1 /*
   2  * Copyright (c) 2007, 2016, Oracle and/or its affiliates. All rights reserved.
   3  * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER.
   4  *
   5  * This code is free software; you can redistribute it and/or modify it
   6  * under the terms of the GNU General Public License version 2 only, as
   7  * published by the Free Software Foundation.  Oracle designates this
   8  * particular file as subject to the "Classpath" exception as provided
   9  * by Oracle in the LICENSE file that accompanied this code.
  10  *
  11  * This code is distributed in the hope that it will be useful, but WITHOUT
  12  * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
  13  * FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public License
  14  * version 2 for more details (a copy is included in the LICENSE file that
  15  * accompanied this code).
  16  *
  17  * You should have received a copy of the GNU General Public License version
  18  * 2 along with this work; if not, write to the Free Software Foundation,
  19  * Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA.
  20  *
  21  * Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA
  22  * or visit www.oracle.com if you need additional information or have any
  23  * questions.
  24  */
  25 
  26 package sun.java2d.marlin;
  27 
  28 import java.util.Arrays;
  29 import sun.awt.geom.PathConsumer2D;
  30 import static sun.java2d.marlin.OffHeapArray.SIZE_INT;
  31 import jdk.internal.misc.Unsafe;
  32 
  33 final class Renderer implements PathConsumer2D, MarlinConst {
  34 
  35     static final boolean DISABLE_RENDER = false;
  36 
  37     static final boolean ENABLE_BLOCK_FLAGS = MarlinProperties.isUseTileFlags();
  38     static final boolean ENABLE_BLOCK_FLAGS_HEURISTICS = MarlinProperties.isUseTileFlagsWithHeuristics();
  39 
  40     private static final int ALL_BUT_LSB = 0xfffffffe;
  41     private static final int ERR_STEP_MAX = 0x7fffffff; // = 2^31 - 1
  42 
  43     private static final double POWER_2_TO_32 = 0x1.0p32;
  44 
  45     // use float to make tosubpix methods faster (no int to float conversion)
  46     public static final float F_SUBPIXEL_POSITIONS_X
  47         = (float) SUBPIXEL_POSITIONS_X;
  48     public static final float F_SUBPIXEL_POSITIONS_Y
  49         = (float) SUBPIXEL_POSITIONS_Y;
  50     public static final int SUBPIXEL_MASK_X = SUBPIXEL_POSITIONS_X - 1;
  51     public static final int SUBPIXEL_MASK_Y = SUBPIXEL_POSITIONS_Y - 1;
  52 
  53     // number of subpixels corresponding to a tile line
  54     private static final int SUBPIXEL_TILE
  55         = TILE_SIZE << SUBPIXEL_LG_POSITIONS_Y;
  56 
  57     // 2048 (pixelSize) pixels (height) x 8 subpixels = 64K
  58     static final int INITIAL_BUCKET_ARRAY
  59         = INITIAL_PIXEL_DIM * SUBPIXEL_POSITIONS_Y;
  60 
  61     // crossing capacity = edges count / 8 ~ 512
  62     static final int INITIAL_CROSSING_COUNT = INITIAL_EDGES_COUNT >> 3;
  63 
  64     public static final int WIND_EVEN_ODD = 0;
  65     public static final int WIND_NON_ZERO = 1;
  66 
  67     // common to all types of input path segments.
  68     // OFFSET as bytes
  69     // only integer values:
  70     public static final long OFF_CURX_OR  = 0;
  71     public static final long OFF_ERROR    = OFF_CURX_OR  + SIZE_INT;
  72     public static final long OFF_BUMP_X   = OFF_ERROR    + SIZE_INT;
  73     public static final long OFF_BUMP_ERR = OFF_BUMP_X   + SIZE_INT;
  74     public static final long OFF_NEXT     = OFF_BUMP_ERR + SIZE_INT;
  75     public static final long OFF_YMAX     = OFF_NEXT     + SIZE_INT;
  76 
  77     // size of one edge in bytes
  78     public static final int SIZEOF_EDGE_BYTES = (int)(OFF_YMAX + SIZE_INT);
  79 
  80     // curve break into lines
  81     // cubic error in subpixels to decrement step
  82     private static final float CUB_DEC_ERR_SUBPIX
  83         = 2.5f * (NORM_SUBPIXELS / 8f); // 2.5 subpixel for typical 8x8 subpixels
  84     // cubic error in subpixels to increment step
  85     private static final float CUB_INC_ERR_SUBPIX
  86         = 1f * (NORM_SUBPIXELS / 8f); // 1 subpixel for typical 8x8 subpixels
  87 
  88     // cubic bind length to decrement step = 8 * error in subpixels
  89     // pisces: 20 / 8
  90     // openjfx pisces: 8 / 3.2
  91     // multiply by 8 = error scale factor:
  92     public static final float CUB_DEC_BND
  93         = 8f * CUB_DEC_ERR_SUBPIX; // 20f means 2.5 subpixel error
  94     // cubic bind length to increment step = 8 * error in subpixels
  95     public static final float CUB_INC_BND
  96         = 8f * CUB_INC_ERR_SUBPIX; // 8f means 1 subpixel error
  97 
  98     // cubic countlg
  99     public static final int CUB_COUNT_LG = 2;
 100     // cubic count = 2^countlg
 101     private static final int CUB_COUNT = 1 << CUB_COUNT_LG;
 102     // cubic count^2 = 4^countlg
 103     private static final int CUB_COUNT_2 = 1 << (2 * CUB_COUNT_LG);
 104     // cubic count^3 = 8^countlg
 105     private static final int CUB_COUNT_3 = 1 << (3 * CUB_COUNT_LG);
 106     // cubic dt = 1 / count
 107     private static final float CUB_INV_COUNT = 1f / CUB_COUNT;
 108     // cubic dt^2 = 1 / count^2 = 1 / 4^countlg
 109     private static final float CUB_INV_COUNT_2 = 1f / CUB_COUNT_2;
 110     // cubic dt^3 = 1 / count^3 = 1 / 8^countlg
 111     private static final float CUB_INV_COUNT_3 = 1f / CUB_COUNT_3;
 112 
 113     // quad break into lines
 114     // quadratic error in subpixels
 115     private static final float QUAD_DEC_ERR_SUBPIX
 116         = 1f * (NORM_SUBPIXELS / 8f); // 1 subpixel for typical 8x8 subpixels
 117 
 118     // quadratic bind length to decrement step = 8 * error in subpixels
 119     // pisces and openjfx pisces: 32
 120     public static final float QUAD_DEC_BND
 121         = 8f * QUAD_DEC_ERR_SUBPIX; // 8f means 1 subpixel error
 122 
 123 //////////////////////////////////////////////////////////////////////////////
 124 //  SCAN LINE
 125 //////////////////////////////////////////////////////////////////////////////
 126     // crossings ie subpixel edge x coordinates
 127     private int[] crossings;
 128     // auxiliary storage for crossings (merge sort)
 129     private int[] aux_crossings;
 130 
 131     // indices into the segment pointer lists. They indicate the "active"
 132     // sublist in the segment lists (the portion of the list that contains
 133     // all the segments that cross the next scan line).
 134     private int edgeCount;
 135     private int[] edgePtrs;
 136     // auxiliary storage for edge pointers (merge sort)
 137     private int[] aux_edgePtrs;
 138 
 139     // max used for both edgePtrs and crossings (stats only)
 140     private int activeEdgeMaxUsed;
 141 
 142     // crossings ref (dirty)
 143     private final IntArrayCache.Reference crossings_ref;
 144     // edgePtrs ref (dirty)
 145     private final IntArrayCache.Reference edgePtrs_ref;
 146     // merge sort initial arrays (large enough to satisfy most usages) (1024)
 147     // aux_crossings ref (dirty)
 148     private final IntArrayCache.Reference aux_crossings_ref;
 149     // aux_edgePtrs ref (dirty)
 150     private final IntArrayCache.Reference aux_edgePtrs_ref;
 151 
 152 //////////////////////////////////////////////////////////////////////////////
 153 //  EDGE LIST
 154 //////////////////////////////////////////////////////////////////////////////
 155     private int edgeMinY = Integer.MAX_VALUE;
 156     private int edgeMaxY = Integer.MIN_VALUE;
 157     private float edgeMinX = Float.POSITIVE_INFINITY;
 158     private float edgeMaxX = Float.NEGATIVE_INFINITY;
 159 
 160     // edges [floats|ints] stored in off-heap memory
 161     private final OffHeapArray edges;
 162 
 163     private int[] edgeBuckets;
 164     private int[] edgeBucketCounts; // 2*newedges + (1 if pruning needed)
 165     // used range for edgeBuckets / edgeBucketCounts
 166     private int buckets_minY;
 167     private int buckets_maxY;
 168     // sum of each edge delta Y (subpixels)
 169     private int edgeSumDeltaY;
 170 
 171     // edgeBuckets ref (clean)
 172     private final IntArrayCache.Reference edgeBuckets_ref;
 173     // edgeBucketCounts ref (clean)
 174     private final IntArrayCache.Reference edgeBucketCounts_ref;
 175 
 176     // Flattens using adaptive forward differencing. This only carries out
 177     // one iteration of the AFD loop. All it does is update AFD variables (i.e.
