diff --git a/src/p25519/arch_ref64/f_impl.h b/src/p25519/arch_ref64/f_impl.h
index 835151a..639826d 100644
--- a/src/p25519/arch_ref64/f_impl.h
+++ b/src/p25519/arch_ref64/f_impl.h
@@ -4,14 +4,12 @@
 #ifndef __P25519_H__
 #define __P25519_H__ 1
 
+#include "f_field.h"
+
 #include <stdint.h>
 #include <assert.h>
 #include <string.h>
 
-#include "decaf/decaf_255.h"
-#include "word.h"
-
-#define LBITS 51
 #define FIELD_LITERAL(a,b,c,d,e) {{ a,b,c,d,e }}
 
 #ifdef __cplusplus
@@ -20,54 +18,29 @@ extern "C" {
 
 /* -------------- Inline functions begin here -------------- */
 
-void
-gf_25519_add_RAW (
-    gf_25519_t out,
-    const gf_25519_t a,
-    const gf_25519_t b
-) {
+void gf_add_RAW (gf out, const gf a, const gf b) {
     unsigned int i;
     for (i=0; i<5; i++) {
         out->limb[i] = a->limb[i] + b->limb[i];
     }
-    gf_25519_weak_reduce(out);
+    gf_weak_reduce(out);
 }
 
-void
-gf_25519_sub_RAW (
-    gf_25519_t out,
-    const gf_25519_t a,
-    const gf_25519_t b
-) {
+void gf_sub_RAW (gf out, const gf a, const gf b) {
     unsigned int i;
     uint64_t co1 = ((1ull<<51)-1)*2, co2 = co1-36;
     for (i=0; i<5; i++) {
         out->limb[i] = a->limb[i] - b->limb[i] + ((i==0) ? co2 : co1);
     }
-    gf_25519_weak_reduce(out);
-}
-
-void
-gf_25519_copy (
-    gf_25519_t out,
-    const gf_25519_t a
-) {
-    memcpy(out,a,sizeof(*a));
+    gf_weak_reduce(out);
 }
 
-void
-gf_25519_bias (
-    gf_25519_t a,
-    int amt
-) {
+void gf_bias (gf a, int amt) {
     (void) a;
     (void) amt;
 }
 
-void
-gf_25519_weak_reduce (
-    gf_25519_t a
-) {
+void gf_weak_reduce (gf a) {
     uint64_t mask = (1ull<<51) - 1;
     uint64_t tmp = a->limb[4] >> 51;
     int i;
diff --git a/src/p25519/arch_x86_64/f_impl.h b/src/p25519/arch_x86_64/f_impl.h
index 24cbe19..1b89171 100644
--- a/src/p25519/arch_x86_64/f_impl.h
+++ b/src/p25519/arch_x86_64/f_impl.h
@@ -4,36 +4,24 @@
 #ifndef __P25519_H__
 #define __P25519_H__ 1
 
+#include "f_field.h"
+
 #include <stdint.h>
 #include <assert.h>
 #include <string.h>
 
-#include "decaf/decaf_255.h"
-#include "word.h"
-
-#define DECAF_255_LIMB_BITS 51
 #define FIELD_LITERAL(a,b,c,d,e) {{ a,b,c,d,e }}
 
 /* -------------- Inline functions begin here -------------- */
 
-void
-gf_25519_add_RAW (
-    gf_25519_t out,
-    const gf_25519_t a,
-    const gf_25519_t b
-) {
+void gf_add_RAW (gf out, const gf a, const gf b) {
     unsigned int i;
     for (i=0; i<5; i++) {
         out->limb[i] = a->limb[i] + b->limb[i];
     }
 }
 
-void
-gf_25519_sub_RAW (
-    gf_25519_t out,
-    const gf_25519_t a,
-    const gf_25519_t b
-) {
+void gf_sub_RAW (gf out, const gf a, const gf b) {
     unsigned int i;
     uint64_t co1 = ((1ull<<51)-1)*2, co2 = co1-36;
     for (i=0; i<5; i++) {
@@ -41,11 +29,7 @@ gf_25519_sub_RAW (
     }
 }
 
-void
-gf_25519_bias (
-    gf_25519_t a,
-    int amt
-) {
+void gf_bias (gf a, int amt) {
     a->limb[0] += ((uint64_t)(amt)<<52) - 38*amt;
     int i;
     for (i=1; i<5; i++) {
@@ -53,10 +37,7 @@ gf_25519_bias (
     }
 }
 
