ___ Cocoa-dev mailing list (Cocoa-dev@lists.apple.com) Please do not post admin requests or moderator comments to the list. Contact the moderators at cocoa-dev-admins(at)lists.apple.com Help/Unsubscribe/Update your Subscription: http://lists.apple.com/mailman/options/cocoa-dev/archive%40mail-archive.com This email sent to [EMAIL PROTECTED]
Re: How To Deal With Rounding Errors
If the user clicks just off the left of the view, does that give you a negative value? Or do you limit it to 0, then divide by 0? What happens if you use a range of 1-2 instead of 0-1? -- Scott Ribe [EMAIL PROTECTED] http://www.killerbytes.com/ (303) 722-0567 voice ___ Cocoa-dev mailing list (Cocoa-dev@lists.apple.com) Please do not post admin requests or moderator comments to the list. Contact the moderators at cocoa-dev-admins(at)lists.apple.com Help/Unsubscribe/Update your Subscription: http://lists.apple.com/mailman/options/cocoa-dev/archive%40mail-archive.com This email sent to [EMAIL PROTECTED]
