The Tor Browser: gfx/cairo/libpixman/src/pixman-matrix.c@b8a032363ba2 (annotated)

gfx/cairo/libpixman/src/pixman-matrix.c@b8a032363ba2 (annotated)

gfx/cairo/libpixman/src/pixman-matrix.c

Thu, 22 Jan 2015 13:21:57 +0100

author: Michael Schloh von Bennewitz <michael@schloh.com>
date: Thu, 22 Jan 2015 13:21:57 +0100
branch: TOR_BUG_9701
changeset 15: b8a032363ba2
permissions: -rw-r--r--

Incorporate requested changes from Mozilla in review:
https://bugzilla.mozilla.org/show_bug.cgi?id=1123480#c6

 /*
  * Copyright © 2008 Keith Packard
  *
  * Permission to use, copy, modify, distribute, and sell this software and its
  * documentation for any purpose is hereby granted without fee, provided that
  * the above copyright notice appear in all copies and that both that copyright
  * notice and this permission notice appear in supporting documentation, and
  * that the name of the copyright holders not be used in advertising or
  * publicity pertaining to distribution of the software without specific,
  * written prior permission.  The copyright holders make no representations
  * about the suitability of this software for any purpose.  It is provided "as
  * is" without express or implied warranty.
  *
  * THE COPYRIGHT HOLDERS DISCLAIM ALL WARRANTIES WITH REGARD TO THIS SOFTWARE,
  * INCLUDING ALL IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS, IN NO
  * EVENT SHALL THE COPYRIGHT HOLDERS BE LIABLE FOR ANY SPECIAL, INDIRECT OR
  * CONSEQUENTIAL DAMAGES OR ANY DAMAGES WHATSOEVER RESULTING FROM LOSS OF USE,
  * DATA OR PROFITS, WHETHER IN AN ACTION OF CONTRACT, NEGLIGENCE OR OTHER
  * TORTIOUS ACTION, ARISING OUT OF OR IN CONNECTION WITH THE USE OR PERFORMANCE
  * OF THIS SOFTWARE.
  */
 /*
  * Matrix interfaces
  */
 #ifdef HAVE_CONFIG_H
 #include <config.h>
 #endif
 #include <math.h>
 #include <string.h>
 #include "pixman-private.h"
 #define F(x)    pixman_int_to_fixed (x)
 static force_inline int
 count_leading_zeros (uint32_t x)
 {
 #ifdef __GNUC__
     return __builtin_clz (x);
 #else
     int n = 0;
     while (x)
     {
         n++;
         x >>= 1;
     }
     return 32 - n;
 #endif
 }
 /*
  * Large signed/unsigned integer division with rounding for the platforms with
  * only 64-bit integer data type supported (no 128-bit data type).
  *
  * Arguments:
  *     hi, lo - high and low 64-bit parts of the dividend
  *     div    - 48-bit divisor
  *
  * Returns: lowest 64 bits of the result as a return value and highest 64
  *          bits of the result to "result_hi" pointer
  */
 /* grade-school unsigned division (128-bit by 48-bit) with rounding to nearest */
 static force_inline uint64_t
 rounded_udiv_128_by_48 (uint64_t  hi,
                         uint64_t  lo,
                         uint64_t  div,
                         uint64_t *result_hi)
 {
     uint64_t tmp, remainder, result_lo;
     assert(div < ((uint64_t)1 << 48));
     remainder = hi % div;
     *result_hi = hi / div;
     tmp = (remainder << 16) + (lo >> 48);
     result_lo = tmp / div;
     remainder = tmp % div;
     tmp = (remainder << 16) + ((lo >> 32) & 0xFFFF);
     result_lo = (result_lo << 16) + (tmp / div);
     remainder = tmp % div;
     tmp = (remainder << 16) + ((lo >> 16) & 0xFFFF);
     result_lo = (result_lo << 16) + (tmp / div);
     remainder = tmp % div;
     tmp = (remainder << 16) + (lo & 0xFFFF);
     result_lo = (result_lo << 16) + (tmp / div);
     remainder = tmp % div;
     /* round to nearest */
     if (remainder * 2 >= div && ++result_lo == 0)
         *result_hi += 1;
     return result_lo;
 }
 /* signed division (128-bit by 49-bit) with rounding to nearest */
 static inline int64_t
 rounded_sdiv_128_by_49 (int64_t   hi,
                         uint64_t  lo,
                         int64_t   div,
                         int64_t  *signed_result_hi)
 {
     uint64_t result_lo, result_hi;
     int sign = 0;
     if (div < 0)
     {
         div = -div;
         sign ^= 1;
     }
     if (hi < 0)
     {
         if (lo != 0)
             hi++;
         hi = -hi;
         lo = -lo;
         sign ^= 1;
     }
     result_lo = rounded_udiv_128_by_48 (hi, lo, div, &result_hi);
     if (sign)
     {
         if (result_lo != 0)
             result_hi++;
         result_hi = -result_hi;
         result_lo = -result_lo;
     }
     if (signed_result_hi)
     {
         *signed_result_hi = result_hi;
     }
     return result_lo;
 }
 /*
  * Multiply 64.16 fixed point value by (2^scalebits) and convert
  * to 128-bit integer.
