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## modules/javafx.graphics/src/main/java/com/sun/marlin/Helpers.java

```*** 1,7 ****
/*
* DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER.
*
* This code is free software; you can redistribute it and/or modify it
* under the terms of the GNU General Public License version 2 only, as
--- 1,7 ----
/*
* DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER.
*
* This code is free software; you can redistribute it and/or modify it
* under the terms of the GNU General Public License version 2 only, as
*** 24,34 ****
*/

package com.sun.marlin;

import com.sun.javafx.geom.PathConsumer2D;
- import static java.lang.Math.PI;
import java.util.Arrays;
import com.sun.marlin.stats.Histogram;
import com.sun.marlin.stats.StatLong;

final class Helpers implements MarlinConst {
--- 24,33 ----
*** 45,61 ****
static boolean within(final double x, final double y, final double err) {
final double d = y - x;
return (d <= err && d >= -err);
}

!     static int quadraticRoots(final float a, final float b,
!                               final float c, float[] zeroes, final int off)
{
int ret = off;
-         float t;
if (a != 0.0f) {
!             final float dis = b*b - 4*a*c;
if (dis > 0.0f) {
final float sqrtDis = (float) Math.sqrt(dis);
// depending on the sign of b we use a slightly different
// algorithm than the traditional one to find one of the roots
// so we can avoid adding numbers of different signs (which
--- 44,72 ----
static boolean within(final double x, final double y, final double err) {
final double d = y - x;
return (d <= err && d >= -err);
}

!     static float evalCubic(final float a, final float b,
!                            final float c, final float d,
!                            final float t)
!     {
!         return t * (t * (t * a + b) + c) + d;
!     }
!
!     static float evalQuad(final float a, final float b,
!                           final float c, final float t)
!     {
!         return t * (t * a + b) + c;
!     }
!
!     static int quadraticRoots(final float a, final float b, final float c,
!                               final float[] zeroes, final int off)
{
int ret = off;
if (a != 0.0f) {
!             final float dis = b*b - 4.0f * a * c;
if (dis > 0.0f) {
final float sqrtDis = (float) Math.sqrt(dis);
// depending on the sign of b we use a slightly different
// algorithm than the traditional one to find one of the roots
// so we can avoid adding numbers of different signs (which
*** 66,172 ****
} else {
zeroes[ret++] = (-b + sqrtDis) / (2.0f * a);
zeroes[ret++] = (2.0f * c) / (-b + sqrtDis);
}
} else if (dis == 0.0f) {
!                 t = (-b) / (2.0f * a);
!                 zeroes[ret++] = t;
!             }
!         } else {
!             if (b != 0.0f) {
!                 t = (-c) / b;
!                 zeroes[ret++] = t;
}
}
return ret - off;
}

// find the roots of g(t) = d*t^3 + a*t^2 + b*t + c in [A,B)
!     static int cubicRootsInAB(float d, float a, float b, float c,
!                               float[] pts, final int off,
final float A, final float B)
{
!         if (d == 0.0f) {
!             int num = quadraticRoots(a, b, c, pts, off);
return filterOutNotInAB(pts, off, num, A, B) - off;
}
// From Graphics Gems:
!         // http://tog.acm.org/resources/GraphicsGems/gems/Roots3And4.c
// (also from awt.geom.CubicCurve2D. But here we don't need as
// much accuracy and we don't want to create arrays so we use
// our own customized version).

// normal form: x^3 + ax^2 + bx + c = 0
!         a /= d;
!         b /= d;
!         c /= d;

//  substitute x = y - A/3 to eliminate quadratic term:
//     x^3 +Px + Q = 0
//
// Since we actually need P/3 and Q/2 for all of the
// calculations that follow, we will calculate
// p = P/3
// q = Q/2
// instead and use those values for simplicity of the code.
