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| From | Ian Kelly <ian.g.kelly@gmail.com> |
| Date | Tue, 4 Mar 2014 04:19:59 -0700 |
| Subject | Re: Working with the set of real numbers (was: Finding size of Variable) |
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Show key headers only | View raw
On Mon, Mar 3, 2014 at 11:35 PM, Chris Angelico <rosuav@gmail.com> wrote:
> In constant space, that will produce the sum of two infinite sequences
> of digits. (And it's constant time, too, except when it gets a stream
> of nines. Adding three thirds together will produce an infinite loop
> as it waits to see if there'll be anything that triggers an infinite
> cascade of carries.) Now, if there's a way to do that for square
> rooting a number, then the CF notation has a distinct benefit over the
> decimal expansion used here. As far as I know, there's no simple way,
> in constant space and/or time, to progressively yield more digits of a
> number's square root, working in decimal.
The code for that looks like this:
def cf_sqrt(n):
"""Yield the terms of the square root of n as a continued fraction."""
m = 0
d = 1
a = a0 = floor_sqrt(n)
while True:
yield a
next_m = d * a - m
next_d = (n - next_m * next_m) // d
if next_d == 0:
break
next_a = (a0 + next_m) // next_d
m, d, a = next_m, next_d, next_a
def floor_sqrt(n):
"""Return the integer part of the square root of n."""
n = int(n)
if n == 0: return 0
lower = 2 ** int(math.log(n, 2) // 2)
upper = lower * 2
while upper - lower > 1:
mid = (upper + lower) // 2
if n < mid * mid:
upper = mid
else:
lower = mid
return lower
The floor_sqrt function is merely doing a simple binary search and
could probably be optimized, but then it's only called once during
initialization anyway. The meat of the loop, as you can see, is just
a constant amount of integer arithmetic. If it were desired to halt
once the continued fraction starts to repeat, that would just be a
matter of checking whether the triple (m, d, a) has been seen already.
Going back to your example of adding generated digits though, I don't
know how to add two continued fractions together without evaluating
them.
Back to comp.lang.python | Previous | Next — Previous in thread | Next in thread | Find similar | Unroll thread
Finding size of Variable Ayushi Dalmia <ayushidalmia2604@gmail.com> - 2014-02-04 03:28 -0800
Re: Finding size of Variable Peter Otten <__peter__@web.de> - 2014-02-04 12:40 +0100
Re: Finding size of Variable Ayushi Dalmia <ayushidalmia2604@gmail.com> - 2014-02-04 04:43 -0800
Re: Finding size of Variable Asaf Las <roegltd@gmail.com> - 2014-02-04 04:53 -0800
Re: Finding size of Variable Ayushi Dalmia <ayushidalmia2604@gmail.com> - 2014-02-04 05:18 -0800
Re: Finding size of Variable Dave Angel <davea@davea.name> - 2014-02-04 08:09 -0500
Re: Finding size of Variable Ayushi Dalmia <ayushidalmia2604@gmail.com> - 2014-02-04 05:19 -0800
Re: Finding size of Variable Dennis Lee Bieber <wlfraed@ix.netcom.com> - 2014-02-04 09:06 -0500
Re: Finding size of Variable Ayushi Dalmia <ayushidalmia2604@gmail.com> - 2014-02-04 21:00 -0800
Re:Finding size of Variable Dave Angel <davea@davea.name> - 2014-02-04 14:21 -0500
