tests/MatrixTest.cpp - platform/external/skqp - Gitiles


 /*
  * Copyright 2011 Google Inc.
  *
  * Use of this source code is governed by a BSD-style license that can be
  * found in the LICENSE file.
  */
 #include "Test.h"
 #include "SkMath.h"
 #include "SkMatrix.h"
 #include "SkRandom.h"

 static bool nearly_equal_scalar(SkScalar a, SkScalar b) {
     // Note that we get more compounded error for multiple operations when
     // SK_SCALAR_IS_FIXED.
 #ifdef SK_SCALAR_IS_FLOAT
     const SkScalar tolerance = SK_Scalar1 / 200000;
 #else
     const SkScalar tolerance = SK_Scalar1 / 1024;
 #endif

     return SkScalarAbs(a - b) <= tolerance;
 }

 static bool nearly_equal(const SkMatrix& a, const SkMatrix& b) {
     for (int i = 0; i < 9; i++) {
         if (!nearly_equal_scalar(a[i], b[i])) {
             printf("not equal %g %g\n", (float)a[i], (float)b[i]);
             return false;
         }
     }
     return true;
 }

 static bool are_equal(skiatest::Reporter* reporter,
                       const SkMatrix& a,
                       const SkMatrix& b) {
     bool equal = a == b;
     bool cheapEqual = a.cheapEqualTo(b);
     if (equal != cheapEqual) {
 #if SK_SCALAR_IS_FLOAT
         if (equal) {
             bool foundZeroSignDiff = false;
             for (int i = 0; i < 9; ++i) {
                 float aVal = a.get(i);
                 float bVal = b.get(i);
                 int aValI = *reinterpret_cast<int*>(&aVal);
                 int bValI = *reinterpret_cast<int*>(&bVal);
                 if (0 == aVal && 0 == bVal && aValI != bValI) {
                     foundZeroSignDiff = true;
                 } else {
                     REPORTER_ASSERT(reporter, aVal == bVal && aValI == aValI);
                 }
             }
             REPORTER_ASSERT(reporter, foundZeroSignDiff);
         } else {
             bool foundNaN = false;
             for (int i = 0; i < 9; ++i) {
                 float aVal = a.get(i);
                 float bVal = b.get(i);
                 int aValI = *reinterpret_cast<int*>(&aVal);
                 int bValI = *reinterpret_cast<int*>(&bVal);
                 if (sk_float_isnan(aVal) && aValI == bValI) {
                     foundNaN = true;
                 } else {
                     REPORTER_ASSERT(reporter, aVal == bVal && aValI == bValI);
                 }
             }
             REPORTER_ASSERT(reporter, foundNaN);
         }
 #else
         REPORTER_ASSERT(reporter, false);
 #endif
     }
     return equal;
 }

 static bool is_identity(const SkMatrix& m) {
     SkMatrix identity;
     identity.reset();
     return nearly_equal(m, identity);
 }

 static void test_flatten(skiatest::Reporter* reporter, const SkMatrix& m) {
     // add 100 in case we have a bug, I don't want to kill my stack in the test
     char buffer[SkMatrix::kMaxFlattenSize + 100];
     uint32_t size1 = m.flatten(NULL);
     uint32_t size2 = m.flatten(buffer);
     REPORTER_ASSERT(reporter, size1 == size2);
     REPORTER_ASSERT(reporter, size1 <= SkMatrix::kMaxFlattenSize);

     SkMatrix m2;
     uint32_t size3 = m2.unflatten(buffer);
     REPORTER_ASSERT(reporter, size1 == size2);
     REPORTER_ASSERT(reporter, are_equal(reporter, m, m2));

     char buffer2[SkMatrix::kMaxFlattenSize + 100];
     size3 = m2.flatten(buffer2);
     REPORTER_ASSERT(reporter, size1 == size2);
     REPORTER_ASSERT(reporter, memcmp(buffer, buffer2, size1) == 0);
 }

 void test_matrix_max_stretch(skiatest::Reporter* reporter) {
     SkMatrix identity;
     identity.reset();
     REPORTER_ASSERT(reporter, SK_Scalar1 == identity.getMaxStretch());

     SkMatrix scale;
     scale.setScale(SK_Scalar1 * 2, SK_Scalar1 * 4);
     REPORTER_ASSERT(reporter, SK_Scalar1 * 4 == scale.getMaxStretch());

     SkMatrix rot90Scale;
     rot90Scale.setRotate(90 * SK_Scalar1);
     rot90Scale.postScale(SK_Scalar1 / 4, SK_Scalar1 / 2);
     REPORTER_ASSERT(reporter, SK_Scalar1 / 2 == rot90Scale.getMaxStretch());

     SkMatrix rotate;
     rotate.setRotate(128 * SK_Scalar1);
     REPORTER_ASSERT(reporter, SkScalarAbs(SK_Scalar1 - rotate.getMaxStretch()) <= SK_ScalarNearlyZero);

     SkMatrix translate;
     translate.setTranslate(10 * SK_Scalar1, -5 * SK_Scalar1);
     REPORTER_ASSERT(reporter, SK_Scalar1 == translate.getMaxStretch());

