path: root/base/gsmatrix.c

/* Copyright (C) 2001-2023 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.
*/


/* Matrix operators for Ghostscript library */
#include "math_.h"
#include "memory_.h"
#include "gx.h"
#include "gserrors.h"
#include "gxfarith.h"
#include "gxfixed.h"
#include "gxmatrix.h"
#include "stream.h"

/* The identity matrix */
static const gs_matrix gs_identity_matrix =
{identity_matrix_body};

/* ------ Matrix creation ------ */

/* Create an identity matrix */
void
gs_make_identity(gs_matrix * pmat)
{
    *pmat = gs_identity_matrix;
}

/* Create a translation matrix */
int
gs_make_translation(double dx, double dy, gs_matrix * pmat)
{
    *pmat = gs_identity_matrix;
    pmat->tx = dx;
    pmat->ty = dy;
    return 0;
}

/* Create a scaling matrix */
int
gs_make_scaling(double sx, double sy, gs_matrix * pmat)
{
    *pmat = gs_identity_matrix;
    pmat->xx = sx;
    pmat->yy = sy;
    return 0;
}

/* Create a rotation matrix. */
/* The angle is in degrees. */
int
gs_make_rotation(double ang, gs_matrix * pmat)
{
    gs_sincos_t sincos;

    gs_sincos_degrees(ang, &sincos);
    pmat->yy = pmat->xx = sincos.cos;
    pmat->xy = sincos.sin;
    pmat->yx = -sincos.sin;
    pmat->tx = pmat->ty = 0.0;
    return 0;
}

/* ------ Matrix arithmetic ------ */

/* Multiply two matrices.  We should check for floating exceptions, */
/* but for the moment it's just too awkward. */
/* Since this is used heavily, we check for shortcuts. */
int
gs_matrix_multiply(const gs_matrix * pm1, const gs_matrix * pm2, gs_matrix * pmr)
{
    double xx1 = pm1->xx, yy1 = pm1->yy;
    double tx1 = pm1->tx, ty1 = pm1->ty;
    double xx2 = pm2->xx, yy2 = pm2->yy;
    double xy2 = pm2->xy, yx2 = pm2->yx;

    if (is_xxyy(pm1)) {
        pmr->tx = tx1 * xx2 + pm2->tx;
        pmr->ty = ty1 * yy2 + pm2->ty;
        if (is_fzero(xy2))
            pmr->xy = 0;
        else
            pmr->xy = xx1 * xy2,
                pmr->ty += tx1 * xy2;
        pmr->xx = xx1 * xx2;
        if (is_fzero(yx2))
            pmr->yx = 0;
        else
            pmr->yx = yy1 * yx2,
                pmr->tx += ty1 * yx2;
        pmr->yy = yy1 * yy2;
    } else {
        double xy1 = pm1->xy, yx1 = pm1->yx;

        pmr->xx = xx1 * xx2 + xy1 * yx2;
        pmr->xy = xx1 * xy2 + xy1 * yy2;
        pmr->yy = yx1 * xy2 + yy1 * yy2;
        pmr->yx = yx1 * xx2 + yy1 * yx2;
        pmr->tx = tx1 * xx2 + ty1 * yx2 + pm2->tx;
        pmr->ty = tx1 * xy2 + ty1 * yy2 + pm2->ty;
    }
    return 0;
}
int
gs_matrix_multiply_double(const gs_matrix_double * pm1, const gs_matrix * pm2, gs_matrix_double * pmr)
{
    double xx1 = pm1->xx, yy1 = pm1->yy;
    double tx1 = pm1->tx, ty1 = pm1->ty;
    double xx2 = pm2->xx, yy2 = pm2->yy;
    double xy2 = pm2->xy, yx2 = pm2->yx;

    if (is_xxyy(pm1)) {
        pmr->tx = tx1 * xx2 + pm2->tx;
        pmr->ty = ty1 * yy2 + pm2->ty;
        if (is_fzero(xy2))
            pmr->xy = 0;
        else
            pmr->xy = xx1 * xy2,
                pmr->ty += tx1 * xy2;
        pmr->xx = xx1 * xx2;
        if (is_fzero(yx2))
            pmr->yx = 0;
        else
            pmr->yx = yy1 * yx2,
                pmr->tx += ty1 * yx2;
        pmr->yy = yy1 * yy2;
    } else {
        double xy1 = pm1->xy, yx1 = pm1->yx;

        pmr->xx = xx1 * xx2 + xy1 * yx2;
        pmr->xy = xx1 * xy2 + xy1 * yy2;
        pmr->yy = yx1 * xy2 + yy1 * yy2;
        pmr->yx = yx1 * xx2 + yy1 * yx2;
        pmr->tx = tx1 * xx2 + ty1 * yx2 + pm2->tx;
        pmr->ty = tx1 * xy2 + ty1 * yy2 + pm2->ty;
    }
    return 0;
}

