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From: SourceForge.net <noreply@so...>  20100806 15:45:31

Bugs item #3040667, was opened at 20100806 17:43 Message generated for change (Settings changed) made by crategus You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=3040667&group_id=4933 Please note that this message will contain a full copy of the comment thread, including the initial issue submission, for this request, not just the latest update. Category: Lisp Core  Trigonometry Group: None Status: Open Resolution: None Priority: 5 Private: No Submitted By: Dieter Kaiser (crategus) Assigned to: Nobody/Anonymous (nobody) >Summary: logarc(acosh(z)) needlessly complicated Initial Comment: I think the implementation of the logarithmic representation of acosh and asech is needlessly complicated. We have: (%i3) acosh(z),logarc; (%o3) 2*log(sqrt(z+1)/sqrt(2)+sqrt(z1)/sqrt(2)) (%i4) asech(z),logarc; (%o4) 2*log(sqrt(1/z+1)/sqrt(2)+sqrt(1/z1)/sqrt(2)) A more simple implementation which corresponds to the definition of the functions is acosh(z) = log(z+sqrt(z1)*sqrt(z+1)) asech(z) = log(1/z+sqrt(1/z1)*sqrt(1+1/z)) Dieter Kaiser  >Comment By: Dieter Kaiser (crategus) Date: 20100806 17:45 Message: Correcting the title. It is the function acosh. Dieter Kaiser  You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=3040667&group_id=4933 
From: SourceForge.net <noreply@so...>  20100806 17:04:40

Bugs item #3040667, was opened at 20100806 11:43 Message generated for change (Comment added) made by rtoy You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=3040667&group_id=4933 Please note that this message will contain a full copy of the comment thread, including the initial issue submission, for this request, not just the latest update. Category: Lisp Core  Trigonometry Group: None Status: Open Resolution: None Priority: 5 Private: No Submitted By: Dieter Kaiser (crategus) Assigned to: Nobody/Anonymous (nobody) Summary: logarc(acosh(z)) needlessly complicated Initial Comment: I think the implementation of the logarithmic representation of acosh and asech is needlessly complicated. We have: (%i3) acosh(z),logarc; (%o3) 2*log(sqrt(z+1)/sqrt(2)+sqrt(z1)/sqrt(2)) (%i4) asech(z),logarc; (%o4) 2*log(sqrt(1/z+1)/sqrt(2)+sqrt(1/z1)/sqrt(2)) A more simple implementation which corresponds to the definition of the functions is acosh(z) = log(z+sqrt(z1)*sqrt(z+1)) asech(z) = log(1/z+sqrt(1/z1)*sqrt(1+1/z)) Dieter Kaiser  >Comment By: Raymond Toy (rtoy) Date: 20100806 13:04 Message: Care must be taken with these because of the potentially different branch cuts in the different definitions. However the two definitions for acosh are the same, I think. The definitions used here were taken from Kahan's nice paper, Branch Cuts for Complex Elementary Functions or Much Ado about Nothing's Sign Bit. The numerical evaluation of the functions were also taken from Kahan's paper.  Comment By: Dieter Kaiser (crategus) Date: 20100806 11:45 Message: Correcting the title. It is the function acosh. Dieter Kaiser  You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=3040667&group_id=4933 
From: SourceForge.net <noreply@so...>  20100806 20:10:57

