From d383dfe91e84bc01f8d72f4d511a7c7ad8d861df Mon Sep 17 00:00:00 2001
From: Michael Hamburg <mike@shiftleft.org>
Date: Thu, 22 Jan 2015 15:35:58 -0800
Subject: [PATCH] going to GMP-style element[1] types

Conflicts:
	src/include/ec_point.h
	src/p448/magic.c
	src/p480/magic.c
	src/p521/magic.c
	test/bench.c
---
 src/arithmetic.c        |   77 ++-
 src/ec_point.c          | 1225 +++++++++++++++++++--------------------
 src/goldilocks.c        |   70 +--
 src/include/ec_point.h  |   97 ++--
 src/include/field.h     |   79 +--
 src/include/magic.h     |    4 +-
 src/include/scalarmul.h |    4 +-
 src/p448/f_arithmetic.c |   54 +-
 src/p448/magic.c        |   22 +-
 src/p480/f_arithmetic.c |   54 +-
 src/p480/magic.c        |   18 +-
 src/p521/f_arithmetic.c |   54 +-
 src/p521/magic.c        |   18 +-
 src/scalarmul.c         |   70 +--
 test/bench.c            |  173 +++---
 test/test.c             |    2 +-
 test/test.h             |    2 +-
 test/test_arithmetic.c  |   94 +--
 test/test_pointops.c    |  120 ++--
 test/test_scalarmul.c   |   90 +--
 20 files changed, 1162 insertions(+), 1165 deletions(-)

diff --git a/src/arithmetic.c b/src/arithmetic.c
index 4530aa3..89be5c4 100644
--- a/src/arithmetic.c
+++ b/src/arithmetic.c
@@ -13,78 +13,75 @@
 
 mask_t
 field_eq (
-    const struct field_t *a,
-    const struct field_t *b
+    const field_a_t a,
+    const field_a_t b
 ) {
-    struct field_t ra, rb;
-    field_copy(&ra, a);
-    field_copy(&rb, b);
-    field_weak_reduce(&ra);
-    field_weak_reduce(&rb);
-    field_sub_RAW(&ra, &ra, &rb);
-    field_bias(&ra, 2);
-    return field_is_zero(&ra);
+    field_a_t ra, rb;
+    field_copy(ra, a);
+    field_copy(rb, b);
+    field_weak_reduce(ra);
+    field_weak_reduce(rb);
+    field_sub_RAW(ra, ra, rb);
+    field_bias(ra, 2);
+    return field_is_zero(ra);
 }
 
 void
 field_inverse (
-    struct field_t*       a,
-    const struct field_t* x
+    field_a_t a,
+    const field_a_t x
 ) {
-    struct field_t L0, L1;
-    field_isr  (   &L0,     x );
-    field_sqr  (   &L1,   &L0 );
-    field_sqr  (   &L0,   &L1 );
-    field_mul  (     a,     x,   &L0 );
+    field_a_t L0, L1;
+    field_isr  (   L0,     x );
+    field_sqr  (   L1,   L0 );
+    field_sqr  (   L0,   L1 );
+    field_mul  (     a,     x,   L0 );
 }
 
 mask_t
 field_is_square (
-    const struct field_t* x
+    const field_a_t x
 ) {
-    mask_t L2, L3;
-    struct field_t L0, L1;
-    field_isr  (   &L0,     x );
-    field_sqr  (   &L1,   &L0 );
-    field_mul  (   &L0,     x,   &L1 );
-    field_subw(   &L0,     1 );
-       L3 = field_is_zero(   &L0 );
-       L2 = field_is_zero(     x );
-    return    L3 |    L2;
+    field_a_t L0, L1;
+    field_isr  (   L0,     x );
+    field_sqr  (   L1,   L0 );
+    field_mul  (   L0,     x,  L1 );
+    field_subw(   L0,     1 );
+    return field_is_zero(   L0 ) | field_is_zero(     x );
 }
 
 void
 field_simultaneous_invert (
-    struct field_t *__restrict__ out,
-    const struct field_t *in,
+    field_a_t *__restrict__ out,
+    const field_a_t *in,
     unsigned int n
 ) {
   if (n==0) {
       return;
   } else if (n==1) {
-      field_inverse(out,in);
+      field_inverse(out[0],in[0]);
       return;
   }
   
-  field_copy(&out[1], &in[0]);
+  field_copy(out[1], in[0]);
   int i;
   for (i=1; i<(int) (n-1); i++) {
-      field_mul(&out[i+1], &out[i], &in[i]);
+      field_mul(out[i+1], out[i], in[i]);
   }
-  field_mul(&out[0], &out[n-1], &in[n-1]);
+  field_mul(out[0], out[n-1], in[n-1]);
   
-  struct field_t tmp;
-  field_inverse(&tmp, &out[0]);
-  field_copy(&out[0], &tmp);
+  field_a_t tmp;
+  field_inverse(tmp, out[0]);
+  field_copy(out[0], tmp);
   
   /* at this point, out[0] = product(in[i]) ^ -1
    * out[i] = product(in[0]..in[i-1]) if i != 0
    */
   for (i=n-1; i>0; i--) {
-      field_mul(&tmp, &out[i], &out[0]);
-      field_copy(&out[i], &tmp);
+      field_mul(tmp, out[i], out[0]);
+      field_copy(out[i], tmp);
       
-      field_mul(&tmp, &out[0], &in[i]);
-      field_copy(&out[0], &tmp);
+      field_mul(tmp, out[0], in[i]);
+      field_copy(out[0], tmp);
   }
 }
diff --git a/src/ec_point.c b/src/ec_point.c
index 48c84b1..aea17ac 100644
--- a/src/ec_point.c
+++ b/src/ec_point.c
@@ -18,20 +18,20 @@ add_tw_niels_to_tw_extensible (
     const struct tw_niels_t* e
 ) {
     ANALYZE_THIS_ROUTINE_CAREFULLY;
-    struct field_t L0, L1;
-    field_sub (   &L1, &d->y, &d->x );
-    field_mul  (   &L0, &e->a,   &L1 );
-    field_add_nr  (   &L1, &d->x, &d->y );
-    field_mul  ( &d->y, &e->b,   &L1 );
-    field_mul  (   &L1, &d->u, &d->t );
-    field_mul  ( &d->x, &e->c,   &L1 );
-    field_add_nr  ( &d->u,   &L0, &d->y );
-    field_subx_nr ( &d->t, &d->y,   &L0 );
-    field_subx_nr ( &d->y, &d->z, &d->x );
-    field_add_nr  (   &L0, &d->x, &d->z );
-    field_mul  ( &d->z,   &L0, &d->y );
-    field_mul  ( &d->x, &d->y, &d->t );
-    field_mul  ( &d->y,   &L0, &d->u );
+    field_a_t L0, L1;
+    field_sub (   L1, d->y, d->x );
+    field_mul  (   L0, e->a,   L1 );
+    field_add_nr  (   L1, d->x, d->y );
+    field_mul  ( d->y, e->b,   L1 );
+    field_mul  (   L1, d->u, d->t );
+    field_mul  ( d->x, e->c,   L1 );
+    field_add_nr  ( d->u,   L0, d->y );
+    field_sub_nr ( d->t, d->y,   L0 );
+    field_sub_nr ( d->y, d->z, d->x );
+    field_add_nr  (   L0, d->x, d->z );
+    field_mul  ( d->z,   L0, d->y );
+    field_mul  ( d->x, d->y, d->t );
+    field_mul  ( d->y,   L0, d->u );
 }
 
 void
@@ -40,20 +40,20 @@ sub_tw_niels_from_tw_extensible (
     const struct tw_niels_t* e
 ) {
     ANALYZE_THIS_ROUTINE_CAREFULLY;
-    struct field_t L0, L1;
-    field_subx_nr (   &L1, &d->y, &d->x );
-    field_mul  (   &L0, &e->b,   &L1 );
-    field_add_nr  (   &L1, &d->x, &d->y );
-    field_mul  ( &d->y, &e->a,   &L1 );
-    field_mul  (   &L1, &d->u, &d->t );
-    field_mul  ( &d->x, &e->c,   &L1 );
-    field_add_nr  ( &d->u,   &L0, &d->y );
-    field_subx_nr ( &d->t, &d->y,   &L0 );
-    field_add_nr  ( &d->y, &d->x, &d->z );
-    field_subx_nr (   &L0, &d->z, &d->x );
-    field_mul  ( &d->z,   &L0, &d->y );
-    field_mul  ( &d->x, &d->y, &d->t );
-    field_mul  ( &d->y,   &L0, &d->u );
+    field_a_t L0, L1;
+    field_sub_nr (   L1, d->y, d->x );
+    field_mul  (   L0, e->b,   L1 );
+    field_add_nr  (   L1, d->x, d->y );
+    field_mul  ( d->y, e->a,   L1 );
+    field_mul  (   L1, d->u, d->t );
+    field_mul  ( d->x, e->c,   L1 );
+    field_add_nr  ( d->u,   L0, d->y );
+    field_sub_nr ( d->t, d->y,   L0 );
+    field_add_nr  ( d->y, d->x, d->z );
+    field_sub_nr (   L0, d->z, d->x );
+    field_mul  ( d->z,   L0, d->y );
+    field_mul  ( d->x, d->y, d->t );
+    field_mul  ( d->y,   L0, d->u );
 }
 
 void
@@ -61,9 +61,9 @@ add_tw_pniels_to_tw_extensible (
     struct tw_extensible_t*   e,
     const struct tw_pniels_t* a
 ) {
-    struct field_t L0;
-    field_mul  (   &L0, &e->z, &a->z );
-    field_copy ( &e->z,   &L0 );
+    field_a_t L0;
+    field_mul  (   L0, e->z, a->z );
+    field_copy ( e->z,   L0 );
     add_tw_niels_to_tw_extensible(     e, &a->n );
 }
 
@@ -72,9 +72,9 @@ sub_tw_pniels_from_tw_extensible (
     struct tw_extensible_t*   e,
     const struct tw_pniels_t* a
 ) {
-    struct field_t L0;
-    field_mul  (   &L0, &e->z, &a->z );
-    field_copy ( &e->z,   &L0 );
+    field_a_t L0;
+    field_mul  (   L0, e->z, a->z );
+    field_copy ( e->z,   L0 );
     sub_tw_niels_from_tw_extensible(     e, &a->n );
 }
 
@@ -83,24 +83,24 @@ double_tw_extensible (
     struct tw_extensible_t* a
 ) {
     ANALYZE_THIS_ROUTINE_CAREFULLY;
-    struct field_t L0, L1, L2;
-    field_sqr  (   &L2, &a->x );
-    field_sqr  (   &L0, &a->y );
-    field_add_nr  ( &a->u,   &L2,   &L0 );
-    field_add_nr  ( &a->t, &a->y, &a->x );
-    field_sqr  (   &L1, &a->t );
-    field_sub_nr  ( &a->t,   &L1, &a->u );
-    field_bias ( &a->t,     3 );
-    IF32( field_weak_reduce( &a->t ) );
-    field_subx_nr (   &L1,   &L0,   &L2 );
-    field_sqr  ( &a->x, &a->z );
-    field_bias ( &a->x,     2-is32 /*is32 ? 1 : 2*/ );
-    field_add_nr  ( &a->z, &a->x, &a->x );
-    field_sub_nr  (   &L0, &a->z,   &L1 );
-    IF32( field_weak_reduce(   &L0 ) );
-    field_mul  ( &a->z,   &L1,   &L0 );
-    field_mul  ( &a->x,   &L0, &a->t );
-    field_mul  ( &a->y,   &L1, &a->u );
+    field_a_t L0, L1, L2;
+    field_sqr  (   L2, a->x );
+    field_sqr  (   L0, a->y );
+    field_add_nr  ( a->u,   L2,   L0 );
+    field_add_nr  ( a->t, a->y, a->x );
+    field_sqr  (   L1, a->t );
+    field_sub_nr  ( a->t,   L1, a->u );
+    field_bias ( a->t,     3 );
+    IF32( field_weak_reduce( a->t ) );
+    field_sub_nr (   L1,   L0,   L2 );
+    field_sqr  ( a->x, a->z );
+    field_bias ( a->x,     2-is32 /*is32 ? 1 : 2*/ );
+    field_add_nr  ( a->z, a->x, a->x );
+    field_sub_nr  (   L0, a->z,   L1 );
+    IF32( field_weak_reduce(   L0 ) );
+    field_mul  ( a->z,   L1,   L0 );
+    field_mul  ( a->x,   L0, a->t );
+    field_mul  ( a->y,   L1, a->u );
 }
 
 void
@@ -108,24 +108,24 @@ double_extensible (
     struct extensible_t* a
 ) {
     ANALYZE_THIS_ROUTINE_CAREFULLY;
-    struct field_t L0, L1, L2;
-    field_sqr  (   &L2, &a->x );
-    field_sqr  (   &L0, &a->y );
-    field_add_nr  (   &L1,   &L2,   &L0 );
-    field_add_nr  ( &a->t, &a->y, &a->x );
-    field_sqr  ( &a->u, &a->t );
-    field_sub_nr  ( &a->t, &a->u,   &L1 );
-    field_bias ( &a->t,     3 );
-    IF32( field_weak_reduce( &a->t ) );
-    field_subx_nr ( &a->u,   &L0,   &L2 );
-    field_sqr  ( &a->x, &a->z );
-    field_bias ( &a->x,     2 );
-    field_add_nr  ( &a->z, &a->x, &a->x );
-    field_sub_nr  (   &L0, &a->z,   &L1 );
-    IF32( field_weak_reduce(   &L0 ) );
-    field_mul  ( &a->z,   &L1,   &L0 );
-    field_mul  ( &a->x,   &L0, &a->t );
-    field_mul  ( &a->y,   &L1, &a->u );
+    field_a_t L0, L1, L2;
+    field_sqr  (   L2, a->x );
+    field_sqr  (   L0, a->y );
+    field_add_nr  (   L1,   L2,   L0 );
+    field_add_nr  ( a->t, a->y, a->x );
+    field_sqr  ( a->u, a->t );
+    field_sub_nr  ( a->t, a->u,   L1 );
+    field_bias ( a->t,     3 );
+    IF32( field_weak_reduce( a->t ) );
+    field_sub_nr ( a->u,   L0,   L2 );
+    field_sqr  ( a->x, a->z );
+    field_bias ( a->x,     2 );
+    field_add_nr  ( a->z, a->x, a->x );
+    field_sub_nr  (   L0, a->z,   L1 );
+    IF32( field_weak_reduce(   L0 ) );
+    field_mul  ( a->z,   L1,   L0 );
+    field_mul  ( a->x,   L0, a->t );
+    field_mul  ( a->y,   L1, a->u );
 }
 
 void
@@ -133,20 +133,20 @@ twist_and_double (
     struct tw_extensible_t*    b,
     const struct extensible_t* a
 ) {
-    struct field_t L0;
-    field_sqr  ( &b->x, &a->x );
-    field_sqr  ( &b->z, &a->y );
-    field_add ( &b->u, &b->x, &b->z );
-    field_add ( &b->t, &a->y, &a->x );
-    field_sqr  (   &L0, &b->t );
-    field_sub ( &b->t,   &L0, &b->u );
-    field_sub (   &L0, &b->z, &b->x );
-    field_sqr  ( &b->x, &a->z );
-    field_add ( &b->z, &b->x, &b->x );
-    field_sub ( &b->y, &b->z, &b->u );
-    field_mul  ( &b->z,   &L0, &b->y );
-    field_mul  ( &b->x, &b->y, &b->t );
-    field_mul  ( &b->y,   &L0, &b->u );
+    field_a_t L0;
+    field_sqr  ( b->x, a->x );
+    field_sqr  ( b->z, a->y );
+    field_add ( b->u, b->x, b->z );
+    field_add ( b->t, a->y, a->x );
+    field_sqr  (   L0, b->t );
+    field_sub ( b->t,   L0, b->u );
+    field_sub (   L0, b->z, b->x );
+    field_sqr  ( b->x, a->z );
+    field_add ( b->z, b->x, b->x );
+    field_sub ( b->y, b->z, b->u );
+    field_mul  ( b->z,   L0, b->y );
+    field_mul  ( b->x, b->y, b->t );
+    field_mul  ( b->y,   L0, b->u );
 }
 
 void
@@ -154,20 +154,20 @@ untwist_and_double (
     struct extensible_t*          b,
     const struct tw_extensible_t* a
 ) {
-    struct field_t L0;
-    field_sqr  ( &b->x, &a->x );
-    field_sqr  ( &b->z, &a->y );
-    field_add (   &L0, &b->x, &b->z );
-    field_add ( &b->t, &a->y, &a->x );
-    field_sqr  ( &b->u, &b->t );
-    field_sub ( &b->t, &b->u,   &L0 );
-    field_sub ( &b->u, &b->z, &b->x );
-    field_sqr  ( &b->x, &a->z );
-    field_add ( &b->z, &b->x, &b->x );
-    field_sub ( &b->y, &b->z, &b->u );
-    field_mul  ( &b->z,   &L0, &b->y );
-    field_mul  ( &b->x, &b->y, &b->t );
-    field_mul  ( &b->y,   &L0, &b->u );
+    field_a_t L0;
+    field_sqr  ( b->x, a->x );
+    field_sqr  ( b->z, a->y );
+    field_add (   L0, b->x, b->z );
+    field_add ( b->t, a->y, a->x );
+    field_sqr  ( b->u, b->t );
+    field_sub ( b->t, b->u,   L0 );
+    field_sub ( b->u, b->z, b->x );
+    field_sqr  ( b->x, a->z );
+    field_add ( b->z, b->x, b->x );
+    field_sub ( b->y, b->z, b->u );
+    field_mul  ( b->z,   L0, b->y );
+    field_mul  ( b->x, b->y, b->t );
+    field_mul  ( b->y,   L0, b->u );
 }
 
 void
@@ -175,11 +175,11 @@ convert_tw_affine_to_tw_pniels (
     struct tw_pniels_t*       b,
     const struct tw_affine_t* a
 ) {
-    field_sub ( &b->n.a, &a->y, &a->x );
-    field_add ( &b->n.b, &a->x, &a->y );
-    field_mul  ( &b->z, &a->y, &a->x );
-    field_mulw_scc_wr ( &b->n.c, &b->z, 2*EDWARDS_D-2 );
-    field_set_ui( &b->z,     2 );
+    field_sub ( b->n.a, a->y, a->x );
+    field_add ( b->n.b, a->x, a->y );
+    field_mul  ( b->z, a->y, a->x );
+    field_mulw_scc_wr ( b->n.c, b->z, 2*EDWARDS_D-2 );
+    field_set_ui( b->z,     2 );
 }
 
 void
@@ -187,11 +187,11 @@ convert_tw_affine_to_tw_extensible (
     struct tw_extensible_t*   b,
     const struct tw_affine_t* a
 ) {
-    field_copy ( &b->x, &a->x );
-    field_copy ( &b->y, &a->y );
-    field_set_ui( &b->z,     1 );
-    field_copy ( &b->t, &a->x );
-    field_copy ( &b->u, &a->y );
+    field_copy ( b->x, a->x );
+    field_copy ( b->y, a->y );
+    field_set_ui( b->z,     1 );
+    field_copy ( b->t, a->x );
+    field_copy ( b->u, a->y );
 }
 
 void
@@ -199,11 +199,11 @@ convert_affine_to_extensible (
     struct extensible_t*   b,
     const struct affine_t* a
 ) {
-    field_copy ( &b->x, &a->x );
-    field_copy ( &b->y, &a->y );
-    field_set_ui( &b->z,     1 );
-    field_copy ( &b->t, &a->x );
-    field_copy ( &b->u, &a->y );
+    field_copy ( b->x, a->x );
+    field_copy ( b->y, a->y );
+    field_set_ui( b->z,     1 );
+    field_copy ( b->t, a->x );
+    field_copy ( b->u, a->y );
 }
 
 void
@@ -211,11 +211,11 @@ convert_tw_extensible_to_tw_pniels (
     struct tw_pniels_t*           b,
     const struct tw_extensible_t* a
 ) {
-    field_sub ( &b->n.a, &a->y, &a->x );
-    field_add ( &b->n.b, &a->x, &a->y );
-    field_mul  ( &b->z, &a->u, &a->t );
-    field_mulw_scc_wr ( &b->n.c, &b->z, 2*EDWARDS_D-2 );
-    field_add ( &b->z, &a->z, &a->z );
+    field_sub ( b->n.a, a->y, a->x );
+    field_add ( b->n.b, a->x, a->y );
+    field_mul  ( b->z, a->u, a->t );
+    field_mulw_scc_wr ( b->n.c, b->z, 2*EDWARDS_D-2 );
+    field_add ( b->z, a->z, a->z );
 }
 
 void
@@ -223,11 +223,11 @@ convert_tw_pniels_to_tw_extensible (
     struct tw_extensible_t*   e,
     const struct tw_pniels_t* d
 ) {
-    field_add ( &e->u, &d->n.b, &d->n.a );
-    field_sub ( &e->t, &d->n.b, &d->n.a );
-    field_mul  ( &e->x, &d->z, &e->t );
-    field_mul  ( &e->y, &d->z, &e->u );
-    field_sqr  ( &e->z, &d->z );
+    field_add ( e->u, d->n.b, d->n.a );
+    field_sub ( e->t, d->n.b, d->n.a );
+    field_mul  ( e->x, d->z, e->t );
+    field_mul  ( e->y, d->z, e->u );
+    field_sqr  ( e->z, d->z );
 }
 
