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README.md

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:

Mathematical Constants

  • NUMBERS_E: Euler's number (e), approximately 2.718, is the base of natural logarithms and is fundamental in calculus, particularly in exponential growth and decay problems.
  • NUMBERS_LOG2E: Logarithm of e to the base 2, approximately 1.443, useful in binary logarithms and data compression algorithms.
  • NUMBERS_LOG10E: Logarithm of e to the base 10, approximately 0.434, commonly used in logarithmic scales (e.g., pH, decibels).
  • NUMBERS_PI: Pi (π), approximately 3.14159, represents the ratio of a circle's circumference to its diameter, fundamental in geometry and trigonometry.
  • NUMBERS_INV_PI: The inverse of π (1/π), approximately 0.318, appears in normalization of Fourier transforms.
  • NUMBERS_INV_SQRTPI: Reciprocal of the square root of π (1/√π), approximately 0.564, used in probability density functions.
  • NUMBERS_LN2: Natural logarithm of 2, approximately 0.693, important in binary systems and entropy calculations.
  • NUMBERS_LN10: Natural logarithm of 10, approximately 2.303, useful in base-10 logarithmic conversions.
  • NUMBERS_SQRT2: Square root of 2, approximately 1.414, represents the diagonal of a unit square.
  • NUMBERS_SQRT3: Square root of 3, approximately 1.732, appears in equilateral triangles and trigonometry.
  • NUMBERS_INV_SQRT3: Reciprocal of the square root of 3 (1/√3), approximately 0.577, used in coordinate transformations.
  • NUMBERS_EGAMMA: Euler-Mascheroni constant (γ), approximately 0.577, a constant in number theory and analysis.
  • NUMBERS_PHI: The golden ratio (φ), approximately 1.618, often seen in art, architecture, and nature.
  • NUMBERS_TAU: Tau (2π), approximately 6.283, an alternative to π in periodic functions.
  • NUMBERS_SQRT5: Square root of 5, approximately 2.236, used in formulas for the golden ratio and Fibonacci numbers.
  • NUMBERS_CUBE_RT2: Cube root of 2, approximately 1.26, used in scaling problems and volume calculations.

Physics Constants

  • NUMBERS_C: Speed of light in a vacuum, 299,792,458 m/s, a cornerstone of relativity and electromagnetic theory.
  • NUMBERS_G: Gravitational constant, approximately 6.67430e-11 m³·kg⁻¹·s⁻², governs the force of gravity between two masses.
  • NUMBERS_PLANCK: Planck's constant, approximately 6.626e-34 J·s, defines the scale of quantum effects.
  • NUMBERS_BOLTZ: Boltzmann constant, approximately 1.380649e-23 J/K, relates temperature to energy.
  • NUMBERS_AVOGADRO: Avogadro's number, 6.022e23 mol⁻¹, defines the number of particles in one mole.
  • NUMBERS_R: Ideal gas constant, 8.314 J/(mol·K), appears in the ideal gas law.

Conversion Factors

Angular Conversion:

  • NUMBERS_DEG_TO_RAD: Converts degrees to radians (π/180), approximately 0.01745.
  • NUMBERS_RAD_TO_DEG: Converts radians to degrees (180/π), approximately 57.296.

Length Conversion:

  • NUMBERS_INCH_TO_CM: Converts inches to centimeters, exact value of 2.54.
  • NUMBERS_CM_TO_INCH: Converts centimeters to inches, approximately 0.3937.

Length and Distance

  • NUMBERS_M_TO_KM: Converts meters to kilometers (1/1000).
  • NUMBERS_KM_TO_M: Converts kilometers to meters (1000).
  • NUMBERS_M_TO_CM: Converts meters to centimeters (100).
  • NUMBERS_CM_TO_M: Converts centimeters to meters (1/100).
  • NUMBERS_FT_TO_M: Converts feet to meters, approximately 0.3048.
  • NUMBERS_M_TO_FT: Converts meters to feet, approximately 3.2808.
  • NUMBERS_YD_TO_M: Converts yards to meters, approximately 0.9144.
  • NUMBERS_M_TO_YD: Converts meters to yards, approximately 1.0936.
  • NUMBERS_MILE_TO_KM: Converts miles to kilometers, approximately 1.609.
  • NUMBERS_KM_TO_MILE: Converts kilometers to miles, approximately 0.621.

