Abs (Absolute Value)

• Syntax: Abs(x)

• Purpose: Returns the absolute value (the distance from zero) of a number x. Ignores whether the number is positive or negative.

• Example:

  a = _Abs(-153)  -- Sets a to 153

Acos (Arccosine)

• Syntax: Acos(x)

• Purpose: Returns the arccosine of x in radians. The arccosine is the inverse function of cosine, meaning it finds the angle whose cosine is x. The result will be between 0 and pi.

• Example:

  x = _Acos(1)   -- result will be 0 (cosine of 0 radians is 1)
  y = _Acos(-1)  -- result will be approximately 3.14159 (cosine of pi radians is -1)

Angle_Between_Two_Points

• Syntax: Angle_Between_Two_Points(From_X, From_Y, To_X, To_Y)

• Purpose: Calculates the angle (in radians) formed by a line drawn between two points. Uses the starting point (From_X, From_Y) as the angle's vertex.

Any_pow (Exponentiation)

• Syntax: Any_pow(x, y)

• Purpose: Calculates x raised to the power of y (x^y). Can also be done using the ^ operator, like x^y.

Any_root (Roots)

• Syntax: Any_root(x, y)

• Purpose: Returns x raised to the power of (1/y). In other words, finds the y-th root of x. Can also be done using the ^ operator, like x^(1/y).

Asin (Arcsine)

• Syntax: Asin(x)

• Purpose: Returns the arcsine of x in radians. Arcsine is the inverse function of sine, finding the angle whose sine is x. The result will be between -pi/2 and pi/2.

• Example:

  _Print_Console(_Asin(1))    -- result will be approx. 1.57079 (sine of pi/2 radians is 1)
  _Print_Console(_Asin(-1))   -- result will be approx. -1.57079 (sine of -pi/2 radians is -1)

Atan (Arctangent)

• Syntax: Atan(x)

• Purpose: Returns the arctangent of x in radians. Arctangent is the inverse function of tangent, finding the angle whose tangent is x. The result will be between -pi/2 and pi/2.

• Example:

  _Print_Console(_Atan(0))   -- result is 0 (tangent of 0 radians is 0) 

Atan2 (Arctangent with Quadrant Handling)

• Syntax: Atan2(y, x)

• Purpose: Similar to Atan, but considers the signs of x and y to determine the correct quadrant of the result. Useful because Atan alone doesn't fully distinguish between some angles. Result will be in the range of -pi to pi radians.

• Example:

  _Print_Console(_Atan2(1, 0))  -- Result will be pi/2

Bin (Binary Conversion)

• Syntax: Bin(num)

• Purpose: Converts a decimal (base-10) number to its binary (base-2) representation.

Bin_to_Dec (Binary to Decimal)

• Syntax: Bin_to_Dec(binNumber)

• Purpose: Converts a binary number (as a string) to its equivalent decimal form.

Ceil (Ceiling)

• Syntax: Ceil(x)

• Purpose: Returns the smallest integer that is greater than or equal to x.

• Example:

  _Print_Console( _Ceil(0.5) )  -- Output: 1
  _Print_Console( _Ceil(-0.5) ) -- Output: 0 

Center_Between_Two_Points

• Syntax: Center_Between_Two_Points(x1, y1, x2, y2)

• Purpose: Calculates the midpoint (the point exactly in between) of a line segment defined by the coordinates (x1, y1) and (x2, y2).

Combination

• Syntax: Combination(n, r)

• Purpose: Calculates the number of ways you can choose a subset of r items from a larger set of n items (where order doesn't matter).

Convert_from_any_base

• Syntax: Convert_from_any_base(number_as_string, nn)

• Purpose: Takes a number represented as a string in any base (nn, from 2 to 54) and converts it to its equivalent decimal (base-10) representation.

• Example:

  _Print_Console( _Convert_from_any_base("11111111", 2) )  -- Output: 255 (binary to decimal)

Convert_to_any_base

• Syntax: Convert_to_any_base(number, nn)

• Purpose: Converts a decimal number into its representation in another base (nn, from 2 to 54).

• Example:

  _Print_Console( _Convert_to_any_base(255, 2) )  -- Output: 11111111 (decimal to binary)

Cos (Cosine)

• Syntax: Cos(x)

• Purpose: Returns the cosine of an angle x (given in radians).

Cosh (Hyperbolic Cosine)

• Syntax: Cosh(x)

• Purpose: Returns the hyperbolic cosine of x. Hyperbolic functions are related to hyperbolas the way trigonometric functions (like cosine) are related to circles.