Re: Finding size of Variable Ayushi Dalmia <ayushidalmia2604@gmail.com> - 2014-02-04 21:15 -0800
Re: Finding size of Variable Peter Otten <__peter__@web.de> - 2014-02-05 09:27 +0100
Re: Finding size of Variable Tim Golden <mail@timgolden.me.uk> - 2014-02-04 19:28 +0000
Re: Finding size of Variable Tim Chase <python.list@tim.thechases.com> - 2014-02-04 13:29 -0600
Re: Finding size of Variable Ayushi Dalmia <ayushidalmia2604@gmail.com> - 2014-02-04 21:35 -0800
Re: Finding size of Variable Rustom Mody <rustompmody@gmail.com> - 2014-02-04 21:45 -0800
Re: Finding size of Variable Ayushi Dalmia <ayushidalmia2604@gmail.com> - 2014-02-04 22:00 -0800
Re: Finding size of Variable Steven D'Aprano <steve+comp.lang.python@pearwood.info> - 2014-02-05 11:00 +0000
Re: Finding size of Variable Chris Angelico <rosuav@gmail.com> - 2014-02-05 22:44 +1100
Re: Finding size of Variable wxjmfauth@gmail.com - 2014-02-06 02:15 -0800
Re: Finding size of Variable Ned Batchelder <ned@nedbatchelder.com> - 2014-02-06 06:10 -0500
Re: Finding size of Variable wxjmfauth@gmail.com - 2014-02-06 05:51 -0800
Re: Finding size of Variable wxjmfauth@gmail.com - 2014-02-06 06:15 -0800
Re: Finding size of Variable Steven D'Aprano <steve+comp.lang.python@pearwood.info> - 2014-02-08 02:48 +0000
Re: Finding size of Variable Ethan Furman <ethan@stoneleaf.us> - 2014-02-07 19:02 -0800
Re: Finding size of Variable Mark Lawrence <breamoreboy@yahoo.co.uk> - 2014-02-08 13:17 +0000
Re: Finding size of Variable David Hutto <dwightdhutto@gmail.com> - 2014-02-08 17:45 -0500
Re: Finding size of Variable Rustom Mody <rustompmody@gmail.com> - 2014-02-08 17:25 -0800
Re: Finding size of Variable David Hutto <dwightdhutto@gmail.com> - 2014-02-08 21:56 -0500
Re: Finding size of Variable Chris Angelico <rosuav@gmail.com> - 2014-02-09 13:59 +1100
Re: Finding size of Variable David Hutto <dwightdhutto@gmail.com> - 2014-02-08 22:07 -0500
Re: Finding size of Variable Ned Batchelder <ned@nedbatchelder.com> - 2014-02-08 22:09 -0500
Re: Finding size of Variable David Hutto <dwightdhutto@gmail.com> - 2014-02-08 22:09 -0500
Re: Finding size of Variable Ned Batchelder <ned@nedbatchelder.com> - 2014-02-08 22:16 -0500
Re: Finding size of Variable Rustom Mody <rustompmody@gmail.com> - 2014-02-08 19:30 -0800
Re: Finding size of Variable wxjmfauth@gmail.com - 2014-02-10 06:07 -0800
Re: Finding size of Variable Asaf Las <roegltd@gmail.com> - 2014-02-10 06:25 -0800
Re: Finding size of Variable Mark Lawrence <breamoreboy@yahoo.co.uk> - 2014-02-10 14:39 +0000
Re: Finding size of Variable Tim Chase <python.list@tim.thechases.com> - 2014-02-10 08:43 -0600
Re: Finding size of Variable wxjmfauth@gmail.com - 2014-02-11 10:53 -0800
Re: Finding size of Variable Mark Lawrence <breamoreboy@yahoo.co.uk> - 2014-02-11 19:04 +0000
Re: Finding size of Variable wxjmfauth@gmail.com - 2014-02-11 23:49 -0800
Re: Finding size of Variable Chris Angelico <rosuav@gmail.com> - 2014-02-12 19:06 +1100
Re: Finding size of Variable Jussi Piitulainen <jpiitula@ling.helsinki.fi> - 2014-02-12 10:57 +0200
Re: Finding size of Variable Chris Angelico <rosuav@gmail.com> - 2014-02-12 20:24 +1100
Re: Finding size of Variable Jussi Piitulainen <jpiitula@ling.helsinki.fi> - 2014-02-12 11:35 +0200
