diff --git a/tools/qfcc/source/expr_algebra.c b/tools/qfcc/source/expr_algebra.c
index d450b46f3..2ee35774a 100644
--- a/tools/qfcc/source/expr_algebra.c
+++ b/tools/qfcc/source/expr_algebra.c
@@ -351,7 +351,7 @@ pga3_x_y_z_w_dot_yz_zx_xy (expr_t **c, expr_t *a, expr_t *b, algebra_t *alg)
 	auto vtype = vector_type (stype, 3);
 	auto dot_type = algebra_mvec_type (alg, 0x01);
 	auto va = offset_cast (vtype, a, 0);
-	c[2] = cross_expr (dot_type, b, va);
+	c[0] = new_extend_expr (cross_expr (vtype, b, va), dot_type, 0, false);
 }
 
 static void
@@ -375,7 +375,6 @@ pga3_x_y_z_w_dot_wxyz (expr_t **c, expr_t *a, expr_t *b, algebra_t *alg)
 	c[5] = new_extend_expr (cv, algebra_mvec_type (alg, 0x20), 0, false);
 }
 
-#define pga3_wzy_wxz_wyx_xyz_dot_x_y_z_w pga3_x_y_z_w_dot_wzy_wxz_wyx_xyz
 static void
 pga3_x_y_z_w_dot_wzy_wxz_wyx_xyz (expr_t **c, expr_t *a, expr_t *b,
 								  algebra_t *alg)
@@ -397,8 +396,8 @@ pga3_yz_zx_xy_dot_x_y_z_w (expr_t **c, expr_t *a, expr_t *b, algebra_t *alg)
 	auto stype = alg->type;
 	auto vtype = vector_type (stype, 3);
 	auto dot_type = algebra_mvec_type (alg, 0x01);
-	auto vb = offset_cast (vtype, a, 0);
-	c[2] = cross_expr (dot_type, a, vb);
+	auto vb = offset_cast (vtype, b, 0);
+	c[0] = new_extend_expr (cross_expr (vtype, vb, a), dot_type, 0, false);
 }
 
 static void
@@ -408,7 +407,6 @@ pga3_yz_zx_xy_dot_yz_zx_xy (expr_t **c, expr_t *a, expr_t *b, algebra_t *alg)
 	c[2] = unary_expr ('-', dot_expr (dot_type, a, b));
 }
 
-#define pga3_wxyz_dot_yz_zx_xy pga3_yz_zx_xy_dot_wxyz
 static void
 pga3_yz_zx_xy_dot_wxyz (expr_t **c, expr_t *a, expr_t *b, algebra_t *alg)
 {
@@ -419,7 +417,6 @@ pga3_yz_zx_xy_dot_wxyz (expr_t **c, expr_t *a, expr_t *b, algebra_t *alg)
 	c[3] = scale_expr (bmtype, va, unary_expr ('-', sb));
 }
 
-#define pga3_wzy_wxz_wyx_xyz_dot_yz_zx_xy pga3_yz_zx_xy_dot_wzy_wxz_wyx_xyz
 static void
 pga3_yz_zx_xy_dot_wzy_wxz_wyx_xyz (expr_t **c, expr_t *a, expr_t *b,
 								   algebra_t *alg)
@@ -443,8 +440,8 @@ pga3_wx_wy_wz_dot_x_y_z_w (expr_t **c, expr_t *a, expr_t *b, algebra_t *alg)
 {
 	auto stype = alg->type;
 	auto vtype = vector_type (stype, 3);
-	auto va = offset_cast (vtype, a, 0);
-	auto cs = dot_expr (stype, b, va);
+	auto vb = offset_cast (vtype, b, 0);
+	auto cs = dot_expr (stype, a, vb);
 	c[0] = new_extend_expr (cs, algebra_mvec_type (alg, 0x01), 0, true);
 }
 
@@ -459,6 +456,16 @@ pga3_wxyz_dot_x_y_z_w (expr_t **c, expr_t *a, expr_t *b, algebra_t *alg)
 	c[5] = scale_expr (dot_type, vb, sa);
 }
 
+static void
+pga3_wxyz_dot_yz_zx_xy (expr_t **c, expr_t *a, expr_t *b, algebra_t *alg)
+{
+	auto stype = alg->type;
+	auto bmtype = algebra_mvec_type (alg, 0x08);
+	auto sa = offset_cast (stype, a, 0);
+	auto vb = offset_cast (bmtype, b, 0);
+	c[3] = scale_expr (bmtype, vb, unary_expr ('-', sa));
+}
+
 static void
 pga3_wxyz_dot_wzy_wxz_wyx_xyz (expr_t **c, expr_t *a, expr_t *b, algebra_t *alg)
 {
@@ -470,12 +477,45 @@ pga3_wxyz_dot_wzy_wxz_wyx_xyz (expr_t **c, expr_t *a, expr_t *b, algebra_t *alg)
 	c[0] = new_extend_expr (cs, algebra_mvec_type (alg, 0x01), 0, true);
 }
 