 void
@@ -235,47 +235,47 @@ convert_tw_niels_to_tw_extensible (
     struct tw_extensible_t*  e,
     const struct tw_niels_t* d
 ) {
-    field_add ( &e->y, &d->b, &d->a );
-    field_sub ( &e->x, &d->b, &d->a );
-    field_set_ui( &e->z,     1 );
-    field_copy ( &e->t, &e->x );
-    field_copy ( &e->u, &e->y );
+    field_add ( e->y, d->b, d->a );
+    field_sub ( e->x, d->b, d->a );
+    field_set_ui( e->z,     1 );
+    field_copy ( e->t, e->x );
+    field_copy ( e->u, e->y );
 }
 
 void
 deserialize_montgomery_decaf (
     struct montgomery_aux_t* a,
-    const struct field_t *s
+    const field_a_t s
 ) {
-    field_copy   ( &a->s0, s );
-    field_copy   ( &a->xa, s );
-    field_set_ui ( &a->za, 1 );
-    field_set_ui ( &a->xd, 1 );
-    field_set_ui ( &a->zd, 0 );
+    field_copy   ( a->s0, s );
+    field_copy   ( a->xa, s );
+    field_set_ui ( a->za, 1 );
+    field_set_ui ( a->xd, 1 );
+    field_set_ui ( a->zd, 0 );
 }
 
 void
 montgomery_aux_step (
     struct montgomery_aux_t* a
 ) {
-    field_add  ( &a->xs, &a->xa, &a->za ); // xs = C
-    field_subx ( &a->zs, &a->xa, &a->za ); // zs = D
-    field_add  ( &a->xa, &a->xd, &a->zd ); // xa = A
-    field_subx ( &a->za, &a->xd, &a->zd ); // za = B
-    field_mul  ( &a->xd, &a->xa, &a->zs ); // xd = DA
-    field_mul  ( &a->zd, &a->xs, &a->za ); // zd = CB
-    field_add  ( &a->xs, &a->xd, &a->zd ); // xs = DA+CB
-    field_subx ( &a->zd, &a->xd, &a->zd ); // zd = DA-CB
-    field_mul  ( &a->zs, &a->zd, &a->s0 ); // zs = (DA-CB)*s0
-    field_sqr  ( &a->zd, &a->xa );         // zd = AA
-    field_sqr  ( &a->xa, &a->za );         // xa = BB
-    field_subx ( &a->za, &a->zd, &a->xa ); // za = E
-    field_mul  ( &a->xd, &a->xa, &a->zd ); // xd final
-    field_mulw_scc_wr ( &a->zd, &a->xa, 1-EDWARDS_D ); // zd = (1-d)*E
-    field_add  ( &a->xa, &a->za, &a->zd ); // BB + (1-d)*E
-    field_mul  ( &a->zd, &a->xa, &a->za ); // zd final
-    field_sqr  ( &a->xa, &a->xs );         // (DA+CB)^2
-    field_sqr  ( &a->za, &a->zs );         // (DA-CB)^2*s0^2
+    field_add  ( a->xs, a->xa, a->za ); // xs = C
+    field_sub ( a->zs, a->xa, a->za ); // zs = D
+    field_add  ( a->xa, a->xd, a->zd ); // xa = A
+    field_sub ( a->za, a->xd, a->zd ); // za = B
+    field_mul  ( a->xd, a->xa, a->zs ); // xd = DA
+    field_mul  ( a->zd, a->xs, a->za ); // zd = CB
+    field_add  ( a->xs, a->xd, a->zd ); // xs = DA+CB
+    field_sub ( a->zd, a->xd, a->zd ); // zd = DA-CB
+    field_mul  ( a->zs, a->zd, a->s0 ); // zs = (DA-CB)*s0
+    field_sqr  ( a->zd, a->xa );         // zd = AA
+    field_sqr  ( a->xa, a->za );         // xa = BB
+    field_sub ( a->za, a->zd, a->xa ); // za = E
+    field_mul  ( a->xd, a->xa, a->zd ); // xd final
+    field_mulw_scc_wr ( a->zd, a->xa, 1-EDWARDS_D ); // zd = (1-d)*E
+    field_add  ( a->xa, a->za, a->zd ); // BB + (1-d)*E
+    field_mul  ( a->zd, a->xa, a->za ); // zd final
+    field_sqr  ( a->xa, a->xs );         // (DA+CB)^2
+    field_sqr  ( a->za, a->zs );         // (DA-CB)^2*s0^2
 }
 
 void
@@ -283,110 +283,110 @@ montgomery_step (
     struct montgomery_t* a
 ) {
     ANALYZE_THIS_ROUTINE_CAREFULLY;
-    struct field_t L0, L1;
-    field_add_nr  (   &L0, &a->zd, &a->xd );
-    field_sub (   &L1, &a->xd, &a->zd );
-    field_sub ( &a->zd, &a->xa, &a->za );
-    field_mul  ( &a->xd,   &L0, &a->zd );
-    field_add_nr  ( &a->zd, &a->za, &a->xa );
-    field_mul  ( &a->za,   &L1, &a->zd );
-    field_add_nr  ( &a->xa, &a->za, &a->xd );
-    field_sqr  ( &a->zd, &a->xa );
-    field_mul  ( &a->xa, &a->z0, &a->zd );
-    field_sub ( &a->zd, &a->xd, &a->za );
-    field_sqr  ( &a->za, &a->zd );
-    field_sqr  ( &a->xd,   &L0 );
-    field_sqr  (   &L0,   &L1 );
-    field_mulw_scc ( &a->zd, &a->xd, 1-EDWARDS_D ); /* FIXME PERF MULW */
-    field_sub (   &L1, &a->xd,   &L0 );
-    field_mul  ( &a->xd,   &L0, &a->zd );
-    field_sub_nr  (   &L0, &a->zd,   &L1 );
-    field_bias (   &L0,     4 - 2*is32 /*is32 ? 2 : 4*/ );
-    IF32( field_weak_reduce(   &L0 ) );
-    field_mul  ( &a->zd,   &L0,   &L1 );
+    field_a_t L0, L1;
+    field_add_nr  (   L0, a->zd, a->xd );
+    field_sub (   L1, a->xd, a->zd );
+    field_sub ( a->zd, a->xa, a->za );
+    field_mul  ( a->xd,   L0, a->zd );
+    field_add_nr  ( a->zd, a->za, a->xa );
+    field_mul  ( a->za,   L1, a->zd );
+    field_add_nr  ( a->xa, a->za, a->xd );
+    field_sqr  ( a->zd, a->xa );
+    field_mul  ( a->xa, a->z0, a->zd );
+    field_sub ( a->zd, a->xd, a->za );
+    field_sqr  ( a->za, a->zd );
+    field_sqr  ( a->xd,   L0 );
+    field_sqr  (   L0,   L1 );
+    field_mulw_scc ( a->zd, a->xd, 1-EDWARDS_D ); /* FIXME PERF MULW */
+    field_sub (   L1, a->xd,   L0 );
+    field_mul  ( a->xd,   L0, a->zd );
+    field_sub_nr  (   L0, a->zd,   L1 );
+    field_bias (   L0,     4 - 2*is32 /*is32 ? 2 : 4*/ );
+    IF32( field_weak_reduce(   L0 ) );
+    field_mul  ( a->zd,   L0,   L1 );
 }
 
 void
 deserialize_montgomery (
     struct montgomery_t* a,
-    const struct field_t* sbz
+    const field_a_t sbz
 ) {
-    field_sqr  ( &a->z0,   sbz );
-    field_set_ui( &a->xd,     1 );
-    field_set_ui( &a->zd,     0 );
-    field_set_ui( &a->xa,     1 );
-    field_copy ( &a->za, &a->z0 );
+    field_sqr  ( a->z0,   sbz );
+    field_set_ui( a->xd,     1 );
+    field_set_ui( a->zd,     0 );
+    field_set_ui( a->xa,     1 );
+    field_copy ( a->za, a->z0 );
 }
 
 mask_t
 serialize_montgomery (
-    struct field_t*             b,
+    field_a_t             b,
     const struct montgomery_t* a,
-    const struct field_t*       sbz
+    const field_a_t       sbz
 ) {
     mask_t L4, L5, L6;
-    struct field_t L0, L1, L2, L3;
-    field_mul  (   &L3, &a->z0, &a->zd );
-    field_sub (   &L1,   &L3, &a->xd );
-    field_mul  (   &L3, &a->za,   &L1 );
-    field_mul  (   &L2, &a->z0, &a->xd );
-    field_sub (   &L1,   &L2, &a->zd );
-    field_mul  (   &L0, &a->xa,   &L1 );
-    field_add (   &L2,   &L0,   &L3 );
-    field_sub (   &L1,   &L3,   &L0 );
-    field_mul  (   &L3,   &L1,   &L2 );
-    field_copy (   &L2, &a->z0 );
-    field_addw (   &L2,     1 );
-    field_sqr  (   &L0,   &L2 );
-    field_mulw_scc_wr (   &L1,   &L0, EDWARDS_D-1 );
-    field_add (   &L2, &a->z0, &a->z0 );
-    field_add (   &L0,   &L2,   &L2 );
-    field_add (   &L2,   &L0,   &L1 );
-    field_mul  (   &L0, &a->xd,   &L2 );
-       L5 = field_is_zero( &a->zd );
+    field_a_t L0, L1, L2, L3;
+    field_mul  (   L3, a->z0, a->zd );
+    field_sub (   L1,   L3, a->xd );
+    field_mul  (   L3, a->za,   L1 );
+    field_mul  (   L2, a->z0, a->xd );
+    field_sub (   L1,   L2, a->zd );
+    field_mul  (   L0, a->xa,   L1 );
+    field_add (   L2,   L0,   L3 );
+    field_sub (   L1,   L3,   L0 );
+    field_mul  (   L3,   L1,   L2 );
+    field_copy (   L2, a->z0 );
+    field_addw (   L2,     1 );
+    field_sqr  (   L0,   L2 );
+    field_mulw_scc_wr (   L1,   L0, EDWARDS_D-1 );
+    field_add (   L2, a->z0, a->z0 );
+    field_add (   L0,   L2,   L2 );
+    field_add (   L2,   L0,   L1 );
+    field_mul  (   L0, a->xd,   L2 );
+       L5 = field_is_zero( a->zd );
        L6 = -   L5;
-    constant_time_mask (   &L1,   &L0, sizeof(L1), L5 );
-    field_add (   &L2,   &L1, &a->zd );
+    constant_time_mask (   L1,   L0, sizeof(L1), L5 );
+    field_add (   L2,   L1, a->zd );
        L4 = ~   L5;
-    field_mul  (   &L1,   sbz,   &L3 );
-    field_addw (   &L1,    L6 );
-    field_mul  (   &L3,   &L2,   &L1 );
-    field_mul  (   &L1,   &L3,   &L2 );
-    field_mul  (   &L2,   &L3, &a->xd );
-    field_mul  (   &L3,   &L1,   &L2 );
-    field_isr  (   &L0,   &L3 );
-    field_mul  (   &L2,   &L1,   &L0 );
-    field_sqr  (   &L1,   &L0 );
-    field_mul  (   &L0,   &L3,   &L1 );
-    constant_time_mask (     b,   &L2, sizeof(L1), L4 );
-    field_subw(   &L0,     1 );
-       L5 = field_is_zero(   &L0 );
+    field_mul  (   L1,   sbz,   L3 );
+    field_addw (   L1,    L6 );
+    field_mul  (   L3,   L2,   L1 );
+    field_mul  (   L1,   L3,   L2 );
+    field_mul  (   L2,   L3, a->xd );
+    field_mul  (   L3,   L1,   L2 );
+    field_isr  (   L0,   L3 );
+    field_mul  (   L2,   L1,   L0 );
+    field_sqr  (   L1,   L0 );
+    field_mul  (   L0,   L3,   L1 );
+    constant_time_mask (     b,   L2, sizeof(L1), L4 );
+    field_subw(   L0,     1 );
+       L5 = field_is_zero(   L0 );
        L4 = field_is_zero(   sbz );
     return    L5 |    L4;
 }
 
 void
 serialize_extensible (
-    struct field_t*             b,
+    field_a_t             b,
     const struct extensible_t* a
 ) {
-    struct field_t L0, L1, L2;
-    field_sub (   &L0, &a->y, &a->z );
-    field_add (     b, &a->z, &a->y );
-    field_mul  (   &L1, &a->z, &a->x );
-    field_mul  (   &L2,   &L0,   &L1 );
-    field_mul  (   &L1,   &L2,   &L0 );
-    field_mul  (   &L0,   &L2,     b );
-    field_mul  (   &L2,   &L1,   &L0 );
-    field_isr  (   &L0,   &L2 );
-    field_mul  (     b,   &L1,   &L0 );
-    field_sqr  (   &L1,   &L0 );
-    field_mul  (   &L0,   &L2,   &L1 );
+    field_a_t L0, L1, L2;
+    field_sub (   L0, a->y, a->z );
+    field_add (     b, a->z, a->y );
+    field_mul  (   L1, a->z, a->x );
+    field_mul  (   L2,   L0,   L1 );
+    field_mul  (   L1,   L2,   L0 );
+    field_mul  (   L0,   L2,     b );
+    field_mul  (   L2,   L1,   L0 );
+    field_isr  (   L0,   L2 );
+    field_mul  (     b,   L1,   L0 );
+    field_sqr  (   L1,   L0 );
+    field_mul  (   L0,   L2,   L1 );
 }
 
 void
 decaf_make_even (
-    struct field_t *a
+    field_a_t a
 ) {
     field_cond_neg ( a, field_low_bit(a) );
     field_strong_reduce ( a );
@@ -394,163 +394,163 @@ decaf_make_even (
 
 void
 decaf_serialize_extensible (
-    struct field_t*            b,
+    field_a_t b,
     const struct extensible_t* a
 ) {
-    struct field_t L0, L1, L2, L3;
-    field_mulw_scc ( &L2, &a->y, EDWARDS_D ); // L2 = d*y
-    field_mul  ( &L3, &L2, &a->t ); // L3 = d*y*t_
-    field_mul  ( &L2, &L3, &a->u ); // L2 = d*y*t
-    field_mul  ( &L0, &a->x, &a->z ); // L0 = x*z
-    field_subx ( &L3, &L2, &L0 ); // L3 = d*y*t - x*z
-    field_add  ( &L0, &a->y, &a->z ); // L0 = y+z
-    field_subx ( &L1, &a->y, &a->z ); // L1 = y-z
-    field_mul  ( &L2, &L1, &L0 );     // L2 = y^2-z^2
-    field_isr  ( &L2, &L2 );          // L2 = 1/sqrt(y^2-z^2)
-    field_sqr  ( &L1, &L2 );          // L1 = 1/(y^2-z^2)
-    field_mul  ( &L0, &L1, &L3 );     // L0 = (d*y*t - z*x)/(y^2-z^2) = 1/x
-    field_mul  ( &L1, &L2, &sqrt_d_minus_1 ); // L1 = sy
-    field_add  ( &L3, &L1, &L1 );     // L3 = 2*sy
-    field_negx ( &L3, &L3 );          // L3 = -2*sy     
-    field_mul  ( &L2, &L3, &a->z );   // L2 = -2*sy*z
-    field_cond_neg ( &L1, field_low_bit(&L2) ); // cond-neg sy
-    field_mul  ( &L2, &L1, &a->y ); // L2 = 2*sy*y
-    field_add  ( b, &L0, &L2 );
+    field_a_t L0, L1, L2, L3;
+    field_mulw_scc ( L2, a->y, EDWARDS_D ); // L2 = d*y
+    field_mul  ( L3, L2, a->t ); // L3 = d*y*t_
+    field_mul  ( L2, L3, a->u ); // L2 = d*y*t
+    field_mul  ( L0, a->x, a->z ); // L0 = x*z
+    field_sub ( L3, L2, L0 ); // L3 = d*y*t - x*z
+    field_add  ( L0, a->y, a->z ); // L0 = y+z
+    field_sub ( L1, a->y, a->z ); // L1 = y-z
+    field_mul  ( L2, L1, L0 );     // L2 = y^2-z^2
+    field_isr  ( L2, L2 );          // L2 = 1/sqrt(y^2-z^2)
+    field_sqr  ( L1, L2 );          // L1 = 1/(y^2-z^2)
+    field_mul  ( L0, L1, L3 );     // L0 = (d*y*t - z*x)/(y^2-z^2) = 1/x
+    field_mul  ( L1, L2, sqrt_d_minus_1 ); // L1 = sy
+    field_add  ( L3, L1, L1 );     // L3 = 2*sy
+    field_neg ( L3, L3 );          // L3 = -2*sy     
+    field_mul  ( L2, L3, a->z );   // L2 = -2*sy*z
+    field_cond_neg ( L1, field_low_bit(L2) ); // cond-neg sy
+    field_mul  ( L2, L1, a->y ); // L2 = 2*sy*y
+    field_add  ( b, L0, L2 );
     decaf_make_even ( b );
 }
 
 void
 decaf_serialize_tw_extensible (
-    struct field_t*            b,
+    field_a_t            b,
     const struct tw_extensible_t* a
 ) {
-    struct field_t L0, L1, L2, L3;
-    field_mulw_scc ( &L2, &a->y, 1-EDWARDS_D ); // L2 = (1-d)*y
-    field_mul  ( &L3, &L2, &a->t ); // L3 = (1-d)*y*t_
-    field_mul  ( &L2, &L3, &a->u ); // L2 = (1-d)*y*t
-    field_mul  ( &L0, &a->x, &a->z ); // L0 = x*z
-    field_subx ( &L3, &L2, &L0 ); // L3 = d*y*t - x*z
-    field_add  ( &L0, &a->z, &a->y ); // L0 = y+z
-    field_subx ( &L1, &a->z, &a->y ); // L1 = z-y
-    field_mul  ( &L2, &L1, &L0 );     // L2 = z^2-y^2
-    field_isr  ( &L2, &L2 );          // L2 = 1/sqrt(z^2-y^2)
-    field_sqr  ( &L1, &L2 );          // L1 = 1/(z^2-y^2)
-    field_mul  ( &L0, &L1, &L3 );     // L0 = ((1-d)*y*t - z*x)/(y^2-z^2) = 1/x
-    field_mul  ( &L1, &L2, &sqrt_minus_d ); // L1 = sy
-    field_add  ( &L3, &L1, &L1 );     // L3 = 2*sy
-    field_negx ( &L3, &L3 );          // L3 = -2*sy     
-    field_mul  ( &L2, &L3, &a->z );   // L2 = -2*sy*z
-    field_cond_neg ( &L1, field_low_bit(&L2) ); // cond-neg sy
-    field_mul  ( &L2, &L1, &a->y ); // L2 = 2*sy*y
-    field_add  ( b, &L0, &L2 );
+    field_a_t L0, L1, L2, L3;
+    field_mulw_scc ( L2, a->y, 1-EDWARDS_D ); // L2 = (1-d)*y
+    field_mul  ( L3, L2, a->t ); // L3 = (1-d)*y*t_
+    field_mul  ( L2, L3, a->u ); // L2 = (1-d)*y*t
+    field_mul  ( L0, a->x, a->z ); // L0 = x*z
+    field_sub ( L3, L2, L0 ); // L3 = d*y*t - x*z
+    field_add  ( L0, a->z, a->y ); // L0 = y+z
+    field_sub ( L1, a->z, a->y ); // L1 = z-y
+    field_mul  ( L2, L1, L0 );     // L2 = z^2-y^2
+    field_isr  ( L2, L2 );          // L2 = 1/sqrt(z^2-y^2)
+    field_sqr  ( L1, L2 );          // L1 = 1/(z^2-y^2)
+    field_mul  ( L0, L1, L3 );     // L0 = ((1-d)*y*t - z*x)/(y^2-z^2) = 1/x
+    field_mul  ( L1, L2, sqrt_minus_d ); // L1 = sy
+    field_add  ( L3, L1, L1 );     // L3 = 2*sy
+    field_neg ( L3, L3 );          // L3 = -2*sy     
+    field_mul  ( L2, L3, a->z );   // L2 = -2*sy*z
+    field_cond_neg ( L1, field_low_bit(L2) ); // cond-neg sy
+    field_mul  ( L2, L1, a->y ); // L2 = 2*sy*y
+    field_add  ( b, L0, L2 );
     decaf_make_even ( b );
 }
 
