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Groups > comp.lang.c++ > #81620
| From | Paavo Helde <myfirstname@osa.pri.ee> |
|---|---|
| Newsgroups | comp.lang.c++ |
| Subject | Re: rational numbers |
| Date | 2021-09-27 11:37 +0300 |
| Organization | A noiseless patient Spider |
| Message-ID | <sirvrp$6jn$1@dont-email.me> (permalink) |
| References | (12 earlier) <sihdr5$12es$1@gioia.aioe.org> <siissf$dqg$1@dont-email.me> <sijkll$m21$1@gioia.aioe.org> <sik536$nus$1@dont-email.me> <sirkkb$gk$1@gioia.aioe.org> |
27.09.2021 08:25 Juha Nieminen kirjutas:
> Paavo Helde <myfirstname@osa.pri.ee> wrote:
>> It appears we are both concerned about efficiency. Alas, we have
>> drastically different opinions about where the inefficiencies lure.
>> Fortunately programming is strongly connected to reality, unlike some
>> other areas of human activity, so one can check the reality to see
>> what's really happening.
>>
>> Here is a test program measuring the two different approaches to
>> streaming: (A) sending 100 million ints to std::ostream separately, and
>> (B) formatting them first into a huge std::string, then sending that to
>> std::ostream in one go. My results are here:
I used std::ostringstream only to exclude disk access from timings.
> You are constructing a string with the contents of the data in both cases.
No. In one case I construct a string with data indeed, but with
to_string() approach I construct this string *twice*! And it's still
faster than the first method!
> This is not what I'm talking about. It's quite obvious (and I have never
> had any illusion otherwise) that std::ostringstream is extraordinarily
> inefficient. Obviously using other methods for constructing a string
> are going to be a million times faster. (I myself pretty much never
> use std::ostringstream if I can avoid it.)
It's the general std::ostream interface which is slow. One can easily
switch to ofstream in my example if this feels better, this won't change
the timings much. Here are the results for std::ofstream:
MSVC++ 2019 x64 Release build:
Traditional streaming: 32367 ms
to_string() streaming: 3979 ms
to_string() is 8.13446 times faster than traditional streaming.
g++ 8.3 on Linux:
$ g++ -Wall -O2 test5.cpp -std=c++17
$ ./a.out
Traditional streaming: 3451 ms
to_string() streaming: 1771 ms
to_string() is 1.94862 times faster than traditional streaming.
Source code below.
>
> But I am not talking about constructing a string from the content of
> the data. In fact, I'm talking about the exact opposite: *Avoiding*
> constructing a string into memory with the data.
Why? In my practice this is a major usage scenario.
>
> How do you add support to the standard output functions for custom
> types without requiring those custom types to create strings from
> their data, and being able to directly output the data?
Why? What's wrong with creating strings?
> Just substitute std::ostream with something more efficient.
I just did. It's called to_string().
> The question remains: How do you add native support for custom
> types to that output method, without requiring the custom types
> to create dynamically allocated strings in memory, and instead
> being able to directly use that output method to print their
> contents (in whichever way they choose)?
Why? A lot of data transfer mechanisms use internal memory buffers,
which often are dynamically allocated.
