diff --git a/tools/qfcc/source/algebra.c b/tools/qfcc/source/algebra.c
index b1537322e..11550d82d 100644
--- a/tools/qfcc/source/algebra.c
+++ b/tools/qfcc/source/algebra.c
@@ -103,9 +103,9 @@ static const char *mvec_2d_names[] = {
 
 static const char *mvec_3d_names[] = {
 	"vec",
-	"scalar"
-	"bvec",
 	"tvec",
+	"bvec",
+	"scalar",
 	0
 };
 
@@ -339,11 +339,11 @@ algebra_init (algebra_t *a)
 		basis_layout_init (&a->layout, 4, a->groups);
 	} else if (p == 2 && m == 0 && z == 1) {
 		// 2d PGA (w squares to 0, x y square to +1):
-		// : yw  xw  xy  1
 		// : x   y   w   wxy
+		// : yw  wx  xy  1
 		basis_blade_t pga_blades[8] = {
-			blades[5], blades[4], blades[6], blades[0],
 			blades[2], blades[3], blades[1], blades[7],
+			blades[5], blades[4], blades[6], blades[0],
 		};
 		a->groups = malloc (sizeof (basis_group_t[4]));
 		a->mvec_types = alloc_mvec_types (4);
diff --git a/tools/qfcc/source/expr_algebra.c b/tools/qfcc/source/expr_algebra.c
index c65fd975f..a3217e7ef 100644
--- a/tools/qfcc/source/expr_algebra.c
+++ b/tools/qfcc/source/expr_algebra.c
@@ -816,7 +816,7 @@ pga2_yw_wx_xy_dot_yw_wx_xy (expr_t **c, expr_t *a, expr_t *b, algebra_t *alg)
 	auto sa = offset_cast (stype, a, 2);
 	auto sb = offset_cast (stype, b, 2);
 
-	c[1] = neg_expr (scale_expr (stype, sa, sb));
+	c[3] = neg_expr (scale_expr (stype, sa, sb));
 }
 
 static void
@@ -825,7 +825,7 @@ pga2_yw_wx_xy_dot_x_y_w (expr_t **c, expr_t *a, expr_t *b, algebra_t *alg)
 	auto stype = alg->type;
 	auto wtype = vector_type (stype, 2);
 	auto vtype = vector_type (stype, 3);
-	auto dot_type = algebra_mvec_type (alg, 0x04);
+	auto dot_type = algebra_mvec_type (alg, 0x01);
 	auto va = offset_cast (wtype, a, 0);
 	auto sa = offset_cast (stype, a, 2);
 	auto vb = offset_cast (wtype, b, 0);
@@ -833,7 +833,7 @@ pga2_yw_wx_xy_dot_x_y_w (expr_t **c, expr_t *a, expr_t *b, algebra_t *alg)
 	auto cs = wedge_expr (stype, vb, va);
 	cv = ext_expr (scale_expr (wtype, cv, sa), vtype, 0, false);
 	cs = ext_expr (cs, dot_type, 0, true);
-	c[2] = sum_expr (dot_type, cv, cs);
+	c[0] = sum_expr (dot_type, cv, cs);
 }
 
 static void
@@ -843,7 +843,7 @@ pga2_yw_wx_xy_dot_wxy (expr_t **c, expr_t *a, expr_t *b, algebra_t *alg)
 	auto sa = offset_cast (stype, a, 2);
 	auto sb = offset_cast (stype, b, 0);
 	auto cs = neg_expr (scale_expr (stype, sa, sb));
-	c[0] = ext_expr (cs, algebra_mvec_type (alg, 0x01), 0, true);
+	c[2] = ext_expr (cs, algebra_mvec_type (alg, 0x04), 0, true);
 }
 
