/* Copyright (C) 2001-2025 Artifex Software, Inc.

   All Rights Reserved.

   This software is provided AS-IS with no warranty, either express or

   implied.

   This software is distributed under license and may not be copied,

   modified or distributed except as expressly authorized under the terms

   of the license contained in the file LICENSE in this distribution.

   Refer to licensing information at http://www.artifex.com or contact

   Artifex Software, Inc.,  39 Mesa Street, Suite 108A, San Francisco,

   CA 94129, USA, for further information.

*/

/* Screen (Type 1) halftone processing for Ghostscript library */

#include "math_.h"

#include "gx.h"

#include "gserrors.h"

#include "gsstruct.h"

#include "gxarith.h"

#include "gzstate.h"

#include "gxdevice.h"           /* for gzht.h */

#include "gzht.h"

/* Define whether to force all halftones to be strip halftones, */

/* for debugging. */

static const bool FORCE_STRIP_HALFTONES = false;

/* Structure descriptors */

private_st_gs_screen_enum();

/* GC procedures */

static

ENUM_PTRS_WITH(screen_enum_enum_ptrs, gs_screen_enum *eptr)

{

    if (index < 1 + st_ht_order_max_ptrs) {

        gs_ptr_type_t ret =

            ENUM_USING(st_ht_order, &eptr->order, sizeof(eptr->order),

                       index - 1);

        if (ret == 0)           /* don't stop early */

            ENUM_RETURN(0);

        return ret;

    }

    return ENUM_USING(st_halftone, &eptr->halftone, sizeof(eptr->halftone),

                      index - (1 + st_ht_order_max_ptrs));

}

ENUM_PTR(0, gs_screen_enum, pgs);

ENUM_PTRS_END

static RELOC_PTRS_WITH(screen_enum_reloc_ptrs, gs_screen_enum *eptr)

{

    RELOC_PTR(gs_screen_enum, pgs);

    RELOC_USING(st_halftone, &eptr->halftone, sizeof(gs_halftone));

    RELOC_USING(st_ht_order, &eptr->order, sizeof(gx_ht_order));

}

RELOC_PTRS_END

/* Default AccurateScreens control */

void

gs_setaccuratescreens(gs_memory_t *mem, bool accurate)

{

    gs_lib_ctx_t *ctx = gs_lib_ctx_get_interp_instance(mem);

    ctx->screen_accurate_screens = accurate;

}

bool

gs_currentaccuratescreens(gs_memory_t *mem)

{

    gs_lib_ctx_t *ctx = gs_lib_ctx_get_interp_instance(mem);

    return ctx->screen_accurate_screens;

}

void

gs_setminscreenlevels(gs_memory_t *mem, uint levels)

{

    gs_lib_ctx_t *ctx = gs_lib_ctx_get_interp_instance(mem);

    ctx->screen_min_screen_levels = levels;

}

uint

gs_currentminscreenlevels(gs_memory_t *mem)

{

    gs_lib_ctx_t *ctx = gs_lib_ctx_get_interp_instance(mem);

    return ctx->screen_min_screen_levels;

}

/* Initialize the screen control statics at startup. */

init_proc(gs_gshtscr_init);     /* check prototype */

int

gs_gshtscr_init(gs_memory_t *mem)

{

    gs_setaccuratescreens(mem, false);

    gs_setminscreenlevels(mem, 1);

    return 0;

}

/*

 * The following implementation notes complement the general discussion of

 * halftone tiles found in gxdht.h.

 *

 * Currently we allow R(') > 1 (i.e., multiple basic cells per multi-cell)

 * only if AccurateScreens is true or if B (the number of pixels in a basic

 * cell) < MinScreenLevels; if AccurateScreens is false and B >=

 * MinScreenLevels, multi-cells and basic cells are the same.

 *

 * To find the smallest super-cell for a given multi-cell size, i.e., the

 * smallest (absolute value) coordinates where the corners of multi-cells

 * lie on the coordinate axes, we compute the values of i and j that give

 * the minimum value of W by:

 *      D = gcd(abs(M'), abs(N)), i = M'/D, j = N/D, W = C / D,

 * and similarly

 *      D' = gcd(abs(M), abs(N')), i' = N'/D', j' = M/D', W' = C / D'.

