glsl: add determinant() functions.

These functions are defined in GLSL 1.50 and GLES 3.00 ES.

The formulas have been extracted from the existing implementation of
inverse().

Reviewed-by: Ian Romanick <ian.d.romanick@intel.com>
Reviewed-by: Kenneth Graunke <kenneth@whitecape.org>
Reviewed-by: Eric Anholt <eric@anholt.net>
Acked-by: Carl Worth <cworth@cworth.org>

diff --git a/src/glsl/builtins/glsl/determinant.glsl b/src/glsl/builtins/glsl/determinant.glsl
new file mode 100644 (file)
index 0000000..32695a8
--- /dev/null
+++ b/src/glsl/builtins/glsl/determinant.glsl
@@ -0,0 +1,70 @@
+/*
+ * Copyright © 2012 Intel Corporation
+ *
+ * Permission is hereby granted, free of charge, to any person obtaining a
+ * copy of this software and associated documentation files (the "Software"),
+ * to deal in the Software without restriction, including without limitation
+ * the rights to use, copy, modify, merge, publish, distribute, sublicense,
+ * and/or sell copies of the Software, and to permit persons to whom the
+ * Software is furnished to do so, subject to the following conditions:
+ *
+ * The above copyright notice and this permission notice (including the next
+ * paragraph) shall be included in all copies or substantial portions of the
+ * Software.
+ *
+ * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+ * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+ * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.  IN NO EVENT SHALL
+ * THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+ * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
+ * FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER
+ * DEALINGS IN THE SOFTWARE.
+ */
+
+#version 120
+float determinant(mat2 m)
+{
+   return m[0][0] * m[1][1] - m[1][0] * m[0][1];
+}
+
+float determinant(mat3 m)
+{
+   return (+ m[0][0] * (m[1][1] * m[2][2] - m[1][2] * m[2][1])
+           - m[0][1] * (m[1][0] * m[2][2] - m[1][2] * m[2][0])
+           + m[0][2] * (m[1][0] * m[2][1] - m[1][1] * m[2][0]));
+}
+
+float determinant(mat4 m)
+{
+   float SubFactor00 = m[2][2] * m[3][3] - m[3][2] * m[2][3];
+   float SubFactor01 = m[2][1] * m[3][3] - m[3][1] * m[2][3];
+   float SubFactor02 = m[2][1] * m[3][2] - m[3][1] * m[2][2];
+   float SubFactor03 = m[2][0] * m[3][3] - m[3][0] * m[2][3];
+   float SubFactor04 = m[2][0] * m[3][2] - m[3][0] * m[2][2];
+   float SubFactor05 = m[2][0] * m[3][1] - m[3][0] * m[2][1];
+   float SubFactor06 = m[1][2] * m[3][3] - m[3][2] * m[1][3];
+   float SubFactor07 = m[1][1] * m[3][3] - m[3][1] * m[1][3];
+   float SubFactor08 = m[1][1] * m[3][2] - m[3][1] * m[1][2];
+   float SubFactor09 = m[1][0] * m[3][3] - m[3][0] * m[1][3];
+   float SubFactor10 = m[1][0] * m[3][2] - m[3][0] * m[1][2];
+   float SubFactor11 = m[1][1] * m[3][3] - m[3][1] * m[1][3];
+   float SubFactor12 = m[1][0] * m[3][1] - m[3][0] * m[1][1];
+   float SubFactor13 = m[1][2] * m[2][3] - m[2][2] * m[1][3];
+   float SubFactor14 = m[1][1] * m[2][3] - m[2][1] * m[1][3];
+   float SubFactor15 = m[1][1] * m[2][2] - m[2][1] * m[1][2];
+   float SubFactor16 = m[1][0] * m[2][3] - m[2][0] * m[1][3];
+   float SubFactor17 = m[1][0] * m[2][2] - m[2][0] * m[1][2];
+   float SubFactor18 = m[1][0] * m[2][1] - m[2][0] * m[1][1];
+
+   vec4 adj_0;
+
+   adj_0[0] = + (m[1][1] * SubFactor00 - m[1][2] * SubFactor01 + m[1][3] * SubFactor02);
+   adj_0[1] = - (m[1][0] * SubFactor00 - m[1][2] * SubFactor03 + m[1][3] * SubFactor04);
+   adj_0[2] = + (m[1][0] * SubFactor01 - m[1][1] * SubFactor03 + m[1][3] * SubFactor05);
+   adj_0[3] = - (m[1][0] * SubFactor02 - m[1][1] * SubFactor04 + m[1][2] * SubFactor05);
+
+   return (+ m[0][0] * adj_0[0]
+           + m[0][1] * adj_0[1]
+           + m[0][2] * adj_0[2]
+           + m[0][3] * adj_0[3]);
+}