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Groups > comp.lang.c++ > #81506

Re: rational numbers

From Paavo Helde <myfirstname@osa.pri.ee>
Newsgroups comp.lang.c++
Subject Re: rational numbers
Date 2021-09-24 12:17 +0300
Organization A noiseless patient Spider
Message-ID <sik536$nus$1@dont-email.me> (permalink)
References (12 earlier) <sihaga$1j77$1@gioia.aioe.org> <sihch6$ms3$1@dont-email.me> <sihdr5$12es$1@gioia.aioe.org> <siissf$dqg$1@dont-email.me> <sijkll$m21$1@gioia.aioe.org>

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24.09.2021 07:37 Juha Nieminen kirjutas:
> Paavo Helde <myfirstname@osa.pri.ee> wrote:
>>> Preferably whatever the solution is, it shouldn't require the type
>>> to dynamically construct a string to be printed, and instead the
>>> type should get an std::ostream (or FILE*, or whatever) that it
>>> can use to directly write whatever it wants there.
>>
>> Why? Is this just because of memory overhead concerns?
> 
> What is this sudden strange attitude of "efficiency doesn't matter"?
> 
> This is C++ we are talking about, not Python, or JavaScript, or PHP,
> or a shell script.
> 

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:

MSVC++ 2019 x64 Release (/O2 optimization):
Traditional streaming: 28561 ms
to_string() streaming: 2663 ms
to_string() is 10.7251 times faster than traditional streaming.

To be honest, g++ 8.3 on Linux (or more exactly, libstdc++) seems to be 
much better with iostreams, but still to_string() beats iostreams:

$ g++ -Wall -O2 test5.cpp -std=c++17
$ ./a.out
Traditional streaming: 4268 ms
to_string() streaming: 2592 ms
to_string() is 1.6466 times faster than traditional streaming.

Source code:

#include <iostream>
#include <string>
#include <sstream>
#include <vector>
#include <numeric>
#include <charconv>
#include <chrono>
#include <cstdint>

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+0, buffer+k, x, 10).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::ostringstream sink1, sink2;
     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";

     // Make use of the results to ensure these were not optimized away.
     return int(sink1.str().size()-sink2.str().size());
}

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Thread

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

csiph-web