 mask_t
 decaf_deserialize_affine (
     struct affine_t       *a,
-    const struct field_t  *s,
+    const field_a_t s,
     mask_t allow_identity
 ) {
-    struct field_t L0, L1, L2, L3, L4, L5;
+    field_a_t L0, L1, L2, L3, L4, L5;
     mask_t succ, zero;
     zero = field_is_zero(s);
     succ = allow_identity | ~zero;
     succ &= ~field_low_bit(s);
-    field_sqr  ( &L0, s );
-    field_copy ( &L1, &L0 );
-    field_addw ( &L1, 1 );
-    field_make_nonzero ( &L1 );
-    field_sqr ( &L2, &L1 );
-    field_mulw_scc_wr ( &L3, &L0, -4*EDWARDS_D );
-    field_add ( &L3, &L3, &L2 );
-    field_mul ( &L4, &L3, &L2 );
-    field_mul ( &L2, &L4, &L0 );
-    field_isr ( &L4, &L2 );
-    field_sqr ( &L5, &L4 );
-    field_mul ( &L0, &L5, &L2 );
-    field_addw( &L0, 1 );
-    succ &= ~field_is_zero( &L0 );
-    field_mul ( &L2, &L3, &L1 );
-    field_mul ( &L3, &L2, &L4 );
-    field_cond_neg ( &L4, field_low_bit(&L3) );
-    field_mul ( &L3, &L4, s );
-    field_sqr ( &L4, &L3 );
-    field_mul ( &L0, &L2, &L4 );
-    field_add ( &L0, &L0, &L0 );
-    field_mul ( &a->x, &L0, s );
-    field_mul ( &L2, &L1, &L3 );
-    field_negx ( &L1, &L1 ); 
-    field_addw ( &L1, 2 );
-    field_mul ( &a->y, &L1, &L2 );
-    field_addw ( &a->y, -zero );
+    field_sqr  ( L0, s );
+    field_copy ( L1, L0 );
+    field_addw ( L1, 1 );
+    field_make_nonzero ( L1 );
+    field_sqr ( L2, L1 );
+    field_mulw_scc_wr ( L3, L0, -4*EDWARDS_D );
+    field_add ( L3, L3, L2 );
+    field_mul ( L4, L3, L2 );
+    field_mul ( L2, L4, L0 );
+    field_isr ( L4, L2 );
+    field_sqr ( L5, L4 );
+    field_mul ( L0, L5, L2 );
+    field_addw( L0, 1 );
+    succ &= ~field_is_zero( L0 );
+    field_mul ( L2, L3, L1 );
+    field_mul ( L3, L2, L4 );
+    field_cond_neg ( L4, field_low_bit(L3) );
+    field_mul ( L3, L4, s );
+    field_sqr ( L4, L3 );
+    field_mul ( L0, L2, L4 );
+    field_add ( L0, L0, L0 );
+    field_mul ( a->x, L0, s );
+    field_mul ( L2, L1, L3 );
+    field_neg ( L1, L1 ); 
+    field_addw ( L1, 2 );
+    field_mul ( a->y, L1, L2 );
+    field_addw ( a->y, -zero );
     return succ;
 }
 
 mask_t
 decaf_deserialize_tw_affine (
     struct tw_affine_t    *a,
-    const struct field_t  *s,
+    const field_a_t s,
     mask_t allow_identity
 ) {
-    struct field_t L0, L1, L2, L3, L4, L5;
+    field_a_t L0, L1, L2, L3, L4, L5;
     mask_t succ, zero;
     zero = field_is_zero(s);
     succ = allow_identity | ~zero;
     succ &= ~field_low_bit(s);
-    field_sqr  ( &L0, s );
-    field_negx ( &L1, &L0 );
-    field_addw ( &L1, 1 );
-    field_make_nonzero ( &L1 );
-    field_sqr ( &L2, &L1 );
-    field_mulw_scc_wr ( &L3, &L0, 4-4*EDWARDS_D );
-    field_add ( &L3, &L3, &L2 );
-    field_mul ( &L4, &L3, &L2 );
-    field_mul ( &L2, &L4, &L0 );
-    field_isr ( &L4, &L2 );
-    field_sqr ( &L5, &L4 );
-    field_mul ( &L0, &L5, &L2 );
-    field_addw( &L0, 1 );
-    succ &= ~field_is_zero( &L0 );
-    field_mul ( &L2, &L3, &L1 );
-    field_mul ( &L3, &L2, &L4 );
-    field_cond_neg ( &L4, field_low_bit(&L3) );
-    field_mul ( &L3, &L4, s );
-    field_sqr ( &L4, &L3 );
-    field_mul ( &L0, &L2, &L4 );
-    field_add ( &L0, &L0, &L0 );
-    field_mul ( &a->x, &L0, s );
-    field_mul ( &L2, &L1, &L3 );
-    field_negx ( &L1, &L1 );      
-    field_addw ( &L1, 2 );
-    field_mul ( &a->y, &L1, &L2 );
-    field_addw ( &a->y, -zero );
+    field_sqr  ( L0, s );
+    field_neg ( L1, L0 );
+    field_addw ( L1, 1 );
+    field_make_nonzero ( L1 );
+    field_sqr ( L2, L1 );
+    field_mulw_scc_wr ( L3, L0, 4-4*EDWARDS_D );
+    field_add ( L3, L3, L2 );
+    field_mul ( L4, L3, L2 );
+    field_mul ( L2, L4, L0 );
+    field_isr ( L4, L2 );
+    field_sqr ( L5, L4 );
+    field_mul ( L0, L5, L2 );
+    field_addw( L0, 1 );
+    succ &= ~field_is_zero( L0 );
+    field_mul ( L2, L3, L1 );
+    field_mul ( L3, L2, L4 );
+    field_cond_neg ( L4, field_low_bit(L3) );
+    field_mul ( L3, L4, s );
+    field_sqr ( L4, L3 );
+    field_mul ( L0, L2, L4 );
+    field_add ( L0, L0, L0 );
+    field_mul ( a->x, L0, s );
+    field_mul ( L2, L1, L3 );
+    field_neg ( L1, L1 );      
+    field_addw ( L1, 2 );
+    field_mul ( a->y, L1, L2 );
+    field_addw ( a->y, -zero );
     return succ;
 }
 
 void
 untwist_and_double_and_serialize (
-    struct field_t*                b,
+    field_a_t                b,
     const struct tw_extensible_t* a
 ) {
-    struct field_t L0, L1, L2, L3;
-    field_mul  (   &L3, &a->y, &a->x );
-    field_add (     b, &a->y, &a->x );
-    field_sqr  (   &L1,     b );
-    field_add (   &L2,   &L3,   &L3 );
-    field_sub (     b,   &L1,   &L2 );
-    field_sqr  (   &L2, &a->z );
-    field_sqr  (   &L1,   &L2 );
+    field_a_t L0, L1, L2, L3;
+    field_mul  (   L3, a->y, a->x );
+    field_add (     b, a->y, a->x );
+    field_sqr  (   L1,     b );
+    field_add (   L2,   L3,   L3 );
+    field_sub (     b,   L1,   L2 );
+    field_sqr  (   L2, a->z );
+    field_sqr  (   L1,   L2 );
     field_add (   b,     b,     b );
-    field_mulw_scc (     &L2,   b, EDWARDS_D-1 );
-    field_mulw_scc (   b,   &L2, EDWARDS_D-1 );
-    field_mul  (   &L0,   &L2,   &L1 );
-    field_mul  (   &L2,     b,   &L0 );
-    field_isr  (   &L0,   &L2 );
-    field_mul  (   &L1,     b,   &L0 );
-    field_sqr  (     b,   &L0 );
-    field_mul  (   &L0,   &L2,     b );
-    field_mul  (     b,   &L1,   &L3 );
+    field_mulw_scc (     L2,   b, EDWARDS_D-1 );
+    field_mulw_scc (   b,   L2, EDWARDS_D-1 );
+    field_mul  (   L0,   L2,   L1 );
+    field_mul  (   L2,     b,   L0 );
+    field_isr  (   L0,   L2 );
+    field_mul  (   L1,     b,   L0 );
+    field_sqr  (     b,   L0 );
+    field_mul  (   L0,   L2,     b );
+    field_mul  (     b,   L1,   L3 );
 }
 
 void
@@ -558,25 +558,25 @@ twist_even (
     struct tw_extensible_t*    b,
     const struct extensible_t* a
 ) {
-    field_sqr  ( &b->y, &a->z );
-    field_sqr  ( &b->z, &a->x );
-    field_sub ( &b->u, &b->y, &b->z );
-    field_sub ( &b->z, &a->z, &a->x );
-    field_mul  ( &b->y, &b->z, &a->y );
-    field_sub ( &b->z, &a->z, &a->y );
-    field_mul  ( &b->x, &b->z, &b->y );
-    field_mul  ( &b->t, &b->x, &b->u );
-    field_mul  ( &b->y, &b->x, &b->t );
-    field_isr  ( &b->t, &b->y );
-    field_mul  ( &b->u, &b->x, &b->t );
-    field_sqr  ( &b->x, &b->t );
-    field_mul  ( &b->t, &b->y, &b->x );
-    field_mul  ( &b->x, &a->x, &b->u );
-    field_mul  ( &b->y, &a->y, &b->u );
-    field_addw ( &b->y,    -field_is_zero( &b->z ) );
-    field_set_ui( &b->z,     1 );
-    field_copy ( &b->t, &b->x );
-    field_copy ( &b->u, &b->y );
+    field_sqr  ( b->y, a->z );
+    field_sqr  ( b->z, a->x );
+    field_sub ( b->u, b->y, b->z );
+    field_sub ( b->z, a->z, a->x );
+    field_mul  ( b->y, b->z, a->y );
+    field_sub ( b->z, a->z, a->y );
+    field_mul  ( b->x, b->z, b->y );
+    field_mul  ( b->t, b->x, b->u );
+    field_mul  ( b->y, b->x, b->t );
+    field_isr  ( b->t, b->y );
+    field_mul  ( b->u, b->x, b->t );
+    field_sqr  ( b->x, b->t );
+    field_mul  ( b->t, b->y, b->x );
+    field_mul  ( b->x, a->x, b->u );
+    field_mul  ( b->y, a->y, b->u );
+    field_addw ( b->y,    -field_is_zero( b->z ) );
+    field_set_ui( b->z,     1 );
+    field_copy ( b->t, b->x );
+    field_copy ( b->u, b->y );
 }
 
 void
@@ -584,135 +584,134 @@ test_only_twist (
     struct tw_extensible_t*    b,
     const struct extensible_t* a
 ) {
-    struct field_t L0, L1;
-    field_sqr  ( &b->u, &a->z );
-    field_sqr  ( &b->y, &a->x );
-    field_sub ( &b->z, &b->u, &b->y );
-    field_add ( &b->y, &b->z, &b->z );
-    field_add ( &b->u, &b->y, &b->y );
-    field_sub ( &b->y, &a->z, &a->x );
-    field_mul  ( &b->x, &b->y, &a->y );
-    field_sub ( &b->z, &a->z, &a->y );
-    field_mul  ( &b->t, &b->z, &b->x );
-    field_mul  (   &L1, &b->t, &b->u );
-    field_mul  ( &b->x, &b->t,   &L1 );
-    field_isr  (   &L0, &b->x );
-    field_mul  ( &b->u, &b->t,   &L0 );
-    field_sqr  (   &L1,   &L0 );
-    field_mul  ( &b->t, &b->x,   &L1 );
-    field_add (   &L1, &a->y, &a->x );
-    field_sub (   &L0, &a->x, &a->y );
-    field_mul  ( &b->x, &b->t,   &L0 );
-    field_add (   &L0, &b->x,   &L1 );
-    field_sub ( &b->t,   &L1, &b->x );
-    field_mul  ( &b->x,   &L0, &b->u );
-    field_addw ( &b->x, -field_is_zero( &b->y ) );
-    field_mul  ( &b->y, &b->t, &b->u );
-    field_addw ( &b->y, -field_is_zero( &b->z ) );
-    field_set_ui( &b->z, 1+field_is_zero( &a->y ) );
-    field_copy ( &b->t, &b->x );
-    field_copy ( &b->u, &b->y );
+    field_a_t L0, L1;
+    field_sqr  ( b->u, a->z );
+    field_sqr  ( b->y, a->x );
+    field_sub ( b->z, b->u, b->y );
+    field_add ( b->y, b->z, b->z );
+    field_add ( b->u, b->y, b->y );
+    field_sub ( b->y, a->z, a->x );
+    field_mul  ( b->x, b->y, a->y );
+    field_sub ( b->z, a->z, a->y );
+    field_mul  ( b->t, b->z, b->x );
+    field_mul  (   L1, b->t, b->u );
+    field_mul  ( b->x, b->t,   L1 );
+    field_isr  (   L0, b->x );
+    field_mul  ( b->u, b->t,   L0 );
+    field_sqr  (   L1,   L0 );
+    field_mul  ( b->t, b->x,   L1 );
+    field_add (   L1, a->y, a->x );
+    field_sub (   L0, a->x, a->y );
+    field_mul  ( b->x, b->t,   L0 );
+    field_add (   L0, b->x,   L1 );
+    field_sub ( b->t,   L1, b->x );
+    field_mul  ( b->x,   L0, b->u );
+    field_addw ( b->x, -field_is_zero( b->y ) );
+    field_mul  ( b->y, b->t, b->u );
+    field_addw ( b->y, -field_is_zero( b->z ) );
+    field_set_ui( b->z, 1+field_is_zero( a->y ) );
+    field_copy ( b->t, b->x );
+    field_copy ( b->u, b->y );
 }
 
 mask_t
 is_even_pt (
     const struct extensible_t* a
 ) {
-    struct field_t L0, L1, L2;
-    field_sqr  (   &L2, &a->z );
-    field_sqr  (   &L1, &a->x );
-    field_sub (   &L0,   &L2,   &L1 );
-    return field_is_square (   &L0 );
+    field_a_t L0, L1, L2;
+    field_sqr  (   L2, a->z );
+    field_sqr  (   L1, a->x );
+    field_sub (   L0,   L2,   L1 );
+    return field_is_square (   L0 );
 }
 
 mask_t
 is_even_tw (
     const struct tw_extensible_t* a
 ) {
-    struct field_t L0, L1, L2;
-    field_sqr  (   &L2, &a->z );
-    field_sqr  (   &L1, &a->x );
-    field_add (   &L0,   &L1,   &L2 );
-    return field_is_square (   &L0 );
+    field_a_t L0, L1, L2;
+    field_sqr  (   L2, a->z );
+    field_sqr  (   L1, a->x );
+    field_add (   L0,   L1,   L2 );
+    return field_is_square (   L0 );
 }
 
 mask_t
 deserialize_affine (
     struct affine_t*     a,
-    const struct field_t* sz
-) {
-    struct field_t L0, L1, L2, L3;
-    field_sqr  (   &L1,    sz );
-    field_copy (   &L3,   &L1 );
-    field_addw (   &L3,     1 );
-    field_sqr  (   &L2,   &L3 );
-    field_mulw_scc (   &a->x,   &L2, EDWARDS_D-1 ); /* PERF MULW */
-    field_add (   &L3,   &L1,   &L1 ); /* FIXME: i adjusted the bias here, was it right? */
-    field_add ( &a->y,   &L3,   &L3 );
-    field_add (   &L3, &a->y, &a->x );
-    field_copy ( &a->y,   &L1 );
-    field_negx ( &a->x, &a->y );
-    field_addw ( &a->x,     1 );
-    field_mul  ( &a->y, &a->x,   &L3 );
-    field_sqr  (   &L2, &a->x );
-    field_mul  (   &L0,   &L2, &a->y );
-    field_mul  ( &a->y, &a->x,   &L0 );
-    field_isr  (   &L3, &a->y );
-    field_mul  ( &a->y,   &L2,   &L3 );
-    field_sqr  (   &L2,   &L3 );
-    field_mul  (   &L3,   &L0,   &L2 );
-    field_mul  (   &L0, &a->x,   &L3 );
-    field_add (   &L2, &a->y, &a->y );
-    field_mul  ( &a->x,    sz,   &L2 );
-    field_addw (   &L1,     1 );
-    field_mul  ( &a->y,   &L1,   &L3 );
-    field_subw(   &L0,     1 );
-    return field_is_zero(   &L0 );
+    const field_a_t sz
+) {
+    field_a_t L0, L1, L2, L3;
+    field_sqr  (   L1,    sz );
+    field_copy (   L3,   L1 );
+    field_addw (   L3,     1 );
+    field_sqr  (   L2,   L3 );
+    field_mulw_scc (   a->x,   L2, EDWARDS_D-1 ); /* PERF MULW */
+    field_add (   L3,   L1,   L1 ); /* FIXME: i adjusted the bias here, was it right? */
+    field_add ( a->y,   L3,   L3 );
+    field_add (   L3, a->y, a->x );
+    field_copy ( a->y,   L1 );
+    field_neg ( a->x, a->y );
+    field_addw ( a->x,     1 );
+    field_mul  ( a->y, a->x,   L3 );
+    field_sqr  (   L2, a->x );
+    field_mul  (   L0,   L2, a->y );
+    field_mul  ( a->y, a->x,   L0 );
+    field_isr  (   L3, a->y );
+    field_mul  ( a->y,   L2,   L3 );
+    field_sqr  (   L2,   L3 );
+    field_mul  (   L3,   L0,   L2 );
+    field_mul  (   L0, a->x,   L3 );
+    field_add (   L2, a->y, a->y );
+    field_mul  ( a->x,    sz,   L2 );
+    field_addw (   L1,     1 );
+    field_mul  ( a->y,   L1,   L3 );
+    field_subw(   L0,     1 );
+    return field_is_zero(   L0 );
 }
 
 mask_t
 deserialize_and_twist_approx (
     struct tw_extensible_t* a,
-    const struct field_t*    sdm1,
-    const struct field_t*    sz
-) {
-    struct field_t L0, L1;
-    field_sqr  ( &a->z,    sz );
-    field_copy ( &a->y, &a->z );
-    field_addw ( &a->y,     1 );
-    field_sqr  ( &L0, &a->y );
-    field_mulw_scc ( &a->x, &L0, EDWARDS_D-1 );
-    field_add ( &a->y, &a->z, &a->z );
-    field_add ( &a->u, &a->y, &a->y );
-    field_add ( &a->y, &a->u, &a->x );
-    field_sqr  ( &a->x, &a->z );
-    field_negx ( &a->u, &a->x );
-    field_addw ( &a->u,     1 );
-    field_mul  ( &a->x,  sdm1, &a->u );
-    field_mul  (   &L0, &a->x, &a->y );
-    field_mul  ( &a->t,   &L0, &a->y );
-    field_mul  ( &a->u, &a->x, &a->t );
-    field_mul  ( &a->t, &a->u,   &L0 );
-    field_mul  ( &a->y, &a->x, &a->t );
-    field_isr  (   &L0, &a->y );
-    field_mul  ( &a->y, &a->u,   &L0 );
-    field_sqr  (   &L1,   &L0 );
-    field_mul  ( &a->u, &a->t,   &L1 );
-    field_mul  ( &a->t, &a->x, &a->u );
-    field_add ( &a->x,    sz,    sz );
-    field_mul  (   &L0, &a->u, &a->x );
-    field_copy ( &a->x, &a->z );
-    field_negx (   &L1, &a->x );
-    field_addw (   &L1,     1 );
-    field_mul  ( &a->x,   &L1,   &L0 );
-    field_mul  (   &L0, &a->u, &a->y );
-    field_addw ( &a->z,     1 );
-    field_mul  ( &a->y, &a->z,   &L0 );
-    field_subw( &a->t,     1 );
-    mask_t ret = field_is_zero( &a->t );
-    field_set_ui( &a->z,     1 );
-    field_copy ( &a->t, &a->x );
-    field_copy ( &a->u, &a->y );
+    const field_a_t    sz
+) {
+    field_a_t L0, L1;
+    field_sqr  ( a->z,    sz );
+    field_copy ( a->y, a->z );
+    field_addw ( a->y,     1 );
+    field_sqr  ( L0, a->y );
+    field_mulw_scc ( a->x, L0, EDWARDS_D-1 );
+    field_add ( a->y, a->z, a->z );
+    field_add ( a->u, a->y, a->y );
+    field_add ( a->y, a->u, a->x );
+    field_sqr  ( a->x, a->z );
+    field_neg ( a->u, a->x );
+    field_addw ( a->u,     1 );
+    field_mul  ( a->x,  sqrt_d_minus_1, a->u );
+    field_mul  (   L0, a->x, a->y );
+    field_mul  ( a->t,   L0, a->y );
+    field_mul  ( a->u, a->x, a->t );
+    field_mul  ( a->t, a->u,   L0 );
+    field_mul  ( a->y, a->x, a->t );
+    field_isr  (   L0, a->y );
+    field_mul  ( a->y, a->u,   L0 );
+    field_sqr  (   L1,   L0 );
+    field_mul  ( a->u, a->t,   L1 );
+    field_mul  ( a->t, a->x, a->u );
+    field_add ( a->x,    sz,    sz );
+    field_mul  (   L0, a->u, a->x );
+    field_copy ( a->x, a->z );
+    field_neg (   L1, a->x );
+    field_addw (   L1,     1 );
+    field_mul  ( a->x,   L1,   L0 );
+    field_mul  (   L0, a->u, a->y );
+    field_addw ( a->z,     1 );
+    field_mul  ( a->y, a->z,   L0 );
+    field_subw( a->t,     1 );
+    mask_t ret = field_is_zero( a->t );
+    field_set_ui( a->z,     1 );
+    field_copy ( a->t, a->x );
+    field_copy ( a->u, a->y );
     return ret;
 }
 
