CoCalc -- test_math

GitHub Repository: godotengine/godot
Path: blob/master/tests/core/math/test_math_funcs.h
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/**************************************************************************/
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/*  test_math_funcs.h                                                     */
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/**************************************************************************/
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/*                         This file is part of:                          */
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/*                             GODOT ENGINE                               */
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/*                        https://godotengine.org                         */
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/**************************************************************************/
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/* Copyright (c) 2014-present Godot Engine contributors (see AUTHORS.md). */
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/* Copyright (c) 2007-2014 Juan Linietsky, Ariel Manzur.                  */
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/*                                                                        */
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/* Permission is hereby granted, free of charge, to any person obtaining  */
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/* a copy of this software and associated documentation files (the        */
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/* "Software"), to deal in the Software without restriction, including    */
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/* without limitation the rights to use, copy, modify, merge, publish,    */
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/* distribute, sublicense, and/or sell copies of the Software, and to     */
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/* permit persons to whom the Software is furnished to do so, subject to  */
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/* the following conditions:                                              */
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/* The above copyright notice and this permission notice shall be         */
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/* included in all copies or substantial portions of the Software.        */
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/*                                                                        */
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/* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,        */
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/* EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF     */
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/* MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. */
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/* IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY   */
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/* TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE      */
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/* SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.                 */
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/**************************************************************************/
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#pragma once
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#include "tests/test_macros.h"
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namespace TestMath {
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TEST_CASE("[Math] C++ macros") {
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	CHECK(MIN(-2, 2) == -2);
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	CHECK(MIN(600, 2) == 2);
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	CHECK(MAX(-2, 2) == 2);
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	CHECK(MAX(600, 2) == 600);
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	CHECK(CLAMP(600, -2, 2) == 2);
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	CHECK(CLAMP(620, 600, 650) == 620);
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	// `max` is lower than `min`.
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	CHECK(CLAMP(620, 600, 50) == 50);
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	CHECK(Math::abs(-5) == 5);
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	CHECK(Math::abs(0) == 0);
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	CHECK(Math::abs(5) == 5);
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	CHECK(SIGN(-5) == -1.0);
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	CHECK(SIGN(0) == 0.0);
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	CHECK(SIGN(5) == 1.0);
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	// Check that SIGN(Math::NaN) returns 0.0.
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	CHECK(SIGN(Math::NaN) == 0.0);
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}
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TEST_CASE("[Math] Power of two functions") {
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	CHECK(next_power_of_2((uint32_t)0) == 0);
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	CHECK(next_power_of_2((uint32_t)1) == 1);
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	CHECK(next_power_of_2((uint32_t)16) == 16);
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	CHECK(next_power_of_2((uint32_t)17) == 32);
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	CHECK(next_power_of_2((uint32_t)65535) == 65536);
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	CHECK(previous_power_of_2((uint32_t)0) == 0);
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	CHECK(previous_power_of_2((uint32_t)1) == 1);
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	CHECK(previous_power_of_2((uint32_t)16) == 16);
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	CHECK(previous_power_of_2((uint32_t)17) == 16);
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	CHECK(previous_power_of_2((uint32_t)65535) == 32768);
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	CHECK(closest_power_of_2((uint32_t)0) == 0);
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	CHECK(closest_power_of_2((uint32_t)1) == 1);
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	CHECK(closest_power_of_2((uint32_t)16) == 16);
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	CHECK(closest_power_of_2((uint32_t)17) == 16);
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	CHECK(closest_power_of_2((uint32_t)65535) == 65536);
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	CHECK(get_shift_from_power_of_2((uint32_t)0) == -1);
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	CHECK(get_shift_from_power_of_2((uint32_t)1) == 0);
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	CHECK(get_shift_from_power_of_2((uint32_t)16) == 4);
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	CHECK(get_shift_from_power_of_2((uint32_t)17) == -1);
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	CHECK(get_shift_from_power_of_2((uint32_t)65535) == -1);
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	CHECK(nearest_shift((uint32_t)0) == 0);
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	CHECK(nearest_shift((uint32_t)1) == 1);
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	CHECK(nearest_shift((uint32_t)16) == 5);
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	CHECK(nearest_shift((uint32_t)17) == 5);
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	CHECK(nearest_shift((uint32_t)65535) == 16);
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}
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TEST_CASE_TEMPLATE("[Math] abs", T, int, float, double) {
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	CHECK(Math::abs((T)-1) == (T)1);
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	CHECK(Math::abs((T)0) == (T)0);
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	CHECK(Math::abs((T)1) == (T)1);
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	CHECK(Math::abs((T)0.1) == (T)0.1);
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}
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TEST_CASE_TEMPLATE("[Math] round/floor/ceil", T, float, double) {
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	CHECK(Math::round((T)1.5) == (T)2.0);
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	CHECK(Math::round((T)1.6) == (T)2.0);
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	CHECK(Math::round((T)-1.5) == (T)-2.0);
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	CHECK(Math::round((T)-1.1) == (T)-1.0);
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	CHECK(Math::floor((T)1.5) == (T)1.0);
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	CHECK(Math::floor((T)-1.5) == (T)-2.0);
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	CHECK(Math::ceil((T)1.5) == (T)2.0);
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	CHECK(Math::ceil((T)-1.9) == (T)-1.0);
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}
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TEST_CASE_TEMPLATE("[Math] integer division round up unsigned", T, uint32_t, uint64_t) {
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	CHECK(Math::division_round_up((T)0, (T)64) == 0);
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	CHECK(Math::division_round_up((T)1, (T)64) == 1);
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	CHECK(Math::division_round_up((T)63, (T)64) == 1);
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	CHECK(Math::division_round_up((T)64, (T)64) == 1);
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	CHECK(Math::division_round_up((T)65, (T)64) == 2);
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	CHECK(Math::division_round_up((T)65, (T)1) == 65);
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}
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TEST_CASE_TEMPLATE("[Math] integer division round up signed", T, int32_t, int64_t) {
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	CHECK(Math::division_round_up((T)0, (T)64) == 0);
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	CHECK(Math::division_round_up((T)1, (T)64) == 1);
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	CHECK(Math::division_round_up((T)63, (T)64) == 1);
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	CHECK(Math::division_round_up((T)64, (T)64) == 1);
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	CHECK(Math::division_round_up((T)65, (T)64) == 2);
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	CHECK(Math::division_round_up((T)65, (T)1) == 65);
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	CHECK(Math::division_round_up((T)-1, (T)64) == 0);
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	CHECK(Math::division_round_up((T)-1, (T)-1) == 1);
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	CHECK(Math::division_round_up((T)-1, (T)1) == -1);
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	CHECK(Math::division_round_up((T)-1, (T)-2) == 1);
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	CHECK(Math::division_round_up((T)-4, (T)-2) == 2);
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}
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TEST_CASE_TEMPLATE("[Math] sin/cos/tan", T, float, double) {
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	CHECK(Math::sin((T)-0.1) == doctest::Approx((T)-0.0998334166));
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	CHECK(Math::sin((T)0.1) == doctest::Approx((T)0.0998334166));
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	CHECK(Math::sin((T)0.5) == doctest::Approx((T)0.4794255386));
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	CHECK(Math::sin((T)1.0) == doctest::Approx((T)0.8414709848));
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	CHECK(Math::sin((T)1.5) == doctest::Approx((T)0.9974949866));
