Remove some conditional branches from division

4 files changed, 2995 insertions, 22 deletions

diff --git a/src/lib/math/bigint/bigint.cpp b/src/lib/math/bigint/bigint.cpp
index a4545e4a1..1a09a92f1 100644
--- a/src/lib/math/bigint/bigint.cpp
+++ b/src/lib/math/bigint/bigint.cpp
@@ -317,7 +317,7 @@ BigInt BigInt::operator-() const
    return x;
    }
 
-void BigInt::reduce_below(const BigInt& p, secure_vector<word>& ws)
+size_t BigInt::reduce_below(const BigInt& p, secure_vector<word>& ws)
    {
    if(p.is_negative())
       throw Invalid_Argument("BigInt::reduce_below mod must be positive");
@@ -332,14 +332,19 @@ void BigInt::reduce_below(const BigInt& p, secure_vector<word>& ws)
 
    clear_mem(ws.data(), ws.size());
 
+   size_t reductions = 0;
+
    for(;;)
       {
       word borrow = bigint_sub3(ws.data(), data(), p_words + 1, p.data(), p_words);
       if(borrow)
          break;
 
+      ++reductions;
       swap_reg(ws);
       }
+
+   return reductions;
    }
 
 /*
diff --git a/src/lib/math/bigint/bigint.h b/src/lib/math/bigint/bigint.h
index f0aa04391..9b7af4169 100644
--- a/src/lib/math/bigint/bigint.h
+++ b/src/lib/math/bigint/bigint.h
@@ -344,7 +344,7 @@ class BOTAN_PUBLIC_API(2,0) BigInt final
      * mod and performs repeated subtractions. It should not be used if
      * *this is much larger than mod, instead use modulo operator.
      */
-     void reduce_below(const BigInt& mod, secure_vector<word> &ws);
+     size_t reduce_below(const BigInt& mod, secure_vector<word> &ws);
 
      /**
      * Zeroize the BigInt. The size of the underlying register is not
diff --git a/src/lib/math/bigint/divide.cpp b/src/lib/math/bigint/divide.cpp
index 2dfb7405e..ed9a12112 100644
--- a/src/lib/math/bigint/divide.cpp
+++ b/src/lib/math/bigint/divide.cpp
@@ -154,6 +154,8 @@ BigInt ct_modulo(const BigInt& x, const BigInt& y)
 
 /*
 * Solve x = q * y + r
+*
+* See Handbook of Applied Cryptography section 14.2.5
 */
 void divide(const BigInt& x, const BigInt& y_arg, BigInt& q_out, BigInt& r_out)
    {
@@ -166,11 +168,12 @@ void divide(const BigInt& x, const BigInt& y_arg, BigInt& q_out, BigInt& r_out)
 
    BigInt r = x;
    BigInt q = 0;
+   secure_vector<word> ws;
 
    r.set_sign(BigInt::Positive);
    y.set_sign(BigInt::Positive);
 
-   if(r >= y)
+   if(r.is_nonzero())
       {
       // Calculate shifts needed to normalize y with high bit set
       const size_t shifts = BOTAN_MP_WORD_BITS - high_bit(y.word_at(y_words-1));
@@ -180,7 +183,7 @@ void divide(const BigInt& x, const BigInt& y_arg, BigInt& q_out, BigInt& r_out)
 
       // we know y has not changed size, since we only shifted up to set high bit
       const size_t t = y_words - 1;
-      const size_t n = r.sig_words() - 1; // r may have changed size however
+      const size_t n = std::max(t, r.sig_words() - 1); // r may have changed size however
 
       BOTAN_ASSERT_NOMSG(n >= t);
 
@@ -190,38 +193,35 @@ void divide(const BigInt& x, const BigInt& y_arg, BigInt& q_out, BigInt& r_out)
 
       BigInt shifted_y = y << (BOTAN_MP_WORD_BITS * (n-t));
 
