1 /*
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   3  * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER.
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   5  * This code is free software; you can redistribute it and/or modify it
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   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  *
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  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).
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  25 
  26 package sun.java2d.marlin;
  27 
  28 import sun.awt.geom.PathConsumer2D;
  29 import static sun.java2d.marlin.OffHeapArray.SIZE_INT;
  30 import jdk.internal.misc.Unsafe;
  31 
  32 final class Renderer implements PathConsumer2D, MarlinRenderer {
  33 
  34     static final boolean DISABLE_RENDER = false;
  35 
  36     static final boolean ENABLE_BLOCK_FLAGS = MarlinProperties.isUseTileFlags();
  37     static final boolean ENABLE_BLOCK_FLAGS_HEURISTICS = MarlinProperties.isUseTileFlagsWithHeuristics();
  38 
  39     private static final int ALL_BUT_LSB = 0xFFFFFFFE;
  40     private static final int ERR_STEP_MAX = 0x7FFFFFFF; // = 2^31 - 1
  41 
  42     private static final double POWER_2_TO_32 = 0x1.0p32d;
  43 
  44     // use float to make tosubpix methods faster (no int to float conversion)
  45     static final float SUBPIXEL_SCALE_X = (float) SUBPIXEL_POSITIONS_X;
  46     static final float SUBPIXEL_SCALE_Y = (float) SUBPIXEL_POSITIONS_Y;
  47     static final int SUBPIXEL_MASK_X = SUBPIXEL_POSITIONS_X - 1;
  48     static final int SUBPIXEL_MASK_Y = SUBPIXEL_POSITIONS_Y - 1;
  49 
  50     static final float RDR_OFFSET_X = 0.501f / SUBPIXEL_SCALE_X;
  51     static final float RDR_OFFSET_Y = 0.501f / SUBPIXEL_SCALE_Y;
  52 
  53     // number of subpixels corresponding to a tile line
  54     private static final int SUBPIXEL_TILE
  55         = TILE_H << 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 / 4 ~ 1024
  62     static final int INITIAL_CROSSING_COUNT = INITIAL_EDGES_COUNT >> 2;
  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         = MarlinProperties.getCubicDecD2() * (NORM_SUBPIXELS / 8.0f); // 1 pixel
  84     // cubic error in subpixels to increment step
  85     private static final float CUB_INC_ERR_SUBPIX
  86         = MarlinProperties.getCubicIncD1() * (NORM_SUBPIXELS / 8.0f); // 0.4 pixel
  87 
  88     // TestNonAARasterization (JDK-8170879): cubics
  89     // bad paths (59294/100000 == 59,29%, 94335 bad pixels (avg = 1,59), 3966 warnings (avg = 0,07)
  90 
  91     // cubic bind length to decrement step
  92     public static final float CUB_DEC_BND
  93         = 8.0f * CUB_DEC_ERR_SUBPIX;
  94     // cubic bind length to increment step
  95     public static final float CUB_INC_BND
  96         = 8.0f * CUB_INC_ERR_SUBPIX;
  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 = 1.0f / CUB_COUNT;
 108     // cubic dt^2 = 1 / count^2 = 1 / 4^countlg
 109     private static final float CUB_INV_COUNT_2 = 1.0f / CUB_COUNT_2;
 110     // cubic dt^3 = 1 / count^3 = 1 / 8^countlg
 111     private static final float CUB_INV_COUNT_3 = 1.0f / CUB_COUNT_3;
 112 
 113     // quad break into lines
 114     // quadratic error in subpixels
 115     private static final float QUAD_DEC_ERR_SUBPIX
 116         = MarlinProperties.getQuadDecD2() * (NORM_SUBPIXELS / 8.0f); // 0.5 pixel
 117 
 118     // TestNonAARasterization (JDK-8170879): quads
 119     // bad paths (62916/100000 == 62,92%, 103818 bad pixels (avg = 1,65), 6514 warnings (avg = 0,10)
 120 
 121     // quadratic bind length to decrement step
 122     public static final float QUAD_DEC_BND
 123         = 8.0f * QUAD_DEC_ERR_SUBPIX;
 124 
 125 //////////////////////////////////////////////////////////////////////////////
 126 //  SCAN LINE
 127 //////////////////////////////////////////////////////////////////////////////
 128     // crossings ie subpixel edge x coordinates
 129     private int[] crossings;
 130     // auxiliary storage for crossings (merge sort)
 131     private int[] aux_crossings;
 132 
 133     // indices into the segment pointer lists. They indicate the "active"
 134     // sublist in the segment lists (the portion of the list that contains
 135     // all the segments that cross the next scan line).
 136     private int edgeCount;
 137     private int[] edgePtrs;
 138     // auxiliary storage for edge pointers (merge sort)
 139     private int[] aux_edgePtrs;
 140 
 141     // max used for both edgePtrs and crossings (stats only)
 142     private int activeEdgeMaxUsed;
 143 
 144     // crossings ref (dirty)
 145     private final IntArrayCache.Reference crossings_ref;
 146     // edgePtrs ref (dirty)
 147     private final IntArrayCache.Reference edgePtrs_ref;
 148     // merge sort initial arrays (large enough to satisfy most usages) (1024)
 149     // aux_crossings ref (dirty)
 150     private final IntArrayCache.Reference aux_crossings_ref;
 151     // aux_edgePtrs ref (dirty)
 152     private final IntArrayCache.Reference aux_edgePtrs_ref;
 153 
 154 //////////////////////////////////////////////////////////////////////////////
 155 //  EDGE LIST
 156 //////////////////////////////////////////////////////////////////////////////
 157     private int edgeMinY = Integer.MAX_VALUE;
 158     private int edgeMaxY = Integer.MIN_VALUE;
 159     private float edgeMinX = Float.POSITIVE_INFINITY;
 160     private float edgeMaxX = Float.NEGATIVE_INFINITY;
 161 
 162     // edges [ints] stored in off-heap memory
 163     private final OffHeapArray edges;
 164 
 165     private int[] edgeBuckets;
 166     private int[] edgeBucketCounts; // 2*newedges + (1 if pruning needed)
 167     // used range for edgeBuckets / edgeBucketCounts
 168     private int buckets_minY;
 169     private int buckets_maxY;
 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 = 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 /= 4.0f; // 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 = 1.0f / 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 = 2.0f * c.dax * icount3;
 250         dddy = 2.0f * 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) + Math.abs(ddy) >= _DEC_BND) {
 266                 dddx /= 8.0f;
 267                 dddy /= 8.0f;
 268                 ddx = ddx / 4.0f - dddx;
 269                 ddy = ddy / 4.0f - dddy;
 270                 dx = (dx - ddx) / 2.0f;
 271                 dy = (dy - ddy) / 2.0f;
 272 
 273                 count <<= 1;
 274                 if (DO_STATS) {
 275                     rdrCtx.stats.stat_rdr_curveBreak_dec.add(count);
 276                 }
 277             }
 278 
 279             // double step:
 280             // can only do this on even "count" values, because we must divide count by 2
 281             while (count % 2 == 0
 282                    && Math.abs(dx) + Math.abs(dy) <= _INC_BND)
 283             {
 284                 dx = 2.0f * dx + ddx;
 285                 dy = 2.0f * dy + ddy;
 286                 ddx = 4.0f * (ddx + dddx);
 287                 ddy = 4.0f * (ddy + dddy);
 288                 dddx *= 8.0f;
 289                 dddy *= 8.0f;
 290 
 291                 count >>= 1;
 292                 if (DO_STATS) {
 293                     rdrCtx.stats.stat_rdr_curveBreak_inc.add(count);
 294                 }
 295             }
 296             if (--count > 0) {
 297                 x1 += dx;
 298                 dx += ddx;
 299                 ddx += dddx;
 300                 y1 += dy;
 301                 dy += ddy;
 302                 ddy += dddy;
 303             } else {
 304                 x1 = x3;
 305                 y1 = y3;
 306             }
 307 
 308             addLine(x0, y0, x1, y1);
 309 
 310             if (DO_STATS) { nL++; }
 311             x0 = x1;
 312             y0 = y1;
 313         }
 314         if (DO_STATS) {
 315             rdrCtx.stats.stat_rdr_curveBreak.add(nL);
 316         }
 317     }
 318 
 319     private void addLine(float x1, float y1, float x2, float y2) {
 320         if (DO_MONITORS) {
 321             rdrCtx.stats.mon_rdr_addLine.start();
 322         }
 323         if (DO_STATS) {
 324             rdrCtx.stats.stat_rdr_addLine.add(1);
 325         }
 326         int or = 1; // orientation of the line. 1 if y increases, 0 otherwise.