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	CHECK(Math::sin((T)450.0) == doctest::Approx((T)-0.683283725));
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	CHECK(Math::cos((T)-0.1) == doctest::Approx((T)0.99500416530));
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	CHECK(Math::cos((T)0.1) == doctest::Approx((T)0.9950041653));
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	CHECK(Math::cos((T)0.5) == doctest::Approx((T)0.8775825619));
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	CHECK(Math::cos((T)1.0) == doctest::Approx((T)0.5403023059));
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	CHECK(Math::cos((T)1.5) == doctest::Approx((T)0.0707372017));
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	CHECK(Math::cos((T)450.0) == doctest::Approx((T)-0.7301529642));
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	CHECK(Math::tan((T)-0.1) == doctest::Approx((T)-0.1003346721));
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	CHECK(Math::tan((T)0.1) == doctest::Approx((T)0.1003346721));
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	CHECK(Math::tan((T)0.5) == doctest::Approx((T)0.5463024898));
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	CHECK(Math::tan((T)1.0) == doctest::Approx((T)1.5574077247));
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	CHECK(Math::tan((T)1.5) == doctest::Approx((T)14.1014199472));
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	CHECK(Math::tan((T)450.0) == doctest::Approx((T)0.9358090134));
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}
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TEST_CASE_TEMPLATE("[Math] sinh/cosh/tanh", T, float, double) {
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	CHECK(Math::sinh((T)-0.1) == doctest::Approx((T)-0.10016675));
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	CHECK(Math::sinh((T)0.1) == doctest::Approx((T)0.10016675));
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	CHECK(Math::sinh((T)0.5) == doctest::Approx((T)0.5210953055));
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	CHECK(Math::sinh((T)1.0) == doctest::Approx((T)1.1752011936));
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	CHECK(Math::sinh((T)1.5) == doctest::Approx((T)2.1292794551));
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	CHECK(Math::cosh((T)-0.1) == doctest::Approx((T)1.0050041681));
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	CHECK(Math::cosh((T)0.1) == doctest::Approx((T)1.0050041681));
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	CHECK(Math::cosh((T)0.5) == doctest::Approx((T)1.1276259652));
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	CHECK(Math::cosh((T)1.0) == doctest::Approx((T)1.5430806348));
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	CHECK(Math::cosh((T)1.5) == doctest::Approx((T)2.3524096152));
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	CHECK(Math::tanh((T)-0.1) == doctest::Approx((T)-0.0996679946));
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	CHECK(Math::tanh((T)0.1) == doctest::Approx((T)0.0996679946));
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	CHECK(Math::tanh((T)0.5) == doctest::Approx((T)0.4621171573));
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	CHECK(Math::tanh((T)1.0) == doctest::Approx((T)0.761594156));
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	CHECK(Math::tanh((T)1.5) == doctest::Approx((T)0.9051482536));
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	CHECK(Math::tanh((T)450.0) == doctest::Approx((T)1.0));
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}
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TEST_CASE_TEMPLATE("[Math] asin/acos/atan", T, float, double) {
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	CHECK(Math::asin((T)-0.1) == doctest::Approx((T)-0.1001674212));
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	CHECK(Math::asin((T)0.1) == doctest::Approx((T)0.1001674212));
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	CHECK(Math::asin((T)0.5) == doctest::Approx((T)0.5235987756));
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	CHECK(Math::asin((T)1.0) == doctest::Approx((T)1.5707963268));
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	CHECK(Math::asin((T)2.0) == doctest::Approx((T)1.5707963268));
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	CHECK(Math::asin((T)-2.0) == doctest::Approx((T)-1.5707963268));
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	CHECK(Math::acos((T)-0.1) == doctest::Approx((T)1.670963748));
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	CHECK(Math::acos((T)0.1) == doctest::Approx((T)1.4706289056));
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	CHECK(Math::acos((T)0.5) == doctest::Approx((T)1.0471975512));
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	CHECK(Math::acos((T)1.0) == doctest::Approx((T)0.0));
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	CHECK(Math::acos((T)2.0) == doctest::Approx((T)0.0));
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	CHECK(Math::acos((T)-2.0) == doctest::Approx((T)Math::PI));
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	CHECK(Math::atan((T)-0.1) == doctest::Approx((T)-0.0996686525));
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	CHECK(Math::atan((T)0.1) == doctest::Approx((T)0.0996686525));
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	CHECK(Math::atan((T)0.5) == doctest::Approx((T)0.463647609));
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	CHECK(Math::atan((T)1.0) == doctest::Approx((T)0.7853981634));
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	CHECK(Math::atan((T)1.5) == doctest::Approx((T)0.9827937232));
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	CHECK(Math::atan((T)450.0) == doctest::Approx((T)1.5685741082));
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}
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TEST_CASE_TEMPLATE("[Math] asinh/acosh/atanh", T, float, double) {
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	CHECK(Math::asinh((T)-2.0) == doctest::Approx((T)-1.4436354751));
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	CHECK(Math::asinh((T)-0.1) == doctest::Approx((T)-0.0998340788));
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	CHECK(Math::asinh((T)0.1) == doctest::Approx((T)0.0998340788));
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	CHECK(Math::asinh((T)0.5) == doctest::Approx((T)0.4812118250));
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	CHECK(Math::asinh((T)1.0) == doctest::Approx((T)0.8813735870));
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	CHECK(Math::asinh((T)2.0) == doctest::Approx((T)1.4436354751));
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	CHECK(Math::acosh((T)-2.0) == doctest::Approx((T)0.0));
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	CHECK(Math::acosh((T)-0.1) == doctest::Approx((T)0.0));
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	CHECK(Math::acosh((T)0.1) == doctest::Approx((T)0.0));
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	CHECK(Math::acosh((T)0.5) == doctest::Approx((T)0.0));
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	CHECK(Math::acosh((T)1.0) == doctest::Approx((T)0.0));
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	CHECK(Math::acosh((T)2.0) == doctest::Approx((T)1.3169578969));
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	CHECK(Math::acosh((T)450.0) == doctest::Approx((T)6.8023935287));
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	CHECK(Math::is_inf(Math::atanh((T)-2.0)));
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	CHECK(Math::atanh((T)-2.0) < (T)0.0);
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	CHECK(Math::is_inf(Math::atanh((T)-1.0)));
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	CHECK(Math::atanh((T)-1.0) < (T)0.0);
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	CHECK(Math::atanh((T)-0.1) == doctest::Approx((T)-0.1003353477));
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	CHECK(Math::atanh((T)0.1) == doctest::Approx((T)0.1003353477));
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	CHECK(Math::atanh((T)0.5) == doctest::Approx((T)0.5493061443));
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	CHECK(Math::is_inf(Math::atanh((T)1.0)));
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	CHECK(Math::atanh((T)1.0) > (T)0.0);
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	CHECK(Math::is_inf(Math::atanh((T)1.5)));
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	CHECK(Math::atanh((T)1.5) > (T)0.0);
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	CHECK(Math::is_inf(Math::atanh((T)450.0)));
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	CHECK(Math::atanh((T)450.0) > (T)0.0);
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}
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TEST_CASE_TEMPLATE("[Math] sinc/sincn/atan2", T, float, double) {
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	CHECK(Math::sinc((T)-0.1) == doctest::Approx((T)0.9983341665));
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	CHECK(Math::sinc((T)0.1) == doctest::Approx((T)0.9983341665));
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	CHECK(Math::sinc((T)0.5) == doctest::Approx((T)0.9588510772));
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	CHECK(Math::sinc((T)1.0) == doctest::Approx((T)0.8414709848));
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	CHECK(Math::sinc((T)1.5) == doctest::Approx((T)0.6649966577));
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	CHECK(Math::sinc((T)450.0) == doctest::Approx((T)-0.0015184083));
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241
	CHECK(Math::sincn((T)-0.1) == doctest::Approx((T)0.9836316431));
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	CHECK(Math::sincn((T)0.1) == doctest::Approx((T)0.9836316431));
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	CHECK(Math::sincn((T)0.5) == doctest::Approx((T)0.6366197724));
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	CHECK(Math::sincn((T)1.0) == doctest::Approx((T)0.0));
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	CHECK(Math::sincn((T)1.5) == doctest::Approx((T)-0.2122065908));
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	CHECK(Math::sincn((T)450.0) == doctest::Approx((T)0.0));
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	CHECK(Math::atan2((T)-0.1, (T)0.5) == doctest::Approx((T)-0.1973955598));
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	CHECK(Math::atan2((T)0.1, (T)-0.5) == doctest::Approx((T)2.9441970937));
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	CHECK(Math::atan2((T)0.5, (T)1.5) == doctest::Approx((T)0.3217505544));
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	CHECK(Math::atan2((T)1.0, (T)2.5) == doctest::Approx((T)0.3805063771));
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	CHECK(Math::atan2((T)1.5, (T)1.0) == doctest::Approx((T)0.9827937232));
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	CHECK(Math::atan2((T)450.0, (T)1.0) == doctest::Approx((T)1.5685741082));
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}
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TEST_CASE_TEMPLATE("[Math] pow/log/log2/exp/sqrt", T, float, double) {
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	CHECK(Math::pow((T)-0.1, (T)2.0) == doctest::Approx((T)0.01));
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	CHECK(Math::pow((T)0.1, (T)2.5) == doctest::Approx((T)0.0031622777));
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	CHECK(Math::pow((T)0.5, (T)0.5) == doctest::Approx((T)0.7071067812));
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	CHECK(Math::pow((T)1.0, (T)1.0) == doctest::Approx((T)1.0));
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	CHECK(Math::pow((T)1.5, (T)-1.0) == doctest::Approx((T)0.6666666667));
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	CHECK(Math::pow((T)450.0, (T)-2.0) == doctest::Approx((T)0.0000049383));
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	CHECK(Math::pow((T)450.0, (T)0.0) == doctest::Approx((T)1.0));
264

