LCOV - code coverage report
Current view: top level - choreo/tower - fd_tower.c (source / functions) Hit Total Coverage
Test: cov.lcov Lines: 88 365 24.1 %
Date: 2025-12-06 04:45:29 Functions: 5 14 35.7 %

          Line data    Source code
       1             : #include <limits.h>
       2             : #include <unistd.h>
       3             : #include <fcntl.h>
       4             : #include <sys/stat.h>
       5             : 
       6             : #include "fd_tower.h"
       7             : #include "../voter/fd_voter.h"
       8             : #include "fd_tower_forks.h"
       9             : #include "../../flamenco/txn/fd_txn_generate.h"
      10             : #include "../../flamenco/runtime/fd_system_ids.h"
      11             : 
      12             : #define LOGGING 0
      13             : 
      14           0 : #define THRESHOLD_DEPTH (8)
      15           0 : #define THRESHOLD_RATIO (2.0 / 3.0)
      16             : #define SWITCH_RATIO    (0.38)
      17             : 
      18             : /* expiration calculates the expiration slot of vote given a slot and
      19             :    confirmation count. */
      20             : 
      21             : static inline ulong
      22          42 : expiration_slot( fd_tower_t const * vote ) {
      23          42 :   ulong lockout = 1UL << vote->conf;
      24          42 :   return vote->slot + lockout;
      25          42 : }
      26             : 
      27             : /* simulate_vote simulates voting for slot, popping all votes from the
      28             :    top that would be consecutively expired by voting for slot. */
      29             : 
      30             : ulong
      31             : simulate_vote( fd_tower_t const * tower,
      32          48 :                ulong              slot ) {
      33          48 :   ulong cnt = fd_tower_cnt( tower );
      34          54 :   while( cnt ) {
      35          42 :     fd_tower_t const * top_vote = fd_tower_peek_index_const( tower, cnt - 1 );
      36          42 :     if( FD_LIKELY( expiration_slot( top_vote ) >= slot ) ) break; /* expire only if consecutive */
      37           6 :     cnt--;
      38           6 :   }
      39          48 :   return cnt;
      40          48 : }
      41             : 
      42             : /* push_vote pushes a new vote for slot onto the tower.  Pops and
      43             :    returns the new root (bottom of the tower) if it reaches max lockout
      44             :    as a result of the new vote.  Otherwise, returns ULONG_MAX.
      45             : 
      46             :    Max lockout is equivalent to 1 << FD_TOWER_VOTE_MAX + 1 (which
      47             :    implies confirmation count is FD_TOWER_VOTE_MAX + 1).  As a result,
      48             :    fd_tower_vote also maintains the invariant that the tower contains at
      49             :    most FD_TOWER_VOTE_MAX votes, because (in addition to vote expiry)
      50             :    there will always be a pop before reaching FD_TOWER_VOTE_MAX + 1. */
      51             : 
      52             : ulong
      53             : push_vote( fd_tower_t * tower,
      54          48 :            ulong        slot ) {
      55             : 
      56          48 : # if FD_TOWER_PARANOID
      57          48 :   fd_tower_t const * vote = fd_tower_peek_tail_const( tower );
      58          48 :   if( FD_UNLIKELY( vote && slot <= vote->slot ) ) FD_LOG_ERR(( "[%s] slot %lu <= vote->slot %lu", __func__, slot, vote->slot )); /* caller error*/
      59          48 : # endif
      60             : 
      61             :   /* Use simulate_vote to determine how many expired votes to pop. */
      62             : 
      63          48 :   ulong cnt = simulate_vote( tower, slot );
      64             : 
      65             :   /* Pop everything that got expired. */
      66             : 
      67          54 :   while( FD_LIKELY( fd_tower_cnt( tower ) > cnt ) ) {
      68           6 :     fd_tower_pop_tail( tower );
      69           6 :   }
      70             : 
      71             :   /* If the tower is still full after expiring, then pop and return the
      72             :      bottom vote slot as the new root because this vote has incremented
      73             :      it to max lockout.  Otherwise this is a no-op and there is no new
      74             :      root (FD_SLOT_NULL). */
      75             : 
      76          48 :   ulong root = FD_SLOT_NULL;
      77          48 :   if( FD_LIKELY( fd_tower_full( tower ) ) ) { /* optimize for full tower */
      78           0 :     root = fd_tower_pop_head( tower ).slot;
      79           0 :   }
      80             : 
      81             :   /* Increment confirmations (double lockouts) for consecutive
      82             :      confirmations in prior votes. */
      83             : 
      84          48 :   ulong prev_conf = 0;
      85          48 :   for( fd_tower_iter_t iter = fd_tower_iter_init_rev( tower       );
      86         147 :                              !fd_tower_iter_done_rev( tower, iter );
      87          99 :                        iter = fd_tower_iter_prev    ( tower, iter ) ) {
      88          99 :     fd_tower_t * vote = fd_tower_iter_ele( tower, iter );
      89          99 :     if( FD_UNLIKELY( vote->conf != ++prev_conf ) ) break;
      90          99 :     vote->conf++;
      91          99 :   }
      92             : 
      93             :   /* Add the new vote to the tower. */
      94             : 
      95          48 :   fd_tower_push_tail( tower, (fd_tower_t){ .slot = slot, .conf = 1 } );
      96             : 
      97             :   /* Return the new root (FD_SLOT_NULL if there is none). */
      98             : 
      99          48 :   return root;
     100          48 : }
     101             : 
     102             : /* lockout_check checks if we are locked out from voting for slot.
