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bird/lib/redblack.h

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/*
* BIRD Internet Routing Daemon -- Red Black Tree
*
* (c) 2018 Maria Matejka <mq@jmq.cz>
* (c) 2018 CZ.NIC z.s.p.o.
*
* Can be freely distributed and used under the terms of the GNU GPL.
*/
#ifndef _BIRD_REDBLACK_H_
#define _BIRD_REDBLACK_H_
/* Assumption: The nodes are always residing on an even address.
* We store the node blackness into the parent pointer LSB. */
/*
* Typical use case:
* struct mystruct {
* whatever;
* REDBLACK_NODE(struct mystruct, myprefix_);
* whatever;
* };
*/
#define REDBLACK_NODE(type, name) type *name[3]
/* Color bit definition */
#define REDBLACK_BLACK 0
#define REDBLACK_RED 1
/* Parent pointer and color composition and resolution */
#define REDBLACK_PARENT_POINTER(name, what) (what)->name[0]
#define REDBLACK_PTR(type, pointer) ((type *) pointer)
#define REDBLACK_PTR_RED(type, pointer) REDBLACK_PTR(type, (((uintptr_t) (pointer)) | 1))
#define REDBLACK_PTR_BLACK(type, pointer) (pointer)
#define REDBLACK_PTR_COLOR(pointer) (((uintptr_t) (pointer)) & 1)
#define REDBLACK_NODE_COLOR(name, what) REDBLACK_PTR_COLOR(REDBLACK_PARENT_POINTER(name, what))
#define REDBLACK_PTR_COMPOSE(type, pointer, color) REDBLACK_PTR(type, (((uintptr_t) (pointer)) | (color)))
#define REDBLACK_PTR_PTR(type, pointer) REDBLACK_PTR(type, (((uintptr_t) (pointer)) & ~1))
#define REDBLACK_PARENT(type, name, what) REDBLACK_PTR_PTR(type, REDBLACK_PARENT_POINTER(name, what))
#define REDBLACK_SET_COLOR(type, name, what, color) \
(REDBLACK_PARENT_POINTER(name, what) = REDBLACK_PTR_COMPOSE(type, REDBLACK_PARENT(type, name, what), color))
/* Left and right direction */
#define REDBLACK_LEFT 1
#define REDBLACK_RIGHT 2
#define REDBLACK_CHILD(name, what, where) (what)->name[where]
#define REDBLACK_CHILDREN(name, what) { (what)->name[REDBLACK_LEFT], (what)->name[REDBLACK_RIGHT] }
#define REDBLACK_LEFT_CHILD(name, what) REDBLACK_CHILD(name, what, REDBLACK_LEFT)
#define REDBLACK_RIGHT_CHILD(name, what) REDBLACK_CHILD(name, what, REDBLACK_RIGHT)
#define REDBLACK_PARENT_SIDE(name, parent, child) ((REDBLACK_LEFT_CHILD(name, parent) == child) ? REDBLACK_LEFT : REDBLACK_RIGHT)
#define REDBLACK_DUMP(type, name, root, dumper) \
do { \
type *n = root; \
int depth = 0, dir = 0; \
while (n) { \
switch (dir) { \
case 0: if (REDBLACK_LEFT_CHILD(name, n)) { \
ASSERT(REDBLACK_PARENT(type, name, REDBLACK_LEFT_CHILD(name, n)) == n); \
n = REDBLACK_LEFT_CHILD(name, n); dir = 0; depth++; break; \
} __attribute__((fallthrough)); \
case 1: dumper(n, REDBLACK_NODE_COLOR(name, n), depth); \
if (REDBLACK_RIGHT_CHILD(name, n)) { \
ASSERT(REDBLACK_PARENT(type, name, REDBLACK_RIGHT_CHILD(name, n)) == n); \
n = REDBLACK_RIGHT_CHILD(name, n); dir = 0; depth++; break; \
} __attribute__((fallthrough)); \
