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haas:fall2017:discrete:projects:pnc0 [2017/07/24 16:22] – [algorithm] wedge | haas:fall2017:discrete:projects:pnc0 [2017/10/15 21:11] (current) – [Programs] wedge | ||
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- | ~~TOC~~ | ||
======Project: | ======Project: | ||
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* 0.2: added an additional requirement to implementation constraints: | * 0.2: added an additional requirement to implementation constraints: | ||
* 0.3: added new check/ | * 0.3: added new check/ | ||
+ | * 0.4: added further explanation to " | ||
+ | * 0.5: for increased readability, | ||
* revision #: < | * revision #: < | ||
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This optimization employs the approximated square root trick (**NOT** utilizing an existing square root function, but using simpler logic you implement to approximate the square root point). | This optimization employs the approximated square root trick (**NOT** utilizing an existing square root function, but using simpler logic you implement to approximate the square root point). | ||
+ | ===Further explanation=== | ||
+ | An optimization to the previous process, which used **sqrt()**, this variation will do the exact same thing, but without using the **sqrt()** function. It will approximate the square root. | ||
+ | |||
+ | We know that a square root (especially a whole numbered square root), is when we have whole number factors that are squared. But in addition, only considering the whole number aspect of the square root, we start seeing series of values with the same whole square root value: | ||
+ | |||
+ | <cli> | ||
+ | lab46:~$ count=0; for ((i=2; i<152; i++)); do printf "[%3d] %2d " " | ||
+ | [ 2] 1 [ 3] 1 [ 4] 2 [ 5] 2 [ 6] 2 [ 7] 2 [ 8] 2 [ 9] 3 [ 10] 3 [ 11] 3 | ||
+ | [ 12] 3 [ 13] 3 [ 14] 3 [ 15] 3 [ 16] 4 [ 17] 4 [ 18] 4 [ 19] 4 [ 20] 4 [ 21] 4 | ||
+ | [ 22] 4 [ 23] 4 [ 24] 4 [ 25] 5 [ 26] 5 [ 27] 5 [ 28] 5 [ 29] 5 [ 30] 5 [ 31] 5 | ||
+ | [ 32] 5 [ 33] 5 [ 34] 5 [ 35] 5 [ 36] 6 [ 37] 6 [ 38] 6 [ 39] 6 [ 40] 6 [ 41] 6 | ||
+ | [ 42] 6 [ 43] 6 [ 44] 6 [ 45] 6 [ 46] 6 [ 47] 6 [ 48] 6 [ 49] 7 [ 50] 7 [ 51] 7 | ||
+ | [ 52] 7 [ 53] 7 [ 54] 7 [ 55] 7 [ 56] 7 [ 57] 7 [ 58] 7 [ 59] 7 [ 60] 7 [ 61] 7 | ||
+ | [ 62] 7 [ 63] 7 [ 64] 8 [ 65] 8 [ 66] 8 [ 67] 8 [ 68] 8 [ 69] 8 [ 70] 8 [ 71] 8 | ||
+ | [ 72] 8 [ 73] 8 [ 74] 8 [ 75] 8 [ 76] 8 [ 77] 8 [ 78] 8 [ 79] 8 [ 80] 8 [ 81] 9 | ||
+ | [ 82] 9 [ 83] 9 [ 84] 9 [ 85] 9 [ 86] 9 [ 87] 9 [ 88] 9 [ 89] 9 [ 90] 9 [ 91] 9 | ||
+ | [ 92] 9 [ 93] 9 [ 94] 9 [ 95] 9 [ 96] 9 [ 97] 9 [ 98] 9 [ 99] 9 [100] 10 [101] 10 | ||
+ | [102] 10 [103] 10 [104] 10 [105] 10 [106] 10 [107] 10 [108] 10 [109] 10 [110] 10 [111] 10 | ||
+ | [112] 10 [113] 10 [114] 10 [115] 10 [116] 10 [117] 10 [118] 10 [119] 10 [120] 10 [121] 11 | ||
+ | [122] 11 [123] 11 [124] 11 [125] 11 [126] 11 [127] 11 [128] 11 [129] 11 [130] 11 [131] 11 | ||
+ | [132] 11 [133] 11 [134] 11 [135] 11 [136] 11 [137] 11 [138] 11 [139] 11 [140] 11 [141] 11 | ||
+ | [142] 11 [143] 11 [144] 12 [145] 12 [146] 12 [147] 12 [148] 12 [149] 12 [150] 12 [151] 12 | ||
+ | </ | ||
+ | |||
+ | Or, if perhaps we instead order by square root value: | ||
+ | |||
+ | <cli> | ||
+ | lab46:~$ oldsqrt=$(echo " | ||
+ | [ 2] 1 [ 3] 1 | ||
+ | [ 4] 2 [ 5] 2 [ 6] 2 [ 7] 2 [ 8] 2 | ||
+ | [ 9] 3 [ 10] 3 [ 11] 3 [ 12] 3 [ 13] 3 [ 14] 3 [ 15] 3 | ||
+ | [ 16] 4 [ 17] 4 [ 18] 4 [ 19] 4 [ 20] 4 [ 21] 4 [ 22] 4 [ 23] 4 [ 24] 4 | ||
+ | [ 25] 5 [ 26] 5 [ 27] 5 [ 28] 5 [ 29] 5 [ 30] 5 [ 31] 5 [ 32] 5 [ 33] 5 [ 34] 5 [ 35] 5 | ||