/* Invert a matrix.  Return gs_error_undefinedresult if not invertible. */
int
gs_matrix_invert(const gs_matrix * pm, gs_matrix * pmr)
{				/* We have to be careful about fetch/store order, */
    /* because pm might be the same as pmr. */
    if (is_xxyy(pm)) {
        if (is_fzero(pm->xx) || is_fzero(pm->yy))
            return_error(gs_error_undefinedresult);
        pmr->tx = -(pmr->xx = 1.0 / pm->xx) * pm->tx;
        pmr->xy = 0.0;
        pmr->yx = 0.0;
        pmr->ty = -(pmr->yy = 1.0 / pm->yy) * pm->ty;
    } else {
        float mxx = pm->xx, myy = pm->yy, mxy = pm->xy, myx = pm->yx;
        float mtx = pm->tx, mty = pm->ty;
        /* we declare det as double since on at least some computer (i.e. peeves)
           declaring it as a float results in different values for pmr depending
           on whether or not optimization is turned on.  I believe this is caused
           by the compiler keeping the det value in an internal register when
           optimization is enable.  As evidence of this if you add a debugging
           statement to print out det the optimized code acts the same as the
           unoptimized code.  declearing det as double does not change the CET 10-09.ps
           output. */
        double det = (float)(mxx * myy) - (float)(mxy * myx);

        /*
         * We are doing the math as floats instead of doubles to reproduce
         * the results in page 1 of CET 10-09.ps
         */
        if (det == 0)
            return_error(gs_error_undefinedresult);
        pmr->xx = myy / det;
        pmr->xy = -mxy / det;
        pmr->yx = -myx / det;
        pmr->yy = mxx / det;
        pmr->tx = (((float)(mty * myx) - (float)(mtx * myy))) / det;
        pmr->ty = (((float)(mtx * mxy) - (float)(mty * mxx))) / det;
    }
    return 0;
}
int
gs_matrix_invert_to_double(const gs_matrix * pm, gs_matrix_double * pmr)
{				/* We have to be careful about fetch/store order, */
    /* because pm might be the same as pmr. */
    if (is_xxyy(pm)) {
        if (is_fzero(pm->xx) || is_fzero(pm->yy))
            return_error(gs_error_undefinedresult);
        pmr->tx = -(pmr->xx = 1.0 / pm->xx) * pm->tx;
        pmr->xy = 0.0;
        pmr->yx = 0.0;
        pmr->ty = -(pmr->yy = 1.0 / pm->yy) * pm->ty;
    } else {
        double mxx = pm->xx, myy = pm->yy, mxy = pm->xy, myx = pm->yx;
        double mtx = pm->tx, mty = pm->ty;
        double det = (mxx * myy) - (mxy * myx);

        /*
         * We are doing the math as floats instead of doubles to reproduce
         * the results in page 1 of CET 10-09.ps
         */
        if (det == 0)
            return_error(gs_error_undefinedresult);
        pmr->xx = myy / det;
        pmr->xy = -mxy / det;
        pmr->yx = -myx / det;
        pmr->yy = mxx / det;
        pmr->tx = (((mty * myx) - (mtx * myy))) / det;
        pmr->ty = (((mtx * mxy) - (mty * mxx))) / det;
    }
    return 0;
}

/* Translate a matrix, possibly in place. */
int
gs_matrix_translate(const gs_matrix * pm, double dx, double dy, gs_matrix * pmr)
{
    gs_point trans;
    int code = gs_distance_transform(dx, dy, pm, &trans);

    if (code < 0)
        return code;
    if (pmr != pm)
        *pmr = *pm;
    pmr->tx += trans.x;
    pmr->ty += trans.y;
    return 0;
}

/* Scale a matrix, possibly in place. */
int
gs_matrix_scale(const gs_matrix * pm, double sx, double sy, gs_matrix * pmr)
{
    pmr->xx = pm->xx * sx;
    pmr->xy = pm->xy * sx;
    pmr->yx = pm->yx * sy;
    pmr->yy = pm->yy * sy;
    if (pmr != pm) {
        pmr->tx = pm->tx;
        pmr->ty = pm->ty;
    }
    return 0;
}

