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skia2/tests/WangsFormulaTest.cpp
Chris Dalton f6bf516926 Reland "Add an implementation and log2 variants for Wang's formula" 
This is a reland of e278e1c1c7

Original change's description:
> Add an implementation and log2 variants for Wang's formula
>
> Wang's formulas for cubics and quadratics (1985) tell us how many line
> segments a curve must be chopped into when tessellating. This CL adds
> an implementation along with optimized log2 variants, as well as tests
> and a benchmark.
>
> Change-Id: I3f777b8d0312c57c3a1cc24307de5945c70be287
> Reviewed-on: https://skia-review.googlesource.com/c/skia/+/288321
> Reviewed-by: Brian Salomon <bsalomon@google.com>
> Commit-Queue: Chris Dalton <csmartdalton@google.com>

TBR=bsalomon@google.com

Change-Id: Ie3822c62439fc579a59ea8adb49583224de41aa5
Reviewed-on: https://skia-review.googlesource.com/c/skia/+/289680
Reviewed-by: Chris Dalton <csmartdalton@google.com>
Commit-Queue: Chris Dalton <csmartdalton@google.com>
2020-05-14 02:57:59 +00:00

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/*
* Copyright 2020 Google Inc.
*
* Use of this source code is governed by a BSD-style license that can be
* found in the LICENSE file.
*/
#include "include/utils/SkRandom.h"
#include "src/core/SkGeometry.h"
#include "src/gpu/tessellate/GrWangsFormula.h"
#include "tests/Test.h"
constexpr static int kIntolerance = 4; // 1/4 pixel max error.
const SkPoint kSerp[4] = {
{285.625f, 499.687f}, {411.625f, 808.188f}, {1064.62f, 135.688f}, {1042.63f, 585.187f}};
const SkPoint kLoop[4] = {
{635.625f, 614.687f}, {171.625f, 236.188f}, {1064.62f, 135.688f}, {516.625f, 570.187f}};
const SkPoint kQuad[4] = {
{460.625f, 557.187f}, {707.121f, 209.688f}, {779.628f, 577.687f}};
DEF_TEST(WangsFormula_nextlog2, r) {
REPORTER_ASSERT(r, GrWangsFormula::nextlog2(-std::numeric_limits<float>::infinity()) == 0);
REPORTER_ASSERT(r, GrWangsFormula::nextlog2(-std::numeric_limits<float>::max()) == 0);
REPORTER_ASSERT(r, GrWangsFormula::nextlog2(-1000.0f) == 0);
REPORTER_ASSERT(r, GrWangsFormula::nextlog2(-0.1f) == 0);
REPORTER_ASSERT(r, GrWangsFormula::nextlog2(-std::numeric_limits<float>::min()) == 0);
REPORTER_ASSERT(r, GrWangsFormula::nextlog2(-std::numeric_limits<float>::denorm_min()) == 0);
REPORTER_ASSERT(r, GrWangsFormula::nextlog2(0.0f) == 0);
REPORTER_ASSERT(r, GrWangsFormula::nextlog2(std::numeric_limits<float>::denorm_min()) == 0);
REPORTER_ASSERT(r, GrWangsFormula::nextlog2(std::numeric_limits<float>::min()) == 0);
REPORTER_ASSERT(r, GrWangsFormula::nextlog2(0.1f) == 0);
REPORTER_ASSERT(r, GrWangsFormula::nextlog2(1.0f) == 0);
REPORTER_ASSERT(r, GrWangsFormula::nextlog2(1.1f) == 1);
REPORTER_ASSERT(r, GrWangsFormula::nextlog2(2.0f) == 1);
REPORTER_ASSERT(r, GrWangsFormula::nextlog2(2.1f) == 2);
REPORTER_ASSERT(r, GrWangsFormula::nextlog2(3.0f) == 2);
REPORTER_ASSERT(r, GrWangsFormula::nextlog2(3.1f) == 2);
REPORTER_ASSERT(r, GrWangsFormula::nextlog2(4.0f) == 2);
REPORTER_ASSERT(r, GrWangsFormula::nextlog2(4.1f) == 3);
REPORTER_ASSERT(r, GrWangsFormula::nextlog2(5.0f) == 3);
REPORTER_ASSERT(r, GrWangsFormula::nextlog2(5.1f) == 3);
REPORTER_ASSERT(r, GrWangsFormula::nextlog2(6.0f) == 3);
REPORTER_ASSERT(r, GrWangsFormula::nextlog2(6.1f) == 3);
REPORTER_ASSERT(r, GrWangsFormula::nextlog2(7.0f) == 3);
