The Tor Browser: gfx/cairo/libpixman/src/pixman-radial-gradient.c@6474c204b198 (annotated)

gfx/cairo/libpixman/src/pixman-radial-gradient.c@6474c204b198 (annotated)

gfx/cairo/libpixman/src/pixman-radial-gradient.c

Wed, 31 Dec 2014 06:09:35 +0100

author: Michael Schloh von Bennewitz <michael@schloh.com>
date: Wed, 31 Dec 2014 06:09:35 +0100
changeset 0: 6474c204b198
permissions: -rw-r--r--

Cloned upstream origin tor-browser at tor-browser-31.3.0esr-4.5-1-build1
revision ID fc1c9ff7c1b2defdbc039f12214767608f46423f for hacking purpose.

 /* -*- Mode: c; c-basic-offset: 4; tab-width: 8; indent-tabs-mode: t; -*- */
 /*
  *
  * Copyright © 2000 Keith Packard, member of The XFree86 Project, Inc.
  * Copyright © 2000 SuSE, Inc.
  *             2005 Lars Knoll & Zack Rusin, Trolltech
  * Copyright © 2007 Red Hat, Inc.
  *
  *
  * Permission to use, copy, modify, distribute, and sell this software and its
  * documentation for any purpose is hereby granted without fee, provided that
  * the above copyright notice appear in all copies and that both that
  * copyright notice and this permission notice appear in supporting
  * documentation, and that the name of Keith Packard not be used in
  * advertising or publicity pertaining to distribution of the software without
  * specific, written prior permission.  Keith Packard makes no
  * representations about the suitability of this software for any purpose.  It
  * is provided "as is" without express or implied warranty.
  *
  * THE COPYRIGHT HOLDERS DISCLAIM ALL WARRANTIES WITH REGARD TO THIS
  * SOFTWARE, INCLUDING ALL IMPLIED WARRANTIES OF MERCHANTABILITY AND
  * FITNESS, IN NO EVENT SHALL THE COPYRIGHT HOLDERS BE LIABLE FOR ANY
  * SPECIAL, INDIRECT OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES
  * WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN
  * AN ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING
  * OUT OF OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS
  * SOFTWARE.
  */
 #ifdef HAVE_CONFIG_H
 #include <config.h>
 #endif
 #include <stdlib.h>
 #include <math.h>
 #include "pixman-private.h"
 #include "pixman-dither.h"
 static inline pixman_fixed_32_32_t
 dot (pixman_fixed_48_16_t x1,
      pixman_fixed_48_16_t y1,
      pixman_fixed_48_16_t z1,
      pixman_fixed_48_16_t x2,
      pixman_fixed_48_16_t y2,
      pixman_fixed_48_16_t z2)
 {
     /*
      * Exact computation, assuming that the input values can
      * be represented as pixman_fixed_16_16_t
      */
     return x1 * x2 + y1 * y2 + z1 * z2;
 }
 static inline double
 fdot (double x1,
       double y1,
       double z1,
       double x2,
       double y2,
       double z2)
 {
     /*
      * Error can be unbound in some special cases.
