text: /*
   * Mesa 3-D graphics library
   * Version:  7.0
   *
   * Copyright (C) 1999-2007  Brian Paul   All Rights Reserved.
   *
   * Permission is hereby granted, free of charge, to any person obtaining a
   * copy of this software and associated documentation files (the "Software"),
   * to deal in the Software without restriction, including without limitation
   * the rights to use, copy, modify, merge, publish, distribute, sublicense,
   * and/or sell copies of the Software, and to permit persons to whom the
   * Software is furnished to do so, subject to the following conditions:
   *
   * The above copyright notice and this permission notice shall be included
   * in all copies or substantial portions of the Software.
   *
   * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
   * OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
   * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.  IN NO EVENT SHALL
   * BRIAN PAUL BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN
   * AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN
   * CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
   */
  
  /*
   * Triangle Rasterizer Template
   *
   * This file is #include'd to generate custom triangle rasterizers.
   *
   * The following macros may be defined to indicate what auxillary information
   * must be interpolated across the triangle:
   *    INTERP_Z        - if defined, interpolate integer Z values
   *    INTERP_RGB      - if defined, interpolate integer RGB values
   *    INTERP_ALPHA    - if defined, interpolate integer Alpha values
   *    INTERP_INT_TEX  - if defined, interpolate integer ST texcoords
   *                         (fast, simple 2-D texture mapping, without
   *                         perspective correction)
   *    INTERP_ATTRIBS  - if defined, interpolate arbitrary attribs (texcoords,
   *                         varying vars, etc)  This also causes W to be
   *                         computed for perspective correction).
   *
   * When one can directly address pixels in the color buffer the following
   * macros can be defined and used to compute pixel addresses during
   * rasterization (see pRow):
   *    PIXEL_TYPE          - the datatype of a pixel (GLubyte, GLushort, GLuint)
   *    BYTES_PER_ROW       - number of bytes per row in the color buffer
   *    PIXEL_ADDRESS(X,Y)  - returns the address of pixel at (X,Y) where
   *                          Y==0 at bottom of screen and increases upward.
   *
   * Similarly, for direct depth buffer access, this type is used for depth
   * buffer addressing (see zRow):
   *    DEPTH_TYPE          - either GLushort or GLuint
   *
   * Optionally, one may provide one-time setup code per triangle:
   *    SETUP_CODE    - code which is to be executed once per triangle
   *
   * The following macro MUST be defined:
   *    RENDER_SPAN(span) - code to write a span of pixels.
   *
   * This code was designed for the origin to be in the lower-left corner.
   *
   * Inspired by triangle rasterizer code written by Allen Akin.  Thanks Allen!
   *
   *
   * Some notes on rasterization accuracy:
   *
   * This code uses fixed point arithmetic (the GLfixed type) to iterate
   * over the triangle edges and interpolate ancillary data (such as Z,
   * color, secondary color, etc).  The number of fractional bits in
   * GLfixed and the value of SUB_PIXEL_BITS has a direct bearing on the
   * accuracy of rasterization.
   *
   * If SUB_PIXEL_BITS=4 then we'll snap the vertices to the nearest
   * 1/16 of a pixel.  If we're walking up a long, nearly vertical edge
   * (dx=1/16, dy=1024) we'll need 4 + 10 = 14 fractional bits in
   * GLfixed to walk the edge without error.  If the maximum viewport
   * height is 4K pixels, then we'll need 4 + 12 = 16 fractional bits.
   *
   * Historically, Mesa has used 11 fractional bits in GLfixed, snaps
   * vertices to 1/16 pixel and allowed a maximum viewport height of 2K
   * pixels.  11 fractional bits is actually insufficient for accurately
   * rasterizing some triangles.  More recently, the maximum viewport
   * height was increased to 4K pixels.  Thus, Mesa should be using 16
   * fractional bits in GLfixed.  Unfortunately, there may be some issues
   * with setting FIXED_FRAC_BITS=16, such as multiplication overflow.
   * This will have to be examined in some detail...
   *
   * For now, if you find rasterization errors, particularly with tall,
   * sliver triangles, try increasing FIXED_FRAC_BITS and/or decreasing
   * SUB_PIXEL_BITS.
   */
  
  
  /*
   * Some code we unfortunately need to prevent negative interpolated colors.
   */
  #ifndef CLAMP_INTERPOLANT
  #define CLAMP_INTERPOLANT(CHANNEL, CHANNELSTEP, LEN)		\
  do {								\
     GLfixed endVal = span.CHANNEL + (LEN) * span.CHANNELSTEP;	\
     if (endVal < 0) {						\
        span.CHANNEL -= endVal;					\
     }								\
     if (span.CHANNEL < 0) {					\
        span.CHANNEL = 0;						\
     }								\
  } while (0)
  #endif
  
  
  static void NAME(struct gl_context *ctx, const SWvertex *v0,
                                   const SWvertex *v1,
                                   const SWvertex *v2 )
  {
     typedef struct {
        const SWvertex *v0, *v1;   /* Y(v0) < Y(v1) */
        GLfloat dx;	/* X(v1) - X(v0) */
        GLfloat dy;	/* Y(v1) - Y(v0) */
        GLfloat dxdy;	/* dx/dy */
        GLfixed fdxdy;	/* dx/dy in fixed-point */
        GLfloat adjy;	/* adjust from v[0]->fy to fsy, scaled */
        GLfixed fsx;	/* first sample point x coord */
        GLfixed fsy;
        GLfixed fx0;	/* fixed pt X of lower endpoint */
        GLint lines;	/* number of lines to be sampled on this edge */
     } EdgeT;
  