 178     // X0, Y0, D*[X|Y], COUNT; not variables used for computing scanline crossings).
 179     private void quadBreakIntoLinesAndAdd(float x0, float y0,
 180                                           final Curve c,
 181                                           final float x2, final float y2)
 182     {
 183         int count = 1; // dt = 1 / count
 184 
 185         // maximum(ddX|Y) = norm(dbx, dby) * dt^2 (= 1)
 186         float maxDD = FloatMath.max(Math.abs(c.dbx), Math.abs(c.dby));
 187 
 188         final float _DEC_BND = QUAD_DEC_BND;
 189 
 190         while (maxDD >= _DEC_BND) {
 191             // divide step by half:
 192             maxDD /= 4f; // error divided by 2^2 = 4
 193 
 194             count <<= 1;
 195             if (DO_STATS) {
 196                 rdrCtx.stats.stat_rdr_quadBreak_dec.add(count);
 197             }
 198         }
 199 
 200         int nL = 0; // line count
 201         if (count > 1) {
 202             final float icount = 1f / count; // dt
 203             final float icount2 = icount * icount; // dt^2
 204 
 205             final float ddx = c.dbx * icount2;
 206             final float ddy = c.dby * icount2;
 207             float dx = c.bx * icount2 + c.cx * icount;
 208             float dy = c.by * icount2 + c.cy * icount;
 209 
 210             float x1, y1;
 211 
 212             while (--count > 0) {
 213                 x1 = x0 + dx;
 214                 dx += ddx;
 215                 y1 = y0 + dy;
 216                 dy += ddy;
 217 
 218                 addLine(x0, y0, x1, y1);
 219 
 220                 if (DO_STATS) { nL++; }
 221                 x0 = x1;
 222                 y0 = y1;
 223             }
 224         }
 225         addLine(x0, y0, x2, y2);
 226 
 227         if (DO_STATS) {
 228             rdrCtx.stats.stat_rdr_quadBreak.add(nL + 1);
 229         }
 230     }
 231 
 232     // x0, y0 and x3,y3 are the endpoints of the curve. We could compute these
 233     // using c.xat(0),c.yat(0) and c.xat(1),c.yat(1), but this might introduce
 234     // numerical errors, and our callers already have the exact values.
 235     // Another alternative would be to pass all the control points, and call
 236     // c.set here, but then too many numbers are passed around.
 237     private void curveBreakIntoLinesAndAdd(float x0, float y0,
 238                                            final Curve c,
 239                                            final float x3, final float y3)
 240     {
 241         int count           = CUB_COUNT;
 242         final float icount  = CUB_INV_COUNT;   // dt
 243         final float icount2 = CUB_INV_COUNT_2; // dt^2
 244         final float icount3 = CUB_INV_COUNT_3; // dt^3
 245 
 246         // the dx and dy refer to forward differencing variables, not the last
 247         // coefficients of the "points" polynomial
 248         float dddx, dddy, ddx, ddy, dx, dy;
 249         dddx = 2f * c.dax * icount3;
 250         dddy = 2f * c.day * icount3;
 251         ddx = dddx + c.dbx * icount2;
 252         ddy = dddy + c.dby * icount2;
 253         dx = c.ax * icount3 + c.bx * icount2 + c.cx * icount;
 254         dy = c.ay * icount3 + c.by * icount2 + c.cy * icount;
 255 
 256         // we use x0, y0 to walk the line
 257         float x1 = x0, y1 = y0;
 258         int nL = 0; // line count
 259 
 260         final float _DEC_BND = CUB_DEC_BND;
 261         final float _INC_BND = CUB_INC_BND;
 262 
 263         while (count > 0) {
 264             // divide step by half:
 265             while (Math.abs(ddx) >= _DEC_BND || Math.abs(ddy) >= _DEC_BND) {
 266                 dddx /= 8f;
 267                 dddy /= 8f;
 268                 ddx = ddx/4f - dddx;
 269                 ddy = ddy/4f - dddy;
 270                 dx = (dx - ddx) / 2f;
 271                 dy = (dy - ddy) / 2f;
 272 
 273                 count <<= 1;
 274                 if (DO_STATS) {
 275                     rdrCtx.stats.stat_rdr_curveBreak_dec.add(count);
 276                 }
 277             }
 278 
 279             // double step:
 280             // TODO: why use first derivative dX|Y instead of second ddX|Y ?
 281             // both scale changes should use speed or acceleration to have the same metric.
 282 
 283             // can only do this on even "count" values, because we must divide count by 2
 284             while (count % 2 == 0
 285                    && Math.abs(dx) <= _INC_BND && Math.abs(dy) <= _INC_BND)
 286             {
 287                 dx = 2f * dx + ddx;
 288                 dy = 2f * dy + ddy;
 289                 ddx = 4f * (ddx + dddx);
 290                 ddy = 4f * (ddy + dddy);
 291                 dddx *= 8f;
 292                 dddy *= 8f;
 293 
 294                 count >>= 1;
 295                 if (DO_STATS) {
 296                     rdrCtx.stats.stat_rdr_curveBreak_inc.add(count);
 297                 }
 298             }
 299             if (--count > 0) {
 300                 x1 += dx;
 301                 dx += ddx;
 302                 ddx += dddx;
 303                 y1 += dy;
 304                 dy += ddy;
 305                 ddy += dddy;
 306             } else {
 307                 x1 = x3;
 308                 y1 = y3;
 309             }
 310 
 311             addLine(x0, y0, x1, y1);
 312 
 313             if (DO_STATS) { nL++; }
 314             x0 = x1;
 315             y0 = y1;
 316         }
 317         if (DO_STATS) {
 318             rdrCtx.stats.stat_rdr_curveBreak.add(nL);
 319         }
 320     }
 321 
 322     private void addLine(float x1, float y1, float x2, float y2) {
 323         if (DO_MONITORS) {
 324             rdrCtx.stats.mon_rdr_addLine.start();
 325         }
 326         if (DO_STATS) {
 327             rdrCtx.stats.stat_rdr_addLine.add(1);
 328         }
 329         int or = 1; // orientation of the line. 1 if y increases, 0 otherwise.