Working with the set of real numbers (was: Finding size of Variable) Ben Finney <ben+python@benfinney.id.au> - 2014-02-12 19:17 +1100
Re: Working with the set of real numbers (was: Finding size of Variable) wxjmfauth@gmail.com - 2014-02-12 00:35 -0800
Re: Working with the set of real numbers (was: Finding size of Variable) wxjmfauth@gmail.com - 2014-02-12 00:46 -0800
Re: Working with the set of real numbers Ben Finney <ben+python@benfinney.id.au> - 2014-02-12 19:52 +1100
Re: Working with the set of real numbers (was: Finding size of Variable) Grant Edwards <invalid@invalid.invalid> - 2014-02-12 15:24 +0000
Re: Working with the set of real numbers (was: Finding size of Variable) "Gisle Vanem" <gvanem@yahoo.no> - 2014-02-12 17:23 +0100
Re: Working with the set of real numbers (was: Finding size of Variable) Chris Angelico <rosuav@gmail.com> - 2014-02-12 19:47 +1100
Re: Working with the set of real numbers (was: Finding size of Variable) Jussi Piitulainen <jpiitula@ling.helsinki.fi> - 2014-02-12 11:23 +0200
Re: Working with the set of real numbers (was: Finding size of Variable) albert@spenarnc.xs4all.nl (Albert van der Horst) - 2014-03-04 02:45 +0000
Re: Working with the set of real numbers (was: Finding size of Variable) Chris Angelico <rosuav@gmail.com> - 2014-03-04 14:02 +1100
Re: Working with the set of real numbers (was: Finding size of Variable) Rustom Mody <rustompmody@gmail.com> - 2014-03-03 19:13 -0800
Re: Working with the set of real numbers (was: Finding size of Variable) Chris Angelico <rosuav@gmail.com> - 2014-03-04 14:46 +1100
Re: Working with the set of real numbers (was: Finding size of Variable) Rustom Mody <rustompmody@gmail.com> - 2014-03-03 21:19 -0800
Re: Working with the set of real numbers (was: Finding size of Variable) Steven D'Aprano <steve@pearwood.info> - 2014-03-04 05:53 +0000
Re: Working with the set of real numbers (was: Finding size of Variable) Chris Angelico <rosuav@gmail.com> - 2014-03-04 17:35 +1100
Re: Working with the set of real numbers Gregory Ewing <greg.ewing@canterbury.ac.nz> - 2014-03-05 00:05 +1300
Re: Working with the set of real numbers Chris Angelico <rosuav@gmail.com> - 2014-03-04 23:43 +1100
Re: Working with the set of real numbers Marko Rauhamaa <marko@pacujo.net> - 2014-03-04 21:49 +0200
Re: Working with the set of real numbers Chris Angelico <rosuav@gmail.com> - 2014-03-05 06:58 +1100
Re: Working with the set of real numbers Oscar Benjamin <oscar.j.benjamin@gmail.com> - 2014-03-04 20:55 +0000
Re: Working with the set of real numbers Marko Rauhamaa <marko@pacujo.net> - 2014-03-04 23:05 +0200
Re: Working with the set of real numbers Oscar Benjamin <oscar.j.benjamin@gmail.com> - 2014-03-04 22:08 +0000
Re: Working with the set of real numbers Chris Angelico <rosuav@gmail.com> - 2014-03-05 08:18 +1100
Re: Working with the set of real numbers Oscar Benjamin <oscar.j.benjamin@gmail.com> - 2014-03-04 22:02 +0000
Re: Working with the set of real numbers Chris Angelico <rosuav@gmail.com> - 2014-03-05 09:18 +1100
Re: Working with the set of real numbers Oscar Benjamin <oscar.j.benjamin@gmail.com> - 2014-03-04 22:54 +0000
