path: root/base/gscie.c

/* Copyright (C) 2001-2021 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.,  1305 Grant Avenue - Suite 200, Novato,
   CA 94945, U.S.A., +1(415)492-9861, for further information.
*/


/* CIE color rendering cache management */
#include "math_.h"
#include "memory_.h"
#include "gx.h"
#include "gserrors.h"
#include "gsstruct.h"
#include "gsmatrix.h"		/* for gscolor2.h */
#include "gxcspace.h"		/* for gxcie.c */
#include "gscolor2.h"		/* for gs_set/currentcolorrendering */
#include "gxarith.h"
#include "gxcie.h"
#include "gxdevice.h"		/* for gxcmap.h */
#include "gxcmap.h"
#include "gzstate.h"
#include "gsicc.h"

/*
 * Define whether to optimize the CIE mapping process by combining steps.
 * This should only be disabled (commented out) for debugging.
 */
#define OPTIMIZE_CIE_MAPPING

/* Forward references */
static int cie_joint_caches_init(gx_cie_joint_caches *,
                                  const gs_cie_common *,
                                  gs_cie_render *);
static void cie_joint_caches_complete(gx_cie_joint_caches *,
                                       const gs_cie_common *,
                                       const gs_cie_abc *,
                                       const gs_cie_render *);
static void cie_cache_restrict(cie_cache_floats *, const gs_range *);
static void cie_invert3(const gs_matrix3 *, gs_matrix3 *);
static void cie_matrix_init(gs_matrix3 *);

/* Allocator structure types */
private_st_joint_caches();
extern_st(st_gs_gstate);

#define RESTRICTED_INDEX(v, n, itemp)\
  ((uint)(itemp = (int)(v)) >= (n) ?\
   (itemp < 0 ? 0 : (n) - 1) : itemp)

/* Define cache interpolation threshold values. */
#ifdef CIE_CACHE_INTERPOLATE
#  ifdef CIE_INTERPOLATE_THRESHOLD
#    define CACHE_THRESHOLD CIE_INTERPOLATE_THRESHOLD
#  else
#    define CACHE_THRESHOLD 0	/* always interpolate */
#  endif
#else
#  define CACHE_THRESHOLD 1.0e6	/* never interpolate */
#endif
#ifdef CIE_RENDER_TABLE_INTERPOLATE
#  define RENDER_TABLE_THRESHOLD 0
#else
#  define RENDER_TABLE_THRESHOLD 1.0e6
#endif

/*
 * Determine whether a function is a linear transformation of the form
 * f(x) = scale * x + origin.
 */
static bool
cache_is_linear(cie_linear_params_t *params, const cie_cache_floats *pcf)
{
    double origin = pcf->values[0];
    double diff = pcf->values[countof(pcf->values) - 1] - origin;
    double scale = diff / (countof(pcf->values) - 1);
    int i;
    double test = origin + scale;

    for (i = 1; i < countof(pcf->values) - 1; ++i, test += scale)
        if (fabs(pcf->values[i] - test) >= 0.5 / countof(pcf->values))
            return (params->is_linear = false);
    params->origin = origin - pcf->params.base;
    params->scale =
        diff * pcf->params.factor / (countof(pcf->values) - 1);
    return (params->is_linear = true);
}

static void
cache_set_linear(cie_cache_floats *pcf)
{
        if (pcf->params.is_identity) {
            if_debug1('c', "[c]is_linear("PRI_INTPTR") = true (is_identity)\n",
                      (intptr_t)pcf);
            pcf->params.linear.is_linear = true;
            pcf->params.linear.origin = 0;
            pcf->params.linear.scale = 1;
        } else if (cache_is_linear(&pcf->params.linear, pcf)) {
            if (pcf->params.linear.origin == 0 &&
                fabs(pcf->params.linear.scale - 1) < 0.00001)
                pcf->params.is_identity = true;
            if_debug4('c',
                      "[c]is_linear("PRI_INTPTR") = true, origin = %g, scale = %g%s\n",
                      (intptr_t)pcf, pcf->params.linear.origin,
                      pcf->params.linear.scale,
                      (pcf->params.is_identity ? " (=> is_identity)" : ""));
        }
#ifdef DEBUG
        else
            if_debug1('c', "[c]linear("PRI_INTPTR") = false\n", (intptr_t)pcf);
#endif
}
static void
cache3_set_linear(gx_cie_vector_cache3_t *pvc)
{
    cache_set_linear(&pvc->caches[0].floats);
    cache_set_linear(&pvc->caches[1].floats);
    cache_set_linear(&pvc->caches[2].floats);
}

#ifdef DEBUG
static void
if_debug_vector3(const char *str, const gs_vector3 *vec)
{
    if_debug4('c', "%s[%g %g %g]\n", str, vec->u, vec->v, vec->w);
}
static void
if_debug_matrix3(const char *str, const gs_matrix3 *mat)
{
    if_debug10('c', "%s [%g %g %g] [%g %g %g] [%g %g %g]\n", str,
               mat->cu.u, mat->cu.v, mat->cu.w,
               mat->cv.u, mat->cv.v, mat->cv.w,
               mat->cw.u, mat->cw.v, mat->cw.w);
}
#else
#  define if_debug_vector3(str, vec) DO_NOTHING
#  define if_debug_matrix3(str, mat) DO_NOTHING
#endif

/* ------ Default values for CIE dictionary elements ------ */

/* Default transformation procedures. */

float
a_identity(double in, const gs_cie_a * pcie)
{
    return in;
}
static float
a_from_cache(double in, const gs_cie_a * pcie)
{
    return gs_cie_cached_value(in, &pcie->caches.DecodeA.floats);
}

float
abc_identity(double in, const gs_cie_abc * pcie)
{
    return in;
}
static float
abc_from_cache_0(double in, const gs_cie_abc * pcie)
{
    return gs_cie_cached_value(in, &pcie->caches.DecodeABC.caches[0].floats);
}
static float
abc_from_cache_1(double in, const gs_cie_abc * pcie)
{
    return gs_cie_cached_value(in, &pcie->caches.DecodeABC.caches[1].floats);
}
static float
abc_from_cache_2(double in, const gs_cie_abc * pcie)
{
    return gs_cie_cached_value(in, &pcie->caches.DecodeABC.caches[2].floats);
}

static float
def_identity(double in, const gs_cie_def * pcie)
{
    return in;
}
static float
def_from_cache_0(double in, const gs_cie_def * pcie)
{
    return gs_cie_cached_value(in, &pcie->caches_def.DecodeDEF[0].floats);
}
static float
def_from_cache_1(double in, const gs_cie_def * pcie)
{
    return gs_cie_cached_value(in, &pcie->caches_def.DecodeDEF[1].floats);
}
static float
def_from_cache_2(double in, const gs_cie_def * pcie)
{
    return gs_cie_cached_value(in, &pcie->caches_def.DecodeDEF[2].floats);
}

static float
defg_identity(double in, const gs_cie_defg * pcie)
{
    return in;
}
static float
defg_from_cache_0(double in, const gs_cie_defg * pcie)
{
    return gs_cie_cached_value(in, &pcie->caches_defg.DecodeDEFG[0].floats);
}
static float
defg_from_cache_1(double in, const gs_cie_defg * pcie)
{
    return gs_cie_cached_value(in, &pcie->caches_defg.DecodeDEFG[1].floats);
}
static float
defg_from_cache_2(double in, const gs_cie_defg * pcie)
{
    return gs_cie_cached_value(in, &pcie->caches_defg.DecodeDEFG[2].floats);
}
static float
defg_from_cache_3(double in, const gs_cie_defg * pcie)
{
    return gs_cie_cached_value(in, &pcie->caches_defg.DecodeDEFG[3].floats);
}

float
common_identity(double in, const gs_cie_common * pcie)
{
    return in;
}
static float
lmn_from_cache_0(double in, const gs_cie_common * pcie)
{
    return gs_cie_cached_value(in, &pcie->caches.DecodeLMN[0].floats);
}
static float
lmn_from_cache_1(double in, const gs_cie_common * pcie)
{
    return gs_cie_cached_value(in, &pcie->caches.DecodeLMN[1].floats);
}
static float
lmn_from_cache_2(double in, const gs_cie_common * pcie)
{
    return gs_cie_cached_value(in, &pcie->caches.DecodeLMN[2].floats);
}