     const SWcontext *swrast = SWRAST_CONTEXT(ctx);
  #ifdef INTERP_Z
     const GLint depthBits = ctx->DrawBuffer->Visual.depthBits;
     const GLint fixedToDepthShift = depthBits <= 16 ? FIXED_SHIFT : 0;
     const GLfloat maxDepth = ctx->DrawBuffer->_DepthMaxF;
  #define FixedToDepth(F)  ((F) >> fixedToDepthShift)
  #endif
     EdgeT eMaj, eTop, eBot;
     GLfloat oneOverArea;
     const SWvertex *vMin, *vMid, *vMax;  /* Y(vMin)<=Y(vMid)<=Y(vMax) */
     GLfloat bf = SWRAST_CONTEXT(ctx)->_BackfaceSign;
     const GLint snapMask = ~((FIXED_ONE / (1 << SUB_PIXEL_BITS)) - 1); /* for x/y coord snapping */
     GLfixed vMin_fx, vMin_fy, vMid_fx, vMid_fy, vMax_fx, vMax_fy;
  
     SWspan span;
  
     (void) swrast;
  
     INIT_SPAN(span, GL_POLYGON);
     span.y = 0; /* silence warnings */
  
  #ifdef INTERP_Z
     (void) fixedToDepthShift;
  #endif
  
     /*
     printf("%s()\n", __FUNCTION__);
     printf("  %g, %g, %g\n",
            v0->attrib[FRAG_ATTRIB_WPOS][0],
            v0->attrib[FRAG_ATTRIB_WPOS][1],
            v0->attrib[FRAG_ATTRIB_WPOS][2]);
     printf("  %g, %g, %g\n",
            v1->attrib[FRAG_ATTRIB_WPOS][0],
            v1->attrib[FRAG_ATTRIB_WPOS][1],
            v1->attrib[FRAG_ATTRIB_WPOS][2]);
     printf("  %g, %g, %g\n",
            v2->attrib[FRAG_ATTRIB_WPOS][0],
            v2->attrib[FRAG_ATTRIB_WPOS][1],
            v2->attrib[FRAG_ATTRIB_WPOS][2]);
     */
  
     /* Compute fixed point x,y coords w/ half-pixel offsets and snapping.
      * And find the order of the 3 vertices along the Y axis.
      */
     {
        const GLfixed fy0 = FloatToFixed(v0->attrib[FRAG_ATTRIB_WPOS][1] - 0.5F) & snapMask;
        const GLfixed fy1 = FloatToFixed(v1->attrib[FRAG_ATTRIB_WPOS][1] - 0.5F) & snapMask;
        const GLfixed fy2 = FloatToFixed(v2->attrib[FRAG_ATTRIB_WPOS][1] - 0.5F) & snapMask;
        if (fy0 <= fy1) {
           if (fy1 <= fy2) {
              /* y0 <= y1 <= y2 */
              vMin = v0;   vMid = v1;   vMax = v2;
              vMin_fy = fy0;  vMid_fy = fy1;  vMax_fy = fy2;
           }
           else if (fy2 <= fy0) {
              /* y2 <= y0 <= y1 */
              vMin = v2;   vMid = v0;   vMax = v1;
              vMin_fy = fy2;  vMid_fy = fy0;  vMax_fy = fy1;
           }
           else {
              /* y0 <= y2 <= y1 */
              vMin = v0;   vMid = v2;   vMax = v1;
              vMin_fy = fy0;  vMid_fy = fy2;  vMax_fy = fy1;
              bf = -bf;
           }
        }
        else {
           if (fy0 <= fy2) {
              /* y1 <= y0 <= y2 */
              vMin = v1;   vMid = v0;   vMax = v2;
              vMin_fy = fy1;  vMid_fy = fy0;  vMax_fy = fy2;
              bf = -bf;
           }
           else if (fy2 <= fy1) {
              /* y2 <= y1 <= y0 */
              vMin = v2;   vMid = v1;   vMax = v0;
              vMin_fy = fy2;  vMid_fy = fy1;  vMax_fy = fy0;
              bf = -bf;
           }
           else {
              /* y1 <= y2 <= y0 */
              vMin = v1;   vMid = v2;   vMax = v0;
              vMin_fy = fy1;  vMid_fy = fy2;  vMax_fy = fy0;
           }
        }
  
        /* fixed point X coords */
        vMin_fx = FloatToFixed(vMin->attrib[FRAG_ATTRIB_WPOS][0] + 0.5F) & snapMask;
        vMid_fx = FloatToFixed(vMid->attrib[FRAG_ATTRIB_WPOS][0] + 0.5F) & snapMask;
        vMax_fx = FloatToFixed(vMax->attrib[FRAG_ATTRIB_WPOS][0] + 0.5F) & snapMask;
     }
  
     /* vertex/edge relationship */
     eMaj.v0 = vMin;   eMaj.v1 = vMax;   /*TODO: .v1's not needed */
     eTop.v0 = vMid;   eTop.v1 = vMax;
     eBot.v0 = vMin;   eBot.v1 = vMid;
  
     /* compute deltas for each edge:  vertex[upper] - vertex[lower] */
     eMaj.dx = FixedToFloat(vMax_fx - vMin_fx);
     eMaj.dy = FixedToFloat(vMax_fy - vMin_fy);
     eTop.dx = FixedToFloat(vMax_fx - vMid_fx);
     eTop.dy = FixedToFloat(vMax_fy - vMid_fy);
     eBot.dx = FixedToFloat(vMid_fx - vMin_fx);
     eBot.dy = FixedToFloat(vMid_fy - vMin_fy);
  
     /* compute area, oneOverArea and perform backface culling */
     {
        const GLfloat area = eMaj.dx * eBot.dy - eBot.dx * eMaj.dy;
  
        if (IS_INF_OR_NAN(area) || area == 0.0F)
           return;
  
        if (area * bf * swrast->_BackfaceCullSign < 0.0)
           return;
  
        oneOverArea = 1.0F / area;
  
