The branch master has been updated
       via  425dde5d75a6ffff9a1027107711b99da39e3519 (commit)
       via  3a17b9a46ecf54a30073534dff04e3223ff98813 (commit)
      from  4ace4ccda2934d2628c3d63d41e79abe041621a7 (commit)


- Log -----------------------------------------------------------------
commit 425dde5d75a6ffff9a1027107711b99da39e3519
Author: Dr. Matthias St. Pierre <matthias.st.pie...@ncp-e.com>
Date:   Tue Dec 4 23:59:24 2018 +0100

    curve25519.c: improve formula alignment
    
    Reviewed-by: Matt Caswell <m...@openssl.org>
    (Merged from https://github.com/openssl/openssl/pull/7750)

commit 3a17b9a46ecf54a30073534dff04e3223ff98813
Author: Dr. Matthias St. Pierre <matthias.st.pie...@ncp-e.com>
Date:   Mon Dec 3 22:01:18 2018 +0100

    curve25519.c: reformat code to follow coding guidelines
    
    Fixes #7698
    
    Reviewed-by: Matt Caswell <m...@openssl.org>
    (Merged from https://github.com/openssl/openssl/pull/7750)

-----------------------------------------------------------------------

Summary of changes:
 crypto/ec/curve25519.c | 4566 +++++++++++++++++++++++++-----------------------
 1 file changed, 2336 insertions(+), 2230 deletions(-)

diff --git a/crypto/ec/curve25519.c b/crypto/ec/curve25519.c
index d2156a2..7d12c5d 100644
--- a/crypto/ec/curve25519.c
+++ b/crypto/ec/curve25519.c
@@ -744,91 +744,99 @@ static void x25519_scalar_mult(uint8_t out[32], const 
uint8_t scalar[32],
 
 /*
  * Reference base 2^25.5 implementation.
- */
-/*
+ *
  * This code is mostly taken from the ref10 version of Ed25519 in SUPERCOP
  * 20141124 (http://bench.cr.yp.to/supercop.html).
  *
  * The field functions are shared by Ed25519 and X25519 where possible.
  */
 
-/* fe means field element. Here the field is \Z/(2^255-19). An element t,
+/*
+ * fe means field element. Here the field is \Z/(2^255-19). An element t,
  * entries t[0]...t[9], represents the integer t[0]+2^26 t[1]+2^51 t[2]+2^77
  * t[3]+2^102 t[4]+...+2^230 t[9]. Bounds on each t[i] vary depending on
- * context.  */
+ * context.
+ */
 typedef int32_t fe[10];
 
+static const int64_t kBottom21Bits =  0x1fffffLL;
 static const int64_t kBottom25Bits = 0x1ffffffLL;
 static const int64_t kBottom26Bits = 0x3ffffffLL;
 static const int64_t kTop39Bits = 0xfffffffffe000000LL;
 static const int64_t kTop38Bits = 0xfffffffffc000000LL;
 
-static uint64_t load_3(const uint8_t *in) {
-  uint64_t result;
-  result = (uint64_t)in[0];
-  result |= ((uint64_t)in[1]) << 8;
-  result |= ((uint64_t)in[2]) << 16;
-  return result;
+static uint64_t load_3(const uint8_t *in)
+{
+    uint64_t result;
+
+    result  = ((uint64_t)in[0]);
+    result |= ((uint64_t)in[1]) << 8;
+    result |= ((uint64_t)in[2]) << 16;
+    return result;
 }
 
-static uint64_t load_4(const uint8_t *in) {
-  uint64_t result;
-  result = (uint64_t)in[0];
-  result |= ((uint64_t)in[1]) << 8;
-  result |= ((uint64_t)in[2]) << 16;
-  result |= ((uint64_t)in[3]) << 24;
-  return result;
+static uint64_t load_4(const uint8_t *in)
+{
+    uint64_t result;
+
+    result  = ((uint64_t)in[0]);
+    result |= ((uint64_t)in[1]) << 8;
+    result |= ((uint64_t)in[2]) << 16;
+    result |= ((uint64_t)in[3]) << 24;
+    return result;
 }
 
-static void fe_frombytes(fe h, const uint8_t *s) {
-  /* Ignores top bit of h. */
-  int64_t h0 = load_4(s);
-  int64_t h1 = load_3(s + 4) << 6;
-  int64_t h2 = load_3(s + 7) << 5;
-  int64_t h3 = load_3(s + 10) << 3;
-  int64_t h4 = load_3(s + 13) << 2;
-  int64_t h5 = load_4(s + 16);
-  int64_t h6 = load_3(s + 20) << 7;
-  int64_t h7 = load_3(s + 23) << 5;
-  int64_t h8 = load_3(s + 26) << 4;
-  int64_t h9 = (load_3(s + 29) & 8388607) << 2;
-  int64_t carry0;
-  int64_t carry1;
-  int64_t carry2;
-  int64_t carry3;
-  int64_t carry4;
-  int64_t carry5;
-  int64_t carry6;
-  int64_t carry7;
-  int64_t carry8;
-  int64_t carry9;
-
-  carry9 = h9 + (1 << 24); h0 += (carry9 >> 25) * 19; h9 -= carry9 & 
kTop39Bits;
-  carry1 = h1 + (1 << 24); h2 += carry1 >> 25; h1 -= carry1 & kTop39Bits;
-  carry3 = h3 + (1 << 24); h4 += carry3 >> 25; h3 -= carry3 & kTop39Bits;
-  carry5 = h5 + (1 << 24); h6 += carry5 >> 25; h5 -= carry5 & kTop39Bits;
-  carry7 = h7 + (1 << 24); h8 += carry7 >> 25; h7 -= carry7 & kTop39Bits;
-
-  carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits;
-  carry2 = h2 + (1 << 25); h3 += carry2 >> 26; h2 -= carry2 & kTop38Bits;
-  carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits;
-  carry6 = h6 + (1 << 25); h7 += carry6 >> 26; h6 -= carry6 & kTop38Bits;
-  carry8 = h8 + (1 << 25); h9 += carry8 >> 26; h8 -= carry8 & kTop38Bits;
-
-  h[0] = (int32_t)h0;
-  h[1] = (int32_t)h1;
-  h[2] = (int32_t)h2;
-  h[3] = (int32_t)h3;
-  h[4] = (int32_t)h4;
-  h[5] = (int32_t)h5;
-  h[6] = (int32_t)h6;
-  h[7] = (int32_t)h7;
-  h[8] = (int32_t)h8;
-  h[9] = (int32_t)h9;
+static void fe_frombytes(fe h, const uint8_t *s)
+{
+    /* Ignores top bit of h. */
+    int64_t h0 =  load_4(s);
+    int64_t h1 =  load_3(s +  4) << 6;
+    int64_t h2 =  load_3(s +  7) << 5;
+    int64_t h3 =  load_3(s + 10) << 3;
+    int64_t h4 =  load_3(s + 13) << 2;
+    int64_t h5 =  load_4(s + 16);
+    int64_t h6 =  load_3(s + 20) << 7;
+    int64_t h7 =  load_3(s + 23) << 5;
+    int64_t h8 =  load_3(s + 26) << 4;
+    int64_t h9 = (load_3(s + 29) & 0x7fffff) << 2;
+    int64_t carry0;
+    int64_t carry1;
+    int64_t carry2;
+    int64_t carry3;
+    int64_t carry4;
+    int64_t carry5;
+    int64_t carry6;
+    int64_t carry7;
+    int64_t carry8;
+    int64_t carry9;
+
+    carry9 = h9 + (1 << 24); h0 += (carry9 >> 25) * 19; h9 -= carry9 & 
kTop39Bits;
+    carry1 = h1 + (1 << 24); h2 += carry1 >> 25; h1 -= carry1 & kTop39Bits;
+    carry3 = h3 + (1 << 24); h4 += carry3 >> 25; h3 -= carry3 & kTop39Bits;
+    carry5 = h5 + (1 << 24); h6 += carry5 >> 25; h5 -= carry5 & kTop39Bits;
+    carry7 = h7 + (1 << 24); h8 += carry7 >> 25; h7 -= carry7 & kTop39Bits;
+
+    carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits;
+    carry2 = h2 + (1 << 25); h3 += carry2 >> 26; h2 -= carry2 & kTop38Bits;
+    carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits;
+    carry6 = h6 + (1 << 25); h7 += carry6 >> 26; h6 -= carry6 & kTop38Bits;
+    carry8 = h8 + (1 << 25); h9 += carry8 >> 26; h8 -= carry8 & kTop38Bits;
+
+    h[0] = (int32_t)h0;
+    h[1] = (int32_t)h1;
+    h[2] = (int32_t)h2;
+    h[3] = (int32_t)h3;
+    h[4] = (int32_t)h4;
+    h[5] = (int32_t)h5;
+    h[6] = (int32_t)h6;
+    h[7] = (int32_t)h7;
+    h[8] = (int32_t)h8;
+    h[9] = (int32_t)h9;
 }
 
-/* Preconditions:
- *  |h| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc.
+/*
+ * Preconditions:
+ *   |h| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc.
  *
  * Write p=2^255-19; q=floor(h/p).
  * Basic claim: q = floor(2^(-255)(h + 19 2^(-25)h9 + 2^(-1))).
@@ -848,102 +856,112 @@ static void fe_frombytes(fe h, const uint8_t *s) {
  *   Then 0<x<2^255 so floor(2^(-255)x) = 0 so floor(q+2^(-255)x) = q.
  *
  *   Have q+2^(-255)x = 2^(-255)(h + 19 2^(-25) h9 + 2^(-1))
- *   so floor(2^(-255)(h + 19 2^(-25) h9 + 2^(-1))) = q. */
-static void fe_tobytes(uint8_t *s, const fe h) {
-  int32_t h0 = h[0];
-  int32_t h1 = h[1];
-  int32_t h2 = h[2];
-  int32_t h3 = h[3];
-  int32_t h4 = h[4];
-  int32_t h5 = h[5];
-  int32_t h6 = h[6];
-  int32_t h7 = h[7];
-  int32_t h8 = h[8];
-  int32_t h9 = h[9];
-  int32_t q;
-
-  q = (19 * h9 + (((int32_t) 1) << 24)) >> 25;
-  q = (h0 + q) >> 26;
-  q = (h1 + q) >> 25;
-  q = (h2 + q) >> 26;
-  q = (h3 + q) >> 25;
-  q = (h4 + q) >> 26;
-  q = (h5 + q) >> 25;
-  q = (h6 + q) >> 26;
-  q = (h7 + q) >> 25;
-  q = (h8 + q) >> 26;
-  q = (h9 + q) >> 25;
-
-  /* Goal: Output h-(2^255-19)q, which is between 0 and 2^255-20. */
-  h0 += 19 * q;
-  /* Goal: Output h-2^255 q, which is between 0 and 2^255-20. */
-
-  h1 += h0 >> 26; h0 &= kBottom26Bits;
-  h2 += h1 >> 25; h1 &= kBottom25Bits;
-  h3 += h2 >> 26; h2 &= kBottom26Bits;
-  h4 += h3 >> 25; h3 &= kBottom25Bits;
-  h5 += h4 >> 26; h4 &= kBottom26Bits;
-  h6 += h5 >> 25; h5 &= kBottom25Bits;
-  h7 += h6 >> 26; h6 &= kBottom26Bits;
-  h8 += h7 >> 25; h7 &= kBottom25Bits;
-  h9 += h8 >> 26; h8 &= kBottom26Bits;
-                  h9 &= kBottom25Bits;
-                  /* h10 = carry9 */
-
-  /* Goal: Output h0+...+2^255 h10-2^255 q, which is between 0 and 2^255-20.
-   * Have h0+...+2^230 h9 between 0 and 2^255-1;
-   * evidently 2^255 h10-2^255 q = 0.
-   * Goal: Output h0+...+2^230 h9.  */
-
-  s[0] = (uint8_t)(h0 >> 0);
-  s[1] = (uint8_t)(h0 >> 8);
-  s[2] = (uint8_t)(h0 >> 16);
-  s[3] = (uint8_t)((h0 >> 24) | ((uint32_t)(h1) << 2));
-  s[4] = (uint8_t)(h1 >> 6);
-  s[5] = (uint8_t)(h1 >> 14);
-  s[6] = (uint8_t)((h1 >> 22) | ((uint32_t)(h2) << 3));
-  s[7] = (uint8_t)(h2 >> 5);
-  s[8] = (uint8_t)(h2 >> 13);
-  s[9] = (uint8_t)((h2 >> 21) | ((uint32_t)(h3) << 5));
-  s[10] = (uint8_t)(h3 >> 3);
-  s[11] = (uint8_t)(h3 >> 11);
-  s[12] = (uint8_t)((h3 >> 19) | ((uint32_t)(h4) << 6));
-  s[13] = (uint8_t)(h4 >> 2);
-  s[14] = (uint8_t)(h4 >> 10);
-  s[15] = (uint8_t)(h4 >> 18);
-  s[16] = (uint8_t)(h5 >> 0);
-  s[17] = (uint8_t)(h5 >> 8);
-  s[18] = (uint8_t)(h5 >> 16);
-  s[19] = (uint8_t)((h5 >> 24) | ((uint32_t)(h6) << 1));
-  s[20] = (uint8_t)(h6 >> 7);
-  s[21] = (uint8_t)(h6 >> 15);
-  s[22] = (uint8_t)((h6 >> 23) | ((uint32_t)(h7) << 3));
-  s[23] = (uint8_t)(h7 >> 5);
-  s[24] = (uint8_t)(h7 >> 13);
-  s[25] = (uint8_t)((h7 >> 21) | ((uint32_t)(h8) << 4));
-  s[26] = (uint8_t)(h8 >> 4);
-  s[27] = (uint8_t)(h8 >> 12);
-  s[28] = (uint8_t)((h8 >> 20) | ((uint32_t)(h9) << 6));
-  s[29] = (uint8_t)(h9 >> 2);
-  s[30] = (uint8_t)(h9 >> 10);
-  s[31] = (uint8_t)(h9 >> 18);
+ *   so floor(2^(-255)(h + 19 2^(-25) h9 + 2^(-1))) = q.
+ */
+static void fe_tobytes(uint8_t *s, const fe h)
+{
+    int32_t h0 = h[0];
+    int32_t h1 = h[1];
+    int32_t h2 = h[2];
+    int32_t h3 = h[3];
+    int32_t h4 = h[4];
+    int32_t h5 = h[5];
+    int32_t h6 = h[6];
+    int32_t h7 = h[7];
+    int32_t h8 = h[8];
+    int32_t h9 = h[9];
+    int32_t q;
+
+    q = (19 * h9 + (((int32_t) 1) << 24)) >> 25;
+    q = (h0 + q) >> 26;
+    q = (h1 + q) >> 25;
+    q = (h2 + q) >> 26;
+    q = (h3 + q) >> 25;
+    q = (h4 + q) >> 26;
+    q = (h5 + q) >> 25;
+    q = (h6 + q) >> 26;
+    q = (h7 + q) >> 25;
+    q = (h8 + q) >> 26;
+    q = (h9 + q) >> 25;
+
+    /* Goal: Output h-(2^255-19)q, which is between 0 and 2^255-20. */
+    h0 += 19 * q;
+    /* Goal: Output h-2^255 q, which is between 0 and 2^255-20. */
+
+    h1 += h0 >> 26; h0 &= kBottom26Bits;
+    h2 += h1 >> 25; h1 &= kBottom25Bits;
+    h3 += h2 >> 26; h2 &= kBottom26Bits;
+    h4 += h3 >> 25; h3 &= kBottom25Bits;
+    h5 += h4 >> 26; h4 &= kBottom26Bits;
+    h6 += h5 >> 25; h5 &= kBottom25Bits;
+    h7 += h6 >> 26; h6 &= kBottom26Bits;
+    h8 += h7 >> 25; h7 &= kBottom25Bits;
+    h9 += h8 >> 26; h8 &= kBottom26Bits;
+                    h9 &= kBottom25Bits;
+    /* h10 = carry9 */
+
+    /*
+     * Goal: Output h0+...+2^255 h10-2^255 q, which is between 0 and 2^255-20.
+     * Have h0+...+2^230 h9 between 0 and 2^255-1;
+     * evidently 2^255 h10-2^255 q = 0.
+     * Goal: Output h0+...+2^230 h9.
+     */
+    s[ 0] = (uint8_t) (h0 >>  0);
+    s[ 1] = (uint8_t) (h0 >>  8);
+    s[ 2] = (uint8_t) (h0 >> 16);
+    s[ 3] = (uint8_t)((h0 >> 24) | ((uint32_t)(h1) << 2));
+    s[ 4] = (uint8_t) (h1 >>  6);
+    s[ 5] = (uint8_t) (h1 >> 14);
+    s[ 6] = (uint8_t)((h1 >> 22) | ((uint32_t)(h2) << 3));
+    s[ 7] = (uint8_t) (h2 >>  5);
+    s[ 8] = (uint8_t) (h2 >> 13);
+    s[ 9] = (uint8_t)((h2 >> 21) | ((uint32_t)(h3) << 5));
+    s[10] = (uint8_t) (h3 >>  3);
+    s[11] = (uint8_t) (h3 >> 11);
+    s[12] = (uint8_t)((h3 >> 19) | ((uint32_t)(h4) << 6));
+    s[13] = (uint8_t) (h4 >>  2);
+    s[14] = (uint8_t) (h4 >> 10);
+    s[15] = (uint8_t) (h4 >> 18);
+    s[16] = (uint8_t) (h5 >>  0);
+    s[17] = (uint8_t) (h5 >>  8);
+    s[18] = (uint8_t) (h5 >> 16);
+    s[19] = (uint8_t)((h5 >> 24) | ((uint32_t)(h6) << 1));
+    s[20] = (uint8_t) (h6 >>  7);
+    s[21] = (uint8_t) (h6 >> 15);
+    s[22] = (uint8_t)((h6 >> 23) | ((uint32_t)(h7) << 3));
+    s[23] = (uint8_t) (h7 >>  5);
+    s[24] = (uint8_t) (h7 >> 13);
+    s[25] = (uint8_t)((h7 >> 21) | ((uint32_t)(h8) << 4));
+    s[26] = (uint8_t) (h8 >>  4);
+    s[27] = (uint8_t) (h8 >> 12);
+    s[28] = (uint8_t)((h8 >> 20) | ((uint32_t)(h9) << 6));
+    s[29] = (uint8_t) (h9 >>  2);
+    s[30] = (uint8_t) (h9 >> 10);
+    s[31] = (uint8_t) (h9 >> 18);
 }
 
 /* h = f */
-static void fe_copy(fe h, const fe f) {
-  memmove(h, f, sizeof(int32_t) * 10);
+static void fe_copy(fe h, const fe f)
+{
+    memmove(h, f, sizeof(int32_t) * 10);
 }
 
 /* h = 0 */
-static void fe_0(fe h) { memset(h, 0, sizeof(int32_t) * 10); }
+static void fe_0(fe h)
+{
+    memset(h, 0, sizeof(int32_t) * 10);
+}
 
 /* h = 1 */
-static void fe_1(fe h) {
-  memset(h, 0, sizeof(int32_t) * 10);
-  h[0] = 1;
+static void fe_1(fe h)
+{
+    memset(h, 0, sizeof(int32_t) * 10);
+    h[0] = 1;
 }
 
-/* h = f + g
+/*
+ * h = f + g
+ *
  * Can overlap h with f or g.
  *
  * Preconditions:
@@ -951,15 +969,20 @@ static void fe_1(fe h) {
  *    |g| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
  *
  * Postconditions:
- *    |h| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc. */
-static void fe_add(fe h, const fe f, const fe g) {
-  unsigned i;
-  for (i = 0; i < 10; i++) {
-    h[i] = f[i] + g[i];
-  }
+ *    |h| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc.
+ */
+static void fe_add(fe h, const fe f, const fe g)
+{
+    unsigned i;
+
+    for (i = 0; i < 10; i++) {
+        h[i] = f[i] + g[i];
+    }
 }
 
-/* h = f - g
+/*
+ * h = f - g
+ *
  * Can overlap h with f or g.
  *
  * Preconditions:
@@ -967,15 +990,20 @@ static void fe_add(fe h, const fe f, const fe g) {
  *    |g| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
  *
  * Postconditions:
- *    |h| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc. */
-static void fe_sub(fe h, const fe f, const fe g) {
-  unsigned i;
-  for (i = 0; i < 10; i++) {
-    h[i] = f[i] - g[i];
-  }
+ *    |h| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc.
+ */
+static void fe_sub(fe h, const fe f, const fe g)
+{
+    unsigned i;
+
+    for (i = 0; i < 10; i++) {
+        h[i] = f[i] - g[i];
+    }
 }
 