     103             :    Returns 1 if we can vote for slot without violating lockout, 0
     104             :    otherwise.
     105             : 
     106             :    After voting for a slot n, we are locked out for 2^k slots, where k
     107             :    is the confirmation count of that vote.  Once locked out, we cannot
     108             :    vote for a different fork until that previously-voted fork expires at
     109             :    slot n+2^k.  This implies the earliest slot in which we can switch
     110             :    from the previously-voted fork is (n+2^k)+1.  We use `ghost` to
     111             :    determine whether `slot` is on the same or different fork as previous
     112             :    vote slots.
     113             : 
     114             :    In the case of the tower, every vote has its own expiration slot
     115             :    depending on confirmations. The confirmation count is the max number
     116             :    of consecutive votes that have been pushed on top of the vote, and
     117             :    not necessarily its current height in the tower.
     118             : 
     119             :    For example, the following is a diagram of a tower pushing and
     120             :    popping with each vote:
     121             : 
     122             : 
     123             :    slot | confirmation count
     124             :    -----|-------------------
     125             :    4    |  1 <- vote
     126             :    3    |  2
     127             :    2    |  3
     128             :    1    |  4
     129             : 
     130             : 
     131             :    slot | confirmation count
     132             :    -----|-------------------
     133             :    9    |  1 <- vote
     134             :    2    |  3
     135             :    1    |  4
     136             : 
     137             : 
     138             :    slot | confirmation count
     139             :    -----|-------------------
     140             :    10   |  1 <- vote
     141             :    9    |  2
     142             :    2    |  3
     143             :    1    |  4
     144             : 
     145             : 
     146             :    slot | confirmation count
     147             :    -----|-------------------
     148             :    11   |  1 <- vote
     149             :    10   |  2
     150             :    9    |  3
     151             :    2    |  4
     152             :    1    |  5
     153             : 
     154             : 
     155             :    slot | confirmation count
     156             :    -----|-------------------
     157             :    18   |  1 <- vote
     158             :    2    |  4
     159             :    1    |  5
     160             : 
     161             : 
     162             :    In the final tower, note the gap in confirmation counts between slot
     163             :    18 and slot 2, even though slot 18 is directly above slot 2. */
     164             : 
     165             : int
     166             : lockout_check( fd_tower_t const * tower,
     167             :                fd_forks_t       * forks,
     168           0 :                ulong              slot ) {
     169             : 
     170           0 :   if( FD_UNLIKELY( fd_tower_empty( tower )                         ) ) return 1; /* always not locked out if we haven't voted. */
     171           0 :   if( FD_UNLIKELY( slot <= fd_tower_peek_tail_const( tower )->slot ) ) return 0; /* always locked out from voting for slot <= last vote slot */
     172             : 
     173             :   /* Simulate a vote to pop off all the votes that would be expired by
     174             :      voting for slot.  Then check if the newly top-of-tower vote is on
     175             :      the same fork as slot (if so this implies we can vote for it). */
     176             : 
     177           0 :   ulong cnt = simulate_vote( tower, slot ); /* pop off votes that would be expired */
     178           0 :   if( FD_UNLIKELY( !cnt ) ) return 1;       /* tower is empty after popping expired votes */
     179             : 
     180           0 :   fd_tower_t const * vote = fd_tower_peek_index_const( tower, cnt - 1 ); /* newly top-of-tower */
     181             : # if LOGGING
     182             :   FD_LOG_NOTICE(( "[%s] lockout_check for slot %lu against vote slot %lu", __func__, slot, vote->slot ));
     183             : # endif
     184           0 :   return fd_forks_is_slot_descendant( forks, vote->slot, slot );   /* check if on same fork */
     185           0 : }
     186             : 
     187             : /* switch_check checks if we can switch to the fork of `slot`.  Returns
     188             :    1 if we can switch, 0 otherwise.  Assumes tower is non-empty.
