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[tor-commits] [tor/master] Use SHL{8, 32, 64} in ed25519/ref10 to avoid left-shifting negative values

To: tor-commits@xxxxxxxxxxxxxxxxxxxx
Subject: [tor-commits] [tor/master] Use SHL{8, 32, 64} in ed25519/ref10 to avoid left-shifting negative values
From: nickm@xxxxxxxxxxxxxx
Date: Mon, 29 Sep 2014 01:01:35 +0000 (UTC)
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Delivery-date: Sun, 28 Sep 2014 21:01:47 -0400
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Patch-author: Nick Mathewson <nickm@xxxxxxxxxxxxxx>
Sender: "tor-commits" <tor-commits-bounces@xxxxxxxxxxxxxxxxxxxx>
commit 6129ff320e6510a453922dba01163824923bc782
Author: Nick Mathewson <nickm@xxxxxxxxxxxxxx>
Date:   Sun Sep 28 20:39:09 2014 -0400

    Use SHL{8,32,64} in ed25519/ref10 to avoid left-shifting negative values
    
    This helps us avoid undefined behavior. It's based on a patch from teor,
    except that I wrote a perl script to regenerate the patch:
    
      #!/usr/bin/perl -p -w -i
    
      BEGIN { %vartypes = (); }
    
      if (/^[{}]/) {
          %vartypes = ();
      }
    
      if (/^ *crypto_int(\d+) +([a-zA-Z_][_a-zA-Z0-9]*)/) {
          $vartypes{$2} = $1;
      } elsif (/^ *(?:signed +)char +([a-zA-Z_][_a-zA-Z0-9]*)/) {
          $vartypes{$1} = '8';
      }
    
      # This fixes at most one shift per line. But that's all the code does.
      if (/([a-zA-Z_][a-zA-Z_0-9]*) *<< *(\d+)/) {
          $v = $1;
          if (exists $vartypes{$v}) {
      	s/$v *<< *(\d+)/SHL$vartypes{$v}($v,$1)/;
          }
      }
    
      # remove extra parenthesis
      s/\(SHL64\((.*)\)\)/SHL64\($1\)/;
      s/\(SHL32\((.*)\)\)/SHL32\($1\)/;
      s/\(SHL8\((.*)\)\)/SHL8\($1\)/;
---
 src/ext/ed25519/ref10/fe_frombytes.c       |   20 ++--
 src/ext/ed25519/ref10/fe_mul.c             |   24 ++---
 src/ext/ed25519/ref10/fe_sq.c              |   24 ++---
 src/ext/ed25519/ref10/fe_sq2.c             |   24 ++---
 src/ext/ed25519/ref10/fe_tobytes.c         |   36 +++----
 src/ext/ed25519/ref10/ge_scalarmult_base.c |    2 +-
 src/ext/ed25519/ref10/sc_muladd.c          |  158 ++++++++++++++--------------
 src/ext/ed25519/ref10/sc_reduce.c          |  112 ++++++++++----------
 8 files changed, 200 insertions(+), 200 deletions(-)

diff --git a/src/ext/ed25519/ref10/fe_frombytes.c b/src/ext/ed25519/ref10/fe_frombytes.c
index 87e2494..98b8e5f 100644
--- a/src/ext/ed25519/ref10/fe_frombytes.c
+++ b/src/ext/ed25519/ref10/fe_frombytes.c
@@ -48,17 +48,17 @@ void fe_frombytes(fe h,const unsigned char *s)
   crypto_int64 carry8;
   crypto_int64 carry9;
 
-  carry9 = (h9 + (crypto_int64) (1<<24)) >> 25; h0 += carry9 * 19; h9 -= carry9 << 25;
-  carry1 = (h1 + (crypto_int64) (1<<24)) >> 25; h2 += carry1; h1 -= carry1 << 25;
-  carry3 = (h3 + (crypto_int64) (1<<24)) >> 25; h4 += carry3; h3 -= carry3 << 25;
-  carry5 = (h5 + (crypto_int64) (1<<24)) >> 25; h6 += carry5; h5 -= carry5 << 25;
-  carry7 = (h7 + (crypto_int64) (1<<24)) >> 25; h8 += carry7; h7 -= carry7 << 25;
+  carry9 = (h9 + (crypto_int64) (1<<24)) >> 25; h0 += carry9 * 19; h9 -= SHL64(carry9,25);
+  carry1 = (h1 + (crypto_int64) (1<<24)) >> 25; h2 += carry1; h1 -= SHL64(carry1,25);
+  carry3 = (h3 + (crypto_int64) (1<<24)) >> 25; h4 += carry3; h3 -= SHL64(carry3,25);
+  carry5 = (h5 + (crypto_int64) (1<<24)) >> 25; h6 += carry5; h5 -= SHL64(carry5,25);
+  carry7 = (h7 + (crypto_int64) (1<<24)) >> 25; h8 += carry7; h7 -= SHL64(carry7,25);
 
-  carry0 = (h0 + (crypto_int64) (1<<25)) >> 26; h1 += carry0; h0 -= carry0 << 26;
-  carry2 = (h2 + (crypto_int64) (1<<25)) >> 26; h3 += carry2; h2 -= carry2 << 26;
-  carry4 = (h4 + (crypto_int64) (1<<25)) >> 26; h5 += carry4; h4 -= carry4 << 26;
-  carry6 = (h6 + (crypto_int64) (1<<25)) >> 26; h7 += carry6; h6 -= carry6 << 26;
-  carry8 = (h8 + (crypto_int64) (1<<25)) >> 26; h9 += carry8; h8 -= carry8 << 26;
+  carry0 = (h0 + (crypto_int64) (1<<25)) >> 26; h1 += carry0; h0 -= SHL64(carry0,26);
+  carry2 = (h2 + (crypto_int64) (1<<25)) >> 26; h3 += carry2; h2 -= SHL64(carry2,26);
+  carry4 = (h4 + (crypto_int64) (1<<25)) >> 26; h5 += carry4; h4 -= SHL64(carry4,26);
+  carry6 = (h6 + (crypto_int64) (1<<25)) >> 26; h7 += carry6; h6 -= SHL64(carry6,26);
+  carry8 = (h8 + (crypto_int64) (1<<25)) >> 26; h9 += carry8; h8 -= SHL64(carry8,26);
 
   h[0] = (crypto_int32) h0;
   h[1] = (crypto_int32) h1;
diff --git a/src/ext/ed25519/ref10/fe_mul.c b/src/ext/ed25519/ref10/fe_mul.c
index d68e210..ace63e6 100644
--- a/src/ext/ed25519/ref10/fe_mul.c
+++ b/src/ext/ed25519/ref10/fe_mul.c
@@ -197,46 +197,46 @@ void fe_mul(fe h,const fe f,const fe g)
     i.e. |h1| <= 1.7*2^59; narrower ranges for h3, h5, h7, h9
   */
 