     SkMatrix perspX;
     perspX.reset();
     perspX.setPerspX(SkScalarToPersp(SK_Scalar1 / 1000));
     REPORTER_ASSERT(reporter, -SK_Scalar1 == perspX.getMaxStretch());

     SkMatrix perspY;
     perspY.reset();
     perspY.setPerspX(SkScalarToPersp(-SK_Scalar1 / 500));
     REPORTER_ASSERT(reporter, -SK_Scalar1 == perspY.getMaxStretch());

     SkMatrix baseMats[] = {scale, rot90Scale, rotate,
                            translate, perspX, perspY};
     SkMatrix mats[2*SK_ARRAY_COUNT(baseMats)];
     for (size_t i = 0; i < SK_ARRAY_COUNT(baseMats); ++i) {
         mats[i] = baseMats[i];
         bool invertable = mats[i].invert(&mats[i + SK_ARRAY_COUNT(baseMats)]);
         REPORTER_ASSERT(reporter, invertable);
     }
     SkRandom rand;
     for (int m = 0; m < 1000; ++m) {
         SkMatrix mat;
         mat.reset();
         for (int i = 0; i < 4; ++i) {
             int x = rand.nextU() % SK_ARRAY_COUNT(mats);
             mat.postConcat(mats[x]);
         }
         SkScalar stretch = mat.getMaxStretch();

         if ((stretch < 0) != mat.hasPerspective()) {
             stretch = mat.getMaxStretch();
         }

         REPORTER_ASSERT(reporter, (stretch < 0) == mat.hasPerspective());

         if (mat.hasPerspective()) {
             m -= 1; // try another non-persp matrix
             continue;
         }

         // test a bunch of vectors. None should be scaled by more than stretch
         // (modulo some error) and we should find a vector that is scaled by
         // almost stretch.
         static const SkScalar gStretchTol = (105 * SK_Scalar1) / 100;
         static const SkScalar gMaxStretchTol = (97 * SK_Scalar1) / 100;
         SkScalar max = 0;
         SkVector vectors[1000];
         for (size_t i = 0; i < SK_ARRAY_COUNT(vectors); ++i) {
             vectors[i].fX = rand.nextSScalar1();
             vectors[i].fY = rand.nextSScalar1();
             if (!vectors[i].normalize()) {
                 i -= 1;
                 continue;
             }
         }
         mat.mapVectors(vectors, SK_ARRAY_COUNT(vectors));
         for (size_t i = 0; i < SK_ARRAY_COUNT(vectors); ++i) {
             SkScalar d = vectors[i].length();
             REPORTER_ASSERT(reporter, SkScalarDiv(d, stretch) < gStretchTol);
             if (max < d) {
                 max = d;
             }
         }
         REPORTER_ASSERT(reporter, SkScalarDiv(max, stretch) >= gMaxStretchTol);
     }
 }

 // This function is extracted from src/gpu/SkGpuDevice.cpp,
 // in order to make sure this function works correctly.
 static bool isSimilarityTransformation(const SkMatrix& matrix,
                                        SkScalar tol = SK_ScalarNearlyZero) {
     if (matrix.isIdentity() || matrix.getType() == SkMatrix::kTranslate_Mask) {
         return true;
     }
     if (matrix.hasPerspective()) {
         return false;
     }

     SkScalar mx = matrix.get(SkMatrix::kMScaleX);
     SkScalar sx = matrix.get(SkMatrix::kMSkewX);
     SkScalar my = matrix.get(SkMatrix::kMScaleY);
     SkScalar sy = matrix.get(SkMatrix::kMSkewY);

     if (mx == 0 && sx == 0 && my == 0 && sy == 0) {
         return false;
     }

     // it has scales or skews, but it could also be rotation, check it out.
     SkVector vec[2];
     vec[0].set(mx, sx);
     vec[1].set(sy, my);

     return SkScalarNearlyZero(vec[0].dot(vec[1]), SkScalarSquare(tol)) &&
            SkScalarNearlyEqual(vec[0].lengthSqd(), vec[1].lengthSqd(),
                 SkScalarSquare(tol));
 }

 void test_matrix_is_similarity_transform(skiatest::Reporter* reporter) {
     SkMatrix mat;

     // identity
     mat.setIdentity();
     REPORTER_ASSERT(reporter, isSimilarityTransformation(mat));

     // translation only
     mat.reset();
     mat.setTranslate(SkIntToScalar(100), SkIntToScalar(100));
     REPORTER_ASSERT(reporter, isSimilarityTransformation(mat));

     // scale with same size
     mat.reset();
     mat.setScale(SkIntToScalar(15), SkIntToScalar(15));
     REPORTER_ASSERT(reporter, isSimilarityTransformation(mat));

     // scale with one negative
     mat.reset();
     mat.setScale(SkIntToScalar(-15), SkIntToScalar(15));
     REPORTER_ASSERT(reporter, isSimilarityTransformation(mat));

     // scale with different size
     mat.reset();
     mat.setScale(SkIntToScalar(15), SkIntToScalar(20));
     REPORTER_ASSERT(reporter, !isSimilarityTransformation(mat));