     189             : 
     190             :    There are two forks of interest: our last vote fork ("vote fork") and
     191             :    the fork we want to switch to ("switch fork").  The switch fork is on
     192             :    the fork of `slot`.
     193             : 
     194             :    In order to switch, FD_TOWER_SWITCH_PCT of stake must have voted for
     195             :    a slot that satisfies the following conditions: the
     196             :    GCA(slot, last_vote) is an ancestor of the switch_slot
     197             : 
     198             :    Recall from the lockout check a validator is locked out from voting
     199             :    for our last vote slot when their last vote slot is on a different
     200             :    fork, and that vote's expiration slot > our last vote slot.
     201             : 
     202             :    The following pseudocode describes the algorithm:
     203             : 
     204             :    ```
     205             :    for every fork f in the fork tree, take the most recently executed
     206             :    slot `s` (the leaf of the fork).
     207             : 
     208             :    Take the greatest common ancestor of the `s` and the our last vote
     209             :    slot. If the switch_slot is a descendant of this GCA, then votes for
     210             :    `s` can count towards the switch threshold.
     211             : 
     212             :      query banks(`s`) for vote accounts in `s`
     213             :        for all vote accounts v in `s`
     214             :           if v's  locked out[1] from voting for our latest vote slot
     215             :              add v's stake to switch stake
     216             : 
     217             :    return switch stake >= FD_TOWER_SWITCH_PCT
     218             :    ```
     219             : 
     220             :    The switch check is used to safeguard optimistic confirmation.
     221             :    Specifically: FD_TOWER_OPT_CONF_PCT + FD_TOWER_SWITCH_PCT >= 1. */
     222             : 
     223             : int
     224             : switch_check( fd_tower_t const  * tower,
     225             :               fd_forks_t        * forks,
     226             :               fd_epoch_stakes_t * epoch_stakes,
     227             :               ulong               total_stake,
     228          33 :               ulong               switch_slot ) {
     229          33 :   ulong switch_stake   = 0;
     230          33 :   ulong last_vote_slot = fd_tower_peek_tail_const( tower )->slot;
     231          33 :   ulong root_slot      = fd_tower_peek_head_const( tower )->slot;
     232          33 :   for ( fd_tower_leaves_dlist_iter_t iter = fd_tower_leaves_dlist_iter_fwd_init( forks->tower_leaves_dlist, forks->tower_leaves_pool );
     233         138 :                                            !fd_tower_leaves_dlist_iter_done( iter, forks->tower_leaves_dlist, forks->tower_leaves_pool );
     234         120 :                                      iter = fd_tower_leaves_dlist_iter_fwd_next( iter, forks->tower_leaves_dlist, forks->tower_leaves_pool ) ) {
     235             : 
     236             :     /* Iterate over all the leaves of all forks */
     237         120 :     fd_tower_leaf_t  * leaf = fd_tower_leaves_dlist_iter_ele( iter, forks->tower_leaves_dlist, forks->tower_leaves_pool );
     238         120 :     ulong candidate_slot = leaf->slot;
     239         120 :     ulong lca = fd_forks_lowest_common_ancestor( forks, candidate_slot, last_vote_slot );
     240             : 
     241         120 :     if( lca != ULONG_MAX && fd_forks_is_slot_descendant( forks, lca, switch_slot ) ) {
     242             : 
     243             :       /* This candidate slot may be considered for the switch proof, if
     244             :          it passes the following conditions:
     245             : 
     246             :          https://github.com/anza-xyz/agave/blob/c7b97bc77addacf03b229c51b47c18650d909576/core/src/consensus.rs#L1117
     247             : 
     248             :          Now for this candidate slot, look at the lockouts that were created at
     249             :          the time that we processed the bank for this candidate slot. */
     250             : 
     251          78 :       for( fd_lockout_slots_t const * slot = fd_lockout_slots_map_ele_query_const( forks->lockout_slots_map, &candidate_slot, NULL, forks->lockout_slots_pool );