 327         if (y2 < y1) {
 328             or = 0;
 329             float tmp = y2;
 330             y2 = y1;
 331             y1 = tmp;
 332             tmp = x2;
 333             x2 = x1;
 334             x1 = tmp;
 335         }
 336 
 337         // convert subpixel coordinates [float] into pixel positions [int]
 338 
 339         // The index of the pixel that holds the next HPC is at ceil(trueY - 0.5)
 340         // Since y1 and y2 are biased by -0.5 in tosubpixy(), this is simply
 341         // ceil(y1) or ceil(y2)
 342         // upper integer (inclusive)
 343         final int firstCrossing = FloatMath.max(FloatMath.ceil_int(y1), boundsMinY);
 344 
 345         // note: use boundsMaxY (last Y exclusive) to compute correct coverage
 346         // upper integer (exclusive)
 347         final int lastCrossing  = FloatMath.min(FloatMath.ceil_int(y2), boundsMaxY);
 348 
 349         /* skip horizontal lines in pixel space and clip edges
 350            out of y range [boundsMinY; boundsMaxY] */
 351         if (firstCrossing >= lastCrossing) {
 352             if (DO_MONITORS) {
 353                 rdrCtx.stats.mon_rdr_addLine.stop();
 354             }
 355             if (DO_STATS) {
 356                 rdrCtx.stats.stat_rdr_addLine_skip.add(1);
 357             }
 358             return;
 359         }
 360 
 361         // edge min/max X/Y are in subpixel space (half-open interval):
 362         // note: Use integer crossings to ensure consistent range within
 363         // edgeBuckets / edgeBucketCounts arrays in case of NaN values (int = 0)
 364         if (firstCrossing < edgeMinY) {
 365             edgeMinY = firstCrossing;
 366         }
 367         if (lastCrossing > edgeMaxY) {
 368             edgeMaxY = lastCrossing;
 369         }
 370 
 371         // Use double-precision for improved accuracy:
 372         final double x1d   = x1;
 373         final double y1d   = y1;
 374         final double slope = (x1d - x2) / (y1d - y2);
 375 
 376         if (slope >= 0.0d) { // <==> x1 < x2
 377             if (x1 < edgeMinX) {
 378                 edgeMinX = x1;
 379             }
 380             if (x2 > edgeMaxX) {
 381                 edgeMaxX = x2;
 382             }
 383         } else {
 384             if (x2 < edgeMinX) {
 385                 edgeMinX = x2;
 386             }
 387             if (x1 > edgeMaxX) {
 388                 edgeMaxX = x1;
 389             }
 390         }
 391 
 392         // local variables for performance:
 393         final int _SIZEOF_EDGE_BYTES = SIZEOF_EDGE_BYTES;
 394 
 395         final OffHeapArray _edges = edges;
 396 
 397         // get free pointer (ie length in bytes)
 398         final int edgePtr = _edges.used;
 399 
 400         // use substraction to avoid integer overflow:
 401         if (_edges.length - edgePtr < _SIZEOF_EDGE_BYTES) {
 402             // suppose _edges.length > _SIZEOF_EDGE_BYTES
 403             // so doubling size is enough to add needed bytes
 404             // note: throw IOOB if neededSize > 2Gb:
 405             final long edgeNewSize = ArrayCacheConst.getNewLargeSize(
 406                                         _edges.length,
 407                                         edgePtr + _SIZEOF_EDGE_BYTES);
 408 
 409             if (DO_STATS) {
 410                 rdrCtx.stats.stat_rdr_edges_resizes.add(edgeNewSize);
 411             }
 412             _edges.resize(edgeNewSize);
 413         }
 414 
 415 
 416         final Unsafe _unsafe = OffHeapArray.UNSAFE;
 417         final long SIZE_INT = 4L;
 418         long addr   = _edges.address + edgePtr;
 419 
 420         // The x value must be bumped up to its position at the next HPC we will evaluate.
 421         // "firstcrossing" is the (sub)pixel number where the next crossing occurs
 422         // thus, the actual coordinate of the next HPC is "firstcrossing + 0.5"
 423         // so the Y distance we cover is "firstcrossing + 0.5 - trueY".
 424         // Note that since y1 (and y2) are already biased by -0.5 in tosubpixy(), we have
 425         // y1 = trueY - 0.5
 426         // trueY = y1 + 0.5
 427         // firstcrossing + 0.5 - trueY = firstcrossing + 0.5 - (y1 + 0.5)
 428         //                             = firstcrossing - y1
 429         // The x coordinate at that HPC is then:
 430         // x1_intercept = x1 + (firstcrossing - y1) * slope
 431         // The next VPC is then given by:
 432         // VPC index = ceil(x1_intercept - 0.5), or alternately
 433         // VPC index = floor(x1_intercept - 0.5 + 1 - epsilon)
 434         // epsilon is hard to pin down in floating point, but easy in fixed point, so if
 435         // we convert to fixed point then these operations get easier:
 436         // long x1_fixed = x1_intercept * 2^32;  (fixed point 32.32 format)
 437         // curx = next VPC = fixed_floor(x1_fixed - 2^31 + 2^32 - 1)
 438         //                 = fixed_floor(x1_fixed + 2^31 - 1)
 439         //                 = fixed_floor(x1_fixed + 0x7FFFFFFF)
 440         // and error       = fixed_fract(x1_fixed + 0x7FFFFFFF)
 441         final double x1_intercept = x1d + (firstCrossing - y1d) * slope;
 442 
 443         // inlined scalb(x1_intercept, 32):
 444         final long x1_fixed_biased = ((long) (POWER_2_TO_32 * x1_intercept))
 445                                      + 0x7FFFFFFFL;
 446         // curx:
 447         // last bit corresponds to the orientation
 448         _unsafe.putInt(addr, (((int) (x1_fixed_biased >> 31L)) & ALL_BUT_LSB) | or);
 449         addr += SIZE_INT;
 450         _unsafe.putInt(addr,  ((int)  x1_fixed_biased) >>> 1);
 451         addr += SIZE_INT;
 452 
 453         // inlined scalb(slope, 32):
 454         final long slope_fixed = (long) (POWER_2_TO_32 * slope);
 455 
 456         // last bit set to 0 to keep orientation:
 457         _unsafe.putInt(addr, (((int) (slope_fixed >> 31L)) & ALL_BUT_LSB));
 458         addr += SIZE_INT;
 459         _unsafe.putInt(addr,  ((int)  slope_fixed) >>> 1);
 460         addr += SIZE_INT;
 461 
 462         final int[] _edgeBuckets      = edgeBuckets;
 463         final int[] _edgeBucketCounts = edgeBucketCounts;
 464 
 465         final int _boundsMinY = boundsMinY;
 466 
 467         // each bucket is a linked list. this method adds ptr to the
 468         // start of the "bucket"th linked list.