Test source code without std::ostringstream:
#include <iostream>
#include <string>
#include <vector>
#include <numeric>
#include <charconv>
#include <chrono>
#include <cstdint>
#include <fstream>
class A {
public:
A();
// traditional operator<<
friend std::ostream& operator<<(std::ostream& os, const A& a);
// tostring() operator
std::string to_string() const;
private:
std::vector<int> data;
};
A::A() {
// Initialize data to something
data.resize(100000000);
std::iota(data.begin(), data.end(), 0);
}
std::ostream& operator<<(std::ostream& os, const A& a) {
for (auto& x: a.data) {
os << x << ' ';
}
return os;
}
std::string A::to_string() const {
const size_t k = 64;
char buffer[k];
std::string result;
for (auto x: data) {
auto q = std::to_chars(buffer, buffer+k, x).ptr;
*q++ = ' ';
result.append(buffer, q-buffer);
}
return result;
}
using sclock = std::chrono::steady_clock;
std::int64_t ms(sclock::duration lapse) {
return
std::chrono::duration_cast<std::chrono::milliseconds>(lapse).count();
}
int main() {
std::ofstream sink1("sink1.txt"), sink2("sink2.txt");
A a;
// traditional streaming
sclock::time_point start1 = sclock::now();
sink1 << a;
sclock::time_point finish1 = sclock::now();
std::cout << "Traditional streaming: " << ms(finish1-start1) << "
ms\n";
// tostring()
sclock::time_point start2 = sclock::now();
sink2 << a.to_string();
sclock::time_point finish2 = sclock::now();
std::cout << "to_string() streaming: " << ms(finish2-start2) << "
ms\n";
double ratio = double(ms(finish1-start1))/ms(finish2-start2);
std::cout << "to_string() is " << ratio << " times " <<
(ratio>1.0 ? "faster" : "slower") << " than traditional
streaming.\n";
}
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rational numbers alessandro volturno <alessandro.volturno@libero.it> - 2021-09-16 14:59 +0200
Re: rational numbers Paavo Helde <myfirstname@osa.pri.ee> - 2021-09-16 16:40 +0300
Re: rational numbers alessandro volturno <alessandro.volturno@libero.it> - 2021-09-16 18:24 +0200
Re: rational numbers scott@slp53.sl.home (Scott Lurndal) - 2021-09-16 17:05 +0000
Re: rational numbers Manfred <noname@add.invalid> - 2021-09-16 19:58 +0200
Re: rational numbers Christian Gollwitzer <auriocus@gmx.de> - 2021-09-17 09:21 +0200
Re: rational numbers David Brown <david.brown@hesbynett.no> - 2021-09-17 10:34 +0200
Re: rational numbers Christian Gollwitzer <auriocus@gmx.de> - 2021-09-17 15:55 +0200
Re: rational numbers David Brown <david.brown@hesbynett.no> - 2021-09-17 17:49 +0200
Re: rational numbers Christian Gollwitzer <auriocus@gmx.de> - 2021-09-17 18:22 +0200
Re: rational numbers Ian Collins <ian-news@hotmail.com> - 2021-09-17 22:07 +1200
Re: rational numbers David Brown <david.brown@hesbynett.no> - 2021-09-17 13:32 +0200
Re: rational numbers Ian Collins <ian-news@hotmail.com> - 2021-09-18 09:15 +1200
Re: rational numbers scott@slp53.sl.home (Scott Lurndal) - 2021-09-17 14:06 +0000
Re: rational numbers David Brown <david.brown@hesbynett.no> - 2021-09-16 20:41 +0200
Re: rational numbers Bart <bc@freeuk.com> - 2021-09-16 21:11 +0100
Re: rational numbers Ben Bacarisse <ben.usenet@bsb.me.uk> - 2021-09-16 21:26 +0100
Re: rational numbers Bart <bc@freeuk.com> - 2021-09-16 21:54 +0100
Re: rational numbers "Alf P. Steinbach" <alf.p.steinbach@gmail.com> - 2021-09-16 23:07 +0200
Re: rational numbers "Alf P. Steinbach" <alf.p.steinbach@gmail.com> - 2021-09-16 23:27 +0200
