First we have some really trivial code that will try to flip a coin one hundred times. We track the number of times that the coin lands as "heads" in a row. We also count when "tails" lands in a row and so therefore we can also know the maximum counts for each. The code will exit when it has a result with the percentage of heads that the user requested. Below you can see the output when the user wants to see a result of 80% heads in the one hundred coin flips. Since the drand48() function is seeded with the nanosec portion of the current time we will see different results every time the code is run. The code had to do the one hundred coin flips 734,308,307 times before we saw 80% of the results being "heads". /* * coin_flip.c : flip a coin one hundred times in a row and wait to * see results with a large percentage of "heads" * * RETURN : This code will return eventually. Maybe. If the * user requests a large percentage of "heads" then * it may run a very long time. There is no promise * that it will ever exit. Good luck. * * UPDATE : A bail out condition was needed to have the code * bail out before the heat death of the universe. * * ------------------------------------------------------------------ * Copyright (c) 2024 Dennis Clarke * * Permission is hereby granted, free of charge, to any person * obtaining a copy of this software and associated documentation * files (the "Software"), to deal in the Software without * restriction, including without limitation the rights to use, * copy, modify, merge, publish, distribute, sublicense, and/or * sell copies of the Software, and to permit persons to whom the * Software is furnished to do so, subject to the following * conditions: * * The above copyright notice and this permission notice shall be * included in all copies or substantial portions of the Software. * * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY * KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE * WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR * PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS * OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR * OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR * OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE * SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. * ------------------------------------------------------------------ */ /********************************************************************* * The Open Group Base Specifications Issue 6 * IEEE Std 1003.1, 2004 Edition * * An XSI-conforming application should ensure that the feature * test macro _XOPEN_SOURCE is defined with the value 600 before * inclusion of any header. This is needed to enable the * functionality described in The _POSIX_C_SOURCE Feature Test * Macro and in addition to enable the XSI extension. * *********************************************************************/ #if ! defined (_XOPEN_SOURCE) #define _XOPEN_SOURCE 600 #endif #include <stdlib.h> #include <stdio.h> #include <math.h> #include <inttypes.h> #include <time.h> #define LIMIT 70 int main ( int argc, char **argv ) { /* this code was written with some beers and while * ranting about uniform distribution results for * a given source of random data. No attempt was * made to make the code well organized and variables * were tossed into the fray at whim. */ int k, bias = 0; uint64_t j; int heads, tails; int head_count, max_heads_in_a_row; int tail_count; int max_tails_in_a_row; int max_heads_when; int max_tails_when; int this_flip; int limit = LIMIT; int64_t loop_up = 0; int64_t loop_last = -1; int bit_shift = 1; double x; struct timespec now_time; /* did the user suggest a given percentage ? */ if ( argc > 1 ) { /* * * * * W A R N I N G * * * * * * There is no checking for reasonable data here. */ limit = atoi(argv[1]); printf("Geez I hope you really want %i\n", limit ); } /* Get the REALTIME_CLOCK time in a timespec struct */ if ( clock_gettime(CLOCK_REALTIME, &now_time ) == -1 ) { /* We could not get the clock. Bail out. */ fprintf(stderr,"ERROR : could not attain CLOCK_REALTIME\n"); return EXIT_FAILURE; } else { /* call srand48() with the nanosecond time data */ srand48( (long) now_time.tv_nsec ); } /* this is the iteration counter */ j = 0; max_heads_in_a_row = 0; max_tails_in_a_row = 0; max_heads_when = 0; max_tails_when = 0; doagain: heads = 0; tails = 0; this_flip = 0; head_count = 0; tail_count = 0; for ( k=0 ; k<100; k++ ) { x = drand48(); if ( x < 0.5 ) { tails += 1; this_flip = 0; } else { heads += 1; this_flip = 1; } if ( this_flip == 1 ) { head_count += 1; tail_count = 0; if ( head_count > max_heads_in_a_row ) { max_heads_in_a_row = head_count; max_heads_when = j; } } else { head_count = 0; tail_count += 1; if ( tail_count > max_tails_in_a_row ) { max_tails_in_a_row = tail_count; max_tails_when = j; } } } if ( heads > limit ) { bias += 1; } j += 1; /* This is just a progress report which will only * happen when j is a perfect power of two. Also * the power of two is increased with a left bit * shift and so you can expect the reports to happen * ever more slowly as the code runs. At least we * see some sign of activity to let the user know * something is running. */ if ( j & bit_shift ) { printf ("\nloop j = %" PRIu64 "\n", j ); printf ("max number of heads in a row was %i\n", max_heads_in_a_row); printf ("max heads happened at loop num %i\n", max_heads_when); printf ("max number of tails in a row was %i\n", max_tails_in_a_row); printf ("max tails happened at loop num %i\n", max_tails_when); bit_shift *= 2; } /* be sure to bail out if we have already run 2^34 loops */ if ( ( bias < 1 ) && ( j < ( 1L<<34 ) ) ) goto doagain; printf ("\nbias events count at %" PRIu64 " for %i%% heads.