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Groups > comp.lang.c > #164258
| From | James Kuyper <jameskuyper@alumni.caltech.edu> |
|---|---|
| Newsgroups | comp.lang.c |
| Subject | Re: How to avoid an overflow during multiplication? |
| Date | 2022-01-04 00:32 -0500 |
| Organization | A noiseless patient Spider |
| Message-ID | <sr0m4h$vu3$1@dont-email.me> (permalink) |
| References | (4 earlier) <sqo86f$a7j$1@dont-email.me> <uint32_t-20220101030736@ram.dialup.fu-berlin.de> <PS-20220101032942@ram.dialup.fu-berlin.de> <sqqroj$4ef$1@dont-email.me> <formula-20220102025135@ram.dialup.fu-berlin.de> |
On 1/1/22 8:58 PM, Stefan Ram wrote:
...
> To determine how large a possible increase in the number of values
> with the correct result is, I wrote a function "muldiv_naive" with
> just "a * b / c" and another function "muldiv_experimental" with
> the formula you mentioned above.
>
> Then I calculate three random numbers a, b, c in a loop and count
> the number of correct results of the naive approach and with the
> formula you mentioned above.
>
> So far, the output of the program shows that the formula you
> mentioned above does indeed yield the correct result in about
> five times more cases than with the naive approach. But on the
> other hand, overall, both find the correct result only in few
> cases if all possible 32 bit values are used for a and c and
> all possible 16 bit values for b.
>
> main.c
>
> #include <limits.h>
> #include <stdint.h>
> #include <stdio.h>
> #include <stdlib.h>
>
> #if RAND_MAX != 32767
> #error "RAND_MAX != 32767"
> #endif
I couldn't use your code unmodified on my system; it has RAND_MAX ==
2147483647.
> #if UINT16_MAX != 65535
> #error "UINT16_MAX != 65535"
> #endif
>
> #if UINT32_MAX != 4294967295
> #error "UINT32_MAX != 4294967295"
> #endif>
> #define TOP ( ( unsigned long long )UINT32_MAX + 1 )
>
> unsigned long long rand32( void )
> { return
> ( ( ( ( unsigned long long )rand() >> 5 )<< 30 )+
> ( ( ( unsigned long long )rand() >> 5 )<< 20 )+
> ( ( ( unsigned long long )rand() >> 5 )<< 10 )+
> ( ( ( unsigned long long )rand() >> 5 )<< 0 ))&
> ( unsigned long long )0xffffffff; }
It would have made more sense to have this return uint32_t, and to use
uint32_t in the calculations.
There's no need to cast the final constant - it's likely to be the
correct type even without the cast, and if it isn't, it will be
implicitly converted to that type anyway, and has a value that will
survive the conversion unchanged.
> unsigned long long rand16( void )
> { return
> ( ( ( ( unsigned long long )rand() >> 5 )<< 10 )+
> ( ( ( unsigned long long )rand() >> 5 )<< 0 ))&
> ( unsigned long long )0xffff; }
Similarly, that should have use uint16_t. And again, there's no need to
cast the final constant, for the same reasons as in rand32().
> void the_exact_result_is_not_representable( void ){}
>
> unsigned long long muldiv_exact
> ( unsigned long long const a,
> unsigned long long const b,
> unsigned long long const c )
> { return a * b / c; }
>
> uint32_t muldiv_naive
> ( uint32_t const a,
> uint16_t const b,
> uint32_t const c )
> { return a * b / c; }
>
> uint32_t muldiv_experimental
> ( uint32_t const a,
> uint16_t const b,
> uint32_t const c )
> { const uint32_t q =( uint32_t )( a / c );
> const uint32_t p =( uint32_t )( q * b );
> const uint32_t r =( uint32_t )( a % c );
> const uint32_t m =( uint32_t )( r * b );
> const uint32_t d =( uint32_t )( m / c );
> const uint32_t s =( uint32_t )( p + d );
Note: those casts are unnecessary - assigning them to variables with
that type causes the same conversion to occur implicitly.