 330         if (y2 < y1) {
 331             or = 0;
 332             float tmp = y2;
 333             y2 = y1;
 334             y1 = tmp;
 335             tmp = x2;
 336             x2 = x1;
 337             x1 = tmp;
 338         }
 339 
 340         // convert subpixel coordinates (float) into pixel positions (int)
 341 
 342         // The index of the pixel that holds the next HPC is at ceil(trueY - 0.5)
 343         // Since y1 and y2 are biased by -0.5 in tosubpixy(), this is simply
 344         // ceil(y1) or ceil(y2)
 345         // upper integer (inclusive)
 346         final int firstCrossing = FloatMath.max(FloatMath.ceil_int(y1), boundsMinY);
 347 
 348         // note: use boundsMaxY (last Y exclusive) to compute correct coverage
 349         // upper integer (exclusive)
 350         final int lastCrossing  = FloatMath.min(FloatMath.ceil_int(y2), boundsMaxY);
 351 
 352         /* skip horizontal lines in pixel space and clip edges
 353            out of y range [boundsMinY; boundsMaxY] */
 354         if (firstCrossing >= lastCrossing) {
 355             if (DO_MONITORS) {
 356                 rdrCtx.stats.mon_rdr_addLine.stop();
 357             }
 358             if (DO_STATS) {
 359                 rdrCtx.stats.stat_rdr_addLine_skip.add(1);
 360             }
 361             return;
 362         }
 363 
 364         // edge min/max X/Y are in subpixel space (inclusive) within bounds:
 365         // note: Use integer crossings to ensure consistent range within
 366         // edgeBuckets / edgeBucketCounts arrays in case of NaN values (int = 0)
 367         if (firstCrossing < edgeMinY) {
 368             edgeMinY = firstCrossing;
 369         }
 370         if (lastCrossing > edgeMaxY) {
 371             edgeMaxY = lastCrossing;
 372         }
 373 
 374         // Use double-precision for improved accuracy:
 375         final double x1d   = x1;
 376         final double y1d   = y1;
 377         final double slope = (x1d - x2) / (y1d - y2);
 378 
 379         if (slope >= 0.0) { // <==> x1 < x2
 380             if (x1 < edgeMinX) {
 381                 edgeMinX = x1;
 382             }
 383             if (x2 > edgeMaxX) {
 384                 edgeMaxX = x2;
 385             }
 386         } else {
 387             if (x2 < edgeMinX) {
 388                 edgeMinX = x2;
 389             }
 390             if (x1 > edgeMaxX) {
 391                 edgeMaxX = x1;
 392             }
 393         }
 394 
 395         // local variables for performance:
 396         final int _SIZEOF_EDGE_BYTES = SIZEOF_EDGE_BYTES;
 397 
 398         final OffHeapArray _edges = edges;
 399 
 400         // get free pointer (ie length in bytes)
 401         final int edgePtr = _edges.used;
 402 
 403         // use substraction to avoid integer overflow:
 404         if (_edges.length - edgePtr < _SIZEOF_EDGE_BYTES) {
 405             // suppose _edges.length > _SIZEOF_EDGE_BYTES
 406             // so doubling size is enough to add needed bytes
 407             // note: throw IOOB if neededSize > 2Gb:
 408             final long edgeNewSize = ArrayCacheConst.getNewLargeSize(
 409                                         _edges.length,
 410                                         edgePtr + _SIZEOF_EDGE_BYTES);
 411 
 412             if (DO_STATS) {
 413                 rdrCtx.stats.stat_rdr_edges_resizes.add(edgeNewSize);
 414             }
 415             _edges.resize(edgeNewSize);
 416         }
 417 
 418 
 419         final Unsafe _unsafe = OffHeapArray.UNSAFE;
 420         final long SIZE_INT = 4L;
 421         long addr   = _edges.address + edgePtr;
 422 
 423         // The x value must be bumped up to its position at the next HPC we will evaluate.
 424         // "firstcrossing" is the (sub)pixel number where the next crossing occurs
 425         // thus, the actual coordinate of the next HPC is "firstcrossing + 0.5"
 426         // so the Y distance we cover is "firstcrossing + 0.5 - trueY".
 427         // Note that since y1 (and y2) are already biased by -0.5 in tosubpixy(), we have
 428         // y1 = trueY - 0.5
 429         // trueY = y1 + 0.5
 430         // firstcrossing + 0.5 - trueY = firstcrossing + 0.5 - (y1 + 0.5)
 431         //                             = firstcrossing - y1
 432         // The x coordinate at that HPC is then:
 433         // x1_intercept = x1 + (firstcrossing - y1) * slope
 434         // The next VPC is then given by:
 435         // VPC index = ceil(x1_intercept - 0.5), or alternately
 436         // VPC index = floor(x1_intercept - 0.5 + 1 - epsilon)
 437         // epsilon is hard to pin down in floating point, but easy in fixed point, so if
 438         // we convert to fixed point then these operations get easier:
 439         // long x1_fixed = x1_intercept * 2^32;  (fixed point 32.32 format)
 440         // curx = next VPC = fixed_floor(x1_fixed - 2^31 + 2^32 - 1)
 441         //                 = fixed_floor(x1_fixed + 2^31 - 1)
 442         //                 = fixed_floor(x1_fixed + 0x7fffffff)
 443         // and error       = fixed_fract(x1_fixed + 0x7fffffff)
 444         final double x1_intercept = x1d + (firstCrossing - y1d) * slope;
 445 
 446         // inlined scalb(x1_intercept, 32):
 447         final long x1_fixed_biased = ((long) (POWER_2_TO_32 * x1_intercept))
 448                                      + 0x7fffffffL;
 449         // curx:
 450         // last bit corresponds to the orientation
 451         _unsafe.putInt(addr, (((int) (x1_fixed_biased >> 31L)) & ALL_BUT_LSB) | or);
 452         addr += SIZE_INT;
 453         _unsafe.putInt(addr,  ((int)  x1_fixed_biased) >>> 1);
 454         addr += SIZE_INT;
 455 
 456         // inlined scalb(slope, 32):
 457         final long slope_fixed = (long) (POWER_2_TO_32 * slope);
 458 
 459         // last bit set to 0 to keep orientation:
 460         _unsafe.putInt(addr, (((int) (slope_fixed >> 31L)) & ALL_BUT_LSB));
 461         addr += SIZE_INT;
 462         _unsafe.putInt(addr,  ((int)  slope_fixed) >>> 1);
 463         addr += SIZE_INT;
 464 
 465         final int[] _edgeBuckets      = edgeBuckets;
 466         final int[] _edgeBucketCounts = edgeBucketCounts;
 467 
 468         final int _boundsMinY = boundsMinY;
 469 
 470         // each bucket is a linked list. this method adds ptr to the
 471         // start of the "bucket"th linked list.
 472         final int bucketIdx = firstCrossing - _boundsMinY;
 473 
 474         // pointer from bucket
 475         _unsafe.putInt(addr, _edgeBuckets[bucketIdx]);
 476         addr += SIZE_INT;
 477         // y max (inclusive)
 478         _unsafe.putInt(addr,  lastCrossing);
 479 
 480         // Update buckets:
 481         // directly the edge struct "pointer"
 482         _edgeBuckets[bucketIdx]       = edgePtr;
 483         _edgeBucketCounts[bucketIdx] += 2; // 1 << 1
 484         // last bit means edge end
 485         _edgeBucketCounts[lastCrossing - _boundsMinY] |= 0x1;
 486 
 487         // update sum of delta Y (subpixels):
 488         edgeSumDeltaY += (lastCrossing - firstCrossing);
 489 
 490         // update free pointer (ie length in bytes)
 491         _edges.used += _SIZEOF_EDGE_BYTES;
 492 
 493         if (DO_MONITORS) {
 494             rdrCtx.stats.mon_rdr_addLine.stop();
 495         }
 496     }
 497 
 498 // END EDGE LIST
 499 //////////////////////////////////////////////////////////////////////////////
 500 
 501     // Cache to store RLE-encoded coverage mask of the current primitive
 502     final MarlinCache cache;
 503 
 504     // Bounds of the drawing region, at subpixel precision.