case 2: { \
type *p = REDBLACK_PARENT(type, name, n); \
if (p) dir = REDBLACK_PARENT_SIDE(name, p, n); \
n = p; \
depth--; \
break; \
} \
} \
} \
} while (0)
#define REDBLACK_MAX_REASONABLE_DEPTH 256
#define REDBLACK_CHECK(type, name, key, compare, root) do { \
if (!root) \
break; \
type *prev = NULL; \
struct redblack_check { \
type *node; \
int state; \
int blackness[2]; \
} stack[REDBLACK_MAX_REASONABLE_DEPTH] = { \
{}, \
{ .node = root } \
}; \
int pos = 1; \
while (pos > 0) { \
switch (stack[pos].state) { \
case 0: \
if (REDBLACK_LEFT_CHILD(name, stack[pos].node)) { \
stack[pos+1] = (struct redblack_check) { .node = REDBLACK_LEFT_CHILD(name, stack[pos].node) }; \
ASSERT(compare(key(stack[pos+1].node), key(stack[pos].node)) < 0); \
pos++; \
continue; \
} \
stack[pos].state++; \
__attribute__((fallthrough)); \
case 1: \
ASSERT(!prev || (compare(key(prev), key(stack[pos].node)) < 0)); \
if (REDBLACK_RIGHT_CHILD(name, stack[pos].node)) { \
stack[pos+1] = (struct redblack_check) { .node = REDBLACK_RIGHT_CHILD(name, stack[pos].node) }; \
ASSERT(compare(key(stack[pos+1].node), key(stack[pos].node)) > 0); \
pos++; \
continue; \
} \
stack[pos].state++; \
__attribute__((fallthrough)); \
case 2: \
ASSERT(stack[pos].blackness[0] == stack[pos].blackness[1]); \
stack[pos-1].blackness[stack[pos-1].state] = stack[pos].blackness[0] + (REDBLACK_NODE_COLOR(name, stack[pos].node) == REDBLACK_BLACK); \
pos--; \
stack[pos].state++; \
} \
} \
/* printf("Redblack check OK. Overall blackness: %d\n", stack[0].blackness[0]); */ \
} while(0)
#define REDBLACK_FIND_POINTER(name, key, compare, root, what, pointer) \
for ( \
int _cmp = !(pointer = &(root)); \
(*pointer) && (_cmp = compare((what), key((*pointer)))); \
pointer = &(REDBLACK_CHILD(name, (*pointer), ((_cmp < 0) ? 1 : 2))) \
)
#define REDBLACK_FIND(type, name, key, compare, root, what) \
({ type **pointer; REDBLACK_FIND_POINTER(name, key, compare, root, what, pointer); *pointer; })
#define REDBLACK_FIND_UP(type, name, key, compare, root, what) ({ \
type **pointer, *prev = NULL, *out; \
REDBLACK_FIND_POINTER(name, key, compare, root, what, pointer) \
prev = *pointer; \
if (!*pointer && prev) \
if (pointer == &(REDBLACK_RIGHT_CHILD(name, prev))) \
out = REDBLACK_NEXT(type, name, prev); \
else \
out = prev; \
else \
out = *pointer; \
out; \
})
#define REDBLACK_FIND_DOWN(type, name, key, compare, root, what) ({ \
type **pointer, *prev = NULL, *out; \
REDBLACK_FIND_POINTER(name, key, compare, root, what, pointer) \
prev = *pointer; \
if (!*pointer && prev) \
if (pointer == &(REDBLACK_LEFT_CHILD(name, prev))) \
out = REDBLACK_PREV(type, name, prev); \
else \
out = prev; \
else \
out = *pointer; \
out; \
})
#define REDBLACK_FIRST(type, name, root) ({ \
type *first = root; \
if (first) \
while (REDBLACK_LEFT_CHILD(name, first)) \