!         double sq_A = a * a;
!         double p = (1.0d/3.0d) * ((-1.0d/3.0d) * sq_A + b);
!         double q = (1.0d/2.0d) * ((2.0d/27.0d) * a * sq_A - (1.0d/3.0d) * a * b + c);

// use Cardano's formula

!         double cb_p = p * p * p;
!         double D = q * q + cb_p;

int num;
if (D < 0.0d) {
// see: http://en.wikipedia.org/wiki/Cubic_function#Trigonometric_.28and_hyperbolic.29_method
!             final double phi = (1.0d/3.0d) * Math.acos(-q / Math.sqrt(-cb_p));
final double t = 2.0d * Math.sqrt(-p);

!             pts[ off+0 ] = (float) ( t * Math.cos(phi));
!             pts[ off+1 ] = (float) (-t * Math.cos(phi + (PI / 3.0d)));
!             pts[ off+2 ] = (float) (-t * Math.cos(phi - (PI / 3.0d)));
num = 3;
} else {
final double sqrt_D = Math.sqrt(D);
final double u =   Math.cbrt(sqrt_D - q);
final double v = - Math.cbrt(sqrt_D + q);

!             pts[ off ] = (float) (u + v);
num = 1;

if (within(D, 0.0d, 1e-8d)) {
!                 pts[off+1] = -(pts[off] / 2.0f);
num = 2;
}
}

-         final float sub = (1.0f/3.0f) * a;
-
-         for (int i = 0; i < num; ++i) {
-             pts[ off+i ] -= sub;
-         }
-
return filterOutNotInAB(pts, off, num, A, B) - off;
}

-     static float evalCubic(final float a, final float b,
-                            final float c, final float d,
-                            final float t)
-     {
-         return t * (t * (t * a + b) + c) + d;
-     }
-
-     static float evalQuad(final float a, final float b,
-                           final float c, final float t)
-     {
-         return t * (t * a + b) + c;
-     }
-
// returns the index 1 past the last valid element remaining after filtering
!     static int filterOutNotInAB(float[] nums, final int off, final int len,
final float a, final float b)
{
int ret = off;
for (int i = off, end = off + len; i < end; i++) {
if (nums[i] >= a && nums[i] < b) {
--- 77,166 ----
} else {
zeroes[ret++] = (-b + sqrtDis) / (2.0f * a);
zeroes[ret++] = (2.0f * c) / (-b + sqrtDis);
}
} else if (dis == 0.0f) {
!                 zeroes[ret++] = -b / (2.0f * a);
}
+         } else if (b != 0.0f) {
+             zeroes[ret++] = -c / b;
}
return ret - off;
}

// find the roots of g(t) = d*t^3 + a*t^2 + b*t + c in [A,B)
!     static int cubicRootsInAB(final float d0, float a0, float b0, float c0,
!                               final float[] pts, final int off,
final float A, final float B)
{
!         if (d0 == 0.0f) {
!             final int num = quadraticRoots(a0, b0, c0, pts, off);
return filterOutNotInAB(pts, off, num, A, B) - off;
}
// From Graphics Gems:
!         // https://github.com/erich666/GraphicsGems/blob/master/gems/Roots3And4.c
// (also from awt.geom.CubicCurve2D. But here we don't need as
// much accuracy and we don't want to create arrays so we use
// our own customized version).

// normal form: x^3 + ax^2 + bx + c = 0
!
!         // 2018.1: Need double precision if d is very small (flat curve) !
!         /*
!          * TODO: cleanup all that code after reading Roots3And4.c
!          */
!         final double a = ((double)a0) / d0;
!         final double b = ((double)b0) / d0;
!         final double c = ((double)c0) / d0;

//  substitute x = y - A/3 to eliminate quadratic term:
//     x^3 +Px + Q = 0
//
// Since we actually need P/3 and Q/2 for all of the
// calculations that follow, we will calculate
// p = P/3
// q = Q/2
// instead and use those values for simplicity of the code.
