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-rw-r--r--libs/pixman-0.40.0/pixman/pixman-matrix.c1073
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diff --git a/libs/pixman-0.40.0/pixman/pixman-matrix.c b/libs/pixman-0.40.0/pixman/pixman-matrix.c
new file mode 100644
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--- /dev/null
+++ b/libs/pixman-0.40.0/pixman/pixman-matrix.c
@@ -0,0 +1,1073 @@
+/*
+ * 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 HAVE_BUILTIN_CLZ
+ 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 = ((uint64_t)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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