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 lab 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 lab page for more information. return 1.0; end Logarithmic_Integral; end Number_Theory;
code 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 lab 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 lab page for more information.
return 1.0;
end Logarithmic_Integral;
end Number_Theory;

 alt="This package contains subprograms for doing number theoretic computations.
It is used in VTC's CIS-2730, Lab #2.
.M
4 v package Number_Theory is
Constant Definitions
..
7
Gamma : constant := 0.57721_56649_01532_86060_65120_90082_40243_10421_59335_93992;
10
11
Type Definitions
12
13
The range of values for which N! can be computed without overflow.
subtype Factorial_Argument_Type is Integer range 0 .. 12;
14
15
16
-- The range of values that might meaningfully be asked: are you prime?
subtype Prime_Argument_Type is Integer range 2 .. Integer'Last;
17
18
19
A floating point type with at least 15 significant decimal digits.
type Floating_Type is digits 15;
20
21
22
23
24
Subprogram Declarations
25
26
27
Returns N!
28
function Factorial(N : Factorial_Argument_Type) return Positive;
29
Returns True if N is prime; False otherwise.
function Is_Prime(N : in Prime_Argument_Type) return Boolean;
32
Returns the number of prime numbers less than or equal to N.
function Prime_Counting(N : in Prime_Argument_Type) return Natural;
33
34
35
-- The logarithmic integral function, which is an approximation of the prime counting function.
function Logarithmic_Integral(N : in Prime_Argument_Type) return Floating_Type;
36
37
38
39
end Number_Theory;
123 tn ON
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Step by step
Solved in 3 steps with 3 images
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