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/*
* Division Algorithm
* (C) 1999-2007,2012,2018 Jack Lloyd
*
* Botan is released under the Simplified BSD License (see license.txt)
*/
#include <botan/divide.h>
#include <botan/internal/mp_core.h>
#include <botan/internal/mp_madd.h>
#include <botan/internal/ct_utils.h>
namespace Botan {
namespace {
/*
* Handle signed operands, if necessary
*/
void sign_fixup(const BigInt& x, const BigInt& y, BigInt& q, BigInt& r)
{
if(x.sign() == BigInt::Negative)
{
q.flip_sign();
if(r.is_nonzero()) { --q; r = y.abs() - r; }
}
if(y.sign() == BigInt::Negative)
q.flip_sign();
}
bool division_check(word q, word y2, word y1,
word x3, word x2, word x1)
{
// Compute (y3,y2,y1) = (y2,y1) * q
word y3 = 0;
y1 = word_madd2(q, y1, &y3);
y2 = word_madd2(q, y2, &y3);
// Return (y3,y2,y1) >? (x3,x2,x1)
if(y3 > x3) return true;
if(y3 < x3) return false;
if(y2 > x2) return true;
if(y2 < x2) return false;
if(y1 > x1) return true;
if(y1 < x1) return false;
return false;
}
}
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);
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);
// y <= r -> r >= y
const auto r_gte_y = bigint_ct_is_lt(y.data(), y_words, r.data(), r.size(), true);
q.conditionally_set_bit(b, r_gte_y.is_set());
bigint_cnd_sub(r_gte_y.value(), r.mutable_data(), r.size(), y.data(), y_words);
}
sign_fixup(x, y, q, r);
r_out = r;
q_out = q;
}
/*
* Solve x = q * y + r
*/
void divide(const BigInt& x, const BigInt& y_arg, BigInt& q, BigInt& r)
{
if(y_arg.is_zero())
throw BigInt::DivideByZero();
BigInt y = y_arg;
const size_t y_words = y.sig_words();
r = x;
q = 0;
r.set_sign(BigInt::Positive);
y.set_sign(BigInt::Positive);
int32_t compare = r.cmp(y);
if(compare == 0)
{
q = 1;
r = 0;
}
else if(compare > 0)
{
size_t shifts = 0;
word y_top = y.word_at(y.sig_words()-1);
while(y_top < MP_WORD_TOP_BIT) { y_top <<= 1; ++shifts; }
y <<= shifts;
r <<= shifts;
const size_t n = r.sig_words() - 1;
const size_t t = y_words - 1;
if(n < t)
throw Internal_Error("BigInt division word sizes");
q.grow_to(n - t + 1);
word* q_words = q.mutable_data();
if(n <= t)
{
while(r > y) { r -= y; ++q; }
r >>= shifts;
sign_fixup(x, y_arg, q, r);
return;
}
BigInt temp = y << (BOTAN_MP_WORD_BITS * (n-t));
while(r >= temp) { r -= temp; q_words[n-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 y_t = y.word_at(t);
if(x_j0 == y_t)
q_words[j-t-1] = MP_WORD_MAX;
else
q_words[j-t-1] = bigint_divop(x_j0, x_j1, y_t);
while(division_check(q_words[j-t-1],
y_t, y.word_at(t-1),
x_j0, x_j1, r.word_at(j-2)))
{
q_words[j-t-1] -= 1;
}
r -= (q_words[j-t-1] * y) << (BOTAN_MP_WORD_BITS * (j-t-1));
if(r.is_negative())
{
r += y << (BOTAN_MP_WORD_BITS * (j-t-1));
q_words[j-t-1] -= 1;
}
}
r >>= shifts;
}
sign_fixup(x, y_arg, q, r);
}
}
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