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Add rational::pseudo_inverse

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This commit is contained in:
Jakob Rath 2022-12-21 12:13:05 +01:00
parent 4a1781d747
commit 8da9850d45
3 changed files with 33 additions and 0 deletions
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8
src/util/mpq.h
View file

@ -490,6 +490,8 @@ public:
void machine_div_rem(mpz const & a, mpz const & b, mpz & c, mpz & d) { mpz_manager<SYNCH>::machine_div_rem(a, b, c, d); }
void machine_div2k(mpz const & a, unsigned k, mpz & c) { mpz_manager<SYNCH>::machine_div2k(a, k, c); }
void div(mpz const & a, mpz const & b, mpz & c) { mpz_manager<SYNCH>::div(a, b, c); }
void rat_div(mpz const & a, mpz const & b, mpq & c) {
@ -516,6 +518,12 @@ public:
machine_div(a.m_num, b.m_num, c);
}
void machine_idiv2k(mpq const & a, unsigned k, mpq & c) {
SASSERT(is_int(a));
machine_div2k(a.m_num, k, c.m_num);
reset_denominator(c);
}
void idiv(mpq const & a, mpq const & b, mpq & c) {
SASSERT(is_int(a) && is_int(b));
div(a.m_num, b.m_num, c.m_num);

18
src/util/rational.cpp
View file

@ -153,3 +153,21 @@ bool rational::mult_inverse(unsigned num_bits, rational & result) const {
return true;
}
/**
* Compute multiplicative pseudo-inverse modulo 2^num_bits:
*
* mod(n * n.pseudo_inverse(bits), 2^bits) == 2^k,
* where k is maximal such that 2^k divides n.
*
* Precondition: number is non-zero.
*/
rational rational::pseudo_inverse(unsigned num_bits) const {
rational result;
rational const& n = *this;
SASSERT(!n.is_zero()); // TODO: or we define pseudo-inverse of 0 as 0.
unsigned const k = n.trailing_zeros();
rational const odd = machine_div2k(n, k);
VERIFY(odd.mult_inverse(num_bits, result));
SASSERT_EQ(mod(n * result, rational::power_of_two(num_bits)), rational::power_of_two(k));
return result;
}

7
src/util/rational.h
View file

@ -229,6 +229,12 @@ public:
return r;
}
friend inline rational machine_div2k(rational const & r1, unsigned k) {
rational r;
rational::m().machine_idiv2k(r1.m_val, k, r.m_val);
return r;
}
friend inline rational mod(rational const & r1, rational const & r2) {
rational r;
rational::m().mod(r1.m_val, r2.m_val, r.m_val);
@ -355,6 +361,7 @@ public:
}
bool mult_inverse(unsigned num_bits, rational & result) const;
rational pseudo_inverse(unsigned num_bits) const;
static rational const & zero() {
return m_zero;