!         final double sub = (1.0d / 3.0d) * a;
!         final double sq_A = a * a;
!         final double p = (1.0d / 3.0d) * ((-1.0d / 3.0d) * sq_A + b);
!         final double q = (1.0d / 2.0d) * ((2.0d / 27.0d) * a * sq_A - sub * b + c);

// use Cardano's formula

!         final double cb_p = p * p * p;
!         final double D = q * q + cb_p;

int num;
if (D < 0.0d) {
// see: http://en.wikipedia.org/wiki/Cubic_function#Trigonometric_.28and_hyperbolic.29_method
!             final double phi = (1.0d / 3.0d) * Math.acos(-q / Math.sqrt(-cb_p));
final double t = 2.0d * Math.sqrt(-p);

!             pts[off    ] = (float) ( t * Math.cos(phi) - sub);
!             pts[off + 1] = (float) (-t * Math.cos(phi + (Math.PI / 3.0d)) - sub);
!             pts[off + 2] = (float) (-t * Math.cos(phi - (Math.PI / 3.0d)) - sub);
num = 3;
} else {
final double sqrt_D = Math.sqrt(D);
final double u =   Math.cbrt(sqrt_D - q);
final double v = - Math.cbrt(sqrt_D + q);

!             pts[off    ] = (float) (u + v - sub);
num = 1;

if (within(D, 0.0d, 1e-8d)) {
!                 pts[off + 1] = (float)((-1.0d / 2.0d) * (u + v) - sub);
num = 2;
}
}

return filterOutNotInAB(pts, off, num, A, B) - off;
}

// returns the index 1 past the last valid element remaining after filtering
!     static int filterOutNotInAB(final float[] nums, final int off, final int len,
final float a, final float b)
{
int ret = off;
for (int i = off, end = off + len; i < end; i++) {
if (nums[i] >= a && nums[i] < b) {
*** 174,212 ****
}
}
return ret;
}

!     static float linelen(float x1, float y1, float x2, float y2) {
!         final float dx = x2 - x1;
!         final float dy = y2 - y1;
!         return (float) Math.sqrt(dx*dx + dy*dy);
}

!     static void subdivide(float[] src, int srcoff, float[] left, int leftoff,
!                           float[] right, int rightoff, int type)
{
switch(type) {
-         case 6:
-             Helpers.subdivideQuad(src, srcoff, left, leftoff, right, rightoff);
-             return;
case 8:
!             Helpers.subdivideCubic(src, srcoff, left, leftoff, right, rightoff);
return;
default:
throw new InternalError("Unsupported curve type");
}
}

!     static void isort(float[] a, int off, int len) {
!         for (int i = off + 1, end = off + len; i < end; i++) {
!             float ai = a[i];
!             int j = i - 1;
!             for (; j >= off && a[j] > ai; j--) {
!                 a[j+1] = a[j];
}
!             a[j+1] = ai;
}
}

// Most of these are copied from classes in java.awt.geom because we need
// both single and double precision variants of these functions, and Line2D,
--- 168,361 ----
}
}
return ret;
}

!     static float fastLineLen(final float x0, final float y0,
!                              final float x1, final float y1)
!     {
!         final float dx = x1 - x0;
!         final float dy = y1 - y0;
!
!         // use manhattan norm:
!         return Math.abs(dx) + Math.abs(dy);
!     }
!
!     static float linelen(final float x0, final float y0,
!                          final float x1, final float y1)
!     {
!         final float dx = x1 - x0;
!         final float dy = y1 - y0;
!         return (float) Math.sqrt(dx * dx + dy * dy);
!     }
!
!     static float fastQuadLen(final float x0, final float y0,
!                              final float x1, final float y1,
!                              final float x2, final float y2)
!     {
!         final float dx1 = x1 - x0;
!         final float dx2 = x2 - x1;
!         final float dy1 = y1 - y0;
!         final float dy2 = y2 - y1;
!
!         // use manhattan norm:
!         return Math.abs(dx1) + Math.abs(dx2)
!              + Math.abs(dy1) + Math.abs(dy2);
!     }
!
!     static float quadlen(final float x0, final float y0,
!                          final float x1, final float y1,
!                          final float x2, final float y2)
!     {
!         return (linelen(x0, y0, x1, y1)
!                 + linelen(x1, y1, x2, y2)
!                 + linelen(x0, y0, x2, y2)) / 2.0f;
!     }
!
!
!     static float fastCurvelen(final float x0, final float y0,
!                               final float x1, final float y1,
!                               final float x2, final float y2,
!                               final float x3, final float y3)
!     {
!         final float dx1 = x1 - x0;
!         final float dx2 = x2 - x1;
!         final float dx3 = x3 - x2;
!         final float dy1 = y1 - y0;
!         final float dy2 = y2 - y1;
!         final float dy3 = y3 - y2;
!
!         // use manhattan norm:
!         return Math.abs(dx1) + Math.abs(dx2) + Math.abs(dx3)
!              + Math.abs(dy1) + Math.abs(dy2) + Math.abs(dy3);
!     }
!
!     static float curvelen(final float x0, final float y0,
!                           final float x1, final float y1,
!                           final float x2, final float y2,
!                           final float x3, final float y3)
!     {
!         return (linelen(x0, y0, x1, y1)
!               + linelen(x1, y1, x2, y2)
!               + linelen(x2, y2, x3, y3)
!               + linelen(x0, y0, x3, y3)) / 2.0f;
!     }
!
!     // finds values of t where the curve in pts should be subdivided in order
!     // to get good offset curves a distance of w away from the middle curve.
!     // Stores the points in ts, and returns how many of them there were.
