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diff --git a/tests/test_math.cpp b/tests/test_math.cpp
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+/*************************************************************************/
+/* test_math.cpp */
+/*************************************************************************/
+/* This file is part of: */
+/* GODOT ENGINE */
+/* https://godotengine.org */
+/*************************************************************************/
+/* Copyright (c) 2007-2020 Juan Linietsky, Ariel Manzur. */
+/* Copyright (c) 2014-2020 Godot Engine contributors (cf. AUTHORS.md). */
+/* */
+/* Permission is hereby granted, free of charge, to any person obtaining */
+/* a copy of this software and associated documentation files (the */
+/* "Software"), to deal in the Software without restriction, including */
+/* without limitation the rights to use, copy, modify, merge, publish, */
+/* distribute, sublicense, and/or sell copies of the Software, and to */
+/* permit persons to whom the Software is furnished to do so, subject to */
+/* the following conditions: */
+/* */
+/* The above copyright notice and this permission notice shall be */
+/* included in all copies or substantial portions of the Software. */
+/* */
+/* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, */
+/* EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF */
+/* MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.*/
+/* IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY */
+/* CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, */
+/* TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE */
+/* SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. */
+/*************************************************************************/
+
+#include "test_math.h"
+
+#include "core/math/basis.h"
+#include "core/math/camera_matrix.h"
+#include "core/math/delaunay_3d.h"
+#include "core/math/geometry_2d.h"
+#include "core/math/math_funcs.h"
+#include "core/math/transform.h"
+#include "core/method_ptrcall.h"
+#include "core/os/file_access.h"
+#include "core/os/keyboard.h"
+#include "core/os/os.h"
+#include "core/print_string.h"
+#include "core/ustring.h"
+#include "core/variant.h"
+#include "core/vmap.h"
+#include "scene/main/node.h"
+#include "scene/resources/texture.h"
+#include "servers/rendering/shader_language.h"
+
+namespace TestMath {
+
+class GetClassAndNamespace {
+ String code;
+ int idx;
+ int line;
+ String error_str;
+ bool error;
+ Variant value;
+
+ String class_name;
+
+ enum Token {
+ TK_BRACKET_OPEN,
+ TK_BRACKET_CLOSE,
+ TK_CURLY_BRACKET_OPEN,
+ TK_CURLY_BRACKET_CLOSE,
+ TK_PERIOD,
+ TK_COLON,
+ TK_COMMA,
+ TK_SYMBOL,
+ TK_IDENTIFIER,
+ TK_STRING,
+ TK_NUMBER,
+ TK_EOF,
+ TK_ERROR
+ };
+
+ Token get_token() {
+ while (true) {
+ switch (code[idx]) {
+ case '\n': {
+ line++;
+ idx++;
+ break;
+ };
+ case 0: {
+ return TK_EOF;
+
+ } break;
+ case '{': {
+ idx++;
+ return TK_CURLY_BRACKET_OPEN;
+ };
+ case '}': {
+ idx++;
+ return TK_CURLY_BRACKET_CLOSE;
+ };
+ case '[': {
+ idx++;
+ return TK_BRACKET_OPEN;
+ };
+ case ']': {
+ idx++;
+ return TK_BRACKET_CLOSE;
+ };
+ case ':': {
+ idx++;
+ return TK_COLON;
+ };
+ case ',': {
+ idx++;
+ return TK_COMMA;
+ };
+ case '.': {
+ idx++;
+ return TK_PERIOD;
+ };
+ case '#': {
+ //compiler directive
+ while (code[idx] != '\n' && code[idx] != 0) {
+ idx++;
+ }
+ continue;
+ } break;
+ case '/': {
+ switch (code[idx + 1]) {
+ case '*': { // block comment
+
+ idx += 2;
+ while (true) {
+ if (code[idx] == 0) {
+ error_str = "Unterminated comment";
+ error = true;
+ return TK_ERROR;
+ } else if (code[idx] == '*' && code[idx + 1] == '/') {
+ idx += 2;
+ break;
+ } else if (code[idx] == '\n') {
+ line++;
+ }
+
+ idx++;
+ }
+
+ } break;
+ case '/': { // line comment skip
+
+ while (code[idx] != '\n' && code[idx] != 0) {
+ idx++;
+ }
+
+ } break;
+ default: {
+ value = "/";
+ idx++;
+ return TK_SYMBOL;
+ }
+ }
+
+ continue; // a comment
+ } break;
+ case '\'':
+ case '"': {
+ CharType begin_str = code[idx];
+ idx++;
+ String tk_string = String();
+ while (true) {
+ if (code[idx] == 0) {
+ error_str = "Unterminated String";
+ error = true;
+ return TK_ERROR;
+ } else if (code[idx] == begin_str) {
+ idx++;
+ break;
+ } else if (code[idx] == '\\') {
+ //escaped characters...
