Deal with {und,ov}erflow issues in QLine's length handling

Use std::hypot() instead of sqrt() of a sum of squares.
This ensures length() can't be zero when isNull() is false.
Use length() in QLine::setLength() rather than duplicating that.

Clarify and expand some documentation; isNull() never said what
constituted validity, nor did unitVector() mention that is should not
be used on a line for which isNull() is true. Make clear that lines of
denormal length cannot be rescaled accurately.

Given that we use fuzzy comparison to determine equality of
end-points, isNull() can be false for a line with displacements less
than sqrt(numeric_limits<qreal>::denorm_min()) between the coordinates
of its end-points (as long as these are not much bigger); squaring
these would give zero, hence a zero length, where using hypot() avoids
the underflow and gives a non-zero length. Having a zero length for a
line with isNull() false would lead to problems in setLength(), which
uses an isNull() pre-test, protecting a call to unitVector().

(It was already possible for a null line to have non-zero length; this
now arises in more cases.)

Restored QLine::setLength() to the form it had before a recent change
to avoid division by zero (which resulted from underflow in computing
the length of a non-null line) but allow for the possibility that the
unit vector it computes as transient may not have length exactly one.

Add tests against {ov,und}erflow problems in QLine. Reworked the test
added during the divide-by-zero fix to make it part of the existing
test.

Pick-to: 5.15 5.12
Change-Id: I7b71d66b872ccc08a64e941acd36b45b0ea15fab
Reviewed-by: Sze Howe Koh <szehowe.koh@gmail.com>

1 files changed, 34 insertions, 24 deletions

diff --git a/tests/auto/corelib/tools/qline/tst_qline.cpp b/tests/auto/corelib/tools/qline/tst_qline.cpp
index 7e07e9d1e2..f4ac51fc24 100644
--- a/tests/auto/corelib/tools/qline/tst_qline.cpp
+++ b/tests/auto/corelib/tools/qline/tst_qline.cpp
@@ -40,8 +40,6 @@ private slots:
     void testLength();
     void testLength_data();
 
-    void testSetLength();
-
     void testCenter();
     void testCenter_data();
 
@@ -214,11 +212,13 @@ void tst_QLine::testLength_data()
     QTest::addColumn<double>("vx");
     QTest::addColumn<double>("vy");
 