+static void
+pga3_wzy_wxz_wyx_xyz_dot_x_y_z_w (expr_t **c, expr_t *a, expr_t *b,
+								  algebra_t *alg)
+{
+	auto stype = alg->type;
+	auto vtype = vector_type (stype, 3);
+	auto bvtype = algebra_mvec_type (alg, 0x02);
+	auto bmtype = algebra_mvec_type (alg, 0x08);
+	auto sa = offset_cast (stype, a, 3);
+	auto va = offset_cast (vtype, a, 0);
+	auto vb = offset_cast (vtype, b, 0);
+	c[1] = scale_expr (bvtype, vb, sa);
+	c[3] = cross_expr (bmtype, va, vb);
+}
+
+static void
+pga3_wzy_wxz_wyx_xyz_dot_yz_zx_xy (expr_t **c, expr_t *a, expr_t *b,
+								   algebra_t *alg)
+{
+	auto stype = alg->type;
+	auto vtype = vector_type (stype, 3);
+	auto dot_type = algebra_mvec_type (alg, 0x01);
+
+	auto va = offset_cast (vtype, a, 0);
+	auto sa = offset_cast (stype, a, 3);
+
+	auto cv = scale_expr (vtype, b, sa);
+	auto cs = dot_expr (stype, b, va);
+
+	c[0] = sum_expr (dot_type, '-', new_extend_expr (cs, dot_type, 0, true),
+									new_extend_expr (cv, dot_type, 0, false));
+}
+
 static void
 pga3_wzy_wxz_wyx_xyz_dot_wxyz (expr_t **c, expr_t *a, expr_t *b, algebra_t *alg)
 {
 	auto stype = alg->type;
-	auto sa = offset_cast (stype, a, 0);
-	auto sb = offset_cast (stype, b, 3);
+	auto sa = offset_cast (stype, a, 3);
+	auto sb = offset_cast (stype, b, 0);
 	auto cs = scale_expr (stype, sa, sb);
 	c[0] = new_extend_expr (cs, algebra_mvec_type (alg, 0x01), 0, true);
 }
diff --git a/tools/qfcc/test/pga3d.r b/tools/qfcc/test/pga3d.r
index 09e10631b..52a7d2d5b 100644
--- a/tools/qfcc/test/pga3d.r
+++ b/tools/qfcc/test/pga3d.r
@@ -27,36 +27,9 @@ typedef union {
 	};
 } oddgrades_t;
 
