diff --git a/tools/qfcc/include/algebra.h b/tools/qfcc/include/algebra.h
index 83f5013b5..72030caf7 100644
--- a/tools/qfcc/include/algebra.h
+++ b/tools/qfcc/include/algebra.h
@@ -68,6 +68,7 @@ typedef struct algebra_s {
 	basis_layout_t layout;
 	basis_group_t *groups;
 	struct type_s **mvec_types;
+	struct symbol_s *mvec_sym;
 	int         num_components;	///< number of componets (2^d)
 	int         dimension;		///< number of dimensions (plus + minus + zero)
 	int         plus;			///< number of elements squaring to +1
@@ -79,6 +80,7 @@ typedef struct multivector_s {
 	int         num_components;
 	int         group_mask;
 	algebra_t  *algebra;
+	struct symbol_s *mvec_sym;	///< null if single group
 } multivector_t;
 
 struct expr_s;
diff --git a/tools/qfcc/source/algebra.c b/tools/qfcc/source/algebra.c
index e0447a0bf..b3babbd23 100644
--- a/tools/qfcc/source/algebra.c
+++ b/tools/qfcc/source/algebra.c
@@ -87,42 +87,49 @@ count_minus (uint32_t minus)
 {
 	return count_bits (minus) & 1 ? -1 : 1;
 }
-#if 0
-static struct_def_t mvec_1d_struct[] = {
-	{"vec", &type_vec2},
-	{}
+
+static const char *mvec_1d_names[] = {
+	"vec",
+	"scalar",
+	0
 };
 
-static struct_def_t mvec_2d_struct[] = {
-	{"vec", &type_vec4},
-	{}
+static const char *mvec_2d_names[] = {
+	"vec",
+	"scalar",
+	"bvec",
+	0
 };
 
-static struct_def_t mvec_3d_struct[] = {
-	{"vec",   &type_vec4},
-	{"bvec",  &type_vec4},
-	{}
+static const char *mvec_3d_names[] = {
+	"vec",
+	"scalar"
+	"bvec",
+	"tvec",
+	0
 };
 
-static struct_def_t mvec_4d_struct[] = {
-	{"vec",   &type_vec4},
-	{"bvecv", &type_vec4},
-	{"bvecm", &type_vec4},
-	{"tvec",  &type_vec4},
-	{}
+static const char *mvec_4d_names[] = {
+	"vec",
+	"bvecv",
+	"scalar",
+	"bvecm",
+	"qvec",
+	"tvec",
+	0
 };
 
-static struct_def_t *mvec_struct[] = {
-	[1] = mvec_1d_struct,
-	[2] = mvec_2d_struct,
-	[3] = mvec_3d_struct,
-	[4] = mvec_4d_struct,
+static const char **mvec_names[] = {
+	[1] = mvec_1d_names,
+	[2] = mvec_2d_names,
+	[3] = mvec_3d_names,
+	[4] = mvec_4d_names,
 };
 
 static symbol_t *
-build_algebra_types (algebra_t *a)
+build_algebra_type (algebra_t *a)
 {
-	auto name = save_string (va (0, "multivector.%s.%d.%d.%d",
+	auto name = save_string (va (0, "multivec.%s(%d.%d.%d)",
 								 a->type->encoding,
 								 a->plus, a->minus, a->zero));
 	int  dim = a->plus + a->minus + a->zero;
@@ -149,13 +156,23 @@ build_algebra_types (algebra_t *a)
 			mvsym->type->alignment = 4;
 		}
 	} else if (dim > 0) {
-		mvsym = make_structure (name, 's', mvec_struct[dim], 0);
+		const char **names = mvec_names[dim];
+		int          count = 0;
+		for (auto n = names; *n; n++, count++) continue;
+		struct_def_t fields[count + 1] = {};
+		for (int i = 0; i < count; i++) {
+			fields[i] = (struct_def_t) {
+				.name = names[i],
+				.type = algebra_mvec_type (a, 1u << i),
+			};
+		};
+		mvsym = make_structure (name, 's', fields, 0);
 	} else {
 		internal_error (0, "invalid number of dimensions");
 	}
 	return mvsym;
 }
-#endif
+
 static void
 basis_blade_init (basis_blade_t *blade, pr_uint_t mask)
 {
@@ -340,6 +357,8 @@ algebra_init (algebra_t *a)
 			algebra_mvec_type (a, g->group_mask);
 		}
 	}
+	a->mvec_sym = build_algebra_type (a);
+	a->mvec_types[(1 << a->dimension) - 1] = a->mvec_sym->type;
 }
 