 static void
@@ -851,7 +851,7 @@ pga2_x_y_w_dot_yw_wx_xy (expr_t **c, expr_t *a, expr_t *b, algebra_t *alg)
 {
 	auto stype = alg->type;
 	auto wtype = vector_type (stype, 2);
-	auto dot_type = algebra_mvec_type (alg, 0x04);
+	auto dot_type = algebra_mvec_type (alg, 0x01);
 	auto va = offset_cast (wtype, a, 0);
 	auto vb = offset_cast (wtype, b, 0);
 	auto sb = offset_cast (stype, b, 2);
@@ -859,7 +859,7 @@ pga2_x_y_w_dot_yw_wx_xy (expr_t **c, expr_t *a, expr_t *b, algebra_t *alg)
 	auto cs = wedge_expr (stype, vb, va);
 	cv = ext_expr (cv, dot_type, 0, false);
 	cs = ext_expr (cs, dot_type, 0, true);
-	c[2] = sum_expr (dot_type, cs, cv);
+	c[0] = sum_expr (dot_type, cs, cv);
 }
 
 static void
@@ -870,7 +870,7 @@ pga2_x_y_w_dot_x_y_w (expr_t **c, expr_t *a, expr_t *b, algebra_t *alg)
 	auto va = offset_cast (vtype, a, 0);
 	auto vb = offset_cast (vtype, b, 0);
 	auto cs = dot_expr (stype, va, vb);
-	c[1] = cs;
+	c[3] = cs;
 }
 
 static void
@@ -878,11 +878,11 @@ pga2_x_y_w_dot_wxy (expr_t **c, expr_t *a, expr_t *b, algebra_t *alg)
 {
 	auto stype = alg->type;
 	auto vtype = vector_type (stype, 2);
-	auto dot_type = algebra_mvec_type (alg, 0x01);
+	auto dot_type = algebra_mvec_type (alg, 0x04);
 	auto va = offset_cast (vtype, a, 0);
 	auto cv = scale_expr (vtype, va, b);
 
-	c[0] = ext_expr (cv, dot_type, 0, false);
+	c[2] = ext_expr (cv, dot_type, 0, false);
 }
 
 static void
@@ -892,7 +892,7 @@ pga2_wxy_dot_yw_wx_xy (expr_t **c, expr_t *a, expr_t *b, algebra_t *alg)
 	auto sa = offset_cast (stype, a, 0);
 	auto sb = offset_cast (stype, b, 2);
 	auto cs = neg_expr (scale_expr (stype, sa, sb));
-	c[0] = ext_expr (cs, algebra_mvec_type (alg, 0x01), 0, true);
+	c[2] = ext_expr (cs, algebra_mvec_type (alg, 0x04), 0, true);
 }
 
 static void
@@ -900,34 +900,37 @@ pga2_wxy_dot_x_y_w (expr_t **c, expr_t *a, expr_t *b, algebra_t *alg)
 {
 	auto stype = alg->type;
 	auto vtype = vector_type (stype, 2);
-	auto dot_type = algebra_mvec_type (alg, 0x01);
+	auto dot_type = algebra_mvec_type (alg, 0x04);
 	auto sa = offset_cast (stype, a, 0);
 	auto vb = offset_cast (vtype, b, 0);
 	auto cv = scale_expr (vtype, vb, sa);
-	c[0] = ext_expr (cv, dot_type, 0, false);
+	c[2] = ext_expr (cv, dot_type, 0, false);
 }
 
 static pga_func pga2_dot_funcs[4][4] = {
 	[0] = {
-		[0] = pga2_yw_wx_xy_dot_yw_wx_xy,
-		[2] = pga2_yw_wx_xy_dot_x_y_w,
-		[3] = pga2_yw_wx_xy_dot_wxy,
+		[0] = pga2_x_y_w_dot_x_y_w,
+		[1] = pga2_x_y_w_dot_wxy,
+		[2] = pga2_x_y_w_dot_yw_wx_xy,
+		[3] = scale_component,
 	},
 	[1] = {
+		[0] = pga2_wxy_dot_x_y_w,
+		[2] = pga2_wxy_dot_yw_wx_xy,
+		[3] = scale_component,
+	},
+	[2] = {
+		[0] = pga2_yw_wx_xy_dot_x_y_w,
+		[1] = pga2_yw_wx_xy_dot_wxy,
+		[2] = pga2_yw_wx_xy_dot_yw_wx_xy,
+		[3] = scale_component,
+	},
+	[3] = {
 		[0] = scale_component,
 		[1] = scale_component,
 		[2] = scale_component,
 		[3] = scale_component,
 	},
-	[2] = {
-		[0] = pga2_x_y_w_dot_yw_wx_xy,
-		[2] = pga2_x_y_w_dot_x_y_w,
-		[3] = pga2_x_y_w_dot_wxy,
-	},
-	[3] = {
-		[0] = pga2_wxy_dot_yw_wx_xy,
-		[2] = pga2_wxy_dot_x_y_w,
-	},
 };
 