 469         final int bucketIdx = firstCrossing - _boundsMinY;
 470 
 471         // pointer from bucket
 472         _unsafe.putInt(addr, _edgeBuckets[bucketIdx]);
 473         addr += SIZE_INT;
 474         // y max (exclusive)
 475         _unsafe.putInt(addr,  lastCrossing);
 476 
 477         // Update buckets:
 478         // directly the edge struct "pointer"
 479         _edgeBuckets[bucketIdx]       = edgePtr;
 480         _edgeBucketCounts[bucketIdx] += 2; // 1 << 1
 481         // last bit means edge end
 482         _edgeBucketCounts[lastCrossing - _boundsMinY] |= 0x1;
 483 
 484         // update free pointer (ie length in bytes)
 485         _edges.used += _SIZEOF_EDGE_BYTES;
 486 
 487         if (DO_MONITORS) {
 488             rdrCtx.stats.mon_rdr_addLine.stop();
 489         }
 490     }
 491 
 492 // END EDGE LIST
 493 //////////////////////////////////////////////////////////////////////////////
 494 
 495     // Cache to store RLE-encoded coverage mask of the current primitive
 496     final MarlinCache cache;
 497 
 498     // Bounds of the drawing region, at subpixel precision.
 499     private int boundsMinX, boundsMinY, boundsMaxX, boundsMaxY;
 500 
 501     // Current winding rule
 502     private int windingRule;
 503 
 504     // Current drawing position, i.e., final point of last segment
 505     private float x0, y0;
 506 
 507     // Position of most recent 'moveTo' command
 508     private float sx0, sy0;
 509 
 510     // per-thread renderer context
 511     final RendererContext rdrCtx;
 512     // dirty curve
 513     private final Curve curve;
 514 
 515     // clean alpha array (zero filled)
 516     private int[] alphaLine;
 517 
 518     // alphaLine ref (clean)
 519     private final IntArrayCache.Reference alphaLine_ref;
 520 
 521     private boolean enableBlkFlags = false;
 522     private boolean prevUseBlkFlags = false;
 523 
 524     /* block flags (0|1) */
 525     private int[] blkFlags;
 526 
 527     // blkFlags ref (clean)
 528     private final IntArrayCache.Reference blkFlags_ref;
 529 
 530     Renderer(final RendererContext rdrCtx) {
 531         this.rdrCtx = rdrCtx;
 532 
 533         this.edges = rdrCtx.newOffHeapArray(INITIAL_EDGES_CAPACITY); // 96K
 534 
 535         this.curve = rdrCtx.curve;
 536 
 537         edgeBuckets_ref      = rdrCtx.newCleanIntArrayRef(INITIAL_BUCKET_ARRAY); // 64K
 538         edgeBucketCounts_ref = rdrCtx.newCleanIntArrayRef(INITIAL_BUCKET_ARRAY); // 64K
 539 
 540         edgeBuckets      = edgeBuckets_ref.initial;
 541         edgeBucketCounts = edgeBucketCounts_ref.initial;
 542 
 543         // 2048 (pixelsize) pixel large
 544         alphaLine_ref = rdrCtx.newCleanIntArrayRef(INITIAL_AA_ARRAY); // 8K
 545         alphaLine     = alphaLine_ref.initial;
 546 
 547         this.cache = rdrCtx.cache;
 548 
 549         crossings_ref     = rdrCtx.newDirtyIntArrayRef(INITIAL_CROSSING_COUNT); // 2K
 550         aux_crossings_ref = rdrCtx.newDirtyIntArrayRef(INITIAL_CROSSING_COUNT); // 2K
 551         edgePtrs_ref      = rdrCtx.newDirtyIntArrayRef(INITIAL_CROSSING_COUNT); // 2K
 552         aux_edgePtrs_ref  = rdrCtx.newDirtyIntArrayRef(INITIAL_CROSSING_COUNT); // 2K
 553 
 554         crossings     = crossings_ref.initial;
 555         aux_crossings = aux_crossings_ref.initial;
 556         edgePtrs      = edgePtrs_ref.initial;
 557         aux_edgePtrs  = aux_edgePtrs_ref.initial;
 558 
 559         blkFlags_ref = rdrCtx.newCleanIntArrayRef(INITIAL_ARRAY); // 1K = 1 tile line
 560         blkFlags     = blkFlags_ref.initial;
 561     }
 562 
 563     Renderer init(final int pix_boundsX, final int pix_boundsY,
 564                   final int pix_boundsWidth, final int pix_boundsHeight,
 565                   final int windingRule)
 566     {
 567         this.windingRule = windingRule;
 568 
 569         // bounds as half-open intervals: minX <= x < maxX and minY <= y < maxY
 570         this.boundsMinX =  pix_boundsX << SUBPIXEL_LG_POSITIONS_X;
 571         this.boundsMaxX =
 572             (pix_boundsX + pix_boundsWidth) << SUBPIXEL_LG_POSITIONS_X;
 573         this.boundsMinY =  pix_boundsY << SUBPIXEL_LG_POSITIONS_Y;
 574         this.boundsMaxY =
 575             (pix_boundsY + pix_boundsHeight) << SUBPIXEL_LG_POSITIONS_Y;
 576 
 577         if (DO_LOG_BOUNDS) {
 578             MarlinUtils.logInfo("boundsXY = [" + boundsMinX + " ... "
 579                                 + boundsMaxX + "[ [" + boundsMinY + " ... "
 580                                 + boundsMaxY + "[");
 581         }
 582 
 583         // see addLine: ceil(boundsMaxY) => boundsMaxY + 1
 584         // +1 for edgeBucketCounts
 585         final int edgeBucketsLength = (boundsMaxY - boundsMinY) + 1;
 586 
 587         if (edgeBucketsLength > INITIAL_BUCKET_ARRAY) {
 588             if (DO_STATS) {
 589                 rdrCtx.stats.stat_array_renderer_edgeBuckets
 590                     .add(edgeBucketsLength);
 591                 rdrCtx.stats.stat_array_renderer_edgeBucketCounts
 592                     .add(edgeBucketsLength);
 593             }
 594             edgeBuckets = edgeBuckets_ref.getArray(edgeBucketsLength);
 595             edgeBucketCounts = edgeBucketCounts_ref.getArray(edgeBucketsLength);
 596         }
 597 
 598         edgeMinY = Integer.MAX_VALUE;
 599         edgeMaxY = Integer.MIN_VALUE;
 600         edgeMinX = Float.POSITIVE_INFINITY;
 601         edgeMaxX = Float.NEGATIVE_INFINITY;
 602 
 603         // reset used mark:
 604         edgeCount = 0;
 605         activeEdgeMaxUsed = 0;
 606         edges.used = 0;
 607 
 608         return this; // fluent API
 609     }
 610 
 611     /**
 612      * Disposes this renderer and recycle it clean up before reusing this instance
 613      */
 614     void dispose() {
 615         if (DO_STATS) {
 616             rdrCtx.stats.stat_rdr_activeEdges.add(activeEdgeMaxUsed);
 617             rdrCtx.stats.stat_rdr_edges.add(edges.used);
 618             rdrCtx.stats.stat_rdr_edges_count.add(edges.used / SIZEOF_EDGE_BYTES);
 619             rdrCtx.stats.hist_rdr_edges_count.add(edges.used / SIZEOF_EDGE_BYTES);
 620             rdrCtx.stats.totalOffHeap += edges.length;
 621         }
 622         // Return arrays:
 623         crossings = crossings_ref.putArray(crossings);
 624         aux_crossings = aux_crossings_ref.putArray(aux_crossings);
 625 
 626         edgePtrs = edgePtrs_ref.putArray(edgePtrs);
 627         aux_edgePtrs = aux_edgePtrs_ref.putArray(aux_edgePtrs);
 628 
 629         alphaLine = alphaLine_ref.putArray(alphaLine, 0, 0); // already zero filled