        /* 0 = front, 1 = back */
        span.facing = oneOverArea * bf > 0.0F;
     }
  
     /* Edge setup.  For a triangle strip these could be reused... */
     {
        eMaj.fsy = FixedCeil(vMin_fy);
        eMaj.lines = FixedToInt(FixedCeil(vMax_fy - eMaj.fsy));
        if (eMaj.lines > 0) {
           eMaj.dxdy = eMaj.dx / eMaj.dy;
           eMaj.fdxdy = SignedFloatToFixed(eMaj.dxdy);
           eMaj.adjy = (GLfloat) (eMaj.fsy - vMin_fy);  /* SCALED! */
           eMaj.fx0 = vMin_fx;
           eMaj.fsx = eMaj.fx0 + (GLfixed) (eMaj.adjy * eMaj.dxdy);
        }
        else {
           return;  /*CULLED*/
        }
  
        eTop.fsy = FixedCeil(vMid_fy);
        eTop.lines = FixedToInt(FixedCeil(vMax_fy - eTop.fsy));
        if (eTop.lines > 0) {
           eTop.dxdy = eTop.dx / eTop.dy;
           eTop.fdxdy = SignedFloatToFixed(eTop.dxdy);
           eTop.adjy = (GLfloat) (eTop.fsy - vMid_fy); /* SCALED! */
           eTop.fx0 = vMid_fx;
           eTop.fsx = eTop.fx0 + (GLfixed) (eTop.adjy * eTop.dxdy);
        }
  
        eBot.fsy = FixedCeil(vMin_fy);
        eBot.lines = FixedToInt(FixedCeil(vMid_fy - eBot.fsy));
        if (eBot.lines > 0) {
           eBot.dxdy = eBot.dx / eBot.dy;
           eBot.fdxdy = SignedFloatToFixed(eBot.dxdy);
           eBot.adjy = (GLfloat) (eBot.fsy - vMin_fy);  /* SCALED! */
           eBot.fx0 = vMin_fx;
           eBot.fsx = eBot.fx0 + (GLfixed) (eBot.adjy * eBot.dxdy);
        }
     }
  
     /*
      * Conceptually, we view a triangle as two subtriangles
      * separated by a perfectly horizontal line.  The edge that is
      * intersected by this line is one with maximal absolute dy; we
      * call it a ``major'' edge.  The other two edges are the
      * ``top'' edge (for the upper subtriangle) and the ``bottom''
      * edge (for the lower subtriangle).  If either of these two
      * edges is horizontal or very close to horizontal, the
      * corresponding subtriangle might cover zero sample points;
      * we take care to handle such cases, for performance as well
      * as correctness.
      *
      * By stepping rasterization parameters along the major edge,
      * we can avoid recomputing them at the discontinuity where
      * the top and bottom edges meet.  However, this forces us to
      * be able to scan both left-to-right and right-to-left.
      * Also, we must determine whether the major edge is at the
      * left or right side of the triangle.  We do this by
      * computing the magnitude of the cross-product of the major
      * and top edges.  Since this magnitude depends on the sine of
      * the angle between the two edges, its sign tells us whether
      * we turn to the left or to the right when travelling along
      * the major edge to the top edge, and from this we infer
      * whether the major edge is on the left or the right.
      *
      * Serendipitously, this cross-product magnitude is also a
      * value we need to compute the iteration parameter
      * derivatives for the triangle, and it can be used to perform
      * backface culling because its sign tells us whether the
      * triangle is clockwise or counterclockwise.  In this code we
      * refer to it as ``area'' because it's also proportional to
      * the pixel area of the triangle.
      */
  
     {
        GLint scan_from_left_to_right;  /* true if scanning left-to-right */
  
        /*
         * Execute user-supplied setup code
         */
  #ifdef SETUP_CODE
        SETUP_CODE
  #endif
  
        scan_from_left_to_right = (oneOverArea < 0.0F);
  