first = REDBLACK_LEFT_CHILD(name, first); \
first; \
})
#define REDBLACK_NEXT(type, name, node) ({ \
type *where = node; \
if (REDBLACK_RIGHT_CHILD(name, where)) { \
where = REDBLACK_RIGHT_CHILD(name, where); \
while (REDBLACK_LEFT_CHILD(name, where)) \
where = REDBLACK_LEFT_CHILD(name, where); \
} else \
while (1) { \
type *p = REDBLACK_PARENT(type, name, where); \
int ps = p ? REDBLACK_PARENT_SIDE(name, p, where) : 0; \
where = p; \
if (ps == REDBLACK_RIGHT) \
continue; \
break; \
} \
where; \
})
#define REDBLACK_PREV(type, name, node) ({ \
type *where = node; \
if (REDBLACK_LEFT_CHILD(name, where)) { \
where = REDBLACK_LEFT_CHILD(name, where); \
while (REDBLACK_RIGHT_CHILD(name, where)) \
where = REDBLACK_RIGHT_CHILD(name, where); \
} else \
while (1) { \
type *p = REDBLACK_PARENT(type, name, where); \
int ps = p ? REDBLACK_PARENT_SIDE(name, p, where) : 0; \
where = p; \
if (ps == REDBLACK_LEFT) \
continue; \
break; \
} \
where; \
})
/* Low level tree manipulation */
/* Connect a node @ch to its new parent @p on side @side, setting color of @ch to @color */
#define REDBLACK_CONNECT_NODE_SET_COLOR(type, name, p, side, ch, color) \
(ch ? (REDBLACK_PARENT_POINTER(name, (REDBLACK_CHILD(name, p, side) = ch)) = REDBLACK_PTR_COMPOSE(type, p, color)) \
: (REDBLACK_CHILD(name, p, side) = NULL))
/* Connect a node @ch to its new parent @p on side @side, keeping its former color */
#define REDBLACK_CONNECT_NODE_KEEP_COLOR(type, name, p, side, ch) \
REDBLACK_CONNECT_NODE_SET_COLOR(type, name, p, side, ch, REDBLACK_NODE_COLOR(name, ch))
/* Opposite side macros (left <=> right) */
#define REDBLACK_OPPOSITE(side) (3-(side))
/* Tree rotation in a given direction.
* Left rotation:
*
* (P) (C)
* / XX XX \
* (A) (C) ---> (P) (D)
* X \ / X
* (B) (D) (A) (B)
*
* Right rotation is in the opposite direction.
*/
#define REDBLACK_ROTATE(type, name, root, p, side) do { \
type *rp = p, \
*rg = REDBLACK_PARENT(type, name, rp), \
*rc = REDBLACK_CHILD(name, rp, REDBLACK_OPPOSITE(side)), \
*rb = REDBLACK_CHILD(name, rc, side); \
int rgs = rg ? REDBLACK_PARENT_SIDE(name, rg, rp) : 0; \
REDBLACK_CONNECT_NODE_KEEP_COLOR(type, name, rc, side, rp); \
REDBLACK_CONNECT_NODE_KEEP_COLOR(type, name, rp, REDBLACK_OPPOSITE(side), rb); \
if (rgs) \
REDBLACK_CONNECT_NODE_KEEP_COLOR(type, name, rg, rgs, rc); \
else { \
REDBLACK_PARENT_POINTER(name, rc) = NULL; \
root = rc; \
} \
} while (0)
#define REDBLACK_INSERT(type, name, key, compare, root, what) do { \
type **where = &(root); \
what->name[0] = what->name[1] = what->name[2] = NULL; \
REDBLACK_FIND_POINTER(name, key, compare, root, key(what), where) \
REDBLACK_PARENT_POINTER(name, what) = REDBLACK_PTR_RED(type, *where); \
ASSERT(!*where); \
*where = what; \
type *n = *where; \
do { \
if (((uintptr_t) REDBLACK_PARENT_POINTER(name, n)) == 1) \
REDBLACK_PARENT_POINTER(name, n) = NULL; \