 630         blkFlags  = blkFlags_ref.putArray(blkFlags, 0, 0); // already zero filled
 631 
 632         if (edgeMinY != Integer.MAX_VALUE) {
 633             // if context is maked as DIRTY:
 634             if (rdrCtx.dirty) {
 635                 // may happen if an exception if thrown in the pipeline processing:
 636                 // clear completely buckets arrays:
 637                 buckets_minY = 0;
 638                 buckets_maxY = boundsMaxY - boundsMinY;
 639             }
 640             // clear only used part
 641             edgeBuckets = edgeBuckets_ref.putArray(edgeBuckets, buckets_minY,
 642                                                                 buckets_maxY);
 643             edgeBucketCounts = edgeBucketCounts_ref.putArray(edgeBucketCounts,
 644                                                              buckets_minY,
 645                                                              buckets_maxY + 1);
 646         } else {
 647             // unused arrays
 648             edgeBuckets = edgeBuckets_ref.putArray(edgeBuckets, 0, 0);
 649             edgeBucketCounts = edgeBucketCounts_ref.putArray(edgeBucketCounts, 0, 0);
 650         }
 651 
 652         // At last: resize back off-heap edges to initial size
 653         if (edges.length != INITIAL_EDGES_CAPACITY) {
 654             // note: may throw OOME:
 655             edges.resize(INITIAL_EDGES_CAPACITY);
 656         }
 657         if (DO_CLEAN_DIRTY) {
 658             // Force zero-fill dirty arrays:
 659             edges.fill(BYTE_0);
 660         }
 661         if (DO_MONITORS) {
 662             rdrCtx.stats.mon_rdr_endRendering.stop();
 663         }
 664         // recycle the RendererContext instance
 665         MarlinRenderingEngine.returnRendererContext(rdrCtx);
 666     }
 667 
 668     private static float tosubpixx(final float pix_x) {
 669         return SUBPIXEL_SCALE_X * pix_x;
 670     }
 671 
 672     private static float tosubpixy(final float pix_y) {
 673         // shift y by -0.5 for fast ceil(y - 0.5):
 674         return SUBPIXEL_SCALE_Y * pix_y - 0.5f;
 675     }
 676 
 677     @Override
 678     public void moveTo(float pix_x0, float pix_y0) {
 679         closePath();
 680         final float sx = tosubpixx(pix_x0);
 681         final float sy = tosubpixy(pix_y0);
 682         this.sx0 = sx;
 683         this.sy0 = sy;
 684         this.x0 = sx;
 685         this.y0 = sy;
 686     }
 687 
 688     @Override
 689     public void lineTo(float pix_x1, float pix_y1) {
 690         final float x1 = tosubpixx(pix_x1);
 691         final float y1 = tosubpixy(pix_y1);
 692         addLine(x0, y0, x1, y1);
 693         x0 = x1;
 694         y0 = y1;
 695     }
 696 
 697     @Override
 698     public void curveTo(float pix_x1, float pix_y1,
 699                         float pix_x2, float pix_y2,
 700                         float pix_x3, float pix_y3)
 701     {
 702         final float xe = tosubpixx(pix_x3);
 703         final float ye = tosubpixy(pix_y3);
 704         curve.set(x0, y0, tosubpixx(pix_x1), tosubpixy(pix_y1),
 705                   tosubpixx(pix_x2), tosubpixy(pix_y2), xe, ye);
 706         curveBreakIntoLinesAndAdd(x0, y0, curve, xe, ye);
 707         x0 = xe;
 708         y0 = ye;
 709     }
 710 
 711     @Override
 712     public void quadTo(float pix_x1, float pix_y1,
 713                        float pix_x2, float pix_y2)
 714     {
 715         final float xe = tosubpixx(pix_x2);
 716         final float ye = tosubpixy(pix_y2);
 717         curve.set(x0, y0, tosubpixx(pix_x1), tosubpixy(pix_y1), xe, ye);
 718         quadBreakIntoLinesAndAdd(x0, y0, curve, xe, ye);
 719         x0 = xe;
 720         y0 = ye;
 721     }
 722 
 723     @Override
 724     public void closePath() {
 725         if (x0 != sx0 || y0 != sy0) {
 726             addLine(x0, y0, sx0, sy0);
 727             x0 = sx0;
 728             y0 = sy0;
 729         }
 730     }
 731 
 732     @Override
 733     public void pathDone() {
 734         closePath();
 735     }
 736 
 737     @Override
 738     public long getNativeConsumer() {
 739         throw new InternalError("Renderer does not use a native consumer.");
 740     }
 741 
 742     private void _endRendering(final int ymin, final int ymax) {
 743         if (DISABLE_RENDER) {
 744             return;
 745         }
 746 
 747         // Get X bounds as true pixel boundaries to compute correct pixel coverage:
 748         final int bboxx0 = bbox_spminX;
 749         final int bboxx1 = bbox_spmaxX;
 750 
 751         final boolean windingRuleEvenOdd = (windingRule == WIND_EVEN_ODD);
 752 
 753         // Useful when processing tile line by tile line
 754         final int[] _alpha = alphaLine;
 755 
 756         // local vars (performance):
 757         final MarlinCache _cache = cache;
 758         final OffHeapArray _edges = edges;
 759         final int[] _edgeBuckets = edgeBuckets;
 760         final int[] _edgeBucketCounts = edgeBucketCounts;
 761 
 762         int[] _crossings = this.crossings;
 763         int[] _edgePtrs  = this.edgePtrs;
 764 
 765         // merge sort auxiliary storage:
 766         int[] _aux_crossings = this.aux_crossings;
 767         int[] _aux_edgePtrs  = this.aux_edgePtrs;
 768 
 769         // copy constants:
 770         final long _OFF_ERROR    = OFF_ERROR;
 771         final long _OFF_BUMP_X   = OFF_BUMP_X;
 772         final long _OFF_BUMP_ERR = OFF_BUMP_ERR;
 773 
 774         final long _OFF_NEXT     = OFF_NEXT;
 775         final long _OFF_YMAX     = OFF_YMAX;
 776 
 777         final int _ALL_BUT_LSB   = ALL_BUT_LSB;
 778         final int _ERR_STEP_MAX  = ERR_STEP_MAX;
 779 
 780         // unsafe I/O:
 781         final Unsafe _unsafe = OffHeapArray.UNSAFE;
 782         final long    addr0  = _edges.address;
 783         long addr;
 784         final int _SUBPIXEL_LG_POSITIONS_X = SUBPIXEL_LG_POSITIONS_X;
 785         final int _SUBPIXEL_LG_POSITIONS_Y = SUBPIXEL_LG_POSITIONS_Y;
 786         final int _SUBPIXEL_MASK_X = SUBPIXEL_MASK_X;
 787         final int _SUBPIXEL_MASK_Y = SUBPIXEL_MASK_Y;
 788         final int _SUBPIXEL_POSITIONS_X = SUBPIXEL_POSITIONS_X;
 789 
 790         final int _MIN_VALUE = Integer.MIN_VALUE;
 791         final int _MAX_VALUE = Integer.MAX_VALUE;
 792 
 793         // Now we iterate through the scanlines. We must tell emitRow the coord
 794         // of the first non-transparent pixel, so we must keep accumulators for
 795         // the first and last pixels of the section of the current pixel row
 796         // that we will emit.
