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aiju 2018-03-17 19:26:26 +00:00
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104
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#pragma lib "libsat.a"
typedef struct SATParam SATParam;
typedef struct SATClause SATClause;
typedef struct SATSolve SATSolve;
typedef struct SATBlock SATBlock;
typedef struct SATVar SATVar;
typedef struct SATLit SATLit;
typedef struct SATConflict SATConflict;
/* user adjustable parameters */
struct SATParam {
void (*errfun)(char *, void *);
void *erraux;
long (*randfn)(void *);
void *randaux;
uint goofprob; /* probability of making a random decision, times 2**31 */
double varρ; /* Δactivity is multiplied by this after a conflict */
double clauseρ; /* Δclactivity is multiplied by this after a conflict */
int trivlim; /* number of extra literals we're willing to tolerate before substituting the trivial clause */
int purgeΔ; /* initial purge interval (number of conflicts before a purge) */
int purgeδ; /* increase in purge interval at purge */
double purgeα; /* α weight factor for purge heuristic */
u32int flushψ; /* agility threshold for restarts */
};
/* each block contains multiple SATClauses consecutively in its data region. each clause is 8 byte aligned and the total size is SATBLOCKSZ (64K) */
struct SATBlock {
SATBlock *next, *prev;
SATClause *last; /* last clause, ==nil for empty blocks */
void *end; /* first byte past the last clause */
uchar data[1];
};
struct SATSolve {
SATParam;
uchar unsat; /* ==1 if unsatisfiable. don't even try to solve. */
uchar scratched; /* <0 if error happened, state undefined */
SATBlock bl[2]; /* two doubly linked list heads: list bl[0] contains user clauses, list bl[1] contains learned clauses */
SATBlock *lastbl; /* the last block we added a learned clause to */
SATClause *cl; /* all clauses are linked together; this is the first user clause */
SATClause *learncl; /* first learned clause */
SATClause **lastp[2]; /* this points towards the last link in each linked list */
int ncl; /* total number of clauses */
int ncl0; /* number of user clauses */
SATVar *var; /* all variables (array with nvar elements) */
SATLit *lit; /* all literals (array with 2*nvar elements) */
int nvar;
int nvaralloc; /* space allocated for variables */
int *trail; /* the trail contains all literals currently assumed true */
int ntrail;
int *decbd; /* decision boundaries. trail[decbd[i]] has the first literal of level i */
int lvl; /* current decision level */
SATVar **heap; /* binary heap with free variables, sorted by activity (nonfree variables are removed lazily and so may also be in it) */
int nheap;
uint *lvlstamp; /* used to "stamp" levels during conflict resolution and purging */
uint stamp; /* current "stamp" counter */
int forptr; /* trail[forptr] is the first literal we haven't explored the implications of yet */
int binptr; /* ditto for binary implications */
int *cflcl; /* during conflict resolution we build the learned clause in here */
int ncflcl;
int cflclalloc; /* space allocated for cflcl */
int cfllvl; /* the maximum level of the literals in cflcl, cflcl[0] excluded */
int cflctr; /* number of unresolved literals during conflict resolution */
double Δactivity; /* activity increment for variables */
double Δclactivity; /* activity increment for clauses */
uvlong conflicts; /* total number of conflicts so far */
uvlong nextpurge; /* purge happens when conflicts >= nextpurge */
uint purgeival; /* increment for nextpurge */
/* during a purge we do a "full run", assigning all variables and recording conflicts rather than resolving them */
SATConflict *fullrcfl; /* conflicts found thus */
int nfullrcfl;
int fullrlvl; /* minimum cfllvl for conflicts found during purging */
int *fullrlits; /* literals implied by conflicts at level fullrlvl */
int nfullrlits;
int rangecnt[256]; /* number of clauses with certain range values */
u64int nextflush; /* flush happens when conflicts >= nextflush */
u32int flushu, flushv, flushθ; /* variables for flush scheduling algorithm */
u32int agility; /* agility is a measure how quickly variables are being flipped. high agility inhibits flushes */
void *scrap; /* auxiliary memory that may need to be freed after a fatal error */
};
SATSolve *satnew(void);
SATSolve *satadd1(SATSolve *, int *, int);
SATSolve *sataddv(SATSolve *, ...);
SATSolve *satrange1(SATSolve *, int *, int, int, int);
SATSolve *satrangev(SATSolve *, int, int, ...);
int satsolve(SATSolve *);
int satmore(SATSolve *);
int satval(SATSolve *, int);
void satfree(SATSolve *);
void satreset(SATSolve *);

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.TH SAT 2
.SH NAME
satnew, satadd1, sataddv, satrange1, satrangev, satsolve, satmore, satval, satreset, satfree \- boolean satisfiability (SAT) solver
.SH SYNOPSIS
.de PB
.PP
.ft L
.nf
..
.PB
#include <u.h>
#include <libc.h>
#include <sat.h>
.PB
struct SATParam {
void (*errfun)(char *msg, void *erraux);
void *erraux;
long (*randfn)(void *randaux);
void *randaux;
/* + finetuning parameters, see sat.h */
};
.PB
struct SATSolve {
SATParam;
/* + internals */
};
.PB
.ta +\w'\fLSATSolve* \fP'u
SATSolve* satnew(void);
void satfree(SATSolve *s);
SATSolve* satadd1(SATSolve *s, int *lit, int nlit);
SATSolve* sataddv(SATSolve *s, ...);
SATSolve* satrange1(SATSolve *s, int *lit, int nlit,
int min, int max);
SATSolve* satrangev(SATSolve *s, int min, int max, ...);
int satsolve(SATSolve *s);
int satmore(SATSolve *s);
int satval(SATSolve *s, int lit);
void satreset(SATSolve *s);
.SH DESCRIPTION
.PP
.I Libsat
is a solver for the boolean satisfiability problem, i.e. given a boolean formula it will either find an assignment to the variables that makes it true, or report that this is impossible.
The input formula must be in conjunctive normal form (CNF), i.e. of the form
.IP
.if t (x\d\s71\s10\u ∨ x\d\s72\s10\u ∨ x\d\s73\s10\u ∨ …) ∧ (y\d\s71\s10\u ∨ y\d\s72\s10\u ∨ y \d\s73\s10\u ∨ …) ∧ …,
.if n (x1 ∨ x2 ∨ x3 ∨ ...) ∧ (y1 ∨ y2 ∨ y3 ∨ ...) ∧ ...,
.PP
where each
.if t x\d\s7i\s10\u or y\d\s7i\s10\u
.if n x_i or y_i
can optionally be negated.
.PP
For example, consider
.IP
.if t (x\d\s71\s10\u ∨ x\d\s72\s10\u ∨ x\d\s73\s10\u) ∧ (¬x\d\s71\s10\u ∨ ¬x\d\s72\s10\u) ∧ (¬x\d\s72\s10\u ∨ ¬x\d\s73\s10\u) ∧ (¬x\d\s71\s10\u ∨ ¬x\d\s73\s10\u).
.if n (x1 ∨ x2 ∨ x3) ∧ (¬x1 ∨ ¬x2) ∧ (¬x2 ∨ ¬x3) ∧ (¬x1 ∨ ¬x3).
.PP
This formula encodes the constraint that exactly one of the three variables be true. To represent this as input for
.I libsat
we assign positive integers to each variable.
Negation is represented by the corresponding negative number, hence our example corresponds to the set of "clauses"
.IP
1, 2, 3
.br
-1, -2
.br
-1, -3
.br
-2, -3
.PP
To actually solve this problem we would create a
.B SATSolve
structure and add clauses one by one using
.I satadd1
or
.I sataddv
(the former takes an
.B int
array, the latter a variadic list terminated by 0).
