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 * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER.

 *

 * This code is free software; you can redistribute it and/or modify it

 * under the terms of the GNU General Public License version 2 only, as

 * published by the Free Software Foundation.  Oracle designates this

 * particular file as subject to the "Classpath" exception as provided

 * by Oracle in the LICENSE file that accompanied this code.

 *

 * This code is distributed in the hope that it will be useful, but WITHOUT

 * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or

 * FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public License

 * version 2 for more details (a copy is included in the LICENSE file that

 * accompanied this code).

 *

 * You should have received a copy of the GNU General Public License version

 * 2 along with this work; if not, write to the Free Software Foundation,

 * Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA.

 *

 * Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA

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package sun.java2d.marlin;

import java.util.Arrays;

import sun.awt.geom.PathConsumer2D;

import sun.java2d.marlin.stats.Histogram;

import sun.java2d.marlin.stats.StatLong;

final class Helpers implements MarlinConst {

    private Helpers() {

        throw new Error("This is a non instantiable class");

    }

    static boolean within(final float x, final float y, final float err) {

        final float d = y - x;

        return (d <= err && d >= -err);

    }

    static boolean within(final double x, final double y, final double err) {

        final double d = y - x;

        return (d <= err && d >= -err);

    }

    static float evalCubic(final float a, final float b,

                           final float c, final float d,

                           final float t)

    {

        return t * (t * (t * a + b) + c) + d;

    }

    static float evalQuad(final float a, final float b,

                          final float c, final float t)

    {

        return t * (t * a + b) + c;

    }

    static int quadraticRoots(final float a, final float b, final float c,

                              final float[] zeroes, final int off)

    {

        int ret = off;

        if (a != 0.0f) {

            final float dis = b*b - 4.0f * a * c;

            if (dis > 0.0f) {

                final float sqrtDis = (float) Math.sqrt(dis);

                // depending on the sign of b we use a slightly different

                // algorithm than the traditional one to find one of the roots

                // so we can avoid adding numbers of different signs (which

                // might result in loss of precision).

                if (b >= 0.0f) {

                    zeroes[ret++] = (2.0f * c) / (-b - sqrtDis);

                    zeroes[ret++] = (-b - sqrtDis) / (2.0f * a);

                } else {

                    zeroes[ret++] = (-b + sqrtDis) / (2.0f * a);

                    zeroes[ret++] = (2.0f * c) / (-b + sqrtDis);

                }

            } else if (dis == 0.0f) {

                zeroes[ret++] = -b / (2.0f * a);

            }

        } else if (b != 0.0f) {

            zeroes[ret++] = -c / b;

        }

        return ret - off;

    }

    // find the roots of g(t) = d*t^3 + a*t^2 + b*t + c in [A,B)

    static int cubicRootsInAB(final float d0, float a0, float b0, float c0,

                              final float[] pts, final int off,

                              final float A, final float B)

    {

        if (d0 == 0.0f) {

            final int num = quadraticRoots(a0, b0, c0, pts, off);

            return filterOutNotInAB(pts, off, num, A, B) - off;

        }

        // From Graphics Gems:

        // https://github.com/erich666/GraphicsGems/blob/master/gems/Roots3And4.c

        // (also from awt.geom.CubicCurve2D. But here we don't need as

        // much accuracy and we don't want to create arrays so we use

        // our own customized version).

        // normal form: x^3 + ax^2 + bx + c = 0

        // 2018.1: Need double precision if d is very small (flat curve) !

        /*

         * TODO: cleanup all that code after reading Roots3And4.c

         */

        final double a = ((double)a0) / d0;

        final double b = ((double)b0) / d0;

        final double c = ((double)c0) / d0;

        //  substitute x = y - A/3 to eliminate quadratic term:

        //     x^3 +Px + Q = 0

        //

        // Since we actually need P/3 and Q/2 for all of the

        // calculations that follow, we will calculate

        // p = P/3

        // q = Q/2

        // instead and use those values for simplicity of the code.

        final double sub = (1.0d / 3.0d) * a;

        final double sq_A = a * a;

        final double p = (1.0d / 3.0d) * ((-1.0d / 3.0d) * sq_A + b);

        final double q = (1.0d / 2.0d) * ((2.0d / 27.0d) * a * sq_A - sub * b + c);