     252          84 :                                       slot;
     253          78 :                                       slot = fd_lockout_slots_map_ele_next_const ( slot, NULL, forks->lockout_slots_pool ) ) {
     254          21 :         ulong interval_end = slot->interval_end;
     255          21 :         ulong key = fd_lockout_interval_key( candidate_slot, interval_end );
     256             : 
     257             :         /* Intervals are keyed by the end of the interval. If the end of
     258             :            the interval is < the last vote slot, then these vote
     259             :            accounts with this particular lockout are NOT locked out from
     260             :            voting for the last vote slot, which means we can skip this
     261             :            set of intervals. */
     262             : 
     263          21 :         if( interval_end < last_vote_slot ) continue;
     264             : 
     265             :         /* At this point we can actually query for the intervals by
     266             :            end interval to get the vote accounts. */
     267             : 
     268          15 :         for( fd_lockout_intervals_t const * interval = fd_lockout_intervals_map_ele_query_const( forks->lockout_intervals_map, &key, NULL, forks->lockout_intervals_pool );
     269          24 :                                             interval;
     270          24 :                                             interval = fd_lockout_intervals_map_ele_next_const( interval, NULL, forks->lockout_intervals_pool ) ) {
     271          24 :           ulong vote_slot            =  interval->interval_start;
     272          24 :           fd_hash_t const * vote_acc = &interval->vote_account_pubkey;
     273             : 
     274          24 :           if( FD_UNLIKELY( !fd_forks_is_slot_descendant( forks, vote_slot, last_vote_slot ) &&
     275          24 :                             vote_slot > root_slot ) ) {
     276          24 :             fd_voter_stake_key_t key = { .vote_account = *vote_acc, .slot = switch_slot };
     277          24 :             fd_voter_stake_t const * voter_stake = fd_voter_stake_map_ele_query_const( epoch_stakes->voter_stake_map, &key, NULL, epoch_stakes->voter_stake_pool );
     278          24 :             if( FD_UNLIKELY( !voter_stake ) ) FD_LOG_CRIT(( "missing voter stake for vote account %s on slot %lu. Is this an error?", FD_BASE58_ENC_32_ALLOCA( vote_acc ), switch_slot ));
     279          24 :             ulong voter_idx = fd_voter_stake_pool_idx( epoch_stakes->voter_stake_pool, voter_stake );
     280             : 
     281             :             /* Don't count this vote account towards the switch cqheck if it has already been used. */
     282          24 :             if( FD_UNLIKELY( fd_used_acc_scratch_test( epoch_stakes->used_acc_scratch, voter_idx ) ) ) continue;
     283             : 
     284          24 :             fd_used_acc_scratch_insert( epoch_stakes->used_acc_scratch, voter_idx );
     285          24 :             switch_stake += voter_stake->stake;
     286          24 :             if( FD_LIKELY( (double)switch_stake >= (double)total_stake * SWITCH_RATIO ) ) {
     287          15 :               fd_used_acc_scratch_null( epoch_stakes->used_acc_scratch );
     288          15 :               FD_LOG_INFO(( "[%s] switch check from slot %lu to slot %lu passed with percentage: %.0lf%%", __func__, last_vote_slot, switch_slot, (double)switch_stake / (double)total_stake * 100.0 ));
     289          15 :               return 1;
     290          15 :             }
     291          24 :           }
     292          24 :         }
     293          15 :       }
     294          78 :     }
     295         120 :   }
     296          18 :   fd_used_acc_scratch_null( epoch_stakes->used_acc_scratch );
     297          18 :   FD_LOG_INFO(( "[%s] switch check from slot %lu to slot %lu failed with percentage: %.0lf%%", __func__, last_vote_slot, switch_slot, (double)switch_stake / (double)total_stake * 100.0 ));
     298          18 :   return 0;
     299          33 : }
     300             : 
     301             : /* threshold_check checks if we pass the threshold required to vote for
     302             :    `slot`.  Returns 1 if we pass the threshold check, 0 otherwise.