The
.B SATSolve
is modified inplace but returned for convenience.
Passing
.B nil
as a first argument will create and return a new structure.
Alternatively,
.I satnew
will create an empty structure.
.PP
Once clauses have been added,
.I satsolve
will invoke the actual solver.
It returns 1 if it found an assignment and 0 if there is no assignment (the formula is unsatisfiable).
If an assignment has been found, further clauses can be added to constrain it further and
.I satsolve
rerun.
.I Satmore
performs this automatically, excluding the current values of the variables.
It is equivalent to
.I satsolve
if no variables have assigned values.
.PP
Once a solution has been found,
.I satval
returns the value of literal
.I lit.
It returns 1 for true, 0 for false and -1 for undetermined.
If the formula is satisfiable, an undetermined variable is one where either value will satisfy the formula.
If the formula is unsatisfiable, all variables are undetermined.
.PP
.I Satrange1
and
.I satrangev
function like their
.I satadd
brethren but rather than adding a single clause they add multiple clauses corresponding to the constraint that at least
.I min
and at most
.I max
literals from the provided array be true.
For example, the clause from above corresponds to
.IP
.B "satrangev(s, 1, 1, 1, 2, 3, 0);"
.PP
.I Satreset
resets all solver state, deleting all learned clauses and variable assignments.
It retains all user provided clauses.
.I Satfree
deletes a solver structure and frees all associated storage.
.PP
There are a number of user-adjustable parameters in the
.B SATParam
structure embedded in
.BR SATSolve .
.I Randfun
is called with argument
.I randaux
to generate random numbers between 0 and
.if t 2\u\s731\s10\d-1;
.if n 2^31-1;
it defaults to
.IR lrand (2).
.I Errfun
is called on fatal errors (see DIAGNOSTICS).
Additionally, a number of finetuning parameters are defined in
.BR sat.h .
By tweaking their values, the run-time for a given problem can be reduced.
.SH EXAMPLE
Find all solutions to the example clause from above:
.PB
.ta .5i 1i 1.5i
SATSolve *s;
s = nil;
s = sataddv(s, 1, 2, 3, 0);
s = sataddv(s, -1, -2, 0);
s = sataddv(s, -1, -3, 0);
s = sataddv(s, -2, -3, 0);
while(satmore(s) > 0)
print("x1=%d x2=%d x3=%d\\n",
satval(s, 1),
satval(s, 2),
satval(s, 3));
satfree(s);
.SH SOURCE
.B /sys/src/libsat
.SH "SEE ALSO"
Donald Knuth, ``The Art of Computer Programming'', Volume 4, Fascicle 6.
.SH DIAGNOSTICS
.I Satnew
returns
.B nil
on certain fatal error conditions (such as
.IR malloc (2)
failure).
Other routines will call
.I errfun
with an error string and
.IR erraux .
If no
.I errfun
is provided or if it returns,
.IR sysfatal (2)
is called.
It is permissible to use
.IR setjmp (2)
to return from an error condition.
Call
.I satfree
to clean up the
.B SATSolve
structure in this case.
Note that calling the
.I satadd
or
.I satrange
routines with
.B nil
first argument will invoke
.I sysfatal
on error, since no
.I errfun
has been defined yet.
.SH BUGS
Variable numbers should be consecutive numbers starting from 1, since variable data is kept in arrays internally.
.PP
Large clauses of several thousand literals are probably inefficient and should be split up using auxiliary variables.
Very large clauses exceeding about 16,000 literals will not work at all.
.PP
There is no way to remove clauses (since it's unclear what the semantics should be).
.PP
The details about the tuning parameters are subject to change.
.PP
Calling
.I satadd
or
.I satrange
after
.I satsolve
or
.I satmore
may reset variable values.
.PP
.I Satmore
will always return 1 when there are no assigned variables in the solution.
.P
Some debugging routines called under "shouldn't happen" conditions are non-reentrant.
.SH HISTORY
.I Libsat
first appeared in 9front in March, 2018.

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#include <u.h>
#include <libc.h>
#include <sat.h>
#include "impl.h"
static SATSolve *globsat;
static int
satclausefmt(Fmt *f)
{
SATClause *c;
char *s;
int i, fl;
fl = f->flags;
c = va_arg(f->args, SATClause *);
if(c == nil)
return fmtstrcpy(f, "Λ");
if(c->n == 0)
return fmtstrcpy(f, "ε");
s = "%s%d";
for(i = 0; i < c->n; i++){
if((fl & FmtSign) != 0)
switch(globsat->lit[c->l[i]].val){
case 1: s = "%s[%d]"; break;
case 0: s = "%s(%d)"; break;
case -1: s = "%s%d"; break;
default: abort();
}
fmtprint(f, s, i != 0 ? " ∨ " : "", signf(c->l[i]));
}
return 0;
}
void
satprintstate(SATSolve *s)
{
int i;
Fmt f;
char buf[512];
SATVar *v;
fmtfdinit(&f, 1, buf, sizeof(buf));
fmtprint(&f, "trail:\n");
for(i = 0; i < s->ntrail; i++){
v = &s->var[VAR(s->trail[i])];
fmtprint(&f, "%c%-8d %- 8d %-8d ", i == s->forptr ? '*' : ' ', i, signf(s->trail[i]), v->lvl);
if(v->isbinreason)
fmtprint(&f, "%d ∨ %d\n", signf(s->trail[i]), signf(v->binreason));
else
fmtprint(&f, "%+Γ\n", v->reason);
}
fmtrune(&f, '\n');
fmtfdflush(&f);
}
void
satsanity(SATSolve *s)
{
int i, j, k, m, tl, s0, s1;
SATVar *v;
SATLit *l;
SATClause *c;
for(c = s->cl; c != nil; c = c->next){
assert(c->n >= 2);
assert((uint)((uchar*)c->next - (uchar*)c) >= sizeof(SATClause) + (c->n - 1) * sizeof(int));
for(j = 0; j < c->n; j++)
assert((uint)c->l[j] < 2*s->nvar);
for(i = 0; i < 2; i++)
c->watch[i] = (void*)((uintptr)c->watch[i] | 1);
}
for(i = 0; i < s->nvar; i++){
tl = -1;
for(j = 0; j < s->ntrail; j++)
if(VAR(s->trail[j]) == i){
assert(tl == -1);
tl = j;
}
v = &s->var[i];
l = &s->lit[2*i];
if(l->val >= 0){
assert(l->val <= 1);
assert(l[0].val + l[1].val == 1);
assert((uint)v->lvl <= s->lvl);
assert(tl != -1);
assert(s->trail[tl] == 2*i+l[1].val);
assert(tl >= s->decbd[v->lvl]);
assert(v->lvl == s->lvl || tl < s->decbd[v->lvl+1]);
}else{
assert(l[0].val == -1 && l[1].val == -1);
assert(v->lvl == -1);
assert(v->heaploc >= 0);
assert(tl == -1);
}
assert(v->heaploc == -1 || (uint)v->heaploc <= s->nheap && s->heap[v->heaploc] == v);
for(j = 0; j < 2; j++){
m = 2 * i + j;
for(c = l[j].watch; c != nil; c = c->watch[k]){
k = c->l[1] == m;
assert(k || c->l[0] == m);
assert((uintptr)c->watch[k] & 1);
c->watch[k] = (void*)((uintptr)c->watch[k] & ~1);
}
}
}
for(c = s->cl; c != nil; c = c->next)
for(i = 0; i < 2; i++)
assert(((uintptr)c->watch[i] & 1) == 0);
if(s->forptr == s->ntrail)
for(c = s->cl; c != nil; c = c->next){
s0 = s->lit[c->l[0]].val;
s1 = s->lit[c->l[1]].val;
if(s0 != 0 && s1 != 0 || s0 == 1 || s1 == 1)
continue;
for(i = 2; i < c->n; i++)
if(s->lit[c->l[i]].val != 0){
satprintstate(s);
print("watchlist error: %+Γ\n", c);
assert(0);
}
}
}
void
satdebuginit(SATSolve *s)
{
globsat = s;
fmtinstall(L'Γ', satclausefmt);
}

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/* note that internally, literals use a representation different from the API.