+ idx++;
+ CharType next = code[idx];
+ if (next == 0) {
+ error_str = "Unterminated String";
+ error = true;
+ return TK_ERROR;
+ }
+ CharType res = 0;
+
+ switch (next) {
+ case 'b':
+ res = 8;
+ break;
+ case 't':
+ res = 9;
+ break;
+ case 'n':
+ res = 10;
+ break;
+ case 'f':
+ res = 12;
+ break;
+ case 'r':
+ res = 13;
+ break;
+ case '\"':
+ res = '\"';
+ break;
+ case '\\':
+ res = '\\';
+ break;
+ default: {
+ res = next;
+ } break;
+ }
+
+ tk_string += res;
+
+ } else {
+ if (code[idx] == '\n') {
+ line++;
+ }
+ tk_string += code[idx];
+ }
+ idx++;
+ }
+
+ value = tk_string;
+
+ return TK_STRING;
+
+ } break;
+ default: {
+ if (code[idx] <= 32) {
+ idx++;
+ break;
+ }
+
+ if ((code[idx] >= 33 && code[idx] <= 47) || (code[idx] >= 58 && code[idx] <= 64) || (code[idx] >= 91 && code[idx] <= 96) || (code[idx] >= 123 && code[idx] <= 127)) {
+ value = String::chr(code[idx]);
+ idx++;
+ return TK_SYMBOL;
+ }
+
+ if (code[idx] == '-' || (code[idx] >= '0' && code[idx] <= '9')) {
+ //a number
+ const CharType *rptr;
+ double number = String::to_double(&code[idx], &rptr);
+ idx += (rptr - &code[idx]);
+ value = number;
+ return TK_NUMBER;
+
+ } else if ((code[idx] >= 'A' && code[idx] <= 'Z') || (code[idx] >= 'a' && code[idx] <= 'z') || code[idx] > 127) {
+ String id;
+
+ while ((code[idx] >= 'A' && code[idx] <= 'Z') || (code[idx] >= 'a' && code[idx] <= 'z') || code[idx] > 127) {
+ id += code[idx];
+ idx++;
+ }
+
+ value = id;
+ return TK_IDENTIFIER;
+ } else {
+ error_str = "Unexpected character.";
+ error = true;
+ return TK_ERROR;
+ }
+ }
+ }
+ }
+ }
+
+public:
+ Error parse(const String &p_code, const String &p_known_class_name = String()) {
+ code = p_code;
+ idx = 0;
+ line = 0;
+ error_str = String();
+ error = false;
+ value = Variant();
+ class_name = String();
+
+ bool use_next_class = false;
+ Token tk = get_token();
+
+ Map<int, String> namespace_stack;
+ int curly_stack = 0;
+
+ while (!error || tk != TK_EOF) {
+ if (tk == TK_BRACKET_OPEN) {
+ tk = get_token();
+ if (tk == TK_IDENTIFIER && String(value) == "ScriptClass") {
+ if (get_token() == TK_BRACKET_CLOSE) {
+ use_next_class = true;
+ }
+ }
+ } else if (tk == TK_IDENTIFIER && String(value) == "class") {
+ tk = get_token();
+ if (tk == TK_IDENTIFIER) {
+ String name = value;
+ if (use_next_class || p_known_class_name == name) {
+ for (Map<int, String>::Element *E = namespace_stack.front(); E; E = E->next()) {
+ class_name += E->get() + ".";
+ }
+ class_name += String(value);
+ break;
+ }
+ }
+
+ } else if (tk == TK_IDENTIFIER && String(value) == "namespace") {
+ String name;
+ int at_level = curly_stack;
+ while (true) {
+ tk = get_token();
+ if (tk == TK_IDENTIFIER) {
+ name += String(value);
+ }
+
+ tk = get_token();
+ if (tk == TK_PERIOD) {
+ name += ".";
+ } else if (tk == TK_CURLY_BRACKET_OPEN) {
+ curly_stack++;
+ break;
+ } else {
+ break; //whathever else
+ }
+ }
+
+ if (name != String()) {
+ namespace_stack[at_level] = name;
+ }
+
+ } else if (tk == TK_CURLY_BRACKET_OPEN) {
+ curly_stack++;