> return s; }
>
> int main( void )
> { unsigned long long naive_correct = 0;
> unsigned long long experimental_correct = 0;
> unsigned long long count = 0;> while( count < 100000000 )
If your count is going to be that small, unsigned long or even long
would be sufficient, there's no need to use unsigned long long for the
counters above.
> { unsigned long long a = rand32();
> unsigned long long b = rand16();
> unsigned long long c = rand32();
Those should have been defined as uint32_t and uint16_t. The only
consequence of defining them as unsigned long long is that it might make
the arithmetic slower - it won't change the calculated results.
> if( c )
> { unsigned long long const exact_result =
> muldiv_exact( a, b, c );
> uint32_t const experimental_result =
> muldiv_experimental( ( uint32_t )a,( uint16_t )b,( uint32_t )c );
> uint32_t const naive_result =
> muldiv_naive( ( uint32_t )a,( uint16_t )b,( uint32_t )c );
Those casts are all unnecessary, with or without the changes I suggested
above, because the specified conversions occur implicitly even without
those casts.
> if( exact_result >= TOP )
> the_exact_result_is_not_representable();
> else
> { if( naive_result == exact_result )
> { ++naive_correct; }
> if( experimental_result == exact_result )
> { ++experimental_correct; }}}
> ++count; }> printf
> ( "count=%llu, naive_correct=%llu, experimental_correct=%llu\n",
> count, naive_correct, experimental_correct );
> printf
> ( "naive percentage: %g\n",
> ( double )naive_correct/( double )count * 100. );
Simpler:
naive_correct * 100.0 / count;
With that change, the needed conversions will occur implicitly, and
similarly for the next calculation:
> printf
> ( "experimental percentage: %g\n",
> ( double )experimental_correct/( double )count * 100. ); }
>
> transcript
>
> count=100000000, naive_correct=19178, experimental_correct=120393
> naive percentage: 0.019178
> experimental percentage: 0.120393
Note first that the experimental percentage is much higher than the
naive percentage, which is what makes that formula useful. The reason
why the experimental percentage is so small is the second term:
(a%c)*b/c. a%c has a value that can be as high as c-1, so the
multiplication has a good chance of wrapping if c > UINT16_MAX,
rendering the formula invalid.
The OP has only given a few indications of the range of values for grouplen:
1. It's passed through a uint32_t interface, implying that it's at least
possible for it to be > UINT16_MAX.
2. He's said it never changes.
3. He gave 15730 as an example of a real-world value.
4. He indicated that tempo/grouplen is typically about 100. Since tempo
is passed as a uint16_t value, that would imply that grouplen is
normally much smaller than UINT16_MAX.
All in all, it sounds likely ticks, tempo, and grouplen usually (though
not necessarily always) have values that allow the formula a*b/c =
(a/c)*b + (a%c)*b/c to be valid when using a 32-bit type.
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How to avoid an overflow during multiplication? Mateusz Viste <mateusz@xyz.invalid> - 2021-12-31 11:02 +0100
Re: How to avoid an overflow during multiplication? Ben Bacarisse <ben.usenet@bsb.me.uk> - 2021-12-31 12:33 +0000
Re: How to avoid an overflow during multiplication? Ben Bacarisse <ben.usenet@bsb.me.uk> - 2021-12-31 12:33 +0000
Re: How to avoid an overflow during multiplication? Mateusz Viste <mateusz@xyz.invalid> - 2021-12-31 14:24 +0100