* variables are numbered from 0 (not 1) and 2v and 2v+1 correspond to v
* and ¬v, resp. */
#define VAR(l) ((l)>>1)
#define NOT(l) ((l)^1)
/* l[0] and l[1] are special: they are the watched literals.
* all clauses that have literal l on their watchlist form a linked list starting with s->lit[l].watch
* and watch[i] having the next clause for l[i] */
struct SATClause {
SATClause *next;
SATClause *watch[2];
double activity; /* activity is increased every time a clause is used to resolve a conflict (tiebreaking heuristic during purging) */
int n; /* >= 2 for learned clauses and > 2 for input clauses (binary input clauses are kept in the bimp tables) */
ushort range; /* heuristic used during purging, low range => keep clause (range 0..256) */
int l[1];
};
struct SATLit {
int *bimp; /* array of literals implied by this literal through binary clauses (Binary IMPlications) */
SATClause *watch; /* linked list of watched clauses */
int nbimp;
char val; /* -1 = not assigned, 0 = false, 1 = true */
};
struct SATVar {
double activity; /* activity is increased every time a variable shows up in a conflict */
union {
SATClause *reason; /* nil for decision and free literals */
int binreason; /* used when isbinreason == 1: the reason is the clause l ∨ l->binreason */
};
int lvl; /* level at which this variable is defined, or -1 for free variables */
int heaploc; /* location in binary heap or -1 when not in heap */
uint stamp; /* "stamp" value used for conflict resolution etc. */
uchar flags; /* see below */
char isbinreason;
};
enum {
VARPHASE = 1, /* for a free variables, VARPHASE is used as a first guess the next time it is picked */
VARUSER = 0x80, /* user assigned variable (unit clause in input) */
};
/* records conflicts during purging */
struct SATConflict {
union {
SATClause *c;
uvlong b;
};
int lvl; /* bit 31 denotes binary conflict */
};
#define CFLLVL(c) ((c).lvl & 0x7fffffff)
enum {
SATBLOCKSZ = 65536,
SATVARALLOC = 64,
CLAUSEALIGN = 8,
CFLCLALLOC = 16,
};
void saterror(SATSolve *, char *, ...);
void sataddtrail(SATSolve *, int);
void satdebuginit(SATSolve *);
void satprintstate(SATSolve *);
void satsanity(SATSolve *);
SATVar *satheaptake(SATSolve *);
void satheapput(SATSolve *, SATVar *);
void satreheap(SATSolve *, SATVar *);
void satheapreset(SATSolve *);
int satnrand(SATSolve *, int);
void *satrealloc(SATSolve *, void *, ulong);
SATClause *satnewclause(SATSolve *, int, int);
SATClause *satreplclause(SATSolve *, int);
void satcleanup(SATSolve *, int);
void satbackjump(SATSolve *, int);
#define signf(l) (((l)<<31>>31|1)*((l)+2>>1))
#pragma varargck type "Γ" SATClause*
#define ε 2.2250738585072014e-308
#define MAXACTIVITY 1e100

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#include <u.h>
#include <libc.h>
#include <sat.h>
#include "impl.h"
SATSolve *
satnew(void)
{
SATSolve *s;
s = calloc(1, sizeof(SATSolve));
if(s == nil) return nil;
s->bl[0].next = s->bl[0].prev = &s->bl[0];
s->bl[1].next = s->bl[1].prev = &s->bl[1];
s->bl[0].end = (uchar*)&s->bl[0] + SATBLOCKSZ; /* this block is "full" */
s->bl[1].end = (uchar*)&s->bl[1] + SATBLOCKSZ;
s->lastp[0] = &s->cl;
s->lastp[1] = &s->learncl;
s->lastbl = &s->bl[1];
s->randfn = (long(*)(void*)) lrand;
s->goofprob = 0.02 * (1UL<<31);
s->varρ = 1/0.9;
s->clauseρ = 1/0.999;
s->trivlim = 10;
s->purgeΔ = 10000;
s->purgeδ = 100;
s->purgeα = 0.2;
s->flushψ = (1ULL<<32)*0.05;
s->Δactivity = 1;
s->Δclactivity = 1;
return s;
}
void
satfree(SATSolve *s)
{
SATBlock *b, *bb;
int i;
if(s == nil) return;
for(i = 0; i < 2; i++)
for(b = s->bl[i].next; b != &s->bl[i]; b = bb){
bb = b->next;
free(b);
}
for(i = 0; i < 2 * s->nvar; i++)
free(s->lit[i].bimp);
free(s->heap);
free(s->trail);
free(s->decbd);
free(s->var);
free(s->lit);
free(s->cflcl);
free(s->fullrcfl);
free(s->fullrlits);
free(s->scrap);
free(s);
}
void
saterror(SATSolve *s, char *msg, ...)
{
char buf[ERRMAX];
va_list va;
va_start(va, msg);
vsnprint(buf, sizeof(buf), msg, va);
va_end(va);
s->scratched = 1;
if(s != nil && s->errfun != nil)
s->errfun(buf, s->erraux);
sysfatal("%s", buf);
}
int
satval(SATSolve *s, int l)
{
int m, v;
if(s->unsat) return -1;
m = l >> 31;
v = (l + m ^ m) - 1;
if(v < 0 || v >= s->nvar) return -1;
return s->lit[2*v+(m&1)].val;
}
int
satnrand(SATSolve *s, int n)
{
long slop, v;
if(n <= 1) return 0;
slop = 0x7fffffff % n;
do
v = s->randfn(s->randaux);
while(v <= slop);
return v % n;
}
void *
satrealloc(SATSolve *s, void *v, ulong n)
{
v = realloc(v, n);
if(v == nil)
saterror(s, "realloc: %r");
return v;
}
#define LEFT(x) (2*(x)+1)
#define RIGHT(x) (2*(x)+2)
#define UP(x) ((x)-1>>1)
static SATVar *
heapswap(SATSolve *s, int i, int j)
{
SATVar *r;
if(i == j) return s->heap[i];
r = s->heap[i];
s->heap[i] = s->heap[j];
s->heap[j] = r;
s->heap[i]->heaploc = i;
s->heap[j]->heaploc = j;
return r;
}
static void
heapup(SATSolve *s, int i)
{
int m;
m = i;
for(;;){
if(LEFT(i) < s->nheap && s->heap[LEFT(i)]->activity > s->heap[m]->activity)
m = LEFT(i);
if(RIGHT(i) < s->nheap && s->heap[RIGHT(i)]->activity > s->heap[m]->activity)
m = RIGHT(i);
if(i == m) break;
heapswap(s, m, i);
i = m;
}
}
static void
heapdown(SATSolve *s, int i)
{
int p;
for(; i > 0 && s->heap[p = UP(i)]->activity < s->heap[i]->activity; i = p)
heapswap(s, i, p);
}
SATVar *
satheaptake(SATSolve *s)
{
SATVar *r;
assert(s->nheap > 0);
