Step by Step solution about How to resolve the algorithm Real constants and functions step by step in the C++ programming language

Code Explanation in Detail:

Code 1:

This code demonstrates the use of standard C++ mathematical functions for various operations:

• euler_e: It defines a static variable initialized with the mathematical constant e (approximately 2.718).
• pi: It defines a static variable initialized with the mathematical constant π (approximately 3.14159).
• main():
  • Prints the values of e, pi, and other mathematical computations to the console, including square root, logarithm, exponentiation, absolute value, floor, ceiling, and power.

Code 2:

This code employs the Boost C++ Libraries to demonstrate the use of more advanced mathematical functions:

• using namespace boost::math::double_constants;: This line imports various mathematical constants and functions defined in the Boost library.
• main():
  • Prints the values of e, π, π², √2, ln(e), and other mathematical computations to the console.

Key Concepts Demonstrated:

Mathematical Constants:

• M_E: Represents the mathematical constant e defined in the <cmath> header.
• M_PI: Represents the mathematical constant π defined in the <cmath> header.
• e and pi from Boost C++ Libraries: These provide high-precision values of mathematical constants.

Mathematical Functions:

• std::sqrt(): Computes the square root.
• std::exp(): Computes the exponential function (e^x).
• std::log(): Computes the natural logarithm (ln).
• std::log10(): Computes the base-10 logarithm (log10).
• std::abs(): Computes the absolute value.
• std::floor(): Computes the largest integer less than or equal to the argument.
• std::ceil(): Computes the smallest integer greater than or equal to the argument.
• std::pow(): Computes the power function (x^y).

Boost C++ Libraries:

• Boost C++ Libraries provide high-precision values and functions for mathematical computations, such as e, pi, pi_sqr, and root_two.

Precision Control:

• std::setprecision(18): Controls the number of decimal places displayed for certain computations.

#include <iostream>
#include <cmath>

#ifdef M_E
static double euler_e = M_E;
#else
static double euler_e = std::exp(1); // standard fallback
#endif

#ifdef M_PI
static double pi = M_PI;
#else
static double pi = std::acos(-1);
#endif

int main()
{
  std::cout << "e = " << euler_e
            << "\npi = " << pi
            << "\nsqrt(2) = " << std::sqrt(2.0)
            << "\nln(e) = " << std::log(euler_e)
            << "\nlg(100) = " << std::log10(100.0)
            << "\nexp(3) = " << std::exp(3.0)
            << "\n|-4.5| = " << std::abs(-4.5)   // or std::fabs(-4.5); both work in C++
            << "\nfloor(4.5) = " << std::floor(4.5)
            << "\nceiling(4.5) = " << std::ceil(4.5)
            << "\npi^2 = " << std::pow(pi,2.0) << std::endl;
}


#include <iostream>
#include <iomanip>
#include <cmath>
#include <boost/math/constants/constants.hpp>

int main()
{
    using namespace boost::math::double_constants;
    std::cout << "e = " << std::setprecision(18) << e
              << "\ne³ = " << std::exp(3.0)
              << "\nπ = " << pi
              << "\nπ² = " << pi_sqr
              << "\n√2 = " << root_two
              << "\nln(e) = " << std::log(e)
              << "\nlg(100) = " << std::log10(100.0)
              << "\n|-4.5| = " << std::abs(-4.5)
              << "\nfloor(4.5) = " << std::floor(4.5)
              << "\nceiling(4.5) = " << std::ceil(4.5) << std::endl;
}