-/* h = f * g
+/*
+ * h = f * g
+ *
  * Can overlap h with f or g.
  *
  * Preconditions:
@@ -1001,224 +1029,228 @@ static void fe_sub(fe h, const fe f, const fe g) {
  * 10 of them are 2-way parallelizable and vectorizable.
  * Can get away with 11 carries, but then data flow is much deeper.
  *
- * With tighter constraints on inputs can squeeze carries into int32. */
-static void fe_mul(fe h, const fe f, const fe g) {
-  int32_t f0 = f[0];
-  int32_t f1 = f[1];
-  int32_t f2 = f[2];
-  int32_t f3 = f[3];
-  int32_t f4 = f[4];
-  int32_t f5 = f[5];
-  int32_t f6 = f[6];
-  int32_t f7 = f[7];
-  int32_t f8 = f[8];
-  int32_t f9 = f[9];
-  int32_t g0 = g[0];
-  int32_t g1 = g[1];
-  int32_t g2 = g[2];
-  int32_t g3 = g[3];
-  int32_t g4 = g[4];
-  int32_t g5 = g[5];
-  int32_t g6 = g[6];
-  int32_t g7 = g[7];
-  int32_t g8 = g[8];
-  int32_t g9 = g[9];
-  int32_t g1_19 = 19 * g1; /* 1.959375*2^29 */
-  int32_t g2_19 = 19 * g2; /* 1.959375*2^30; still ok */
-  int32_t g3_19 = 19 * g3;
-  int32_t g4_19 = 19 * g4;
-  int32_t g5_19 = 19 * g5;
-  int32_t g6_19 = 19 * g6;
-  int32_t g7_19 = 19 * g7;
-  int32_t g8_19 = 19 * g8;
-  int32_t g9_19 = 19 * g9;
-  int32_t f1_2 = 2 * f1;
-  int32_t f3_2 = 2 * f3;
-  int32_t f5_2 = 2 * f5;
-  int32_t f7_2 = 2 * f7;
-  int32_t f9_2 = 2 * f9;
-  int64_t f0g0    = f0   * (int64_t) g0;
-  int64_t f0g1    = f0   * (int64_t) g1;
-  int64_t f0g2    = f0   * (int64_t) g2;
-  int64_t f0g3    = f0   * (int64_t) g3;
-  int64_t f0g4    = f0   * (int64_t) g4;
-  int64_t f0g5    = f0   * (int64_t) g5;
-  int64_t f0g6    = f0   * (int64_t) g6;
-  int64_t f0g7    = f0   * (int64_t) g7;
-  int64_t f0g8    = f0   * (int64_t) g8;
-  int64_t f0g9    = f0   * (int64_t) g9;
-  int64_t f1g0    = f1   * (int64_t) g0;
-  int64_t f1g1_2  = f1_2 * (int64_t) g1;
-  int64_t f1g2    = f1   * (int64_t) g2;
-  int64_t f1g3_2  = f1_2 * (int64_t) g3;
-  int64_t f1g4    = f1   * (int64_t) g4;
-  int64_t f1g5_2  = f1_2 * (int64_t) g5;
-  int64_t f1g6    = f1   * (int64_t) g6;
-  int64_t f1g7_2  = f1_2 * (int64_t) g7;
-  int64_t f1g8    = f1   * (int64_t) g8;
-  int64_t f1g9_38 = f1_2 * (int64_t) g9_19;
-  int64_t f2g0    = f2   * (int64_t) g0;
-  int64_t f2g1    = f2   * (int64_t) g1;
-  int64_t f2g2    = f2   * (int64_t) g2;
-  int64_t f2g3    = f2   * (int64_t) g3;
-  int64_t f2g4    = f2   * (int64_t) g4;
-  int64_t f2g5    = f2   * (int64_t) g5;
-  int64_t f2g6    = f2   * (int64_t) g6;
-  int64_t f2g7    = f2   * (int64_t) g7;
-  int64_t f2g8_19 = f2   * (int64_t) g8_19;
-  int64_t f2g9_19 = f2   * (int64_t) g9_19;
-  int64_t f3g0    = f3   * (int64_t) g0;
-  int64_t f3g1_2  = f3_2 * (int64_t) g1;
-  int64_t f3g2    = f3   * (int64_t) g2;
-  int64_t f3g3_2  = f3_2 * (int64_t) g3;
-  int64_t f3g4    = f3   * (int64_t) g4;
-  int64_t f3g5_2  = f3_2 * (int64_t) g5;
-  int64_t f3g6    = f3   * (int64_t) g6;
-  int64_t f3g7_38 = f3_2 * (int64_t) g7_19;
-  int64_t f3g8_19 = f3   * (int64_t) g8_19;
-  int64_t f3g9_38 = f3_2 * (int64_t) g9_19;
-  int64_t f4g0    = f4   * (int64_t) g0;
-  int64_t f4g1    = f4   * (int64_t) g1;
-  int64_t f4g2    = f4   * (int64_t) g2;
-  int64_t f4g3    = f4   * (int64_t) g3;
-  int64_t f4g4    = f4   * (int64_t) g4;
-  int64_t f4g5    = f4   * (int64_t) g5;
-  int64_t f4g6_19 = f4   * (int64_t) g6_19;
-  int64_t f4g7_19 = f4   * (int64_t) g7_19;
-  int64_t f4g8_19 = f4   * (int64_t) g8_19;
-  int64_t f4g9_19 = f4   * (int64_t) g9_19;
-  int64_t f5g0    = f5   * (int64_t) g0;
-  int64_t f5g1_2  = f5_2 * (int64_t) g1;
-  int64_t f5g2    = f5   * (int64_t) g2;
-  int64_t f5g3_2  = f5_2 * (int64_t) g3;
-  int64_t f5g4    = f5   * (int64_t) g4;
-  int64_t f5g5_38 = f5_2 * (int64_t) g5_19;
-  int64_t f5g6_19 = f5   * (int64_t) g6_19;
-  int64_t f5g7_38 = f5_2 * (int64_t) g7_19;
-  int64_t f5g8_19 = f5   * (int64_t) g8_19;
-  int64_t f5g9_38 = f5_2 * (int64_t) g9_19;
-  int64_t f6g0    = f6   * (int64_t) g0;
-  int64_t f6g1    = f6   * (int64_t) g1;
-  int64_t f6g2    = f6   * (int64_t) g2;
-  int64_t f6g3    = f6   * (int64_t) g3;
-  int64_t f6g4_19 = f6   * (int64_t) g4_19;
-  int64_t f6g5_19 = f6   * (int64_t) g5_19;
-  int64_t f6g6_19 = f6   * (int64_t) g6_19;
-  int64_t f6g7_19 = f6   * (int64_t) g7_19;
-  int64_t f6g8_19 = f6   * (int64_t) g8_19;
-  int64_t f6g9_19 = f6   * (int64_t) g9_19;
-  int64_t f7g0    = f7   * (int64_t) g0;
-  int64_t f7g1_2  = f7_2 * (int64_t) g1;
-  int64_t f7g2    = f7   * (int64_t) g2;
-  int64_t f7g3_38 = f7_2 * (int64_t) g3_19;
-  int64_t f7g4_19 = f7   * (int64_t) g4_19;
-  int64_t f7g5_38 = f7_2 * (int64_t) g5_19;
-  int64_t f7g6_19 = f7   * (int64_t) g6_19;
-  int64_t f7g7_38 = f7_2 * (int64_t) g7_19;
-  int64_t f7g8_19 = f7   * (int64_t) g8_19;
-  int64_t f7g9_38 = f7_2 * (int64_t) g9_19;
-  int64_t f8g0    = f8   * (int64_t) g0;
-  int64_t f8g1    = f8   * (int64_t) g1;
-  int64_t f8g2_19 = f8   * (int64_t) g2_19;
-  int64_t f8g3_19 = f8   * (int64_t) g3_19;
-  int64_t f8g4_19 = f8   * (int64_t) g4_19;
-  int64_t f8g5_19 = f8   * (int64_t) g5_19;
-  int64_t f8g6_19 = f8   * (int64_t) g6_19;
-  int64_t f8g7_19 = f8   * (int64_t) g7_19;
-  int64_t f8g8_19 = f8   * (int64_t) g8_19;
-  int64_t f8g9_19 = f8   * (int64_t) g9_19;
-  int64_t f9g0    = f9   * (int64_t) g0;
-  int64_t f9g1_38 = f9_2 * (int64_t) g1_19;
-  int64_t f9g2_19 = f9   * (int64_t) g2_19;
-  int64_t f9g3_38 = f9_2 * (int64_t) g3_19;
-  int64_t f9g4_19 = f9   * (int64_t) g4_19;
-  int64_t f9g5_38 = f9_2 * (int64_t) g5_19;
-  int64_t f9g6_19 = f9   * (int64_t) g6_19;
-  int64_t f9g7_38 = f9_2 * (int64_t) g7_19;
-  int64_t f9g8_19 = f9   * (int64_t) g8_19;
-  int64_t f9g9_38 = f9_2 * (int64_t) g9_19;
-  int64_t h0 = 
f0g0+f1g9_38+f2g8_19+f3g7_38+f4g6_19+f5g5_38+f6g4_19+f7g3_38+f8g2_19+f9g1_38;
-  int64_t h1 = f0g1+f1g0   
+f2g9_19+f3g8_19+f4g7_19+f5g6_19+f6g5_19+f7g4_19+f8g3_19+f9g2_19;
-  int64_t h2 = f0g2+f1g1_2 +f2g0   
+f3g9_38+f4g8_19+f5g7_38+f6g6_19+f7g5_38+f8g4_19+f9g3_38;
-  int64_t h3 = f0g3+f1g2   +f2g1   +f3g0   
+f4g9_19+f5g8_19+f6g7_19+f7g6_19+f8g5_19+f9g4_19;
-  int64_t h4 = f0g4+f1g3_2 +f2g2   +f3g1_2 +f4g0   
+f5g9_38+f6g8_19+f7g7_38+f8g6_19+f9g5_38;
-  int64_t h5 = f0g5+f1g4   +f2g3   +f3g2   +f4g1   +f5g0   
+f6g9_19+f7g8_19+f8g7_19+f9g6_19;
-  int64_t h6 = f0g6+f1g5_2 +f2g4   +f3g3_2 +f4g2   +f5g1_2 +f6g0   
+f7g9_38+f8g8_19+f9g7_38;
-  int64_t h7 = f0g7+f1g6   +f2g5   +f3g4   +f4g3   +f5g2   +f6g1   +f7g0   
+f8g9_19+f9g8_19;
-  int64_t h8 = f0g8+f1g7_2 +f2g6   +f3g5_2 +f4g4   +f5g3_2 +f6g2   +f7g1_2 
+f8g0   +f9g9_38;
-  int64_t h9 = f0g9+f1g8   +f2g7   +f3g6   +f4g5   +f5g4   +f6g3   +f7g2   
+f8g1   +f9g0   ;
-  int64_t carry0;
-  int64_t carry1;
-  int64_t carry2;
-  int64_t carry3;
-  int64_t carry4;
-  int64_t carry5;
-  int64_t carry6;
-  int64_t carry7;
-  int64_t carry8;
-  int64_t carry9;
-
-  /* |h0| <= (1.65*1.65*2^52*(1+19+19+19+19)+1.65*1.65*2^50*(38+38+38+38+38))
-   *   i.e. |h0| <= 1.4*2^60; narrower ranges for h2, h4, h6, h8
-   * |h1| <= (1.65*1.65*2^51*(1+1+19+19+19+19+19+19+19+19))
-   *   i.e. |h1| <= 1.7*2^59; narrower ranges for h3, h5, h7, h9 */
-
-  carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits;
-  carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits;
-  /* |h0| <= 2^25 */
-  /* |h4| <= 2^25 */
-  /* |h1| <= 1.71*2^59 */
-  /* |h5| <= 1.71*2^59 */
-
-  carry1 = h1 + (1 << 24); h2 += carry1 >> 25; h1 -= carry1 & kTop39Bits;
-  carry5 = h5 + (1 << 24); h6 += carry5 >> 25; h5 -= carry5 & kTop39Bits;
-  /* |h1| <= 2^24; from now on fits into int32 */
-  /* |h5| <= 2^24; from now on fits into int32 */
-  /* |h2| <= 1.41*2^60 */
-  /* |h6| <= 1.41*2^60 */
-
-  carry2 = h2 + (1 << 25); h3 += carry2 >> 26; h2 -= carry2 & kTop38Bits;
-  carry6 = h6 + (1 << 25); h7 += carry6 >> 26; h6 -= carry6 & kTop38Bits;
-  /* |h2| <= 2^25; from now on fits into int32 unchanged */
-  /* |h6| <= 2^25; from now on fits into int32 unchanged */
-  /* |h3| <= 1.71*2^59 */
-  /* |h7| <= 1.71*2^59 */
-
-  carry3 = h3 + (1 << 24); h4 += carry3 >> 25; h3 -= carry3 & kTop39Bits;
-  carry7 = h7 + (1 << 24); h8 += carry7 >> 25; h7 -= carry7 & kTop39Bits;
-  /* |h3| <= 2^24; from now on fits into int32 unchanged */
-  /* |h7| <= 2^24; from now on fits into int32 unchanged */
-  /* |h4| <= 1.72*2^34 */
-  /* |h8| <= 1.41*2^60 */
-
-  carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits;
-  carry8 = h8 + (1 << 25); h9 += carry8 >> 26; h8 -= carry8 & kTop38Bits;
-  /* |h4| <= 2^25; from now on fits into int32 unchanged */
-  /* |h8| <= 2^25; from now on fits into int32 unchanged */
-  /* |h5| <= 1.01*2^24 */
-  /* |h9| <= 1.71*2^59 */
-
-  carry9 = h9 + (1 << 24); h0 += (carry9 >> 25) * 19; h9 -= carry9 & 
kTop39Bits;
-  /* |h9| <= 2^24; from now on fits into int32 unchanged */
-  /* |h0| <= 1.1*2^39 */
-
-  carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits;
-  /* |h0| <= 2^25; from now on fits into int32 unchanged */
-  /* |h1| <= 1.01*2^24 */
-
-  h[0] = (int32_t)h0;
-  h[1] = (int32_t)h1;
-  h[2] = (int32_t)h2;
-  h[3] = (int32_t)h3;
-  h[4] = (int32_t)h4;
-  h[5] = (int32_t)h5;
-  h[6] = (int32_t)h6;
-  h[7] = (int32_t)h7;
-  h[8] = (int32_t)h8;
-  h[9] = (int32_t)h9;
+ * With tighter constraints on inputs can squeeze carries into int32.
+ */
+static void fe_mul(fe h, const fe f, const fe g)
+{
+    int32_t f0 = f[0];
+    int32_t f1 = f[1];
+    int32_t f2 = f[2];
+    int32_t f3 = f[3];
+    int32_t f4 = f[4];
+    int32_t f5 = f[5];
+    int32_t f6 = f[6];
+    int32_t f7 = f[7];
+    int32_t f8 = f[8];
+    int32_t f9 = f[9];
+    int32_t g0 = g[0];
+    int32_t g1 = g[1];
+    int32_t g2 = g[2];
+    int32_t g3 = g[3];
+    int32_t g4 = g[4];
+    int32_t g5 = g[5];
+    int32_t g6 = g[6];
+    int32_t g7 = g[7];
+    int32_t g8 = g[8];
+    int32_t g9 = g[9];
+    int32_t g1_19 = 19 * g1; /* 1.959375*2^29 */
+    int32_t g2_19 = 19 * g2; /* 1.959375*2^30; still ok */
+    int32_t g3_19 = 19 * g3;
+    int32_t g4_19 = 19 * g4;
+    int32_t g5_19 = 19 * g5;
+    int32_t g6_19 = 19 * g6;
+    int32_t g7_19 = 19 * g7;
+    int32_t g8_19 = 19 * g8;
+    int32_t g9_19 = 19 * g9;
+    int32_t f1_2 = 2 * f1;
+    int32_t f3_2 = 2 * f3;
+    int32_t f5_2 = 2 * f5;
+    int32_t f7_2 = 2 * f7;
+    int32_t f9_2 = 2 * f9;
+    int64_t f0g0    = f0   * (int64_t) g0;
+    int64_t f0g1    = f0   * (int64_t) g1;
+    int64_t f0g2    = f0   * (int64_t) g2;
+    int64_t f0g3    = f0   * (int64_t) g3;
+    int64_t f0g4    = f0   * (int64_t) g4;
+    int64_t f0g5    = f0   * (int64_t) g5;
+    int64_t f0g6    = f0   * (int64_t) g6;
+    int64_t f0g7    = f0   * (int64_t) g7;
+    int64_t f0g8    = f0   * (int64_t) g8;
+    int64_t f0g9    = f0   * (int64_t) g9;
+    int64_t f1g0    = f1   * (int64_t) g0;
+    int64_t f1g1_2  = f1_2 * (int64_t) g1;
+    int64_t f1g2    = f1   * (int64_t) g2;
+    int64_t f1g3_2  = f1_2 * (int64_t) g3;
+    int64_t f1g4    = f1   * (int64_t) g4;
+    int64_t f1g5_2  = f1_2 * (int64_t) g5;
+    int64_t f1g6    = f1   * (int64_t) g6;
+    int64_t f1g7_2  = f1_2 * (int64_t) g7;
+    int64_t f1g8    = f1   * (int64_t) g8;
+    int64_t f1g9_38 = f1_2 * (int64_t) g9_19;
+    int64_t f2g0    = f2   * (int64_t) g0;
+    int64_t f2g1    = f2   * (int64_t) g1;
+    int64_t f2g2    = f2   * (int64_t) g2;
+    int64_t f2g3    = f2   * (int64_t) g3;
+    int64_t f2g4    = f2   * (int64_t) g4;
+    int64_t f2g5    = f2   * (int64_t) g5;
+    int64_t f2g6    = f2   * (int64_t) g6;
+    int64_t f2g7    = f2   * (int64_t) g7;
+    int64_t f2g8_19 = f2   * (int64_t) g8_19;
+    int64_t f2g9_19 = f2   * (int64_t) g9_19;
+    int64_t f3g0    = f3   * (int64_t) g0;
+    int64_t f3g1_2  = f3_2 * (int64_t) g1;
+    int64_t f3g2    = f3   * (int64_t) g2;
+    int64_t f3g3_2  = f3_2 * (int64_t) g3;
+    int64_t f3g4    = f3   * (int64_t) g4;
+    int64_t f3g5_2  = f3_2 * (int64_t) g5;
+    int64_t f3g6    = f3   * (int64_t) g6;
+    int64_t f3g7_38 = f3_2 * (int64_t) g7_19;
+    int64_t f3g8_19 = f3   * (int64_t) g8_19;
+    int64_t f3g9_38 = f3_2 * (int64_t) g9_19;
+    int64_t f4g0    = f4   * (int64_t) g0;
+    int64_t f4g1    = f4   * (int64_t) g1;
+    int64_t f4g2    = f4   * (int64_t) g2;
+    int64_t f4g3    = f4   * (int64_t) g3;
+    int64_t f4g4    = f4   * (int64_t) g4;
+    int64_t f4g5    = f4   * (int64_t) g5;
+    int64_t f4g6_19 = f4   * (int64_t) g6_19;
+    int64_t f4g7_19 = f4   * (int64_t) g7_19;
+    int64_t f4g8_19 = f4   * (int64_t) g8_19;
+    int64_t f4g9_19 = f4   * (int64_t) g9_19;
+    int64_t f5g0    = f5   * (int64_t) g0;
+    int64_t f5g1_2  = f5_2 * (int64_t) g1;
+    int64_t f5g2    = f5   * (int64_t) g2;
+    int64_t f5g3_2  = f5_2 * (int64_t) g3;
+    int64_t f5g4    = f5   * (int64_t) g4;
+    int64_t f5g5_38 = f5_2 * (int64_t) g5_19;
+    int64_t f5g6_19 = f5   * (int64_t) g6_19;
+    int64_t f5g7_38 = f5_2 * (int64_t) g7_19;
+    int64_t f5g8_19 = f5   * (int64_t) g8_19;
+    int64_t f5g9_38 = f5_2 * (int64_t) g9_19;
+    int64_t f6g0    = f6   * (int64_t) g0;
+    int64_t f6g1    = f6   * (int64_t) g1;
+    int64_t f6g2    = f6   * (int64_t) g2;
+    int64_t f6g3    = f6   * (int64_t) g3;
+    int64_t f6g4_19 = f6   * (int64_t) g4_19;
+    int64_t f6g5_19 = f6   * (int64_t) g5_19;
+    int64_t f6g6_19 = f6   * (int64_t) g6_19;
+    int64_t f6g7_19 = f6   * (int64_t) g7_19;
+    int64_t f6g8_19 = f6   * (int64_t) g8_19;
+    int64_t f6g9_19 = f6   * (int64_t) g9_19;
+    int64_t f7g0    = f7   * (int64_t) g0;
+    int64_t f7g1_2  = f7_2 * (int64_t) g1;
+    int64_t f7g2    = f7   * (int64_t) g2;
+    int64_t f7g3_38 = f7_2 * (int64_t) g3_19;
+    int64_t f7g4_19 = f7   * (int64_t) g4_19;
+    int64_t f7g5_38 = f7_2 * (int64_t) g5_19;
+    int64_t f7g6_19 = f7   * (int64_t) g6_19;
+    int64_t f7g7_38 = f7_2 * (int64_t) g7_19;
+    int64_t f7g8_19 = f7   * (int64_t) g8_19;
+    int64_t f7g9_38 = f7_2 * (int64_t) g9_19;
+    int64_t f8g0    = f8   * (int64_t) g0;
+    int64_t f8g1    = f8   * (int64_t) g1;
+    int64_t f8g2_19 = f8   * (int64_t) g2_19;
+    int64_t f8g3_19 = f8   * (int64_t) g3_19;
+    int64_t f8g4_19 = f8   * (int64_t) g4_19;
+    int64_t f8g5_19 = f8   * (int64_t) g5_19;
+    int64_t f8g6_19 = f8   * (int64_t) g6_19;
+    int64_t f8g7_19 = f8   * (int64_t) g7_19;
+    int64_t f8g8_19 = f8   * (int64_t) g8_19;
+    int64_t f8g9_19 = f8   * (int64_t) g9_19;
+    int64_t f9g0    = f9   * (int64_t) g0;
+    int64_t f9g1_38 = f9_2 * (int64_t) g1_19;
+    int64_t f9g2_19 = f9   * (int64_t) g2_19;
+    int64_t f9g3_38 = f9_2 * (int64_t) g3_19;
+    int64_t f9g4_19 = f9   * (int64_t) g4_19;
+    int64_t f9g5_38 = f9_2 * (int64_t) g5_19;
+    int64_t f9g6_19 = f9   * (int64_t) g6_19;
+    int64_t f9g7_38 = f9_2 * (int64_t) g7_19;
+    int64_t f9g8_19 = f9   * (int64_t) g8_19;
+    int64_t f9g9_38 = f9_2 * (int64_t) g9_19;
+    int64_t h0 = f0g0 + f1g9_38 + f2g8_19 + f3g7_38 + f4g6_19 + f5g5_38 + 
f6g4_19 + f7g3_38 + f8g2_19 + f9g1_38;
+    int64_t h1 = f0g1 + f1g0    + f2g9_19 + f3g8_19 + f4g7_19 + f5g6_19 + 
f6g5_19 + f7g4_19 + f8g3_19 + f9g2_19;
+    int64_t h2 = f0g2 + f1g1_2  + f2g0    + f3g9_38 + f4g8_19 + f5g7_38 + 
f6g6_19 + f7g5_38 + f8g4_19 + f9g3_38;
+    int64_t h3 = f0g3 + f1g2    + f2g1    + f3g0    + f4g9_19 + f5g8_19 + 
f6g7_19 + f7g6_19 + f8g5_19 + f9g4_19;
+    int64_t h4 = f0g4 + f1g3_2  + f2g2    + f3g1_2  + f4g0    + f5g9_38 + 
f6g8_19 + f7g7_38 + f8g6_19 + f9g5_38;
+    int64_t h5 = f0g5 + f1g4    + f2g3    + f3g2    + f4g1    + f5g0    + 
f6g9_19 + f7g8_19 + f8g7_19 + f9g6_19;
+    int64_t h6 = f0g6 + f1g5_2  + f2g4    + f3g3_2  + f4g2    + f5g1_2  + f6g0 
   + f7g9_38 + f8g8_19 + f9g7_38;
+    int64_t h7 = f0g7 + f1g6    + f2g5    + f3g4    + f4g3    + f5g2    + f6g1 
   + f7g0    + f8g9_19 + f9g8_19;
+    int64_t h8 = f0g8 + f1g7_2  + f2g6    + f3g5_2  + f4g4    + f5g3_2  + f6g2 
   + f7g1_2  + f8g0    + f9g9_38;
+    int64_t h9 = f0g9 + f1g8    + f2g7    + f3g6    + f4g5    + f5g4    + f6g3 
   + f7g2    + f8g1    + f9g0   ;
+    int64_t carry0;
+    int64_t carry1;
+    int64_t carry2;
+    int64_t carry3;
+    int64_t carry4;
+    int64_t carry5;
+    int64_t carry6;
+    int64_t carry7;
+    int64_t carry8;
+    int64_t carry9;
+
+    /* |h0| <= (1.65*1.65*2^52*(1+19+19+19+19)+1.65*1.65*2^50*(38+38+38+38+38))
+     *   i.e. |h0| <= 1.4*2^60; narrower ranges for h2, h4, h6, h8
+     * |h1| <= (1.65*1.65*2^51*(1+1+19+19+19+19+19+19+19+19))
+     *   i.e. |h1| <= 1.7*2^59; narrower ranges for h3, h5, h7, h9 */
+
+    carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits;
+    carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits;
+    /* |h0| <= 2^25 */
+    /* |h4| <= 2^25 */
+    /* |h1| <= 1.71*2^59 */
+    /* |h5| <= 1.71*2^59 */
+
+    carry1 = h1 + (1 << 24); h2 += carry1 >> 25; h1 -= carry1 & kTop39Bits;
+    carry5 = h5 + (1 << 24); h6 += carry5 >> 25; h5 -= carry5 & kTop39Bits;
+    /* |h1| <= 2^24; from now on fits into int32 */
+    /* |h5| <= 2^24; from now on fits into int32 */
+    /* |h2| <= 1.41*2^60 */
+    /* |h6| <= 1.41*2^60 */
+
+    carry2 = h2 + (1 << 25); h3 += carry2 >> 26; h2 -= carry2 & kTop38Bits;
+    carry6 = h6 + (1 << 25); h7 += carry6 >> 26; h6 -= carry6 & kTop38Bits;
+    /* |h2| <= 2^25; from now on fits into int32 unchanged */
+    /* |h6| <= 2^25; from now on fits into int32 unchanged */
+    /* |h3| <= 1.71*2^59 */
+    /* |h7| <= 1.71*2^59 */
+
+    carry3 = h3 + (1 << 24); h4 += carry3 >> 25; h3 -= carry3 & kTop39Bits;
+    carry7 = h7 + (1 << 24); h8 += carry7 >> 25; h7 -= carry7 & kTop39Bits;
+    /* |h3| <= 2^24; from now on fits into int32 unchanged */
+    /* |h7| <= 2^24; from now on fits into int32 unchanged */
+    /* |h4| <= 1.72*2^34 */
+    /* |h8| <= 1.41*2^60 */
+
+    carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits;
+    carry8 = h8 + (1 << 25); h9 += carry8 >> 26; h8 -= carry8 & kTop38Bits;
+    /* |h4| <= 2^25; from now on fits into int32 unchanged */
+    /* |h8| <= 2^25; from now on fits into int32 unchanged */
+    /* |h5| <= 1.01*2^24 */
+    /* |h9| <= 1.71*2^59 */
+
+    carry9 = h9 + (1 << 24); h0 += (carry9 >> 25) * 19; h9 -= carry9 & 
kTop39Bits;
+    /* |h9| <= 2^24; from now on fits into int32 unchanged */
+    /* |h0| <= 1.1*2^39 */
+
+    carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits;
+    /* |h0| <= 2^25; from now on fits into int32 unchanged */
+    /* |h1| <= 1.01*2^24 */
+
+    h[0] = (int32_t)h0;
+    h[1] = (int32_t)h1;
+    h[2] = (int32_t)h2;
+    h[3] = (int32_t)h3;
+    h[4] = (int32_t)h4;
+    h[5] = (int32_t)h5;
+    h[6] = (int32_t)h6;
+    h[7] = (int32_t)h7;
+    h[8] = (int32_t)h8;
+    h[9] = (int32_t)h9;
 }
 