r = heapswap(s, 0, --s->nheap);
heapup(s, 0);
r->heaploc = -1;
return r;
}
void
satheapput(SATSolve *s, SATVar *v)
{
assert(s->nheap < s->nvar);
v->heaploc = s->nheap;
s->heap[s->nheap++] = v;
heapdown(s, s->nheap - 1);
}
void
satreheap(SATSolve *s, SATVar *v)
{
int i;
i = v->heaploc;
if(i < 0) return;
heapup(s, i);
heapdown(s, i);
}
void
satheapreset(SATSolve *s)
{
int i, n, j;
s->heap = satrealloc(s, s->heap, s->nvar * sizeof(SATVar *));
n = s->nvar;
s->nheap = n;
for(i = 0; i < n; i++){
s->heap[i] = &s->var[i];
s->heap[i]->heaploc = i;
}
for(i = 0; i < n - 1; i++){
j = i + satnrand(s, n - i);
heapswap(s, i, j);
heapdown(s, i);
}
heapdown(s, n - 1);
}

22
sys/src/libsat/mkfile Normal file
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</$objtype/mkfile
LIB=/$objtype/lib/libsat.a
OFILES=\
misc.$O \
satadd.$O \
satrange.$O \
satsolve.$O \
satmore.$O \
debug.$O \
HFILES=\
/sys/include/sat.h\
impl.h\
UPDATE=\
mkfile\
$HFILES\
${OFILES:%.$O=%.c}\
</sys/src/cmd/mksyslib

230
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#include <u.h>
#include <libc.h>
#include <sat.h>
#include "impl.h"
static SATBlock *
newblock(SATSolve *s, int learned)
{
SATBlock *b;
b = calloc(1, SATBLOCKSZ);
if(b == nil)
saterror(s, "malloc: %r");
b->prev = s->bl[learned].prev;
b->next = &s->bl[learned];
b->next->prev = b;
b->prev->next = b;
b->end = (void*) b->data;
return b;
}
SATClause *
satnewclause(SATSolve *s, int n, int learned)
{
SATBlock *b;
SATClause *c;
int f, sz;
sz = sizeof(SATClause) + (n - 1) * sizeof(int);
assert(sz <= SATBLOCKSZ);
if(learned)
b = s->lastbl;
else
b = s->bl[0].prev;
for(;;){
f = (uchar*)b + SATBLOCKSZ - (uchar*)b->end;
if(f >= sz) break;
b = b->next;
if(b == &s->bl[learned])
b = newblock(s, learned);
}
c = b->end;
memset(c, 0, sizeof(SATClause));
b->end = (void *)((uintptr)b->end + sz + CLAUSEALIGN - 1 & -CLAUSEALIGN);
b->last = c;
if(learned){
if(s->lastp[1] == &s->learncl)
*s->lastp[0] = c;
s->lastbl = b;
}else
c->next = s->learncl;
*s->lastp[learned] = c;
s->lastp[learned] = &c->next;
s->ncl++;
return c;
}
/* this is currently only used to subsume clauses, i.e. n is guaranteed to be less than the last n */
SATClause *
satreplclause(SATSolve *s, int n)
{
SATBlock *b;
SATClause *c, **wp;
int f, sz, i, l;
assert(s->lastbl != nil && s->lastbl->last != nil);
b = s->lastbl;
c = b->last;
f = (uchar*)b + SATBLOCKSZ - (uchar*)c;
sz = sizeof(SATClause) + (n - 1) * sizeof(int);
assert(f >= sz);
b->end = (void *)((uintptr)c + sz + CLAUSEALIGN - 1 & -CLAUSEALIGN);
for(i = 0; i < 2; i++){
l = c->l[i];
for(wp = &s->lit[l].watch; *wp != nil && *wp != c; wp = &(*wp)->watch[(*wp)->l[1] == l])
;
assert(*wp != nil);
*wp = c->watch[i];
}
memset(c, 0, sizeof(SATClause));
return c;
}
static int
litconv(SATSolve *s, int l)
{
int v, m, n;
SATVar *vp;
SATLit *lp;
m = l >> 31;
v = (l + m ^ m) - 1;
if(v >= s->nvaralloc){
n = -(-(v+1) & -SATVARALLOC);
s->var = vp = satrealloc(s, s->var, n * sizeof(SATVar));
s->lit = lp = satrealloc(s, s->lit, 2 * n * sizeof(SATLit));
memset(vp += s->nvaralloc, 0, (n - s->nvaralloc) * sizeof(SATVar));
memset(lp += 2*s->nvaralloc, 0, 2 * (n - s->nvaralloc) * sizeof(SATLit));
for(; vp < s->var + n; vp++){
vp->lvl = -1;
vp->flags = VARPHASE;
}
for(; lp < s->lit + 2 * n; lp++)
lp->val = -1;
s->nvaralloc = n;
}
if(v >= s->nvar)
s->nvar = v + 1;
return v << 1 | m & 1;
}
static void
addbimp(SATSolve *s, int l0, int l1)
{
SATLit *lp;
lp = &s->lit[NOT(l0)];
lp->bimp = satrealloc(s, lp->bimp, (lp->nbimp + 1) * sizeof(int));
lp->bimp[lp->nbimp++] = l1;
}
static SATSolve *
satadd1special(SATSolve *s, int *a, int n)
{
int i, l0, l1;
if(n == 0){
s->unsat = 1;
return s;
}
l0 = a[0];
l1 = 0;
for(i = 1; i < n; i++)
if(a[i] != l0){
l1 = a[i];
break;
}
if(l1 == 0){
l0 = litconv(s, l0);
assert(s->lvl == 0);
switch(s->lit[l0].val){
case 0:
s->unsat = 1;
return s;
case -1:
s->trail = satrealloc(s, s->trail, sizeof(int) * s->nvar);
memmove(&s->trail[1], s->trail, sizeof(int) * s->ntrail);
s->trail[0] = l0;
s->ntrail++;
s->var[VAR(l0)].flags |= VARUSER;
s->var[VAR(l0)].lvl = 0;
s->lit[l0].val = 1;
s->lit[NOT(l0)].val = 0;
}
return s;
}
if(l0 + l1 == 0) return s;
l0 = litconv(s, l0);
l1 = litconv(s, l1);
addbimp(s, l0, l1);
addbimp(s, l1, l0);
return s;
}
SATSolve *
satadd1(SATSolve *s, int *a, int n)
{
SATClause *c;
int i, j, l, u;
SATVar *v;
if(s == nil){
s = satnew();
if(s == nil)
saterror(nil, "satnew: %r");
}
if(n < 0)
for(n = 0; a[n] != 0; n++)
;
for(i = 0; i < n; i++)
if(a[i] == 0)
saterror(s, "satadd1(%p, %p, %d): a[%d]==0, callerpc=%p", s, a, n, i, getcallerpc(&s));
satbackjump(s, 0);
if(n <= 2)
return satadd1special(s, a, n);
/* use stamps to detect repeated literals and tautological clauses */
if(s->stamp >= (uint)-6){
for(i = 0; i < s->nvar; i++)
s->var[i].stamp = 0;
s->stamp = 1;
}else
s->stamp += 3;
u = 0;
for(i = 0; i < n; i++){
l = litconv(s, a[i]);
v = &s->var[VAR(l)];
if(v->stamp < s->stamp) u++;
if(v->stamp == s->stamp + (~l & 1))
return s; /* tautological */
v->stamp = s->stamp + (l & 1);
}
if(u <= 2)
return satadd1special(s, a, n);
s->stamp += 3;
c = satnewclause(s, u, 0);
c->n = u;
for(i = 0, j = 0; i < n; i++){
l = litconv(s, a[i]);
v = &s->var[VAR(l)];
if(v->stamp < s->stamp){
c->l[j++] = l;
v->stamp = s->stamp;
}
}
assert(j == u);
s->ncl0++;
return s;
}
SATSolve *
sataddv(SATSolve *s, ...)
