Rearranged lfsr_rbyd_append to have a single sprial loop with black recoloring during deletes

Preliminary comparisons show a minor improvement to code size at the cost
of stack usage. Really this boils down to a toss up, I'm currently
leaning towards this implementation of lfsr_rbyd_append as it has the
fewest moving parts, reusing the core rbyd loop for all mutating
operations.

Note these numbers are _very_ rough, there are likely some low-hanging
optimizations/cleanup and the rbyd size measurements are simply found
from fuzzing 1000 random permutations:

               commit size                       rbyd size
               code  stack  append/removes  create/deletes
spiralrb:      3178    664            1609            1621
spiralb:       3058    664            1609            1606 (current)
2stepb:        3284    632            1609            1606
This commit is contained in:
Christopher Haster
2023-01-30 20:30:16 -06:00
parent d3d340c426
commit 739a6e6d98
+314 -285
View File
@@ -2100,15 +2100,17 @@ static int lfsr_rbyd_append(lfs_t *lfs, lfsr_rbyd_t *rbyd_,
// this gets a bit confusing as we also may need to keep
// track of both the lower and upper bounds of diverging paths
// in the case of range deletions
//bool diverged = false;
bool diverged = false;
bool flipped = false;
uint8_t found = 0;
// TODO bool flipped? bool found?
lfsr_sid_t lower_lower_id = -1;
lfsr_sid_t lower_upper_id = rbyd_->weight;
lfsr_sid_t upper_lower_id = upper_lower_id;
lfsr_sid_t upper_upper_id = upper_upper_id;
lfsr_tag_t lower_lower_tag = 0;
lfsr_tag_t lower_upper_tag = 0xffff;
lfsr_tag_t upper_lower_tag = upper_lower_tag;
lfsr_sid_t upper_lower_id = lower_lower_id;
lfsr_sid_t upper_upper_id = lower_upper_id;
lfsr_tag_t upper_lower_tag = lower_lower_tag;
lfsr_tag_t upper_upper_tag = lower_upper_tag;
// queue of pending alts we can emulate rotations with
@@ -2120,19 +2122,17 @@ static int lfsr_rbyd_append(lfs_t *lfs, lfsr_rbyd_t *rbyd_,
// descend down tree, building alt pointers
while (true) {
// // do we need to flip bounds?
// if (diverged
// && !lfsr_tag_isfound(upper_tag_)
// && (!p_alts[0] || lfsr_tag_isblack(p_alts[0]))) {
// LFS_ASSERT(false);
// lfs_swap16(&lower_tag_, &upper_tag_);
// lfs_swaps32(&lower_id_, &upper_id_);
// lfs_swap32(&lower_branch, &upper_branch);
// lfs_swaps32(&lower_lower_id, &upper_lower_id);
// lfs_swaps32(&lower_upper_id, &upper_upper_id);
// lfs_swap16(&lower_lower_tag, &upper_lower_tag);
// lfs_swap16(&lower_upper_tag, &upper_upper_tag);
// }
// do we need to flip bounds?
if (diverged && found < 1) {
flipped = !flipped;
lfs_swap16(&lower_tag_, &upper_tag_);
lfs_swaps32(&lower_id_, &upper_id_);
lfs_swap32(&lower_branch, &upper_branch);
lfs_swaps32(&lower_lower_id, &upper_lower_id);
lfs_swaps32(&lower_upper_id, &upper_upper_id);
lfs_swap16(&lower_lower_tag, &upper_lower_tag);
lfs_swap16(&lower_upper_tag, &upper_upper_tag);
}
// read the alt pointer
lfsr_tag_t alt;
@@ -2147,14 +2147,23 @@ static int lfsr_rbyd_append(lfs_t *lfs, lfsr_rbyd_t *rbyd_,
// found an alt?