 static void
@@ -1204,35 +1207,35 @@ static pga_func pga3_wedge_funcs[6][6] = {
 static void
 pga2_yw_wx_xy_wedge_x_y_w (expr_t **c, expr_t *a, expr_t *b, algebra_t *alg)
 {
-	c[3] = dot_expr (algebra_mvec_type (alg, 0x08), a, b);
+	c[1] = dot_expr (algebra_mvec_type (alg, 0x02), a, b);
 }
 
 static void
 pga2_x_y_w_wedge_x_y_w (expr_t **c, expr_t *a, expr_t *b, algebra_t *alg)
 {
-	auto wedge_type = algebra_mvec_type (alg, 0x01);
-	c[0] = cross_expr (wedge_type, a, b);
+	auto wedge_type = algebra_mvec_type (alg, 0x04);
+	c[2] = cross_expr (wedge_type, a, b);
 }
 
 static pga_func pga2_wedge_funcs[4][4] = {
 	[0] = {
-		[1] = scale_component,
-		[2] = pga2_yw_wx_xy_wedge_x_y_w,
+		[0] = pga2_x_y_w_wedge_x_y_w,
+		[2] = pga2_x_y_w_wedge_yw_wx_xy,
+		[3] = scale_component,
 	},
 	[1] = {
+		[3] = scale_component,
+	},
+	[2] = {
+		[0] = pga2_yw_wx_xy_wedge_x_y_w,
+		[3] = scale_component,
+	},
+	[3] = {
 		[0] = scale_component,
 		[1] = scale_component,
 		[2] = scale_component,
 		[3] = scale_component,
 	},
-	[2] = {
-		[0] = pga2_x_y_w_wedge_yw_wx_xy,
-		[1] = scale_component,
-		[2] = pga2_x_y_w_wedge_x_y_w,
-	},
-	[3] = {
-		[1] = scale_component,
-	},
 };
 
 static void
@@ -1654,13 +1657,13 @@ pga2_yw_wx_xy_geom_yw_wx_xy (expr_t **c, expr_t *a, expr_t *b, algebra_t *alg)
 	auto stype = alg->type;
 	auto vtype = vector_type (stype, 3);
 	auto ctype = vector_type (stype, 2);
-	auto geom_type = algebra_mvec_type (alg, 0x01);
+	auto geom_type = algebra_mvec_type (alg, 0x04);
 	auto sa = offset_cast (stype, a, 2);
 	auto sb = offset_cast (stype, b, 2);
 	auto cv = alias_expr (ctype, cross_expr (vtype, b, a), 0);
 
-	c[0] = ext_expr (cv, geom_type, 0, false);
-	c[1] = neg_expr (scale_expr (algebra_mvec_type (alg, 0x02), sa, sb));
+	c[2] = ext_expr (cv, geom_type, 0, false);
+	c[3] = neg_expr (scale_expr (algebra_mvec_type (alg, 0x08), sa, sb));
 }
 
 static void
@@ -1669,7 +1672,7 @@ pga2_yw_wx_xy_geom_x_y_w (expr_t **c, expr_t *a, expr_t *b, algebra_t *alg)
 	auto stype = alg->type;
 	auto wtype = vector_type (stype, 2);
 	auto vtype = vector_type (stype, 3);
-	auto geom_type = algebra_mvec_type (alg, 0x04);
+	auto geom_type = algebra_mvec_type (alg, 0x01);
 	auto va = offset_cast (wtype, a, 0);
 	auto sa = offset_cast (stype, a, 2);
 	auto vb = offset_cast (wtype, b, 0);
@@ -1677,8 +1680,8 @@ pga2_yw_wx_xy_geom_x_y_w (expr_t **c, expr_t *a, expr_t *b, algebra_t *alg)
 	auto cs = wedge_expr (stype, vb, va);
 	cs = ext_expr (cs, geom_type, 0, true);
 	cv = ext_expr (scale_expr (wtype, cv, sa), vtype, 0, false);
-	c[2] = sum_expr (geom_type, cv, cs);
-	c[3] = dot_expr (algebra_mvec_type (alg, 0x08), a, b);
+	c[0] = sum_expr (geom_type, cv, cs);
+	c[1] = dot_expr (algebra_mvec_type (alg, 0x02), a, b);
 }
 