  */
 static force_inline void
 fixed_64_16_to_int128 (int64_t  hi,
                        int64_t  lo,
                        int64_t *rhi,
                        int64_t *rlo,
                        int      scalebits)
 {
     /* separate integer and fractional parts */
     hi += lo >> 16;
     lo &= 0xFFFF;
     if (scalebits <= 0)
     {
         *rlo = hi >> (-scalebits);
         *rhi = *rlo >> 63;
     }
     else
     {
         *rhi = hi >> (64 - scalebits);
         *rlo = (uint64_t)hi << scalebits;
         if (scalebits < 16)
             *rlo += lo >> (16 - scalebits);
         else
             *rlo += lo << (scalebits - 16);
     }
 }
 /*
  * Convert 112.16 fixed point value to 48.16 with clamping for the out
  * of range values.
  */
 static force_inline pixman_fixed_48_16_t
 fixed_112_16_to_fixed_48_16 (int64_t hi, int64_t lo, pixman_bool_t *clampflag)
 {
     if ((lo >> 63) != hi)
     {
         *clampflag = TRUE;
         return hi >= 0 ? INT64_MAX : INT64_MIN;
     }
     else
     {
         return lo;
     }
 }
 /*
  * Transform a point with 31.16 fixed point coordinates from the destination
  * space to a point with 48.16 fixed point coordinates in the source space.
  * No overflows are possible for affine transformations and the results are
  * accurate including the least significant bit. Projective transformations
  * may overflow, in this case the results are just clamped to return maximum
  * or minimum 48.16 values (so that the caller can at least handle the NONE
  * and PAD repeats correctly) and the return value is FALSE to indicate that
  * such clamping has happened.
  */
 PIXMAN_EXPORT pixman_bool_t
 pixman_transform_point_31_16 (const pixman_transform_t    *t,
                               const pixman_vector_48_16_t *v,
                               pixman_vector_48_16_t       *result)
 {
     pixman_bool_t clampflag = FALSE;
     int i;
     int64_t tmp[3][2], divint;
     uint16_t divfrac;
     /* input vector values must have no more than 31 bits (including sign)
      * in the integer part */
     assert (v->v[0] <   ((pixman_fixed_48_16_t)1 << (30 + 16)));
     assert (v->v[0] >= -((pixman_fixed_48_16_t)1 << (30 + 16)));
     assert (v->v[1] <   ((pixman_fixed_48_16_t)1 << (30 + 16)));
     assert (v->v[1] >= -((pixman_fixed_48_16_t)1 << (30 + 16)));
     assert (v->v[2] <   ((pixman_fixed_48_16_t)1 << (30 + 16)));
     assert (v->v[2] >= -((pixman_fixed_48_16_t)1 << (30 + 16)));
     for (i = 0; i < 3; i++)
     {
         tmp[i][0] = (int64_t)t->matrix[i][0] * (v->v[0] >> 16);
         tmp[i][1] = (int64_t)t->matrix[i][0] * (v->v[0] & 0xFFFF);
         tmp[i][0] += (int64_t)t->matrix[i][1] * (v->v[1] >> 16);
         tmp[i][1] += (int64_t)t->matrix[i][1] * (v->v[1] & 0xFFFF);
         tmp[i][0] += (int64_t)t->matrix[i][2] * (v->v[2] >> 16);
         tmp[i][1] += (int64_t)t->matrix[i][2] * (v->v[2] & 0xFFFF);
     }
     /*
      * separate 64-bit integer and 16-bit fractional parts for the divisor,
      * which is also scaled by 65536 after fixed point multiplication.