@@ -720,30 +719,30 @@ void
 set_identity_extensible (
     struct extensible_t* a
 ) {
-    field_set_ui( &a->x,     0 );
-    field_set_ui( &a->y,     1 );
-    field_set_ui( &a->z,     1 );
-    field_set_ui( &a->t,     0 );
-    field_set_ui( &a->u,     0 );
+    field_set_ui( a->x,     0 );
+    field_set_ui( a->y,     1 );
+    field_set_ui( a->z,     1 );
+    field_set_ui( a->t,     0 );
+    field_set_ui( a->u,     0 );
 }
 
 void
 set_identity_tw_extensible (
     struct tw_extensible_t* a
 ) {
-    field_set_ui( &a->x,     0 );
-    field_set_ui( &a->y,     1 );
-    field_set_ui( &a->z,     1 );
-    field_set_ui( &a->t,     0 );
-    field_set_ui( &a->u,     0 );
+    field_set_ui( a->x,     0 );
+    field_set_ui( a->y,     1 );
+    field_set_ui( a->z,     1 );
+    field_set_ui( a->t,     0 );
+    field_set_ui( a->u,     0 );
 }
 
 void
 set_identity_affine (
     struct affine_t* a
 ) {
-    field_set_ui( &a->x,     0 );
-    field_set_ui( &a->y,     1 );
+    field_set_ui( a->x,     0 );
+    field_set_ui( a->y,     1 );
 }
 
 mask_t
@@ -751,12 +750,12 @@ decaf_eq_extensible (
     const struct extensible_t* a,
     const struct extensible_t* b
 ) {
-    struct field_t L0, L1, L2;
-    field_mul  (   &L2, &b->y, &a->x );
-    field_mul  (   &L1, &a->y, &b->x );
-    field_sub  (   &L0,   &L2,   &L1 );
-    field_bias (   &L0,     2 );
-    return field_is_zero ( &L0 );
+    field_a_t L0, L1, L2;
+    field_mul  (   L2, b->y, a->x );
+    field_mul  (   L1, a->y, b->x );
+    field_sub  (   L0,   L2,   L1 );
+    field_bias (   L0,     2 );
+    return field_is_zero ( L0 );
 }
 
 mask_t
@@ -764,12 +763,12 @@ decaf_eq_tw_extensible (
     const struct tw_extensible_t* a,
     const struct tw_extensible_t* b
 ) {
-    struct field_t L0, L1, L2;
-    field_mul  (   &L2, &b->y, &a->x );
-    field_mul  (   &L1, &a->y, &b->x );
-    field_sub  (   &L0,   &L2,   &L1 );
-    field_bias (   &L0,     2 );
-    return field_is_zero ( &L0 );
+    field_a_t L0, L1, L2;
+    field_mul  (   L2, b->y, a->x );
+    field_mul  (   L1, a->y, b->x );
+    field_sub  (   L0, L2, L1 );
+    field_bias (   L0, 2 );
+    return field_is_zero ( L0 );
 }
 
 mask_t
@@ -778,11 +777,11 @@ eq_affine (
     const struct affine_t* b
 ) {
     mask_t L1, L2;
-    struct field_t L0;
-    field_sub (   &L0, &a->x, &b->x );
-       L2 = field_is_zero(   &L0 );
-    field_sub (   &L0, &a->y, &b->y );
-       L1 = field_is_zero(   &L0 );
+    field_a_t L0;
+    field_sub (   L0, a->x, b->x );
+       L2 = field_is_zero(   L0 );
+    field_sub (   L0, a->y, b->y );
+       L1 = field_is_zero(   L0 );
     return    L2 &    L1;
 }
 
@@ -792,15 +791,15 @@ eq_extensible (
     const struct extensible_t* b
 ) {
     mask_t L3, L4;
-    struct field_t L0, L1, L2;
-    field_mul  (   &L2, &b->z, &a->x );
-    field_mul  (   &L1, &a->z, &b->x );
-    field_sub (   &L0,   &L2,   &L1 );
-       L4 = field_is_zero(   &L0 );
-    field_mul  (   &L2, &b->z, &a->y );
-    field_mul  (   &L1, &a->z, &b->y );
-    field_sub (   &L0,   &L2,   &L1 );
-       L3 = field_is_zero(   &L0 );
+    field_a_t L0, L1, L2;
+    field_mul  (   L2, b->z, a->x );
+    field_mul  (   L1, a->z, b->x );
+    field_sub (   L0,   L2,   L1 );
+       L4 = field_is_zero(   L0 );
+    field_mul  (   L2, b->z, a->y );
+    field_mul  (   L1, a->z, b->y );
+    field_sub (   L0,   L2,   L1 );
+       L3 = field_is_zero(   L0 );
     return    L4 &    L3;
 }
 
@@ -810,39 +809,39 @@ eq_tw_extensible (
     const struct tw_extensible_t* b
 ) {
     mask_t L3, L4;
-    struct field_t L0, L1, L2;
-    field_mul  (   &L2, &b->z, &a->x );
-    field_mul  (   &L1, &a->z, &b->x );
-    field_sub (   &L0,   &L2,   &L1 );
-       L4 = field_is_zero(   &L0 );
-    field_mul  (   &L2, &b->z, &a->y );
-    field_mul  (   &L1, &a->z, &b->y );
-    field_sub (   &L0,   &L2,   &L1 );
-       L3 = field_is_zero(   &L0 );
+    field_a_t L0, L1, L2;
+    field_mul  (   L2, b->z, a->x );
+    field_mul  (   L1, a->z, b->x );
+    field_sub (   L0,   L2,   L1 );
+       L4 = field_is_zero(   L0 );
+    field_mul  (   L2, b->z, a->y );
+    field_mul  (   L1, a->z, b->y );
+    field_sub (   L0,   L2,   L1 );
+       L3 = field_is_zero(   L0 );
     return    L4 &    L3;
 }
 
 void
 elligator_2s_inject (
     struct affine_t*     a,
-    const struct field_t* r
-) {
-    struct field_t L2, L3, L4, L5, L6, L7, L8;
-    field_sqr  ( &a->x,     r );
-    field_sqr  (   &L3, &a->x );
-    field_copy ( &a->y,   &L3 );
-    field_negx (   &L4, &a->y );
-    field_addw (   &L4,     1 );
-    field_sqr  (   &L2,   &L4 );
-    field_mulw (   &L7,   &L2, (EDWARDS_D-1)*(EDWARDS_D-1) );
-    field_mulw (   &L8,   &L3, 4*(EDWARDS_D+1)*(EDWARDS_D+1) );
-    field_add ( &a->y,   &L8,   &L7 );
-    field_mulw (   &L8,   &L2, 4*(EDWARDS_D)*(EDWARDS_D-1) );
-    field_sub (   &L7, &a->y,   &L8 );
-    field_mulw_scc (   &L6, &a->y, -2-2*EDWARDS_D );
-    field_mul  (   &L5,   &L7,   &L6 );
+    const field_a_t r
+) {
+    field_a_t L2, L3, L4, L5, L6, L7, L8;
+    field_sqr  ( a->x,     r );
+    field_sqr  (   L3, a->x );
+    field_copy ( a->y,   L3 );
+    field_neg (   L4, a->y );
+    field_addw (   L4,     1 );
+    field_sqr  (   L2,   L4 );
+    field_mulw (   L7,   L2, (EDWARDS_D-1)*(EDWARDS_D-1) );
+    field_mulw (   L8,   L3, 4*(EDWARDS_D+1)*(EDWARDS_D+1) );
+    field_add ( a->y,   L8,   L7 );
+    field_mulw (   L8,   L2, 4*(EDWARDS_D)*(EDWARDS_D-1) );
+    field_sub (   L7, a->y,   L8 );
+    field_mulw_scc (   L6, a->y, -2-2*EDWARDS_D );
+    field_mul  (   L5,   L7,   L6 );
         /* FIXME Stability problem (API stability, not crash) / possible bug.
-         * change to: p448_mul  (   &L5,   &L7,   &L4 ); ?
+         * change to: p448_mul  (   L5,   L7,   L4 ); ?
          * This isn't a deep change: it's for sign adjustment.
          * Need to check which one leads to the correct sign, probably by writig
          * the invert routine.
@@ -853,47 +852,47 @@ elligator_2s_inject (
          * Could compute be, (be)^2, (be)^3, a b^3 e^3, a b^3 e^4. = 4M+S
          * instead of 6M.
          */
-    field_mul  (   &L8,   &L5,   &L4 );
-    field_mul  (   &L4,   &L5,   &L6 );
-    field_mul  (   &L5,   &L7,   &L8 );
-    field_mul  (   &L8,   &L5,   &L4 );
-    field_mul  (   &L4,   &L7,   &L8 );
-    field_isr  (   &L6,   &L4 );
-    field_mul  (   &L4,   &L5,   &L6 );
-    field_sqr  (   &L5,   &L6 );
-    field_mul  (   &L6,   &L8,   &L5 );
-    field_mul  (   &L8,   &L7,   &L6 );
-    field_mul  (   &L7,   &L8,   &L6 );
-    field_copy (   &L6, &a->x );
-    field_addw ( &a->x,     1 );
-    field_mul  (   &L5, &a->x,   &L8 );
-    field_addw (   &L5,     1 );
-    field_sub ( &a->x,   &L6,   &L5 );
-    field_mul  (   &L5,   &L4, &a->x );
-    field_mulw_scc_wr (   &a->x,   &L5, -2-2*EDWARDS_D );
-    field_add (   &L4,   &L3,   &L3 );
-    field_add (   &L3,   &L4,   &L2 );
-    field_subw(   &L3,     2 );
-    field_mul  (   &L2,   &L3,   &L8 );
-    field_mulw (   &L3,   &L2, 2*(EDWARDS_D+1)*(EDWARDS_D-1) );
-    field_add (   &L2,   &L3, &a->y );
-    field_mul  ( &a->y,   &L7,   &L2 );
-    field_addw ( &a->y,    -field_is_zero( &L8 ) );
+    field_mul  (   L8,   L5,   L4 );
+    field_mul  (   L4,   L5,   L6 );
+    field_mul  (   L5,   L7,   L8 );
+    field_mul  (   L8,   L5,   L4 );
+    field_mul  (   L4,   L7,   L8 );
+    field_isr  (   L6,   L4 );
+    field_mul  (   L4,   L5,   L6 );
+    field_sqr  (   L5,   L6 );
+    field_mul  (   L6,   L8,   L5 );
+    field_mul  (   L8,   L7,   L6 );
+    field_mul  (   L7,   L8,   L6 );
+    field_copy (   L6, a->x );
+    field_addw ( a->x,     1 );
+    field_mul  (   L5, a->x,   L8 );
+    field_addw (   L5,     1 );
+    field_sub ( a->x,   L6,   L5 );
+    field_mul  (   L5,   L4, a->x );
+    field_mulw_scc_wr (   a->x,   L5, -2-2*EDWARDS_D );
+    field_add (   L4,   L3,   L3 );
+    field_add (   L3,   L4,   L2 );
+    field_subw(   L3,     2 );
+    field_mul  (   L2,   L3,   L8 );
+    field_mulw (   L3,   L2, 2*(EDWARDS_D+1)*(EDWARDS_D-1) );
+    field_add (   L2,   L3, a->y );
+    field_mul  ( a->y,   L7,   L2 );
+    field_addw ( a->y,    -field_is_zero( L8 ) );
 }
 
 mask_t
 validate_affine (
     const struct affine_t* a
 ) {
-    struct field_t L0, L1, L2, L3;
-    field_sqr  (   &L0, &a->y );
-    field_sqr  (   &L1, &a->x );
-    field_add (   &L3,   &L1,   &L0 );
-    field_mulw_scc (   &L2,   &L1, EDWARDS_D );
-    field_mul  (   &L1,   &L0,   &L2 );
-    field_addw (   &L1,     1 );
-    field_sub (   &L0,   &L3,   &L1 );
-    return field_is_zero(   &L0 );
+    field_a_t L0, L1, L2, L3;
+    field_sqr  (   L0, a->y );
+    field_sqr  (   L1, a->x );
+    field_add (   L3,   L1,   L0 );
+    field_mulw_scc (   L2,   L1, EDWARDS_D );
+    field_mul  (   L1,   L0,   L2 );
+    field_addw (   L1,     1 );
+    field_sub (   L0,   L3,   L1 );
+    return field_is_zero(   L0 );
 }
 
 mask_t
@@ -901,36 +900,36 @@ validate_tw_extensible (
     const struct tw_extensible_t* ext
 ) {
     mask_t L4, L5;
-    struct field_t L0, L1, L2, L3;
+    field_a_t L0, L1, L2, L3;
     /*
      * Check invariant:
      * 0 = -x*y + z*t*u
      */
-    field_mul  (   &L1, &ext->t, &ext->u );
-    field_mul  (   &L2, &ext->z,   &L1 );
-    field_mul  (   &L0, &ext->x, &ext->y );
-    field_negx (   &L1,   &L0 );
-    field_add (   &L0,   &L1,   &L2 );
-       L5 = field_is_zero(   &L0 );
+    field_mul  (   L1, ext->t, ext->u );
+    field_mul  (   L2, ext->z,   L1 );
+    field_mul  (   L0, ext->x, ext->y );
+    field_neg (   L1,   L0 );
+    field_add (   L0,   L1,   L2 );
+       L5 = field_is_zero(   L0 );
     /*
      * Check invariant:
      * 0 = d*t^2*u^2 + x^2 - y^2 + z^2 - t^2*u^2
      */
-    field_sqr  (   &L2, &ext->y );
-    field_negx (   &L1,   &L2 );
-    field_sqr  (   &L0, &ext->x );
-    field_add (   &L2,   &L0,   &L1 );
-    field_sqr  (   &L3, &ext->u );
-    field_sqr  (   &L0, &ext->t );
-    field_mul  (   &L1,   &L0,   &L3 );
-    field_mulw_scc (   &L3,   &L1, EDWARDS_D );
-    field_add (   &L0,   &L3,   &L2 );
-    field_negx (   &L3,   &L1 );
-    field_add (   &L2,   &L3,   &L0 );
-    field_sqr  (   &L1, &ext->z );
-    field_add (   &L0,   &L1,   &L2 );
-       L4 = field_is_zero(   &L0 );
-    return    L5 & L4 &~ field_is_zero(&ext->z);
+    field_sqr  (   L2, ext->y );
+    field_neg (   L1,   L2 );
+    field_sqr  (   L0, ext->x );
+    field_add (   L2,   L0,   L1 );
+    field_sqr  (   L3, ext->u );
+    field_sqr  (   L0, ext->t );
+    field_mul  (   L1,   L0,   L3 );
+    field_mulw_scc (   L3,   L1, EDWARDS_D );
+    field_add (   L0,   L3,   L2 );
+    field_neg (   L3,   L1 );
+    field_add (   L2,   L3,   L0 );
+    field_sqr  (   L1, ext->z );
+    field_add (   L0,   L1,   L2 );
+       L4 = field_is_zero(   L0 );
+    return    L5 & L4 &~ field_is_zero(ext->z);
 }
 
 mask_t
@@ -938,33 +937,33 @@ validate_extensible (
     const struct extensible_t* ext
 ) {
     mask_t L4, L5;
-    struct field_t L0, L1, L2, L3;
+    field_a_t L0, L1, L2, L3;
     /*
      * Check invariant:
      * 0 = d*t^2*u^2 - x^2 - y^2 + z^2
      */
-    field_sqr  (   &L2, &ext->y );
-    field_negx (   &L1,   &L2 );
-    field_sqr  (   &L0, &ext->z );
-    field_add (   &L2,   &L0,   &L1 );
-    field_sqr  (   &L3, &ext->u );
-    field_sqr  (   &L0, &ext->t );
-    field_mul  (   &L1,   &L0,   &L3 );
-    field_mulw_scc (   &L0,   &L1, EDWARDS_D );
-    field_add (   &L1,   &L0,   &L2 );
-    field_sqr  (   &L0, &ext->x );
-    field_negx (   &L2,   &L0 );
-    field_add (   &L0,   &L2,   &L1 );
-       L5 = field_is_zero(   &L0 );
+    field_sqr  (   L2, ext->y );
+    field_neg (   L1,   L2 );
+    field_sqr  (   L0, ext->z );
+    field_add (   L2,   L0,   L1 );
+    field_sqr  (   L3, ext->u );
+    field_sqr  (   L0, ext->t );
+    field_mul  (   L1,   L0,   L3 );
+    field_mulw_scc (   L0,   L1, EDWARDS_D );
+    field_add (   L1,   L0,   L2 );
+    field_sqr  (   L0, ext->x );
+    field_neg (   L2,   L0 );
+    field_add (   L0,   L2,   L1 );
+       L5 = field_is_zero(   L0 );
     /*
      * Check invariant:
      * 0 = -x*y + z*t*u
      */
-    field_mul  (   &L1, &ext->t, &ext->u );
-    field_mul  (   &L2, &ext->z,   &L1 );
-    field_mul  (   &L0, &ext->x, &ext->y );
-    field_negx (   &L1,   &L0 );
-    field_add (   &L0,   &L1,   &L2 );
-       L4 = field_is_zero(   &L0 );
-    return L5 & L4 &~ field_is_zero(&ext->z);
+    field_mul  (   L1, ext->t, ext->u );
+    field_mul  (   L2, ext->z,   L1 );
+    field_mul  (   L0, ext->x, ext->y );
+    field_neg (   L1,   L0 );
+    field_add (   L0,   L1,   L2 );
+       L4 = field_is_zero(   L0 );
+    return L5 & L4 &~ field_is_zero(ext->z);
 }
diff --git a/src/goldilocks.c b/src/goldilocks.c
index f86e1ab..7cba9c4 100644
--- a/src/goldilocks.c
+++ b/src/goldilocks.c
@@ -162,7 +162,7 @@ goldilocks_derive_private_key (
     
     struct sha512_ctx_t ctx;
     struct tw_extensible_t exta;
-    struct field_t pk;
+    field_a_t pk;
     
     sha512_init(&ctx);
     sha512_update(&ctx, (const unsigned char *)"derivepk", GOLDI_DIVERSIFY_BYTES);
@@ -173,9 +173,9 @@ goldilocks_derive_private_key (
     barrett_serialize(privkey->opaque, sk, GOLDI_FIELD_BYTES);
 
     scalarmul_fixed_base(&exta, sk, GOLDI_SCALAR_BITS, &goldilocks_global.fixed_base);
-    untwist_and_double_and_serialize(&pk, &exta);
+    untwist_and_double_and_serialize(pk, &exta);
     
-    field_serialize(&privkey->opaque[GOLDI_FIELD_BYTES], &pk);
+    field_serialize(&privkey->opaque[GOLDI_FIELD_BYTES], pk);
     
     return GOLDI_EOK;
 }
@@ -225,11 +225,11 @@ goldilocks_private_to_public (
     struct goldilocks_public_key_t *pubkey,
     const struct goldilocks_private_key_t *privkey
 ) {
-    struct field_t pk;
-    mask_t msucc = field_deserialize(&pk,&privkey->opaque[GOLDI_FIELD_BYTES]);
+    field_a_t pk;
+    mask_t msucc = field_deserialize(pk,&privkey->opaque[GOLDI_FIELD_BYTES]);
     
     if (msucc) {
-        field_serialize(pubkey->opaque, &pk);
+        field_serialize(pubkey->opaque, pk);
         return GOLDI_EOK;
     } else {
         return GOLDI_ECORRUPT;
@@ -252,15 +252,15 @@ goldilocks_shared_secret_core (
     assert(GOLDI_SHARED_SECRET_BYTES == SHA512_OUTPUT_BYTES);
     
     word_t sk[GOLDI_FIELD_WORDS];
-    struct field_t pk;
+    field_a_t pk;
     
-    mask_t succ = field_deserialize(&pk,your_pubkey->opaque), msucc = -1;
+    mask_t succ = field_deserialize(pk,your_pubkey->opaque), msucc = -1;
     
 #ifdef EXPERIMENT_ECDH_STIR_IN_PUBKEYS
-    struct field_t sum, prod;
-    msucc &= field_deserialize(&sum,&my_privkey->opaque[GOLDI_FIELD_BYTES]);
-    field_mul(&prod,&pk,&sum);
-    field_add(&sum,&pk,&sum);
+    field_a_t sum, prod;
+    msucc &= field_deserialize(sum,&my_privkey->opaque[GOLDI_FIELD_BYTES]);
+    field_mul(prod,pk,sum);
+    field_add(sum,pk,sum);
 #endif
     
     msucc &= barrett_deserialize(sk,my_privkey->opaque,&curve_prime_order);
@@ -269,17 +269,17 @@ goldilocks_shared_secret_core (
     if (pre) {
         struct tw_extensible_t tw;
         succ &= scalarmul_fixed_base(&tw, sk, GOLDI_SCALAR_BITS, &pre->table);
-        untwist_and_double_and_serialize(&pk, &tw);
+        untwist_and_double_and_serialize(pk, &tw);
     } else {
-        succ &= montgomery_ladder(&pk,&pk,sk,GOLDI_SCALAR_BITS,1);
+        succ &= montgomery_ladder(pk,pk,sk,GOLDI_SCALAR_BITS,1);
     }
 #else
     (void)pre;
-    succ &= montgomery_ladder(&pk,&pk,sk,GOLDI_SCALAR_BITS,1);
+    succ &= montgomery_ladder(pk,pk,sk,GOLDI_SCALAR_BITS,1);
 #endif
     