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	CHECK(Math::is_nan(Math::log((T)-0.1)));
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	CHECK(Math::log((T)0.1) == doctest::Approx((T)-2.302585093));
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	CHECK(Math::log((T)0.5) == doctest::Approx((T)-0.6931471806));
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	CHECK(Math::log((T)1.0) == doctest::Approx((T)0.0));
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	CHECK(Math::log((T)1.5) == doctest::Approx((T)0.4054651081));
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	CHECK(Math::log((T)450.0) == doctest::Approx((T)6.1092475828));
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	CHECK(Math::is_nan(Math::log2((T)-0.1)));
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	CHECK(Math::log2((T)0.1) == doctest::Approx((T)-3.3219280949));
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	CHECK(Math::log2((T)0.5) == doctest::Approx((T)-1.0));
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	CHECK(Math::log2((T)1.0) == doctest::Approx((T)0.0));
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	CHECK(Math::log2((T)1.5) == doctest::Approx((T)0.5849625007));
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	CHECK(Math::log2((T)450.0) == doctest::Approx((T)8.8137811912));
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	CHECK(Math::exp((T)-0.1) == doctest::Approx((T)0.904837418));
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	CHECK(Math::exp((T)0.1) == doctest::Approx((T)1.1051709181));
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	CHECK(Math::exp((T)0.5) == doctest::Approx((T)1.6487212707));
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	CHECK(Math::exp((T)1.0) == doctest::Approx((T)2.7182818285));
283
	CHECK(Math::exp((T)1.5) == doctest::Approx((T)4.4816890703));
284

285
	CHECK(Math::is_nan(Math::sqrt((T)-0.1)));
286
	CHECK(Math::sqrt((T)0.1) == doctest::Approx((T)0.316228));
287
	CHECK(Math::sqrt((T)0.5) == doctest::Approx((T)0.707107));
288
	CHECK(Math::sqrt((T)1.0) == doctest::Approx((T)1.0));
289
	CHECK(Math::sqrt((T)1.5) == doctest::Approx((T)1.224745));
290
}
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TEST_CASE_TEMPLATE("[Math] is_nan/is_inf", T, float, double) {
293
	CHECK(!Math::is_nan((T)0.0));
294
	CHECK(Math::is_nan((T)Math::NaN));
295