-  carry0 = (h0 + (crypto_int64) (1<<25)) >> 26; h1 += carry0; h0 -= carry0 << 26;
-  carry4 = (h4 + (crypto_int64) (1<<25)) >> 26; h5 += carry4; h4 -= carry4 << 26;
+  carry0 = (h0 + (crypto_int64) (1<<25)) >> 26; h1 += carry0; h0 -= SHL64(carry0,26);
+  carry4 = (h4 + (crypto_int64) (1<<25)) >> 26; h5 += carry4; h4 -= SHL64(carry4,26);
   /* |h0| <= 2^25 */
   /* |h4| <= 2^25 */
   /* |h1| <= 1.71*2^59 */
   /* |h5| <= 1.71*2^59 */
 
-  carry1 = (h1 + (crypto_int64) (1<<24)) >> 25; h2 += carry1; h1 -= carry1 << 25;
-  carry5 = (h5 + (crypto_int64) (1<<24)) >> 25; h6 += carry5; h5 -= carry5 << 25;
+  carry1 = (h1 + (crypto_int64) (1<<24)) >> 25; h2 += carry1; h1 -= SHL64(carry1,25);
+  carry5 = (h5 + (crypto_int64) (1<<24)) >> 25; h6 += carry5; h5 -= SHL64(carry5,25);
   /* |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 + (crypto_int64) (1<<25)) >> 26; h3 += carry2; h2 -= carry2 << 26;
-  carry6 = (h6 + (crypto_int64) (1<<25)) >> 26; h7 += carry6; h6 -= carry6 << 26;
+  carry2 = (h2 + (crypto_int64) (1<<25)) >> 26; h3 += carry2; h2 -= SHL64(carry2,26);
+  carry6 = (h6 + (crypto_int64) (1<<25)) >> 26; h7 += carry6; h6 -= SHL64(carry6,26);
   /* |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 + (crypto_int64) (1<<24)) >> 25; h4 += carry3; h3 -= carry3 << 25;
-  carry7 = (h7 + (crypto_int64) (1<<24)) >> 25; h8 += carry7; h7 -= carry7 << 25;
+  carry3 = (h3 + (crypto_int64) (1<<24)) >> 25; h4 += carry3; h3 -= SHL64(carry3,25);
+  carry7 = (h7 + (crypto_int64) (1<<24)) >> 25; h8 += carry7; h7 -= SHL64(carry7,25);
   /* |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 + (crypto_int64) (1<<25)) >> 26; h5 += carry4; h4 -= carry4 << 26;
-  carry8 = (h8 + (crypto_int64) (1<<25)) >> 26; h9 += carry8; h8 -= carry8 << 26;
+  carry4 = (h4 + (crypto_int64) (1<<25)) >> 26; h5 += carry4; h4 -= SHL64(carry4,26);
+  carry8 = (h8 + (crypto_int64) (1<<25)) >> 26; h9 += carry8; h8 -= SHL64(carry8,26);
   /* |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 + (crypto_int64) (1<<24)) >> 25; h0 += carry9 * 19; h9 -= carry9 << 25;
+  carry9 = (h9 + (crypto_int64) (1<<24)) >> 25; h0 += carry9 * 19; h9 -= SHL64(carry9,25);
   /* |h9| <= 2^24; from now on fits into int32 unchanged */
   /* |h0| <= 1.1*2^39 */
 
-  carry0 = (h0 + (crypto_int64) (1<<25)) >> 26; h1 += carry0; h0 -= carry0 << 26;
+  carry0 = (h0 + (crypto_int64) (1<<25)) >> 26; h1 += carry0; h0 -= SHL64(carry0,26);
   /* |h0| <= 2^25; from now on fits into int32 unchanged */
   /* |h1| <= 1.01*2^24 */
 
diff --git a/src/ext/ed25519/ref10/fe_sq.c b/src/ext/ed25519/ref10/fe_sq.c
index 54a3949..0022a17 100644
--- a/src/ext/ed25519/ref10/fe_sq.c
+++ b/src/ext/ed25519/ref10/fe_sq.c
@@ -117,24 +117,24 @@ void fe_sq(fe h,const fe f)
   crypto_int64 carry8;
   crypto_int64 carry9;
 
-  carry0 = (h0 + (crypto_int64) (1<<25)) >> 26; h1 += carry0; h0 -= carry0 << 26;
-  carry4 = (h4 + (crypto_int64) (1<<25)) >> 26; h5 += carry4; h4 -= carry4 << 26;
+  carry0 = (h0 + (crypto_int64) (1<<25)) >> 26; h1 += carry0; h0 -= SHL64(carry0,26);
+  carry4 = (h4 + (crypto_int64) (1<<25)) >> 26; h5 += carry4; h4 -= SHL64(carry4,26);
 
-  carry1 = (h1 + (crypto_int64) (1<<24)) >> 25; h2 += carry1; h1 -= carry1 << 25;
-  carry5 = (h5 + (crypto_int64) (1<<24)) >> 25; h6 += carry5; h5 -= carry5 << 25;
+  carry1 = (h1 + (crypto_int64) (1<<24)) >> 25; h2 += carry1; h1 -= SHL64(carry1,25);
+  carry5 = (h5 + (crypto_int64) (1<<24)) >> 25; h6 += carry5; h5 -= SHL64(carry5,25);
 
-  carry2 = (h2 + (crypto_int64) (1<<25)) >> 26; h3 += carry2; h2 -= carry2 << 26;
-  carry6 = (h6 + (crypto_int64) (1<<25)) >> 26; h7 += carry6; h6 -= carry6 << 26;
+  carry2 = (h2 + (crypto_int64) (1<<25)) >> 26; h3 += carry2; h2 -= SHL64(carry2,26);
+  carry6 = (h6 + (crypto_int64) (1<<25)) >> 26; h7 += carry6; h6 -= SHL64(carry6,26);
 
-  carry3 = (h3 + (crypto_int64) (1<<24)) >> 25; h4 += carry3; h3 -= carry3 << 25;
-  carry7 = (h7 + (crypto_int64) (1<<24)) >> 25; h8 += carry7; h7 -= carry7 << 25;
+  carry3 = (h3 + (crypto_int64) (1<<24)) >> 25; h4 += carry3; h3 -= SHL64(carry3,25);
+  carry7 = (h7 + (crypto_int64) (1<<24)) >> 25; h8 += carry7; h7 -= SHL64(carry7,25);
 
-  carry4 = (h4 + (crypto_int64) (1<<25)) >> 26; h5 += carry4; h4 -= carry4 << 26;
-  carry8 = (h8 + (crypto_int64) (1<<25)) >> 26; h9 += carry8; h8 -= carry8 << 26;
+  carry4 = (h4 + (crypto_int64) (1<<25)) >> 26; h5 += carry4; h4 -= SHL64(carry4,26);
+  carry8 = (h8 + (crypto_int64) (1<<25)) >> 26; h9 += carry8; h8 -= SHL64(carry8,26);
 