/* Transformation procedures for accessing an already-loaded cache. */

float
gs_cie_cached_value(double in, const cie_cache_floats *pcache)
{
    /*
     * We need to get the same results when we sample an already-loaded
     * cache, so we need to round the index just a tiny bit.
     */
    int index =
        (int)((in - pcache->params.base) * pcache->params.factor + 0.0001);

    CIE_CLAMP_INDEX(index);
    return pcache->values[index];
}

/* Default vectors and matrices. */

const gs_range3 Range3_default = {
    { {0, 1}, {0, 1}, {0, 1} }
};
const gs_range4 Range4_default = {
    { {0, 1}, {0, 1}, {0, 1}, {0, 1} }
};
const gs_cie_defg_proc4 DecodeDEFG_default = {
    {defg_identity, defg_identity, defg_identity, defg_identity}
};
const gs_cie_defg_proc4 DecodeDEFG_from_cache = {
    {defg_from_cache_0, defg_from_cache_1, defg_from_cache_2, defg_from_cache_3}
};
const gs_cie_def_proc3 DecodeDEF_default = {
    {def_identity, def_identity, def_identity}
};
const gs_cie_def_proc3 DecodeDEF_from_cache = {
    {def_from_cache_0, def_from_cache_1, def_from_cache_2}
};
const gs_cie_abc_proc3 DecodeABC_default = {
    {abc_identity, abc_identity, abc_identity}
};
const gs_cie_abc_proc3 DecodeABC_from_cache = {
    {abc_from_cache_0, abc_from_cache_1, abc_from_cache_2}
};
const gs_cie_common_proc3 DecodeLMN_default = {
    {common_identity, common_identity, common_identity}
};
const gs_cie_common_proc3 DecodeLMN_from_cache = {
    {lmn_from_cache_0, lmn_from_cache_1, lmn_from_cache_2}
};
const gs_matrix3 Matrix3_default = {
    {1, 0, 0},
    {0, 1, 0},
    {0, 0, 1},
    1 /*true */
};
const gs_range RangeA_default = {0, 1};
const gs_cie_a_proc DecodeA_default = a_identity;
const gs_cie_a_proc DecodeA_from_cache = a_from_cache;
const gs_vector3 MatrixA_default = {1, 1, 1};
const gs_vector3 BlackPoint_default = {0, 0, 0};

/* Initialize a CIE color. */
/* This only happens on setcolorspace. */
void
gx_init_CIE(gs_client_color * pcc, const gs_color_space * pcs)
{
    gx_init_paint_4(pcc, pcs);
    /* (0...) may not be within the range of allowable values. */
    (*pcs->type->restrict_color)(pcc, pcs);
}

/* Restrict CIE colors. */

static inline void
cie_restrict(float *pv, const gs_range *range)
{
    if (*pv <= range->rmin)
        *pv = range->rmin;
    else if (*pv >= range->rmax)
        *pv = range->rmax;
}

void
gx_restrict_CIEDEFG(gs_client_color * pcc, const gs_color_space * pcs)
{
    const gs_cie_defg *pcie = pcs->params.defg;

    cie_restrict(&pcc->paint.values[0], &pcie->RangeDEFG.ranges[0]);
    cie_restrict(&pcc->paint.values[1], &pcie->RangeDEFG.ranges[1]);
    cie_restrict(&pcc->paint.values[2], &pcie->RangeDEFG.ranges[2]);
    cie_restrict(&pcc->paint.values[3], &pcie->RangeDEFG.ranges[3]);
}
void
gx_restrict_CIEDEF(gs_client_color * pcc, const gs_color_space * pcs)
{
    const gs_cie_def *pcie = pcs->params.def;

    cie_restrict(&pcc->paint.values[0], &pcie->RangeDEF.ranges[0]);
    cie_restrict(&pcc->paint.values[1], &pcie->RangeDEF.ranges[1]);
    cie_restrict(&pcc->paint.values[2], &pcie->RangeDEF.ranges[2]);
}
void
gx_restrict_CIEABC(gs_client_color * pcc, const gs_color_space * pcs)
{
    const gs_cie_abc *pcie = pcs->params.abc;

    cie_restrict(&pcc->paint.values[0], &pcie->RangeABC.ranges[0]);
    cie_restrict(&pcc->paint.values[1], &pcie->RangeABC.ranges[1]);
    cie_restrict(&pcc->paint.values[2], &pcie->RangeABC.ranges[2]);
}
void
gx_restrict_CIEA(gs_client_color * pcc, const gs_color_space * pcs)
{
    const gs_cie_a *pcie = pcs->params.a;

    cie_restrict(&pcc->paint.values[0], &pcie->RangeA);
}

/* ================ Table setup ================ */

/* ------ Install a CIE color space ------ */

static void cie_cache_mult(gx_cie_vector_cache *, const gs_vector3 *,
                            const cie_cache_floats *, double);
static bool cie_cache_mult3(gx_cie_vector_cache3_t *,
                             const gs_matrix3 *, double);

int
gx_install_cie_abc(gs_cie_abc *pcie, gs_gstate * pgs)
{
    if_debug_matrix3("[c]CIE MatrixABC =", &pcie->MatrixABC);
    cie_matrix_init(&pcie->MatrixABC);
    CIE_LOAD_CACHE_BODY(pcie->caches.DecodeABC.caches, pcie->RangeABC.ranges,
                        &pcie->DecodeABC, DecodeABC_default, pcie,
                        "DecodeABC");
    gx_cie_load_common_cache(&pcie->common, pgs);
    gs_cie_abc_complete(pcie);
    return gs_cie_cs_complete(pgs, true);
}

int
gx_install_CIEDEFG(gs_color_space * pcs, gs_gstate * pgs)
{
    gs_cie_defg *pcie = pcs->params.defg;

    CIE_LOAD_CACHE_BODY(pcie->caches_defg.DecodeDEFG, pcie->RangeDEFG.ranges,
                        &pcie->DecodeDEFG, DecodeDEFG_default, pcie,
                        "DecodeDEFG");
    return gx_install_cie_abc((gs_cie_abc *)pcie, pgs);
}

int
gx_install_CIEDEF(gs_color_space * pcs, gs_gstate * pgs)
{
    gs_cie_def *pcie = pcs->params.def;

    CIE_LOAD_CACHE_BODY(pcie->caches_def.DecodeDEF, pcie->RangeDEF.ranges,
                        &pcie->DecodeDEF, DecodeDEF_default, pcie,
                        "DecodeDEF");
    return gx_install_cie_abc((gs_cie_abc *)pcie, pgs);
}

int
gx_install_CIEABC(gs_color_space * pcs, gs_gstate * pgs)
{
    return gx_install_cie_abc(pcs->params.abc, pgs);
}

int
gx_install_CIEA(gs_color_space * pcs, gs_gstate * pgs)
{
    gs_cie_a *pcie = pcs->params.a;
    gs_sample_loop_params_t lp;
    int i;

    gs_cie_cache_init(&pcie->caches.DecodeA.floats.params, &lp,
                      &pcie->RangeA, "DecodeA");
    for (i = 0; i <= lp.N; ++i) {
        float in = SAMPLE_LOOP_VALUE(i, lp);

        pcie->caches.DecodeA.floats.values[i] = (*pcie->DecodeA)(in, pcie);
        if_debug3m('C', pgs->memory, "[C]DecodeA[%d] = %g => %g\n",
                   i, in, pcie->caches.DecodeA.floats.values[i]);
    }
    gx_cie_load_common_cache(&pcie->common, pgs);
    gs_cie_a_complete(pcie);
    return gs_cie_cs_complete(pgs, true);
}