-/* h = f * f
+/*
+ * h = f * f
+ *
  * Can overlap h with f.
  *
  * Preconditions:
@@ -1227,286 +1259,307 @@ static void fe_mul(fe h, const fe f, const fe g) {
  * Postconditions:
  *    |h| bounded by 1.01*2^25,1.01*2^24,1.01*2^25,1.01*2^24,etc.
  *
- * See fe_mul.c for discussion of implementation strategy. */
-static void fe_sq(fe h, const fe f) {
-  int32_t f0 = f[0];
-  int32_t f1 = f[1];
-  int32_t f2 = f[2];
-  int32_t f3 = f[3];
-  int32_t f4 = f[4];
-  int32_t f5 = f[5];
-  int32_t f6 = f[6];
-  int32_t f7 = f[7];
-  int32_t f8 = f[8];
-  int32_t f9 = f[9];
-  int32_t f0_2 = 2 * f0;
-  int32_t f1_2 = 2 * f1;
-  int32_t f2_2 = 2 * f2;
-  int32_t f3_2 = 2 * f3;
-  int32_t f4_2 = 2 * f4;
-  int32_t f5_2 = 2 * f5;
-  int32_t f6_2 = 2 * f6;
-  int32_t f7_2 = 2 * f7;
-  int32_t f5_38 = 38 * f5; /* 1.959375*2^30 */
-  int32_t f6_19 = 19 * f6; /* 1.959375*2^30 */
-  int32_t f7_38 = 38 * f7; /* 1.959375*2^30 */
-  int32_t f8_19 = 19 * f8; /* 1.959375*2^30 */
-  int32_t f9_38 = 38 * f9; /* 1.959375*2^30 */
-  int64_t f0f0    = f0   * (int64_t) f0;
-  int64_t f0f1_2  = f0_2 * (int64_t) f1;
-  int64_t f0f2_2  = f0_2 * (int64_t) f2;
-  int64_t f0f3_2  = f0_2 * (int64_t) f3;
-  int64_t f0f4_2  = f0_2 * (int64_t) f4;
-  int64_t f0f5_2  = f0_2 * (int64_t) f5;
-  int64_t f0f6_2  = f0_2 * (int64_t) f6;
-  int64_t f0f7_2  = f0_2 * (int64_t) f7;
-  int64_t f0f8_2  = f0_2 * (int64_t) f8;
-  int64_t f0f9_2  = f0_2 * (int64_t) f9;
-  int64_t f1f1_2  = f1_2 * (int64_t) f1;
-  int64_t f1f2_2  = f1_2 * (int64_t) f2;
-  int64_t f1f3_4  = f1_2 * (int64_t) f3_2;
-  int64_t f1f4_2  = f1_2 * (int64_t) f4;
-  int64_t f1f5_4  = f1_2 * (int64_t) f5_2;
-  int64_t f1f6_2  = f1_2 * (int64_t) f6;
-  int64_t f1f7_4  = f1_2 * (int64_t) f7_2;
-  int64_t f1f8_2  = f1_2 * (int64_t) f8;
-  int64_t f1f9_76 = f1_2 * (int64_t) f9_38;
-  int64_t f2f2    = f2   * (int64_t) f2;
-  int64_t f2f3_2  = f2_2 * (int64_t) f3;
-  int64_t f2f4_2  = f2_2 * (int64_t) f4;
-  int64_t f2f5_2  = f2_2 * (int64_t) f5;
-  int64_t f2f6_2  = f2_2 * (int64_t) f6;
-  int64_t f2f7_2  = f2_2 * (int64_t) f7;
-  int64_t f2f8_38 = f2_2 * (int64_t) f8_19;
-  int64_t f2f9_38 = f2   * (int64_t) f9_38;
-  int64_t f3f3_2  = f3_2 * (int64_t) f3;
-  int64_t f3f4_2  = f3_2 * (int64_t) f4;
-  int64_t f3f5_4  = f3_2 * (int64_t) f5_2;
-  int64_t f3f6_2  = f3_2 * (int64_t) f6;
-  int64_t f3f7_76 = f3_2 * (int64_t) f7_38;
-  int64_t f3f8_38 = f3_2 * (int64_t) f8_19;
-  int64_t f3f9_76 = f3_2 * (int64_t) f9_38;
-  int64_t f4f4    = f4   * (int64_t) f4;
-  int64_t f4f5_2  = f4_2 * (int64_t) f5;
-  int64_t f4f6_38 = f4_2 * (int64_t) f6_19;
-  int64_t f4f7_38 = f4   * (int64_t) f7_38;
-  int64_t f4f8_38 = f4_2 * (int64_t) f8_19;
-  int64_t f4f9_38 = f4   * (int64_t) f9_38;
-  int64_t f5f5_38 = f5   * (int64_t) f5_38;
-  int64_t f5f6_38 = f5_2 * (int64_t) f6_19;
-  int64_t f5f7_76 = f5_2 * (int64_t) f7_38;
-  int64_t f5f8_38 = f5_2 * (int64_t) f8_19;
-  int64_t f5f9_76 = f5_2 * (int64_t) f9_38;
-  int64_t f6f6_19 = f6   * (int64_t) f6_19;
-  int64_t f6f7_38 = f6   * (int64_t) f7_38;
-  int64_t f6f8_38 = f6_2 * (int64_t) f8_19;
-  int64_t f6f9_38 = f6   * (int64_t) f9_38;
-  int64_t f7f7_38 = f7   * (int64_t) f7_38;
-  int64_t f7f8_38 = f7_2 * (int64_t) f8_19;
-  int64_t f7f9_76 = f7_2 * (int64_t) f9_38;
-  int64_t f8f8_19 = f8   * (int64_t) f8_19;
-  int64_t f8f9_38 = f8   * (int64_t) f9_38;
-  int64_t f9f9_38 = f9   * (int64_t) f9_38;
-  int64_t h0 = f0f0  +f1f9_76+f2f8_38+f3f7_76+f4f6_38+f5f5_38;
-  int64_t h1 = f0f1_2+f2f9_38+f3f8_38+f4f7_38+f5f6_38;
-  int64_t h2 = f0f2_2+f1f1_2 +f3f9_76+f4f8_38+f5f7_76+f6f6_19;
-  int64_t h3 = f0f3_2+f1f2_2 +f4f9_38+f5f8_38+f6f7_38;
-  int64_t h4 = f0f4_2+f1f3_4 +f2f2   +f5f9_76+f6f8_38+f7f7_38;
-  int64_t h5 = f0f5_2+f1f4_2 +f2f3_2 +f6f9_38+f7f8_38;
-  int64_t h6 = f0f6_2+f1f5_4 +f2f4_2 +f3f3_2 +f7f9_76+f8f8_19;
-  int64_t h7 = f0f7_2+f1f6_2 +f2f5_2 +f3f4_2 +f8f9_38;
-  int64_t h8 = f0f8_2+f1f7_4 +f2f6_2 +f3f5_4 +f4f4   +f9f9_38;
-  int64_t h9 = f0f9_2+f1f8_2 +f2f7_2 +f3f6_2 +f4f5_2;
-  int64_t carry0;
-  int64_t carry1;
-  int64_t carry2;
-  int64_t carry3;
-  int64_t carry4;
-  int64_t carry5;
-  int64_t carry6;
-  int64_t carry7;
-  int64_t carry8;
-  int64_t carry9;
-
-  carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits;
-  carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits;
-
-  carry1 = h1 + (1 << 24); h2 += carry1 >> 25; h1 -= carry1 & kTop39Bits;
-  carry5 = h5 + (1 << 24); h6 += carry5 >> 25; h5 -= carry5 & kTop39Bits;
-
-  carry2 = h2 + (1 << 25); h3 += carry2 >> 26; h2 -= carry2 & kTop38Bits;
-  carry6 = h6 + (1 << 25); h7 += carry6 >> 26; h6 -= carry6 & kTop38Bits;
-
-  carry3 = h3 + (1 << 24); h4 += carry3 >> 25; h3 -= carry3 & kTop39Bits;
-  carry7 = h7 + (1 << 24); h8 += carry7 >> 25; h7 -= carry7 & kTop39Bits;
-
-  carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits;
-  carry8 = h8 + (1 << 25); h9 += carry8 >> 26; h8 -= carry8 & kTop38Bits;
-
-  carry9 = h9 + (1 << 24); h0 += (carry9 >> 25) * 19; h9 -= carry9 & 
kTop39Bits;
-
-  carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits;
-
-  h[0] = (int32_t)h0;
-  h[1] = (int32_t)h1;
-  h[2] = (int32_t)h2;
-  h[3] = (int32_t)h3;
-  h[4] = (int32_t)h4;
-  h[5] = (int32_t)h5;
-  h[6] = (int32_t)h6;
-  h[7] = (int32_t)h7;
-  h[8] = (int32_t)h8;
-  h[9] = (int32_t)h9;
+ * See fe_mul.c for discussion of implementation strategy.
+ */
+static void fe_sq(fe h, const fe f)
+{
+    int32_t f0 = f[0];
+    int32_t f1 = f[1];
+    int32_t f2 = f[2];
+    int32_t f3 = f[3];
+    int32_t f4 = f[4];
+    int32_t f5 = f[5];
+    int32_t f6 = f[6];
+    int32_t f7 = f[7];
+    int32_t f8 = f[8];
+    int32_t f9 = f[9];
+    int32_t f0_2 = 2 * f0;
+    int32_t f1_2 = 2 * f1;
+    int32_t f2_2 = 2 * f2;
+    int32_t f3_2 = 2 * f3;
+    int32_t f4_2 = 2 * f4;
+    int32_t f5_2 = 2 * f5;
+    int32_t f6_2 = 2 * f6;
+    int32_t f7_2 = 2 * f7;
+    int32_t f5_38 = 38 * f5; /* 1.959375*2^30 */
+    int32_t f6_19 = 19 * f6; /* 1.959375*2^30 */
+    int32_t f7_38 = 38 * f7; /* 1.959375*2^30 */
+    int32_t f8_19 = 19 * f8; /* 1.959375*2^30 */
+    int32_t f9_38 = 38 * f9; /* 1.959375*2^30 */
+    int64_t f0f0    = f0   * (int64_t) f0;
+    int64_t f0f1_2  = f0_2 * (int64_t) f1;
+    int64_t f0f2_2  = f0_2 * (int64_t) f2;
+    int64_t f0f3_2  = f0_2 * (int64_t) f3;
+    int64_t f0f4_2  = f0_2 * (int64_t) f4;
+    int64_t f0f5_2  = f0_2 * (int64_t) f5;
+    int64_t f0f6_2  = f0_2 * (int64_t) f6;
+    int64_t f0f7_2  = f0_2 * (int64_t) f7;
+    int64_t f0f8_2  = f0_2 * (int64_t) f8;
+    int64_t f0f9_2  = f0_2 * (int64_t) f9;
+    int64_t f1f1_2  = f1_2 * (int64_t) f1;
+    int64_t f1f2_2  = f1_2 * (int64_t) f2;
+    int64_t f1f3_4  = f1_2 * (int64_t) f3_2;
+    int64_t f1f4_2  = f1_2 * (int64_t) f4;
+    int64_t f1f5_4  = f1_2 * (int64_t) f5_2;
+    int64_t f1f6_2  = f1_2 * (int64_t) f6;
+    int64_t f1f7_4  = f1_2 * (int64_t) f7_2;
+    int64_t f1f8_2  = f1_2 * (int64_t) f8;
+    int64_t f1f9_76 = f1_2 * (int64_t) f9_38;
+    int64_t f2f2    = f2   * (int64_t) f2;
+    int64_t f2f3_2  = f2_2 * (int64_t) f3;
+    int64_t f2f4_2  = f2_2 * (int64_t) f4;
+    int64_t f2f5_2  = f2_2 * (int64_t) f5;
+    int64_t f2f6_2  = f2_2 * (int64_t) f6;
+    int64_t f2f7_2  = f2_2 * (int64_t) f7;
+    int64_t f2f8_38 = f2_2 * (int64_t) f8_19;
+    int64_t f2f9_38 = f2   * (int64_t) f9_38;
+    int64_t f3f3_2  = f3_2 * (int64_t) f3;
+    int64_t f3f4_2  = f3_2 * (int64_t) f4;
+    int64_t f3f5_4  = f3_2 * (int64_t) f5_2;
+    int64_t f3f6_2  = f3_2 * (int64_t) f6;
+    int64_t f3f7_76 = f3_2 * (int64_t) f7_38;
+    int64_t f3f8_38 = f3_2 * (int64_t) f8_19;
+    int64_t f3f9_76 = f3_2 * (int64_t) f9_38;
+    int64_t f4f4    = f4   * (int64_t) f4;
+    int64_t f4f5_2  = f4_2 * (int64_t) f5;
+    int64_t f4f6_38 = f4_2 * (int64_t) f6_19;
+    int64_t f4f7_38 = f4   * (int64_t) f7_38;
+    int64_t f4f8_38 = f4_2 * (int64_t) f8_19;
+    int64_t f4f9_38 = f4   * (int64_t) f9_38;
+    int64_t f5f5_38 = f5   * (int64_t) f5_38;
+    int64_t f5f6_38 = f5_2 * (int64_t) f6_19;
+    int64_t f5f7_76 = f5_2 * (int64_t) f7_38;
+    int64_t f5f8_38 = f5_2 * (int64_t) f8_19;
+    int64_t f5f9_76 = f5_2 * (int64_t) f9_38;
+    int64_t f6f6_19 = f6   * (int64_t) f6_19;
+    int64_t f6f7_38 = f6   * (int64_t) f7_38;
+    int64_t f6f8_38 = f6_2 * (int64_t) f8_19;
+    int64_t f6f9_38 = f6   * (int64_t) f9_38;
+    int64_t f7f7_38 = f7   * (int64_t) f7_38;
+    int64_t f7f8_38 = f7_2 * (int64_t) f8_19;
+    int64_t f7f9_76 = f7_2 * (int64_t) f9_38;
+    int64_t f8f8_19 = f8   * (int64_t) f8_19;
+    int64_t f8f9_38 = f8   * (int64_t) f9_38;
+    int64_t f9f9_38 = f9   * (int64_t) f9_38;
+    int64_t h0 = f0f0   + f1f9_76 + f2f8_38 + f3f7_76 + f4f6_38 + f5f5_38;
+    int64_t h1 = f0f1_2 + f2f9_38 + f3f8_38 + f4f7_38 + f5f6_38;
+    int64_t h2 = f0f2_2 + f1f1_2  + f3f9_76 + f4f8_38 + f5f7_76 + f6f6_19;
+    int64_t h3 = f0f3_2 + f1f2_2  + f4f9_38 + f5f8_38 + f6f7_38;
+    int64_t h4 = f0f4_2 + f1f3_4  + f2f2    + f5f9_76 + f6f8_38 + f7f7_38;
+    int64_t h5 = f0f5_2 + f1f4_2  + f2f3_2  + f6f9_38 + f7f8_38;
+    int64_t h6 = f0f6_2 + f1f5_4  + f2f4_2  + f3f3_2  + f7f9_76 + f8f8_19;
+    int64_t h7 = f0f7_2 + f1f6_2  + f2f5_2  + f3f4_2  + f8f9_38;
+    int64_t h8 = f0f8_2 + f1f7_4  + f2f6_2  + f3f5_4  + f4f4    + f9f9_38;
+    int64_t h9 = f0f9_2 + f1f8_2  + f2f7_2  + f3f6_2  + f4f5_2;
+    int64_t carry0;
+    int64_t carry1;
+    int64_t carry2;
+    int64_t carry3;
+    int64_t carry4;
+    int64_t carry5;
+    int64_t carry6;
+    int64_t carry7;
+    int64_t carry8;
+    int64_t carry9;
+
+    carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits;
+    carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits;
+
+    carry1 = h1 + (1 << 24); h2 += carry1 >> 25; h1 -= carry1 & kTop39Bits;
+    carry5 = h5 + (1 << 24); h6 += carry5 >> 25; h5 -= carry5 & kTop39Bits;
+
+    carry2 = h2 + (1 << 25); h3 += carry2 >> 26; h2 -= carry2 & kTop38Bits;
+    carry6 = h6 + (1 << 25); h7 += carry6 >> 26; h6 -= carry6 & kTop38Bits;
+
+    carry3 = h3 + (1 << 24); h4 += carry3 >> 25; h3 -= carry3 & kTop39Bits;
+    carry7 = h7 + (1 << 24); h8 += carry7 >> 25; h7 -= carry7 & kTop39Bits;
+
+    carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits;
+    carry8 = h8 + (1 << 25); h9 += carry8 >> 26; h8 -= carry8 & kTop38Bits;
+
+    carry9 = h9 + (1 << 24); h0 += (carry9 >> 25) * 19; h9 -= carry9 & 
kTop39Bits;
+
+    carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits;
+
+    h[0] = (int32_t)h0;
+    h[1] = (int32_t)h1;
+    h[2] = (int32_t)h2;
+    h[3] = (int32_t)h3;
+    h[4] = (int32_t)h4;
+    h[5] = (int32_t)h5;
+    h[6] = (int32_t)h6;
+    h[7] = (int32_t)h7;
+    h[8] = (int32_t)h8;
+    h[9] = (int32_t)h9;
 }
 
-static void fe_invert(fe out, const fe z) {
-  fe t0;
-  fe t1;
-  fe t2;
-  fe t3;
-  int i;
+static void fe_invert(fe out, const fe z)
+{
+    fe t0;
+    fe t1;
+    fe t2;
+    fe t3;
+    int i;
 
-  /*
-   * Compute z ** -1 = z ** (2 ** 255 - 19 - 2) with the exponent as
-   * 2 ** 255 - 21 = (2 ** 5) * (2 ** 250 - 1) + 11.
-   */
+    /*
+     * Compute z ** -1 = z ** (2 ** 255 - 19 - 2) with the exponent as
+     * 2 ** 255 - 21 = (2 ** 5) * (2 ** 250 - 1) + 11.
+     */
 
-  /* t0 = z ** 2 */
-  fe_sq(t0, z);
+    /* t0 = z ** 2 */
+    fe_sq(t0, z);
 
-  /* t1 = t0 ** (2 ** 2) = z ** 8 */
-  fe_sq(t1, t0);
-  fe_sq(t1, t1);
+    /* t1 = t0 ** (2 ** 2) = z ** 8 */
+    fe_sq(t1, t0);
+    fe_sq(t1, t1);
 
-  /* t1 = z * t1 = z ** 9 */
-  fe_mul(t1, z, t1);
-  /* t0 = t0 * t1 = z ** 11 -- stash t0 away for the end. */
-  fe_mul(t0, t0, t1);
+    /* t1 = z * t1 = z ** 9 */
+    fe_mul(t1, z, t1);
+    /* t0 = t0 * t1 = z ** 11 -- stash t0 away for the end. */
+    fe_mul(t0, t0, t1);
 
-  /* t2 = t0 ** 2 = z ** 22 */
-  fe_sq(t2, t0);
+    /* t2 = t0 ** 2 = z ** 22 */
+    fe_sq(t2, t0);
 
-  /* t1 = t1 * t2 = z ** (2 ** 5 - 1) */
-  fe_mul(t1, t1, t2);
+    /* t1 = t1 * t2 = z ** (2 ** 5 - 1) */
+    fe_mul(t1, t1, t2);
 
-  /* t2 = t1 ** (2 ** 5) = z ** ((2 ** 5) * (2 ** 5 - 1)) */
-  fe_sq(t2, t1);
-  for (i = 1; i < 5; ++i) {
-    fe_sq(t2, t2);
-  }
+    /* t2 = t1 ** (2 ** 5) = z ** ((2 ** 5) * (2 ** 5 - 1)) */
+    fe_sq(t2, t1);
+    for (i = 1; i < 5; ++i) {
+        fe_sq(t2, t2);
+    }
 
-  /* t1 = t1 * t2 = z ** ((2 ** 5 + 1) * (2 ** 5 - 1)) = z ** (2 ** 10 - 1) */
-  fe_mul(t1, t2, t1);
+    /* t1 = t1 * t2 = z ** ((2 ** 5 + 1) * (2 ** 5 - 1)) = z ** (2 ** 10 - 1) 
*/
+    fe_mul(t1, t2, t1);
 
-  /* Continuing similarly... */
+    /* Continuing similarly... */
 
-  /* t2 = z ** (2 ** 20 - 1) */
-  fe_sq(t2, t1);
-  for (i = 1; i < 10; ++i) {
-    fe_sq(t2, t2);
-  }
-  fe_mul(t2, t2, t1);
-
-  /* t2 = z ** (2 ** 40 - 1) */
-  fe_sq(t3, t2);
-  for (i = 1; i < 20; ++i) {
-    fe_sq(t3, t3);
-  }
-  fe_mul(t2, t3, t2);
-
-  /* t2 = z ** (2 ** 10) * (2 ** 40 - 1) */
-  for (i = 0; i < 10; ++i) {
-    fe_sq(t2, t2);
-  }
-  /* t1 = z ** (2 ** 50 - 1) */
-  fe_mul(t1, t2, t1);
+    /* t2 = z ** (2 ** 20 - 1) */
+    fe_sq(t2, t1);
+    for (i = 1; i < 10; ++i) {
+        fe_sq(t2, t2);
+    }
+    fe_mul(t2, t2, t1);
 
-  /* t2 = z ** (2 ** 100 - 1) */
-  fe_sq(t2, t1);
-  for (i = 1; i < 50; ++i) {
-    fe_sq(t2, t2);
-  }
-  fe_mul(t2, t2, t1);
-
-  /* t2 = z ** (2 ** 200 - 1) */
-  fe_sq(t3, t2);
-  for (i = 1; i < 100; ++i) {
-    fe_sq(t3, t3);
-  }
-  fe_mul(t2, t3, t2);
-
-  /* t2 = z ** ((2 ** 50) * (2 ** 200 - 1) */
-  fe_sq(t2, t2);
-  for (i = 1; i < 50; ++i) {
+    /* t2 = z ** (2 ** 40 - 1) */
+    fe_sq(t3, t2);
+    for (i = 1; i < 20; ++i) {
+        fe_sq(t3, t3);
+    }
+    fe_mul(t2, t3, t2);
+
+    /* t2 = z ** (2 ** 10) * (2 ** 40 - 1) */
+    for (i = 0; i < 10; ++i) {
+        fe_sq(t2, t2);
+    }
+    /* t1 = z ** (2 ** 50 - 1) */
+    fe_mul(t1, t2, t1);
+
+    /* t2 = z ** (2 ** 100 - 1) */
+    fe_sq(t2, t1);
+    for (i = 1; i < 50; ++i) {
+        fe_sq(t2, t2);
+    }
+    fe_mul(t2, t2, t1);
+
+    /* t2 = z ** (2 ** 200 - 1) */
+    fe_sq(t3, t2);
+    for (i = 1; i < 100; ++i) {
+        fe_sq(t3, t3);
+    }
+    fe_mul(t2, t3, t2);
+
+    /* t2 = z ** ((2 ** 50) * (2 ** 200 - 1) */
     fe_sq(t2, t2);
-  }
+    for (i = 1; i < 50; ++i) {
+        fe_sq(t2, t2);
+    }
 
-  /* t1 = z ** (2 ** 250 - 1) */
-  fe_mul(t1, t2, t1);
+    /* t1 = z ** (2 ** 250 - 1) */
+    fe_mul(t1, t2, t1);
 
-  /* t1 = z ** ((2 ** 5) * (2 ** 250 - 1)) */
-  fe_sq(t1, t1);
-  for (i = 1; i < 5; ++i) {
+    /* t1 = z ** ((2 ** 5) * (2 ** 250 - 1)) */
     fe_sq(t1, t1);
-  }
+    for (i = 1; i < 5; ++i) {
+        fe_sq(t1, t1);
+    }
 
-  /* Recall t0 = z ** 11; out = z ** (2 ** 255 - 21) */
-  fe_mul(out, t1, t0);
+    /* Recall t0 = z ** 11; out = z ** (2 ** 255 - 21) */
+    fe_mul(out, t1, t0);
 }
 
-/* h = -f
+/*
+ * h = -f
  *
  * Preconditions:
  *    |f| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
  *
  * Postconditions:
- *    |h| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc. */
-static void fe_neg(fe h, const fe f) {
-  unsigned i;
-  for (i = 0; i < 10; i++) {
-    h[i] = -f[i];
-  }
+ *    |h| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
+ */
+static void fe_neg(fe h, const fe f)
+{
+    unsigned i;
+
+    for (i = 0; i < 10; i++) {
+        h[i] = -f[i];
+    }
 }
 
-/* Replace (f,g) with (g,g) if b == 1;
+/*
+ * Replace (f,g) with (g,g) if b == 1;
  * replace (f,g) with (f,g) if b == 0.
  *
- * Preconditions: b in {0,1}. */
-static void fe_cmov(fe f, const fe g, unsigned b) {
-  size_t i;
-  b = 0-b;
-  for (i = 0; i < 10; i++) {
-    int32_t x = f[i] ^ g[i];
-    x &= b;
-    f[i] ^= x;
-  }
+ * Preconditions: b in {0,1}.
+ */
+static void fe_cmov(fe f, const fe g, unsigned b)
+{
+    size_t i;
+
+    b = 0-b;
+    for (i = 0; i < 10; i++) {
+        int32_t x = f[i] ^ g[i];
+        x &= b;
+        f[i] ^= x;
+    }
 }
 
-/* return 0 if f == 0
+/*
+ * return 0 if f == 0
  * return 1 if f != 0
  *
  * Preconditions:
- *    |f| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc. */
-static int fe_isnonzero(const fe f) {
-  uint8_t s[32];
-  static const uint8_t zero[32] = {0};
-  fe_tobytes(s, f);
+ *    |f| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc.
+ */
+static int fe_isnonzero(const fe f)
+{
+    uint8_t s[32];
+    static const uint8_t zero[32] = {0};
 
-  return CRYPTO_memcmp(s, zero, sizeof(zero)) != 0;
+    fe_tobytes(s, f);
+
+    return CRYPTO_memcmp(s, zero, sizeof(zero)) != 0;
 }
 
-/* return 1 if f is in {1,3,5,...,q-2}
+/*
+ * return 1 if f is in {1,3,5,...,q-2}
  * return 0 if f is in {0,2,4,...,q-1}
  *
  * Preconditions:
- *    |f| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc. */
-static int fe_isnegative(const fe f) {
-  uint8_t s[32];
-  fe_tobytes(s, f);
-  return s[0] & 1;
+ *    |f| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc.
+ */
+static int fe_isnegative(const fe f)
+{
+    uint8_t s[32];
+
+    fe_tobytes(s, f);
+    return s[0] & 1;
 }
 
-/* h = 2 * f * f
+/*
+ * h = 2 * f * f
+ *
  * Can overlap h with f.
  *
  * Preconditions:
@@ -1515,208 +1568,212 @@ static int fe_isnegative(const fe f) {
  * Postconditions:
  *    |h| bounded by 1.01*2^25,1.01*2^24,1.01*2^25,1.01*2^24,etc.
  *
- * See fe_mul.c for discussion of implementation strategy. */
-static void fe_sq2(fe h, const fe f) {
-  int32_t f0 = f[0];
-  int32_t f1 = f[1];
-  int32_t f2 = f[2];
-  int32_t f3 = f[3];
-  int32_t f4 = f[4];
-  int32_t f5 = f[5];
-  int32_t f6 = f[6];
-  int32_t f7 = f[7];
-  int32_t f8 = f[8];
-  int32_t f9 = f[9];
-  int32_t f0_2 = 2 * f0;
-  int32_t f1_2 = 2 * f1;
-  int32_t f2_2 = 2 * f2;
-  int32_t f3_2 = 2 * f3;
-  int32_t f4_2 = 2 * f4;
-  int32_t f5_2 = 2 * f5;
-  int32_t f6_2 = 2 * f6;
-  int32_t f7_2 = 2 * f7;
-  int32_t f5_38 = 38 * f5; /* 1.959375*2^30 */
-  int32_t f6_19 = 19 * f6; /* 1.959375*2^30 */
-  int32_t f7_38 = 38 * f7; /* 1.959375*2^30 */
-  int32_t f8_19 = 19 * f8; /* 1.959375*2^30 */
-  int32_t f9_38 = 38 * f9; /* 1.959375*2^30 */
-  int64_t f0f0    = f0   * (int64_t) f0;
-  int64_t f0f1_2  = f0_2 * (int64_t) f1;
-  int64_t f0f2_2  = f0_2 * (int64_t) f2;
-  int64_t f0f3_2  = f0_2 * (int64_t) f3;
-  int64_t f0f4_2  = f0_2 * (int64_t) f4;
-  int64_t f0f5_2  = f0_2 * (int64_t) f5;
-  int64_t f0f6_2  = f0_2 * (int64_t) f6;
-  int64_t f0f7_2  = f0_2 * (int64_t) f7;
-  int64_t f0f8_2  = f0_2 * (int64_t) f8;
-  int64_t f0f9_2  = f0_2 * (int64_t) f9;
-  int64_t f1f1_2  = f1_2 * (int64_t) f1;
-  int64_t f1f2_2  = f1_2 * (int64_t) f2;
-  int64_t f1f3_4  = f1_2 * (int64_t) f3_2;
-  int64_t f1f4_2  = f1_2 * (int64_t) f4;
-  int64_t f1f5_4  = f1_2 * (int64_t) f5_2;
-  int64_t f1f6_2  = f1_2 * (int64_t) f6;
-  int64_t f1f7_4  = f1_2 * (int64_t) f7_2;
-  int64_t f1f8_2  = f1_2 * (int64_t) f8;
-  int64_t f1f9_76 = f1_2 * (int64_t) f9_38;
-  int64_t f2f2    = f2   * (int64_t) f2;
-  int64_t f2f3_2  = f2_2 * (int64_t) f3;
-  int64_t f2f4_2  = f2_2 * (int64_t) f4;
-  int64_t f2f5_2  = f2_2 * (int64_t) f5;
-  int64_t f2f6_2  = f2_2 * (int64_t) f6;
-  int64_t f2f7_2  = f2_2 * (int64_t) f7;
-  int64_t f2f8_38 = f2_2 * (int64_t) f8_19;
-  int64_t f2f9_38 = f2   * (int64_t) f9_38;
-  int64_t f3f3_2  = f3_2 * (int64_t) f3;
-  int64_t f3f4_2  = f3_2 * (int64_t) f4;
-  int64_t f3f5_4  = f3_2 * (int64_t) f5_2;
-  int64_t f3f6_2  = f3_2 * (int64_t) f6;
-  int64_t f3f7_76 = f3_2 * (int64_t) f7_38;
-  int64_t f3f8_38 = f3_2 * (int64_t) f8_19;
-  int64_t f3f9_76 = f3_2 * (int64_t) f9_38;
-  int64_t f4f4    = f4   * (int64_t) f4;
-  int64_t f4f5_2  = f4_2 * (int64_t) f5;
-  int64_t f4f6_38 = f4_2 * (int64_t) f6_19;
-  int64_t f4f7_38 = f4   * (int64_t) f7_38;
-  int64_t f4f8_38 = f4_2 * (int64_t) f8_19;
-  int64_t f4f9_38 = f4   * (int64_t) f9_38;
-  int64_t f5f5_38 = f5   * (int64_t) f5_38;
-  int64_t f5f6_38 = f5_2 * (int64_t) f6_19;
-  int64_t f5f7_76 = f5_2 * (int64_t) f7_38;
-  int64_t f5f8_38 = f5_2 * (int64_t) f8_19;
-  int64_t f5f9_76 = f5_2 * (int64_t) f9_38;
-  int64_t f6f6_19 = f6   * (int64_t) f6_19;
-  int64_t f6f7_38 = f6   * (int64_t) f7_38;
-  int64_t f6f8_38 = f6_2 * (int64_t) f8_19;
-  int64_t f6f9_38 = f6   * (int64_t) f9_38;
-  int64_t f7f7_38 = f7   * (int64_t) f7_38;
-  int64_t f7f8_38 = f7_2 * (int64_t) f8_19;
-  int64_t f7f9_76 = f7_2 * (int64_t) f9_38;
-  int64_t f8f8_19 = f8   * (int64_t) f8_19;
-  int64_t f8f9_38 = f8   * (int64_t) f9_38;
-  int64_t f9f9_38 = f9   * (int64_t) f9_38;
-  int64_t h0 = f0f0  +f1f9_76+f2f8_38+f3f7_76+f4f6_38+f5f5_38;
-  int64_t h1 = f0f1_2+f2f9_38+f3f8_38+f4f7_38+f5f6_38;
-  int64_t h2 = f0f2_2+f1f1_2 +f3f9_76+f4f8_38+f5f7_76+f6f6_19;
-  int64_t h3 = f0f3_2+f1f2_2 +f4f9_38+f5f8_38+f6f7_38;
-  int64_t h4 = f0f4_2+f1f3_4 +f2f2   +f5f9_76+f6f8_38+f7f7_38;
-  int64_t h5 = f0f5_2+f1f4_2 +f2f3_2 +f6f9_38+f7f8_38;
-  int64_t h6 = f0f6_2+f1f5_4 +f2f4_2 +f3f3_2 +f7f9_76+f8f8_19;
-  int64_t h7 = f0f7_2+f1f6_2 +f2f5_2 +f3f4_2 +f8f9_38;
-  int64_t h8 = f0f8_2+f1f7_4 +f2f6_2 +f3f5_4 +f4f4   +f9f9_38;
-  int64_t h9 = f0f9_2+f1f8_2 +f2f7_2 +f3f6_2 +f4f5_2;
-  int64_t carry0;
-  int64_t carry1;
-  int64_t carry2;
-  int64_t carry3;
-  int64_t carry4;
-  int64_t carry5;
-  int64_t carry6;
-  int64_t carry7;
-  int64_t carry8;
-  int64_t carry9;
-
-  h0 += h0;
-  h1 += h1;
-  h2 += h2;
-  h3 += h3;
-  h4 += h4;
-  h5 += h5;
-  h6 += h6;
-  h7 += h7;
-  h8 += h8;
-  h9 += h9;
-
-  carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits;
-  carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits;
-
-  carry1 = h1 + (1 << 24); h2 += carry1 >> 25; h1 -= carry1 & kTop39Bits;
-  carry5 = h5 + (1 << 24); h6 += carry5 >> 25; h5 -= carry5 & kTop39Bits;
-
-  carry2 = h2 + (1 << 25); h3 += carry2 >> 26; h2 -= carry2 & kTop38Bits;
-  carry6 = h6 + (1 << 25); h7 += carry6 >> 26; h6 -= carry6 & kTop38Bits;
-
-  carry3 = h3 + (1 << 24); h4 += carry3 >> 25; h3 -= carry3 & kTop39Bits;
-  carry7 = h7 + (1 << 24); h8 += carry7 >> 25; h7 -= carry7 & kTop39Bits;
-
-  carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits;
-  carry8 = h8 + (1 << 25); h9 += carry8 >> 26; h8 -= carry8 & kTop38Bits;
-
-  carry9 = h9 + (1 << 24); h0 += (carry9 >> 25) * 19; h9 -= carry9 & 
kTop39Bits;
-
-  carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits;
-
-  h[0] = (int32_t)h0;
-  h[1] = (int32_t)h1;
-  h[2] = (int32_t)h2;
-  h[3] = (int32_t)h3;
-  h[4] = (int32_t)h4;
-  h[5] = (int32_t)h5;
-  h[6] = (int32_t)h6;
-  h[7] = (int32_t)h7;
-  h[8] = (int32_t)h8;
-  h[9] = (int32_t)h9;
+ * See fe_mul.c for discussion of implementation strategy.
+ */
+static void fe_sq2(fe h, const fe f)
+{
+    int32_t f0 = f[0];
+    int32_t f1 = f[1];
+    int32_t f2 = f[2];
+    int32_t f3 = f[3];
+    int32_t f4 = f[4];
+    int32_t f5 = f[5];
+    int32_t f6 = f[6];
+    int32_t f7 = f[7];
+    int32_t f8 = f[8];
+    int32_t f9 = f[9];
+    int32_t f0_2 = 2 * f0;
+    int32_t f1_2 = 2 * f1;
+    int32_t f2_2 = 2 * f2;
+    int32_t f3_2 = 2 * f3;
+    int32_t f4_2 = 2 * f4;
+    int32_t f5_2 = 2 * f5;
+    int32_t f6_2 = 2 * f6;
+    int32_t f7_2 = 2 * f7;
+    int32_t f5_38 = 38 * f5; /* 1.959375*2^30 */
+    int32_t f6_19 = 19 * f6; /* 1.959375*2^30 */
+    int32_t f7_38 = 38 * f7; /* 1.959375*2^30 */
+    int32_t f8_19 = 19 * f8; /* 1.959375*2^30 */
+    int32_t f9_38 = 38 * f9; /* 1.959375*2^30 */
+    int64_t f0f0    = f0   * (int64_t) f0;
+    int64_t f0f1_2  = f0_2 * (int64_t) f1;
+    int64_t f0f2_2  = f0_2 * (int64_t) f2;
+    int64_t f0f3_2  = f0_2 * (int64_t) f3;
+    int64_t f0f4_2  = f0_2 * (int64_t) f4;
+    int64_t f0f5_2  = f0_2 * (int64_t) f5;
+    int64_t f0f6_2  = f0_2 * (int64_t) f6;
+    int64_t f0f7_2  = f0_2 * (int64_t) f7;
+    int64_t f0f8_2  = f0_2 * (int64_t) f8;
+    int64_t f0f9_2  = f0_2 * (int64_t) f9;
+    int64_t f1f1_2  = f1_2 * (int64_t) f1;
+    int64_t f1f2_2  = f1_2 * (int64_t) f2;
+    int64_t f1f3_4  = f1_2 * (int64_t) f3_2;
+    int64_t f1f4_2  = f1_2 * (int64_t) f4;
+    int64_t f1f5_4  = f1_2 * (int64_t) f5_2;
+    int64_t f1f6_2  = f1_2 * (int64_t) f6;
+    int64_t f1f7_4  = f1_2 * (int64_t) f7_2;
+    int64_t f1f8_2  = f1_2 * (int64_t) f8;
+    int64_t f1f9_76 = f1_2 * (int64_t) f9_38;
+    int64_t f2f2    = f2   * (int64_t) f2;
+    int64_t f2f3_2  = f2_2 * (int64_t) f3;
+    int64_t f2f4_2  = f2_2 * (int64_t) f4;
+    int64_t f2f5_2  = f2_2 * (int64_t) f5;
+    int64_t f2f6_2  = f2_2 * (int64_t) f6;
+    int64_t f2f7_2  = f2_2 * (int64_t) f7;
+    int64_t f2f8_38 = f2_2 * (int64_t) f8_19;
+    int64_t f2f9_38 = f2   * (int64_t) f9_38;
+    int64_t f3f3_2  = f3_2 * (int64_t) f3;
+    int64_t f3f4_2  = f3_2 * (int64_t) f4;
+    int64_t f3f5_4  = f3_2 * (int64_t) f5_2;
+    int64_t f3f6_2  = f3_2 * (int64_t) f6;
+    int64_t f3f7_76 = f3_2 * (int64_t) f7_38;
+    int64_t f3f8_38 = f3_2 * (int64_t) f8_19;
+    int64_t f3f9_76 = f3_2 * (int64_t) f9_38;
+    int64_t f4f4    = f4   * (int64_t) f4;
+    int64_t f4f5_2  = f4_2 * (int64_t) f5;
+    int64_t f4f6_38 = f4_2 * (int64_t) f6_19;
+    int64_t f4f7_38 = f4   * (int64_t) f7_38;
+    int64_t f4f8_38 = f4_2 * (int64_t) f8_19;
+    int64_t f4f9_38 = f4   * (int64_t) f9_38;
+    int64_t f5f5_38 = f5   * (int64_t) f5_38;
+    int64_t f5f6_38 = f5_2 * (int64_t) f6_19;
+    int64_t f5f7_76 = f5_2 * (int64_t) f7_38;
+    int64_t f5f8_38 = f5_2 * (int64_t) f8_19;
+    int64_t f5f9_76 = f5_2 * (int64_t) f9_38;
+    int64_t f6f6_19 = f6   * (int64_t) f6_19;
+    int64_t f6f7_38 = f6   * (int64_t) f7_38;
+    int64_t f6f8_38 = f6_2 * (int64_t) f8_19;
+    int64_t f6f9_38 = f6   * (int64_t) f9_38;
+    int64_t f7f7_38 = f7   * (int64_t) f7_38;
+    int64_t f7f8_38 = f7_2 * (int64_t) f8_19;
+    int64_t f7f9_76 = f7_2 * (int64_t) f9_38;
+    int64_t f8f8_19 = f8   * (int64_t) f8_19;
+    int64_t f8f9_38 = f8   * (int64_t) f9_38;
+    int64_t f9f9_38 = f9   * (int64_t) f9_38;
+    int64_t h0 = f0f0   + f1f9_76 + f2f8_38 + f3f7_76 + f4f6_38 + f5f5_38;
+    int64_t h1 = f0f1_2 + f2f9_38 + f3f8_38 + f4f7_38 + f5f6_38;
+    int64_t h2 = f0f2_2 + f1f1_2  + f3f9_76 + f4f8_38 + f5f7_76 + f6f6_19;
+    int64_t h3 = f0f3_2 + f1f2_2  + f4f9_38 + f5f8_38 + f6f7_38;
+    int64_t h4 = f0f4_2 + f1f3_4  + f2f2    + f5f9_76 + f6f8_38 + f7f7_38;
+    int64_t h5 = f0f5_2 + f1f4_2  + f2f3_2  + f6f9_38 + f7f8_38;
+    int64_t h6 = f0f6_2 + f1f5_4  + f2f4_2  + f3f3_2  + f7f9_76 + f8f8_19;
+    int64_t h7 = f0f7_2 + f1f6_2  + f2f5_2  + f3f4_2  + f8f9_38;
+    int64_t h8 = f0f8_2 + f1f7_4  + f2f6_2  + f3f5_4  + f4f4    + f9f9_38;
+    int64_t h9 = f0f9_2 + f1f8_2  + f2f7_2  + f3f6_2  + f4f5_2;
+    int64_t carry0;
+    int64_t carry1;
+    int64_t carry2;
+    int64_t carry3;
+    int64_t carry4;
+    int64_t carry5;
+    int64_t carry6;
+    int64_t carry7;
+    int64_t carry8;
+    int64_t carry9;
+
+    h0 += h0;
+    h1 += h1;
+    h2 += h2;
+    h3 += h3;
+    h4 += h4;
+    h5 += h5;
+    h6 += h6;
+    h7 += h7;
+    h8 += h8;
+    h9 += h9;
+
+    carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits;
+    carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits;
+
+    carry1 = h1 + (1 << 24); h2 += carry1 >> 25; h1 -= carry1 & kTop39Bits;
+    carry5 = h5 + (1 << 24); h6 += carry5 >> 25; h5 -= carry5 & kTop39Bits;
+
+    carry2 = h2 + (1 << 25); h3 += carry2 >> 26; h2 -= carry2 & kTop38Bits;
+    carry6 = h6 + (1 << 25); h7 += carry6 >> 26; h6 -= carry6 & kTop38Bits;
+
+    carry3 = h3 + (1 << 24); h4 += carry3 >> 25; h3 -= carry3 & kTop39Bits;
+    carry7 = h7 + (1 << 24); h8 += carry7 >> 25; h7 -= carry7 & kTop39Bits;
+
+    carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits;
+    carry8 = h8 + (1 << 25); h9 += carry8 >> 26; h8 -= carry8 & kTop38Bits;
+
+    carry9 = h9 + (1 << 24); h0 += (carry9 >> 25) * 19; h9 -= carry9 & 
kTop39Bits;
+
+    carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits;
+
+    h[0] = (int32_t)h0;
+    h[1] = (int32_t)h1;
+    h[2] = (int32_t)h2;
+    h[3] = (int32_t)h3;
+    h[4] = (int32_t)h4;
+    h[5] = (int32_t)h5;
+    h[6] = (int32_t)h6;
+    h[7] = (int32_t)h7;
+    h[8] = (int32_t)h8;
+    h[9] = (int32_t)h9;
 }
 
