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https://github.com/Z3Prover/z3
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This commit is contained in:
Nikolaj Bjorner
parent
e19a7f71aa
commit
c0e885931c
2 changed files with 147 additions and 24 deletions
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@ -34,10 +34,71 @@ u256 u256::operator*(u256 const& other) const {
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return u256(result);
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}
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u256 u256::operator<<(uint64_t sh) const {
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u256 r;
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if (0 == sh || sh >= 256)
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;
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else if (sh >= 176)
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r.m_num[3] = m_num[0] << (sh - 176);
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else if (sh >= 128) {
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sh -= 128;
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r.m_num[2] = m_num[0] << sh;
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r.m_num[3] = (m_num[1] << sh) | (m_num[0] >> (64 - sh));
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}
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else if (sh >= 64) {
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sh -= 64;
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r.m_num[1] = m_num[0] << sh;
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r.m_num[2] = (m_num[1] << sh) | (m_num[0] >> (64 - sh));
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r.m_num[3] = (m_num[2] << sh) | (m_num[1] >> (64 - sh));
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}
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else {
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r.m_num[0] = m_num[0] << sh;
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r.m_num[1] = (m_num[1] << sh) | (m_num[0] >> (64 - sh));
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r.m_num[2] = (m_num[2] << sh) | (m_num[1] >> (64 - sh));
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r.m_num[3] = (m_num[3] << sh) | (m_num[2] >> (64 - sh));
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}
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return r;
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}
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u256 u256::operator>>(uint64_t sh) const {
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u256 r;
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if (0 == sh || sh >= 256)
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;
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else if (sh >= 176)
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r.m_num[0] = m_num[3] >> (sh - 176);
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else if (sh >= 128) {
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sh -= 128;
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r.m_num[0] = (m_num[2] >> sh) | (m_num[3] << (64 - sh));
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r.m_num[1] = (m_num[3] >> sh);
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}
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else if (sh >= 64) {
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sh -= 64;
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r.m_num[0] = (m_num[1] >> sh) | (m_num[2] << (64 - sh));
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r.m_num[1] = (m_num[2] >> sh) | (m_num[3] << (64 - sh));
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r.m_num[2] = (m_num[3] >> sh);
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}
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else {
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r.m_num[0] = (m_num[0] >> sh) | (m_num[1] << (64 - sh));
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r.m_num[1] = (m_num[1] >> sh) | (m_num[2] << (64 - sh));
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r.m_num[2] = (m_num[2] >> sh) | (m_num[3] << (64 - sh));
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r.m_num[3] = (m_num[3] >> sh);
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}
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return r;
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}
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u256 u256::operator&(u256 const& other) const {
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u256 r;
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for (unsigned i = 0; i < 4; ++i)
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r.m_num[i] = m_num[i] & other.m_num[i];
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return r;
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}
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u256& u256::operator*=(u256 const& other) {
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uint64_t result[8];
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Hacl_Bignum256_mul(const_cast<uint64_t*>(m_num), const_cast<uint64_t*>(other.m_num), result);
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std::uninitialized_copy(m_num, m_num + sizeof(*this), result);
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std::uninitialized_copy(m_num, m_num + 4, result);
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return *this;
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}
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@ -58,22 +119,34 @@ u256& u256::inv() {
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return *this;
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}
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u256 u256::mod(u256 const& other) const {
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if (other.is_zero())
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throw default_exception("mod 0 is not defined");
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if (other.is_one())
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return u256();
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u256 r;
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uint64_t a[8];
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a[4] = a[5] = a[6] = a[7] = 0;
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if (!other.is_even()) {
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std::uninitialized_copy(m_num, m_num + 4, a);
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VERIFY(Hacl_Bignum256_mod(const_cast<uint64_t*>(other.m_num), a, r.m_num));
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return r;
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}
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unsigned tz = other.trailing_zeros();
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u256 thz = *this >> tz;
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u256 n = other >> tz;
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SASSERT(!n.is_even() && n > 1);
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std::uninitialized_copy(thz.m_num, thz.m_num + 4, a);
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VERIFY(Hacl_Bignum256_mod(const_cast<uint64_t*>(n.m_num), a, r.m_num));
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r = r << tz;
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r += *this & ((u256(1) << tz) - 1);
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return r;
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}
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u256 u256::mul_inverse() const {
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NOT_IMPLEMENTED_YET();
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/*
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Write `a mod n` in `res`.