{
va_list va;
va_start(va, s);
/* horrible hack */
s = satadd1(s, (int*)va, -1);
va_end(va);
return s;
}

24
sys/src/libsat/satmore.c Normal file
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#include <u.h>
#include <libc.h>
#include <sat.h>
#include "impl.h"
int
satmore(SATSolve *s)
{
int *a, i, n;
if(s == nil) return 1;
s->scrap = a = satrealloc(s, nil, s->nvar * sizeof(int));
n = 0;
for(i = 0; i < s->nvar; i++)
switch(s->lit[2*i].val){
case 0: a[n++] = i+1; break;
case 1: a[n++] = -(i+1); break;
}
if(n > 0)
satadd1(s, a, n);
free(a);
s->scrap = nil;
return satsolve(s);
}

68
sys/src/libsat/satrange.c Normal file
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#include <u.h>
#include <libc.h>
#include <sat.h>
#include "impl.h"
static SATSolve *
satmin(SATSolve *s, int *a, int n, int *id, int *l, int m, int mul)
{
int i;
if(m > n) return s;
for(i = 0; i < m; i++)
id[i] = i;
for(;;){
for(i = 0; i < m; i++)
l[i] = a[id[i]] * mul;
s = satadd1(s, l, m);
for(i = m-1; i >= 0; i--){
if(++id[i] < n+i+1-m)
break;
if(i == 0)
return s;
}
while(++i < m)
id[i] = id[i-1]+1;
}
}
SATSolve *
satrange1(SATSolve *s, int *a, int n, int min, int max)
{
int sz, na;
if(s == nil){
s = satnew();
if(s == nil)
saterror(nil, "satnew: %r");
}
if(n < 0)
for(n = 0; a[n] != 0; n++)
;
if(min > n || max < 0)
return sataddv(s, 0);
if(min < 0) min = 0;
if(max > n) max = n;
sz = n+1-min;
if(min == 0 || max != n && sz < max+1) sz = max+1;
if(s->cflclalloc < 2*sz){
na = -(-2*sz & -CFLCLALLOC);
s->cflcl = satrealloc(s, s->cflcl, na * sizeof(int));
s->cflclalloc = na;
}
s = satmin(s, a, n, s->cflcl, s->cflcl+sz, max+1, -1);
s = satmin(s, a, n, s->cflcl, s->cflcl+sz, n+1-min, 1);
return s;
}
SATSolve *
satrangev(SATSolve *s, int min, int max, ...)
{
va_list va;
va_start(va, max);
/* horrible hack */
s = satrange1(s, (int*)va, -1, min, max);
va_end(va);
return s;
}

887
sys/src/libsat/satsolve.c Normal file
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#include <u.h>
#include <libc.h>
#include <sat.h>
#include "impl.h"
/* the solver follows Algorithm C from Knuth's The Art of Computer Programming, Vol. 4, Fascicle 6 */
#define verbosestate 0
#define verboseforcing 0
#define verboseconflict 0
#define paranoia 0
#define sanity(s) if(paranoia) satsanity(s)
void
sataddtrail(SATSolve *s, int l)
{
s->trail[s->ntrail++] = l;
s->lit[l].val = 1;
s->lit[NOT(l)].val = 0;
s->var[VAR(l)].lvl = s->lvl;
s->agility -= s->agility >> 13;
if(((s->var[VAR(l)].flags ^ l) & 1) != 0)
s->agility += 1<<19;
if(verbosestate) satprintstate(s);
}
/* compute watchlists from scratch */
static void
rewatch(SATSolve *s)
{
SATLit *l;
SATClause *c;
int i, j, x;
for(l = s->lit; l < s->lit + 2*s->nvar; l++)
l->watch = nil;
for(c = s->cl; c != nil; c = c->next)
for(i = 0; i < 2; i++){
if(s->lit[c->l[i]].val == 0)
for(j = 2; j < c->n; j++)
if(s->lit[c->l[j]].val != 0){
x = c->l[i], c->l[i] = c->l[j], c->l[j] = x;
break;
}
c->watch[i] = s->lit[c->l[i]].watch;
s->lit[c->l[i]].watch = c;
}
}
/* jump back to decision level d */
void
satbackjump(SATSolve *s, int d)
{
int l;
SATVar *v;
if(s->lvl == d) return;
while(s->ntrail > s->decbd[d + 1]){
l = s->trail[--s->ntrail];
v = &s->var[VAR(l)];
if((v->flags & VARUSER) != 0){ /* don't delete user assignments */
s->ntrail++;
break;
}
s->lit[l].val = -1;
s->lit[NOT(l)].val = -1;
v->flags = v->flags & ~1 | l & 1;
v->lvl = -1;
v->reason = nil;
v->isbinreason = 0;
if(v->heaploc < 0)
satheapput(s, v);
}
s->lvl = d;
if(s->forptr > s->ntrail) s->forptr = s->ntrail;
if(s->binptr > s->ntrail) s->binptr = s->ntrail;
if(verbosestate) satprintstate(s);
}
static void
solvinit(SATSolve *s)
{
satdebuginit(s);
satheapreset(s);
s->decbd = satrealloc(s, s->decbd, s->nvar * sizeof(int));
s->decbd[0] = 0;
s->trail = satrealloc(s, s->trail, sizeof(int) * s->nvar);
s->fullrlits = satrealloc(s, s->fullrlits, sizeof(int) * s->nvar);
s->lvlstamp = satrealloc(s, s->lvlstamp, sizeof(int) * s->nvar);
memset(s->lvlstamp, 0, sizeof(int) * s->nvar);
if(s->cflclalloc == 0){
s->cflcl = satrealloc(s, s->cflcl, CFLCLALLOC * sizeof(int));
s->cflclalloc = CFLCLALLOC;
}
rewatch(s);
s->conflicts = 0;
s->nextpurge = s->purgeΔ;
s->purgeival = s->purgeΔ;
s->nextflush = 1;
s->flushu = 1;
s->flushv = 1;
s->flushθ = s->flushψ;
s->agility = 0;
satbackjump(s, 0);
s->forptr = 0;
s->binptr = 0;
}
void
satcleanup(SATSolve *s, int all)
{
SATBlock *b, *bn;
if(all){
*s->lastp[0] = nil;
s->learncl = nil;
s->lastp[1] = &s->learncl;
s->ncl = s->ncl0;
}
for(b = s->bl[1].next; b != &s->bl[1]; b = bn){
bn = b->next;
if(b->last != nil && !all) continue;
b->next->prev = b->prev;
b->prev->next = b->next;
free(b);
}
s->lastbl = s->bl[1].prev;
free(s->fullrlits);
s->fullrlits = nil;
free(s->lvlstamp);
s->lvlstamp = nil;
free(s->cflcl);
s->cflcl = nil;
s->cflclalloc = 0;
}
static void
stampoverflow(SATSolve *s)
{
int i;
for(i = 0; i < s->nvar; i++){
s->var[i].stamp = 0;
s->lvlstamp[i] = 0;
}
s->stamp = -2;
}
/* "bump" the variable, i.e. increase its activity score. reduce all score when one exceeds MAXACTIVITY (1e100) */
static void
varbump(SATSolve *s, SATVar *v)
{
v->activity += s->Δactivity;
satreheap(s, v);
if(v->activity < MAXACTIVITY) return;
for(v = s->var; v < s->var + s->nvar; v++)
if(v->activity != 0){
v->activity /= MAXACTIVITY;
if(v->activity < ε)
v->activity = ε;
}
s->Δactivity /= MAXACTIVITY;
}
/* ditto for clauses */
static void
clausebump(SATSolve *s, SATClause *c)
{
c->activity += s->Δclactivity;
if(c->activity < MAXACTIVITY) return;
for(c = s->cl; c != nil; c = c->next)
if(c->activity != 0){
c->activity /= MAXACTIVITY;
if(c->activity < ε)
c->activity = ε;
}
s->Δclactivity /= MAXACTIVITY;
}
/* pick a literal. normally we pick the variable with highest activity from the heap. sometimes we goof and pick a random one. */
static void
decision(SATSolve *s)
{
SATVar *v;
s->decbd[++s->lvl] = s->ntrail;
if((uint)s->randfn(s->randaux) < s->goofprob){
v = s->heap[satnrand(s, s->nheap)];
if(v->lvl < 0)
goto gotv;
}
do
v = satheaptake(s);
while(v->lvl >= 0);
gotv:
sataddtrail(s, 2 * (v - s->var) + (v->flags & VARPHASE));