REPORTER_ASSERT(r, GrWangsFormula::nextlog2(7.1f) == 3);
REPORTER_ASSERT(r, GrWangsFormula::nextlog2(8.0f) == 3);
REPORTER_ASSERT(r, GrWangsFormula::nextlog2(8.1f) == 4);
REPORTER_ASSERT(r, GrWangsFormula::nextlog2(9.0f) == 4);
REPORTER_ASSERT(r, GrWangsFormula::nextlog2(9.1f) == 4);
REPORTER_ASSERT(r, GrWangsFormula::nextlog2(std::numeric_limits<float>::max()) == 128);
REPORTER_ASSERT(r, GrWangsFormula::nextlog2(std::numeric_limits<float>::infinity()) > 0);
REPORTER_ASSERT(r, GrWangsFormula::nextlog2(std::numeric_limits<float>::quiet_NaN()) >= 0);
for (int i = 0; i < 100; ++i) {
float pow2 = std::ldexp(1, i);
float epsilon = std::ldexp(SK_ScalarNearlyZero, i);
REPORTER_ASSERT(r, GrWangsFormula::nextlog2(pow2) == i);
REPORTER_ASSERT(r, GrWangsFormula::nextlog2(pow2 + epsilon) == i + 1);
REPORTER_ASSERT(r, GrWangsFormula::nextlog2(pow2 - epsilon) == i);
}
}
void for_random_matrices(SkRandom* rand, std::function<void(const SkMatrix&)> f) {
SkMatrix m;
m.setIdentity();
f(m);
for (int i = -10; i <= 30; ++i) {
for (int j = -10; j <= 30; ++j) {
m.setScaleX(std::ldexp(1 + rand->nextF(), i));
m.setSkewX(0);
m.setSkewY(0);
m.setScaleY(std::ldexp(1 + rand->nextF(), j));
f(m);
m.setScaleX(std::ldexp(1 + rand->nextF(), i));
m.setSkewX(std::ldexp(1 + rand->nextF(), (j + i) / 2));
m.setSkewY(std::ldexp(1 + rand->nextF(), (j + i) / 2));
m.setScaleY(std::ldexp(1 + rand->nextF(), j));
f(m);
}
}
}
void for_random_beziers(int numPoints, SkRandom* rand, std::function<void(const SkPoint[])> f) {
SkASSERT(numPoints <= 4);
SkPoint pts[4];
for (int i = -10; i <= 30; ++i) {
for (int j = 0; j < numPoints; ++j) {
pts[j].set(std::ldexp(1 + rand->nextF(), i), std::ldexp(1 + rand->nextF(), i));
}
f(pts);
}
}
// Ensure the optimized "*_log2" versions return the same value as ceil(std::log2(f)).
DEF_TEST(WangsFormula_log2, r) {
// Constructs a cubic such that the 'length' term in wang's formula == term.
//
// f = sqrt(k * length(max(abs(p0 - p1*2 + p2),
// abs(p1 - p2*2 + p3))));
auto setupCubicLengthTerm = [](int seed, SkPoint pts[], float term) {
memset(pts, 0, sizeof(SkPoint) * 4);
SkPoint term2d = (seed & 1) ?
SkPoint::Make(term, 0) : SkPoint::Make(.5f, std::sqrt(3)/2) * term;
seed >>= 1;
if (seed & 1) {
term2d.fX = -term2d.fX;
}
seed >>= 1;
if (seed & 1) {
std::swap(term2d.fX, term2d.fY);
}
seed >>= 1;
switch (seed % 4) {
case 0:
pts[0] = term2d;
pts[3] = term2d * .75f;
return;
case 1:
pts[1] = term2d * -.5f;
return;
case 2:
pts[1] = term2d * -.5f;
return;
case 3:
pts[3] = term2d;
pts[0] = term2d * .75f;
return;
}
};
// Constructs a quadratic such that the 'length' term in wang's formula == term.
//
// f = sqrt(k * length(p0 - p1*2 + p2));
auto setupQuadraticLengthTerm = [](int seed, SkPoint pts[], float term) {
memset(pts, 0, sizeof(SkPoint) * 3);
SkPoint term2d = (seed & 1) ?
SkPoint::Make(term, 0) : SkPoint::Make(.5f, std::sqrt(3)/2) * term;
seed >>= 1;
if (seed & 1) {
term2d.fX = -term2d.fX;
}
seed >>= 1;
if (seed & 1) {
std::swap(term2d.fX, term2d.fY);
}
seed >>= 1;
switch (seed % 3) {
case 0:
pts[0] = term2d;
return;
case 1:
pts[1] = term2d * -.5f;
return;
case 2:
pts[2] = term2d;
return;
}
};
for (int level = 0; level < 30; ++level) {
float epsilon = std::ldexp(SK_ScalarNearlyZero, level * 2);
SkPoint pts[4];
{
// Test cubic boundaries.