 505     private int boundsMinX, boundsMinY, boundsMaxX, boundsMaxY;
 506 
 507     // Current winding rule
 508     private int windingRule;
 509 
 510     // Current drawing position, i.e., final point of last segment
 511     private float x0, y0;
 512 
 513     // Position of most recent 'moveTo' command
 514     private float sx0, sy0;
 515 
 516     // per-thread renderer context
 517     final RendererContext rdrCtx;
 518     // dirty curve
 519     private final Curve curve;
 520 
 521     // clean alpha array (zero filled)
 522     private int[] alphaLine;
 523 
 524     // alphaLine ref (clean)
 525     private final IntArrayCache.Reference alphaLine_ref;
 526 
 527     private boolean enableBlkFlags = false;
 528     private boolean prevUseBlkFlags = false;
 529 
 530     /* block flags (0|1) */
 531     private int[] blkFlags;
 532 
 533     // blkFlags ref (clean)
 534     private final IntArrayCache.Reference blkFlags_ref;
 535 
 536     Renderer(final RendererContext rdrCtx) {
 537         this.rdrCtx = rdrCtx;
 538 
 539         this.edges = rdrCtx.newOffHeapArray(INITIAL_EDGES_CAPACITY); // 96K
 540 
 541         this.curve = rdrCtx.curve;
 542 
 543         edgeBuckets_ref      = rdrCtx.newCleanIntArrayRef(INITIAL_BUCKET_ARRAY); // 64K
 544         edgeBucketCounts_ref = rdrCtx.newCleanIntArrayRef(INITIAL_BUCKET_ARRAY); // 64K
 545 
 546         edgeBuckets      = edgeBuckets_ref.initial;
 547         edgeBucketCounts = edgeBucketCounts_ref.initial;
 548 
 549         // 2048 (pixelsize) pixel large
 550         alphaLine_ref = rdrCtx.newCleanIntArrayRef(INITIAL_AA_ARRAY); // 8K
 551         alphaLine     = alphaLine_ref.initial;
 552 
 553         this.cache = rdrCtx.cache;
 554 
 555         crossings_ref     = rdrCtx.newDirtyIntArrayRef(INITIAL_CROSSING_COUNT); // 2K
 556         aux_crossings_ref = rdrCtx.newDirtyIntArrayRef(INITIAL_CROSSING_COUNT); // 2K
 557         edgePtrs_ref      = rdrCtx.newDirtyIntArrayRef(INITIAL_CROSSING_COUNT); // 2K
 558         aux_edgePtrs_ref  = rdrCtx.newDirtyIntArrayRef(INITIAL_CROSSING_COUNT); // 2K
 559 
 560         crossings     = crossings_ref.initial;
 561         aux_crossings = aux_crossings_ref.initial;
 562         edgePtrs      = edgePtrs_ref.initial;
 563         aux_edgePtrs  = aux_edgePtrs_ref.initial;
 564 
 565         blkFlags_ref = rdrCtx.newCleanIntArrayRef(INITIAL_ARRAY); // 1K = 1 tile line
 566         blkFlags     = blkFlags_ref.initial;
 567     }
 568 
 569     Renderer init(final int pix_boundsX, final int pix_boundsY,
 570                   final int pix_boundsWidth, final int pix_boundsHeight,
 571                   final int windingRule) {
 572 
 573         this.windingRule = windingRule;
 574 
 575         // bounds as half-open intervals: minX <= x < maxX and minY <= y < maxY
 576         this.boundsMinX =  pix_boundsX << SUBPIXEL_LG_POSITIONS_X;
 577         this.boundsMaxX =
 578             (pix_boundsX + pix_boundsWidth) << SUBPIXEL_LG_POSITIONS_X;
 579         this.boundsMinY =  pix_boundsY << SUBPIXEL_LG_POSITIONS_Y;
 580         this.boundsMaxY =
 581             (pix_boundsY + pix_boundsHeight) << SUBPIXEL_LG_POSITIONS_Y;
 582 
 583         if (DO_LOG_BOUNDS) {
 584             MarlinUtils.logInfo("boundsXY = [" + boundsMinX + " ... "
 585                                 + boundsMaxX + "[ [" + boundsMinY + " ... "
 586                                 + boundsMaxY + "[");
 587         }
 588 
 589         // see addLine: ceil(boundsMaxY) => boundsMaxY + 1
 590         // +1 for edgeBucketCounts
 591         final int edgeBucketsLength = (boundsMaxY - boundsMinY) + 1;
 592 
 593         if (edgeBucketsLength > INITIAL_BUCKET_ARRAY) {
 594             if (DO_STATS) {
 595                 rdrCtx.stats.stat_array_renderer_edgeBuckets
 596                     .add(edgeBucketsLength);
 597                 rdrCtx.stats.stat_array_renderer_edgeBucketCounts
 598                     .add(edgeBucketsLength);
 599             }
 600             edgeBuckets = edgeBuckets_ref.getArray(edgeBucketsLength);
 601             edgeBucketCounts = edgeBucketCounts_ref.getArray(edgeBucketsLength);
 602         }
 603 
 604         edgeMinY = Integer.MAX_VALUE;
 605         edgeMaxY = Integer.MIN_VALUE;
 606         edgeMinX = Float.POSITIVE_INFINITY;
 607         edgeMaxX = Float.NEGATIVE_INFINITY;
 608 
 609         // reset used mark:
 610         edgeCount = 0;
 611         activeEdgeMaxUsed = 0;
 612         edges.used = 0;
 613 
 614         edgeSumDeltaY = 0;
 615 
 616         return this; // fluent API
 617     }
 618 
 619     /**
 620      * Disposes this renderer and recycle it clean up before reusing this instance
 621      */
 622     void dispose() {
 623         if (DO_STATS) {
 624             rdrCtx.stats.stat_rdr_activeEdges.add(activeEdgeMaxUsed);
 625             rdrCtx.stats.stat_rdr_edges.add(edges.used);
 626             rdrCtx.stats.stat_rdr_edges_count.add(edges.used / SIZEOF_EDGE_BYTES);
 627             rdrCtx.stats.hist_rdr_edges_count.add(edges.used / SIZEOF_EDGE_BYTES);
 628             rdrCtx.stats.totalOffHeap += edges.length;
 629         }
 630         // Return arrays:
 631         crossings = crossings_ref.putArray(crossings);
 632         aux_crossings = aux_crossings_ref.putArray(aux_crossings);
 633 
 634         edgePtrs = edgePtrs_ref.putArray(edgePtrs);
 635         aux_edgePtrs = aux_edgePtrs_ref.putArray(aux_edgePtrs);
 636 
 637         alphaLine = alphaLine_ref.putArray(alphaLine, 0, 0); // already zero filled
 638         blkFlags  = blkFlags_ref.putArray(blkFlags, 0, 0); // already zero filled
 639 
 640         if (edgeMinY != Integer.MAX_VALUE) {
 641             // if context is maked as DIRTY:
 642             if (rdrCtx.dirty) {
 643                 // may happen if an exception if thrown in the pipeline processing:
 644                 // clear completely buckets arrays:
 645                 buckets_minY = 0;
 646                 buckets_maxY = boundsMaxY - boundsMinY;
 647             }
 648             // clear only used part
 649             edgeBuckets = edgeBuckets_ref.putArray(edgeBuckets, buckets_minY,
 650                                                                 buckets_maxY);
 651             edgeBucketCounts = edgeBucketCounts_ref.putArray(edgeBucketCounts,
 652                                                              buckets_minY,
 653                                                              buckets_maxY + 1);
 654         } else {
 655             // unused arrays
 656             edgeBuckets = edgeBuckets_ref.putArray(edgeBuckets, 0, 0);
 657             edgeBucketCounts = edgeBucketCounts_ref.putArray(edgeBucketCounts, 0, 0);
 658         }
 659 
 660         // At last: resize back off-heap edges to initial size
 661         if (edges.length != INITIAL_EDGES_CAPACITY) {
 662             // note: may throw OOME:
 663             edges.resize(INITIAL_EDGES_CAPACITY);
 664         }
 665         if (DO_CLEAN_DIRTY) {
 666             // Force zero-fill dirty arrays:
 667             edges.fill(BYTE_0);
 668         }
 669         if (DO_MONITORS) {
 670             rdrCtx.stats.mon_rdr_endRendering.stop();
 671         }
 672     }
 673 
 674     private static float tosubpixx(final float pix_x) {
 675         return F_SUBPIXEL_POSITIONS_X * pix_x;
 676     }
 677 
 678     private static float tosubpixy(final float pix_y) {
 679         // shift y by -0.5 for fast ceil(y - 0.5):
 680         return F_SUBPIXEL_POSITIONS_Y * pix_y - 0.5f;
 681     }
 682 
 683     @Override
 684     public void moveTo(float pix_x0, float pix_y0) {
 685         closePath();
 686         final float sx = tosubpixx(pix_x0);
 687         final float sy = tosubpixy(pix_y0);
 688         this.sx0 = sx;
 689         this.sy0 = sy;
 690         this.x0 = sx;
 691         this.y0 = sy;
 692     }
 693 
 694     @Override
 695     public void lineTo(float pix_x1, float pix_y1) {
 696         final float x1 = tosubpixx(pix_x1);
 697         final float y1 = tosubpixy(pix_y1);
 698         addLine(x0, y0, x1, y1);
 699         x0 = x1;
 700         y0 = y1;
 701     }
 702 
 703     @Override
 704     public void curveTo(float x1, float y1,
 705             float x2, float y2,
 706             float x3, float y3)
 707     {
 708         final float xe = tosubpixx(x3);
 709         final float ye = tosubpixy(y3);
 710         curve.set(x0, y0, tosubpixx(x1), tosubpixy(y1),
 711                           tosubpixx(x2), tosubpixy(y2), xe, ye);
 712         curveBreakIntoLinesAndAdd(x0, y0, curve, xe, ye);
 713         x0 = xe;
 714         y0 = ye;
 715     }
 716 
 717     @Override
 718     public void quadTo(float x1, float y1, float x2, float y2) {
 719         final float xe = tosubpixx(x2);
 720         final float ye = tosubpixy(y2);
 721         curve.set(x0, y0, tosubpixx(x1), tosubpixy(y1), xe, ye);
 722         quadBreakIntoLinesAndAdd(x0, y0, curve, xe, ye);
 723         x0 = xe;
 724         y0 = ye;
 725     }
 726 
 727     @Override
 728     public void closePath() {
 729         addLine(x0, y0, sx0, sy0);
 730         x0 = sx0;
 731         y0 = sy0;
 732     }
 733 
 734     @Override
 735     public void pathDone() {
 736         closePath();
 737     }
 738 
 739     @Override
 740     public long getNativeConsumer() {
 741         throw new InternalError("Renderer does not use a native consumer.");
