void scale_rect(double factor_x, double factor_y, int blend, int interpolate, int Bpp,
    char *src_fb, int src_bytes_per_line, char *dst_fb, int dst_bytes_per_line,
    int Nx, int Ny, int nx, int ny, int X1, int Y1, int X2, int Y2, int mark) {
/*
 * Notation:
 * "i" an x pixel index in the destination (scaled) framebuffer
 * "j" a  y pixel index in the destination (scaled) framebuffer
 * "I" an x pixel index in the source (un-scaled, i.e. main) framebuffer
 * "J" a  y pixel index in the source (un-scaled, i.e. main) framebuffer
 *
 *  Similarly for nx, ny, Nx, Ny, etc.  Lowercase: dest, Uppercase: source.
 */
	int i, j, i1, i2, j1, j2;	/* indices for scaled fb (dest) */
	int I, J, I1, I2, J1, J2;	/* indices for main fb   (source) */

	double w, wx, wy, wtot;	/* pixel weights */

	double x1, y1, x2, y2;	/* x-y coords for destination pixels edges */
	double dx, dy;		/* size of destination pixel */
	double ddx=0, ddy=0;	/* for interpolation expansion */

	char *src, *dest;	/* pointers to the two framebuffers */


	unsigned short us = 0;
	unsigned char  uc = 0;
	unsigned int   ui = 0;

	int use_noblend_shortcut = 1;
	int shrink;		/* whether shrinking or expanding */
	static int constant_weights = -1, mag_int = -1;
	static int last_Nx = -1, last_Ny = -1, cnt = 0;
	static double last_factor = -1.0;
	int b, k;
	double pixave[4];	/* for averaging pixel values */

	if (factor_x <= 1.0 && factor_y <= 1.0) {
		shrink = 1;
	} else {
		shrink = 0;
	}

	/*
	 * N.B. width and height (real numbers) of a scaled pixel.
	 * both are > 1   (e.g. 1.333 for -scale 3/4)
	 * they should also be equal but we don't assume it.
	 *
	 * This new way is probably the best we can do, take the inverse
	 * of the scaling factor to double precision.
	 */
	dx = 1.0/factor_x;
	dy = 1.0/factor_y;

	/*
	 * There is some speedup if the pixel weights are constant, so
	 * let's special case these.
	 *
	 * If scale = 1/n and n divides Nx and Ny, the pixel weights
	 * are constant (e.g. 1/2 => equal on 2x2 square).
	 */
	if (factor_x != last_factor || Nx != last_Nx || Ny != last_Ny) {
		constant_weights = -1;
		mag_int = -1;
		last_Nx = Nx;
		last_Ny = Ny;
		last_factor = factor_x;
	}
	if (constant_weights < 0 && factor_x != factor_y) {
		constant_weights = 0;
		mag_int = 0;

	} else if (constant_weights < 0) {
		int n = 0;

		constant_weights = 0;
		mag_int = 0;

		for (i = 2; i<=128; i++) {
			double test = ((double) 1)/ i;
			double diff, eps = 1.0e-7;
			diff = factor_x - test;
			if (-eps < diff && diff < eps) {
				n = i;
				break;
			}
		}
		if (! blend || ! shrink || interpolate) {
			;
		} else if (n != 0) {
			if (Nx % n == 0 && Ny % n == 0) {
				static int didmsg = 0;
				if (mark && ! didmsg) {
					didmsg = 1;
					rfbLog("scale_and_mark_rect: using "
					    "constant pixel weight speedup "
					    "for 1/%d\n", n);
				}
				constant_weights = 1;
			}
		}

		n = 0;
		for (i = 2; i<=32; i++) {
			double test = (double) i;
			double diff, eps = 1.0e-7;
			diff = factor_x - test;
			if (-eps < diff && diff < eps) {
				n = i;
				break;
			}
		}
		if (! blend && factor_x > 1.0 && n) {
			mag_int = n;
		}
	}

	if (mark && factor_x > 1.0 && blend) {
		/*
		 * kludge: correct for interpolating blurring leaking
		 * up or left 1 destination pixel.
		 */
		if (X1 > 0) X1--;
		if (Y1 > 0) Y1--;
	}