-static void fe_pow22523(fe out, const fe z) {
-  fe t0;
-  fe t1;
-  fe t2;
-  int i;
+static void fe_pow22523(fe out, const fe z)
+{
+    fe t0;
+    fe t1;
+    fe t2;
+    int i;
 
-  fe_sq(t0, z);
-  fe_sq(t1, t0);
-  for (i = 1; i < 2; ++i) {
-    fe_sq(t1, t1);
-  }
-  fe_mul(t1, z, t1);
-  fe_mul(t0, t0, t1);
-  fe_sq(t0, t0);
-  fe_mul(t0, t1, t0);
-  fe_sq(t1, t0);
-  for (i = 1; i < 5; ++i) {
-    fe_sq(t1, t1);
-  }
-  fe_mul(t0, t1, t0);
-  fe_sq(t1, t0);
-  for (i = 1; i < 10; ++i) {
-    fe_sq(t1, t1);
-  }
-  fe_mul(t1, t1, t0);
-  fe_sq(t2, t1);
-  for (i = 1; i < 20; ++i) {
-    fe_sq(t2, t2);
-  }
-  fe_mul(t1, t2, t1);
-  fe_sq(t1, t1);
-  for (i = 1; i < 10; ++i) {
-    fe_sq(t1, t1);
-  }
-  fe_mul(t0, t1, t0);
-  fe_sq(t1, t0);
-  for (i = 1; i < 50; ++i) {
+    fe_sq(t0, z);
+    fe_sq(t1, t0);
+    for (i = 1; i < 2; ++i) {
+        fe_sq(t1, t1);
+    }
+    fe_mul(t1, z, t1);
+    fe_mul(t0, t0, t1);
+    fe_sq(t0, t0);
+    fe_mul(t0, t1, t0);
+    fe_sq(t1, t0);
+    for (i = 1; i < 5; ++i) {
+        fe_sq(t1, t1);
+    }
+    fe_mul(t0, t1, t0);
+    fe_sq(t1, t0);
+    for (i = 1; i < 10; ++i) {
+        fe_sq(t1, t1);
+    }
+    fe_mul(t1, t1, t0);
+    fe_sq(t2, t1);
+    for (i = 1; i < 20; ++i) {
+        fe_sq(t2, t2);
+    }
+    fe_mul(t1, t2, t1);
     fe_sq(t1, t1);
-  }
-  fe_mul(t1, t1, t0);
-  fe_sq(t2, t1);
-  for (i = 1; i < 100; ++i) {
-    fe_sq(t2, t2);
-  }
-  fe_mul(t1, t2, t1);
-  fe_sq(t1, t1);
-  for (i = 1; i < 50; ++i) {
+    for (i = 1; i < 10; ++i) {
+        fe_sq(t1, t1);
+    }
+    fe_mul(t0, t1, t0);
+    fe_sq(t1, t0);
+    for (i = 1; i < 50; ++i) {
+        fe_sq(t1, t1);
+    }
+    fe_mul(t1, t1, t0);
+    fe_sq(t2, t1);
+    for (i = 1; i < 100; ++i) {
+        fe_sq(t2, t2);
+    }
+    fe_mul(t1, t2, t1);
     fe_sq(t1, t1);
-  }
-  fe_mul(t0, t1, t0);
-  fe_sq(t0, t0);
-  for (i = 1; i < 2; ++i) {
+    for (i = 1; i < 50; ++i) {
+        fe_sq(t1, t1);
+    }
+    fe_mul(t0, t1, t0);
     fe_sq(t0, t0);
-  }
-  fe_mul(out, t0, z);
+    for (i = 1; i < 2; ++i) {
+        fe_sq(t0, t0);
+    }
+    fe_mul(out, t0, z);
 }
 
-/* ge means group element.
-
+/*
+ * ge means group element.
+ *
  * Here the group is the set of pairs (x,y) of field elements (see fe.h)
  * satisfying -x^2 + y^2 = 1 + d x^2y^2
  * where d = -121665/121666.
@@ -1725,268 +1782,292 @@ static void fe_pow22523(fe out, const fe z) {
  *   ge_p2 (projective): (X:Y:Z) satisfying x=X/Z, y=Y/Z
  *   ge_p3 (extended): (X:Y:Z:T) satisfying x=X/Z, y=Y/Z, XY=ZT
  *   ge_p1p1 (completed): ((X:Z),(Y:T)) satisfying x=X/Z, y=Y/T
- *   ge_precomp (Duif): (y+x,y-x,2dxy) */
-
+ *   ge_precomp (Duif): (y+x,y-x,2dxy)
+ */
 typedef struct {
-  fe X;
-  fe Y;
-  fe Z;
+    fe X;
+    fe Y;
+    fe Z;
 } ge_p2;
 
 typedef struct {
-  fe X;
-  fe Y;
-  fe Z;
-  fe T;
+    fe X;
+    fe Y;
+    fe Z;
+    fe T;
 } ge_p3;
 
 typedef struct {
-  fe X;
-  fe Y;
-  fe Z;
-  fe T;
+    fe X;
+    fe Y;
+    fe Z;
+    fe T;
 } ge_p1p1;
 
 typedef struct {
-  fe yplusx;
-  fe yminusx;
-  fe xy2d;
+    fe yplusx;
+    fe yminusx;
+    fe xy2d;
 } ge_precomp;
 
 typedef struct {
-  fe YplusX;
-  fe YminusX;
-  fe Z;
-  fe T2d;
+    fe YplusX;
+    fe YminusX;
+    fe Z;
+    fe T2d;
 } ge_cached;
 
-static void ge_tobytes(uint8_t *s, const ge_p2 *h) {
-  fe recip;
-  fe x;
-  fe y;
+static void ge_tobytes(uint8_t *s, const ge_p2 *h)
+{
+    fe recip;
+    fe x;
+    fe y;
+
+    fe_invert(recip, h->Z);
+    fe_mul(x, h->X, recip);
+    fe_mul(y, h->Y, recip);
+    fe_tobytes(s, y);
+    s[31] ^= fe_isnegative(x) << 7;
+}
 
-  fe_invert(recip, h->Z);
-  fe_mul(x, h->X, recip);
-  fe_mul(y, h->Y, recip);
-  fe_tobytes(s, y);
-  s[31] ^= fe_isnegative(x) << 7;
+static void ge_p3_tobytes(uint8_t *s, const ge_p3 *h)
+{
+    fe recip;
+    fe x;
+    fe y;
+
+    fe_invert(recip, h->Z);
+    fe_mul(x, h->X, recip);
+    fe_mul(y, h->Y, recip);
+    fe_tobytes(s, y);
+    s[31] ^= fe_isnegative(x) << 7;
 }
 
-static void ge_p3_tobytes(uint8_t *s, const ge_p3 *h) {
-  fe recip;
-  fe x;
-  fe y;
+static const fe d = {
+    -10913610, 13857413, -15372611, 6949391,   114729,
+    -8787816,  -6275908, -3247719,  -18696448, -12055116
+};
 
-  fe_invert(recip, h->Z);
-  fe_mul(x, h->X, recip);
-  fe_mul(y, h->Y, recip);
-  fe_tobytes(s, y);
-  s[31] ^= fe_isnegative(x) << 7;
-}
+static const fe sqrtm1 = {
+    -32595792, -7943725,  9377950,  3500415, 12389472,
+    -272473,   -25146209, -2005654, 326686,  11406482
+};
 
-static const fe d = {-10913610, 13857413, -15372611, 6949391,   114729,
-                     -8787816,  -6275908, -3247719,  -18696448, -12055116};
-
-static const fe sqrtm1 = {-32595792, -7943725,  9377950,  3500415, 12389472,
-                          -272473,   -25146209, -2005654, 326686,  11406482};
-
-static int ge_frombytes_vartime(ge_p3 *h, const uint8_t *s) {
-  fe u;
-  fe v;
-  fe v3;
-  fe vxx;
-  fe check;
-
-  fe_frombytes(h->Y, s);
-  fe_1(h->Z);
-  fe_sq(u, h->Y);
-  fe_mul(v, u, d);
-  fe_sub(u, u, h->Z); /* u = y^2-1 */
-  fe_add(v, v, h->Z); /* v = dy^2+1 */
-
-  fe_sq(v3, v);
-  fe_mul(v3, v3, v); /* v3 = v^3 */
-  fe_sq(h->X, v3);
-  fe_mul(h->X, h->X, v);
-  fe_mul(h->X, h->X, u); /* x = uv^7 */
-
-  fe_pow22523(h->X, h->X); /* x = (uv^7)^((q-5)/8) */
-  fe_mul(h->X, h->X, v3);
-  fe_mul(h->X, h->X, u); /* x = uv^3(uv^7)^((q-5)/8) */
-
-  fe_sq(vxx, h->X);
-  fe_mul(vxx, vxx, v);
-  fe_sub(check, vxx, u); /* vx^2-u */
-  if (fe_isnonzero(check)) {
-    fe_add(check, vxx, u); /* vx^2+u */
+static int ge_frombytes_vartime(ge_p3 *h, const uint8_t *s)
+{
+    fe u;
+    fe v;
+    fe v3;
+    fe vxx;
+    fe check;
+
+    fe_frombytes(h->Y, s);
+    fe_1(h->Z);
+    fe_sq(u, h->Y);
+    fe_mul(v, u, d);
+    fe_sub(u, u, h->Z); /* u = y^2-1 */
+    fe_add(v, v, h->Z); /* v = dy^2+1 */
+
+    fe_sq(v3, v);
+    fe_mul(v3, v3, v); /* v3 = v^3 */
+    fe_sq(h->X, v3);
+    fe_mul(h->X, h->X, v);
+    fe_mul(h->X, h->X, u); /* x = uv^7 */
+
+    fe_pow22523(h->X, h->X); /* x = (uv^7)^((q-5)/8) */
+    fe_mul(h->X, h->X, v3);
+    fe_mul(h->X, h->X, u); /* x = uv^3(uv^7)^((q-5)/8) */
+
+    fe_sq(vxx, h->X);
+    fe_mul(vxx, vxx, v);
+    fe_sub(check, vxx, u); /* vx^2-u */
     if (fe_isnonzero(check)) {
-      return -1;
+        fe_add(check, vxx, u); /* vx^2+u */
+        if (fe_isnonzero(check)) {
+            return -1;
+        }
+        fe_mul(h->X, h->X, sqrtm1);
     }
-    fe_mul(h->X, h->X, sqrtm1);
-  }
 
-  if (fe_isnegative(h->X) != (s[31] >> 7)) {
-    fe_neg(h->X, h->X);
-  }
+    if (fe_isnegative(h->X) != (s[31] >> 7)) {
+        fe_neg(h->X, h->X);
+    }
 
-  fe_mul(h->T, h->X, h->Y);
-  return 0;
+    fe_mul(h->T, h->X, h->Y);
+    return 0;
 }
 
-static void ge_p2_0(ge_p2 *h) {
-  fe_0(h->X);
-  fe_1(h->Y);
-  fe_1(h->Z);
+static void ge_p2_0(ge_p2 *h)
+{
+    fe_0(h->X);
+    fe_1(h->Y);
+    fe_1(h->Z);
 }
 
-static void ge_p3_0(ge_p3 *h) {
-  fe_0(h->X);
-  fe_1(h->Y);
-  fe_1(h->Z);
-  fe_0(h->T);
+static void ge_p3_0(ge_p3 *h)
+{
+    fe_0(h->X);
+    fe_1(h->Y);
+    fe_1(h->Z);
+    fe_0(h->T);
 }
 
-static void ge_precomp_0(ge_precomp *h) {
-  fe_1(h->yplusx);
-  fe_1(h->yminusx);
-  fe_0(h->xy2d);
+static void ge_precomp_0(ge_precomp *h)
+{
+    fe_1(h->yplusx);
+    fe_1(h->yminusx);
+    fe_0(h->xy2d);
 }
 
 /* r = p */
-static void ge_p3_to_p2(ge_p2 *r, const ge_p3 *p) {
-  fe_copy(r->X, p->X);
-  fe_copy(r->Y, p->Y);
-  fe_copy(r->Z, p->Z);
+static void ge_p3_to_p2(ge_p2 *r, const ge_p3 *p)
+{
+    fe_copy(r->X, p->X);
+    fe_copy(r->Y, p->Y);
+    fe_copy(r->Z, p->Z);
 }
 
-static const fe d2 = {-21827239, -5839606,  -30745221, 13898782, 229458,
-                      15978800,  -12551817, -6495438,  29715968, 9444199};
+static const fe d2 = {
+    -21827239, -5839606,  -30745221, 13898782, 229458,
+    15978800,  -12551817, -6495438,  29715968, 9444199
+};
 
 /* r = p */
-static void ge_p3_to_cached(ge_cached *r, const ge_p3 *p) {
-  fe_add(r->YplusX, p->Y, p->X);
-  fe_sub(r->YminusX, p->Y, p->X);
-  fe_copy(r->Z, p->Z);
-  fe_mul(r->T2d, p->T, d2);
+static void ge_p3_to_cached(ge_cached *r, const ge_p3 *p)
+{
+    fe_add(r->YplusX, p->Y, p->X);
+    fe_sub(r->YminusX, p->Y, p->X);
+    fe_copy(r->Z, p->Z);
+    fe_mul(r->T2d, p->T, d2);
 }
 
 /* r = p */
-static void ge_p1p1_to_p2(ge_p2 *r, const ge_p1p1 *p) {
-  fe_mul(r->X, p->X, p->T);
-  fe_mul(r->Y, p->Y, p->Z);
-  fe_mul(r->Z, p->Z, p->T);
+static void ge_p1p1_to_p2(ge_p2 *r, const ge_p1p1 *p)
+{
+    fe_mul(r->X, p->X, p->T);
+    fe_mul(r->Y, p->Y, p->Z);
+    fe_mul(r->Z, p->Z, p->T);
 }
 
 /* r = p */
-static void ge_p1p1_to_p3(ge_p3 *r, const ge_p1p1 *p) {
-  fe_mul(r->X, p->X, p->T);
-  fe_mul(r->Y, p->Y, p->Z);
-  fe_mul(r->Z, p->Z, p->T);
-  fe_mul(r->T, p->X, p->Y);
+static void ge_p1p1_to_p3(ge_p3 *r, const ge_p1p1 *p)
+{
+    fe_mul(r->X, p->X, p->T);
+    fe_mul(r->Y, p->Y, p->Z);
+    fe_mul(r->Z, p->Z, p->T);
+    fe_mul(r->T, p->X, p->Y);
 }
 
 /* r = 2 * p */
-static void ge_p2_dbl(ge_p1p1 *r, const ge_p2 *p) {
-  fe t0;
-
-  fe_sq(r->X, p->X);
-  fe_sq(r->Z, p->Y);
-  fe_sq2(r->T, p->Z);
-  fe_add(r->Y, p->X, p->Y);
-  fe_sq(t0, r->Y);
-  fe_add(r->Y, r->Z, r->X);
-  fe_sub(r->Z, r->Z, r->X);
-  fe_sub(r->X, t0, r->Y);
-  fe_sub(r->T, r->T, r->Z);
+static void ge_p2_dbl(ge_p1p1 *r, const ge_p2 *p)
+{
+    fe t0;
+
+    fe_sq(r->X, p->X);
+    fe_sq(r->Z, p->Y);
+    fe_sq2(r->T, p->Z);
+    fe_add(r->Y, p->X, p->Y);
+    fe_sq(t0, r->Y);
+    fe_add(r->Y, r->Z, r->X);
+    fe_sub(r->Z, r->Z, r->X);
+    fe_sub(r->X, t0, r->Y);
+    fe_sub(r->T, r->T, r->Z);
 }
 
 /* r = 2 * p */
-static void ge_p3_dbl(ge_p1p1 *r, const ge_p3 *p) {
-  ge_p2 q;
-  ge_p3_to_p2(&q, p);
-  ge_p2_dbl(r, &q);
+static void ge_p3_dbl(ge_p1p1 *r, const ge_p3 *p)
+{
+    ge_p2 q;
+    ge_p3_to_p2(&q, p);
+    ge_p2_dbl(r, &q);
 }
 
 /* r = p + q */
-static void ge_madd(ge_p1p1 *r, const ge_p3 *p, const ge_precomp *q) {
-  fe t0;
-
-  fe_add(r->X, p->Y, p->X);
-  fe_sub(r->Y, p->Y, p->X);
-  fe_mul(r->Z, r->X, q->yplusx);
-  fe_mul(r->Y, r->Y, q->yminusx);
-  fe_mul(r->T, q->xy2d, p->T);
-  fe_add(t0, p->Z, p->Z);
-  fe_sub(r->X, r->Z, r->Y);
-  fe_add(r->Y, r->Z, r->Y);
-  fe_add(r->Z, t0, r->T);
-  fe_sub(r->T, t0, r->T);
+static void ge_madd(ge_p1p1 *r, const ge_p3 *p, const ge_precomp *q)
+{
+    fe t0;
+
+    fe_add(r->X, p->Y, p->X);
+    fe_sub(r->Y, p->Y, p->X);
+    fe_mul(r->Z, r->X, q->yplusx);
+    fe_mul(r->Y, r->Y, q->yminusx);
+    fe_mul(r->T, q->xy2d, p->T);
+    fe_add(t0, p->Z, p->Z);
+    fe_sub(r->X, r->Z, r->Y);
+    fe_add(r->Y, r->Z, r->Y);
+    fe_add(r->Z, t0, r->T);
+    fe_sub(r->T, t0, r->T);
 }
 
 /* r = p - q */
-static void ge_msub(ge_p1p1 *r, const ge_p3 *p, const ge_precomp *q) {
-  fe t0;
-
-  fe_add(r->X, p->Y, p->X);
-  fe_sub(r->Y, p->Y, p->X);
-  fe_mul(r->Z, r->X, q->yminusx);
-  fe_mul(r->Y, r->Y, q->yplusx);
-  fe_mul(r->T, q->xy2d, p->T);
-  fe_add(t0, p->Z, p->Z);
-  fe_sub(r->X, r->Z, r->Y);
-  fe_add(r->Y, r->Z, r->Y);
-  fe_sub(r->Z, t0, r->T);
-  fe_add(r->T, t0, r->T);
+static void ge_msub(ge_p1p1 *r, const ge_p3 *p, const ge_precomp *q)
+{
+    fe t0;
+
+    fe_add(r->X, p->Y, p->X);
+    fe_sub(r->Y, p->Y, p->X);
+    fe_mul(r->Z, r->X, q->yminusx);
+    fe_mul(r->Y, r->Y, q->yplusx);
+    fe_mul(r->T, q->xy2d, p->T);
+    fe_add(t0, p->Z, p->Z);
+    fe_sub(r->X, r->Z, r->Y);
+    fe_add(r->Y, r->Z, r->Y);
+    fe_sub(r->Z, t0, r->T);
+    fe_add(r->T, t0, r->T);
 }
 
 /* r = p + q */
-static void ge_add(ge_p1p1 *r, const ge_p3 *p, const ge_cached *q) {
-  fe t0;
-
-  fe_add(r->X, p->Y, p->X);
-  fe_sub(r->Y, p->Y, p->X);
-  fe_mul(r->Z, r->X, q->YplusX);
-  fe_mul(r->Y, r->Y, q->YminusX);
-  fe_mul(r->T, q->T2d, p->T);
-  fe_mul(r->X, p->Z, q->Z);
-  fe_add(t0, r->X, r->X);
-  fe_sub(r->X, r->Z, r->Y);
-  fe_add(r->Y, r->Z, r->Y);
-  fe_add(r->Z, t0, r->T);
-  fe_sub(r->T, t0, r->T);
+static void ge_add(ge_p1p1 *r, const ge_p3 *p, const ge_cached *q)
+{
+    fe t0;
+
+    fe_add(r->X, p->Y, p->X);
+    fe_sub(r->Y, p->Y, p->X);
+    fe_mul(r->Z, r->X, q->YplusX);
+    fe_mul(r->Y, r->Y, q->YminusX);
+    fe_mul(r->T, q->T2d, p->T);
+    fe_mul(r->X, p->Z, q->Z);
+    fe_add(t0, r->X, r->X);
+    fe_sub(r->X, r->Z, r->Y);
+    fe_add(r->Y, r->Z, r->Y);
+    fe_add(r->Z, t0, r->T);
+    fe_sub(r->T, t0, r->T);
 }
 