     
-    field_serialize(gxy,&pk);
+    field_serialize(gxy,pk);
     
     /* obliterate records of our failure by adjusting with obliteration key */
     struct sha512_ctx_t ctx;
@@ -300,9 +300,9 @@ goldilocks_shared_secret_core (
 #ifdef EXPERIMENT_ECDH_STIR_IN_PUBKEYS
     /* stir in the sum and product of the pubkeys. */
     uint8_t a_pk[GOLDI_FIELD_BYTES];
-    field_serialize(a_pk, &sum);
+    field_serialize(a_pk, sum);
     sha512_update(&ctx, a_pk, GOLDI_FIELD_BYTES);
-    field_serialize(a_pk, &prod);
+    field_serialize(a_pk, prod);
     sha512_update(&ctx, a_pk, GOLDI_FIELD_BYTES);
 #endif
        
@@ -383,11 +383,11 @@ goldilocks_sign (
     /* 4[nonce]G */
     uint8_t signature_tmp[GOLDI_FIELD_BYTES];
     struct tw_extensible_t exta;
-    struct field_t gsk;
+    field_a_t gsk;
     scalarmul_fixed_base(&exta, tk, GOLDI_SCALAR_BITS, &goldilocks_global.fixed_base);
     double_tw_extensible(&exta);
-    untwist_and_double_and_serialize(&gsk, &exta);
-    field_serialize(signature_tmp, &gsk);
+    untwist_and_double_and_serialize(gsk, &exta);
+    field_serialize(signature_tmp, gsk);
     
     word_t challenge[GOLDI_FIELD_WORDS];
     goldilocks_derive_challenge (
@@ -437,10 +437,10 @@ goldilocks_verify (
         return GOLDI_EUNINIT;
     }
     
-    struct field_t pk;
+    field_a_t pk;
     word_t s[GOLDI_FIELD_WORDS];
     
-    mask_t succ = field_deserialize(&pk,pubkey->opaque);
+    mask_t succ = field_deserialize(pk,pubkey->opaque);
     if (!succ) return GOLDI_EINVAL;
     
     succ = barrett_deserialize(s, &signature[GOLDI_FIELD_BYTES], &curve_prime_order);
@@ -449,14 +449,14 @@ goldilocks_verify (
     word_t challenge[GOLDI_FIELD_WORDS];
     goldilocks_derive_challenge(challenge, pubkey->opaque, signature, message, message_len);
     
-    struct field_t eph;
+    field_a_t eph;
     struct tw_extensible_t pk_text;
     
     /* deserialize [nonce]G */
-    succ = field_deserialize(&eph, signature);
+    succ = field_deserialize(eph, signature);
     if (!succ) return GOLDI_EINVAL;
     
-    succ = deserialize_and_twist_approx(&pk_text, &sqrt_d_minus_1, &pk);
+    succ = deserialize_and_twist_approx(&pk_text, pk);
     if (!succ) return GOLDI_EINVAL;
     
     linear_combo_var_fixed_vt( &pk_text,
@@ -464,9 +464,9 @@ goldilocks_verify (
         s, GOLDI_SCALAR_BITS,
         goldilocks_global.wnafs, WNAF_PRECMP_BITS );
     
-    untwist_and_double_and_serialize( &pk, &pk_text );
+    untwist_and_double_and_serialize( pk, &pk_text );
 
-    succ = field_eq(&eph, &pk);
+    succ = field_eq(eph, pk);
     return succ ? 0 : GOLDI_EINVAL;
 }
 #endif
@@ -485,14 +485,14 @@ goldilocks_precompute_public_key (
     
     struct tw_extensible_t pk_text;
     
-    struct field_t pk;
-    mask_t succ = field_deserialize(&pk, pub->opaque);
+    field_a_t pk;
+    mask_t succ = field_deserialize(pk, pub->opaque);
     if (!succ) {
         free(precom);
         return NULL;
     }
     
-    succ = deserialize_and_twist_approx(&pk_text, &sqrt_d_minus_1, &pk);
+    succ = deserialize_and_twist_approx(&pk_text, pk);
     if (!succ) {
         free(precom);
         return NULL;
@@ -538,11 +538,11 @@ goldilocks_verify_precomputed (
     word_t challenge[GOLDI_FIELD_WORDS];
     goldilocks_derive_challenge(challenge, pubkey->pub.opaque, signature, message, message_len);
     
-    struct field_t eph, pk;
+    field_a_t eph, pk;
     struct tw_extensible_t pk_text;
     
     /* deserialize [nonce]G */
-    succ = field_deserialize(&eph, signature);
+    succ = field_deserialize(eph, signature);
     if (!succ) return GOLDI_EINVAL;
         
     succ = linear_combo_combs_vt (
@@ -552,9 +552,9 @@ goldilocks_verify_precomputed (
     );
     if (!succ) return GOLDI_EINVAL;
     
-    untwist_and_double_and_serialize( &pk, &pk_text );
+    untwist_and_double_and_serialize( pk, &pk_text );
 
-    succ = field_eq(&eph, &pk);
+    succ = field_eq(eph, pk);
     return succ ? 0 : GOLDI_EINVAL;
 }
 
diff --git a/src/include/ec_point.h b/src/include/ec_point.h
index 0391928..f91216d 100644
--- a/src/include/ec_point.h
+++ b/src/include/ec_point.h
@@ -21,28 +21,28 @@ extern "C" {
  * Affine point on an Edwards curve.
  */
 struct affine_t {
-    struct field_t x, y;
+    field_a_t x, y;
 };
 
 /**
  * Affine point on a twisted Edwards curve.
  */
 struct tw_affine_t {
-    struct field_t x, y;
+    field_a_t x, y;
 };
 
 /**
  * Montgomery buffer.
  */
 struct montgomery_t {
-    struct field_t z0, xd, zd, xa, za;
+    field_a_t z0, xd, zd, xa, za;
 };
 
 /**
  * Montgomery buffer, augmented version.
  */
 struct montgomery_aux_t {
-    struct field_t s0, xd, zd, xa, za, xs, zs;
+    field_a_t s0, xd, zd, xa, za, xs, zs;
 };
 
 /**
@@ -64,7 +64,7 @@ struct montgomery_aux_t {
  * instead.
  */
 struct extensible_t {
-    struct field_t x, y, z, t, u;
+    field_a_t x, y, z, t, u;
 };
 
 /**
@@ -72,7 +72,7 @@ struct extensible_t {
  * suitable for accumulators.
  */
 struct tw_extensible_t {
-    struct field_t x, y, z, t, u;
+    field_a_t x, y, z, t, u;
 };
 
 /**
@@ -81,7 +81,7 @@ struct tw_extensible_t {
  * Good for mixed readdition; suitable for fixed tables.
  */
 struct tw_niels_t {
-    struct field_t a, b, c;
+    field_a_t a, b, c;
 };
 
 /**
@@ -91,7 +91,7 @@ struct tw_niels_t {
  */
 struct tw_pniels_t {
     struct tw_niels_t n;
-    struct field_t z;
+    field_a_t z;
 };
 
 
@@ -285,20 +285,20 @@ montgomery_aux_step (
 void
 deserialize_montgomery (
     struct montgomery_t* a,
-    const struct field_t* sbz
+    const field_a_t sbz
 );
 
 mask_t
 serialize_montgomery (
-    struct field_t*             b,
+    field_a_t             b,
     const struct montgomery_t* a,
-    const struct field_t*       sbz
+    const field_a_t       sbz
 );
     
 void
 deserialize_montgomery_decaf (
     struct montgomery_aux_t* a,
-    const struct field_t *s
+    const field_a_t s
 );
 
 /**
@@ -314,7 +314,7 @@ deserialize_montgomery_decaf (
  */
 void
 serialize_extensible (
-    struct field_t*             b,
+    field_a_t             b,
     const struct extensible_t* a
 );
 
@@ -323,7 +323,7 @@ serialize_extensible (
  */
 void
 untwist_and_double_and_serialize (
-    struct field_t*                b,
+    field_a_t                b,
     const struct tw_extensible_t* a
 );
 
@@ -363,7 +363,7 @@ test_only_twist (
 
 mask_t
 field_is_square (
-    const struct field_t* x
+    const field_a_t x
 );
 
 mask_t
@@ -382,7 +382,7 @@ is_even_tw (
 mask_t
 deserialize_affine (
     struct affine_t*     a,
-    const struct field_t* sz
+    const field_a_t sz
 );
 
 /**
@@ -395,22 +395,21 @@ deserialize_affine (
 mask_t
 deserialize_and_twist_approx (
     struct tw_extensible_t* a,
-    const struct field_t*    sdm1,
-    const struct field_t*    sz
+    const field_a_t sz
 )
 __attribute__((warn_unused_result));
 
 mask_t
 decaf_deserialize_affine (
-    struct affine_t       *a,
-    const struct field_t  *s,
+    struct affine_t *a,
+    const field_a_t s,
     mask_t allow_identity
 )
 __attribute__((warn_unused_result));
     
 void
 decaf_serialize_extensible (
-    struct field_t*            b,
+    field_a_t b,
     const struct extensible_t* a
 );
 
@@ -418,14 +417,14 @@ decaf_serialize_extensible (
 mask_t
 decaf_deserialize_tw_affine (
     struct tw_affine_t       *a,
-    const struct field_t  *s,
+    const field_a_t s,
     mask_t allow_identity
 )
 __attribute__((warn_unused_result));
 
 void
 decaf_serialize_tw_extensible (
-    struct field_t*            b,
+    field_a_t            b,
     const struct tw_extensible_t* a
 );
 
@@ -465,7 +464,7 @@ eq_tw_extensible (
 void
 elligator_2s_inject (
     struct affine_t*     a,
-    const struct field_t* r
+    const field_a_t r
 );
 
 mask_t
@@ -516,8 +515,8 @@ cond_negate_tw_niels (
     struct tw_niels_t *n,
     mask_t doNegate
 ) {
-    constant_time_cond_swap(&n->a, &n->b, sizeof(n->a), doNegate);
-    field_cond_neg(&n->c, doNegate);
+    constant_time_cond_swap(n->a, n->b, sizeof(n->a), doNegate);
+    field_cond_neg(n->c, doNegate);
 }
 
 /**
@@ -537,8 +536,8 @@ copy_affine (
     struct affine_t*       a,
     const struct affine_t* ds
 ) {
-    field_copy ( &a->x, &ds->x );
-    field_copy ( &a->y, &ds->y );
+    field_copy ( a->x, ds->x );
+    field_copy ( a->y, ds->y );
 }
 
 void
@@ -546,8 +545,8 @@ copy_tw_affine (
     struct tw_affine_t*       a,
     const struct tw_affine_t* ds
 ) {
-    field_copy ( &a->x, &ds->x );
-    field_copy ( &a->y, &ds->y );
+    field_copy ( a->x, ds->x );
+    field_copy ( a->y, ds->y );
 }
 
 void
@@ -555,11 +554,11 @@ copy_montgomery (
     struct montgomery_t*       a,
     const struct montgomery_t* ds
 ) {
-    field_copy ( &a->z0, &ds->z0 );
-    field_copy ( &a->xd, &ds->xd );
-    field_copy ( &a->zd, &ds->zd );
-    field_copy ( &a->xa, &ds->xa );
-    field_copy ( &a->za, &ds->za );
+    field_copy ( a->z0, ds->z0 );
+    field_copy ( a->xd, ds->xd );
+    field_copy ( a->zd, ds->zd );
+    field_copy ( a->xa, ds->xa );
+    field_copy ( a->za, ds->za );
 }
 
 void
@@ -567,11 +566,11 @@ copy_extensible (
     struct extensible_t*       a,
     const struct extensible_t* ds
 ) {
-    field_copy ( &a->x, &ds->x );
-    field_copy ( &a->y, &ds->y );
-    field_copy ( &a->z, &ds->z );
-    field_copy ( &a->t, &ds->t );
-    field_copy ( &a->u, &ds->u );
+    field_copy ( a->x, ds->x );
+    field_copy ( a->y, ds->y );
+    field_copy ( a->z, ds->z );
+    field_copy ( a->t, ds->t );
+    field_copy ( a->u, ds->u );
 }
 
 void
@@ -579,11 +578,11 @@ copy_tw_extensible (
     struct tw_extensible_t*       a,
     const struct tw_extensible_t* ds
 ) {
-    field_copy ( &a->x, &ds->x );
-    field_copy ( &a->y, &ds->y );
-    field_copy ( &a->z, &ds->z );
-    field_copy ( &a->t, &ds->t );
-    field_copy ( &a->u, &ds->u );
+    field_copy ( a->x, ds->x );
+    field_copy ( a->y, ds->y );
+    field_copy ( a->z, ds->z );
+    field_copy ( a->t, ds->t );
+    field_copy ( a->u, ds->u );
 }
 
 void
@@ -591,9 +590,9 @@ copy_tw_niels (
     struct tw_niels_t*       a,
     const struct tw_niels_t* ds
 ) {
-    field_copy ( &a->a, &ds->a );
-    field_copy ( &a->b, &ds->b );
-    field_copy ( &a->c, &ds->c );
+    field_copy ( a->a, ds->a );
+    field_copy ( a->b, ds->b );
+    field_copy ( a->c, ds->c );
 }
 
 void
@@ -602,7 +601,7 @@ copy_tw_pniels (
     const struct tw_pniels_t* ds
 ) {
     copy_tw_niels( &a->n, &ds->n );
-    field_copy ( &a->z, &ds->z );
+    field_copy ( a->z, ds->z );
 }
 
 #ifdef __cplusplus
diff --git a/src/include/field.h b/src/include/field.h
index 77aa2a0..212eda5 100644
--- a/src/include/field.h
+++ b/src/include/field.h
@@ -14,6 +14,9 @@
 #include "f_field.h"
 #include <string.h>
 
+typedef struct field_t field_a_t[1];
+#define field_a_restrict_t struct field_t *__restrict__
+
 #define is32 (GOLDI_BITS == 32 || FIELD_BITS != 448)
 #if (is32)
 #define IF32(s) (s)
@@ -54,8 +57,8 @@ extern const uint8_t FIELD_MODULUS[FIELD_BYTES];
 static inline void
 __attribute__((unused,always_inline))        
 field_copy (
-    struct field_t *__restrict__ a,
-    const struct field_t *__restrict__ b
+    field_a_restrict_t a,
+    const field_a_restrict_t b
 ) {
     memcpy(a,b,sizeof(*a));
 }
@@ -70,8 +73,8 @@ field_copy (
  */
 void
 field_isr (
-    struct field_t*       a,
-    const struct field_t* x
+    field_a_t       a,
+    const field_a_t x
 );
     
 /**
@@ -81,8 +84,8 @@ field_isr (
  */     
 void
 field_simultaneous_invert (
-    struct field_t *__restrict__ out,
-    const struct field_t *in,
+    field_a_t *__restrict__ out,
+    const field_a_t *in,
     unsigned int n
 );
 
@@ -93,8 +96,8 @@ field_simultaneous_invert (
  */
 void
 field_inverse (
-    struct field_t*       a,
-    const struct field_t* x
+    field_a_t       a,
+    const field_a_t x
 );
 
 /**
@@ -102,8 +105,8 @@ field_inverse (
  */
 mask_t
 field_eq (
-    const struct field_t *a,
-    const struct field_t *b
+    const field_a_t a,
+    const field_a_t b
 );
     
 /**
@@ -112,23 +115,23 @@ field_eq (
 static __inline__ void
 __attribute__((unused,always_inline))
 field_sqrn (
-    field_t *__restrict__ y,
-    const field_t *x,
+    field_a_restrict_t y,
+    const field_a_t x,
     int n
 ) {
-    field_t tmp;
+    field_a_t tmp;
     assert(n>0);
     if (n&1) {
         field_sqr(y,x);
         n--;
     } else {
-        field_sqr(&tmp,x);
-        field_sqr(y,&tmp);
+        field_sqr(tmp,x);
+        field_sqr(y,tmp);
         n-=2;
     }
     for (; n; n-=2) {
-        field_sqr(&tmp,y);
-        field_sqr(y,&tmp);
+        field_sqr(tmp,y);
+        field_sqr(y,tmp);
     }
 }
 
@@ -152,8 +155,8 @@ field_make_nonzero (struct field_t *f) {
 /* Multiply by signed curve constant */
 static __inline__ void
 field_mulw_scc (
-    struct field_t* __restrict__ out,
-    const struct field_t *a,
+    field_a_restrict_t out,
+    const field_a_t a,
     int64_t scc
 ) {
     if (scc >= 0) {
@@ -168,8 +171,8 @@ field_mulw_scc (
 /* Multiply by signed curve constant and weak reduce if biased */
 static __inline__ void
 field_mulw_scc_wr (
-    struct field_t* __restrict__ out,
-    const struct field_t *a,
+    field_a_restrict_t out,
+    const field_a_t a,
     int64_t scc
 ) {
     field_mulw_scc(out, a, scc);
@@ -179,9 +182,9 @@ field_mulw_scc_wr (
 
 static __inline__ void
 field_subx_RAW (
-    struct field_t *d,
-    const struct field_t *a,
-    const struct field_t *b
+    field_a_t d,
+    const field_a_t a,
+    const field_a_t b
 ) {
     field_sub_RAW ( d, a, b );
     field_bias( d, 2 );
@@ -190,9 +193,9 @@ field_subx_RAW (
 
 static __inline__ void
 field_sub (
-    struct field_t *d,
-    const struct field_t *a,
-    const struct field_t *b
+    field_a_t d,
+    const field_a_t a,
+    const field_a_t b
 ) {
     field_sub_RAW ( d, a, b );
     field_bias( d, 2 );
@@ -201,9 +204,9 @@ field_sub (
 
 static __inline__ void
 field_add (
-    struct field_t *d,
-    const struct field_t *a,
-    const struct field_t *b
+    field_a_t d,
+    const field_a_t a,
+    const field_a_t b
 ) {
     field_add_RAW ( d, a, b );
     field_weak_reduce ( d );
@@ -211,7 +214,7 @@ field_add (
 
 static __inline__ void
 field_subw (
-    struct field_t *d,
+    field_a_t d,
     word_t c
 ) {
     field_subw_RAW ( d, c );
@@ -220,9 +223,9 @@ field_subw (
 }
 
 static __inline__ void
-field_negx (
-    struct field_t *d,
-    const struct field_t *a
+field_neg (
+    field_a_t d,
+    const field_a_t a
 ) {
     field_neg_RAW ( d, a );
     field_bias( d, 2 );
@@ -235,12 +238,12 @@ field_negx (
 static inline void
 __attribute__((unused,always_inline)) 
 field_cond_neg (
-    field_t *a,
+    field_a_t a,
     mask_t doNegate
 ) {
-	struct field_t negated;
-    field_negx(&negated, a);
-	constant_time_select(a, &negated, a, sizeof(negated), doNegate);
+	field_a_t negated;
+    field_neg(negated, a);
+	constant_time_select(a, negated, a, sizeof(negated), doNegate);
 }
 
 /** Require the warning annotation on raw routines */
diff --git a/src/include/magic.h b/src/include/magic.h
index badf484..551060e 100644
--- a/src/include/magic.h
+++ b/src/include/magic.h
@@ -45,12 +45,12 @@
 /**
  * @brief sqrt(d-1), used for point formats and twisting.
  */
-extern const struct field_t sqrt_d_minus_1;
+extern const field_a_t sqrt_d_minus_1;
 
 /**
  * @brief sqrt(-d), used for point formats and twisting.
  */
-extern const struct field_t sqrt_minus_d;
+extern const field_a_t sqrt_minus_d;
 