Mass and Weight

  • NUMBERS_KG_TO_LB: Converts kilograms to pounds, approximately 2.205.
  • NUMBERS_LB_TO_KG: Converts pounds to kilograms, approximately 0.4536.
  • NUMBERS_OZ_TO_GRAM: Converts ounces to grams, approximately 28.35.
  • NUMBERS_GRAM_TO_OZ: Converts grams to ounces, approximately 0.03527.
  • NUMBERS_TON_TO_KG: Converts metric tons to kilograms (1000).
  • NUMBERS_KG_TO_TON: Converts kilograms to metric tons (1/1000).

Area

  • NUMBERS_SQFT_TO_SQM: Converts square feet to square meters, approximately 0.0929.
  • NUMBERS_SQM_TO_SQFT: Converts square meters to square feet, approximately 10.764.
  • NUMBERS_ACRE_TO_SQM: Converts acres to square meters, approximately 4046.856.
  • NUMBERS_SQM_TO_ACRE: Converts square meters to acres, approximately 0.000247.
  • NUMBERS_HECTARE_TO_SQM: Converts hectares to square meters (10,000).
  • NUMBERS_SQM_TO_HECTARE: Converts square meters to hectares (1/10,000).

Volume

  • NUMBERS_L_TO_ML: Converts liters to milliliters (1000).
  • NUMBERS_ML_TO_L: Converts milliliters to liters (1/1000).
  • NUMBERS_GAL_TO_L: Converts US gallons to liters, approximately 3.785.
  • NUMBERS_L_TO_GAL: Converts liters to US gallons, approximately 0.264.
  • NUMBERS_CUBIC_M_TO_L: Converts cubic meters to liters (1000).
  • NUMBERS_L_TO_CUBIC_M: Converts liters to cubic meters (1/1000).
  • NUMBERS_CUBIC_IN_TO_L: Converts cubic inches to liters, approximately 0.01639.
  • NUMBERS_L_TO_CUBIC_IN: Converts liters to cubic inches, approximately 61.024.

Speed

  • NUMBERS_MPS_TO_KMPH: Converts meters per second to kilometers per hour (3.6).
  • NUMBERS_KMPH_TO_MPS: Converts kilometers per hour to meters per second (1/3.6).
  • NUMBERS_MPH_TO_KMPH: Converts miles per hour to kilometers per hour, approximately 1.609.
  • NUMBERS_KMPH_TO_MPH: Converts kilometers per hour to miles per hour, approximately 0.621.
  • NUMBERS_KNOT_TO_KMPH: Converts knots to kilometers per hour, approximately 1.852.
  • NUMBERS_KMPH_TO_KNOT: Converts kilometers per hour to knots, approximately 0.54.

Temperature

  • NUMBERS_C_TO_K: Converts Celsius to Kelvin (add 273.15).
  • NUMBERS_K_TO_C: Converts Kelvin to Celsius (subtract 273.15).
  • NUMBERS_F_TO_C_MULT: Multiplier for Fahrenheit to Celsius conversion (5/9).
  • NUMBERS_C_TO_F_MULT: Multiplier for Celsius to Fahrenheit conversion (9/5).
  • NUMBERS_F_TO_C_OFFSET: Offset to subtract 32 in Fahrenheit to Celsius conversion.
  • NUMBERS_C_TO_F_OFFSET: Offset to add 32 in Celsius to Fahrenheit conversion.

Energy and Power

  • NUMBERS_J_TO_CAL: Converts joules to calories, approximately 0.239.
  • NUMBERS_CAL_TO_J: Converts calories to joules (4.184).
  • NUMBERS_J_TO_KWH: Converts joules to kilowatt-hours, approximately 2.778e-7.
  • NUMBERS_KWH_TO_J: Converts kilowatt-hours to joules (3.6e6).
  • NUMBERS_W_TO_HP: Converts watts to horsepower, approximately 0.00134.
  • NUMBERS_HP_TO_W: Converts horsepower to watts, approximately 745.7.