 */

/* Compute the derived values of a halftone tile. */

void

gx_compute_cell_values(gx_ht_cell_params_t * phcp)

{

    const int M = phcp->M, N = phcp->N, M1 = phcp->M1, N1 = phcp->N1;

    const uint m = any_abs(M), n = any_abs(N);

    const uint m1 = any_abs(M1), n1 = any_abs(N1);

    const ulong C = phcp->C = (ulong)m * m1 + (ulong)n * n1;

    const int D = phcp->D = igcd(m1, n);

    const int D1 = phcp->D1 = igcd(m, n1);

    phcp->W = C / D, phcp->W1 = C / D1;

    /* Compute the shift value. */

    /* If M1 or N is zero, the shift is zero. */

    if (M1 && N) {

        int h = 0, k = 0, dy = 0;

        int shift;

        /*

         * There may be a faster way to do this: see Knuth vol. 2,

         * section 4.5.2, Algorithm X (p. 302) and exercise 15

         * (p. 315, solution p. 523).

         */

        while (dy != D)

            if (dy > D) {

                if (M1 > 0)

                    ++k;

                else

                    --k;

                dy -= m1;

            } else {

                if (N > 0)

                    ++h;

                else

                    --h;

                dy += n;

            }

        shift = h * M + k * N1;

        /* We just computed what amounts to a right shift; */

        /* what we want is a left shift. */

        phcp->S = imod(-shift, phcp->W);

    } else

        phcp->S = 0;

    if_debug12('h', "[h]MNR=(%d,%d)/%d, M'N'R'=(%d,%d)/%d => C=%lu, D=%d, D'=%d, W=%u, W'=%u, S=%d\n",

               M, N, phcp->R, M1, N1, phcp->R1,

               C, D, D1, phcp->W, phcp->W1, phcp->S);

}

/* Forward references */

static int pick_cell_size(gs_screen_halftone * ph,

     const gs_matrix * pmat, ulong max_size, uint min_levels, bool accurate,

                           gx_ht_cell_params_t * phcp);

/* Allocate a screen enumerator. */

gs_screen_enum *

gs_screen_enum_alloc(gs_memory_t * mem, client_name_t cname)

{

    return gs_alloc_struct(mem, gs_screen_enum, &st_gs_screen_enum, cname);

}

/* Set up for halftone sampling. */

int

gs_screen_init(gs_screen_enum * penum, gs_gstate * pgs,

               gs_screen_halftone * phsp)

{

    gs_lib_ctx_t *ctx = gs_lib_ctx_get_interp_instance(pgs->memory);

    return gs_screen_init_accurate(penum, pgs, phsp,

                                   ctx->screen_accurate_screens);

}

int

gs_screen_init_memory(gs_screen_enum * penum, gs_gstate * pgs,

                gs_screen_halftone * phsp, bool accurate, gs_memory_t * mem)

{

    int code =

    gs_screen_order_init_memory(&penum->order, pgs, phsp, accurate, mem);

    if (code < 0)

        return code;

    return

        gs_screen_enum_init_memory(penum, &penum->order, pgs, phsp, mem);

}

/* Allocate and initialize a spot screen. */

/* This is the first half of gs_screen_init_accurate. */

int

gs_screen_order_alloc(gx_ht_order *porder, gs_memory_t *mem)

{

    uint num_levels = porder->params.W * porder->params.D;

    int code;

    if (!FORCE_STRIP_HALFTONES &&

        ((ulong)porder->params.W1 * bitmap_raster(porder->params.W) +

           (ulong)num_levels * sizeof(*porder->levels) +

           (ulong)porder->params.W * porder->params.W1 * sizeof(gx_ht_bit)) <=

        porder->screen_params.max_size) {

        /*

         * Allocate an order for the entire tile, but only sample one

         * strip.  Note that this causes the order parameters to be

         * self-inconsistent until gx_ht_construct_spot_order fixes them

         * up: see gxdht.h for more information.

