Groups | Search | Server Info | Keyboard shortcuts | Login | Register [http] [https] [nntp] [nntps]
| From | James Kuyper <jameskuyper@verizon.net> |
|---|---|
| Newsgroups | comp.lang.c |
| Subject | Re: How to write this sign function in Delphi. |
| Date | 2015-09-28 15:31 -0400 |
| Organization | Self |
| Message-ID | <56099589.3050705@verizon.net> (permalink) |
| References | (15 earlier) <muatrp$8kg$1@dont-email.me> <mub0oi$ije$1@dont-email.me> <mub51i$23e$1@dont-email.me> <lntwqesb25.fsf@kst-u.example.com> <mubv24$d7g$1@dont-email.me> |
On 09/28/2015 01:59 PM, Richard Heathfield wrote: ... > The important question in the present context is: what is the largest > integer that double is required to be able to represent precisely, such > that all smaller (positive) integers can also be represented? > > It was my belief that this number is considerably lower than 2^53, but > it is now only my opinion. I don't quite see how to get the relevant > number from the Linear B description of floating point provided in the > Standard. From 5.2.4.2.2p2, "A floating-point number (x) is defined by the following model: x = s*b^e * (the sum from k=1 to p of (f_k * b^(-k)) )" [Note: the model actually given relies upon sub-scripts, super-scripts, one greek letter, and three levels of printing, none of which are guaranteed to display meaningfully in a usenet message. I've therefore taken the liberty of re-writing it to avoid those problems, without changing the underlying meaning. f_k corresponds to 'k' being a subscript of f, b^e corresponds to pow(b,e), and I've converted a three-level sigma symbol into English words.] For any given x, you can represent x+1 by increasing f_e by 1 - if the result is b, then replace it by 0 and carry on to the next digit. But you can only do this only if f_e exists. Therefore, the smallest positive (so s==1) integer x such that x+1 can't be represented has e==p+1, f_0==1, and f_k==0 for all other values of k. That number has the value 1*b^(p+1)*1*b^(-1), or simply b^p. 5.2.4.2.2p13 says that DBL_EPSILON == b^(1-p) == FLT_RADIX/(b^p). Therefore, the number you're looking for is FLT_RADIX/DBL_EPSILON. The smallest permitted value for FLT_RADIX is 2; the largest permitted value of DBL_EPSILON is 1e-9, so the number you're looking for can't be smaller than 2e9. You can get exactly that limit using p=1, b=2e9. That would require 31 bits to store the significand, and only 3 bits for the exponent, with e_min==-3 and e_max=4, so it would fit in 35 bits. b=2^31 would make more efficient use of that amount of space. I can't vouch for the accuracy of the above analysis - I'm too error prone; but if it is in error, it should at least be correctable to give the right answer.
Back to comp.lang.c | Previous | Next — Previous in thread | Next in thread | Find similar | Unroll thread
How to write this sign function in Delphi. "Skybuck Flying" <skybuck2000@hotmail.com> - 2015-09-21 20:17 +0200
Re: How to write this sign function in Delphi. "Skybuck Flying" <skybuck2000@hotmail.com> - 2015-09-21 20:43 +0200
Re: How to write this sign function in Delphi. Ben Bacarisse <ben.usenet@bsb.me.uk> - 2015-09-21 19:51 +0100
Re: How to write this sign function in Delphi. "Skybuck Flying" <skybuck2000@hotmail.com> - 2015-09-21 23:26 +0200
Re: How to write this sign function in Delphi. Ben Bacarisse <ben.usenet@bsb.me.uk> - 2015-09-21 22:47 +0100
Re: How to write this sign function in Delphi. "Skybuck Flying" <skybuck2000@hotmail.com> - 2015-09-22 16:29 +0200
Re: How to write this sign function in Delphi. Ben Bacarisse <ben.usenet@bsb.me.uk> - 2015-09-22 16:11 +0100
Re: How to write this sign function in Delphi. "Skybuck Flying" <skybuck2000@hotmail.com> - 2015-09-23 11:18 +0200