 797         // We also need to accumulate pix_bbox, but the iterator does it
 798         // for us. We will just get the values from it once this loop is done
 799         int minX = _MAX_VALUE;
 800         int maxX = _MIN_VALUE;
 801 
 802         int y = ymin;
 803         int bucket = y - boundsMinY;
 804 
 805         int numCrossings = this.edgeCount;
 806         int edgePtrsLen = _edgePtrs.length;
 807         int crossingsLen = _crossings.length;
 808         int _arrayMaxUsed = activeEdgeMaxUsed;
 809         int ptrLen = 0, newCount, ptrEnd;
 810 
 811         int bucketcount, i, j, ecur;
 812         int cross, lastCross;
 813         int x0, x1, tmp, sum, prev, curx, curxo, crorientation, err;
 814         int pix_x, pix_xmaxm1, pix_xmax;
 815 
 816         int low, high, mid, prevNumCrossings;
 817         boolean useBinarySearch;
 818 
 819         final int[] _blkFlags = blkFlags;
 820         final int _BLK_SIZE_LG = BLOCK_SIZE_LG;
 821         final int _BLK_SIZE = BLOCK_SIZE;
 822 
 823         final boolean _enableBlkFlagsHeuristics = ENABLE_BLOCK_FLAGS_HEURISTICS && this.enableBlkFlags;
 824 
 825         // Use block flags if large pixel span and few crossings:
 826         // ie mean(distance between crossings) is high
 827         boolean useBlkFlags = this.prevUseBlkFlags;
 828 
 829         final int stroking = rdrCtx.stroking;
 830 
 831         int lastY = -1; // last emited row
 832 
 833 
 834         // Iteration on scanlines
 835         for (; y < ymax; y++, bucket++) {
 836             // --- from former ScanLineIterator.next()
 837             bucketcount = _edgeBucketCounts[bucket];
 838 
 839             // marker on previously sorted edges:
 840             prevNumCrossings = numCrossings;
 841 
 842             // bucketCount indicates new edge / edge end:
 843             if (bucketcount != 0) {
 844                 if (DO_STATS) {
 845                     rdrCtx.stats.stat_rdr_activeEdges_updates.add(numCrossings);
 846                 }
 847 
 848                 // last bit set to 1 means that edges ends
 849                 if ((bucketcount & 0x1) != 0) {
 850                     // eviction in active edge list
 851                     // cache edges[] address + offset
 852                     addr = addr0 + _OFF_YMAX;
 853 
 854                     for (i = 0, newCount = 0; i < numCrossings; i++) {
 855                         // get the pointer to the edge
 856                         ecur = _edgePtrs[i];
 857                         // random access so use unsafe:
 858                         if (_unsafe.getInt(addr + ecur) > y) {
 859                             _edgePtrs[newCount++] = ecur;
 860                         }
 861                     }
 862                     // update marker on sorted edges minus removed edges:
 863                     prevNumCrossings = numCrossings = newCount;
 864                 }
 865 
 866                 ptrLen = bucketcount >> 1; // number of new edge
 867 
 868                 if (ptrLen != 0) {
 869                     if (DO_STATS) {
 870                         rdrCtx.stats.stat_rdr_activeEdges_adds.add(ptrLen);
 871                         if (ptrLen > 10) {
 872                             rdrCtx.stats.stat_rdr_activeEdges_adds_high.add(ptrLen);
 873                         }
 874                     }
 875                     ptrEnd = numCrossings + ptrLen;
 876 
 877                     if (edgePtrsLen < ptrEnd) {
 878                         if (DO_STATS) {
 879                             rdrCtx.stats.stat_array_renderer_edgePtrs.add(ptrEnd);
 880                         }
 881                         this.edgePtrs = _edgePtrs
 882                             = edgePtrs_ref.widenArray(_edgePtrs, numCrossings,
 883                                                       ptrEnd);
 884 
 885                         edgePtrsLen = _edgePtrs.length;
 886                         // Get larger auxiliary storage:
 887                         aux_edgePtrs_ref.putArray(_aux_edgePtrs);
 888 
 889                         // use ArrayCache.getNewSize() to use the same growing
 890                         // factor than widenArray():
 891                         if (DO_STATS) {
 892                             rdrCtx.stats.stat_array_renderer_aux_edgePtrs.add(ptrEnd);
 893                         }
 894                         this.aux_edgePtrs = _aux_edgePtrs
 895                             = aux_edgePtrs_ref.getArray(
 896                                 ArrayCacheConst.getNewSize(numCrossings, ptrEnd)
 897                             );
 898                     }
 899 
 900                     // cache edges[] address + offset
 901                     addr = addr0 + _OFF_NEXT;
 902 
 903                     // add new edges to active edge list:
 904                     for (ecur = _edgeBuckets[bucket];
 905                          numCrossings < ptrEnd; numCrossings++)
 906                     {
 907                         // store the pointer to the edge
 908                         _edgePtrs[numCrossings] = ecur;
 909                         // random access so use unsafe:
 910                         ecur = _unsafe.getInt(addr + ecur);
 911                     }
 912 
 913                     if (crossingsLen < numCrossings) {
 914                         // Get larger array:
 915                         crossings_ref.putArray(_crossings);
 916 
 917                         if (DO_STATS) {
 918                             rdrCtx.stats.stat_array_renderer_crossings
 919                                 .add(numCrossings);
 920                         }
 921                         this.crossings = _crossings
 922                             = crossings_ref.getArray(numCrossings);
 923 
 924                         // Get larger auxiliary storage:
 925                         aux_crossings_ref.putArray(_aux_crossings);
 926 
 927                         if (DO_STATS) {
 928                             rdrCtx.stats.stat_array_renderer_aux_crossings
 929                                 .add(numCrossings);
 930                         }
 931                         this.aux_crossings = _aux_crossings
 932                             = aux_crossings_ref.getArray(numCrossings);
 933 
 934                         crossingsLen = _crossings.length;
 935                     }
 936                     if (DO_STATS) {
 937                         // update max used mark
 938                         if (numCrossings > _arrayMaxUsed) {
 939                             _arrayMaxUsed = numCrossings;
 940                         }
 941                     }
 942                 } // ptrLen != 0
 943             } // bucketCount != 0
 944 
 945 
 946             if (numCrossings != 0) {
 947                 /*
 948                  * thresholds to switch to optimized merge sort
 949                  * for newly added edges + final merge pass.
 950                  */
 951                 if ((ptrLen < 10) || (numCrossings < 40)) {
 952                     if (DO_STATS) {
 953                         rdrCtx.stats.hist_rdr_crossings.add(numCrossings);
 954                         rdrCtx.stats.hist_rdr_crossings_adds.add(ptrLen);
 955                     }
 956 
 957                     /*
 958                      * threshold to use binary insertion sort instead of
 959                      * straight insertion sort (to reduce minimize comparisons).