/* Load the common caches when installing the color space. */
/* This routine is exported for the benefit of gsicc.c */
void
gx_cie_load_common_cache(gs_cie_common * pcie, gs_gstate * pgs)
{
    if_debug_matrix3("[c]CIE MatrixLMN =", &pcie->MatrixLMN);
    cie_matrix_init(&pcie->MatrixLMN);
    CIE_LOAD_CACHE_BODY(pcie->caches.DecodeLMN, pcie->RangeLMN.ranges,
                        &pcie->DecodeLMN, DecodeLMN_default, pcie,
                        "DecodeLMN");
}

/* Complete loading the common caches. */
/* This routine is exported for the benefit of gsicc.c */
void
gx_cie_common_complete(gs_cie_common *pcie)
{
    int i;

    for (i = 0; i < 3; ++i)
        cache_set_linear(&pcie->caches.DecodeLMN[i].floats);
}

/*
 * Restrict the DecodeDEF[G] cache according to RangeHIJ[K], and scale to
 * the dimensions of Table.
 */
static void
gs_cie_defx_scale(float *values, const gs_range *range, int dim)
{
    double scale = (dim - 1.0) / (range->rmax - range->rmin);
    int i;

    for (i = 0; i < gx_cie_cache_size; ++i) {
        float value = values[i];

        values[i] =
            (value <= range->rmin ? 0 :
             value >= range->rmax ? dim - 1 :
             (value - range->rmin) * scale);
    }
}

/* Complete loading a CIEBasedDEFG color space. */
/* This routine is NOT idempotent. */
void
gs_cie_defg_complete(gs_cie_defg * pcie)
{
    int j;

    for (j = 0; j < 4; ++j)
        gs_cie_defx_scale(pcie->caches_defg.DecodeDEFG[j].floats.values,
                          &pcie->RangeHIJK.ranges[j], pcie->Table.dims[j]);
    gs_cie_abc_complete((gs_cie_abc *)pcie);
}

/* Complete loading a CIEBasedDEF color space. */
/* This routine is NOT idempotent. */
void
gs_cie_def_complete(gs_cie_def * pcie)
{
    int j;

    for (j = 0; j < 3; ++j)
        gs_cie_defx_scale(pcie->caches_def.DecodeDEF[j].floats.values,
                          &pcie->RangeHIJ.ranges[j], pcie->Table.dims[j]);
    gs_cie_abc_complete((gs_cie_abc *)pcie);
}

/* Complete loading a CIEBasedABC color space. */
/* This routine is idempotent. */
void
gs_cie_abc_complete(gs_cie_abc * pcie)
{
    cache3_set_linear(&pcie->caches.DecodeABC);
    pcie->caches.skipABC =
        cie_cache_mult3(&pcie->caches.DecodeABC, &pcie->MatrixABC,
                        CACHE_THRESHOLD);
    gx_cie_common_complete((gs_cie_common *)pcie);
}

/* Complete loading a CIEBasedA color space. */
/* This routine is idempotent. */
void
gs_cie_a_complete(gs_cie_a * pcie)
{
    cie_cache_mult(&pcie->caches.DecodeA, &pcie->MatrixA,
                   &pcie->caches.DecodeA.floats,
                   CACHE_THRESHOLD);
    cache_set_linear(&pcie->caches.DecodeA.floats);
    gx_cie_common_complete((gs_cie_common *)pcie);
}

/*
 * Set the ranges where interpolation is required in a vector cache.
 * This procedure is idempotent.
 */
typedef struct cie_cache_range_temp_s {
    cie_cached_value prev;
    int imin, imax;
} cie_cache_range_temp_t;
static inline void
check_interpolation_required(cie_cache_range_temp_t *pccr,
                             cie_cached_value cur, int i, double threshold)
{
    cie_cached_value prev = pccr->prev;

    if (cie_cached_abs(cur - prev) > threshold * min(cie_cached_abs(prev), cie_cached_abs(cur))) {
        if (i - 1 < pccr->imin)
            pccr->imin = i - 1;
        if (i > pccr->imax)
            pccr->imax = i;
    }
    pccr->prev = cur;
}
static void
cie_cache_set_interpolation(gx_cie_vector_cache *pcache, double threshold)
{
    cie_cached_value base = pcache->vecs.params.base;
    cie_cached_value factor = pcache->vecs.params.factor;
    cie_cache_range_temp_t temp[3];
    int i, j;

    for (j = 0; j < 3; ++j)
        temp[j].imin = gx_cie_cache_size, temp[j].imax = -1;
    temp[0].prev = pcache->vecs.values[0].u;
    temp[1].prev = pcache->vecs.values[0].v;
    temp[2].prev = pcache->vecs.values[0].w;

    for (i = 0; i < gx_cie_cache_size; ++i) {
        check_interpolation_required(&temp[0], pcache->vecs.values[i].u, i,
                                     threshold);
        check_interpolation_required(&temp[1], pcache->vecs.values[i].v, i,
                                     threshold);
        check_interpolation_required(&temp[2], pcache->vecs.values[i].w, i,
                                     threshold);
    }

    for (j = 0; j < 3; ++j) {
        pcache->vecs.params.interpolation_ranges[j].rmin =
            base + (cie_cached_value)((double)temp[j].imin / factor);
        pcache->vecs.params.interpolation_ranges[j].rmax =
            base + (cie_cached_value)((double)temp[j].imax / factor);
        if_debug3('c', "[c]interpolation_ranges[%d] = %g, %g\n", j,
                  cie_cached2float(pcache->vecs.params.interpolation_ranges[j].rmin),
                  cie_cached2float(pcache->vecs.params.interpolation_ranges[j].rmax));
    }

}

/*
 * Convert a scalar cache to a vector cache by multiplying the scalar
 * values by a vector.  Also set the range where interpolation is needed.
 * This procedure is idempotent.
 */
static void
cie_cache_mult(gx_cie_vector_cache * pcache, const gs_vector3 * pvec,
               const cie_cache_floats * pcf, double threshold)
{
    float u = pvec->u, v = pvec->v, w = pvec->w;
    int i;

    pcache->vecs.params.base = float2cie_cached(pcf->params.base);
    pcache->vecs.params.factor = float2cie_cached(pcf->params.factor);
    pcache->vecs.params.limit =
        float2cie_cached((gx_cie_cache_size - 1) / pcf->params.factor +
                         pcf->params.base);
    for (i = 0; i < gx_cie_cache_size; ++i) {
        float f = pcf->values[i];

        pcache->vecs.values[i].u = float2cie_cached(f * u);
        pcache->vecs.values[i].v = float2cie_cached(f * v);
        pcache->vecs.values[i].w = float2cie_cached(f * w);
    }
    cie_cache_set_interpolation(pcache, threshold);
}

/*
 * Set the interpolation ranges in a 3-vector cache, based on the ranges in
 * the individual vector caches.  This procedure is idempotent.
 */
static void
cie_cache3_set_interpolation(gx_cie_vector_cache3_t * pvc)
{
    int j, k;

    /* Iterate over output components. */
    for (j = 0; j < 3; ++j) {
        /* Iterate over sub-caches. */
        cie_interpolation_range_t *p =
                &pvc->caches[0].vecs.params.interpolation_ranges[j];
        cie_cached_value rmin = p->rmin, rmax = p->rmax;

        for (k = 1; k < 3; ++k) {
            p = &pvc->caches[k].vecs.params.interpolation_ranges[j];
            rmin = min(rmin, p->rmin), rmax = max(rmax, p->rmax);
        }
        pvc->interpolation_ranges[j].rmin = rmin;
        pvc->interpolation_ranges[j].rmax = rmax;
        if_debug3('c', "[c]Merged interpolation_ranges[%d] = %g, %g\n",
                  j, rmin, rmax);
    }
}