        // use Cardano's formula

        final double cb_p = p * p * p;

        final double D = q * q + cb_p;

        int num;

        if (D < 0.0d) {

            // see: http://en.wikipedia.org/wiki/Cubic_function#Trigonometric_.28and_hyperbolic.29_method

            final double phi = (1.0d / 3.0d) * Math.acos(-q / Math.sqrt(-cb_p));

            final double t = 2.0d * Math.sqrt(-p);

            pts[off    ] = (float) ( t * Math.cos(phi) - sub);

            pts[off + 1] = (float) (-t * Math.cos(phi + (Math.PI / 3.0d)) - sub);

            pts[off + 2] = (float) (-t * Math.cos(phi - (Math.PI / 3.0d)) - sub);

            num = 3;

        } else {

            final double sqrt_D = Math.sqrt(D);

            final double u =   Math.cbrt(sqrt_D - q);

            final double v = - Math.cbrt(sqrt_D + q);

            pts[off    ] = (float) (u + v - sub);

            num = 1;

            if (within(D, 0.0d, 1e-8d)) {

                pts[off + 1] = (float)((-1.0d / 2.0d) * (u + v) - sub);

                num = 2;

            }

        }

        return filterOutNotInAB(pts, off, num, A, B) - off;

    }

    // returns the index 1 past the last valid element remaining after filtering

    static int filterOutNotInAB(final float[] nums, final int off, final int len,

                                final float a, final float b)

    {

        int ret = off;

        for (int i = off, end = off + len; i < end; i++) {

            if (nums[i] >= a && nums[i] < b) {

                nums[ret++] = nums[i];

            }

        }

        return ret;

    }

    static float fastLineLen(final float x0, final float y0,

                             final float x1, final float y1)

    {

        final float dx = x1 - x0;

        final float dy = y1 - y0;

        // use manhattan norm:

        return Math.abs(dx) + Math.abs(dy);

    }

    static float linelen(final float x0, final float y0,

                         final float x1, final float y1)

    {

        final float dx = x1 - x0;

        final float dy = y1 - y0;

        return (float) Math.sqrt(dx * dx + dy * dy);

    }

    static float fastQuadLen(final float x0, final float y0,

                             final float x1, final float y1,

                             final float x2, final float y2)

    {

        final float dx1 = x1 - x0;

        final float dx2 = x2 - x1;

        final float dy1 = y1 - y0;

        final float dy2 = y2 - y1;

        // use manhattan norm:

        return Math.abs(dx1) + Math.abs(dx2)

             + Math.abs(dy1) + Math.abs(dy2);

    }

    static float quadlen(final float x0, final float y0,

                         final float x1, final float y1,

                         final float x2, final float y2)

    {

        return (linelen(x0, y0, x1, y1)

                + linelen(x1, y1, x2, y2)

                + linelen(x0, y0, x2, y2)) / 2.0f;

    }

    static float fastCurvelen(final float x0, final float y0,

                              final float x1, final float y1,

                              final float x2, final float y2,

                              final float x3, final float y3)

    {

        final float dx1 = x1 - x0;

        final float dx2 = x2 - x1;

        final float dx3 = x3 - x2;

        final float dy1 = y1 - y0;

        final float dy2 = y2 - y1;

        final float dy3 = y3 - y2;

        // use manhattan norm:

        return Math.abs(dx1) + Math.abs(dx2) + Math.abs(dx3)

             + Math.abs(dy1) + Math.abs(dy2) + Math.abs(dy3);

    }

    static float curvelen(final float x0, final float y0,

                          final float x1, final float y1,

                          final float x2, final float y2,

                          final float x3, final float y3)

    {

        return (linelen(x0, y0, x1, y1)

              + linelen(x1, y1, x2, y2)

              + linelen(x2, y2, x3, y3)

              + linelen(x0, y0, x3, y3)) / 2.0f;

    }

    // finds values of t where the curve in pts should be subdivided in order

    // to get good offset curves a distance of w away from the middle curve.

    // Stores the points in ts, and returns how many of them there were.

    static int findSubdivPoints(final Curve c, final float[] pts,

                                final float[] ts, final int type,

                                final float w2)

    {

        final float x12 = pts[2] - pts[0];

        final float y12 = pts[3] - pts[1];

        // if the curve is already parallel to either axis we gain nothing

        // from rotating it.

