{"id":7097,"date":"2025-08-09T00:01:10","date_gmt":"2025-08-09T07:01:10","guid":{"rendered":"https:\/\/c-for-dummies.com\/blog\/?p=7097"},"modified":"2025-08-16T08:12:28","modified_gmt":"2025-08-16T15:12:28","slug":"fun-with-the-exp-function","status":"publish","type":"post","link":"https:\/\/c-for-dummies.com\/blog\/?p=7097","title":{"rendered":"Fun with the exp()<\/em> Function"},"content":{"rendered":"

Deep in the crevasse of oddball math functions is one that raises Euler’s number (e<\/em>) to a given power. This calculation is vital enough in programming that it sports its own function, exp()<\/em>. And I would ignore this function with exuberant glee were it not for a trick someone showed me a long time ago.
\n
\nEuler’s number is approximately 2.71828. I’ve written about it before<\/a> on this blog, specifically how to calculate it.<\/p>\n

The most important thing to remember about Euler’s number is that Euler<\/em> is pronounced “oil-er.” Beyond that, lots of mathy interesting things happen with this number e<\/em>, including using it as the base for an exponential expression, en<\/sup><\/em>. It’s such a big deal that it has its own name, the exponential function<\/a>.<\/p>\n

Do yourself a favor: If you’re ever at a nerd cocktail party and some mathematician starts off on the exponential function quickly run away<\/em>! Lots of things go on with this function, but it does have an interesting effect in programming that I’ve played with to much delight.<\/p>\n

The following code demonstrates the exp()<\/em> function by outputting a buncha values:<\/p>\n

2025_08_09-Lesson.c<\/a><\/h3>\n
\r\n#include <stdio.h>\r\n#include <math.h>\r\n\r\nint main()\r\n{\r\n    int x;\r\n    double b;\r\n\r\n    for( x=0; x<64; x++ )\r\n    {\r\n        b = exp( (double)x\/20.0 );\r\n        printf(\"%f\\n\",b);\r\n    }\r\n\r\n    return 0;\r\n}<\/pre>\n
Looping variable x<\/code> is an integer; it’s not a good idea to use real numbers as looping values. In the exp()<\/em> function, x<\/code> is cast as double<\/em> because the exp()<\/em> function requires a double<\/em> as its argument. The function returns a double<\/em>, the value of the expression e<\/em> raised to the x\/20.0<\/code> power.<\/p>\n
Remember to link in the math library when building this program in Linux. At the command prompt, the switch is -lm<\/code> (little L, little M), which I add last:<\/p>\n
clang 2025_08_09-Lesson.c -lm<\/code><\/p>\n
Here is the output:<\/p>\n
1.000000
\n1.051271
\n1.105171
\n1.161834
\n1.221403
\n1.284025
\n1.349859
\n1.419068
\n1.491825
\n1.568312
\n1.648721
\n1.733253
\n1.822119
\n1.915541
\n2.013753
\n2.117000
\n2.225541
\n2.339647
\n2.459603
\n2.585710
\n2.718282
\n2.857651
\n3.004166
\n3.158193
\n3.320117
\n3.490343
\n3.669297
\n3.857426
\n4.055200
\n4.263115
\n4.481689
\n4.711470
\n4.953032
\n5.206980
\n5.473947
\n5.754603
\n6.049647
\n6.359820
\n6.685894
\n7.028688
\n7.389056
\n7.767901
\n8.166170
\n8.584858
\n9.025013
\n9.487736
\n9.974182
\n10.485570
\n11.023176
\n11.588347
\n12.182494
\n12.807104
\n13.463738
\n14.154039
\n14.879732
\n15.642632
\n16.444647
\n17.287782
\n18.174145
\n19.105954
\n20.085537
\n21.115344
\n22.197951
\n23.336065<\/code><\/p>\n
Thank you for scrolling down.<\/p>\n
In the big picture, values output are teensy tiny at first, but grow larger as the loop progresses. Near the end, values increase at a faster rate. It’s this rate that makes the exp()<\/em> function’s output interesting to me. As another programmer pointed out years go, you can use these values to simulate a bouncing ball.<\/p>\n
The video player below shows an animation from code that uses the exp()<\/em> function to help bounce an asterisk across the terminal window.<\/p>\n
https:\/\/c-for-dummies.com\/blog\/wp-content\/uploads\/2025\/08\/0809-video_1.mp4<\/a><\/video><\/div>\n
In the video, you see the ball start out slowly, then accelerate as it “drops” to the bottom of the screen. The vertical positions echo the output shown above and at the same rate.<\/p>\n
I’ve also animated the asterisk to move left-to-right across the screen, though it stops after 1013 movements. I’ll explain more as I continue to work with the exp()<\/em> function over the next few lessons.<\/p>\n
In next week’s Lesson<\/a>, I borrow some screen manipulating and timing functions from other Lessons in this blog to help animate the asterisk. Plus I put the loop shown in this lesson’s code to work to make the ball “bounce.”<\/p>\n","protected":false},"excerpt":{"rendered":"
Of what possible use could there be fore a function en<\/sup><\/em>? 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":[2],"tags":[],"class_list":["post-7097","post","type-post","status-publish","format-standard","hentry","category-main"],"_links":{"self":[{"href":"https:\/\/c-for-dummies.com\/blog\/index.php?rest_route=\/wp\/v2\/posts\/7097","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=7097"}],"version-history":[{"count":10,"href":"https:\/\/c-for-dummies.com\/blog\/index.php?rest_route=\/wp\/v2\/posts\/7097\/revisions"}],"predecessor-version":[{"id":7126,"href":"https:\/\/c-for-dummies.com\/blog\/index.php?rest_route=\/wp\/v2\/posts\/7097\/revisions\/7126"}],"wp:attachment":[{"href":"https:\/\/c-for-dummies.com\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=7097"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/c-for-dummies.com\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=7097"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/c-for-dummies.com\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=7097"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}