tdf#143877 Fix failing tests caused by floating point precision

Due to different imlementation of floating-point unit (FPU),
on different CPU platforms, the floating point numbers could
could be different.
https://stackoverflow.com/questions/64036879/differing-floating-point-calculation-results-between-x86-64-and-armv8-2-a
https://mcuoneclipse.com/2019/03/29/be-aware-floating-point-operations-on-arm-cortex-m4f/

With this path I have changed the tested images,
to use floating point numbers which are easily represented
by floating numbers (multiplied/divided by 2), like:
- change tension to values: 0.125, 0.25, 0.5, 1.0, 1.5 ...
- change position of curve to of control points to 256.0, 384.0 512.0

Previous values was hard to represent by floating numbers,
for example tension:
- 0.4 has been written as 0.399999976158142
- 0.1 has been written as 0.099999994039535

More information:
https://observablehq.com/@benaubin/floating-point

Additionally the precision of numbers were
increased to double.

Change-Id: I5725c1f2f474d0c00821edaa9bb2102cb172093f
Reviewed-on: https://gerrit.libreoffice.org/c/core/+/152838
Reviewed-by: Stephan Bergmann <sbergman@redhat.com>
Tested-by: Bartosz Kosiorek <gang65@poczta.onet.pl>

1 files changed, 19 insertions, 23 deletions

diff --git a/drawinglayer/source/tools/emfppath.cxx b/drawinglayer/source/tools/emfppath.cxx
index bd5b2d357b0f..e7c4a5512c76 100644
--- a/drawinglayer/source/tools/emfppath.cxx
+++ b/drawinglayer/source/tools/emfppath.cxx
@@ -34,7 +34,12 @@ namespace
 
 namespace emfplushelper
 {
-    typedef float matrix [4][4];
+    typedef double matrix [4][4];
+
+    constexpr sal_uInt32 nDetails = 8;
+    constexpr double alpha[nDetails]
+        = { 1. / nDetails, 2. / nDetails, 3. / nDetails, 4. / nDetails,
+            5. / nDetails, 6. / nDetails, 7. / nDetails, 8. / nDetails };
 
     // see 2.2.2.21 EmfPlusInteger7
     //     2.2.2.22 EmfPlusInteger15
@@ -232,21 +237,20 @@ namespace emfplushelper
         m[0][2] = tension - 2.;
         m[1][0] = 2. * tension;
         m[1][1] = tension - 3.;
-        m[1][2] = 3. - 2 * tension;
+        m[1][2] = 3. - 2. * tension;
         m[3][1] = 1.;
         m[0][3] = m[2][2] = tension;
         m[0][0] = m[1][3] = m[2][0] = -tension;
         m[2][1] = m[2][3] = m[3][0] = m[3][2] = m[3][3] = 0.;
     }
 
-    static float calculateSplineCoefficients(float p0, float p1, float p2, float p3, float alpha, matrix m)
+    static double calculateSplineCoefficients(float p0, float p1, float p2, float p3, sal_uInt32 step, matrix m)
     {
-        float a, b, c, d;
-        a = m[0][0] * p0 + m[0][1] * p1 + m[0][2] * p2 + m[0][3] * p3;
-        b = m[1][0] * p0 + m[1][1] * p1 + m[1][2] * p2 + m[1][3] * p3;
-        c = m[2][0] * p0 + m[2][2] * p2;
-        d = p1;
-        return (d + alpha * (c + alpha * (b + alpha * a)));
+        double a = m[0][0] * p0 + m[0][1] * p1 + m[0][2] * p2 + m[0][3] * p3;
+        double b = m[1][0] * p0 + m[1][1] * p1 + m[1][2] * p2 + m[1][3] * p3;
+        double c = m[2][0] * p0 + m[2][2] * p2;
+        double d = p1;
+        return (d + alpha[step] * (c + alpha[step] * (b + alpha[step] * a)));
     }
 
     ::basegfx::B2DPolyPolygon& EMFPPath::GetCardinalSpline(EmfPlusHelperData const& rR, float fTension,
@@ -254,11 +258,7 @@ namespace emfplushelper
     {
         ::basegfx::B2DPolygon polygon;
         matrix mat;
-        float x, y;
-        constexpr sal_uInt32 nDetails = 8;
-        constexpr float alpha[nDetails]
-            = { 1. / nDetails, 2. / nDetails, 3. / nDetails, 4. / nDetails,
-                5. / nDetails, 6. / nDetails, 7. / nDetails, 8. / nDetails };
+        double x, y;
         if (aNumSegments >= nPoints)
             aNumSegments = nPoints - 1;
         GetCardinalMatrix(fTension, mat);
@@ -274,9 +274,9 @@ namespace emfplushelper
             for (sal_uInt32 s = 0; s < nDetails; s++)
             {
                 x = calculateSplineCoefficients(xPoints[i - 3], xPoints[i - 2], xPoints[i - 1],
-                                                xPoints[i], alpha[s], mat);
+                                                xPoints[i], s, mat);
                 y = calculateSplineCoefficients(yPoints[i - 3], yPoints[i - 2], yPoints[i - 1],
-                                                yPoints[i], alpha[s], mat);
+                                                yPoints[i], s, mat);
                 polygon.append(rR.Map(x, y));
             }
         }
@@ -289,11 +289,7 @@ namespace emfplushelper
     {
         ::basegfx::B2DPolygon polygon;
         matrix mat;
-        float x, y;
-        constexpr sal_uInt32 nDetails = 8;
-        constexpr float alpha[nDetails]
-            = { 1. / nDetails, 2. / nDetails, 3. / nDetails, 4. / nDetails,
-                5. / nDetails, 6. / nDetails, 7. / nDetails, 8. / nDetails };
+        double x, y;
         GetCardinalMatrix(fTension, mat);
         // add three first points at the end
         xPoints.push_back(xPoints[0]);
@@ -308,9 +304,9 @@ namespace emfplushelper
             for (sal_uInt32 s = 0; s < nDetails; s++)
             {
                 x = calculateSplineCoefficients(xPoints[i - 3], xPoints[i - 2], xPoints[i - 1],
-                                                xPoints[i], alpha[s], mat);
+                                                xPoints[i], s, mat);
                 y = calculateSplineCoefficients(yPoints[i - 3], yPoints[i - 2], yPoints[i - 1],
-                                                yPoints[i], alpha[s], mat);
+                                                yPoints[i], s, mat);
                 polygon.append(rR.Map(x, y));
             }
         }