if (lfsr_tag_isalt(alt)) {
// TODO get rid of weight_
lfs_size_t weight_ = weight + 1;
// make jump absolute
jump = lower_branch - jump;
lfs_off_t branch_ = lower_branch + delta;
// go ahead and make alt black, this isn't perfect but it's
// simpler and compact will take care of any balance issues
// that may occur
if (diverged) {
LFS_ASSERT(!p_alts[0] || lfsr_tag_isblack(p_alts[0]));
alt = lfsr_tag_mkblack(alt);
}
// do bounds want to take different paths? begin cutting
if (/*!diverged
&&*/ lfsr_tag_follow2(alt, weight_,
if (!diverged
&& lfsr_tag_follow2(alt, weight_,
p_alts[0], p_weights[0],
lower_lower_id, lower_upper_id,
lower_tag_, lower_id_)
@@ -2176,15 +2185,17 @@ static int lfsr_rbyd_append(lfs_t *lfs, lfsr_rbyd_t *rbyd_,
goto diverging_red;
}
//diverged = true;
diverged = true;
LFS_ASSERT(!p_alts[0] || lfsr_tag_isblack(p_alts[0]));
alt = lfsr_tag_mkblack(alt);
upper_branch = lower_branch;
upper_lower_id = lower_lower_id;
upper_upper_id = lower_upper_id;
upper_lower_id = lower_lower_id;
upper_upper_id = lower_upper_id;
upper_lower_tag = lower_lower_tag;
upper_upper_tag = lower_upper_tag;
goto diverged;
//goto diverged;
// // make sure upper path is in sync with red alts!
@@ -2297,6 +2308,7 @@ diverging_red:
lower_branch = jump;
continue;
}
}
// // cut while following
// } else if (diverged
@@ -2388,7 +2400,7 @@ diverging_red:
// lower_branch = branch_;
// continue;
// }
}
// }
// two reds makes a yellow, split?
if (lfsr_tag_isred(alt)
@@ -2531,30 +2543,33 @@ diverging_red:
lfs_swap32(&jump, &branch_);
}
// push alt onto queue
LFS_ASSERT((lfs_ssize_t)weight_ >= 0);
// printf("pushed alt%c%s 0x%x w%d 0x%x\n",
// lfsr_tag_isred(alt) ? 'r' : 'b',
// lfsr_tag_isgt(alt) ? "gt" : "le",
// lfsr_tag_key(alt),
// weight_,
// jump);
int err = lfsr_rbyd_p_push(lfs, rbyd_,
p_alts, p_weights, p_jumps,
alt, weight_, jump);
if (err) {
return err;
}
// continue to next alt
// TODO move this up?
// trim alt from our current bounds
if (lfsr_tag_isblack(alt)) {
lfsr_tag_trim2(
alt, weight_,
p_alts[0], p_weights[0],
p_alts[1], p_weights[1],
&lower_lower_id, &lower_upper_id,
&lower_lower_tag, &lower_upper_tag);
}
if (!diverged || flipped == lfsr_tag_isgt(alt)) {
// push alts onto our queue
LFS_ASSERT((lfs_ssize_t)weight_ >= 0);
// printf("pushed alt%c%s 0x%x w%d 0x%x\n",
// lfsr_tag_isred(alt) ? 'r' : 'b',
// lfsr_tag_isgt(alt) ? "gt" : "le",
// lfsr_tag_key(alt),
// weight_,
// jump);
int err = lfsr_rbyd_p_push(lfs, rbyd_,
p_alts, p_weights, p_jumps,
alt, weight_, jump);
if (err) {
return err;
}
}
// continue to next alt
graft = lower_branch;
lower_branch = branch_;
@@ -2584,264 +2599,278 @@ diverging_red:
// found end of tree?
} else {
// update the tag id, marking as found
lower_tag_ = lfsr_tag_mkfound(alt);
lower_tag_ = alt;
lower_id_ = lower_upper_id-1;
// // if we diverged, we also need to find the other bound
// if (diverged && !lfsr_tag_isfound(upper_tag_)) {
// continue;
// }
// if we hit this we didn't diverge, and need to update upper bound
upper_tag_ = lower_tag_;
upper_id_ = lower_id_;
upper_branch = lower_branch;
upper_lower_id = lower_lower_id;
upper_upper_id = lower_upper_id;
upper_lower_tag = lower_lower_tag;
upper_upper_tag = lower_upper_tag;
// TODO deduplicate flips somehow?