// f = sqrt(k * length(max(abs(p0 - p1*2 + p2),
// abs(p1 - p2*2 + p3))));
constexpr static float k = (3 * 2) / (8 * (1.f/kIntolerance));
float x = std::ldexp(1, level * 2) / k;
setupCubicLengthTerm(level << 1, pts, x - epsilon);
REPORTER_ASSERT(r,
std::ceil(std::log2(GrWangsFormula::cubic(kIntolerance, pts))) == level);
REPORTER_ASSERT(r, GrWangsFormula::cubic_log2(kIntolerance, pts) == level);
setupCubicLengthTerm(level << 1, pts, x + epsilon);
REPORTER_ASSERT(r,
std::ceil(std::log2(GrWangsFormula::cubic(kIntolerance, pts))) == level + 1);
REPORTER_ASSERT(r, GrWangsFormula::cubic_log2(kIntolerance, pts) == level + 1);
}
{
// Test quadratic boundaries.
// f = std::sqrt(k * Length(p0 - p1*2 + p2));
constexpr static float k = 2 / (8 * (1.f/kIntolerance));
float x = std::ldexp(1, level * 2) / k;
setupQuadraticLengthTerm(level << 1, pts, x - epsilon);
REPORTER_ASSERT(r,
std::ceil(std::log2(GrWangsFormula::quadratic(kIntolerance, pts))) == level);
REPORTER_ASSERT(r, GrWangsFormula::quadratic_log2(kIntolerance, pts) == level);
setupQuadraticLengthTerm(level << 1, pts, x + epsilon);
REPORTER_ASSERT(r,
std::ceil(std::log2(GrWangsFormula::quadratic(kIntolerance, pts))) == level+1);
REPORTER_ASSERT(r, GrWangsFormula::quadratic_log2(kIntolerance, pts) == level + 1);
}
}
auto check_cubic_log2 = [&](const SkPoint* pts) {
float f = std::max(1.f, GrWangsFormula::cubic(kIntolerance, pts));
int f_log2 = GrWangsFormula::cubic_log2(kIntolerance, pts);
REPORTER_ASSERT(r, SkScalarCeilToInt(std::log2(f)) == f_log2);
};
auto check_quadratic_log2 = [&](const SkPoint* pts) {
float f = std::max(1.f, GrWangsFormula::quadratic(kIntolerance, pts));
int f_log2 = GrWangsFormula::quadratic_log2(kIntolerance, pts);
REPORTER_ASSERT(r, SkScalarCeilToInt(std::log2(f)) == f_log2);
};
SkRandom rand;
for_random_matrices(&rand, [&](const SkMatrix& m) {
SkPoint pts[4];
m.mapPoints(pts, kSerp, 4);
check_cubic_log2(pts);
m.mapPoints(pts, kLoop, 4);
check_cubic_log2(pts);
m.mapPoints(pts, kQuad, 3);
check_quadratic_log2(pts);
});
for_random_beziers(4, &rand, [&](const SkPoint pts[]) {
check_cubic_log2(pts);
});
for_random_beziers(3, &rand, [&](const SkPoint pts[]) {
check_quadratic_log2(pts);
});
}
// Ensure using transformations gives the same result as pre-transforming all points.
DEF_TEST(WangsFormula_vectorXforms, r) {
auto check_cubic_log2_with_transform = [&](const SkPoint* pts, const SkMatrix& m){
SkPoint ptsXformed[4];
m.mapPoints(ptsXformed, pts, 4);
int expected = GrWangsFormula::cubic_log2(kIntolerance, ptsXformed);
int actual = GrWangsFormula::cubic_log2(kIntolerance, pts, GrVectorXform(m));
REPORTER_ASSERT(r, actual == expected);
};
auto check_quadratic_log2_with_transform = [&](const SkPoint* pts, const SkMatrix& m) {
SkPoint ptsXformed[3];
m.mapPoints(ptsXformed, pts, 3);
int expected = GrWangsFormula::quadratic_log2(kIntolerance, ptsXformed);
int actual = GrWangsFormula::quadratic_log2(kIntolerance, pts, GrVectorXform(m));
REPORTER_ASSERT(r, actual == expected);
};
SkRandom rand;
for_random_matrices(&rand, [&](const SkMatrix& m) {
check_cubic_log2_with_transform(kSerp, m);
check_cubic_log2_with_transform(kLoop, m);
check_quadratic_log2_with_transform(kQuad, m);
for_random_beziers(4, &rand, [&](const SkPoint pts[]) {
check_cubic_log2_with_transform(pts, m);
});
for_random_beziers(3, &rand, [&](const SkPoint pts[]) {
check_quadratic_log2_with_transform(pts, m);
});
});
}
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