Re: How to avoid an overflow during multiplication? Mateusz Viste <mateusz@xyz.invalid> - 2021-12-31 15:00 +0100
Re: How to avoid an overflow during multiplication? Keith Thompson <Keith.S.Thompson+u@gmail.com> - 2021-12-31 11:38 -0800
Re: How to avoid an overflow during multiplication? Mateusz Viste <mateusz@xyz.invalid> - 2021-12-31 20:49 +0100
Re: How to avoid an overflow during multiplication? James Kuyper <jameskuyper@alumni.caltech.edu> - 2021-12-31 18:37 -0500
Re: How to avoid an overflow during multiplication? Mateusz Viste <mateusz@xyz.invalid> - 2022-01-01 17:48 +0100
Re: How to avoid an overflow during multiplication? Tim Rentsch <tr.17687@z991.linuxsc.com> - 2022-01-21 05:51 -0800
Re: How to avoid an overflow during multiplication? Mateusz Viste <mateusz@xyz.invalid> - 2022-01-21 15:59 +0100
Re: How to avoid an overflow during multiplication? David Brown <david.brown@hesbynett.no> - 2022-01-21 16:19 +0100
Re: How to avoid an overflow during multiplication? Mateusz Viste <mateusz@xyz.invalid> - 2022-01-21 16:51 +0100
Re: How to avoid an overflow during multiplication? James Kuyper <jameskuyper@alumni.caltech.edu> - 2022-01-21 12:08 -0500
Re: How to avoid an overflow during multiplication? David Brown <david.brown@hesbynett.no> - 2022-01-21 18:14 +0100
Re: How to avoid an overflow during multiplication? Mateusz Viste <mateusz@xyz.invalid> - 2022-01-21 18:25 +0100
Re: How to avoid an overflow during multiplication? David Brown <david.brown@hesbynett.no> - 2022-01-21 20:53 +0100
Re: How to avoid an overflow during multiplication? Mateusz Viste <mateusz@xyz.invalid> - 2022-01-21 22:22 +0100
Re: How to avoid an overflow during multiplication? David Brown <david.brown@hesbynett.no> - 2022-01-22 13:05 +0100
Re: How to avoid an overflow during multiplication? Mateusz Viste <mateusz@xyz.invalid> - 2022-01-22 13:53 +0100
Re: How to avoid an overflow during multiplication? Richard Damon <Richard@Damon-Family.org> - 2022-01-22 08:31 -0500
Re: How to avoid an overflow during multiplication? Mateusz Viste <mateusz@xyz.invalid> - 2022-01-22 15:53 +0100
Re: How to avoid an overflow during multiplication? David Brown <david.brown@hesbynett.no> - 2022-01-22 16:46 +0100
Re: How to avoid an overflow during multiplication? Mateusz Viste <mateusz@xyz.invalid> - 2022-01-24 09:33 +0100
Re: How to avoid an overflow during multiplication? David Brown <david.brown@hesbynett.no> - 2022-01-24 10:15 +0100
Re: How to avoid an overflow during multiplication? Tim Rentsch <tr.17687@z991.linuxsc.com> - 2022-01-22 10:03 -0800
Re: How to avoid an overflow during multiplication? David Brown <david.brown@hesbynett.no> - 2022-01-23 12:28 +0100
Re: How to avoid an overflow during multiplication? Bart <bc@freeuk.com> - 2022-01-23 11:48 +0000
Re: How to avoid an overflow during multiplication? Öö Tiib <ootiib@hot.ee> - 2022-01-23 08:36 -0800
Re: How to avoid an overflow during multiplication? Bart <bc@freeuk.com> - 2022-01-23 16:55 +0000
Re: How to avoid an overflow during multiplication? Tim Rentsch <tr.17687@z991.linuxsc.com> - 2022-01-23 19:17 -0800
Re: How to avoid an overflow during multiplication? James Kuyper <jameskuyper@alumni.caltech.edu> - 2022-01-21 12:11 -0500
Re: How to avoid an overflow during multiplication? Mateusz Viste <mateusz@xyz.invalid> - 2022-01-21 18:28 +0100