  
        /* compute d?/dx and d?/dy derivatives */
  #ifdef INTERP_Z
        span.interpMask |= SPAN_Z;
        {
           GLfloat eMaj_dz = vMax->attrib[FRAG_ATTRIB_WPOS][2] - vMin->attrib[FRAG_ATTRIB_WPOS][2];
           GLfloat eBot_dz = vMid->attrib[FRAG_ATTRIB_WPOS][2] - vMin->attrib[FRAG_ATTRIB_WPOS][2];
           span.attrStepX[FRAG_ATTRIB_WPOS][2] = oneOverArea * (eMaj_dz * eBot.dy - eMaj.dy * eBot_dz);
           if (span.attrStepX[FRAG_ATTRIB_WPOS][2] > maxDepth ||
               span.attrStepX[FRAG_ATTRIB_WPOS][2] < -maxDepth) {
              /* probably a sliver triangle */
              span.attrStepX[FRAG_ATTRIB_WPOS][2] = 0.0;
              span.attrStepY[FRAG_ATTRIB_WPOS][2] = 0.0;
           }
           else {
              span.attrStepY[FRAG_ATTRIB_WPOS][2] = oneOverArea * (eMaj.dx * eBot_dz - eMaj_dz * eBot.dx);
           }
           if (depthBits <= 16)
              span.zStep = SignedFloatToFixed(span.attrStepX[FRAG_ATTRIB_WPOS][2]);
           else
              span.zStep = (GLint) span.attrStepX[FRAG_ATTRIB_WPOS][2];
        }
  #endif
  #ifdef INTERP_RGB
        span.interpMask |= SPAN_RGBA;
        if (ctx->Light.ShadeModel == GL_SMOOTH) {
           GLfloat eMaj_dr = (GLfloat) (vMax->color[RCOMP] - vMin->color[RCOMP]);
           GLfloat eBot_dr = (GLfloat) (vMid->color[RCOMP] - vMin->color[RCOMP]);
           GLfloat eMaj_dg = (GLfloat) (vMax->color[GCOMP] - vMin->color[GCOMP]);
           GLfloat eBot_dg = (GLfloat) (vMid->color[GCOMP] - vMin->color[GCOMP]);
           GLfloat eMaj_db = (GLfloat) (vMax->color[BCOMP] - vMin->color[BCOMP]);
           GLfloat eBot_db = (GLfloat) (vMid->color[BCOMP] - vMin->color[BCOMP]);
  #  ifdef INTERP_ALPHA
           GLfloat eMaj_da = (GLfloat) (vMax->color[ACOMP] - vMin->color[ACOMP]);
           GLfloat eBot_da = (GLfloat) (vMid->color[ACOMP] - vMin->color[ACOMP]);
  #  endif
           span.attrStepX[FRAG_ATTRIB_COL0][0] = oneOverArea * (eMaj_dr * eBot.dy - eMaj.dy * eBot_dr);
           span.attrStepY[FRAG_ATTRIB_COL0][0] = oneOverArea * (eMaj.dx * eBot_dr - eMaj_dr * eBot.dx);
           span.attrStepX[FRAG_ATTRIB_COL0][1] = oneOverArea * (eMaj_dg * eBot.dy - eMaj.dy * eBot_dg);
           span.attrStepY[FRAG_ATTRIB_COL0][1] = oneOverArea * (eMaj.dx * eBot_dg - eMaj_dg * eBot.dx);
           span.attrStepX[FRAG_ATTRIB_COL0][2] = oneOverArea * (eMaj_db * eBot.dy - eMaj.dy * eBot_db);
           span.attrStepY[FRAG_ATTRIB_COL0][2] = oneOverArea * (eMaj.dx * eBot_db - eMaj_db * eBot.dx);
           span.redStep   = SignedFloatToFixed(span.attrStepX[FRAG_ATTRIB_COL0][0]);
           span.greenStep = SignedFloatToFixed(span.attrStepX[FRAG_ATTRIB_COL0][1]);
           span.blueStep  = SignedFloatToFixed(span.attrStepX[FRAG_ATTRIB_COL0][2]);
  #  ifdef INTERP_ALPHA
           span.attrStepX[FRAG_ATTRIB_COL0][3] = oneOverArea * (eMaj_da * eBot.dy - eMaj.dy * eBot_da);
           span.attrStepY[FRAG_ATTRIB_COL0][3] = oneOverArea * (eMaj.dx * eBot_da - eMaj_da * eBot.dx);
           span.alphaStep = SignedFloatToFixed(span.attrStepX[FRAG_ATTRIB_COL0][3]);
  #  endif /* INTERP_ALPHA */
        }
        else {
           ASSERT(ctx->Light.ShadeModel == GL_FLAT);
           span.interpMask |= SPAN_FLAT;
           span.attrStepX[FRAG_ATTRIB_COL0][0] = span.attrStepY[FRAG_ATTRIB_COL0][0] = 0.0F;
           span.attrStepX[FRAG_ATTRIB_COL0][1] = span.attrStepY[FRAG_ATTRIB_COL0][1] = 0.0F;
           span.attrStepX[FRAG_ATTRIB_COL0][2] = span.attrStepY[FRAG_ATTRIB_COL0][2] = 0.0F;
  	 span.redStep   = 0;
  	 span.greenStep = 0;
  	 span.blueStep  = 0;
  #  ifdef INTERP_ALPHA
           span.attrStepX[FRAG_ATTRIB_COL0][3] = span.attrStepY[FRAG_ATTRIB_COL0][3] = 0.0F;
  	 span.alphaStep = 0;
  #  endif
        }
  #endif /* INTERP_RGB */
  #ifdef INTERP_INT_TEX
        {
           GLfloat eMaj_ds = (vMax->attrib[FRAG_ATTRIB_TEX0][0] - vMin->attrib[FRAG_ATTRIB_TEX0][0]) * S_SCALE;
           GLfloat eBot_ds = (vMid->attrib[FRAG_ATTRIB_TEX0][0] - vMin->attrib[FRAG_ATTRIB_TEX0][0]) * S_SCALE;
           GLfloat eMaj_dt = (vMax->attrib[FRAG_ATTRIB_TEX0][1] - vMin->attrib[FRAG_ATTRIB_TEX0][1]) * T_SCALE;
           GLfloat eBot_dt = (vMid->attrib[FRAG_ATTRIB_TEX0][1] - vMin->attrib[FRAG_ATTRIB_TEX0][1]) * T_SCALE;
           span.attrStepX[FRAG_ATTRIB_TEX0][0] = oneOverArea * (eMaj_ds * eBot.dy - eMaj.dy * eBot_ds);
           span.attrStepY[FRAG_ATTRIB_TEX0][0] = oneOverArea * (eMaj.dx * eBot_ds - eMaj_ds * eBot.dx);
           span.attrStepX[FRAG_ATTRIB_TEX0][1] = oneOverArea * (eMaj_dt * eBot.dy - eMaj.dy * eBot_dt);
           span.attrStepY[FRAG_ATTRIB_TEX0][1] = oneOverArea * (eMaj.dx * eBot_dt - eMaj_dt * eBot.dx);
           span.intTexStep[0] = SignedFloatToFixed(span.attrStepX[FRAG_ATTRIB_TEX0][0]);
           span.intTexStep[1] = SignedFloatToFixed(span.attrStepX[FRAG_ATTRIB_TEX0][1]);
        }
  #endif
  #ifdef INTERP_ATTRIBS
        {
           /* attrib[FRAG_ATTRIB_WPOS][3] is 1/W */
           const GLfloat wMax = vMax->attrib[FRAG_ATTRIB_WPOS][3];
           const GLfloat wMin = vMin->attrib[FRAG_ATTRIB_WPOS][3];
           const GLfloat wMid = vMid->attrib[FRAG_ATTRIB_WPOS][3];
           {
              const GLfloat eMaj_dw = wMax - wMin;
              const GLfloat eBot_dw = wMid - wMin;
              span.attrStepX[FRAG_ATTRIB_WPOS][3] = oneOverArea * (eMaj_dw * eBot.dy - eMaj.dy * eBot_dw);
              span.attrStepY[FRAG_ATTRIB_WPOS][3] = oneOverArea * (eMaj.dx * eBot_dw - eMaj_dw * eBot.dx);
           }
           ATTRIB_LOOP_BEGIN
              if (swrast->_InterpMode[attr] == GL_FLAT) {
                 ASSIGN_4V(span.attrStepX[attr], 0.0, 0.0, 0.0, 0.0);
                 ASSIGN_4V(span.attrStepY[attr], 0.0, 0.0, 0.0, 0.0);
              }
              else {
                 GLuint c;
                 for (c = 0; c < 4; c++) {
                    GLfloat eMaj_da = vMax->attrib[attr][c] * wMax - vMin->attrib[attr][c] * wMin;
                    GLfloat eBot_da = vMid->attrib[attr][c] * wMid - vMin->attrib[attr][c] * wMin;
                    span.attrStepX[attr][c] = oneOverArea * (eMaj_da * eBot.dy - eMaj.dy * eBot_da);
                    span.attrStepY[attr][c] = oneOverArea * (eMaj.dx * eBot_da - eMaj_da * eBot.dx);
                 }
              }
           ATTRIB_LOOP_END
        }
  #endif
  