}
/* go through the watchlist of a literal that just turned out false. */
/* full == 1 records the first conflict and goes on rather than aborting immediately */
static SATClause *
forcing(SATSolve *s, int l, int full)
{
SATClause **cp, *rc, *c, *xp;
int v0;
int x, j;
cp = &s->lit[l].watch;
rc = nil;
if(verboseforcing) print("forcing literal %d\n", signf(l));
while(c = *cp, c != nil){
if(l == c->l[0]){
/* this swap implies that the reason r for a literal l always has r->l[0]==l */
x = c->l[1], c->l[1] = c->l[0], c->l[0] = x;
xp = c->watch[1], c->watch[1] = c->watch[0], c->watch[0] = xp;
}
assert(c->l[1] == l);
v0 = s->lit[c->l[0]].val;
if(v0 > 0) /* the clause is true anyway */
goto next;
for(j = 2; j < c->n; j++)
if(s->lit[c->l[j]].val != 0){
/* found another literal to watch for this clause */
if(verboseforcing) print("moving clause %+Γ onto watchlist %d\n", c, signf(c->l[j]));
*cp = c->watch[1];
x = c->l[j], c->l[j] = c->l[1], c->l[1] = x;
c->watch[1] = s->lit[x].watch;
s->lit[x].watch = c;
goto cont;
}
if(v0 == 0){
/* conflict */
if(!full) return c;
if(rc == nil) rc = c;
goto next;
}
if(verboseforcing) print("inferring %d using clause %+Γ\n", signf(c->l[0]), c);
sataddtrail(s, c->l[0]);
s->var[VAR(c->l[0])].reason = c;
next:
cp = &c->watch[1];
cont: ;
}
return rc;
}
/* forcing() for binary implications */
static uvlong
binforcing(SATSolve *s, int l, int full)
{
SATLit *lp;
int i, m;
uvlong rc;
lp = &s->lit[l];
rc = 0;
if(verboseforcing && lp->nbimp > 0) print("forcing literal %d (binary)\n", signf(l));
for(i = 0; i < lp->nbimp; i++){
m = lp->bimp[i];
switch(s->lit[m].val){
case -1:
if(verboseforcing) print("inferring %d using binary clause (%d) ∨ %d\n", signf(m), -signf(l), signf(m));
sataddtrail(s, m);
s->var[VAR(m)].binreason = NOT(l);
s->var[VAR(m)].isbinreason = 1;
break;
case 0:
if(verboseforcing) print("conflict (%d) ∨ (%d)\n", -signf(l), signf(m));
if(rc == 0) rc = (uvlong)NOT(l) << 32 | (uint)m;
if(!full) return rc;
break;
}
}
return rc;
}
/* check if we can discard the previously learned clause because the current one subsumes it */
static int
checkdiscard(SATSolve *s)
{
SATClause *c;
SATVar *v;
int q, j;
if(s->lastp[1] == &s->learncl) return 0;
c = (SATClause*) ((uchar*) s->lastp[1] - (uchar*) &((SATClause*)0)->next);
if(s->lit[c->l[0]].val >= 0) return 0; /* clause is a reason, hands off */
q = s->ncflcl;
for(j = c->n - 1; q > 0 && j >= q; j--){
v = &s->var[VAR(c->l[j])];
/* check if literal is in the current clause */
if(c->l[j] == s->cflcl[0] || (uint)v->lvl <= s->cfllvl && v->stamp == s->stamp)
q--;
}
return q == 0;
}
/* add the clause we just learned to our collection */
static SATClause *
learn(SATSolve *s, int notriv)
{
SATClause *r;
int i, l, triv;
/* clauses that are too complicated are not worth it. learn the trivial clause (all decisions negated) instead */
if(triv = !notriv && s->ncflcl > s->lvl + s->trivlim){
assert(s->lvl + 1 <= s->cflclalloc);
for(i = 1; i <= s->lvl; i++)
s->cflcl[i] = NOT(s->trail[s->decbd[s->lvl + 1 - i]]);
s->ncflcl = s->lvl + 1;
}
if(s->ncflcl == 1) /* unit clauses are handled by putting them on the trail in conflict() */
return nil;
if(!triv && checkdiscard(s))
r = satreplclause(s, s->ncflcl);
else
r = satnewclause(s, s->ncflcl, 1);
r->n = s->ncflcl;
memcpy(r->l, s->cflcl, s->ncflcl * sizeof(int));
for(i = 0; i < 2; i++){
l = r->l[i];
r->watch[i] = s->lit[l].watch;
s->lit[l].watch = r;
}
return r;
}
/* recursive procedure to determine if a literal is redundant.
* to avoid repeated work, each known redundant literal is stamped with stamp+1
* and each known nonredundant literal is stamped with stamp+2.
*/
static int
redundant(SATSolve *s, int l)
{
SATVar *v, *w;
SATClause *c;
int i, r;
v = &s->var[VAR(l)];
if(v->isbinreason){
/* stupid special case code */
r = v->binreason;
w = &s->var[VAR(r)];
if(w->lvl != 0){
if(w->stamp == s->stamp + 2)
return 0;
if(w->stamp < s->stamp && (s->lvlstamp[w->lvl] < s->stamp || !redundant(s, r))){
w->stamp = s->stamp + 2;
return 0;
}
}
v->stamp = s->stamp + 1;
return 1;
}
if(v->reason == nil) return 0; /* decision literals are never redundant */
c = v->reason;
for(i = 0; i < c->n; i++){
if(c->l[i] == NOT(l)) continue;
w = &s->var[VAR(c->l[i])];
if(w->lvl == 0)
continue; /* literals at level 0 are redundant */
if(w->stamp == s->stamp + 2)
return 0;
/* if the literal is not in the clause or known redundant, check if it is redundant */
/* we can skip the check if the level is not stamped: */
/* if there are no literals at the same level in the clause, it must be nonredundant */
if(w->stamp < s->stamp && (s->lvlstamp[w->lvl] < s->stamp || !redundant(s, c->l[i]))){
w->stamp = s->stamp + 2;
return 0;
}
}
v->stamp = s->stamp + 1;
return 1;
}
/* "blitting" a literal means to either add it to the conflict clause
* (if v->lvl < s->lvl) or to increment the counter of literals to be
* resolved, plus some bookkeeping. */
static void
blit(SATSolve *s, int l)
{
SATVar *v;
int p;
v = &s->var[VAR(l)];
if(v->stamp == s->stamp) return;
v->stamp = s->stamp;
p = v->lvl;
if(p == 0) return;
if(verboseconflict) print("stamp %d %s (ctr=%d)\n", signf(l), p == s->lvl ? "and increment" : "and collect", s->cflctr);
varbump(s, v);
if(p == s->lvl){
s->cflctr++;
return;
}
if(s->ncflcl >= s->cflclalloc){
s->cflcl = satrealloc(s, s->cflcl, (s->cflclalloc + CFLCLALLOC) * sizeof(int));
s->cflclalloc += CFLCLALLOC;
}
s->cflcl[s->ncflcl++] = l;
if(p > s->cfllvl) s->cfllvl = p;
/* lvlstamp[p] == stamp if there is exactly one literal and ==stamp+1 if there is more than one literal on level p */
if(s->lvlstamp[p] <= s->stamp)
s->lvlstamp[p] = s->stamp + (s->lvlstamp[p] == s->stamp);
}
/* to resolve a conflict, we start with the conflict clause and use
* resolution (a ∨ b and ¬a ∨ c imply b ∨ c) with the reasons for the
* literals to remove all but one literal at the current level. this
* gives a new "learned" clause with all literals false and we jump back
* to the second-highest level in it. at this point, the clause implies
* the one remaining literal and we can continue.
