MathTrigonometry

// This source code is subject to the terms of the Mozilla Public License 2.0 at https://mozilla.org/MPL/2.0/
// © RicardoSantos

//@version=5

// @description Trigonometric methods.
library("MathTrigonometry")
// reference:
//      https://www.brighthubeducation.com/homework-math-help/72270-trigonometry-functions-a-trig-functions-list/
//      https://github.com/mathnet/mathnet-numerics/blob/a50d68d52def605a53d129cc60ea3371a2e97548/src/Numerics/Trigonometry.cs

// @function Normalized sinc function.
// @param value float, value.
// @returns float.
export sinc (float value) => //{
    float _z = math.pi * value
    if math.abs(_z) <= 1.0e-15 // almost equal
    	1.0
    else
        math.sin(_z) / _z
//}

//######################################

// @function Cotangent of value.
// @param value float, value.
// @returns float.
export cot (float value) => //{
	1.0 / math.tan(value)
//}

// @function Cosecant of value.
// @param value float, value.
// @returns float.
export csc (float value) => //{
	1.0 / math.sin(value)
//}

// @function Secant of value.
// @param value float, value.
// @returns float.
export sec (float value) => //{
	1.0 / math.cos(value)
//}

///#################

// @function Arc cotangent of value.
// @param value float, adjacent value.
// @returns float.
export acot (float value) => //{
	math.atan(1.0 / value)
//}

// @function Arc secant of value.
// @param value float, hypotenuse value.
// @returns float.
export asec (float value) => //{
	math.acos(1.0 / value)
//}

// @function Arc cosecant of value.
// @param value float, hipotenuse value.
// @returns float.
export acsc (float value) => //{
	math.atan(1.0 / value)
//}

//################

// @function Hyperbolic sine of angle.
// @param angle float, value.
// @returns float.
export sinh (float angle) => //{
	(math.exp(angle) - math.exp(-angle)) / 2.0
//}

// @function Hyperbolic cosine of angle.
// @param angle float, value.
// @returns float.
export cosh (float angle) => //{
	(math.exp(angle) + math.exp(-angle)) / 2.0
//}

// @function Hyperbolic tangent of angle.
// @param angle float, value.
// @returns float.
export tanh (float angle) => //{
    if angle > 19.1
        1.0
    else if angle -19.1
        -1.0
    else
	    float _e1 = math.exp(angle)
	    float _e2 = math.exp(-angle)
	    (_e1 - _e2) / (_e1 + _e2)
//}

// @function Hyperbolic cotangent of angle.
// @param angle float, value.
// @returns float.
export coth (float angle) => //{
    if angle > 19.1
        1.0
    else if angle -19.1
        -1.0
    else
	    float _e1 = math.exp(angle)
	    float _e2 = math.exp(-angle)
	    (_e1 + _e2) / (_e1 - _e2)
//}

// @function Hyperbolic secant of angle.
// @param angle float, value.
// @returns float.
export sech (float angle) => //{
    1.0 / cosh(angle)
//}

// @function Hyperbolic cosecant of angle.
// @param angle float, value.
// @returns float.
export csch (float angle) => //{
    1.0 / sinh(angle)
//}

//#############################

// @function Hyperbolic area sine.
// @param value float, value.
// @returns float.
export asinh (float value) => //{
    //https://github.com/mathnet/mathnet-numerics/blob/a50d68d52def605a53d129cc60ea3371a2e97548/src/Numerics/Trigonometry.cs#L711
    float _absv = math.abs(value)
    if _absv >= 268435456.0
        math.sign(value) * (math.log(_absv) + math.log(2.0))
    else
        math.sign(value) * math.log(_absv + math.sqrt(1.0 + math.pow(value, 2.0)))
//}

// @function Hyperbolic area cosine.
// @param value float, value.
// @returns float.
export acosh (float value) => //{
    //https://github.com/mathnet/mathnet-numerics/blob/a50d68d52def605a53d129cc60ea3371a2e97548/src/Numerics/Trigonometry.cs#L737
    float _absv = math.abs(value)
    if _absv >= 268435456.0
        math.log(value) + math.log(2.0)
    else
        math.log(value + (math.sqrt(value -1.0) * math.sqrt(value + 1.0)))
//}

// @function Hyperbolic area tangent.
// @param value float, value.
// @returns float.
export atanh (float value) => //{
    0.5 * math.log((value + 1.0) / (value - 1.0))
//}

// @function Hyperbolic area cotangent.
// @param value float, value.
// @returns float.
export acoth (float value) => //{
    0.5 * math.log((value + 1.0) / (value - 1.0))
//}

// @function Hyperbolic area secant.
// @param value float, value.
// @returns float.
export asech (float value) => //{
    acosh(1.0 / value)
//}

// @function Hyperbolic area cosecant.
// @param value float, value.
// @returns float.
export acsch (float value) => //{
    asinh(1.0 / value)
//}