From 0d0c6a199c5b631299c72dce80d66ac0f4936a64 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.

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.
---
 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 643c9867e..b644dec82 100644
--- a/src/cairo-matrix.c
+++ b/src/cairo-matrix.c
@@ -525,9 +525,33 @@ _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))