-      while(r >= shifted_y)
-         {
-         r -= shifted_y;
-         q_words[n-t] += 1;
-         }
+      // Set q_{n-t} to number of times r > shifted_y
+      q_words[n-t] = r.reduce_below(shifted_y, ws);
+
+      const word y_t0  = y.word_at(t);
+      const word y_t1  = y.word_at(t-1);
 
       for(size_t j = n; j != t; --j)
          {
          const word x_j0  = r.word_at(j);
          const word x_j1 = r.word_at(j-1);
          const word x_j2 = r.word_at(j-2);
-         const word y_t0  = y.word_at(t);
-         const word y_t1  = y.word_at(t-1);
 
-         word qjt = (x_j0 == y_t0) ? MP_WORD_MAX : bigint_divop(x_j0, x_j1, y_t0);
+         word qjt = bigint_divop(x_j0, x_j1, y_t0);
+
+         qjt = CT::Mask<word>::is_equal(x_j0, y_t0).select(MP_WORD_MAX, qjt);
 
-         while(division_check(qjt, y_t0, y_t1, x_j0, x_j1, x_j2))
-            {
-            qjt -= 1;
-            }
+         // Per HAC 14.23, this operation is required at most twice
+         qjt -= division_check(qjt, y_t0, y_t1, x_j0, x_j1, x_j2);
+         qjt -= division_check(qjt, y_t0, y_t1, x_j0, x_j1, x_j2);
+         BOTAN_DEBUG_ASSERT(division_check(qjt, y_t0, y_t1, x_j0, x_j1, x_j2) == false);
 
          shifted_y >>= BOTAN_MP_WORD_BITS;
          // Now shifted_y == y << (BOTAN_MP_WORD_BITS * (j-t-1))
 
          r -= qjt * shifted_y;
 
-         if(r.is_negative())
-            {
-            // overcorrected
-            qjt -= 1;
-            r += shifted_y;
-            }
+         // TODO this could be better
+         qjt -= r.is_negative();
+         r += static_cast<word>(r.is_negative()) * shifted_y;
 
          q_words[j-t-1] = qjt;
          }
diff --git a/src/tests/data/bn/divide.vec b/src/tests/data/bn/divide.vec
index 0a6dd2423..b7195a8e4 100644
--- a/src/tests/data/bn/divide.vec
+++ b/src/tests/data/bn/divide.vec
@@ -163,3 +163,2971 @@ In1 = 1996953214196350189568
 In2 = 13331618315827609940
 Output = 149
 