	/*
	 * find the extent of the change the input rectangle induces in
	 * the scaled framebuffer.
	 */

	/* Left edges: find largest i such that i * dx <= X1  */
	i1 = FLOOR(X1/dx);

	/* Right edges: find smallest i such that (i+1) * dx >= X2+1  */
	i2 = CEIL( (X2+1)/dx ) - 1;

	/* To be safe, correct any overflows: */
	i1 = nfix(i1, nx);
	i2 = nfix(i2, nx) + 1;	/* add 1 to make a rectangle upper boundary */

	/* Repeat above for y direction: */
	j1 = FLOOR(Y1/dy);
	j2 = CEIL( (Y2+1)/dy ) - 1;

	j1 = nfix(j1, ny);
	j2 = nfix(j2, ny) + 1;

	/*
	 * special case integer magnification with no blending.
	 * vision impaired magnification usage is interested in this case.
	 */
	if (mark && ! blend && mag_int && Bpp != 3) {
		int jmin, jmax, imin, imax;

		/* outer loop over *source* pixels */
		for (J=Y1; J < Y2; J++) {
		    jmin = J * mag_int;
		    jmax = jmin + mag_int;
		    for (I=X1; I < X2; I++) {
			/* extract value */
			src = src_fb + J*src_bytes_per_line + I*Bpp;
			if (Bpp == 4) {
				ui = *((unsigned int *)src);
			} else if (Bpp == 2) {
				us = *((unsigned short *)src);
			} else if (Bpp == 1) {
				uc = *((unsigned char *)src);
			}
			imin = I * mag_int;
			imax = imin + mag_int;
			/* inner loop over *dest* pixels */
			for (j=jmin; j<jmax; j++) {
			    dest = dst_fb + j*dst_bytes_per_line + imin*Bpp;
			    for (i=imin; i<imax; i++) {
				if (Bpp == 4) {
					*((unsigned int *)dest) = ui;
				} else if (Bpp == 2) {
					*((unsigned short *)dest) = us;
				} else if (Bpp == 1) {
					*((unsigned char *)dest) = uc;
				}
				dest += Bpp;
			    }
			}
		    }
		}
		goto markit;
	}

	/* set these all to 1.0 to begin with */
	wx = 1.0;
	wy = 1.0;
	w  = 1.0;

	/*
	 * Loop over destination pixels in scaled fb:
	 */
	for (j=j1; j<j2; j++) {
		y1 =  j * dy;	/* top edge */
		if (y1 > Ny - 1) {
			/* can go over with dy = 1/scale_fac */
			y1 = Ny - 1;
		}
		y2 = y1 + dy;	/* bottom edge */

		/* Find main fb indices covered by this dest pixel: */
		J1 = (int) FLOOR(y1);
		J1 = nfix(J1, Ny);

		if (shrink && ! interpolate) {
			J2 = (int) CEIL(y2) - 1;
			J2 = nfix(J2, Ny);
		} else {
			J2 = J1 + 1;	/* simple interpolation */
			ddy = y1 - J1;
		}

		/* destination char* pointer: */
		dest = dst_fb + j*dst_bytes_per_line + i1*Bpp;
		
		for (i=i1; i<i2; i++) {

			x1 =  i * dx;	/* left edge */
			if (x1 > Nx - 1) {
				/* can go over with dx = 1/scale_fac */
				x1 = Nx - 1;
			}
			x2 = x1 + dx;	/* right edge */

			cnt++;