-  carry9 = (h9 + (crypto_int64) (1<<24)) >> 25; h0 += carry9 * 19; h9 -= carry9 << 25;
+  carry9 = (h9 + (crypto_int64) (1<<24)) >> 25; h0 += carry9 * 19; h9 -= SHL64(carry9,25);
 
-  carry0 = (h0 + (crypto_int64) (1<<25)) >> 26; h1 += carry0; h0 -= carry0 << 26;
+  carry0 = (h0 + (crypto_int64) (1<<25)) >> 26; h1 += carry0; h0 -= SHL64(carry0,26);
 
   h[0] = (crypto_int32) h0;
   h[1] = (crypto_int32) h1;
diff --git a/src/ext/ed25519/ref10/fe_sq2.c b/src/ext/ed25519/ref10/fe_sq2.c
index 01b149f..e8faa69 100644
--- a/src/ext/ed25519/ref10/fe_sq2.c
+++ b/src/ext/ed25519/ref10/fe_sq2.c
@@ -128,24 +128,24 @@ void fe_sq2(fe h,const fe f)
   h8 += h8;
   h9 += h9;
 
-  carry0 = (h0 + (crypto_int64) (1<<25)) >> 26; h1 += carry0; h0 -= carry0 << 26;
-  carry4 = (h4 + (crypto_int64) (1<<25)) >> 26; h5 += carry4; h4 -= carry4 << 26;
+  carry0 = (h0 + (crypto_int64) (1<<25)) >> 26; h1 += carry0; h0 -= SHL64(carry0,26);
+  carry4 = (h4 + (crypto_int64) (1<<25)) >> 26; h5 += carry4; h4 -= SHL64(carry4,26);
 
-  carry1 = (h1 + (crypto_int64) (1<<24)) >> 25; h2 += carry1; h1 -= carry1 << 25;
-  carry5 = (h5 + (crypto_int64) (1<<24)) >> 25; h6 += carry5; h5 -= carry5 << 25;
+  carry1 = (h1 + (crypto_int64) (1<<24)) >> 25; h2 += carry1; h1 -= SHL64(carry1,25);
+  carry5 = (h5 + (crypto_int64) (1<<24)) >> 25; h6 += carry5; h5 -= SHL64(carry5,25);
 
-  carry2 = (h2 + (crypto_int64) (1<<25)) >> 26; h3 += carry2; h2 -= carry2 << 26;
-  carry6 = (h6 + (crypto_int64) (1<<25)) >> 26; h7 += carry6; h6 -= carry6 << 26;
+  carry2 = (h2 + (crypto_int64) (1<<25)) >> 26; h3 += carry2; h2 -= SHL64(carry2,26);
+  carry6 = (h6 + (crypto_int64) (1<<25)) >> 26; h7 += carry6; h6 -= SHL64(carry6,26);
 
-  carry3 = (h3 + (crypto_int64) (1<<24)) >> 25; h4 += carry3; h3 -= carry3 << 25;
-  carry7 = (h7 + (crypto_int64) (1<<24)) >> 25; h8 += carry7; h7 -= carry7 << 25;
+  carry3 = (h3 + (crypto_int64) (1<<24)) >> 25; h4 += carry3; h3 -= SHL64(carry3,25);
+  carry7 = (h7 + (crypto_int64) (1<<24)) >> 25; h8 += carry7; h7 -= SHL64(carry7,25);
 
-  carry4 = (h4 + (crypto_int64) (1<<25)) >> 26; h5 += carry4; h4 -= carry4 << 26;
-  carry8 = (h8 + (crypto_int64) (1<<25)) >> 26; h9 += carry8; h8 -= carry8 << 26;
+  carry4 = (h4 + (crypto_int64) (1<<25)) >> 26; h5 += carry4; h4 -= SHL64(carry4,26);
+  carry8 = (h8 + (crypto_int64) (1<<25)) >> 26; h9 += carry8; h8 -= SHL64(carry8,26);
 
-  carry9 = (h9 + (crypto_int64) (1<<24)) >> 25; h0 += carry9 * 19; h9 -= carry9 << 25;
+  carry9 = (h9 + (crypto_int64) (1<<24)) >> 25; h0 += carry9 * 19; h9 -= SHL64(carry9,25);
 
-  carry0 = (h0 + (crypto_int64) (1<<25)) >> 26; h1 += carry0; h0 -= carry0 << 26;
+  carry0 = (h0 + (crypto_int64) (1<<25)) >> 26; h1 += carry0; h0 -= SHL64(carry0,26);
 
   h[0] = (crypto_int32) h0;
   h[1] = (crypto_int32) h1;
diff --git a/src/ext/ed25519/ref10/fe_tobytes.c b/src/ext/ed25519/ref10/fe_tobytes.c
index 0a63baf..3c7f389 100644
--- a/src/ext/ed25519/ref10/fe_tobytes.c
+++ b/src/ext/ed25519/ref10/fe_tobytes.c
@@ -65,16 +65,16 @@ void fe_tobytes(unsigned char *s,const fe h)
   h0 += 19 * q;
   /* Goal: Output h-2^255 q, which is between 0 and 2^255-20. */
 
-  carry0 = h0 >> 26; h1 += carry0; h0 -= carry0 << 26;
-  carry1 = h1 >> 25; h2 += carry1; h1 -= carry1 << 25;
-  carry2 = h2 >> 26; h3 += carry2; h2 -= carry2 << 26;
-  carry3 = h3 >> 25; h4 += carry3; h3 -= carry3 << 25;
-  carry4 = h4 >> 26; h5 += carry4; h4 -= carry4 << 26;
-  carry5 = h5 >> 25; h6 += carry5; h5 -= carry5 << 25;
-  carry6 = h6 >> 26; h7 += carry6; h6 -= carry6 << 26;
-  carry7 = h7 >> 25; h8 += carry7; h7 -= carry7 << 25;
-  carry8 = h8 >> 26; h9 += carry8; h8 -= carry8 << 26;
-  carry9 = h9 >> 25;               h9 -= carry9 << 25;
+  carry0 = h0 >> 26; h1 += carry0; h0 -= SHL32(carry0,26);
+  carry1 = h1 >> 25; h2 += carry1; h1 -= SHL32(carry1,25);
+  carry2 = h2 >> 26; h3 += carry2; h2 -= SHL32(carry2,26);
+  carry3 = h3 >> 25; h4 += carry3; h3 -= SHL32(carry3,25);
+  carry4 = h4 >> 26; h5 += carry4; h4 -= SHL32(carry4,26);
+  carry5 = h5 >> 25; h6 += carry5; h5 -= SHL32(carry5,25);
+  carry6 = h6 >> 26; h7 += carry6; h6 -= SHL32(carry6,26);
+  carry7 = h7 >> 25; h8 += carry7; h7 -= SHL32(carry7,25);
+  carry8 = h8 >> 26; h9 += carry8; h8 -= SHL32(carry8,26);
+  carry9 = h9 >> 25;               h9 -= SHL32(carry9,25);
                   /* h10 = carry9 */
 