+ | [ 36] 6 [ 37] 6 [ 38] 6 [ 39] 6 [ 40] 6 [ 41] 6 [ 42] 6 [ 43] 6 [ 44] 6 [ 45] 6 [ 46] 6 [ 47] 6 [ 48] 6 | ||
+ | </ | ||
+ | |||
+ | We see that the square root of 36 is 6, but so is the square root of 37, 38, 39... etc. up until we hit 49 (where the whole number square root increments to 7). | ||
+ | |||
+ | Therefore, if we were checking 42 to be prime, we'd only have to check up to 6. | ||
+ | |||
+ | We don't need a **sqrt()** function to tell us this, we can determine the approximate square root point ourselves- by squaring the current factor being tested, and so long as it hasn't exceeded the value we're checking, we know to continue. | ||
+ | |||
+ | There are some important lessons at play here: | ||
+ | |||
+ | * approximation can be powerful | ||
+ | * approximation can result in a simpler algorithm, improving runtime | ||
+ | * **sqrt()** is more complex than you may be aware, not to mention it is in a function. By avoiding that function call, we eliminate some overhead, and that can make a difference in runtime performance. | ||
+ | |||
+ | Depending on how you implement this and the original sqrt() algorithms, this version may have a noticeable performance difference. If, on the other hand, you were really optimal in both implementations, | ||
+ | |||
====primeregbm==== | ====primeregbm==== | ||
To get a taste for combining optimizations, | To get a taste for combining optimizations, | ||
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It is your task to write the following prime number variants: | It is your task to write the following prime number variants: | ||
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====Program Specifications==== | ====Program Specifications==== | ||
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The various " | The various " | ||
- | |||
- | The " | ||
- | * qtynorm: a normal quantity run (2-max) | ||
- | * ./primealg 2048 1 2 0 | ||
- | * qtypart: an offset quantity run (24-max) | ||
- | * ./primealg 2048 1 24 0 | ||
- | * rngnorm: a normal range run (2-max) | ||
- | * ./primealg 0 1 2 2048 | ||
- | * rngpart: an offset range run (24-max) | ||
- | * ./primealg 0 1 24 2048 | ||
- | * coop: both qty and upper bounds set (q: 2048, ub: 8192) | ||
- | * ./primealg 2048 1 2 8192 | ||
- | * coop2: | ||
- | * ./primealg 512 1 2 8192 | ||
- | * coop3: | ||
- | * ./primealg 2048 1 24 8192 | ||
- | * noargs: | ||
- | * ./primealg | ||
- | * invargs: insufficient number of arguments provided (invokes error) | ||
- | * ./primealg 128 | ||
- | * invqty: | ||
- | * ./primealg -2 1 | ||
- | * invnary: invalid value given for n-ary (invokes error) | ||
- | * ./primealg 128 2 | ||
- | * invlow: | ||
- | * ./primealg 128 1 1 | ||
- | * invhigh: invalid value given for upper bound (invokes error) | ||
- | * ./primealg 128 1 32 24 | ||
Just another "nice thing" we deserve. | Just another "nice thing" we deserve. | ||
=====Command-Line Arguments===== | =====Command-Line Arguments===== | ||
- | To automate our comparisons, | + | To automate our comparisons, |
====header files==== | ====header files==== | ||
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int main(int argc, char **argv) | int main(int argc, char **argv) | ||
</ | </ | ||
+ | |||
+ | There are two very important variables involved here (the types are actually what are important, the names given to the variables are actually quite, variable; you may see other references refer to them as things like " | ||
+ | |||
+ | * int argc: the count (an integer) of tokens given on the command line (program name + arguments) | ||
+ | * < | ||
The arguments are accessible via the argv array, in the order they were specified: | The arguments are accessible via the argv array, in the order they were specified: | ||