     // scale with same size at a pivot point
     mat.reset();
     mat.setScale(SkIntToScalar(15), SkIntToScalar(15),
                  SkIntToScalar(2), SkIntToScalar(2));
     REPORTER_ASSERT(reporter, isSimilarityTransformation(mat));

     // scale with different size at a pivot point
     mat.reset();
     mat.setScale(SkIntToScalar(15), SkIntToScalar(20),
                  SkIntToScalar(2), SkIntToScalar(2));
     REPORTER_ASSERT(reporter, !isSimilarityTransformation(mat));

     // skew with same size
     mat.reset();
     mat.setSkew(SkIntToScalar(15), SkIntToScalar(15));
     REPORTER_ASSERT(reporter, !isSimilarityTransformation(mat));

     // skew with different size
     mat.reset();
     mat.setSkew(SkIntToScalar(15), SkIntToScalar(20));
     REPORTER_ASSERT(reporter, !isSimilarityTransformation(mat));

     // skew with same size at a pivot point
     mat.reset();
     mat.setSkew(SkIntToScalar(15), SkIntToScalar(15),
                 SkIntToScalar(2), SkIntToScalar(2));
     REPORTER_ASSERT(reporter, !isSimilarityTransformation(mat));

     // skew with different size at a pivot point
     mat.reset();
     mat.setSkew(SkIntToScalar(15), SkIntToScalar(20),
                 SkIntToScalar(2), SkIntToScalar(2));
     REPORTER_ASSERT(reporter, !isSimilarityTransformation(mat));

     // perspective x
     mat.reset();
     mat.setPerspX(SkScalarToPersp(SK_Scalar1 / 2));
     REPORTER_ASSERT(reporter, !isSimilarityTransformation(mat));

     // perspective y
     mat.reset();
     mat.setPerspY(SkScalarToPersp(SK_Scalar1 / 2));
     REPORTER_ASSERT(reporter, !isSimilarityTransformation(mat));

 #if SK_SCALAR_IS_FLOAT
     /* We bypass the following tests for SK_SCALAR_IS_FIXED build.
      * The long discussion can be found in this issue:
      *     http://codereview.appspot.com/5999050/
      * In short, we haven't found a perfect way to fix the precision
      * issue, i.e. the way we use tolerance in isSimilarityTransformation
      * is incorrect. The situation becomes worse in fixed build, so
      * we disabled rotation related tests for fixed build.
      */

     // rotate
     for (int angle = 0; angle < 360; ++angle) {
         mat.reset();
         mat.setRotate(SkIntToScalar(angle));
         REPORTER_ASSERT(reporter, isSimilarityTransformation(mat));
     }

     // see if there are any accumulated precision issues
     mat.reset();
     for (int i = 1; i < 360; i++) {
         mat.postRotate(SkIntToScalar(1));
     }
     REPORTER_ASSERT(reporter, isSimilarityTransformation(mat));

     // rotate + translate
     mat.reset();
     mat.setRotate(SkIntToScalar(30));
     mat.postTranslate(SkIntToScalar(10), SkIntToScalar(20));
     REPORTER_ASSERT(reporter, isSimilarityTransformation(mat));

     // rotate + uniform scale
     mat.reset();
     mat.setRotate(SkIntToScalar(30));
     mat.postScale(SkIntToScalar(2), SkIntToScalar(2));
     REPORTER_ASSERT(reporter, isSimilarityTransformation(mat));

     // rotate + non-uniform scale
     mat.reset();
     mat.setRotate(SkIntToScalar(30));
     mat.postScale(SkIntToScalar(3), SkIntToScalar(2));
     REPORTER_ASSERT(reporter, !isSimilarityTransformation(mat));
 #endif

     // all zero
     mat.setAll(0, 0, 0, 0, 0, 0, 0, 0, 0);
     REPORTER_ASSERT(reporter, !isSimilarityTransformation(mat));

     // all zero except perspective
     mat.setAll(0, 0, 0, 0, 0, 0, 0, 0, SK_Scalar1);
     REPORTER_ASSERT(reporter, !isSimilarityTransformation(mat));

     // scales zero, only skews
     mat.setAll(0, SK_Scalar1, 0,
                SK_Scalar1, 0, 0,
                0, 0, SkMatrix::I()[8]);
     REPORTER_ASSERT(reporter, isSimilarityTransformation(mat));
 }

 void TestMatrix(skiatest::Reporter* reporter) {
     SkMatrix    mat, inverse, iden1, iden2;

     mat.reset();
     mat.setTranslate(SK_Scalar1, SK_Scalar1);
     REPORTER_ASSERT(reporter, mat.invert(&inverse));
     iden1.setConcat(mat, inverse);
     REPORTER_ASSERT(reporter, is_identity(iden1));

     mat.setScale(SkIntToScalar(2), SkIntToScalar(2));
     REPORTER_ASSERT(reporter, mat.invert(&inverse));
     iden1.setConcat(mat, inverse);
     REPORTER_ASSERT(reporter, is_identity(iden1));
     test_flatten(reporter, mat);

