Math

#Square root, nth root, arc sin, arc tan, and arc cos functions courtesy of "bi0qaw" (http://dev.bukkit.org/profiles/bi0qaw/)
#Rotation function courtesy of "Cool3303" (http://dev.bukkit.org/profiles/Cool3303/)
#These commands should be able to approximate the functions of the number argument passed to them to an accuracy of about {@accuracy}
#Remember to change your "number accuracy:" in your Skript config file to {@accuracy} for best results.

Options:
  accuracy: 10 #How accurate should our numbers be? 10 is accurate to 7-10 decimal places usually
  permission: "math.calc" #Permission node required to execute the math commands
  message: "true" #Whether or not to message the results to the player executing the command
  e: 2.7182818284
  pi: 3.14159265358979323846

#Calculate the square root of a number by exponentiating by 0.5
Command /sqrt <number>:
	Permission: {@permission}
	Trigger:
		Set {_x} to number-argument
		If {_x} is smaller than 0:
			If {@message} is "true":
				Send "You cannot square root a negative number!"
			Stop
		Set {_x} to {_x}^0.5
		Set {sqrt.value} to {_x}
		If {@message} is "true":
			Send "%{sqrt.value.%player%}%" to player

#Calculate the nth-root of a number by exponentiating by 1/n
Command /rt <integer> <number>:
	Permission: {@permission}
	Usage:	/rt <root-number> <number>
	Trigger:
		Set {_x} to number-argument-2
		Set {_n} to integer-argument-1
		If {_x} is smaller than 0:
			If {@message} is "true":
				Send "You cannot root a negative number!"
			Stop
		Set {_x} to {_x}^(1/{_n})
		Set {rt.value} to {_x}
		If {@message} is "true":
			Send "%{rt.value.%player%}%" to player

#Calculate the factorial of a number
Command /fact <number>:
	Permission: {@permission}
	Trigger:
		Set {_x} to number-argument
		Set {_i} to {_x} - 1
		Loop {_i} times:
			Set {_x} to {_x} * {_i}
			Subtract 1 from {_i}
		Set {fact.value} to {_x}
		If {@message} is "true":
			Send "%{fact.value.%player%}%" to player

#Calculate the sine of a degree by converting it to radians and looping through a Taylor Series formula
Command /sin <number>:
	Permission: {@permission}
	Trigger:
		Set {_x} to (number-argument / 180) * {@pi}
		Set {_s} to {_x}
		Loop {@accuracy} times:
			Set {_n} to loop-number * 2 + 1
			Execute console command "/fact %{_n}%"
			Set {_f} to {fact.value}
			Set {_s} to {_s} + (({_x} ^ {_n}) / {_f})  * (-1 ^ loop-number)
		Set {sin.value} to {_s}
		If {@message} is "true":
			Send "%{sin.value}%" to player

#Calculate the cosine of a degree by converting it to radians and looping through a Taylor Series formula
Command /cos <number>:
	Permission: {@permission}
	Trigger:
		Set {_x} to (number-argument / 180) * {@pi}
		Set {_c} to 1
		Loop {@accuracy} times:
			Set {_n} to loop-number * 2
			Execute console command "/fact %{_n}%"
			Set {_f} to {fact.value}
			Set {_c} to {_c} + (({_x} ^ {_n}) / {_f}) * (-1 ^ loop-number)
		Set {cos.value} to {_c}
		If {@message} is "true":
			Send "%{cos.value}%" to player

#Calculate the tangent of a degree
Command /tan <number>:
	Permission: {@permission}
	Trigger:
		Execute console command "/sin %number-argument%"
		Set {_sin} to {sin.value}
		Execute console command "/cos %number-argument%"
		Set {_cos} to {cos.value}
		Set {_t} to {_sin} / {_cos}
		Set {tan.value} to {_t}
		If {@message} is "true":
			Send "%{tan.value}%" to player