/* Rotate a matrix, possibly in place.  The angle is in degrees. */
int
gs_matrix_rotate(const gs_matrix * pm, double ang, gs_matrix * pmr)
{
    double mxx, mxy;
    gs_sincos_t sincos;

    gs_sincos_degrees(ang, &sincos);
    mxx = pm->xx, mxy = pm->xy;
    pmr->xx = sincos.cos * mxx + sincos.sin * pm->yx;
    pmr->xy = sincos.cos * mxy + sincos.sin * pm->yy;
    pmr->yx = sincos.cos * pm->yx - sincos.sin * mxx;
    pmr->yy = sincos.cos * pm->yy - sincos.sin * mxy;
    if (pmr != pm) {
        pmr->tx = pm->tx;
        pmr->ty = pm->ty;
    }
    return 0;
}

/* ------ Coordinate transformations (floating point) ------ */

/* Note that all the transformation routines take separate */
/* x and y arguments, but return their result in a point. */

/* Transform a point. */
int
gs_point_transform(double x, double y, const gs_matrix * pmat,
                   gs_point * ppt)
{
    /*
     * The float casts are there to reproduce results in CET 10-01.ps
     * page 4.
     */
    ppt->x = (float)(x * pmat->xx) + pmat->tx;
    ppt->y = (float)(y * pmat->yy) + pmat->ty;
    if (!is_fzero(pmat->yx))
        ppt->x += (float)(y * pmat->yx);
    if (!is_fzero(pmat->xy))
        ppt->y += (float)(x * pmat->xy);
    return 0;
}

/* Inverse-transform a point. */
/* Return gs_error_undefinedresult if the matrix is not invertible. */
int
gs_point_transform_inverse(double x, double y, const gs_matrix * pmat,
                           gs_point * ppt)
{
    if (is_xxyy(pmat)) {
        if (is_fzero(pmat->xx) || is_fzero(pmat->yy))
            return_error(gs_error_undefinedresult);
        ppt->x = (x - pmat->tx) / pmat->xx;
        ppt->y = (y - pmat->ty) / pmat->yy;
        return 0;
    } else if (is_xyyx(pmat)) {
        if (is_fzero(pmat->xy) || is_fzero(pmat->yx))
            return_error(gs_error_undefinedresult);
        ppt->x = (y - pmat->ty) / pmat->xy;
        ppt->y = (x - pmat->tx) / pmat->yx;
        return 0;
    } else {			/* There are faster ways to do this, */
        /* but we won't implement one unless we have to. */
        gs_matrix imat;
        int code = gs_matrix_invert(pmat, &imat);

        if (code < 0)
            return code;
        return gs_point_transform(x, y, &imat, ppt);
    }
}

/* Transform a distance. */
int
gs_distance_transform(double dx, double dy, const gs_matrix * pmat,
                      gs_point * pdpt)
{
    pdpt->x = dx * pmat->xx;
    pdpt->y = dy * pmat->yy;
    if (!is_fzero(pmat->yx))
        pdpt->x += dy * pmat->yx;
    if (!is_fzero(pmat->xy))
        pdpt->y += dx * pmat->xy;
    return 0;
}

/* Inverse-transform a distance. */
/* Return gs_error_undefinedresult if the matrix is not invertible. */
int
gs_distance_transform_inverse(double dx, double dy,
                              const gs_matrix * pmat, gs_point * pdpt)
{
    if (is_xxyy(pmat)) {
        if (is_fzero(pmat->xx) || is_fzero(pmat->yy))
            return_error(gs_error_undefinedresult);
        pdpt->x = dx / pmat->xx;
        pdpt->y = dy / pmat->yy;
    } else if (is_xyyx(pmat)) {
        if (is_fzero(pmat->xy) || is_fzero(pmat->yx))
            return_error(gs_error_undefinedresult);
        pdpt->x = dy / pmat->xy;
        pdpt->y = dx / pmat->yx;
    } else {
        double det = pmat->xx * pmat->yy - pmat->xy * pmat->yx;

        if (det == 0)
            return_error(gs_error_undefinedresult);
        pdpt->x = (dx * pmat->yy - dy * pmat->yx) / det;
        pdpt->y = (dy * pmat->xx - dx * pmat->xy) / det;
    }
    return 0;
}

