From 540de34453d16092acd2978b513831a02f01f59f Mon Sep 17 00:00:00 2001
From: Chris Wilson <chris@chris-wilson.co.uk>
Date: Sun, 26 Oct 2008 12:53:29 +0000
Subject: [PATCH] [matrix] Optimise invert for simple scaling|translation
 matrices.

Peter Hercek reported, and provided a very useful test case for, a bug
that caused his applications to crash with Cairo detecting an
non-invertible pattern matrix and thus asserting the impossible happened.
Bisecting revealed that the bug first appeared with 3c18d95 and
disappeared with 0d0c6a1. Since neither of these explain the crash,
further investigation revealed a compiler bug (gcc 4.3.3 20081130,
earlier versions have different bugs!) that caused the matrix inversion
to be invalid iff _cairo_matrix_scalar_multiply() was inlined (i.e. -O0,
or an explicit noinline atttribute on that function prevented the bug, as
did -msse.) So we apply this workaround to hide the bug in the stable
series...

The matrix is quite often just a simple scale and translate (or even
identity!). For this class of matrix, we can skip the full adjoint
rearrangement and determinant calculation and just compute the inverse
directly.
(cherry picked from commit 0d0c6a199c5b631299c72dce80d66ac0f4936a64)
---
 src/cairo-matrix.c | 26 +++++++++++++++++++++++++-
 1 file changed, 25 insertions(+), 1 deletion(-)

diff --git a/src/cairo-matrix.c b/src/cairo-matrix.c
index ca1832306..6a29aeccb 100644
--- a/src/cairo-matrix.c
+++ b/src/cairo-matrix.c
@@ -485,9 +485,33 @@ _cairo_matrix_compute_adjoint (cairo_matrix_t *matrix)
 cairo_status_t
 cairo_matrix_invert (cairo_matrix_t *matrix)
 {
-    /* inv (A) = 1/det (A) * adj (A) */
     double det;
 
+    /* Simple scaling|translation matrices are quite common... */
+    if (matrix->xy == 0. && matrix->yx == 0.) {
+	matrix->x0 = -matrix->x0;
+	matrix->y0 = -matrix->y0;
+
+	if (matrix->xx != 1.) {
+	    if (matrix->xx == 0.)
+		return _cairo_error (CAIRO_STATUS_INVALID_MATRIX);
+
+	    matrix->xx = 1. / matrix->xx;
+	    matrix->x0 *= matrix->xx;
+	}
+
+	if (matrix->yy != 1.) {
+	    if (matrix->yy == 0.)
+		return _cairo_error (CAIRO_STATUS_INVALID_MATRIX);
+
+	    matrix->yy = 1. / matrix->yy;
+	    matrix->y0 *= matrix->yy;
+	}
+
+	return CAIRO_STATUS_SUCCESS;
+    }
+
+    /* inv (A) = 1/det (A) * adj (A) */
     det = _cairo_matrix_compute_determinant (matrix);
 
     if (! ISFINITE (det))