math.rock

(Pi constant)
Put 3.1415926535897932 into the pi
Put 2.7182818284590452 into the e
Put the pi times 2 into the tau

(Convert degrees to radians)
DegToRad takes the degrees
Give back the degrees times the tau over 360


(Convert radians to degrees)
RadToDeg takes the radian
Give back the radian times 360 over the tau


(Factorial: n!)
Factorial takes the number
Put 0 into the zero
If the number is the zero
Give back 1

If the number is less than the zero
Give back -1

Put 1 into the iterator
Put 1 into the answer
While the iterator is as little as the number
Put the iterator of the answer into the answer
Build the iterator up

Give back the answer


(Abs value)
Absolute Value takes The number
If The number is less than 0
Put The number times -1 into The number
Give back The number

Give back The number


(Is-close)
Is Close takes the a and the b
Put 0.0000000001 into the relativetolerance (to be changed to an optional argument)
Put 0 into the absolutetolerance (to be changed to an optional argument)
Put Absolute Value taking the a into the largest
If Absolute Value taking the b is greater than the largest
Put Absolute Value taking the b into the largest

Put the relativetolerance times the largest into the scalefactor
If the absolutetolerance is greater than the scalefactor
Put the absolutetolerance into the threshold
Else
Put the scalefactor into the threshold

Put the a minus the b into the difference
Put Absolute Value taking the difference into the difference
If the difference is as little as the threshold
Give back true
Else
Give back false


(Mod: a % m)
Mod takes the number and the modulo
If the number is greater than 0
While the number is as great as the modulo
Put the number minus the modulo into the number

Give back the number

If the number is less than 0
While the number is less than 0
Put the number plus the modulo into the number

Give back the number

Give back the number


(Gcd)
Gcd takes the x and the y
If Mod taking the x, 1 is not 0 or Mod taking the y, 1 is not 0
Give back "Error: the input must be two integer numbers"

Put Absolute Value taking the x into the x
Put Absolute Value taking the y into the y
If the x is 0
Give back the y

If the y is 0
Give back the x

While the x is not the y
If the x is greater than the y
Put the x minus the y into the x
Else
Put the y minus the x into the y


Give back the x


(Floor)
Floor takes the number
Put the number minus Mod taking the number, 1 into the number
Give back the number


(Ceil)
Ceil takes the number
Put -1 times the number into the number
Put -1 times Floor taking the number into the number
Give back the number


(Power: a^x)
Power takes the base and the exponent
If the exponent is less than 0
Put -1 times the exponent into the newexponent
Give back 1 over Power taking the base, the newexponent

If the exponent is 0
Give back 1

If the base is 0
Give back 0

If Mod taking the exponent, 1 is 0
Give back PowerIntegerExponent taking the base, the exponent
Else
Give back PowerRealExponent taking the base, the exponent


(PowerIntegerExponent: should rather be named PowerPositiveIntegerExponent)
PowerIntegerExponent takes the base and the exponent
Put 0 into the iterator
Put the 1 into the answer
While the iterator is smaller than the exponent (Probably can also use divide and conquer exponentiation -> e^n + e^m + ....)
Put the base times the answer into the answer
Build the iterator up

Give back the answer


(PowerRealExponent)
PowerRealExponent takes the base and the exponent
Put the exponent times LN taking the base into the argument
Give back Exp taking the argument


(Exp)
Exp takes the x
Put 666 into the prevanswer
Put 1 into the nextanswer
Put 1 into the iterator
While the iterator is less than 2000 and Is Close taking the prevanswer, the nextanswer is false
Put the nextanswer into the prevanswer
Put Power taking the x, the iterator into the numerator
Put Factorial taking the iterator into the denominator
Put the numerator over the denominator into the term
Put the prevanswer plus the term into the nextanswer
Build the iterator up

Give back the nextanswer


(Natural Logarithm, always base e)
LN takes the number
Put the number minus 1 into the top
Put the number plus 1 into the bottom
Put the top over the bottom into the x
Put 1 into the iterator
Put 0 into the answer
While the iterator is less than 10 (get reasonable starting point for Halley's method)
Put Power taking the x, the iterator into the term
Put the term over the iterator into the term
Put the answer plus the term into the answer
Build the iterator up
Build the iterator up

Put the answer times 2 into the nextanswer (end power expansion, start Halley's cubic convergence)
Put 666 into the prevanswer
Put 0 into the iterator
While the iterator is less than 2000 and Is Close taking the prevanswer, the nextanswer is false
Put the nextanswer into the prevanswer
Put the number minus Exp taking the prevanswer into the numerator
Put the number plus Exp taking the prevanswer into the denominator
Put 2 times the numerator over the denominator into the term
Put the prevanswer plus the term into the nextanswer
Build the iterator up

Give back the nextanswer


(Log with number and base)
LOG takes the number and the base
Put LN taking the number into the top
Put LN taking the base into the bottom
Give back the top over the bottom