/* Compute the bounding box of 4 points. */
int
gs_points_bbox(const gs_point pts[4], gs_rect * pbox)
{
#define assign_min_max(vmin, vmax, v0, v1)\
  if ( v0 < v1 ) vmin = v0, vmax = v1; else vmin = v1, vmax = v0
#define assign_min_max_4(vmin, vmax, v0, v1, v2, v3)\
  { double min01, max01, min23, max23;\
    assign_min_max(min01, max01, v0, v1);\
    assign_min_max(min23, max23, v2, v3);\
    vmin = min(min01, min23);\
    vmax = max(max01, max23);\
  }
    assign_min_max_4(pbox->p.x, pbox->q.x,
                     pts[0].x, pts[1].x, pts[2].x, pts[3].x);
    assign_min_max_4(pbox->p.y, pbox->q.y,
                     pts[0].y, pts[1].y, pts[2].y, pts[3].y);
#undef assign_min_max
#undef assign_min_max_4
    return 0;
}

/* Transform or inverse-transform a bounding box. */
/* Return gs_error_undefinedresult if the matrix is not invertible. */
static int
bbox_transform_either_only(const gs_rect * pbox_in, const gs_matrix * pmat,
                           gs_point pts[4],
     int (*point_xform) (double, double, const gs_matrix *, gs_point *))
{
    int code;

    if ((code = (*point_xform) (pbox_in->p.x, pbox_in->p.y, pmat, &pts[0])) < 0 ||
        (code = (*point_xform) (pbox_in->p.x, pbox_in->q.y, pmat, &pts[1])) < 0 ||
        (code = (*point_xform) (pbox_in->q.x, pbox_in->p.y, pmat, &pts[2])) < 0 ||
     (code = (*point_xform) (pbox_in->q.x, pbox_in->q.y, pmat, &pts[3])) < 0
        )
        DO_NOTHING;
    return code;
}

static int
bbox_transform_either(const gs_rect * pbox_in, const gs_matrix * pmat,
                      gs_rect * pbox_out,
     int (*point_xform) (double, double, const gs_matrix *, gs_point *))
{
    int code;

    /*
     * In principle, we could transform only one point and two
     * distance vectors; however, because of rounding, we will only
     * get fully consistent results if we transform all 4 points.
     * We must compute the max and min after transforming,
     * since a rotation may be involved.
     */
    gs_point pts[4];

    if ((code = bbox_transform_either_only(pbox_in, pmat, pts, point_xform)) < 0)
        return code;
    return gs_points_bbox(pts, pbox_out);
}
int
gs_bbox_transform(const gs_rect * pbox_in, const gs_matrix * pmat,
                  gs_rect * pbox_out)
{
    return bbox_transform_either(pbox_in, pmat, pbox_out,
                                 gs_point_transform);
}
int
gs_bbox_transform_only(const gs_rect * pbox_in, const gs_matrix * pmat,
                       gs_point points[4])
{
    return bbox_transform_either_only(pbox_in, pmat, points,
                                      gs_point_transform);
}
int
gs_bbox_transform_inverse(const gs_rect * pbox_in, const gs_matrix * pmat,
                          gs_rect * pbox_out)
{
    int code = bbox_transform_either(pbox_in, pmat, pbox_out,
                                 gs_point_transform_inverse);

    return code;
}

/* ------ Coordinate transformations (to fixed point) ------ */

#define f_fits_in_fixed(f) f_fits_in_bits(f, fixed_int_bits)

/* Make a gs_matrix_fixed from a gs_matrix. */
int
gs_matrix_fixed_from_matrix(gs_matrix_fixed *pfmat, const gs_matrix *pmat)
{
    *(gs_matrix *)pfmat = *pmat;
    if (f_fits_in_fixed(pmat->tx) && f_fits_in_fixed(pmat->ty)) {
        pfmat->tx = fixed2float(pfmat->tx_fixed = float2fixed(pmat->tx));
        pfmat->ty = fixed2float(pfmat->ty_fixed = float2fixed(pmat->ty));
        pfmat->txy_fixed_valid = true;
    } else {
        pfmat->txy_fixed_valid = false;
    }
    return 0;
}