!     static int findSubdivPoints(final Curve c, final float[] pts,
!                                 final float[] ts, final int type,
!                                 final float w2)
!     {
!         final float x12 = pts[2] - pts[0];
!         final float y12 = pts[3] - pts[1];
!         // if the curve is already parallel to either axis we gain nothing
!         // from rotating it.
!         if ((y12 != 0.0f && x12 != 0.0f)) {
!             // we rotate it so that the first vector in the control polygon is
!             // parallel to the x-axis. This will ensure that rotated quarter
!             // circles won't be subdivided.
!             final float hypot = (float)Math.sqrt(x12 * x12 + y12 * y12);
!             final float cos = x12 / hypot;
!             final float sin = y12 / hypot;
!             final float x1 = cos * pts[0] + sin * pts[1];
!             final float y1 = cos * pts[1] - sin * pts[0];
!             final float x2 = cos * pts[2] + sin * pts[3];
!             final float y2 = cos * pts[3] - sin * pts[2];
!             final float x3 = cos * pts[4] + sin * pts[5];
!             final float y3 = cos * pts[5] - sin * pts[4];
!
!             switch(type) {
!             case 8:
!                 final float x4 = cos * pts[6] + sin * pts[7];
!                 final float y4 = cos * pts[7] - sin * pts[6];
!                 c.set(x1, y1, x2, y2, x3, y3, x4, y4);
!                 break;
!             case 6:
!                 c.set(x1, y1, x2, y2, x3, y3);
!                 break;
!             default:
!             }
!         } else {
!             c.set(pts, type);
!         }
!
!         int ret = 0;
!         // we subdivide at values of t such that the remaining rotated
!         // curves are monotonic in x and y.
!         ret += c.dxRoots(ts, ret);
!         ret += c.dyRoots(ts, ret);
!
!         // subdivide at inflection points.
!         if (type == 8) {
!             // quadratic curves can't have inflection points
!             ret += c.infPoints(ts, ret);
!         }
!
!         // now we must subdivide at points where one of the offset curves will have
!         // a cusp. This happens at ts where the radius of curvature is equal to w.
!         ret += c.rootsOfROCMinusW(ts, ret, w2, 0.0001f);
!
!         ret = filterOutNotInAB(ts, 0, ret, 0.0001f, 0.9999f);
!         isort(ts, ret);
!         return ret;
!     }
!
!     // finds values of t where the curve in pts should be subdivided in order
!     // to get intersections with the given clip rectangle.
!     // Stores the points in ts, and returns how many of them there were.
!     static int findClipPoints(final Curve curve, final float[] pts,
!                               final float[] ts, final int type,
!                               final int outCodeOR,
!                               final float[] clipRect)
!     {
!         curve.set(pts, type);
!
!         // clip rectangle (ymin, ymax, xmin, xmax)
!         int ret = 0;
!
!         if ((outCodeOR & OUTCODE_LEFT) != 0) {
!             ret += curve.xPoints(ts, ret, clipRect[2]);
!         }
!         if ((outCodeOR & OUTCODE_RIGHT) != 0) {
!             ret += curve.xPoints(ts, ret, clipRect[3]);
!         }
!         if ((outCodeOR & OUTCODE_TOP) != 0) {
!             ret += curve.yPoints(ts, ret, clipRect[0]);
!         }
!         if ((outCodeOR & OUTCODE_BOTTOM) != 0) {
!             ret += curve.yPoints(ts, ret, clipRect[1]);
!         }
!         isort(ts, ret);
!         return ret;
}

!     static void subdivide(final float[] src,
!                           final float[] left, final float[] right,
!                           final int type)
{
switch(type) {
case 8:
!             subdivideCubic(src, left, right);
!             return;
!         case 6:
return;
default:
throw new InternalError("Unsupported curve type");
}
}

!     static void isort(final float[] a, final int len) {
!         for (int i = 1, j; i < len; i++) {
!             final float ai = a[i];
!             j = i - 1;
!             for (; j >= 0 && a[j] > ai; j--) {
!                 a[j + 1] = a[j];
}
!             a[j + 1] = ai;
}
}

// Most of these are copied from classes in java.awt.geom because we need
// both single and double precision variants of these functions, and Line2D,
*** 225,434 ****
* it is possible to pass the same array for <code>left</code>
* and <code>right</code> and to use offsets, such as <code>rightoff</code>
* equals (<code>leftoff</code> + 6), in order
* to avoid allocating extra storage for this common point.