Re: How to write this sign function in Delphi. David Brown <david.brown@hesbynett.no> - 2015-09-23 13:01 +0200
Re: How to write this sign function in Delphi. "Skybuck Flying" <skybuck2000@hotmail.com> - 2015-09-21 20:53 +0200
Re: How to write this sign function in Delphi. "Skybuck Flying" <skybuck2000@hotmail.com> - 2015-09-21 20:54 +0200
Re: How to write this sign function in Delphi. "Skybuck Flying" <skybuck2000@hotmail.com> - 2015-09-21 20:58 +0200
Re: How to write this sign function in Delphi. M Philbrook <jamie_ka1lpa@charter.net> - 2015-09-21 18:15 -0400
Re: How to write this sign function in Delphi. supercat@casperkitty.com - 2015-09-21 15:21 -0700
Re: How to write this sign function in Delphi. Robert Wessel <robertwessel2@yahoo.com> - 2015-09-21 17:51 -0500
Re: How to write this sign function in Delphi. James Kuyper <jameskuyper@verizon.net> - 2015-09-21 19:15 -0400
Re: How to write this sign function in Delphi. Robert Wessel <robertwessel2@yahoo.com> - 2015-09-21 23:59 -0500
Re: How to write this sign function in Delphi. supercat@casperkitty.com - 2015-09-22 09:22 -0700
Re: How to write this sign function in Delphi. Keith Thompson <kst-u@mib.org> - 2015-09-22 10:32 -0700
Re: How to write this sign function in Delphi. jt@toerring.de (Jens Thoms Toerring) - 2015-09-22 18:17 +0000
Re: How to write this sign function in Delphi. supercat@casperkitty.com - 2015-09-22 12:25 -0700
Re: How to write this sign function in Delphi. jt@toerring.de (Jens Thoms Toerring) - 2015-09-22 22:33 +0000
Re: How to write this sign function in Delphi. supercat@casperkitty.com - 2015-09-22 15:52 -0700
Re: How to write this sign function in Delphi. raltbos@xs4all.nl (Richard Bos) - 2015-09-22 23:09 +0000
Re: How to write this sign function in Delphi. supercat@casperkitty.com - 2015-09-23 09:07 -0700
Re: How to write this sign function in Delphi. Jorgen Grahn <grahn+nntp@snipabacken.se> - 2015-09-23 16:55 +0000
Re: How to write this sign function in Delphi. supercat@casperkitty.com - 2015-09-23 10:46 -0700
Re: How to write this sign function in Delphi. jt@toerring.de (Jens Thoms Toerring) - 2015-09-23 23:18 +0000
Re: How to write this sign function in Delphi. James Kuyper <jameskuyper@verizon.net> - 2015-09-23 22:29 -0400
Re: How to write this sign function in Delphi. Ben Bacarisse <ben.usenet@bsb.me.uk> - 2015-09-24 11:09 +0100
Re: How to write this sign function in Delphi. Malcolm McLean <malcolm.mclean5@btinternet.com> - 2015-09-27 18:23 -0700
Re: How to write this sign function in Delphi. glen herrmannsfeldt <gah@ugcs.caltech.edu> - 2015-09-28 05:20 +0000
Re: How to write this sign function in Delphi. Malcolm McLean <malcolm.mclean5@btinternet.com> - 2015-09-27 23:23 -0700
Re: How to write this sign function in Delphi. Richard Heathfield <rjh@cpax.org.uk> - 2015-09-28 09:03 +0100
Re: How to write this sign function in Delphi. Malcolm McLean <malcolm.mclean5@btinternet.com> - 2015-09-28 01:24 -0700
Re: How to write this sign function in Delphi. Richard Heathfield <rjh@cpax.org.uk> - 2015-09-28 09:32 +0100
Re: How to write this sign function in Delphi. Bartc <bc@freeuk.com> - 2015-09-28 10:22 +0100
Re: How to write this sign function in Delphi. Richard Heathfield <rjh@cpax.org.uk> - 2015-09-28 11:35 +0100
Re: How to write this sign function in Delphi. Keith Thompson <kst-u@mib.org> - 2015-09-28 10:33 -0700
Re: How to write this sign function in Delphi. Richard Heathfield <rjh@cpax.org.uk> - 2015-09-28 18:59 +0100
Re: How to write this sign function in Delphi. Rosario19 <Ros@invalid.invalid> - 2015-09-28 20:09 +0200
Re: How to write this sign function in Delphi. Robert Wessel <robertwessel2@yahoo.com> - 2015-09-28 13:39 -0500