Re: How to avoid an overflow during multiplication? James Kuyper <jameskuyper@alumni.caltech.edu> - 2022-01-21 12:59 -0500
Re: How to avoid an overflow during multiplication? scott@slp53.sl.home (Scott Lurndal) - 2022-01-21 17:23 +0000
Re: How to avoid an overflow during multiplication? Mateusz Viste <mateusz@xyz.invalid> - 2022-01-21 18:35 +0100
Re: How to avoid an overflow during multiplication? scott@slp53.sl.home (Scott Lurndal) - 2022-01-21 18:06 +0000
Re: How to avoid an overflow during multiplication? Mateusz Viste <mateusz@xyz.invalid> - 2022-01-21 20:04 +0100
Re: How to avoid an overflow during multiplication? scott@slp53.sl.home (Scott Lurndal) - 2022-01-21 19:14 +0000
Re: How to avoid an overflow during multiplication? Tim Rentsch <tr.17687@z991.linuxsc.com> - 2022-01-21 17:02 -0800
Re: How to avoid an overflow during multiplication? scott@slp53.sl.home (Scott Lurndal) - 2022-01-22 16:59 +0000
Re: How to avoid an overflow during multiplication? Tim Rentsch <tr.17687@z991.linuxsc.com> - 2022-01-24 08:01 -0800
Re: How to avoid an overflow during multiplication? scott@slp53.sl.home (Scott Lurndal) - 2022-01-24 16:24 +0000
Re: How to avoid an overflow during multiplication? scott@slp53.sl.home (Scott Lurndal) - 2022-01-24 17:38 +0000
Re: How to avoid an overflow during multiplication? Tim Rentsch <tr.17687@z991.linuxsc.com> - 2022-01-24 11:28 -0800
Re: How to avoid an overflow during multiplication? scott@slp53.sl.home (Scott Lurndal) - 2022-01-24 22:44 +0000
Re: How to avoid an overflow during multiplication? Keith Thompson <Keith.S.Thompson+u@gmail.com> - 2022-01-24 15:34 -0800
Re: How to avoid an overflow during multiplication? scott@slp53.sl.home (Scott Lurndal) - 2022-01-25 14:50 +0000
Re: How to avoid an overflow during multiplication? Ben Bacarisse <ben.usenet@bsb.me.uk> - 2022-01-25 18:30 +0000
Re: How to avoid an overflow during multiplication? scott@slp53.sl.home (Scott Lurndal) - 2022-01-25 18:50 +0000
Re: How to avoid an overflow during multiplication? Keith Thompson <Keith.S.Thompson+u@gmail.com> - 2022-01-25 14:42 -0800
Re: How to avoid an overflow during multiplication? scott@slp53.sl.home (Scott Lurndal) - 2022-01-25 23:05 +0000
Re: How to avoid an overflow during multiplication? Tim Rentsch <tr.17687@z991.linuxsc.com> - 2022-01-29 04:54 -0800
Re: How to avoid an overflow during multiplication? James Kuyper <jameskuyper@alumni.caltech.edu> - 2022-01-24 21:50 -0500
Re: How to avoid an overflow during multiplication? Manfred <invalid@invalid.add> - 2022-01-25 19:24 +0100
Re: How to avoid an overflow during multiplication? scott@slp53.sl.home (Scott Lurndal) - 2022-01-25 18:35 +0000
Re: How to avoid an overflow during multiplication? Tim Rentsch <tr.17687@z991.linuxsc.com> - 2022-01-29 10:05 -0800
Re: How to avoid an overflow during multiplication? Ben Bacarisse <ben.usenet@bsb.me.uk> - 2022-01-21 20:46 +0000
Re: How to avoid an overflow during multiplication? Tim Rentsch <tr.17687@z991.linuxsc.com> - 2022-01-21 17:32 -0800
Re: How to avoid an overflow during multiplication? Mateusz Viste <mateusz@xyz.invalid> - 2022-01-22 09:57 +0100
Re: How to avoid an overflow during multiplication? Tim Rentsch <tr.17687@z991.linuxsc.com> - 2022-01-22 09:44 -0800
Re: How to avoid an overflow during multiplication? James Kuyper <jameskuyper@alumni.caltech.edu> - 2022-01-22 15:26 -0500
Re: How to avoid an overflow during multiplication? Tim Rentsch <tr.17687@z991.linuxsc.com> - 2022-01-22 14:44 -0800