/*
 * Convert 3 scalar caches to vector caches by multiplying by a matrix.
 * Return true iff the resulting cache is an identity transformation.
 * This procedure is idempotent.
 */
static bool
cie_cache_mult3(gx_cie_vector_cache3_t * pvc, const gs_matrix3 * pmat,
                double threshold)
{
    cie_cache_mult(&pvc->caches[0], &pmat->cu, &pvc->caches[0].floats, threshold);
    cie_cache_mult(&pvc->caches[1], &pmat->cv, &pvc->caches[1].floats, threshold);
    cie_cache_mult(&pvc->caches[2], &pmat->cw, &pvc->caches[2].floats, threshold);
    cie_cache3_set_interpolation(pvc);
    return pmat->is_identity & pvc->caches[0].floats.params.is_identity &
        pvc->caches[1].floats.params.is_identity &
        pvc->caches[2].floats.params.is_identity;
}

/* ------ Install a rendering dictionary ------ */

bool
vector_equal(const gs_vector3 *p1, const gs_vector3 *p2)
{
    if (p1->u != p2->u)
        return false;
    if (p1->v != p2->v)
        return false;
    if (p1->w != p2->w)
        return false;
    return true;
}

bool
matrix_equal(const gs_matrix3 *p1, const gs_matrix3 *p2)
{
    if (p1->is_identity != p2->is_identity)
        return false;
    if (!vector_equal(&(p1->cu), &(p2->cu)))
        return false;
    if (!vector_equal(&(p1->cv), &(p2->cv)))
        return false;
    if (!vector_equal(&(p1->cw), &(p2->cw)))
        return false;
    return true;
}

static bool
transform_equal(const gs_cie_transform_proc3 *p1, const gs_cie_transform_proc3 *p2)
{
    if (p1->proc != p2->proc)
        return false;
    if (p1->proc_data.size != p2->proc_data.size)
        return false;
    if (memcmp(p1->proc_data.data, p2->proc_data.data, p1->proc_data.size) != 0)
        return false;
    if (p1->driver_name != p2->driver_name)
        return false;
    if (p1->proc_name != p2->proc_name)
        return false;
    return true;
}

bool
range_equal(const gs_range3 *p1, const gs_range3 *p2)
{
    int k;

    for (k = 0; k < 3; k++) {
        if (p1->ranges[k].rmax != p2->ranges[k].rmax)
            return false;
        if (p1->ranges[k].rmin != p2->ranges[k].rmin)
            return false;
    }
    return true;
}

/* setcolorrendering */
int
gs_setcolorrendering(gs_gstate * pgs, gs_cie_render * pcrd)
{
    int code = gs_cie_render_complete(pcrd);
    const gs_cie_render *pcrd_old = pgs->cie_render;
    bool joint_ok;

    if (code < 0)
        return code;
    if (pcrd_old != 0 && pcrd->id == pcrd_old->id)
        return 0;		/* detect needless reselecting */
    joint_ok =
        pcrd_old != 0 &&
        vector_equal(&pcrd->points.WhitePoint, &pcrd_old->points.WhitePoint) &&
        vector_equal(&pcrd->points.BlackPoint, &pcrd_old->points.BlackPoint) &&
        matrix_equal(&pcrd->MatrixPQR, &pcrd_old->MatrixPQR) &&
        range_equal(&pcrd->RangePQR, &pcrd_old->RangePQR) &&
        transform_equal(&pcrd->TransformPQR, &pcrd_old->TransformPQR);
    rc_assign(pgs->cie_render, pcrd, "gs_setcolorrendering");
    /* Initialize the joint caches if needed. */
    if (!joint_ok)
        code = gs_cie_cs_complete(pgs, true);
    gx_unset_dev_color(pgs);
    return code;
}

/* currentcolorrendering */
const gs_cie_render *
gs_currentcolorrendering(const gs_gstate * pgs)
{
    return pgs->cie_render;
}

/* Unshare (allocating if necessary) the joint caches. */
gx_cie_joint_caches *
gx_unshare_cie_caches(gs_gstate * pgs)
{
    gx_cie_joint_caches *pjc = pgs->cie_joint_caches;

    rc_unshare_struct(pgs->cie_joint_caches, gx_cie_joint_caches,
                      &st_joint_caches, pgs->memory,
                      return 0, "gx_unshare_cie_caches");
    if (pgs->cie_joint_caches != pjc) {
        pjc = pgs->cie_joint_caches;
        pjc->cspace_id = pjc->render_id = gs_no_id;
        pjc->id_status = pjc->status = CIE_JC_STATUS_BUILT;
    }
    return pjc;
}

gx_cie_joint_caches *
gx_get_cie_caches_ref(gs_gstate * pgs, gs_memory_t * mem)
{
    gx_cie_joint_caches *pjc = pgs->cie_joint_caches;

    /* Take a reference here, to allow for the one that
     * rc_unshare_struct might drop if it has to copy it.
     * Whatever happens we will have taken 1 net new
     * reference which we return to the caller. */
    rc_increment(pgs->cie_joint_caches);
    rc_unshare_struct(pjc, gx_cie_joint_caches,
                      &st_joint_caches, mem,
                      return NULL, "gx_unshare_cie_caches");
    return pjc;
}

/* Compute the parameters for loading a cache, setting base and factor. */
/* This procedure is idempotent. */
void
gs_cie_cache_init(cie_cache_params * pcache, gs_sample_loop_params_t * pslp,
                  const gs_range * domain, client_name_t cname)
{
    /*
      We need to map the values in the range [domain->rmin..domain->rmax].
      However, if rmin < 0 < rmax and the function is non-linear, this can
      lead to anomalies at zero, which is the default value for CIE colors.
      The "correct" way to approach this is to run the mapping functions on
      demand, but we don't want to deal with the complexities of the
      callbacks this would involve (especially in the middle of rendering
      images); instead, we adjust the range so that zero maps precisely to a
      cache slot.  Define:

      A = domain->rmin;
      B = domain->rmax;
      N = gx_cie_cache_size - 1;

      R = B - A;
      h(v) = N * (v - A) / R;		// the index of v in the cache
      X = h(0).

      If X is not an integer, we can decrease A and/increase B to make it
      one.  Let A' and B' be the adjusted values of A and B respectively,
      and let K be the integer derived from X (either floor(X) or ceil(X)).
      Define

      f(K) = (K * B' + (N - K) * A') / N).

      We want f(K) = 0.  This occurs precisely when, for any real number
      C != 0,

      A' = -K * C;
      B' = (N - K) * C.

      In order to ensure A' <= A and B' >= B, we require

      C >= -A / K;
      C >= B / (N - K).