   /*
@@ -87,32 +87,32 @@ void fe_tobytes(unsigned char *s,const fe h)
   s[0] = h0 >> 0;
   s[1] = h0 >> 8;
   s[2] = h0 >> 16;
-  s[3] = (h0 >> 24) | (h1 << 2);
+  s[3] = (h0 >> 24) | SHL32(h1,2);
   s[4] = h1 >> 6;
   s[5] = h1 >> 14;
-  s[6] = (h1 >> 22) | (h2 << 3);
+  s[6] = (h1 >> 22) | SHL32(h2,3);
   s[7] = h2 >> 5;
   s[8] = h2 >> 13;
-  s[9] = (h2 >> 21) | (h3 << 5);
+  s[9] = (h2 >> 21) | SHL32(h3,5);
   s[10] = h3 >> 3;
   s[11] = h3 >> 11;
-  s[12] = (h3 >> 19) | (h4 << 6);
+  s[12] = (h3 >> 19) | SHL32(h4,6);
   s[13] = h4 >> 2;
   s[14] = h4 >> 10;
   s[15] = h4 >> 18;
   s[16] = h5 >> 0;
   s[17] = h5 >> 8;
   s[18] = h5 >> 16;
-  s[19] = (h5 >> 24) | (h6 << 1);
+  s[19] = (h5 >> 24) | SHL32(h6,1);
   s[20] = h6 >> 7;
   s[21] = h6 >> 15;
-  s[22] = (h6 >> 23) | (h7 << 3);
+  s[22] = (h6 >> 23) | SHL32(h7,3);
   s[23] = h7 >> 5;
   s[24] = h7 >> 13;
-  s[25] = (h7 >> 21) | (h8 << 4);
+  s[25] = (h7 >> 21) | SHL32(h8,4);
   s[26] = h8 >> 4;
   s[27] = h8 >> 12;
-  s[28] = (h8 >> 20) | (h9 << 6);
+  s[28] = (h8 >> 20) | SHL32(h9,6);
   s[29] = h9 >> 2;
   s[30] = h9 >> 10;
   s[31] = h9 >> 18;
diff --git a/src/ext/ed25519/ref10/ge_scalarmult_base.c b/src/ext/ed25519/ref10/ge_scalarmult_base.c
index ad7aae4..3ede0ad 100644
--- a/src/ext/ed25519/ref10/ge_scalarmult_base.c
+++ b/src/ext/ed25519/ref10/ge_scalarmult_base.c
@@ -86,7 +86,7 @@ void ge_scalarmult_base(ge_p3 *h,const unsigned char *a)
     e[i] += carry;
     carry = e[i] + 8;
     carry >>= 4;
-    e[i] -= carry << 4;
+    e[i] -= SHL8(carry,4);
   }
   e[63] += carry;
   /* each e[i] is between -8 and 8 */
diff --git a/src/ext/ed25519/ref10/sc_muladd.c b/src/ext/ed25519/ref10/sc_muladd.c
index 6f1e9d0..20b94c1 100644
--- a/src/ext/ed25519/ref10/sc_muladd.c
+++ b/src/ext/ed25519/ref10/sc_muladd.c
@@ -144,30 +144,30 @@ void sc_muladd(unsigned char *s,const unsigned char *a,const unsigned char *b,co
   s22 = a11*b11;
   s23 = 0;
 
-  carry0 = (s0 + (1<<20)) >> 21; s1 += carry0; s0 -= carry0 << 21;
-  carry2 = (s2 + (1<<20)) >> 21; s3 += carry2; s2 -= carry2 << 21;
-  carry4 = (s4 + (1<<20)) >> 21; s5 += carry4; s4 -= carry4 << 21;
-  carry6 = (s6 + (1<<20)) >> 21; s7 += carry6; s6 -= carry6 << 21;
-  carry8 = (s8 + (1<<20)) >> 21; s9 += carry8; s8 -= carry8 << 21;
-  carry10 = (s10 + (1<<20)) >> 21; s11 += carry10; s10 -= carry10 << 21;
-  carry12 = (s12 + (1<<20)) >> 21; s13 += carry12; s12 -= carry12 << 21;
-  carry14 = (s14 + (1<<20)) >> 21; s15 += carry14; s14 -= carry14 << 21;
-  carry16 = (s16 + (1<<20)) >> 21; s17 += carry16; s16 -= carry16 << 21;
-  carry18 = (s18 + (1<<20)) >> 21; s19 += carry18; s18 -= carry18 << 21;
-  carry20 = (s20 + (1<<20)) >> 21; s21 += carry20; s20 -= carry20 << 21;
-  carry22 = (s22 + (1<<20)) >> 21; s23 += carry22; s22 -= carry22 << 21;
+  carry0 = (s0 + (1<<20)) >> 21; s1 += carry0; s0 -= SHL64(carry0,21);
+  carry2 = (s2 + (1<<20)) >> 21; s3 += carry2; s2 -= SHL64(carry2,21);
+  carry4 = (s4 + (1<<20)) >> 21; s5 += carry4; s4 -= SHL64(carry4,21);
+  carry6 = (s6 + (1<<20)) >> 21; s7 += carry6; s6 -= SHL64(carry6,21);
+  carry8 = (s8 + (1<<20)) >> 21; s9 += carry8; s8 -= SHL64(carry8,21);
+  carry10 = (s10 + (1<<20)) >> 21; s11 += carry10; s10 -= SHL64(carry10,21);
+  carry12 = (s12 + (1<<20)) >> 21; s13 += carry12; s12 -= SHL64(carry12,21);
+  carry14 = (s14 + (1<<20)) >> 21; s15 += carry14; s14 -= SHL64(carry14,21);
+  carry16 = (s16 + (1<<20)) >> 21; s17 += carry16; s16 -= SHL64(carry16,21);
+  carry18 = (s18 + (1<<20)) >> 21; s19 += carry18; s18 -= SHL64(carry18,21);
+  carry20 = (s20 + (1<<20)) >> 21; s21 += carry20; s20 -= SHL64(carry20,21);
+  carry22 = (s22 + (1<<20)) >> 21; s23 += carry22; s22 -= SHL64(carry22,21);
 