* @param src the array holding the coordinates for the source curve
-      * @param srcoff the offset into the array of the beginning of the
-      * the 6 source coordinates
* @param left the array for storing the coordinates for the first
* half of the subdivided curve
-      * @param leftoff the offset into the array of the beginning of the
-      * the 6 left coordinates
* @param right the array for storing the coordinates for the second
* half of the subdivided curve
-      * @param rightoff the offset into the array of the beginning of the
-      * the 6 right coordinates
* @since 1.7
*/
!     static void subdivideCubic(float[] src, int srcoff,
!                                float[] left, int leftoff,
!                                float[] right, int rightoff)
!     {
!         float x1 = src[srcoff + 0];
!         float y1 = src[srcoff + 1];
!         float ctrlx1 = src[srcoff + 2];
!         float ctrly1 = src[srcoff + 3];
!         float ctrlx2 = src[srcoff + 4];
!         float ctrly2 = src[srcoff + 5];
!         float x2 = src[srcoff + 6];
!         float y2 = src[srcoff + 7];
!         if (left != null) {
!             left[leftoff + 0] = x1;
!             left[leftoff + 1] = y1;
!         }
!         if (right != null) {
!             right[rightoff + 6] = x2;
!             right[rightoff + 7] = y2;
!         }
!         x1 = (x1 + ctrlx1) / 2.0f;
!         y1 = (y1 + ctrly1) / 2.0f;
!         x2 = (x2 + ctrlx2) / 2.0f;
!         y2 = (y2 + ctrly2) / 2.0f;
!         float centerx = (ctrlx1 + ctrlx2) / 2.0f;
!         float centery = (ctrly1 + ctrly2) / 2.0f;
!         ctrlx1 = (x1 + centerx) / 2.0f;
!         ctrly1 = (y1 + centery) / 2.0f;
!         ctrlx2 = (x2 + centerx) / 2.0f;
!         ctrly2 = (y2 + centery) / 2.0f;
!         centerx = (ctrlx1 + ctrlx2) / 2.0f;
!         centery = (ctrly1 + ctrly2) / 2.0f;
!         if (left != null) {
!             left[leftoff + 2] = x1;
!             left[leftoff + 3] = y1;
!             left[leftoff + 4] = ctrlx1;
!             left[leftoff + 5] = ctrly1;
!             left[leftoff + 6] = centerx;
!             left[leftoff + 7] = centery;
!         }
!         if (right != null) {
!             right[rightoff + 0] = centerx;
!             right[rightoff + 1] = centery;
!             right[rightoff + 2] = ctrlx2;
!             right[rightoff + 3] = ctrly2;
!             right[rightoff + 4] = x2;
!             right[rightoff + 5] = y2;
!         }
!     }
!
!
!     static void subdivideCubicAt(float t, float[] src, int srcoff,
!                                  float[] left, int leftoff,
!                                  float[] right, int rightoff)
!     {
!         float x1 = src[srcoff + 0];
!         float y1 = src[srcoff + 1];
!         float ctrlx1 = src[srcoff + 2];
!         float ctrly1 = src[srcoff + 3];
!         float ctrlx2 = src[srcoff + 4];
!         float ctrly2 = src[srcoff + 5];
!         float x2 = src[srcoff + 6];
!         float y2 = src[srcoff + 7];
!         if (left != null) {
!             left[leftoff + 0] = x1;
!             left[leftoff + 1] = y1;
!         }
!         if (right != null) {
!             right[rightoff + 6] = x2;
!             right[rightoff + 7] = y2;
!         }
!         x1 = x1 + t * (ctrlx1 - x1);
!         y1 = y1 + t * (ctrly1 - y1);
!         x2 = ctrlx2 + t * (x2 - ctrlx2);
!         y2 = ctrly2 + t * (y2 - ctrly2);
!         float centerx = ctrlx1 + t * (ctrlx2 - ctrlx1);
!         float centery = ctrly1 + t * (ctrly2 - ctrly1);
!         ctrlx1 = x1 + t * (centerx - x1);
!         ctrly1 = y1 + t * (centery - y1);
!         ctrlx2 = centerx + t * (x2 - centerx);
!         ctrly2 = centery + t * (y2 - centery);
!         centerx = ctrlx1 + t * (ctrlx2 - ctrlx1);
!         centery = ctrly1 + t * (ctrly2 - ctrly1);
!         if (left != null) {
!             left[leftoff + 2] = x1;
!             left[leftoff + 3] = y1;
!             left[leftoff + 4] = ctrlx1;
!             left[leftoff + 5] = ctrly1;
!             left[leftoff + 6] = centerx;
!             left[leftoff + 7] = centery;
!         }
!         if (right != null) {
!             right[rightoff + 0] = centerx;
!             right[rightoff + 1] = centery;
!             right[rightoff + 2] = ctrlx2;
!             right[rightoff + 3] = ctrly2;
!             right[rightoff + 4] = x2;
!             right[rightoff + 5] = y2;
!         }
!     }
!