        /*
         * We always sample at pixel centers.  However, we avoid
         * explicit half-pixel offsets in this code by incorporating
         * the proper offset in each of x and y during the
         * transformation to window coordinates.
         *
         * We also apply the usual rasterization rules to prevent
         * cracks and overlaps.  A pixel is considered inside a
         * subtriangle if it meets all of four conditions: it is on or
         * to the right of the left edge, strictly to the left of the
         * right edge, on or below the top edge, and strictly above
         * the bottom edge.  (Some edges may be degenerate.)
         *
         * The following discussion assumes left-to-right scanning
         * (that is, the major edge is on the left); the right-to-left
         * case is a straightforward variation.
         *
         * We start by finding the half-integral y coordinate that is
         * at or below the top of the triangle.  This gives us the
         * first scan line that could possibly contain pixels that are
         * inside the triangle.
         *
         * Next we creep down the major edge until we reach that y,
         * and compute the corresponding x coordinate on the edge.
         * Then we find the half-integral x that lies on or just
         * inside the edge.  This is the first pixel that might lie in
         * the interior of the triangle.  (We won't know for sure
         * until we check the other edges.)
         *
         * As we rasterize the triangle, we'll step down the major
         * edge.  For each step in y, we'll move an integer number
         * of steps in x.  There are two possible x step sizes, which
         * we'll call the ``inner'' step (guaranteed to land on the
         * edge or inside it) and the ``outer'' step (guaranteed to
         * land on the edge or outside it).  The inner and outer steps
         * differ by one.  During rasterization we maintain an error
         * term that indicates our distance from the true edge, and
         * select either the inner step or the outer step, whichever
         * gets us to the first pixel that falls inside the triangle.
         *
         * All parameters (z, red, etc.) as well as the buffer
         * addresses for color and z have inner and outer step values,
         * so that we can increment them appropriately.  This method
         * eliminates the need to adjust parameters by creeping a
         * sub-pixel amount into the triangle at each scanline.
         */
  
        {
           GLint subTriangle;
           GLfixed fxLeftEdge = 0, fxRightEdge = 0;
           GLfixed fdxLeftEdge = 0, fdxRightEdge = 0;
           GLfixed fError = 0, fdError = 0;
  #ifdef PIXEL_ADDRESS
           PIXEL_TYPE *pRow = NULL;
           GLint dPRowOuter = 0, dPRowInner;  /* offset in bytes */
  #endif
  #ifdef INTERP_Z
  #  ifdef DEPTH_TYPE
           struct gl_renderbuffer *zrb
              = ctx->DrawBuffer->Attachment[BUFFER_DEPTH].Renderbuffer;
           DEPTH_TYPE *zRow = NULL;
           GLint dZRowOuter = 0, dZRowInner;  /* offset in bytes */
  #  endif
           GLuint zLeft = 0;
           GLfixed fdzOuter = 0, fdzInner;
  #endif
  #ifdef INTERP_RGB
           GLint rLeft = 0, fdrOuter = 0, fdrInner;
           GLint gLeft = 0, fdgOuter = 0, fdgInner;
           GLint bLeft = 0, fdbOuter = 0, fdbInner;
  #endif
  #ifdef INTERP_ALPHA
           GLint aLeft = 0, fdaOuter = 0, fdaInner;
  #endif
  #ifdef INTERP_INT_TEX
           GLfixed sLeft=0, dsOuter=0, dsInner;
           GLfixed tLeft=0, dtOuter=0, dtInner;
  #endif
  #ifdef INTERP_ATTRIBS
           GLfloat wLeft = 0, dwOuter = 0, dwInner;
           GLfloat attrLeft[FRAG_ATTRIB_MAX][4];
           GLfloat daOuter[FRAG_ATTRIB_MAX][4], daInner[FRAG_ATTRIB_MAX][4];
  #endif
  
           for (subTriangle=0; subTriangle<=1; subTriangle++) {
              EdgeT *eLeft, *eRight;
              int setupLeft, setupRight;
              int lines;
  