      * Using clever dot product algorithms (for example compensated
      * dot product) would improve this but make the code much less
      * obvious
      */
     return x1 * x2 + y1 * y2 + z1 * z2;
 }
 static uint32_t
 radial_compute_color (double                    a,
 		      double                    b,
 		      double                    c,
 		      double                    inva,
 		      double                    dr,
 		      double                    mindr,
 		      pixman_gradient_walker_t *walker,
 		      pixman_repeat_t           repeat)
 {
     /*
      * In this function error propagation can lead to bad results:
      *  - discr can have an unbound error (if b*b-a*c is very small),
      *    potentially making it the opposite sign of what it should have been
      *    (thus clearing a pixel that would have been colored or vice-versa)
      *    or propagating the error to sqrtdiscr;
      *    if discr has the wrong sign or b is very small, this can lead to bad
      *    results
      *
      *  - the algorithm used to compute the solutions of the quadratic
      *    equation is not numerically stable (but saves one division compared
      *    to the numerically stable one);
      *    this can be a problem if a*c is much smaller than b*b
      *
      *  - the above problems are worse if a is small (as inva becomes bigger)
      */
     double discr;
     if (a == 0)
     {
 	double t;
 	if (b == 0)
 	    return 0;
 	t = pixman_fixed_1 / 2 * c / b;
 	if (repeat == PIXMAN_REPEAT_NONE)
 	{
 	    if (0 <= t && t <= pixman_fixed_1)
 		return _pixman_gradient_walker_pixel (walker, t);
 	}
 	else
 	{
 	    if (t * dr >= mindr)
 		return _pixman_gradient_walker_pixel (walker, t);
 	}
 	return 0;
     }
     discr = fdot (b, a, 0, b, -c, 0);
     if (discr >= 0)
     {
 	double sqrtdiscr, t0, t1;
 	sqrtdiscr = sqrt (discr);
 	t0 = (b + sqrtdiscr) * inva;
 	t1 = (b - sqrtdiscr) * inva;
 	/*
 	 * The root that must be used is the biggest one that belongs
 	 * to the valid range ([0,1] for PIXMAN_REPEAT_NONE, any
 	 * solution that results in a positive radius otherwise).
 	 *
 	 * If a > 0, t0 is the biggest solution, so if it is valid, it
 	 * is the correct result.
 	 *
 	 * If a < 0, only one of the solutions can be valid, so the
 	 * order in which they are tested is not important.
 	 */
 	if (repeat == PIXMAN_REPEAT_NONE)
 	{
 	    if (0 <= t0 && t0 <= pixman_fixed_1)
 		return _pixman_gradient_walker_pixel (walker, t0);
 	    else if (0 <= t1 && t1 <= pixman_fixed_1)
 		return _pixman_gradient_walker_pixel (walker, t1);
 	}
 	else
 	{
 	    if (t0 * dr >= mindr)
 		return _pixman_gradient_walker_pixel (walker, t0);
 	    else if (t1 * dr >= mindr)
 		return _pixman_gradient_walker_pixel (walker, t1);
 	}
     }
     return 0;
 }
 static uint32_t *
 radial_get_scanline_narrow (pixman_iter_t *iter, const uint32_t *mask)
 {
     /*
      * Implementation of radial gradients following the PDF specification.
      * See section 8.7.4.5.4 Type 3 (Radial) Shadings of the PDF Reference
      * Manual (PDF 32000-1:2008 at the time of this writing).
      *
      * In the radial gradient problem we are given two circles (c₁,r₁) and
      * (c₂,r₂) that define the gradient itself.
      *
      * Mathematically the gradient can be defined as the family of circles
      *
      *     ((1-t)·c₁ + t·(c₂), (1-t)·r₁ + t·r₂)
      *
      * excluding those circles whose radius would be < 0. When a point
      * belongs to more than one circle, the one with a bigger t is the only
      * one that contributes to its color. When a point does not belong
      * to any of the circles, it is transparent black, i.e. RGBA (0, 0, 0, 0).
      * Further limitations on the range of values for t are imposed when
      * the gradient is not repeated, namely t must belong to [0,1].
      *
      * The graphical result is the same as drawing the valid (radius > 0)
      * circles with increasing t in [-inf, +inf] (or in [0,1] if the gradient
      * is not repeated) using SOURCE operator composition.
      *
      * It looks like a cone pointing towards the viewer if the ending circle
      * is smaller than the starting one, a cone pointing inside the page if
      * the starting circle is the smaller one and like a cylinder if they
      * have the same radius.