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* argv[3]: conditionally optional; represents lower bound | * argv[3]: conditionally optional; represents lower bound | ||
* argv[4]: conditionally optional; represents upper bound | * argv[4]: conditionally optional; represents upper bound | ||
+ | |||
+ | Additionally, | ||
+ | |||
+ | ===example=== | ||
+ | For example, if we were to execute the **primereg** program: | ||
+ | |||
+ | <cli> | ||
+ | lab46: | ||
+ | </ | ||
+ | |||
+ | We'd have: | ||
+ | |||
+ | * < | ||
+ | * < | ||
+ | * < | ||
+ | * < | ||
+ | * < | ||
+ | |||
+ | and let's not forget: | ||
+ | |||
+ | * argc: 5 | ||
+ | |||
+ | With the conditionally optional arguments as part of the program spec, for a valid execution of the program, argc could be a value anywhere from 3 to 5. | ||
====Simple argument checks==== | ====Simple argument checks==== | ||
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</ | </ | ||
+ | ===verifyall tests=== | ||
+ | The " | ||
+ | * **qtynorm**: | ||
+ | * **./ | ||
+ | * **qtypart**: | ||
+ | * **./ | ||
+ | * **rngnorm**: | ||
+ | * **./ | ||
+ | * **rngpart**: | ||
+ | * **./ | ||
+ | * **coop**: both qty and upper bounds set (q: 2048, ub: 8192) | ||
+ | * **./ | ||
+ | * **coop2**: both qty and upper bounds set (q: 512, ub: 8192) | ||
+ | * **./ | ||
+ | * **coop3**: both qty and upper bounds set, offset start (24-max, q: 2048, ub: 8192) | ||
+ | * **./ | ||
+ | * **noargs**: | ||
+ | * **./ | ||
+ | * **invargs**: | ||
+ | * **./ | ||
+ | * **invqty**: invalid value for quantity argument given (invokes error) | ||
+ | * **./ | ||
+ | * **invnary**: | ||
+ | * **./ | ||
+ | * **invlow**: invalid value given for lower bound (invokes error) | ||
+ | * **./ | ||
+ | * **invhigh**: | ||
+ | * **./ | ||
+ | |||
+ | If you'd actually to see the output your program' | ||
+ | |||
+ | For example, if you wanted to see the intended output of the **invnary** test, that would be found in: | ||
+ | |||
+ | * **/ | ||
+ | |||
+ | You could easily run your program with the stated arguments for the test, then use **cat** to display the test results and do a visual comparison. | ||
====In general==== | ====In general==== | ||
Analyze the times you see... do they make sense, especially when comparing the algorithm used and the quantity being processed? These are related to some very important core Computer Science considerations we need to be increasingly mindful of as we design our programs and implement our solutions. Algorithmic complexity and algorithmic efficiency will be common themes in all we do. | Analyze the times you see... do they make sense, especially when comparing the algorithm used and the quantity being processed? These are related to some very important core Computer Science considerations we need to be increasingly mindful of as we design our programs and implement our solutions. Algorithmic complexity and algorithmic efficiency will be common themes in all we do. | ||
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====Evaluation Criteria==== | ====Evaluation Criteria==== | ||
- | What I will be looking for: | + | Grand total points: |
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</ | </ | ||
+ | |||
+ | What I will be looking for (for each file): | ||
+ | |||
+ | < | ||
+ | *: | ||
+ | *: | ||
+ | *: | ||
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+ | </ | ||
+ | |||
+ | As the optimizations improve upon others, some evaluations will be based upon differences between a baseline (in some cases, primereg) and the optimization. |