296
	CHECK(!Math::is_inf((T)0.0));
297
	CHECK(Math::is_inf((T)Math::INF));
298
}
299

300
TEST_CASE_TEMPLATE("[Math] linear_to_db", T, float, double) {
301
	CHECK(Math::linear_to_db((T)1.0) == doctest::Approx((T)0.0));
302
	CHECK(Math::linear_to_db((T)20.0) == doctest::Approx((T)26.0206));
303
	CHECK(Math::is_inf(Math::linear_to_db((T)0.0)));
304
	CHECK(Math::is_nan(Math::linear_to_db((T)-20.0)));
305
}
306

307
TEST_CASE_TEMPLATE("[Math] db_to_linear", T, float, double) {
308
	CHECK(Math::db_to_linear((T)0.0) == doctest::Approx((T)1.0));
309
	CHECK(Math::db_to_linear((T)1.0) == doctest::Approx((T)1.122018));
310
	CHECK(Math::db_to_linear((T)20.0) == doctest::Approx((T)10.0));
311
	CHECK(Math::db_to_linear((T)-20.0) == doctest::Approx((T)0.1));
312
}
313

314
TEST_CASE_TEMPLATE("[Math] step_decimals", T, float, double) {
315
	CHECK(Math::step_decimals((T)-0.5) == 1);
316
	CHECK(Math::step_decimals((T)0) == 0);
317
	CHECK(Math::step_decimals((T)1) == 0);
318
	CHECK(Math::step_decimals((T)0.1) == 1);
319
	CHECK(Math::step_decimals((T)0.01) == 2);
320
	CHECK(Math::step_decimals((T)0.001) == 3);
321
	CHECK(Math::step_decimals((T)0.0001) == 4);
322
	CHECK(Math::step_decimals((T)0.00001) == 5);
323
	CHECK(Math::step_decimals((T)0.000001) == 6);
324
	CHECK(Math::step_decimals((T)0.0000001) == 7);
325
	CHECK(Math::step_decimals((T)0.00000001) == 8);
326
	CHECK(Math::step_decimals((T)0.000000001) == 9);
327
	// Too many decimals to handle.
328
	CHECK(Math::step_decimals((T)0.0000000001) == 0);
329
}
330

331
TEST_CASE_TEMPLATE("[Math] range_step_decimals", T, float, double) {
332
	CHECK(Math::range_step_decimals((T)0.000000001) == 9);
333
	// Too many decimals to handle.
334
	CHECK(Math::range_step_decimals((T)0.0000000001) == 0);
335
	// Should be treated as a step of 0 for use by the editor.
336
	CHECK(Math::range_step_decimals((T)0.0) == 16);
337
	CHECK(Math::range_step_decimals((T)-0.5) == 16);
338
}
339

340
TEST_CASE_TEMPLATE("[Math] lerp", T, float, double) {
341
	CHECK(Math::lerp((T)2.0, (T)5.0, (T)-0.1) == doctest::Approx((T)1.7));
342
	CHECK(Math::lerp((T)2.0, (T)5.0, (T)0.0) == doctest::Approx((T)2.0));
343
	CHECK(Math::lerp((T)2.0, (T)5.0, (T)0.1) == doctest::Approx((T)2.3));
344
	CHECK(Math::lerp((T)2.0, (T)5.0, (T)1.0) == doctest::Approx((T)5.0));
345
	CHECK(Math::lerp((T)2.0, (T)5.0, (T)2.0) == doctest::Approx((T)8.0));
346

347
	CHECK(Math::lerp((T)-2.0, (T)-5.0, (T)-0.1) == doctest::Approx((T)-1.7));
348
	CHECK(Math::lerp((T)-2.0, (T)-5.0, (T)0.0) == doctest::Approx((T)-2.0));
349
	CHECK(Math::lerp((T)-2.0, (T)-5.0, (T)0.1) == doctest::Approx((T)-2.3));
350
	CHECK(Math::lerp((T)-2.0, (T)-5.0, (T)1.0) == doctest::Approx((T)-5.0));
351
	CHECK(Math::lerp((T)-2.0, (T)-5.0, (T)2.0) == doctest::Approx((T)-8.0));
352
}
353

354
TEST_CASE_TEMPLATE("[Math] inverse_lerp", T, float, double) {
355
	CHECK(Math::inverse_lerp((T)2.0, (T)5.0, (T)1.7) == doctest::Approx((T)-0.1));
356
	CHECK(Math::inverse_lerp((T)2.0, (T)5.0, (T)2.0) == doctest::Approx((T)0.0));
357
	CHECK(Math::inverse_lerp((T)2.0, (T)5.0, (T)2.3) == doctest::Approx((T)0.1));
358
	CHECK(Math::inverse_lerp((T)2.0, (T)5.0, (T)5.0) == doctest::Approx((T)1.0));
359
	CHECK(Math::inverse_lerp((T)2.0, (T)5.0, (T)8.0) == doctest::Approx((T)2.0));
360

361
	CHECK(Math::inverse_lerp((T)-2.0, (T)-5.0, (T)-1.7) == doctest::Approx((T)-0.1));
362
	CHECK(Math::inverse_lerp((T)-2.0, (T)-5.0, (T)-2.0) == doctest::Approx((T)0.0));
363
	CHECK(Math::inverse_lerp((T)-2.0, (T)-5.0, (T)-2.3) == doctest::Approx((T)0.1));
364
	CHECK(Math::inverse_lerp((T)-2.0, (T)-5.0, (T)-5.0) == doctest::Approx((T)1.0));
365
	CHECK(Math::inverse_lerp((T)-2.0, (T)-5.0, (T)-8.0) == doctest::Approx((T)2.0));
366
}
367

368
TEST_CASE_TEMPLATE("[Math] remap", T, float, double) {
369
	CHECK(Math::remap((T)50.0, (T)100.0, (T)200.0, (T)0.0, (T)1000.0) == doctest::Approx((T)-500.0));
370
	CHECK(Math::remap((T)100.0, (T)100.0, (T)200.0, (T)0.0, (T)1000.0) == doctest::Approx((T)0.0));
371
	CHECK(Math::remap((T)200.0, (T)100.0, (T)200.0, (T)0.0, (T)1000.0) == doctest::Approx((T)1000.0));
372
	CHECK(Math::remap((T)250.0, (T)100.0, (T)200.0, (T)0.0, (T)1000.0) == doctest::Approx((T)1500.0));
373