              if (subTriangle==0) {
                 /* bottom half */
                 if (scan_from_left_to_right) {
                    eLeft = &eMaj;
                    eRight = &eBot;
                    lines = eRight->lines;
                    setupLeft = 1;
                    setupRight = 1;
                 }
                 else {
                    eLeft = &eBot;
                    eRight = &eMaj;
                    lines = eLeft->lines;
                    setupLeft = 1;
                    setupRight = 1;
                 }
              }
              else {
                 /* top half */
                 if (scan_from_left_to_right) {
                    eLeft = &eMaj;
                    eRight = &eTop;
                    lines = eRight->lines;
                    setupLeft = 0;
                    setupRight = 1;
                 }
                 else {
                    eLeft = &eTop;
                    eRight = &eMaj;
                    lines = eLeft->lines;
                    setupLeft = 1;
                    setupRight = 0;
                 }
                 if (lines == 0)
                    return;
              }
  
              if (setupLeft && eLeft->lines > 0) {
                 const SWvertex *vLower = eLeft->v0;
                 const GLfixed fsy = eLeft->fsy;
                 const GLfixed fsx = eLeft->fsx;  /* no fractional part */
                 const GLfixed fx = FixedCeil(fsx);  /* no fractional part */
                 const GLfixed adjx = (GLfixed) (fx - eLeft->fx0); /* SCALED! */
                 const GLfixed adjy = (GLfixed) eLeft->adjy;      /* SCALED! */
                 GLint idxOuter;
                 GLfloat dxOuter;
                 GLfixed fdxOuter;
  
                 fError = fx - fsx - FIXED_ONE;
                 fxLeftEdge = fsx - FIXED_EPSILON;
                 fdxLeftEdge = eLeft->fdxdy;
                 fdxOuter = FixedFloor(fdxLeftEdge - FIXED_EPSILON);
                 fdError = fdxOuter - fdxLeftEdge + FIXED_ONE;
                 idxOuter = FixedToInt(fdxOuter);
                 dxOuter = (GLfloat) idxOuter;
                 span.y = FixedToInt(fsy);
  
                 /* silence warnings on some compilers */
                 (void) dxOuter;
                 (void) adjx;
                 (void) adjy;
                 (void) vLower;
  
  #ifdef PIXEL_ADDRESS
                 {
                    pRow = (PIXEL_TYPE *) PIXEL_ADDRESS(FixedToInt(fxLeftEdge), span.y);
                    dPRowOuter = -((int)BYTES_PER_ROW) + idxOuter * sizeof(PIXEL_TYPE);
                    /* negative because Y=0 at bottom and increases upward */
                 }
  #endif
                 /*
                  * Now we need the set of parameter (z, color, etc.) values at
                  * the point (fx, fsy).  This gives us properly-sampled parameter
                  * values that we can step from pixel to pixel.  Furthermore,
                  * although we might have intermediate results that overflow
                  * the normal parameter range when we step temporarily outside
                  * the triangle, we shouldn't overflow or underflow for any
                  * pixel that's actually inside the triangle.
                  */
  
  #ifdef INTERP_Z
                 {
                    GLfloat z0 = vLower->attrib[FRAG_ATTRIB_WPOS][2];
                    if (depthBits <= 16) {
                       /* interpolate fixed-pt values */
                       GLfloat tmp = (z0 * FIXED_SCALE
                                      + span.attrStepX[FRAG_ATTRIB_WPOS][2] * adjx
                                      + span.attrStepY[FRAG_ATTRIB_WPOS][2] * adjy) + FIXED_HALF;
                       if (tmp < MAX_GLUINT / 2)
                          zLeft = (GLfixed) tmp;
                       else
                          zLeft = MAX_GLUINT / 2;
                       fdzOuter = SignedFloatToFixed(span.attrStepY[FRAG_ATTRIB_WPOS][2] +
                                                     dxOuter * span.attrStepX[FRAG_ATTRIB_WPOS][2]);
                    }
                    else {
                       /* interpolate depth values w/out scaling */
                       zLeft = (GLuint) (z0 + span.attrStepX[FRAG_ATTRIB_WPOS][2] * FixedToFloat(adjx)
                                            + span.attrStepY[FRAG_ATTRIB_WPOS][2] * FixedToFloat(adjy));
                       fdzOuter = (GLint) (span.attrStepY[FRAG_ATTRIB_WPOS][2] +
                                           dxOuter * span.attrStepX[FRAG_ATTRIB_WPOS][2]);
                    }
  #  ifdef DEPTH_TYPE
                    zRow = (DEPTH_TYPE *)
                      _swrast_pixel_address(zrb, FixedToInt(fxLeftEdge), span.y);
                    dZRowOuter = (ctx->DrawBuffer->Width + idxOuter) * sizeof(DEPTH_TYPE);
  #  endif
                 }
  #endif
  #ifdef INTERP_RGB
                 if (ctx->Light.ShadeModel == GL_SMOOTH) {
                    rLeft = (GLint)(ChanToFixed(vLower->color[RCOMP])
                                    + span.attrStepX[FRAG_ATTRIB_COL0][0] * adjx
                                    + span.attrStepY[FRAG_ATTRIB_COL0][0] * adjy) + FIXED_HALF;
                    gLeft = (GLint)(ChanToFixed(vLower->color[GCOMP])
                                    + span.attrStepX[FRAG_ATTRIB_COL0][1] * adjx
                                    + span.attrStepY[FRAG_ATTRIB_COL0][1] * adjy) + FIXED_HALF;
                    bLeft = (GLint)(ChanToFixed(vLower->color[BCOMP])
                                    + span.attrStepX[FRAG_ATTRIB_COL0][2] * adjx
                                    + span.attrStepY[FRAG_ATTRIB_COL0][2] * adjy) + FIXED_HALF;
                    fdrOuter = SignedFloatToFixed(span.attrStepY[FRAG_ATTRIB_COL0][0]
                                                  + dxOuter * span.attrStepX[FRAG_ATTRIB_COL0][0]);
                    fdgOuter = SignedFloatToFixed(span.attrStepY[FRAG_ATTRIB_COL0][1]
                                                  + dxOuter * span.attrStepX[FRAG_ATTRIB_COL0][1]);
                    fdbOuter = SignedFloatToFixed(span.attrStepY[FRAG_ATTRIB_COL0][2]
                                                  + dxOuter * span.attrStepX[FRAG_ATTRIB_COL0][2]);
  #  ifdef INTERP_ALPHA
                    aLeft = (GLint)(ChanToFixed(vLower->color[ACOMP])
                                    + span.attrStepX[FRAG_ATTRIB_COL0][3] * adjx
                                    + span.attrStepY[FRAG_ATTRIB_COL0][3] * adjy) + FIXED_HALF;
                    fdaOuter = SignedFloatToFixed(span.attrStepY[FRAG_ATTRIB_COL0][3]
                                                  + dxOuter * span.attrStepX[FRAG_ATTRIB_COL0][3]);
  #  endif
                 }
                 else {
                    ASSERT(ctx->Light.ShadeModel == GL_FLAT);
                    rLeft = ChanToFixed(v2->color[RCOMP]);
                    gLeft = ChanToFixed(v2->color[GCOMP]);
                    bLeft = ChanToFixed(v2->color[BCOMP]);
                    fdrOuter = fdgOuter = fdbOuter = 0;
  #  ifdef INTERP_ALPHA
                    aLeft = ChanToFixed(v2->color[ACOMP]);
                    fdaOuter = 0;
  #  endif
                 }
  #endif /* INTERP_RGB */
  