         */

        code = gx_ht_alloc_order(porder, porder->params.W,

                                 porder->params.W1, 0,

                                 num_levels, mem);

        porder->height = porder->orig_height = porder->params.D;

        porder->shift = porder->orig_shift = porder->params.S;

    } else {

        /* Just allocate the order for a single strip. */

        code = gx_ht_alloc_order(porder, porder->params.W,

                                 porder->params.D, porder->params.S,

                                 num_levels, mem);

    }

    return code;

}

int

gs_screen_order_init_memory(gx_ht_order * porder, const gs_gstate * pgs,

                            gs_screen_halftone * phsp, bool accurate,

                            gs_memory_t * mem)

{

    gs_matrix imat;

    ulong max_size = gx_ht_cache_default_bits_size();

    int code;

    gs_lib_ctx_t *ctx = gs_lib_ctx_get_interp_instance(mem);

    if (phsp->frequency < 0.1)

        return_error(gs_error_rangecheck);

    gs_deviceinitialmatrix(gs_currentdevice(pgs), &imat);

    code = pick_cell_size(phsp, &imat, max_size,

                          ctx->screen_min_screen_levels, accurate,

                          &porder->params);

    if (code < 0)

        return code;

    gx_compute_cell_values(&porder->params);

    porder->screen_params.matrix = imat;

    porder->screen_params.max_size = max_size;

    return gs_screen_order_alloc(porder, mem);

}

/*

 * Given a desired frequency, angle, and minimum number of levels, a maximum

 * cell size, and an AccurateScreens flag, pick values for M('), N('), and

 * R(').  We want to get a good fit to the requested frequency and angle,

 * provide at least the requested minimum number of levels, and keep

 * rendering as fast as possible; trading these criteria off against each

 * other is what makes the code complicated.

 *

 * We compute trial values u and v from the original values of F and A.

 * Normally these will not be integers.  We then examine the 4 pairs of

 * integers obtained by rounding each of u and v independently up or down,

 * and pick the pair U, V that yields the closest match to the requested

 * F and A values and doesn't require more than max_size storage for a

 * single tile.  If no pair

 * yields an acceptably small W, we divide both u and v by 2 and try again.

 * Then we run the equations backward to obtain the actual F and A.

 * This is fairly easy given that we require either xx = yy = 0 or

 * xy = yx = 0.  In the former case, we have

 *      U = (72 / F * xx) * cos(A);

 *      V = (72 / F * yy) * sin(A);

 * from which immediately

 *      A = arctan((V / yy) / (U / xx)),

 * or equivalently

 *      A = arctan((V * xx) / (U * yy)).

 * We can then obtain F as

 *      F = (72 * xx / U) * cos(A),

 * or equivalently

 *      F = (72 * yy / V) * sin(A).

 * For landscape devices, we replace xx by yx, yy by xy, and interchange

 * sin and cos, resulting in

 *      A = arctan((U * xy) / (V * yx))

 * and

 *      F = (72 * yx / U) * sin(A)

 * or

 *      F = (72 * xy / V) * cos(A).

 */

/* ph->frequency and ph->angle are input parameters; */

/* the routine sets ph->actual_frequency and ph->actual_angle. */

static int

pick_cell_size(gs_screen_halftone * ph, const gs_matrix * pmat, ulong max_size,

               uint min_levels, bool accurate, gx_ht_cell_params_t * phcp)

{

    const bool landscape = (pmat->xy != 0.0 || pmat->yx != 0.0);

    /* Account for a possibly reflected coordinate system. */

    /* See gxstroke.c for the algorithm. */

    const bool reflected = pmat->xy * pmat->yx > pmat->xx * pmat->yy;

    const int reflection = (reflected ? -1 : 1);

    const int rotation =

    (landscape ? (pmat->yx < 0 ? 90 : -90) : pmat->xx < 0 ? 180 : 0);

    const double f0 = ph->frequency, a0 = ph->angle;

    double T = 1.0;

    gs_point uv0;

#define u0 uv0.x

#define v0 uv0.y

    int rt = 1;

    double f = 0, a = 0;

    double e_best = 1000;

    bool better;

    if (landscape) {

        if (pmat->xy)

            T = fabs(pmat->yx / pmat->xy);

    } else {

        if (pmat->yy)

            T = fabs(pmat->xx / pmat->yy);

    }

    /*

     * We need to find a vector in device space whose length is

     * 1 inch / ph->frequency and whose angle is ph->angle.