     mat.setScale(SK_Scalar1/2, SK_Scalar1/2);
     REPORTER_ASSERT(reporter, mat.invert(&inverse));
     iden1.setConcat(mat, inverse);
     REPORTER_ASSERT(reporter, is_identity(iden1));
     test_flatten(reporter, mat);

     mat.setScale(SkIntToScalar(3), SkIntToScalar(5), SkIntToScalar(20), 0);
     mat.postRotate(SkIntToScalar(25));
     REPORTER_ASSERT(reporter, mat.invert(NULL));
     REPORTER_ASSERT(reporter, mat.invert(&inverse));
     iden1.setConcat(mat, inverse);
     REPORTER_ASSERT(reporter, is_identity(iden1));
     iden2.setConcat(inverse, mat);
     REPORTER_ASSERT(reporter, is_identity(iden2));
     test_flatten(reporter, mat);
     test_flatten(reporter, iden2);

     // rectStaysRect test
     {
         static const struct {
             SkScalar    m00, m01, m10, m11;
             bool        mStaysRect;
         }
         gRectStaysRectSamples[] = {
             {          0,          0,          0,           0, false },
             {          0,          0,          0,  SK_Scalar1, false },
             {          0,          0, SK_Scalar1,           0, false },
             {          0,          0, SK_Scalar1,  SK_Scalar1, false },
             {          0, SK_Scalar1,          0,           0, false },
             {          0, SK_Scalar1,          0,  SK_Scalar1, false },
             {          0, SK_Scalar1, SK_Scalar1,           0, true },
             {          0, SK_Scalar1, SK_Scalar1,  SK_Scalar1, false },
             { SK_Scalar1,          0,          0,           0, false },
             { SK_Scalar1,          0,          0,  SK_Scalar1, true },
             { SK_Scalar1,          0, SK_Scalar1,           0, false },
             { SK_Scalar1,          0, SK_Scalar1,  SK_Scalar1, false },
             { SK_Scalar1, SK_Scalar1,          0,           0, false },
             { SK_Scalar1, SK_Scalar1,          0,  SK_Scalar1, false },
             { SK_Scalar1, SK_Scalar1, SK_Scalar1,           0, false },
             { SK_Scalar1, SK_Scalar1, SK_Scalar1,  SK_Scalar1, false }
         };

         for (size_t i = 0; i < SK_ARRAY_COUNT(gRectStaysRectSamples); i++) {
             SkMatrix    m;

             m.reset();
             m.set(SkMatrix::kMScaleX, gRectStaysRectSamples[i].m00);
             m.set(SkMatrix::kMSkewX,  gRectStaysRectSamples[i].m01);
             m.set(SkMatrix::kMSkewY,  gRectStaysRectSamples[i].m10);
             m.set(SkMatrix::kMScaleY, gRectStaysRectSamples[i].m11);
             REPORTER_ASSERT(reporter,
                     m.rectStaysRect() == gRectStaysRectSamples[i].mStaysRect);
         }
     }

     mat.reset();
     mat.set(SkMatrix::kMScaleX, SkIntToScalar(1));
     mat.set(SkMatrix::kMSkewX,  SkIntToScalar(2));
     mat.set(SkMatrix::kMTransX, SkIntToScalar(3));
     mat.set(SkMatrix::kMSkewY,  SkIntToScalar(4));
     mat.set(SkMatrix::kMScaleY, SkIntToScalar(5));
     mat.set(SkMatrix::kMTransY, SkIntToScalar(6));
     SkScalar affine[6];
     REPORTER_ASSERT(reporter, mat.asAffine(affine));

     #define affineEqual(e) affine[SkMatrix::kA##e] == mat.get(SkMatrix::kM##e)
     REPORTER_ASSERT(reporter, affineEqual(ScaleX));
     REPORTER_ASSERT(reporter, affineEqual(SkewY));
     REPORTER_ASSERT(reporter, affineEqual(SkewX));
     REPORTER_ASSERT(reporter, affineEqual(ScaleY));
     REPORTER_ASSERT(reporter, affineEqual(TransX));
     REPORTER_ASSERT(reporter, affineEqual(TransY));
     #undef affineEqual

     mat.set(SkMatrix::kMPersp1, SkScalarToPersp(SK_Scalar1 / 2));
     REPORTER_ASSERT(reporter, !mat.asAffine(affine));

     SkMatrix mat2;
     mat2.reset();
     mat.reset();
     SkScalar zero = 0;
     mat.set(SkMatrix::kMSkewX, -zero);
     REPORTER_ASSERT(reporter, are_equal(reporter, mat, mat2));

     mat2.reset();
     mat.reset();
     mat.set(SkMatrix::kMSkewX, SK_ScalarNaN);
     mat2.set(SkMatrix::kMSkewX, SK_ScalarNaN);
     // fixed pt doesn't have the property that NaN does not equal itself.
 #ifdef SK_SCALAR_IS_FIXED
     REPORTER_ASSERT(reporter, are_equal(reporter, mat, mat2));
 #else
     REPORTER_ASSERT(reporter, !are_equal(reporter, mat, mat2));
 #endif

     test_matrix_max_stretch(reporter);
     test_matrix_is_similarity_transform(reporter);
 }