     303             : 
     304             :    The following psuedocode describes the algorithm:
     305             : 
     306             :    ```
     307             :    simulate that we have voted for `slot`
     308             : 
     309             :    for all vote accounts in the current epoch
     310             : 
     311             :       simulate that the vote account has voted for `slot`
     312             : 
     313             :       pop all votes expired by that simulated vote
     314             : 
     315             :       if the validator's latest tower vote after expiry >= our threshold
     316             :       slot ie. our vote from THRESHOLD_DEPTH back also after simulating,
     317             :       then add validator's stake to threshold_stake.
     318             : 
     319             :    return threshold_stake >= FD_TOWER_THRESHOLD_RATIO
     320             :    ```
     321             : 
     322             :    The threshold check simulates voting for the current slot to expire
     323             :    stale votes.  This is to prevent validators that haven't voted in a
     324             :    long time from counting towards the threshold stake. */
     325             : 
     326             : int
     327             : threshold_check( fd_tower_t       const * tower,
     328             :                  fd_tower_accts_t const * accts,
     329             :                  ulong                    total_stake,
     330           0 :                  ulong                    slot ) {
     331             : 
     332           0 :   uchar __attribute__((aligned(FD_TOWER_ALIGN))) scratch[ FD_TOWER_FOOTPRINT ];
     333           0 :   fd_tower_t * scratch_tower = fd_tower_join( fd_tower_new( scratch ) );
     334             : 
     335             :   /* First, simulate a vote on our tower, popping off everything that
     336             :      would be expired by voting for slot. */
     337             : 
     338           0 :   ulong cnt = simulate_vote( tower, slot );
     339             : 
     340             :   /* We can always vote if our tower is not at least THRESHOLD_DEPTH
     341             :      deep after simulating. */
     342             : 
     343           0 :   if( FD_UNLIKELY( cnt < THRESHOLD_DEPTH ) ) return 1;
     344             : 
     345             :   /* Get the vote slot from THRESHOLD_DEPTH back. Note THRESHOLD_DEPTH
     346             :      is the 8th index back _including_ the simulated vote at index 0. */
     347             : 
     348           0 :   ulong threshold_slot  = fd_tower_peek_index_const( tower, cnt - THRESHOLD_DEPTH )->slot;
     349           0 :   ulong threshold_stake = 0;
     350           0 :   for( fd_tower_accts_iter_t iter = fd_tower_accts_iter_init( accts       );
     351           0 :                                    !fd_tower_accts_iter_done( accts, iter );
     352           0 :                              iter = fd_tower_accts_iter_next( accts, iter ) ) {
     353           0 :     fd_tower_accts_t const * acct = fd_tower_accts_iter_ele_const( accts, iter );
     354           0 :     fd_tower_remove_all( scratch_tower );
     355           0 :     fd_tower_from_vote_acc( scratch_tower, acct->data );
     356             : 
     357           0 :     ulong cnt = simulate_vote( scratch_tower, slot ); /* expire votes */
     358           0 :     if( FD_UNLIKELY( !cnt ) ) continue;               /* no votes left after expiry */
     359             : 
     360             :     /* Count their stake towards the threshold check if their last vote
     361             :        slot >= our threshold slot.
     362             : 
     363             :        We know these votes are for our own fork because towers are
     364             :        sourced from vote _accounts_, not vote _transactions_.
     365             : 
     366             :        Because we are iterating vote accounts on the same fork that we
     367             :        we want to vote for, we know these slots must all occur along the
     368             :        same fork ancestry.