if (diverged && found < 2) {
found += 1;
flipped = !flipped;
lfs_swap16(&lower_tag_, &upper_tag_);
lfs_swaps32(&lower_id_, &upper_id_);
lfs_swap32(&lower_branch, &upper_branch);
lfs_swaps32(&lower_lower_id, &upper_lower_id);
lfs_swaps32(&lower_upper_id, &upper_upper_id);
lfs_swap16(&lower_lower_tag, &upper_lower_tag);
lfs_swap16(&lower_upper_tag, &upper_upper_tag);
continue;
}
// almost done, we just need to insert a new alt pointer
// to connect our leaf to the tree
goto stem;
//// // if we diverged, we also need to find the other bound
//// if (diverged && !lfsr_tag_isfound(upper_tag_)) {
//// continue;
//// }
//
// // if we hit this we didn't diverge, and need to update upper bound
// upper_tag_ = lower_tag_;
// upper_id_ = lower_id_;
// upper_branch = lower_branch;
// upper_lower_id = lower_lower_id;
// upper_upper_id = lower_upper_id;
// upper_lower_tag = lower_lower_tag;
// upper_upper_tag = lower_upper_tag;
}
}
diverged:;
// descend down two branches of the tree, trimming inner branches
// and building alt pointers
while (!lfsr_tag_isfound(lower_tag_) || !lfsr_tag_isfound(upper_tag_)) {
// // do we need to flip bounds?
// if (diverged
// && !lfsr_tag_isfound(upper_tag_)
// && (!p_alts[0] || lfsr_tag_isblack(p_alts[0]))) {
// lfs_swap16(&lower_tag_, &upper_tag_);
// lfs_swaps32(&lower_id_, &upper_id_);
// lfs_swap32(&lower_branch, &upper_branch);
// lfs_swaps32(&lower_lower_id, &upper_lower_id);
// lfs_swaps32(&lower_upper_id, &upper_upper_id);
// lfs_swap16(&lower_lower_tag, &upper_lower_tag);
// lfs_swap16(&lower_upper_tag, &upper_upper_tag);
//diverged:;
// // descend down two branches of the tree, trimming inner branches
// // and building alt pointers
// while (!lfsr_tag_isfound(lower_tag_) || !lfsr_tag_isfound(upper_tag_)) {
//// // do we need to flip bounds?
//// if (diverged
//// && !lfsr_tag_isfound(upper_tag_)
//// && (!p_alts[0] || lfsr_tag_isblack(p_alts[0]))) {
//// lfs_swap16(&lower_tag_, &upper_tag_);
//// lfs_swaps32(&lower_id_, &upper_id_);
//// lfs_swap32(&lower_branch, &upper_branch);
//// lfs_swaps32(&lower_lower_id, &upper_lower_id);
//// lfs_swaps32(&lower_upper_id, &upper_upper_id);
//// lfs_swap16(&lower_lower_tag, &upper_lower_tag);
//// lfs_swap16(&lower_upper_tag, &upper_upper_tag);
//// }
//
// // lower bound
// if (!lfsr_tag_isfound(lower_tag_)) {
// // read the alt pointer
// lfsr_tag_t alt;
// lfsr_sid_t weight;
// lfs_off_t jump;
// lfs_ssize_t delta = lfsr_rbyd_readtag(lfs,
// &lfs->pcache, &lfs->rcache, 0,
// rbyd_->block, lower_branch, &alt, &weight, &jump, NULL);
// if (delta < 0) {
// return delta;
// }
//
// // found an alt?
// if (lfsr_tag_isalt(alt)) {
// // TODO get rid of weight_
// lfs_size_t weight_ = weight + 1;
// // make jump absolute
// jump = lower_branch - jump;
// lfs_off_t branch_ = lower_branch + delta;
//
// // go ahead and make alt black, this isn't perfect but it's
// // simpler and compact will take care of any balance issues
// // that may occur
// alt = lfsr_tag_mkblack(alt);
//
// // prune?
// // <b >b
// // .-'| .-'|
// // <y | | |
// // .-------'| | | |
// // | <r | => | <b
// // | .----' | .-----------|-'|
// // | | <b | <b |
// // | | .----'| | .----'| |
// // 1 2 3 4 4 1 2 3 4 4 2
// // TODO prune1?
// if (lfsr_tag_prune2(
// alt, weight_,
// p_alts[0], p_weights[0],
// lower_lower_id, lower_upper_id,
// lower_lower_tag, lower_upper_tag)) {
// LFS_ASSERT(!lfsr_tag_isred(p_alts[0]));
//// if (p_alts[0] && lfsr_tag_isred(p_alts[0])) {
//// alt = lfsr_tag_mkblack(p_alts[0]);
//// weight_ = p_weights[0];
//// branch_ = jump;
//// jump = p_jumps[0];
//// lfsr_rbyd_p_pop(p_alts, p_weights, p_jumps);
//// } else {
// // TODO does this ever happen with normal prunes?