-void
-gf_25519_weak_reduce (
-    gf_25519_t a
-) {
+void gf_weak_reduce (gf a) {
     uint64_t mask = (1ull<<51) - 1;
     uint64_t tmp = a->limb[4] >> 51;
     int i;
diff --git a/src/p448/arch_32/f_impl.h b/src/p448/arch_32/f_impl.h
index 7d343e0..d6abb12 100644
--- a/src/p448/arch_32/f_impl.h
+++ b/src/p448/arch_32/f_impl.h
@@ -4,17 +4,12 @@
 #ifndef __P448_H__
 #define __P448_H__ 1
 
-#include "word.h"
+#include "f_field.h"
 
 #include <stdint.h>
 #include <assert.h>
 
-typedef struct gf_448_s {
-  uint32_t limb[16];
-} __attribute__((aligned(32))) gf_448_s, gf_448_t[1];
-
-#define LBITS 28
-#define LIMB(x) (x##ull)&((1ull<<LBITS)-1), (x##ull)>>LBITS
+#define LIMB(x) (x##ull)&((1ull<<28)-1), (x##ull)>>28
 #define FIELD_LITERAL(a,b,c,d,e,f,g,h) \
     {{LIMB(a),LIMB(b),LIMB(c),LIMB(d),LIMB(e),LIMB(f),LIMB(g),LIMB(h)}}
 
@@ -24,12 +19,7 @@ extern "C" {
 
 /* -------------- Inline functions begin here -------------- */
 
-void
-gf_448_add_RAW (
-    gf_448_t out,
-    const gf_448_t a,
-    const gf_448_t b
-) {
+void gf_add_RAW (gf out, const gf a, const gf b) {
     unsigned int i;
     for (i=0; i<sizeof(*out)/sizeof(uint32xn_t); i++) {
         ((uint32xn_t*)out)[i] = ((const uint32xn_t*)a)[i] + ((const uint32xn_t*)b)[i];
@@ -42,12 +32,7 @@ gf_448_add_RAW (
     */
 }
 
-void
-gf_448_sub_RAW (
-    gf_448_t out,
-    const gf_448_t a,
-    const gf_448_t b
-) {
+void gf_sub_RAW (gf out, const gf a, const gf b) {
     unsigned int i;
     for (i=0; i<sizeof(*out)/sizeof(uint32xn_t); i++) {
         ((uint32xn_t*)out)[i] = ((const uint32xn_t*)a)[i] - ((const uint32xn_t*)b)[i];
@@ -60,11 +45,7 @@ gf_448_sub_RAW (
     */
 }
 
-void
-gf_448_bias (
-    gf_448_t a,
-    int amt
-) {
+void gf_bias (gf a, int amt) {
     uint32_t co1 = ((1ull<<28)-1)*amt, co2 = co1-amt;
     uint32x4_t lo = {co1,co1,co1,co1}, hi = {co2,co1,co1,co1};
     uint32x4_t *aa = (uint32x4_t*) a;
@@ -74,10 +55,7 @@ gf_448_bias (
     aa[3] += lo;
 }
 
-void
-gf_448_weak_reduce (
-    gf_448_t a
-) {
+void gf_weak_reduce (gf a) {
     uint64_t mask = (1ull<<28) - 1;
     uint64_t tmp = a->limb[15] >> 28;
     int i;
diff --git a/src/p448/arch_arm_32/f_impl.h b/src/p448/arch_arm_32/f_impl.h
index 7d343e0..d6abb12 100644
--- a/src/p448/arch_arm_32/f_impl.h
+++ b/src/p448/arch_arm_32/f_impl.h
@@ -4,17 +4,12 @@
 #ifndef __P448_H__
 #define __P448_H__ 1
 
-#include "word.h"
+#include "f_field.h"
 
 #include <stdint.h>
 #include <assert.h>
 
-typedef struct gf_448_s {
-  uint32_t limb[16];
-} __attribute__((aligned(32))) gf_448_s, gf_448_t[1];
-
-#define LBITS 28
-#define LIMB(x) (x##ull)&((1ull<<LBITS)-1), (x##ull)>>LBITS
+#define LIMB(x) (x##ull)&((1ull<<28)-1), (x##ull)>>28
 #define FIELD_LITERAL(a,b,c,d,e,f,g,h) \
     {{LIMB(a),LIMB(b),LIMB(c),LIMB(d),LIMB(e),LIMB(f),LIMB(g),LIMB(h)}}
 