Re: rational numbers Paavo Helde <myfirstname@osa.pri.ee> - 2021-09-16 23:12 +0300
Re: rational numbers alessandro volturno <alessandro.volturno@libero.it> - 2021-09-17 09:50 +0200
Re: rational numbers David Brown <david.brown@hesbynett.no> - 2021-09-17 11:15 +0200
Re: rational numbers alessandro volturno <alessandro.volturno@libero.it> - 2021-09-17 19:19 +0200
Re: rational numbers James Kuyper <jameskuyper@alumni.caltech.edu> - 2021-09-17 19:00 -0400
Re: rational numbers David Brown <david.brown@hesbynett.no> - 2021-09-18 11:39 +0200
Re: rational numbers alessandro volturno <alessandro.volturno@libero.it> - 2021-09-18 11:56 +0200
Re: rational numbers Bart <bc@freeuk.com> - 2021-09-18 11:01 +0100
Re: rational numbers Juha Nieminen <nospam@thanks.invalid> - 2021-09-17 05:36 +0000
Re: rational numbers alessandro volturno <alessandro.volturno@libero.it> - 2021-09-17 09:55 +0200
Re: rational numbers Juha Nieminen <nospam@thanks.invalid> - 2021-09-17 11:16 +0000
Re: rational numbers alessandro volturno <alessandro.volturno@libero.it> - 2021-09-17 18:33 +0200
Re: rational numbers Tim Rentsch <tr.17687@z991.linuxsc.com> - 2021-10-06 13:06 -0700
Re: rational numbers scott@slp53.sl.home (Scott Lurndal) - 2021-09-17 14:03 +0000
Re: rational numbers Christian Gollwitzer <auriocus@gmx.de> - 2021-09-17 17:12 +0200
Re: rational numbers Christian Gollwitzer <auriocus@gmx.de> - 2021-09-17 17:16 +0200
Re: rational numbers Manfred <noname@add.invalid> - 2021-09-17 18:59 +0200
Re: rational numbers scott@slp53.sl.home (Scott Lurndal) - 2021-09-17 17:13 +0000
Re: rational numbers Juha Nieminen <nospam@thanks.invalid> - 2021-09-19 10:17 +0000
Re: rational numbers scott@slp53.sl.home (Scott Lurndal) - 2021-09-19 14:07 +0000
Re: rational numbers Juha Nieminen <nospam@thanks.invalid> - 2021-09-19 15:58 +0000
Re: rational numbers scott@slp53.sl.home (Scott Lurndal) - 2021-09-19 21:53 +0000
Re: rational numbers Ian Collins <ian-news@hotmail.com> - 2021-09-18 09:34 +1200
Re: rational numbers David Brown <david.brown@hesbynett.no> - 2021-09-18 12:00 +0200
Re: rational numbers scott@slp53.sl.home (Scott Lurndal) - 2021-09-18 14:54 +0000
Re: rational numbers Bart <bc@freeuk.com> - 2021-09-18 17:36 +0100
Re: rational numbers Christian Gollwitzer <auriocus@gmx.de> - 2021-09-18 23:29 +0200
Re: rational numbers Bart <bc@freeuk.com> - 2021-09-19 01:09 +0100
Re: rational numbers red floyd <no.spam.here@its.invalid> - 2021-09-18 23:45 -0700
Re: rational numbers scott@slp53.sl.home (Scott Lurndal) - 2021-09-18 22:48 +0000
Re: rational numbers Bart <bc@freeuk.com> - 2021-09-19 00:46 +0100
Re: rational numbers Christian Gollwitzer <auriocus@gmx.de> - 2021-09-19 08:06 +0200
Re: rational numbers Bart <bc@freeuk.com> - 2021-09-19 10:26 +0100
Re: rational numbers Juha Nieminen <nospam@thanks.invalid> - 2021-09-19 10:23 +0000
Re: rational numbers Bart <bc@freeuk.com> - 2021-09-19 12:04 +0100
Re: rational numbers Juha Nieminen <nospam@thanks.invalid> - 2021-09-19 16:01 +0000
Re: rational numbers Bart <bc@freeuk.com> - 2021-09-19 17:39 +0100
Re: rational numbers Juha Nieminen <nospam@thanks.invalid> - 2021-09-20 05:25 +0000
Re: rational numbers Bart <bc@freeuk.com> - 2021-09-20 10:37 +0100
Re: rational numbers Juha Nieminen <nospam@thanks.invalid> - 2021-09-22 04:58 +0000
Re: rational numbers Bart <bc@freeuk.com> - 2021-09-22 11:26 +0100
Re: rational numbers Ian Collins <ian-news@hotmail.com> - 2021-09-22 23:13 +1200