      *
      * What we actually do is, given the point whose color we are interested
      * in, compute the t values for that point, solving for t in:
      *
      *     length((1-t)·c₁ + t·(c₂) - p) = (1-t)·r₁ + t·r₂
      *
      * Let's rewrite it in a simpler way, by defining some auxiliary
      * variables:
      *
      *     cd = c₂ - c₁
      *     pd = p - c₁
      *     dr = r₂ - r₁
      *     length(t·cd - pd) = r₁ + t·dr
      *
      * which actually means
      *
      *     hypot(t·cdx - pdx, t·cdy - pdy) = r₁ + t·dr
      *
      * or
      *
      *     ⎷((t·cdx - pdx)² + (t·cdy - pdy)²) = r₁ + t·dr.
      *
      * If we impose (as stated earlier) that r₁ + t·dr >= 0, it becomes:
      *
      *     (t·cdx - pdx)² + (t·cdy - pdy)² = (r₁ + t·dr)²
      *
      * where we can actually expand the squares and solve for t:
      *
      *     t²cdx² - 2t·cdx·pdx + pdx² + t²cdy² - 2t·cdy·pdy + pdy² =
      *       = r₁² + 2·r₁·t·dr + t²·dr²
      *
      *     (cdx² + cdy² - dr²)t² - 2(cdx·pdx + cdy·pdy + r₁·dr)t +
      *         (pdx² + pdy² - r₁²) = 0
      *
      *     A = cdx² + cdy² - dr²
      *     B = pdx·cdx + pdy·cdy + r₁·dr
      *     C = pdx² + pdy² - r₁²
      *     At² - 2Bt + C = 0
      *
      * The solutions (unless the equation degenerates because of A = 0) are:
      *
      *     t = (B ± ⎷(B² - A·C)) / A
      *
      * The solution we are going to prefer is the bigger one, unless the
      * radius associated to it is negative (or it falls outside the valid t
      * range).
      *
      * Additional observations (useful for optimizations):
      * A does not depend on p
      *
      * A < 0 <=> one of the two circles completely contains the other one
      *   <=> for every p, the radiuses associated with the two t solutions
      *       have opposite sign
      */
     pixman_image_t *image = iter->image;
     int x = iter->x;
     int y = iter->y;
     int width = iter->width;
     uint32_t *buffer = iter->buffer;
     gradient_t *gradient = (gradient_t *)image;
     radial_gradient_t *radial = (radial_gradient_t *)image;
     uint32_t *end = buffer + width;
     pixman_gradient_walker_t walker;
     pixman_vector_t v, unit;
     /* reference point is the center of the pixel */
     v.vector[0] = pixman_int_to_fixed (x) + pixman_fixed_1 / 2;
     v.vector[1] = pixman_int_to_fixed (y) + pixman_fixed_1 / 2;
     v.vector[2] = pixman_fixed_1;
     _pixman_gradient_walker_init (&walker, gradient, image->common.repeat);
     if (image->common.transform)
     {
 	if (!pixman_transform_point_3d (image->common.transform, &v))
 	    return iter->buffer;
 	unit.vector[0] = image->common.transform->matrix[0][0];
 	unit.vector[1] = image->common.transform->matrix[1][0];
 	unit.vector[2] = image->common.transform->matrix[2][0];
     }
     else
     {
 	unit.vector[0] = pixman_fixed_1;
 	unit.vector[1] = 0;
 	unit.vector[2] = 0;
     }
     if (unit.vector[2] == 0 && v.vector[2] == pixman_fixed_1)
     {
 	/*
 	 * Given:
 	 *
 	 * t = (B ± ⎷(B² - A·C)) / A
 	 *
 	 * where
 	 *
 	 * A = cdx² + cdy² - dr²
 	 * B = pdx·cdx + pdy·cdy + r₁·dr
 	 * C = pdx² + pdy² - r₁²
 	 * det = B² - A·C
 	 *
 	 * Since we have an affine transformation, we know that (pdx, pdy)
 	 * increase linearly with each pixel,
 	 *
 	 * pdx = pdx₀ + n·ux,
 	 * pdy = pdy₀ + n·uy,
 	 *
 	 * we can then express B, C and det through multiple differentiation.
