blob: 95fe78c32db794dbb57d7010323c033861e320bf [file] [log] [blame]
/*
* Copyright 2023 Google LLC
*
* Use of this source code is governed by a BSD-style license that can be
* found in the LICENSE file.
*/
#include "include/core/SkSpan.h"
#include "include/core/SkTypes.h"
#include "include/private/base/SkFloatingPoint.h"
#include "src/base/SkQuads.h"
#include "src/pathops/SkPathOpsQuad.h"
#include "tests/Test.h"
#include <algorithm>
#include <cstddef>
#include <cfloat>
#include <cmath>
#include <iterator>
#include <string>
static void testQuadRootsReal(skiatest::Reporter* reporter, std::string name,
double A, double B, double C,
SkSpan<const double> expectedRoots) {
skiatest::ReporterContext subtest(reporter, name);
// Validate test case
REPORTER_ASSERT(reporter, expectedRoots.size() <= 2,
"Invalid test case, up to 2 roots allowed");
for (size_t i = 0; i < expectedRoots.size(); i++) {
double x = expectedRoots[i];
// A*x^2 + B*x + C should equal 0
double y = A * x * x + B * x + C;
REPORTER_ASSERT(reporter, sk_double_nearly_zero(y),
"Invalid test case root %zu. %.16f != 0", i, y);
if (i > 0) {
REPORTER_ASSERT(reporter, expectedRoots[i-1] <= expectedRoots[i],
"Invalid test case root %zu. Roots should be sorted in ascending order", i);
}
}
{
skiatest::ReporterContext subsubtest(reporter, "Pathops Implementation");
double roots[2] = {0, 0};
int rootCount = SkDQuad::RootsReal(A, B, C, roots);
REPORTER_ASSERT(reporter, expectedRoots.size() == size_t(rootCount),
"Wrong number of roots returned %zu != %d", expectedRoots.size(),
rootCount);
// We don't care which order the roots are returned from the algorithm.
// For determinism, we will sort them (and ensure the provided solutions are also sorted).
std::sort(std::begin(roots), std::begin(roots) + rootCount);
for (int i = 0; i < rootCount; i++) {
if (sk_double_nearly_zero(expectedRoots[i])) {
REPORTER_ASSERT(reporter, sk_double_nearly_zero(roots[i]),
"0 != %.16f at index %d", roots[i], i);
} else {
REPORTER_ASSERT(reporter,
sk_doubles_nearly_equal_ulps(expectedRoots[i], roots[i], 64),
"%.16f != %.16f at index %d", expectedRoots[i], roots[i], i);
}
}
}
{
skiatest::ReporterContext subsubtest(reporter, "SkQuads Implementation");
double roots[2] = {0, 0};
int rootCount = SkQuads::RootsReal(A, B, C, roots);
REPORTER_ASSERT(reporter, expectedRoots.size() == size_t(rootCount),
"Wrong number of roots returned %zu != %d", expectedRoots.size(),
rootCount);
// We don't care which order the roots are returned from the algorithm.
// For determinism, we will sort them (and ensure the provided solutions are also sorted).
std::sort(std::begin(roots), std::begin(roots) + rootCount);
for (int i = 0; i < rootCount; i++) {
if (sk_double_nearly_zero(expectedRoots[i])) {
REPORTER_ASSERT(reporter, sk_double_nearly_zero(roots[i]),
"0 != %.16f at index %d", roots[i], i);
} else {
REPORTER_ASSERT(reporter,
sk_doubles_nearly_equal_ulps(expectedRoots[i], roots[i], 64),
"%.16f != %.16f at index %d", expectedRoots[i], roots[i], i);
}
}
}
}
DEF_TEST(QuadRootsReal_ActualQuadratics, reporter) {
// All answers are given with 16 significant digits (max for a double) or as an integer
// when the answer is exact.
testQuadRootsReal(reporter, "two roots 3x^2 - 20x - 40",
3, -20, -40,
{-1.610798991397109,
//-1.610798991397108632474265 from Wolfram Alpha
8.277465658063775,
// 8.277465658063775299140932 from Wolfram Alpha
});
// (2x - 4)(x + 17)
testQuadRootsReal(reporter, "two roots 2x^2 + 30x - 68",
2, 30, -68,
{-17, 2});
testQuadRootsReal(reporter, "two roots x^2 - 5",
1, 0, -5,
{-2.236067977499790,
//-2.236067977499789696409174 from Wolfram Alpha
2.236067977499790,
// 2.236067977499789696409174 from Wolfram Alpha
});
testQuadRootsReal(reporter, "one root x^2 - 2x + 1",
1, -2, 1,
{1});
testQuadRootsReal(reporter, "no roots 5x^2 + 6x + 7",
5, 6, 7,
{});
testQuadRootsReal(reporter, "no roots 4x^2 + 1",
4, 0, 1,
{});
testQuadRootsReal(reporter, "one root is zero, another is big",
14, -13, 0,
{0,
0.9285714285714286
//0.9285714285714285714285714 from Wolfram Alpha
});
// Values from a failing test case observed during testing.
testQuadRootsReal(reporter, "one root is zero, another is small",
0.2929016490705016, 0.0000030451558069, 0,
{-0.00001039651301576329, 0});
testQuadRootsReal(reporter, "b and c are zero, a is positive 4x^2",
4, 0, 0,
{0});
testQuadRootsReal(reporter, "b and c are zero, a is negative -4x^2",
-4, 0, 0,
{0});
testQuadRootsReal(reporter, "a and b are huge, c is zero",
4.3719914983870202e+291, 1.0269509510194551e+152, 0,
// One solution is 0, the other is so close to zero it returns
// true for sk_double_nearly_zero, so it is collapsed into one.
{0});
}
DEF_TEST(QuadRootsReal_Linear, reporter) {
testQuadRootsReal(reporter, "positive slope 5x + 6",
0, 5, 6,
{-1.2});
testQuadRootsReal(reporter, "negative slope -3x - 9",
0, -3, -9,
{-3.});
}
DEF_TEST(QuadRootsReal_Constant, reporter) {
testQuadRootsReal(reporter, "No intersections y = -10",
0, 0, -10,
{});
testQuadRootsReal(reporter, "Infinite solutions y = 0",
0, 0, 0,
{0.});
}
DEF_TEST(QuadRootsReal_NonFiniteNumbers, reporter) {
// The Pathops implementation does not check for infinities nor nans in all cases.
double roots[2];
REPORTER_ASSERT(reporter,
SkQuads::RootsReal(DBL_MAX, 0, DBL_MAX, roots) == 0,
"Discriminant is negative infinity"
);
REPORTER_ASSERT(reporter,
SkQuads::RootsReal(1, DBL_MAX, 0, roots) == 0,
"Discriminant is positive infinity"
);
REPORTER_ASSERT(reporter,
SkQuads::RootsReal(DBL_MAX, DBL_MAX, DBL_MAX, roots) == 0,
"Double Overflow"
);
REPORTER_ASSERT(reporter,
SkQuads::RootsReal(1, NAN, -3, roots) == 0,
"Nan quadratic"
);
REPORTER_ASSERT(reporter,
SkQuads::RootsReal(0, NAN, 3, roots) == 0,
"Nan linear"
);
REPORTER_ASSERT(reporter,
SkQuads::RootsReal(0, 0, NAN, roots) == 0,
"Nan constant"
);
}