Re: How to write this sign function in Delphi. Richard Heathfield <rjh@cpax.org.uk> - 2015-09-28 20:04 +0100
Re: How to write this sign function in Delphi. Robert Wessel <robertwessel2@yahoo.com> - 2015-09-28 16:43 -0500
Re: How to write this sign function in Delphi. Martin Shobe <martin.shobe@yahoo.com> - 2015-09-28 18:55 -0500
Re: How to write this sign function in Delphi. Robert Wessel <robertwessel2@yahoo.com> - 2015-09-28 19:31 -0500
Re: How to write this sign function in Delphi. supercat@casperkitty.com - 2015-09-28 12:16 -0700
Re: How to write this sign function in Delphi. Keith Thompson <kst-u@mib.org> - 2015-09-28 14:31 -0700
Re: How to write this sign function in Delphi. Robert Wessel <robertwessel2@yahoo.com> - 2015-09-28 16:47 -0500
Re: How to write this sign function in Delphi. supercat@casperkitty.com - 2015-09-29 11:54 -0700
Re: How to write this sign function in Delphi. Robert Wessel <robertwessel2@yahoo.com> - 2015-10-01 00:36 -0500
Re: How to write this sign function in Delphi. raltbos@xs4all.nl (Richard Bos) - 2015-10-02 10:53 +0000
Re: How to write this sign function in Delphi. supercat@casperkitty.com - 2015-10-02 09:48 -0700
Re: How to write this sign function in Delphi. Robert Wessel <robertwessel2@yahoo.com> - 2015-10-03 11:27 -0500
Re: How to write this sign function in Delphi. supercat@casperkitty.com - 2015-10-03 12:32 -0700
Re: How to write this sign function in Delphi. Robert Wessel <robertwessel2@yahoo.com> - 2015-10-03 11:26 -0500
Re: How to write this sign function in Delphi. Tim Rentsch <txr@alumni.caltech.edu> - 2015-10-04 16:46 -0700
Re: How to write this sign function in Delphi. Keith Thompson <kst-u@mib.org> - 2015-09-28 14:23 -0700
Re: How to write this sign function in Delphi. Robert Wessel <robertwessel2@yahoo.com> - 2015-09-28 16:52 -0500
Re: How to write this sign function in Delphi. Tim Rentsch <txr@alumni.caltech.edu> - 2015-09-30 01:39 -0700
Re: How to write this sign function in Delphi. Keith Thompson <kst-u@mib.org> - 2015-09-30 12:37 -0700
Re: How to write this sign function in Delphi. glen herrmannsfeldt <gah@ugcs.caltech.edu> - 2015-09-30 21:28 +0000
Re: How to write this sign function in Delphi. James Kuyper <jameskuyper@verizon.net> - 2015-09-30 17:54 -0400
Re: How to write this sign function in Delphi. glen herrmannsfeldt <gah@ugcs.caltech.edu> - 2015-10-01 03:59 +0000
Re: How to write this sign function in Delphi. James Kuyper <jameskuyper@verizon.net> - 2015-10-01 01:42 -0400
Re: How to write this sign function in Delphi. Keith Thompson <kst-u@mib.org> - 2015-09-30 16:20 -0700
Re: How to write this sign function in Delphi. Tim Rentsch <txr@alumni.caltech.edu> - 2015-10-04 16:39 -0700
Re: How to write this sign function in Delphi. glen herrmannsfeldt <gah@ugcs.caltech.edu> - 2015-09-28 23:23 +0000
Re: How to write this sign function in Delphi. supercat@casperkitty.com - 2015-09-29 09:35 -0700
Re: How to write this sign function in Delphi. raltbos@xs4all.nl (Richard Bos) - 2015-10-02 11:06 +0000
Re: How to write this sign function in Delphi. supercat@casperkitty.com - 2015-10-02 09:23 -0700
Re: How to write this sign function in Delphi. Martin Shobe <martin.shobe@yahoo.com> - 2015-10-02 12:07 -0500
Re: How to write this sign function in Delphi. supercat@casperkitty.com - 2015-10-02 10:47 -0700
Re: How to write this sign function in Delphi. Keith Thompson <kst-u@mib.org> - 2015-10-02 17:48 -0700
Re: How to write this sign function in Delphi. Richard Heathfield <rjh@cpax.org.uk> - 2015-10-03 16:46 +0100
Re: How to write this sign function in Delphi. Martin Shobe <martin.shobe@yahoo.com> - 2015-10-05 10:41 -0500
Re: How to write this sign function in Delphi. James Kuyper <jameskuyper@verizon.net> - 2015-09-28 15:31 -0400