 960                      */
 961                     useBinarySearch = (numCrossings >= 20);
 962 
 963                     // if small enough:
 964                     lastCross = _MIN_VALUE;
 965 
 966                     for (i = 0; i < numCrossings; i++) {
 967                         // get the pointer to the edge
 968                         ecur = _edgePtrs[i];
 969 
 970                         /* convert subpixel coordinates into pixel
 971                             positions for coming scanline */
 972                         /* note: it is faster to always update edges even
 973                            if it is removed from AEL for coming or last scanline */
 974 
 975                         // random access so use unsafe:
 976                         addr = addr0 + ecur; // ecur + OFF_F_CURX
 977 
 978                         // get current crossing:
 979                         curx = _unsafe.getInt(addr);
 980 
 981                         // update crossing with orientation at last bit:
 982                         cross = curx;
 983 
 984                         // Increment x using DDA (fixed point):
 985                         curx += _unsafe.getInt(addr + _OFF_BUMP_X);
 986 
 987                         // Increment error:
 988                         err  =  _unsafe.getInt(addr + _OFF_ERROR)
 989                               + _unsafe.getInt(addr + _OFF_BUMP_ERR);
 990 
 991                         // Manual carry handling:
 992                         // keep sign and carry bit only and ignore last bit (preserve orientation):
 993                         _unsafe.putInt(addr,               curx - ((err >> 30) & _ALL_BUT_LSB));
 994                         _unsafe.putInt(addr + _OFF_ERROR, (err & _ERR_STEP_MAX));
 995 
 996                         if (DO_STATS) {
 997                             rdrCtx.stats.stat_rdr_crossings_updates.add(numCrossings);
 998                         }
 999 
1000                         // insertion sort of crossings:
1001                         if (cross < lastCross) {
1002                             if (DO_STATS) {
1003                                 rdrCtx.stats.stat_rdr_crossings_sorts.add(i);
1004                             }
1005 
1006                             /* use binary search for newly added edges
1007                                in crossings if arrays are large enough */
1008                             if (useBinarySearch && (i >= prevNumCrossings)) {
1009                                 if (DO_STATS) {
1010                                     rdrCtx.stats.stat_rdr_crossings_bsearch.add(i);
1011                                 }
1012                                 low = 0;
1013                                 high = i - 1;
1014 
1015                                 do {
1016                                     // note: use signed shift (not >>>) for performance
1017                                     // as indices are small enough to exceed Integer.MAX_VALUE
1018                                     mid = (low + high) >> 1;
1019 
1020                                     if (_crossings[mid] < cross) {
1021                                         low = mid + 1;
1022                                     } else {
1023                                         high = mid - 1;
1024                                     }
1025                                 } while (low <= high);
1026 
1027                                 for (j = i - 1; j >= low; j--) {
1028                                     _crossings[j + 1] = _crossings[j];
1029                                     _edgePtrs [j + 1] = _edgePtrs[j];
1030                                 }
1031                                 _crossings[low] = cross;
1032                                 _edgePtrs [low] = ecur;
1033 
1034                             } else {
1035                                 j = i - 1;
1036                                 _crossings[i] = _crossings[j];
1037                                 _edgePtrs[i] = _edgePtrs[j];
1038 
1039                                 while ((--j >= 0) && (_crossings[j] > cross)) {
1040                                     _crossings[j + 1] = _crossings[j];
1041                                     _edgePtrs [j + 1] = _edgePtrs[j];
1042                                 }
1043                                 _crossings[j + 1] = cross;
1044                                 _edgePtrs [j + 1] = ecur;
1045                             }
1046 
1047                         } else {
1048                             _crossings[i] = lastCross = cross;
1049                         }
1050                     }
1051                 } else {
1052                     if (DO_STATS) {
1053                         rdrCtx.stats.stat_rdr_crossings_msorts.add(numCrossings);
1054                         rdrCtx.stats.hist_rdr_crossings_ratio
1055                             .add((1000 * ptrLen) / numCrossings);
1056                         rdrCtx.stats.hist_rdr_crossings_msorts.add(numCrossings);
1057                         rdrCtx.stats.hist_rdr_crossings_msorts_adds.add(ptrLen);
1058                     }
1059 
1060                     // Copy sorted data in auxiliary arrays
1061                     // and perform insertion sort on almost sorted data
1062                     // (ie i < prevNumCrossings):
1063 
1064                     lastCross = _MIN_VALUE;
1065 
1066                     for (i = 0; i < numCrossings; i++) {
1067                         // get the pointer to the edge
1068                         ecur = _edgePtrs[i];
1069 
1070                         /* convert subpixel coordinates into pixel
1071                             positions for coming scanline */
1072                         /* note: it is faster to always update edges even
1073                            if it is removed from AEL for coming or last scanline */
1074 
1075                         // random access so use unsafe:
1076                         addr = addr0 + ecur; // ecur + OFF_F_CURX
1077 
1078                         // get current crossing:
1079                         curx = _unsafe.getInt(addr);
1080 
1081                         // update crossing with orientation at last bit:
1082                         cross = curx;
1083 
1084                         // Increment x using DDA (fixed point):
1085                         curx += _unsafe.getInt(addr + _OFF_BUMP_X);
1086 
1087                         // Increment error:
1088                         err  =  _unsafe.getInt(addr + _OFF_ERROR)
1089                               + _unsafe.getInt(addr + _OFF_BUMP_ERR);
1090 
1091                         // Manual carry handling:
1092                         // keep sign and carry bit only and ignore last bit (preserve orientation):
1093                         _unsafe.putInt(addr,               curx - ((err >> 30) & _ALL_BUT_LSB));
1094                         _unsafe.putInt(addr + _OFF_ERROR, (err & _ERR_STEP_MAX));
1095 
1096                         if (DO_STATS) {
1097                             rdrCtx.stats.stat_rdr_crossings_updates.add(numCrossings);
1098                         }
1099 
1100                         if (i >= prevNumCrossings) {
1101                             // simply store crossing as edgePtrs is in-place:
1102                             // will be copied and sorted efficiently by mergesort later:
1103                             _crossings[i]     = cross;
1104 
1105                         } else if (cross < lastCross) {
1106                             if (DO_STATS) {
1107                                 rdrCtx.stats.stat_rdr_crossings_sorts.add(i);
1108                             }
1109 
1110                             // (straight) insertion sort of crossings:
1111                             j = i - 1;
1112                             _aux_crossings[i] = _aux_crossings[j];
1113                             _aux_edgePtrs[i] = _aux_edgePtrs[j];
1114 
1115                             while ((--j >= 0) && (_aux_crossings[j] > cross)) {
1116                                 _aux_crossings[j + 1] = _aux_crossings[j];
1117                                 _aux_edgePtrs [j + 1] = _aux_edgePtrs[j];
1118                             }
1119                             _aux_crossings[j + 1] = cross;
1120                             _aux_edgePtrs [j + 1] = ecur;
1121 
1122                         } else {
1123                             // auxiliary storage:
1124                             _aux_crossings[i] = lastCross = cross;
1125                             _aux_edgePtrs [i] = ecur;
1126                         }
1127                     }
1128 
1129                     // use Mergesort using auxiliary arrays (sort only right part)
1130                     MergeSort.mergeSortNoCopy(_crossings,     _edgePtrs,
1131                                               _aux_crossings, _aux_edgePtrs,
1132                                               numCrossings,   prevNumCrossings);
1133                 }
1134 
1135                 // reset ptrLen
1136                 ptrLen = 0;
1137                 // --- from former ScanLineIterator.next()
1138 
1139 
1140                 /* note: bboxx0 and bboxx1 must be pixel boundaries
1141                    to have correct coverage computation */
1142 
1143                 // right shift on crossings to get the x-coordinate:
1144                 curxo = _crossings[0];
1145                 x0    = curxo >> 1;
1146                 if (x0 < minX) {
1147                     minX = x0; // subpixel coordinate
1148                 }
1149 
1150                 x1 = _crossings[numCrossings - 1] >> 1;
1151                 if (x1 > maxX) {
1152                     maxX = x1; // subpixel coordinate
1153                 }
1154 
1155 
1156                 // compute pixel coverages
1157                 prev = curx = x0;
1158                 // to turn {0, 1} into {-1, 1}, multiply by 2 and subtract 1.
1159                 // last bit contains orientation (0 or 1)
1160                 crorientation = ((curxo & 0x1) << 1) - 1;
1161 
1162                 if (windingRuleEvenOdd) {
1163                     sum = crorientation;
1164 
1165                     // Even Odd winding rule: take care of mask ie sum(orientations)
1166                     for (i = 1; i < numCrossings; i++) {
1167                         curxo = _crossings[i];
1168                         curx  =  curxo >> 1;
1169                         // to turn {0, 1} into {-1, 1}, multiply by 2 and subtract 1.
1170                         // last bit contains orientation (0 or 1)
1171                         crorientation = ((curxo & 0x1) << 1) - 1;
1172 
1173                         if ((sum & 0x1) != 0) {
1174                             // TODO: perform line clipping on left-right sides
1175                             // to avoid such bound checks:
1176                             x0 = (prev > bboxx0) ? prev : bboxx0;
1177 
1178                             if (curx < bboxx1) {
1179                                 x1 = curx;
1180                             } else {
1181                                 x1 = bboxx1;
1182                                 // skip right side (fast exit loop):
1183                                 i = numCrossings;
1184                             }
1185 
1186                             if (x0 < x1) {
1187                                 x0 -= bboxx0; // turn x0, x1 from coords to indices
1188                                 x1 -= bboxx0; // in the alpha array.