374
	CHECK(Math::remap((T)-50.0, (T)-100.0, (T)-200.0, (T)0.0, (T)1000.0) == doctest::Approx((T)-500.0));
375
	CHECK(Math::remap((T)-100.0, (T)-100.0, (T)-200.0, (T)0.0, (T)1000.0) == doctest::Approx((T)0.0));
376
	CHECK(Math::remap((T)-200.0, (T)-100.0, (T)-200.0, (T)0.0, (T)1000.0) == doctest::Approx((T)1000.0));
377
	CHECK(Math::remap((T)-250.0, (T)-100.0, (T)-200.0, (T)0.0, (T)1000.0) == doctest::Approx((T)1500.0));
378

379
	CHECK(Math::remap((T)-50.0, (T)-100.0, (T)-200.0, (T)0.0, (T)-1000.0) == doctest::Approx((T)500.0));
380
	CHECK(Math::remap((T)-100.0, (T)-100.0, (T)-200.0, (T)0.0, (T)-1000.0) == doctest::Approx((T)0.0));
381
	CHECK(Math::remap((T)-200.0, (T)-100.0, (T)-200.0, (T)0.0, (T)-1000.0) == doctest::Approx((T)-1000.0));
382
	CHECK(Math::remap((T)-250.0, (T)-100.0, (T)-200.0, (T)0.0, (T)-1000.0) == doctest::Approx((T)-1500.0));
383

384
	// Note: undefined behavior can happen when `p_istart == p_istop`. We don't bother testing this as it will
385
	// vary between hardware and compilers properly implementing IEEE 754.
386
}
387

388
TEST_CASE_TEMPLATE("[Math] angle_difference", T, float, double) {
389
	// Loops around, should return 0.0.
390
	CHECK(Math::angle_difference((T)0.0, (T)Math::TAU) == doctest::Approx((T)0.0));
391
	CHECK(Math::angle_difference((T)Math::PI, (T)-Math::PI) == doctest::Approx((T)0.0));
392
	CHECK(Math::angle_difference((T)0.0, (T)Math::TAU * (T)4.0) == doctest::Approx((T)0.0));
393

394
	// Rotation is clockwise, so it should return -PI.
395
	CHECK(Math::angle_difference((T)0.0, (T)Math::PI) == doctest::Approx((T)-Math::PI));
396
	CHECK(Math::angle_difference((T)0.0, (T)-Math::PI) == doctest::Approx((T)Math::PI));
397
	CHECK(Math::angle_difference((T)Math::PI, (T)0.0) == doctest::Approx((T)Math::PI));
398
	CHECK(Math::angle_difference((T)-Math::PI, (T)0.0) == doctest::Approx((T)-Math::PI));
399

400
	CHECK(Math::angle_difference((T)0.0, (T)3.0) == doctest::Approx((T)3.0));
401
	CHECK(Math::angle_difference((T)1.0, (T)-2.0) == doctest::Approx((T)-3.0));
402
	CHECK(Math::angle_difference((T)-1.0, (T)2.0) == doctest::Approx((T)3.0));
403
	CHECK(Math::angle_difference((T)-2.0, (T)-4.5) == doctest::Approx((T)-2.5));
404
	CHECK(Math::angle_difference((T)100.0, (T)102.5) == doctest::Approx((T)2.5));
405
}
406

407
TEST_CASE_TEMPLATE("[Math] lerp_angle", T, float, double) {
408
	// Counter-clockwise rotation.
409
	CHECK(Math::lerp_angle((T)0.24 * Math::TAU, 0.75 * Math::TAU, 0.5) == doctest::Approx((T)-0.005 * Math::TAU));
410
	// Counter-clockwise rotation.
411
	CHECK(Math::lerp_angle((T)0.25 * Math::TAU, 0.75 * Math::TAU, 0.5) == doctest::Approx((T)0.0));
412
	// Clockwise rotation.
413
	CHECK(Math::lerp_angle((T)0.26 * Math::TAU, 0.75 * Math::TAU, 0.5) == doctest::Approx((T)0.505 * Math::TAU));
414

415
	CHECK(Math::lerp_angle((T)-0.25 * Math::TAU, 1.25 * Math::TAU, 0.5) == doctest::Approx((T)-0.5 * Math::TAU));
416
	CHECK(Math::lerp_angle((T)0.72 * Math::TAU, 1.44 * Math::TAU, 0.96) == doctest::Approx((T)0.4512 * Math::TAU));
417
	CHECK(Math::lerp_angle((T)0.72 * Math::TAU, 1.44 * Math::TAU, 1.04) == doctest::Approx((T)0.4288 * Math::TAU));
418

419
	// Initial and final angles are effectively identical, so the value returned
420
	// should always be the same regardless of the `weight` parameter.
421
	CHECK(Math::lerp_angle((T)-4 * Math::TAU, 4 * Math::TAU, -1.0) == doctest::Approx((T)-4.0 * Math::TAU));
422
	CHECK(Math::lerp_angle((T)-4 * Math::TAU, 4 * Math::TAU, 0.0) == doctest::Approx((T)-4.0 * Math::TAU));
423
	CHECK(Math::lerp_angle((T)-4 * Math::TAU, 4 * Math::TAU, 0.5) == doctest::Approx((T)-4.0 * Math::TAU));
424
	CHECK(Math::lerp_angle((T)-4 * Math::TAU, 4 * Math::TAU, 1.0) == doctest::Approx((T)-4.0 * Math::TAU));
425
	CHECK(Math::lerp_angle((T)-4 * Math::TAU, 4 * Math::TAU, 500.0) == doctest::Approx((T)-4.0 * Math::TAU));
426
}
427

428
TEST_CASE_TEMPLATE("[Math] move_toward", T, float, double) {
429
	CHECK(Math::move_toward(2.0, 5.0, -1.0) == doctest::Approx((T)1.0));
430
	CHECK(Math::move_toward(2.0, 5.0, 2.5) == doctest::Approx((T)4.5));
431
	CHECK(Math::move_toward(2.0, 5.0, 4.0) == doctest::Approx((T)5.0));
432
	CHECK(Math::move_toward(-2.0, -5.0, -1.0) == doctest::Approx((T)-1.0));
433
	CHECK(Math::move_toward(-2.0, -5.0, 2.5) == doctest::Approx((T)-4.5));
434
	CHECK(Math::move_toward(-2.0, -5.0, 4.0) == doctest::Approx((T)-5.0));
435
}
436