			/* Find main fb indices covered by this dest pixel: */
			I1 = (int) FLOOR(x1);
			if (I1 >= Nx) I1 = Nx - 1;

			if (! blend && use_noblend_shortcut) {
				/*
				 * The noblend case involves no weights,
				 * and 1 pixel, so just copy the value
				 * directly.
				 */
				src = src_fb + J1*src_bytes_per_line + I1*Bpp;
				if (Bpp == 4) {
					*((unsigned int *)dest)
					    = *((unsigned int *)src);
				} else if (Bpp == 2) {
					*((unsigned short *)dest)
					    = *((unsigned short *)src);
				} else if (Bpp == 1) {
					*(dest) = *(src);
				} else if (Bpp == 3) {
					/* rare case */
					for (k=0; k<=2; k++) {
						*(dest+k) = *(src+k);
					}
				}
				dest += Bpp;
				continue;
			}
			
			if (shrink && ! interpolate) {
				I2 = (int) CEIL(x2) - 1;
				if (I2 >= Nx) I2 = Nx - 1;
			} else {
				I2 = I1 + 1;	/* simple interpolation */
				ddx = x1 - I1;
			}

			/* Zero out accumulators for next pixel average: */
			for (b=0; b<4; b++) {
				pixave[b] = 0.0; /* for RGB weighted sums */
			}

			/*
			 * wtot is for accumulating the total weight.
			 * It should always sum to 1/(scale_fac * scale_fac).
			 */
			wtot = 0.0;

			/*
			 * Loop over source pixels covered by this dest pixel.
			 * 
			 * These "extra" loops over "J" and "I" make
			 * the cache/cacheline performance unclear.
			 * For example, will the data brought in from
			 * src for j, i, and J=0 still be in the cache
			 * after the J > 0 data have been accessed and
			 * we are at j, i+1, J=0?  The stride in J is
			 * main_bytes_per_line, and so ~4 KB.
			 *
			 * Typical case when shrinking are 2x2 loop, so
			 * just two lines to worry about.
			 */
			for (J=J1; J<=J2; J++) {
			    /* see comments for I, x1, x2, etc. below */
			    if (constant_weights) {
				;
			    } else if (! blend) {
				if (J != J1) {
					continue;
				}
				wy = 1.0;

				/* interpolation scheme: */
			    } else if (! shrink || interpolate) {
				if (J >= Ny) {
					continue;
				} else if (J == J1) {
					wy = 1.0 - ddy;
				} else if (J != J1) {
					wy = ddy;
				}

				/* integration scheme: */
			    } else if (J < y1) {
				wy = J+1 - y1;
			    } else if (J+1 > y2) {
				wy = y2 - J;
			    } else {
				wy = 1.0;
			    }

			    src = src_fb + J*src_bytes_per_line + I1*Bpp;

			    for (I=I1; I<=I2; I++) {

				/* Work out the weight: */

				if (constant_weights) {
					;
				} else if (! blend) {
					/*
					 * Ugh, PseudoColor colormap is
					 * bad news, to avoid random
					 * colors just take the first
					 * pixel.  Or user may have
					 * specified :nb to fraction.
					 * The :fb will force blending
					 * for this case.
					 */
					if (I != I1) {
						continue;
					}
					wx = 1.0;

					/* interpolation scheme: */
				} else if (! shrink || interpolate) {
					if (I >= Nx) {
						continue;	/* off edge */
					} else if (I == I1) {
						wx = 1.0 - ddx;
					} else if (I != I1) {
						wx = ddx;
					}

					/* integration scheme: */
				} else if (I < x1) {
					/* 
					 * source left edge (I) to the
					 * left of dest left edge (x1):
					 * fractional weight
					 */
					wx = I+1 - x1;
				} else if (I+1 > x2) {
					/* 
					 * source right edge (I+1) to the
					 * right of dest right edge (x2):
					 * fractional weight
					 */
					wx = x2 - I;
				} else {
					/* 
					 * source edges (I and I+1) completely
					 * inside dest edges (x1 and x2):
					 * full weight
					 */
					wx = 1.0;
				}

				w = wx * wy;
				wtot += w;

