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#include <assert.h>
#include <math.h>
#include "CubicUtilities.h"
#include "Intersection_Tests.h"
namespace QuarticRootTest {
#include "QuarticRoot.cpp"
}
double mulA[] = {-3, -1, 1, 3};
size_t mulACount = sizeof(mulA) / sizeof(mulA[0]);
double rootB[] = {-9, -6, -3, -1, 0, 1, 3, 6, 9};
size_t rootBCount = sizeof(rootB) / sizeof(rootB[0]);
double rootC[] = {-8, -6, -2, -1, 0, 1, 2, 6, 8};
size_t rootCCount = sizeof(rootC) / sizeof(rootC[0]);
double rootD[] = {-7, -4, -1, 0, 1, 2, 5};
size_t rootDCount = sizeof(rootD) / sizeof(rootD[0]);
double rootE[] = {-5, -1, 0, 1, 7};
size_t rootECount = sizeof(rootE) / sizeof(rootE[0]);
static void quadraticTest() {
// (x - a)(x - b) == x^2 - (a + b)x + ab
for (size_t aIndex = 0; aIndex < mulACount; ++aIndex) {
for (size_t bIndex = 0; bIndex < rootBCount; ++bIndex) {
for (size_t cIndex = 0; cIndex < rootCCount; ++cIndex) {
const double A = mulA[aIndex];
const double B = rootB[bIndex];
const double C = rootC[cIndex];
const double b = A * (B + C);
const double c = A * B * C;
double roots[2];
const int rootCount = QuarticRootTest::quadraticRootsX(A, b, c, roots);
const int expected = 1 + (B != C);
assert(rootCount == expected);
assert(approximately_equal(roots[0], -B)
|| approximately_equal(roots[0], -C));
if (B != C) {
assert(!approximately_equal(roots[0], roots[1]));
assert(approximately_equal(roots[1], -B)
|| approximately_equal(roots[1], -C));
}
}
}
}
}
static void cubicTest() {
// (x - a)(x - b)(x - c) == x^3 - (a + b + c)x^2 + (ab + bc + ac)x - abc
for (size_t aIndex = 0; aIndex < mulACount; ++aIndex) {
for (size_t bIndex = 0; bIndex < rootBCount; ++bIndex) {
for (size_t cIndex = 0; cIndex < rootCCount; ++cIndex) {
for (size_t dIndex = 0; dIndex < rootDCount; ++dIndex) {
const double A = mulA[aIndex];
const double B = rootB[bIndex];
const double C = rootC[cIndex];
const double D = rootD[dIndex];
const double b = A * (B + C + D);
const double c = A * (B * C + C * D + B * D);
const double d = A * B * C * D;
double roots[3];
const int rootCount = QuarticRootTest::cubicRootsX(A, b, c, d, roots);
const int expected = 1 + (B != C) + (B != D && C != D);
assert(rootCount == expected);
assert(approximately_equal(roots[0], -B)
|| approximately_equal(roots[0], -C)
|| approximately_equal(roots[0], -D));
if (expected > 1) {
assert(!approximately_equal(roots[0], roots[1]));
assert(approximately_equal(roots[1], -B)
|| approximately_equal(roots[1], -C)
|| approximately_equal(roots[1], -D));
if (expected > 2) {
assert(!approximately_equal(roots[0], roots[2])
&& !approximately_equal(roots[1], roots[2]));
assert(approximately_equal(roots[2], -B)
|| approximately_equal(roots[2], -C)
|| approximately_equal(roots[2], -D));
}
}
}
}
}
}
}
static void quarticTest() {
// (x - a)(x - b)(x - c)(x - d) == x^4 - (a + b + c + d)x^3
// + (ab + bc + cd + ac + bd + cd)x^2 - (abc + bcd + abd + acd) * x + abcd
for (size_t aIndex = 0; aIndex < mulACount; ++aIndex) {
for (size_t bIndex = 0; bIndex < rootBCount; ++bIndex) {
for (size_t cIndex = 0; cIndex < rootCCount; ++cIndex) {
for (size_t dIndex = 0; dIndex < rootDCount; ++dIndex) {
for (size_t eIndex = 0; eIndex < rootECount; ++eIndex) {
const double A = mulA[aIndex];
const double B = rootB[bIndex];
const double C = rootC[cIndex];
const double D = rootD[dIndex];
const double E = rootE[eIndex];
const double b = A * (B + C + D + E);
const double c = A * (B * C + C * D + B * D + B * E + C * E + D * E);
const double d = A * (B * C * D + B * C * E + B * D * E + C * D * E);
const double e = A * B * C * D * E;
double roots[4];
const int rootCount = QuarticRootTest::quarticRoots(A, b, c, d, e, roots);
const int expected = 1 + (B != C) + (B != D && C != D) + (B != E && C != E && D != E);
assert(rootCount == expected);
assert(approximately_equal(roots[0], -B)
|| approximately_equal(roots[0], -C)
|| approximately_equal(roots[0], -D)
|| approximately_equal(roots[0], -E));
if (expected > 1) {
assert(!approximately_equal(roots[0], roots[1]));
assert(approximately_equal(roots[1], -B)
|| approximately_equal(roots[1], -C)
|| approximately_equal(roots[1], -D)
|| approximately_equal(roots[1], -E));
if (expected > 2) {
assert(!approximately_equal(roots[0], roots[2])
&& !approximately_equal(roots[1], roots[2]));
assert(approximately_equal(roots[2], -B)
|| approximately_equal(roots[2], -C)
|| approximately_equal(roots[2], -D)
|| approximately_equal(roots[2], -E));
if (expected > 3) {
assert(!approximately_equal(roots[0], roots[3])
&& !approximately_equal(roots[1], roots[3])
&& !approximately_equal(roots[2], roots[3]));
assert(approximately_equal(roots[3], -B)
|| approximately_equal(roots[3], -C)
|| approximately_equal(roots[3], -D)
|| approximately_equal(roots[3], -E));
}
}
}
}
}
}
}
}
}
void QuarticRoot_Test() {
quadraticTest();
cubicTest();
quarticTest();
}
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