      */
     divint  = tmp[2][0] + (tmp[2][1] >> 16);
     divfrac = tmp[2][1] & 0xFFFF;
     if (divint == pixman_fixed_1 && divfrac == 0)
     {
         /*
          * this is a simple affine transformation
          */
         result->v[0] = tmp[0][0] + ((tmp[0][1] + 0x8000) >> 16);
         result->v[1] = tmp[1][0] + ((tmp[1][1] + 0x8000) >> 16);
         result->v[2] = pixman_fixed_1;
     }
     else if (divint == 0 && divfrac == 0)
     {
         /*
          * handle zero divisor (if the values are non-zero, set the
          * results to maximum positive or minimum negative)
          */
         clampflag = TRUE;
         result->v[0] = tmp[0][0] + ((tmp[0][1] + 0x8000) >> 16);
         result->v[1] = tmp[1][0] + ((tmp[1][1] + 0x8000) >> 16);
         if (result->v[0] > 0)
             result->v[0] = INT64_MAX;
         else if (result->v[0] < 0)
             result->v[0] = INT64_MIN;
         if (result->v[1] > 0)
             result->v[1] = INT64_MAX;
         else if (result->v[1] < 0)
             result->v[1] = INT64_MIN;
     }
     else
     {
         /*
          * projective transformation, analyze the top 32 bits of the divisor
          */
         int32_t hi32divbits = divint >> 32;
         if (hi32divbits < 0)
             hi32divbits = ~hi32divbits;
         if (hi32divbits == 0)
         {
             /* the divisor is small, we can actually keep all the bits */
             int64_t hi, rhi, lo, rlo;
             int64_t div = (divint << 16) + divfrac;
             fixed_64_16_to_int128 (tmp[0][0], tmp[0][1], &hi, &lo, 32);
             rlo = rounded_sdiv_128_by_49 (hi, lo, div, &rhi);
             result->v[0] = fixed_112_16_to_fixed_48_16 (rhi, rlo, &clampflag);
             fixed_64_16_to_int128 (tmp[1][0], tmp[1][1], &hi, &lo, 32);
             rlo = rounded_sdiv_128_by_49 (hi, lo, div, &rhi);
             result->v[1] = fixed_112_16_to_fixed_48_16 (rhi, rlo, &clampflag);
         }
         else
         {
             /* the divisor needs to be reduced to 48 bits */
             int64_t hi, rhi, lo, rlo, div;
             int shift = 32 - count_leading_zeros (hi32divbits);
             fixed_64_16_to_int128 (divint, divfrac, &hi, &div, 16 - shift);
             fixed_64_16_to_int128 (tmp[0][0], tmp[0][1], &hi, &lo, 32 - shift);
             rlo = rounded_sdiv_128_by_49 (hi, lo, div, &rhi);
             result->v[0] = fixed_112_16_to_fixed_48_16 (rhi, rlo, &clampflag);
             fixed_64_16_to_int128 (tmp[1][0], tmp[1][1], &hi, &lo, 32 - shift);
             rlo = rounded_sdiv_128_by_49 (hi, lo, div, &rhi);
             result->v[1] = fixed_112_16_to_fixed_48_16 (rhi, rlo, &clampflag);
         }
     }
     result->v[2] = pixman_fixed_1;
     return !clampflag;
 }
 PIXMAN_EXPORT void
 pixman_transform_point_31_16_affine (const pixman_transform_t    *t,
                                      const pixman_vector_48_16_t *v,
                                      pixman_vector_48_16_t       *result)
 {
     int64_t hi0, lo0, hi1, lo1;
     /* input vector values must have no more than 31 bits (including sign)
      * in the integer part */
     assert (v->v[0] <   ((pixman_fixed_48_16_t)1 << (30 + 16)));
     assert (v->v[0] >= -((pixman_fixed_48_16_t)1 << (30 + 16)));
     assert (v->v[1] <   ((pixman_fixed_48_16_t)1 << (30 + 16)));
     assert (v->v[1] >= -((pixman_fixed_48_16_t)1 << (30 + 16)));
     hi0  = (int64_t)t->matrix[0][0] * (v->v[0] >> 16);
     lo0  = (int64_t)t->matrix[0][0] * (v->v[0] & 0xFFFF);
     hi0 += (int64_t)t->matrix[0][1] * (v->v[1] >> 16);
     lo0 += (int64_t)t->matrix[0][1] * (v->v[1] & 0xFFFF);
     hi0 += (int64_t)t->matrix[0][2];
     hi1  = (int64_t)t->matrix[1][0] * (v->v[0] >> 16);
     lo1  = (int64_t)t->matrix[1][0] * (v->v[0] & 0xFFFF);