Time

  • NUMBERS_SEC_TO_MIN: Converts seconds to minutes (1/60).
  • NUMBERS_MIN_TO_SEC: Converts minutes to seconds (60).
  • NUMBERS_MIN_TO_HOUR: Converts minutes to hours (1/60).
  • NUMBERS_HOUR_TO_MIN: Converts hours to minutes (60).
  • NUMBERS_DAY_TO_HOUR: Converts days to hours (24).
  • NUMBERS_HOUR_TO_DAY: Converts hours to days (1/24).
  • NUMBERS_YEAR_TO_SEC: Converts years to seconds, approximately 31,556,952 (based on 365.2425 days/year).

Examples

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

#include "numbers/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;
}

Result

Amount after 10 years: $1648.72

Example 2: Converting Radians to Degrees Using Pi

#include "numbers/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;
}

Result

1.00 radians is equal to 57.30 degrees

Example 3: Using the Golden Ratio (Phi)

#include "numbers/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;
}

Result

Approximate 10th Fibonacci number: 55

Example 4: Calculate Distance Traveled by Light in Vacuum

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

int main() {
    double time_seconds = 10.0; 
    double distance = NUMBERS_C * time_seconds; 

    fmt_printf("Light travels %.2e meters in %.2f seconds.\n", distance, time_seconds);
    return 0;
}

Result

Light travels 3.00e+09 meters in 10.00 seconds.

Example 5: Gravitational Force Between Two Masses

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

int main() {
    double mass1 = 5.0;     
    double mass2 = 10.0;    
    double distance = 2.0;  

    double force = (NUMBERS_G * mass1 * mass2) / (distance * distance);

    fmt_printf("Gravitational force: %.2e N\n", force);
    return 0;
}

Result

Gravitational force: 8.34e-10 N

Example 6: Calculate Energy Using Planck's Constant

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

int main() {
    double frequency = 5.0e14; 
    double energy = NUMBERS_PLANCK * frequency;

    fmt_printf("Energy of photon: %.2e J\n", energy);
    return 0;
}

Result

Energy of photon: 3.31e-19 J

Example 7: Convert Temperature from Fahrenheit to Celsius

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

int main() {
    double fahrenheit = 98.6;
    double celsius = (fahrenheit + NUMBERS_F_TO_C_OFFSET) * NUMBERS_F_TO_C_MULT;

    fmt_printf("%.2f°F is %.2f°C\n", fahrenheit, celsius);
    return 0;
}

Result

98.60F is 37.00C

Example 8: Convert Speed from Kilometers per Hour to Miles per Hour

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

int main() {
    double speed_kmph = 100.0;
    double speed_mph = speed_kmph * NUMBERS_KMPH_TO_MPH;

    fmt_printf("%.2f km/h is %.2f mph\n", speed_kmph, speed_mph);
    return 0;
}

Result

100.00 km/h is 62.14 mph

Example 9: Approximate Area of a Circle

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

int main() {
    double radius = 5.0; 
    double area = NUMBERS_PI * radius * radius;

    fmt_printf("Area of a circle with radius %.2f meters: %.2f square meters\n", radius, area);
    return 0;
}

Result

Area of a circle with radius 5.00 meters: 78.54 square meters

Example 10: Calculating Natural Logarithm Using NUMBERS_LN2

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

int main() {
    double x = 8.0;
    // Using change of base formula: ln(x) = log2(x) * NUMBERS_LN2
    double ln_x = log2(x) * NUMBERS_LN2;

    fmt_printf("Natural logarithm of %.2f is approximately %.4f\n", x, ln_x);
    return 0;
}

Result

Natural logarithm of 8.00 is approximately 2.0794

Example 11: Converting Inches to Centimeters Using NUMBERS_INCH_TO_CM

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

int main() {
    double length_in_inches = 12.0; // Length in inches
    double length_in_cm = length_in_inches * NUMBERS_INCH_TO_CM; // Convert to centimeters

    fmt_printf("%.2f inches is equal to %.2f centimeters\n", length_in_inches, length_in_cm);
    return 0;
}

Result

12.00 inches is equal to 30.48 centimeters

Example 12: Calculating Energy from Temperature Using Boltzmann Constant

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

int main() {
    double temperature = 300.0; // Temperature in Kelvin
    double energy = NUMBERS_BOLTZ * temperature; // Energy in joules

    fmt_printf("Thermal energy at %.2f K is %.2e J\n", temperature, energy);
    return 0;
}

Result

Thermal energy at 300.00 K is 4.14e-21 J

License

This project is open-source and available under [ISC License].