@@ -24,12 +19,7 @@ extern "C" {
 
 /* -------------- Inline functions begin here -------------- */
 
-void
-gf_448_add_RAW (
-    gf_448_t out,
-    const gf_448_t a,
-    const gf_448_t b
-) {
+void gf_add_RAW (gf out, const gf a, const gf b) {
     unsigned int i;
     for (i=0; i<sizeof(*out)/sizeof(uint32xn_t); i++) {
         ((uint32xn_t*)out)[i] = ((const uint32xn_t*)a)[i] + ((const uint32xn_t*)b)[i];
@@ -42,12 +32,7 @@ gf_448_add_RAW (
     */
 }
 
-void
-gf_448_sub_RAW (
-    gf_448_t out,
-    const gf_448_t a,
-    const gf_448_t b
-) {
+void gf_sub_RAW (gf out, const gf a, const gf b) {
     unsigned int i;
     for (i=0; i<sizeof(*out)/sizeof(uint32xn_t); i++) {
         ((uint32xn_t*)out)[i] = ((const uint32xn_t*)a)[i] - ((const uint32xn_t*)b)[i];
@@ -60,11 +45,7 @@ gf_448_sub_RAW (
     */
 }
 
-void
-gf_448_bias (
-    gf_448_t a,
-    int amt
-) {
+void gf_bias (gf a, int amt) {
     uint32_t co1 = ((1ull<<28)-1)*amt, co2 = co1-amt;
     uint32x4_t lo = {co1,co1,co1,co1}, hi = {co2,co1,co1,co1};
     uint32x4_t *aa = (uint32x4_t*) a;
@@ -74,10 +55,7 @@ gf_448_bias (
     aa[3] += lo;
 }
 
-void
-gf_448_weak_reduce (
-    gf_448_t a
-) {
+void gf_weak_reduce (gf a) {
     uint64_t mask = (1ull<<28) - 1;
     uint64_t tmp = a->limb[15] >> 28;
     int i;
diff --git a/src/p448/arch_neon_experimental/f_impl.h b/src/p448/arch_neon_experimental/f_impl.h
index a88dec2..2ed616b 100644
--- a/src/p448/arch_neon_experimental/f_impl.h
+++ b/src/p448/arch_neon_experimental/f_impl.h
@@ -4,20 +4,15 @@
 #ifndef __P448_H__
 #define __P448_H__ 1
 
-#include "word.h"
+#include "f_field.h"
 
 #include <stdint.h>
 #include <assert.h>
 
-typedef struct gf_448_s {
-  uint32_t limb[16];
-} __attribute__((aligned(32))) gf_448_s, gf_448_t[1];
-
 #define LIMBPERM(x) (((x)<<1 | (x)>>3) & 15)
 #define USE_NEON_PERM 1
-#define LBITS 28
-#define LIMBHI(x) ((x##ull)>>LBITS)
-#define LIMBLO(x) ((x##ull)&((1ull<<LBITS)-1))
+#define LIMBHI(x) ((x##ull)>>28)
+#define LIMBLO(x) ((x##ull)&((1ull<<28)-1))
 #  define FIELD_LITERAL(a,b,c,d,e,f,g,h) \
     {{LIMBLO(a),LIMBLO(e), LIMBHI(a),LIMBHI(e), \
       LIMBLO(b),LIMBLO(f), LIMBHI(b),LIMBHI(f), \
@@ -30,24 +25,14 @@ extern "C" {
     
 /* -------------- Inline functions begin here -------------- */
 
-void
-gf_448_add_RAW (
-    gf_448_t out,
-    const gf_448_t a,
-    const gf_448_t b
-) {
+void gf_add_RAW (gf out, const gf a, const gf b) {
     unsigned int i;
     for (i=0; i<sizeof(*out)/sizeof(uint32xn_t); i++) {
         ((uint32xn_t*)out)[i] = ((const uint32xn_t*)a)[i] + ((const uint32xn_t*)b)[i];
     }
 }
 
-void
-gf_448_sub_RAW (
-    gf_448_t out,
-    const gf_448_t a,
-    const gf_448_t b
-) {
+void gf_sub_RAW (gf out, const gf a, const gf b) {
     unsigned int i;
     for (i=0; i<sizeof(*out)/sizeof(uint32xn_t); i++) {
         ((uint32xn_t*)out)[i] = ((const uint32xn_t*)a)[i] - ((const uint32xn_t*)b)[i];
@@ -60,11 +45,7 @@ gf_448_sub_RAW (
     */
 }
 