      Since A' and B' must be exactly representable as floats, we round C
      upward to ensure that it has no more than M mantissa bits, where

      M = ARCH_FLOAT_MANTISSA_BITS - ceil(log2(N)).
    */
    float A = domain->rmin, B = domain->rmax;
    double R = B - A, delta;
#define NN (gx_cie_cache_size - 1) /* 'N' is a member name, see end of proc */
#define N NN
#define CEIL_LOG2_N CIE_LOG2_CACHE_SIZE

    /* Adjust the range if necessary. */
    if (A < 0 && B >= 0) {
        const double X = -N * A / R;	/* know X > 0 */
        /* Choose K to minimize range expansion. */
        const int K = (int)(A + B < 0 ? floor(X) : ceil(X)); /* know 0 < K < N */
        const double Ca = -A / K, Cb = B / (N - K); /* know Ca, Cb > 0 */
        double C = max(Ca, Cb);	/* know C > 0 */
        const int M = ARCH_FLOAT_MANTISSA_BITS - CEIL_LOG2_N;
        int cexp;
        const double cfrac = frexp(C, &cexp);

        if_debug4('c', "[c]adjusting cache_init(%8g, %8g), X = %8g, K = %d:\n",
                  A, B, X, K);
        /* Round C to no more than M significant bits.  See above. */
        C = ldexp(ceil(ldexp(cfrac, M)), cexp - M);
        /* Finally, compute A' and B'. */
        A = -K * C;
        B = (N - K) * C;
        if_debug2('c', "[c]  => %8g, %8g\n", A, B);
        R = B - A;
    }
    delta = R / N;
#ifdef CIE_CACHE_INTERPOLATE
    pcache->base = A;		/* no rounding */
#else
    pcache->base = A - delta / 2;	/* so lookup will round */
#endif
    /*
     * If size of the domain is zero, then use 1.0 as the scaling
     * factor.  This prevents divide by zero errors in later calculations.
     * This should only occurs with zero matrices.  It does occur with
     * Genoa test file 050-01.ps.
     */
    pcache->factor = (any_abs(delta) < 1e-30 ? 1.0 : N / R);
    if_debug4('c', "[c]cache %s "PRI_INTPTR" base=%g, factor=%g\n",
              (const char *)cname, (intptr_t)pcache,
              pcache->base, pcache->factor);
    pslp->A = A;
    pslp->B = B;
#undef N
    pslp->N = NN;
#undef NN
}

/* ------ Complete a rendering structure ------ */

/*
 * Compute the derived values in a CRD that don't involve the cached
 * procedure values.  This procedure is idempotent.
 */
static void cie_transform_range3(const gs_range3 *, const gs_matrix3 *,
                                  gs_range3 *);
int
gs_cie_render_init(gs_cie_render * pcrd)
{
    gs_matrix3 PQR_inverse;

    if (pcrd->status >= CIE_RENDER_STATUS_INITED)
        return 0;		/* init already done */
    if_debug_matrix3("[c]CRD MatrixLMN =", &pcrd->MatrixLMN);
    cie_matrix_init(&pcrd->MatrixLMN);
    if_debug_matrix3("[c]CRD MatrixABC =", &pcrd->MatrixABC);
    cie_matrix_init(&pcrd->MatrixABC);
    if_debug_matrix3("[c]CRD MatrixPQR =", &pcrd->MatrixPQR);
    cie_matrix_init(&pcrd->MatrixPQR);
    cie_invert3(&pcrd->MatrixPQR, &PQR_inverse);
    cie_matrix_mult3(&pcrd->MatrixLMN, &PQR_inverse,
                     &pcrd->MatrixPQR_inverse_LMN);
    cie_transform_range3(&pcrd->RangePQR, &pcrd->MatrixPQR_inverse_LMN,
                         &pcrd->DomainLMN);
    cie_transform_range3(&pcrd->RangeLMN, &pcrd->MatrixABC,
                         &pcrd->DomainABC);
    cie_mult3(&pcrd->points.WhitePoint, &pcrd->MatrixPQR, &pcrd->wdpqr);
    cie_mult3(&pcrd->points.BlackPoint, &pcrd->MatrixPQR, &pcrd->bdpqr);
    pcrd->status = CIE_RENDER_STATUS_INITED;
    return 0;
}

/*
 * Sample the EncodeLMN, EncodeABC, and RenderTableT CRD procedures, and
 * load the caches.  This procedure is idempotent.
 */
int
gs_cie_render_sample(gs_cie_render * pcrd)
{
    int code;

    if (pcrd->status >= CIE_RENDER_STATUS_SAMPLED)
        return 0;		/* sampling already done */
    code = gs_cie_render_init(pcrd);
    if (code < 0)
        return code;
    CIE_LOAD_CACHE_BODY(pcrd->caches.EncodeLMN.caches, pcrd->DomainLMN.ranges,
                        &pcrd->EncodeLMN, Encode_default, pcrd, "EncodeLMN");
    cache3_set_linear(&pcrd->caches.EncodeLMN);
    CIE_LOAD_CACHE_BODY(pcrd->caches.EncodeABC, pcrd->DomainABC.ranges,
                        &pcrd->EncodeABC, Encode_default, pcrd, "EncodeABC");
    if (pcrd->RenderTable.lookup.table != 0) {
        int i, j, m = pcrd->RenderTable.lookup.m;
        gs_sample_loop_params_t lp;
        bool is_identity = true;

        for (j = 0; j < m; j++) {
            gs_cie_cache_init(&pcrd->caches.RenderTableT[j].fracs.params,
                              &lp, &Range3_default.ranges[0],
                              "RenderTableT");
            is_identity &= pcrd->RenderTable.T.procs[j] ==
                RenderTableT_default.procs[j];
        }
        pcrd->caches.RenderTableT_is_identity = is_identity;
        /*
         * Unfortunately, we defined the first argument of the RenderTable
         * T procedures as being a byte, limiting the number of distinct
         * cache entries to 256 rather than gx_cie_cache_size.
         * We confine this decision to this loop, rather than propagating
         * it to the procedures that use the cached data, so that we can
         * change it more easily at some future time.
         */
        for (i = 0; i < gx_cie_cache_size; i++) {
#if gx_cie_log2_cache_size >= 8
            byte value = i >> (gx_cie_log2_cache_size - 8);
#else
            byte value = (i << (8 - gx_cie_log2_cache_size)) +
                (i >> (gx_cie_log2_cache_size * 2 - 8));
#endif
            for (j = 0; j < m; j++) {
                pcrd->caches.RenderTableT[j].fracs.values[i] =
                    (*pcrd->RenderTable.T.procs[j])(value, pcrd);
                if_debug3('C', "[C]RenderTableT[%d,%d] = %g\n",
                          i, j,
                          frac2float(pcrd->caches.RenderTableT[j].fracs.values[i]));
            }
        }
    }
    pcrd->status = CIE_RENDER_STATUS_SAMPLED;
    return 0;
}

/* Transform a set of ranges. */
static void
cie_transform_range(const gs_range3 * in, double mu, double mv, double mw,
                    gs_range * out)
{
    float umin = mu * in->ranges[0].rmin, umax = mu * in->ranges[0].rmax;
    float vmin = mv * in->ranges[1].rmin, vmax = mv * in->ranges[1].rmax;
    float wmin = mw * in->ranges[2].rmin, wmax = mw * in->ranges[2].rmax;
    float temp;

    if (umin > umax)
        temp = umin, umin = umax, umax = temp;
    if (vmin > vmax)
        temp = vmin, vmin = vmax, vmax = temp;
    if (wmin > wmax)
        temp = wmin, wmin = wmax, wmax = temp;
    out->rmin = umin + vmin + wmin;
    out->rmax = umax + vmax + wmax;
}
static void
cie_transform_range3(const gs_range3 * in, const gs_matrix3 * mat,
                     gs_range3 * out)
{
    cie_transform_range(in, mat->cu.u, mat->cv.u, mat->cw.u,
                        &out->ranges[0]);
    cie_transform_range(in, mat->cu.v, mat->cv.v, mat->cw.v,
                        &out->ranges[1]);
    cie_transform_range(in, mat->cu.w, mat->cv.w, mat->cw.w,
                        &out->ranges[2]);
}