#Calculate the arcsine of a sine of a degree
Command /arcsin <number>:
	Permission: {@permission}
	Usage: /arcsin <sin(degree)>
	Trigger:
		Set {_x} to number-argument
		If {_x} is smaller than -1:
			Send "The value has to be bigger/equal to -1" to player
		If {_x} is bigger than 1:
			Send "The value has to be smaller/equal to 1" to player
		Execute console command "/arccos %{_x}%"
		Set {_ac} to {arccos.value}
		Set {_ac} to {_ac} * 2 * {@pi} / 360
		Set {_as} to ({@pi} / 2 - {_ac}) * 360 / (2 * {@pi})
		Set {arcsin.value} to {_as}
		If {@message} is "true":
			Send "%{arcsin.value}%" to player

#Calculate the arccosine of a cosine of a degree
Command /arccos <number>:
	Permission: {@permission}
	Usage: /arccos <cos(degree)>
	Trigger:
		Set {_x} to number-argument
		If {_x} is smaller than -1:
			Send "The value has to be bigger/equal to -1" to player
		If {_x} is bigger than 1:
			Send "The value has to be smaller/equal to 1" to player
		Set {_ac} to ((-0.69813170079773212 * {_x} * {_x} - 0.87266462599716477) * {_x} + 1.5707963267948966) * 360 / (2 * {@pi})
		Set {arccos.value} to {_ac}
		IF {@message} is "true":
			Send "%{arccos.value}%" to player

#Calculate the arctangent of a tangent of a degree
Command /arctan <number>:
	Permission: {@permission}
	Usage: /arctan <tan(degree)>
	Trigger:
		Set {_x} to number-argument
		If {_x} is smaller than -1:
			Send "The value has to be bigger/equal to -1" to player
			stop
		If {_x} is bigger than 1:
			Send "The value has to be smaller/equal to 1" to player
			stop
		Set {_absx} to ({_x} ^ 2) ^ 0.5
		Set {_at} to ({@pi} / 4 * {_x} - ({_absx} - 1) * (0.2447 + 0.0663 * {_absx})) * 360 / (2 * {@pi})
		Set {arctan.value} to {_at}
		If {@message} is "true":
			Send "%{arctan.value}%" to player

#Calculate a rotation
Command /rotate <number> <number>:
	Permission: {@permission}
	Trigger:
		Set {_Radius} to argument 1
		Set {_Angle} to argument 2
		Set {_Number} to floor( 360 / {_Angle} )
		Loop {_Number} times:
			If {_Current} is not set:
				Set {_Current} to 0
			Else:
				Add {_Angle} to {_Current}
			Set {_x} to ( {_Current} / 180 ) * 3.14159265358979323846
			Set {_c} to 1
			Loop 10 times:
				Set {_n} to loop-number-2 * 2
				Set {_f} to {_n}
				Set {_i} to {_f} - 1
				Loop {_i} times:
					Set {_f} to {_f} * {_i}
					Subtract 1 from {_i}
				Set {_c} to {_c} + (({_x} ^ {_n}) / {_f}) * (-1 ^ loop-number-2)
			Set {_c} to ( {_c} * {_Radius})
			Set {_s} to {_x}
			Loop 10 times:
				Set {_n} to loop-number-2 * 2 + 1
				Set {_f} to {_n}
				Set {_i} to {_f} - 1
				Loop {_i} times:
					Set {_f} to {_f} * {_i}
					Subtract 1 from {_i}
				Set {_s} to {_s} + (({_x} ^ {_n}) / {_f}) * (-1 ^ loop-number-2)
			Set {_s} to ( {_s} * {_Radius})
			Set {_Particlespawn} to location of player
			Increase x-coordinate of {_Particlespawn} by {_c}
			Increase Z-coordinate of {_Particlespawn} by {_s}
			Set {rotate.value} to {_Particlespawn}
			If {@message} is "true":
				Broadcast "%{_Particlespawn}%"