-void
-gf_448_bias (
-    gf_448_t a,
-    int amt
-) {
+void gf_bias (gf a, int amt) {
     uint32_t co1 = ((1ull<<28)-1)*amt, co2 = co1-amt;
     uint32x4_t lo = {co1,co2,co1,co1}, hi = {co1,co1,co1,co1};
     uint32x4_t *aa = (uint32x4_t*) a;
@@ -74,10 +55,7 @@ gf_448_bias (
     aa[3] += hi;
 }
 
-void
-gf_448_weak_reduce (
-    gf_448_t a
-) {
+void gf_weak_reduce (gf a) {
 
     uint32x2_t *aa = (uint32x2_t*) a, vmask = {(1ull<<28)-1, (1ull<<28)-1}, vm2 = {0,-1},
        tmp = vshr_n_u32(aa[7],28);
diff --git a/src/p448/arch_ref64/f_impl.h b/src/p448/arch_ref64/f_impl.h
index cf84d72..0f9af8b 100644
--- a/src/p448/arch_ref64/f_impl.h
+++ b/src/p448/arch_ref64/f_impl.h
@@ -4,17 +4,12 @@
 #ifndef __P448_H__
 #define __P448_H__ 1
 
+#include "f_field.h"
+
 #include <stdint.h>
 #include <assert.h>
 #include <string.h>
 
-#include "word.h"
-
-typedef struct gf_448_s {
-  uint64_t limb[8];
-} __attribute__((aligned(32))) gf_448_s, gf_448_t[1];
-
-#define LBITS 56
 #define FIELD_LITERAL(a,b,c,d,e,f,g,h) {{a,b,c,d,e,f,g,h}}
 
 #ifdef __cplusplus
@@ -23,46 +18,29 @@ extern "C" {
 
 /* -------------- Inline functions begin here -------------- */
 
-void
-gf_448_add_RAW (
-    gf_448_t out,
-    const gf_448_t a,
-    const gf_448_t b
-) {
+void gf_add_RAW (gf  out, const gf  a, const gf  b) {
     unsigned int i;
     for (i=0; i<8; i++) {
         out->limb[i] = a->limb[i] + b->limb[i];
     }
-    gf_448_weak_reduce(out);
+    gf_weak_reduce(out);
 }
 
-void
-gf_448_sub_RAW (
-    gf_448_t out,
-    const gf_448_t a,
-    const gf_448_t b
-) {
+void gf_sub_RAW (gf  out, const gf  a, const gf  b) {
     unsigned int i;
     uint64_t co1 = ((1ull<<56)-1)*2, co2 = co1-2;
     for (i=0; i<8; i++) {
         out->limb[i] = a->limb[i] - b->limb[i] + ((i==4) ? co2 : co1);
     }
-    gf_448_weak_reduce(out);
+    gf_weak_reduce(out);
 }
 
-void
-gf_448_bias (
-    gf_448_t a,
-    int amt
-) {
+void gf_bias (gf  a, int amt) {
     (void) a;
     (void) amt;
 }
 
-void
-gf_448_weak_reduce (
-    gf_448_t a
-) {
+void gf_weak_reduce (gf  a) {
     uint64_t mask = (1ull<<56) - 1;
     uint64_t tmp = a->limb[7] >> 56;
     int i;
diff --git a/src/p448/arch_x86_64/f_impl.h b/src/p448/arch_x86_64/f_impl.h
index 0593398..8f1b40c 100644
--- a/src/p448/arch_x86_64/f_impl.h
+++ b/src/p448/arch_x86_64/f_impl.h
@@ -4,13 +4,11 @@
 #ifndef __P448_H__
 #define __P448_H__ 1
 
+#include "f_field.h"
+
 #include <stdint.h>
 #include <assert.h>
 
-#include "decaf/decaf_448.h"
-#include "word.h"
-
-#define LBITS 56
 #define FIELD_LITERAL(a,b,c,d,e,f,g,h) {{a,b,c,d,e,f,g,h}}
 