/*
 * Finish preparing a CRD for installation, by restricting and/or
 * transforming the cached procedure values.
 * This procedure is idempotent.
 */
int
gs_cie_render_complete(gs_cie_render * pcrd)
{
    int code;

    if (pcrd->status >= CIE_RENDER_STATUS_COMPLETED)
        return 0;		/* completion already done */
    code = gs_cie_render_sample(pcrd);
    if (code < 0)
        return code;
    /*
     * Since range restriction happens immediately after
     * the cache lookup, we can save a step by restricting
     * the values in the cache entries.
     *
     * If there is no lookup table, we want the final ABC values
     * to be fracs; if there is a table, we want them to be
     * appropriately scaled ints.
     */
    pcrd->MatrixABCEncode = pcrd->MatrixABC;
    {
        int c;
        double f;

        for (c = 0; c < 3; c++) {
            gx_cie_float_fixed_cache *pcache = &pcrd->caches.EncodeABC[c];

            cie_cache_restrict(&pcrd->caches.EncodeLMN.caches[c].floats,
                               &pcrd->RangeLMN.ranges[c]);
            cie_cache_restrict(&pcrd->caches.EncodeABC[c].floats,
                               &pcrd->RangeABC.ranges[c]);
            if (pcrd->RenderTable.lookup.table == 0) {
                cie_cache_restrict(&pcache->floats,
                                   &Range3_default.ranges[0]);
                gs_cie_cache_to_fracs(&pcache->floats, &pcache->fixeds.fracs);
                pcache->fixeds.fracs.params.is_identity = false;
            } else {
                int i;
                int n = pcrd->RenderTable.lookup.dims[c];

#ifdef CIE_RENDER_TABLE_INTERPOLATE
#  define SCALED_INDEX(f, n, itemp)\
     RESTRICTED_INDEX(f * (1 << _cie_interpolate_bits),\
                      (n) << _cie_interpolate_bits, itemp)
#else
                int m = pcrd->RenderTable.lookup.m;
                int k =
                    (c == 0 ? 1 : c == 1 ?
                     m * pcrd->RenderTable.lookup.dims[2] : m);
#  define SCALED_INDEX(f, n, itemp)\
     (RESTRICTED_INDEX(f, n, itemp) * k)
#endif
                const gs_range *prange = pcrd->RangeABC.ranges + c;
                double scale = (n - 1) / (prange->rmax - prange->rmin);

                for (i = 0; i < gx_cie_cache_size; ++i) {
                    float v =
                        (pcache->floats.values[i] - prange->rmin) * scale
#ifndef CIE_RENDER_TABLE_INTERPOLATE
                        + 0.5
#endif
                        ;
                    int itemp;

                    if_debug5('c',
                              "[c]cache[%d][%d] = %g => %g => %d\n",
                              c, i, pcache->floats.values[i], v,
                              SCALED_INDEX(v, n, itemp));
                    pcache->fixeds.ints.values[i] =
                        SCALED_INDEX(v, n, itemp);
                }
                pcache->fixeds.ints.params = pcache->floats.params;
                pcache->fixeds.ints.params.is_identity = false;
#undef SCALED_INDEX
            }
        }
        /* Fold the scaling of the EncodeABC cache index */
        /* into MatrixABC. */
#define MABC(i, t)\
  f = pcrd->caches.EncodeABC[i].floats.params.factor;\
  pcrd->MatrixABCEncode.cu.t *= f;\
  pcrd->MatrixABCEncode.cv.t *= f;\
  pcrd->MatrixABCEncode.cw.t *= f;\
  pcrd->EncodeABC_base[i] =\
    float2cie_cached(pcrd->caches.EncodeABC[i].floats.params.base * f)
        MABC(0, u);
        MABC(1, v);
        MABC(2, w);
#undef MABC
        pcrd->MatrixABCEncode.is_identity = 0;
    }
    cie_cache_mult3(&pcrd->caches.EncodeLMN, &pcrd->MatrixABCEncode,
                    CACHE_THRESHOLD);
    pcrd->status = CIE_RENDER_STATUS_COMPLETED;
    return 0;
}

/* Apply a range restriction to a cache. */
static void
cie_cache_restrict(cie_cache_floats * pcache, const gs_range * prange)
{
    int i;

    for (i = 0; i < gx_cie_cache_size; i++) {
        float v = pcache->values[i];

        if (v < prange->rmin)
            pcache->values[i] = prange->rmin;
        else if (v > prange->rmax)
            pcache->values[i] = prange->rmax;
    }
}

/* Convert a cache from floats to fracs. */
/* Note that the two may be aliased. */
void
gs_cie_cache_to_fracs(const cie_cache_floats *pfloats, cie_cache_fracs *pfracs)
{
    int i;

    /* Loop from bottom to top so that we don't */
    /* overwrite elements before they're used. */
    for (i = 0; i < gx_cie_cache_size; ++i)
        pfracs->values[i] = float2frac(pfloats->values[i]);
    pfracs->params = pfloats->params;
}

/* ------ Fill in the joint cache ------ */

/* If the current color space is a CIE space, or has a CIE base space, */
/* return a pointer to the common part of the space; otherwise return 0. */
static const gs_cie_common *
cie_cs_common_abc(const gs_color_space *pcs_orig, const gs_cie_abc **ppabc)
{
    const gs_color_space *pcs = pcs_orig;

    *ppabc = 0;
    do {
        switch (pcs->type->index) {
        case gs_color_space_index_CIEDEF:
            *ppabc = (const gs_cie_abc *)pcs->params.def;
            return &pcs->params.def->common;
        case gs_color_space_index_CIEDEFG:
            *ppabc = (const gs_cie_abc *)pcs->params.defg;
            return &pcs->params.defg->common;
        case gs_color_space_index_CIEABC:
            *ppabc = pcs->params.abc;
            return &pcs->params.abc->common;
        case gs_color_space_index_CIEA:
            return &pcs->params.a->common;
        default:
            pcs = gs_cspace_base_space(pcs);
            break;
        }
    } while (pcs != 0);

    return 0;
}
const gs_cie_common *
gs_cie_cs_common(const gs_gstate * pgs)
{
    const gs_cie_abc *ignore_pabc;

    return cie_cs_common_abc(gs_currentcolorspace_inline(pgs), &ignore_pabc);
}

/*
 * Mark the joint caches as needing completion.  This is done lazily,
 * when a color is being mapped.  However, make sure the joint caches
 * exist now.
 */
int
gs_cie_cs_complete(gs_gstate * pgs, bool init)
{
    gx_cie_joint_caches *pjc = gx_unshare_cie_caches(pgs);

    if (pjc == 0)
        return_error(gs_error_VMerror);
    pjc->status = (init ? CIE_JC_STATUS_BUILT : CIE_JC_STATUS_INITED);
    return 0;
}
/* Actually complete the joint caches. */
int
gs_cie_jc_complete(const gs_gstate *pgs, const gs_color_space *pcs)
{
    const gs_cie_abc *pabc;
    const gs_cie_common *common = cie_cs_common_abc(pcs, &pabc);
    gs_cie_render *pcrd = pgs->cie_render;
    gx_cie_joint_caches *pjc = pgs->cie_joint_caches;

    if (pjc->cspace_id == pcs->id &&
        pjc->render_id == pcrd->id)
        pjc->status = pjc->id_status;
    switch (pjc->status) {
    case CIE_JC_STATUS_BUILT: {
        int code = cie_joint_caches_init(pjc, common, pcrd);

        if (code < 0)
            return code;
    }
        /* falls through */
    case CIE_JC_STATUS_INITED:
        cie_joint_caches_complete(pjc, common, pabc, pcrd);
        pjc->cspace_id = pcs->id;
        pjc->render_id = pcrd->id;
        pjc->id_status = pjc->status = CIE_JC_STATUS_COMPLETED;
        /* falls through */
    case CIE_JC_STATUS_COMPLETED:
        break;
    }
    return 0;
}

/*
 * Compute the source and destination WhitePoint and BlackPoint for
 * the TransformPQR procedure.
 */
int
gs_cie_compute_points_sd(gx_cie_joint_caches *pjc,
                         const gs_cie_common * pcie,
                         const gs_cie_render * pcrd)
{
    gs_cie_wbsd *pwbsd = &pjc->points_sd;

    pwbsd->ws.xyz = pcie->points.WhitePoint;
    cie_mult3(&pwbsd->ws.xyz, &pcrd->MatrixPQR, &pwbsd->ws.pqr);
    pwbsd->bs.xyz = pcie->points.BlackPoint;
    cie_mult3(&pwbsd->bs.xyz, &pcrd->MatrixPQR, &pwbsd->bs.pqr);
    pwbsd->wd.xyz = pcrd->points.WhitePoint;
    pwbsd->wd.pqr = pcrd->wdpqr;
    pwbsd->bd.xyz = pcrd->points.BlackPoint;
    pwbsd->bd.pqr = pcrd->bdpqr;
    return 0;
}