Re: How to avoid an overflow during multiplication? Tim Rentsch <tr.17687@z991.linuxsc.com> - 2022-01-21 23:37 -0800
Re: How to avoid an overflow during multiplication? Tim Rentsch <tr.17687@z991.linuxsc.com> - 2022-01-22 12:04 -0800
Re: How to avoid an overflow during multiplication? Mateusz Viste <mateusz@xyz.invalid> - 2022-01-24 09:59 +0100
Re: How to avoid an overflow during multiplication? Tim Rentsch <tr.17687@z991.linuxsc.com> - 2022-02-03 10:24 -0800
Re: How to avoid an overflow during multiplication? Mateusz Viste <mateusz@xyz.invalid> - 2022-02-03 21:34 +0100
Re: How to avoid an overflow during multiplication? Keith Thompson <Keith.S.Thompson+u@gmail.com> - 2022-02-03 13:33 -0800
Re: How to avoid an overflow during multiplication? Mateusz Viste <mateusz@xyz.invalid> - 2022-02-03 22:57 +0100
Re: How to avoid an overflow during multiplication? Vir Campestris <vir.campestris@invalid.invalid> - 2022-02-03 22:28 +0000
Re: How to avoid an overflow during multiplication? Mateusz Viste <mateusz@xyz.invalid> - 2022-02-03 23:48 +0100
Re: How to avoid an overflow during multiplication? James Kuyper <jameskuyper@alumni.caltech.edu> - 2022-02-03 22:17 -0500
Re: How to avoid an overflow during multiplication? Öö Tiib <ootiib@hot.ee> - 2022-02-04 00:36 -0800
Re: How to avoid an overflow during multiplication? Mateusz Viste <mateusz@xyz.invalid> - 2022-02-04 10:49 +0100
Re: How to avoid an overflow during multiplication? Öö Tiib <ootiib@hot.ee> - 2022-02-04 09:03 -0800
Re: How to avoid an overflow during multiplication? Tim Rentsch <tr.17687@z991.linuxsc.com> - 2022-02-07 00:52 -0800
Re: How to avoid an overflow during multiplication? Bart <bc@freeuk.com> - 2022-02-07 10:03 +0000
Re: How to avoid an overflow during multiplication? Ben Bacarisse <ben.usenet@bsb.me.uk> - 2022-02-07 11:22 +0000
Re: How to avoid an overflow during multiplication? Bart <bc@freeuk.com> - 2022-02-07 14:58 +0000
Re: How to avoid an overflow during multiplication? Tim Rentsch <tr.17687@z991.linuxsc.com> - 2022-02-07 09:06 -0800
Re: How to avoid an overflow during multiplication? Mateusz Viste <mateusz@xyz.invalid> - 2022-02-04 09:44 +0100
Re: How to avoid an overflow during multiplication? David Brown <david.brown@hesbynett.no> - 2022-02-04 11:06 +0100
Re: How to avoid an overflow during multiplication? Malcolm McLean <malcolm.arthur.mclean@gmail.com> - 2022-02-04 05:53 -0800
Re: How to avoid an overflow during multiplication? David Brown <david.brown@hesbynett.no> - 2022-02-04 15:27 +0100
Re: How to avoid an overflow during multiplication? Mateusz Viste <mateusz@xyz.invalid> - 2022-02-04 15:53 +0100
Re: How to avoid an overflow during multiplication? David Brown <david.brown@hesbynett.no> - 2022-02-05 14:11 +0100
Re: How to avoid an overflow during multiplication? Malcolm McLean <malcolm.arthur.mclean@gmail.com> - 2022-02-05 09:15 -0800
Re: How to avoid an overflow during multiplication? Bart <bc@freeuk.com> - 2022-02-04 19:38 +0000
Re: How to avoid an overflow during multiplication? David Brown <david.brown@hesbynett.no> - 2022-02-05 14:23 +0100
Re: How to avoid an overflow during multiplication? Bart <bc@freeuk.com> - 2022-02-05 15:16 +0000
Re: How to avoid an overflow during multiplication? David Brown <david.brown@hesbynett.no> - 2022-02-05 17:27 +0100
Re: How to avoid an overflow during multiplication? Bart <bc@freeuk.com> - 2022-02-05 16:41 +0000