Re: rational numbers Bart <bc@freeuk.com> - 2021-09-22 13:45 +0100
Re: rational numbers Ian Collins <ian-news@hotmail.com> - 2021-09-24 21:37 +1200
Re: rational numbers Paavo Helde <myfirstname@osa.pri.ee> - 2021-09-22 15:29 +0300
Re: rational numbers Juha Nieminen <nospam@thanks.invalid> - 2021-09-23 07:26 +0000
Re: rational numbers scott@slp53.sl.home (Scott Lurndal) - 2021-09-19 21:54 +0000
Re: rational numbers Bart <bc@freeuk.com> - 2021-09-20 00:31 +0100
Re: rational numbers David Brown <david.brown@hesbynett.no> - 2021-09-20 08:33 +0200
Re: rational numbers Bart <bc@freeuk.com> - 2021-09-20 16:11 +0100
Re: rational numbers David Brown <david.brown@hesbynett.no> - 2021-09-20 18:08 +0200
Re: rational numbers Bart <bc@freeuk.com> - 2021-09-20 18:39 +0100
Re: rational numbers David Brown <david.brown@hesbynett.no> - 2021-09-20 19:49 +0200
Re: rational numbers Bart <bc@freeuk.com> - 2021-09-20 19:04 +0100
Re: rational numbers David Brown <david.brown@hesbynett.no> - 2021-09-20 21:35 +0200
Re: rational numbers Bart <bc@freeuk.com> - 2021-09-20 21:38 +0100
Re: rational numbers Ian Collins <ian-news@hotmail.com> - 2021-09-21 10:28 +1200
Re: rational numbers Bo Persson <bo@bo-persson.se> - 2021-09-21 09:08 +0200
Re: rational numbers David Brown <david.brown@hesbynett.no> - 2021-09-21 09:39 +0200
Re: rational numbers Bart <bc@freeuk.com> - 2021-09-21 11:12 +0100
Re: rational numbers Paavo Helde <myfirstname@osa.pri.ee> - 2021-09-21 15:45 +0300
Re: rational numbers Bart <bc@freeuk.com> - 2021-09-21 14:37 +0100
Re: rational numbers Paavo Helde <myfirstname@osa.pri.ee> - 2021-09-21 17:09 +0300
Re: rational numbers Bart <bc@freeuk.com> - 2021-09-21 16:26 +0100
Re: rational numbers David Brown <david.brown@hesbynett.no> - 2021-09-21 18:04 +0200
Re: rational numbers Keith Thompson <Keith.S.Thompson+u@gmail.com> - 2021-09-21 11:51 -0700
Re: rational numbers David Brown <david.brown@hesbynett.no> - 2021-09-22 11:09 +0200
Re: rational numbers scott@slp53.sl.home (Scott Lurndal) - 2021-09-21 15:38 +0000
Re: rational numbers scott@slp53.sl.home (Scott Lurndal) - 2021-09-21 15:36 +0000
Re: rational numbers HorseyWorsey@the_stables.com - 2021-09-21 15:49 +0000
Re: rational numbers scott@slp53.sl.home (Scott Lurndal) - 2021-09-21 16:21 +0000
Re: rational numbers HorseyWorsey@the_stables.com - 2021-09-22 09:21 +0000
Re: rational numbers Bart <bc@freeuk.com> - 2021-09-21 17:45 +0100
Re: rational numbers scott@slp53.sl.home (Scott Lurndal) - 2021-09-21 17:02 +0000
Re: rational numbers Bart <bc@freeuk.com> - 2021-09-21 18:16 +0100
Re: rational numbers Keith Thompson <Keith.S.Thompson+u@gmail.com> - 2021-09-21 11:53 -0700
Re: rational numbers Bart <bc@freeuk.com> - 2021-09-21 20:48 +0100
Re: rational numbers scott@slp53.sl.home (Scott Lurndal) - 2021-09-21 20:23 +0000
Re: rational numbers Bart <bc@freeuk.com> - 2021-09-21 23:29 +0100
Re: rational numbers Keith Thompson <Keith.S.Thompson+u@gmail.com> - 2021-09-21 13:47 -0700
Re: rational numbers Paavo Helde <myfirstname@osa.pri.ee> - 2021-09-21 20:11 +0300
Re: rational numbers Bart <bc@freeuk.com> - 2021-09-21 18:33 +0100
Re: rational numbers Paavo Helde <myfirstname@osa.pri.ee> - 2021-09-21 20:43 +0300
Re: rational numbers Bart <bc@freeuk.com> - 2021-09-21 18:59 +0100
Re: rational numbers Paavo Helde <myfirstname@osa.pri.ee> - 2021-09-21 21:20 +0300
