/*

* Division Algorithm

* (C) 1999-2007,2012,2018 Jack Lloyd

*

* Botan is released under the Simplified BSD License (see license.txt)

*/

#include <botan/internal/divide.h>

#include <botan/internal/mp_core.h>

#include <botan/internal/mp_madd.h>

#include <botan/internal/ct_utils.h>

#include <botan/internal/bit_ops.h>

namespace Botan {

namespace {

/*

* Handle signed operands, if necessary

*/

void sign_fixup(const BigInt& x, const BigInt& y, BigInt& q, BigInt& r)

   {

   q.cond_flip_sign(x.sign() != y.sign());

   if(x.is_negative() && r.is_nonzero())

      {

      q -= 1;

      r = y.abs() - r;

      }

   }

inline bool division_check(word q, word y2, word y1,

                           word x3, word x2, word x1)

   {

   /*

   Compute (y3,y2,y1) = (y2,y1) * q

   and return true if (y3,y2,y1) > (x3,x2,x1)

   */

   word y3 = 0;

   y1 = word_madd2(q, y1, &y3);

   y2 = word_madd2(q, y2, &y3);

   const word x[3] = { x1, x2, x3 };

   const word y[3] = { y1, y2, y3 };

   return bigint_ct_is_lt(x, 3, y, 3).is_set();

   }

}

void ct_divide(const BigInt& x, const BigInt& y, BigInt& q_out, BigInt& r_out)

   {

   const size_t x_words = x.sig_words();

   const size_t y_words = y.sig_words();

   const size_t x_bits = x.bits();

   BigInt q(BigInt::Positive, x_words);

   BigInt r(BigInt::Positive, y_words);

   BigInt t(BigInt::Positive, y_words); // a temporary

   for(size_t i = 0; i != x_bits; ++i)

      {

      const size_t b = x_bits - 1 - i;

      const bool x_b = x.get_bit(b);

      r *= 2;

      r.conditionally_set_bit(0, x_b);

      const bool r_gte_y = bigint_sub3(t.mutable_data(), r.data(), r.size(), y.data(), y_words) == 0;

      q.conditionally_set_bit(b, r_gte_y);

      r.ct_cond_swap(r_gte_y, t);

      }

   sign_fixup(x, y, q, r);

   r_out = r;

   q_out = q;

   }

void ct_divide_u8(const BigInt& x, uint8_t y, BigInt& q_out, uint8_t& r_out)

   {

   const size_t x_words = x.sig_words();

   const size_t x_bits = x.bits();

   BigInt q(BigInt::Positive, x_words);

   uint32_t r = 0;

   for(size_t i = 0; i != x_bits; ++i)

      {

      const size_t b = x_bits - 1 - i;

      const bool x_b = x.get_bit(b);

      r *= 2;

      r += x_b;

      const auto r_gte_y = CT::Mask<uint32_t>::is_gte(r, y);

      q.conditionally_set_bit(b, r_gte_y.is_set());

      r = r_gte_y.select(r - y, r);

      }

   if(x.is_negative())

      {

      q.flip_sign();

      if(r != 0)

         {

         --q;

         r = y - r;

         }

      }

   r_out = static_cast<uint8_t>(r);

   q_out = q;

   }

BigInt ct_modulo(const BigInt& x, const BigInt& y)

   {

   if(y.is_negative() || y.is_zero())

      throw Invalid_Argument("ct_modulo requires y > 0");

   const size_t y_words = y.sig_words();

   const size_t x_bits = x.bits();

   BigInt r(BigInt::Positive, y_words);

   BigInt t(BigInt::Positive, y_words);

   for(size_t i = 0; i != x_bits; ++i)

      {

      const size_t b = x_bits - 1 - i;

      const bool x_b = x.get_bit(b);

      r *= 2;

      r.conditionally_set_bit(0, x_b);

      const bool r_gte_y = bigint_sub3(t.mutable_data(), r.data(), r.size(), y.data(), y_words) == 0;

      r.ct_cond_swap(r_gte_y, t);

      }

   if(x.is_negative())

      {

      if(r.is_nonzero())

         {

         r = y - r;

         }

      }

   return r;

   }

/*

* Solve x = q * y + r

*

* See Handbook of Applied Cryptography section 14.2.5

*/

void vartime_divide(const BigInt& x, const BigInt& y_arg, BigInt& q_out, BigInt& r_out)

   {

   if(y_arg.is_zero())

      throw Invalid_Argument("vartime_divide: cannot divide by zero");

   const size_t y_words = y_arg.sig_words();

   BOTAN_ASSERT_NOMSG(y_words > 0);

   BigInt y = y_arg;

   BigInt r = x;

   BigInt q = 0;

   secure_vector<word> ws;

   r.set_sign(BigInt::Positive);

   y.set_sign(BigInt::Positive);

   // Calculate shifts needed to normalize y with high bit set

   const size_t shifts = y.top_bits_free();

   y <<= shifts;

   r <<= shifts;

   // 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 = std::max(y_words, r.sig_words()) - 1; // r may have changed size however

   BOTAN_ASSERT_NOMSG(n >= t);

   q.grow_to(n - t + 1);

   word* q_words = q.mutable_data();

   BigInt shifted_y = y << (BOTAN_MP_WORD_BITS * (n-t));

   // 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);

   BOTAN_DEBUG_ASSERT((y_t0 >> (BOTAN_MP_WORD_BITS-1)) == 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);

      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);

      // 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))

      // TODO this sequence could be better

      r -= qjt * shifted_y;

      qjt -= r.is_negative();

      r += static_cast<word>(r.is_negative()) * shifted_y;

      q_words[j-t-1] = qjt;

      }

   r >>= shifts;

   sign_fixup(x, y_arg, q, r);

   r_out = r;

   q_out = q;

   }

}