* to do this quickly, rather than explicitly apply resolution, we keep a
* counter of literals at the highest level (unresolved literals) and an
* array with all other literals (which will become the learned clause). */
static void
conflict(SATSolve *s, SATClause *c, uvlong bin, int full)
{
int i, j, l, p, *nl, found;
SATVar *v;
SATClause *r;
if(verboseconflict) satprintstate(s);
/* choose a new unique stamp value */
if(s->stamp >= (uint)-3)
stampoverflow(s);
s->stamp += 3;
s->ncflcl = 1;
s->cflctr = 0;
s->cfllvl = 0;
/* we start by blitting each literal in the conflict clause */
if(c != nil){
clausebump(s, c);
for(i = 0; i < c->n; i++)
blit(s, c->l[i]);
/* if there is only one literal l at the current level, we should have inferred ¬l at a lower level (bug). */
if(s->cflctr <= 1){
satprintstate(s);
print("conflict clause %+Γ\n", c);
assert(s->cflctr > 1);
}
}else{
blit(s, bin);
blit(s, bin>>32);
if(s->cflctr <= 1){
satprintstate(s);
print("binary conflict clause %d ∨ %d\n", (int)(bin>>32), (int)bin);
assert(s->cflctr > 1);
}
}
/* now we go backwards through the trail, decrementing the unresolved literal counter at each stamped literal */
/* and blitting the literals in their reason */
for(i = s->ntrail; --i >= 0; ){
v = &s->var[VAR(s->trail[i])];
if(v->stamp != s->stamp) continue;
if(verboseconflict) print("trail literal %d\n", signf(s->trail[i]));
if(--s->cflctr == 0) break;
if(v->isbinreason)
blit(s, v->binreason);
else if((r = v->reason) != nil){
clausebump(s, r);
for(j = 0; j < r->n; j++)
blit(s, r->l[j]);
}
}
/* i should point to the one remaining literal at the current level */
assert(i >= 0);
nl = s->cflcl;
nl[0] = NOT(s->trail[i]);
found = 0;
/* delete redundant literals. note we must watch a literal at cfllvl, so put it in l[1]. */
for(i = 1, j = 1; i < s->ncflcl; i++){
l = nl[i];
p = s->var[VAR(nl[i])].lvl;
/* lvlstamp[p] != s->stamp + 1 => only one literal at level p => must be nonredundant */
if(s->lvlstamp[p] != s->stamp + 1 || !redundant(s, l))
if(found || p < s->cfllvl)
nl[j++] = nl[i];
else{
/* watch this literal */
l = nl[i], nl[j++] = nl[1], nl[1] = l;
found = 1;
}
}
s->ncflcl = j;
if(!full){
/* normal mode: jump back and add to trail right away */
satbackjump(s, s->cfllvl);
sataddtrail(s, nl[0]);
}else{
/* purging: record minimum cfllvl and literals at that level */
if(s->cfllvl < s->fullrlvl){
s->fullrlvl = s->cfllvl;
s->nfullrlits = 0;
}
s->fullrlits[s->nfullrlits++] = nl[0];
}
r = learn(s, full);
if(!full && r != nil)
s->var[VAR(nl[0])].reason = r;
if(verboseconflict)
if(r != nil)
print("learned %+Γ\n", r);
else
print("learned %d\n", signf(nl[0]));
s->Δactivity *= s->varρ;
s->Δclactivity *= s->clauseρ;
s->conflicts++;
}
/* to purge, we need a fullrun that assigns values to all variables.
* during this we record the first conflict at each level, to be resolved
* later. otherwise this is just a copy of the main loop which never
* purges or flushes. */
static int
fullrun(SATSolve *s)
{
int l;
uvlong b;
SATClause *c;
while(s->ntrail < s->nvar){
decision(s);
re:
while(s->binptr < s->ntrail){
l = s->trail[s->binptr++];
b = binforcing(s, l, 1);
if(b != 0){
if(s->lvl == 0){
s->unsat = 1;
return -1;
}
if(s->nfullrcfl == 0 || s->lvl > CFLLVL(s->fullrcfl[s->nfullrcfl-1])){
s->fullrcfl = satrealloc(s, s->fullrcfl, sizeof(SATConflict) * (s->nfullrcfl + 1));
s->fullrcfl[s->nfullrcfl].lvl = 1<<31 | s->lvl;
s->fullrcfl[s->nfullrcfl++].b = b;
}
}
sanity(s);
}
while(s->forptr < s->ntrail){
l = s->trail[s->forptr++];
c = forcing(s, NOT(l), 1);
if(c != nil){
if(s->lvl == 0){
s->unsat = 1;
return -1;
}
if(s->nfullrcfl == 0 || s->lvl > CFLLVL(s->fullrcfl[s->nfullrcfl-1])){
s->fullrcfl = satrealloc(s, s->fullrcfl, sizeof(SATConflict) * (s->nfullrcfl + 1));
s->fullrcfl[s->nfullrcfl].lvl = s->lvl;
s->fullrcfl[s->nfullrcfl++].c = c;
}
}
}
if(s->binptr < s->ntrail) goto re;
}
return 0;
}
/* assign range scores to all clauses.
* p == number of levels that have positive literals in the clause.
* r == number of levels that have literals in the clause.
* range == min(floor(16 * (p + α (r - p))), 255) with magic constant α. */
static void
ranges(SATSolve *s)
{
SATClause *c;
int p, r, k, l, v;
uint ci;
ci = 2;
memset(s->lvlstamp, 0, sizeof(int) * s->nvar);
memset(s->rangecnt, 0, sizeof(s->rangecnt));
for(c = s->learncl; c != nil; c = c->next, ci += 2){
if(!s->var[VAR(c->l[0])].binreason && s->var[VAR(c->l[0])].reason == c){
c->range = 0;
s->rangecnt[0]++;
continue;
}
p = 0;
r = 0;
for(k = 0; k < c->n; k++){
l = c->l[k];
v = s->var[VAR(l)].lvl;
if(v == 0){
if(s->lit[l].val == 1){
c->range = 256;
goto next;
}
}else{
if(s->lvlstamp[v] < ci){
s->lvlstamp[v] = ci;
r++;
}
if(s->lvlstamp[v] == ci && s->lit[l].val == 1){
s->lvlstamp[v] = ci + 1;
p++;
}
}
}
r = 16 * (p + s->purgeα * (r - p));
if(r > 255) r = 255;
c->range = r;
s->rangecnt[r]++;
next: ;
}
}
/* resolve conflicts found during fullrun() */
static void
fullrconflicts(SATSolve *s)
{
SATConflict *cfl;
int i;
s->fullrlvl = s->lvl;
s->nfullrlits = 0;
for(cfl = &s->fullrcfl[s->nfullrcfl - 1]; cfl >= s->fullrcfl; cfl--){
satbackjump(s, CFLLVL(*cfl));
if(cfl->lvl < 0)
conflict(s, nil, cfl->b, 1);
else
conflict(s, cfl->c, 0, 1);
}
satbackjump(s, 0);
if(s->fullrlvl == 0)
for(i = 0; i < s->nfullrlits; i++)
sataddtrail(s, s->fullrlits[i]);
free(s->fullrcfl);
s->fullrcfl = nil;
}
/* note that nil > *, this simplifies the algorithm by having nil "bubble" to the top */
static int
actgt(SATClause *a, SATClause *b)
{
if(b == nil) return 0;
if(a == nil) return 1;
return a->activity > b->activity || a->activity == b->activity && a > b;
}
/* select n clauses to keep
* first we find the upper limit j on the range score
* to get the exact number, we move htot clauses from j to j+1
* to this end, we put them in a max-heap of size htot, sorted by activity,
* continually replacing the largest element if we find a less active clause.