     * Because device pixels may not be square, we can't simply

     * map the length to device space and then rotate it;

     * instead, since we know that user space is uniform in X and Y,

     * we calculate the correct angle in user space before rotation.

     */

    /* Compute trial values of u and v. */

    if (f0 == 0)

        return_error(gs_error_rangecheck);

    {

        gs_matrix rmat;

        gs_make_rotation(a0 * reflection + rotation, &rmat);

        gs_distance_transform(72.0 / f0, 0.0, &rmat, &uv0);

        gs_distance_transform(u0, v0, pmat, &uv0);

        if_debug10('h', "[h]Requested: f=%g a=%g mat=[%g %g %g %g] max_size=%lu min_levels=%u =>\n     u=%g v=%g\n",

                   ph->frequency, ph->angle,

                   pmat->xx, pmat->xy, pmat->yx, pmat->yy,

                   max_size, min_levels, u0, v0);

    }

    /* Adjust u and v to reasonable values. */

    if (u0 == 0 && v0 == 0)

        return_error(gs_error_rangecheck);

    /* We increment rt in a loop below until (u+v) * rt

     * is at least 4. Make sure that rt has enough range

     * to satisfy that calculation. If it doesn't then

     * give up (silly values).

     */

    if ((fabs(u0) + fabs(v0)) < ((double)5.0 / max_int))

        return_error(gs_error_rangecheck);

    while ((fabs(u0) + fabs(v0)) * rt < 4)

        ++rt;

    phcp->C = 0;

  try_size:

    better = false;

    {

        double fm0 = u0 * rt;

        double fn0 = v0 * rt;

        int m0 = (int)floor(u0 * rt + 0.0001);

        int n0 = (int)floor(v0 * rt + 0.0001);

        gx_ht_cell_params_t p;

        p.R = p.R1 = rt;

        for (p.M = m0 + 1; p.M >= m0; p.M--)

            for (p.N = n0 + 1; p.N >= n0; p.N--) {

                long raster, wt;

#ifdef DEBUG

                long wt_size;

#endif

                double fr, ar, ft, at, f_diff, a_diff, f_err, a_err;

                p.M1 = (int)floor(p.M / T + 0.5);

                p.N1 = (int)floor(p.N * T + 0.5);

                if (p.M1 == 0 && p.N1 == 0)

                    return_error(gs_error_rangecheck);

                gx_compute_cell_values(&p);

                if_debug3('h', "[h]trying m=%d, n=%d, r=%d\n", p.M, p.N, rt);

                wt = p.W;

                if (wt >= max_short)

                    continue;

                /* Calculations below involve dividing by one or more of these values

                 * make sure we can't get a divide by zero.

                 */

                if (wt == 0 || p.D == 0 || (p.M == 0 && p.N == 0))

                    continue;

                /* Check the strip size, not the full tile size, */

                /* against max_size. */

                raster = bitmap_raster(wt);

                if (raster > max_size / p.D || raster > max_long / wt)

                    continue;

#ifdef DEBUG

                wt_size = raster * wt;

#endif

                /* Compute the corresponding values of F and A. */

                if (landscape)

                    ar = atan2(p.M * (double)pmat->xy,

                               p.N * (double)pmat->yx),

                        fr = 72.0 * (p.M == 0 ? pmat->xy / p.N * cos(ar) :

                                     pmat->yx / p.M * sin(ar));

                else

                    ar = atan2(p.N * (double)pmat->xx,

                               p.M * (double)pmat->yy),

                        fr = 72.0 * (p.M == 0 ? pmat->yy / p.N * sin(ar) :

                                     pmat->xx / p.M * cos(ar));

                ft = fabs(fr) * rt;

                /* Normalize the angle to the requested quadrant. */

                at = (ar * radians_to_degrees - rotation) * reflection;

                at -= floor(at / 180.0) * 180.0;

                at += floor(a0 / 180.0) * 180.0;

                f_diff = fabs(ft - f0);

                a_diff = fabs(at - a0);

                f_err = f_diff / fabs(f0);

                /*

                 * We used to compute the percentage difference here:

                 *      a_err = (a0 == 0 ? a_diff : a_diff / fabs(a0));

                 * but using the angle difference makes more sense:

                 */

                a_err = a_diff;

                if_debug5('h', " ==> d=%d, wt=%ld, wt_size=%ld, f=%g, a=%g\n",

                          p.D, wt, bitmap_raster(wt) * wt, ft, at);

                {

                    /*

                     * Compute the error in position between ideal location.