Re: How to write this sign function in Delphi. Robert Wessel <robertwessel2@yahoo.com> - 2015-09-28 16:40 -0500
Re: How to write this sign function in Delphi. James Kuyper <jameskuyper@verizon.net> - 2015-09-28 18:17 -0400
Re: How to write this sign function in Delphi. Tim Rentsch <txr@alumni.caltech.edu> - 2015-09-30 02:49 -0700
Re: How to write this sign function in Delphi. supercat@casperkitty.com - 2015-09-30 06:27 -0700
Re: How to write this sign function in Delphi. Tim Rentsch <txr@alumni.caltech.edu> - 2015-09-29 10:43 -0700
Re: How to write this sign function in Delphi. glen herrmannsfeldt <gah@ugcs.caltech.edu> - 2015-09-28 22:51 +0000
Re: How to write this sign function in Delphi. Tim Rentsch <txr@alumni.caltech.edu> - 2015-09-30 02:11 -0700
Re: How to write this sign function in Delphi. glen herrmannsfeldt <gah@ugcs.caltech.edu> - 2015-09-28 22:48 +0000
Re: How to write this sign function in Delphi. Robert Wessel <robertwessel2@yahoo.com> - 2015-09-28 22:03 -0500
Re: How to write this sign function in Delphi. Tim Rentsch <txr@alumni.caltech.edu> - 2015-09-30 01:13 -0700
Re: How to write this sign function in Delphi. Bartc <bc@freeuk.com> - 2015-09-30 17:06 +0100
Re: How to write this sign function in Delphi. Richard Heathfield <rjh@cpax.org.uk> - 2015-09-30 17:26 +0100
Re: How to write this sign function in Delphi. Keith Thompson <kst-u@mib.org> - 2015-09-30 13:04 -0700
Re: How to write this sign function in Delphi. glen herrmannsfeldt <gah@ugcs.caltech.edu> - 2015-09-28 09:12 +0000
Re: How to write this sign function in Delphi. David Brown <david.brown@hesbynett.no> - 2015-09-28 12:28 +0200
Re: How to write this sign function in Delphi. Ben Bacarisse <ben.usenet@bsb.me.uk> - 2015-09-28 20:44 +0100
Re: How to write this sign function in Delphi. Malcolm McLean <malcolm.mclean5@btinternet.com> - 2015-10-01 01:39 -0700
Re: How to write this sign function in Delphi. Keith Thompson <kst-u@mib.org> - 2015-10-01 08:55 -0700
Re: How to write this sign function in Delphi. supercat@casperkitty.com - 2015-10-01 09:02 -0700
Re: How to write this sign function in Delphi. Malcolm McLean <malcolm.mclean5@btinternet.com> - 2015-10-01 14:55 -0700
Re: How to write this sign function in Delphi. supercat@casperkitty.com - 2015-10-01 16:48 -0700
Re: How to write this sign function in Delphi. raltbos@xs4all.nl (Richard Bos) - 2015-10-02 11:46 +0000
Re: How to write this sign function in Delphi. Malcolm McLean <malcolm.mclean5@btinternet.com> - 2015-10-06 00:15 -0700
Re: How to write this sign function in Delphi. Les Cargill <lcargill99@comcast.com> - 2015-10-06 02:43 -0500
Re: How to write this sign function in Delphi. David Brown <david.brown@hesbynett.no> - 2015-10-06 10:13 +0200
Re: How to write this sign function in Delphi. Les Cargill <lcargill99@comcast.com> - 2015-10-06 19:14 -0500
Re: How to write this sign function in Delphi. supercat@casperkitty.com - 2015-10-06 21:36 -0700
Re: How to write this sign function in Delphi. Ben Bacarisse <ben.usenet@bsb.me.uk> - 2015-10-06 09:25 +0100
Re: How to write this sign function in Delphi. supercat@casperkitty.com - 2015-10-06 09:28 -0700
Re: How to write this sign function in Delphi. Keith Thompson <kst-u@mib.org> - 2015-10-06 13:11 -0700
Re: How to write this sign function in Delphi. supercat@casperkitty.com - 2015-10-06 13:56 -0700
Re: How to write this sign function in Delphi. glen herrmannsfeldt <gah@ugcs.caltech.edu> - 2015-10-07 00:25 +0000
Re: How to write this sign function in Delphi. supercat@casperkitty.com - 2015-10-06 09:44 -0700
Re: How to write this sign function in Delphi. Malcolm McLean <malcolm.mclean5@btinternet.com> - 2015-10-06 10:08 -0700
