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fixes for division

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This commit is contained in:
Nikolaj Bjorner 2022-08-12 11:54:26 -04:00
parent f989521a8c
commit d272becade
1 changed files with 32 additions and 38 deletions
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60
src/math/simplex/model_based_opt.cpp
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@ -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) {
if (lub_index != UINT_MAX)
result = solve_for(lub_index, x, true);
}
else if (glb_index != UINT_MAX) {
else if (glb_index != UINT_MAX)
result = solve_for(glb_index, x, true);
}
else {
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) {
if (lub_size <= glb_size)
result = def(m_rows[lub_index], x);
}
else {
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;
}
//