the code is in ada with Ada.Numerics.Generic_Elementary_Functions;package body Number_Theory is -- Instantiate the library for floating point math using Floating_Type. package Floating_Functions is new Ada.Numerics.Generic_Elementary_Functions(Floating_Type); use Floating_Functions; function Factorial(N : in Factorial_Argument_Type) return Positive is begin -- TODO: Finish me! -- -- 0! is 1 -- N! is N * (N-1) * (N-2) * ... * 1 return 1; end Factorial; function Is_Prime(N : in Prime_Argument_Type) return Boolean is Upper_Bound : Prime_Argument_Type; Current_Divisor : Prime_Argument_Type; begin -- Handle 2 as a special case. if N = 2 then return True; end if; Upper_Bound := N - 1; Current_Divisor := 2; while Current_Divisor < Upper_Bound loop if N rem Current_Divisor = 0 then return False; end if; Upper_Bound := N / Current_Divisor; end loop; return True; end Is_Prime; function Prime_Counting(N : in Prime_Argument_Type) return Natural is begin -- TODO: Finish me! -- -- See the page for more information. return 0; end Prime_Counting; function Logarithmic_Integral(N : in Prime_Argument_Type) return Floating_Type is begin -- TODO: Finish me! -- -- See the page for more information. return 1.0; end Logarithmic_Integral;end Number_Theory; 2. Number theory is a branch of mathematics that concerns itself with the properties of the integers. One function of considerable interest in number theory is the prime countingfunction. It is traditionally given the name n (but it has nothing to do with circles). For example T(6) = 3 because there are three prime numbers less than or equal to 6 (namely, 2, 3,and 5).Start by adding a function to package Number_Theory that computes n(n) for positive values n greater than or equal to 2. Note that the package already has a function Is_Prime thatyou will no doubt find useful. You might also want to make use of the defined subtype Prime_Argument_Type. Ada allows you to use Greek letters in variable names, but I suggest usingthe name Prime_Counting for n instead.3. Modify the main file main.adb to exercise your function (ask the user to input a value n and then output (n)). Here are some values of n(n) you can check.T(n)104100251_00016810_0001_229100_0009_5921_000_00078_49810_000_000664_579100_000_000 5_761_4551_000_000_000 50_847_534 4. Computing n(n) exactly can be time-consuming, especially for large values of n (note: you should be able to double the speed of your implementation by skipping even numbers...don't forget to handle 2 as a special case). It turns out there is an approximation formula for computing n(n) that is much faster to calculate. It entails evaluating an infinite series thatuses the natural logarithm function. Here is the series:v + 1n(1n(n)) + In'(n)/(1*1!) + In?(n)/(2*2!) + 1n (n)/(3*3!) + ...Here y (gamma) is Euler's constant and has the value (approximately):y = 0.57721_56649_01532_86060_65120_90082_40243_10421_59335_93992Although the series has infinitely many terms you don't need to add them all because the terms get smaller and smaller. This series is called the "logarithmic integral function" andgoes by the name li(n). It is an amazing fact that n(n) is roughly equal to li(n).Add a function to your package Number_Theory that computes li(n). Call your function Logarithmic_Integral.The package Ada.Numerics.Generic_Elementary_Functions contains a function Log which computes the natural logarithm (shown as 'In' in the formula above). Note that thelogarithmic integral is computed using floating point numbers, so you'll need some type conversions to go back and forth between integers and floating point values. For example if Nis an integer of some kind, you can convert its value to the floating point type declared in Number_Theory by doing Floating_Type (N).

the code is in ada with Ada.Numerics.Generic_Elementary_Functions; package body Number_Theory is -- Instantiate the library for floating point math using Floating_Type. package Floating_Functions is new Ada.Numerics.Generic_Elementary_Functions(Floating_Type); use Floating_Functions; function Factorial(N : in Factorial_Argument_Type) return Positive is begin -- TODO: Finish me! -- -- 0! is 1 -- N! is N * (N-1) * (N-2) * ... * 1 return 1; end Factorial; function Is_Prime(N : in Prime_Argument_Type) return Boolean is Upper_Bound : Prime_Argument_Type; Current_Divisor : Prime_Argument_Type; begin -- Handle 2 as a special case. if N = 2 then return True; end if; Upper_Bound := N - 1; Current_Divisor := 2; while Current_Divisor < Upper_Bound loop if N rem Current_Divisor = 0 then return False; end if; Upper_Bound := N / Current_Divisor; end loop; return True; end Is_Prime; function Prime_Counting(N : in Prime_Argument_Type) return Natural is begin -- TODO: Finish me! -- -- See the page for more information. return 0; end Prime_Counting; function Logarithmic_Integral(N : in Prime_Argument_Type) return Floating_Type is begin -- TODO: Finish me! -- -- See the page for more information. return 1.0; end Logarithmic_Integral; end Number_Theory;

7th Edition

ISBN:9780133594140

Author:James Kurose, Keith Ross

Publisher:James Kurose, Keith Ross

Chapter1: Computer Networks And The Internet

Section: Chapter Questions

Problem R1RQ: What is the difference between a host and an end system? List several different types of end...