 #ifdef __cplusplus
@@ -19,12 +17,7 @@ extern "C" {
 
 /* -------------- Inline functions begin here -------------- */
 
-void
-gf_448_add_RAW (
-    gf_448_t out,
-    const gf_448_t a,
-    const gf_448_t b
-) {
+void gf_add_RAW (gf  out, const gf  a, const gf  b) {
     unsigned int i;
     for (i=0; i<sizeof(*out)/sizeof(uint64xn_t); i++) {
         ((uint64xn_t*)out)[i] = ((const uint64xn_t*)a)[i] + ((const uint64xn_t*)b)[i];
@@ -37,12 +30,7 @@ gf_448_add_RAW (
     */
 }
 
-void
-gf_448_sub_RAW (
-    gf_448_t out,
-    const gf_448_t a,
-    const gf_448_t b
-) {
+void gf_sub_RAW (gf  out, const gf  a, const gf  b) {
     unsigned int i;
     for (i=0; i<sizeof(*out)/sizeof(uint64xn_t); i++) {
         ((uint64xn_t*)out)[i] = ((const uint64xn_t*)a)[i] - ((const uint64xn_t*)b)[i];
@@ -55,11 +43,7 @@ gf_448_sub_RAW (
     */
 }
 
-void
-gf_448_bias (
-    gf_448_t a,
-    int amt
-) {
+void gf_bias (gf  a, int amt) {
     uint64_t co1 = ((1ull<<56)-1)*amt, co2 = co1-amt;
     
 #if __AVX2__
@@ -82,10 +66,7 @@ gf_448_bias (
 #endif
 }
 
-void
-gf_448_weak_reduce (
-    gf_448_t a
-) {
+void gf_weak_reduce (gf  a) {
     /* PERF: use pshufb/palignr if anyone cares about speed of this */
     uint64_t mask = (1ull<<56) - 1;
     uint64_t tmp = a->limb[7] >> 56;
diff --git a/src/p480/arch_x86_64/f_impl.h b/src/p480/arch_x86_64/f_impl.h
index b55ba97..7c1867c 100644
--- a/src/p480/arch_x86_64/f_impl.h
+++ b/src/p480/arch_x86_64/f_impl.h
@@ -1,78 +1,23 @@
 /* Copyright (c) 2014 Cryptography Research, Inc.
  * Released under the MIT License.  See LICENSE.txt for license information.
  */
-#ifndef __gf_480_H__
-#define __gf_480_H__ 1
+#ifndef __gf_H__
+#define __gf_H__ 1
+
+#include "f_field.h"
 
 #include <stdint.h>
 #include <assert.h>
 
 #include "word.h"
 
-typedef struct gf_480_t {
-  uint64_t limb[8];
-} __attribute__((aligned(32))) gf_480_t;
-
 #ifdef __cplusplus
 extern "C" {
 #endif
-             
-static __inline__ void
-gf_480_weak_reduce (
-    gf_480_t *inout
-) __attribute__((unused,always_inline));
-             
-void
-gf_480_strong_reduce (
-    gf_480_t *inout
-);
-  
-static __inline__ void
-gf_480_bias (
-    gf_480_t *inout,
-    int amount
-) __attribute__((unused,always_inline));
-         
-void
-gf_480_mul (
-    gf_480_t *__restrict__ out,
-    const gf_480_t *a,
-    const gf_480_t *b
-);
-
-void
-gf_480_mulw (
-    gf_480_t *__restrict__ out,
-    const gf_480_t *a,
-    uint64_t b
-);
-
-void
-gf_480_sqr (
-    gf_480_t *__restrict__ out,
-    const gf_480_t *a
-);
-
-void
-gf_480_serialize (
-    uint8_t *serial,
-    const struct gf_480_t *x
-);
-
-mask_t
-gf_480_deserialize (
-    gf_480_t *x,
-    const uint8_t serial[60]
-);
 
 /* -------------- Inline functions begin here -------------- */
 
-void
-gf_480_add_RAW (
-    gf_480_t *out,
-    const gf_480_t *a,
-    const gf_480_t *b
-) {
+void gf_add_RAW (gf  *out, const gf  *a, const gf  *b) {
     unsigned int i;
     for (i=0; i<sizeof(*out)/sizeof(uint64xn_t); i++) {
         ((uint64xn_t*)out)[i] = ((const uint64xn_t*)a)[i] + ((const uint64xn_t*)b)[i];
@@ -85,12 +30,7 @@ gf_480_add_RAW (
     */
 }
 