/*
 * Sample the TransformPQR procedure for the joint caches.
 * This routine is idempotent.
 */
static int
cie_joint_caches_init(gx_cie_joint_caches * pjc,
                      const gs_cie_common * pcie,
                      gs_cie_render * pcrd)
{
    bool is_identity;
    int j;

    gs_cie_compute_points_sd(pjc, pcie, pcrd);
    /*
     * If a client pre-loaded the cache, we can't adjust the range.
     * ****** WRONG ******
     */
    if (pcrd->TransformPQR.proc == TransformPQR_from_cache.proc)
        return 0;
    is_identity = pcrd->TransformPQR.proc == TransformPQR_default.proc;
    for (j = 0; j < 3; j++) {
        int i;
        gs_sample_loop_params_t lp;

        gs_cie_cache_init(&pjc->TransformPQR.caches[j].floats.params, &lp,
                          &pcrd->RangePQR.ranges[j], "TransformPQR");
        for (i = 0; i <= lp.N; ++i) {
            float in = SAMPLE_LOOP_VALUE(i, lp);
            float out;
            int code = (*pcrd->TransformPQR.proc)(j, in, &pjc->points_sd,
                                                  pcrd, &out);

            if (code < 0)
                return code;
            pjc->TransformPQR.caches[j].floats.values[i] = out;
            if_debug4('C', "[C]TransformPQR[%d,%d] = %g => %g\n",
                      j, i, in, out);
        }
        pjc->TransformPQR.caches[j].floats.params.is_identity = is_identity;
    }
    return 0;
}

/*
 * Complete the loading of the joint caches.
 * This routine is idempotent.
 */
static void
cie_joint_caches_complete(gx_cie_joint_caches * pjc,
                          const gs_cie_common * pcie,
                          const gs_cie_abc * pabc /* NULL if CIEA */,
                          const gs_cie_render * pcrd)
{
    gs_matrix3 mat3, mat2;
    gs_matrix3 MatrixLMN_PQR;
    int j;

    pjc->remap_finish = gx_cie_real_remap_finish;

    /*
     * We number the pipeline steps as follows:
     *   1 - DecodeABC/MatrixABC
     *   2 - DecodeLMN/MatrixLMN/MatrixPQR
     *   3 - TransformPQR/MatrixPQR'/MatrixLMN
     *   4 - EncodeLMN/MatrixABC
     *   5 - EncodeABC, RenderTable (we don't do anything with this here)
     * We work from back to front, combining steps where possible.
     * Currently we only combine steps if a procedure is the identity
     * transform, but we could do it whenever the procedure is linear.
     * A project for another day....
     */

        /* Step 4 */

#ifdef OPTIMIZE_CIE_MAPPING
    if (pcrd->caches.EncodeLMN.caches[0].floats.params.is_identity &&
        pcrd->caches.EncodeLMN.caches[1].floats.params.is_identity &&
        pcrd->caches.EncodeLMN.caches[2].floats.params.is_identity
        ) {
        /* Fold step 4 into step 3. */
        if_debug0('c', "[c]EncodeLMN is identity, folding MatrixABC(Encode) into MatrixPQR'+LMN.\n");
        cie_matrix_mult3(&pcrd->MatrixABCEncode, &pcrd->MatrixPQR_inverse_LMN,
                         &mat3);
        pjc->skipEncodeLMN = true;
    } else
#endif /* OPTIMIZE_CIE_MAPPING */
    {
        if_debug0('c', "[c]EncodeLMN is not identity.\n");
        mat3 = pcrd->MatrixPQR_inverse_LMN;
        pjc->skipEncodeLMN = false;
    }

        /* Step 3 */

    cache3_set_linear(&pjc->TransformPQR);
    cie_matrix_mult3(&pcrd->MatrixPQR, &pcie->MatrixLMN,
                     &MatrixLMN_PQR);

#ifdef OPTIMIZE_CIE_MAPPING
    if (pjc->TransformPQR.caches[0].floats.params.is_identity &
        pjc->TransformPQR.caches[1].floats.params.is_identity &
        pjc->TransformPQR.caches[2].floats.params.is_identity
        ) {
        /* Fold step 3 into step 2. */
        if_debug0('c', "[c]TransformPQR is identity, folding MatrixPQR'+LMN into MatrixLMN+PQR.\n");
        cie_matrix_mult3(&mat3, &MatrixLMN_PQR, &mat2);
        pjc->skipPQR = true;
    } else
#endif /* OPTIMIZE_CIE_MAPPING */
    {
        if_debug0('c', "[c]TransformPQR is not identity.\n");
        mat2 = MatrixLMN_PQR;
        for (j = 0; j < 3; j++) {
            cie_cache_restrict(&pjc->TransformPQR.caches[j].floats,
                               &pcrd->RangePQR.ranges[j]);
        }
        cie_cache_mult3(&pjc->TransformPQR, &mat3, CACHE_THRESHOLD);
        pjc->skipPQR = false;
    }

        /* Steps 2 & 1 */

#ifdef OPTIMIZE_CIE_MAPPING
    if (pcie->caches.DecodeLMN[0].floats.params.is_identity &
        pcie->caches.DecodeLMN[1].floats.params.is_identity &
        pcie->caches.DecodeLMN[2].floats.params.is_identity
        ) {
        if_debug0('c', "[c]DecodeLMN is identity, folding MatrixLMN+PQR into MatrixABC.\n");
        if (!pabc) {
            pjc->skipDecodeLMN = mat2.is_identity;
            pjc->skipDecodeABC = false;
            if (!pjc->skipDecodeLMN) {
                for (j = 0; j < 3; j++) {
                    cie_cache_mult(&pjc->DecodeLMN.caches[j], &mat2.cu + j,
                                   &pcie->caches.DecodeLMN[j].floats,
                                   CACHE_THRESHOLD);
                }
                cie_cache3_set_interpolation(&pjc->DecodeLMN);
            }
        } else {
            /*
             * Fold step 2 into step 1.  This is a little different because
             * the data for step 1 are in the color space structure.
             */
            gs_matrix3 mat1;

            cie_matrix_mult3(&mat2, &pabc->MatrixABC, &mat1);
            for (j = 0; j < 3; j++) {
                cie_cache_mult(&pjc->DecodeLMN.caches[j], &mat1.cu + j,
                               &pabc->caches.DecodeABC.caches[j].floats,
                               CACHE_THRESHOLD);
            }
            cie_cache3_set_interpolation(&pjc->DecodeLMN);
            pjc->skipDecodeLMN = false;
            pjc->skipDecodeABC = true;
        }
    } else
#endif /* OPTIMIZE_CIE_MAPPING */
    {
        if_debug0('c', "[c]DecodeLMN is not identity.\n");
        for (j = 0; j < 3; j++) {
            cie_cache_mult(&pjc->DecodeLMN.caches[j], &mat2.cu + j,
                           &pcie->caches.DecodeLMN[j].floats,
                           CACHE_THRESHOLD);
        }
        cie_cache3_set_interpolation(&pjc->DecodeLMN);
        pjc->skipDecodeLMN = false;
        pjc->skipDecodeABC = pabc != 0 && pabc->caches.skipABC;
    }

