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fp:lab02 [2022/02/24 11:32]
pdmatei 		fp:lab02 [2023/03/10 10:16] (current)
pdmatei
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 <code scala> <code scala>
-def fact (n: Integer): Integer ​= { +def fact (n: Int): Int = { 
-   def aux_fact(n: Integer, acc: Integer): Integer ​= +   def aux_fact(i: Int, acc: Int): Int = 
        if (???) acc        if (???) acc
        else ???        else ???
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 **2.5.** Implement the function ''​nthGuess''​ which starts with $math[x_0 = 1] and computes the nth estimate $math[x_n] of $math[\sqrt{a}]:​ **2.5.** Implement the function ''​nthGuess''​ which starts with $math[x_0 = 1] and computes the nth estimate $math[x_n] of $math[\sqrt{a}]:​
 <code scala> <code scala>
-def nth_guess(n: ​Double, a: Double): Double = ???+def nth_guess(n: ​Int, a: Double): Double = ???
 </​code>​ </​code>​
  
 Note that: Note that:
-  * for smaller $math[a], there is no need to compute $math[n] estimations ​(as $math[(x_n)_n] converges quite fast to $math[\sqrt{a}]. ​+  * for smaller $math[a], there is no need to compute $math[n] estimations as $math[(x_n)_n] converges quite fast to $math[\sqrt{a}]. ​
    
 **2.6.** Thus, implement the function ''​acceptable''​ which returns ''​true''​ iff $math[\mid x_n^2 - a \mid \leq 0.001]. (Hint, google the ''​abs''​ function in Scala. Don't forget to import ''​scala.math._''​). **2.6.** Thus, implement the function ''​acceptable''​ which returns ''​true''​ iff $math[\mid x_n^2 - a \mid \leq 0.001]. (Hint, google the ''​abs''​ function in Scala. Don't forget to import ''​scala.math._''​).
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 } }
 </​code>​ </​code>​
 +
 +**2.8. (!) **  Try out your code for: ''​2.0e50''​ (which is $math[2.0\cdot 10^{50}]) or ''​2.0e-50''​. The code will likely take a very long time to finish. The reason is that $math[xn^2 - a] will suffer from rounding error which may be larger than 0.001. Can you find a different implementation for the function ''​acceptable''​ which takes that into account? (Hint: the code is just as simple as the original one). 
 +