{"id":4166,"date":"2020-06-08T00:01:24","date_gmt":"2020-06-08T07:01:24","guid":{"rendered":"https:\/\/c-for-dummies.com\/blog\/?p=4166"},"modified":"2020-06-06T11:23:57","modified_gmt":"2020-06-06T18:23:57","slug":"getting-to-eulers-number-solution","status":"publish","type":"post","link":"https:\/\/c-for-dummies.com\/blog\/?p=4166","title":{"rendered":"Getting to Euler’s Number – Solution"},"content":{"rendered":"

The challenge for this month’s Exercise<\/a> is not only to calculate Euler’s number, e<\/em>, but to count how many loops a program must endure before your e<\/em> value calculation matches the defined constant M_E<\/code>. I hope you didn’t find this challenge too difficult.
\n
\nYes, I wanted you to write code that loops to calculate the value. Bernoulli’s equation is illustrated in Figure 1. It contains the expression lim n→\u221e<\/strong>. This mathematical dingus translates into a loop in the C language, not to infinity but to some bignum.<\/p>\n

\"\"

Figure 1. Bernoulli’s equation, which Euler (or Gauss) calculated to the value of e<\/em>.<\/p><\/div>\n

Here is how I write Bernoulli’s equation in C:<\/p>\n

count = 0;
\nwhile(1)
\n{
\n    count++;
\n    e = pow( (1.0\/(double)count + 1), (double)count );
\n}<\/code><\/p>\n

Variable count<\/code> is a long<\/em> integer. It’s initialized to zero and incremented through the loop.<\/p>\n

The pow()<\/em> function raises 1.0\/(double)count+1<\/code> to the (double)count<\/code> power, which is the essence of Bernoulli’s equation. Of course, he put it as 1 + 1.0\/(double)count<\/code>, but I reversed it for clarity and precedence and fancy stuff like that.<\/p>\n

The double<\/em> typecasts are required in the expression because using a floating point value as a looping counter is bad practice.<\/p>\n

The loop as presented above has no exit condition. To make one, I use the second part of the Exercise’s challenge, which is to match the value you calculate, stored in variable e<\/code>, with the M_E<\/code> defined constant. Here is the full code for my solution:<\/p>\n

2020_06-Exercise.c<\/a><\/h3>\n
\r\n\/* link with -lm on Linux *\/<\/span>\r\n#include <stdio.h>\r\n#include <math.h>\r\n\r\nint main()\r\n{\r\n    long count;\r\n    double e;\r\n\r\n    count = 0;\r\n    while(1)\r\n    {\r\n        count++;\r\n        e = pow( (1.0\/(double)count + 1), (double)count );\r\n        if( e==M_E )\r\n            break;\r\n    }\r\n    printf(\"The computer calculated %f after %ld loops\\n\",\r\n            e,\r\n            count\r\n          );\r\n\r\n    return(0);\r\n}<\/pre>\n
Variable e<\/code> holds the calculated value of Euler’s number, conveniently also called e<\/em>. The pow()<\/em> function within the while<\/em> loop repeats, refining the value over and over as it approaches, or “tends to,” the value stored in M_E<\/code>.<\/p>\n
Of course, the program can be written without a loop. I mean, the expression does say lim n→\u221e<\/strong>. So if you just plug in \u221e as a value, it works. Right? (Don’t blanch if you’re a mathematician.) The highest value for an unsigned long int<\/em> is 4,294,967,295. Why not use it? This code does:<\/p>\n
2020_06-Exercise-alt.c<\/a><\/h3>\n
\r\n\/* link with -lm on Linux *\/<\/span>\r\n#include <stdio.h>\r\n#include <math.h>\r\n\r\nint main()\r\n{\r\n    double e;\r\n    unsigned long count = 4294967295L;\r\n\r\n    e = pow( (1.0\/(double)count + 1), (double)count );\r\n    printf(\"The computer calculated %f for %f\\n\",\r\n            e,\r\n            M_E\r\n          );\r\n\r\n    return(0);\r\n}<\/pre>\n
No loop is used above. Instead, the maximum size of a long int<\/em> is specified at Line 8, 4294967295L<\/code>, the L<\/code> suffix identifying the value as a long<\/em> literal. No looping. No waiting. No telling, except for the output:<\/p>\n
The computer calculated 2.718282 for 2.718282<\/code><\/p>\n
Presto.<\/p>\n
Still, the looping approach is what I wanted in your solution. If you say, “To hell with him and his silly directions” and concocted a solution similar to my alternative shown above, okay. Still, the notion was to plod through the equation, as the lim n→\u221e<\/strong> expression implies. Mathematically, it wouldn’t be any fun otherwise.<\/p>\n","protected":false},"excerpt":{"rendered":"
The challenge for this month’s Exercise is not only to calculate Euler’s number, e, but to count how many loops a program must endure before your e value calculation matches the defined constant M_E. I hope you didn’t find this … Continue reading →<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[5],"tags":[],"class_list":["post-4166","post","type-post","status-publish","format-standard","hentry","category-solution"],"_links":{"self":[{"href":"https:\/\/c-for-dummies.com\/blog\/index.php?rest_route=\/wp\/v2\/posts\/4166","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/c-for-dummies.com\/blog\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/c-for-dummies.com\/blog\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/c-for-dummies.com\/blog\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/c-for-dummies.com\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=4166"}],"version-history":[{"count":6,"href":"https:\/\/c-for-dummies.com\/blog\/index.php?rest_route=\/wp\/v2\/posts\/4166\/revisions"}],"predecessor-version":[{"id":4204,"href":"https:\/\/c-for-dummies.com\/blog\/index.php?rest_route=\/wp\/v2\/posts\/4166\/revisions\/4204"}],"wp:attachment":[{"href":"https:\/\/c-for-dummies.com\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=4166"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/c-for-dummies.com\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=4166"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/c-for-dummies.com\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=4166"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}