Re: rational numbers Bart <bc@freeuk.com> - 2021-09-21 20:32 +0100
Re: rational numbers scott@slp53.sl.home (Scott Lurndal) - 2021-09-21 20:24 +0000
Re: rational numbers scott@slp53.sl.home (Scott Lurndal) - 2021-09-21 18:52 +0000
Re: rational numbers Bo Persson <bo@bo-persson.se> - 2021-09-21 18:34 +0200
Re: rational numbers Paavo Helde <myfirstname@osa.pri.ee> - 2021-09-21 01:16 +0300
Re: rational numbers Bart <bc@freeuk.com> - 2021-09-21 00:39 +0100
Re: rational numbers Manfred <noname@add.invalid> - 2021-09-22 23:45 +0200
Re: rational numbers David Brown <david.brown@hesbynett.no> - 2021-09-22 23:51 +0200
Re: rational numbers Manfred <noname@add.invalid> - 2021-09-23 18:42 +0200
Re: rational numbers David Brown <david.brown@hesbynett.no> - 2021-09-23 21:52 +0200
Re: rational numbers Bart <bc@freeuk.com> - 2021-09-23 00:17 +0100
Re: rational numbers Branimir Maksimovic <branimir.maksimovic@gmail.com> - 2021-09-23 02:03 +0000
Re: rational numbers Bart <bc@freeuk.com> - 2021-09-23 11:18 +0100
Re: rational numbers HorseyWorsey@the_stables.com - 2021-09-23 10:26 +0000
Re: rational numbers Bart <bc@freeuk.com> - 2021-09-23 12:21 +0100
Re: rational numbers Bart <bc@freeuk.com> - 2021-09-23 12:40 +0100
Re: rational numbers Richard Damon <Richard@Damon-Family.org> - 2021-09-23 08:05 -0400
Re: rational numbers Bart <bc@freeuk.com> - 2021-09-23 15:02 +0100
Re: rational numbers Ian Collins <ian-news@hotmail.com> - 2021-09-24 08:48 +1200
Re: rational numbers Bart <bc@freeuk.com> - 2021-09-23 23:05 +0100
Re: rational numbers Branimir Maksimovic <branimir.maksimovic@gmail.com> - 2021-09-23 23:47 +0000
Re: rational numbers Keith Thompson <Keith.S.Thompson+u@gmail.com> - 2021-09-23 16:56 -0700
Re: rational numbers Bart <bc@freeuk.com> - 2021-09-24 01:58 +0100
Re: rational numbers Branimir Maksimovic <branimir.maksimovic@gmail.com> - 2021-09-24 01:40 +0000
Re: rational numbers Keith Thompson <Keith.S.Thompson+u@gmail.com> - 2021-09-23 19:35 -0700
Re: rational numbers "daniel...@gmail.com" <danielaparker@gmail.com> - 2021-09-24 09:07 -0700
Re: rational numbers "daniel...@gmail.com" <danielaparker@gmail.com> - 2021-09-24 09:21 -0700
Re: rational numbers HorseyWorsey@the_stables.com - 2021-09-23 14:58 +0000
Re: rational numbers Bart <bc@freeuk.com> - 2021-09-23 17:02 +0100
Re: rational numbers HorseyWorsey@the_stables.com - 2021-09-23 16:21 +0000
Re: rational numbers Bart <bc@freeuk.com> - 2021-09-23 18:31 +0100
Re: rational numbers HorseyWorsey@the_stables.com - 2021-09-24 09:12 +0000
Re: rational numbers Bart <bc@freeuk.com> - 2021-09-24 12:10 +0100
Re: rational numbers Branimir Maksimovic <branimir.maksimovic@gmail.com> - 2021-09-24 11:23 +0000
Re: rational numbers HorseyWorsey@the_stables.com - 2021-09-24 15:19 +0000
Re: rational numbers Bart <bc@freeuk.com> - 2021-09-24 17:25 +0100
Re: rational numbers HorseyWorsey@the_stables.com - 2021-09-25 09:27 +0000
Re: rational numbers Bart <bc@freeuk.com> - 2021-09-25 11:07 +0100
Re: rational numbers HorseyWorsey@the_stables.com - 2021-09-25 10:14 +0000
Re: rational numbers Bart <bc@freeuk.com> - 2021-09-25 11:53 +0100
Re: rational numbers HorseyWorsey@the_stables.com - 2021-09-25 11:23 +0000
Re: rational numbers Branimir Maksimovic <branimir.maksimovic@gmail.com> - 2021-09-25 12:34 +0000
Re: rational numbers Paavo Helde <myfirstname@osa.pri.ee> - 2021-09-25 15:37 +0300
Re: rational numbers Bart <bc@freeuk.com> - 2021-09-25 15:46 +0100