 742     }
 743 
 744     private void _endRendering(final int ymin, final int ymax) {
 745         if (DISABLE_RENDER) {
 746             return;
 747         }
 748 
 749         // Get X bounds as true pixel boundaries to compute correct pixel coverage:
 750         final int bboxx0 = bbox_spminX;
 751         final int bboxx1 = bbox_spmaxX;
 752 
 753         final boolean windingRuleEvenOdd = (windingRule == WIND_EVEN_ODD);
 754 
 755         // Useful when processing tile line by tile line
 756         final int[] _alpha = alphaLine;
 757 
 758         // local vars (performance):
 759         final MarlinCache _cache = cache;
 760         final OffHeapArray _edges = edges;
 761         final int[] _edgeBuckets = edgeBuckets;
 762         final int[] _edgeBucketCounts = edgeBucketCounts;
 763 
 764         int[] _crossings = this.crossings;
 765         int[] _edgePtrs  = this.edgePtrs;
 766 
 767         // merge sort auxiliary storage:
 768         int[] _aux_crossings = this.aux_crossings;
 769         int[] _aux_edgePtrs  = this.aux_edgePtrs;
 770 
 771         // copy constants:
 772         final long _OFF_ERROR    = OFF_ERROR;
 773         final long _OFF_BUMP_X   = OFF_BUMP_X;
 774         final long _OFF_BUMP_ERR = OFF_BUMP_ERR;
 775 
 776         final long _OFF_NEXT     = OFF_NEXT;
 777         final long _OFF_YMAX     = OFF_YMAX;
 778 
 779         final int _ALL_BUT_LSB   = ALL_BUT_LSB;
 780         final int _ERR_STEP_MAX  = ERR_STEP_MAX;
 781 
 782         // unsafe I/O:
 783         final Unsafe _unsafe = OffHeapArray.UNSAFE;
 784         final long    addr0  = _edges.address;
 785         long addr;
 786         final int _SUBPIXEL_LG_POSITIONS_X = SUBPIXEL_LG_POSITIONS_X;
 787         final int _SUBPIXEL_LG_POSITIONS_Y = SUBPIXEL_LG_POSITIONS_Y;
 788         final int _SUBPIXEL_MASK_X = SUBPIXEL_MASK_X;
 789         final int _SUBPIXEL_MASK_Y = SUBPIXEL_MASK_Y;
 790         final int _SUBPIXEL_POSITIONS_X = SUBPIXEL_POSITIONS_X;
 791 
 792         final int _MIN_VALUE = Integer.MIN_VALUE;
 793         final int _MAX_VALUE = Integer.MAX_VALUE;
 794 
 795         // Now we iterate through the scanlines. We must tell emitRow the coord
 796         // of the first non-transparent pixel, so we must keep accumulators for
 797         // the first and last pixels of the section of the current pixel row
 798         // that we will emit.
 799         // We also need to accumulate pix_bbox, but the iterator does it
 800         // for us. We will just get the values from it once this loop is done
 801         int minX = _MAX_VALUE;
 802         int maxX = _MIN_VALUE;
 803 
 804         int y = ymin;
 805         int bucket = y - boundsMinY;
 806 
 807         int numCrossings = this.edgeCount;
 808         int edgePtrsLen = _edgePtrs.length;
 809         int crossingsLen = _crossings.length;
 810         int _arrayMaxUsed = activeEdgeMaxUsed;
 811         int ptrLen = 0, newCount, ptrEnd;
 812 
 813         int bucketcount, i, j, ecur;
 814         int cross, lastCross;
 815         int x0, x1, tmp, sum, prev, curx, curxo, crorientation, err;
 816         int pix_x, pix_xmaxm1, pix_xmax;
 817 
 818         int low, high, mid, prevNumCrossings;
 819         boolean useBinarySearch;
 820 
 821         final int[] _blkFlags = blkFlags;
 822         final int _BLK_SIZE_LG = BLOCK_SIZE_LG;
 823         final int _BLK_SIZE = BLOCK_SIZE;
 824 
 825         final boolean _enableBlkFlagsHeuristics = ENABLE_BLOCK_FLAGS_HEURISTICS && this.enableBlkFlags;
 826 
 827         // Use block flags if large pixel span and few crossings:
 828         // ie mean(distance between crossings) is high
 829         boolean useBlkFlags = this.prevUseBlkFlags;
 830 
 831         final int stroking = rdrCtx.stroking;
 832 
 833         int lastY = -1; // last emited row
 834 
 835 
 836         // Iteration on scanlines
 837         for (; y < ymax; y++, bucket++) {
 838             // --- from former ScanLineIterator.next()
 839             bucketcount = _edgeBucketCounts[bucket];
 840 
 841             // marker on previously sorted edges:
 842             prevNumCrossings = numCrossings;
 843 
 844             // bucketCount indicates new edge / edge end:
 845             if (bucketcount != 0) {
 846                 if (DO_STATS) {
 847                     rdrCtx.stats.stat_rdr_activeEdges_updates.add(numCrossings);
 848                 }
 849 
 850                 // last bit set to 1 means that edges ends
 851                 if ((bucketcount & 0x1) != 0) {
 852                     // eviction in active edge list
 853                     // cache edges[] address + offset
 854                     addr = addr0 + _OFF_YMAX;
 855 
 856                     for (i = 0, newCount = 0; i < numCrossings; i++) {
 857                         // get the pointer to the edge
 858                         ecur = _edgePtrs[i];
 859                         // random access so use unsafe:
 860                         if (_unsafe.getInt(addr + ecur) > y) {
 861                             _edgePtrs[newCount++] = ecur;
 862                         }
 863                     }
 864                     // update marker on sorted edges minus removed edges:
 865                     prevNumCrossings = numCrossings = newCount;
 866                 }
 867 
 868                 ptrLen = bucketcount >> 1; // number of new edge
 869 
 870                 if (ptrLen != 0) {
 871                     if (DO_STATS) {
 872                         rdrCtx.stats.stat_rdr_activeEdges_adds.add(ptrLen);
 873                         if (ptrLen > 10) {
 874                             rdrCtx.stats.stat_rdr_activeEdges_adds_high.add(ptrLen);
 875                         }
 876                     }
 877                     ptrEnd = numCrossings + ptrLen;
 878 
 879                     if (edgePtrsLen < ptrEnd) {
 880                         if (DO_STATS) {
 881                             rdrCtx.stats.stat_array_renderer_edgePtrs.add(ptrEnd);
 882                         }
 883                         this.edgePtrs = _edgePtrs
 884                             = edgePtrs_ref.widenArray(_edgePtrs, numCrossings,
 885                                                       ptrEnd);
 886 
 887                         edgePtrsLen = _edgePtrs.length;
 888                         // Get larger auxiliary storage:
 889                         aux_edgePtrs_ref.putArray(_aux_edgePtrs);
 890 
 891                         // use ArrayCache.getNewSize() to use the same growing
 892                         // factor than widenArray():
 893                         if (DO_STATS) {
 894                             rdrCtx.stats.stat_array_renderer_aux_edgePtrs.add(ptrEnd);
 895                         }
 896                         this.aux_edgePtrs = _aux_edgePtrs
 897                             = aux_edgePtrs_ref.getArray(
 898                                 ArrayCacheConst.getNewSize(numCrossings, ptrEnd)
 899                             );
 900                     }
 901 
 902                     // cache edges[] address + offset
 903                     addr = addr0 + _OFF_NEXT;
 904 
 905                     // add new edges to active edge list:
 906                     for (ecur = _edgeBuckets[bucket];
 907                          numCrossings < ptrEnd; numCrossings++)
 908                     {
 909                         // store the pointer to the edge
 910                         _edgePtrs[numCrossings] = ecur;
 911                         // random access so use unsafe:
 912                         ecur = _unsafe.getInt(addr + ecur);
 913                     }
 914 
 915                     if (crossingsLen < numCrossings) {
 916                         // Get larger array:
 917                         crossings_ref.putArray(_crossings);
 918 
 919                         if (DO_STATS) {
 920                             rdrCtx.stats.stat_array_renderer_crossings
 921                                 .add(numCrossings);
 922                         }
 923                         this.crossings = _crossings
 924                             = crossings_ref.getArray(numCrossings);
 925 
 926                         // Get larger auxiliary storage:
 927                         aux_crossings_ref.putArray(_aux_crossings);
 928 
 929                         if (DO_STATS) {
 930                             rdrCtx.stats.stat_array_renderer_aux_crossings
 931                                 .add(numCrossings);
 932                         }
 933                         this.aux_crossings = _aux_crossings
 934                             = aux_crossings_ref.getArray(numCrossings);
 935 
 936                         crossingsLen = _crossings.length;
 937                     }
 938                     if (DO_STATS) {
 939                         // update max used mark
 940                         if (numCrossings > _arrayMaxUsed) {
 941                             _arrayMaxUsed = numCrossings;
 942                         }
 943                     }
 944                 } // ptrLen != 0
 945             } // bucketCount != 0
 946 
 947 
 948             if (numCrossings != 0) {
 949                 /*
 950                  * thresholds to switch to optimized merge sort
 951                  * for newly added edges + final merge pass.