                     * and the current integer location.

                     */

                    double error =

                        (fn0 - p.N) * (fn0 - p.N) + (fm0 - p.M) * (fm0 - p.M);

                    /*

                     * Adjust the error by the length of the vector.  This gives

                     * a slight bias toward larger cell sizzes.

                     */

                    error /= p.N * p.N + p.M * p.M;

                    error = sqrt(error); /* The previous calcs. gave value squared */

                    if (error > e_best)

                        continue;

                    e_best = error;

                }

                *phcp = p;

                f = ft, a = at;

                better = true;

                if_debug3('h', "*** best wt_size=%ld, f_diff=%g, a_diff=%g\n",

                          wt_size, f_diff, a_diff);

                /*

                 * We want a maximum relative frequency error of 1% and a

                 * maximum angle error of 1% (of 90 degrees).

                 */

                if (f_err <= 0.01 && a_err <= 0.9 /*degrees*/)

                    goto done;

            }

    }

    /* It is possible (for ridiculous halftone screens) to reach this point without ever

     * having been able to find a suitable screen. In that case we will not have set

     * phcp and so phcp->C will be undefined. We can detect this condition by checking rt

     * is 1 (so its the first attempt to find a screen) and better is false (we didn't find

     * a better match). If that happens, exit with an error.

     */

    if (rt == 1 && !better)

        return_error(gs_error_rangecheck);

    if (phcp->C < min_levels) { /* We don't have enough levels yet.  Keep going. */

        ++rt;

        goto try_size;

    }

    if (better) {               /* If we want accurate screens, continue till we fail. */

        if (accurate) {

            ++rt;

            goto try_size;

        }

    } else {                    /*

                                 * We couldn't find an acceptable M and N.  If R > 1,

                                 * take what we've got; if R = 1, give up.

                                 */

        if (rt == 1)

            return_error(gs_error_rangecheck);

    }

    /* Deliver the results. */

  done:

    if_debug5('h', "[h]Chosen: f=%g a=%g M=%d N=%d R=%d\n",

              f, a, phcp->M, phcp->N, phcp->R);

    ph->actual_frequency = f;

    ph->actual_angle = a;

    return 0;

#undef u0

#undef v0

}

/* Prepare to sample a spot screen. */

/* This is the second half of gs_screen_init_accurate. */

int

gs_screen_enum_init_memory(gs_screen_enum * penum, const gx_ht_order * porder,

                           gs_gstate * pgs, const gs_screen_halftone * phsp,

                           gs_memory_t * mem)

{

    int code;

    penum->pgs = pgs;           /* ensure clean for GC */

    if (&penum->order != porder) /* Pacify Valgrind */

        penum->order = *porder;

    penum->halftone.rc.memory = mem;

    penum->halftone.type = ht_type_screen;

    penum->halftone.params.screen = *phsp;

    penum->x = penum->y = 0;

    penum->strip = porder->num_levels / porder->width;

    penum->shift = porder->shift;

    /*

     * We want a transformation matrix that maps the parallelogram

     * (0,0), (U,V), (U-V',V+U'), (-V',U') to the square (+/-1, +/-1).

     * If the coefficients are [a b c d e f] and we let

     *      u = U = M/R, v = V = N/R,

     *      r = -V' = -N'/R', s = U' = M'/R',

     * then we just need to solve the equations:

     *      a*0 + c*0 + e = -1      b*0 + d*0 + f = -1

     *      a*u + c*v + e = 1       b*u + d*v + f = 1

     *      a*r + c*s + e = -1      b*r + d*s + f = 1

     * This has the following solution:

     *      Q = 2 / (M*M' + N*N')

     *      a = Q * R * M'

     *      b = -Q * R' * N

     *      c = Q * R * N'