 /**
  * @brief The base point for Goldilocks.
diff --git a/src/include/scalarmul.h b/src/include/scalarmul.h
index bd97cc9..ecb1782 100644
--- a/src/include/scalarmul.h
+++ b/src/include/scalarmul.h
@@ -90,8 +90,8 @@ struct fixed_base_table_t {
  */
 mask_t
 montgomery_ladder (
-    struct field_t *out,
-    const struct field_t *in,
+    field_a_t out,
+    const field_a_t in,
     const word_t *scalar,
     unsigned int nbits,
     unsigned int n_extra_doubles
diff --git a/src/p448/f_arithmetic.c b/src/p448/f_arithmetic.c
index 82f35b8..c9b87e5 100644
--- a/src/p448/f_arithmetic.c
+++ b/src/p448/f_arithmetic.c
@@ -12,32 +12,32 @@
 
 void 
 field_isr (
-    struct field_t*       a,
-    const struct field_t* x
+    field_a_t a,
+    const field_a_t x
 ) {
-    struct field_t L0, L1, L2;
-    field_sqr  (   &L1,     x );
-    field_mul  (   &L2,     x,   &L1 );
-    field_sqr  (   &L1,   &L2 );
-    field_mul  (   &L2,     x,   &L1 );
-    field_sqrn (   &L1,   &L2,     3 );
-    field_mul  (   &L0,   &L2,   &L1 );
-    field_sqrn (   &L1,   &L0,     3 );
-    field_mul  (   &L0,   &L2,   &L1 );
-    field_sqrn (   &L2,   &L0,     9 );
-    field_mul  (   &L1,   &L0,   &L2 );
-    field_sqr  (   &L0,   &L1 );
-    field_mul  (   &L2,     x,   &L0 );
-    field_sqrn (   &L0,   &L2,    18 );
-    field_mul  (   &L2,   &L1,   &L0 );
-    field_sqrn (   &L0,   &L2,    37 );
-    field_mul  (   &L1,   &L2,   &L0 );
-    field_sqrn (   &L0,   &L1,    37 );
-    field_mul  (   &L1,   &L2,   &L0 );
-    field_sqrn (   &L0,   &L1,   111 );
-    field_mul  (   &L2,   &L1,   &L0 );
-    field_sqr  (   &L0,   &L2 );
-    field_mul  (   &L1,     x,   &L0 );
-    field_sqrn (   &L0,   &L1,   223 );
-    field_mul  (     a,   &L2,   &L0 );
+    field_a_t L0, L1, L2;
+    field_sqr  (   L1,     x );
+    field_mul  (   L2,     x,   L1 );
+    field_sqr  (   L1,   L2 );
+    field_mul  (   L2,     x,   L1 );
+    field_sqrn (   L1,   L2,     3 );
+    field_mul  (   L0,   L2,   L1 );
+    field_sqrn (   L1,   L0,     3 );
+    field_mul  (   L0,   L2,   L1 );
+    field_sqrn (   L2,   L0,     9 );
+    field_mul  (   L1,   L0,   L2 );
+    field_sqr  (   L0,   L1 );
+    field_mul  (   L2,     x,   L0 );
+    field_sqrn (   L0,   L2,    18 );
+    field_mul  (   L2,   L1,   L0 );
+    field_sqrn (   L0,   L2,    37 );
+    field_mul  (   L1,   L2,   L0 );
+    field_sqrn (   L0,   L1,    37 );
+    field_mul  (   L1,   L2,   L0 );
+    field_sqrn (   L0,   L1,   111 );
+    field_mul  (   L2,   L1,   L0 );
+    field_sqr  (   L0,   L2 );
+    field_mul  (   L1,     x,   L0 );
+    field_sqrn (   L0,   L1,   223 );
+    field_mul  (     a,   L2,   L0 );
 }
diff --git a/src/p448/magic.c b/src/p448/magic.c
index 42db98f..9258614 100644
--- a/src/p448/magic.c
+++ b/src/p448/magic.c
@@ -35,17 +35,17 @@ const word_t SCALARMUL_FIXED_WINDOW_ADJUSTMENT[2*SCALAR_WORDS] = {
 
 const struct affine_t goldilocks_base_point = {
 #ifdef USE_NEON_PERM
-    {{ 0xaed939f,0xc59d070,0xf0de840,0x5f065c3, 0xf4ba0c7,0xdf73324,0xc170033,0x3a6a26a,
+    {{{ 0xaed939f,0xc59d070,0xf0de840,0x5f065c3, 0xf4ba0c7,0xdf73324,0xc170033,0x3a6a26a,
        0x4c63d96,0x4609845,0xf3932d9,0x1b4faff, 0x6147eaa,0xa2692ff,0x9cecfa9,0x297ea0e
-    }},
+    }}},
 #else
-    {{ U56LE(0xf0de840aed939f), U56LE(0xc170033f4ba0c7),
+    {{{ U56LE(0xf0de840aed939f), U56LE(0xc170033f4ba0c7),
        U56LE(0xf3932d94c63d96), U56LE(0x9cecfa96147eaa),
        U56LE(0x5f065c3c59d070), U56LE(0x3a6a26adf73324),
        U56LE(0x1b4faff4609845), U56LE(0x297ea0ea2692ff)
-    }},
+    }}},
 #endif
-    {{ 19 }}
+    {{{ 19 }}}
 };
 
 static const word_t curve_prime_order_lo[(224+WORD_BITS-1)/WORD_BITS] = {
@@ -61,8 +61,8 @@ const struct barrett_prime_t curve_prime_order = {
     curve_prime_order_lo
 };
 
-const struct field_t
-sqrt_d_minus_1 = {{
+const field_a_t
+sqrt_d_minus_1 = {{{
 #ifdef USE_NEON_PERM
     0x6749f46,0x24d9770,0xd2e2183,0xa49f7b4,
     0xb4f0179,0x8c5f656,0x888db42,0xdcac462,
@@ -78,10 +78,10 @@ sqrt_d_minus_1 = {{
     U56LE(0x49443b8748734a),
     U56LE(0x12fec0c0b25b7a)
 #endif
-}};
+}}};
 
-const struct field_t
-sqrt_minus_d = {{
+const field_a_t
+sqrt_minus_d = {{{
 #ifdef USE_NEON_PERM
     0x5572736,0x4a2d780,0x42ef0f4,0xb8d54b6,
     0x0ce5296,0x1a7b8a5,0x7bf6aa2,0x6aa0a1f,
@@ -97,4 +97,4 @@ sqrt_minus_d = {{
     U56LE(0x683bf68d722fa2),
     U56LE(0x22d962fbeb24f7)
 #endif
-}};
+}}};
diff --git a/src/p480/f_arithmetic.c b/src/p480/f_arithmetic.c
index d616e42..bc8e657 100644
--- a/src/p480/f_arithmetic.c
+++ b/src/p480/f_arithmetic.c
@@ -12,32 +12,32 @@
 
 void 
 field_isr (
-    struct field_t*       a,
-    const struct field_t* x
+    field_a_t a,
+    const field_a_t x
 ) {
-    struct field_t L0, L1, L2, L3;
-    field_sqr  (   &L2,     x );
-    field_mul  (   &L1,     x,   &L2 );
-    field_sqrn (   &L0,   &L1,     2 );
-    field_mul  (   &L2,   &L1,   &L0 );
-    field_sqrn (   &L0,   &L2,     4 );
-    field_mul  (   &L1,   &L2,   &L0 );
-    field_sqr  (   &L0,   &L1 );
-    field_mul  (   &L2,     x,   &L0 );
-    field_sqrn (   &L0,   &L2,     8 );
-    field_mul  (   &L2,   &L1,   &L0 );
-    field_sqrn (   &L0,   &L2,    17 );
-    field_mul  (   &L1,   &L2,   &L0 );
-    field_sqrn (   &L0,   &L1,    17 );
-    field_mul  (   &L1,   &L2,   &L0 );
-    field_sqrn (   &L3,   &L1,    17 );
-    field_mul  (   &L0,   &L2,   &L3 );
-    field_sqrn (   &L2,   &L0,    51 );
-    field_mul  (   &L0,   &L1,   &L2 );
-    field_sqrn (   &L1,   &L0,   119 );
-    field_mul  (   &L2,   &L0,   &L1 );
-    field_sqr  (   &L0,   &L2 );
-    field_mul  (   &L1,     x,   &L0 );
-    field_sqrn (   &L0,   &L1,   239 );
-    field_mul  (     a,   &L2,   &L0 );
+    field_a_t L0, L1, L2, L3;
+    field_sqr  (   L2,     x );
+    field_mul  (   L1,     x,   L2 );
+    field_sqrn (   L0,   L1,     2 );
+    field_mul  (   L2,   L1,   L0 );
+    field_sqrn (   L0,   L2,     4 );
+    field_mul  (   L1,   L2,   L0 );
+    field_sqr  (   L0,   L1 );
+    field_mul  (   L2,     x,   L0 );
+    field_sqrn (   L0,   L2,     8 );
+    field_mul  (   L2,   L1,   L0 );
+    field_sqrn (   L0,   L2,    17 );
+    field_mul  (   L1,   L2,   L0 );
+    field_sqrn (   L0,   L1,    17 );
+    field_mul  (   L1,   L2,   L0 );
+    field_sqrn (   L3,   L1,    17 );
+    field_mul  (   L0,   L2,   L3 );
+    field_sqrn (   L2,   L0,    51 );
+    field_mul  (   L0,   L1,   L2 );
+    field_sqrn (   L1,   L0,   119 );
+    field_mul  (   L2,   L0,   L1 );
+    field_sqr  (   L0,   L2 );
+    field_mul  (   L1,     x,   L0 );
+    field_sqrn (   L0,   L1,   239 );
+    field_mul  (     a,   L2,   L0 );
 }
diff --git a/src/p480/magic.c b/src/p480/magic.c
index fbb3011..db6ba43 100644
--- a/src/p480/magic.c
+++ b/src/p480/magic.c
@@ -36,7 +36,7 @@ const word_t SCALARMUL_FIXED_WINDOW_ADJUSTMENT[2*SCALAR_WORDS] = {
 };
 
 const struct affine_t goldilocks_base_point = {
-    {{
+    {{{
         U60LE(0x849ff7f845c30d3),
         U60LE(0x7dda488553a4c5b),
         U60LE(0x1d3a2d9844831ea),
@@ -45,8 +45,8 @@ const struct affine_t goldilocks_base_point = {
         U60LE(0xfc955e59aeefa65),
         U60LE(0x3ab247cd530013c),
         U60LE(0x7ca42af3d564280)
-    }},
-    {{ 5 }}
+    }}},
+    {{{ 5 }}}
 };
 
 static const word_t curve_prime_order_lo[(240+WORD_BITS-1)/WORD_BITS] = {
@@ -62,13 +62,13 @@ const struct barrett_prime_t curve_prime_order = {
     curve_prime_order_lo
 };
 
-const struct field_t
-sqrt_d_minus_1 = {{
+const field_a_t
+sqrt_d_minus_1 = {{{
     232 /* Whoa, it comes out even. */
-}};
+}}};
 
-const struct field_t
-sqrt_minus_d = {{
+const field_a_t
+sqrt_minus_d = {{{
     U60LE(0xf098fba8d880ec0),
     U60LE(0x9d6ea1b2774d3e9),
     U60LE(0x1a52c44c0154b38),
@@ -77,4 +77,4 @@ sqrt_minus_d = {{
     U60LE(0xb9d4b5edcfee721),
     U60LE(0x65275d687c7215d),
     U60LE(0x3458ffa5bbfdea5)
-}};
+}}};
diff --git a/src/p521/f_arithmetic.c b/src/p521/f_arithmetic.c
index 7fbdfb8..37c0b50 100644
--- a/src/p521/f_arithmetic.c
+++ b/src/p521/f_arithmetic.c
@@ -12,32 +12,32 @@
 
 void 
 field_isr (
-    struct field_t*       a,
-    const struct field_t* x
+    field_a_t a,
+    const field_a_t x
 ) {
-    struct field_t L0, L1, L2;
-    field_sqr  (   &L1,     x );
-    field_mul  (   &L0,     x,   &L1 );
-    field_sqrn (   &L2,   &L0,     2 );
-    field_mul  (   &L1,   &L0,   &L2 );
-    field_sqrn (   &L2,   &L1,     4 );
-    field_mul  (   &L0,   &L1,   &L2 );
-    field_sqrn (   &L2,   &L0,     8 );
-    field_mul  (   &L1,   &L0,   &L2 );
-    field_sqrn (   &L2,   &L1,    16 );
-    field_mul  (   &L0,   &L1,   &L2 );
-    field_sqrn (   &L2,   &L0,    32 );
-    field_mul  (   &L1,   &L0,   &L2 );
-    field_sqr  (   &L2,   &L1 );
-    field_mul  (   &L0,     x,   &L2 );
-    field_sqrn (   &L2,   &L0,    64 );
-    field_mul  (   &L0,   &L1,   &L2 );
-    field_sqrn (   &L2,   &L0,   129 );
-    field_mul  (   &L1,   &L0,   &L2 );
-    field_sqr  (   &L2,   &L1 );
-    field_mul  (   &L0,     x,   &L2 );
-    field_sqrn (   &L2,   &L0,   259 );
-    field_mul  (   &L1,   &L0,   &L2 );
-    field_sqr  (   &L0,   &L1 );
-    field_mul  (     a,     x,   &L0 );
+    field_a_t L0, L1, L2;
+    field_sqr  (   L1,     x );
+    field_mul  (   L0,     x,   L1 );
+    field_sqrn (   L2,   L0,     2 );
+    field_mul  (   L1,   L0,   L2 );
+    field_sqrn (   L2,   L1,     4 );
+    field_mul  (   L0,   L1,   L2 );
+    field_sqrn (   L2,   L0,     8 );
+    field_mul  (   L1,   L0,   L2 );
+    field_sqrn (   L2,   L1,    16 );
+    field_mul  (   L0,   L1,   L2 );
+    field_sqrn (   L2,   L0,    32 );
+    field_mul  (   L1,   L0,   L2 );
+    field_sqr  (   L2,   L1 );
+    field_mul  (   L0,     x,   L2 );
+    field_sqrn (   L2,   L0,    64 );
+    field_mul  (   L0,   L1,   L2 );
+    field_sqrn (   L2,   L0,   129 );
+    field_mul  (   L1,   L0,   L2 );
+    field_sqr  (   L2,   L1 );
+    field_mul  (   L0,     x,   L2 );
+    field_sqrn (   L2,   L0,   259 );
+    field_mul  (   L1,   L0,   L2 );
+    field_sqr  (   L0,   L1 );
+    field_mul  (     a,     x,   L0 );
 }
diff --git a/src/p521/magic.c b/src/p521/magic.c
index 5319f6c..1ab3293 100644
--- a/src/p521/magic.c
+++ b/src/p521/magic.c
@@ -39,7 +39,7 @@ const word_t SCALARMUL_FIXED_WINDOW_ADJUSTMENT[2*SCALAR_WORDS] = {
 };
 
 const struct affine_t goldilocks_base_point = {
-    {{
+    {{{
 #ifdef USE_P521_3x3_TRANSPOSE
         U58LE(0x02a940a2f19ba6c),
         U58LE(0x3331c90d2c6ba52),
@@ -64,8 +64,8 @@ const struct affine_t goldilocks_base_point = {
         U58LE(0x06277e432c8a5ac),
         U58LE(0x0752cb45c48648b)
 #endif
-    }},
-    {{ 12 }}
+    }}},
+    {{{ 12 }}}
 };
 
 static const word_t curve_prime_order_lo[(261+WORD_BITS-1)/WORD_BITS] = {
@@ -82,8 +82,8 @@ const struct barrett_prime_t curve_prime_order = {
     curve_prime_order_lo
 };
 
-const struct field_t
-sqrt_d_minus_1 = {{
+const field_a_t
+sqrt_d_minus_1 = {{{
 #ifdef USE_P521_3x3_TRANSPOSE
     U58LE(0x1e2be72c1c81990),
     U58LE(0x207dfc238a33e46),
@@ -108,10 +108,10 @@ sqrt_d_minus_1 = {{
     U58LE(0x0524b9e715937f5),
     U58LE(0x0a9ea3ac10d6aed)
 #endif
-}};
+}}};
 
-const struct field_t
-sqrt_minus_d = {{
+const field_a_t
+sqrt_minus_d = {{{
 #ifdef USE_P521_3x3_TRANSPOSE
     U58LE(0x375d668ef98910e),
     U58LE(0x2e033a89e955dfc),
@@ -136,4 +136,4 @@ sqrt_minus_d = {{
     U58LE(0x009993c0e8ee528),
     U58LE(0x0d07656ee612ae6)
 #endif
-}};
+}}};
diff --git a/src/scalarmul.c b/src/scalarmul.c
index b85a42c..cf95984 100644
--- a/src/scalarmul.c
+++ b/src/scalarmul.c
@@ -15,8 +15,8 @@
 
 mask_t
 montgomery_ladder (
-    struct field_t *out,
-    const struct field_t *in,
+    field_a_t out,
+    const field_a_t in,
     const word_t *scalar,
     unsigned int nbits,
     unsigned int n_extra_doubles
@@ -30,15 +30,15 @@ montgomery_ladder (
         word_t w = scalar[j];
         for (i=n; i>=0; i--) {
             mask_t flip = -((w>>i)&1);
-            constant_time_cond_swap(&mont.xa,&mont.xd,sizeof(mont.xd),flip^pflip);
-            constant_time_cond_swap(&mont.za,&mont.zd,sizeof(mont.xd),flip^pflip);
+            constant_time_cond_swap(mont.xa,mont.xd,sizeof(mont.xd),flip^pflip);
+            constant_time_cond_swap(mont.za,mont.zd,sizeof(mont.xd),flip^pflip);
             montgomery_step(&mont);
             pflip = flip;
         }
         n = WORD_BITS-1;
     }
-    constant_time_cond_swap(&mont.xa,&mont.xd,sizeof(mont.xd),pflip);
-    constant_time_cond_swap(&mont.za,&mont.zd,sizeof(mont.xd),pflip);
+    constant_time_cond_swap(mont.xa,mont.xd,sizeof(mont.xd),pflip);
+    constant_time_cond_swap(mont.za,mont.zd,sizeof(mont.xd),pflip);
     
     assert(n_extra_doubles < INT_MAX);
     for (j=0; j<(int)n_extra_doubles; j++) {
@@ -475,8 +475,8 @@ precompute_fixed_base (
     struct tw_pniels_t pn_tmp;
   
     struct tw_pniels_t *doubles = (struct tw_pniels_t *) malloc_vector(sizeof(*doubles) * (t-1));
-    struct field_t *zs  = (struct field_t *) malloc_vector(sizeof(*zs) * (n<<(t-1)));
-    struct field_t *zis = (struct field_t *) malloc_vector(sizeof(*zis) * (n<<(t-1)));
+    field_a_t *zs  = (field_a_t *) malloc_vector(sizeof(*zs) * (n<<(t-1)));
+    field_a_t *zis = (field_a_t *) malloc_vector(sizeof(*zis) * (n<<(t-1)));
     
     struct tw_niels_t *table = prealloc;
     if (prealloc) {
@@ -562,7 +562,7 @@ precompute_fixed_base (
 
             convert_tw_extensible_to_tw_pniels(&pn_tmp, &start);
             copy_tw_niels(&table[idx], &pn_tmp.n);
-            field_copy(&zs[idx], &pn_tmp.z);
+            field_copy(zs[idx], pn_tmp.z);
 			
             if (j >= (1u<<(t-1)) - 1) break;
             int delta = (j+1) ^ ((j+1)>>1) ^ gray;
@@ -584,22 +584,22 @@ precompute_fixed_base (
 	
     field_simultaneous_invert(zis, zs, n<<(t-1));
 
-    field_t product;
+    field_a_t product;
     for (i=0; i<n<<(t-1); i++) {
-        field_mul(&product, &table[i].a, &zis[i]);
-        field_strong_reduce(&product);
-        field_copy(&table[i].a, &product);
+        field_mul(product, table[i].a, zis[i]);
+        field_strong_reduce(product);
+        field_copy(table[i].a, product);
         
-        field_mul(&product, &table[i].b, &zis[i]);
-        field_strong_reduce(&product);
-        field_copy(&table[i].b, &product);
+        field_mul(product, table[i].b, zis[i]);
+        field_strong_reduce(product);
+        field_copy(table[i].b, product);
         
-        field_mul(&product, &table[i].c, &zis[i]);
-        field_strong_reduce(&product);
-        field_copy(&table[i].c, &product);
+        field_mul(product, table[i].c, zis[i]);
+        field_strong_reduce(product);
+        field_copy(table[i].c, product);
     }
 	
-	mask_t ret = ~field_is_zero(&zis[0]);
+	mask_t ret = ~field_is_zero(zis[0]);
 
     free(doubles);
     free(zs);
@@ -635,8 +635,8 @@ precompute_fixed_base_wnaf (
     unsigned int tbits
 ) {
     int i;
-    struct field_t *zs  = (struct field_t *) malloc_vector(sizeof(*zs)<<tbits);
-    struct field_t *zis = (struct field_t *) malloc_vector(sizeof(*zis)<<tbits);
+    field_a_t *zs  = (field_a_t *) malloc_vector(sizeof(*zs)<<tbits);
+    field_a_t *zis = (field_a_t *) malloc_vector(sizeof(*zis)<<tbits);
 
     if (!zs || !zis) {
         free(zs);
@@ -650,7 +650,7 @@ precompute_fixed_base_wnaf (
     struct tw_pniels_t twop, tmp;
     
     convert_tw_extensible_to_tw_pniels(&tmp, &base);
-    field_copy(&zs[0], &tmp.z);
+    field_copy(zs[0], tmp.z);
     copy_tw_niels(&out[0], &tmp.n);
 
     if (tbits > 0) {
@@ -659,32 +659,32 @@ precompute_fixed_base_wnaf (
         add_tw_pniels_to_tw_extensible(&base, &tmp);
         
         convert_tw_extensible_to_tw_pniels(&tmp, &base);
-        field_copy(&zs[1], &tmp.z);
+        field_copy(zs[1], tmp.z);
         copy_tw_niels(&out[1], &tmp.n);
 
         for (i=2; i < 1<<tbits; i++) {
             add_tw_pniels_to_tw_extensible(&base, &twop);
             convert_tw_extensible_to_tw_pniels(&tmp, &base);
-            field_copy(&zs[i], &tmp.z);
+            field_copy(zs[i], tmp.z);
             copy_tw_niels(&out[i], &tmp.n);
         }
     }
     
     field_simultaneous_invert(zis, zs, 1<<tbits);
 