+ } else if (tk == TK_CURLY_BRACKET_CLOSE) {
+ curly_stack--;
+ if (namespace_stack.has(curly_stack)) {
+ namespace_stack.erase(curly_stack);
+ }
+ }
+
+ tk = get_token();
+ }
+
+ if (error) {
+ return ERR_PARSE_ERROR;
+ }
+
+ return OK;
+ }
+
+ String get_error() {
+ return error_str;
+ }
+
+ String get_class() {
+ return class_name;
+ }
+};
+
+void test_vec(Plane p_vec) {
+ CameraMatrix cm;
+ cm.set_perspective(45, 1, 0, 100);
+ Plane v0 = cm.xform4(p_vec);
+
+ print_line("out: " + v0);
+ v0.normal.z = (v0.d / 100.0 * 2.0 - 1.0) * v0.d;
+ print_line("out_F: " + v0);
+}
+
+uint32_t ihash(uint32_t a) {
+ a = (a + 0x7ed55d16) + (a << 12);
+ a = (a ^ 0xc761c23c) ^ (a >> 19);
+ a = (a + 0x165667b1) + (a << 5);
+ a = (a + 0xd3a2646c) ^ (a << 9);
+ a = (a + 0xfd7046c5) + (a << 3);
+ a = (a ^ 0xb55a4f09) ^ (a >> 16);
+ return a;
+}
+
+uint32_t ihash2(uint32_t a) {
+ a = (a ^ 61) ^ (a >> 16);
+ a = a + (a << 3);
+ a = a ^ (a >> 4);
+ a = a * 0x27d4eb2d;
+ a = a ^ (a >> 15);
+ return a;
+}
+
+uint32_t ihash3(uint32_t a) {
+ a = (a + 0x479ab41d) + (a << 8);
+ a = (a ^ 0xe4aa10ce) ^ (a >> 5);
+ a = (a + 0x9942f0a6) - (a << 14);
+ a = (a ^ 0x5aedd67d) ^ (a >> 3);
+ a = (a + 0x17bea992) + (a << 7);
+ return a;
+}
+
+MainLoop *test() {
+ {
+ Vector<Vector3> points;
+ points.push_back(Vector3(0, 0, 0));
+ points.push_back(Vector3(0, 0, 1));
+ points.push_back(Vector3(0, 1, 0));
+ points.push_back(Vector3(0, 1, 1));
+ points.push_back(Vector3(1, 1, 0));
+ points.push_back(Vector3(1, 0, 0));
+ points.push_back(Vector3(1, 0, 1));
+ points.push_back(Vector3(1, 1, 1));
+
+ for (int i = 0; i < 800; i++) {
+ points.push_back(Vector3(Math::randf() * 2.0 - 1.0, Math::randf() * 2.0 - 1.0, Math::randf() * 2.0 - 1.0) * Vector3(25, 30, 33));
+ }
+
+ Vector<Delaunay3D::OutputSimplex> os = Delaunay3D::tetrahedralize(points);
+ print_line("simplices in the end: " + itos(os.size()));
+ for (int i = 0; i < os.size(); i++) {
+ print_line("Simplex " + itos(i) + ": ");
+ print_line(points[os[i].points[0]]);
+ print_line(points[os[i].points[1]]);
+ print_line(points[os[i].points[2]]);
+ print_line(points[os[i].points[3]]);
+ }
+
+ {
+ FileAccessRef f = FileAccess::open("res://bsp.obj", FileAccess::WRITE);
+ for (int i = 0; i < os.size(); i++) {
+ f->store_line("o Simplex" + itos(i));
+ for (int j = 0; j < 4; j++) {
+ f->store_line(vformat("v %f %f %f", points[os[i].points[j]].x, points[os[i].points[j]].y, points[os[i].points[j]].z));
+ }
+ static const int face_order[4][3] = {
+ { 1, 2, 3 },
+ { 1, 3, 4 },
+ { 1, 2, 4 },
+ { 2, 3, 4 }
+ };
+
+ for (int j = 0; j < 4; j++) {
+ f->store_line(vformat("f %d %d %d", 4 * i + face_order[j][0], 4 * i + face_order[j][1], 4 * i + face_order[j][2]));
+ }
+ }
+ f->close();
+ }
+
+ return nullptr;
+ }
+
+ {
+ float r = 1;
+ float g = 0.5;
+ float b = 0.1;
+
+ const float pow2to9 = 512.0f;
+ const float B = 15.0f;
+ const float N = 9.0f;
+
+ float sharedexp = 65408.000f;
+
+ float cRed = MAX(0.0f, MIN(sharedexp, r));
+ float cGreen = MAX(0.0f, MIN(sharedexp, g));