Re: How to avoid an overflow during multiplication? David Brown <david.brown@hesbynett.no> - 2022-02-06 12:01 +0100
Re: How to avoid an overflow during multiplication? Bart <bc@freeuk.com> - 2022-02-06 13:24 +0000
Re: How to avoid an overflow during multiplication? Manfred <invalid@add.invalid> - 2022-02-05 23:18 +0100
Re: How to avoid an overflow during multiplication? James Kuyper <jameskuyper@alumni.caltech.edu> - 2022-02-06 00:11 -0500
Re: How to avoid an overflow during multiplication? Manfred <noname@add.invalid> - 2022-02-06 18:43 +0100
Re: How to avoid an overflow during multiplication? David Brown <david.brown@hesbynett.no> - 2022-02-06 15:03 +0100
Re: How to avoid an overflow during multiplication? "james...@alumni.caltech.edu" <jameskuyper@alumni.caltech.edu> - 2022-02-05 09:38 -0800
Re: How to avoid an overflow during multiplication? Bart <bc@freeuk.com> - 2022-02-05 17:57 +0000
Re: How to avoid an overflow during multiplication? Richard Damon <Richard@Damon-Family.org> - 2022-02-05 13:29 -0500
Re: How to avoid an overflow during multiplication? David Brown <david.brown@hesbynett.no> - 2022-02-06 15:15 +0100
Re: How to avoid an overflow during multiplication? Bart <bc@freeuk.com> - 2022-02-06 14:34 +0000
Re: How to avoid an overflow during multiplication? Keith Thompson <Keith.S.Thompson+u@gmail.com> - 2022-02-06 12:56 -0800
Re: How to avoid an overflow during multiplication? "james...@alumni.caltech.edu" <jameskuyper@alumni.caltech.edu> - 2022-02-05 09:50 -0800
Re: How to avoid an overflow during multiplication? Bart <bc@freeuk.com> - 2022-02-05 18:09 +0000
Re: How to avoid an overflow during multiplication? James Kuyper <jameskuyper@alumni.caltech.edu> - 2022-02-04 11:06 -0500
Re: How to avoid an overflow during multiplication? Malcolm McLean <malcolm.arthur.mclean@gmail.com> - 2022-02-04 09:02 -0800
Re: How to avoid an overflow during multiplication? Keith Thompson <Keith.S.Thompson+u@gmail.com> - 2022-02-04 11:12 -0800
Re: How to avoid an overflow during multiplication? James Kuyper <jameskuyper@alumni.caltech.edu> - 2022-02-04 19:36 -0500
Re: How to avoid an overflow during multiplication? scott@slp53.sl.home (Scott Lurndal) - 2022-02-04 16:38 +0000
Re: How to avoid an overflow during multiplication? Vir Campestris <vir.campestris@invalid.invalid> - 2022-02-06 22:08 +0000
Re: How to avoid an overflow during multiplication? Mateusz Viste <mateusz@xyz.invalid> - 2022-02-07 09:11 +0100
Re: How to avoid an overflow during multiplication? Mateusz Viste <mateusz@xyz.invalid> - 2022-02-07 09:13 +0100
Re: How to avoid an overflow during multiplication? Mateusz Viste <mateusz@xyz.invalid> - 2022-02-07 09:14 +0100
Re: How to avoid an overflow during multiplication? Vir Campestris <vir.campestris@invalid.invalid> - 2022-02-07 21:42 +0000
Re: How to avoid an overflow during multiplication? Mateusz Viste <mateusz@xyz.invalid> - 2022-02-07 23:43 +0100
Re: How to avoid an overflow during multiplication? James Kuyper <jameskuyper@alumni.caltech.edu> - 2022-02-03 22:35 -0500
Re: How to avoid an overflow during multiplication? Tim Rentsch <tr.17687@z991.linuxsc.com> - 2022-02-04 21:14 -0800
Re: How to avoid an overflow during multiplication? Mateusz Viste <mateusz@xyz.invalid> - 2022-02-05 11:40 +0100
Re: How to avoid an overflow during multiplication? James Kuyper <jameskuyper@alumni.caltech.edu> - 2022-02-05 13:46 -0500