437
TEST_CASE_TEMPLATE("[Math] rotate_toward", T, float, double) {
438
	// Rotate toward.
439
	CHECK(Math::rotate_toward((T)0.0, (T)Math::PI * (T)0.75, (T)1.5) == doctest::Approx((T)1.5));
440
	CHECK(Math::rotate_toward((T)-2.0, (T)1.0, (T)2.5) == doctest::Approx((T)0.5));
441
	CHECK(Math::rotate_toward((T)-2.0, (T)Math::PI, (T)Math::PI) == doctest::Approx((T)-Math::PI));
442
	CHECK(Math::rotate_toward((T)1.0, (T)Math::PI, (T)20.0) == doctest::Approx((T)Math::PI));
443

444
	// Rotate away.
445
	CHECK(Math::rotate_toward((T)0.0, (T)0.0, (T)-1.5) == doctest::Approx((T)-1.5));
446
	CHECK(Math::rotate_toward((T)0.0, (T)0.0, (T)-Math::PI) == doctest::Approx((T)-Math::PI));
447
	CHECK(Math::rotate_toward((T)3.0, (T)Math::PI, (T)-Math::PI) == doctest::Approx((T)0.0));
448
	CHECK(Math::rotate_toward((T)2.0, (T)Math::PI, (T)-1.5) == doctest::Approx((T)0.5));
449
	CHECK(Math::rotate_toward((T)1.0, (T)2.0, (T)-0.5) == doctest::Approx((T)0.5));
450
	CHECK(Math::rotate_toward((T)2.5, (T)2.0, (T)-0.5) == doctest::Approx((T)3.0));
451
	CHECK(Math::rotate_toward((T)-1.0, (T)1.0, (T)-1.0) == doctest::Approx((T)-2.0));
452
}
453

454
TEST_CASE_TEMPLATE("[Math] smoothstep", T, float, double) {
455
	CHECK(Math::smoothstep((T)0.0, (T)2.0, (T)-5.0) == doctest::Approx((T)0.0));
456
	CHECK(Math::smoothstep((T)0.0, (T)2.0, (T)0.5) == doctest::Approx((T)0.15625));
457
	CHECK(Math::smoothstep((T)0.0, (T)2.0, (T)1.0) == doctest::Approx((T)0.5));
458
	CHECK(Math::smoothstep((T)0.0, (T)2.0, (T)2.0) == doctest::Approx((T)1.0));
459
}
460

461
TEST_CASE("[Math] ease") {
462
	CHECK(Math::ease(0.1, 1.0) == doctest::Approx(0.1));
463
	CHECK(Math::ease(0.1, 2.0) == doctest::Approx(0.01));
464
	CHECK(Math::ease(0.1, 0.5) == doctest::Approx(0.19));
465
	CHECK(Math::ease(0.1, 0.0) == doctest::Approx(0));
466
	CHECK(Math::ease(0.1, -0.5) == doctest::Approx(0.2236067977));
467
	CHECK(Math::ease(0.1, -1.0) == doctest::Approx(0.1));
468
	CHECK(Math::ease(0.1, -2.0) == doctest::Approx(0.02));
469

470
	CHECK(Math::ease(-1.0, 1.0) == doctest::Approx(0));
471
	CHECK(Math::ease(-1.0, 2.0) == doctest::Approx(0));
472
	CHECK(Math::ease(-1.0, 0.5) == doctest::Approx(0));
473
	CHECK(Math::ease(-1.0, 0.0) == doctest::Approx(0));
474
	CHECK(Math::ease(-1.0, -0.5) == doctest::Approx(0));
475
	CHECK(Math::ease(-1.0, -1.0) == doctest::Approx(0));
476
	CHECK(Math::ease(-1.0, -2.0) == doctest::Approx(0));
477
}
478

479
TEST_CASE("[Math] snapped") {
480
	CHECK(Math::snapped(0.5, 0.04) == doctest::Approx(0.52));
481
	CHECK(Math::snapped(-0.5, 0.04) == doctest::Approx(-0.48));
482
	CHECK(Math::snapped(0.0, 0.04) == doctest::Approx(0));
483
	CHECK(Math::snapped(128'000.025, 0.04) == doctest::Approx(128'000.04));
484

485
	CHECK(Math::snapped(0.5, 400) == doctest::Approx(0));
486
	CHECK(Math::snapped(-0.5, 400) == doctest::Approx(0));
487
	CHECK(Math::snapped(0.0, 400) == doctest::Approx(0));
488
	CHECK(Math::snapped(128'000.025, 400) == doctest::Approx(128'000.0));
489

490
	CHECK(Math::snapped(0.5, 0.0) == doctest::Approx(0.5));
491
	CHECK(Math::snapped(-0.5, 0.0) == doctest::Approx(-0.5));
492
	CHECK(Math::snapped(0.0, 0.0) == doctest::Approx(0.0));
493
	CHECK(Math::snapped(128'000.025, 0.0) == doctest::Approx(128'000.0));
494

495
	CHECK(Math::snapped(0.5, -1.0) == doctest::Approx(0));
496
	CHECK(Math::snapped(-0.5, -1.0) == doctest::Approx(-1.0));
497
	CHECK(Math::snapped(0.0, -1.0) == doctest::Approx(0));
498
	CHECK(Math::snapped(128'000.025, -1.0) == doctest::Approx(128'000.0));
499
}
500

501
TEST_CASE("[Math] larger_prime") {
502
	CHECK(Math::larger_prime(0) == 5);
503
	CHECK(Math::larger_prime(1) == 5);
504
	CHECK(Math::larger_prime(2) == 5);
505
	CHECK(Math::larger_prime(5) == 13);
506
	CHECK(Math::larger_prime(500) == 769);
507
	CHECK(Math::larger_prime(1'000'000) == 1'572'869);
508
	CHECK(Math::larger_prime(1'000'000'000) == 1'610'612'741);
509

510
	// The next prime is larger than `INT32_MAX` and is not present in the built-in prime table.
511
	ERR_PRINT_OFF;
512
	CHECK(Math::larger_prime(2'000'000'000) == 0);
513
	ERR_PRINT_ON;
514
}
515

516
TEST_CASE_TEMPLATE("[Math] fmod", T, float, double) {
517
	CHECK(Math::fmod((T)-2.0, (T)0.3) == doctest::Approx((T)-0.2));
518
	CHECK(Math::fmod((T)0.0, (T)0.3) == doctest::Approx((T)0.0));
519
	CHECK(Math::fmod((T)2.0, (T)0.3) == doctest::Approx((T)0.2));
520