 	 */
 	pixman_fixed_32_32_t b, db, c, dc, ddc;
 	/* warning: this computation may overflow */
 	v.vector[0] -= radial->c1.x;
 	v.vector[1] -= radial->c1.y;
 	/*
 	 * B and C are computed and updated exactly.
 	 * If fdot was used instead of dot, in the worst case it would
 	 * lose 11 bits of precision in each of the multiplication and
 	 * summing up would zero out all the bit that were preserved,
 	 * thus making the result 0 instead of the correct one.
 	 * This would mean a worst case of unbound relative error or
 	 * about 2^10 absolute error
 	 */
 	b = dot (v.vector[0], v.vector[1], radial->c1.radius,
 		 radial->delta.x, radial->delta.y, radial->delta.radius);
 	db = dot (unit.vector[0], unit.vector[1], 0,
 		  radial->delta.x, radial->delta.y, 0);
 	c = dot (v.vector[0], v.vector[1],
 		 -((pixman_fixed_48_16_t) radial->c1.radius),
 		 v.vector[0], v.vector[1], radial->c1.radius);
 	dc = dot (2 * (pixman_fixed_48_16_t) v.vector[0] + unit.vector[0],
 * (pixman_fixed_48_16_t) v.vector[1] + unit.vector[1],
 ,
 		  unit.vector[0], unit.vector[1], 0);
 	ddc = 2 * dot (unit.vector[0], unit.vector[1], 0,
 		       unit.vector[0], unit.vector[1], 0);
 	while (buffer < end)
 	{
 	    if (!mask || *mask++)
 	    {
 		*buffer = radial_compute_color (radial->a, b, c,
 						radial->inva,
 						radial->delta.radius,
 						radial->mindr,
 						&walker,
 						image->common.repeat);
 	    }
 	    b += db;
 	    c += dc;
 	    dc += ddc;
 	    ++buffer;
 	}
     }
     else
     {
 	/* projective */
 	/* Warning:
 	 * error propagation guarantees are much looser than in the affine case
 	 */
 	while (buffer < end)
 	{
 	    if (!mask || *mask++)
 	    {
 		if (v.vector[2] != 0)
 		{
 		    double pdx, pdy, invv2, b, c;
 		    invv2 = 1. * pixman_fixed_1 / v.vector[2];
 		    pdx = v.vector[0] * invv2 - radial->c1.x;
 		    /*    / pixman_fixed_1 */
 		    pdy = v.vector[1] * invv2 - radial->c1.y;
 		    /*    / pixman_fixed_1 */
 		    b = fdot (pdx, pdy, radial->c1.radius,
 			      radial->delta.x, radial->delta.y,
 			      radial->delta.radius);
 		    /*  / pixman_fixed_1 / pixman_fixed_1 */
 		    c = fdot (pdx, pdy, -radial->c1.radius,
 			      pdx, pdy, radial->c1.radius);
 		    /*  / pixman_fixed_1 / pixman_fixed_1 */
 		    *buffer = radial_compute_color (radial->a, b, c,
 						    radial->inva,
 						    radial->delta.radius,
 						    radial->mindr,
 						    &walker,
 						    image->common.repeat);
 		}
 		else
 		{
 		    *buffer = 0;
 		}
 	    }
 	    ++buffer;
 	    v.vector[0] += unit.vector[0];
 	    v.vector[1] += unit.vector[1];
 	    v.vector[2] += unit.vector[2];
 	}
     }
     iter->y++;
     return iter->buffer;
 }
 static uint32_t *
 radial_get_scanline_16 (pixman_iter_t *iter, const uint32_t *mask)
 {
     /*
      * Implementation of radial gradients following the PDF specification.
      * See section 8.7.4.5.4 Type 3 (Radial) Shadings of the PDF Reference
      * Manual (PDF 32000-1:2008 at the time of this writing).