-    field_t product;
+    field_a_t product;
     for (i=0; i<1<<tbits; i++) {
-        field_mul(&product, &out[i].a, &zis[i]);
-        field_strong_reduce(&product);
-        field_copy(&out[i].a, &product);
+        field_mul(product, out[i].a, zis[i]);
+        field_strong_reduce(product);
+        field_copy(out[i].a, product);
         
-        field_mul(&product, &out[i].b, &zis[i]);
-        field_strong_reduce(&product);
-        field_copy(&out[i].b, &product);
+        field_mul(product, out[i].b, zis[i]);
+        field_strong_reduce(product);
+        field_copy(out[i].b, product);
         
-        field_mul(&product, &out[i].c, &zis[i]);
-        field_strong_reduce(&product);
-        field_copy(&out[i].c, &product);
+        field_mul(product, out[i].c, zis[i]);
+        field_strong_reduce(product);
+        field_copy(out[i].c, product);
     }
 
     free(zs);
diff --git a/test/bench.c b/test/bench.c
index e3f3b52..79d93a6 100644
--- a/test/bench.c
+++ b/test/bench.c
@@ -29,7 +29,7 @@ static double now(void) {
   return tv.tv_sec + tv.tv_usec/1000000.0;
 }
 
-static void field_randomize( struct crandom_state_t *crand, struct field_t *a ) {
+static void field_randomize( struct crandom_state_t *crand, field_a_t a ) {
     crandom_generate(crand, (unsigned char *)a, sizeof(*a));
     field_strong_reduce(a);
 }
@@ -38,7 +38,7 @@ static void q448_randomize( struct crandom_state_t *crand, word_t sk[SCALAR_WORD
     crandom_generate(crand, (unsigned char *)sk, SCALAR_BYTES);
 }
 
-static void field_print( const char *descr, const struct field_t *a ) {
+static void field_print( const char *descr, const field_a_t a ) {
     int j;
     unsigned char ser[FIELD_BYTES];
     field_serialize(ser,a);
@@ -52,7 +52,7 @@ static void field_print( const char *descr, const struct field_t *a ) {
 static void __attribute__((unused))
 field_print_full (
     const char *descr,
-    const struct field_t *a
+    const field_a_t a
 ) {
     int j;
     printf("%s = 0x", descr);
@@ -87,8 +87,7 @@ int main(int argc, char **argv) {
     struct affine_t affine;
     struct montgomery_t mb;
     struct montgomery_aux_t mba;
-    struct field_t a,b,c,d;
-    
+    field_a_t a,b,c,d;
     
     double when;
     int i;
@@ -107,42 +106,42 @@ int main(int argc, char **argv) {
     word_t sk[SCALAR_WORDS],tk[SCALAR_WORDS];
     q448_randomize(&crand, sk);
     
-    memset(&a,0,sizeof(a));
-    memset(&b,0,sizeof(b));
-    memset(&c,0,sizeof(c));
-    memset(&d,0,sizeof(d));
+    memset(a,0,sizeof(a));
+    memset(b,0,sizeof(b));
+    memset(c,0,sizeof(c));
+    memset(d,0,sizeof(d));
     when = now();
     for (i=0; i<nbase*5000; i++) {
-        field_mul(&c, &b, &a);
+        field_mul(c, b, a);
     }
     when = now() - when;
     printf("mul:         %5.1fns\n", when * 1e9 / i);
     
     when = now();
     for (i=0; i<nbase*5000; i++) {
-        field_sqr(&c, &a);
+        field_sqr(c, a);
     }
     when = now() - when;
     printf("sqr:         %5.1fns\n", when * 1e9 / i);
     
     when = now();
     for (i=0; i<nbase*5000; i++) {
-        field_mulw(&c, &b, 1234562);
+        field_mulw(c, b, 1234562);
     }
     when = now() - when;
     printf("mulw:        %5.1fns\n", when * 1e9 / i);
     
     when = now();
     for (i=0; i<nbase*500; i++) {
-        field_mul(&c, &b, &a);
-        field_mul(&a, &b, &c);
+        field_mul(c, b, a);
+        field_mul(a, b, c);
     }
     when = now() - when;
     printf("mul dep:     %5.1fns\n", when * 1e9 / i / 2);
     
     when = now();
     for (i=0; i<nbase*10; i++) {
-        field_randomize(&crand, &a);
+        field_randomize(&crand, a);
     }
     when = now() - when;
     printf("rand448:     %5.1fns\n", when * 1e9 / i);
@@ -166,46 +165,46 @@ int main(int argc, char **argv) {
     
     when = now();
     for (i=0; i<nbase; i++) {
-        field_isr(&c, &a);
+        field_isr(c, a);
     }
     when = now() - when;
     printf("isr auto:    %5.1fµs\n", when * 1e6 / i);
     
     for (i=0; i<100; i++) {
-        field_randomize(&crand, &a);
-        field_isr(&d,&a);
-        field_sqr(&b,&d);
-        field_mul(&c,&b,&a);
-        field_sqr(&b,&c);
-        field_subw(&b,1);
-        if (!field_is_zero(&b)) {
+        field_randomize(&crand, a);
+        field_isr(d,a);
+        field_sqr(b,d);
+        field_mul(c,b,a);
+        field_sqr(b,c);
+        field_subw(b,1);
+        if (!field_is_zero(b)) {
             printf("ISR validation failure!\n");
-            field_print("a", &a);
-            field_print("s", &d);
+            field_print("a", a);
+            field_print("s", d);
         }
     }
     
     when = now();
     for (i=0; i<nbase; i++) {
-        elligator_2s_inject(&affine, &a);
+        elligator_2s_inject(&affine, a);
     }
     when = now() - when;
     printf("elligator:   %5.1fµs\n", when * 1e6 / i);
     
     for (i=0; i<100; i++) {
-        field_randomize(&crand, &a);
-        elligator_2s_inject(&affine, &a);
+        field_randomize(&crand, a);
+        elligator_2s_inject(&affine, a);
         if (!validate_affine(&affine)) {
             printf("Elligator validation failure!\n");
-            field_print("a", &a);
-            field_print("x", &affine.x);
-            field_print("y", &affine.y);
+            field_print("a", a);
+            field_print("x", affine.x);
+            field_print("y", affine.y);
         }
     }
     
     when = now();
     for (i=0; i<nbase; i++) {
-        deserialize_affine(&affine, &a);
+        deserialize_affine(&affine, a);
     }
     when = now() - when;
     printf("decompress:  %5.1fµs\n", when * 1e6 / i);
@@ -213,34 +212,34 @@ int main(int argc, char **argv) {
     convert_affine_to_extensible(&exta, &affine);
     when = now();
     for (i=0; i<nbase; i++) {
-        serialize_extensible(&a, &exta);
+        serialize_extensible(a, &exta);
     }
     when = now() - when;
     printf("compress:    %5.1fµs\n", when * 1e6 / i);
     
     int goods = 0;
     for (i=0; i<100; i++) {
-        field_randomize(&crand, &a);
-        mask_t good = deserialize_affine(&affine, &a);
+        field_randomize(&crand, a);
+        mask_t good = deserialize_affine(&affine, a);
         if (good & !validate_affine(&affine)) {
             printf("Deserialize validation failure!\n");
-            field_print("a", &a);
-            field_print("x", &affine.x);
-            field_print("y", &affine.y);
+            field_print("a", a);
+            field_print("x", affine.x);
+            field_print("y", affine.y);
         } else if (good) {
             goods++;
             convert_affine_to_extensible(&exta,&affine);
-            serialize_extensible(&b, &exta);
-            field_sub(&c,&b,&a);
-            if (!field_is_zero(&c)) {
+            serialize_extensible(b, &exta);
+            field_sub(c,b,a);
+            if (!field_is_zero(c)) {
                 printf("Reserialize validation failure!\n");
-                field_print("a", &a);
-                field_print("x", &affine.x);
-                field_print("y", &affine.y);
-                deserialize_affine(&affine, &b);
-                field_print("b", &b);
-                field_print("x", &affine.x);
-                field_print("y", &affine.y);
+                field_print("a", a);
+                field_print("x", affine.x);
+                field_print("y", affine.y);
+                deserialize_affine(&affine, b);
+                field_print("b", b);
+                field_print("x", affine.x);
+                field_print("y", affine.y);
                 printf("\n");
             }
         }
@@ -322,7 +321,7 @@ int main(int argc, char **argv) {
 	
     when = now();
     for (i=0; i<nbase/10; i++) {
-        ignore_result(montgomery_ladder(&a,&b,sk,FIELD_BITS,0));
+        ignore_result(montgomery_ladder(a,b,sk,FIELD_BITS,0));
     }
     when = now() - when;
     printf("full ladder: %5.1fµs\n", when * 1e6 / i);
@@ -344,7 +343,7 @@ int main(int argc, char **argv) {
     when = now();
     for (i=0; i<nbase/10; i++) {
         scalarmul(&ext,sk);
-        untwist_and_double_and_serialize(&a,&ext);
+        untwist_and_double_and_serialize(a,&ext);
     }
     when = now() - when;
     printf("edwards smc: %5.1fµs\n", when * 1e6 / i);
@@ -414,12 +413,12 @@ int main(int argc, char **argv) {
     
     when = now();
     for (i=0; i<nbase/10; i++) {
-        deserialize_affine(&affine, &a);
+        deserialize_affine(&affine, a);
         convert_affine_to_extensible(&exta,&affine);
         twist_and_double(&ext,&exta);
         scalarmul(&ext,sk);
         untwist_and_double(&exta,&ext);
-        serialize_extensible(&b, &exta);
+        serialize_extensible(b, &exta);
     }
     when = now() - when;
     printf("edwards sm:  %5.1fµs\n", when * 1e6 / i);
@@ -427,8 +426,8 @@ int main(int argc, char **argv) {
     struct fixed_base_table_t t_5_5_18, t_3_5_30, t_8_4_14, t_5_3_30, t_15_3_10;
 
     while (1) {
-        field_randomize(&crand, &a);
-        if (deserialize_affine(&affine, &a)) break;
+        field_randomize(&crand, a);
+        if (deserialize_affine(&affine, a)) break;
     }
     convert_affine_to_extensible(&exta,&affine);
     twist_and_double(&ext,&exta);
@@ -625,9 +624,9 @@ int main(int argc, char **argv) {
     
     failures=0; successes = 0;
     for (i=0; i<nbase/10; i++) {
-        field_randomize(&crand, &a);
+        field_randomize(&crand, a);
 		word_t two = 2;
-        mask_t good = montgomery_ladder(&b,&a,&two,2,0);
+        mask_t good = montgomery_ladder(b,a,&two,2,0);
 		if (!good) continue;
 		
 		word_t x,y;
@@ -637,17 +636,17 @@ int main(int argc, char **argv) {
         y = (hword_t)y;
         word_t z=x*y;
         
-    	ignore_result(montgomery_ladder(&b,&a,&x,WORD_BITS,0));
-        ignore_result(montgomery_ladder(&c,&b,&y,WORD_BITS,0));
-        ignore_result(montgomery_ladder(&b,&a,&z,WORD_BITS,0));
+    	ignore_result(montgomery_ladder(b,a,&x,WORD_BITS,0));
+        ignore_result(montgomery_ladder(c,b,&y,WORD_BITS,0));
+        ignore_result(montgomery_ladder(b,a,&z,WORD_BITS,0));
         
-        field_sub(&d,&b,&c);
-		if (!field_is_zero(&d)) {
+        field_sub(d,b,c);
+		if (!field_is_zero(d)) {
             printf("Odd ladder validation failure %d!\n", ++failures);
-            field_print("a", &a);
+            field_print("a", a);
             printf("x=%"PRIxWORD", y=%"PRIxWORD", z=%"PRIxWORD"\n", x,y,z);
-            field_print("c", &c);
-            field_print("b", &b);
+            field_print("c", c);
+            field_print("b", b);
 			printf("\n");
 		}
 	}
@@ -656,23 +655,23 @@ int main(int argc, char **argv) {
     for (i=0; i<nbase/10; i++) {
         mask_t good;
         do {
-            field_randomize(&crand, &a);
-            good = deserialize_affine(&affine, &a);
+            field_randomize(&crand, a);
+            good = deserialize_affine(&affine, a);
         } while (!good);
         
         convert_affine_to_extensible(&exta,&affine);
         twist_and_double(&ext,&exta);
         untwist_and_double(&exta,&ext);
-        serialize_extensible(&b, &exta);
-        untwist_and_double_and_serialize(&c, &ext);
+        serialize_extensible(b, &exta);
+        untwist_and_double_and_serialize(c, &ext);
         
-        field_sub(&d,&b,&c);
+        field_sub(d,b,c);
         
-        if (good && !field_is_zero(&d)){
+        if (good && !field_is_zero(d)){
             printf("Iso+serial validation failure %d!\n", ++failures);
-            field_print("a", &a);
-            field_print("b", &b);
-            field_print("c", &c);
+            field_print("a", a);
+            field_print("b", b);
+            field_print("c", c);
             printf("\n");
         } else if (good) {
             successes ++;
@@ -684,23 +683,23 @@ int main(int argc, char **argv) {
     
     successes = failures = 0;
     for (i=0; i<nbase/10; i++) {
-        struct field_t aa;
+        field_a_t aa;
         struct tw_extensible_t exu,exv,exw;
         
         mask_t good;
         do {
-            field_randomize(&crand, &a);
-            good = deserialize_affine(&affine, &a);
+            field_randomize(&crand, a);
+            good = deserialize_affine(&affine, a);
             convert_affine_to_extensible(&exta,&affine);
             twist_and_double(&ext,&exta);
         } while (!good);
         do {
-            field_randomize(&crand, &aa);
-            good = deserialize_affine(&affine, &aa);
+            field_randomize(&crand, aa);
+            good = deserialize_affine(&affine, aa);
             convert_affine_to_extensible(&exta,&affine);
             twist_and_double(&exu,&exta);
         } while (!good);
-        field_randomize(&crand, &aa);
+        field_randomize(&crand, aa);
         
         q448_randomize(&crand, sk);
 		if (i==0 || i==2) memset(&sk, 0, sizeof(sk));
@@ -714,23 +713,23 @@ int main(int argc, char **argv) {
         convert_tw_extensible_to_tw_pniels(&pniels, &exw);
         add_tw_pniels_to_tw_extensible(&exv,&pniels);
         untwist_and_double(&exta,&exv);
-        serialize_extensible(&b, &exta);
+        serialize_extensible(b, &exta);
 
         ignore_result(precompute_fixed_base_wnaf(wnaft,&exu,5));
         linear_combo_var_fixed_vt(&ext,sk,FIELD_BITS,tk,FIELD_BITS,wnaft,5);
         untwist_and_double(&exta,&exv);
-        serialize_extensible(&c, &exta);
+        serialize_extensible(c, &exta);
         
-        field_sub(&d,&b,&c);
+        field_sub(d,b,c);
         
-        if (!field_is_zero(&d)){
+        if (!field_is_zero(d)){
             printf("PreWNAF combo validation failure %d!\n", ++failures);
-            field_print("a", &a);
-            field_print("A", &aa);
+            field_print("a", a);
+            field_print("A", aa);
             q448_print("s", sk);
             q448_print("t", tk);
-            field_print("c", &c);
-            field_print("b", &b);
+            field_print("c", c);
+            field_print("b", b);
             printf("\n\n");
         } else if (good) {
             successes ++;
diff --git a/test/test.c b/test/test.c
index 3111a74..7ef3d8f 100644
--- a/test/test.c
+++ b/test/test.c
@@ -82,7 +82,7 @@ hexprint (
 
 void field_print (
     const char *descr,
-    const struct field_t *a
+    const field_a_t a
 ) {
     int j;
     unsigned char ser[FIELD_BYTES];
diff --git a/test/test.h b/test/test.h
index 4776b79..03f2844 100644
--- a/test/test.h
+++ b/test/test.h
@@ -20,7 +20,7 @@ hexprint (
     
 void field_print (
     const char *descr,
-    const struct field_t *a
+    const field_a_t a
 );
     
 void scalar_print (
diff --git a/test/test_arithmetic.c b/test/test_arithmetic.c
index 7c45407..d1bc3f2 100644
--- a/test/test_arithmetic.c
+++ b/test/test_arithmetic.c
@@ -7,7 +7,7 @@
 mpz_t mp_field;
 
 static mask_t mpz_to_field (
-    struct field_t *out,
+    field_a_t out,
     const mpz_t in
 ) {
     uint8_t ser[FIELD_BYTES];
@@ -27,9 +27,9 @@ static inline int BRANCH_ON_CONSTANT(int x) {
 
 static mask_t field_assert_eq_gmp(
     const char *descr,
-    const struct field_t *a,
-    const struct field_t *b,
-    const struct field_t *x,
+    const field_a_t a,
+    const field_a_t b,
+    const field_a_t x,
     const mpz_t y,
     float lowBound,
     float highBound
@@ -88,32 +88,32 @@ static mask_t test_add_sub_RAW (
     const mpz_t y,
     word_t word
 ) {
-    struct field_t xx,yy,tt;
+    field_a_t xx,yy,tt;
     mpz_t t;
     mask_t succ = MASK_SUCCESS;
-    succ  = mpz_to_field(&xx,x);
-    succ &= mpz_to_field(&yy,y);
+    succ  = mpz_to_field(xx,x);
+    succ &= mpz_to_field(yy,y);
     mpz_init(t);
     
-    field_add_RAW(&tt,&xx,&yy);
+    field_add_RAW(tt,xx,yy);
     mpz_add(t,x,y);
-    succ &= field_assert_eq_gmp("add",&xx,&yy,&tt,t,0,2.1);
+    succ &= field_assert_eq_gmp("add",xx,yy,tt,t,0,2.1);
     
-    field_sub_RAW(&tt,&xx,&yy);
-    field_bias(&tt,2);
+    field_sub_RAW(tt,xx,yy);
+    field_bias(tt,2);
     mpz_sub(t,x,y);
-    succ &= field_assert_eq_gmp("sub",&xx,&yy,&tt,t,0,3.1);
+    succ &= field_assert_eq_gmp("sub",xx,yy,tt,t,0,3.1);
     
-    field_copy(&tt,&xx);
-    field_addw(&tt,word);
+    field_copy(tt,xx);
+    field_addw(tt,word);
     mpz_add_ui(t,x,word);
-    succ &= field_assert_eq_gmp("addw",&xx,&yy,&tt,t,0,2.1);
+    succ &= field_assert_eq_gmp("addw",xx,yy,tt,t,0,2.1);
     
-    field_copy(&tt,&xx);
-    field_subw(&tt,word);
-    field_bias(&tt,1);
+    field_copy(tt,xx);
+    field_subw(tt,word);
+    field_bias(tt,1);
     mpz_sub_ui(t,x,word);
-    succ &= field_assert_eq_gmp("subw",&xx,&yy,&tt,t,0,2.1);
+    succ &= field_assert_eq_gmp("subw",xx,yy,tt,t,0,2.1);
 
     /*
     if (!succ) {
@@ -132,32 +132,32 @@ static mask_t test_mul_sqr (
     const mpz_t y,
     word_t word
 ) {
-    struct field_t xx,yy,tt;
+    field_a_t xx,yy,tt;
     mpz_t t;
     mask_t succ = MASK_SUCCESS;
-    succ  = mpz_to_field(&xx,x);
-    succ &= mpz_to_field(&yy,y);
+    succ  = mpz_to_field(xx,x);
+    succ &= mpz_to_field(yy,y);
     mpz_init(t);
     
-    field_mul(&tt,&xx,&yy);
+    field_mul(tt,xx,yy);
     mpz_mul(t,x,y);
-    succ &= field_assert_eq_gmp("mul",&xx,&yy,&tt,t,0,1.1);
+    succ &= field_assert_eq_gmp("mul",xx,yy,tt,t,0,1.1);
     
-    field_mulw(&tt,&xx,word);
+    field_mulw(tt,xx,word);
     mpz_mul_ui(t,x,word);
-    succ &= field_assert_eq_gmp("mulw",&xx,&yy,&tt,t,0,1.1);
+    succ &= field_assert_eq_gmp("mulw",xx,yy,tt,t,0,1.1);
     
-    field_sqr(&tt,&xx);
+    field_sqr(tt,xx);
     mpz_mul(t,x,x);
-    succ &= field_assert_eq_gmp("sqrx",&xx,&yy,&tt,t,0,1.1);
+    succ &= field_assert_eq_gmp("sqrx",xx,yy,tt,t,0,1.1);
     
-    field_sqr(&tt,&yy);
+    field_sqr(tt,yy);
     mpz_mul(t,y,y);
-    succ &= field_assert_eq_gmp("sqy",&xx,&yy,&tt,t,0,1.1);
+    succ &= field_assert_eq_gmp("sqy",xx,yy,tt,t,0,1.1);
     
     if (!succ) {
-        field_print("    x", &xx);
-        field_print("    y", &yy);
+        field_print("    x", xx);
+        field_print("    y", yy);
     }
     
     mpz_clear(t);
@@ -168,28 +168,28 @@ static mask_t test_mul_sqr (
 static mask_t test_isr (
     const mpz_t x
 ) {
-    struct field_t xx,yy,ss,tt;
+    field_a_t xx,yy,ss,tt;
     mask_t succ = 0;
-    succ  = mpz_to_field(&xx,x);
+    succ  = mpz_to_field(xx,x);
     
