In this assignment, you will implement a program that computes $\backslash (\backslash$mathrm$\{$a$\}^\{\backslash$mathrm$\{$b$\}\}\backslash ),$ where a is the base and b is the exponent. The program must handle both positive and negative integer exponents. It will dynamically allocate memory for all intermediate results, manage overflow or precision issues, and transition between different data types based on the value of $\backslash ($ b $\backslash ).$

If $\backslash (\backslash$mathrm$\{$b$\}\backslash$geq $0\backslash ),$ the program will start by using an array of long integers and will transition to array of double numbers if overflow occurs. For negative exponents $($b the program will begin with an array of double numbers.

The program should compute powers based on the formula $\backslash ($ a$^\{$b$\}=$a$^\{2\}$ a$^\{$b$-1\}\backslash ).$ However, the calculation must be non$-$recursive. Instead of using recursion, the program should store intermediate results in an array and compule each power using the previously computed value.

Demo Run $1$:

This program calculates anb using dynamic memory allocation.

Please enter the base $($a$)$: $5$

Please enter the exponent $($b$)$: $2$

Final Result $($long$)$: $25$

Demo Run $2$:

This program calculates $\backslash ($ a$^\{$n$\}\backslash$mathrm$\{$~b$\}\backslash )$ using dynamic memory allocation.

Please enter the base $($a$)$: $5$

Please enter the exponent $($b$)100$

Detected long overflow at power $28.$ Switching to double precision!

Final Result $($double$)$: $7\mathrm{.}8886090622101228$e$+69$

Demo Run $3$:

This program calculates $\backslash (\backslash$mathrm$\{$a$\}^\{$n$\}\backslash$mathrm$\{$~b$\}\backslash )$ using dynamic memory allocation.

Please enter the base $($a$)$: $5$

Please enter the exponent $($b$)-4$

Final Result $($double$)$: $0\mathrm{.}0016$

Demo Run $4$:

This program calculates an b using dynamic memory allocation.

Please enter the base $($a$)$: $-3$

Please enter the exponent $($b$)-11$

Final Result $($double$)$: $\backslash (-5\mathrm{.}6450292694767622\backslash$mathrm$\{$e$\}-06\backslash )$

Demo Run $5$:

This program calculates $\backslash (\backslash$mathrm$\{$a$\}^\{$n$\}\backslash$mathrm$\{$~b$\}\backslash )$ using dynamic memory allocation.

Please enter the base $($a$)$: $-3$

Please enter the exponent $($b$)-1000$

Detected double overflow at power $647.$ Unable to compute.

Last computed value at power $646$ was $\backslash (6\mathrm{.}021011422323151$ e$-309\backslash )$

Demo Run $6$:

This program calculates $\backslash ($ a$^\{$n$\}\backslash$mathrm$\{$~b$\}\backslash )$ using dynamic memory allocation.

Please enter the base $($a$)$: $-4$

Please enter the exponent $($b$)$: $19999$

Detected long overflow at power $32.$ Switching to double precision!

Detected double overflow at power $512.$ Unable to compute.

Last computed value at power $511$ was $\backslash (-4\mathrm{.}4942328371557898$ e$+307\backslash )$