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The argument a is meant to be a 512-bit bignum, i.e. uint64_t[8].
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The argument n and the outparam res are meant to be 256-bit bignums, i.e. uint64_t[4].
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The function returns false if any of the following preconditions are violated,
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true otherwise.
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• 1 < n
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• n % 2 = 1
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VERIFY(Hacl_Bignum256_mod(uint64_t *n, uint64_t *a, uint64_t *res));
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*/
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return *this;
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}
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@ -88,10 +161,56 @@ unsigned u256::trailing_zeros() const {
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}
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u256 u256::gcd(u256 const& other) const {
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NOT_IMPLEMENTED_YET();
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return *this;
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if (is_zero())
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return other;
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if (other.is_zero())
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return *this;
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if (is_one())
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return *this;
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if (other.is_one())
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return other;
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u256 x = *this;
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u256 y = other;
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unsigned tz = x.trailing_zeros();
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unsigned shift = std::min(y.trailing_zeros(), tz);
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x = x >> tz;
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if (x == 1)
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return x << shift;
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if (y == 1)
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return y << shift;
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if (x == y)
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return x << shift;
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do {
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tz = y.trailing_zeros();
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y = y >> tz;
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if (x > y)
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std::swap(x, y);
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y -= x;
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}
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while (!y.is_zero());
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return x << shift;
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}
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bool u256::operator<(u256 const& other) const {
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return 0 != Hacl_Bignum256_lt_mask(const_cast<uint64_t*>(m_num), const_cast<uint64_t*>(other.m_num));
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}
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bool u256::operator<(uint64_t other) const {
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uint64_t _other[4];
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_other[0] = other;
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_other[1] = _other[2] = _other[3] = 0;
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return 0 != Hacl_Bignum256_lt_mask(const_cast<uint64_t*>(m_num), _other);
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}
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bool u256::operator>(uint64_t other) const {
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uint64_t _other[4];
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_other[0] = other;
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_other[1] = _other[2] = _other[3] = 0;
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return 0 != Hacl_Bignum256_lt_mask(_other, const_cast<uint64_t*>(m_num));
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}
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std::ostream& u256::display(std::ostream& out) const {
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rational n;
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for (unsigned i = 0; i < 4; ++i)
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@ -14,7 +14,11 @@ public:
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u256 operator+(u256 const& other) const { u256 r = *this; return r += other; }
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u256 operator-(u256 const& other) const { u256 r = *this; return r -= other; }
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u256 operator-() const { u256 r = *this; return r.inv(); }
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u256 operator<<(uint64_t sh) const;
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u256 operator>>(uint64_t sh) const;
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u256 operator&(u256 const& other) const;
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u256 mod(u256 const& other) const;
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u256 mul_inverse() const;
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unsigned trailing_zeros() const;
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u256 gcd(u256 const& other) const;
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@ -27,17 +31,17 @@ public:
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u256& inv(); /* unary minus */
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// comparisons
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bool operator==(u256 const& other) const;
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bool operator!=(u256 const& other) const;
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bool operator==(u256 const& other) const { return m_num[0] == other.m_num[0] && m_num[1] == other.m_num[1] && m_num[2] == other.m_num[2] && m_num[3] == other.m_num[3]; }
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bool operator!=(u256 const& other) const { return !(*this == other); }
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bool operator<(u256 const& other) const;
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bool operator<=(u256 const& other) const;
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bool operator>(u256 const& other) const;
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bool operator>=(u256 const& other) const;
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bool operator<=(u256 const& other) const { return !(other < *this); }
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bool operator>(u256 const& other) const { return other < *this; }
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bool operator>=(u256 const& other) const { return !(*this < other); }
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bool operator<(uint64_t other) const;
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bool operator<=(uint64_t other) const;
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bool operator<=(uint64_t other) const { return !(*this > other); }
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bool operator>(uint64_t other) const;
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bool operator>=(uint64_t other) const;
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bool operator>=(uint64_t other) const { return !(*this < other); }
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bool is_zero() const { return m_num[0] == 0 && m_num[1] == 0 && m_num[2] == 0 && m_num[3] == 0; }
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bool is_one() const { return m_num[0] == 1 && m_num[1] == 0 && m_num[2] == 0 && m_num[3] == 0; }
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