-    QTest::newRow("[1,0]*2") << 0.0 << 0.0 << 1.0 << 0.0 << 1.0 << 2.0 << 2.0 << 0.0;
-    QTest::newRow("[0,1]*2") << 0.0 << 0.0 << 0.0 << 1.0 << 1.0 << 2.0 << 0.0 << 2.0;
-    QTest::newRow("[-1,0]*2") << 0.0 << 0.0 << -1.0 << 0.0 << 1.0 << 2.0 << -2.0 << 0.0;
-    QTest::newRow("[0,-1]*2") << 0.0 << 0.0 << 0.0 << -1.0 << 1.0 << 2.0 << 0.0 << -2.0;
-    QTest::newRow("[1,1]->|1|") << 0.0 << 0.0 << 1.0 << 1.0
+    // Test name: [dx,dy]->|lenToSet| (x1,x2)
+    // with the last part omitted if (0,0)
+    QTest::newRow("[1,0]->|2|") << 0.0 << 0.0 << 1.0 << 0.0 << 1.0 << 2.0 << 2.0 << 0.0;
+    QTest::newRow("[0,1]->|2|") << 0.0 << 0.0 << 0.0 << 1.0 << 1.0 << 2.0 << 0.0 << 2.0;
+    QTest::newRow("[-1,0]->|2|") << 0.0 << 0.0 << -1.0 << 0.0 << 1.0 << 2.0 << -2.0 << 0.0;
+    QTest::newRow("[0,-1]->|2|") << 0.0 << 0.0 << 0.0 << -1.0 << 1.0 << 2.0 << 0.0 << -2.0;
+    QTest::newRow("[1,1]->->|1|") << 0.0 << 0.0 << 1.0 << 1.0
                              << M_SQRT2 << 1.0 << M_SQRT1_2 << M_SQRT1_2;
     QTest::newRow("[-1,1]->|1|") << 0.0 << 0.0 << -1.0 << 1.0
                              << M_SQRT2 << 1.0 << -M_SQRT1_2 << M_SQRT1_2;
@@ -226,10 +226,10 @@ void tst_QLine::testLength_data()
                              << M_SQRT2 << 1.0 << M_SQRT1_2 << -M_SQRT1_2;
     QTest::newRow("[-1,-1]->|1|") << 0.0 << 0.0 << -1.0 << -1.0
                              << M_SQRT2 << 1.0 << -M_SQRT1_2 << -M_SQRT1_2;
-    QTest::newRow("[1,0]*2 (2,2)") << 2.0 << 2.0 << 3.0 << 2.0 << 1.0 << 2.0 << 2.0 << 0.0;
-    QTest::newRow("[0,1]*2 (2,2)") << 2.0 << 2.0 << 2.0 << 3.0 << 1.0 << 2.0 << 0.0 << 2.0;
-    QTest::newRow("[-1,0]*2 (2,2)") << 2.0 << 2.0 << 1.0 << 2.0 << 1.0 << 2.0 << -2.0 << 0.0;
-    QTest::newRow("[0,-1]*2 (2,2)") << 2.0 << 2.0 << 2.0 << 1.0 << 1.0 << 2.0 << 0.0 << -2.0;
+    QTest::newRow("[1,0]->|2| (2,2)") << 2.0 << 2.0 << 3.0 << 2.0 << 1.0 << 2.0 << 2.0 << 0.0;
+    QTest::newRow("[0,1]->|2| (2,2)") << 2.0 << 2.0 << 2.0 << 3.0 << 1.0 << 2.0 << 0.0 << 2.0;
+    QTest::newRow("[-1,0]->|2| (2,2)") << 2.0 << 2.0 << 1.0 << 2.0 << 1.0 << 2.0 << -2.0 << 0.0;
+    QTest::newRow("[0,-1]->|2| (2,2)") << 2.0 << 2.0 << 2.0 << 1.0 << 1.0 << 2.0 << 0.0 << -2.0;
     QTest::newRow("[1,1]->|1| (2,2)") << 2.0 << 2.0 << 3.0 << 3.0
                                    << M_SQRT2 << 1.0 << M_SQRT1_2 << M_SQRT1_2;
     QTest::newRow("[-1,1]->|1| (2,2)") << 2.0 << 2.0 << 1.0 << 3.0
@@ -238,6 +238,20 @@ void tst_QLine::testLength_data()
                                     << M_SQRT2 << 1.0 << M_SQRT1_2 << -M_SQRT1_2;
     QTest::newRow("[-1,-1]->|1| (2,2)") << 2.0 << 2.0 << 1.0 << 1.0
                                      << M_SQRT2 << 1.0 << -M_SQRT1_2 << -M_SQRT1_2;
+    const double small = qSqrt(std::numeric_limits<qreal>::denorm_min()) / 8;
+    QTest::newRow("[small,small]->|2| (-small/2,-small/2)")
+        << -(small * .5) << -(small * .5) << (small * .5) << (small * .5)
+        << (small * M_SQRT2) << (2 * M_SQRT2) << 2.0 << 2.0;
+    const double tiny = std::numeric_limits<qreal>::min() / 2;
+    QTest::newRow("[tiny,tiny]->|2| (-tiny/2,-tiny/2)")
+        << -(tiny * .5) << -(tiny * .5) << (tiny * .5) << (tiny * .5)
+        << (tiny * M_SQRT2) << (2 * M_SQRT2) << 2.0 << 2.0;
+    QTest::newRow("[1+3e-13,1+4e-13]|1895| (1, 1)")
+        << 1.0 << 1.0 << (1 + 3e-13) << (1 + 4e-13) // isNull(), so ignores setLength()
+        << 5e-13 << 1895.0 << 3e-13 << 4e-13;
+    QTest::newRow("[4e-323,5e-324]|1892|") // Unavoidable underflow: denormals
+        << 0.0 << 0.0 << 4e-323 << 5e-324
+        << 4e-323 << 1892.0 << 4e-323 << 5e-324; // vx, vy values ignored
 }
 
 void tst_QLine::testLength()
@@ -252,21 +266,17 @@ void tst_QLine::testLength()
     QFETCH(double, vy);
 
     QLineF l(x1, y1, x2, y2);
-    QCOMPARE(l.length(), qreal(length));
+    const bool wasNull = l.isNull();
+    if (!wasNull)
+        QCOMPARE(l.length(), qreal(length));
 
     l.setLength(lengthToSet);
-    QCOMPARE(l.length(), qreal(lengthToSet));
-    QCOMPARE(l.dx(), qreal(vx));
-    QCOMPARE(l.dy(), qreal(vy));
-}
-
-void tst_QLine::testSetLength()
-{
-    QLineF l(0, 0, 4e-323, 5e-324);
-    const qreal newLength = 1892;
-    const qreal oldLength = l.length();
-    l.setLength(newLength);
-    QCOMPARE(l.length(), oldLength ? newLength : 0);
+    QCOMPARE(l.length(), wasNull ? qreal(length) : qreal(lengthToSet));
+    // Scaling tiny values up to big can be imprecise: don't try to test vx, vy
+    if (wasNull || !qFuzzyIsNull(length)) {
+        QCOMPARE(l.dx(), qreal(vx));
+        QCOMPARE(l.dy(), qreal(vy));
+    }
 }
 
 void tst_QLine::testCenter()