\n
\nTo understand tetration, start with exponentiation. The expression 23<\/sup> reads as “two to the third power.” It’s shorthand for
2 * 2 * 2<\/code>. Tetration takes this concept higher, but first consider this operation:<\/p>\n235<\/sup><\/sup><\/p>\nThe expression above is valid. It’s calculated as 35<\/sup>, which is 243. Then you get 2243<\/sup>, which is 1.4134776518227074636666380005943e+73. Neat-o.<\/p>\nStacking powers in this manner is called nesting exponents. They work from the top-down. Tetration works similarly, but with a singe value:<\/p>\n
222<\/sup><\/sup><\/p>\nThis expression is evaluated the same: 22<\/sup> is 4, and 24<\/sup> is 16: 222<\/sup><\/sup> = 16.<\/p>\nOne way to express tetration is to use this notation: 2<\/sup>2, with the exponent coming before the number. Another way is to use Knuth’s up-arrow notation: 2\u2191\u21912. In computerdom, two carets are often used: 2^^2.<\/p>\nRegardless of the notation, with tetration values can get quite large quickly. Peruse this YouTube video<\/a> is you want to completely blow your brain. After watching, you may understand why this topic isn’t taught in school or why a tetration function isn’t available in the standard C library. But that doesn’t mean you can’t write one yourself!<\/p>\nThis month’s C programming Exercise is to write a tertration function. Pass to the function the base value and the tetration exponent. For the expression 5<\/sup>2, the base is 2 and the exponent is 5. This is the same expression depicted in Figure 1. Your function must calculate and return the result.<\/p>\n![\"\"](\"https:\/\/c-for-dummies.com\/blog\/wp-content\/uploads\/2023\/12\/12ex-figure1.png\")
Figure 1. Examples of tetration notation.<\/p><\/div>\n
You can ignore base values less than 2. I’m unaware whether a rule exists, but I’ve seen nothing regarding a tetration expression like 1<\/sup>2, which is just two squared, 22<\/sup>, or 0<\/sup>2, which would be one (or would it be two?). Because I’ve not found any documentation to address these low tetration values, just cut off the exponent values below two in your solution.<\/p>\nHere is output from my solution:<\/p>\n
Base: 4
\nExponent: 3
\n4^^3 = 13407807929942597099574024998205846127479365820592393377723561443721764030073546976801874298166903427690031858186486050853753882811946569946433649006084096<\/code><\/p>\nThese numbers get huge quickly! Many of them cannot be calculated when using the standard C library. For example, from Figure 1:<\/p>\n
Base: 2
\nExponent: 5
\n2^^5 = inf<\/code><\/p>\nDon’t worry about using a large number library<\/a> to obtain the results, as that’s not part of this exercise.<\/p>\nPlease try this challenge on your own. My solution is available here<\/a>.<\/p>\n","protected":false},"excerpt":{"rendered":"How to generate huge values with very little effort. Continue reading