+In1 = 0xA
+In2 = 0xA
+Output = 0x1
+
+In1 = 0x2020
+In2 = 0xA00
+Output = 0x3
+
+In1 = 0xA0A
+In2 = 0x1
+Output = 0xA0A
+
+In1 = 0xA
+In2 = 0x1
+Output = 0xA
+
+In1 = 0xA00
+In2 = 0x100
+Output = 0xA
+
+In1 = 0xC700
+In2 = 0x100
+Output = 0xC7
+
+In1 = 0x6000
+In2 = 0xA
+Output = 0x999
+
+In1 = 0x2235
+In2 = 0xA00
+Output = 0x3
+
+In1 = 0xE00A
+In2 = 0xA20
+Output = 0x16
+
+In1 = 0x6000
+In2 = 0xEC
+Output = 0x68
+
+In1 = 0x100
+In2 = 0xC7
+Output = 0x1
+
+In1 = 0xE00A
+In2 = 0x20
+Output = 0x700
+
+In1 = 0xE0E0
+In2 = 0xA20
+Output = 0x16
+
+In1 = 0xE00E
+In2 = 0x20
+Output = 0x700
+
+In1 = 0xE00A
+In2 = 0x1A20
+Output = 0x8
+
+In1 = 0xE0E0
+In2 = 0x3A20
+Output = 0x3
+
+In1 = 0x2C
+In2 = 0x7
+Output = 0x6
+
+In1 = 0xE0E0
+In2 = 0xE00A
+Output = 0x1
+
+In1 = 0xE0E0
+In2 = 0x930A
+Output = 0x1
+
+In1 = 0x6C
+In2 = 0x31
+Output = 0x2
+
+In1 = 0xFF0A
+In2 = 0xA1C
+Output = 0x19
+
+In1 = 0x203B
+In2 = 0x22
+Output = 0xF2
+
+In1 = 0xA0A
+In2 = 0x101
+Output = 0xA
+
+In1 = 0xE0
+In2 = 0xA
+Output = 0x16
+
+In1 = 0xC7C7
+In2 = 0x2020
+Output = 0x6
+
+In1 = 0xE00A
+In2 = 0xAEA
+Output = 0x14
+
+In1 = 0x60
+In2 = 0x20
+Output = 0x3
+
+In1 = 0x8801
+In2 = 0xA00
+Output = 0xD
+
+In1 = 0xE00A
+In2 = 0xA00
+Output = 0x16
+
+In1 = 0xE0A1
+In2 = 0x20E0
+Output = 0x6
+
+In1 = 0x4320
+In2 = 0xAE0
+Output = 0x6
+
+In1 = 0x100
+In2 = 0x41
+Output = 0x3
+
+In1 = 0x6000
+In2 = 0xE
+Output = 0x6DB
+
+In1 = 0xC7C7
+In2 = 0x20A0
+Output = 0x6
+
+In1 = 0xEC19
+In2 = 0xA
+Output = 0x179C
+
+In1 = 0x1900
+In2 = 0x232
+Output = 0xB
+
+In1 = 0xE0A1
+In2 = 0xE0A1
+Output = 0x1
+
+In1 = 0xA0A
+In2 = 0xA0A
+Output = 0x1
+
+In1 = 0x20F6
+In2 = 0x20E0
+Output = 0x1
+
+In1 = 0x3A00
+In2 = 0x2000
+Output = 0x1
+
+In1 = 0xA70E
+In2 = 0x6000
+Output = 0x1
+
+In1 = 0x6000
+In2 = 0xF
+Output = 0x666
+
+In1 = 0x400
+In2 = 0x100
+Output = 0x4
+
+In1 = 0x22
+In2 = 0x2
+Output = 0x11
+
+In1 = 0x2ADF
+In2 = 0xEFE
+Output = 0x2
+
+In1 = 0x20
+In2 = 0xA
+Output = 0x3
+
+In1 = 0xE0
+In2 = 0x5D
+Output = 0x2
+
+In1 = 0xFE
+In2 = 0x20
+Output = 0x7
+
+In1 = 0xE7F5
+In2 = 0x2600
+Output = 0x6
+
+In1 = 0xE0
+In2 = 0xA1
+Output = 0x1
+
+In1 = 0xE80E
+In2 = 0x2020
+Output = 0x7
+
+In1 = 0x3522
