Numbers Library in C

Author: amin tahmasebi Release Date: 2024 License: ISC License

The Numbers library in C provides constants for common mathematical values, analogous to the <numbers> header introduced in C++20. It offers a simple way to access important mathematical constants in C programming, enhancing the precision and readability of mathematical computations.

Compilation

To compile the Numbers library with your main program, include the numbers.h file in your project and use a standard GCC compilation command. If other libraries are needed, include their .c files in the command:

gcc -std=c11 -O3 -march=native -flto -funroll-loops -Wall -Wextra -pedantic -s -o main ./main.c 

Make sure that GCC is installed on your system and that the numbers.h file is in the correct directory.

Usage

To use the Numbers library, simply include the numbers.h header file in your C source files:

#include "numbers.h"

Constants Description

Each constant in the numbers.h library represents a fundamental mathematical value, providing high precision for mathematical calculations:

• NUMBERS_E: Represents Euler's number, the base of natural logarithms, approximately 2.718.
• NUMBERS_LOG2E: The logarithm base 2 of Euler's number, approximately 1.442.
• NUMBERS_LOG10E: The logarithm base 10 of Euler's number, approximately 0.434.
• NUMBERS_PI: Represents the mathematical constant pi, the ratio of the circumference of a circle to its diameter, approximately 3.14159.
• NUMBERS_INV_PI: The multiplicative inverse of pi, approximately 0.318.
• NUMBERS_INV_SQRTPI: The inverse of the square root of pi, approximately 0.564.
• NUMBERS_LN2: The natural logarithm of 2, approximately 0.693.
• NUMBERS_LN10: The natural logarithm of 10, approximately 2.303.
• NUMBERS_SQRT2: The square root of 2, representing the length of the diagonal of a square with side length 1, approximately 1.414.
• NUMBERS_SQRT3: The square root of 3, important in various geometrical and trigonometric contexts, approximately 1.732.
• NUMBERS_INV_SQRT3: The inverse of the square root of 3, approximately 0.577.
• NUMBERS_EGAMMA: Euler-Mascheroni constant, a recurring constant in number theory and analysis, approximately 0.577.
• NUMBERS_PHI: The golden ratio, a special number that appears in various areas of mathematics and art, approximately 1.618.

Example 1: Calculating Compound Interest Using Euler's Number (e)

#include "numbers.h"
#include "fmt/fmt.h"
#include <math.h>

int main() {
    double principal = 1000.0; // Initial investment
    double rate = 0.05;        // Annual interest rate
    int years = 10;            // Number of years

    // Compound interest formula: A = P * e^(rt)
    double amount = principal * pow(NUMBERS_E, rate * years);

    fmt_printf("Amount after %d years: $%.2f\n", years, amount);
    return 0;
}

Example 2: Converting Radians to Degrees Using Pi

#include "numbers.h"
#include "fmt/fmt.h"

int main() {
    double radians = 1.0; // Radians
    double degrees = radians * (180.0 / NUMBERS_PI); // Convert to degrees

    fmt_printf("%.2f radians is equal to %.2f degrees\n", radians, degrees);
    return 0;
}

Example 3: Using the Golden Ratio (Phi)

#include "numbers.h"
#include "fmt/fmt.h"
#include <math.h>

int main() {
    int n = 10; // nth position in Fibonacci sequence
    // Approximating the nth Fibonacci number using Golden Ratio
    double fib_n = (pow(NUMBERS_PHI, n) - pow(-NUMBERS_PHI, -n)) / sqrt(5);

    fmt_printf("Approximate %dth Fibonacci number: %.0f\n", n, fib_n);
    return 0;
}