     369             : 
     370             :        Therefore, if their latest vote slot >= our threshold slot, we
     371             :        know that vote must be for the threshold slot itself or one of
     372             :        threshold slot's descendants. */
     373             : 
     374           0 :     ulong last_vote = fd_tower_peek_index_const( scratch_tower, cnt - 1 )->slot;
     375           0 :     if( FD_LIKELY( last_vote >= threshold_slot ) ) threshold_stake += acct->stake;
     376           0 :   }
     377             : 
     378           0 :   double threshold_pct = (double)threshold_stake / (double)total_stake;
     379             : # if LOGGING
     380             :   FD_LOG_NOTICE(( "[%s] ok? %d. top: %lu. threshold: %lu. stake: %.0lf%%.", __func__, threshold_pct > THRESHOLD_RATIO, fd_tower_peek_tail_const( tower )->slot, threshold_slot, threshold_pct * 100.0 ));
     381             : # endif
     382           0 :   return threshold_pct > THRESHOLD_RATIO;
     383           0 : }
     384             : 
     385             : int
     386             : propagated_check( fd_notar_t * notar,
     387           0 :                   ulong        slot ) {
     388             : 
     389           0 :   fd_notar_slot_t * notar_slot = fd_notar_slot_query( notar->slot_map, slot, NULL );
     390           0 :   if( FD_UNLIKELY( !notar_slot ) ) return 1;
     391             : 
     392           0 :   if( FD_LIKELY( notar_slot->is_leader                   ) ) return 1; /* can always vote for slot in which we're leader */
     393           0 :   if( FD_LIKELY( notar_slot->prev_leader_slot==ULONG_MAX ) ) return 1; /* haven't been leader yet */
     394             : 
     395           0 :   fd_notar_slot_t * prev_leader_notar_slot = fd_notar_slot_query( notar->slot_map, notar_slot->prev_leader_slot, NULL );
     396           0 :   if( FD_LIKELY( !prev_leader_notar_slot ) ) return 1; /* already pruned rooted */
     397             : 
     398           0 :   return prev_leader_notar_slot->is_propagated;
     399           0 : }
     400             : 
     401             : fd_tower_out_t
     402             : fd_tower_vote_and_reset( fd_tower_t        * tower,
     403             :                          fd_tower_accts_t  * accts,
     404             :                          fd_epoch_stakes_t * epoch_stakes,
     405             :                          fd_forks_t        * forks,
     406             :                          fd_ghost_t        * ghost,
     407           0 :                          fd_notar_t        * notar ) {
     408             : 
     409           0 :   uchar                  flags     = 0;
     410           0 :   fd_ghost_blk_t const * best_blk  = fd_ghost_best( ghost, fd_ghost_root( ghost ) );
     411           0 :   fd_ghost_blk_t const * reset_blk = NULL;
     412           0 :   fd_ghost_blk_t const * vote_blk  = NULL;
     413             : 
     414             :   /* Case 0: if we haven't voted yet then we can always vote and reset
     415             :      to ghost_best.
     416             : 
     417             :      https://github.com/anza-xyz/agave/blob/v2.3.7/core/src/consensus.rs#L933-L935 */
     418             : 
     419           0 :   if( FD_UNLIKELY( fd_tower_empty( tower ) ) ) {
     420           0 :     fd_tower_forks_t * fork = fd_forks_query( forks, best_blk->slot );
     421           0 :     fork->voted             = 1;
     422           0 :     fork->voted_block_id    = best_blk->id;
     423           0 :     return (fd_tower_out_t){
     424           0 :       .flags          = flags,
     425           0 :       .reset_slot     = best_blk->slot,
     426           0 :       .reset_block_id = best_blk->id,
     427           0 :       .vote_slot      = best_blk->slot,
     428           0 :       .vote_block_id  = best_blk->id,
     429           0 :       .root_slot      = push_vote( tower, best_blk->slot )
     430           0 :     };
     431           0 :   }
     432             : 
     433           0 :   ulong              prev_vote_slot     = fd_tower_peek_tail_const( tower )->slot;
     434           0 :   fd_tower_forks_t * prev_vote_fork     = fd_forks_query( forks, prev_vote_slot );
     435           0 :   fd_hash_t        * prev_vote_block_id = &prev_vote_fork->voted_block_id;
     436           0 :   fd_ghost_blk_t   * prev_vote_blk      = fd_ghost_query( ghost, prev_vote_block_id );
     437             : 
     438             :   /* Case 1: if an ancestor of our prev vote (including prev vote
     439             :      itself) is an unconfirmed duplicate, then our prev vote was on a
     440             :      duplicate fork.
     441             : 
     442             :      There are two subcases to check. */
     443             : 
     444           0 :   int invalid_ancestor = !!fd_ghost_invalid_ancestor( ghost, prev_vote_blk );
     445           0 :   if( FD_UNLIKELY( invalid_ancestor ) ) { /* do we have an invalid ancestor? */
     446             : 
     447             :     /* Case 1a: ghost_best is an ancestor of prev vote.  This means
     448             :        ghost_best is rolling back to an ancestor that precedes the
     449             :        duplicate ancestor on the same fork as our prev vote.  In this
     450             :        case, we can't vote on our ancestor, but we do reset to that
     451             :        ancestor.