 bool
@@ -461,23 +480,41 @@ algebra_mvec_type (algebra_t *algebra, pr_uint_t group_mask)
 	}
 	if (!algebra->mvec_types[group_mask]) {
 		int count = 0;
+		int components = 0;
 		for (int i = 0; i < algebra->layout.count; i++) {
 			if (group_mask & (1 << i)) {
-				count += algebra->layout.groups[i].count;
+				components += algebra->layout.groups[i].count;
+				count++;
 			}
 		}
+		symbol_t   *mvec_sym = 0;
+		if (group_mask & (group_mask - 1)) {
+			struct_def_t fields[count + 1] = {};
+			for (int i = 0, c = 0; i < algebra->layout.count; i++) {
+				pr_uint_t   mask = 1 << i;
+				if (group_mask & mask) {
+					fields[c] = (struct_def_t) {
+						.name = save_string (va (0, "group_%d", i)),
+						.type = algebra_mvec_type (algebra, mask),
+					};
+					c++;
+				};
+			};
+			mvec_sym = make_structure (0, 's', fields, 0);
+		}
 		multivector_t *mvec = malloc (sizeof (multivector_t));
 		*mvec = (multivector_t) {
-			.num_components = count,
+			.num_components = components,
 			.group_mask = group_mask,
 			.algebra = algebra,
+			.mvec_sym = mvec_sym,
 		};
 		algebra->mvec_types[group_mask] = new_type ();
 		*algebra->mvec_types[group_mask] = (type_t) {
 			.type = algebra->type->type,
 			.name = "basis group",
-			.alignment = algebra_alignment (algebra->type, count),
-			.width = count,
+			.alignment = algebra_alignment (algebra->type, components),
+			.width = components,
 			.meta = ty_algebra,
 			.t.algebra = (algebra_t *) mvec,
 			.freeable = true,
diff --git a/tools/qfcc/source/expr_algebra.c b/tools/qfcc/source/expr_algebra.c
index 977fcb29c..33a1a9950 100644
--- a/tools/qfcc/source/expr_algebra.c
+++ b/tools/qfcc/source/expr_algebra.c
@@ -33,6 +33,7 @@
 #include "tools/qfcc/include/algebra.h"
 #include "tools/qfcc/include/diagnostic.h"
 #include "tools/qfcc/include/expr.h"
+#include "tools/qfcc/include/symtab.h"
 #include "tools/qfcc/include/type.h"
 #include "tools/qfcc/include/value.h"
 
@@ -65,6 +66,18 @@ offset_cast (type_t *type, expr_t *expr, int offset)
 	return new_offset_alias_expr (type, expr, offset);
 }
 