     hi1 += (int64_t)t->matrix[1][1] * (v->v[1] >> 16);
     lo1 += (int64_t)t->matrix[1][1] * (v->v[1] & 0xFFFF);
     hi1 += (int64_t)t->matrix[1][2];
     result->v[0] = hi0 + ((lo0 + 0x8000) >> 16);
     result->v[1] = hi1 + ((lo1 + 0x8000) >> 16);
     result->v[2] = pixman_fixed_1;
 }
 PIXMAN_EXPORT void
 pixman_transform_point_31_16_3d (const pixman_transform_t    *t,
                                  const pixman_vector_48_16_t *v,
                                  pixman_vector_48_16_t       *result)
 {
     int i;
     int64_t tmp[3][2];
     /* input vector values must have no more than 31 bits (including sign)
      * in the integer part */
     assert (v->v[0] <   ((pixman_fixed_48_16_t)1 << (30 + 16)));
     assert (v->v[0] >= -((pixman_fixed_48_16_t)1 << (30 + 16)));
     assert (v->v[1] <   ((pixman_fixed_48_16_t)1 << (30 + 16)));
     assert (v->v[1] >= -((pixman_fixed_48_16_t)1 << (30 + 16)));
     assert (v->v[2] <   ((pixman_fixed_48_16_t)1 << (30 + 16)));
     assert (v->v[2] >= -((pixman_fixed_48_16_t)1 << (30 + 16)));
     for (i = 0; i < 3; i++)
     {
         tmp[i][0] = (int64_t)t->matrix[i][0] * (v->v[0] >> 16);
         tmp[i][1] = (int64_t)t->matrix[i][0] * (v->v[0] & 0xFFFF);
         tmp[i][0] += (int64_t)t->matrix[i][1] * (v->v[1] >> 16);
         tmp[i][1] += (int64_t)t->matrix[i][1] * (v->v[1] & 0xFFFF);
         tmp[i][0] += (int64_t)t->matrix[i][2] * (v->v[2] >> 16);
         tmp[i][1] += (int64_t)t->matrix[i][2] * (v->v[2] & 0xFFFF);
     }
     result->v[0] = tmp[0][0] + ((tmp[0][1] + 0x8000) >> 16);
     result->v[1] = tmp[1][0] + ((tmp[1][1] + 0x8000) >> 16);
     result->v[2] = tmp[2][0] + ((tmp[2][1] + 0x8000) >> 16);
 }
 PIXMAN_EXPORT void
 pixman_transform_init_identity (struct pixman_transform *matrix)
 {
     int i;
     memset (matrix, '\0', sizeof (struct pixman_transform));
     for (i = 0; i < 3; i++)
 	matrix->matrix[i][i] = F (1);
 }
 typedef pixman_fixed_32_32_t pixman_fixed_34_30_t;
 PIXMAN_EXPORT pixman_bool_t
 pixman_transform_point_3d (const struct pixman_transform *transform,
                            struct pixman_vector *         vector)
 {
     pixman_vector_48_16_t tmp;
     tmp.v[0] = vector->vector[0];
     tmp.v[1] = vector->vector[1];
     tmp.v[2] = vector->vector[2];
     pixman_transform_point_31_16_3d (transform, &tmp, &tmp);
     vector->vector[0] = tmp.v[0];
     vector->vector[1] = tmp.v[1];
     vector->vector[2] = tmp.v[2];
     return vector->vector[0] == tmp.v[0] &&
            vector->vector[1] == tmp.v[1] &&
            vector->vector[2] == tmp.v[2];
 }
 PIXMAN_EXPORT pixman_bool_t
 pixman_transform_point (const struct pixman_transform *transform,
                         struct pixman_vector *         vector)
 {
     pixman_vector_48_16_t tmp;
     tmp.v[0] = vector->vector[0];
     tmp.v[1] = vector->vector[1];
     tmp.v[2] = vector->vector[2];
     if (!pixman_transform_point_31_16 (transform, &tmp, &tmp))
         return FALSE;
     vector->vector[0] = tmp.v[0];
     vector->vector[1] = tmp.v[1];
     vector->vector[2] = tmp.v[2];
     return vector->vector[0] == tmp.v[0] &&
            vector->vector[1] == tmp.v[1] &&
            vector->vector[2] == tmp.v[2];
 }
 PIXMAN_EXPORT pixman_bool_t
 pixman_transform_multiply (struct pixman_transform *      dst,
                            const struct pixman_transform *l,
                            const struct pixman_transform *r)
 {
     struct pixman_transform d;
     int dx, dy;
     int o;
     for (dy = 0; dy < 3; dy++)
     {
 	for (dx = 0; dx < 3; dx++)
 	{
 	    pixman_fixed_48_16_t v;
 	    pixman_fixed_32_32_t partial;
 	    v = 0;
 	    for (o = 0; o < 3; o++)
 	    {
 		partial =
 		    (pixman_fixed_32_32_t) l->matrix[dy][o] *