 static void
@@ -1688,7 +1691,7 @@ pga2_yw_wx_xy_geom_wxy (expr_t **c, expr_t *a, expr_t *b, algebra_t *alg)
 	auto sa = offset_cast (stype, a, 2);
 	auto sb = offset_cast (stype, b, 0);
 	auto cs = neg_expr (scale_expr (stype, sa, sb));
-	c[0] = ext_expr (cs, algebra_mvec_type (alg, 0x01), 0, true);
+	c[2] = ext_expr (cs, algebra_mvec_type (alg, 0x04), 0, true);
 }
 
 static void
@@ -1697,7 +1700,7 @@ pga2_x_y_w_geom_yw_wx_xy (expr_t **c, expr_t *a, expr_t *b, algebra_t *alg)
 	auto stype = alg->type;
 	auto wtype = vector_type (stype, 2);
 	auto vtype = vector_type (stype, 3);
-	auto geom_type = algebra_mvec_type (alg, 0x04);
+	auto geom_type = algebra_mvec_type (alg, 0x01);
 	auto va = offset_cast (wtype, a, 0);
 	auto vb = offset_cast (wtype, b, 0);
 	auto sb = offset_cast (stype, b, 2);
@@ -1705,8 +1708,8 @@ pga2_x_y_w_geom_yw_wx_xy (expr_t **c, expr_t *a, expr_t *b, algebra_t *alg)
 	auto cs = wedge_expr (stype, vb, va);
 	cs = ext_expr (cs, geom_type, 0, true);
 	cv = ext_expr (scale_expr (wtype, cv, sb), vtype, 0, false);
-	c[2] = sum_expr (geom_type, cv, cs);
-	c[3] = dot_expr (algebra_mvec_type (alg, 0x08), a, b);
+	c[0] = sum_expr (geom_type, cv, cs);
+	c[1] = dot_expr (algebra_mvec_type (alg, 0x02), a, b);
 }
 
 static void
@@ -1714,11 +1717,11 @@ pga2_x_y_w_geom_x_y_w (expr_t **c, expr_t *a, expr_t *b, algebra_t *alg)
 {
 	auto stype = alg->type;
 	auto vtype = vector_type (stype, 2);
-	auto geom_type = algebra_mvec_type (alg, 0x01);
+	auto geom_type = algebra_mvec_type (alg, 0x04);
 	auto va = offset_cast (vtype, a, 0);
 	auto vb = offset_cast (vtype, b, 0);
-	c[1] = dot_expr (stype, va, vb);
-	c[0] = cross_expr (geom_type, a, b);
+	c[3] = dot_expr (stype, va, vb);
+	c[2] = cross_expr (geom_type, a, b);
 }
 
 static void
@@ -1726,11 +1729,11 @@ pga2_x_y_w_geom_wxy (expr_t **c, expr_t *a, expr_t *b, algebra_t *alg)
 {
 	auto stype = alg->type;
 	auto vtype = vector_type (stype, 2);
-	auto geom_type = algebra_mvec_type (alg, 0x01);
+	auto geom_type = algebra_mvec_type (alg, 0x04);
 	auto va = offset_cast (vtype, a, 0);
 	auto cv = scale_expr (vtype, va, b);
 