+ float cBlue = MAX(0.0f, MIN(sharedexp, b));
+
+ float cMax = MAX(cRed, MAX(cGreen, cBlue));
+
+ float expp = MAX(-B - 1.0f, floor(Math::log(cMax) / Math_LN2)) + 1.0f + B;
+
+ float sMax = (float)floor((cMax / Math::pow(2.0f, expp - B - N)) + 0.5f);
+
+ float exps = expp + 1.0f;
+
+ if (0.0 <= sMax && sMax < pow2to9) {
+ exps = expp;
+ }
+
+ float sRed = Math::floor((cRed / pow(2.0f, exps - B - N)) + 0.5f);
+ float sGreen = Math::floor((cGreen / pow(2.0f, exps - B - N)) + 0.5f);
+ float sBlue = Math::floor((cBlue / pow(2.0f, exps - B - N)) + 0.5f);
+
+ print_line("R: " + rtos(sRed) + " G: " + rtos(sGreen) + " B: " + rtos(sBlue) + " EXP: " + rtos(exps));
+
+ uint32_t rgbe = (Math::fast_ftoi(sRed) & 0x1FF) | ((Math::fast_ftoi(sGreen) & 0x1FF) << 9) | ((Math::fast_ftoi(sBlue) & 0x1FF) << 18) | ((Math::fast_ftoi(exps) & 0x1F) << 27);
+
+ float rb = rgbe & 0x1ff;
+ float gb = (rgbe >> 9) & 0x1ff;
+ float bb = (rgbe >> 18) & 0x1ff;
+ float eb = (rgbe >> 27);
+ float mb = Math::pow(2.0, eb - 15.0 - 9.0);
+ float rd = rb * mb;
+ float gd = gb * mb;
+ float bd = bb * mb;
+
+ print_line("RGBE: " + Color(rd, gd, bd));
+ }
+
+ Vector<int> ints;
+ ints.resize(20);
+
+ {
+ int *w;
+ w = ints.ptrw();
+ for (int i = 0; i < ints.size(); i++) {
+ w[i] = i;
+ }
+ }
+
+ Vector<int> posho = ints;
+
+ {
+ const int *r = posho.ptr();
+ for (int i = 0; i < posho.size(); i++) {
+ print_line(itos(i) + " : " + itos(r[i]));
+ }
+ }
+
+ List<String> cmdlargs = OS::get_singleton()->get_cmdline_args();
+
+ if (cmdlargs.empty()) {
+ //try editor!
+ return nullptr;
+ }
+
+ String test = cmdlargs.back()->get();
+ if (test == "math") {
+ // Not a file name but the test name, abort.
+ // FIXME: This test is ugly as heck, needs fixing :)
+ return nullptr;
+ }
+
+ FileAccess *fa = FileAccess::open(test, FileAccess::READ);
+ ERR_FAIL_COND_V_MSG(!fa, nullptr, "Could not open file: " + test);
+
+ Vector<uint8_t> buf;
+ int flen = fa->get_len();
+ buf.resize(fa->get_len() + 1);
+ fa->get_buffer(buf.ptrw(), flen);
+ buf.write[flen] = 0;
+
+ String code;
+ code.parse_utf8((const char *)&buf[0]);
+
+ GetClassAndNamespace getclass;
+ if (getclass.parse(code)) {
+ print_line("Parse error: " + getclass.get_error());
+ } else {
+ print_line("Found class: " + getclass.get_class());
+ }
+
+ {
+ Vector<int> hashes;
+ List<StringName> tl;
+ ClassDB::get_class_list(&tl);
+
+ for (List<StringName>::Element *E = tl.front(); E; E = E->next()) {
+ Vector<uint8_t> m5b = E->get().operator String().md5_buffer();
+ hashes.push_back(hashes.size());
+ }
+
+ for (int i = nearest_shift(hashes.size()); i < 20; i++) {
+ bool success = true;
+ for (int s = 0; s < 10000; s++) {
+ Set<uint32_t> existing;
+ success = true;
+
+ for (int j = 0; j < hashes.size(); j++) {
+ uint32_t eh = ihash2(ihash3(hashes[j] + ihash(s) + s)) & ((1 << i) - 1);
+ if (existing.has(eh)) {
+ success = false;
+ break;
+ }
+ existing.insert(eh);
+ }
+
+ if (success) {
+ print_line("success at " + itos(i) + "/" + itos(nearest_shift(hashes.size())) + " shift " + itos(s));