Re: Working with the set of real numbers Chris Angelico <rosuav@gmail.com> - 2014-03-05 10:01 +1100
Re: Working with the set of real numbers Dave Angel <davea@davea.name> - 2014-03-04 18:20 -0500
Re: Working with the set of real numbers Oscar Benjamin <oscar.j.benjamin@gmail.com> - 2014-03-05 11:59 +0000
Re: Working with the set of real numbers Dave Angel <davea@davea.name> - 2014-03-05 07:57 -0500
Re: Working with the set of real numbers Dave Angel <davea@davea.name> - 2014-03-05 08:32 -0500
Re: Working with the set of real numbers Oscar Benjamin <oscar.j.benjamin@gmail.com> - 2014-03-06 12:27 +0000
Re: Working with the set of real numbers Chris Angelico <rosuav@gmail.com> - 2014-03-07 00:16 +1100
Re: Working with the set of real numbers (was: Finding size of Variable) Ian Kelly <ian.g.kelly@gmail.com> - 2014-03-04 04:19 -0700
Re: Working with the set of real numbers (was: Finding size of Variable) albert@spenarnc.xs4all.nl (Albert van der Horst) - 2014-03-05 02:27 +0000
Re: Working with the set of real numbers (was: Finding size of Variable) Ian Kelly <ian.g.kelly@gmail.com> - 2014-03-04 04:23 -0700
Re: Working with the set of real numbers (was: Finding size of Variable) albert@spenarnc.xs4all.nl (Albert van der Horst) - 2014-03-05 02:15 +0000
Re: Working with the set of real numbers (was: Finding size of Variable) Steven D'Aprano <steve@pearwood.info> - 2014-03-05 03:41 +0000
Re: Working with the set of real numbers (was: Finding size of Variable) Rustom Mody <rustompmody@gmail.com> - 2014-03-04 20:15 -0800
Re: Working with the set of real numbers (was: Finding size of Variable) Roy Smith <roy@panix.com> - 2014-03-04 23:25 -0500
Re: Working with the set of real numbers Ben Finney <ben+python@benfinney.id.au> - 2014-03-05 15:37 +1100
Re: Working with the set of real numbers Rustom Mody <rustompmody@gmail.com> - 2014-03-04 20:57 -0800
Re: Working with the set of real numbers Roy Smith <roy@panix.com> - 2014-03-05 00:29 -0500
Re: Working with the set of real numbers (was: Finding size of Variable) Steven D'Aprano <steve@pearwood.info> - 2014-03-05 07:52 +0000
Re: Working with the set of real numbers (was: Finding size of Variable) Steven D'Aprano <steve@pearwood.info> - 2014-03-05 08:38 +0000
Re: Working with the set of real numbers (was: Finding size of Variable) wxjmfauth@gmail.com - 2014-03-05 01:00 -0800
Re: Working with the set of real numbers Ned Batchelder <ned@nedbatchelder.com> - 2014-03-05 06:23 -0500
Re: Working with the set of real numbers (was: Finding size of Variable) Oscar Benjamin <oscar.j.benjamin@gmail.com> - 2014-03-05 12:21 +0000
Re: Working with the set of real numbers (was: Finding size of Variable) Steven D'Aprano <steve+comp.lang.python@pearwood.info> - 2014-03-05 17:43 +0000
Re: Working with the set of real numbers (was: Finding size of Variable) Chris Angelico <rosuav@gmail.com> - 2014-03-06 05:01 +1100
Re: Working with the set of real numbers (was: Finding size of Variable) Chris Kaynor <ckaynor@zindagigames.com> - 2014-03-05 10:03 -0800
Re: Working with the set of real numbers (was: Finding size of Variable) Grant Edwards <invalid@invalid.invalid> - 2014-03-05 19:13 +0000