 /* r = p - q */
-static void ge_sub(ge_p1p1 *r, const ge_p3 *p, const ge_cached *q) {
-  fe t0;
-
-  fe_add(r->X, p->Y, p->X);
-  fe_sub(r->Y, p->Y, p->X);
-  fe_mul(r->Z, r->X, q->YminusX);
-  fe_mul(r->Y, r->Y, q->YplusX);
-  fe_mul(r->T, q->T2d, p->T);
-  fe_mul(r->X, p->Z, q->Z);
-  fe_add(t0, r->X, r->X);
-  fe_sub(r->X, r->Z, r->Y);
-  fe_add(r->Y, r->Z, r->Y);
-  fe_sub(r->Z, t0, r->T);
-  fe_add(r->T, t0, r->T);
+static void ge_sub(ge_p1p1 *r, const ge_p3 *p, const ge_cached *q)
+{
+    fe t0;
+
+    fe_add(r->X, p->Y, p->X);
+    fe_sub(r->Y, p->Y, p->X);
+    fe_mul(r->Z, r->X, q->YminusX);
+    fe_mul(r->Y, r->Y, q->YplusX);
+    fe_mul(r->T, q->T2d, p->T);
+    fe_mul(r->X, p->Z, q->Z);
+    fe_add(t0, r->X, r->X);
+    fe_sub(r->X, r->Z, r->Y);
+    fe_add(r->Y, r->Z, r->Y);
+    fe_sub(r->Z, t0, r->T);
+    fe_add(r->T, t0, r->T);
 }
 
-static uint8_t equal(signed char b, signed char c) {
-  uint8_t ub = b;
-  uint8_t uc = c;
-  uint8_t x = ub ^ uc; /* 0: yes; 1..255: no */
-  uint32_t y = x;      /* 0: yes; 1..255: no */
-  y -= 1;              /* 4294967295: yes; 0..254: no */
-  y >>= 31;            /* 1: yes; 0: no */
-  return y;
+static uint8_t equal(signed char b, signed char c)
+{
+    uint8_t ub = b;
+    uint8_t uc = c;
+    uint8_t x = ub ^ uc; /* 0: yes; 1..255: no */
+    uint32_t y = x;      /* 0: yes; 1..255: no */
+    y -= 1;              /* 4294967295: yes; 0..254: no */
+    y >>= 31;            /* 1: yes; 0: no */
+    return y;
 }
 
-static void cmov(ge_precomp *t, const ge_precomp *u, uint8_t b) {
-  fe_cmov(t->yplusx, u->yplusx, b);
-  fe_cmov(t->yminusx, u->yminusx, b);
-  fe_cmov(t->xy2d, u->xy2d, b);
+static void cmov(ge_precomp *t, const ge_precomp *u, uint8_t b)
+{
+    fe_cmov(t->yplusx, u->yplusx, b);
+    fe_cmov(t->yminusx, u->yminusx, b);
+    fe_cmov(t->xy2d, u->xy2d, b);
 }
 
 /* k25519Precomp[i][j] = (j+1)*256^i*B */
@@ -4105,257 +4186,273 @@ static const ge_precomp k25519Precomp[32][8] = {
     },
 };
 
-static uint8_t negative(signed char b) {
-  uint32_t x = b;
-  x >>= 31; /* 1: yes; 0: no */
-  return x;
+static uint8_t negative(signed char b)
+{
+    uint32_t x = b;
+
+    x >>= 31; /* 1: yes; 0: no */
+    return x;
 }
 
-static void table_select(ge_precomp *t, int pos, signed char b) {
-  ge_precomp minust;
-  uint8_t bnegative = negative(b);
-  uint8_t babs = b - ((uint8_t)((-bnegative) & b) << 1);
-
-  ge_precomp_0(t);
-  cmov(t, &k25519Precomp[pos][0], equal(babs, 1));
-  cmov(t, &k25519Precomp[pos][1], equal(babs, 2));
-  cmov(t, &k25519Precomp[pos][2], equal(babs, 3));
-  cmov(t, &k25519Precomp[pos][3], equal(babs, 4));
-  cmov(t, &k25519Precomp[pos][4], equal(babs, 5));
-  cmov(t, &k25519Precomp[pos][5], equal(babs, 6));
-  cmov(t, &k25519Precomp[pos][6], equal(babs, 7));
-  cmov(t, &k25519Precomp[pos][7], equal(babs, 8));
-  fe_copy(minust.yplusx, t->yminusx);
-  fe_copy(minust.yminusx, t->yplusx);
-  fe_neg(minust.xy2d, t->xy2d);
-  cmov(t, &minust, bnegative);
+static void table_select(ge_precomp *t, int pos, signed char b)
+{
+    ge_precomp minust;
+    uint8_t bnegative = negative(b);
+    uint8_t babs = b - ((uint8_t)((-bnegative) & b) << 1);
+
+    ge_precomp_0(t);
+    cmov(t, &k25519Precomp[pos][0], equal(babs, 1));
+    cmov(t, &k25519Precomp[pos][1], equal(babs, 2));
+    cmov(t, &k25519Precomp[pos][2], equal(babs, 3));
+    cmov(t, &k25519Precomp[pos][3], equal(babs, 4));
+    cmov(t, &k25519Precomp[pos][4], equal(babs, 5));
+    cmov(t, &k25519Precomp[pos][5], equal(babs, 6));
+    cmov(t, &k25519Precomp[pos][6], equal(babs, 7));
+    cmov(t, &k25519Precomp[pos][7], equal(babs, 8));
+    fe_copy(minust.yplusx, t->yminusx);
+    fe_copy(minust.yminusx, t->yplusx);
+    fe_neg(minust.xy2d, t->xy2d);
+    cmov(t, &minust, bnegative);
 }
 
-/* h = a * B
+/*
+ * h = a * B
+ *
  * where a = a[0]+256*a[1]+...+256^31 a[31]
  * B is the Ed25519 base point (x,4/5) with x positive.
  *
  * Preconditions:
- *   a[31] <= 127 */
-static void ge_scalarmult_base(ge_p3 *h, const uint8_t *a) {
-  signed char e[64];
-  signed char carry;
-  ge_p1p1 r;
-  ge_p2 s;
-  ge_precomp t;
-  int i;
-
-  for (i = 0; i < 32; ++i) {
-    e[2 * i + 0] = (a[i] >> 0) & 15;
-    e[2 * i + 1] = (a[i] >> 4) & 15;
-  }
-  /* each e[i] is between 0 and 15 */
-  /* e[63] is between 0 and 7 */
-
-  carry = 0;
-  for (i = 0; i < 63; ++i) {
-    e[i] += carry;
-    carry = e[i] + 8;
-    carry >>= 4;
-    e[i] -= carry << 4;
-  }
-  e[63] += carry;
-  /* each e[i] is between -8 and 8 */
-
-  ge_p3_0(h);
-  for (i = 1; i < 64; i += 2) {
-    table_select(&t, i / 2, e[i]);
-    ge_madd(&r, h, &t);
-    ge_p1p1_to_p3(h, &r);
-  }
-
-  ge_p3_dbl(&r, h);
-  ge_p1p1_to_p2(&s, &r);
-  ge_p2_dbl(&r, &s);
-  ge_p1p1_to_p2(&s, &r);
-  ge_p2_dbl(&r, &s);
-  ge_p1p1_to_p2(&s, &r);
-  ge_p2_dbl(&r, &s);
-  ge_p1p1_to_p3(h, &r);
-
-  for (i = 0; i < 64; i += 2) {
-    table_select(&t, i / 2, e[i]);
-    ge_madd(&r, h, &t);
+ *   a[31] <= 127
+ */
+static void ge_scalarmult_base(ge_p3 *h, const uint8_t *a)
+{
+    signed char e[64];
+    signed char carry;
+    ge_p1p1 r;
+    ge_p2 s;
+    ge_precomp t;
+    int i;
+
+    for (i = 0; i < 32; ++i) {
+        e[2 * i + 0] = (a[i] >> 0) & 15;
+        e[2 * i + 1] = (a[i] >> 4) & 15;
+    }
+    /* each e[i] is between 0 and 15 */
+    /* e[63] is between 0 and 7 */
+
+    carry = 0;
+    for (i = 0; i < 63; ++i) {
+        e[i] += carry;
+        carry = e[i] + 8;
+        carry >>= 4;
+        e[i] -= carry << 4;
+    }
+    e[63] += carry;
+    /* each e[i] is between -8 and 8 */
+
+    ge_p3_0(h);
+    for (i = 1; i < 64; i += 2) {
+        table_select(&t, i / 2, e[i]);
+        ge_madd(&r, h, &t);
+        ge_p1p1_to_p3(h, &r);
+    }
+
+    ge_p3_dbl(&r, h);
+    ge_p1p1_to_p2(&s, &r);
+    ge_p2_dbl(&r, &s);
+    ge_p1p1_to_p2(&s, &r);
+    ge_p2_dbl(&r, &s);
+    ge_p1p1_to_p2(&s, &r);
+    ge_p2_dbl(&r, &s);
     ge_p1p1_to_p3(h, &r);
-  }
 
-  OPENSSL_cleanse(e, sizeof(e));
+    for (i = 0; i < 64; i += 2) {
+        table_select(&t, i / 2, e[i]);
+        ge_madd(&r, h, &t);
+        ge_p1p1_to_p3(h, &r);
+    }
+
+    OPENSSL_cleanse(e, sizeof(e));
 }
 
 #if !defined(BASE_2_51_IMPLEMENTED)
-/* Replace (f,g) with (g,f) if b == 1;
+/*
+ * Replace (f,g) with (g,f) if b == 1;
  * replace (f,g) with (f,g) if b == 0.
  *
- * Preconditions: b in {0,1}. */
-static void fe_cswap(fe f, fe g, unsigned int b) {
-  size_t i;
-  b = 0-b;
-  for (i = 0; i < 10; i++) {
-    int32_t x = f[i] ^ g[i];
-    x &= b;
-    f[i] ^= x;
-    g[i] ^= x;
-  }
+ * Preconditions: b in {0,1}.
+ */
+static void fe_cswap(fe f, fe g, unsigned int b)
+{
+    size_t i;
+
+    b = 0-b;
+    for (i = 0; i < 10; i++) {
+        int32_t x = f[i] ^ g[i];
+        x &= b;
+        f[i] ^= x;
+        g[i] ^= x;
+    }
 }
 
-/* h = f * 121666
+/*
+ * h = f * 121666
+ *
  * Can overlap h with f.
  *
  * Preconditions:
  *    |f| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc.
  *
  * Postconditions:
- *    |h| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc. */
-static void fe_mul121666(fe h, fe f) {
-  int32_t f0 = f[0];
-  int32_t f1 = f[1];
-  int32_t f2 = f[2];
-  int32_t f3 = f[3];
-  int32_t f4 = f[4];
-  int32_t f5 = f[5];
-  int32_t f6 = f[6];
-  int32_t f7 = f[7];
-  int32_t f8 = f[8];
-  int32_t f9 = f[9];
-  int64_t h0 = f0 * (int64_t) 121666;
-  int64_t h1 = f1 * (int64_t) 121666;
-  int64_t h2 = f2 * (int64_t) 121666;
-  int64_t h3 = f3 * (int64_t) 121666;
-  int64_t h4 = f4 * (int64_t) 121666;
-  int64_t h5 = f5 * (int64_t) 121666;
-  int64_t h6 = f6 * (int64_t) 121666;
-  int64_t h7 = f7 * (int64_t) 121666;
-  int64_t h8 = f8 * (int64_t) 121666;
-  int64_t h9 = f9 * (int64_t) 121666;
-  int64_t carry0;
-  int64_t carry1;
-  int64_t carry2;
-  int64_t carry3;
-  int64_t carry4;
-  int64_t carry5;
-  int64_t carry6;
-  int64_t carry7;
-  int64_t carry8;
-  int64_t carry9;
-
-  carry9 = h9 + (1 << 24); h0 += (carry9 >> 25) * 19; h9 -= carry9 & 
kTop39Bits;
-  carry1 = h1 + (1 << 24); h2 += carry1 >> 25; h1 -= carry1 & kTop39Bits;
-  carry3 = h3 + (1 << 24); h4 += carry3 >> 25; h3 -= carry3 & kTop39Bits;
-  carry5 = h5 + (1 << 24); h6 += carry5 >> 25; h5 -= carry5 & kTop39Bits;
-  carry7 = h7 + (1 << 24); h8 += carry7 >> 25; h7 -= carry7 & kTop39Bits;
-
-  carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits;
-  carry2 = h2 + (1 << 25); h3 += carry2 >> 26; h2 -= carry2 & kTop38Bits;
-  carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits;
-  carry6 = h6 + (1 << 25); h7 += carry6 >> 26; h6 -= carry6 & kTop38Bits;
-  carry8 = h8 + (1 << 25); h9 += carry8 >> 26; h8 -= carry8 & kTop38Bits;
-
-  h[0] = (int32_t)h0;
-  h[1] = (int32_t)h1;
-  h[2] = (int32_t)h2;
-  h[3] = (int32_t)h3;
-  h[4] = (int32_t)h4;
-  h[5] = (int32_t)h5;
-  h[6] = (int32_t)h6;
-  h[7] = (int32_t)h7;
-  h[8] = (int32_t)h8;
-  h[9] = (int32_t)h9;
+ *    |h| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
+ */
+static void fe_mul121666(fe h, fe f)
+{
+    int32_t f0 = f[0];
+    int32_t f1 = f[1];
+    int32_t f2 = f[2];
+    int32_t f3 = f[3];
+    int32_t f4 = f[4];
+    int32_t f5 = f[5];
+    int32_t f6 = f[6];
+    int32_t f7 = f[7];
+    int32_t f8 = f[8];
+    int32_t f9 = f[9];
+    int64_t h0 = f0 * (int64_t) 121666;
+    int64_t h1 = f1 * (int64_t) 121666;
+    int64_t h2 = f2 * (int64_t) 121666;
+    int64_t h3 = f3 * (int64_t) 121666;
+    int64_t h4 = f4 * (int64_t) 121666;
+    int64_t h5 = f5 * (int64_t) 121666;
+    int64_t h6 = f6 * (int64_t) 121666;
+    int64_t h7 = f7 * (int64_t) 121666;
+    int64_t h8 = f8 * (int64_t) 121666;
+    int64_t h9 = f9 * (int64_t) 121666;
+    int64_t carry0;
+    int64_t carry1;
+    int64_t carry2;
+    int64_t carry3;
+    int64_t carry4;
+    int64_t carry5;
+    int64_t carry6;
+    int64_t carry7;
+    int64_t carry8;
+    int64_t carry9;
+
+    carry9 = h9 + (1 << 24); h0 += (carry9 >> 25) * 19; h9 -= carry9 & 
kTop39Bits;
+    carry1 = h1 + (1 << 24); h2 += carry1 >> 25; h1 -= carry1 & kTop39Bits;
+    carry3 = h3 + (1 << 24); h4 += carry3 >> 25; h3 -= carry3 & kTop39Bits;
+    carry5 = h5 + (1 << 24); h6 += carry5 >> 25; h5 -= carry5 & kTop39Bits;
+    carry7 = h7 + (1 << 24); h8 += carry7 >> 25; h7 -= carry7 & kTop39Bits;
+
+    carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits;
+    carry2 = h2 + (1 << 25); h3 += carry2 >> 26; h2 -= carry2 & kTop38Bits;
+    carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits;
+    carry6 = h6 + (1 << 25); h7 += carry6 >> 26; h6 -= carry6 & kTop38Bits;
+    carry8 = h8 + (1 << 25); h9 += carry8 >> 26; h8 -= carry8 & kTop38Bits;
+
+    h[0] = (int32_t)h0;
+    h[1] = (int32_t)h1;
+    h[2] = (int32_t)h2;
+    h[3] = (int32_t)h3;
+    h[4] = (int32_t)h4;
+    h[5] = (int32_t)h5;
+    h[6] = (int32_t)h6;
+    h[7] = (int32_t)h7;
+    h[8] = (int32_t)h8;
+    h[9] = (int32_t)h9;
 }
 
 static void x25519_scalar_mult_generic(uint8_t out[32],
                                        const uint8_t scalar[32],
                                        const uint8_t point[32]) {
-  fe x1, x2, z2, x3, z3, tmp0, tmp1;
-  uint8_t e[32];
-  unsigned swap = 0;
-  int pos;
-
-  memcpy(e, scalar, 32);
-  e[0] &= 248;
-  e[31] &= 127;
-  e[31] |= 64;
-  fe_frombytes(x1, point);
-  fe_1(x2);
-  fe_0(z2);
-  fe_copy(x3, x1);
-  fe_1(z3);
-
-  for (pos = 254; pos >= 0; --pos) {
-    unsigned b = 1 & (e[pos / 8] >> (pos & 7));
-    swap ^= b;
-    fe_cswap(x2, x3, swap);
-    fe_cswap(z2, z3, swap);
-    swap = b;
-    fe_sub(tmp0, x3, z3);
-    fe_sub(tmp1, x2, z2);
-    fe_add(x2, x2, z2);
-    fe_add(z2, x3, z3);
-    fe_mul(z3, tmp0, x2);
-    fe_mul(z2, z2, tmp1);
-    fe_sq(tmp0, tmp1);
-    fe_sq(tmp1, x2);
-    fe_add(x3, z3, z2);
-    fe_sub(z2, z3, z2);
-    fe_mul(x2, tmp1, tmp0);
-    fe_sub(tmp1, tmp1, tmp0);
-    fe_sq(z2, z2);
-    fe_mul121666(z3, tmp1);
-    fe_sq(x3, x3);
-    fe_add(tmp0, tmp0, z3);
-    fe_mul(z3, x1, z2);
-    fe_mul(z2, tmp1, tmp0);
-  }
-
-  fe_invert(z2, z2);
-  fe_mul(x2, x2, z2);
-  fe_tobytes(out, x2);
-
-  OPENSSL_cleanse(e, sizeof(e));
+    fe x1, x2, z2, x3, z3, tmp0, tmp1;
+    uint8_t e[32];
+    unsigned swap = 0;
+    int pos;
+
+    memcpy(e, scalar, 32);
+    e[0] &= 248;
+    e[31] &= 127;
+    e[31] |= 64;
+    fe_frombytes(x1, point);
+    fe_1(x2);
+    fe_0(z2);
+    fe_copy(x3, x1);
+    fe_1(z3);
+
+    for (pos = 254; pos >= 0; --pos) {
+        unsigned b = 1 & (e[pos / 8] >> (pos & 7));
+        swap ^= b;
+        fe_cswap(x2, x3, swap);
+        fe_cswap(z2, z3, swap);
+        swap = b;
+        fe_sub(tmp0, x3, z3);
+        fe_sub(tmp1, x2, z2);
+        fe_add(x2, x2, z2);
+        fe_add(z2, x3, z3);
+        fe_mul(z3, tmp0, x2);
+        fe_mul(z2, z2, tmp1);
+        fe_sq(tmp0, tmp1);
+        fe_sq(tmp1, x2);
+        fe_add(x3, z3, z2);
+        fe_sub(z2, z3, z2);
+        fe_mul(x2, tmp1, tmp0);
+        fe_sub(tmp1, tmp1, tmp0);
+        fe_sq(z2, z2);
+        fe_mul121666(z3, tmp1);
+        fe_sq(x3, x3);
+        fe_add(tmp0, tmp0, z3);
+        fe_mul(z3, x1, z2);
+        fe_mul(z2, tmp1, tmp0);
+    }
+
+    fe_invert(z2, z2);
+    fe_mul(x2, x2, z2);
+    fe_tobytes(out, x2);
+
+    OPENSSL_cleanse(e, sizeof(e));
 }
 
 static void x25519_scalar_mult(uint8_t out[32], const uint8_t scalar[32],
                                const uint8_t point[32]) {
-  x25519_scalar_mult_generic(out, scalar, point);
+    x25519_scalar_mult_generic(out, scalar, point);
 }
 #endif
 
-static void slide(signed char *r, const uint8_t *a) {
-  int i;
-  int b;
-  int k;
-
-  for (i = 0; i < 256; ++i) {
-    r[i] = 1 & (a[i >> 3] >> (i & 7));
-  }
-
-  for (i = 0; i < 256; ++i) {
-    if (r[i]) {
-      for (b = 1; b <= 6 && i + b < 256; ++b) {
-        if (r[i + b]) {
-          if (r[i] + (r[i + b] << b) <= 15) {
-            r[i] += r[i + b] << b;
-            r[i + b] = 0;
-          } else if (r[i] - (r[i + b] << b) >= -15) {
-            r[i] -= r[i + b] << b;
-            for (k = i + b; k < 256; ++k) {
-              if (!r[k]) {
-                r[k] = 1;
-                break;
-              }
-              r[k] = 0;
+static void slide(signed char *r, const uint8_t *a)
+{
+    int i;
+    int b;
+    int k;
+
+    for (i = 0; i < 256; ++i) {
+        r[i] = 1 & (a[i >> 3] >> (i & 7));
+    }
+
+    for (i = 0; i < 256; ++i) {
+        if (r[i]) {
+            for (b = 1; b <= 6 && i + b < 256; ++b) {
+                if (r[i + b]) {
+                    if (r[i] + (r[i + b] << b) <= 15) {
+                        r[i] += r[i + b] << b;
+                        r[i + b] = 0;
+                    } else if (r[i] - (r[i + b] << b) >= -15) {
+                        r[i] -= r[i + b] << b;
+                        for (k = i + b; k < 256; ++k) {
+                            if (!r[k]) {
+                                r[k] = 1;
+                                break;
+                            }
+                            r[k] = 0;
+                        }
+                    } else {
+                        break;
+                    }
+                }
             }
-          } else {
-            break;
-          }
         }
-      }
     }
-  }
 }
 
 static const ge_precomp Bi[8] = {
@@ -4425,1066 +4522,1075 @@ static const ge_precomp Bi[8] = {
     },
 };
 
-/* r = a * A + b * B
+/*
+ * r = a * A + b * B
+ *
  * where a = a[0]+256*a[1]+...+256^31 a[31].
  * and b = b[0]+256*b[1]+...+256^31 b[31].
- * B is the Ed25519 base point (x,4/5) with x positive. */
+ * B is the Ed25519 base point (x,4/5) with x positive.
+ */
 static void ge_double_scalarmult_vartime(ge_p2 *r, const uint8_t *a,
-                                         const ge_p3 *A, const uint8_t *b) {
-  signed char aslide[256];
-  signed char bslide[256];
-  ge_cached Ai[8]; /* A,3A,5A,7A,9A,11A,13A,15A */
-  ge_p1p1 t;
-  ge_p3 u;
-  ge_p3 A2;
-  int i;
-
-  slide(aslide, a);
-  slide(bslide, b);
-
-  ge_p3_to_cached(&Ai[0], A);
-  ge_p3_dbl(&t, A);
-  ge_p1p1_to_p3(&A2, &t);
-  ge_add(&t, &A2, &Ai[0]);
-  ge_p1p1_to_p3(&u, &t);
-  ge_p3_to_cached(&Ai[1], &u);
-  ge_add(&t, &A2, &Ai[1]);
-  ge_p1p1_to_p3(&u, &t);
-  ge_p3_to_cached(&Ai[2], &u);
-  ge_add(&t, &A2, &Ai[2]);
-  ge_p1p1_to_p3(&u, &t);
-  ge_p3_to_cached(&Ai[3], &u);
-  ge_add(&t, &A2, &Ai[3]);
-  ge_p1p1_to_p3(&u, &t);
-  ge_p3_to_cached(&Ai[4], &u);
-  ge_add(&t, &A2, &Ai[4]);
-  ge_p1p1_to_p3(&u, &t);
-  ge_p3_to_cached(&Ai[5], &u);
-  ge_add(&t, &A2, &Ai[5]);
-  ge_p1p1_to_p3(&u, &t);
-  ge_p3_to_cached(&Ai[6], &u);
-  ge_add(&t, &A2, &Ai[6]);
-  ge_p1p1_to_p3(&u, &t);
-  ge_p3_to_cached(&Ai[7], &u);
-
-  ge_p2_0(r);
-
-  for (i = 255; i >= 0; --i) {
-    if (aslide[i] || bslide[i]) {
-      break;
+                                         const ge_p3 *A, const uint8_t *b)
+{
+    signed char aslide[256];
+    signed char bslide[256];
+    ge_cached Ai[8]; /* A,3A,5A,7A,9A,11A,13A,15A */
+    ge_p1p1 t;
+    ge_p3 u;
+    ge_p3 A2;
+    int i;
+
+    slide(aslide, a);
+    slide(bslide, b);
+
+    ge_p3_to_cached(&Ai[0], A);
+    ge_p3_dbl(&t, A);
+    ge_p1p1_to_p3(&A2, &t);
+    ge_add(&t, &A2, &Ai[0]);
+    ge_p1p1_to_p3(&u, &t);
+    ge_p3_to_cached(&Ai[1], &u);
+    ge_add(&t, &A2, &Ai[1]);
+    ge_p1p1_to_p3(&u, &t);
+    ge_p3_to_cached(&Ai[2], &u);
+    ge_add(&t, &A2, &Ai[2]);
+    ge_p1p1_to_p3(&u, &t);
+    ge_p3_to_cached(&Ai[3], &u);
+    ge_add(&t, &A2, &Ai[3]);
+    ge_p1p1_to_p3(&u, &t);
+    ge_p3_to_cached(&Ai[4], &u);
+    ge_add(&t, &A2, &Ai[4]);
+    ge_p1p1_to_p3(&u, &t);
+    ge_p3_to_cached(&Ai[5], &u);
+    ge_add(&t, &A2, &Ai[5]);
+    ge_p1p1_to_p3(&u, &t);
+    ge_p3_to_cached(&Ai[6], &u);
+    ge_add(&t, &A2, &Ai[6]);
+    ge_p1p1_to_p3(&u, &t);
+    ge_p3_to_cached(&Ai[7], &u);
+
+    ge_p2_0(r);
+
+    for (i = 255; i >= 0; --i) {
+        if (aslide[i] || bslide[i]) {
+            break;
+        }
     }
-  }
 
-  for (; i >= 0; --i) {
-    ge_p2_dbl(&t, r);
+    for (; i >= 0; --i) {
+        ge_p2_dbl(&t, r);
 
-    if (aslide[i] > 0) {
-      ge_p1p1_to_p3(&u, &t);
-      ge_add(&t, &u, &Ai[aslide[i] / 2]);
-    } else if (aslide[i] < 0) {
-      ge_p1p1_to_p3(&u, &t);
-      ge_sub(&t, &u, &Ai[(-aslide[i]) / 2]);
-    }
+        if (aslide[i] > 0) {
+            ge_p1p1_to_p3(&u, &t);
+            ge_add(&t, &u, &Ai[aslide[i] / 2]);
+        } else if (aslide[i] < 0) {
+            ge_p1p1_to_p3(&u, &t);
+            ge_sub(&t, &u, &Ai[(-aslide[i]) / 2]);
+        }
 
-    if (bslide[i] > 0) {
-      ge_p1p1_to_p3(&u, &t);
-      ge_madd(&t, &u, &Bi[bslide[i] / 2]);
-    } else if (bslide[i] < 0) {
-      ge_p1p1_to_p3(&u, &t);
-      ge_msub(&t, &u, &Bi[(-bslide[i]) / 2]);
-    }
+        if (bslide[i] > 0) {
+            ge_p1p1_to_p3(&u, &t);
+            ge_madd(&t, &u, &Bi[bslide[i] / 2]);
+        } else if (bslide[i] < 0) {
+            ge_p1p1_to_p3(&u, &t);
+            ge_msub(&t, &u, &Bi[(-bslide[i]) / 2]);
+        }
 
