Pakeji Hesabu (Math Package)

Pakeji Hesabu is a math package written in pure Nuru by VictorKariuki.

This package provides various mathematical functions and constants implemented in nuru programming language. It includes methods for trigonometric functions, logarithmic functions, array operations, and utility functions.

Usage

To use the pakeji hesabu package follow the steps below:

1. Copy the hesabu.nr file and any required third-party package files into the same directory as your project.

2. Ensure that the package file names end with the .nr extension and match the package names. For example, if the package name is hesabu, the corresponding file name should be hesabu.nr.

3. You can directly import the hesabu.nr package and any required third-party packages in your Nuru code using the tumia keyword. For example:

   tumia "hesabu"
   

   Example of calling the package methods:

   andika(hesabu.e())
   

What is in

This package covers a wide range of mathematical operations, including basic arithmetic, trigonometry, exponential and logarithmic functions, rounding and comparison operations, as well as some utility and array operations.

The methods provided in the hesabu package can be classified into different categories based on their functionalities. Here is a classification of the methods:

1. Trigonometric Functions:

   • cos(x)
   • sin(x)
   • tan(x)
   • acos(x)
   • asin(x)
   • atan(x)

2. Hyperbolic Functions:

   • cosh(x)
   • sinh(x)
   • tanh(x)
   • acosh(x)
   • asinh(x)
   • atanh(x)

3. Exponential and Logarithmic Functions:

   • exp(x)
   • expm1(x)
   • log(x)
   • log10(x)
   • log1p(x)

4. Other Mathematical Functions:

   • abs(namba)
   • ceil(x)
   • floor(x)
   • sqrt(x)
   • cbrt(x)
   • root(x, n)
   • hypot(values)
   • factorial(n)

5. Rounding and Comparison Functions:

   • round(x, method)
   • max(numbers)
   • min(numbers)

6. Utility Functions:

   • sign(x)
   • isNegative(num)
   • isInteger(num)
   • getIntegerPart(num)

7. Array and List Operations:

   • list(first, last, interval)
   • reduce(iterator, callback, initialValue)

1. Constants:

• PI: Represents the mathematical constant π.
• e: Represents Euler's Number.
• phi: Represents the Golden Ratio.
• ln10: Represents the natural logarithm of 10.
• ln2: Represents the natural logarithm of 2.
• log10e: Represents the base 10 logarithms of Euler's number (e).
• log2e: Represents the base 2 logarithm of Euler's number (e).
• sqrt1_2: Represents the square root of 1/2.
• sqrt2: Represents the square root of 2.
• sqrt3: Represents the square root of 3.
• sqrt5: Represents the square root of 5.
• EPSILON: Represents a small value (2.220446049250313e-16).

2. Methods:

1. abs(namba)

   • Description: Calculates the absolute value of a number.
   • Example: hesabu.abs(-42) returns 42.

2. acos(x)

   • Description: Calculates the arccosine of a number.
   • Example: hesabu.acos(0.5) returns 1.0471975511965979.

3. acosh(x)

   • Description: Calculates the inverse hyperbolic cosine of a number.
   • Example: hesabu.acosh(2) returns 1.3169578969248166.

4. asin(x)

   • Description: Calculates the arcsine of a number using the Taylor series.
   • Example: hesabu.arcsin(0.5) returns 0.5235987755982989.

5. asinh(x)

   • Description: Calculates the inverse hyperbolic sine of a number.
   • Example: hesabu.arsinh(2) returns 1.4436354751788103.

6. atan(x)

   • Description: Calculates the arctangent of a number using the Taylor series.
   • Example: hesabu.atan(1) returns 0.7853981633974485.

7. atan2(y, x)

   • Description: Calculates the arctangent of the quotient of its arguments.
   • Example: hesabu.atan2(1, 1) returns 0.7853981633974483.

8. atanh(x)

   • Description: Calculates the inverse hyperbolic tangent of a number.
   • Example: hesabu.atanh(0.5) returns 0.5493061443340549.

9. cbrt(x)

   • Description: Calculates the cube root of a number.
   • Example: hesabu.cbrt(8) returns 2.

10. root(x, n)

    • Description: Calculates the nth root of a number using the Newton-Raphson method.
    • Example: hesabu.root(27, 3) returns 3.

11. ceil(x)

    • Description: Rounds up to the smallest integer greater than or equal to a given number.
    • Example: hesabu.ceil(4.3) returns 5.