      *
      * In the radial gradient problem we are given two circles (c₁,r₁) and
      * (c₂,r₂) that define the gradient itself.
      *
      * Mathematically the gradient can be defined as the family of circles
      *
      *     ((1-t)·c₁ + t·(c₂), (1-t)·r₁ + t·r₂)
      *
      * excluding those circles whose radius would be < 0. When a point
      * belongs to more than one circle, the one with a bigger t is the only
      * one that contributes to its color. When a point does not belong
      * to any of the circles, it is transparent black, i.e. RGBA (0, 0, 0, 0).
      * Further limitations on the range of values for t are imposed when
      * the gradient is not repeated, namely t must belong to [0,1].
      *
      * The graphical result is the same as drawing the valid (radius > 0)
      * circles with increasing t in [-inf, +inf] (or in [0,1] if the gradient
      * is not repeated) using SOURCE operator composition.
      *
      * It looks like a cone pointing towards the viewer if the ending circle
      * is smaller than the starting one, a cone pointing inside the page if
      * the starting circle is the smaller one and like a cylinder if they
      * have the same radius.
      *
      * What we actually do is, given the point whose color we are interested
      * in, compute the t values for that point, solving for t in:
      *
      *     length((1-t)·c₁ + t·(c₂) - p) = (1-t)·r₁ + t·r₂
      *
      * Let's rewrite it in a simpler way, by defining some auxiliary
      * variables:
      *
      *     cd = c₂ - c₁
      *     pd = p - c₁
      *     dr = r₂ - r₁
      *     length(t·cd - pd) = r₁ + t·dr
      *
      * which actually means
      *
      *     hypot(t·cdx - pdx, t·cdy - pdy) = r₁ + t·dr
      *
      * or
      *
      *     ⎷((t·cdx - pdx)² + (t·cdy - pdy)²) = r₁ + t·dr.
      *
      * If we impose (as stated earlier) that r₁ + t·dr >= 0, it becomes:
      *
      *     (t·cdx - pdx)² + (t·cdy - pdy)² = (r₁ + t·dr)²
      *
      * where we can actually expand the squares and solve for t:
      *
      *     t²cdx² - 2t·cdx·pdx + pdx² + t²cdy² - 2t·cdy·pdy + pdy² =
      *       = r₁² + 2·r₁·t·dr + t²·dr²
      *
      *     (cdx² + cdy² - dr²)t² - 2(cdx·pdx + cdy·pdy + r₁·dr)t +
      *         (pdx² + pdy² - r₁²) = 0
      *
      *     A = cdx² + cdy² - dr²
      *     B = pdx·cdx + pdy·cdy + r₁·dr
      *     C = pdx² + pdy² - r₁²
      *     At² - 2Bt + C = 0
      *
      * The solutions (unless the equation degenerates because of A = 0) are:
      *
      *     t = (B ± ⎷(B² - A·C)) / A
      *
      * The solution we are going to prefer is the bigger one, unless the
      * radius associated to it is negative (or it falls outside the valid t
      * range).