            // we rotate it so that the first vector in the control polygon is

            // parallel to the x-axis. This will ensure that rotated quarter

            // circles won't be subdivided.

            final float hypot = (float)Math.sqrt(x12 * x12 + y12 * y12);

            final float cos = x12 / hypot;

            final float sin = y12 / hypot;

            final float x1 = cos * pts[0] + sin * pts[1];

            final float y1 = cos * pts[1] - sin * pts[0];

            final float x2 = cos * pts[2] + sin * pts[3];

            final float y2 = cos * pts[3] - sin * pts[2];

            final float x3 = cos * pts[4] + sin * pts[5];

            final float y3 = cos * pts[5] - sin * pts[4];

            switch(type) {

            case 8:

                final float x4 = cos * pts[6] + sin * pts[7];

                final float y4 = cos * pts[7] - sin * pts[6];

                c.set(x1, y1, x2, y2, x3, y3, x4, y4);

                break;

            case 6:

                c.set(x1, y1, x2, y2, x3, y3);

                break;

            default:

            }

        } else {

            c.set(pts, type);

        }

        int ret = 0;

        // we subdivide at values of t such that the remaining rotated

        // curves are monotonic in x and y.

        ret += c.dxRoots(ts, ret);

        ret += c.dyRoots(ts, ret);

        // subdivide at inflection points.

        if (type == 8) {

            // quadratic curves can't have inflection points

            ret += c.infPoints(ts, ret);

        }

        // now we must subdivide at points where one of the offset curves will have

        // a cusp. This happens at ts where the radius of curvature is equal to w.

        ret += c.rootsOfROCMinusW(ts, ret, w2, 0.0001f);

        ret = filterOutNotInAB(ts, 0, ret, 0.0001f, 0.9999f);

        isort(ts, ret);

        return ret;

    }

    // finds values of t where the curve in pts should be subdivided in order

    // to get intersections with the given clip rectangle.

    // Stores the points in ts, and returns how many of them there were.

    static int findClipPoints(final Curve curve, final float[] pts,

                              final float[] ts, final int type,

                              final int outCodeOR,

                              final float[] clipRect)

    {

        curve.set(pts, type);

        // clip rectangle (ymin, ymax, xmin, xmax)

        int ret = 0;

        if ((outCodeOR & OUTCODE_LEFT) != 0) {

            ret += curve.xPoints(ts, ret, clipRect[2]);

        }

        if ((outCodeOR & OUTCODE_RIGHT) != 0) {

            ret += curve.xPoints(ts, ret, clipRect[3]);

        }

        if ((outCodeOR & OUTCODE_TOP) != 0) {

            ret += curve.yPoints(ts, ret, clipRect[0]);

        }

        if ((outCodeOR & OUTCODE_BOTTOM) != 0) {

            ret += curve.yPoints(ts, ret, clipRect[1]);

        }

        isort(ts, ret);

        return ret;

    }

    static void subdivide(final float[] src,

                          final float[] left, final float[] right,

                          final int type)

    {

        switch(type) {

        case 8:

            subdivideCubic(src, left, right);

            return;

        case 6:

            subdivideQuad(src, left, right);

            return;

        default:

            throw new InternalError("Unsupported curve type");

        }

    }

    static void isort(final float[] a, final int len) {

        for (int i = 1, j; i < len; i++) {

            final float ai = a[i];

            j = i - 1;

            for (; j >= 0 && a[j] > ai; j--) {

                a[j + 1] = a[j];

            }

            a[j + 1] = ai;

        }

    }

    // Most of these are copied from classes in java.awt.geom because we need

    // both single and double precision variants of these functions, and Line2D,

    // CubicCurve2D, QuadCurve2D don't provide them.

    /**

     * Subdivides the cubic curve specified by the coordinates

     * stored in the <code>src</code> array at indices <code>srcoff</code>

     * through (<code>srcoff</code>&nbsp;+&nbsp;7) and stores the

     * resulting two subdivided curves into the two result arrays at the

     * corresponding indices.

     * Either or both of the <code>left</code> and <code>right</code>

     * arrays may be <code>null</code> or a reference to the same array

     * as the <code>src</code> array.