Re: How to avoid an overflow during multiplication? Ben Bacarisse <ben.usenet@bsb.me.uk> - 2022-02-05 23:30 +0000
Re: How to avoid an overflow during multiplication? James Kuyper <jameskuyper@alumni.caltech.edu> - 2022-02-06 00:17 -0500
Re: How to avoid an overflow during multiplication? David Brown <david.brown@hesbynett.no> - 2022-02-06 15:21 +0100
Re: How to avoid an overflow during multiplication? dave_thompson_2@comcast.net - 2022-05-14 12:34 -0400
Re: How to avoid an overflow during multiplication? Tim Rentsch <tr.17687@z991.linuxsc.com> - 2022-05-15 07:19 -0700
Re: How to avoid an overflow during multiplication? Andrey Tarasevich <andreytarasevich@hotmail.com> - 2022-05-14 12:04 -0700
Re: How to avoid an overflow during multiplication? Andrey Tarasevich <andreytarasevich@hotmail.com> - 2022-05-14 12:15 -0700
Re: How to avoid an overflow during multiplication? Tim Rentsch <tr.17687@z991.linuxsc.com> - 2022-05-15 07:25 -0700
Re: How to avoid an overflow during multiplication? Keith Thompson <Keith.S.Thompson+u@gmail.com> - 2021-12-31 15:41 -0800
Re: How to avoid an overflow during multiplication? David Brown <david.brown@hesbynett.no> - 2021-12-31 16:17 +0100
Re: How to avoid an overflow during multiplication? Mateusz Viste <mateusz@xyz.invalid> - 2021-12-31 16:22 +0100
Re: How to avoid an overflow during multiplication? Guillaume <message@bottle.org> - 2021-12-31 19:35 +0100
Re: How to avoid an overflow during multiplication? Bonita Montero <Bonita.Montero@gmail.com> - 2021-12-31 13:53 +0100
Re: How to avoid an overflow during multiplication? Öö Tiib <ootiib@hot.ee> - 2021-12-31 05:10 -0800
Re: How to avoid an overflow during multiplication? Bonita Montero <Bonita.Montero@gmail.com> - 2021-12-31 14:25 +0100
Re: How to avoid an overflow during multiplication? scott@slp53.sl.home (Scott Lurndal) - 2021-12-31 16:16 +0000
Re: How to avoid an overflow during multiplication? Mateusz Viste <mateusz@xyz.invalid> - 2021-12-31 17:32 +0100
Re: How to avoid an overflow during multiplication? Mateusz Viste <mateusz@xyz.invalid> - 2021-12-31 14:31 +0100
Re: How to avoid an overflow during multiplication? Bonita Montero <Bonita.Montero@gmail.com> - 2021-12-31 14:37 +0100
Re: How to avoid an overflow during multiplication? "james...@alumni.caltech.edu" <jameskuyper@alumni.caltech.edu> - 2021-12-31 15:21 -0800
Re: How to avoid an overflow during multiplication? David Brown <david.brown@hesbynett.no> - 2022-01-01 13:50 +0100
Re: How to avoid an overflow during multiplication? Michael S <already5chosen@yahoo.com> - 2022-01-01 10:31 -0800
Re: How to avoid an overflow during multiplication? Bonita Montero <Bonita.Montero@gmail.com> - 2022-01-01 20:03 +0100
Re: How to avoid an overflow during multiplication? Bart <bc@freeuk.com> - 2022-01-01 19:18 +0000
Re: How to avoid an overflow during multiplication? David Brown <david.brown@hesbynett.no> - 2022-01-02 13:38 +0100
Re: How to avoid an overflow during multiplication? Michael S <already5chosen@yahoo.com> - 2021-12-31 05:37 -0800
Re: How to avoid an overflow during multiplication? Mateusz Viste <mateusz@xyz.invalid> - 2021-12-31 14:55 +0100
Re: How to avoid an overflow during multiplication? Michael S <already5chosen@yahoo.com> - 2021-12-31 06:12 -0800
Re: How to avoid an overflow during multiplication? Mateusz Viste <mateusz@xyz.invalid> - 2021-12-31 16:11 +0100