 		    (pixman_fixed_32_32_t) r->matrix[o][dx];
 		v += (partial + 0x8000) >> 16;
 	    }
 	    if (v > pixman_max_fixed_48_16 || v < pixman_min_fixed_48_16)
 		return FALSE;
 	    d.matrix[dy][dx] = (pixman_fixed_t) v;
 	}
     }
     *dst = d;
     return TRUE;
 }
 PIXMAN_EXPORT void
 pixman_transform_init_scale (struct pixman_transform *t,
                              pixman_fixed_t           sx,
                              pixman_fixed_t           sy)
 {
     memset (t, '\0', sizeof (struct pixman_transform));
     t->matrix[0][0] = sx;
     t->matrix[1][1] = sy;
     t->matrix[2][2] = F (1);
 }
 static pixman_fixed_t
 fixed_inverse (pixman_fixed_t x)
 {
     return (pixman_fixed_t) ((((pixman_fixed_48_16_t) F (1)) * F (1)) / x);
 }
 PIXMAN_EXPORT pixman_bool_t
 pixman_transform_scale (struct pixman_transform *forward,
                         struct pixman_transform *reverse,
                         pixman_fixed_t           sx,
                         pixman_fixed_t           sy)
 {
     struct pixman_transform t;
     if (sx == 0 || sy == 0)
 	return FALSE;
     if (forward)
     {
 	pixman_transform_init_scale (&t, sx, sy);
 	if (!pixman_transform_multiply (forward, &t, forward))
 	    return FALSE;
     }
     if (reverse)
     {
 	pixman_transform_init_scale (&t, fixed_inverse (sx),
 	                             fixed_inverse (sy));
 	if (!pixman_transform_multiply (reverse, reverse, &t))
 	    return FALSE;
     }
     return TRUE;
 }
 PIXMAN_EXPORT void
 pixman_transform_init_rotate (struct pixman_transform *t,
                               pixman_fixed_t           c,
                               pixman_fixed_t           s)
 {
     memset (t, '\0', sizeof (struct pixman_transform));
     t->matrix[0][0] = c;
     t->matrix[0][1] = -s;
     t->matrix[1][0] = s;
     t->matrix[1][1] = c;
     t->matrix[2][2] = F (1);
 }
 PIXMAN_EXPORT pixman_bool_t
 pixman_transform_rotate (struct pixman_transform *forward,
                          struct pixman_transform *reverse,
                          pixman_fixed_t           c,
                          pixman_fixed_t           s)
 {
     struct pixman_transform t;
     if (forward)
     {
 	pixman_transform_init_rotate (&t, c, s);
 	if (!pixman_transform_multiply (forward, &t, forward))
 	    return FALSE;
     }
     if (reverse)
     {
 	pixman_transform_init_rotate (&t, c, -s);
 	if (!pixman_transform_multiply (reverse, reverse, &t))
 	    return FALSE;
     }
     return TRUE;
 }
 PIXMAN_EXPORT void
 pixman_transform_init_translate (struct pixman_transform *t,
                                  pixman_fixed_t           tx,
                                  pixman_fixed_t           ty)
 {
     memset (t, '\0', sizeof (struct pixman_transform));
     t->matrix[0][0] = F (1);
     t->matrix[0][2] = tx;
     t->matrix[1][1] = F (1);
     t->matrix[1][2] = ty;
     t->matrix[2][2] = F (1);
 }
 PIXMAN_EXPORT pixman_bool_t
 pixman_transform_translate (struct pixman_transform *forward,
                             struct pixman_transform *reverse,
                             pixman_fixed_t           tx,
                             pixman_fixed_t           ty)
 {
     struct pixman_transform t;
     if (forward)
     {
 	pixman_transform_init_translate (&t, tx, ty);
 	if (!pixman_transform_multiply (forward, &t, forward))
 	    return FALSE;
     }
     if (reverse)
     {
 	pixman_transform_init_translate (&t, -tx, -ty);
 	if (!pixman_transform_multiply (reverse, reverse, &t))
 	    return FALSE;
     }
     return TRUE;
 }
 PIXMAN_EXPORT pixman_bool_t
 pixman_transform_bounds (const struct pixman_transform *matrix,
                          struct pixman_box16 *          b)
 {
     struct pixman_vector v[4];
     int i;
     int x1, y1, x2, y2;