Cubic_root

• Syntax: Cubic_root(x)

• Purpose: Finds the cube root of x (equivalent to x^(1/3)).

DMS (Degrees, Minutes, Seconds Conversion)

• Syntax: DMS(g)

• Purpose: Converts an angle given in decimal degrees into its equivalent representation using degrees, minutes, and seconds.

Decrement

• Syntax: Decrement(Object_Name, Decrement_Value, Minimum_Value)

• Purpose: Decreases the value stored in Object_Name by Decrement_Value. Ensures the value doesn't go below Minimum_Value. Likely designed for use with GUI objects within your program.

Deg (Degrees to Radians)

• Syntax: Deg(x)

• Purpose: Converts an angle x from degrees to radians.

• Example:

  _Print_Console(_Deg(180))  -- Output:  3.14159... (pi)

Distance_Between_Two_Points

• Syntax: Distance_Between_Two_Points (x1, y1, x2, y2)

• Purpose: Calculates the straight-line distance between two points with coordinates (x1, y1) and (x2, y2).

Exp (Natural Exponent)

• Syntax: Exp(x)

• Purpose: Returns the value of e (the mathematical constant approximately 2.718) raised to the power of x.

• Example:

  _Print_Console(_Exp(0))  -- Output: 1
  _Print_Console(_Exp(1))  -- Output: approx. 2.71828

Factorial

• Syntax: Factorial(x)

• Purpose: Calculates the factorial of a non-negative integer x. Factorial is the product of all positive integers less than or equal to x (e.g., 5! = 5 * 4 * 3 * 2 * 1 = 120).

Floor

• Syntax: Floor(x)

• Purpose: Returns the largest integer that is less than or equal to x.

• Example:

  _Print_Console( _Floor(0.5) )  -- Output: 0
  _Print_Console( _Floor(-0.5) ) -- Output: -1 

Fmod (Floating-Point Modulus)

• Syntax: Fmod(x, y)

• Purpose: Returns the remainder after dividing x by y, with special handling to ensure an accurate result even when dealing with floating-point numbers (numbers with decimals).

Frac (Fractional Part)

• Syntax: Frac(nValue)

• Purpose: Returns just the decimal portion of a number.

• Example:

  _Print_Console(_Frac(3.14159))  -- Output: 0.14159

Frexp (Fraction and Exponent Split)

• Syntax: Frexp(x)

• Purpose: Splits a number x into two parts: a normalized fraction (m) and an exponent (e). The fraction m will always be between 0.5 and 1, and the result follows the formula x = m * 2^e.

• Example:

  fraction, exponent = _Frexp(128) 
  _Print_Console(fraction)   -- Output: 0.5
  _Print_Console(exponent)   -- Output:  8

Hex (Hexadecimal Conversion)

• Syntax: Hex(number)

• Purpose: Converts a decimal (base-10) number to its hexadecimal (base-16) representation.

Hex_to_Dec (Hexadecimal to Decimal)

• Syntax: Hex_to_Dec(hexNumber)

• Purpose: Converts a hexadecimal number (as a string) to its equivalent decimal form.

Hyp_Cos (Hyperbolic Cosine)

• Syntax: Hyp_Cos(x)

• Purpose: Returns the hyperbolic cosine of x. For a deeper explanation, see the Cosh function.

Hyp_Sin (Hyperbolic Sine)

• Syntax: Hyp_Sin(x)

• Purpose: Returns the hyperbolic sine of x. See the Cosh function for more context.

Hyp_Tan (Hyperbolic Tangent)

• Syntax: Hyp_Tan(x)

• Purpose: Returns the hyperbolic tangent of x. See the Cosh function for more context.

Increment

• Syntax: Increment(Object_Name, Increment_Value)

• Purpose: Increases the value stored in Object_Name by Increment_Value. Likely designed for use with GUI objects within your program.

Int (Truncation)

• Syntax: Int(n)

• Purpose: Essentially the same as Floor. Returns the integer part of n by removing any decimals.

Is_Bin (Binary Number Check)

• Syntax: Is_Bin(string)

• Purpose: Returns true if the provided string contains a valid binary number, and false otherwise.

Is_Hex (Hexadecimal Number Check)

• Syntax: Is_Hex(string)

• Purpose: Returns true if the provided string contains a valid hexadecimal number, and false otherwise.

Is_Number

• Syntax: Is_Number(test_number)

• Purpose: Returns true if the provided test_number is a valid numerical value, and false otherwise.

Is_Oct (Octal Number Check)

• Syntax: Is_Oct(string)

• Purpose: Returns true if the provided string contains a valid octal number (base-8) and false otherwise.