      *
      * Additional observations (useful for optimizations):
      * A does not depend on p
      *
      * A < 0 <=> one of the two circles completely contains the other one
      *   <=> for every p, the radiuses associated with the two t solutions
      *       have opposite sign
      */
     pixman_image_t *image = iter->image;
     int x = iter->x;
     int y = iter->y;
     int width = iter->width;
     uint16_t *buffer = iter->buffer;
     pixman_bool_t toggle = ((x ^ y) & 1);
     gradient_t *gradient = (gradient_t *)image;
     radial_gradient_t *radial = (radial_gradient_t *)image;
     uint16_t *end = buffer + width;
     pixman_gradient_walker_t walker;
     pixman_vector_t v, unit;
     /* reference point is the center of the pixel */
     v.vector[0] = pixman_int_to_fixed (x) + pixman_fixed_1 / 2;
     v.vector[1] = pixman_int_to_fixed (y) + pixman_fixed_1 / 2;
     v.vector[2] = pixman_fixed_1;
     _pixman_gradient_walker_init (&walker, gradient, image->common.repeat);
     if (image->common.transform)
     {
 	if (!pixman_transform_point_3d (image->common.transform, &v))
 	    return iter->buffer;
 	unit.vector[0] = image->common.transform->matrix[0][0];
 	unit.vector[1] = image->common.transform->matrix[1][0];
 	unit.vector[2] = image->common.transform->matrix[2][0];
     }
     else
     {
 	unit.vector[0] = pixman_fixed_1;
 	unit.vector[1] = 0;
 	unit.vector[2] = 0;
     }
     if (unit.vector[2] == 0 && v.vector[2] == pixman_fixed_1)
     {
 	/*
 	 * Given:
 	 *
 	 * t = (B ± ⎷(B² - A·C)) / A
 	 *
 	 * where
 	 *
 	 * A = cdx² + cdy² - dr²
 	 * B = pdx·cdx + pdy·cdy + r₁·dr
 	 * C = pdx² + pdy² - r₁²
 	 * det = B² - A·C
 	 *
 	 * Since we have an affine transformation, we know that (pdx, pdy)
 	 * increase linearly with each pixel,
 	 *
 	 * pdx = pdx₀ + n·ux,
 	 * pdy = pdy₀ + n·uy,
 	 *
 	 * we can then express B, C and det through multiple differentiation.
 	 */
 	pixman_fixed_32_32_t b, db, c, dc, ddc;
 	/* warning: this computation may overflow */
 	v.vector[0] -= radial->c1.x;
 	v.vector[1] -= radial->c1.y;
 	/*
 	 * B and C are computed and updated exactly.
 	 * If fdot was used instead of dot, in the worst case it would
 	 * lose 11 bits of precision in each of the multiplication and
 	 * summing up would zero out all the bit that were preserved,
 	 * thus making the result 0 instead of the correct one.
 	 * This would mean a worst case of unbound relative error or
 	 * about 2^10 absolute error
 	 */
 	b = dot (v.vector[0], v.vector[1], radial->c1.radius,
 		 radial->delta.x, radial->delta.y, radial->delta.radius);
 	db = dot (unit.vector[0], unit.vector[1], 0,
 		  radial->delta.x, radial->delta.y, 0);
 	c = dot (v.vector[0], v.vector[1],
 		 -((pixman_fixed_48_16_t) radial->c1.radius),
 		 v.vector[0], v.vector[1], radial->c1.radius);
 	dc = dot (2 * (pixman_fixed_48_16_t) v.vector[0] + unit.vector[0],
 * (pixman_fixed_48_16_t) v.vector[1] + unit.vector[1],
 ,
 		  unit.vector[0], unit.vector[1], 0);
 	ddc = 2 * dot (unit.vector[0], unit.vector[1], 0,
 		       unit.vector[0], unit.vector[1], 0);
 	while (buffer < end)
 	{
 	    if (!mask || *mask++)
 	    {
 		*buffer = dither_8888_to_0565(
 			  radial_compute_color (radial->a, b, c,
 						radial->inva,
 						radial->delta.radius,
 						radial->mindr,
 						&walker,
 						image->common.repeat),
 			  toggle);
 	    }
 	    toggle ^= 1;
 	    b += db;
 	    c += dc;
 	    dc += ddc;
 	    ++buffer;
 	}
     }
     else
     {
 	/* projective */
 	/* Warning:
 	 * error propagation guarantees are much looser than in the affine case