if (REDBLACK_PARENT_POINTER(name, n) == NULL) \
break; \
type *p = REDBLACK_PARENT(type, name, n); \
if (REDBLACK_NODE_COLOR(name, p) == REDBLACK_BLACK) \
break; \
type *g = REDBLACK_PARENT(type, name, p); \
type *u = REDBLACK_CHILD(name, g, REDBLACK_OPPOSITE(REDBLACK_PARENT_SIDE(name, g, p))); \
if (u && REDBLACK_NODE_COLOR(name, u) == REDBLACK_RED) { \
REDBLACK_SET_COLOR(type, name, u, REDBLACK_BLACK); \
REDBLACK_SET_COLOR(type, name, p, REDBLACK_BLACK); \
REDBLACK_SET_COLOR(type, name, g, REDBLACK_RED); \
n = g; \
continue; \
} \
int gc = REDBLACK_PARENT_SIDE(name, g, p); \
int pc = REDBLACK_PARENT_SIDE(name, p, n); \
if (gc != pc) { \
REDBLACK_ROTATE(type, name, root, p, gc); \
REDBLACK_SET_COLOR(type, name, n, REDBLACK_BLACK); \
} else \
REDBLACK_SET_COLOR(type, name, p, REDBLACK_BLACK); \
REDBLACK_ROTATE(type, name, root, g, REDBLACK_OPPOSITE(gc)); \
REDBLACK_SET_COLOR(type, name, g, REDBLACK_RED); \
break; \
} while (1); \
} while (0)
#define REDBLACK_EXCHANGE(type, name, root, aa, bb) do { \
type *a = aa, *b = bb; \
type *ap = REDBLACK_PARENT(type, name, a), *al = REDBLACK_LEFT_CHILD(name, a), *ar = REDBLACK_RIGHT_CHILD(name, a); \
type *bp = REDBLACK_PARENT(type, name, b), *bl = REDBLACK_LEFT_CHILD(name, b), *br = REDBLACK_RIGHT_CHILD(name, b); \
int as = ap ? REDBLACK_PARENT_SIDE(name, ap, a) : 0, bs = bp ? REDBLACK_PARENT_SIDE(name, bp, b) : 0; \
if ((ap != b) || (as != REDBLACK_LEFT)) \
REDBLACK_CONNECT_NODE_KEEP_COLOR(type, name, a, REDBLACK_LEFT, bl); \
if ((bp != a) || (bs != REDBLACK_LEFT)) \
REDBLACK_CONNECT_NODE_KEEP_COLOR(type, name, b, REDBLACK_LEFT, al); \
if ((ap != b) || (as != REDBLACK_RIGHT)) \
REDBLACK_CONNECT_NODE_KEEP_COLOR(type, name, a, REDBLACK_RIGHT, br); \
if ((bp != a) || (bs != REDBLACK_RIGHT)) \
REDBLACK_CONNECT_NODE_KEEP_COLOR(type, name, b, REDBLACK_RIGHT, ar); \
int ac = REDBLACK_NODE_COLOR(name, a), bc = REDBLACK_NODE_COLOR(name, b); \
if (a == bp) \
bp = b; \
if (b == ap) \
ap = a; \
if (ap) \
REDBLACK_CONNECT_NODE_SET_COLOR(type, name, ap, as, b, ac); \
else { \
REDBLACK_PARENT_POINTER(name, b) = NULL; \
root = b; \
} \
if (bp) \
REDBLACK_CONNECT_NODE_SET_COLOR(type, name, bp, bs, a, bc); \
else { \
REDBLACK_PARENT_POINTER(name, a) = NULL; \
root = a; \
} \
} while (0)
#define REDBLACK_DELETE(type, name, root, what_) do { \
type *what = what_; \
type *cl = REDBLACK_LEFT_CHILD(name, what); \
type *cr = REDBLACK_RIGHT_CHILD(name, what); \
if (cl && cr) { \
type *s = cl; \
while (REDBLACK_RIGHT_CHILD(name, s)) s = REDBLACK_RIGHT_CHILD(name, s); \
REDBLACK_EXCHANGE(type, name, root, s, what); \
cl = REDBLACK_LEFT_CHILD(name, what); \
cr = REDBLACK_RIGHT_CHILD(name, what); \
} \
type *p = REDBLACK_PARENT(type, name, what); \
if (!p) { \
/* Deleting root in almost empty tree */ \
if (cl) { \
root = cl; \
REDBLACK_PARENT_POINTER(name, cl) = NULL; \