+ break;
+ }
+ }
+ if (success) {
+ break;
+ }
+ }
+
+ print_line("DONE");
+ }
+
+ {
+ print_line("NUM: " + itos(-128));
+ }
+
+ {
+ Vector3 v(1, 2, 3);
+ v.normalize();
+ float a = 0.3;
+
+ Basis m(v, a);
+
+ Vector3 v2(7, 3, 1);
+ v2.normalize();
+ float a2 = 0.8;
+
+ Basis m2(v2, a2);
+
+ Quat q = m;
+ Quat q2 = m2;
+
+ Basis m3 = m.inverse() * m2;
+ Quat q3 = (q.inverse() * q2); //.normalized();
+
+ print_line(Quat(m3));
+ print_line(q3);
+
+ print_line("before v: " + v + " a: " + rtos(a));
+ q.get_axis_angle(v, a);
+ print_line("after v: " + v + " a: " + rtos(a));
+ }
+
+ String ret;
+
+ List<String> args;
+ args.push_back("-l");
+ Error err = OS::get_singleton()->execute("/bin/ls", args, true, nullptr, &ret);
+ print_line("error: " + itos(err));
+ print_line(ret);
+
+ Basis m3;
+ m3.rotate(Vector3(1, 0, 0), 0.2);
+ m3.rotate(Vector3(0, 1, 0), 1.77);
+ m3.rotate(Vector3(0, 0, 1), 212);
+ Basis m32;
+ m32.set_euler(m3.get_euler());
+ print_line("ELEULEEEEEEEEEEEEEEEEEER: " + m3.get_euler() + " vs " + m32.get_euler());
+
+ {
+ Dictionary d;
+ d["momo"] = 1;
+ Dictionary b = d;
+ b["44"] = 4;
+ }
+
+ print_line("inters: " + rtos(Geometry2D::segment_intersects_circle(Vector2(-5, 0), Vector2(-2, 0), Vector2(), 1.0)));
+
+ print_line("cross: " + Vector3(1, 2, 3).cross(Vector3(4, 5, 7)));
+ print_line("dot: " + rtos(Vector3(1, 2, 3).dot(Vector3(4, 5, 7))));
+ print_line("abs: " + Vector3(-1, 2, -3).abs());
+ print_line("distance_to: " + rtos(Vector3(1, 2, 3).distance_to(Vector3(4, 5, 7))));
+ print_line("distance_squared_to: " + rtos(Vector3(1, 2, 3).distance_squared_to(Vector3(4, 5, 7))));
+ print_line("plus: " + (Vector3(1, 2, 3) + Vector3(Vector3(4, 5, 7))));
+ print_line("minus: " + (Vector3(1, 2, 3) - Vector3(Vector3(4, 5, 7))));
+ print_line("mul: " + (Vector3(1, 2, 3) * Vector3(Vector3(4, 5, 7))));
+ print_line("div: " + (Vector3(1, 2, 3) / Vector3(Vector3(4, 5, 7))));
+ print_line("mul scalar: " + (Vector3(1, 2, 3) * 2.0));
+ print_line("premul scalar: " + (2.0 * Vector3(1, 2, 3)));
+ print_line("div scalar: " + (Vector3(1, 2, 3) / 3.0));
+ print_line("length: " + rtos(Vector3(1, 2, 3).length()));
+ print_line("length squared: " + rtos(Vector3(1, 2, 3).length_squared()));
+ print_line("normalized: " + Vector3(1, 2, 3).normalized());
+ print_line("inverse: " + Vector3(1, 2, 3).inverse());
+
+ {
+ Vector3 v(4, 5, 7);
+ v.normalize();
+ print_line("normalize: " + v);
+ }
+
+ {
+ Vector3 v(4, 5, 7);
+ v += Vector3(1, 2, 3);
+ print_line("+=: " + v);
+ }
+
+ {
+ Vector3 v(4, 5, 7);
+ v -= Vector3(1, 2, 3);
+ print_line("-=: " + v);
+ }
+
+ {
+ Vector3 v(4, 5, 7);
+ v *= Vector3(1, 2, 3);
+ print_line("*=: " + v);
+ }
+
+ {
+ Vector3 v(4, 5, 7);
+ v /= Vector3(1, 2, 3);
+ print_line("/=: " + v);
+ }
+
+ {
+ Vector3 v(4, 5, 7);
+ v *= 2.0;
+ print_line("scalar *=: " + v);
+ }
+
+ {
+ Vector3 v(4, 5, 7);
+ v /= 2.0;
+ print_line("scalar /=: " + v);
+ }
+
+ return nullptr;
+}
+
+} // namespace TestMath
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