 #include "TestClassDef.h"
 DEFINE_TESTCLASS("Matrix", MatrixTestClass, TestMatrix)

	/*
	* Copyright 2011 Google Inc.
	*
	* Use of this source code is governed by a BSD-style license that can be
	* found in the LICENSE file.
	*/
	#include "Test.h"
	#include "SkMath.h"
	#include "SkMatrix.h"
	#include "SkRandom.h"

	static bool nearly_equal_scalar(SkScalar a, SkScalar b) {
	// Note that we get more compounded error for multiple operations when
	// SK_SCALAR_IS_FIXED.
	#ifdef SK_SCALAR_IS_FLOAT
	const SkScalar tolerance = SK_Scalar1 / 200000;
	#else
	const SkScalar tolerance = SK_Scalar1 / 1024;
	#endif

	return SkScalarAbs(a - b) <= tolerance;
	}

	static bool nearly_equal(const SkMatrix& a, const SkMatrix& b) {
	for (int i = 0; i < 9; i++) {
	if (!nearly_equal_scalar(a[i], b[i])) {
	printf("not equal %g %g\n", (float)a[i], (float)b[i]);
	return false;
	}
	}
	return true;
	}

	static bool are_equal(skiatest::Reporter* reporter,
	const SkMatrix& a,
	const SkMatrix& b) {
	bool equal = a == b;
	bool cheapEqual = a.cheapEqualTo(b);
	if (equal != cheapEqual) {
	#if SK_SCALAR_IS_FLOAT
	if (equal) {
	bool foundZeroSignDiff = false;
	for (int i = 0; i < 9; ++i) {
	float aVal = a.get(i);
	float bVal = b.get(i);
	int aValI = reinterpret_cast<int>(&aVal);
	int bValI = reinterpret_cast<int>(&bVal);
	if (0 == aVal && 0 == bVal && aValI != bValI) {
	foundZeroSignDiff = true;
	} else {
	REPORTER_ASSERT(reporter, aVal == bVal && aValI == aValI);
	}
	}
	REPORTER_ASSERT(reporter, foundZeroSignDiff);
	} else {
	bool foundNaN = false;
	for (int i = 0; i < 9; ++i) {
	float aVal = a.get(i);
	float bVal = b.get(i);
	int aValI = reinterpret_cast<int>(&aVal);
	int bValI = reinterpret_cast<int>(&bVal);
	if (sk_float_isnan(aVal) && aValI == bValI) {
	foundNaN = true;
	} else {
	REPORTER_ASSERT(reporter, aVal == bVal && aValI == bValI);
	}
	}
	REPORTER_ASSERT(reporter, foundNaN);
	}
	#else
	REPORTER_ASSERT(reporter, false);
	#endif
	}
	return equal;
	}

	static bool is_identity(const SkMatrix& m) {
	SkMatrix identity;
	identity.reset();
	return nearly_equal(m, identity);
	}

	static void test_flatten(skiatest::Reporter* reporter, const SkMatrix& m) {
	// add 100 in case we have a bug, I don't want to kill my stack in the test
	char buffer[SkMatrix::kMaxFlattenSize + 100];
	uint32_t size1 = m.flatten(NULL);
	uint32_t size2 = m.flatten(buffer);
	REPORTER_ASSERT(reporter, size1 == size2);
	REPORTER_ASSERT(reporter, size1 <= SkMatrix::kMaxFlattenSize);

	SkMatrix m2;
	uint32_t size3 = m2.unflatten(buffer);
	REPORTER_ASSERT(reporter, size1 == size2);
	REPORTER_ASSERT(reporter, are_equal(reporter, m, m2));

	char buffer2[SkMatrix::kMaxFlattenSize + 100];
	size3 = m2.flatten(buffer2);
	REPORTER_ASSERT(reporter, size1 == size2);
	REPORTER_ASSERT(reporter, memcmp(buffer, buffer2, size1) == 0);
	}

	void test_matrix_max_stretch(skiatest::Reporter* reporter) {
	SkMatrix identity;
	identity.reset();
	REPORTER_ASSERT(reporter, SK_Scalar1 == identity.getMaxStretch());

	SkMatrix scale;
	scale.setScale(SK_Scalar1 * 2, SK_Scalar1 * 4);
	REPORTER_ASSERT(reporter, SK_Scalar1 * 4 == scale.getMaxStretch());

	SkMatrix rot90Scale;
	rot90Scale.setRotate(90 * SK_Scalar1);
	rot90Scale.postScale(SK_Scalar1 / 4, SK_Scalar1 / 2);
	REPORTER_ASSERT(reporter, SK_Scalar1 / 2 == rot90Scale.getMaxStretch());

	SkMatrix rotate;
	rotate.setRotate(128 * SK_Scalar1);
	REPORTER_ASSERT(reporter, SkScalarAbs(SK_Scalar1 - rotate.getMaxStretch()) <= SK_ScalarNearlyZero);

	SkMatrix translate;
	translate.setTranslate(10 * SK_Scalar1, -5 * SK_Scalar1);
	REPORTER_ASSERT(reporter, SK_Scalar1 == translate.getMaxStretch());

