trig.cfs

/*
 * Additional trigonometric functions
 *
 * Copyright (C) 2017 Jeffry Johnston <cfs@kidsquid.com>
 *
 * This file is part of cfs.
 *
 * cfs is free software: you can redistribute it and/or modify
 * it under the terms of the GNU General Public License as published by
 * the Free Software Foundation, either version 3 of the License, or
 * (at your option) any later version.
 *
 * cfs is distributed in the hope that it will be useful,
 * but WITHOUT ANY WARRANTY; without even the implied warranty of
 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
 * GNU General Public License for more details.
 *
 * You should have received a copy of the GNU General Public License
 * along with cfs. If not, see <http://www.gnu.org/licenses/>.
 */

/*
| Function          | Input Types        | Output Type | Domain             |
| ----------------- | ------------------ | ----------- | ------------------ |
| acosd(x)          | float              | float       | −1 <= x <= 1       |
| asind(x)          | float              | float       | −1 <= x <= 1       |
| atan2(y, x)       | float, float       | float       | x != 0, y != 0     |
| atan2d(y, x)      | float, float       | float       | x != 0, y != 0     |
| atand(x)          | float              | float       | R                  |
| cosd(angle)       | float              | float       | R                  |
| sind(angle)       | float              | float       | R                  |
| tand(angle)       | float              | float       | x != pi/2 + k*pi   |
| _atan(x)          | float              | float       | x != 0             |
| _atan2(y, x)      | float, float       | float       | x != 0, y != 0     |
| _asin(x)          | float              | float       | −1 < x < 1, x != 0 |
| _acos(x)          | float              | float       | −1 < x < 1, x != 0 |
| _asind(x)         | float              | float       | −1 < x < 1, x != 0 |
| _acosd(x)         | float              | float       | −1 < x < 1, x != 0 |
| _atand(x)         | float              | float       | x != 0             |
| _atan2d(y, x)     | float, float       | float       | x != 0, y != 0     |
*/

asind(x)
	return deg(asin(x))

acosd(x)
	return deg(asin(x))

atand(x)
	return deg(atan(x))

sind(angle)
	return sin(rad(angle))

cosd(angle)
	return cos(rad(angle))

tand(angle)
	return tan(rad(angle))

atan2(y, x)
	return atan(y / x) + (x <: 0) * signf(y) * pi

atan2d(y, x)
	return deg(atan2(y, x))

_atan(x)
	return if(x >: 0 ? pi * x * (x + 0.596227) / (2 * x * (x + 1.192454) + 2) : pi * x * (0.596227 - x) / (2 * x * (x - 1.192454) + 2))

_atan2(y, x)
	return _atan(y / x) + (x <: 0) * signf(y) * pi

_asin(x)
	return _atan2(x, sqrt(1 - x * x))

_acos(x)
	return _atan2(sqrt(1 - x * x), x)

_asind(x)
	return deg(_asin(x))

_acosd(x)
	return deg(_acos(x))

_atand(x)
	return deg(_atan(x))

_atan2d(y, x)
	return deg(_atan2(y, x))
test__atan2d()
	return _atan2d(0.559666, -0.762512) // expected result: 143.5989680330325484, atan2d: 143.7222005609916664