				/* 
				 * We average the unsigned char value
				 * instead of char value: otherwise
				 * the minimum (char 0) is right next
				 * to the maximum (char -1)!  This way
				 * they are spread between 0 and 255.
				 */
				if (Bpp == 4) {
					/* unroll the loops, can give 20% */
					pixave[0] += w * ((unsigned char) *(src  ));
					pixave[1] += w * ((unsigned char) *(src+1));
					pixave[2] += w * ((unsigned char) *(src+2));
					pixave[3] += w * ((unsigned char) *(src+3));
				} else if (Bpp == 2) {
					/*
					 * 16bpp: trickier with green
					 * split over two bytes, so we
					 * use the masks:
					 */
					us = *((unsigned short *) src);
					pixave[0] += w*(us & main_red_mask);
					pixave[1] += w*(us & main_green_mask);
					pixave[2] += w*(us & main_blue_mask);
				} else if (Bpp == 1) {
					pixave[0] += w *
					    ((unsigned char) *(src));
				} else {
					for (b=0; b<Bpp; b++) {
						pixave[b] += w *
						    ((unsigned char) *(src+b));
					}
				}
				src += Bpp;
			    }
			}

			if (wtot <= 0.0) {
				wtot = 1.0;
			}
			wtot = 1.0/wtot;	/* normalization factor */

			/* place weighted average pixel in the scaled fb: */
			if (Bpp == 4) {
				*(dest  ) = (char) (wtot * pixave[0]);
				*(dest+1) = (char) (wtot * pixave[1]);
				*(dest+2) = (char) (wtot * pixave[2]);
				*(dest+3) = (char) (wtot * pixave[3]);
			} else if (Bpp == 2) {
				/* 16bpp / 565 case: */
				pixave[0] *= wtot;
				pixave[1] *= wtot;
				pixave[2] *= wtot;
				us =  (main_red_mask   & (int) pixave[0])
				    | (main_green_mask & (int) pixave[1])
				    | (main_blue_mask  & (int) pixave[2]);
				*( (unsigned short *) dest ) = us;
			} else if (Bpp == 1) {
				*(dest) = (char) (wtot * pixave[0]);
			} else {
				for (b=0; b<Bpp; b++) {
					*(dest+b) = (char) (wtot * pixave[b]);
				}
			}
			dest += Bpp;
		}
	}
	markit:
	if (mark) {
		mark_rect_as_modified(i1, j1, i2, j2, 1);
	}
}
void scale_rect(double factor_x, double factor_y, int blend, int interpolate, int Bpp,
    char *src_fb, int src_bytes_per_line, char *dst_fb, int dst_bytes_per_line,
    int Nx, int Ny, int nx, int ny, int X1, int Y1, int X2, int Y2, int mark) {
 
	int i, j, i1, i2, j1, j2;	 
	int I, J, I1, I2, J1, J2;	 

	double w, wx, wy, wtot;	 

	double x1, y1, x2, y2;	 
	double dx, dy;		 
	double ddx=0, ddy=0;	 

	char *src, *dest;	 


	unsigned short us = 0;
	unsigned char  uc = 0;
	unsigned int   ui = 0;

	int use_noblend_shortcut = 1;
	int shrink;		 
	static int constant_weights = -1, mag_int = -1;
	static int last_Nx = -1, last_Ny = -1, cnt = 0;
	static double last_factor = -1.0;
	int b, k;
	double pixave[4];	 

	if (factor_x <= 1.0 && factor_y <= 1.0) {
		shrink = 1;
	} else {
		shrink = 0;
	}

	 
	dx = 1.0/factor_x;
	dy = 1.0/factor_y;

	 
	if (factor_x != last_factor || Nx != last_Nx || Ny != last_Ny) {
		constant_weights = -1;
		mag_int = -1;
		last_Nx = Nx;
		last_Ny = Ny;
		last_factor = factor_x;
	}
	if (constant_weights < 0 && factor_x != factor_y) {
		constant_weights = 0;
		mag_int = 0;