-    ge_p1p1_to_p2(r, &t);
-  }
+        ge_p1p1_to_p2(r, &t);
+    }
 }
 
-/* The set of scalars is \Z/l
- * where l = 2^252 + 27742317777372353535851937790883648493. */
-
-/* Input:
+/*
+ * The set of scalars is \Z/l
+ * where l = 2^252 + 27742317777372353535851937790883648493.
+ *
+ * Input:
  *   s[0]+256*s[1]+...+256^63*s[63] = s
  *
  * Output:
  *   s[0]+256*s[1]+...+256^31*s[31] = s mod l
  *   where l = 2^252 + 27742317777372353535851937790883648493.
- *   Overwrites s in place. */
-static void x25519_sc_reduce(uint8_t *s) {
-  int64_t s0 = 2097151 & load_3(s);
-  int64_t s1 = 2097151 & (load_4(s + 2) >> 5);
-  int64_t s2 = 2097151 & (load_3(s + 5) >> 2);
-  int64_t s3 = 2097151 & (load_4(s + 7) >> 7);
-  int64_t s4 = 2097151 & (load_4(s + 10) >> 4);
-  int64_t s5 = 2097151 & (load_3(s + 13) >> 1);
-  int64_t s6 = 2097151 & (load_4(s + 15) >> 6);
-  int64_t s7 = 2097151 & (load_3(s + 18) >> 3);
-  int64_t s8 = 2097151 & load_3(s + 21);
-  int64_t s9 = 2097151 & (load_4(s + 23) >> 5);
-  int64_t s10 = 2097151 & (load_3(s + 26) >> 2);
-  int64_t s11 = 2097151 & (load_4(s + 28) >> 7);
-  int64_t s12 = 2097151 & (load_4(s + 31) >> 4);
-  int64_t s13 = 2097151 & (load_3(s + 34) >> 1);
-  int64_t s14 = 2097151 & (load_4(s + 36) >> 6);
-  int64_t s15 = 2097151 & (load_3(s + 39) >> 3);
-  int64_t s16 = 2097151 & load_3(s + 42);
-  int64_t s17 = 2097151 & (load_4(s + 44) >> 5);
-  int64_t s18 = 2097151 & (load_3(s + 47) >> 2);
-  int64_t s19 = 2097151 & (load_4(s + 49) >> 7);
-  int64_t s20 = 2097151 & (load_4(s + 52) >> 4);
-  int64_t s21 = 2097151 & (load_3(s + 55) >> 1);
-  int64_t s22 = 2097151 & (load_4(s + 57) >> 6);
-  int64_t s23 = (load_4(s + 60) >> 3);
-  int64_t carry0;
-  int64_t carry1;
-  int64_t carry2;
-  int64_t carry3;
-  int64_t carry4;
-  int64_t carry5;
-  int64_t carry6;
-  int64_t carry7;
-  int64_t carry8;
-  int64_t carry9;
-  int64_t carry10;
-  int64_t carry11;
-  int64_t carry12;
-  int64_t carry13;
-  int64_t carry14;
-  int64_t carry15;
-  int64_t carry16;
-
-  s11 += s23 * 666643;
-  s12 += s23 * 470296;
-  s13 += s23 * 654183;
-  s14 -= s23 * 997805;
-  s15 += s23 * 136657;
-  s16 -= s23 * 683901;
-  s23 = 0;
-
-  s10 += s22 * 666643;
-  s11 += s22 * 470296;
-  s12 += s22 * 654183;
-  s13 -= s22 * 997805;
-  s14 += s22 * 136657;
-  s15 -= s22 * 683901;
-  s22 = 0;
-
-  s9 += s21 * 666643;
-  s10 += s21 * 470296;
-  s11 += s21 * 654183;
-  s12 -= s21 * 997805;
-  s13 += s21 * 136657;
-  s14 -= s21 * 683901;
-  s21 = 0;
-
-  s8 += s20 * 666643;
-  s9 += s20 * 470296;
-  s10 += s20 * 654183;
-  s11 -= s20 * 997805;
-  s12 += s20 * 136657;
-  s13 -= s20 * 683901;
-  s20 = 0;
-
-  s7 += s19 * 666643;
-  s8 += s19 * 470296;
-  s9 += s19 * 654183;
-  s10 -= s19 * 997805;
-  s11 += s19 * 136657;
-  s12 -= s19 * 683901;
-  s19 = 0;
-
-  s6 += s18 * 666643;
-  s7 += s18 * 470296;
-  s8 += s18 * 654183;
-  s9 -= s18 * 997805;
-  s10 += s18 * 136657;
-  s11 -= s18 * 683901;
-  s18 = 0;
-
-  carry6 = (s6 + (1 << 20)) >> 21;
-  s7 += carry6;
-  s6 -= carry6 * (1 << 21);
-  carry8 = (s8 + (1 << 20)) >> 21;
-  s9 += carry8;
-  s8 -= carry8 * (1 << 21);
-  carry10 = (s10 + (1 << 20)) >> 21;
-  s11 += carry10;
-  s10 -= carry10 * (1 << 21);
-  carry12 = (s12 + (1 << 20)) >> 21;
-  s13 += carry12;
-  s12 -= carry12 * (1 << 21);
-  carry14 = (s14 + (1 << 20)) >> 21;
-  s15 += carry14;
-  s14 -= carry14 * (1 << 21);
-  carry16 = (s16 + (1 << 20)) >> 21;
-  s17 += carry16;
-  s16 -= carry16 * (1 << 21);
-
-  carry7 = (s7 + (1 << 20)) >> 21;
-  s8 += carry7;
-  s7 -= carry7 * (1 << 21);
-  carry9 = (s9 + (1 << 20)) >> 21;
-  s10 += carry9;
-  s9 -= carry9 * (1 << 21);
-  carry11 = (s11 + (1 << 20)) >> 21;
-  s12 += carry11;
-  s11 -= carry11 * (1 << 21);
-  carry13 = (s13 + (1 << 20)) >> 21;
-  s14 += carry13;
-  s13 -= carry13 * (1 << 21);
-  carry15 = (s15 + (1 << 20)) >> 21;
-  s16 += carry15;
-  s15 -= carry15 * (1 << 21);
-
-  s5 += s17 * 666643;
-  s6 += s17 * 470296;
-  s7 += s17 * 654183;
-  s8 -= s17 * 997805;
-  s9 += s17 * 136657;
-  s10 -= s17 * 683901;
-  s17 = 0;
-
-  s4 += s16 * 666643;
-  s5 += s16 * 470296;
-  s6 += s16 * 654183;
-  s7 -= s16 * 997805;
-  s8 += s16 * 136657;
-  s9 -= s16 * 683901;
-  s16 = 0;
-
-  s3 += s15 * 666643;
-  s4 += s15 * 470296;
-  s5 += s15 * 654183;
-  s6 -= s15 * 997805;
-  s7 += s15 * 136657;
-  s8 -= s15 * 683901;
-  s15 = 0;
-
-  s2 += s14 * 666643;
-  s3 += s14 * 470296;
-  s4 += s14 * 654183;
-  s5 -= s14 * 997805;
-  s6 += s14 * 136657;
-  s7 -= s14 * 683901;
-  s14 = 0;
-
-  s1 += s13 * 666643;
-  s2 += s13 * 470296;
-  s3 += s13 * 654183;
-  s4 -= s13 * 997805;
-  s5 += s13 * 136657;
-  s6 -= s13 * 683901;
-  s13 = 0;
-
-  s0 += s12 * 666643;
-  s1 += s12 * 470296;
-  s2 += s12 * 654183;
-  s3 -= s12 * 997805;
-  s4 += s12 * 136657;
-  s5 -= s12 * 683901;
-  s12 = 0;
-
-  carry0 = (s0 + (1 << 20)) >> 21;
-  s1 += carry0;
-  s0 -= carry0 * (1 << 21);
-  carry2 = (s2 + (1 << 20)) >> 21;
-  s3 += carry2;
-  s2 -= carry2 * (1 << 21);
-  carry4 = (s4 + (1 << 20)) >> 21;
-  s5 += carry4;
-  s4 -= carry4 * (1 << 21);
-  carry6 = (s6 + (1 << 20)) >> 21;
-  s7 += carry6;
-  s6 -= carry6 * (1 << 21);
-  carry8 = (s8 + (1 << 20)) >> 21;
-  s9 += carry8;
-  s8 -= carry8 * (1 << 21);
-  carry10 = (s10 + (1 << 20)) >> 21;
-  s11 += carry10;
-  s10 -= carry10 * (1 << 21);
-
-  carry1 = (s1 + (1 << 20)) >> 21;
-  s2 += carry1;
-  s1 -= carry1 * (1 << 21);
-  carry3 = (s3 + (1 << 20)) >> 21;
-  s4 += carry3;
-  s3 -= carry3 * (1 << 21);
-  carry5 = (s5 + (1 << 20)) >> 21;
-  s6 += carry5;
-  s5 -= carry5 * (1 << 21);
-  carry7 = (s7 + (1 << 20)) >> 21;
-  s8 += carry7;
-  s7 -= carry7 * (1 << 21);
-  carry9 = (s9 + (1 << 20)) >> 21;
-  s10 += carry9;
-  s9 -= carry9 * (1 << 21);
-  carry11 = (s11 + (1 << 20)) >> 21;
-  s12 += carry11;
-  s11 -= carry11 * (1 << 21);
-
-  s0 += s12 * 666643;
-  s1 += s12 * 470296;
-  s2 += s12 * 654183;
-  s3 -= s12 * 997805;
-  s4 += s12 * 136657;
-  s5 -= s12 * 683901;
-  s12 = 0;
-
-  carry0 = s0 >> 21;
-  s1 += carry0;
-  s0 -= carry0 * (1 << 21);
-  carry1 = s1 >> 21;
-  s2 += carry1;
-  s1 -= carry1 * (1 << 21);
-  carry2 = s2 >> 21;
-  s3 += carry2;
-  s2 -= carry2 * (1 << 21);
-  carry3 = s3 >> 21;
-  s4 += carry3;
-  s3 -= carry3 * (1 << 21);
-  carry4 = s4 >> 21;
-  s5 += carry4;
-  s4 -= carry4 * (1 << 21);
-  carry5 = s5 >> 21;
-  s6 += carry5;
-  s5 -= carry5 * (1 << 21);
-  carry6 = s6 >> 21;
-  s7 += carry6;
-  s6 -= carry6 * (1 << 21);
-  carry7 = s7 >> 21;
-  s8 += carry7;
-  s7 -= carry7 * (1 << 21);
-  carry8 = s8 >> 21;
-  s9 += carry8;
-  s8 -= carry8 * (1 << 21);
-  carry9 = s9 >> 21;
-  s10 += carry9;
-  s9 -= carry9 * (1 << 21);
-  carry10 = s10 >> 21;
-  s11 += carry10;
-  s10 -= carry10 * (1 << 21);
-  carry11 = s11 >> 21;
-  s12 += carry11;
-  s11 -= carry11 * (1 << 21);
-
-  s0 += s12 * 666643;
-  s1 += s12 * 470296;
-  s2 += s12 * 654183;
-  s3 -= s12 * 997805;
-  s4 += s12 * 136657;
-  s5 -= s12 * 683901;
-  s12 = 0;
-
-  carry0 = s0 >> 21;
-  s1 += carry0;
-  s0 -= carry0 * (1 << 21);
-  carry1 = s1 >> 21;
-  s2 += carry1;
-  s1 -= carry1 * (1 << 21);
-  carry2 = s2 >> 21;
-  s3 += carry2;
-  s2 -= carry2 * (1 << 21);
-  carry3 = s3 >> 21;
-  s4 += carry3;
-  s3 -= carry3 * (1 << 21);
-  carry4 = s4 >> 21;
-  s5 += carry4;
-  s4 -= carry4 * (1 << 21);
-  carry5 = s5 >> 21;
-  s6 += carry5;
-  s5 -= carry5 * (1 << 21);
-  carry6 = s6 >> 21;
-  s7 += carry6;
-  s6 -= carry6 * (1 << 21);
-  carry7 = s7 >> 21;
-  s8 += carry7;
-  s7 -= carry7 * (1 << 21);
-  carry8 = s8 >> 21;
-  s9 += carry8;
-  s8 -= carry8 * (1 << 21);
-  carry9 = s9 >> 21;
-  s10 += carry9;
-  s9 -= carry9 * (1 << 21);
-  carry10 = s10 >> 21;
-  s11 += carry10;
-  s10 -= carry10 * (1 << 21);
-
-  s[0] = (uint8_t)(s0 >> 0);
-  s[1] = (uint8_t)(s0 >> 8);
-  s[2] = (uint8_t)((s0 >> 16) | (s1 << 5));
-  s[3] = (uint8_t)(s1 >> 3);
-  s[4] = (uint8_t)(s1 >> 11);
-  s[5] = (uint8_t)((s1 >> 19) | (s2 << 2));
-  s[6] = (uint8_t)(s2 >> 6);
-  s[7] = (uint8_t)((s2 >> 14) | (s3 << 7));
-  s[8] = (uint8_t)(s3 >> 1);
-  s[9] = (uint8_t)(s3 >> 9);
-  s[10] = (uint8_t)((s3 >> 17) | (s4 << 4));
-  s[11] = (uint8_t)(s4 >> 4);
-  s[12] = (uint8_t)(s4 >> 12);
-  s[13] = (uint8_t)((s4 >> 20) | (s5 << 1));
-  s[14] = (uint8_t)(s5 >> 7);
-  s[15] = (uint8_t)((s5 >> 15) | (s6 << 6));
-  s[16] = (uint8_t)(s6 >> 2);
-  s[17] = (uint8_t)(s6 >> 10);
-  s[18] = (uint8_t)((s6 >> 18) | (s7 << 3));
-  s[19] = (uint8_t)(s7 >> 5);
-  s[20] = (uint8_t)(s7 >> 13);
-  s[21] = (uint8_t)(s8 >> 0);
-  s[22] = (uint8_t)(s8 >> 8);
-  s[23] = (uint8_t)((s8 >> 16) | (s9 << 5));
-  s[24] = (uint8_t)(s9 >> 3);
-  s[25] = (uint8_t)(s9 >> 11);
-  s[26] = (uint8_t)((s9 >> 19) | (s10 << 2));
-  s[27] = (uint8_t)(s10 >> 6);
-  s[28] = (uint8_t)((s10 >> 14) | (s11 << 7));
-  s[29] = (uint8_t)(s11 >> 1);
-  s[30] = (uint8_t)(s11 >> 9);
-  s[31] = (uint8_t)(s11 >> 17);
+ *   Overwrites s in place.
+*/
+static void x25519_sc_reduce(uint8_t *s)
+{
+    int64_t s0  = kBottom21Bits &  load_3(s);
+    int64_t s1  = kBottom21Bits & (load_4(s +  2) >> 5);
+    int64_t s2  = kBottom21Bits & (load_3(s +  5) >> 2);
+    int64_t s3  = kBottom21Bits & (load_4(s +  7) >> 7);
+    int64_t s4  = kBottom21Bits & (load_4(s + 10) >> 4);
+    int64_t s5  = kBottom21Bits & (load_3(s + 13) >> 1);
+    int64_t s6  = kBottom21Bits & (load_4(s + 15) >> 6);
+    int64_t s7  = kBottom21Bits & (load_3(s + 18) >> 3);
+    int64_t s8  = kBottom21Bits &  load_3(s + 21);
+    int64_t s9  = kBottom21Bits & (load_4(s + 23) >> 5);
+    int64_t s10 = kBottom21Bits & (load_3(s + 26) >> 2);
+    int64_t s11 = kBottom21Bits & (load_4(s + 28) >> 7);
+    int64_t s12 = kBottom21Bits & (load_4(s + 31) >> 4);
+    int64_t s13 = kBottom21Bits & (load_3(s + 34) >> 1);
+    int64_t s14 = kBottom21Bits & (load_4(s + 36) >> 6);
+    int64_t s15 = kBottom21Bits & (load_3(s + 39) >> 3);
+    int64_t s16 = kBottom21Bits &  load_3(s + 42);
+    int64_t s17 = kBottom21Bits & (load_4(s + 44) >> 5);
+    int64_t s18 = kBottom21Bits & (load_3(s + 47) >> 2);
+    int64_t s19 = kBottom21Bits & (load_4(s + 49) >> 7);
+    int64_t s20 = kBottom21Bits & (load_4(s + 52) >> 4);
+    int64_t s21 = kBottom21Bits & (load_3(s + 55) >> 1);
+    int64_t s22 = kBottom21Bits & (load_4(s + 57) >> 6);
+    int64_t s23 =                 (load_4(s + 60) >> 3);
+    int64_t carry0;
+    int64_t carry1;
+    int64_t carry2;
+    int64_t carry3;
+    int64_t carry4;
+    int64_t carry5;
+    int64_t carry6;
+    int64_t carry7;
+    int64_t carry8;
+    int64_t carry9;
+    int64_t carry10;
+    int64_t carry11;
+    int64_t carry12;
+    int64_t carry13;
+    int64_t carry14;
+    int64_t carry15;
+    int64_t carry16;
+
+    s11 += s23 * 666643;
+    s12 += s23 * 470296;
+    s13 += s23 * 654183;
+    s14 -= s23 * 997805;
+    s15 += s23 * 136657;
+    s16 -= s23 * 683901;
+    s23  = 0;
+
+    s10 += s22 * 666643;
+    s11 += s22 * 470296;
+    s12 += s22 * 654183;
+    s13 -= s22 * 997805;
+    s14 += s22 * 136657;
+    s15 -= s22 * 683901;
+    s22  = 0;
+
+    s9  += s21 * 666643;
+    s10 += s21 * 470296;
+    s11 += s21 * 654183;
+    s12 -= s21 * 997805;
+    s13 += s21 * 136657;
+    s14 -= s21 * 683901;
+    s21  = 0;
+
+    s8  += s20 * 666643;
+    s9  += s20 * 470296;
+    s10 += s20 * 654183;
+    s11 -= s20 * 997805;
+    s12 += s20 * 136657;
+    s13 -= s20 * 683901;
+    s20  = 0;
+
+    s7  += s19 * 666643;
+    s8  += s19 * 470296;
+    s9  += s19 * 654183;
+    s10 -= s19 * 997805;
+    s11 += s19 * 136657;
+    s12 -= s19 * 683901;
+    s19  = 0;
+
+    s6  += s18 * 666643;
+    s7  += s18 * 470296;
+    s8  += s18 * 654183;
+    s9  -= s18 * 997805;
+    s10 += s18 * 136657;
+    s11 -= s18 * 683901;
+    s18  = 0;
+
+    carry6 = (s6 + (1 << 20)) >> 21;
+    s7  += carry6;
+    s6  -= carry6 * (1 << 21);
+    carry8 = (s8 + (1 << 20)) >> 21;
+    s9  += carry8;
+    s8  -= carry8 * (1 << 21);
+    carry10 = (s10 + (1 << 20)) >> 21;
+    s11 += carry10;
+    s10 -= carry10 * (1 << 21);
+    carry12 = (s12 + (1 << 20)) >> 21;
+    s13 += carry12;
+    s12 -= carry12 * (1 << 21);
+    carry14 = (s14 + (1 << 20)) >> 21;
+    s15 += carry14;
+    s14 -= carry14 * (1 << 21);
+    carry16 = (s16 + (1 << 20)) >> 21;
+    s17 += carry16;
+    s16 -= carry16 * (1 << 21);
+
+    carry7 = (s7 + (1 << 20)) >> 21;
+    s8  += carry7;
+    s7  -= carry7 * (1 << 21);
+    carry9 = (s9 + (1 << 20)) >> 21;
+    s10 += carry9;
+    s9  -= carry9 * (1 << 21);
+    carry11 = (s11 + (1 << 20)) >> 21;
+    s12 += carry11;
+    s11 -= carry11 * (1 << 21);
+    carry13 = (s13 + (1 << 20)) >> 21;
+    s14 += carry13;
+    s13 -= carry13 * (1 << 21);
+    carry15 = (s15 + (1 << 20)) >> 21;
+    s16 += carry15;
+    s15 -= carry15 * (1 << 21);
+
+    s5  += s17 * 666643;
+    s6  += s17 * 470296;
+    s7  += s17 * 654183;
+    s8  -= s17 * 997805;
+    s9  += s17 * 136657;
+    s10 -= s17 * 683901;
+    s17  = 0;
+
+    s4  += s16 * 666643;
+    s5  += s16 * 470296;
+    s6  += s16 * 654183;
+    s7  -= s16 * 997805;
+    s8  += s16 * 136657;
+    s9  -= s16 * 683901;
+    s16  = 0;
+
+    s3  += s15 * 666643;
+    s4  += s15 * 470296;
+    s5  += s15 * 654183;
+    s6  -= s15 * 997805;
+    s7  += s15 * 136657;
+    s8  -= s15 * 683901;
+    s15  = 0;
+
+    s2  += s14 * 666643;
+    s3  += s14 * 470296;
+    s4  += s14 * 654183;
+    s5  -= s14 * 997805;
+    s6  += s14 * 136657;
+    s7  -= s14 * 683901;
+    s14  = 0;
+
+    s1  += s13 * 666643;
+    s2  += s13 * 470296;
+    s3  += s13 * 654183;
+    s4  -= s13 * 997805;
+    s5  += s13 * 136657;
+    s6  -= s13 * 683901;
+    s13  = 0;
+
+    s0  += s12 * 666643;
+    s1  += s12 * 470296;
+    s2  += s12 * 654183;
+    s3  -= s12 * 997805;
+    s4  += s12 * 136657;
+    s5  -= s12 * 683901;
+    s12  = 0;
+
+    carry0 = (s0 + (1 << 20)) >> 21;
+    s1  += carry0;
+    s0  -= carry0 * (1 << 21);
+    carry2 = (s2 + (1 << 20)) >> 21;
+    s3  += carry2;
+    s2  -= carry2 * (1 << 21);
+    carry4 = (s4 + (1 << 20)) >> 21;
+    s5  += carry4;
+    s4  -= carry4 * (1 << 21);
+    carry6 = (s6 + (1 << 20)) >> 21;
+    s7 += carry6;
+    s6 -= carry6 * (1 << 21);
+    carry8 = (s8 + (1 << 20)) >> 21;
+    s9  += carry8;
+    s8  -= carry8 * (1 << 21);
+    carry10 = (s10 + (1 << 20)) >> 21;
+    s11 += carry10;
+    s10 -= carry10 * (1 << 21);
+
+    carry1 = (s1 + (1 << 20)) >> 21;
+    s2  += carry1;
+    s1  -= carry1 * (1 << 21);
+    carry3 = (s3 + (1 << 20)) >> 21;
+    s4  += carry3;
+    s3  -= carry3 * (1 << 21);
+    carry5 = (s5 + (1 << 20)) >> 21;
+    s6  += carry5;
+    s5  -= carry5 * (1 << 21);
+    carry7 = (s7 + (1 << 20)) >> 21;
+    s8  += carry7;
+    s7  -= carry7 * (1 << 21);
+    carry9 = (s9 + (1 << 20)) >> 21;
+    s10 += carry9;
+    s9  -= carry9 * (1 << 21);
+    carry11 = (s11 + (1 << 20)) >> 21;
+    s12 += carry11;
+    s11 -= carry11 * (1 << 21);
+
+    s0  += s12 * 666643;
+    s1  += s12 * 470296;
+    s2  += s12 * 654183;
+    s3  -= s12 * 997805;
+    s4  += s12 * 136657;
+    s5  -= s12 * 683901;
+    s12  = 0;
+
+    carry0 = s0 >> 21;
+    s1  += carry0;
+    s0  -= carry0 * (1 << 21);
+    carry1 = s1 >> 21;
+    s2  += carry1;
+    s1  -= carry1 * (1 << 21);
+    carry2 = s2 >> 21;
+    s3  += carry2;
+    s2  -= carry2 * (1 << 21);
+    carry3 = s3 >> 21;
+    s4  += carry3;
+    s3  -= carry3 * (1 << 21);
+    carry4 = s4 >> 21;
+    s5  += carry4;
+    s4  -= carry4 * (1 << 21);
+    carry5 = s5 >> 21;
+    s6  += carry5;
+    s5  -= carry5 * (1 << 21);
+    carry6 = s6 >> 21;
+    s7  += carry6;
+    s6  -= carry6 * (1 << 21);
+    carry7 = s7 >> 21;
+    s8  += carry7;
+    s7  -= carry7 * (1 << 21);
+    carry8 = s8 >> 21;
+    s9  += carry8;
+    s8  -= carry8 * (1 << 21);
+    carry9 = s9 >> 21;
+    s10 += carry9;
+    s9  -= carry9 * (1 << 21);
+    carry10 = s10 >> 21;
+    s11 += carry10;
+    s10 -= carry10 * (1 << 21);
+    carry11 = s11 >> 21;
+    s12 += carry11;
+    s11 -= carry11 * (1 << 21);
+
+    s0  += s12 * 666643;
+    s1  += s12 * 470296;
+    s2  += s12 * 654183;
+    s3  -= s12 * 997805;
+    s4  += s12 * 136657;
+    s5  -= s12 * 683901;
+    s12  = 0;
+
+    carry0 = s0 >> 21;
+    s1  += carry0;
+    s0  -= carry0 * (1 << 21);
+    carry1 = s1 >> 21;
+    s2  += carry1;
+    s1  -= carry1 * (1 << 21);
+    carry2 = s2 >> 21;
+    s3  += carry2;
+    s2  -= carry2 * (1 << 21);
+    carry3 = s3 >> 21;
+    s4  += carry3;
+    s3  -= carry3 * (1 << 21);
+    carry4 = s4 >> 21;
+    s5  += carry4;
+    s4  -= carry4 * (1 << 21);
+    carry5 = s5 >> 21;
+    s6  += carry5;
+    s5  -= carry5 * (1 << 21);
+    carry6 = s6 >> 21;
+    s7  += carry6;
+    s6  -= carry6 * (1 << 21);
+    carry7 = s7 >> 21;
+    s8  += carry7;
+    s7  -= carry7 * (1 << 21);
+    carry8 = s8 >> 21;
+    s9  += carry8;
+    s8  -= carry8 * (1 << 21);
+    carry9 = s9 >> 21;
+    s10 += carry9;
+    s9  -= carry9 * (1 << 21);
+    carry10 = s10 >> 21;
+    s11 += carry10;
+    s10 -= carry10 * (1 << 21);
+
+    s[ 0] = (uint8_t) (s0  >>  0);
+    s[ 1] = (uint8_t) (s0  >>  8);
+    s[ 2] = (uint8_t)((s0  >> 16) | (s1  <<  5));
+    s[ 3] = (uint8_t) (s1  >>  3);
+    s[ 4] = (uint8_t) (s1  >> 11);
+    s[ 5] = (uint8_t)((s1  >> 19) | (s2  <<  2));
+    s[ 6] = (uint8_t) (s2  >>  6);
+    s[ 7] = (uint8_t)((s2  >> 14) | (s3  <<  7));
+    s[ 8] = (uint8_t) (s3  >>  1);
+    s[ 9] = (uint8_t) (s3  >>  9);
+    s[10] = (uint8_t)((s3  >> 17) | (s4  <<  4));
+    s[11] = (uint8_t) (s4  >>  4);
+    s[12] = (uint8_t) (s4  >> 12);
+    s[13] = (uint8_t)((s4  >> 20) | (s5  <<  1));
+    s[14] = (uint8_t) (s5  >>  7);
+    s[15] = (uint8_t)((s5  >> 15) | (s6  <<  6));
+    s[16] = (uint8_t) (s6  >>  2);
+    s[17] = (uint8_t) (s6  >> 10);
+    s[18] = (uint8_t)((s6  >> 18) | (s7  <<  3));
+    s[19] = (uint8_t) (s7  >>  5);
+    s[20] = (uint8_t) (s7  >> 13);
+    s[21] = (uint8_t) (s8  >>  0);
+    s[22] = (uint8_t) (s8  >>  8);
+    s[23] = (uint8_t)((s8  >> 16) | (s9  <<  5));
+    s[24] = (uint8_t) (s9  >>  3);
+    s[25] = (uint8_t) (s9  >> 11);
+    s[26] = (uint8_t)((s9  >> 19) | (s10 <<  2));
+    s[27] = (uint8_t) (s10 >>  6);
+    s[28] = (uint8_t)((s10 >> 14) | (s11 <<  7));
+    s[29] = (uint8_t) (s11 >>  1);
+    s[30] = (uint8_t) (s11 >>  9);
+    s[31] = (uint8_t) (s11 >> 17);
 }
 