Re: rational numbers HorseyWorsey@the_stables.com - 2021-09-25 15:19 +0000
Re: rational numbers Branimir Maksimovic <branimir.maksimovic@gmail.com> - 2021-09-25 17:16 +0000
Re: rational numbers Christian Gollwitzer <auriocus@gmx.de> - 2021-09-27 23:51 +0200
Re: rational numbers Bart <bc@freeuk.com> - 2021-09-27 23:41 +0100
Re: rational numbers Branimir Maksimovic <branimir.maksimovic@gmail.com> - 2021-09-23 10:26 +0000
Re: rational numbers scott@slp53.sl.home (Scott Lurndal) - 2021-09-23 14:04 +0000
Re: rational numbers Manfred <noname@add.invalid> - 2021-09-23 17:47 +0200
Re: rational numbers scott@slp53.sl.home (Scott Lurndal) - 2021-09-23 17:07 +0000
Re: rational numbers scott@slp53.sl.home (Scott Lurndal) - 2021-09-23 17:08 +0000
Re: rational numbers Manfred <noname@add.invalid> - 2021-09-23 19:30 +0200
Re: rational numbers Ian Collins <ian-news@hotmail.com> - 2021-09-24 10:06 +1200
Re: rational numbers Juha Nieminen <nospam@thanks.invalid> - 2021-09-22 05:06 +0000
Re: rational numbers Bart <bc@freeuk.com> - 2021-09-22 10:51 +0100
Re: rational numbers HorseyWorsey@the_stables.com - 2021-09-22 10:54 +0000
Re: rational numbers Bart <bc@freeuk.com> - 2021-09-22 11:59 +0100
Re: rational numbers HorseyWorsey@the_stables.com - 2021-09-22 11:04 +0000
Re: rational numbers "Alf P. Steinbach" <alf.p.steinbach@gmail.com> - 2021-09-22 14:17 +0200
Re: rational numbers Bart <bc@freeuk.com> - 2021-09-22 14:32 +0100
Re: rational numbers "Alf P. Steinbach" <alf.p.steinbach@gmail.com> - 2021-09-22 16:23 +0200
Re: rational numbers Paavo Helde <myfirstname@osa.pri.ee> - 2021-09-22 15:18 +0300
Re: rational numbers "Alf P. Steinbach" <alf.p.steinbach@gmail.com> - 2021-09-22 16:16 +0200
Re: rational numbers HorseyWorsey@the_stables.com - 2021-09-22 15:15 +0000
Re: rational numbers "Alf P. Steinbach" <alf.p.steinbach@gmail.com> - 2021-09-22 17:57 +0200
Re: rational numbers HorseyWorsey@the_stables.com - 2021-09-22 16:05 +0000
Re: rational numbers Keith Thompson <Keith.S.Thompson+u@gmail.com> - 2021-09-22 14:13 -0700
Re: rational numbers HorseyWorsey@the_stables.com - 2021-09-23 09:01 +0000
Re: rational numbers James Kuyper <jameskuyper@alumni.caltech.edu> - 2021-09-23 12:08 -0400
Re: rational numbers Keith Thompson <Keith.S.Thompson+u@gmail.com> - 2021-09-23 10:55 -0700
Re: rational numbers Paavo Helde <myfirstname@osa.pri.ee> - 2021-09-22 20:46 +0300
Re: rational numbers "daniel...@gmail.com" <danielaparker@gmail.com> - 2021-09-22 14:42 -0700
Re: rational numbers Paavo Helde <myfirstname@osa.pri.ee> - 2021-09-23 09:15 +0300
Re: rational numbers scott@slp53.sl.home (Scott Lurndal) - 2021-09-22 14:04 +0000
Re: rational numbers Keith Thompson <Keith.S.Thompson+u@gmail.com> - 2021-09-22 07:18 -0700
Re: rational numbers Juha Nieminen <nospam@thanks.invalid> - 2021-09-23 07:31 +0000
Re: rational numbers Paavo Helde <myfirstname@osa.pri.ee> - 2021-09-23 11:05 +0300
Re: rational numbers Juha Nieminen <nospam@thanks.invalid> - 2021-09-23 08:28 +0000
Re: rational numbers Paavo Helde <myfirstname@osa.pri.ee> - 2021-09-24 00:51 +0300
Re: rational numbers Juha Nieminen <nospam@thanks.invalid> - 2021-09-24 04:37 +0000
Re: rational numbers Branimir Maksimovic <branimir.maksimovic@gmail.com> - 2021-09-24 07:46 +0000
Re: rational numbers "daniel...@gmail.com" <danielaparker@gmail.com> - 2021-09-24 08:59 -0700
Re: rational numbers Paavo Helde <myfirstname@osa.pri.ee> - 2021-09-24 22:49 +0300