-void
-gf_480_sub_RAW (
-    gf_480_t *out,
-    const gf_480_t *a,
-    const gf_480_t *b
-) {
+void gf_sub_RAW (gf  *out, const gf  *a, const gf  *b) {
     unsigned int i;
     for (i=0; i<sizeof(*out)/sizeof(uint64xn_t); i++) {
         ((uint64xn_t*)out)[i] = ((const uint64xn_t*)a)[i] - ((const uint64xn_t*)b)[i];
@@ -103,21 +43,15 @@ gf_480_sub_RAW (
     */
 }
 
-void
-gf_480_copy (
-    gf_480_t *out,
-    const gf_480_t *a
-) {
+void gf_copy (gf  *out, const gf  *a) {
     unsigned int i;
     for (i=0; i<sizeof(*out)/sizeof(big_register_t); i++) {
         ((big_register_t *)out)[i] = ((const big_register_t *)a)[i];
     }
 }
 
-void
-gf_480_bias (
-    gf_480_t *a,
-    int amt
+void gf_bias (
+    gf  *a, int amt
 ) {
     uint64_t co1 = ((1ull<<60)-1)*amt, co2 = co1-amt;
     
@@ -141,10 +75,7 @@ gf_480_bias (
 #endif
 }
 
-void
-gf_480_weak_reduce (
-    gf_480_t *a
-) {
+void gf_weak_reduce (gf  *a) {
     /* PERF: use pshufb/palignr if anyone cares about speed of this */
     uint64_t mask = (1ull<<60) - 1;
     uint64_t tmp = a->limb[7] >> 60;
@@ -160,4 +91,4 @@ gf_480_weak_reduce (
 }; /* extern "C" */
 #endif
 
-#endif /* __gf_480_H__ */
+#endif /* __gf_H__ */
diff --git a/src/p521/arch_ref64/f_impl.h b/src/p521/arch_ref64/f_impl.h
index 512b1d9..ddb784f 100644
--- a/src/p521/arch_ref64/f_impl.h
+++ b/src/p521/arch_ref64/f_impl.h
@@ -4,118 +4,41 @@
 #ifndef __P521_H__
 #define __P521_H__ 1
 
+#include "f_field.h"
+
 #include <stdint.h>
 #include <assert.h>
 #include <string.h>
 
-#include "word.h"
-
-typedef struct gf_521_t {
-  uint64_t limb[9];
-} gf_521_t;
-
 #ifdef __cplusplus
 extern "C" {
 #endif
-             
-static __inline__ void
-gf_521_weak_reduce (
-    gf_521_t *inout
-) __attribute__((unused));
-             
-void
-gf_521_strong_reduce (
-    gf_521_t *inout
-);
-
-static __inline__ void
-gf_521_bias (
-    gf_521_t *inout,
-    int amount
-) __attribute__((unused));
-         
-void
-gf_521_mul (
-    gf_521_t *__restrict__ out,
-    const gf_521_t *a,
-    const gf_521_t *b
-);
-
-void
-gf_521_mulw (
-    gf_521_t *__restrict__ out,
-    const gf_521_t *a,
-    uint64_t b
-);
-
-void
-gf_521_sqr (
-    gf_521_t *__restrict__ out,
-    const gf_521_t *a
-);
-
-void
-gf_521_serialize (
-    uint8_t *serial,
-    const struct gf_521_t *x
-);
-
-mask_t
-gf_521_deserialize (
-    gf_521_t *x,
-    const uint8_t serial[66]
-);
 
 /* -------------- Inline functions begin here -------------- */
 
-void
-gf_521_add_RAW (
-    gf_521_t *out,
-    const gf_521_t *a,
-    const gf_521_t *b
-) {
+void gf_add_RAW (gf  *out, const gf  *a, const gf  *b) {
     unsigned int i;
     for (i=0; i<9; i++) {
         out->limb[i] = a->limb[i] + b->limb[i];
     }
-    gf_521_weak_reduce(out);
+    gf_weak_reduce(out);
 }
 
-void
-gf_521_sub_RAW (
-    gf_521_t *out,
-    const gf_521_t *a,
-    const gf_521_t *b
-) {
+void gf_sub_RAW (gf  *out, const gf  *a, const gf  *b) {
     unsigned int i;
     uint64_t co1 = ((1ull<<58)-1)*4, co2 = ((1ull<<57)-1)*4;
     for (i=0; i<9; i++) {
         out->limb[i] = a->limb[i] - b->limb[i] + ((i==8) ? co2 : co1);
     }
-    gf_521_weak_reduce(out);
-}
-
-void
-gf_521_copy (
-    gf_521_t *out,
-    const gf_521_t *a
-) {
-    memcpy(out,a,sizeof(*a));
+    gf_weak_reduce(out);
 }
 