1189 
1190                                 pix_x      =  x0      >> _SUBPIXEL_LG_POSITIONS_X;
1191                                 pix_xmaxm1 = (x1 - 1) >> _SUBPIXEL_LG_POSITIONS_X;
1192 
1193                                 if (pix_x == pix_xmaxm1) {
1194                                     // Start and end in same pixel
1195                                     tmp = (x1 - x0); // number of subpixels
1196                                     _alpha[pix_x    ] += tmp;
1197                                     _alpha[pix_x + 1] -= tmp;
1198 
1199                                     if (useBlkFlags) {
1200                                         // flag used blocks:
1201                                         // note: block processing handles extra pixel:
1202                                         _blkFlags[pix_x    >> _BLK_SIZE_LG] = 1;
1203                                     }
1204                                 } else {
1205                                     tmp = (x0 & _SUBPIXEL_MASK_X);
1206                                     _alpha[pix_x    ]
1207                                         += (_SUBPIXEL_POSITIONS_X - tmp);
1208                                     _alpha[pix_x + 1]
1209                                         += tmp;
1210 
1211                                     pix_xmax = x1 >> _SUBPIXEL_LG_POSITIONS_X;
1212 
1213                                     tmp = (x1 & _SUBPIXEL_MASK_X);
1214                                     _alpha[pix_xmax    ]
1215                                         -= (_SUBPIXEL_POSITIONS_X - tmp);
1216                                     _alpha[pix_xmax + 1]
1217                                         -= tmp;
1218 
1219                                     if (useBlkFlags) {
1220                                         // flag used blocks:
1221                                         // note: block processing handles extra pixel:
1222                                         _blkFlags[pix_x    >> _BLK_SIZE_LG] = 1;
1223                                         _blkFlags[pix_xmax >> _BLK_SIZE_LG] = 1;
1224                                     }
1225                                 }
1226                             }
1227                         }
1228 
1229                         sum += crorientation;
1230                         prev = curx;
1231                     }
1232                 } else {
1233                     // Non-zero winding rule: optimize that case (default)
1234                     // and avoid processing intermediate crossings
1235                     for (i = 1, sum = 0;; i++) {
1236                         sum += crorientation;
1237 
1238                         if (sum != 0) {
1239                             // prev = min(curx)
1240                             if (prev > curx) {
1241                                 prev = curx;
1242                             }
1243                         } else {
1244                             // TODO: perform line clipping on left-right sides
1245                             // to avoid such bound checks:
1246                             x0 = (prev > bboxx0) ? prev : bboxx0;
1247 
1248                             if (curx < bboxx1) {
1249                                 x1 = curx;
1250                             } else {
1251                                 x1 = bboxx1;
1252                                 // skip right side (fast exit loop):
1253                                 i = numCrossings;
1254                             }
1255 
1256                             if (x0 < x1) {
1257                                 x0 -= bboxx0; // turn x0, x1 from coords to indices
1258                                 x1 -= bboxx0; // in the alpha array.
1259 
1260                                 pix_x      =  x0      >> _SUBPIXEL_LG_POSITIONS_X;
1261                                 pix_xmaxm1 = (x1 - 1) >> _SUBPIXEL_LG_POSITIONS_X;
1262 
1263                                 if (pix_x == pix_xmaxm1) {
1264                                     // Start and end in same pixel
1265                                     tmp = (x1 - x0); // number of subpixels
1266                                     _alpha[pix_x    ] += tmp;
1267                                     _alpha[pix_x + 1] -= tmp;
1268 
1269                                     if (useBlkFlags) {
1270                                         // flag used blocks:
1271                                         // note: block processing handles extra pixel:
1272                                         _blkFlags[pix_x    >> _BLK_SIZE_LG] = 1;
1273                                     }
1274                                 } else {
1275                                     tmp = (x0 & _SUBPIXEL_MASK_X);
1276                                     _alpha[pix_x    ]
1277                                         += (_SUBPIXEL_POSITIONS_X - tmp);
1278                                     _alpha[pix_x + 1]
1279                                         += tmp;
1280 
1281                                     pix_xmax = x1 >> _SUBPIXEL_LG_POSITIONS_X;
1282 
1283                                     tmp = (x1 & _SUBPIXEL_MASK_X);
1284                                     _alpha[pix_xmax    ]
1285                                         -= (_SUBPIXEL_POSITIONS_X - tmp);
1286                                     _alpha[pix_xmax + 1]
1287                                         -= tmp;
1288 
1289                                     if (useBlkFlags) {
1290                                         // flag used blocks:
1291                                         // note: block processing handles extra pixel:
1292                                         _blkFlags[pix_x    >> _BLK_SIZE_LG] = 1;
1293                                         _blkFlags[pix_xmax >> _BLK_SIZE_LG] = 1;
1294                                     }
1295                                 }
1296                             }
1297                             prev = _MAX_VALUE;
1298                         }
1299 
1300                         if (i == numCrossings) {
1301                             break;
1302                         }
1303 
1304                         curxo = _crossings[i];
1305                         curx  =  curxo >> 1;
1306                         // to turn {0, 1} into {-1, 1}, multiply by 2 and subtract 1.
1307                         // last bit contains orientation (0 or 1)
1308                         crorientation = ((curxo & 0x1) << 1) - 1;
1309                     }
1310                 }
1311             } // numCrossings > 0
1312 
1313             // even if this last row had no crossings, alpha will be zeroed
1314             // from the last emitRow call. But this doesn't matter because
1315             // maxX < minX, so no row will be emitted to the MarlinCache.
1316             if ((y & _SUBPIXEL_MASK_Y) == _SUBPIXEL_MASK_Y) {
1317                 lastY = y >> _SUBPIXEL_LG_POSITIONS_Y;
1318 
1319                 // convert subpixel to pixel coordinate within boundaries:
1320                 minX = FloatMath.max(minX, bboxx0) >> _SUBPIXEL_LG_POSITIONS_X;
1321                 maxX = FloatMath.min(maxX, bboxx1) >> _SUBPIXEL_LG_POSITIONS_X;
1322 
1323                 if (maxX >= minX) {
1324                     // note: alpha array will be zeroed by copyAARow()
1325                     // +1 because alpha [pix_minX; pix_maxX[
1326                     // fix range [x0; x1[
1327                     // note: if x1=bboxx1, then alpha is written up to bboxx1+1
1328                     // inclusive: alpha[bboxx1] ignored, alpha[bboxx1+1] == 0
1329                     // (normally so never cleared below)
1330                     copyAARow(_alpha, lastY, minX, maxX + 1, useBlkFlags);
1331 
1332                     // speculative for next pixel row (scanline coherence):
1333                     if (_enableBlkFlagsHeuristics) {
1334                         // Use block flags if large pixel span and few crossings:
1335                         // ie mean(distance between crossings) is larger than
1336                         // 1 block size;
1337 
1338                         // fast check width:
1339                         maxX -= minX;
1340 