(Square Root Function)
Square Root takes the number
Put 666 into the prevanswer
Put 0.5 times the number into the nextanswer
Put 1 into the iterator
Put 1.0 times the number into the number
While the iterator is less than 2000 and Is Close taking the prevanswer, the nextanswer is false
Put the nextanswer into the prevanswer
Put the number over the prevanswer plus the prevanswer into the term
Put 0.5 times the term into the nextanswer
Build the iterator up

Give back the nextanswer


(Sine)
Sine takes the radian
Put 1 into the iterator
Put 666 into the prevanswer
Put 0 into the nextanswer
Put 1 into the sign
While the iterator is less than 2000 and Is Close taking the prevanswer, the nextanswer is false
Put the nextanswer into the prevanswer
Put Power taking the radian, the iterator over Factorial taking the iterator into the term
Put the term times the sign into the term
Put the prevanswer plus the term into the nextanswer
Build the iterator up
Build the iterator up
Put the sign times -1 into the sign

Give back the nextanswer


(Cos)
Cos takes the radian
Put 0 into the iterator
Put 666 into the prevanswer
Put 0 into the nextanswer
Put 1 into the sign
While the iterator is less than 2000 and Is Close taking the prevanswer, the nextanswer is false
Put the nextanswer into the prevanswer
Put Power taking the radian, the iterator over Factorial taking the iterator into the term
Put the term times the sign into the term
Put the prevanswer plus the term into the nextanswer
Build the iterator up
Build the iterator up
Put the sign times -1 into the sign

Give back the nextanswer


(Tan)
Tan takes the radian
Put Sine taking the radian into the numerator
Put Cos taking the radian into the denominator
Give back the numerator over the denominator


(Arctan)
Arctan takes the number
Put 1 into the iterator
Put 666 into the prevanswer
Put 0 into the nextanswer
Put 1 into the sign
While the iterator is less than 2000 and Is Close taking the prevanswer, the nextanswer is false
Put the nextanswer into the prevanswer
Put Power taking the number, the iterator over the iterator into the term
Put the term times the sign into the term
Put the prevanswer plus the term into the nextanswer
Build the iterator up
Build the iterator up
Put the sign times -1 into the sign

Give back the nextanswer


(Arcsin)
Arcsin takes the number
Put 0 into the iterator
Put 666 into the prevanswer
Put 0 into the nextanswer
While the iterator is less than 2000 and Is Close taking the prevanswer, the nextanswer is false
Put the nextanswer into the prevanswer
Put 2 times the iterator into the placeholder
Put Factorial taking the placeholder into the numerator
Put 2 times the iterator plus 1 into the exponent
Put the numerator times Power taking the number, the exponent into the numerator
Put Power taking 4, the iterator into the firstdenominator
Put Factorial taking the iterator into the placeholder
Put Power taking the placeholder, 2 into the seconddenominator
Put 2 times the iterator plus 1 into the thirddenominator
Put the firstdenominator times the seconddenominator times the thirddenominator into the denominator
Put the numerator over the denominator into the term
Put the prevanswer plus the term into the nextanswer
Build the iterator up

Give back the nextanswer


(Arccos)
Arccos takes the number
Put the pi over 2 into the answer
Put the answer minus Arcsin taking the number into the answer
Give back the answer


(Sinh)
Sinh takes the number
Put 1 into the iterator
Put 666 into the prevanswer
Put 0 into the nextanswer
While the iterator is less than 2000 and Is Close taking the prevanswer, the nextanswer is false
Put the nextanswer into the prevanswer
Put Power taking the number, the iterator over Factorial taking the iterator into the term
Put the prevanswer plus the term into the nextanswer
Build the iterator up
Build the iterator up

Give back the nextanswer


(Cosh)
Cosh takes the number
Put 0 into the iterator
Put 666 into the prevanswer
Put 0 into the nextanswer
While the iterator is less than 2000 and Is Close taking the prevanswer, the nextanswer is false
Put the nextanswer into the prevanswer
Put Power taking the number, the iterator over Factorial taking the iterator into the term
Put the prevanswer plus the term into the nextanswer
Build the iterator up
Build the iterator up

Give back the nextanswer


(Tanh)
Tanh takes the number
Put Sinh taking the number into the numerator
Put Cosh taking the number into the denominator
Give back the numerator over the denominator


(Arcsinh)
Arcsinh takes the number
Put Power taking the number, 2 into the term
Put the term plus 1 into the term
Put the number plus Square Root taking the term into the argument
Give back LN taking the argument


(Arccosh)
Arccosh takes the number
Put Power taking the number, 2 into the term
Put the term minus 1 into the term
Put the number plus Square Root taking the term into the argument
Give back LN taking the argument


(Arctanh)
Arctanh takes the number
Put 1 plus the number into the numerator
Put 1 minus the number into the denominator
Put the numerator over the denominator into the argument
Give back LN taking the argument over 2


(Get binary from decimal)
DecToBin takes the number
If the number is as little as 1
If the number is 0
Give back "0"

Give back "1"

Put Mod taking the number, 2 into the temp
If the temp is 0
Put "0" into the temp
Else
Put "1" into the temp

Put the number over 2 into the number
Give back the temp plus DecToBin taking the number  (doesn't work until we have integer division)