+static symbol_t *
+get_mvec_sym (type_t *type)
+{
+	symbol_t   *sym = 0;
+	if (type->type == ev_invalid) {
+		sym = type->t.algebra->mvec_sym;
+	} else {
+		sym = type->t.multivec->mvec_sym;
+	}
+	return sym->type->t.symtab->symbols;
+}
+
 static expr_t *
 mvec_expr (expr_t *expr, algebra_t *algebra)
 {
@@ -91,16 +104,10 @@ mvec_expr (expr_t *expr, algebra_t *algebra)
 		.algebra = algebra,
 	};
 	expr_t **c = &mvec->e.multivec.components;
-	int comp_offset = 0;
-	for (int i = 0; i < layout->count; i++) {
-		pr_uint_t   mask = 1u << i;
-		if (mask & group_mask) {
-			auto comp_type = algebra_mvec_type (algebra, mask);
-			*c = offset_cast (comp_type, expr, comp_offset);
-			c = &(*c)->next;
-			mvec->e.multivec.count++;
-			comp_offset += algebra->layout.groups[i].count;
-		}
+	for (auto sym = get_mvec_sym (mvtype); sym; sym = sym->next) {
+		*c = new_offset_alias_expr (sym->type, expr, sym->s.offset);
+		c = &(*c)->next;
+		mvec->e.multivec.count++;
 	}
 
 	return mvec;
@@ -1580,7 +1587,7 @@ algebra_assign_expr (expr_t *dst, expr_t *src)
 	type_t *dstType = get_type (dst);
 
 	if (src->type != ex_multivec) {
-		if (type_size (srcType) == type_size (dstType)) {
+		if (srcType == dstType) {
 			return new_assign_expr (dst, src);
 		}
 	}
@@ -1594,31 +1601,27 @@ algebra_assign_expr (expr_t *dst, expr_t *src)
 	src = mvec_expr (src, algebra);
 	mvec_scatter (components, src, algebra);
 
+	auto sym = get_mvec_sym (dstType);
 	auto block = new_block_expr ();
 	int  memset_base = 0;
-	int  memset_size = 0;
-	int  offset = 0;
 	for (int i = 0; i < layout->count; i++) {
-		if (components[i]) {
-			if (memset_size) {
-				zero_components (block, dst, memset_base, memset_size);
-				memset_size = 0;
-			}
-			auto dst_type = algebra_mvec_type (algebra, 1 << i);
-			auto dst_alias = new_offset_alias_expr (dst_type, dst, offset);
-			append_expr (block, new_assign_expr (dst_alias, components[i]));
-			offset += type_size (dst_type);
-			memset_base = offset;
-		} else {
-			if (dstType->type == ev_invalid) {
-				auto dst_type = algebra_mvec_type (algebra, 1 << i);
-				offset += type_size (dst_type);
-				memset_size += type_size (dst_type);
-			}
+		if (!components[i]) {
+			continue;
 		}
+		while (sym->type != get_type (components[i])) {
+			sym = sym->next;
+		}
+		int size = sym->s.offset - memset_base;
+		if (size) {
+			zero_components (block, dst, memset_base, size);
+		}
+		auto dst_alias = new_offset_alias_expr (sym->type, dst, sym->s.offset);
+		append_expr (block, new_assign_expr (dst_alias, components[i]));
+		memset_base = sym->s.offset + type_size (sym->type);
 	}
-	if (memset_size) {
-		zero_components (block, dst, memset_base, memset_size);
+	if (type_size (dstType) - memset_base) {
+		zero_components (block, dst, memset_base,
+						 type_size (dstType) - memset_base);
 	}
 	return block;
 }
diff --git a/tools/qfcc/test/Makemodule.am b/tools/qfcc/test/Makemodule.am
index 7d8455446..ab161b953 100644
--- a/tools/qfcc/test/Makemodule.am
+++ b/tools/qfcc/test/Makemodule.am
@@ -45,6 +45,7 @@ test_progs_dat=\
 	tools/qfcc/test/overload.dat \
 	tools/qfcc/test/paramret.dat \
 	tools/qfcc/test/pga2d.dat \
+	tools/qfcc/test/pga3d.dat \
 	tools/qfcc/test/postop.dat \
 	tools/qfcc/test/ptraliasenc.dat \
 	tools/qfcc/test/ptrfunc.dat \
@@ -554,6 +555,16 @@ tools/qfcc/test/pga2d.run: $(qfcc_test_run_deps)
 include $(pga2d_dep) # am--include-marker
 r_depfiles_remade += $(pga2d_dep)
 