12. cos(x)

    • Description: Calculates the cosine of an angle in radians using the Taylor series.
    • Example: hesabu.cos(5) returns 0.28366218546322464.

13. cosh(x)

    • Description: Calculates the hyperbolic cosine of a number.
    • Example: hesabu.cosh(5) returns 74.20994842490012.

14. exp(x)

    • Description: Calculates the value of Euler's number raised to the power of a given number.
    • Example: hesabu.exp(2) returns 7.389056098930649.

15. expm1(x)

    • Description: Calculates Euler's number raised to the power of a number minus 1.
    • Example: hesabu.expm1(1) returns 1.7182818284590455.

16. floor(x)

    • Description: Rounds down to the largest integer less than or equal to a given number.
    • Example: hesabu.floor(4.7) returns 4.

17. hypot(values)

    • Description: Calculates the square root of the sum of squares of the given values.
    • Example: hesabu.hypot([3, 4]) returns 5.

18. log(x)

    • Description: Calculates the natural logarithm of a number.
    • Example: hesabu.log(2) returns 0.69314718056.

19. log10(x)

    • Description: Calculates the base 10 logarithm of a number.
    • Example: hesabu.log10(100) returns 1.9999999999573126.

20. log1p(x)

    • Description: Calculates the natural logarithm of 1 plus the given number.
    • Example: hesabu.log1p(1) returns 0.6931471805599451.

21. log2(x)

    • Description: Calculates the base 2 logarithm of a number.
    • Example: hesabu.log2(8) returns 3.

22. max(numbers)

    • Description: Finds the maximum value in a list of numbers.
    • Example: hesabu.max([4, 2, 9, 5]) returns 9.

23. min(numbers)

    • Description: Finds the minimum value in a list of numbers.
    • Example: hesabu.min([4, 2, 9, 5]) returns 2.

24. round(x, method)

    • Description: Rounds a number to the nearest integer using the specified method.
    • supported methods:
      • "rpi" (round to the nearest integer using the principle of rounding half to the nearest even)
      • "rni" (round to the nearest integer using the principle of rounding half away from zero)
      • "ri" (round to the nearest integer using the standard rounding method)
      • An invalid method results in returning NaN (Not a Number)
    • Example: hesabu.round(4.6, "rpi") returns 5.

25. sign(x)

    • Description: Determines the sign of a number.
    • Example: hesabu.sign(-5) returns -1.

26. sin(x)

    • Description: Calculates the sine of an angle in radians using the Taylor series.
    • Example: hesabu.sin(1) returns 0.8414709848078965.

27. sinh(x)

    • Description: Calculates the hyperbolic sine of a number.
    • Example: hesabu.sinh(0) returns 0.

28. sqrt(x)

    • Description: Calculates the square root of a number.
    • Example: hesabu.sqrt(4) returns 2.

29. tan(x)

    • Description: Calculates the tangent of an angle in radians.
    • Example: hesabu.tan(1) returns 1.557407724654902.

30. tanh(x)

    • Description: Calculates the hyperbolic tangent of a number.
    • Example: hesabu.tanh(0) returns 0.

31. factorial(n)

    • Description: Calculates the factorial of a number.
    • Example: hesabu.factorial(5) returns 120.

32. isNegative(num)

    • Description: Checks if a number is negative.
    • Example: hesabu.isNegative(-5) returns kweli.

33. isInteger(num)

    • Description: Checks if a number is an integer.
    • Example: hesabu.isInteger(4.5) returns sikweli.

34. getIntegerPart(num)

    • Description: Gets the integer part of a number.
    • Example: hesabu.getIntegerPart(4.5) returns 4.

35. list(first, last, interval)

    • Description: Creates a list of numbers with the specified interval between them.
    • Example: hesabu.list(1, 5, 1) returns [1, 2, 3, 4].

36. reduce(iterator, callback, initialValue)

    • Description: Reduces the elements of an array to a single value using a specified callback function.
    • Example: hesabu.reduce([1, 2, 3, 4], [callback function], 0)

      fanya callback = unda(accumulator, currentValue){
          rudisha accumulator + currentValue;
      }
    
      andika(hesabu.reduce([1, 2, 3, 4], callback, 0)) \\ returns 10.

Contributing

Contributions to the pakeji hesabu package are welcome. If you have any improvements or bug fixes, feel free to create a pull request.

License

This package is available under the MIT License. See the LICENSE file for more information.