-  carry1 = (s1 + (1<<20)) >> 21; s2 += carry1; s1 -= carry1 << 21;
-  carry3 = (s3 + (1<<20)) >> 21; s4 += carry3; s3 -= carry3 << 21;
-  carry5 = (s5 + (1<<20)) >> 21; s6 += carry5; s5 -= carry5 << 21;
-  carry7 = (s7 + (1<<20)) >> 21; s8 += carry7; s7 -= carry7 << 21;
-  carry9 = (s9 + (1<<20)) >> 21; s10 += carry9; s9 -= carry9 << 21;
-  carry11 = (s11 + (1<<20)) >> 21; s12 += carry11; s11 -= carry11 << 21;
-  carry13 = (s13 + (1<<20)) >> 21; s14 += carry13; s13 -= carry13 << 21;
-  carry15 = (s15 + (1<<20)) >> 21; s16 += carry15; s15 -= carry15 << 21;
-  carry17 = (s17 + (1<<20)) >> 21; s18 += carry17; s17 -= carry17 << 21;
-  carry19 = (s19 + (1<<20)) >> 21; s20 += carry19; s19 -= carry19 << 21;
-  carry21 = (s21 + (1<<20)) >> 21; s22 += carry21; s21 -= carry21 << 21;
+  carry1 = (s1 + (1<<20)) >> 21; s2 += carry1; s1 -= SHL64(carry1,21);
+  carry3 = (s3 + (1<<20)) >> 21; s4 += carry3; s3 -= SHL64(carry3,21);
+  carry5 = (s5 + (1<<20)) >> 21; s6 += carry5; s5 -= SHL64(carry5,21);
+  carry7 = (s7 + (1<<20)) >> 21; s8 += carry7; s7 -= SHL64(carry7,21);
+  carry9 = (s9 + (1<<20)) >> 21; s10 += carry9; s9 -= SHL64(carry9,21);
+  carry11 = (s11 + (1<<20)) >> 21; s12 += carry11; s11 -= SHL64(carry11,21);
+  carry13 = (s13 + (1<<20)) >> 21; s14 += carry13; s13 -= SHL64(carry13,21);
+  carry15 = (s15 + (1<<20)) >> 21; s16 += carry15; s15 -= SHL64(carry15,21);
+  carry17 = (s17 + (1<<20)) >> 21; s18 += carry17; s17 -= SHL64(carry17,21);
+  carry19 = (s19 + (1<<20)) >> 21; s20 += carry19; s19 -= SHL64(carry19,21);
+  carry21 = (s21 + (1<<20)) >> 21; s22 += carry21; s21 -= SHL64(carry21,21);
 
   s11 += s23 * 666643;
   s12 += s23 * 470296;
@@ -217,18 +217,18 @@ void sc_muladd(unsigned char *s,const unsigned char *a,const unsigned char *b,co
   s11 -= s18 * 683901;
   s18 = 0;
 
-  carry6 = (s6 + (1<<20)) >> 21; s7 += carry6; s6 -= carry6 << 21;
-  carry8 = (s8 + (1<<20)) >> 21; s9 += carry8; s8 -= carry8 << 21;
-  carry10 = (s10 + (1<<20)) >> 21; s11 += carry10; s10 -= carry10 << 21;
-  carry12 = (s12 + (1<<20)) >> 21; s13 += carry12; s12 -= carry12 << 21;
-  carry14 = (s14 + (1<<20)) >> 21; s15 += carry14; s14 -= carry14 << 21;
-  carry16 = (s16 + (1<<20)) >> 21; s17 += carry16; s16 -= carry16 << 21;
+  carry6 = (s6 + (1<<20)) >> 21; s7 += carry6; s6 -= SHL64(carry6,21);
+  carry8 = (s8 + (1<<20)) >> 21; s9 += carry8; s8 -= SHL64(carry8,21);
+  carry10 = (s10 + (1<<20)) >> 21; s11 += carry10; s10 -= SHL64(carry10,21);
+  carry12 = (s12 + (1<<20)) >> 21; s13 += carry12; s12 -= SHL64(carry12,21);
+  carry14 = (s14 + (1<<20)) >> 21; s15 += carry14; s14 -= SHL64(carry14,21);
+  carry16 = (s16 + (1<<20)) >> 21; s17 += carry16; s16 -= SHL64(carry16,21);
 
-  carry7 = (s7 + (1<<20)) >> 21; s8 += carry7; s7 -= carry7 << 21;
-  carry9 = (s9 + (1<<20)) >> 21; s10 += carry9; s9 -= carry9 << 21;
-  carry11 = (s11 + (1<<20)) >> 21; s12 += carry11; s11 -= carry11 << 21;
-  carry13 = (s13 + (1<<20)) >> 21; s14 += carry13; s13 -= carry13 << 21;
-  carry15 = (s15 + (1<<20)) >> 21; s16 += carry15; s15 -= carry15 << 21;
+  carry7 = (s7 + (1<<20)) >> 21; s8 += carry7; s7 -= SHL64(carry7,21);
+  carry9 = (s9 + (1<<20)) >> 21; s10 += carry9; s9 -= SHL64(carry9,21);
+  carry11 = (s11 + (1<<20)) >> 21; s12 += carry11; s11 -= SHL64(carry11,21);
+  carry13 = (s13 + (1<<20)) >> 21; s14 += carry13; s13 -= SHL64(carry13,21);
+  carry15 = (s15 + (1<<20)) >> 21; s16 += carry15; s15 -= SHL64(carry15,21);
 
   s5 += s17 * 666643;
   s6 += s17 * 470296;
@@ -278,19 +278,19 @@ void sc_muladd(unsigned char *s,const unsigned char *a,const unsigned char *b,co
   s5 -= s12 * 683901;
   s12 = 0;
 
-  carry0 = (s0 + (1<<20)) >> 21; s1 += carry0; s0 -= carry0 << 21;
-  carry2 = (s2 + (1<<20)) >> 21; s3 += carry2; s2 -= carry2 << 21;
-  carry4 = (s4 + (1<<20)) >> 21; s5 += carry4; s4 -= carry4 << 21;
-  carry6 = (s6 + (1<<20)) >> 21; s7 += carry6; s6 -= carry6 << 21;
-  carry8 = (s8 + (1<<20)) >> 21; s9 += carry8; s8 -= carry8 << 21;
-  carry10 = (s10 + (1<<20)) >> 21; s11 += carry10; s10 -= carry10 << 21;
+  carry0 = (s0 + (1<<20)) >> 21; s1 += carry0; s0 -= SHL64(carry0,21);
+  carry2 = (s2 + (1<<20)) >> 21; s3 += carry2; s2 -= SHL64(carry2,21);
+  carry4 = (s4 + (1<<20)) >> 21; s5 += carry4; s4 -= SHL64(carry4,21);
+  carry6 = (s6 + (1<<20)) >> 21; s7 += carry6; s6 -= SHL64(carry6,21);
+  carry8 = (s8 + (1<<20)) >> 21; s9 += carry8; s8 -= SHL64(carry8,21);
+  carry10 = (s10 + (1<<20)) >> 21; s11 += carry10; s10 -= SHL64(carry10,21);
 