 952                  */
 953                 if ((ptrLen < 10) || (numCrossings < 40)) {
 954                     if (DO_STATS) {
 955                         rdrCtx.stats.hist_rdr_crossings.add(numCrossings);
 956                         rdrCtx.stats.hist_rdr_crossings_adds.add(ptrLen);
 957                     }
 958 
 959                     /*
 960                      * threshold to use binary insertion sort instead of
 961                      * straight insertion sort (to reduce minimize comparisons).
 962                      */
 963                     useBinarySearch = (numCrossings >= 20);
 964 
 965                     // if small enough:
 966                     lastCross = _MIN_VALUE;
 967 
 968                     for (i = 0; i < numCrossings; i++) {
 969                         // get the pointer to the edge
 970                         ecur = _edgePtrs[i];
 971 
 972                         /* convert subpixel coordinates (float) into pixel
 973                             positions (int) for coming scanline */
 974                         /* note: it is faster to always update edges even
 975                            if it is removed from AEL for coming or last scanline */
 976 
 977                         // random access so use unsafe:
 978                         addr = addr0 + ecur; // ecur + OFF_F_CURX
 979 
 980                         // get current crossing:
 981                         curx = _unsafe.getInt(addr);
 982 
 983                         // update crossing with orientation at last bit:
 984                         cross = curx;
 985 
 986                         // Increment x using DDA (fixed point):
 987                         curx += _unsafe.getInt(addr + _OFF_BUMP_X);
 988 
 989                         // Increment error:
 990                         err  =  _unsafe.getInt(addr + _OFF_ERROR)
 991                               + _unsafe.getInt(addr + _OFF_BUMP_ERR);
 992 
 993                         // Manual carry handling:
 994                         // keep sign and carry bit only and ignore last bit (preserve orientation):
 995                         _unsafe.putInt(addr,               curx - ((err >> 30) & _ALL_BUT_LSB));
 996                         _unsafe.putInt(addr + _OFF_ERROR, (err & _ERR_STEP_MAX));
 997 
 998                         if (DO_STATS) {
 999                             rdrCtx.stats.stat_rdr_crossings_updates.add(numCrossings);
1000                         }
1001 
1002                         // insertion sort of crossings:
1003                         if (cross < lastCross) {
1004                             if (DO_STATS) {
1005                                 rdrCtx.stats.stat_rdr_crossings_sorts.add(i);
1006                             }
1007 
1008                             /* use binary search for newly added edges
1009                                in crossings if arrays are large enough */
1010                             if (useBinarySearch && (i >= prevNumCrossings)) {
1011                                 if (DO_STATS) {
1012                                     rdrCtx.stats.stat_rdr_crossings_bsearch.add(i);
1013                                 }
1014                                 low = 0;
1015                                 high = i - 1;
1016 
1017                                 do {
1018                                     // note: use signed shift (not >>>) for performance
1019                                     // as indices are small enough to exceed Integer.MAX_VALUE
1020                                     mid = (low + high) >> 1;
1021 
1022                                     if (_crossings[mid] < cross) {
1023                                         low = mid + 1;
1024                                     } else {
1025                                         high = mid - 1;
1026                                     }
1027                                 } while (low <= high);
1028 
1029                                 for (j = i - 1; j >= low; j--) {
1030                                     _crossings[j + 1] = _crossings[j];
1031                                     _edgePtrs [j + 1] = _edgePtrs[j];
1032                                 }
1033                                 _crossings[low] = cross;
1034                                 _edgePtrs [low] = ecur;
1035 
1036                             } else {
1037                                 j = i - 1;
1038                                 _crossings[i] = _crossings[j];
1039                                 _edgePtrs[i] = _edgePtrs[j];
1040 
1041                                 while ((--j >= 0) && (_crossings[j] > cross)) {
1042                                     _crossings[j + 1] = _crossings[j];
1043                                     _edgePtrs [j + 1] = _edgePtrs[j];
1044                                 }
1045                                 _crossings[j + 1] = cross;
1046                                 _edgePtrs [j + 1] = ecur;
1047                             }
1048 
1049                         } else {
1050                             _crossings[i] = lastCross = cross;
1051                         }
1052                     }
1053                 } else {
1054                     if (DO_STATS) {
1055                         rdrCtx.stats.stat_rdr_crossings_msorts.add(numCrossings);
1056                         rdrCtx.stats.hist_rdr_crossings_ratio
1057                             .add((1000 * ptrLen) / numCrossings);
1058                         rdrCtx.stats.hist_rdr_crossings_msorts.add(numCrossings);
1059                         rdrCtx.stats.hist_rdr_crossings_msorts_adds.add(ptrLen);
1060                     }
1061 
1062                     // Copy sorted data in auxiliary arrays
1063                     // and perform insertion sort on almost sorted data
1064                     // (ie i < prevNumCrossings):
1065 
1066                     lastCross = _MIN_VALUE;
1067 
1068                     for (i = 0; i < numCrossings; i++) {
1069                         // get the pointer to the edge
1070                         ecur = _edgePtrs[i];
1071 
1072                         /* convert subpixel coordinates (float) into pixel
1073                             positions (int) for coming scanline */
1074                         /* note: it is faster to always update edges even
1075                            if it is removed from AEL for coming or last scanline */
1076 
1077                         // random access so use unsafe:
1078                         addr = addr0 + ecur; // ecur + OFF_F_CURX
1079 
1080                         // get current crossing:
1081                         curx = _unsafe.getInt(addr);
1082 
1083                         // update crossing with orientation at last bit:
1084                         cross = curx;
1085 
1086                         // Increment x using DDA (fixed point):
1087                         curx += _unsafe.getInt(addr + _OFF_BUMP_X);
1088 
1089                         // Increment error:
1090                         err  =  _unsafe.getInt(addr + _OFF_ERROR)
1091                               + _unsafe.getInt(addr + _OFF_BUMP_ERR);
1092 
1093                         // Manual carry handling:
1094                         // keep sign and carry bit only and ignore last bit (preserve orientation):
1095                         _unsafe.putInt(addr,               curx - ((err >> 30) & _ALL_BUT_LSB));
1096                         _unsafe.putInt(addr + _OFF_ERROR, (err & _ERR_STEP_MAX));
1097 
1098                         if (DO_STATS) {
1099                             rdrCtx.stats.stat_rdr_crossings_updates.add(numCrossings);
1100                         }
1101 
1102                         if (i >= prevNumCrossings) {
1103                             // simply store crossing as edgePtrs is in-place:
1104                             // will be copied and sorted efficiently by mergesort later:
1105                             _crossings[i]     = cross;
1106 
1107                         } else if (cross < lastCross) {
1108                             if (DO_STATS) {
1109                                 rdrCtx.stats.stat_rdr_crossings_sorts.add(i);
1110                             }
1111 
1112                             // (straight) insertion sort of crossings:
1113                             j = i - 1;
1114                             _aux_crossings[i] = _aux_crossings[j];
1115                             _aux_edgePtrs[i] = _aux_edgePtrs[j];
1116 
1117                             while ((--j >= 0) && (_aux_crossings[j] > cross)) {
1118                                 _aux_crossings[j + 1] = _aux_crossings[j];
1119                                 _aux_edgePtrs [j + 1] = _aux_edgePtrs[j];
1120                             }
1121                             _aux_crossings[j + 1] = cross;
1122                             _aux_edgePtrs [j + 1] = ecur;
1123 
1124                         } else {
1125                             // auxiliary storage:
1126                             _aux_crossings[i] = lastCross = cross;
1127                             _aux_edgePtrs [i] = ecur;
1128                         }
1129                     }
1130 
1131                     // use Mergesort using auxiliary arrays (sort only right part)
1132                     MergeSort.mergeSortNoCopy(_crossings,     _edgePtrs,
1133                                               _aux_crossings, _aux_edgePtrs,
1134                                               numCrossings,   prevNumCrossings);
1135                 }
1136 
1137                 // reset ptrLen
1138                 ptrLen = 0;
1139                 // --- from former ScanLineIterator.next()
1140 
1141 
1142                 /* note: bboxx0 and bboxx1 must be pixel boundaries
1143                    to have correct coverage computation */
1144 
1145                 // right shift on crossings to get the x-coordinate:
1146                 curxo = _crossings[0];
1147                 x0    = curxo >> 1;
1148                 if (x0 < minX) {
1149                     minX = x0; // subpixel coordinate
1150                 }
1151 
1152                 x1 = _crossings[numCrossings - 1] >> 1;
1153                 if (x1 > maxX) {
1154                     maxX = x1; // subpixel coordinate
1155                 }
1156 
1157 
1158                 // compute pixel coverages
1159                 prev = curx = x0;
1160                 // to turn {0, 1} into {-1, 1}, multiply by 2 and subtract 1.