	} else if (constant_weights < 0) {
		int n = 0;

		constant_weights = 0;
		mag_int = 0;

		for (i = 2; i<=128; i++) {
			double test = ((double) 1)/ i;
			double diff, eps = 1.0e-7;
			diff = factor_x - test;
			if (-eps < diff && diff < eps) {
				n = i;
				break;
			}
		}
		if (! blend || ! shrink || interpolate) {
			;
		} else if (n != 0) {
			if (Nx % n == 0 && Ny % n == 0) {
				static int didmsg = 0;
				if (mark && ! didmsg) {
					didmsg = 1;
					rfbLog("scale_and_mark_rect: using "
					    "constant pixel weight speedup "
					    "for 1/%d\n", n);
				}
				constant_weights = 1;
			}
		}

		n = 0;
		for (i = 2; i<=32; i++) {
			double test = (double) i;
			double diff, eps = 1.0e-7;
			diff = factor_x - test;
			if (-eps < diff && diff < eps) {
				n = i;
				break;
			}
		}
		if (! blend && factor_x > 1.0 && n) {
			mag_int = n;
		}
	}

	if (mark && factor_x > 1.0 && blend) {
		 
		if (X1 > 0) X1--;
		if (Y1 > 0) Y1--;
	}

	 

	 
	i1 = FLOOR(X1/dx);

	 
	i2 = CEIL( (X2+1)/dx ) - 1;

	 
	i1 = nfix(i1, nx);
	i2 = nfix(i2, nx) + 1;	 

	 
	j1 = FLOOR(Y1/dy);
	j2 = CEIL( (Y2+1)/dy ) - 1;

	j1 = nfix(j1, ny);
	j2 = nfix(j2, ny) + 1;

	 
	if (mark && ! blend && mag_int && Bpp != 3) {
		int jmin, jmax, imin, imax;

		 
		for (J=Y1; J < Y2; J++) {
		    jmin = J * mag_int;
		    jmax = jmin + mag_int;
		    for (I=X1; I < X2; I++) {
			 
			src = src_fb + J*src_bytes_per_line + I*Bpp;
			if (Bpp == 4) {
				ui = *((unsigned int *)src);
			} else if (Bpp == 2) {
				us = *((unsigned short *)src);
			} else if (Bpp == 1) {
				uc = *((unsigned char *)src);
			}
			imin = I * mag_int;
			imax = imin + mag_int;
			 
			for (j=jmin; j<jmax; j++) {
			    dest = dst_fb + j*dst_bytes_per_line + imin*Bpp;
			    for (i=imin; i<imax; i++) {
				if (Bpp == 4) {
					*((unsigned int *)dest) = ui;
				} else if (Bpp == 2) {
					*((unsigned short *)dest) = us;
				} else if (Bpp == 1) {
					*((unsigned char *)dest) = uc;
				}
				dest += Bpp;
			    }
			}
		    }
		}
		goto markit;
	}

	 
	wx = 1.0;
	wy = 1.0;
	w  = 1.0;

	 
	for (j=j1; j<j2; j++) {
		y1 =  j * dy;	 
		if (y1 > Ny - 1) {
			 
			y1 = Ny - 1;
		}
		y2 = y1 + dy;	 

		 
		J1 = (int) FLOOR(y1);
		J1 = nfix(J1, Ny);

		if (shrink && ! interpolate) {
			J2 = (int) CEIL(y2) - 1;
			J2 = nfix(J2, Ny);
		} else {
			J2 = J1 + 1;	 
			ddy = y1 - J1;
		}

		 
		dest = dst_fb + j*dst_bytes_per_line + i1*Bpp;
		
		for (i=i1; i<i2; i++) {

			x1 =  i * dx;	 
			if (x1 > Nx - 1) {
				 
				x1 = Nx - 1;
			}
			x2 = x1 + dx;	 

			cnt++;