!     static void subdivideQuad(float[] src, int srcoff,
!                               float[] left, int leftoff,
!                               float[] right, int rightoff)
!     {
!         float x1 = src[srcoff + 0];
!         float y1 = src[srcoff + 1];
!         float ctrlx = src[srcoff + 2];
!         float ctrly = src[srcoff + 3];
!         float x2 = src[srcoff + 4];
!         float y2 = src[srcoff + 5];
!         if (left != null) {
!             left[leftoff + 0] = x1;
!             left[leftoff + 1] = y1;
!         }
!         if (right != null) {
!             right[rightoff + 4] = x2;
!             right[rightoff + 5] = y2;
!         }
!         x1 = (x1 + ctrlx) / 2.0f;
!         y1 = (y1 + ctrly) / 2.0f;
!         x2 = (x2 + ctrlx) / 2.0f;
!         y2 = (y2 + ctrly) / 2.0f;
!         ctrlx = (x1 + x2) / 2.0f;
!         ctrly = (y1 + y2) / 2.0f;
!         if (left != null) {
!             left[leftoff + 2] = x1;
!             left[leftoff + 3] = y1;
!             left[leftoff + 4] = ctrlx;
!             left[leftoff + 5] = ctrly;
!         }
!         if (right != null) {
!             right[rightoff + 0] = ctrlx;
!             right[rightoff + 1] = ctrly;
!             right[rightoff + 2] = x2;
!             right[rightoff + 3] = y2;
!         }
!     }
!
!     static void subdivideQuadAt(float t, float[] src, int srcoff,
!                                 float[] left, int leftoff,
!                                 float[] right, int rightoff)
!     {
!         float x1 = src[srcoff + 0];
!         float y1 = src[srcoff + 1];
!         float ctrlx = src[srcoff + 2];
!         float ctrly = src[srcoff + 3];
!         float x2 = src[srcoff + 4];
!         float y2 = src[srcoff + 5];
!         if (left != null) {
!             left[leftoff + 0] = x1;
!             left[leftoff + 1] = y1;
!         }
!         if (right != null) {
!             right[rightoff + 4] = x2;
!             right[rightoff + 5] = y2;
!         }
!         x1 = x1 + t * (ctrlx - x1);
!         y1 = y1 + t * (ctrly - y1);
!         x2 = ctrlx + t * (x2 - ctrlx);
!         y2 = ctrly + t * (y2 - ctrly);
!         ctrlx = x1 + t * (x2 - x1);
!         ctrly = y1 + t * (y2 - y1);
!         if (left != null) {
!             left[leftoff + 2] = x1;
!             left[leftoff + 3] = y1;
!             left[leftoff + 4] = ctrlx;
!             left[leftoff + 5] = ctrly;
!         }
!         if (right != null) {
!             right[rightoff + 0] = ctrlx;
!             right[rightoff + 1] = ctrly;
!             right[rightoff + 2] = x2;
!             right[rightoff + 3] = y2;
!         }
!     }
!
!     static void subdivideAt(float t, float[] src, int srcoff,
!                             float[] left, int leftoff,
!                             float[] right, int rightoff, int size)
!     {
!         switch(size) {
!         case 8:
!             subdivideCubicAt(t, src, srcoff, left, leftoff, right, rightoff);
!             return;
!         case 6:
!             subdivideQuadAt(t, src, srcoff, left, leftoff, right, rightoff);
!             return;
}
}

// From sun.java2d.loops.GeneralRenderer:

--- 374,593 ----
* it is possible to pass the same array for <code>left</code>
* and <code>right</code> and to use offsets, such as <code>rightoff</code>
* equals (<code>leftoff</code> + 6), in order
* to avoid allocating extra storage for this common point.