 	 */
 	while (buffer < end)
 	{
 	    if (!mask || *mask++)
 	    {
 		if (v.vector[2] != 0)
 		{
 		    double pdx, pdy, invv2, b, c;
 		    invv2 = 1. * pixman_fixed_1 / v.vector[2];
 		    pdx = v.vector[0] * invv2 - radial->c1.x;
 		    /*    / pixman_fixed_1 */
 		    pdy = v.vector[1] * invv2 - radial->c1.y;
 		    /*    / pixman_fixed_1 */
 		    b = fdot (pdx, pdy, radial->c1.radius,
 			      radial->delta.x, radial->delta.y,
 			      radial->delta.radius);
 		    /*  / pixman_fixed_1 / pixman_fixed_1 */
 		    c = fdot (pdx, pdy, -radial->c1.radius,
 			      pdx, pdy, radial->c1.radius);
 		    /*  / pixman_fixed_1 / pixman_fixed_1 */
 		    *buffer = dither_8888_to_0565 (
 			      radial_compute_color (radial->a, b, c,
 						    radial->inva,
 						    radial->delta.radius,
 						    radial->mindr,
 						    &walker,
 						    image->common.repeat),
 			      toggle);
 		}
 		else
 		{
 		    *buffer = 0;
 		}
 	    }
 	    ++buffer;
 	    toggle ^= 1;
 	    v.vector[0] += unit.vector[0];
 	    v.vector[1] += unit.vector[1];
 	    v.vector[2] += unit.vector[2];
 	}
     }
     iter->y++;
     return iter->buffer;
 }
 static uint32_t *
 radial_get_scanline_wide (pixman_iter_t *iter, const uint32_t *mask)
 {
     uint32_t *buffer = radial_get_scanline_narrow (iter, NULL);
     pixman_expand_to_float (
 	(argb_t *)buffer, buffer, PIXMAN_a8r8g8b8, iter->width);
     return buffer;
 }
 void
 _pixman_radial_gradient_iter_init (pixman_image_t *image, pixman_iter_t *iter)
 {
     if (iter->iter_flags & ITER_16)
 	iter->get_scanline = radial_get_scanline_16;
     else if (iter->iter_flags & ITER_NARROW)
 	iter->get_scanline = radial_get_scanline_narrow;
     else
 	iter->get_scanline = radial_get_scanline_wide;
 }
 PIXMAN_EXPORT pixman_image_t *
 pixman_image_create_radial_gradient (const pixman_point_fixed_t *  inner,
                                      const pixman_point_fixed_t *  outer,
                                      pixman_fixed_t                inner_radius,
                                      pixman_fixed_t                outer_radius,
                                      const pixman_gradient_stop_t *stops,
                                      int                           n_stops)
 {
     pixman_image_t *image;
     radial_gradient_t *radial;
     image = _pixman_image_allocate ();
     if (!image)
 	return NULL;
     radial = &image->radial;
     if (!_pixman_init_gradient (&radial->common, stops, n_stops))
     {
 	free (image);
 	return NULL;
     }
     image->type = RADIAL;
     radial->c1.x = inner->x;
     radial->c1.y = inner->y;
     radial->c1.radius = inner_radius;
     radial->c2.x = outer->x;
     radial->c2.y = outer->y;
     radial->c2.radius = outer_radius;
     /* warning: this computations may overflow */
     radial->delta.x = radial->c2.x - radial->c1.x;
     radial->delta.y = radial->c2.y - radial->c1.y;
     radial->delta.radius = radial->c2.radius - radial->c1.radius;
     /* computed exactly, then cast to double -> every bit of the double
        representation is correct (53 bits) */
     radial->a = dot (radial->delta.x, radial->delta.y, -radial->delta.radius,
 		     radial->delta.x, radial->delta.y, radial->delta.radius);
     if (radial->a != 0)
 	radial->inva = 1. * pixman_fixed_1 / radial->a;
     radial->mindr = -1. * pixman_fixed_1 * radial->c1.radius;
     return image;
 }

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gfx/cairo/libpixman/src/pixman-radial-gradient.c@6474c204b198 (annotated)

gfx/cairo/libpixman/src/pixman-radial-gradient.c