+In2 = 0xA00
+Output = 0x5
+
+In1 = 0x870E
+In2 = 0x602D
+Output = 0x1
+
+In1 = 0x5AD8
+In2 = 0xEFE
+Output = 0x6
+
+In1 = 0x20F7
+In2 = 0x20E8
+Output = 0x1
+
+In1 = 0x5AD8
+In2 = 0x3AFE
+Output = 0x1
+
+In1 = 0x5AD8
+In2 = 0x3208
+Output = 0x1
+
+In1 = 0x3293
+In2 = 0x1F0A
+Output = 0x1
+
+In1 = 0x400
+In2 = 0x180
+Output = 0x2
+
+In1 = 0x4
+In2 = 0x4
+Output = 0x1
+
+In1 = 0x262C
+In2 = 0x1
+Output = 0x262C
+
+In1 = 0x8001
+In2 = 0xA00
+Output = 0xC
+
+In1 = 0x2C01
+In2 = 0x169F
+Output = 0x1
+
+In1 = 0xA3E0
+In2 = 0xA20
+Output = 0x10
+
+In1 = 0x2C
+In2 = 0x1
+Output = 0x2C
+
+In1 = 0xFFFF
+In2 = 0xAFF
+Output = 0x17
+
+In1 = 0xFF03
+In2 = 0x4
+Output = 0x3FC0
+
+In1 = 0x3801
+In2 = 0xA
+Output = 0x599
+
+In1 = 0x32C7
+In2 = 0x1F5A
+Output = 0x1
+
+In1 = 0x6000
+In2 = 0x90A
+Output = 0xA
+
+In1 = 0x2B01
+In2 = 0xA00
+Output = 0x4
+
+In1 = 0xE0C7
+In2 = 0x1E0
+Output = 0x77
+
+In1 = 0x8D01
+In2 = 0x4A00
+Output = 0x1
+
+In1 = 0xC7FF
+In2 = 0x700
+Output = 0x1C
+
+In1 = 0xE001
+In2 = 0x93
+Output = 0x186
+
+In1 = 0x5F
+In2 = 0x35
+Output = 0x1
+
+In1 = 0xF6DF
+In2 = 0xD5FF
+Output = 0x1
+
+In1 = 0xC760
+In2 = 0x220A
+Output = 0x5
+
+In1 = 0x4100
+In2 = 0xC3
+Output = 0x55
+
+In1 = 0x2C
+In2 = 0x3
+Output = 0xE
+
+In1 = 0xFC02
+In2 = 0x100
+Output = 0xFC
+
+In1 = 0x89C7
+In2 = 0x1760
+Output = 0x5
+
+In1 = 0x1
+In2 = 0x1
+Output = 0x1
+
+In1 = 0x100
+In2 = 0x83
+Output = 0x1
+
+In1 = 0xFFE0
+In2 = 0x5DD9
+Output = 0x2
+
+In1 = 0x3320
+In2 = 0x300
+Output = 0x11
+
+In1 = 0x5AD8
+In2 = 0x1E0E
+Output = 0x3
+
+In1 = 0x6000
+In2 = 0x4F
+Output = 0x137
+
+In1 = 0xE7F5
+In2 = 0x600
+Output = 0x26
+
+In1 = 0xDFFE
+In2 = 0x60
+Output = 0x255
+
+In1 = 0x89
+In2 = 0x4E
+Output = 0x1
+
+In1 = 0x3801
+In2 = 0x80A
+Output = 0x6
+
+In1 = 0xDFE0
+In2 = 0xE0
+Output = 0xFF
+
+In1 = 0x35D8
+In2 = 0xEFE
+Output = 0x3
+
+In1 = 0xA3E0
+In2 = 0x2C20
+Output = 0x3
+
+In1 = 0x3A0A
+In2 = 0xA
+Output = 0x5CD
+
+In1 = 0x8440
+In2 = 0xEFC
+Output = 0x8
+
+In1 = 0xDE
+In2 = 0x10
+Output = 0xD
+
+In1 = 0x52
+In2 = 0xE
+Output = 0x5
+
+In1 = 0xFF2B
+In2 = 0xFF2B
+Output = 0x1
+
+In1 = 0xA70E
+In2 = 0xA0F7
+Output = 0x1
+
+In1 = 0xF8F6
+In2 = 0xC50A
+Output = 0x1