// //LFS_ASSERT(false);
// lower_branch = jump;
// continue;
//// }
// }
//
// // take alt? needs a flip
// // <b >b
// // .-'| => .-'|
// // 1 2 1 2 1
// if (lfsr_tag_follow(
// alt, weight_,
// lower_lower_id, lower_upper_id,
// lower_tag_, lower_id_)) {
// alt = lfsr_tag_flipalt(alt);
// weight_ = lfsr_tag_flipweight(weight_,
// lower_lower_id, lower_upper_id);
// lfs_swap32(&jump, &branch_);
// }
//
// // only keep outer alts, push onto queue
// if (lfsr_tag_isle(alt)) {
// LFS_ASSERT((lfs_ssize_t)weight_ >= 0);
// int err = lfsr_rbyd_p_push(lfs, rbyd_,
// p_alts, p_weights, p_jumps,
// alt, weight_, jump);
// if (err) {
// return err;
// }
// }
//
// // continue to next alt
// lfsr_tag_trim__(
// alt, weight_,
// &lower_lower_id, &lower_upper_id,
// &lower_lower_tag, &lower_upper_tag);
// lower_branch = branch_;
//
// // found end of tree?
// } else {
// // update the tag id, marking as found
// lower_tag_ = lfsr_tag_mkfound(alt);
// lower_id_ = lower_upper_id-1;
// }
// }
// lower bound
if (!lfsr_tag_isfound(lower_tag_)) {
// read the alt pointer
lfsr_tag_t alt;
lfsr_sid_t weight;
lfs_off_t jump;
lfs_ssize_t delta = lfsr_rbyd_readtag(lfs,
&lfs->pcache, &lfs->rcache, 0,
rbyd_->block, lower_branch, &alt, &weight, &jump, NULL);
if (delta < 0) {
return delta;
}
// found an alt?
if (lfsr_tag_isalt(alt)) {
// TODO get rid of weight_
lfs_size_t weight_ = weight + 1;
// make jump absolute
jump = lower_branch - jump;
lfs_off_t branch_ = lower_branch + delta;
// go ahead and make alt black, this isn't perfect but it's
// simpler and compact will take care of any balance issues
// that may occur
alt = lfsr_tag_mkblack(alt);
// prune?
// <b >b
// .-'| .-'|
// <y | | |
// .-------'| | | |
// | <r | => | <b
// | .----' | .-----------|-'|
// | | <b | <b |
// | | .----'| | .----'| |
// 1 2 3 4 4 1 2 3 4 4 2
// TODO prune1?
if (lfsr_tag_prune2(
alt, weight_,
p_alts[0], p_weights[0],
lower_lower_id, lower_upper_id,
lower_lower_tag, lower_upper_tag)) {
LFS_ASSERT(!lfsr_tag_isred(p_alts[0]));
// if (p_alts[0] && lfsr_tag_isred(p_alts[0])) {
// alt = lfsr_tag_mkblack(p_alts[0]);
// weight_ = p_weights[0];
// branch_ = jump;
// jump = p_jumps[0];
// lfsr_rbyd_p_pop(p_alts, p_weights, p_jumps);
// } else {
// TODO does this ever happen with normal prunes?
//LFS_ASSERT(false);
lower_branch = jump;
continue;
//
// // upper bound
// if (!lfsr_tag_isfound(upper_tag_)) {
// // read the alt pointer
// lfsr_tag_t alt;
// lfsr_sid_t weight;
// lfs_off_t jump;
// lfs_ssize_t delta = lfsr_rbyd_readtag(lfs,
// &lfs->pcache, &lfs->rcache, 0,
// rbyd_->block, upper_branch, &alt, &weight, &jump, NULL);
// if (delta < 0) {
// return delta;
// }
//
// // found an alt?
// if (lfsr_tag_isalt(alt)) {
// // TODO get rid of weight_
// lfs_size_t weight_ = weight + 1;
// // make jump absolute
// jump = upper_branch - jump;
// lfs_off_t branch_ = upper_branch + delta;
//
// // go ahead and make alt black, this isn't perfect but it's
// // simpler and compact will take care of any balance issues
// // that may occur
// alt = lfsr_tag_mkblack(alt);
//
// // prune?