  
  #ifdef INTERP_INT_TEX
                 {
                    GLfloat s0, t0;
                    s0 = vLower->attrib[FRAG_ATTRIB_TEX0][0] * S_SCALE;
                    sLeft = (GLfixed)(s0 * FIXED_SCALE + span.attrStepX[FRAG_ATTRIB_TEX0][0] * adjx
                                   + span.attrStepY[FRAG_ATTRIB_TEX0][0] * adjy) + FIXED_HALF;
                    dsOuter = SignedFloatToFixed(span.attrStepY[FRAG_ATTRIB_TEX0][0]
                                                 + dxOuter * span.attrStepX[FRAG_ATTRIB_TEX0][0]);
  
                    t0 = vLower->attrib[FRAG_ATTRIB_TEX0][1] * T_SCALE;
                    tLeft = (GLfixed)(t0 * FIXED_SCALE + span.attrStepX[FRAG_ATTRIB_TEX0][1] * adjx
                                   + span.attrStepY[FRAG_ATTRIB_TEX0][1] * adjy) + FIXED_HALF;
                    dtOuter = SignedFloatToFixed(span.attrStepY[FRAG_ATTRIB_TEX0][1]
                                                 + dxOuter * span.attrStepX[FRAG_ATTRIB_TEX0][1]);
                 }
  #endif
  #ifdef INTERP_ATTRIBS
                 {
                    const GLuint attr = FRAG_ATTRIB_WPOS;
                    wLeft = vLower->attrib[FRAG_ATTRIB_WPOS][3]
                          + (span.attrStepX[attr][3] * adjx
                             + span.attrStepY[attr][3] * adjy) * (1.0F/FIXED_SCALE);
                    dwOuter = span.attrStepY[attr][3] + dxOuter * span.attrStepX[attr][3];
                 }
                 ATTRIB_LOOP_BEGIN
                    const GLfloat invW = vLower->attrib[FRAG_ATTRIB_WPOS][3];
                    if (swrast->_InterpMode[attr] == GL_FLAT) {
                       GLuint c;
                       for (c = 0; c < 4; c++) {
                          attrLeft[attr][c] = v2->attrib[attr][c] * invW;
                          daOuter[attr][c] = 0.0;
                       }
                    }
                    else {
                       GLuint c;
                       for (c = 0; c < 4; c++) {
                          const GLfloat a = vLower->attrib[attr][c] * invW;
                          attrLeft[attr][c] = a + (  span.attrStepX[attr][c] * adjx
                                                   + span.attrStepY[attr][c] * adjy) * (1.0F/FIXED_SCALE);
                          daOuter[attr][c] = span.attrStepY[attr][c] + dxOuter * span.attrStepX[attr][c];
                       }
                    }
                 ATTRIB_LOOP_END
  #endif
              } /*if setupLeft*/
  
  
              if (setupRight && eRight->lines>0) {
                 fxRightEdge = eRight->fsx - FIXED_EPSILON;
                 fdxRightEdge = eRight->fdxdy;
              }
  
              if (lines==0) {
                 continue;
              }
  
  
              /* Rasterize setup */
  #ifdef PIXEL_ADDRESS
              dPRowInner = dPRowOuter + sizeof(PIXEL_TYPE);
  #endif
  #ifdef INTERP_Z
  #  ifdef DEPTH_TYPE
              dZRowInner = dZRowOuter + sizeof(DEPTH_TYPE);
  #  endif
              fdzInner = fdzOuter + span.zStep;
  #endif
  #ifdef INTERP_RGB
              fdrInner = fdrOuter + span.redStep;
              fdgInner = fdgOuter + span.greenStep;
              fdbInner = fdbOuter + span.blueStep;
  #endif
  #ifdef INTERP_ALPHA
              fdaInner = fdaOuter + span.alphaStep;
  #endif
  #ifdef INTERP_INT_TEX
              dsInner = dsOuter + span.intTexStep[0];
              dtInner = dtOuter + span.intTexStep[1];
  #endif
  #ifdef INTERP_ATTRIBS
              dwInner = dwOuter + span.attrStepX[FRAG_ATTRIB_WPOS][3];
              ATTRIB_LOOP_BEGIN
                 GLuint c;
                 for (c = 0; c < 4; c++) {
                    daInner[attr][c] = daOuter[attr][c] + span.attrStepX[attr][c];
                 }
              ATTRIB_LOOP_END
  #endif
  
              while (lines > 0) {
                 /* initialize the span interpolants to the leftmost value */
                 /* ff = fixed-pt fragment */
                 const GLint right = FixedToInt(fxRightEdge);
                 span.x = FixedToInt(fxLeftEdge);
                 if (right <= span.x)
                    span.end = 0;
                 else
                    span.end = right - span.x;
  