-  carry1 = (s1 + (1<<20)) >> 21; s2 += carry1; s1 -= carry1 << 21;
-  carry3 = (s3 + (1<<20)) >> 21; s4 += carry3; s3 -= carry3 << 21;
-  carry5 = (s5 + (1<<20)) >> 21; s6 += carry5; s5 -= carry5 << 21;
-  carry7 = (s7 + (1<<20)) >> 21; s8 += carry7; s7 -= carry7 << 21;
-  carry9 = (s9 + (1<<20)) >> 21; s10 += carry9; s9 -= carry9 << 21;
-  carry11 = (s11 + (1<<20)) >> 21; s12 += carry11; s11 -= carry11 << 21;
+  carry1 = (s1 + (1<<20)) >> 21; s2 += carry1; s1 -= SHL64(carry1,21);
+  carry3 = (s3 + (1<<20)) >> 21; s4 += carry3; s3 -= SHL64(carry3,21);
+  carry5 = (s5 + (1<<20)) >> 21; s6 += carry5; s5 -= SHL64(carry5,21);
+  carry7 = (s7 + (1<<20)) >> 21; s8 += carry7; s7 -= SHL64(carry7,21);
+  carry9 = (s9 + (1<<20)) >> 21; s10 += carry9; s9 -= SHL64(carry9,21);
+  carry11 = (s11 + (1<<20)) >> 21; s12 += carry11; s11 -= SHL64(carry11,21);
 
   s0 += s12 * 666643;
   s1 += s12 * 470296;
@@ -300,18 +300,18 @@ void sc_muladd(unsigned char *s,const unsigned char *a,const unsigned char *b,co
   s5 -= s12 * 683901;
   s12 = 0;
 
-  carry0 = s0 >> 21; s1 += carry0; s0 -= carry0 << 21;
-  carry1 = s1 >> 21; s2 += carry1; s1 -= carry1 << 21;
-  carry2 = s2 >> 21; s3 += carry2; s2 -= carry2 << 21;
-  carry3 = s3 >> 21; s4 += carry3; s3 -= carry3 << 21;
-  carry4 = s4 >> 21; s5 += carry4; s4 -= carry4 << 21;
-  carry5 = s5 >> 21; s6 += carry5; s5 -= carry5 << 21;
-  carry6 = s6 >> 21; s7 += carry6; s6 -= carry6 << 21;
-  carry7 = s7 >> 21; s8 += carry7; s7 -= carry7 << 21;
-  carry8 = s8 >> 21; s9 += carry8; s8 -= carry8 << 21;
-  carry9 = s9 >> 21; s10 += carry9; s9 -= carry9 << 21;
-  carry10 = s10 >> 21; s11 += carry10; s10 -= carry10 << 21;
-  carry11 = s11 >> 21; s12 += carry11; s11 -= carry11 << 21;
+  carry0 = s0 >> 21; s1 += carry0; s0 -= SHL64(carry0,21);
+  carry1 = s1 >> 21; s2 += carry1; s1 -= SHL64(carry1,21);
+  carry2 = s2 >> 21; s3 += carry2; s2 -= SHL64(carry2,21);
+  carry3 = s3 >> 21; s4 += carry3; s3 -= SHL64(carry3,21);
+  carry4 = s4 >> 21; s5 += carry4; s4 -= SHL64(carry4,21);
+  carry5 = s5 >> 21; s6 += carry5; s5 -= SHL64(carry5,21);
+  carry6 = s6 >> 21; s7 += carry6; s6 -= SHL64(carry6,21);
+  carry7 = s7 >> 21; s8 += carry7; s7 -= SHL64(carry7,21);
+  carry8 = s8 >> 21; s9 += carry8; s8 -= SHL64(carry8,21);
+  carry9 = s9 >> 21; s10 += carry9; s9 -= SHL64(carry9,21);
+  carry10 = s10 >> 21; s11 += carry10; s10 -= SHL64(carry10,21);
+  carry11 = s11 >> 21; s12 += carry11; s11 -= SHL64(carry11,21);
 
   s0 += s12 * 666643;
   s1 += s12 * 470296;
@@ -321,47 +321,47 @@ void sc_muladd(unsigned char *s,const unsigned char *a,const unsigned char *b,co
   s5 -= s12 * 683901;
   s12 = 0;
 
-  carry0 = s0 >> 21; s1 += carry0; s0 -= carry0 << 21;
-  carry1 = s1 >> 21; s2 += carry1; s1 -= carry1 << 21;
-  carry2 = s2 >> 21; s3 += carry2; s2 -= carry2 << 21;
-  carry3 = s3 >> 21; s4 += carry3; s3 -= carry3 << 21;
-  carry4 = s4 >> 21; s5 += carry4; s4 -= carry4 << 21;
-  carry5 = s5 >> 21; s6 += carry5; s5 -= carry5 << 21;
-  carry6 = s6 >> 21; s7 += carry6; s6 -= carry6 << 21;
-  carry7 = s7 >> 21; s8 += carry7; s7 -= carry7 << 21;
-  carry8 = s8 >> 21; s9 += carry8; s8 -= carry8 << 21;
-  carry9 = s9 >> 21; s10 += carry9; s9 -= carry9 << 21;
-  carry10 = s10 >> 21; s11 += carry10; s10 -= carry10 << 21;
+  carry0 = s0 >> 21; s1 += carry0; s0 -= SHL64(carry0,21);
+  carry1 = s1 >> 21; s2 += carry1; s1 -= SHL64(carry1,21);
+  carry2 = s2 >> 21; s3 += carry2; s2 -= SHL64(carry2,21);
+  carry3 = s3 >> 21; s4 += carry3; s3 -= SHL64(carry3,21);
+  carry4 = s4 >> 21; s5 += carry4; s4 -= SHL64(carry4,21);
+  carry5 = s5 >> 21; s6 += carry5; s5 -= SHL64(carry5,21);
+  carry6 = s6 >> 21; s7 += carry6; s6 -= SHL64(carry6,21);
+  carry7 = s7 >> 21; s8 += carry7; s7 -= SHL64(carry7,21);
+  carry8 = s8 >> 21; s9 += carry8; s8 -= SHL64(carry8,21);
+  carry9 = s9 >> 21; s10 += carry9; s9 -= SHL64(carry9,21);
+  carry10 = s10 >> 21; s11 += carry10; s10 -= SHL64(carry10,21);
 
   s[0] = s0 >> 0;
   s[1] = s0 >> 8;
-  s[2] = (s0 >> 16) | (s1 << 5);
+  s[2] = (s0 >> 16) | SHL64(s1,5);
   s[3] = s1 >> 3;
   s[4] = s1 >> 11;
-  s[5] = (s1 >> 19) | (s2 << 2);
+  s[5] = (s1 >> 19) | SHL64(s2,2);
   s[6] = s2 >> 6;
-  s[7] = (s2 >> 14) | (s3 << 7);
+  s[7] = (s2 >> 14) | SHL64(s3,7);
   s[8] = s3 >> 1;
   s[9] = s3 >> 9;
-  s[10] = (s3 >> 17) | (s4 << 4);
+  s[10] = (s3 >> 17) | SHL64(s4,4);
   s[11] = s4 >> 4;
   s[12] = s4 >> 12;
-  s[13] = (s4 >> 20) | (s5 << 1);
+  s[13] = (s4 >> 20) | SHL64(s5,1);
   s[14] = s5 >> 7;
-  s[15] = (s5 >> 15) | (s6 << 6);
+  s[15] = (s5 >> 15) | SHL64(s6,6);
   s[16] = s6 >> 2;
   s[17] = s6 >> 10;
-  s[18] = (s6 >> 18) | (s7 << 3);
+  s[18] = (s6 >> 18) | SHL64(s7,3);
   s[19] = s7 >> 5;
   s[20] = s7 >> 13;
   s[21] = s8 >> 0;
   s[22] = s8 >> 8;
-  s[23] = (s8 >> 16) | (s9 << 5);
+  s[23] = (s8 >> 16) | SHL64(s9,5);
   s[24] = s9 >> 3;
   s[25] = s9 >> 11;
-  s[26] = (s9 >> 19) | (s10 << 2);
+  s[26] = (s9 >> 19) | SHL64(s10,2);
   s[27] = s10 >> 6;
-  s[28] = (s10 >> 14) | (s11 << 7);
+  s[28] = (s10 >> 14) | SHL64(s11,7);
   s[29] = s11 >> 1;
   s[30] = s11 >> 9;
   s[31] = s11 >> 17;
diff --git a/src/ext/ed25519/ref10/sc_reduce.c b/src/ext/ed25519/ref10/sc_reduce.c
index d01f5a5..c5afa53 100644
--- a/src/ext/ed25519/ref10/sc_reduce.c
+++ b/src/ext/ed25519/ref10/sc_reduce.c
@@ -124,18 +124,18 @@ void sc_reduce(unsigned char *s)
   s11 -= s18 * 683901;
   s18 = 0;
 