-	c[0] = ext_expr (cv, geom_type, 0, false);
+	c[2] = ext_expr (cv, geom_type, 0, false);
 }
 
 static void
@@ -1740,7 +1743,7 @@ pga2_wxy_geom_yw_wx_xy (expr_t **c, expr_t *a, expr_t *b, algebra_t *alg)
 	auto sa = offset_cast (stype, a, 0);
 	auto sb = offset_cast (stype, b, 2);
 	auto cs = neg_expr (scale_expr (stype, sa, sb));
-	c[0] = ext_expr (cs, algebra_mvec_type (alg, 0x01), 0, true);
+	c[2] = ext_expr (cs, algebra_mvec_type (alg, 0x04), 0, true);
 }
 
 static void
@@ -1748,37 +1751,37 @@ pga2_wxy_geom_x_y_w (expr_t **c, expr_t *a, expr_t *b, algebra_t *alg)
 {
 	auto stype = alg->type;
 	auto vtype = vector_type (stype, 2);
-	auto geom_type = algebra_mvec_type (alg, 0x01);
+	auto geom_type = algebra_mvec_type (alg, 0x04);
 	auto vb = offset_cast (vtype, b, 0);
 	auto cv = scale_expr (vtype, vb, a);
 
-	c[0] = ext_expr (cv, geom_type, 0, false);
+	c[2] = ext_expr (cv, geom_type, 0, false);
 }
 
 static pga_func pga2_geometric_funcs[6][6] = {
 	[0] = {
-		[0] = pga2_yw_wx_xy_geom_yw_wx_xy,
-		[1] = scale_component,
-		[2] = pga2_yw_wx_xy_geom_x_y_w,
-		[3] = pga2_yw_wx_xy_geom_wxy,
+		[0] = pga2_x_y_w_geom_x_y_w,
+		[1] = pga2_x_y_w_geom_wxy,
+		[2] = pga2_x_y_w_geom_yw_wx_xy,
+		[3] = scale_component,
 	},
 	[1] = {
+		[0] = pga2_wxy_geom_x_y_w,
+		[2] = pga2_wxy_geom_yw_wx_xy,
+		[3] = scale_component,
+	},
+	[2] = {
+		[0] = pga2_yw_wx_xy_geom_x_y_w,
+		[1] = pga2_yw_wx_xy_geom_wxy,
+		[2] = pga2_yw_wx_xy_geom_yw_wx_xy,
+		[3] = scale_component,
+	},
+	[3] = {
 		[0] = scale_component,
 		[1] = scale_component,
 		[2] = scale_component,
 		[3] = scale_component,
 	},
-	[2] = {
-		[0] = pga2_x_y_w_geom_yw_wx_xy,
-		[1] = scale_component,
-		[2] = pga2_x_y_w_geom_x_y_w,
-		[3] = pga2_x_y_w_geom_wxy,
-	},
-	[3] = {
-		[0] = pga2_wxy_geom_yw_wx_xy,
-		[1] = scale_component,
-		[2] = pga2_wxy_geom_x_y_w,
-	},
 };
 
 static void
diff --git a/tools/qfcc/test/pga2d.r b/tools/qfcc/test/pga2d.r
index c2c427d2b..09f869090 100644
--- a/tools/qfcc/test/pga2d.r
+++ b/tools/qfcc/test/pga2d.r
@@ -1,19 +1,19 @@
 #include "test-harness.h"
 #pragma warn no-vararg-integer
 typedef @algebra(double(2,0,1)) PGA;
-typedef PGA.group_mask(0x02) scalar_t;
-typedef PGA.group_mask(0x04) vector_t;
-typedef PGA.group_mask(0x01) bivector_t;
-typedef PGA.group_mask(0x08) trivector_t;
+typedef PGA.group_mask(0x08) scalar_t;
+typedef PGA.group_mask(0x01) vector_t;
+typedef PGA.group_mask(0x04) bivector_t;
+typedef PGA.group_mask(0x02) trivector_t;
 typedef union {
-	PGA.group_mask(0x03) mvec;
+	PGA.group_mask(0x0c) mvec;
 	struct {
 		bivector_t bvec;
 		scalar_t   scalar;
 	};
 } evengrades_t;
 typedef union {
-	PGA.group_mask(0x0c) mvec;
+	PGA.group_mask(0x03) mvec;
 	struct {
 		vector_t vec;
 		trivector_t tvec;