Is_Range

• Syntax: Is_Range(n, Initial_Range, Final_Range)

• Purpose: Returns true if the number n falls within the inclusive range between Initial_Range and Final_Range, and false otherwise.

Ldexp (Combine Fraction and Exponent)

• Syntax: Ldexp(m, e)

• Purpose: The opposite of Frexp. Combines a fraction m (between 0.5 and 1) and an exponent e and returns the result according to the formula x = m * 2^e.

Ln (Natural Logarithm)

• Syntax: Ln(x)

• Purpose: Returns the natural logarithm (base-e logarithm) of x.

Log (Natural Logarithm - Alias)

• Syntax: Log(x)

• Purpose: Exactly the same as Ln(x). Returns the natural logarithm (base-e logarithm) of x.

Log10 (Base-10 Logarithm)

• Syntax: Log10(x)

• Purpose: Returns the base-10 logarithm of x.

Minus (Negation)

• Syntax: Minus(x)

• Purpose: Returns the negative of x (equivalent to x * -1).

Mod (Modulus)

• Syntax: Mod(x, y)

• Purpose: Calculates the modulus, which is the remainder after division of x by y.

Modf (Split into Integer and Fraction)

• Syntax: Modf(x)

• Purpose: Splits a number x into two parts: its integer portion and its fractional portion.

• Example:

   integerPart, fractionalPart = _Modf(5.3)
   _Print_Console(integerPart)    -- Output: 5
   _Print_Console(fractionalPart) -- Output: 0.3

Oct (Octal Conversion)

• Syntax: Oct(number)

• Purpose: Converts a decimal (base-10) number to its octal (base-8) representation.

Oct_to_Dec (Octal to Decimal)

• Syntax: Oct_to_Dec(octNumber)

• Purpose: Converts an octal number (as a string) to its equivalent decimal form.

Permutation

• Syntax: Permutation(n, r)

• Purpose: Calculates the number of ways you can order r items out of a set of n items (where order matters).

Pi

• Syntax: Pi()

• Purpose: Returns the mathematical constant pi (approximately 3.14159).

Point_In_Polygon

• Syntax: Point_In_Polygon(x, y, polygon)

• Purpose: Determines whether a point with coordinates (x, y) lies inside a polygon defined by an array of points named polygon. Useful for geographic applications!

Pow (Exponentiation - Alias)

• Syntax: Pow(x, y)

• Purpose: Exactly the same as Any_pow(x, y). Calculates x to the power of y.

Pow_minus_one (Reciprocal)

• Syntax: Pow_minus_one(x)

• Purpose: Calculates the reciprocal of x (equivalent to 1/x or x^(-1)).

Pow_three (Cubing)

• Syntax: Pow_three(x)

• Purpose: Calculates x to the power of 3 (equivalent to x^3).

Rad (Radians to Degrees)

• Syntax: Rad(x)

• Purpose: The opposite of Deg. Converts an angle x from radians to degrees.

RandomSeed

• Syntax: RandomSeed(x)

• Purpose: Sets the starting point ("seed") for the pseudo-random number generator. Using the same seed repeatedly will produce the same sequence of random numbers, which can be useful for testing.

Rnd (Random Number between 0 and 1)

• Syntax: Rnd()

• Purpose: Returns a pseudo-random decimal number between 0 (inclusive) and 1 (exclusive).

Rnd_Between (Random Number within Range)

• Syntax: Rnd_Between(r1, r2)

• Purpose: Returns a pseudo-random number between r1 and r2 (inclusive).

Round

• Syntax: Round(x)

• Purpose: Rounds a number x to the nearest integer. For numbers with a fractional part exactly equal to 0.5, it rounds up.

Sin (Sine)

• Syntax: Sin(x)

• Purpose: Returns the sine of an angle x (given in radians).

Sinh (Hyperbolic Sine)

• Syntax: Sinh(x)

• Purpose: Returns the hyperbolic sine of x. See the Cosh function for more context.

Sqrt (Square Root)

• Syntax: Sqrt(x)

• Purpose: Calculates the principal square root of x (the non-negative root).

Tan (Tangent)

• Syntax: Tan(x)

• Purpose: Returns the tangent of an angle x (given in radians).

Tanh (Hyperbolic Tangent)

• Syntax: Tanh(x)

• Purpose: Returns the hyperbolic tangent of x. See the Cosh function for more context.

Val (String to Number)

• Syntax: Val(string)

• Purpose: Converts a string representation of a number into its numerical equivalent.

aCos, aSin, aTan, pi

• These appear to be alternative names or potential typos. They likely function the same as Acos, Asin, Atan, and Pi respectively.