-  carry6 = (s6 + (1<<20)) >> 21; s7 += carry6; s6 -= carry6 << 21;
-  carry8 = (s8 + (1<<20)) >> 21; s9 += carry8; s8 -= carry8 << 21;
-  carry10 = (s10 + (1<<20)) >> 21; s11 += carry10; s10 -= carry10 << 21;
-  carry12 = (s12 + (1<<20)) >> 21; s13 += carry12; s12 -= carry12 << 21;
-  carry14 = (s14 + (1<<20)) >> 21; s15 += carry14; s14 -= carry14 << 21;
-  carry16 = (s16 + (1<<20)) >> 21; s17 += carry16; s16 -= carry16 << 21;
+  carry6 = (s6 + (1<<20)) >> 21; s7 += carry6; s6 -= SHL64(carry6,21);
+  carry8 = (s8 + (1<<20)) >> 21; s9 += carry8; s8 -= SHL64(carry8,21);
+  carry10 = (s10 + (1<<20)) >> 21; s11 += carry10; s10 -= SHL64(carry10,21);
+  carry12 = (s12 + (1<<20)) >> 21; s13 += carry12; s12 -= SHL64(carry12,21);
+  carry14 = (s14 + (1<<20)) >> 21; s15 += carry14; s14 -= SHL64(carry14,21);
+  carry16 = (s16 + (1<<20)) >> 21; s17 += carry16; s16 -= SHL64(carry16,21);
 
-  carry7 = (s7 + (1<<20)) >> 21; s8 += carry7; s7 -= carry7 << 21;
-  carry9 = (s9 + (1<<20)) >> 21; s10 += carry9; s9 -= carry9 << 21;
-  carry11 = (s11 + (1<<20)) >> 21; s12 += carry11; s11 -= carry11 << 21;
-  carry13 = (s13 + (1<<20)) >> 21; s14 += carry13; s13 -= carry13 << 21;
-  carry15 = (s15 + (1<<20)) >> 21; s16 += carry15; s15 -= carry15 << 21;
+  carry7 = (s7 + (1<<20)) >> 21; s8 += carry7; s7 -= SHL64(carry7,21);
+  carry9 = (s9 + (1<<20)) >> 21; s10 += carry9; s9 -= SHL64(carry9,21);
+  carry11 = (s11 + (1<<20)) >> 21; s12 += carry11; s11 -= SHL64(carry11,21);
+  carry13 = (s13 + (1<<20)) >> 21; s14 += carry13; s13 -= SHL64(carry13,21);
+  carry15 = (s15 + (1<<20)) >> 21; s16 += carry15; s15 -= SHL64(carry15,21);
 
   s5 += s17 * 666643;
   s6 += s17 * 470296;
@@ -185,19 +185,19 @@ void sc_reduce(unsigned char *s)
   s5 -= s12 * 683901;
   s12 = 0;
 
-  carry0 = (s0 + (1<<20)) >> 21; s1 += carry0; s0 -= carry0 << 21;
-  carry2 = (s2 + (1<<20)) >> 21; s3 += carry2; s2 -= carry2 << 21;
-  carry4 = (s4 + (1<<20)) >> 21; s5 += carry4; s4 -= carry4 << 21;
-  carry6 = (s6 + (1<<20)) >> 21; s7 += carry6; s6 -= carry6 << 21;
-  carry8 = (s8 + (1<<20)) >> 21; s9 += carry8; s8 -= carry8 << 21;
-  carry10 = (s10 + (1<<20)) >> 21; s11 += carry10; s10 -= carry10 << 21;
+  carry0 = (s0 + (1<<20)) >> 21; s1 += carry0; s0 -= SHL64(carry0,21);
+  carry2 = (s2 + (1<<20)) >> 21; s3 += carry2; s2 -= SHL64(carry2,21);
+  carry4 = (s4 + (1<<20)) >> 21; s5 += carry4; s4 -= SHL64(carry4,21);
+  carry6 = (s6 + (1<<20)) >> 21; s7 += carry6; s6 -= SHL64(carry6,21);
+  carry8 = (s8 + (1<<20)) >> 21; s9 += carry8; s8 -= SHL64(carry8,21);
+  carry10 = (s10 + (1<<20)) >> 21; s11 += carry10; s10 -= SHL64(carry10,21);
 
-  carry1 = (s1 + (1<<20)) >> 21; s2 += carry1; s1 -= carry1 << 21;
-  carry3 = (s3 + (1<<20)) >> 21; s4 += carry3; s3 -= carry3 << 21;
-  carry5 = (s5 + (1<<20)) >> 21; s6 += carry5; s5 -= carry5 << 21;
-  carry7 = (s7 + (1<<20)) >> 21; s8 += carry7; s7 -= carry7 << 21;
-  carry9 = (s9 + (1<<20)) >> 21; s10 += carry9; s9 -= carry9 << 21;
-  carry11 = (s11 + (1<<20)) >> 21; s12 += carry11; s11 -= carry11 << 21;
+  carry1 = (s1 + (1<<20)) >> 21; s2 += carry1; s1 -= SHL64(carry1,21);
+  carry3 = (s3 + (1<<20)) >> 21; s4 += carry3; s3 -= SHL64(carry3,21);
+  carry5 = (s5 + (1<<20)) >> 21; s6 += carry5; s5 -= SHL64(carry5,21);
+  carry7 = (s7 + (1<<20)) >> 21; s8 += carry7; s7 -= SHL64(carry7,21);
+  carry9 = (s9 + (1<<20)) >> 21; s10 += carry9; s9 -= SHL64(carry9,21);
+  carry11 = (s11 + (1<<20)) >> 21; s12 += carry11; s11 -= SHL64(carry11,21);
 
   s0 += s12 * 666643;
   s1 += s12 * 470296;
@@ -207,18 +207,18 @@ void sc_reduce(unsigned char *s)
   s5 -= s12 * 683901;
   s12 = 0;
 