// // <b >b
// // .-'| .-'|
// // <y | | |
// // .-------'| | | |
// // | <r | => | <b
// // | .----' | .-----------|-'|
// // | | <b | <b |
// // | | .----'| | .----'| |
// // 1 2 3 4 4 1 2 3 4 4 2
// // TODO prune1?
// if (lfsr_tag_prune2(
// alt, weight_,
// p_alts[0], p_weights[0],
// upper_lower_id, upper_upper_id,
// upper_lower_tag, upper_upper_tag)) {
// LFS_ASSERT(!lfsr_tag_isred(p_alts[0]));
//// if (p_alts[0] && lfsr_tag_isred(p_alts[0])) {
//// alt = lfsr_tag_mkblack(p_alts[0]);
//// weight_ = p_weights[0];
//// branch_ = jump;
//// jump = p_jumps[0];
//// lfsr_rbyd_p_pop(p_alts, p_weights, p_jumps);
//// } else {
// // TODO does this ever happen with normal prunes?
// //LFS_ASSERT(false);
// upper_branch = jump;
// continue;
//// }
// }
//
// // take alt? needs a flip
// // <b >b
// // .-'| => .-'|
// // 1 2 1 2 1
// if (lfsr_tag_follow(
// alt, weight_,
// upper_lower_id, upper_upper_id,
// upper_tag_, upper_id_)) {
// alt = lfsr_tag_flipalt(alt);
// weight_ = lfsr_tag_flipweight(weight_,
// upper_lower_id, upper_upper_id);
// lfs_swap32(&jump, &branch_);
// }
//
// // only keep outer alts, push onto queue
// if (lfsr_tag_isgt(alt)) {
// LFS_ASSERT((lfs_ssize_t)weight_ >= 0);
// int err = lfsr_rbyd_p_push(lfs, rbyd_,
// p_alts, p_weights, p_jumps,
// alt, weight_, jump);
// if (err) {
// return err;
// }
}
// take alt? needs a flip
// <b >b
// .-'| => .-'|
// 1 2 1 2 1
if (lfsr_tag_follow(
alt, weight_,
lower_lower_id, lower_upper_id,
lower_tag_, lower_id_)) {
alt = lfsr_tag_flipalt(alt);
weight_ = lfsr_tag_flipweight(weight_,
lower_lower_id, lower_upper_id);
lfs_swap32(&jump, &branch_);
}
// only keep outer alts, push onto queue
if (lfsr_tag_isle(alt)) {
LFS_ASSERT((lfs_ssize_t)weight_ >= 0);
int err = lfsr_rbyd_p_push(lfs, rbyd_,
p_alts, p_weights, p_jumps,
alt, weight_, jump);
if (err) {
return err;
}
}
// continue to next alt
lfsr_tag_trim__(
alt, weight_,
&lower_lower_id, &lower_upper_id,
&lower_lower_tag, &lower_upper_tag);
lower_branch = branch_;
// found end of tree?
} else {
// update the tag id, marking as found
lower_tag_ = lfsr_tag_mkfound(alt);
lower_id_ = lower_upper_id-1;
}
}
// upper bound
if (!lfsr_tag_isfound(upper_tag_)) {
// read the alt pointer
lfsr_tag_t alt;
lfsr_sid_t weight;
lfs_off_t jump;
lfs_ssize_t delta = lfsr_rbyd_readtag(lfs,
&lfs->pcache, &lfs->rcache, 0,
rbyd_->block, upper_branch, &alt, &weight, &jump, NULL);
if (delta < 0) {
return delta;
}
// found an alt?
if (lfsr_tag_isalt(alt)) {
// TODO get rid of weight_
lfs_size_t weight_ = weight + 1;
// make jump absolute
jump = upper_branch - jump;
lfs_off_t branch_ = upper_branch + delta;
// go ahead and make alt black, this isn't perfect but it's
// simpler and compact will take care of any balance issues
// that may occur
alt = lfsr_tag_mkblack(alt);
// prune?