	SkMatrix perspX;
	perspX.reset();
	perspX.setPerspX(SkScalarToPersp(SK_Scalar1 / 1000));
	REPORTER_ASSERT(reporter, -SK_Scalar1 == perspX.getMaxStretch());

	SkMatrix perspY;
	perspY.reset();
	perspY.setPerspX(SkScalarToPersp(-SK_Scalar1 / 500));
	REPORTER_ASSERT(reporter, -SK_Scalar1 == perspY.getMaxStretch());

	SkMatrix baseMats[] = {scale, rot90Scale, rotate,
	translate, perspX, perspY};
	SkMatrix mats[2*SK_ARRAY_COUNT(baseMats)];
	for (size_t i = 0; i < SK_ARRAY_COUNT(baseMats); ++i) {
	mats[i] = baseMats[i];
	bool invertable = mats[i].invert(&mats[i + SK_ARRAY_COUNT(baseMats)]);
	REPORTER_ASSERT(reporter, invertable);
	}
	SkRandom rand;
	for (int m = 0; m < 1000; ++m) {
	SkMatrix mat;
	mat.reset();
	for (int i = 0; i < 4; ++i) {
	int x = rand.nextU() % SK_ARRAY_COUNT(mats);
	mat.postConcat(mats[x]);
	}
	SkScalar stretch = mat.getMaxStretch();

	if ((stretch < 0) != mat.hasPerspective()) {
	stretch = mat.getMaxStretch();
	}

	REPORTER_ASSERT(reporter, (stretch < 0) == mat.hasPerspective());

	if (mat.hasPerspective()) {
	m -= 1; // try another non-persp matrix
	continue;
	}

	// test a bunch of vectors. None should be scaled by more than stretch
	// (modulo some error) and we should find a vector that is scaled by
	// almost stretch.
	static const SkScalar gStretchTol = (105 * SK_Scalar1) / 100;
	static const SkScalar gMaxStretchTol = (97 * SK_Scalar1) / 100;
	SkScalar max = 0;
	SkVector vectors[1000];
	for (size_t i = 0; i < SK_ARRAY_COUNT(vectors); ++i) {
	vectors[i].fX = rand.nextSScalar1();
	vectors[i].fY = rand.nextSScalar1();
	if (!vectors[i].normalize()) {
	i -= 1;
	continue;
	}
	}
	mat.mapVectors(vectors, SK_ARRAY_COUNT(vectors));
	for (size_t i = 0; i < SK_ARRAY_COUNT(vectors); ++i) {
	SkScalar d = vectors[i].length();
	REPORTER_ASSERT(reporter, SkScalarDiv(d, stretch) < gStretchTol);
	if (max < d) {
	max = d;
	}
	}
	REPORTER_ASSERT(reporter, SkScalarDiv(max, stretch) >= gMaxStretchTol);
	}
	}

	// This function is extracted from src/gpu/SkGpuDevice.cpp,
	// in order to make sure this function works correctly.
	static bool isSimilarityTransformation(const SkMatrix& matrix,
	SkScalar tol = SK_ScalarNearlyZero) {
	if (matrix.isIdentity() \|\| matrix.getType() == SkMatrix::kTranslate_Mask) {
	return true;
	}
	if (matrix.hasPerspective()) {
	return false;
	}

	SkScalar mx = matrix.get(SkMatrix::kMScaleX);
	SkScalar sx = matrix.get(SkMatrix::kMSkewX);
	SkScalar my = matrix.get(SkMatrix::kMScaleY);
	SkScalar sy = matrix.get(SkMatrix::kMSkewY);

	if (mx == 0 && sx == 0 && my == 0 && sy == 0) {
	return false;
	}

	// it has scales or skews, but it could also be rotation, check it out.
	SkVector vec[2];
	vec[0].set(mx, sx);
	vec[1].set(sy, my);

	return SkScalarNearlyZero(vec[0].dot(vec[1]), SkScalarSquare(tol)) &&
	SkScalarNearlyEqual(vec[0].lengthSqd(), vec[1].lengthSqd(),
	SkScalarSquare(tol));
	}

	void test_matrix_is_similarity_transform(skiatest::Reporter* reporter) {
	SkMatrix mat;

	// identity
	mat.setIdentity();
	REPORTER_ASSERT(reporter, isSimilarityTransformation(mat));

	// translation only
	mat.reset();
	mat.setTranslate(SkIntToScalar(100), SkIntToScalar(100));
	REPORTER_ASSERT(reporter, isSimilarityTransformation(mat));

	// scale with same size
	mat.reset();
	mat.setScale(SkIntToScalar(15), SkIntToScalar(15));
	REPORTER_ASSERT(reporter, isSimilarityTransformation(mat));

	// scale with one negative
	mat.reset();
	mat.setScale(SkIntToScalar(-15), SkIntToScalar(15));
	REPORTER_ASSERT(reporter, isSimilarityTransformation(mat));

	// scale with different size
	mat.reset();
	mat.setScale(SkIntToScalar(15), SkIntToScalar(20));
	REPORTER_ASSERT(reporter, !isSimilarityTransformation(mat));