/* Transform a point with a fixed-point result. */
int
gs_point_transform2fixed(const gs_matrix_fixed * pmat,
                         double x, double y, gs_fixed_point * ppt)
{
    fixed px, py, t;
    double xtemp, ytemp;
    int code;

    if (!pmat->txy_fixed_valid) {	/* The translation is out of range.  Do the */
        /* computation in floating point, and convert to */
        /* fixed at the end. */
        gs_point fpt;

        gs_point_transform(x, y, (const gs_matrix *)pmat, &fpt);
        if (!(f_fits_in_fixed(fpt.x) && f_fits_in_fixed(fpt.y)))
            return_error(gs_error_limitcheck);
        ppt->x = float2fixed(fpt.x);
        ppt->y = float2fixed(fpt.y);
        return 0;
    }
    if (!is_fzero(pmat->xy)) {	/* Hope for 90 degree rotation */
        if ((code = CHECK_DFMUL2FIXED_VARS(px, y, pmat->yx, xtemp)) < 0 ||
            (code = CHECK_DFMUL2FIXED_VARS(py, x, pmat->xy, ytemp)) < 0
            )
            return code;
        FINISH_DFMUL2FIXED_VARS(px, xtemp);
        FINISH_DFMUL2FIXED_VARS(py, ytemp);
        if (!is_fzero(pmat->xx)) {
            if ((code = CHECK_DFMUL2FIXED_VARS(t, x, pmat->xx, xtemp)) < 0)
                return code;
            FINISH_DFMUL2FIXED_VARS(t, xtemp);
            if ((code = CHECK_SET_FIXED_SUM(px, px, t)) < 0)
                return code;
        }
        if (!is_fzero(pmat->yy)) {
            if ((code = CHECK_DFMUL2FIXED_VARS(t, y, pmat->yy, ytemp)) < 0)
                return code;
            FINISH_DFMUL2FIXED_VARS(t, ytemp);
            if ((code = CHECK_SET_FIXED_SUM(py, py, t)) < 0)
                return code;
        }
    } else {
        if ((code = CHECK_DFMUL2FIXED_VARS(px, x, pmat->xx, xtemp)) < 0 ||
            (code = CHECK_DFMUL2FIXED_VARS(py, y, pmat->yy, ytemp)) < 0
            )
            return code;
        FINISH_DFMUL2FIXED_VARS(px, xtemp);
        FINISH_DFMUL2FIXED_VARS(py, ytemp);
        if (!is_fzero(pmat->yx)) {
            if ((code = CHECK_DFMUL2FIXED_VARS(t, y, pmat->yx, ytemp)) < 0)
                return code;
            FINISH_DFMUL2FIXED_VARS(t, ytemp);
            if ((code = CHECK_SET_FIXED_SUM(px, px, t)) < 0)
                return code;
        }
    }
    if (((code = CHECK_SET_FIXED_SUM(ppt->x, px, pmat->tx_fixed)) < 0) ||
        ((code = CHECK_SET_FIXED_SUM(ppt->y, py, pmat->ty_fixed)) < 0) )
        return code;
    return 0;
}

#if PRECISE_CURRENTPOINT
/* Transform a point with a fixed-point result. */
/* Used for the best precision of the current point,
   see comment in clamp_point_aux. */
int
gs_point_transform2fixed_rounding(const gs_matrix_fixed * pmat,
                         double x, double y, gs_fixed_point * ppt)
{
    gs_point fpt;

    gs_point_transform(x, y, (const gs_matrix *)pmat, &fpt);
    if (!(f_fits_in_fixed(fpt.x) && f_fits_in_fixed(fpt.y)))
        return_error(gs_error_limitcheck);
    ppt->x = float2fixed_rounded(fpt.x);
    ppt->y = float2fixed_rounded(fpt.y);
    return 0;
}
#endif

/* Transform a distance with a fixed-point result. */
int
gs_distance_transform2fixed(const gs_matrix_fixed * pmat,
                            double dx, double dy, gs_fixed_point * ppt)
{
    fixed px, py, t;
    double xtemp, ytemp;
    int code;

    if ((code = CHECK_DFMUL2FIXED_VARS(px, dx, pmat->xx, xtemp)) < 0 ||
        (code = CHECK_DFMUL2FIXED_VARS(py, dy, pmat->yy, ytemp)) < 0
        )
        return code;
    FINISH_DFMUL2FIXED_VARS(px, xtemp);
    FINISH_DFMUL2FIXED_VARS(py, ytemp);
    if (!is_fzero(pmat->yx)) {
        if ((code = CHECK_DFMUL2FIXED_VARS(t, dy, pmat->yx, ytemp)) < 0)
            return code;
        FINISH_DFMUL2FIXED_VARS(t, ytemp);
        if ((code = CHECK_SET_FIXED_SUM(px, px, t)) < 0)
            return code;
    }
    if (!is_fzero(pmat->xy)) {
        if ((code = CHECK_DFMUL2FIXED_VARS(t, dx, pmat->xy, xtemp)) < 0)
            return code;
        FINISH_DFMUL2FIXED_VARS(t, xtemp);
        if ((code = CHECK_SET_FIXED_SUM(py, py, t)) < 0)
            return code;
    }
    ppt->x = px;
    ppt->y = py;
    return 0;
}