* @param src the array holding the coordinates for the source curve
* @param left the array for storing the coordinates for the first
* half of the subdivided curve
* @param right the array for storing the coordinates for the second
* half of the subdivided curve
* @since 1.7
*/
!     static void subdivideCubic(final float[] src,
!                                final float[] left,
!                                final float[] right)
!     {
!         float  x1 = src[0];
!         float  y1 = src[1];
!         float cx1 = src[2];
!         float cy1 = src[3];
!         float cx2 = src[4];
!         float cy2 = src[5];
!         float  x2 = src[6];
!         float  y2 = src[7];
!
!         left[0]  = x1;
!         left[1]  = y1;
!
!         right[6] = x2;
!         right[7] = y2;
!
!         x1 = (x1 + cx1) / 2.0f;
!         y1 = (y1 + cy1) / 2.0f;
!         x2 = (x2 + cx2) / 2.0f;
!         y2 = (y2 + cy2) / 2.0f;
!
!         float cx = (cx1 + cx2) / 2.0f;
!         float cy = (cy1 + cy2) / 2.0f;
!
!         cx1 = (x1 + cx) / 2.0f;
!         cy1 = (y1 + cy) / 2.0f;
!         cx2 = (x2 + cx) / 2.0f;
!         cy2 = (y2 + cy) / 2.0f;
!         cx  = (cx1 + cx2) / 2.0f;
!         cy  = (cy1 + cy2) / 2.0f;
!
!         left[2] = x1;
!         left[3] = y1;
!         left[4] = cx1;
!         left[5] = cy1;
!         left[6] = cx;
!         left[7] = cy;
!
!         right[0] = cx;
!         right[1] = cy;
!         right[2] = cx2;
!         right[3] = cy2;
!         right[4] = x2;
!         right[5] = y2;
!     }
!
!     static void subdivideCubicAt(final float t,
!                                  final float[] src, final int offS,
!                                  final float[] pts, final int offL, final int offR)
!     {
!         float  x1 = src[offS    ];
!         float  y1 = src[offS + 1];
!         float cx1 = src[offS + 2];
!         float cy1 = src[offS + 3];
!         float cx2 = src[offS + 4];
!         float cy2 = src[offS + 5];
!         float  x2 = src[offS + 6];
!         float  y2 = src[offS + 7];
!
!         pts[offL    ] = x1;
!         pts[offL + 1] = y1;
!
!         pts[offR + 6] = x2;
!         pts[offR + 7] = y2;
!
!         x1 =  x1 + t * (cx1 - x1);
!         y1 =  y1 + t * (cy1 - y1);
!         x2 = cx2 + t * (x2 - cx2);
!         y2 = cy2 + t * (y2 - cy2);
!
!         float cx = cx1 + t * (cx2 - cx1);
!         float cy = cy1 + t * (cy2 - cy1);
!
!         cx1 =  x1 + t * (cx - x1);
!         cy1 =  y1 + t * (cy - y1);
!         cx2 =  cx + t * (x2 - cx);
!         cy2 =  cy + t * (y2 - cy);
!         cx  = cx1 + t * (cx2 - cx1);
!         cy  = cy1 + t * (cy2 - cy1);
!
!         pts[offL + 2] = x1;
!         pts[offL + 3] = y1;
!         pts[offL + 4] = cx1;
!         pts[offL + 5] = cy1;
!         pts[offL + 6] = cx;
!         pts[offL + 7] = cy;
!
!         pts[offR    ] = cx;
!         pts[offR + 1] = cy;
!         pts[offR + 2] = cx2;
!         pts[offR + 3] = cy2;
!         pts[offR + 4] = x2;
!         pts[offR + 5] = y2;
!     }
!
!     static void subdivideQuad(final float[] src,
!                               final float[] left,
!                               final float[] right)
!     {
!         float x1 = src[0];
!         float y1 = src[1];
!         float cx = src[2];
!         float cy = src[3];
!         float x2 = src[4];
!         float y2 = src[5];
!
!         left[0]  = x1;
!         left[1]  = y1;
!
!         right[4] = x2;
!         right[5] = y2;
!
!         x1 = (x1 + cx) / 2.0f;
!         y1 = (y1 + cy) / 2.0f;
!         x2 = (x2 + cx) / 2.0f;
!         y2 = (y2 + cy) / 2.0f;
!         cx = (x1 + x2) / 2.0f;
!         cy = (y1 + y2) / 2.0f;
!
!         left[2] = x1;
!         left[3] = y1;
!         left[4] = cx;
!         left[5] = cy;
!
!         right[0] = cx;
!         right[1] = cy;
!         right[2] = x2;
!         right[3] = y2;
!     }
!