-    field_isr(&ss,&xx);
-    field_sqr(&tt,&ss);
-    field_mul(&yy,&xx,&tt);
+    field_isr(ss,xx);
+    field_sqr(tt,ss);
+    field_mul(yy,xx,tt);
     
-    field_addw(&tt,1);
-    succ |= field_is_zero(&tt);
+    field_addw(tt,1);
+    succ |= field_is_zero(tt);
     
-    field_subw(&tt,2);
-    field_bias(&tt,1);
-    succ |= field_is_zero(&tt);
+    field_subw(tt,2);
+    field_bias(tt,1);
+    succ |= field_is_zero(tt);
     
-    field_addw(&tt,1);
+    field_addw(tt,1);
     if (~succ) {
         youfail();
         printf("ISR failure.\n");
-        field_print("    x", &xx);
-        field_print("    s", &ss);
-        field_print("    t", &tt);
+        field_print("    x", xx);
+        field_print("    s", ss);
+        field_print("    t", tt);
     }
     
     return succ;
@@ -214,7 +214,7 @@ int test_arithmetic (void) {
     
     mask_t succ = MASK_SUCCESS;
     
-    int radix_bits = sizeof(word_t) * FIELD_BITS / sizeof(field_t);
+    int radix_bits = sizeof(word_t) * FIELD_BITS / sizeof(field_a_t);
     
     for (j=0; j<ntests; j++) {
         if (j<256) {
diff --git a/test/test_pointops.c b/test/test_pointops.c
index b377fd6..e893774 100644
--- a/test/test_pointops.c
+++ b/test/test_pointops.c
@@ -12,15 +12,15 @@ static void
 failprint_ext (
     const struct extensible_t *a
 ) {
-    struct field_t zi, scaled;
-    field_print("    x", &a->x);
-    field_print("    y", &a->y);
-    field_print("    z", &a->z);
-    field_inverse(&zi, &a->z);
-    field_mul(&scaled, &zi, &a->x);
-    field_print("    X", &scaled);
-    field_mul(&scaled, &zi, &a->y);
-    field_print("    Y", &scaled);
+    field_a_t zi, scaled;
+    field_print("    x", a->x);
+    field_print("    y", a->y);
+    field_print("    z", a->z);
+    field_inverse(zi, a->z);
+    field_mul(scaled, zi, a->x);
+    field_print("    X", scaled);
+    field_mul(scaled, zi, a->y);
+    field_print("    Y", scaled);
     printf("\n");
 }
 
@@ -165,10 +165,10 @@ add_double_test (
     
     if (~succ) {
         printf("    Bases were:\n");
-        field_print("    x1", &base1->x);
-        field_print("    y1", &base1->y);
-        field_print("    x2", &base2->x);
-        field_print("    y2", &base2->y);
+        field_print("    x1", base1->x);
+        field_print("    y1", base1->y);
+        field_print("    x2", base2->x);
+        field_print("    y2", base2->y);
     }
     
     return succ ? 0 : -1;
@@ -211,18 +211,18 @@ single_twisting_test (
         succ = 0;
     } /* FUTURE: quadness */
     
-    field_t sera,serb;
-    untwist_and_double_and_serialize(&sera,&text);
+    field_a_t sera,serb;
+    untwist_and_double_and_serialize(sera,&text);
     copy_extensible(&tmpext,&exb);
     double_extensible(&tmpext);
-    serialize_extensible(&serb,&tmpext);
+    serialize_extensible(serb,&tmpext);
     
     /* check that their (doubled; FUTURE?) serializations are equal */
-    if (~field_eq(&sera,&serb)) {
+    if (~field_eq(sera,serb)) {
         youfail();
         printf("    Different serialization from twist + double ()\n");
-        field_print("    t", &sera);
-        field_print("    b", &serb);
+        field_print("    t", sera);
+        field_print("    b", serb);
         succ = 0;
     }
     
@@ -242,8 +242,8 @@ single_twisting_test (
     
     if (~succ) {
         printf("    Base was:\n");
-        field_print("    x", &base->x);
-        field_print("    y", &base->y);
+        field_print("    x", base->x);
+        field_print("    y", base->y);
     }
     
     
@@ -253,7 +253,7 @@ single_twisting_test (
 int test_decaf (void) {
     struct affine_t base;
     struct tw_affine_t tw_base;
-    struct field_t serf;
+    field_a_t serf;
     
     struct crandom_state_t crand;
     crandom_init_from_buffer(&crand, "my test_decaf random initializer");
@@ -267,87 +267,87 @@ int test_decaf (void) {
         #endif
         ser[0] &= ~1;
 
-        mask_t succ = field_deserialize(&serf, ser);
+        mask_t succ = field_deserialize(serf, ser);
         if (!succ) {
             youfail();
             printf("   Unlikely: fail at field_deserialize\n");
             return -1;
         }
         
-        succ &= decaf_deserialize_affine(&base, &serf, 0);
+        succ &= decaf_deserialize_affine(&base, serf, 0);
         if (!succ) continue;
         
         hits++;
-        struct field_t serf2;
+        field_a_t serf2;
         struct extensible_t ext;
         convert_affine_to_extensible(&ext, &base);
-        decaf_serialize_extensible(&serf2, &ext);
+        decaf_serialize_extensible(serf2, &ext);
         
         if (~validate_affine(&base)) {
             youfail();
             printf("Invalid decaf deser:\n");
-            field_print("    s", &serf);
-            field_print("    x", &base.x);
-            field_print("    y", &base.y);
+            field_print("    s", serf);
+            field_print("    x", base.x);
+            field_print("    y", base.y);
             fails ++;
-        } else if (~field_eq(&serf, &serf2)) {
+        } else if (~field_eq(serf, serf2)) {
             youfail();
             printf("Fail round-trip through decaf ser:\n");
-            field_print("    s", &serf);
-            field_print("    x", &base.x);
-            field_print("    y", &base.y);
+            field_print("    s", serf);
+            field_print("    x", base.x);
+            field_print("    y", base.y);
             printf("    deser is %s\n", validate_affine(&base) ? "valid" : "invalid");
-            field_print("    S", &serf2);
+            field_print("    S", serf2);
             fails ++;
         } else if (~is_even_pt(&ext)) {
             youfail();
             printf("Decaf deser isn't even:\n");
-            field_print("    s", &serf);
-            field_print("    x", &base.x);
-            field_print("    y", &base.y);
+            field_print("    s", serf);
+            field_print("    x", base.x);
+            field_print("    y", base.y);
             fails ++;
         }
         
-        succ = decaf_deserialize_tw_affine(&tw_base, &serf, 0);
+        succ = decaf_deserialize_tw_affine(&tw_base, serf, 0);
         struct tw_extensible_t tw_ext, tw_ext2;
         convert_tw_affine_to_tw_extensible(&tw_ext, &tw_base);
-        decaf_serialize_tw_extensible(&serf2, &tw_ext);
+        decaf_serialize_tw_extensible(serf2, &tw_ext);
         
         twist_even(&tw_ext2, &ext);
 
         if (~validate_tw_extensible(&tw_ext)) {
             youfail();
             printf("Invalid decaf tw deser:\n");
-            field_print("    s", &serf);
-            field_print("    x", &tw_base.x);
-            field_print("    y", &tw_base.y);
+            field_print("    s", serf);
+            field_print("    x", tw_base.x);
+            field_print("    y", tw_base.y);
             fails ++;
-        } else if (~field_eq(&serf, &serf2)) {
+        } else if (~field_eq(serf, serf2)) {
             youfail();
             printf("Fail round-trip through decaf ser:\n");
-            field_print("    s", &serf);
-            field_print("    x", &tw_base.x);
-            field_print("    y", &tw_base.y);
+            field_print("    s", serf);
+            field_print("    x", tw_base.x);
+            field_print("    y", tw_base.y);
             printf("    tw deser is %s\n", validate_tw_extensible(&tw_ext) ? "valid" : "invalid");
-            field_print("    S", &serf2);
+            field_print("    S", serf2);
             fails ++;
         } else if (~is_even_tw(&tw_ext)) {
             youfail();
             printf("Decaf tw deser isn't even:\n");
-            field_print("    s", &serf);
-            field_print("    x", &tw_base.x);
-            field_print("    y", &tw_base.y);
+            field_print("    s", serf);
+            field_print("    x", tw_base.x);
+            field_print("    y", tw_base.y);
             fails ++;
         } else if (~decaf_eq_tw_extensible(&tw_ext,&tw_ext2)) {
             youfail();
             printf("Decaf tw doesn't equal ext:\n");
-            field_print("    s", &serf);
-            field_print("    x1", &base.x);
-            field_print("    y1", &base.y);
-            field_print("    x2", &tw_base.x);
-            field_print("    y2", &tw_base.y);
-            field_print("    X2", &tw_ext2.x);
-            field_print("    Y2", &tw_ext2.y);
+            field_print("    s",  serf);
+            field_print("    x1", base.x);
+            field_print("    y1", base.y);
+            field_print("    x2", tw_base.x);
+            field_print("    y2", tw_base.y);
+            field_print("    X2", tw_ext2.x);
+            field_print("    Y2", tw_ext2.y);
             fails ++;
         }
         
@@ -365,7 +365,7 @@ int test_decaf (void) {
 
 int test_pointops (void) {
     struct affine_t base, pbase;
-    struct field_t serf;
+    field_a_t serf;
     
     struct crandom_state_t crand;
     crandom_init_from_buffer(&crand, "test_pointops random initializer");
@@ -390,7 +390,7 @@ int test_pointops (void) {
         #endif
         
         /* TODO: we need a field generate, which can return random or pathological. */
-        mask_t succ = field_deserialize(&serf, ser);
+        mask_t succ = field_deserialize(serf, ser);
         if (!succ) {
             youfail();
             printf("   Unlikely: fail at field_deserialize\n");
@@ -400,7 +400,7 @@ int test_pointops (void) {
         if (i) {
             copy_affine(&pbase, &base);
         }
-        elligator_2s_inject(&base, &serf);
+        elligator_2s_inject(&base, serf);
         
         if (i) {
             ret = add_double_test(&base, &pbase);
diff --git a/test/test_scalarmul.c b/test/test_scalarmul.c
index 89db764..d21be13 100644
--- a/test/test_scalarmul.c
+++ b/test/test_scalarmul.c
@@ -12,19 +12,19 @@
 /* 0 = succeed, 1 = inval, -1 = fail */
 static int
 single_scalarmul_compatibility_test (
-    const struct field_t *base,
+    const field_a_t base,
     const word_t *scalar,
     int nbits
 ) {
     struct tw_extensible_t text, work;
-    struct field_t mont, ct, vl, vt;
+    field_a_t mont, ct, vl, vt;
     
     int ret = 0, i;
     mask_t succ, succm;
     
-    succ = deserialize_and_twist_approx(&text, &sqrt_d_minus_1, base);
+    succ = deserialize_and_twist_approx(&text, base);
     
-    succm = montgomery_ladder(&mont,base,scalar,nbits,1);
+    succm = montgomery_ladder(mont,base,scalar,nbits,1);
     
     if (succ != succm) {
         youfail();
@@ -52,7 +52,7 @@ single_scalarmul_compatibility_test (
     const int nparams = sizeof(params)/sizeof(params[0]);
     struct fixed_base_table_t fbt;
     const int nsizes = 6;
-    struct field_t fbout[nparams], wout[nsizes];
+    field_a_t fbout[nparams], wout[nsizes];
     memset(&fbt, 0, sizeof(fbt));
     memset(&fbout, 0, sizeof(fbout));
     memset(&wout, 0, sizeof(wout));
@@ -75,7 +75,7 @@ single_scalarmul_compatibility_test (
             continue;
         }
         
-        untwist_and_double_and_serialize(&fbout[i], &work);
+        untwist_and_double_and_serialize(fbout[i], &work);
     }
     
     /* compute using precomp wNAF */
@@ -91,7 +91,7 @@ single_scalarmul_compatibility_test (
         
         scalarmul_fixed_base_wnaf_vt(&work, scalar, nbits, pre, i);
         
-        untwist_and_double_and_serialize(&wout[i], &work);
+        untwist_and_double_and_serialize(wout[i], &work);
     }
     
     mask_t consistent = MASK_SUCCESS;
@@ -100,31 +100,31 @@ single_scalarmul_compatibility_test (
         /* window methods currently only work on FIELD_BITS bits. */
         copy_tw_extensible(&work, &text);
         scalarmul(&work, scalar);
-        untwist_and_double_and_serialize(&ct, &work);
+        untwist_and_double_and_serialize(ct, &work);
         
         copy_tw_extensible(&work, &text);
         scalarmul_vlook(&work, scalar);
-        untwist_and_double_and_serialize(&vl, &work);
+        untwist_and_double_and_serialize(vl, &work);
         
         copy_tw_extensible(&work, &text);
         scalarmul_vt(&work, scalar, nbits);
-        untwist_and_double_and_serialize(&vt, &work);
+        untwist_and_double_and_serialize(vt, &work);
         
     
         /* check consistency mont vs window */
-        consistent &= field_eq(&mont, &ct);
-        consistent &= field_eq(&mont, &vl);
-        consistent &= field_eq(&mont, &vt);
+        consistent &= field_eq(mont, ct);
+        consistent &= field_eq(mont, vl);
+        consistent &= field_eq(mont, vt);
     }
     
     /* check consistency mont vs combs */
     for (i=0; i<nparams; i++) {
-        consistent &= field_eq(&mont,&fbout[i]);
+        consistent &= field_eq(mont,fbout[i]);
     }
     
     /* check consistency mont vs wNAF */
     for (i=0; i<nsizes; i++) {
-        consistent &= field_eq(&mont,&wout[i]);
+        consistent &= field_eq(mont,wout[i]);
     }
     
     /* If inconsistent, complain. */
@@ -133,23 +133,23 @@ single_scalarmul_compatibility_test (
         printf("    Failed scalarmul consistency test with nbits=%d.\n",nbits);
         field_print("    base", base);
         scalar_print("    scal", scalar, (nbits+WORD_BITS-1)/WORD_BITS);
-        field_print("    mont", &mont);
+        field_print("    mont", mont);
         
         for (i=0; i<nparams; i++) {
             printf("    With n=%d, t=%d, s=%d:\n", params[i].n, params[i].t, params[i].s);
-            field_print("    out ", &fbout[i]);
+            field_print("    out ", fbout[i]);
         }
         
         for (i=0; i<nsizes; i++) {
             printf("    With w=%d:\n",i);
-            field_print("    wNAF", &wout[i]);
+            field_print("    wNAF", wout[i]);
         }
         
     
         if (nbits == FIELD_BITS) {
-            field_print("    ct ", &ct);
-            field_print("    vl ", &vl);
-            field_print("    vt ", &vt);
+            field_print("    ct ", ct);
+            field_print("    vl ", vl);
+            field_print("    vt ", vt);
         }
         
         ret = -1;
@@ -160,20 +160,20 @@ single_scalarmul_compatibility_test (
 
 static int
 single_linear_combo_test (
-    const struct field_t *base1,
+    const field_a_t base1,
     const word_t *scalar1,
     int nbits1,
-    const struct field_t *base2,
+    const field_a_t base2,
     const word_t *scalar2,
     int nbits2
 ) { 
     struct tw_extensible_t text1, text2, working;
     struct tw_pniels_t pn;
-    struct field_t result_comb, result_combo, result_wnaf;
+    field_a_t result_comb, result_combo, result_wnaf;
     
     mask_t succ = 
-        deserialize_and_twist_approx(&text1, &sqrt_d_minus_1, base1)
-      & deserialize_and_twist_approx(&text2, &sqrt_d_minus_1, base2);
+        deserialize_and_twist_approx(&text1, base1)
+      & deserialize_and_twist_approx(&text2, base2);
     if (!succ) return 1;
     
     struct fixed_base_table_t t1, t2;
@@ -194,22 +194,22 @@ single_linear_combo_test (
     /* use the dedicated wNAF linear combo algorithm */
     copy_tw_extensible(&working, &text1);
     linear_combo_var_fixed_vt(&working, scalar1, nbits1, scalar2, nbits2, wnaf, 5);
-    untwist_and_double_and_serialize(&result_wnaf, &working);
+    untwist_and_double_and_serialize(result_wnaf, &working);
     
     /* use the dedicated combs algorithm */
     succ &= linear_combo_combs_vt(&working, scalar1, nbits1, &t1, scalar2, nbits2, &t2);
-    untwist_and_double_and_serialize(&result_combo, &working);
+    untwist_and_double_and_serialize(result_combo, &working);
     
     /* use two combs */
     succ &= scalarmul_fixed_base(&working, scalar1, nbits1, &t1);
     convert_tw_extensible_to_tw_pniels(&pn, &working);
     succ &= scalarmul_fixed_base(&working, scalar2, nbits2, &t2);
     add_tw_pniels_to_tw_extensible(&working, &pn);
-    untwist_and_double_and_serialize(&result_comb, &working);
+    untwist_and_double_and_serialize(result_comb, &working);
     
     mask_t consistent = MASK_SUCCESS;
-    consistent &= field_eq(&result_combo, &result_wnaf);
-    consistent &= field_eq(&result_comb,  &result_wnaf);
+    consistent &= field_eq(result_combo, result_wnaf);
+    consistent &= field_eq(result_comb,  result_wnaf);
     
     if (!succ || !consistent) {
         youfail();
@@ -219,9 +219,9 @@ single_linear_combo_test (
         scalar_print("    scal1", scalar1, (nbits1+WORD_BITS-1)/WORD_BITS);
         field_print("    base2", base2);
         scalar_print("    scal2", scalar2, (nbits1+WORD_BITS-1)/WORD_BITS);
-        field_print("    combs", &result_comb);
-        field_print("    combo", &result_combo);
-        field_print("    wNAFs", &result_wnaf);
+        field_print("    combs", result_comb);
+        field_print("    combo", result_combo);
+        field_print("    wNAFs", result_wnaf);
         return -1;
     }
     
@@ -234,7 +234,7 @@ single_linear_combo_test (
 /* 0 = succeed, 1 = inval, -1 = fail */
 static int
 single_scalarmul_commutativity_test (
-    const struct field_t *base,
+    const field_a_t base,
     const word_t *scalar1,
     int nbits1,
     int ned1,
@@ -242,12 +242,12 @@ single_scalarmul_commutativity_test (
     int nbits2,
     int ned2
 ) {
-    struct field_t m12, m21, tmp1, tmp2;
-    mask_t succ12a = montgomery_ladder(&tmp1,base,scalar1,nbits1,ned1);
-    mask_t succ12b = montgomery_ladder(&m12,&tmp1,scalar2,nbits2,ned2);
+    field_a_t m12, m21, tmp1, tmp2;
+    mask_t succ12a = montgomery_ladder(tmp1,base,scalar1,nbits1,ned1);
+    mask_t succ12b = montgomery_ladder(m12,tmp1,scalar2,nbits2,ned2);
     
-    mask_t succ21a = montgomery_ladder(&tmp2,base,scalar2,nbits2,ned2);
-    mask_t succ21b = montgomery_ladder(&m21,&tmp2,scalar1,nbits1,ned1);
+    mask_t succ21a = montgomery_ladder(tmp2,base,scalar2,nbits2,ned2);
+    mask_t succ21b = montgomery_ladder(m21,tmp2,scalar1,nbits1,ned1);
     
     mask_t succ12 = succ12a & succ12b, succ21 = succ21a & succ21b;
     
@@ -256,8 +256,8 @@ single_scalarmul_commutativity_test (
         printf("    Failed scalarmul commutativity test with (nbits,ned) = (%d,%d), (%d,%d).\n",
             nbits1,ned1,nbits2,ned2);
         field_print("    base", base);
-        field_print("    tmp1", &tmp1);
-        field_print("    tmp2", &tmp2);
+        field_print("    tmp1", tmp1);
+        field_print("    tmp2", tmp2);
         scalar_print("    sca1", scalar1, (nbits1+WORD_BITS-1)/WORD_BITS);
         scalar_print("    sca2", scalar2, (nbits1+WORD_BITS-1)/WORD_BITS);
         printf("    good = ((%d,%d),(%d,%d))\n", (int)-succ12a,
@@ -269,7 +269,7 @@ single_scalarmul_commutativity_test (
         return 1;
     }
     
-    mask_t consistent = field_eq(&m12,&m21);
+    mask_t consistent = field_eq(m12,m21);
     if (consistent) {
         return 0;
     } else {
@@ -279,8 +279,8 @@ single_scalarmul_commutativity_test (
         field_print("    base", base);
         scalar_print("    sca1", scalar1, (nbits1+WORD_BITS-1)/WORD_BITS);
         scalar_print("    sca2", scalar2, (nbits1+WORD_BITS-1)/WORD_BITS);
-        field_print("    m12 ", &m12);
-        field_print("    m21 ", &m21);
+        field_print("    m12 ", m12);
+        field_print("    m21 ", m21);
         return -1;
     }
 }