	// scale with same size at a pivot point
	mat.reset();
	mat.setScale(SkIntToScalar(15), SkIntToScalar(15),
	SkIntToScalar(2), SkIntToScalar(2));
	REPORTER_ASSERT(reporter, isSimilarityTransformation(mat));

	// scale with different size at a pivot point
	mat.reset();
	mat.setScale(SkIntToScalar(15), SkIntToScalar(20),
	SkIntToScalar(2), SkIntToScalar(2));
	REPORTER_ASSERT(reporter, !isSimilarityTransformation(mat));

	// skew with same size
	mat.reset();
	mat.setSkew(SkIntToScalar(15), SkIntToScalar(15));
	REPORTER_ASSERT(reporter, !isSimilarityTransformation(mat));

	// skew with different size
	mat.reset();
	mat.setSkew(SkIntToScalar(15), SkIntToScalar(20));
	REPORTER_ASSERT(reporter, !isSimilarityTransformation(mat));

	// skew with same size at a pivot point
	mat.reset();
	mat.setSkew(SkIntToScalar(15), SkIntToScalar(15),
	SkIntToScalar(2), SkIntToScalar(2));
	REPORTER_ASSERT(reporter, !isSimilarityTransformation(mat));

	// skew with different size at a pivot point
	mat.reset();
	mat.setSkew(SkIntToScalar(15), SkIntToScalar(20),
	SkIntToScalar(2), SkIntToScalar(2));
	REPORTER_ASSERT(reporter, !isSimilarityTransformation(mat));

	// perspective x
	mat.reset();
	mat.setPerspX(SkScalarToPersp(SK_Scalar1 / 2));
	REPORTER_ASSERT(reporter, !isSimilarityTransformation(mat));

	// perspective y
	mat.reset();
	mat.setPerspY(SkScalarToPersp(SK_Scalar1 / 2));
	REPORTER_ASSERT(reporter, !isSimilarityTransformation(mat));

	#if SK_SCALAR_IS_FLOAT
	/* We bypass the following tests for SK_SCALAR_IS_FIXED build.
	* The long discussion can be found in this issue:
	* http://codereview.appspot.com/5999050/
	* In short, we haven't found a perfect way to fix the precision
	* issue, i.e. the way we use tolerance in isSimilarityTransformation
	* is incorrect. The situation becomes worse in fixed build, so
	* we disabled rotation related tests for fixed build.
	*/

	// rotate
	for (int angle = 0; angle < 360; ++angle) {
	mat.reset();
	mat.setRotate(SkIntToScalar(angle));
	REPORTER_ASSERT(reporter, isSimilarityTransformation(mat));
	}

	// see if there are any accumulated precision issues
	mat.reset();
	for (int i = 1; i < 360; i++) {
	mat.postRotate(SkIntToScalar(1));
	}
	REPORTER_ASSERT(reporter, isSimilarityTransformation(mat));

	// rotate + translate
	mat.reset();
	mat.setRotate(SkIntToScalar(30));
	mat.postTranslate(SkIntToScalar(10), SkIntToScalar(20));
	REPORTER_ASSERT(reporter, isSimilarityTransformation(mat));

	// rotate + uniform scale
	mat.reset();
	mat.setRotate(SkIntToScalar(30));
	mat.postScale(SkIntToScalar(2), SkIntToScalar(2));
	REPORTER_ASSERT(reporter, isSimilarityTransformation(mat));

	// rotate + non-uniform scale
	mat.reset();
	mat.setRotate(SkIntToScalar(30));
	mat.postScale(SkIntToScalar(3), SkIntToScalar(2));
	REPORTER_ASSERT(reporter, !isSimilarityTransformation(mat));
	#endif

	// all zero
	mat.setAll(0, 0, 0, 0, 0, 0, 0, 0, 0);
	REPORTER_ASSERT(reporter, !isSimilarityTransformation(mat));

	// all zero except perspective
	mat.setAll(0, 0, 0, 0, 0, 0, 0, 0, SK_Scalar1);
	REPORTER_ASSERT(reporter, !isSimilarityTransformation(mat));

	// scales zero, only skews
	mat.setAll(0, SK_Scalar1, 0,
	SK_Scalar1, 0, 0,
	0, 0, SkMatrix::I()[8]);
	REPORTER_ASSERT(reporter, isSimilarityTransformation(mat));
	}

	void TestMatrix(skiatest::Reporter* reporter) {
	SkMatrix mat, inverse, iden1, iden2;

	mat.reset();
	mat.setTranslate(SK_Scalar1, SK_Scalar1);
	REPORTER_ASSERT(reporter, mat.invert(&inverse));
	iden1.setConcat(mat, inverse);
	REPORTER_ASSERT(reporter, is_identity(iden1));

	mat.setScale(SkIntToScalar(2), SkIntToScalar(2));
	REPORTER_ASSERT(reporter, mat.invert(&inverse));
	iden1.setConcat(mat, inverse);
	REPORTER_ASSERT(reporter, is_identity(iden1));
	test_flatten(reporter, mat);

	mat.setScale(SK_Scalar1/2, SK_Scalar1/2);
	REPORTER_ASSERT(reporter, mat.invert(&inverse));
	iden1.setConcat(mat, inverse);
	REPORTER_ASSERT(reporter, is_identity(iden1));
	test_flatten(reporter, mat);

	mat.setScale(SkIntToScalar(3), SkIntToScalar(5), SkIntToScalar(20), 0);
	mat.postRotate(SkIntToScalar(25));
	REPORTER_ASSERT(reporter, mat.invert(NULL));
	REPORTER_ASSERT(reporter, mat.invert(&inverse));
	iden1.setConcat(mat, inverse);
	REPORTER_ASSERT(reporter, is_identity(iden1));
	iden2.setConcat(inverse, mat);
	REPORTER_ASSERT(reporter, is_identity(iden2));
	test_flatten(reporter, mat);
	test_flatten(reporter, iden2);