/* ------ Serialization ------ */

/*
 * For maximum conciseness in band lists, we write a matrix as a control
 * byte followed by 0 to 6 values.  The control byte has the format
 * AABBCD00.  AA and BB control (xx,yy) and (xy,yx) as follows:
 *	00 = values are (0.0, 0.0)
 *	01 = values are (V, V) [1 value follows]
 *	10 = values are (V, -V) [1 value follows]
 *	11 = values are (U, V) [2 values follow]
 * C and D control tx and ty as follows:
 *	0 = value is 0.0
 *	1 = value follows
 * The following code is the only place that knows this representation.
 */

/* Put a matrix on a stream. */
int
sput_matrix(stream *s, const gs_matrix *pmat)
{
    byte buf[1 + 6 * sizeof(float)];
    byte *cp = buf + 1;
    byte b = 0;
    float coeff[6];
    int i;
    uint ignore;

    coeff[0] = pmat->xx;
    coeff[1] = pmat->xy;
    coeff[2] = pmat->yx;
    coeff[3] = pmat->yy;
    coeff[4] = pmat->tx;
    coeff[5] = pmat->ty;
    for (i = 0; i < 4; i += 2) {
        float u = coeff[i], v = coeff[i ^ 3];

        b <<= 2;
        if (u != 0 || v != 0) {
            memcpy(cp, &u, sizeof(float));
            cp += sizeof(float);

            if (v == u)
                b += 1;
            else if (v == -u)
                b += 2;
            else {
                b += 3;
                memcpy(cp, &v, sizeof(float));
                cp += sizeof(float);
            }
        }
    }
    for (; i < 6; ++i) {
        float v = coeff[i];

        b <<= 1;
        if (v != 0) {
            ++b;
            memcpy(cp, &v, sizeof(float));
            cp += sizeof(float);
        }
    }
    buf[0] = b << 2;
    return sputs(s, buf, cp - buf, &ignore);
}

/* Get a matrix from a stream. */
int
sget_matrix(stream *s, gs_matrix *pmat)
{
    int b = sgetc(s);
    float coeff[6];
    int i;
    int status;
    uint nread;

    if (b < 0)
        return b;
    for (i = 0; i < 4; i += 2, b <<= 2)
        if (!(b & 0xc0))
            coeff[i] = coeff[i ^ 3] = 0.0;
        else {
            float value;

            status = sgets(s, (byte *)&value, sizeof(value), &nread);
            if (status < 0 && status != EOFC)
                return_error(gs_error_ioerror);
            coeff[i] = value;
            switch ((b >> 6) & 3) {
                case 1:
                    coeff[i ^ 3] = value;
                    break;
                case 2:
                    coeff[i ^ 3] = -value;
                    break;
                case 3:
                    status = sgets(s, (byte *)&coeff[i ^ 3],
                                   sizeof(coeff[0]), &nread);
                    if (status < 0 && status != EOFC)
                        return_error(gs_error_ioerror);
            }
        }
    for (; i < 6; ++i, b <<= 1)
        if (b & 0x80) {
            status = sgets(s, (byte *)&coeff[i], sizeof(coeff[0]), &nread);
            if (status < 0 && status != EOFC)
                return_error(gs_error_ioerror);
        } else
            coeff[i] = 0.0;
    pmat->xx = coeff[0];
    pmat->xy = coeff[1];
    pmat->yx = coeff[2];
    pmat->yy = coeff[3];
    pmat->tx = coeff[4];
    pmat->ty = coeff[5];
    return 0;
}

/* Compare two matrices */
int
gs_matrix_compare(const gs_matrix *pmat1, const gs_matrix *pmat2) {
  if (pmat1->xx != pmat2->xx)
    return(1);
  if (pmat1->xy != pmat2->xy)
    return(1);
  if (pmat1->yx != pmat2->yx)
    return(1);
  if (pmat1->yy != pmat2->yy)
    return(1);
  if (pmat1->tx != pmat2->tx)
    return(1);
  if (pmat1->ty != pmat2->ty)
    return(1);
  return(0);
}