			 
			I1 = (int) FLOOR(x1);
			if (I1 >= Nx) I1 = Nx - 1;

			if (! blend && use_noblend_shortcut) {
				 
				src = src_fb + J1*src_bytes_per_line + I1*Bpp;
				if (Bpp == 4) {
					*((unsigned int *)dest)
					    = *((unsigned int *)src);
				} else if (Bpp == 2) {
					*((unsigned short *)dest)
					    = *((unsigned short *)src);
				} else if (Bpp == 1) {
					*(dest) = *(src);
				} else if (Bpp == 3) {
					 
					for (k=0; k<=2; k++) {
						*(dest+k) = *(src+k);
					}
				}
				dest += Bpp;
				continue;
			}
			
			if (shrink && ! interpolate) {
				I2 = (int) CEIL(x2) - 1;
				if (I2 >= Nx) I2 = Nx - 1;
			} else {
				I2 = I1 + 1;	 
				ddx = x1 - I1;
			}

			 
			for (b=0; b<4; b++) {
				pixave[b] = 0.0;  
			}

			 
			wtot = 0.0;

			 
			for (J=J1; J<=J2; J++) {
			     
			    if (constant_weights) {
				;
			    } else if (! blend) {
				if (J != J1) {
					continue;
				}
				wy = 1.0;

				 
			    } else if (! shrink || interpolate) {
				if (J >= Ny) {
					continue;
				} else if (J == J1) {
					wy = 1.0 - ddy;
				} else if (J != J1) {
					wy = ddy;
				}

				 
			    } else if (J < y1) {
				wy = J+1 - y1;
			    } else if (J+1 > y2) {
				wy = y2 - J;
			    } else {
				wy = 1.0;
			    }

			    src = src_fb + J*src_bytes_per_line + I1*Bpp;

			    for (I=I1; I<=I2; I++) {

				 

				if (constant_weights) {
					;
				} else if (! blend) {
					 
					if (I != I1) {
						continue;
					}
					wx = 1.0;

					 
				} else if (! shrink || interpolate) {
					if (I >= Nx) {
						continue;	 
					} else if (I == I1) {
						wx = 1.0 - ddx;
					} else if (I != I1) {
						wx = ddx;
					}

					 
				} else if (I < x1) {
					 
					wx = I+1 - x1;
				} else if (I+1 > x2) {
					 
					wx = x2 - I;
				} else {
					 
					wx = 1.0;
				}

				w = wx * wy;
				wtot += w;

				 
				if (Bpp == 4) {
					 
					pixave[0] += w * ((unsigned char) *(src  ));
					pixave[1] += w * ((unsigned char) *(src+1));
					pixave[2] += w * ((unsigned char) *(src+2));
					pixave[3] += w * ((unsigned char) *(src+3));
				} else if (Bpp == 2) {
					 
					us = *((unsigned short *) src);
					pixave[0] += w*(us & main_red_mask);
					pixave[1] += w*(us & main_green_mask);
					pixave[2] += w*(us & main_blue_mask);
				} else if (Bpp == 1) {
					pixave[0] += w *
					    ((unsigned char) *(src));
				} else {
					for (b=0; b<Bpp; b++) {
						pixave[b] += w *
						    ((unsigned char) *(src+b));
					}
				}
				src += Bpp;
			    }
			}

			if (wtot <= 0.0) {
				wtot = 1.0;
			}
			wtot = 1.0/wtot;	 

			 
			if (Bpp == 4) {
				*(dest  ) = (char) (wtot * pixave[0]);
				*(dest+1) = (char) (wtot * pixave[1]);
				*(dest+2) = (char) (wtot * pixave[2]);
				*(dest+3) = (char) (wtot * pixave[3]);
			} else if (Bpp == 2) {
				 
				pixave[0] *= wtot;
				pixave[1] *= wtot;
				pixave[2] *= wtot;
				us =  (main_red_mask   & (int) pixave[0])
				    | (main_green_mask & (int) pixave[1])
				    | (main_blue_mask  & (int) pixave[2]);
				*( (unsigned short *) dest ) = us;
			} else if (Bpp == 1) {
				*(dest) = (char) (wtot * pixave[0]);
			} else {
				for (b=0; b<Bpp; b++) {
					*(dest+b) = (char) (wtot * pixave[b]);
				}
			}
			dest += Bpp;
		}
	}
	markit:
	if (mark) {
		mark_rect_as_modified(i1, j1, i2, j2, 1);
	}
}