}

/*
 * Initialize (just enough of) an gs_gstate so that "concretizing" colors
 * using this gs_gstate will do only the CIE->XYZ mapping.  This is a
 * semi-hack for the PDF writer.
 */
int
gx_cie_to_xyz_alloc(gs_gstate **ppgs, const gs_color_space *pcs,
                    gs_memory_t *mem)
{
    /*
     * In addition to the gs_gstate itself, we need the joint caches.
     */
    gs_gstate *pgs =
        gs_alloc_struct(mem, gs_gstate, &st_gs_gstate,
                        "gx_cie_to_xyz_alloc(gs_gstate)");
    gx_cie_joint_caches *pjc;
    const gs_cie_abc *pabc;
    const gs_cie_common *pcie = cie_cs_common_abc(pcs, &pabc);
    int j;

    if (pgs == 0)
        return_error(gs_error_VMerror);
    memset(pgs, 0, sizeof(*pgs));	/* mostly paranoia */
    pgs->memory = mem;
    GS_STATE_INIT_VALUES(pgs, 1.0);
    gs_gstate_initialize(pgs, mem);

    pjc = gs_alloc_struct(mem, gx_cie_joint_caches, &st_joint_caches,
                          "gx_cie_to_xyz_free(joint caches)");
    if (pjc == 0) {
        gs_free_object(mem, pgs, "gx_cie_to_xyz_alloc(gs_gstate)");
        return_error(gs_error_VMerror);
    }
    rc_init(pjc, mem, 1);

    /*
     * Perform an abbreviated version of cie_joint_caches_complete.
     * Don't bother with any optimizations.
     */
    for (j = 0; j < 3; j++) {
        cie_cache_mult(&pjc->DecodeLMN.caches[j], &pcie->MatrixLMN.cu + j,
                       &pcie->caches.DecodeLMN[j].floats,
                       CACHE_THRESHOLD);
    }
    cie_cache3_set_interpolation(&pjc->DecodeLMN);
    pjc->skipDecodeLMN = false;
    pjc->skipDecodeABC = pabc != 0 && pabc->caches.skipABC;
    /* Mark the joint caches as completed. */
    pjc->remap_finish = gx_cie_xyz_remap_finish;
    pjc->cspace_id = pcs->id;
    pjc->status = CIE_JC_STATUS_COMPLETED;
    pgs->cie_joint_caches = pjc;
    pgs->cie_to_xyz = true;
    *ppgs = pgs;
    return 0;
}
void
gx_cie_to_xyz_free(gs_gstate *pgs)
{
    gs_memory_t *mem = pgs->memory;

    rc_decrement(pgs->cie_joint_caches,"gx_cie_to_xyz_free");

    /* Free up the ICC objects if created */		/* FIXME: does this need to be thread safe */
    if (pgs->icc_link_cache != NULL) {
        rc_decrement(pgs->icc_link_cache,"gx_cie_to_xyz_free");
    }
    if (pgs->icc_manager != NULL) {
        rc_decrement(pgs->icc_manager,"gx_cie_to_xyz_free");
    }
    if (pgs->icc_profile_cache != NULL) {
        rc_decrement(pgs->icc_profile_cache,"gx_cie_to_xyz_free");
    }
    gs_free_object(mem, pgs, "gx_cie_to_xyz_free(gs_gstate)");
}

/* ================ Utilities ================ */

/* Multiply a vector by a matrix. */
/* Note that we are computing M * V where v is a column vector. */
void
cie_mult3(const gs_vector3 * in, register const gs_matrix3 * mat,
          gs_vector3 * out)
{
    if_debug_vector3("[c]mult", in);
    if_debug_matrix3("	*", mat);
    {
        float u = in->u, v = in->v, w = in->w;

        out->u = (u * mat->cu.u) + (v * mat->cv.u) + (w * mat->cw.u);
        out->v = (u * mat->cu.v) + (v * mat->cv.v) + (w * mat->cw.v);
        out->w = (u * mat->cu.w) + (v * mat->cv.w) + (w * mat->cw.w);
    }
    if_debug_vector3("	=", out);
}

/*
 * Multiply two matrices.  Note that the composition of the transformations
 * M1 followed by M2 is M2 * M1, not M1 * M2.  (See gscie.h for details.)
 */
void
cie_matrix_mult3(const gs_matrix3 *ma, const gs_matrix3 *mb, gs_matrix3 *mc)
{
    gs_matrix3 mprod;
    gs_matrix3 *mp = (mc == ma || mc == mb ? &mprod : mc);

    if_debug_matrix3("[c]matrix_mult", ma);
    if_debug_matrix3("             *", mb);
    cie_mult3(&mb->cu, ma, &mp->cu);
    cie_mult3(&mb->cv, ma, &mp->cv);
    cie_mult3(&mb->cw, ma, &mp->cw);
    cie_matrix_init(mp);
    if_debug_matrix3("             =", mp);
    if (mp != mc)
        *mc = *mp;
}

/*
 * Transpose a 3x3 matrix. In and out can not be the same
 */
void
cie_matrix_transpose3(const gs_matrix3 *in, gs_matrix3 *out)
{
    out->cu.u = in->cu.u;
    out->cu.v = in->cv.u;
    out->cu.w = in->cw.u;

    out->cv.u = in->cu.v;
    out->cv.v = in->cv.v;
    out->cv.w = in->cw.v;

    out->cw.u = in->cu.w;
    out->cw.v = in->cv.w;
    out->cw.w = in->cw.w;
}

/* Invert a matrix. */
/* The output must not be an alias for the input. */
static void
cie_invert3(const gs_matrix3 *in, gs_matrix3 *out)
{	/* This is a brute force algorithm; maybe there are better. */
    /* We label the array elements */
    /*   [ A B C ]   */
    /*   [ D E F ]   */
    /*   [ G H I ]   */
#define A cu.u
#define B cv.u
#define C cw.u
#define D cu.v
#define E cv.v
#define F cw.v
#define G cu.w
#define H cv.w
#define I cw.w
    double coA = in->E * in->I - in->F * in->H;
    double coB = in->F * in->G - in->D * in->I;
    double coC = in->D * in->H - in->E * in->G;
    double det = in->A * coA + in->B * coB + in->C * coC;

    if_debug_matrix3("[c]invert", in);
    out->A = coA / det;
    out->D = coB / det;
    out->G = coC / det;
    out->B = (in->C * in->H - in->B * in->I) / det;
    out->E = (in->A * in->I - in->C * in->G) / det;
    out->H = (in->B * in->G - in->A * in->H) / det;
    out->C = (in->B * in->F - in->C * in->E) / det;
    out->F = (in->C * in->D - in->A * in->F) / det;
    out->I = (in->A * in->E - in->B * in->D) / det;
    if_debug_matrix3("        =", out);
#undef A
#undef B
#undef C
#undef D
#undef E
#undef F
#undef G
#undef H
#undef I
    out->is_identity = in->is_identity;
}

/* Set the is_identity flag that accelerates multiplication. */
static void
cie_matrix_init(register gs_matrix3 * mat)
{
    mat->is_identity =
        mat->cu.u == 1.0 && is_fzero2(mat->cu.v, mat->cu.w) &&
        mat->cv.v == 1.0 && is_fzero2(mat->cv.u, mat->cv.w) &&
        mat->cw.w == 1.0 && is_fzero2(mat->cw.u, mat->cw.v);
}

bool
gx_color_space_needs_cie_caches(const gs_color_space * pcs)
{
    switch (pcs->type->index) {
        case gs_color_space_index_CIEDEFG:
        case gs_color_space_index_CIEDEF:
        case gs_color_space_index_CIEABC:
        case gs_color_space_index_CIEA:
            return true;
        case gs_color_space_index_ICC:
            return false;
        case gs_color_space_index_DevicePixel:
        case gs_color_space_index_DeviceN:
        case gs_color_space_index_Separation:
        case gs_color_space_index_Indexed:
        case gs_color_space_index_Pattern:
            return gx_color_space_needs_cie_caches(pcs->base_space);
        default:
            return false;
    }
}