     v[0].vector[0] = F (b->x1);
     v[0].vector[1] = F (b->y1);
     v[0].vector[2] = F (1);
     v[1].vector[0] = F (b->x2);
     v[1].vector[1] = F (b->y1);
     v[1].vector[2] = F (1);
     v[2].vector[0] = F (b->x2);
     v[2].vector[1] = F (b->y2);
     v[2].vector[2] = F (1);
     v[3].vector[0] = F (b->x1);
     v[3].vector[1] = F (b->y2);
     v[3].vector[2] = F (1);
     for (i = 0; i < 4; i++)
     {
 	if (!pixman_transform_point (matrix, &v[i]))
 	    return FALSE;
 	x1 = pixman_fixed_to_int (v[i].vector[0]);
 	y1 = pixman_fixed_to_int (v[i].vector[1]);
 	x2 = pixman_fixed_to_int (pixman_fixed_ceil (v[i].vector[0]));
 	y2 = pixman_fixed_to_int (pixman_fixed_ceil (v[i].vector[1]));
 	if (i == 0)
 	{
 	    b->x1 = x1;
 	    b->y1 = y1;
 	    b->x2 = x2;
 	    b->y2 = y2;
 	}
 	else
 	{
 	    if (x1 < b->x1) b->x1 = x1;
 	    if (y1 < b->y1) b->y1 = y1;
 	    if (x2 > b->x2) b->x2 = x2;
 	    if (y2 > b->y2) b->y2 = y2;
 	}
     }
     return TRUE;
 }
 PIXMAN_EXPORT pixman_bool_t
 pixman_transform_invert (struct pixman_transform *      dst,
                          const struct pixman_transform *src)
 {
     struct pixman_f_transform m;
     pixman_f_transform_from_pixman_transform (&m, src);
     if (!pixman_f_transform_invert (&m, &m))
 	return FALSE;
     if (!pixman_transform_from_pixman_f_transform (dst, &m))
 	return FALSE;
     return TRUE;
 }
 static pixman_bool_t
 within_epsilon (pixman_fixed_t a,
                 pixman_fixed_t b,
                 pixman_fixed_t epsilon)
 {
     pixman_fixed_t t = a - b;
     if (t < 0)
 	t = -t;
     return t <= epsilon;
 }
 #define EPSILON (pixman_fixed_t) (2)
 #define IS_SAME(a, b) (within_epsilon (a, b, EPSILON))
 #define IS_ZERO(a)    (within_epsilon (a, 0, EPSILON))
 #define IS_ONE(a)     (within_epsilon (a, F (1), EPSILON))
 #define IS_UNIT(a)			    \
     (within_epsilon (a, F (1), EPSILON) ||  \
      within_epsilon (a, F (-1), EPSILON) || \
      IS_ZERO (a))
 #define IS_INT(a)    (IS_ZERO (pixman_fixed_frac (a)))
 PIXMAN_EXPORT pixman_bool_t
 pixman_transform_is_identity (const struct pixman_transform *t)
 {
     return (IS_SAME (t->matrix[0][0], t->matrix[1][1]) &&
 	    IS_SAME (t->matrix[0][0], t->matrix[2][2]) &&
 	    !IS_ZERO (t->matrix[0][0]) &&
 	    IS_ZERO (t->matrix[0][1]) &&
 	    IS_ZERO (t->matrix[0][2]) &&
 	    IS_ZERO (t->matrix[1][0]) &&
 	    IS_ZERO (t->matrix[1][2]) &&
 	    IS_ZERO (t->matrix[2][0]) &&
 	    IS_ZERO (t->matrix[2][1]));
 }
 PIXMAN_EXPORT pixman_bool_t
 pixman_transform_is_scale (const struct pixman_transform *t)
 {
     return (!IS_ZERO (t->matrix[0][0]) &&
             IS_ZERO (t->matrix[0][1]) &&
             IS_ZERO (t->matrix[0][2]) &&
             IS_ZERO (t->matrix[1][0]) &&
             !IS_ZERO (t->matrix[1][1]) &&
             IS_ZERO (t->matrix[1][2]) &&
             IS_ZERO (t->matrix[2][0]) &&
             IS_ZERO (t->matrix[2][1]) &&
             !IS_ZERO (t->matrix[2][2]));
 }
 PIXMAN_EXPORT pixman_bool_t
 pixman_transform_is_int_translate (const struct pixman_transform *t)
 {
     return (IS_ONE (t->matrix[0][0]) &&
             IS_ZERO (t->matrix[0][1]) &&
             IS_INT (t->matrix[0][2]) &&
             IS_ZERO (t->matrix[1][0]) &&
             IS_ONE (t->matrix[1][1]) &&
             IS_INT (t->matrix[1][2]) &&
             IS_ZERO (t->matrix[2][0]) &&
             IS_ZERO (t->matrix[2][1]) &&
             IS_ONE (t->matrix[2][2]));
 }
 PIXMAN_EXPORT pixman_bool_t
 pixman_transform_is_inverse (const struct pixman_transform *a,
                              const struct pixman_transform *b)
 {
     struct pixman_transform t;
     if (!pixman_transform_multiply (&t, a, b))
 	return FALSE;
     return pixman_transform_is_identity (&t);
 }
 PIXMAN_EXPORT void