+tools_qfcc_test_pga3d_dat_SOURCES=tools/qfcc/test/pga3d.r
+pga3d_obj=$(tools_qfcc_test_pga3d_dat_SOURCES:.r=.o)
+pga3d_dep=$(call qcautodep,$(tools_qfcc_test_pga3d_dat_SOURCES))
+tools/qfcc/test/pga3d.dat$(EXEEXT): $(pga3d_obj) $(QFCC_DEP)
+	$(V_QFCCLD)$(QLINK) -o $@ $(pga3d_obj)
+tools/qfcc/test/pga3d.run: $(qfcc_test_run_deps)
+	@$(top_srcdir)/tools/qfcc/test/build-run $@
+include $(pga3d_dep) # am--include-marker
+r_depfiles_remade += $(pga3d_dep)
+
 tools_qfcc_test_postop_dat_SOURCES=tools/qfcc/test/postop.r
 postop_obj=$(tools_qfcc_test_postop_dat_SOURCES:.r=.o)
 postop_dep=$(call qcautodep,$(tools_qfcc_test_postop_dat_SOURCES))
diff --git a/tools/qfcc/test/pga3d.r b/tools/qfcc/test/pga3d.r
new file mode 100644
index 000000000..e42bcad88
--- /dev/null
+++ b/tools/qfcc/test/pga3d.r
@@ -0,0 +1,99 @@
+#include "test-harness.h"
+#pragma warn no-vararg-integer
+typedef @algebra(float(3,0,1)) PGA;
+typedef PGA.group_mask(0x04) scalar_t;
+typedef PGA.group_mask(0x01) vector_t;
+typedef PGA.group_mask(0x20) trivector_t;
+typedef PGA.group_mask(0x10) quadvector_t;
+typedef union {
+	PGA.group_mask(0x0a) bvec;
+	struct {
+		PGA.group_mask(0x02) dir;
+		PGA.group_mask(0x08) mom;
+	};
+} bivector_t;
+typedef union {
+	PGA.group_mask(0x1e) mvec;
+	struct {
+		bivector_t bvec;
+		scalar_t   scalar;
+	};
+} evengrades_t;
+typedef union {
+	PGA.group_mask(0x21) mvec;
+	struct {
+		vector_t vec;
+		trivector_t tvec;
+	};
+} oddgrades_t;
+
+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;
+	}
+
+	scalar_t scalar;
+	vector_t vec, vecb;
+	bivector_t bvec, bvecb;
+	trivector_t tvec, tvecb;
+	quadvector_t qvec, qvecb;
+	@algebra (PGA) {
+		scalar = 42;
+		vec = 3*e1 - 2*e2 + e0;
+		bvec.bvec = 4*e20 - 3*e01 + 2*e12;
+		tvec = 7*e012;
+		qvec = 8*e0123;
+
+		vecb = 5*e1 + 12*e2 - 13*e0;
+		bvecb.bvec = 6*e20 + 4*e01 + 1*e12;
+		tvecb = 3*e032;
+		qvecb = 1*e0123;
+	}
+
+	if (scalar != 42) {
+		printf ("scalar != 42: %g\n", scalar);
+		return 1;
+	}
+	if ((vec4)vec != '3 -2 0 1') {
+		printf ("vec != '3 -2 0 1': %q\n", vec);
+		return 1;
+	}
+	if ((vec3)bvec.dir != '0 0 2' || (vec3)bvec.mom != '-3 -4 0') {
+		printf ("bvec != '0 0 2' '-3 -4 0': %v %v\n", bvec.dir, bvec.mom);
+		return 1;
+	}
+	if ((vec4)tvec != '0 0 -7 0') {
+		printf ("tvec != '0 0 -7': %g\n", tvec);
+		return 1;
+	}
+	if ((scalar_t)qvec != 8) {
+		printf ("tvec != 8: %g\n", (scalar_t) qvec);
+		return 1;
+	}
+	return 0;		// to survive and prevail :)
+}