-  carry0 = s0 >> 21; s1 += carry0; s0 -= carry0 << 21;
-  carry1 = s1 >> 21; s2 += carry1; s1 -= carry1 << 21;
-  carry2 = s2 >> 21; s3 += carry2; s2 -= carry2 << 21;
-  carry3 = s3 >> 21; s4 += carry3; s3 -= carry3 << 21;
-  carry4 = s4 >> 21; s5 += carry4; s4 -= carry4 << 21;
-  carry5 = s5 >> 21; s6 += carry5; s5 -= carry5 << 21;
-  carry6 = s6 >> 21; s7 += carry6; s6 -= carry6 << 21;
-  carry7 = s7 >> 21; s8 += carry7; s7 -= carry7 << 21;
-  carry8 = s8 >> 21; s9 += carry8; s8 -= carry8 << 21;
-  carry9 = s9 >> 21; s10 += carry9; s9 -= carry9 << 21;
-  carry10 = s10 >> 21; s11 += carry10; s10 -= carry10 << 21;
-  carry11 = s11 >> 21; s12 += carry11; s11 -= carry11 << 21;
+  carry0 = s0 >> 21; s1 += carry0; s0 -= SHL64(carry0,21);
+  carry1 = s1 >> 21; s2 += carry1; s1 -= SHL64(carry1,21);
+  carry2 = s2 >> 21; s3 += carry2; s2 -= SHL64(carry2,21);
+  carry3 = s3 >> 21; s4 += carry3; s3 -= SHL64(carry3,21);
+  carry4 = s4 >> 21; s5 += carry4; s4 -= SHL64(carry4,21);
+  carry5 = s5 >> 21; s6 += carry5; s5 -= SHL64(carry5,21);
+  carry6 = s6 >> 21; s7 += carry6; s6 -= SHL64(carry6,21);
+  carry7 = s7 >> 21; s8 += carry7; s7 -= SHL64(carry7,21);
+  carry8 = s8 >> 21; s9 += carry8; s8 -= SHL64(carry8,21);
+  carry9 = s9 >> 21; s10 += carry9; s9 -= SHL64(carry9,21);
+  carry10 = s10 >> 21; s11 += carry10; s10 -= SHL64(carry10,21);
+  carry11 = s11 >> 21; s12 += carry11; s11 -= SHL64(carry11,21);
 
   s0 += s12 * 666643;
   s1 += s12 * 470296;
@@ -228,47 +228,47 @@ void sc_reduce(unsigned char *s)
   s5 -= s12 * 683901;
   s12 = 0;
 
-  carry0 = s0 >> 21; s1 += carry0; s0 -= carry0 << 21;
-  carry1 = s1 >> 21; s2 += carry1; s1 -= carry1 << 21;
-  carry2 = s2 >> 21; s3 += carry2; s2 -= carry2 << 21;
-  carry3 = s3 >> 21; s4 += carry3; s3 -= carry3 << 21;
-  carry4 = s4 >> 21; s5 += carry4; s4 -= carry4 << 21;
-  carry5 = s5 >> 21; s6 += carry5; s5 -= carry5 << 21;
-  carry6 = s6 >> 21; s7 += carry6; s6 -= carry6 << 21;
-  carry7 = s7 >> 21; s8 += carry7; s7 -= carry7 << 21;
-  carry8 = s8 >> 21; s9 += carry8; s8 -= carry8 << 21;
-  carry9 = s9 >> 21; s10 += carry9; s9 -= carry9 << 21;
-  carry10 = s10 >> 21; s11 += carry10; s10 -= carry10 << 21;
+  carry0 = s0 >> 21; s1 += carry0; s0 -= SHL64(carry0,21);
+  carry1 = s1 >> 21; s2 += carry1; s1 -= SHL64(carry1,21);
+  carry2 = s2 >> 21; s3 += carry2; s2 -= SHL64(carry2,21);
+  carry3 = s3 >> 21; s4 += carry3; s3 -= SHL64(carry3,21);
+  carry4 = s4 >> 21; s5 += carry4; s4 -= SHL64(carry4,21);
+  carry5 = s5 >> 21; s6 += carry5; s5 -= SHL64(carry5,21);
+  carry6 = s6 >> 21; s7 += carry6; s6 -= SHL64(carry6,21);
+  carry7 = s7 >> 21; s8 += carry7; s7 -= SHL64(carry7,21);
+  carry8 = s8 >> 21; s9 += carry8; s8 -= SHL64(carry8,21);
+  carry9 = s9 >> 21; s10 += carry9; s9 -= SHL64(carry9,21);
+  carry10 = s10 >> 21; s11 += carry10; s10 -= SHL64(carry10,21);
 
   s[0] = s0 >> 0;
   s[1] = s0 >> 8;
-  s[2] = (s0 >> 16) | (s1 << 5);
+  s[2] = (s0 >> 16) | SHL64(s1,5);
   s[3] = s1 >> 3;
   s[4] = s1 >> 11;
-  s[5] = (s1 >> 19) | (s2 << 2);
+  s[5] = (s1 >> 19) | SHL64(s2,2);
   s[6] = s2 >> 6;
-  s[7] = (s2 >> 14) | (s3 << 7);
+  s[7] = (s2 >> 14) | SHL64(s3,7);
   s[8] = s3 >> 1;
   s[9] = s3 >> 9;
-  s[10] = (s3 >> 17) | (s4 << 4);
+  s[10] = (s3 >> 17) | SHL64(s4,4);
   s[11] = s4 >> 4;
   s[12] = s4 >> 12;
-  s[13] = (s4 >> 20) | (s5 << 1);
+  s[13] = (s4 >> 20) | SHL64(s5,1);
   s[14] = s5 >> 7;
-  s[15] = (s5 >> 15) | (s6 << 6);
+  s[15] = (s5 >> 15) | SHL64(s6,6);
   s[16] = s6 >> 2;
   s[17] = s6 >> 10;
-  s[18] = (s6 >> 18) | (s7 << 3);
+  s[18] = (s6 >> 18) | SHL64(s7,3);
   s[19] = s7 >> 5;
   s[20] = s7 >> 13;
   s[21] = s8 >> 0;
   s[22] = s8 >> 8;
-  s[23] = (s8 >> 16) | (s9 << 5);
+  s[23] = (s8 >> 16) | SHL64(s9,5);
   s[24] = s9 >> 3;
   s[25] = s9 >> 11;
-  s[26] = (s9 >> 19) | (s10 << 2);
+  s[26] = (s9 >> 19) | SHL64(s10,2);
   s[27] = s10 >> 6;
-  s[28] = (s10 >> 14) | (s11 << 7);
+  s[28] = (s10 >> 14) | SHL64(s11,7);
   s[29] = s11 >> 1;
   s[30] = s11 >> 9;
   s[31] = s11 >> 17;



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