-/* Input:
+/*
+ * Input:
  *   a[0]+256*a[1]+...+256^31*a[31] = a
  *   b[0]+256*b[1]+...+256^31*b[31] = b
  *   c[0]+256*c[1]+...+256^31*c[31] = c
  *
  * Output:
  *   s[0]+256*s[1]+...+256^31*s[31] = (ab+c) mod l
- *   where l = 2^252 + 27742317777372353535851937790883648493. */
+ *   where l = 2^252 + 27742317777372353535851937790883648493.
+ */
 static void sc_muladd(uint8_t *s, const uint8_t *a, const uint8_t *b,
-                      const uint8_t *c) {
-  int64_t a0 = 2097151 & load_3(a);
-  int64_t a1 = 2097151 & (load_4(a + 2) >> 5);
-  int64_t a2 = 2097151 & (load_3(a + 5) >> 2);
-  int64_t a3 = 2097151 & (load_4(a + 7) >> 7);
-  int64_t a4 = 2097151 & (load_4(a + 10) >> 4);
-  int64_t a5 = 2097151 & (load_3(a + 13) >> 1);
-  int64_t a6 = 2097151 & (load_4(a + 15) >> 6);
-  int64_t a7 = 2097151 & (load_3(a + 18) >> 3);
-  int64_t a8 = 2097151 & load_3(a + 21);
-  int64_t a9 = 2097151 & (load_4(a + 23) >> 5);
-  int64_t a10 = 2097151 & (load_3(a + 26) >> 2);
-  int64_t a11 = (load_4(a + 28) >> 7);
-  int64_t b0 = 2097151 & load_3(b);
-  int64_t b1 = 2097151 & (load_4(b + 2) >> 5);
-  int64_t b2 = 2097151 & (load_3(b + 5) >> 2);
-  int64_t b3 = 2097151 & (load_4(b + 7) >> 7);
-  int64_t b4 = 2097151 & (load_4(b + 10) >> 4);
-  int64_t b5 = 2097151 & (load_3(b + 13) >> 1);
-  int64_t b6 = 2097151 & (load_4(b + 15) >> 6);
-  int64_t b7 = 2097151 & (load_3(b + 18) >> 3);
-  int64_t b8 = 2097151 & load_3(b + 21);
-  int64_t b9 = 2097151 & (load_4(b + 23) >> 5);
-  int64_t b10 = 2097151 & (load_3(b + 26) >> 2);
-  int64_t b11 = (load_4(b + 28) >> 7);
-  int64_t c0 = 2097151 & load_3(c);
-  int64_t c1 = 2097151 & (load_4(c + 2) >> 5);
-  int64_t c2 = 2097151 & (load_3(c + 5) >> 2);
-  int64_t c3 = 2097151 & (load_4(c + 7) >> 7);
-  int64_t c4 = 2097151 & (load_4(c + 10) >> 4);
-  int64_t c5 = 2097151 & (load_3(c + 13) >> 1);
-  int64_t c6 = 2097151 & (load_4(c + 15) >> 6);
-  int64_t c7 = 2097151 & (load_3(c + 18) >> 3);
-  int64_t c8 = 2097151 & load_3(c + 21);
-  int64_t c9 = 2097151 & (load_4(c + 23) >> 5);
-  int64_t c10 = 2097151 & (load_3(c + 26) >> 2);
-  int64_t c11 = (load_4(c + 28) >> 7);
-  int64_t s0;
-  int64_t s1;
-  int64_t s2;
-  int64_t s3;
-  int64_t s4;
-  int64_t s5;
-  int64_t s6;
-  int64_t s7;
-  int64_t s8;
-  int64_t s9;
-  int64_t s10;
-  int64_t s11;
-  int64_t s12;
-  int64_t s13;
-  int64_t s14;
-  int64_t s15;
-  int64_t s16;
-  int64_t s17;
-  int64_t s18;
-  int64_t s19;
-  int64_t s20;
-  int64_t s21;
-  int64_t s22;
-  int64_t s23;
-  int64_t carry0;
-  int64_t carry1;
-  int64_t carry2;
-  int64_t carry3;
-  int64_t carry4;
-  int64_t carry5;
-  int64_t carry6;
-  int64_t carry7;
-  int64_t carry8;
-  int64_t carry9;
-  int64_t carry10;
-  int64_t carry11;
-  int64_t carry12;
-  int64_t carry13;
-  int64_t carry14;
-  int64_t carry15;
-  int64_t carry16;
-  int64_t carry17;
-  int64_t carry18;
-  int64_t carry19;
-  int64_t carry20;
-  int64_t carry21;
-  int64_t carry22;
-
-  s0 = c0 + a0 * b0;
-  s1 = c1 + a0 * b1 + a1 * b0;
-  s2 = c2 + a0 * b2 + a1 * b1 + a2 * b0;
-  s3 = c3 + a0 * b3 + a1 * b2 + a2 * b1 + a3 * b0;
-  s4 = c4 + a0 * b4 + a1 * b3 + a2 * b2 + a3 * b1 + a4 * b0;
-  s5 = c5 + a0 * b5 + a1 * b4 + a2 * b3 + a3 * b2 + a4 * b1 + a5 * b0;
-  s6 = c6 + a0 * b6 + a1 * b5 + a2 * b4 + a3 * b3 + a4 * b2 + a5 * b1 + a6 * 
b0;
-  s7 = c7 + a0 * b7 + a1 * b6 + a2 * b5 + a3 * b4 + a4 * b3 + a5 * b2 +
-       a6 * b1 + a7 * b0;
-  s8 = c8 + a0 * b8 + a1 * b7 + a2 * b6 + a3 * b5 + a4 * b4 + a5 * b3 +
-       a6 * b2 + a7 * b1 + a8 * b0;
-  s9 = c9 + a0 * b9 + a1 * b8 + a2 * b7 + a3 * b6 + a4 * b5 + a5 * b4 +
-       a6 * b3 + a7 * b2 + a8 * b1 + a9 * b0;
-  s10 = c10 + a0 * b10 + a1 * b9 + a2 * b8 + a3 * b7 + a4 * b6 + a5 * b5 +
-        a6 * b4 + a7 * b3 + a8 * b2 + a9 * b1 + a10 * b0;
-  s11 = c11 + a0 * b11 + a1 * b10 + a2 * b9 + a3 * b8 + a4 * b7 + a5 * b6 +
-        a6 * b5 + a7 * b4 + a8 * b3 + a9 * b2 + a10 * b1 + a11 * b0;
-  s12 = a1 * b11 + a2 * b10 + a3 * b9 + a4 * b8 + a5 * b7 + a6 * b6 + a7 * b5 +
-        a8 * b4 + a9 * b3 + a10 * b2 + a11 * b1;
-  s13 = a2 * b11 + a3 * b10 + a4 * b9 + a5 * b8 + a6 * b7 + a7 * b6 + a8 * b5 +
-        a9 * b4 + a10 * b3 + a11 * b2;
-  s14 = a3 * b11 + a4 * b10 + a5 * b9 + a6 * b8 + a7 * b7 + a8 * b6 + a9 * b5 +
-        a10 * b4 + a11 * b3;
-  s15 = a4 * b11 + a5 * b10 + a6 * b9 + a7 * b8 + a8 * b7 + a9 * b6 + a10 * b5 
+
-        a11 * b4;
-  s16 = a5 * b11 + a6 * b10 + a7 * b9 + a8 * b8 + a9 * b7 + a10 * b6 + a11 * 
b5;
-  s17 = a6 * b11 + a7 * b10 + a8 * b9 + a9 * b8 + a10 * b7 + a11 * b6;
-  s18 = a7 * b11 + a8 * b10 + a9 * b9 + a10 * b8 + a11 * b7;
-  s19 = a8 * b11 + a9 * b10 + a10 * b9 + a11 * b8;
-  s20 = a9 * b11 + a10 * b10 + a11 * b9;
-  s21 = a10 * b11 + a11 * b10;
-  s22 = a11 * b11;
-  s23 = 0;
-
-  carry0 = (s0 + (1 << 20)) >> 21;
-  s1 += carry0;
-  s0 -= carry0 * (1 << 21);
-  carry2 = (s2 + (1 << 20)) >> 21;
-  s3 += carry2;
-  s2 -= carry2 * (1 << 21);
-  carry4 = (s4 + (1 << 20)) >> 21;
-  s5 += carry4;
-  s4 -= carry4 * (1 << 21);
-  carry6 = (s6 + (1 << 20)) >> 21;
-  s7 += carry6;
-  s6 -= carry6 * (1 << 21);
-  carry8 = (s8 + (1 << 20)) >> 21;
-  s9 += carry8;
-  s8 -= carry8 * (1 << 21);
-  carry10 = (s10 + (1 << 20)) >> 21;
-  s11 += carry10;
-  s10 -= carry10 * (1 << 21);
-  carry12 = (s12 + (1 << 20)) >> 21;
-  s13 += carry12;
-  s12 -= carry12 * (1 << 21);
-  carry14 = (s14 + (1 << 20)) >> 21;
-  s15 += carry14;
-  s14 -= carry14 * (1 << 21);
-  carry16 = (s16 + (1 << 20)) >> 21;
-  s17 += carry16;
-  s16 -= carry16 * (1 << 21);
-  carry18 = (s18 + (1 << 20)) >> 21;
-  s19 += carry18;
-  s18 -= carry18 * (1 << 21);
-  carry20 = (s20 + (1 << 20)) >> 21;
-  s21 += carry20;
-  s20 -= carry20 * (1 << 21);
-  carry22 = (s22 + (1 << 20)) >> 21;
-  s23 += carry22;
-  s22 -= carry22 * (1 << 21);
-
-  carry1 = (s1 + (1 << 20)) >> 21;
-  s2 += carry1;
-  s1 -= carry1 * (1 << 21);
-  carry3 = (s3 + (1 << 20)) >> 21;
-  s4 += carry3;
-  s3 -= carry3 * (1 << 21);
-  carry5 = (s5 + (1 << 20)) >> 21;
-  s6 += carry5;
-  s5 -= carry5 * (1 << 21);
-  carry7 = (s7 + (1 << 20)) >> 21;
-  s8 += carry7;
-  s7 -= carry7 * (1 << 21);
-  carry9 = (s9 + (1 << 20)) >> 21;
-  s10 += carry9;
-  s9 -= carry9 * (1 << 21);
-  carry11 = (s11 + (1 << 20)) >> 21;
-  s12 += carry11;
-  s11 -= carry11 * (1 << 21);
-  carry13 = (s13 + (1 << 20)) >> 21;
-  s14 += carry13;
-  s13 -= carry13 * (1 << 21);
-  carry15 = (s15 + (1 << 20)) >> 21;
-  s16 += carry15;
-  s15 -= carry15 * (1 << 21);
-  carry17 = (s17 + (1 << 20)) >> 21;
-  s18 += carry17;
-  s17 -= carry17 * (1 << 21);
-  carry19 = (s19 + (1 << 20)) >> 21;
-  s20 += carry19;
-  s19 -= carry19 * (1 << 21);
-  carry21 = (s21 + (1 << 20)) >> 21;
-  s22 += carry21;
-  s21 -= carry21 * (1 << 21);
-
-  s11 += s23 * 666643;
-  s12 += s23 * 470296;
-  s13 += s23 * 654183;
-  s14 -= s23 * 997805;
-  s15 += s23 * 136657;
-  s16 -= s23 * 683901;
-  s23 = 0;
-
-  s10 += s22 * 666643;
-  s11 += s22 * 470296;
-  s12 += s22 * 654183;
-  s13 -= s22 * 997805;
-  s14 += s22 * 136657;
-  s15 -= s22 * 683901;
-  s22 = 0;
-
-  s9 += s21 * 666643;
-  s10 += s21 * 470296;
-  s11 += s21 * 654183;
-  s12 -= s21 * 997805;
-  s13 += s21 * 136657;
-  s14 -= s21 * 683901;
-  s21 = 0;
-
-  s8 += s20 * 666643;
-  s9 += s20 * 470296;
-  s10 += s20 * 654183;
-  s11 -= s20 * 997805;
-  s12 += s20 * 136657;
-  s13 -= s20 * 683901;
-  s20 = 0;
-
-  s7 += s19 * 666643;
-  s8 += s19 * 470296;
-  s9 += s19 * 654183;
-  s10 -= s19 * 997805;
-  s11 += s19 * 136657;
-  s12 -= s19 * 683901;
-  s19 = 0;
-
-  s6 += s18 * 666643;
-  s7 += s18 * 470296;
-  s8 += s18 * 654183;
-  s9 -= s18 * 997805;
-  s10 += s18 * 136657;
-  s11 -= s18 * 683901;
-  s18 = 0;
-
-  carry6 = (s6 + (1 << 20)) >> 21;
-  s7 += carry6;
-  s6 -= carry6 * (1 << 21);
-  carry8 = (s8 + (1 << 20)) >> 21;
-  s9 += carry8;
-  s8 -= carry8 * (1 << 21);
-  carry10 = (s10 + (1 << 20)) >> 21;
-  s11 += carry10;
-  s10 -= carry10 * (1 << 21);
-  carry12 = (s12 + (1 << 20)) >> 21;
-  s13 += carry12;
-  s12 -= carry12 * (1 << 21);
-  carry14 = (s14 + (1 << 20)) >> 21;
-  s15 += carry14;
-  s14 -= carry14 * (1 << 21);
-  carry16 = (s16 + (1 << 20)) >> 21;
-  s17 += carry16;
-  s16 -= carry16 * (1 << 21);
-
-  carry7 = (s7 + (1 << 20)) >> 21;
-  s8 += carry7;
-  s7 -= carry7 * (1 << 21);
-  carry9 = (s9 + (1 << 20)) >> 21;
-  s10 += carry9;
-  s9 -= carry9 * (1 << 21);
-  carry11 = (s11 + (1 << 20)) >> 21;
-  s12 += carry11;
-  s11 -= carry11 * (1 << 21);
-  carry13 = (s13 + (1 << 20)) >> 21;
-  s14 += carry13;
-  s13 -= carry13 * (1 << 21);
-  carry15 = (s15 + (1 << 20)) >> 21;
-  s16 += carry15;
-  s15 -= carry15 * (1 << 21);
-
-  s5 += s17 * 666643;
-  s6 += s17 * 470296;
-  s7 += s17 * 654183;
-  s8 -= s17 * 997805;
-  s9 += s17 * 136657;
-  s10 -= s17 * 683901;
-  s17 = 0;
-
-  s4 += s16 * 666643;
-  s5 += s16 * 470296;
-  s6 += s16 * 654183;
-  s7 -= s16 * 997805;
-  s8 += s16 * 136657;
-  s9 -= s16 * 683901;
-  s16 = 0;
-
-  s3 += s15 * 666643;
-  s4 += s15 * 470296;
-  s5 += s15 * 654183;
-  s6 -= s15 * 997805;
-  s7 += s15 * 136657;
-  s8 -= s15 * 683901;
-  s15 = 0;
-
-  s2 += s14 * 666643;
-  s3 += s14 * 470296;
-  s4 += s14 * 654183;
-  s5 -= s14 * 997805;
-  s6 += s14 * 136657;
-  s7 -= s14 * 683901;
-  s14 = 0;
-
-  s1 += s13 * 666643;
-  s2 += s13 * 470296;
-  s3 += s13 * 654183;
-  s4 -= s13 * 997805;
-  s5 += s13 * 136657;
-  s6 -= s13 * 683901;
-  s13 = 0;
-
-  s0 += s12 * 666643;
-  s1 += s12 * 470296;
-  s2 += s12 * 654183;
-  s3 -= s12 * 997805;
-  s4 += s12 * 136657;
-  s5 -= s12 * 683901;
-  s12 = 0;
-
-  carry0 = (s0 + (1 << 20)) >> 21;
-  s1 += carry0;
-  s0 -= carry0 * (1 << 21);
-  carry2 = (s2 + (1 << 20)) >> 21;
-  s3 += carry2;
-  s2 -= carry2 * (1 << 21);
-  carry4 = (s4 + (1 << 20)) >> 21;
-  s5 += carry4;
-  s4 -= carry4 * (1 << 21);
-  carry6 = (s6 + (1 << 20)) >> 21;
-  s7 += carry6;
-  s6 -= carry6 * (1 << 21);
-  carry8 = (s8 + (1 << 20)) >> 21;
-  s9 += carry8;
-  s8 -= carry8 * (1 << 21);
-  carry10 = (s10 + (1 << 20)) >> 21;
-  s11 += carry10;
-  s10 -= carry10 * (1 << 21);
-
-  carry1 = (s1 + (1 << 20)) >> 21;
-  s2 += carry1;
-  s1 -= carry1 * (1 << 21);
-  carry3 = (s3 + (1 << 20)) >> 21;
-  s4 += carry3;
-  s3 -= carry3 * (1 << 21);
-  carry5 = (s5 + (1 << 20)) >> 21;
-  s6 += carry5;
-  s5 -= carry5 * (1 << 21);
-  carry7 = (s7 + (1 << 20)) >> 21;
-  s8 += carry7;
-  s7 -= carry7 * (1 << 21);
-  carry9 = (s9 + (1 << 20)) >> 21;
-  s10 += carry9;
-  s9 -= carry9 * (1 << 21);
-  carry11 = (s11 + (1 << 20)) >> 21;
-  s12 += carry11;
-  s11 -= carry11 * (1 << 21);
-
-  s0 += s12 * 666643;
-  s1 += s12 * 470296;
-  s2 += s12 * 654183;
-  s3 -= s12 * 997805;
-  s4 += s12 * 136657;
-  s5 -= s12 * 683901;
-  s12 = 0;
-
-  carry0 = s0 >> 21;
-  s1 += carry0;
-  s0 -= carry0 * (1 << 21);
-  carry1 = s1 >> 21;
-  s2 += carry1;
-  s1 -= carry1 * (1 << 21);
-  carry2 = s2 >> 21;
-  s3 += carry2;
-  s2 -= carry2 * (1 << 21);
-  carry3 = s3 >> 21;
-  s4 += carry3;
-  s3 -= carry3 * (1 << 21);
-  carry4 = s4 >> 21;
-  s5 += carry4;
-  s4 -= carry4 * (1 << 21);
-  carry5 = s5 >> 21;
-  s6 += carry5;
-  s5 -= carry5 * (1 << 21);
-  carry6 = s6 >> 21;
-  s7 += carry6;
-  s6 -= carry6 * (1 << 21);
-  carry7 = s7 >> 21;
-  s8 += carry7;
-  s7 -= carry7 * (1 << 21);
-  carry8 = s8 >> 21;
-  s9 += carry8;
-  s8 -= carry8 * (1 << 21);
-  carry9 = s9 >> 21;
-  s10 += carry9;
-  s9 -= carry9 * (1 << 21);
-  carry10 = s10 >> 21;
-  s11 += carry10;
-  s10 -= carry10 * (1 << 21);
-  carry11 = s11 >> 21;
-  s12 += carry11;
-  s11 -= carry11 * (1 << 21);
-
-  s0 += s12 * 666643;
-  s1 += s12 * 470296;
-  s2 += s12 * 654183;
-  s3 -= s12 * 997805;
-  s4 += s12 * 136657;
-  s5 -= s12 * 683901;
-  s12 = 0;
-
-  carry0 = s0 >> 21;
-  s1 += carry0;
-  s0 -= carry0 * (1 << 21);
-  carry1 = s1 >> 21;
-  s2 += carry1;
-  s1 -= carry1 * (1 << 21);
-  carry2 = s2 >> 21;
-  s3 += carry2;
-  s2 -= carry2 * (1 << 21);
-  carry3 = s3 >> 21;
-  s4 += carry3;
-  s3 -= carry3 * (1 << 21);
-  carry4 = s4 >> 21;
-  s5 += carry4;
-  s4 -= carry4 * (1 << 21);
-  carry5 = s5 >> 21;
-  s6 += carry5;
-  s5 -= carry5 * (1 << 21);
-  carry6 = s6 >> 21;
-  s7 += carry6;
-  s6 -= carry6 * (1 << 21);
-  carry7 = s7 >> 21;
-  s8 += carry7;
-  s7 -= carry7 * (1 << 21);
-  carry8 = s8 >> 21;
-  s9 += carry8;
-  s8 -= carry8 * (1 << 21);
-  carry9 = s9 >> 21;
-  s10 += carry9;
-  s9 -= carry9 * (1 << 21);
-  carry10 = s10 >> 21;
-  s11 += carry10;
-  s10 -= carry10 * (1 << 21);
-
-  s[0] = (uint8_t)(s0 >> 0);
-  s[1] = (uint8_t)(s0 >> 8);
-  s[2] = (uint8_t)((s0 >> 16) | (s1 << 5));
-  s[3] = (uint8_t)(s1 >> 3);
-  s[4] = (uint8_t)(s1 >> 11);
-  s[5] = (uint8_t)((s1 >> 19) | (s2 << 2));
-  s[6] = (uint8_t)(s2 >> 6);
-  s[7] = (uint8_t)((s2 >> 14) | (s3 << 7));
-  s[8] = (uint8_t)(s3 >> 1);
-  s[9] = (uint8_t)(s3 >> 9);
-  s[10] = (uint8_t)((s3 >> 17) | (s4 << 4));
-  s[11] = (uint8_t)(s4 >> 4);
-  s[12] = (uint8_t)(s4 >> 12);
-  s[13] = (uint8_t)((s4 >> 20) | (s5 << 1));
-  s[14] = (uint8_t)(s5 >> 7);
-  s[15] = (uint8_t)((s5 >> 15) | (s6 << 6));
-  s[16] = (uint8_t)(s6 >> 2);
-  s[17] = (uint8_t)(s6 >> 10);
-  s[18] = (uint8_t)((s6 >> 18) | (s7 << 3));
-  s[19] = (uint8_t)(s7 >> 5);
-  s[20] = (uint8_t)(s7 >> 13);
-  s[21] = (uint8_t)(s8 >> 0);
-  s[22] = (uint8_t)(s8 >> 8);
-  s[23] = (uint8_t)((s8 >> 16) | (s9 << 5));
-  s[24] = (uint8_t)(s9 >> 3);
-  s[25] = (uint8_t)(s9 >> 11);
-  s[26] = (uint8_t)((s9 >> 19) | (s10 << 2));
-  s[27] = (uint8_t)(s10 >> 6);
-  s[28] = (uint8_t)((s10 >> 14) | (s11 << 7));
-  s[29] = (uint8_t)(s11 >> 1);
-  s[30] = (uint8_t)(s11 >> 9);
-  s[31] = (uint8_t)(s11 >> 17);
+                      const uint8_t *c)
+{
+    int64_t a0  = kBottom21Bits &  load_3(a);
+    int64_t a1  = kBottom21Bits & (load_4(a +  2) >> 5);
+    int64_t a2  = kBottom21Bits & (load_3(a +  5) >> 2);
+    int64_t a3  = kBottom21Bits & (load_4(a +  7) >> 7);
+    int64_t a4  = kBottom21Bits & (load_4(a + 10) >> 4);
+    int64_t a5  = kBottom21Bits & (load_3(a + 13) >> 1);
+    int64_t a6  = kBottom21Bits & (load_4(a + 15) >> 6);
+    int64_t a7  = kBottom21Bits & (load_3(a + 18) >> 3);
+    int64_t a8  = kBottom21Bits &  load_3(a + 21);
+    int64_t a9  = kBottom21Bits & (load_4(a + 23) >> 5);
+    int64_t a10 = kBottom21Bits & (load_3(a + 26) >> 2);
+    int64_t a11 =                 (load_4(a + 28) >> 7);
+    int64_t b0  = kBottom21Bits &  load_3(b);
+    int64_t b1  = kBottom21Bits & (load_4(b +  2) >> 5);
+    int64_t b2  = kBottom21Bits & (load_3(b +  5) >> 2);
+    int64_t b3  = kBottom21Bits & (load_4(b +  7) >> 7);
+    int64_t b4  = kBottom21Bits & (load_4(b + 10) >> 4);
+    int64_t b5  = kBottom21Bits & (load_3(b + 13) >> 1);
+    int64_t b6  = kBottom21Bits & (load_4(b + 15) >> 6);
+    int64_t b7  = kBottom21Bits & (load_3(b + 18) >> 3);
+    int64_t b8  = kBottom21Bits &  load_3(b + 21);
+    int64_t b9  = kBottom21Bits & (load_4(b + 23) >> 5);
+    int64_t b10 = kBottom21Bits & (load_3(b + 26) >> 2);
+    int64_t b11 =                 (load_4(b + 28) >> 7);
+    int64_t c0  = kBottom21Bits &  load_3(c);
+    int64_t c1  = kBottom21Bits & (load_4(c +  2) >> 5);
+    int64_t c2  = kBottom21Bits & (load_3(c +  5) >> 2);
+    int64_t c3  = kBottom21Bits & (load_4(c +  7) >> 7);
+    int64_t c4  = kBottom21Bits & (load_4(c + 10) >> 4);
+    int64_t c5  = kBottom21Bits & (load_3(c + 13) >> 1);
+    int64_t c6  = kBottom21Bits & (load_4(c + 15) >> 6);
+    int64_t c7  = kBottom21Bits & (load_3(c + 18) >> 3);
+    int64_t c8  = kBottom21Bits &  load_3(c + 21);
+    int64_t c9  = kBottom21Bits & (load_4(c + 23) >> 5);
+    int64_t c10 = kBottom21Bits & (load_3(c + 26) >> 2);
+    int64_t c11 =                 (load_4(c + 28) >> 7);
+    int64_t s0;
+    int64_t s1;
+    int64_t s2;
+    int64_t s3;
+    int64_t s4;
+    int64_t s5;
+    int64_t s6;
+    int64_t s7;
+    int64_t s8;
+    int64_t s9;
+    int64_t s10;
+    int64_t s11;
+    int64_t s12;
+    int64_t s13;
+    int64_t s14;
+    int64_t s15;
+    int64_t s16;
+    int64_t s17;
+    int64_t s18;
+    int64_t s19;
+    int64_t s20;
+    int64_t s21;
+    int64_t s22;
+    int64_t s23;
+    int64_t carry0;
+    int64_t carry1;
+    int64_t carry2;
+    int64_t carry3;
+    int64_t carry4;
+    int64_t carry5;
+    int64_t carry6;
+    int64_t carry7;
+    int64_t carry8;
+    int64_t carry9;
+    int64_t carry10;
+    int64_t carry11;
+    int64_t carry12;
+    int64_t carry13;
+    int64_t carry14;
+    int64_t carry15;
+    int64_t carry16;
+    int64_t carry17;
+    int64_t carry18;
+    int64_t carry19;
+    int64_t carry20;
+    int64_t carry21;
+    int64_t carry22;
+
+    s0  = c0   +   a0 * b0;
+    s1  = c1   +   a0 * b1   +   a1 * b0;
+    s2  = c2   +   a0 * b2   +   a1 * b1   +   a2 * b0;
+    s3  = c3   +   a0 * b3   +   a1 * b2   +   a2 * b1  +   a3 * b0;
+    s4  = c4   +   a0 * b4   +   a1 * b3   +   a2 * b2  +   a3 * b1  +   a4 * 
b0;
+    s5  = c5   +   a0 * b5   +   a1 * b4   +   a2 * b3  +   a3 * b2  +   a4 * 
b1  +   a5 * b0;
+    s6  = c6   +   a0 * b6   +   a1 * b5   +   a2 * b4  +   a3 * b3  +   a4 * 
b2  +   a5 * b1 +   a6 * b0;
+    s7  = c7   +   a0 * b7   +   a1 * b6   +   a2 * b5  +   a3 * b4  +   a4 * 
b3  +   a5 * b2 +   a6 * b1   +   a7 * b0;
+    s8  = c8   +   a0 * b8   +   a1 * b7   +   a2 * b6  +   a3 * b5  +   a4 * 
b4  +   a5 * b3 +   a6 * b2   +   a7 * b1   +   a8 * b0;
+    s9  = c9   +   a0 * b9   +   a1 * b8   +   a2 * b7  +   a3 * b6  +   a4 * 
b5  +   a5 * b4 +   a6 * b3   +   a7 * b2   +   a8 * b1  +   a9 * b0;
+    s10 = c10  +   a0 * b10  +   a1 * b9   +   a2 * b8  +   a3 * b7  +   a4 * 
b6  +   a5 * b5 +   a6 * b4   +   a7 * b3   +   a8 * b2  +   a9 * b1  +  a10 * 
b0;
+    s11 = c11  +   a0 * b11  +   a1 * b10  +   a2 * b9  +   a3 * b8  +   a4 * 
b7  +   a5 * b6 +   a6 * b5   +   a7 * b4   +   a8 * b3  +   a9 * b2  +  a10 * 
b1  +  a11 * b0;
+    s12 =          a1 * b11  +   a2 * b10  +   a3 * b9  +   a4 * b8  +   a5 * 
b7  +   a6 * b6 +   a7 * b5   +   a8 * b4   +   a9 * b3  +  a10 * b2  +  a11 * 
b1;
+    s13 =          a2 * b11  +   a3 * b10  +   a4 * b9  +   a5 * b8  +   a6 * 
b7  +   a7 * b6 +   a8 * b5   +   a9 * b4   +  a10 * b3  +  a11 * b2;
+    s14 =          a3 * b11  +   a4 * b10  +   a5 * b9  +   a6 * b8  +   a7 * 
b7  +   a8 * b6 +   a9 * b5   +  a10 * b4   +  a11 * b3;
+    s15 =          a4 * b11  +   a5 * b10  +   a6 * b9  +   a7 * b8  +   a8 * 
b7  +   a9 * b6 +  a10 * b5   +  a11 * b4;
+    s16 =          a5 * b11  +   a6 * b10  +   a7 * b9  +   a8 * b8  +   a9 * 
b7  +  a10 * b6 +  a11 * b5;
+    s17 =          a6 * b11  +   a7 * b10  +   a8 * b9  +   a9 * b8  +  a10 * 
b7  +  a11 * b6;
+    s18 =          a7 * b11  +   a8 * b10  +   a9 * b9  +  a10 * b8  +  a11 * 
b7;
+    s19 =          a8 * b11  +   a9 * b10  +  a10 * b9  +  a11 * b8;
+    s20 =          a9 * b11  +  a10 * b10  +  a11 * b9;
+    s21 =         a10 * b11  +  a11 * b10;
+    s22 =         a11 * b11;
+    s23 =         0;
+
+    carry0 = (s0 + (1 << 20)) >> 21;
+    s1  += carry0;
+    s0  -= carry0 * (1 << 21);
+    carry2 = (s2 + (1 << 20)) >> 21;
+    s3  += carry2;
+    s2  -= carry2 * (1 << 21);
+    carry4 = (s4 + (1 << 20)) >> 21;
+    s5  += carry4;
+    s4  -= carry4 * (1 << 21);
+    carry6 = (s6 + (1 << 20)) >> 21;
+    s7  += carry6;
+    s6  -= carry6 * (1 << 21);
+    carry8 = (s8 + (1 << 20)) >> 21;
+    s9  += carry8;
+    s8  -= carry8 * (1 << 21);
+    carry10 = (s10 + (1 << 20)) >> 21;
+    s11 += carry10;
+    s10 -= carry10 * (1 << 21);
+    carry12 = (s12 + (1 << 20)) >> 21;
+    s13 += carry12;
+    s12 -= carry12 * (1 << 21);
+    carry14 = (s14 + (1 << 20)) >> 21;
+    s15 += carry14;
+    s14 -= carry14 * (1 << 21);
+    carry16 = (s16 + (1 << 20)) >> 21;
+    s17 += carry16;
+    s16 -= carry16 * (1 << 21);
+    carry18 = (s18 + (1 << 20)) >> 21;
+    s19 += carry18;
+    s18 -= carry18 * (1 << 21);
+    carry20 = (s20 + (1 << 20)) >> 21;
+    s21 += carry20;
+    s20 -= carry20 * (1 << 21);
+    carry22 = (s22 + (1 << 20)) >> 21;
+    s23 += carry22;
+    s22 -= carry22 * (1 << 21);
+
+    carry1 = (s1 + (1 << 20)) >> 21;
+    s2  += carry1;
+    s1  -= carry1 * (1 << 21);
+    carry3 = (s3 + (1 << 20)) >> 21;
+    s4  += carry3;
+    s3  -= carry3 * (1 << 21);
+    carry5 = (s5 + (1 << 20)) >> 21;
+    s6  += carry5;
+    s5  -= carry5 * (1 << 21);
+    carry7 = (s7 + (1 << 20)) >> 21;
+    s8  += carry7;
+    s7  -= carry7 * (1 << 21);
+    carry9 = (s9 + (1 << 20)) >> 21;
+    s10 += carry9;
+    s9  -= carry9 * (1 << 21);
+    carry11 = (s11 + (1 << 20)) >> 21;
+    s12 += carry11;
+    s11 -= carry11 * (1 << 21);
+    carry13 = (s13 + (1 << 20)) >> 21;
+    s14 += carry13;
+    s13 -= carry13 * (1 << 21);
+    carry15 = (s15 + (1 << 20)) >> 21;
+    s16 += carry15;
+    s15 -= carry15 * (1 << 21);
+    carry17 = (s17 + (1 << 20)) >> 21;
+    s18 += carry17;
+    s17 -= carry17 * (1 << 21);
+    carry19 = (s19 + (1 << 20)) >> 21;
+    s20 += carry19;
+    s19 -= carry19 * (1 << 21);
+    carry21 = (s21 + (1 << 20)) >> 21;
+    s22 += carry21;
+    s21 -= carry21 * (1 << 21);
+
+    s11 += s23 * 666643;
+    s12 += s23 * 470296;
+    s13 += s23 * 654183;
+    s14 -= s23 * 997805;
+    s15 += s23 * 136657;
+    s16 -= s23 * 683901;
+    s23  = 0;
+
+    s10 += s22 * 666643;
+    s11 += s22 * 470296;
+    s12 += s22 * 654183;
+    s13 -= s22 * 997805;
+    s14 += s22 * 136657;
+    s15 -= s22 * 683901;
+    s22  = 0;
+
+    s9  += s21 * 666643;
+    s10 += s21 * 470296;
+    s11 += s21 * 654183;
+    s12 -= s21 * 997805;
+    s13 += s21 * 136657;
+    s14 -= s21 * 683901;
+    s21  = 0;
+
+    s8  += s20 * 666643;
+    s9  += s20 * 470296;
+    s10 += s20 * 654183;
+    s11 -= s20 * 997805;
+    s12 += s20 * 136657;
+    s13 -= s20 * 683901;
+    s20  = 0;
+
+    s7  += s19 * 666643;
+    s8  += s19 * 470296;
+    s9  += s19 * 654183;
+    s10 -= s19 * 997805;
+    s11 += s19 * 136657;
+    s12 -= s19 * 683901;
+    s19  = 0;
+
+    s6  += s18 * 666643;
+    s7  += s18 * 470296;
+    s8  += s18 * 654183;
+    s9  -= s18 * 997805;
+    s10 += s18 * 136657;
+    s11 -= s18 * 683901;
+    s18  = 0;
+
+    carry6 = (s6 + (1 << 20)) >> 21;
+    s7  += carry6;
+    s6  -= carry6 * (1 << 21);
+    carry8 = (s8 + (1 << 20)) >> 21;
+    s9  += carry8;
+    s8  -= carry8 * (1 << 21);
+    carry10 = (s10 + (1 << 20)) >> 21;
+    s11 += carry10;
+    s10 -= carry10 * (1 << 21);
+    carry12 = (s12 + (1 << 20)) >> 21;
+    s13 += carry12;
+    s12 -= carry12 * (1 << 21);
+    carry14 = (s14 + (1 << 20)) >> 21;
+    s15 += carry14;
+    s14 -= carry14 * (1 << 21);
+    carry16 = (s16 + (1 << 20)) >> 21;
+    s17 += carry16;
+    s16 -= carry16 * (1 << 21);
+
+    carry7 = (s7 + (1 << 20)) >> 21;
+    s8  += carry7;
+    s7  -= carry7 * (1 << 21);
+    carry9 = (s9 + (1 << 20)) >> 21;
+    s10 += carry9;
+    s9  -= carry9 * (1 << 21);
+    carry11 = (s11 + (1 << 20)) >> 21;
+    s12 += carry11;
+    s11 -= carry11 * (1 << 21);
+    carry13 = (s13 + (1 << 20)) >> 21;
+    s14 += carry13;
+    s13 -= carry13 * (1 << 21);
+    carry15 = (s15 + (1 << 20)) >> 21;
+    s16 += carry15;
+    s15 -= carry15 * (1 << 21);
+
+    s5  += s17 * 666643;
+    s6  += s17 * 470296;
+    s7  += s17 * 654183;
+    s8  -= s17 * 997805;
+    s9  += s17 * 136657;
+    s10 -= s17 * 683901;
+    s17  = 0;
+
+    s4  += s16 * 666643;
+    s5  += s16 * 470296;
+    s6  += s16 * 654183;
+    s7  -= s16 * 997805;
+    s8  += s16 * 136657;
+    s9  -= s16 * 683901;
+    s16  = 0;
+
+    s3  += s15 * 666643;
+    s4  += s15 * 470296;
+    s5  += s15 * 654183;
+    s6  -= s15 * 997805;
+    s7  += s15 * 136657;
+    s8  -= s15 * 683901;
+    s15  = 0;
+
+    s2  += s14 * 666643;
+    s3  += s14 * 470296;
+    s4  += s14 * 654183;
+    s5  -= s14 * 997805;
+    s6  += s14 * 136657;
+    s7  -= s14 * 683901;
+    s14  = 0;
+
+    s1  += s13 * 666643;
+    s2  += s13 * 470296;
+    s3  += s13 * 654183;
+    s4  -= s13 * 997805;
+    s5  += s13 * 136657;
+    s6  -= s13 * 683901;
+    s13  = 0;
+
+    s0  += s12 * 666643;
+    s1  += s12 * 470296;
+    s2  += s12 * 654183;
+    s3  -= s12 * 997805;
+    s4  += s12 * 136657;
+    s5  -= s12 * 683901;
+    s12 = 0;
+
+    carry0 = (s0 + (1 << 20)) >> 21;
+    s1  += carry0;
+    s0  -= carry0 * (1 << 21);
+    carry2 = (s2 + (1 << 20)) >> 21;
+    s3  += carry2;
+    s2  -= carry2 * (1 << 21);
+    carry4 = (s4 + (1 << 20)) >> 21;
+    s5  += carry4;
+    s4  -= carry4 * (1 << 21);
+    carry6 = (s6 + (1 << 20)) >> 21;
+    s7  += carry6;
+    s6  -= carry6 * (1 << 21);
+    carry8 = (s8 + (1 << 20)) >> 21;
+    s9  += carry8;
+    s8  -= carry8 * (1 << 21);
+    carry10 = (s10 + (1 << 20)) >> 21;
+    s11 += carry10;
+    s10 -= carry10 * (1 << 21);
+
+    carry1 = (s1 + (1 << 20)) >> 21;
+    s2  += carry1;
+    s1  -= carry1 * (1 << 21);
+    carry3 = (s3 + (1 << 20)) >> 21;
+    s4  += carry3;
+    s3  -= carry3 * (1 << 21);
+    carry5 = (s5 + (1 << 20)) >> 21;
+    s6  += carry5;
+    s5  -= carry5 * (1 << 21);
+    carry7 = (s7 + (1 << 20)) >> 21;
+    s8  += carry7;
+    s7  -= carry7 * (1 << 21);
+    carry9 = (s9 + (1 << 20)) >> 21;
+    s10 += carry9;
+    s9  -= carry9 * (1 << 21);
+    carry11 = (s11 + (1 << 20)) >> 21;
+    s12 += carry11;
+    s11 -= carry11 * (1 << 21);
+
+    s0  += s12 * 666643;
+    s1  += s12 * 470296;
+    s2  += s12 * 654183;
+    s3  -= s12 * 997805;
+    s4  += s12 * 136657;
+    s5  -= s12 * 683901;
+    s12  = 0;
+
+    carry0 = s0 >> 21;
+    s1  += carry0;
+    s0  -= carry0 * (1 << 21);
+    carry1 = s1 >> 21;
+    s2  += carry1;
+    s1  -= carry1 * (1 << 21);
+    carry2 = s2 >> 21;
+    s3  += carry2;
+    s2  -= carry2 * (1 << 21);
+    carry3 = s3 >> 21;
+    s4  += carry3;
+    s3  -= carry3 * (1 << 21);
+    carry4 = s4 >> 21;
+    s5  += carry4;
+    s4  -= carry4 * (1 << 21);
+    carry5 = s5 >> 21;
+    s6  += carry5;
+    s5  -= carry5 * (1 << 21);
+    carry6 = s6 >> 21;
+    s7  += carry6;
+    s6  -= carry6 * (1 << 21);
+    carry7 = s7 >> 21;
+    s8  += carry7;
+    s7  -= carry7 * (1 << 21);
+    carry8 = s8 >> 21;
+    s9  += carry8;
+    s8  -= carry8 * (1 << 21);
+    carry9 = s9 >> 21;
+    s10 += carry9;
+    s9  -= carry9 * (1 << 21);
+    carry10 = s10 >> 21;
+    s11 += carry10;
+    s10 -= carry10 * (1 << 21);
+    carry11 = s11 >> 21;
+    s12 += carry11;
+    s11 -= carry11 * (1 << 21);
+
+    s0  += s12 * 666643;
+    s1  += s12 * 470296;
+    s2  += s12 * 654183;
+    s3  -= s12 * 997805;
+    s4  += s12 * 136657;
+    s5  -= s12 * 683901;
+    s12  = 0;
+
+    carry0 = s0 >> 21;
+    s1  += carry0;
+    s0  -= carry0 * (1 << 21);
+    carry1 = s1 >> 21;
+    s2  += carry1;
+    s1  -= carry1 * (1 << 21);
+    carry2 = s2 >> 21;
+    s3  += carry2;
+    s2  -= carry2 * (1 << 21);
+    carry3 = s3 >> 21;
+    s4  += carry3;
+    s3  -= carry3 * (1 << 21);
+    carry4 = s4 >> 21;
+    s5  += carry4;
+    s4  -= carry4 * (1 << 21);
+    carry5 = s5 >> 21;
+    s6  += carry5;
+    s5  -= carry5 * (1 << 21);
+    carry6 = s6 >> 21;
+    s7  += carry6;
+    s6  -= carry6 * (1 << 21);
+    carry7 = s7 >> 21;
+    s8  += carry7;
+    s7  -= carry7 * (1 << 21);
+    carry8 = s8 >> 21;
+    s9  += carry8;
+    s8  -= carry8 * (1 << 21);
+    carry9 = s9 >> 21;
+    s10 += carry9;
+    s9  -= carry9 * (1 << 21);
+    carry10 = s10 >> 21;
+    s11 += carry10;
+    s10 -= carry10 * (1 << 21);
+
+    s[ 0] = (uint8_t) (s0  >>  0);
+    s[ 1] = (uint8_t) (s0  >>  8);
+    s[ 2] = (uint8_t)((s0  >> 16) | (s1 << 5));
+    s[ 3] = (uint8_t) (s1  >>  3);
+    s[ 4] = (uint8_t) (s1  >> 11);
+    s[ 5] = (uint8_t)((s1  >> 19) | (s2 << 2));
+    s[ 6] = (uint8_t) (s2  >>  6);
+    s[ 7] = (uint8_t)((s2  >> 14) | (s3 << 7));
+    s[ 8] = (uint8_t) (s3  >>  1);
+    s[ 9] = (uint8_t) (s3  >>  9);
+    s[10] = (uint8_t)((s3  >> 17) | (s4 << 4));
+    s[11] = (uint8_t) (s4  >>  4);
+    s[12] = (uint8_t) (s4  >> 12);
+    s[13] = (uint8_t)((s4  >> 20) | (s5 << 1));
+    s[14] = (uint8_t) (s5  >>  7);
+    s[15] = (uint8_t)((s5  >> 15) | (s6 << 6));
+    s[16] = (uint8_t) (s6  >>  2);
+    s[17] = (uint8_t) (s6  >> 10);
+    s[18] = (uint8_t)((s6  >> 18) | (s7 << 3));
+    s[19] = (uint8_t) (s7  >>  5);
+    s[20] = (uint8_t) (s7  >> 13);
+    s[21] = (uint8_t) (s8  >>  0);
+    s[22] = (uint8_t) (s8  >>  8);
+    s[23] = (uint8_t)((s8  >> 16) | (s9 << 5));
+    s[24] = (uint8_t) (s9  >>  3);
+    s[25] = (uint8_t) (s9  >> 11);
+    s[26] = (uint8_t)((s9  >> 19) | (s10 << 2));
+    s[27] = (uint8_t) (s10 >>  6);
+    s[28] = (uint8_t)((s10 >> 14) | (s11 << 7));
+    s[29] = (uint8_t) (s11 >>  1);
+    s[30] = (uint8_t) (s11 >>  9);
+    s[31] = (uint8_t) (s11 >> 17);
 }
 