* the heap starts out filled with nil and the nil are replaced during the first
* htot iterations. */
#define LEFT(i) (2*(i)+1)
#define RIGHT(i) (2*(i)+2)
static int
judgement(SATSolve *s, int n)
{
int cnt, i, j, htot, m;
SATClause *c, **h, *z;
cnt = 0;
for(j = 0; j < 256; j++){
cnt += s->rangecnt[j];
if(cnt >= n) break;
}
if(j == 256) return j;
if(cnt > n){
htot = cnt - n;
h = satrealloc(s, nil, sizeof(SATClause *) * htot);
memset(h, 0, sizeof(SATClause *) * htot);
for(c = s->learncl; c != nil; c = c->next){
if(c->range != j || actgt(c, h[0])) continue;
h[0] = c;
m = 0;
for(;;){
i = m;
if(LEFT(i) < htot && actgt(h[LEFT(i)], h[m])) m = LEFT(i);
if(RIGHT(i) < htot && actgt(h[RIGHT(i)], h[m])) m = RIGHT(i);
if(i == m) break;
z = h[i], h[i] = h[m], h[m] = z;
}
}
for(i = 0; i < htot; i++)
if(h[i] != nil)
h[i]->range = j + 1;
free(h);
}
return j;
}
/* during purging we remove permanently false literals from learned clauses.
* returns 1 if the clause can be deleted entirely. */
static int
cleanupclause(SATSolve *s, SATClause *c)
{
int i, k;
for(i = 0; i < c->n; i++)
if(s->lit[c->l[i]].val == 0)
break;
if(i == c->n) return 0;
for(k = i; i < c->n; i++)
if(s->lit[c->l[i]].val != 0)
c->l[k++] = c->l[i];
c->n = k;
if(k > 1) return 0;
if(k == 0)
s->unsat = 1;
else if(s->lit[c->l[0]].val < 0)
sataddtrail(s, c->l[0]);
return 1;
}
/* delete clauses by overwriting them. don't delete empty blocks; we're going to fill them up soon enough again. */
static void
execution(SATSolve *s, int j)
{
SATClause *c, *n, **cp, *p;
SATBlock *b;
SATVar *v0;
int f, sz;
b = s->bl[1].next;
p = (SATClause*) b->data;
s->ncl = s->ncl0;
cp = &s->learncl;
for(c = p; c != nil; c = n){
n = c->next;
if(c->range > j || cleanupclause(s, c))
continue;
sz = sizeof(SATClause) + (c->n - 1) * sizeof(int);
f = (uchar*)b + SATBLOCKSZ - (uchar*)p;
if(f < sz){
memset(p, 0, f);
b = b->next;
assert(b != &s->bl[1]);
p = (SATClause *) b->data;
}
b->last = p;
/* update reason field of the first variable (if applicable) */
v0 = &s->var[VAR(c->l[0])];
if(!v0->isbinreason && v0->reason == c)
v0->reason = p;
memmove(p, c, sz);
*cp = p;
cp = &p->next;
p = (void*)((uintptr)p + sz + CLAUSEALIGN - 1 & -CLAUSEALIGN);
b->end = p;
s->ncl++;
}
*cp = nil;
*s->lastp[0] = s->learncl;
s->lastp[1] = cp;
s->lastbl = b;
f = (uchar*)b + SATBLOCKSZ - (uchar*)p;
memset(p, 0, f);
for(b = b->next; b != &s->bl[1]; b = b->next){
b->last = nil;
b->end = b->data;
}
}
static void
thepurge(SATSolve *s)
{
int nkeep, i, j;
SATVar *v;
s->purgeival += s->purgeδ;
s->nextpurge = s->conflicts + s->purgeival;
nkeep = (s->ncl - s->ncl0) / 2;
for(i = 0; i < s->ntrail; i++){
v = &s->var[VAR(s->trail[i])];
if(!v->isbinreason && v->reason != nil)
nkeep++;
}
if(nkeep <= 0) return; /* shouldn't happen */
s->nfullrcfl = 0;
if(fullrun(s) < 0){ /* accidentally determined UNSAT during fullrun() */
free(s->fullrcfl);
s->fullrcfl = nil;
return;
}
ranges(s);
fullrconflicts(s);
j = judgement(s, nkeep);
execution(s, j);
rewatch(s);
}
/* to avoid getting stuck, flushing backs up the trail to remove low activity variables.
* don't worry about throwing out high activity ones, they'll get readded quickly. */
static void
theflush(SATSolve *s)
{
double actk;
int dd, l;
/* "reluctant doubling" wizardry to determine when to flush */
if((s->flushu & -s->flushu) == s->flushv){
s->flushu++;
s->flushv = 1;
s->flushθ = s->flushψ;
}else{
s->flushv *= 2;
s->flushθ += s->flushθ >> 4;
}
s->nextflush = s->conflicts + s->flushv;
if(s->agility > s->flushθ) return; /* don't flush when we're too busy */
/* clean up the heap so that a free variable is at the top */
while(s->nheap > 0 && s->heap[0]->lvl >= 0)
satheaptake(s);
if(s->nheap == 0) return; /* shouldn't happen */
actk = s->heap[0]->activity;
for(dd = 0; dd < s->lvl; dd++){
l = s->trail[s->decbd[dd+1]];
if(s->var[VAR(l)].activity < actk)
break;
}
satbackjump(s, dd);
}
int
satsolve(SATSolve *s)
{
int l;
SATClause *c;
uvlong b;
if(s == nil) return 1;
if(s->scratched) return -1;
if(s->nvar == 0) return 1;
solvinit(s);
while(!s->unsat){
re:
while(s->binptr < s->ntrail){
l = s->trail[s->binptr++];
b = binforcing(s, l, 0);
sanity(s);
if(b != 0){
if(s->lvl == 0) goto unsat;
conflict(s, nil, b, 0);
sanity(s);
}
}
while(s->forptr < s->ntrail){
l = s->trail[s->forptr++];
c = forcing(s, NOT(l), 0);
sanity(s);
if(c != nil){
if(s->lvl == 0) goto unsat;
conflict(s, c, 0, 0);
sanity(s);
}
}
if(s->binptr < s->ntrail) goto re;
if(s->ntrail == s->nvar) goto out;
if(s->conflicts >= s->nextpurge)
thepurge(s);
else if(s->conflicts >= s->nextflush)
theflush(s);
else
decision(s);
}
unsat:
s->unsat = 1;
out:
satcleanup(s, 0);
return !s->unsat;
}
void
satreset(SATSolve *s)
{
int i;
if(s == nil || s->decbd == nil) return;
satbackjump(s, -1);
s->lvl = 0;
for(i = 0; i < s->nvar; i++){
s->var[i].activity = 0;
s->var[i].flags |= VARPHASE;
}
satcleanup(s, 1);
s->Δactivity = 1;
s->Δclactivity = 1;
}

1
sys/src/mkfile
View file

@ -30,6 +30,7 @@ LIBS=\
libndb\
libplumb\
libregexp\
libsat\
libscribble\
libsec\
libstdio\