1161                 // last bit contains orientation (0 or 1)
1162                 crorientation = ((curxo & 0x1) << 1) - 1;
1163 
1164                 if (windingRuleEvenOdd) {
1165                     sum = crorientation;
1166 
1167                     // Even Odd winding rule: take care of mask ie sum(orientations)
1168                     for (i = 1; i < numCrossings; i++) {
1169                         curxo = _crossings[i];
1170                         curx  =  curxo >> 1;
1171                         // to turn {0, 1} into {-1, 1}, multiply by 2 and subtract 1.
1172                         // last bit contains orientation (0 or 1)
1173                         crorientation = ((curxo & 0x1) << 1) - 1;
1174 
1175                         if ((sum & 0x1) != 0) {
1176                             // TODO: perform line clipping on left-right sides
1177                             // to avoid such bound checks:
1178                             x0 = (prev > bboxx0) ? prev : bboxx0;
1179                             x1 = (curx < bboxx1) ? curx : bboxx1;
1180 
1181                             if (x0 < x1) {
1182                                 x0 -= bboxx0; // turn x0, x1 from coords to indices
1183                                 x1 -= bboxx0; // in the alpha array.
1184 
1185                                 pix_x      =  x0      >> _SUBPIXEL_LG_POSITIONS_X;
1186                                 pix_xmaxm1 = (x1 - 1) >> _SUBPIXEL_LG_POSITIONS_X;
1187 
1188                                 if (pix_x == pix_xmaxm1) {
1189                                     // Start and end in same pixel
1190                                     tmp = (x1 - x0); // number of subpixels
1191                                     _alpha[pix_x    ] += tmp;
1192                                     _alpha[pix_x + 1] -= tmp;
1193 
1194                                     if (useBlkFlags) {
1195                                         // flag used blocks:
1196                                         _blkFlags[pix_x >> _BLK_SIZE_LG] = 1;
1197                                     }
1198                                 } else {
1199                                     tmp = (x0 & _SUBPIXEL_MASK_X);
1200                                     _alpha[pix_x    ]
1201                                         += (_SUBPIXEL_POSITIONS_X - tmp);
1202                                     _alpha[pix_x + 1]
1203                                         += tmp;
1204 
1205                                     pix_xmax = x1 >> _SUBPIXEL_LG_POSITIONS_X;
1206 
1207                                     tmp = (x1 & _SUBPIXEL_MASK_X);
1208                                     _alpha[pix_xmax    ]
1209                                         -= (_SUBPIXEL_POSITIONS_X - tmp);
1210                                     _alpha[pix_xmax + 1]
1211                                         -= tmp;
1212 
1213                                     if (useBlkFlags) {
1214                                         // flag used blocks:
1215                                         _blkFlags[pix_x    >> _BLK_SIZE_LG] = 1;
1216                                         _blkFlags[pix_xmax >> _BLK_SIZE_LG] = 1;
1217                                     }
1218                                 }
1219                             }
1220                         }
1221 
1222                         sum += crorientation;
1223                         prev = curx;
1224                     }
1225                 } else {
1226                     // Non-zero winding rule: optimize that case (default)
1227                     // and avoid processing intermediate crossings
1228                     for (i = 1, sum = 0;; i++) {
1229                         sum += crorientation;
1230 
1231                         if (sum != 0) {
1232                             // prev = min(curx)
1233                             if (prev > curx) {
1234                                 prev = curx;
1235                             }
1236                         } else {
1237                             // TODO: perform line clipping on left-right sides
1238                             // to avoid such bound checks:
1239                             x0 = (prev > bboxx0) ? prev : bboxx0;
1240                             x1 = (curx < bboxx1) ? curx : bboxx1;
1241 
1242                             if (x0 < x1) {
1243                                 x0 -= bboxx0; // turn x0, x1 from coords to indices
1244                                 x1 -= bboxx0; // in the alpha array.
1245 
1246                                 pix_x      =  x0      >> _SUBPIXEL_LG_POSITIONS_X;
1247                                 pix_xmaxm1 = (x1 - 1) >> _SUBPIXEL_LG_POSITIONS_X;
1248 
1249                                 if (pix_x == pix_xmaxm1) {
1250                                     // Start and end in same pixel
1251                                     tmp = (x1 - x0); // number of subpixels
1252                                     _alpha[pix_x    ] += tmp;
1253                                     _alpha[pix_x + 1] -= tmp;
1254 
1255                                     if (useBlkFlags) {
1256                                         // flag used blocks:
1257                                         _blkFlags[pix_x >> _BLK_SIZE_LG] = 1;
1258                                     }
1259                                 } else {
1260                                     tmp = (x0 & _SUBPIXEL_MASK_X);
1261                                     _alpha[pix_x    ]
1262                                         += (_SUBPIXEL_POSITIONS_X - tmp);
1263                                     _alpha[pix_x + 1]
1264                                         += tmp;
1265 
1266                                     pix_xmax = x1 >> _SUBPIXEL_LG_POSITIONS_X;
1267 
1268                                     tmp = (x1 & _SUBPIXEL_MASK_X);
1269                                     _alpha[pix_xmax    ]
1270                                         -= (_SUBPIXEL_POSITIONS_X - tmp);
1271                                     _alpha[pix_xmax + 1]
1272                                         -= tmp;
1273 
1274                                     if (useBlkFlags) {
1275                                         // flag used blocks:
1276                                         _blkFlags[pix_x    >> _BLK_SIZE_LG] = 1;
1277                                         _blkFlags[pix_xmax >> _BLK_SIZE_LG] = 1;
1278                                     }
1279                                 }
1280                             }
1281                             prev = _MAX_VALUE;
1282                         }
1283 
1284                         if (i == numCrossings) {
1285                             break;
1286                         }
1287 
1288                         curxo = _crossings[i];
1289                         curx  =  curxo >> 1;
1290                         // to turn {0, 1} into {-1, 1}, multiply by 2 and subtract 1.
1291                         // last bit contains orientation (0 or 1)
1292                         crorientation = ((curxo & 0x1) << 1) - 1;
1293                     }
1294                 }
1295             } // numCrossings > 0
1296 
1297             // even if this last row had no crossings, alpha will be zeroed
1298             // from the last emitRow call. But this doesn't matter because
1299             // maxX < minX, so no row will be emitted to the MarlinCache.