-void
-gf_521_bias (
-    gf_521_t *a,
-    int amt
-) {
+void gf_bias (gf *a, int amt) {
     (void) a;
     (void) amt;
 }
 
-void
-gf_521_weak_reduce (
-    gf_521_t *a
-) {
+void gf_weak_reduce (gf  *a) {
     uint64_t mask = (1ull<<58) - 1;
     uint64_t tmp = a->limb[8] >> 57;
     int i;
diff --git a/src/p521/arch_x86_64_r12/f_impl.h b/src/p521/arch_x86_64_r12/f_impl.h
index 4616b71..6dce421 100644
--- a/src/p521/arch_x86_64_r12/f_impl.h
+++ b/src/p521/arch_x86_64_r12/f_impl.h
@@ -4,20 +4,18 @@
 #ifndef __P521_H__
 #define __P521_H__ 1
 
+#include "f_field.h"
+
 #include <stdint.h>
 #include <assert.h>
 #include <string.h>
 
-#include "word.h"
 #include "constant_time.h"
 
+/* FIXME: Currenmtlty desn't work at all, because the struct is declared [9] and not [12] */
 #define LIMBPERM(x) (((x)%3)*4 + (x)/3)
 #define USE_P521_3x3_TRANSPOSE
 
-typedef struct gf_521_s {
-  uint64_t limb[12];
-} __attribute__((aligned(32))) gf_521_t;
-
 #ifdef __cplusplus
 extern "C" {
 #endif
@@ -29,43 +27,25 @@ typedef uint64x4_t uint64x3_t; /* fit it in a vector register */
 static const uint64x3_t mask58 = { (1ull<<58) - 1, (1ull<<58) - 1, (1ull<<58) - 1, 0 };
 
 /* Currently requires CLANG.  Sorry. */
-static inline uint64x3_t
-__attribute__((unused))
-timesW (
-  uint64x3_t u
-) {
-  return u.zxyw + u.zwww;
+static inline uint64x3_t timesW (uint64x3_t u) {
+    return u.zxyw + u.zwww;
 }
 
-void
-gf_521_add_RAW (
-    gf_521_t *out,
-    const gf_521_t *a,
-    const gf_521_t *b
-) {
+void gf_add_RAW (gf  *out, const gf  *a, const gf  *b) {
     unsigned int i;
     for (i=0; i<sizeof(*out)/sizeof(uint64xn_t); i++) {
         ((uint64xn_t*)out)[i] = ((const uint64xn_t*)a)[i] + ((const uint64xn_t*)b)[i];
     }
 }
 
-void
-gf_521_sub_RAW (
-    gf_521_t *out,
-    const gf_521_t *a,
-    const gf_521_t *b
-) {
+void gf_sub_RAW (gf  *out, const gf  *a, const gf  *b) {
     unsigned int i;
     for (i=0; i<sizeof(*out)/sizeof(uint64xn_t); i++) {
         ((uint64xn_t*)out)[i] = ((const uint64xn_t*)a)[i] - ((const uint64xn_t*)b)[i];
     }
 }
 
-void
-gf_521_bias (
-    gf_521_t *a,
-    int amt
-) {
+void gf_bias (gf  *a, int amt) {
     uint64_t co0 = ((1ull<<58)-2)*amt, co1 = ((1ull<<58)-1)*amt;
     uint64x4_t vlo = { co0, co1, co1, 0 }, vhi = { co1, co1, co1, 0 };
     ((uint64x4_t*)a)[0] += vlo;
@@ -73,10 +53,7 @@ gf_521_bias (
     ((uint64x4_t*)a)[2] += vhi;
 }
 
-void
-gf_521_weak_reduce (
-    gf_521_t *a
-) {
+void gf_weak_reduce (gf  *a) {
 #if 0
     int i;
     assert(a->limb[3] == 0 && a->limb[7] == 0 && a->limb[11] == 0);
@@ -84,7 +61,6 @@ gf_521_weak_reduce (
         assert(a->limb[i] < 3ull<<61);
     }
 #endif
-    
     uint64x3_t
         ot0 = ((uint64x4_t*)a)[0],
         ot1 = ((uint64x4_t*)a)[1],