     * Note that the last point in the first subdivided curve is the

     * same as the first point in the second subdivided curve. Thus,

     * it is possible to pass the same array for <code>left</code>

     * and <code>right</code> and to use offsets, such as <code>rightoff</code>

     * equals (<code>leftoff</code> + 6), in order

     * to avoid allocating extra storage for this common point.

     * @param src the array holding the coordinates for the source curve

     * @param left the array for storing the coordinates for the first

     * half of the subdivided curve

     * @param right the array for storing the coordinates for the second

     * half of the subdivided curve

     * @since 1.7

     */

    static void subdivideCubic(final float[] src,

                               final float[] left,

                               final float[] right)

    {

        float  x1 = src[0];

        float  y1 = src[1];

        float cx1 = src[2];

        float cy1 = src[3];

        float cx2 = src[4];

        float cy2 = src[5];

        float  x2 = src[6];

        float  y2 = src[7];

        left[0]  = x1;

        left[1]  = y1;

        right[6] = x2;

        right[7] = y2;

        x1 = (x1 + cx1) / 2.0f;

        y1 = (y1 + cy1) / 2.0f;

        x2 = (x2 + cx2) / 2.0f;

        y2 = (y2 + cy2) / 2.0f;

        float cx = (cx1 + cx2) / 2.0f;

        float cy = (cy1 + cy2) / 2.0f;

        cx1 = (x1 + cx) / 2.0f;

        cy1 = (y1 + cy) / 2.0f;

        cx2 = (x2 + cx) / 2.0f;

        cy2 = (y2 + cy) / 2.0f;

        cx  = (cx1 + cx2) / 2.0f;

        cy  = (cy1 + cy2) / 2.0f;

        left[2] = x1;

        left[3] = y1;

        left[4] = cx1;

        left[5] = cy1;

        left[6] = cx;

        left[7] = cy;

        right[0] = cx;

        right[1] = cy;

        right[2] = cx2;

        right[3] = cy2;

        right[4] = x2;

        right[5] = y2;

    }

    static void subdivideCubicAt(final float t,

                                 final float[] src, final int offS,

                                 final float[] pts, final int offL, final int offR)

    {

        float  x1 = src[offS    ];

        float  y1 = src[offS + 1];

        float cx1 = src[offS + 2];

        float cy1 = src[offS + 3];

        float cx2 = src[offS + 4];

        float cy2 = src[offS + 5];

        float  x2 = src[offS + 6];

        float  y2 = src[offS + 7];

        pts[offL    ] = x1;

        pts[offL + 1] = y1;

        pts[offR + 6] = x2;

        pts[offR + 7] = y2;

        x1 =  x1 + t * (cx1 - x1);

        y1 =  y1 + t * (cy1 - y1);

        x2 = cx2 + t * (x2 - cx2);

        y2 = cy2 + t * (y2 - cy2);

        float cx = cx1 + t * (cx2 - cx1);

        float cy = cy1 + t * (cy2 - cy1);

        cx1 =  x1 + t * (cx - x1);

        cy1 =  y1 + t * (cy - y1);

        cx2 =  cx + t * (x2 - cx);

        cy2 =  cy + t * (y2 - cy);

        cx  = cx1 + t * (cx2 - cx1);

        cy  = cy1 + t * (cy2 - cy1);

        pts[offL + 2] = x1;

        pts[offL + 3] = y1;

        pts[offL + 4] = cx1;

        pts[offL + 5] = cy1;

        pts[offL + 6] = cx;

        pts[offL + 7] = cy;

        pts[offR    ] = cx;

        pts[offR + 1] = cy;

        pts[offR + 2] = cx2;

        pts[offR + 3] = cy2;

        pts[offR + 4] = x2;

        pts[offR + 5] = y2;

    }

    static void subdivideQuad(final float[] src,

                              final float[] left,

                              final float[] right)

    {

        float x1 = src[0];

        float y1 = src[1];

        float cx = src[2];

        float cy = src[3];

        float x2 = src[4];

        float y2 = src[5];

        left[0]  = x1;

        left[1]  = y1;

        right[4] = x2;

        right[5] = y2;

        x1 = (x1 + cx) / 2.0f;

        y1 = (y1 + cy) / 2.0f;