Bugs item #3040667, was opened at 20100806 17:43 Message generated for change (Comment added) made by crategus You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=3040667&group_id=4933 Please note that this message will contain a full copy of the comment thread, including the initial issue submission, for this request, not just the latest update. Category: Lisp Core  Trigonometry Group: None Status: Open Resolution: None Priority: 5 Private: No Submitted By: Dieter Kaiser (crategus) Assigned to: Nobody/Anonymous (nobody) Summary: logarc(acosh(z)) needlessly complicated Initial Comment: I think the implementation of the logarithmic representation of acosh and asech is needlessly complicated. We have: (%i3) acosh(z),logarc; (%o3) 2*log(sqrt(z+1)/sqrt(2)+sqrt(z1)/sqrt(2)) (%i4) asech(z),logarc; (%o4) 2*log(sqrt(1/z+1)/sqrt(2)+sqrt(1/z1)/sqrt(2)) A more simple implementation which corresponds to the definition of the functions is acosh(z) = log(z+sqrt(z1)*sqrt(z+1)) asech(z) = log(1/z+sqrt(1/z1)*sqrt(1+1/z)) Dieter Kaiser  >Comment By: Dieter Kaiser (crategus) Date: 20100806 22:10 Message: Thank you for the comment. When I am right, the implemented formula is optimized for numerical evaluation of the acosh function. Perhaps, the definition is log(z+sqrt(z1)*sqrt(z+1) is more suitable for symbolic calculations. I have observed the difference when looking at expressions which involve power functions of arctrig functions. This is what we have: (%i12) exp(acosh(z)),logarc; (%o12) (sqrt(z+1)/sqrt(2)+sqrt(z1)/sqrt(2))^2 This might be the equivalent result: (%i5) exp(acosh(z)),logarc; (%o5) sqrt(z1)*sqrt(z+1)+z Dieter Kaiser  Comment By: Raymond Toy (rtoy) Date: 20100806 19:04 Message: Care must be taken with these because of the potentially different branch cuts in the different definitions. However the two definitions for acosh are the same, I think. The definitions used here were taken from Kahan's nice paper, Branch Cuts for Complex Elementary Functions or Much Ado about Nothing's Sign Bit. The numerical evaluation of the functions were also taken from Kahan's paper.  Comment By: Dieter Kaiser (crategus) Date: 20100806 17:45 Message: Correcting the title. It is the function acosh. Dieter Kaiser  You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=3040667&group_id=4933 
From: SourceForge.net <noreply@so...>  20100912 17:17:39

Bugs item #3040667, was opened at 20100806 17:43 Message generated for change (Comment added) made by crategus You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=3040667&group_id=4933 Please note that this message will contain a full copy of the comment thread, including the initial issue submission, for this request, not just the latest update. Category: Lisp Core  Trigonometry Group: None >Status: Closed >Resolution: Fixed Priority: 5 Private: No Submitted By: Dieter Kaiser (crategus) Assigned to: Nobody/Anonymous (nobody) Summary: logarc(acosh(z)) needlessly complicated Initial Comment: I think the implementation of the logarithmic representation of acosh and asech is needlessly complicated. We have: (%i3) acosh(z),logarc; (%o3) 2*log(sqrt(z+1)/sqrt(2)+sqrt(z1)/sqrt(2)) (%i4) asech(z),logarc; (%o4) 2*log(sqrt(1/z+1)/sqrt(2)+sqrt(1/z1)/sqrt(2)) A more simple implementation which corresponds to the definition of the functions is acosh(z) = log(z+sqrt(z1)*sqrt(z+1)) asech(z) = log(1/z+sqrt(1/z1)*sqrt(1+1/z)) Dieter Kaiser  >Comment By: Dieter Kaiser (crategus) Date: 20100912 19:17 Message: Fixed in logarc.lisp revision 1.10. Closing this bug report as fixed. Dieter Kaiser  Comment By: Dieter Kaiser (crategus) Date: 20100806 22:10 Message: Thank you for the comment. When I am right, the implemented formula is optimized for numerical evaluation of the acosh function. Perhaps, the definition is log(z+sqrt(z1)*sqrt(z+1) is more suitable for symbolic calculations. I have observed the difference when looking at expressions which involve power functions of arctrig functions. This is what we have: (%i12) exp(acosh(z)),logarc; (%o12) (sqrt(z+1)/sqrt(2)+sqrt(z1)/sqrt(2))^2 This might be the equivalent result: (%i5) exp(acosh(z)),logarc; (%o5) sqrt(z1)*sqrt(z+1)+z Dieter Kaiser  Comment By: Raymond Toy (rtoy) Date: 20100806 19:04 Message: Care must be taken with these because of the potentially different branch cuts in the different definitions. However the two definitions for acosh are the same, I think. The definitions used here were taken from Kahan's nice paper, Branch Cuts for Complex Elementary Functions or Much Ado about Nothing's Sign Bit. The numerical evaluation of the functions were also taken from Kahan's paper.  Comment By: Dieter Kaiser (crategus) Date: 20100806 17:45 Message: Correcting the title. It is the function acosh. Dieter Kaiser  You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=3040667&group_id=4933 