+
+In1 = 0xFFFF
+In2 = 0xEB8
+Output = 0x11
+
+In1 = 0x5AFA
+In2 = 0x40A
+Output = 0x16
+
+In1 = 0x3320
+In2 = 0x500
+Output = 0xA
+
+In1 = 0x6000
+In2 = 0x14F
+Output = 0x49
+
+In1 = 0xD8
+In2 = 0x8
+Output = 0x1B
+
+In1 = 0xC7FF
+In2 = 0x710
+Output = 0x1C
+
+In1 = 0xFF2A
+In2 = 0xC57
+Output = 0x14
+
+In1 = 0x502E
+In2 = 0x12C
+Output = 0x44
+
+In1 = 0x8041
+In2 = 0x4140
+Output = 0x1
+
+In1 = 0xD5DF
+In2 = 0xD5D5
+Output = 0x1
+
+In1 = 0x7F56
+In2 = 0x7EDD
+Output = 0x1
+
+In1 = 0x20E0
+In2 = 0xAE0
+Output = 0x3
+
+In1 = 0xB00
+In2 = 0x4E0
+Output = 0x2
+
+In1 = 0x601
+In2 = 0x10
+Output = 0x60
+
+In1 = 0x1040
+In2 = 0x4
+Output = 0x410
+
+In1 = 0x6B33
+In2 = 0x1
+Output = 0x6B33
+
+In1 = 0xE001
+In2 = 0x97
+Output = 0x17B
+
+In1 = 0x3500
+In2 = 0x4F
+Output = 0xAB
+
+In1 = 0xFED1
+In2 = 0x100
+Output = 0xFE
+
+In1 = 0x20F2
+In2 = 0x20E8
+Output = 0x1
+
+In1 = 0xBA0A
+In2 = 0x8
+Output = 0x1741
+
+In1 = 0x40D8
+In2 = 0xE35
+Output = 0x4
+
+In1 = 0x5E2E
+In2 = 0x12C
+Output = 0x50
+
+In1 = 0x2
+In2 = 0x2
+Output = 0x1
+
+In1 = 0x89C7
+In2 = 0x760
+Output = 0x12
+
+In1 = 0xFFFF
+In2 = 0x400
+Output = 0x3F
+
+In1 = 0x5BF5
+In2 = 0x600
+Output = 0xF
+
+In1 = 0x6
+In2 = 0x1
+Output = 0x6
+
+In1 = 0x7F56
+In2 = 0x3ADD
+Output = 0x2
+
+In1 = 0x500
+In2 = 0x180
+Output = 0x3
+
+In1 = 0x406
+In2 = 0x12C
+Output = 0x3
+
+In1 = 0x29DE
+In2 = 0xC50
+Output = 0x3
+
+In1 = 0xDFE0
+In2 = 0xA0A
+Output = 0x16
+
+In1 = 0x2800
+In2 = 0x400
+Output = 0xA
+
+In1 = 0xE0
+In2 = 0x87
+Output = 0x1
+
+In1 = 0x3B2C
+In2 = 0x1
+Output = 0x3B2C
+
+In1 = 0x3B2C
+In2 = 0xB
+Output = 0x561
+
+In1 = 0xE0
+In2 = 0xE
+Output = 0x10
+
+In1 = 0x3B3B
+In2 = 0x2C2C
+Output = 0x1
+
+In1 = 0x2ADF
+In2 = 0x2ADF
+Output = 0x1
+
+In1 = 0xFFFF
+In2 = 0x1
+Output = 0xFFFF
+
+In1 = 0x800A
+In2 = 0x1
+Output = 0x800A
+
+In1 = 0x41
+In2 = 0x41
+Output = 0x1
+
+In1 = 0xDB02FCDB00
+In2 = 0xDB02FCDB
+Output = 0x100
+
+In1 = 0x6B00
+In2 = 0x1
+Output = 0x6B00
+
+In1 = 0xE0E0
+In2 = 0xE0
+Output = 0x101
+
+In1 = 0xA0
+In2 = 0xB
+Output = 0xE
+
+In1 = 0xA24
+In2 = 0x100
+Output = 0xA
+
+In1 = 0xE0E0
+In2 = 0xE6
+Output = 0xFA
+
+In1 = 0x6B2F
+In2 = 0x1
+Output = 0x6B2F
+
+In1 = 0x20