Re: How to avoid an overflow during multiplication? Manfred <noname@add.invalid> - 2021-12-31 20:54 +0100
Re: How to avoid an overflow during multiplication? Mateusz Viste <mateusz@xyz.invalid> - 2021-12-31 21:19 +0100
Re: How to avoid an overflow during multiplication? Kaz Kylheku <480-992-1380@kylheku.com> - 2021-12-31 15:19 +0000
Re: How to avoid an overflow during multiplication? Mateusz Viste <mateusz@xyz.invalid> - 2021-12-31 16:24 +0100
Re: How to avoid an overflow during multiplication? Kaz Kylheku <480-992-1380@kylheku.com> - 2021-12-31 15:13 +0000
Re: How to avoid an overflow during multiplication? Mateusz Viste <mateusz@xyz.invalid> - 2021-12-31 17:00 +0100
Re: How to avoid an overflow during multiplication? Richard Damon <Richard@Damon-Family.org> - 2021-12-31 12:16 -0500
Re: How to avoid an overflow during multiplication? Tim Rentsch <tr.17687@z991.linuxsc.com> - 2021-12-31 10:28 -0800
Re: How to avoid an overflow during multiplication? pa@see.signature.invalid (Pierre Asselin) - 2021-12-31 20:18 +0000
Re: How to avoid an overflow during multiplication? Manfred <noname@add.invalid> - 2021-12-31 21:27 +0100
Re: How to avoid an overflow during multiplication? Mateusz Viste <mateusz@xyz.invalid> - 2021-12-31 21:39 +0100
Re: How to avoid an overflow during multiplication? Tim Rentsch <tr.17687@z991.linuxsc.com> - 2022-01-20 19:41 -0800
Re: How to avoid an overflow during multiplication? Mateusz Viste <mateusz@xyz.invalid> - 2021-12-31 21:31 +0100
Re: How to avoid an overflow during multiplication? Tim Rentsch <tr.17687@z991.linuxsc.com> - 2021-12-31 17:39 -0800
Re: How to avoid an overflow during multiplication? Tim Rentsch <tr.17687@z991.linuxsc.com> - 2022-01-02 09:08 -0800
Re: How to avoid an overflow during multiplication? James Kuyper <jameskuyper@alumni.caltech.edu> - 2021-12-31 19:08 -0500
Re: How to avoid an overflow during multiplication? James Kuyper <jameskuyper@alumni.caltech.edu> - 2021-12-31 19:45 -0500
Re: How to avoid an overflow during multiplication? Mateusz Viste <mateusz@xyz.invalid> - 2022-01-01 18:24 +0100
Re: How to avoid an overflow during multiplication? James Kuyper <jameskuyper@alumni.caltech.edu> - 2022-01-01 19:31 -0500
Re: How to avoid an overflow during multiplication? "james...@alumni.caltech.edu" <jameskuyper@alumni.caltech.edu> - 2022-01-01 16:53 -0800
Re: How to avoid an overflow during multiplication? James Kuyper <jameskuyper@alumni.caltech.edu> - 2022-01-04 00:32 -0500
Re: How to avoid an overflow during multiplication? Mateusz Viste <mateusz@xyz.invalid> - 2022-01-04 09:43 +0100
Re: How to avoid an overflow during multiplication? Tim Rentsch <tr.17687@z991.linuxsc.com> - 2022-01-04 07:20 -0800
Re: How to avoid an overflow during multiplication? Mateusz Viste <mateusz@xyz.invalid> - 2022-01-04 18:19 +0100
Re: How to avoid an overflow during multiplication? James Kuyper <jameskuyper@alumni.caltech.edu> - 2022-01-04 10:50 -0500
Re: How to avoid an overflow during multiplication? Mateusz Viste <mateusz@xyz.invalid> - 2022-01-04 17:37 +0100
Re: How to avoid an overflow during multiplication? James Kuyper <jameskuyper@alumni.caltech.edu> - 2022-01-04 15:01 -0500
Re: How to avoid an overflow during multiplication? Mateusz Viste <mateusz@xyz.invalid> - 2022-01-04 21:45 +0100
Re: How to avoid an overflow during multiplication? Keith Thompson <Keith.S.Thompson+u@gmail.com> - 2022-01-04 14:21 -0800
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