 int ED25519_sign(uint8_t *out_sig, const uint8_t *message, size_t message_len,
-                 const uint8_t public_key[32], const uint8_t private_key[32]) {
-  uint8_t az[SHA512_DIGEST_LENGTH];
-  uint8_t nonce[SHA512_DIGEST_LENGTH];
-  ge_p3 R;
-  uint8_t hram[SHA512_DIGEST_LENGTH];
-  SHA512_CTX hash_ctx;
-
-  SHA512_Init(&hash_ctx);
-  SHA512_Update(&hash_ctx, private_key, 32);
-  SHA512_Final(az, &hash_ctx);
-
-  az[0] &= 248;
-  az[31] &= 63;
-  az[31] |= 64;
-
-  SHA512_Init(&hash_ctx);
-  SHA512_Update(&hash_ctx, az + 32, 32);
-  SHA512_Update(&hash_ctx, message, message_len);
-  SHA512_Final(nonce, &hash_ctx);
-
-  x25519_sc_reduce(nonce);
-  ge_scalarmult_base(&R, nonce);
-  ge_p3_tobytes(out_sig, &R);
-
-  SHA512_Init(&hash_ctx);
-  SHA512_Update(&hash_ctx, out_sig, 32);
-  SHA512_Update(&hash_ctx, public_key, 32);
-  SHA512_Update(&hash_ctx, message, message_len);
-  SHA512_Final(hram, &hash_ctx);
-
-  x25519_sc_reduce(hram);
-  sc_muladd(out_sig + 32, hram, az, nonce);
-
-  OPENSSL_cleanse(&hash_ctx, sizeof(hash_ctx));
-  OPENSSL_cleanse(nonce, sizeof(nonce));
-  OPENSSL_cleanse(az, sizeof(az));
-
-  return 1;
+                 const uint8_t public_key[32], const uint8_t private_key[32])
+{
+    uint8_t az[SHA512_DIGEST_LENGTH];
+    uint8_t nonce[SHA512_DIGEST_LENGTH];
+    ge_p3 R;
+    uint8_t hram[SHA512_DIGEST_LENGTH];
+    SHA512_CTX hash_ctx;
+
+    SHA512_Init(&hash_ctx);
+    SHA512_Update(&hash_ctx, private_key, 32);
+    SHA512_Final(az, &hash_ctx);
+
+    az[0] &= 248;
+    az[31] &= 63;
+    az[31] |= 64;
+
+    SHA512_Init(&hash_ctx);
+    SHA512_Update(&hash_ctx, az + 32, 32);
+    SHA512_Update(&hash_ctx, message, message_len);
+    SHA512_Final(nonce, &hash_ctx);
+
+    x25519_sc_reduce(nonce);
+    ge_scalarmult_base(&R, nonce);
+    ge_p3_tobytes(out_sig, &R);
+
+    SHA512_Init(&hash_ctx);
+    SHA512_Update(&hash_ctx, out_sig, 32);
+    SHA512_Update(&hash_ctx, public_key, 32);
+    SHA512_Update(&hash_ctx, message, message_len);
+    SHA512_Final(hram, &hash_ctx);
+
+    x25519_sc_reduce(hram);
+    sc_muladd(out_sig + 32, hram, az, nonce);
+
+    OPENSSL_cleanse(&hash_ctx, sizeof(hash_ctx));
+    OPENSSL_cleanse(nonce, sizeof(nonce));
+    OPENSSL_cleanse(az, sizeof(az));
+
+    return 1;
 }
 
 static const char allzeroes[15];
 
 int ED25519_verify(const uint8_t *message, size_t message_len,
-                   const uint8_t signature[64], const uint8_t public_key[32]) {
-  int i;
-  ge_p3 A;
-  const uint8_t *r, *s;
-  SHA512_CTX hash_ctx;
-  ge_p2 R;
-  uint8_t rcheck[32];
-  uint8_t h[SHA512_DIGEST_LENGTH];
-  /* 27742317777372353535851937790883648493 in little endian format */
-  const uint8_t l_low[16] = {
-    0xED, 0xD3, 0xF5, 0x5C, 0x1A, 0x63, 0x12, 0x58, 0xD6, 0x9C, 0xF7, 0xA2,
-    0xDE, 0xF9, 0xDE, 0x14
-  };
-
-  r = signature;
-  s = signature + 32;
-
-  /*
-   * Check 0 <= s < L where L = 2^252 + 27742317777372353535851937790883648493
-   *
-   * If not the signature is publicly invalid. Since it's public we can do the
-   * check in variable time.
-   *
-   * First check the most significant byte
-   */
-  if (s[31] > 0x10)
-    return 0;
-  if (s[31] == 0x10) {
-      /*
-       * Most significant byte indicates a value close to 2^252 so check the
-       * rest
-       */
-      if (memcmp(s + 16, allzeroes, sizeof(allzeroes)) != 0)
+                   const uint8_t signature[64], const uint8_t public_key[32])
+{
+    int i;
+    ge_p3 A;
+    const uint8_t *r, *s;
+    SHA512_CTX hash_ctx;
+    ge_p2 R;
+    uint8_t rcheck[32];
+    uint8_t h[SHA512_DIGEST_LENGTH];
+    /* 27742317777372353535851937790883648493 in little endian format */
+    const uint8_t l_low[16] = {
+        0xED, 0xD3, 0xF5, 0x5C, 0x1A, 0x63, 0x12, 0x58, 0xD6, 0x9C, 0xF7, 0xA2,
+        0xDE, 0xF9, 0xDE, 0x14
+    };
+
+    r = signature;
+    s = signature + 32;
+
+    /*
+     * Check 0 <= s < L where L = 2^252 + 
27742317777372353535851937790883648493
+     *
+     * If not the signature is publicly invalid. Since it's public we can do 
the
+     * check in variable time.
+     *
+     * First check the most significant byte
+     */
+    if (s[31] > 0x10)
         return 0;
-      for (i = 15; i >= 0; i--) {
-          if (s[i] < l_low[i])
-            break;
-          if (s[i] > l_low[i])
+    if (s[31] == 0x10) {
+        /*
+         * Most significant byte indicates a value close to 2^252 so check the
+         * rest
+         */
+        if (memcmp(s + 16, allzeroes, sizeof(allzeroes)) != 0)
             return 0;
-      }
-      if (i < 0)
-        return 0;
-  }
+        for (i = 15; i >= 0; i--) {
+            if (s[i] < l_low[i])
+                break;
+            if (s[i] > l_low[i])
+                return 0;
+        }
+        if (i < 0)
+            return 0;
+    }
 
-  if (ge_frombytes_vartime(&A, public_key) != 0) {
-    return 0;
-  }
+    if (ge_frombytes_vartime(&A, public_key) != 0) {
+        return 0;
+    }
 
-  fe_neg(A.X, A.X);
-  fe_neg(A.T, A.T);
+    fe_neg(A.X, A.X);
+    fe_neg(A.T, A.T);
 
-  SHA512_Init(&hash_ctx);
-  SHA512_Update(&hash_ctx, r, 32);
-  SHA512_Update(&hash_ctx, public_key, 32);
-  SHA512_Update(&hash_ctx, message, message_len);
-  SHA512_Final(h, &hash_ctx);
+    SHA512_Init(&hash_ctx);
+    SHA512_Update(&hash_ctx, r, 32);
+    SHA512_Update(&hash_ctx, public_key, 32);
+    SHA512_Update(&hash_ctx, message, message_len);
+    SHA512_Final(h, &hash_ctx);
 
-  x25519_sc_reduce(h);
+    x25519_sc_reduce(h);
 
-  ge_double_scalarmult_vartime(&R, h, &A, s);
+    ge_double_scalarmult_vartime(&R, h, &A, s);
 
-  ge_tobytes(rcheck, &R);
+    ge_tobytes(rcheck, &R);
 
-  return CRYPTO_memcmp(rcheck, r, sizeof(rcheck)) == 0;
+    return CRYPTO_memcmp(rcheck, r, sizeof(rcheck)) == 0;
 }
 
 void ED25519_public_from_private(uint8_t out_public_key[32],
-                                 const uint8_t private_key[32]) {
-  uint8_t az[SHA512_DIGEST_LENGTH];
-  ge_p3 A;
+                                 const uint8_t private_key[32])
+{
+    uint8_t az[SHA512_DIGEST_LENGTH];
+    ge_p3 A;
 
-  SHA512(private_key, 32, az);
+    SHA512(private_key, 32, az);
 
-  az[0] &= 248;
-  az[31] &= 63;
-  az[31] |= 64;
+    az[0] &= 248;
+    az[31] &= 63;
+    az[31] |= 64;
 
-  ge_scalarmult_base(&A, az);
-  ge_p3_tobytes(out_public_key, &A);
+    ge_scalarmult_base(&A, az);
+    ge_p3_tobytes(out_public_key, &A);
 
-  OPENSSL_cleanse(az, sizeof(az));
+    OPENSSL_cleanse(az, sizeof(az));
 }
 
 int X25519(uint8_t out_shared_key[32], const uint8_t private_key[32],
-           const uint8_t peer_public_value[32]) {
-  static const uint8_t kZeros[32] = {0};
-  x25519_scalar_mult(out_shared_key, private_key, peer_public_value);
-  /* The all-zero output results when the input is a point of small order. */
-  return CRYPTO_memcmp(kZeros, out_shared_key, 32) != 0;
+           const uint8_t peer_public_value[32])
+{
+    static const uint8_t kZeros[32] = {0};
+    x25519_scalar_mult(out_shared_key, private_key, peer_public_value);
+    /* The all-zero output results when the input is a point of small order. */
+    return CRYPTO_memcmp(kZeros, out_shared_key, 32) != 0;
 }
 
 void X25519_public_from_private(uint8_t out_public_value[32],
-                                const uint8_t private_key[32]) {
-  uint8_t e[32];
-  ge_p3 A;
-  fe zplusy, zminusy, zminusy_inv;
-
-  memcpy(e, private_key, 32);
-  e[0] &= 248;
-  e[31] &= 127;
-  e[31] |= 64;
-
-  ge_scalarmult_base(&A, e);
-
-  /* We only need the u-coordinate of the curve25519 point. The map is
-   * u=(y+1)/(1-y). Since y=Y/Z, this gives u=(Z+Y)/(Z-Y). */
-  fe_add(zplusy, A.Z, A.Y);
-  fe_sub(zminusy, A.Z, A.Y);
-  fe_invert(zminusy_inv, zminusy);
-  fe_mul(zplusy, zplusy, zminusy_inv);
-  fe_tobytes(out_public_value, zplusy);
-
-  OPENSSL_cleanse(e, sizeof(e));
+                                const uint8_t private_key[32])
+{
+    uint8_t e[32];
+    ge_p3 A;
+    fe zplusy, zminusy, zminusy_inv;
+
+    memcpy(e, private_key, 32);
+    e[0] &= 248;
+    e[31] &= 127;
+    e[31] |= 64;
+
+    ge_scalarmult_base(&A, e);
+
+    /*
+     * We only need the u-coordinate of the curve25519 point.
+     * The map is u=(y+1)/(1-y). Since y=Y/Z, this gives
+     * u=(Z+Y)/(Z-Y).
+     */
+    fe_add(zplusy, A.Z, A.Y);
+    fe_sub(zminusy, A.Z, A.Y);
+    fe_invert(zminusy_inv, zminusy);
+    fe_mul(zplusy, zplusy, zminusy_inv);
+    fe_tobytes(out_public_value, zplusy);
+
+    OPENSSL_cleanse(e, sizeof(e));
 }
_____
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