521
	CHECK(Math::fmod((T)-2.0, (T)-0.3) == doctest::Approx((T)-0.2));
522
	CHECK(Math::fmod((T)0.0, (T)-0.3) == doctest::Approx((T)0.0));
523
	CHECK(Math::fmod((T)2.0, (T)-0.3) == doctest::Approx((T)0.2));
524
}
525

526
TEST_CASE_TEMPLATE("[Math] fposmod", T, float, double) {
527
	CHECK(Math::fposmod((T)-2.0, (T)0.3) == doctest::Approx((T)0.1));
528
	CHECK(Math::fposmod((T)0.0, (T)0.3) == doctest::Approx((T)0.0));
529
	CHECK(Math::fposmod((T)2.0, (T)0.3) == doctest::Approx((T)0.2));
530

531
	CHECK(Math::fposmod((T)-2.0, (T)-0.3) == doctest::Approx((T)-0.2));
532
	CHECK(Math::fposmod((T)0.0, (T)-0.3) == doctest::Approx((T)0.0));
533
	CHECK(Math::fposmod((T)2.0, (T)-0.3) == doctest::Approx((T)-0.1));
534
}
535

536
TEST_CASE_TEMPLATE("[Math] fposmodp", T, float, double) {
537
	CHECK(Math::fposmodp((T)-2.0, (T)0.3) == doctest::Approx((T)0.1));
538
	CHECK(Math::fposmodp((T)0.0, (T)0.3) == doctest::Approx((T)0.0));
539
	CHECK(Math::fposmodp((T)2.0, (T)0.3) == doctest::Approx((T)0.2));
540

541
	CHECK(Math::fposmodp((T)-2.0, (T)-0.3) == doctest::Approx((T)-0.5));
542
	CHECK(Math::fposmodp((T)0.0, (T)-0.3) == doctest::Approx((T)0.0));
543
	CHECK(Math::fposmodp((T)2.0, (T)-0.3) == doctest::Approx((T)0.2));
544
}
545

546
TEST_CASE("[Math] posmod") {
547
	CHECK(Math::posmod(-20, 3) == 1);
548
	CHECK(Math::posmod(0, 3) == 0);
549
	CHECK(Math::posmod(20, 3) == 2);
550
	CHECK(Math::posmod(-20, -3) == -2);
551
	CHECK(Math::posmod(0, -3) == 0);
552
	CHECK(Math::posmod(20, -3) == -1);
553
}
554

555
TEST_CASE("[Math] wrapi") {
556
	CHECK(Math::wrapi(-30, -20, 160) == 150);
557
	CHECK(Math::wrapi(30, -20, 160) == 30);
558
	CHECK(Math::wrapi(300, -20, 160) == 120);
559
	CHECK(Math::wrapi(300'000'000'000, -20, 160) == 120);
560
}
561

562
TEST_CASE_TEMPLATE("[Math] wrapf", T, float, double) {
563
	CHECK(Math::wrapf((T)-30.0, (T)-20.0, (T)160.0) == doctest::Approx((T)150.0));
564
	CHECK(Math::wrapf((T)30.0, (T)-2.0, (T)160.0) == doctest::Approx((T)30.0));
565
	CHECK(Math::wrapf((T)300.0, (T)-20.0, (T)160.0) == doctest::Approx((T)120.0));
566

567
	CHECK(Math::wrapf(300'000'000'000.0, -20.0, 160.0) == doctest::Approx((T)120.0));
568
	// float's precision is too low for 300'000'000'000.0, so we reduce it by a factor of 1000.
569
	CHECK(Math::wrapf((float)15'000'000.0, (float)-20.0, (float)160.0) == doctest::Approx((T)60.0));
570
}
571

572
TEST_CASE_TEMPLATE("[Math] fract", T, float, double) {
573
	CHECK(Math::fract((T)1.0) == doctest::Approx((T)0.0));
574
	CHECK(Math::fract((T)77.8) == doctest::Approx((T)0.8));
575
	CHECK(Math::fract((T)-10.1) == doctest::Approx((T)0.9));
576
}
577

578
TEST_CASE_TEMPLATE("[Math] pingpong", T, float, double) {
579
	CHECK(Math::pingpong((T)0.0, (T)0.0) == doctest::Approx((T)0.0));
580
	CHECK(Math::pingpong((T)1.0, (T)1.0) == doctest::Approx((T)1.0));
581
	CHECK(Math::pingpong((T)0.5, (T)2.0) == doctest::Approx((T)0.5));
582
	CHECK(Math::pingpong((T)3.5, (T)2.0) == doctest::Approx((T)0.5));
583
	CHECK(Math::pingpong((T)11.5, (T)2.0) == doctest::Approx((T)0.5));
584
	CHECK(Math::pingpong((T)-2.5, (T)2.0) == doctest::Approx((T)1.5));
585
}
586

587
TEST_CASE_TEMPLATE("[Math] deg_to_rad/rad_to_deg", T, float, double) {
588
	CHECK(Math::deg_to_rad((T)180.0) == doctest::Approx((T)Math::PI));
589
	CHECK(Math::deg_to_rad((T)-27.0) == doctest::Approx((T)-0.471239));
590

591
	CHECK(Math::rad_to_deg((T)Math::PI) == doctest::Approx((T)180.0));
592
	CHECK(Math::rad_to_deg((T)-1.5) == doctest::Approx((T)-85.94366927));
593
}
594

595
TEST_CASE_TEMPLATE("[Math] cubic_interpolate", T, float, double) {
596
	CHECK(Math::cubic_interpolate((T)0.2, (T)0.8, (T)0.0, (T)1.0, (T)0.0) == doctest::Approx((T)0.2));
597
	CHECK(Math::cubic_interpolate((T)0.2, (T)0.8, (T)0.0, (T)1.0, (T)0.25) == doctest::Approx((T)0.33125));
598
	CHECK(Math::cubic_interpolate((T)0.2, (T)0.8, (T)0.0, (T)1.0, (T)0.5) == doctest::Approx((T)0.5));
599
	CHECK(Math::cubic_interpolate((T)0.2, (T)0.8, (T)0.0, (T)1.0, (T)0.75) == doctest::Approx((T)0.66875));
600
	CHECK(Math::cubic_interpolate((T)0.2, (T)0.8, (T)0.0, (T)1.0, (T)1.0) == doctest::Approx((T)0.8));
601