Re: Working with the set of real numbers (was: Finding size of Variable) Oscar Benjamin <oscar.j.benjamin@gmail.com> - 2014-03-05 21:22 +0000
Re: Working with the set of real numbers (was: Finding size of Variable) Roy Smith <roy@panix.com> - 2014-03-05 21:31 -0500
Re: Working with the set of real numbers (was: Finding size of Variable) Steven D'Aprano <steve+comp.lang.python@pearwood.info> - 2014-03-06 03:06 +0000
Re: Working with the set of real numbers (was: Finding size of Variable) Chris Angelico <rosuav@gmail.com> - 2014-03-06 14:14 +1100
Re: Working with the set of real numbers (was: Finding size of Variable) Roy Smith <roy@panix.com> - 2014-03-05 23:05 -0500
Re: Working with the set of real numbers (was: Finding size of Variable) Grant Edwards <invalid@invalid.invalid> - 2014-03-06 03:34 +0000
Re: Working with the set of real numbers Mark Lawrence <breamoreboy@yahoo.co.uk> - 2014-03-05 12:50 +0000
Re: Working with the set of real numbers Steven D'Aprano <steve+comp.lang.python@pearwood.info> - 2014-03-05 17:49 +0000
Re: Working with the set of real numbers Ben Finney <ben+python@benfinney.id.au> - 2014-02-12 19:56 +1100
Re: Working with the set of real numbers Chris Angelico <rosuav@gmail.com> - 2014-02-12 20:16 +1100
Re: Working with the set of real numbers Ben Finney <ben+python@benfinney.id.au> - 2014-02-12 21:07 +1100
Re: Working with the set of real numbers Rustom Mody <rustompmody@gmail.com> - 2014-02-12 06:11 -0800
Re: Working with the set of real numbers Ian Kelly <ian.g.kelly@gmail.com> - 2014-02-12 13:45 -0700
Re: Working with the set of real numbers Rustom Mody <rustompmody@gmail.com> - 2014-02-12 17:47 -0800
Re: Working with the set of real numbers Gregory Ewing <greg.ewing@canterbury.ac.nz> - 2014-02-13 11:09 +1300
Re: Working with the set of real numbers Steven D'Aprano <steve@pearwood.info> - 2014-02-13 03:31 +0000
Re: Working with the set of real numbers Ben Finney <ben+python@benfinney.id.au> - 2014-02-13 14:45 +1100
Re: Working with the set of real numbers Chris Angelico <rosuav@gmail.com> - 2014-02-13 15:17 +1100
Re: Working with the set of real numbers Chris Angelico <rosuav@gmail.com> - 2014-02-12 21:20 +1100
Re: Working with the set of real numbers wxjmfauth@gmail.com - 2014-02-12 02:55 -0800
Re: Working with the set of real numbers Ned Batchelder <ned@nedbatchelder.com> - 2014-02-12 06:55 -0500
Re: Working with the set of real numbers Marko Rauhamaa <marko@pacujo.net> - 2014-02-12 14:48 +0200
Re: Working with the set of real numbers Chris Angelico <rosuav@gmail.com> - 2014-02-13 00:20 +1100
Re: Working with the set of real numbers Marko Rauhamaa <marko@pacujo.net> - 2014-02-12 16:13 +0200
Re: Working with the set of real numbers Chris Angelico <rosuav@gmail.com> - 2014-02-13 04:52 +1100
Re: Working with the set of real numbers Gregory Ewing <greg.ewing@canterbury.ac.nz> - 2014-02-13 11:24 +1300
Re: Working with the set of real numbers Dave Angel <davea@davea.name> - 2014-02-12 17:56 -0500
Re: Working with the set of real numbers Gregory Ewing <greg.ewing@canterbury.ac.nz> - 2014-02-14 18:26 +1300
Re: Working with the set of real numbers Ben Finney <ben+python@benfinney.id.au> - 2014-02-12 22:44 +1100