Re: How to write this sign function in Delphi. supercat@casperkitty.com - 2015-10-06 12:00 -0700
Re: How to write this sign function in Delphi. Malcolm McLean <malcolm.mclean5@btinternet.com> - 2015-10-07 01:58 -0700
Re: How to write this sign function in Delphi. Richard Heathfield <rjh@cpax.org.uk> - 2015-10-07 10:12 +0100
Re: How to write this sign function in Delphi. supercat@casperkitty.com - 2015-10-08 00:40 -0700
Re: How to write this sign function in Delphi. Philip Lantz <prl@canterey.us> - 2015-10-03 12:29 -0700
Re: How to write this sign function in Delphi. supercat@casperkitty.com - 2015-10-03 13:20 -0700
Re: How to write this sign function in Delphi. Philip Lantz <prl@canterey.us> - 2015-10-03 12:33 -0700
Re: How to write this sign function in Delphi. James Kuyper <jameskuyper@verizon.net> - 2015-10-03 17:02 -0400
Re: How to write this sign function in Delphi. supercat@casperkitty.com - 2015-10-03 15:04 -0700
Re: How to write this sign function in Delphi. glen herrmannsfeldt <gah@ugcs.caltech.edu> - 2015-10-04 05:12 +0000
Re: How to write this sign function in Delphi. supercat@casperkitty.com - 2015-10-04 12:58 -0700
Re: How to write this sign function in Delphi. Philip Lantz <prl@canterey.us> - 2015-10-03 12:37 -0700
Re: How to write this sign function in Delphi. James Kuyper <jameskuyper@verizon.net> - 2015-10-03 16:21 -0400
Re: How to write this sign function in Delphi. supercat@casperkitty.com - 2015-10-03 16:05 -0700
Re: How to write this sign function in Delphi. supercat@casperkitty.com - 2015-10-03 14:02 -0700
Re: How to write this sign function in Delphi. supercat@casperkitty.com - 2015-09-24 09:39 -0700
Re: How to write this sign function in Delphi. raltbos@xs4all.nl (Richard Bos) - 2015-09-27 16:26 +0000
Re: How to write this sign function in Delphi. M Philbrook <jamie_ka1lpa@charter.net> - 2015-09-21 22:06 -0400
Re: How to write this sign function in Delphi. James Kuyper <jameskuyper@verizon.net> - 2015-09-22 10:17 -0400
Re: How to write this sign function in Delphi. M Philbrook <jamie_ka1lpa@charter.net> - 2015-09-22 19:48 -0400
Re: How to write this sign function in Delphi. Noob <root@127.0.0.1> - 2015-09-23 13:15 +0200
Re: How to write this sign function in Delphi. "Skybuck Flying" <skybuck2000@hotmail.com> - 2015-09-21 21:25 +0200
Re: How to write this sign function in Delphi. "Skybuck Flying" <skybuck2000@hotmail.com> - 2015-09-21 21:54 +0200
Re: How to write this sign function in Delphi. "Skybuck Flying" <skybuck2000@hotmail.com> - 2015-09-21 22:02 +0200
Re: How to write this sign function in Delphi. "Skybuck Flying" <skybuck2000@hotmail.com> - 2015-09-21 21:50 +0200
Re: How to write this sign function in Delphi. M Philbrook <jamie_ka1lpa@charter.net> - 2015-09-21 18:08 -0400
Re: How to write this sign function in Delphi. "Skybuck Flying" <skybuck2000@hotmail.com> - 2015-09-22 08:31 +0200
Re: How to write this sign function in Delphi. "Skybuck Flying" <skybuck2000@hotmail.com> - 2015-09-22 10:18 +0200
Re: How to write this sign function in Delphi. "Skybuck Flying" <skybuck2000@hotmail.com> - 2015-09-22 10:50 +0200
Re: How to write this sign function in Delphi. "Skybuck Flying" <skybuck2000@hotmail.com> - 2015-09-22 11:00 +0200
Re: How to write this sign function in Delphi. "Skybuck Flying" <skybuck2000@hotmail.com> - 2015-09-22 11:07 +0200
Re: How to write this sign function in Delphi. "Skybuck Flying" <skybuck2000@hotmail.com> - 2015-09-22 11:20 +0200
Re: How to write this sign function in Delphi. "Skybuck Flying" <skybuck2000@hotmail.com> - 2015-09-22 11:15 +0200
Re: How to write this sign function in Delphi. "Skybuck Flying" <skybuck2000@hotmail.com> - 2015-09-22 11:23 +0200
csiph-web