\n", j, limit ); printf ("max number of heads in a row was %i\n", max_heads_in_a_row); printf ("max heads happened at loop num %i\n", max_heads_when); printf ("max number of tails in a row was %i\n", max_tails_in_a_row); printf ("max tails happened at loop num %i\n", max_tails_when); /* Please see "The Hitch Hikers Guide to the Galaxy" */ return 42; } io$ /usr/bin/time -p /usr/bin/nice -n +18 ./coin_flip 80 Geez I hope you really want 80 loop j = 1 max number of heads in a row was 5 max heads happened at loop num 0 max number of tails in a row was 6 max tails happened at loop num 0 loop j = 2 max number of heads in a row was 6 max heads happened at loop num 1 max number of tails in a row was 6 max tails happened at loop num 0 loop j = 4 max number of heads in a row was 6 max heads happened at loop num 1 max number of tails in a row was 6 max tails happened at loop num 0 loop j = 8 max number of heads in a row was 10 max heads happened at loop num 4 max number of tails in a row was 6 max tails happened at loop num 0 loop j = 16 max number of heads in a row was 11 max heads happened at loop num 11 max number of tails in a row was 10 max tails happened at loop num 10 loop j = 32 max number of heads in a row was 11 max heads happened at loop num 11 max number of tails in a row was 10 max tails happened at loop num 10 loop j = 64 max number of heads in a row was 11 max heads happened at loop num 11 max number of tails in a row was 10 max tails happened at loop num 10 loop j = 128 max number of heads in a row was 11 max heads happened at loop num 11 max number of tails in a row was 11 max tails happened at loop num 65 loop j = 256 max number of heads in a row was 12 max heads happened at loop num 152 max number of tails in a row was 14 max tails happened at loop num 139 loop j = 512 max number of heads in a row was 16 max heads happened at loop num 490 max number of tails in a row was 14 max tails happened at loop num 139 loop j = 1024 max number of heads in a row was 16 max heads happened at loop num 490 max number of tails in a row was 15 max tails happened at loop num 861 loop j = 2048 max number of heads in a row was 17 max heads happened at loop num 1339 max number of tails in a row was 15 max tails happened at loop num 861 loop j = 4096 max number of heads in a row was 19 max heads happened at loop num 3968 max number of tails in a row was 19 max tails happened at loop num 3061 loop j = 8192 max number of heads in a row was 19 max heads happened at loop num 3968 max number of tails in a row was 19 max tails happened at loop num 3061 loop j = 16384 max number of heads in a row was 19 max heads happened at loop num 3968 max number of tails in a row was 19 max tails happened at loop num 3061 loop j = 32768 max number of heads in a row was 19 max heads happened at loop num 3968 max number of tails in a row was 21 max tails happened at loop num 24344 loop j = 65536 max number of heads in a row was 20 max heads happened at loop num 34721 max number of tails in a row was 21 max tails happened at loop num 24344 loop j = 131072 max number of heads in a row was 20 max heads happened at loop num 34721 max number of tails in a row was 22 max tails happened at loop num 86671 loop j = 262144 max number of heads in a row was 21 max heads happened at loop num 191800 max number of tails in a row was 22 max tails happened at loop num 86671 loop j = 524288 max number of heads in a row was 27 max heads happened at loop num 434509 max number of tails in a row was 23 max tails happened at loop num 386110 loop j = 1048576 max number of heads in a row was 27 max heads happened at loop num 434509 max number of tails in a row was 23 max tails happened at loop num 386110 loop j = 2097152 max number of heads in a row was 27 max heads happened at loop num 434509 max number of tails in a row was 25 max tails happened at loop num 1558459 loop j = 4194304 max number of heads in a row was 27 max heads happened at loop num 434509 max number of tails in a row was 25 max tails happened at loop num 1558459 loop j = 8388608 max number of heads in a row was 28 max heads happened at loop num 5492543 max number of tails in a row was 26 max tails happened at loop num 6296002 loop j = 16777216 max number of heads in a row was 29 max heads happened at loop num 15368274 max number of tails in a row was 31 max tails happened at loop num 15353233 loop j = 33554432 max number of heads in a row was 29 max heads happened at loop num 15368274 max number of tails in a row was 31 max tails happened at loop num 15353233 loop j = 67108864 max number of heads in a row was 30 max heads happened at loop num 49032334 max number of tails in a row was 31 max tails happened at loop num 15353233 loop j = 134217728 max number of heads in a row was 30 max heads happened at loop num 49032334 max number of tails in a row was 31 max tails happened at loop num 15353233 loop j = 268435456 max number of heads in a row was 36 max heads happened at loop num 250497298 max number of tails in a row was 34 max tails happened at loop num 163736586 loop j = 536870912 max number of heads in a row was 36 max heads happened at loop num 250497298 max number of tails in a row was 34 max tails happened at loop num 163736586 loop j = 1073741824 max number of heads in a row was 36 max heads happened at loop num 250497298 max number of tails in a row was 35 max tails happened at loop num 976052969 loop j = 2147483648 max number of heads in a row was 36 max heads happened at loop num 250497298 max number of tails in a row was 36 max tails happened at loop num 1894472577 bias events count at 4245791664 for 80% heads. max number of heads in a row was 36 max heads happened at loop num 250497298 max number of tails in a row was 36 max tails happened at loop num 1894472577 real 31481.86 user 31474.83 sys 0.04 io$

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