	// rectStaysRect test
	{
	static const struct {
	SkScalar m00, m01, m10, m11;
	bool mStaysRect;
	}
	gRectStaysRectSamples[] = {
	{ 0, 0, 0, 0, false },
	{ 0, 0, 0, SK_Scalar1, false },
	{ 0, 0, SK_Scalar1, 0, false },
	{ 0, 0, SK_Scalar1, SK_Scalar1, false },
	{ 0, SK_Scalar1, 0, 0, false },
	{ 0, SK_Scalar1, 0, SK_Scalar1, false },
	{ 0, SK_Scalar1, SK_Scalar1, 0, true },
	{ 0, SK_Scalar1, SK_Scalar1, SK_Scalar1, false },
	{ SK_Scalar1, 0, 0, 0, false },
	{ SK_Scalar1, 0, 0, SK_Scalar1, true },
	{ SK_Scalar1, 0, SK_Scalar1, 0, false },
	{ SK_Scalar1, 0, SK_Scalar1, SK_Scalar1, false },
	{ SK_Scalar1, SK_Scalar1, 0, 0, false },
	{ SK_Scalar1, SK_Scalar1, 0, SK_Scalar1, false },
	{ SK_Scalar1, SK_Scalar1, SK_Scalar1, 0, false },
	{ SK_Scalar1, SK_Scalar1, SK_Scalar1, SK_Scalar1, false }
	};

	for (size_t i = 0; i < SK_ARRAY_COUNT(gRectStaysRectSamples); i++) {
	SkMatrix m;

	m.reset();
	m.set(SkMatrix::kMScaleX, gRectStaysRectSamples[i].m00);
	m.set(SkMatrix::kMSkewX, gRectStaysRectSamples[i].m01);
	m.set(SkMatrix::kMSkewY, gRectStaysRectSamples[i].m10);
	m.set(SkMatrix::kMScaleY, gRectStaysRectSamples[i].m11);
	REPORTER_ASSERT(reporter,
	m.rectStaysRect() == gRectStaysRectSamples[i].mStaysRect);
	}
	}

	mat.reset();
	mat.set(SkMatrix::kMScaleX, SkIntToScalar(1));
	mat.set(SkMatrix::kMSkewX, SkIntToScalar(2));
	mat.set(SkMatrix::kMTransX, SkIntToScalar(3));
	mat.set(SkMatrix::kMSkewY, SkIntToScalar(4));
	mat.set(SkMatrix::kMScaleY, SkIntToScalar(5));
	mat.set(SkMatrix::kMTransY, SkIntToScalar(6));
	SkScalar affine[6];
	REPORTER_ASSERT(reporter, mat.asAffine(affine));

	#define affineEqual(e) affine[SkMatrix::kA##e] == mat.get(SkMatrix::kM##e)
	REPORTER_ASSERT(reporter, affineEqual(ScaleX));
	REPORTER_ASSERT(reporter, affineEqual(SkewY));
	REPORTER_ASSERT(reporter, affineEqual(SkewX));
	REPORTER_ASSERT(reporter, affineEqual(ScaleY));
	REPORTER_ASSERT(reporter, affineEqual(TransX));
	REPORTER_ASSERT(reporter, affineEqual(TransY));
	#undef affineEqual

	mat.set(SkMatrix::kMPersp1, SkScalarToPersp(SK_Scalar1 / 2));
	REPORTER_ASSERT(reporter, !mat.asAffine(affine));

	SkMatrix mat2;
	mat2.reset();
	mat.reset();
	SkScalar zero = 0;
	mat.set(SkMatrix::kMSkewX, -zero);
	REPORTER_ASSERT(reporter, are_equal(reporter, mat, mat2));

	mat2.reset();
	mat.reset();
	mat.set(SkMatrix::kMSkewX, SK_ScalarNaN);
	mat2.set(SkMatrix::kMSkewX, SK_ScalarNaN);
	// fixed pt doesn't have the property that NaN does not equal itself.
	#ifdef SK_SCALAR_IS_FIXED
	REPORTER_ASSERT(reporter, are_equal(reporter, mat, mat2));
	#else
	REPORTER_ASSERT(reporter, !are_equal(reporter, mat, mat2));
	#endif

	test_matrix_max_stretch(reporter);
	test_matrix_is_similarity_transform(reporter);
	}

	#include "TestClassDef.h"
	DEFINE_TESTCLASS("Matrix", MatrixTestClass, TestMatrix)