+In2 = 0x1
+Output = 0x20
+
+In1 = 0x3B
+In2 = 0x2C
+Output = 0x1
+
+In1 = 0x502
+In2 = 0x101
+Output = 0x4
+
+In1 = 0x312F
+In2 = 0x1
+Output = 0x312F
+
+In1 = 0x8001
+In2 = 0x1
+Output = 0x8001
+
+In1 = 0xC8
+In2 = 0x8
+Output = 0x19
+
+In1 = 0x3A
+In2 = 0x20
+Output = 0x1
+
+In1 = 0xB
+In2 = 0xA
+Output = 0x1
+
+In1 = 0xA0A
+In2 = 0x800
+Output = 0x1
+
+In1 = 0x41E400
+In2 = 0x2223
+Output = 0x1EE
+
+In1 = 0xDB02FC
+In2 = 0x1C808
+Output = 0x7A
+
+In1 = 0xDB022C
+In2 = 0x108
+Output = 0xD45F
+
+In1 = 0xFFFFFF
+In2 = 0xFFDA2E
+Output = 0x1
+
+In1 = 0x80FFFF
+In2 = 0x10401
+Output = 0x7F
+
+In1 = 0xAD802
+In2 = 0xA0108
+Output = 0x1
+
+In1 = 0x3B020A
+In2 = 0xA8903
+Output = 0x5
+
+In1 = 0xE3220
+In2 = 0x30042
+Output = 0x4
+
+In1 = 0xE02401
+In2 = 0x1
+Output = 0xE02401
+
+In1 = 0x2F0006
+In2 = 0x1
+Output = 0x2F0006
+
+In1 = 0xFFE0E000
+In2 = 0xE00E0000
+Output = 0x1
+
+In1 = 0x91023120
+In2 = 0x32030002
+Output = 0x2
+
+In1 = 0xFFFFFFFF
+In2 = 0xFFFFFF02
+Output = 0x1
+
+In1 = 0xE02401
+In2 = 0x1001
+Output = 0xE01
+
+In1 = 0x41E4FF00
+In2 = 0x2241E423
+Output = 0x1
+
+In1 = 0x2F000001
+In2 = 0x1
+Output = 0x2F000001
+
+In1 = 0x6BFF00FF
+In2 = 0x10000
+Output = 0x6BFF
+
+In1 = 0x6BFF4F0100
+In2 = 0x2400
+Output = 0x2FFFB15
+
+In1 = 0x490601E400
+In2 = 0x1C8E40022
+Output = 0x28
+
+In1 = 0xFEFEFE0000
+In2 = 0x4FEFEFE
+Output = 0x330A
+
+In1 = 0xFFFFFF0A31
+In2 = 0x2022E4C760
+Output = 0x7
+
+In1 = 0xFFFFFFFFFF
+In2 = 0xFFFF02C760
+Output = 0x1
+
+In1 = 0xFFFFFF0000
+In2 = 0x2C760
+Output = 0x5C2034
+
+In1 = 0xE0BF00
+In2 = 0x101
+Output = 0xDFDF
+
+In1 = 0x6B00000100
+In2 = 0x2400
+Output = 0x2F8E38E
+
+In1 = 0x10000FA00
+In2 = 0x2C760
+Output = 0x5C20
+
+In1 = 0xFFF7FFFFFF
+In2 = 0xF7FF02C760
+Output = 0x1
+
+In1 = 0x3BFFFFFFFF
+In2 = 0x3BFFFF2C2C
+Output = 0x1
+
+In1 = 0x41FF000000
+In2 = 0x2C760
+Output = 0x17BFF1
+
+In1 = 0x100000000
+In2 = 0xFEFE
+Output = 0x10103
+
+In1 = 0x6B40FF4F00
+In2 = 0x100000000
+Output = 0x6B
+
+In1 = 0x4100000000
+In2 = 0xFEFE
+Output = 0x4141C4
+
+In1 = 0xFFF721FFFF
+In2 = 0xF7FF02C760
+Output = 0x1
+
+In1 = 0x3F2C07AF00
+In2 = 0x101000000
+Output = 0x3E
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