Re: Working with the set of real numbers Chris Angelico <rosuav@gmail.com> - 2014-02-12 22:58 +1100
Re: Working with the set of real numbers Gregory Ewing <greg.ewing@canterbury.ac.nz> - 2014-02-13 11:32 +1300
Re: Working with the set of real numbers Grant Edwards <invalid@invalid.invalid> - 2014-02-12 23:23 +0000
Re: Finding size of Variable Mark Lawrence <breamoreboy@yahoo.co.uk> - 2014-02-12 14:04 +0000
Re: Finding size of Variable Rustom Mody <rustompmody@gmail.com> - 2014-02-12 06:14 -0800
Re: Finding size of Variable Mark Lawrence <breamoreboy@yahoo.co.uk> - 2014-02-12 14:25 +0000
Re: Finding size of Variable Rustom Mody <rustompmody@gmail.com> - 2014-02-12 06:32 -0800
Re: Working with the set of real numbers Oscar Benjamin <oscar.j.benjamin@gmail.com> - 2014-02-13 12:48 +0000
Re: Working with the set of real numbers Marko Rauhamaa <marko@pacujo.net> - 2014-02-13 16:00 +0200
Re: Working with the set of real numbers Chris Angelico <rosuav@gmail.com> - 2014-02-14 06:25 +1100
Re: Working with the set of real numbers Marko Rauhamaa <marko@pacujo.net> - 2014-02-13 21:47 +0200
Re: Working with the set of real numbers Chris Angelico <rosuav@gmail.com> - 2014-02-14 07:08 +1100
Re: Working with the set of real numbers Devin Jeanpierre <jeanpierreda@gmail.com> - 2014-02-13 22:05 -0800
Re: Working with the set of real numbers Gregory Ewing <greg.ewing@canterbury.ac.nz> - 2014-02-15 00:30 +1300
Re: Working with the set of real numbers Devin Jeanpierre <jeanpierreda@gmail.com> - 2014-02-14 16:26 -0800
Re: Working with the set of real numbers albert@spenarnc.xs4all.nl (Albert van der Horst) - 2014-03-05 02:38 +0000
Re: Working with the set of real numbers Gregory Ewing <greg.ewing@canterbury.ac.nz> - 2014-02-14 19:37 +1300
Re: Working with the set of real numbers Chris Angelico <rosuav@gmail.com> - 2014-02-14 17:44 +1100
Re: Working with the set of real numbers Rustom Mody <rustompmody@gmail.com> - 2014-02-14 07:13 -0800
Re: Working with the set of real numbers Dave Angel <davea@davea.name> - 2014-02-14 07:30 -0500
Re: Working with the set of real numbers Grant Edwards <invalid@invalid.invalid> - 2014-02-14 15:09 +0000
Re: Working with the set of real numbers Rotwang <sg552@hotmail.co.uk> - 2014-02-13 21:29 +0000
Re: Working with the set of real numbers Marko Rauhamaa <marko@pacujo.net> - 2014-02-14 00:00 +0200
Re: Working with the set of real numbers Rotwang <sg552@hotmail.co.uk> - 2014-02-13 22:21 +0000
Re: Working with the set of real numbers Marko Rauhamaa <marko@pacujo.net> - 2014-02-14 01:16 +0200
Re: Working with the set of real numbers Ben Finney <ben+python@benfinney.id.au> - 2014-02-14 03:57 +1100
Re: Finding size of Variable Ned Batchelder <ned@nedbatchelder.com> - 2014-02-10 10:02 -0500
Re: Finding size of Variable Neil Cerutti <neilc@norwich.edu> - 2014-02-11 14:29 +0000
Re: Finding size of Variable Dennis Lee Bieber <wlfraed@ix.netcom.com> - 2014-02-05 22:14 -0500
Re: Finding size of Variable Dave Angel <davea@davea.name> - 2014-02-05 08:43 -0500
Re: Finding size of Variable Ayushi Dalmia <ayushidalmia2604@gmail.com> - 2014-02-05 06:33 -0800
Re: Finding size of Variable Mark Lawrence <breamoreboy@yahoo.co.uk> - 2014-02-05 15:22 +0000
csiph-web