602
	CHECK(Math::cubic_interpolate((T)20.2, (T)30.1, (T)-100.0, (T)32.0, (T)-50.0) == doctest::Approx((T)-6662732.3));
603
	CHECK(Math::cubic_interpolate((T)20.2, (T)30.1, (T)-100.0, (T)32.0, (T)-5.0) == doctest::Approx((T)-9356.3));
604
	CHECK(Math::cubic_interpolate((T)20.2, (T)30.1, (T)-100.0, (T)32.0, (T)0.0) == doctest::Approx((T)20.2));
605
	CHECK(Math::cubic_interpolate((T)20.2, (T)30.1, (T)-100.0, (T)32.0, (T)1.0) == doctest::Approx((T)30.1));
606
	CHECK(Math::cubic_interpolate((T)20.2, (T)30.1, (T)-100.0, (T)32.0, (T)4.0) == doctest::Approx((T)1853.2));
607
}
608

609
TEST_CASE_TEMPLATE("[Math] cubic_interpolate_angle", T, float, double) {
610
	CHECK(Math::cubic_interpolate_angle((T)(Math::PI * (1.0 / 6.0)), (T)(Math::PI * (5.0 / 6.0)), (T)0.0, (T)Math::PI, (T)0.0) == doctest::Approx((T)Math::PI * (1.0 / 6.0)));
611
	CHECK(Math::cubic_interpolate_angle((T)(Math::PI * (1.0 / 6.0)), (T)(Math::PI * (5.0 / 6.0)), (T)0.0, (T)Math::PI, (T)0.25) == doctest::Approx((T)0.973566));
612
	CHECK(Math::cubic_interpolate_angle((T)(Math::PI * (1.0 / 6.0)), (T)(Math::PI * (5.0 / 6.0)), (T)0.0, (T)Math::PI, (T)0.5) == doctest::Approx((T)Math::PI / 2.0));
613
	CHECK(Math::cubic_interpolate_angle((T)(Math::PI * (1.0 / 6.0)), (T)(Math::PI * (5.0 / 6.0)), (T)0.0, (T)Math::PI, (T)0.75) == doctest::Approx((T)2.16803));
614
	CHECK(Math::cubic_interpolate_angle((T)(Math::PI * (1.0 / 6.0)), (T)(Math::PI * (5.0 / 6.0)), (T)0.0, (T)Math::PI, (T)1.0) == doctest::Approx((T)Math::PI * (5.0 / 6.0)));
615
}
616

617
TEST_CASE_TEMPLATE("[Math] cubic_interpolate_in_time", T, float, double) {
618
	CHECK(Math::cubic_interpolate_in_time((T)0.2, (T)0.8, (T)0.0, (T)1.0, (T)0.0, (T)0.5, (T)0.0, (T)1.0) == doctest::Approx((T)0.0));
619
	CHECK(Math::cubic_interpolate_in_time((T)0.2, (T)0.8, (T)0.0, (T)1.0, (T)0.25, (T)0.5, (T)0.0, (T)1.0) == doctest::Approx((T)0.1625));
620
	CHECK(Math::cubic_interpolate_in_time((T)0.2, (T)0.8, (T)0.0, (T)1.0, (T)0.5, (T)0.5, (T)0.0, (T)1.0) == doctest::Approx((T)0.4));
621
	CHECK(Math::cubic_interpolate_in_time((T)0.2, (T)0.8, (T)0.0, (T)1.0, (T)0.75, (T)0.5, (T)0.0, (T)1.0) == doctest::Approx((T)0.6375));
622
	CHECK(Math::cubic_interpolate_in_time((T)0.2, (T)0.8, (T)0.0, (T)1.0, (T)1.0, (T)0.5, (T)0.0, (T)1.0) == doctest::Approx((T)0.8));
623
}
624

625
TEST_CASE_TEMPLATE("[Math] cubic_interpolate_angle_in_time", T, float, double) {
626
	CHECK(Math::cubic_interpolate_angle_in_time((T)(Math::PI * (1.0 / 6.0)), (T)(Math::PI * (5.0 / 6.0)), (T)0.0, (T)Math::PI, (T)0.0, (T)0.5, (T)0.0, (T)1.0) == doctest::Approx((T)0.0));
627
	CHECK(Math::cubic_interpolate_angle_in_time((T)(Math::PI * (1.0 / 6.0)), (T)(Math::PI * (5.0 / 6.0)), (T)0.0, (T)Math::PI, (T)0.25, (T)0.5, (T)0.0, (T)1.0) == doctest::Approx((T)0.494964));
628
	CHECK(Math::cubic_interpolate_angle_in_time((T)(Math::PI * (1.0 / 6.0)), (T)(Math::PI * (5.0 / 6.0)), (T)0.0, (T)Math::PI, (T)0.5, (T)0.5, (T)0.0, (T)1.0) == doctest::Approx((T)1.27627));
629
	CHECK(Math::cubic_interpolate_angle_in_time((T)(Math::PI * (1.0 / 6.0)), (T)(Math::PI * (5.0 / 6.0)), (T)0.0, (T)Math::PI, (T)0.75, (T)0.5, (T)0.0, (T)1.0) == doctest::Approx((T)2.07394));
630
	CHECK(Math::cubic_interpolate_angle_in_time((T)(Math::PI * (1.0 / 6.0)), (T)(Math::PI * (5.0 / 6.0)), (T)0.0, (T)Math::PI, (T)1.0, (T)0.5, (T)0.0, (T)1.0) == doctest::Approx((T)Math::PI * (5.0 / 6.0)));
631
}
632

633
TEST_CASE_TEMPLATE("[Math] bezier_interpolate", T, float, double) {
634
	CHECK(Math::bezier_interpolate((T)0.0, (T)0.2, (T)0.8, (T)1.0, (T)0.0) == doctest::Approx((T)0.0));
635
	CHECK(Math::bezier_interpolate((T)0.0, (T)0.2, (T)0.8, (T)1.0, (T)0.25) == doctest::Approx((T)0.2125));
636
	CHECK(Math::bezier_interpolate((T)0.0, (T)0.2, (T)0.8, (T)1.0, (T)0.5) == doctest::Approx((T)0.5));
637
	CHECK(Math::bezier_interpolate((T)0.0, (T)0.2, (T)0.8, (T)1.0, (T)0.75) == doctest::Approx((T)0.7875));
638
	CHECK(Math::bezier_interpolate((T)0.0, (T)0.2, (T)0.8, (T)1.0, (T)1.0) == doctest::Approx((T)1.0));
639
}
640

641
} // namespace TestMath
642

643
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