1341                         // if stroking: numCrossings /= 2
1342                         // => shift numCrossings by 1
1343                         // condition = (width / (numCrossings - 1)) > blockSize
1344                         useBlkFlags = (maxX > _BLK_SIZE) && (maxX >
1345                             (((numCrossings >> stroking) - 1) << _BLK_SIZE_LG));
1346 
1347                         if (DO_STATS) {
1348                             tmp = FloatMath.max(1,
1349                                     ((numCrossings >> stroking) - 1));
1350                             rdrCtx.stats.hist_tile_generator_encoding_dist
1351                                 .add(maxX / tmp);
1352                         }
1353                     }
1354                 } else {
1355                     _cache.clearAARow(lastY);
1356                 }
1357                 minX = _MAX_VALUE;
1358                 maxX = _MIN_VALUE;
1359             }
1360         } // scan line iterator
1361 
1362         // Emit final row
1363         y--;
1364         y >>= _SUBPIXEL_LG_POSITIONS_Y;
1365 
1366         // convert subpixel to pixel coordinate within boundaries:
1367         minX = FloatMath.max(minX, bboxx0) >> _SUBPIXEL_LG_POSITIONS_X;
1368         maxX = FloatMath.min(maxX, bboxx1) >> _SUBPIXEL_LG_POSITIONS_X;
1369 
1370         if (maxX >= minX) {
1371             // note: alpha array will be zeroed by copyAARow()
1372             // +1 because alpha [pix_minX; pix_maxX[
1373             // fix range [x0; x1[
1374             // note: if x1=bboxx1, then alpha is written up to bboxx1+1
1375             // inclusive: alpha[bboxx1] ignored then cleared and
1376             // alpha[bboxx1+1] == 0 (normally so never cleared after)
1377             copyAARow(_alpha, y, minX, maxX + 1, useBlkFlags);
1378         } else if (y != lastY) {
1379             _cache.clearAARow(y);
1380         }
1381 
1382         // update member:
1383         edgeCount = numCrossings;
1384         prevUseBlkFlags = useBlkFlags;
1385 
1386         if (DO_STATS) {
1387             // update max used mark
1388             activeEdgeMaxUsed = _arrayMaxUsed;
1389         }
1390     }
1391 
1392     boolean endRendering() {
1393         if (DO_MONITORS) {
1394             rdrCtx.stats.mon_rdr_endRendering.start();
1395         }
1396         if (edgeMinY == Integer.MAX_VALUE) {
1397             return false; // undefined edges bounds
1398         }
1399 
1400         // bounds as half-open intervals
1401         final int spminX = FloatMath.max(FloatMath.ceil_int(edgeMinX - 0.5f), boundsMinX);
1402         final int spmaxX = FloatMath.min(FloatMath.ceil_int(edgeMaxX - 0.5f), boundsMaxX);
1403 
1404         // edge Min/Max Y are already rounded to subpixels within bounds:
1405         final int spminY = edgeMinY;
1406         final int spmaxY = edgeMaxY;
1407 
1408         buckets_minY = spminY - boundsMinY;
1409         buckets_maxY = spmaxY - boundsMinY;
1410 
1411         if (DO_LOG_BOUNDS) {
1412             MarlinUtils.logInfo("edgesXY = [" + edgeMinX + " ... " + edgeMaxX
1413                                 + "[ [" + edgeMinY + " ... " + edgeMaxY + "[");
1414             MarlinUtils.logInfo("spXY    = [" + spminX + " ... " + spmaxX
1415                                 + "[ [" + spminY + " ... " + spmaxY + "[");
1416         }
1417 
1418         // test clipping for shapes out of bounds
1419         if ((spminX >= spmaxX) || (spminY >= spmaxY)) {
1420             return false;
1421         }
1422 
1423         // half open intervals
1424         // inclusive:
1425         final int pminX =  spminX                    >> SUBPIXEL_LG_POSITIONS_X;
1426         // exclusive:
1427         final int pmaxX = (spmaxX + SUBPIXEL_MASK_X) >> SUBPIXEL_LG_POSITIONS_X;
1428         // inclusive:
1429         final int pminY =  spminY                    >> SUBPIXEL_LG_POSITIONS_Y;
1430         // exclusive:
1431         final int pmaxY = (spmaxY + SUBPIXEL_MASK_Y) >> SUBPIXEL_LG_POSITIONS_Y;
1432 
1433         // store BBox to answer ptg.getBBox():
1434         this.cache.init(pminX, pminY, pmaxX, pmaxY);
1435 
1436         // Heuristics for using block flags:
1437         if (ENABLE_BLOCK_FLAGS) {
1438             enableBlkFlags = this.cache.useRLE;
1439             prevUseBlkFlags = enableBlkFlags && !ENABLE_BLOCK_FLAGS_HEURISTICS;
1440 
1441             if (enableBlkFlags) {
1442                 // ensure blockFlags array is large enough:
1443                 // note: +2 to ensure enough space left at end
1444                 final int blkLen = ((pmaxX - pminX) >> BLOCK_SIZE_LG) + 2;
1445                 if (blkLen > INITIAL_ARRAY) {
1446                     blkFlags = blkFlags_ref.getArray(blkLen);
1447                 }
1448             }
1449         }
1450 
1451         // memorize the rendering bounding box:
1452         /* note: bbox_spminX and bbox_spmaxX must be pixel boundaries
1453            to have correct coverage computation */
1454         // inclusive:
1455         bbox_spminX = pminX << SUBPIXEL_LG_POSITIONS_X;
1456         // exclusive:
1457         bbox_spmaxX = pmaxX << SUBPIXEL_LG_POSITIONS_X;
1458         // inclusive:
1459         bbox_spminY = spminY;
1460         // exclusive:
1461         bbox_spmaxY = spmaxY;
1462 
1463         if (DO_LOG_BOUNDS) {
1464             MarlinUtils.logInfo("pXY       = [" + pminX + " ... " + pmaxX
1465                                 + "[ [" + pminY + " ... " + pmaxY + "[");
1466             MarlinUtils.logInfo("bbox_spXY = [" + bbox_spminX + " ... "
1467                                 + bbox_spmaxX + "[ [" + bbox_spminY + " ... "
1468                                 + bbox_spmaxY + "[");
1469         }
1470 
1471         // Prepare alpha line:
1472         // add 2 to better deal with the last pixel in a pixel row.
1473         final int width = (pmaxX - pminX) + 2;
1474 
1475         // Useful when processing tile line by tile line
1476         if (width > INITIAL_AA_ARRAY) {
1477             if (DO_STATS) {
1478                 rdrCtx.stats.stat_array_renderer_alphaline.add(width);
1479             }
1480             alphaLine = alphaLine_ref.getArray(width);
1481         }
1482 
1483         // process first tile line:
1484         endRendering(pminY);
1485 
1486         return true;
1487     }
1488 
1489     private int bbox_spminX, bbox_spmaxX, bbox_spminY, bbox_spmaxY;
1490 
1491     void endRendering(final int pminY) {
1492         if (DO_MONITORS) {
1493             rdrCtx.stats.mon_rdr_endRendering_Y.start();
1494         }
1495 
1496         final int spminY       = pminY << SUBPIXEL_LG_POSITIONS_Y;
1497         final int fixed_spminY = FloatMath.max(bbox_spminY, spminY);
1498 
1499         // avoid rendering for last call to nextTile()
1500         if (fixed_spminY < bbox_spmaxY) {
1501             // process a complete tile line ie scanlines for 32 rows
1502             final int spmaxY = FloatMath.min(bbox_spmaxY, spminY + SUBPIXEL_TILE);
1503 
1504             // process tile line [0 - 32]
1505             cache.resetTileLine(pminY);
1506 
1507             // Process only one tile line:
1508             _endRendering(fixed_spminY, spmaxY);
1509         }
1510         if (DO_MONITORS) {
1511             rdrCtx.stats.mon_rdr_endRendering_Y.stop();
1512         }
1513     }
1514 
1515     void copyAARow(final int[] alphaRow,
1516                    final int pix_y, final int pix_from, final int pix_to,
1517                    final boolean useBlockFlags)
1518     {
1519         if (DO_MONITORS) {
1520             rdrCtx.stats.mon_rdr_copyAARow.start();
1521         }
1522         if (useBlockFlags) {
1523             if (DO_STATS) {
1524                 rdrCtx.stats.hist_tile_generator_encoding.add(1);
1525             }
1526             cache.copyAARowRLE_WithBlockFlags(blkFlags, alphaRow, pix_y, pix_from, pix_to);
1527         } else {
1528             if (DO_STATS) {
1529                 rdrCtx.stats.hist_tile_generator_encoding.add(0);
1530             }
1531             cache.copyAARowNoRLE(alphaRow, pix_y, pix_from, pix_to);
1532         }
1533         if (DO_MONITORS) {
1534             rdrCtx.stats.mon_rdr_copyAARow.stop();
1535         }
1536     }
1537 }