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#include "CubicUtilities.h"
#include "Intersection_Tests.h"
#include "QuadraticUtilities.h"
#include "QuarticRoot.h"
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(bool limit) {
// (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];
double B = rootB[bIndex];
double C = rootC[cIndex];
if (limit) {
B = (B - 6) / 12;
C = (C - 6) / 12;
}
const double b = A * (B + C);
const double c = A * B * C;
double roots[2];
const int rootCount = limit ? quadraticRootsValidT(A, b, c, roots)
: quadraticRootsReal(A, b, c, roots);
int expected;
if (limit) {
expected = B <= 0 && B >= -1;
expected += B != C && C <= 0 && C >= -1;
} else {
expected = 1 + (B != C);
}
SkASSERT(rootCount == expected);
if (!rootCount) {
continue;
}
SkASSERT(approximately_equal(roots[0], -B)
|| approximately_equal(roots[0], -C));
if (expected > 1) {
SkASSERT(!approximately_equal(roots[0], roots[1]));
SkASSERT(approximately_equal(roots[1], -B)
|| approximately_equal(roots[1], -C));
}
}
}
}
}
static void testOneCubic(bool limit, size_t aIndex, size_t bIndex, size_t cIndex, size_t dIndex) {
const double A = mulA[aIndex];
double B = rootB[bIndex];
double C = rootC[cIndex];
double D = rootD[dIndex];
if (limit) {
B = (B - 6) / 12;
C = (C - 6) / 12;
D = (C - 2) / 6;
}
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 = limit ? cubicRootsValidT(A, b, c, d, roots)
: cubicRootsReal(A, b, c, d, roots);
int expected;
if (limit) {
expected = B <= 0 && B >= -1;
expected += B != C && C <= 0 && C >= -1;
expected += B != D && C != D && D <= 0 && D >= -1;
} else {
expected = 1 + (B != C) + (B != D && C != D);
}
SkASSERT(rootCount == expected);
if (!rootCount) {
return;
}
SkASSERT(approximately_equal(roots[0], -B)
|| approximately_equal(roots[0], -C)
|| approximately_equal(roots[0], -D));
if (expected <= 1) {
return;
}
SkASSERT(!approximately_equal(roots[0], roots[1]));
SkASSERT(approximately_equal(roots[1], -B)
|| approximately_equal(roots[1], -C)
|| approximately_equal(roots[1], -D));
if (expected <= 2) {
return;
}
SkASSERT(!approximately_equal(roots[0], roots[2])
&& !approximately_equal(roots[1], roots[2]));
SkASSERT(approximately_equal(roots[2], -B)
|| approximately_equal(roots[2], -C)
|| approximately_equal(roots[2], -D));
}
static void cubicTest(bool limit) {
// (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) {
testOneCubic(limit, aIndex, bIndex, cIndex, dIndex);
}
}
}
}
}
static void testOneQuartic(size_t aIndex, size_t bIndex, size_t cIndex, size_t dIndex,
size_t 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];
bool oneHint = approximately_zero(A + b + c + d + e);
int rootCount = reducedQuarticRoots(A, b, c, d, e, oneHint, roots);
if (rootCount < 0) {
rootCount = quarticRootsReal(0, A, b, c, d, e, roots);
}
const int expected = 1 + (B != C) + (B != D && C != D) + (B != E && C != E && D != E);
SkASSERT(rootCount == expected);
SkASSERT(AlmostEqualUlps(roots[0], -B)
|| AlmostEqualUlps(roots[0], -C)
|| AlmostEqualUlps(roots[0], -D)
|| AlmostEqualUlps(roots[0], -E));
if (expected <= 1) {
return;
}
SkASSERT(!AlmostEqualUlps(roots[0], roots[1]));
SkASSERT(AlmostEqualUlps(roots[1], -B)
|| AlmostEqualUlps(roots[1], -C)
|| AlmostEqualUlps(roots[1], -D)
|| AlmostEqualUlps(roots[1], -E));
if (expected <= 2) {
return;
}
SkASSERT(!AlmostEqualUlps(roots[0], roots[2])
&& !AlmostEqualUlps(roots[1], roots[2]));
SkASSERT(AlmostEqualUlps(roots[2], -B)
|| AlmostEqualUlps(roots[2], -C)
|| AlmostEqualUlps(roots[2], -D)
|| AlmostEqualUlps(roots[2], -E));
if (expected <= 3) {
return;
}
SkASSERT(!AlmostEqualUlps(roots[0], roots[3])
&& !AlmostEqualUlps(roots[1], roots[3])
&& !AlmostEqualUlps(roots[2], roots[3]));
SkASSERT(AlmostEqualUlps(roots[3], -B)
|| AlmostEqualUlps(roots[3], -C)
|| AlmostEqualUlps(roots[3], -D)
|| AlmostEqualUlps(roots[3], -E));
}
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) {
testOneQuartic(aIndex, bIndex, cIndex, dIndex, eIndex);
}
}
}
}
}
}
void QuarticRoot_Test() {
testOneCubic(false, 0, 5, 5, 4);
testOneQuartic(0, 0, 2, 4, 3);
quadraticTest(true);
quadraticTest(false);
cubicTest(true);
cubicTest(false);
quarticTest();
}
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