  #ifdef INTERP_Z
                 span.z = zLeft;
  #endif
  #ifdef INTERP_RGB
                 span.red = rLeft;
                 span.green = gLeft;
                 span.blue = bLeft;
  #endif
  #ifdef INTERP_ALPHA
                 span.alpha = aLeft;
  #endif
  #ifdef INTERP_INT_TEX
                 span.intTex[0] = sLeft;
                 span.intTex[1] = tLeft;
  #endif
  
  #ifdef INTERP_ATTRIBS
                 span.attrStart[FRAG_ATTRIB_WPOS][3] = wLeft;
                 ATTRIB_LOOP_BEGIN
                    GLuint c;
                    for (c = 0; c < 4; c++) {
                       span.attrStart[attr][c] = attrLeft[attr][c];
                    }
                 ATTRIB_LOOP_END
  #endif
  
                 /* This is where we actually generate fragments */
                 /* XXX the test for span.y > 0 _shouldn't_ be needed but
                  * it fixes a problem on 64-bit Opterons (bug 4842).
                  */
                 if (span.end > 0 && span.y >= 0) {
                    const GLint len = span.end - 1;
                    (void) len;
  #ifdef INTERP_RGB
                    CLAMP_INTERPOLANT(red, redStep, len);
                    CLAMP_INTERPOLANT(green, greenStep, len);
                    CLAMP_INTERPOLANT(blue, blueStep, len);
  #endif
  #ifdef INTERP_ALPHA
                    CLAMP_INTERPOLANT(alpha, alphaStep, len);
  #endif
                    {
                       RENDER_SPAN( span );
                    }
                 }
  
                 /*
                  * Advance to the next scan line.  Compute the
                  * new edge coordinates, and adjust the
                  * pixel-center x coordinate so that it stays
                  * on or inside the major edge.
                  */
                 span.y++;
                 lines--;
  
                 fxLeftEdge += fdxLeftEdge;
                 fxRightEdge += fdxRightEdge;
  
                 fError += fdError;
                 if (fError >= 0) {
                    fError -= FIXED_ONE;
  
  #ifdef PIXEL_ADDRESS
                    pRow = (PIXEL_TYPE *) ((GLubyte *) pRow + dPRowOuter);
  #endif
  #ifdef INTERP_Z
  #  ifdef DEPTH_TYPE
                    zRow = (DEPTH_TYPE *) ((GLubyte *) zRow + dZRowOuter);
  #  endif
                    zLeft += fdzOuter;
  #endif
  #ifdef INTERP_RGB
                    rLeft += fdrOuter;
                    gLeft += fdgOuter;
                    bLeft += fdbOuter;
  #endif
  #ifdef INTERP_ALPHA
                    aLeft += fdaOuter;
  #endif
  #ifdef INTERP_INT_TEX
                    sLeft += dsOuter;
                    tLeft += dtOuter;
  #endif
  #ifdef INTERP_ATTRIBS
                    wLeft += dwOuter;
                    ATTRIB_LOOP_BEGIN
                       GLuint c;
                       for (c = 0; c < 4; c++) {
                          attrLeft[attr][c] += daOuter[attr][c];
                       }
                    ATTRIB_LOOP_END
  #endif
                 }
                 else {
  #ifdef PIXEL_ADDRESS
                    pRow = (PIXEL_TYPE *) ((GLubyte *) pRow + dPRowInner);
  #endif
  #ifdef INTERP_Z
  #  ifdef DEPTH_TYPE
                    zRow = (DEPTH_TYPE *) ((GLubyte *) zRow + dZRowInner);
  #  endif
                    zLeft += fdzInner;
  #endif
  #ifdef INTERP_RGB
                    rLeft += fdrInner;
                    gLeft += fdgInner;
                    bLeft += fdbInner;
  #endif
  #ifdef INTERP_ALPHA
                    aLeft += fdaInner;
  #endif
  #ifdef INTERP_INT_TEX
                    sLeft += dsInner;
                    tLeft += dtInner;
  #endif
  #ifdef INTERP_ATTRIBS
                    wLeft += dwInner;
                    ATTRIB_LOOP_BEGIN
                       GLuint c;
                       for (c = 0; c < 4; c++) {
                          attrLeft[attr][c] += daInner[attr][c];
                       }
                    ATTRIB_LOOP_END
  #endif
                 }
              } /*while lines>0*/
  
           } /* for subTriangle */
  
        }
     }
  }
  
  #undef SETUP_CODE
  #undef RENDER_SPAN
  
  #undef PIXEL_TYPE
  #undef BYTES_PER_ROW
  #undef PIXEL_ADDRESS
  #undef DEPTH_TYPE
  
  #undef INTERP_Z
  #undef INTERP_RGB
  #undef INTERP_ALPHA
  #undef INTERP_INT_TEX
  #undef INTERP_ATTRIBS
  
  #undef S_SCALE
  #undef T_SCALE
  
  #undef FixedToDepth
  
  #undef NAME
  