Re: rational numbers Branimir Maksimovic <branimir.maksimovic@gmail.com> - 2021-09-25 00:55 +0000
Re: rational numbers Paavo Helde <myfirstname@osa.pri.ee> - 2021-09-24 12:17 +0300
Re: rational numbers Juha Nieminen <nospam@thanks.invalid> - 2021-09-27 05:25 +0000
Re: rational numbers Paavo Helde <myfirstname@osa.pri.ee> - 2021-09-27 11:37 +0300
Re: rational numbers Juha Nieminen <nospam@thanks.invalid> - 2021-09-28 04:49 +0000
Re: rational numbers Bart <bc@freeuk.com> - 2021-09-23 11:29 +0100
Re: rational numbers Juha Nieminen <nospam@thanks.invalid> - 2021-09-24 04:38 +0000
Re: rational numbers Bart <bc@freeuk.com> - 2021-09-24 11:15 +0100
Re: rational numbers Branimir Maksimovic <branimir.maksimovic@gmail.com> - 2021-09-24 10:19 +0000
Re: rational numbers Juha Nieminen <nospam@thanks.invalid> - 2021-09-27 05:34 +0000
Re: rational numbers scott@slp53.sl.home (Scott Lurndal) - 2021-09-23 14:07 +0000
Re: rational numbers Branimir Maksimovic <branimir.maksimovic@gmail.com> - 2021-09-23 14:50 +0000
Re: rational numbers Juha Nieminen <nospam@thanks.invalid> - 2021-09-20 05:20 +0000
Re: rational numbers Ian Collins <ian-news@hotmail.com> - 2021-09-24 21:45 +1200
Re: rational numbers Paavo Helde <myfirstname@osa.pri.ee> - 2021-09-25 16:15 +0300
Re: rational numbers Juha Nieminen <nospam@thanks.invalid> - 2021-09-27 05:36 +0000
Re: rational numbers Paavo Helde <myfirstname@osa.pri.ee> - 2021-09-27 11:19 +0300
Re: rational numbers Ian Collins <ian-news@hotmail.com> - 2021-09-27 21:27 +1300
Re: rational numbers Paavo Helde <myfirstname@osa.pri.ee> - 2021-09-27 15:49 +0300
Re: rational numbers Juha Nieminen <nospam@thanks.invalid> - 2021-09-28 04:53 +0000
Re: rational numbers Bart <bc@freeuk.com> - 2021-09-28 10:16 +0100
Re: rational numbers Juha Nieminen <nospam@thanks.invalid> - 2021-09-29 12:10 +0000
Re: rational numbers Bart <bc@freeuk.com> - 2021-09-29 14:34 +0100
Re: rational numbers Bart <bc@freeuk.com> - 2021-09-29 15:54 +0100
Re: rational numbers Paavo Helde <myfirstname@osa.pri.ee> - 2021-09-28 13:23 +0300
Re: rational numbers Ian Collins <ian-news@hotmail.com> - 2021-09-29 10:34 +1300
Re: rational numbers Paavo Helde <myfirstname@osa.pri.ee> - 2021-09-29 12:18 +0300
Re: rational numbers Ian Collins <ian-news@hotmail.com> - 2021-09-29 22:46 +1300
Re: rational numbers Paavo Helde <myfirstname@osa.pri.ee> - 2021-09-29 13:07 +0300
Re: rational numbers Paavo Helde <myfirstname@osa.pri.ee> - 2021-10-02 22:57 +0300
Re: rational numbers Juha Nieminen <nospam@thanks.invalid> - 2021-09-29 12:16 +0000
Re: rational numbers Paavo Helde <myfirstname@osa.pri.ee> - 2021-09-29 20:15 +0300
Re: rational numbers Juha Nieminen <nospam@thanks.invalid> - 2021-09-30 04:46 +0000
Re: rational numbers Ian Collins <ian-news@hotmail.com> - 2021-09-19 11:03 +1200
Re: rational numbers Juha Nieminen <nospam@thanks.invalid> - 2021-09-19 10:12 +0000
Re: rational numbers Siri Cruise <chine.bleu@yahoo.com> - 2021-09-23 07:38 -0700
Re: rational numbers alessandro volturno <alessandro.volturno@libero.it> - 2021-09-24 09:45 +0200
Re: rational numbers Branimir Maksimovic <branimir.maksimovic@gmail.com> - 2021-09-24 07:50 +0000
Re: rational numbers David Brown <david.brown@hesbynett.no> - 2021-09-24 10:58 +0200
Re: rational numbers Siri Cruise <chine.bleu@yahoo.com> - 2021-09-24 02:48 -0700
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