// <b >b
// .-'| .-'|
// <y | | |
// .-------'| | | |
// | <r | => | <b
// | .----' | .-----------|-'|
// | | <b | <b |
// | | .----'| | .----'| |
// 1 2 3 4 4 1 2 3 4 4 2
// TODO prune1?
if (lfsr_tag_prune2(
alt, weight_,
p_alts[0], p_weights[0],
upper_lower_id, upper_upper_id,
upper_lower_tag, upper_upper_tag)) {
LFS_ASSERT(!lfsr_tag_isred(p_alts[0]));
// if (p_alts[0] && lfsr_tag_isred(p_alts[0])) {
// alt = lfsr_tag_mkblack(p_alts[0]);
// weight_ = p_weights[0];
// branch_ = jump;
// jump = p_jumps[0];
// lfsr_rbyd_p_pop(p_alts, p_weights, p_jumps);
// } else {
// TODO does this ever happen with normal prunes?
//LFS_ASSERT(false);
upper_branch = jump;
continue;
// }
}
// take alt? needs a flip
// <b >b
// .-'| => .-'|
// 1 2 1 2 1
if (lfsr_tag_follow(
alt, weight_,
upper_lower_id, upper_upper_id,
upper_tag_, upper_id_)) {
alt = lfsr_tag_flipalt(alt);
weight_ = lfsr_tag_flipweight(weight_,
upper_lower_id, upper_upper_id);
lfs_swap32(&jump, &branch_);
}
// only keep outer alts, push onto queue
if (lfsr_tag_isgt(alt)) {
LFS_ASSERT((lfs_ssize_t)weight_ >= 0);
int err = lfsr_rbyd_p_push(lfs, rbyd_,
p_alts, p_weights, p_jumps,
alt, weight_, jump);
if (err) {
return err;
}
}
// continue to next alt
lfsr_tag_trim__(
alt, weight_,
&upper_lower_id, &upper_upper_id,
&upper_lower_tag, &upper_upper_tag);
upper_branch = branch_;
// found end of tree?
} else {
// update the tag id, marking as found
upper_tag_ = lfsr_tag_mkfound(alt);
upper_id_ = upper_upper_id-1;
}
}
}
// }
//
// // continue to next alt
// lfsr_tag_trim__(
// alt, weight_,
// &upper_lower_id, &upper_upper_id,
// &upper_lower_tag, &upper_upper_tag);
// upper_branch = branch_;
//
// // found end of tree?
// } else {
// // update the tag id, marking as found
// upper_tag_ = lfsr_tag_mkfound(alt);
// upper_id_ = upper_upper_id-1;
// }
// }
// }
//
stem:;
LFS_ASSERT(!p_alts[0] || lfsr_tag_isblack(p_alts[0]));
// // TODO need this?
// // unflip our bounds so lower_lower/upper_upper is correct
// if (!diverged) {
// upper_tag_ = lower_tag_;
// upper_id_ = lower_id_;
// upper_branch = lower_branch;
// upper_lower_id = lower_lower_id;
// upper_upper_id = lower_upper_id;
// upper_lower_tag = lower_lower_tag;
// upper_upper_tag = lower_upper_tag;
//// } else if (lower_id_ > upper_id_
//// || (lower_id_ == upper_id_ && lower_tag_ > upper_tag_)) {
//// lfs_swap16(&lower_tag_, &upper_tag_);
//// lfs_swaps32(&lower_id_, &upper_id_);
//// lfs_swap32(&lower_branch, &upper_branch);
//// lfs_swaps32(&lower_lower_id, &upper_lower_id);
//// lfs_swaps32(&lower_upper_id, &upper_upper_id);
//// lfs_swap16(&lower_lower_tag, &upper_lower_tag);
//// lfs_swap16(&lower_upper_tag, &upper_upper_tag);
// }
// TODO can this be done more simply? min/max maybe?
// unflip our bounds so lower_lower/upper_upper is correct
if (!diverged) {
upper_tag_ = lower_tag_;
upper_id_ = lower_id_;
upper_branch = lower_branch;
upper_lower_id = lower_lower_id;
upper_upper_id = lower_upper_id;
upper_lower_tag = lower_lower_tag;
upper_upper_tag = lower_upper_tag;
} else if (flipped) {
lfs_swap16(&lower_tag_, &upper_tag_);
lfs_swaps32(&lower_id_, &upper_id_);
lfs_swap32(&lower_branch, &upper_branch);
lfs_swaps32(&lower_lower_id, &upper_lower_id);
lfs_swaps32(&lower_upper_id, &upper_upper_id);
lfs_swap16(&lower_lower_tag, &upper_lower_tag);
lfs_swap16(&lower_upper_tag, &upper_upper_tag);
}
// split leaf nodes?
//