 pixman_f_transform_from_pixman_transform (struct pixman_f_transform *    ft,
                                           const struct pixman_transform *t)
 {
     int i, j;
     for (j = 0; j < 3; j++)
     {
 	for (i = 0; i < 3; i++)
 	    ft->m[j][i] = pixman_fixed_to_double (t->matrix[j][i]);
     }
 }
 PIXMAN_EXPORT pixman_bool_t
 pixman_transform_from_pixman_f_transform (struct pixman_transform *        t,
                                           const struct pixman_f_transform *ft)
 {
     int i, j;
     for (j = 0; j < 3; j++)
     {
 	for (i = 0; i < 3; i++)
 	{
 	    double d = ft->m[j][i];
 	    if (d < -32767.0 || d > 32767.0)
 		return FALSE;
 	    d = d * 65536.0 + 0.5;
 	    t->matrix[j][i] = (pixman_fixed_t) floor (d);
 	}
     }
     return TRUE;
 }
 PIXMAN_EXPORT pixman_bool_t
 pixman_f_transform_invert (struct pixman_f_transform *      dst,
                            const struct pixman_f_transform *src)
 {
     static const int a[3] = { 2, 2, 1 };
     static const int b[3] = { 1, 0, 0 };
     pixman_f_transform_t d;
     double det;
     int i, j;
     det = 0;
     for (i = 0; i < 3; i++)
     {
 	double p;
 	int ai = a[i];
 	int bi = b[i];
 	p = src->m[i][0] * (src->m[ai][2] * src->m[bi][1] -
 	                    src->m[ai][1] * src->m[bi][2]);
 	if (i == 1)
 	    p = -p;
 	det += p;
     }
     if (det == 0)
 	return FALSE;
     det = 1 / det;
     for (j = 0; j < 3; j++)
     {
 	for (i = 0; i < 3; i++)
 	{
 	    double p;
 	    int ai = a[i];
 	    int aj = a[j];
 	    int bi = b[i];
 	    int bj = b[j];
 	    p = (src->m[ai][aj] * src->m[bi][bj] -
 	         src->m[ai][bj] * src->m[bi][aj]);
 	    if (((i + j) & 1) != 0)
 		p = -p;
 	    d.m[j][i] = det * p;
 	}
     }
     *dst = d;
     return TRUE;
 }
 PIXMAN_EXPORT pixman_bool_t
 pixman_f_transform_point (const struct pixman_f_transform *t,
                           struct pixman_f_vector *         v)
 {
     struct pixman_f_vector result;
     int i, j;
     double a;
     for (j = 0; j < 3; j++)
     {
 	a = 0;
 	for (i = 0; i < 3; i++)
 	    a += t->m[j][i] * v->v[i];
 	result.v[j] = a;
     }
     if (!result.v[2])
 	return FALSE;
     for (j = 0; j < 2; j++)
 	v->v[j] = result.v[j] / result.v[2];
     v->v[2] = 1;
     return TRUE;
 }
 PIXMAN_EXPORT void
 pixman_f_transform_point_3d (const struct pixman_f_transform *t,
                              struct pixman_f_vector *         v)
 {
     struct pixman_f_vector result;
     int i, j;
     double a;
     for (j = 0; j < 3; j++)
     {
 	a = 0;
 	for (i = 0; i < 3; i++)
 	    a += t->m[j][i] * v->v[i];
 	result.v[j] = a;
     }
     *v = result;
 }
 PIXMAN_EXPORT void
 pixman_f_transform_multiply (struct pixman_f_transform *      dst,
                              const struct pixman_f_transform *l,
                              const struct pixman_f_transform *r)
 {
     struct pixman_f_transform d;
     int dx, dy;
     int o;
     for (dy = 0; dy < 3; dy++)
     {
 	for (dx = 0; dx < 3; dx++)
 	{
 	    double v = 0;
 	    for (o = 0; o < 3; o++)
 		v += l->m[dy][o] * r->m[o][dx];
 	    d.m[dy][dx] = v;
 	}
     }
     *dst = d;
 }
 PIXMAN_EXPORT void
 pixman_f_transform_init_scale (struct pixman_f_transform *t,
                                double                     sx,
                                double                     sy)
 {
     t->m[0][0] = sx;
     t->m[0][1] = 0;
     t->m[0][2] = 0;
     t->m[1][0] = 0;
     t->m[1][1] = sy;
     t->m[1][2] = 0;
     t->m[2][0] = 0;
     t->m[2][1] = 0;
     t->m[2][2] = 1;
 }
 PIXMAN_EXPORT pixman_bool_t
 pixman_f_transform_scale (struct pixman_f_transform *forward,
                           struct pixman_f_transform *reverse,
                           double                     sx,
                           double                     sy)
