mirror of
https://github.com/Z3Prover/z3
synced 2025-04-08 18:31:49 +00:00
fixes for division
This commit is contained in:
parent
f989521a8c
commit
d272becade
|
@ -1101,15 +1101,12 @@ namespace opt {
|
|||
// There are only upper or only lower bounds.
|
||||
if (row_index == UINT_MAX) {
|
||||
if (compute_def) {
|
||||
if (lub_index != UINT_MAX) {
|
||||
result = solve_for(lub_index, x, true);
|
||||
}
|
||||
else if (glb_index != UINT_MAX) {
|
||||
result = solve_for(glb_index, x, true);
|
||||
}
|
||||
else {
|
||||
result = def() + m_var2value[x];
|
||||
}
|
||||
if (lub_index != UINT_MAX)
|
||||
result = solve_for(lub_index, x, true);
|
||||
else if (glb_index != UINT_MAX)
|
||||
result = solve_for(glb_index, x, true);
|
||||
else
|
||||
result = def() + m_var2value[x];
|
||||
SASSERT(eval(result) == eval(x));
|
||||
}
|
||||
else {
|
||||
|
@ -1122,12 +1119,10 @@ namespace opt {
|
|||
SASSERT(lub_index != UINT_MAX);
|
||||
SASSERT(glb_index != UINT_MAX);
|
||||
if (compute_def) {
|
||||
if (lub_size <= glb_size) {
|
||||
result = def(m_rows[lub_index], x);
|
||||
}
|
||||
else {
|
||||
result = def(m_rows[glb_index], x);
|
||||
}
|
||||
if (lub_size <= glb_size)
|
||||
result = def(m_rows[lub_index], x);
|
||||
else
|
||||
result = def(m_rows[glb_index], x);
|
||||
}
|
||||
|
||||
// The number of matching lower and upper bounds is small.
|
||||
|
@ -1148,7 +1143,8 @@ namespace opt {
|
|||
}
|
||||
}
|
||||
}
|
||||
for (unsigned row_id : lub_rows) retire_row(row_id);
|
||||
for (unsigned row_id : lub_rows)
|
||||
retire_row(row_id);
|
||||
|
||||
return result;
|
||||
}
|
||||
|
@ -1281,13 +1277,14 @@ namespace opt {
|
|||
|
||||
//
|
||||
// Given v = a*x + b div m
|
||||
// Replace x |-> m*y + a_inv*z
|
||||
// Replace x |-> m*y + z
|
||||
// - w = b div m
|
||||
// - v = ((m*y + g*z) + b) div m
|
||||
// = a*y + (a_inv*z + b) div m
|
||||
// = a*y + b div m + (b mod m + g*z) div m
|
||||
// - v = ((a*m*y + a*z) + b) div m
|
||||
// = a*y + (a*z + b) div m
|
||||
// = a*y + b div m + (b mod m + a*z) div m
|
||||
// = a*y + b div m + k
|
||||
// where k := (b.value mod m + g*z.value) div m
|
||||
// where k := (b.value mod m + a*z.value) div m
|
||||
// k is between 0 and a
|
||||
//
|
||||
model_based_opt::def model_based_opt::solve_div(unsigned x, unsigned_vector const& div_rows, bool compute_def) {
|
||||
def result;
|
||||
|
@ -1302,32 +1299,24 @@ namespace opt {
|
|||
replace_var(row_index, x, rational::zero());
|
||||
rational b_value = m_rows[row_index].m_value;
|
||||
|
||||
// compute a_inv
|
||||
rational a_inv, m_inv;
|
||||
rational g = gcd(a, m, a_inv, m_inv);
|
||||
if (a_inv.is_neg())
|
||||
a_inv = mod(a_inv, m);
|
||||
SASSERT(mod(a_inv * a, m) == g);
|
||||
|
||||
// solve for x_value = m*y_value + a^-1*z_value, 0 <= z_value < m.
|
||||
// solve for x_value = m*y_value + z_value, 0 <= z_value < m.
|
||||
rational z_value = mod(x_value, m);
|
||||
rational y_value = div(x_value, m) - div(a_inv*z_value, m);
|
||||
SASSERT(x_value == m*y_value + a_inv*z_value);
|
||||
rational y_value = div(x_value, m);
|
||||
SASSERT(x_value == m*y_value + z_value);
|
||||
SASSERT(0 <= z_value && z_value < m);
|
||||
|
||||
// add new variables
|
||||
unsigned y = add_var(y_value, true);
|
||||
unsigned z = add_var(z_value, true);
|
||||
// TODO: we could recycle x by either y or z.
|
||||
|
||||
// replace x by m*y + a^-1*z in other rows.
|
||||
// replace x by m*y + z in other rows.
|
||||
unsigned_vector const& row_ids = m_var2row_ids[x];
|
||||
uint_set visited;
|
||||
visited.insert(row_index);
|
||||
for (unsigned row_id : row_ids) {
|
||||
if (visited.contains(row_id))
|
||||
continue;
|
||||
replace_var(row_id, x, m, y, a_inv, z);
|
||||
replace_var(row_id, x, m, y, rational::one(), z);
|
||||
visited.insert(row_id);
|
||||
normalize(row_id);
|
||||
}
|
||||
|
@ -1339,9 +1328,16 @@ namespace opt {
|
|||
// add w = b div m
|
||||
vector<var> coeffs = m_rows[row_index].m_vars;
|
||||
rational coeff = m_rows[row_index].m_coeff;
|
||||
|
||||
unsigned w = add_div(coeffs, coeff, m);
|
||||
rational k = div(g*z_value + mod(b_value, m), m);
|
||||
|
||||
|
||||
//
|
||||
// w = b div m
|
||||
// v = a*y + w + k
|
||||
// k = (a*z_value + (b_value mod m)) div m
|
||||
//
|
||||
|
||||
rational k = div(a*z_value + mod(b_value, m), m);
|
||||
vector<var> div_coeffs;
|
||||
div_coeffs.push_back(var(v, rational::minus_one()));
|
||||
div_coeffs.push_back(var(y, a));
|
||||
|
@ -1358,9 +1354,7 @@ namespace opt {
|
|||
result = (y_def * m) + z_def;
|
||||
m_var2value[x] = eval(result);
|
||||
}
|
||||
|
||||
return result;
|
||||
|
||||
}
|
||||
|
||||
//
|
||||
|
|
Loading…
Reference in a new issue