     *      d = Q * R' * M

     *      e = -1

     *      f = -1

     */

    {

        const int M = porder->params.M, N = porder->params.N, R = porder->params.R;

        const int M1 = porder->params.M1, N1 = porder->params.N1, R1 = porder->params.R1;

        double Q = 2.0 / ((long)M * M1 + (long)N * N1);

        penum->mat.xx = Q * (R * M1);

        penum->mat.xy = Q * (-R1 * N);

        penum->mat.yx = Q * (R * N1);

        penum->mat.yy = Q * (R1 * M);

        penum->mat.tx = -1.0;

        penum->mat.ty = -1.0;

        code = gs_matrix_invert(&penum->mat, &penum->mat_inv);

    }

    if_debug7('h', "[h]Screen: (%dx%d)/%d [%f %f %f %f]\n",

              porder->width, porder->height, porder->params.R,

              penum->mat.xx, penum->mat.xy,

              penum->mat.yx, penum->mat.yy);

    return code;

}

/* Report current point for sampling */

int

gs_screen_currentpoint(gs_screen_enum * penum, gs_point * ppt)

{

    gs_point pt;

    int code;

    double sx, sy; /* spot center in spot coords (integers) */

    gs_point spot_center; /* device coords */

    if (penum->y >= penum->strip) {     /* all done */

        gx_ht_construct_spot_order(&penum->order);

        return 1;

    }

    /* We displace the sampled coordinates very slightly */

    /* in order to reduce the likely number of points */

    /* for which the spot function returns the same value. */

    if ((code = gs_point_transform(penum->x + 0.501, penum->y + 0.498, &penum->mat, &pt)) < 0)

        return code;

    /* find the spot center in device coords : */

    sx = ceil( pt.x / 2 ) * 2;

    sy = ceil( pt.y / 2 ) * 2;

    if ((code = gs_point_transform(sx, sy, &penum->mat_inv, &spot_center)) < 0)

        return code;

    /* shift the spot center to nearest pixel center : */

    spot_center.x = floor(spot_center.x) + 0.5;

    spot_center.y = floor(spot_center.y) + 0.5;

    /* compute the spot function arguments for the shifted spot : */

    if ((code = gs_distance_transform(penum->x - spot_center.x + 0.501,

                                      penum->y - spot_center.y + 0.498,

                                      &penum->mat, &pt)) < 0)

        return code;

    pt.x += 1;

    pt.y += 1;

    if (pt.x < -1.0)

        pt.x += ((int)(-ceil(pt.x)) + 1) & ~1;

    else if (pt.x >= 1.0)

        pt.x -= ((int)pt.x + 1) & ~1;

    if (pt.y < -1.0)

        pt.y += ((int)(-ceil(pt.y)) + 1) & ~1;

    else if (pt.y >= 1.0)

        pt.y -= ((int)pt.y + 1) & ~1;

    *ppt = pt;

    return 0;

}

/* Record next halftone sample */

int

gs_screen_next(gs_screen_enum * penum, double value)

{

    ht_sample_t sample;

    int width = penum->order.width;

    gx_ht_bit *bits = (gx_ht_bit *)penum->order.bit_data;

    if (value < -1.0 || value > 1.0)

        return_error(gs_error_rangecheck);

    sample = (ht_sample_t) ((value + 1) * max_ht_sample);

#if defined(DEBUG)

    if (gs_debug_c('H')) {

        gs_point pt;

        gs_screen_currentpoint(penum, &pt);

        dlprintf6("[H]sample x=%d y=%d (%f,%f): %f -> %u\n",

                  penum->x, penum->y, pt.x, pt.y, value, sample);

    }

#endif

    bits[penum->y * width + penum->x].mask = sample;

    if (++(penum->x) >= width)

        penum->x = 0, ++(penum->y);

    return 0;

}

/* Install a fully constructed screen in the gstate. */

int

gs_screen_install(gs_screen_enum * penum)

{

    gx_device_halftone dev_ht;

    int code;

    dev_ht.rc.memory = penum->halftone.rc.memory;

    dev_ht.order = penum->order;

    dev_ht.components = 0;

    penum->halftone.objtype = HT_OBJTYPE_DEFAULT;

    if ((code = gx_ht_install(penum->pgs, &penum->halftone, &dev_ht)) < 0)

        gx_device_halftone_release(&dev_ht, dev_ht.rc.memory);

    return code;

}