1300             if ((y & _SUBPIXEL_MASK_Y) == _SUBPIXEL_MASK_Y) {
1301                 lastY = y >> _SUBPIXEL_LG_POSITIONS_Y;
1302 
1303                 // convert subpixel to pixel coordinate within boundaries:
1304                 minX = FloatMath.max(minX, bboxx0) >> _SUBPIXEL_LG_POSITIONS_X;
1305                 maxX = FloatMath.min(maxX, bboxx1) >> _SUBPIXEL_LG_POSITIONS_X;
1306 
1307                 if (maxX >= minX) {
1308                     // note: alpha array will be zeroed by copyAARow()
1309                     // +2 because alpha [pix_minX; pix_maxX+1]
1310                     // fix range [x0; x1[
1311                     copyAARow(_alpha, lastY, minX, maxX + 2, useBlkFlags);
1312 
1313                     // speculative for next pixel row (scanline coherence):
1314                     if (_enableBlkFlagsHeuristics) {
1315                         // Use block flags if large pixel span and few crossings:
1316                         // ie mean(distance between crossings) is larger than
1317                         // 1 block size;
1318 
1319                         // fast check width:
1320                         maxX -= minX;
1321 
1322                         // if stroking: numCrossings /= 2
1323                         // => shift numCrossings by 1
1324                         // condition = (width / (numCrossings - 1)) > blockSize
1325                         useBlkFlags = (maxX > _BLK_SIZE) && (maxX >
1326                             (((numCrossings >> stroking) - 1) << _BLK_SIZE_LG));
1327 
1328                         if (DO_STATS) {
1329                             tmp = FloatMath.max(1,
1330                                     ((numCrossings >> stroking) - 1));
1331                             rdrCtx.stats.hist_tile_generator_encoding_dist
1332                                 .add(maxX / tmp);
1333                         }
1334                     }
1335                 } else {
1336                     _cache.clearAARow(lastY);
1337                 }
1338                 minX = _MAX_VALUE;
1339                 maxX = _MIN_VALUE;
1340             }
1341         } // scan line iterator
1342 
1343         // Emit final row
1344         y--;
1345         y >>= _SUBPIXEL_LG_POSITIONS_Y;
1346 
1347         // convert subpixel to pixel coordinate within boundaries:
1348         minX = FloatMath.max(minX, bboxx0) >> _SUBPIXEL_LG_POSITIONS_X;
1349         maxX = FloatMath.min(maxX, bboxx1) >> _SUBPIXEL_LG_POSITIONS_X;
1350 
1351         if (maxX >= minX) {
1352             // note: alpha array will be zeroed by copyAARow()
1353             // +2 because alpha [pix_minX; pix_maxX+1]
1354             // fix range [x0; x1[
1355             copyAARow(_alpha, y, minX, maxX + 2, useBlkFlags);
1356         } else if (y != lastY) {
1357             _cache.clearAARow(y);
1358         }
1359 
1360         // update member:
1361         edgeCount = numCrossings;
1362         prevUseBlkFlags = useBlkFlags;
1363 
1364         if (DO_STATS) {
1365             // update max used mark
1366             activeEdgeMaxUsed = _arrayMaxUsed;
1367         }
1368     }
1369 
1370     boolean endRendering() {
1371         if (DO_MONITORS) {
1372             rdrCtx.stats.mon_rdr_endRendering.start();
1373         }
1374         if (edgeMinY == Integer.MAX_VALUE) {
1375             return false; // undefined edges bounds
1376         }
1377 
1378         final int _boundsMinY = boundsMinY;
1379         final int _boundsMaxY = boundsMaxY;
1380 
1381         // bounds as inclusive intervals
1382         final int spminX = FloatMath.max(FloatMath.ceil_int(edgeMinX - 0.5f), boundsMinX);
1383         final int spmaxX = FloatMath.min(FloatMath.ceil_int(edgeMaxX - 0.5f), boundsMaxX - 1);
1384 
1385         // edge Min/Max Y are already rounded to subpixels within bounds:
1386         final int spminY = edgeMinY;
1387         final int spmaxY;
1388         int maxY = edgeMaxY;
1389 
1390         if (maxY <= _boundsMaxY - 1) {
1391             spmaxY = maxY;
1392         } else {
1393             spmaxY = _boundsMaxY - 1;
1394             maxY   = _boundsMaxY;
1395         }
1396         buckets_minY = spminY - _boundsMinY;
1397         buckets_maxY = maxY   - _boundsMinY;
1398 
1399         if (DO_LOG_BOUNDS) {
1400             MarlinUtils.logInfo("edgesXY = [" + edgeMinX + " ... " + edgeMaxX
1401                                 + "][" + edgeMinY + " ... " + edgeMaxY + "]");
1402             MarlinUtils.logInfo("spXY    = [" + spminX + " ... " + spmaxX
1403                                 + "][" + spminY + " ... " + spmaxY + "]");
1404         }
1405 
1406         // test clipping for shapes out of bounds
1407         if ((spminX > spmaxX) || (spminY > spmaxY)) {
1408             return false;
1409         }
1410 
1411         // half open intervals
1412         // inclusive:
1413         final int pminX =  spminX                    >> SUBPIXEL_LG_POSITIONS_X;
1414         // exclusive:
1415         final int pmaxX = (spmaxX + SUBPIXEL_MASK_X) >> SUBPIXEL_LG_POSITIONS_X;
1416         // inclusive:
1417         final int pminY =  spminY                    >> SUBPIXEL_LG_POSITIONS_Y;
1418         // exclusive:
1419         final int pmaxY = (spmaxY + SUBPIXEL_MASK_Y) >> SUBPIXEL_LG_POSITIONS_Y;
1420 
1421         // store BBox to answer ptg.getBBox():
1422         this.cache.init(pminX, pminY, pmaxX, pmaxY, edgeSumDeltaY);
1423 
1424         // Heuristics for using block flags:
1425         if (ENABLE_BLOCK_FLAGS) {
1426             enableBlkFlags = this.cache.useRLE;
1427             prevUseBlkFlags = enableBlkFlags && !ENABLE_BLOCK_FLAGS_HEURISTICS;
1428 
1429             if (enableBlkFlags) {
1430                 // ensure blockFlags array is large enough:
1431                 // note: +2 to ensure enough space left at end
1432                 final int nxTiles = ((pmaxX - pminX) >> TILE_SIZE_LG) + 2;
1433                 if (nxTiles > INITIAL_ARRAY) {
1434                     blkFlags = blkFlags_ref.getArray(nxTiles);
1435                 }
1436             }
1437         }
1438 
1439         // memorize the rendering bounding box:
1440         /* note: bbox_spminX and bbox_spmaxX must be pixel boundaries
1441            to have correct coverage computation */
1442         // inclusive:
1443         bbox_spminX = pminX << SUBPIXEL_LG_POSITIONS_X;
1444         // exclusive:
1445         bbox_spmaxX = pmaxX << SUBPIXEL_LG_POSITIONS_X;
1446         // inclusive:
1447         bbox_spminY = spminY;
1448         // exclusive:
1449         bbox_spmaxY = FloatMath.min(spmaxY + 1, pmaxY << SUBPIXEL_LG_POSITIONS_Y);
1450 
1451         if (DO_LOG_BOUNDS) {
1452             MarlinUtils.logInfo("pXY       = [" + pminX + " ... " + pmaxX
1453                                 + "[ [" + pminY + " ... " + pmaxY + "[");
1454             MarlinUtils.logInfo("bbox_spXY = [" + bbox_spminX + " ... "
1455                                 + bbox_spmaxX + "[ [" + bbox_spminY + " ... "
1456                                 + bbox_spmaxY + "[");
1457         }
1458 
1459         // Prepare alpha line:
1460         // add 2 to better deal with the last pixel in a pixel row.
1461         final int width = (pmaxX - pminX) + 2;
1462 
1463         // Useful when processing tile line by tile line
1464         if (width > INITIAL_AA_ARRAY) {
1465             if (DO_STATS) {
1466                 rdrCtx.stats.stat_array_renderer_alphaline.add(width);
1467             }
1468             alphaLine = alphaLine_ref.getArray(width);
1469         }
1470 
1471         // process first tile line:
1472         endRendering(pminY);
1473 
1474         return true;
1475     }
1476 
1477     private int bbox_spminX, bbox_spmaxX, bbox_spminY, bbox_spmaxY;
1478 
1479     void endRendering(final int pminY) {
1480         if (DO_MONITORS) {
1481             rdrCtx.stats.mon_rdr_endRendering_Y.start();
1482         }
1483 
1484         final int spminY       = pminY << SUBPIXEL_LG_POSITIONS_Y;
1485         final int fixed_spminY = FloatMath.max(bbox_spminY, spminY);
1486 
1487         // avoid rendering for last call to nextTile()
1488         if (fixed_spminY < bbox_spmaxY) {
1489             // process a complete tile line ie scanlines for 32 rows
1490             final int spmaxY = FloatMath.min(bbox_spmaxY, spminY + SUBPIXEL_TILE);
1491 
1492             // process tile line [0 - 32]
1493             cache.resetTileLine(pminY);
1494 
1495             // Process only one tile line:
1496             _endRendering(fixed_spminY, spmaxY);
1497         }
1498         if (DO_MONITORS) {
1499             rdrCtx.stats.mon_rdr_endRendering_Y.stop();
1500         }
1501     }
1502 
1503     void copyAARow(final int[] alphaRow,
1504                    final int pix_y, final int pix_from, final int pix_to,
1505                    final boolean useBlockFlags)
1506     {
1507         if (useBlockFlags) {
1508             if (DO_STATS) {
1509                 rdrCtx.stats.hist_tile_generator_encoding.add(1);
1510             }
1511             cache.copyAARowRLE_WithBlockFlags(blkFlags, alphaRow, pix_y, pix_from, pix_to);
1512         } else {
1513             if (DO_STATS) {
1514                 rdrCtx.stats.hist_tile_generator_encoding.add(0);
1515             }
1516             cache.copyAARowNoRLE(alphaRow, pix_y, pix_from, pix_to);
1517         }
1518     }
1519 }