!     static void subdivideQuadAt(final float t,
!                                 final float[] src, final int offS,
!                                 final float[] pts, final int offL, final int offR)
!     {
!         float x1 = src[offS    ];
!         float y1 = src[offS + 1];
!         float cx = src[offS + 2];
!         float cy = src[offS + 3];
!         float x2 = src[offS + 4];
!         float y2 = src[offS + 5];
!
!         pts[offL    ] = x1;
!         pts[offL + 1] = y1;
!
!         pts[offR + 4] = x2;
!         pts[offR + 5] = y2;
!
!         x1 = x1 + t * (cx - x1);
!         y1 = y1 + t * (cy - y1);
!         x2 = cx + t * (x2 - cx);
!         y2 = cy + t * (y2 - cy);
!         cx = x1 + t * (x2 - x1);
!         cy = y1 + t * (y2 - y1);
!
!         pts[offL + 2] = x1;
!         pts[offL + 3] = y1;
!         pts[offL + 4] = cx;
!         pts[offL + 5] = cy;
!
!         pts[offR    ] = cx;
!         pts[offR + 1] = cy;
!         pts[offR + 2] = x2;
!         pts[offR + 3] = y2;
!     }
!
!     static void subdivideLineAt(final float t,
!                                 final float[] src, final int offS,
!                                 final float[] pts, final int offL, final int offR)
!     {
!         float x1 = src[offS    ];
!         float y1 = src[offS + 1];
!         float x2 = src[offS + 2];
!         float y2 = src[offS + 3];
!
!         pts[offL    ] = x1;
!         pts[offL + 1] = y1;
!
!         pts[offR + 2] = x2;
!         pts[offR + 3] = y2;
!
!         x1 = x1 + t * (x2 - x1);
!         y1 = y1 + t * (y2 - y1);
!
!         pts[offL + 2] = x1;
!         pts[offL + 3] = y1;
!
!         pts[offR    ] = x1;
!         pts[offR + 1] = y1;
!     }
!
!     static void subdivideAt(final float t,
!                             final float[] src, final int offS,
!                             final float[] pts, final int offL, final int type)
!     {
!         // if instead of switch (perf + most probable cases first)
!         if (type == 8) {
!             subdivideCubicAt(t, src, offS, pts, offL, offL + type);
!         } else if (type == 4) {
!             subdivideLineAt(t, src, offS, pts, offL, offL + type);
!         } else {
!             subdivideQuadAt(t, src, offS, pts, offL, offL + type);
}
}

// From sun.java2d.loops.GeneralRenderer:

*** 611,631 ****
switch(_curveTypes[i]) {
case TYPE_LINETO:
io.lineTo(_curves[e], _curves[e+1]);
e += 2;
continue;
-                               _curves[e+2], _curves[e+3]);
-                     e += 4;
-                     continue;
case TYPE_CUBICTO:
!                     io.curveTo(_curves[e+0], _curves[e+1],
_curves[e+2], _curves[e+3],
_curves[e+4], _curves[e+5]);
e += 6;
continue;
default:
}
}
numCurves = 0;
end = 0;
--- 770,790 ----
switch(_curveTypes[i]) {
case TYPE_LINETO:
io.lineTo(_curves[e], _curves[e+1]);
e += 2;
continue;
case TYPE_CUBICTO:
!                     io.curveTo(_curves[e],   _curves[e+1],
_curves[e+2], _curves[e+3],
_curves[e+4], _curves[e+5]);
e += 6;
continue;
+                               _curves[e+2], _curves[e+3]);
+                     e += 4;
+                     continue;
default:
}
}
numCurves = 0;
end = 0;
*** 653,673 ****
switch(_curveTypes[--nc]) {
case TYPE_LINETO:
e -= 2;
io.lineTo(_curves[e], _curves[e+1]);
continue;
-                     e -= 4;
-                               _curves[e+2], _curves[e+3]);
-                     continue;
case TYPE_CUBICTO:
e -= 6;
!                     io.curveTo(_curves[e+0], _curves[e+1],
_curves[e+2], _curves[e+3],
_curves[e+4], _curves[e+5]);
continue;
default:
}
}
numCurves = 0;
end = 0;
--- 812,832 ----
switch(_curveTypes[--nc]) {
case TYPE_LINETO:
e -= 2;
io.lineTo(_curves[e], _curves[e+1]);
continue;
case TYPE_CUBICTO:
e -= 6;
!                     io.curveTo(_curves[e],   _curves[e+1],
_curves[e+2], _curves[e+3],
_curves[e+4], _curves[e+5]);
continue;