-int
-main (void)
+static int
+test_wedge (void)
 {
-	if (sizeof (scalar_t) != sizeof (float)) {
-		printf ("scalar has wrong size: %d\n", sizeof (scalar_t));
-		return 1;
-	}
-	if (sizeof (vector_t) != 4 * sizeof (scalar_t)) {
-		printf ("bivector has wrong size: %d\n", sizeof (vector_t));
-		return 1;
-	}
-	// the pair of vec3s in a bivector have an alignment of 4
-	if (sizeof (bivector_t) != 8 * sizeof (scalar_t)) {
-		printf ("bivector has wrong size: %d\n", sizeof (bivector_t));
-		return 1;
-	}
-	if (sizeof (bivector_t) != sizeof (PGA.group_mask(0x0a))) {
-		printf ("bivector group has wrong size: %d\n",
-				sizeof (PGA.group_mask(0x0a)));
-		return 1;
-	}
-	if (sizeof (trivector_t) != 4 * sizeof (scalar_t)) {
-		printf ("trivector has wrong size: %d\n", sizeof (trivector_t));
-		return 1;
-	}
-	if (sizeof (quadvector_t) != sizeof (scalar_t)) {
-		printf ("quadvector has wrong size: %d\n", sizeof (quadvector_t));
-		return 1;
-	}
-
 	scalar_t scalar;
 	vector_t vec, vecb, vecc, vecd;
 	bivector_t bvec, bvecb;
@@ -147,6 +120,163 @@ main (void)
 		printf ("(vecd ∧ vecc) ∧ a != 742': %g\n", (scalar_t) c);
 		return 1;
 	}
+	return 0;
+}
+
+static int
+test_dot (void)
+{
+	scalar_t scalar;
+	vector_t vec, vecb, vecc, vecd;
+	bivector_t bvec, bvecb;
+	trivector_t tvec, tvecb;
+	quadvector_t qvec, qvecb;
+	@algebra (PGA) {
+		scalar = 42;
+		vec = 3*e1 - 2*e2 + 4*e3 + e0;
+		bvec.bvec = -3*e01 + 5*e02 + 7*e03 + 11*e23 - 4*e31 + 2*e12;
+		tvec = 1*e032 + 4*e013 + 7*e021 - 2*e123;
+		qvec = 8*e0123;
+
+		vecb = 5*e1 + 12*e2 - 13*e0;
+		bvecb.bvec = 6*e20 + 4*e01 + 1*e12;
+		tvecb = 3*e032;
+		qvecb = 1*e0123;
+
+		vecc = 5*e1 + 4*e2 - 3*e3 + 4*e0;
+		vecd = e1 + e2 + e3 + e0;
+	}
+
+	if (qvec • qvecb != 0) {
+		printf ("(qvec • qvecb) != 0': %g\n", qvec • qvecb);
+		return 1;
+	}
+
+	auto a = tvec • qvec;
+	if ((vec4)a != '0 0 0 -16') {
+		printf ("vec • vecb != '0 0 0 -16': %v\n", a);
+		return 1;
+	}
+
+	bivector_t b = { .mom = bvec.bvec • qvec };
+	if ((vec3)b.dir != '0 0 0' || (vec3)b.mom != '-88 32 -16') {
+		printf ("bvec • qvec != '0 0 0' '-88 32 -16': %v %v\n", b.dir, b.mom);
+		return 1;
+	}
+
+	auto c = vec • qvec;
+	if ((vec4)c != '24 -16 32 0') {
+		printf ("vec • qvec != '24 -16 32 0': %v\n", c);
+		return 1;
+	}
+
+	a = bvec.bvec • tvec;
+	if ((vec4)a != '22 -8 4 9') {
+		printf ("bvec • tvec != '22 -8 4 9': %v\n", a);
+		return 1;
+	}
+
+	b.bvec = vec • tvec;
+	if ((vec3)b.dir != '-6 4 -8' || (vec3)b.mom != '30 17 -14') {
+		printf ("vec • tvec != '-6 4 -8' '30 17 -14': %v %v\n", b.dir, b.mom);
+		return 1;
+	}
+
+	if (bvec.bvec • bvec.bvec != -141) {
+		printf ("(bvec • bvec) != -141': %g\n", bvec.bvec • bvec.bvec);
+		return 1;
+	}
+
+	a = vec • bvec.bvec;
+	if ((vec4)a != '-12 -38 -10 -9') {
+		printf ("vec • bvec != '-12 -38 -10 -9': %v\n", a);
+		return 1;
+	}
+
+	if (vec • vecb != -9) {
+		printf ("(vec • vecb) != -9': %g\n", vec • vecb);
+		return 1;
+	}
+
+	a = qvec • tvec;
+	if ((vec4)a != '0 0 0 16') {
+		printf ("vec • vecb != '0 0 0 16': %v\n", a);
+		return 1;
+	}
+
+	b.dir = nil;//FIXME allow bvec = mom
+	b.mom = qvec • bvec.bvec;
+	if ((vec3)b.dir != '0 0 0' || (vec3)b.mom != '-88 32 -16') {
+		printf ("qvec • bvec != '0 0 0' '-88 32 -16': %v %v\n", b.dir, b.mom);
+		return 1;
+	}
+
+	c = qvec • vec;
+	if ((vec4)c != '-24 16 -32 0') {
+		printf ("vec • qvec != '-24 16 -32 0': %v\n", c);
+		return 1;
+	}
+
+	a = tvec • bvec.bvec;
+	if ((vec4)a != '22 -8 4 9') {
+		printf ("tvec • vec != '22 -8 4 9': %v\n", a);
+		return 1;
+	}
+
+	b.bvec = tvec • vec;
+	if ((vec3)b.dir != '-6 4 -8' || (vec3)b.mom != '30 17 -14') {
+		printf ("tvec • vec != '-6 4 -8' '30 17 -14': %v %v\n", b.dir, b.mom);
+		return 1;
+	}
+
+	a = bvec.bvec • vec;
+	if ((vec4)a != '12 38 10 9') {
+		printf ("bvec • vec != '12 38 10 9': %q\n", a);
+		return 1;
+	}
+
+	return 0;
+}
+
+int
+main (void)
+{
+	if (sizeof (scalar_t) != sizeof (float)) {
+		printf ("scalar has wrong size: %d\n", sizeof (scalar_t));
+		return 1;
+	}
+	if (sizeof (vector_t) != 4 * sizeof (scalar_t)) {
+		printf ("bivector has wrong size: %d\n", sizeof (vector_t));
+		return 1;
+	}
+	// the pair of vec3s in a bivector have an alignment of 4
+	if (sizeof (bivector_t) != 8 * sizeof (scalar_t)) {
+		printf ("bivector has wrong size: %d\n", sizeof (bivector_t));
+		return 1;
+	}
+	if (sizeof (bivector_t) != sizeof (PGA.group_mask(0x0a))) {
+		printf ("bivector group has wrong size: %d\n",
+				sizeof (PGA.group_mask(0x0a)));
+		return 1;
+	}
+	if (sizeof (trivector_t) != 4 * sizeof (scalar_t)) {
+		printf ("trivector has wrong size: %d\n", sizeof (trivector_t));
+		return 1;
+	}
+	if (sizeof (quadvector_t) != sizeof (scalar_t)) {
+		printf ("quadvector has wrong size: %d\n", sizeof (quadvector_t));
+		return 1;
+	}
+
+	if (test_wedge ()) {
+		printf ("wedge products failed\n");
+		return 1;
+	}
+
+	if (test_dot ()) {
+		printf ("dot products failed\n");
+		return 1;
+	}
 
 	return 0;		// to survive and prevail :)
 }