break; \
} \
if (cr) { \
root = cr; \
REDBLACK_PARENT_POINTER(name, cr) = NULL; \
break; \
} \
root = NULL; \
break; \
} \
int ps = REDBLACK_PARENT_SIDE(name, p, what); \
if (REDBLACK_NODE_COLOR(name, what) == REDBLACK_RED) { \
ASSERT((cl == NULL) && (cr == NULL)); \
REDBLACK_CHILD(name, p, ps) = NULL; \
break; \
} \
/* The only child now must be red */ \
if (cl) { \
REDBLACK_CONNECT_NODE_SET_COLOR(type, name, p, ps, cl, REDBLACK_BLACK); \
break; \
} \
if (cr) { \
REDBLACK_CONNECT_NODE_SET_COLOR(type, name, p, ps, cr, REDBLACK_BLACK); \
break; \
} \
type *drop = what; \
while (1) { /* Invariant: what is black */ \
if (what == root) { /* Case 1 */ \
if (drop) \
root = NULL; \
break; \
} \
type *p = REDBLACK_PARENT(type, name, what); \
int ws = REDBLACK_PARENT_SIDE(name, p, what); \
type *s = REDBLACK_CHILD(name, p, REDBLACK_OPPOSITE(ws)); \
/* Case 2 */ \
if (s && (REDBLACK_NODE_COLOR(name, s) == REDBLACK_RED)) { /* Therefore p is black also in case 2 */ \
REDBLACK_ROTATE(type, name, root, p, ws); \
REDBLACK_SET_COLOR(type, name, p, REDBLACK_RED); \
REDBLACK_SET_COLOR(type, name, s, REDBLACK_BLACK); \
/* Now what's sibling is also black, let's try once again */ \
continue; \
} \
if (drop) drop = REDBLACK_CHILD(name, p, ws) = NULL; \
type *sc[2] = REDBLACK_CHILDREN(name, s); \
/* Case 3 & 4: sc[0] and sc[1] are both black; s is black from case 2 */ \
if ((!sc[0] || REDBLACK_NODE_COLOR(name, sc[0]) == REDBLACK_BLACK) && \
(!sc[1] || REDBLACK_NODE_COLOR(name, sc[1]) == REDBLACK_BLACK)) { \
if (REDBLACK_NODE_COLOR(name, p) == REDBLACK_BLACK) { /* Case 3 */ \
/* No red node nearby, pushing the change up the tree */ \
REDBLACK_SET_COLOR(type, name, s, REDBLACK_RED); \
what = p; \
continue; \
} else { /* Case 4: p is red */ \
/* Moving the red down the other tree */ \
REDBLACK_SET_COLOR(type, name, p, REDBLACK_BLACK); \
REDBLACK_SET_COLOR(type, name, s, REDBLACK_RED); \
break; \
} \
} \
/* Now sc[0] or sc[1] must be red (one or both) */ \
/* Case 5: the niece on the opposite side is black */ \
int nop = (REDBLACK_OPPOSITE(ws) == REDBLACK_RIGHT); \
if (!sc[nop] || (REDBLACK_NODE_COLOR(name, sc[nop]) == REDBLACK_BLACK)) { \
REDBLACK_SET_COLOR(type, name, s, REDBLACK_RED); \
REDBLACK_SET_COLOR(type, name, sc[1-nop], REDBLACK_BLACK); \
REDBLACK_ROTATE(type, name, root, s, REDBLACK_OPPOSITE(ws)); \
s = REDBLACK_CHILD(name, p, REDBLACK_OPPOSITE(ws)); \
sc[0] = REDBLACK_LEFT_CHILD(name, s); \
sc[1] = REDBLACK_RIGHT_CHILD(name, s); \
} \
/* Case 6: the niece on the opposite side is red */ \
REDBLACK_ROTATE(type, name, root, p, ws); \
REDBLACK_SET_COLOR(type, name, s, REDBLACK_NODE_COLOR(name, p)); \
REDBLACK_SET_COLOR(type, name, p, REDBLACK_BLACK); \
REDBLACK_SET_COLOR(type, name, sc[nop], REDBLACK_BLACK); \
break; \
} \
} while (0)
#endif
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