 {
     struct pixman_f_transform t;
     if (sx == 0 || sy == 0)
 	return FALSE;
     if (forward)
     {
 	pixman_f_transform_init_scale (&t, sx, sy);
 	pixman_f_transform_multiply (forward, &t, forward);
     }
     if (reverse)
     {
 	pixman_f_transform_init_scale (&t, 1 / sx, 1 / sy);
 	pixman_f_transform_multiply (reverse, reverse, &t);
     }
     return TRUE;
 }
 PIXMAN_EXPORT void
 pixman_f_transform_init_rotate (struct pixman_f_transform *t,
                                 double                     c,
                                 double                     s)
 {
     t->m[0][0] = c;
     t->m[0][1] = -s;
     t->m[0][2] = 0;
     t->m[1][0] = s;
     t->m[1][1] = c;
     t->m[1][2] = 0;
     t->m[2][0] = 0;
     t->m[2][1] = 0;
     t->m[2][2] = 1;
 }
 PIXMAN_EXPORT pixman_bool_t
 pixman_f_transform_rotate (struct pixman_f_transform *forward,
                            struct pixman_f_transform *reverse,
                            double                     c,
                            double                     s)
 {
     struct pixman_f_transform t;
     if (forward)
     {
 	pixman_f_transform_init_rotate (&t, c, s);
 	pixman_f_transform_multiply (forward, &t, forward);
     }
     if (reverse)
     {
 	pixman_f_transform_init_rotate (&t, c, -s);
 	pixman_f_transform_multiply (reverse, reverse, &t);
     }
     return TRUE;
 }
 PIXMAN_EXPORT void
 pixman_f_transform_init_translate (struct pixman_f_transform *t,
                                    double                     tx,
                                    double                     ty)
 {
     t->m[0][0] = 1;
     t->m[0][1] = 0;
     t->m[0][2] = tx;
     t->m[1][0] = 0;
     t->m[1][1] = 1;
     t->m[1][2] = ty;
     t->m[2][0] = 0;
     t->m[2][1] = 0;
     t->m[2][2] = 1;
 }
 PIXMAN_EXPORT pixman_bool_t
 pixman_f_transform_translate (struct pixman_f_transform *forward,
                               struct pixman_f_transform *reverse,
                               double                     tx,
                               double                     ty)
 {
     struct pixman_f_transform t;
     if (forward)
     {
 	pixman_f_transform_init_translate (&t, tx, ty);
 	pixman_f_transform_multiply (forward, &t, forward);
     }
     if (reverse)
     {
 	pixman_f_transform_init_translate (&t, -tx, -ty);
 	pixman_f_transform_multiply (reverse, reverse, &t);
     }
     return TRUE;
 }
 PIXMAN_EXPORT pixman_bool_t
 pixman_f_transform_bounds (const struct pixman_f_transform *t,
                            struct pixman_box16 *            b)
 {
     struct pixman_f_vector v[4];
     int i;
     int x1, y1, x2, y2;
     v[0].v[0] = b->x1;
     v[0].v[1] = b->y1;
     v[0].v[2] = 1;
     v[1].v[0] = b->x2;
     v[1].v[1] = b->y1;
     v[1].v[2] = 1;
     v[2].v[0] = b->x2;
     v[2].v[1] = b->y2;
     v[2].v[2] = 1;
     v[3].v[0] = b->x1;
     v[3].v[1] = b->y2;
     v[3].v[2] = 1;
     for (i = 0; i < 4; i++)
     {
 	if (!pixman_f_transform_point (t, &v[i]))
 	    return FALSE;
 	x1 = floor (v[i].v[0]);
 	y1 = floor (v[i].v[1]);
 	x2 = ceil (v[i].v[0]);
 	y2 = ceil (v[i].v[1]);
 	if (i == 0)
 	{
 	    b->x1 = x1;
 	    b->y1 = y1;
 	    b->x2 = x2;
 	    b->y2 = y2;
 	}
 	else
 	{
 	    if (x1 < b->x1) b->x1 = x1;
 	    if (y1 < b->y1) b->y1 = y1;
 	    if (x2 > b->x2) b->x2 = x2;
 	    if (y2 > b->y2) b->y2 = y2;
 	}
     }
     return TRUE;
 }
 PIXMAN_EXPORT void
 pixman_f_transform_init_identity (struct pixman_f_transform *t)
 {
     int i, j;
     for (j = 0; j < 3; j++)
     {
 	for (i = 0; i < 3; i++)
 	    t->m[j][i] = i == j ? 1 : 0;
     }
 }

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gfx/cairo/libpixman/src/pixman-matrix.c@b8a032363ba2 (annotated)

gfx/cairo/libpixman/src/pixman-matrix.c