     452             : 
     453             :        https://github.com/anza-xyz/agave/blob/v2.3.7/core/src/consensus.rs#L1016-L1019 */
     454             : 
     455           0 :     int ancestor_rollback = prev_vote_blk != best_blk && !!fd_ghost_ancestor( ghost, prev_vote_blk, &best_blk->id );
     456           0 :     if( FD_LIKELY( ancestor_rollback ) ) {
     457           0 :       flags     = fd_uchar_set_bit( flags, FD_TOWER_FLAG_ANCESTOR_ROLLBACK );
     458           0 :       reset_blk = best_blk;
     459           0 :     }
     460             : 
     461             :     /* Case 1b: ghost_best is not an ancestor, but prev_vote is a
     462             :        duplicate and we've confirmed its duplicate sibling.  In this
     463             :        case, we allow switching to ghost_best without a switch proof.
     464             : 
     465             :        Example: slot 5 is a duplicate.  We first receive, replay and
     466             :        vote for block 5, so that is our prev vote.  We later receive
     467             :        block 5' and observe that it is duplicate confirmed.  ghost_best
     468             :        now returns block 5' and we both vote and reset to block 5'
     469             :        regardless of the switch check.
     470             : 
     471             :        https://github.com/anza-xyz/agave/blob/v2.3.7/core/src/consensus.rs#L1021-L1024 */
     472             : 
     473           0 :     int sibling_confirmed = 0!=memcmp( &prev_vote_fork->voted_block_id, &prev_vote_fork->confirmed_block_id, sizeof(fd_hash_t) );
     474           0 :     if( FD_LIKELY( sibling_confirmed ) ) {
     475           0 :       flags     = fd_uchar_set_bit( flags, FD_TOWER_FLAG_SIBLING_CONFIRMED );
     476           0 :       reset_blk = best_blk;
     477           0 :       vote_blk  = best_blk;
     478           0 :     }
     479             : 
     480             :     /* At this point our prev vote was on a duplicate fork but didn't
     481             :        match either of the above subcases.
     482             : 
     483             :        In this case, we have to pass the switch check to reset to a
     484             :        different fork from prev vote (same as non-duplicate case). */
     485           0 :   }
     486             : 
     487             :   /* Case 3: if our prev vote slot is an ancestor of the best slot, then
     488             :      they are on the same fork and we can both reset to it.  We can also
     489             :      vote for it if we pass the can_vote checks.
     490             : 
     491             :      https://github.com/anza-xyz/agave/blob/v2.3.7/core/src/consensus.rs#L1057 */
     492             : 
     493           0 :   else if( FD_LIKELY( fd_forks_is_slot_ancestor( forks, best_blk->slot, prev_vote_slot ) ) ) {
     494           0 :     flags     = fd_uchar_set_bit( flags, FD_TOWER_FLAG_SAME_FORK );
     495           0 :     reset_blk = best_blk;
     496           0 :     vote_blk  = best_blk;
     497           0 :   }
     498             : 
     499             :   /* Case 4: if our prev vote is not an ancestor of the best block, then
     500             :      it is on a different fork.  If we pass the switch check, we can
     501             :      reset to it.  If we additionally pass the lockout check, we can
     502             :      also vote for it.
     503             : 
     504             :      https://github.com/anza-xyz/agave/blob/v2.3.7/core/src/consensus.rs#L1208-L1215
     505             : 
     506             :      Note also Agave uses the best blk's total stake for checking the
     507             :      threshold.
     508             : 
     509             :      https://github.com/anza-xyz/agave/blob/v2.3.7/core/src/consensus/fork_choice.rs#L443-L445 */
     510             : 
     511           0 :   else if( FD_LIKELY( switch_check( tower, forks, epoch_stakes, best_blk->total_stake, best_blk->slot ) ) ) {
     512           0 :     flags     = fd_uchar_set_bit( flags, FD_TOWER_FLAG_SWITCH_PASS );
     513           0 :     reset_blk = best_blk;
     514           0 :     vote_blk  = best_blk;
     515           0 :   }
     516             : 
     517             :   /* Case 5: same as case 4 but we didn't pass the switch check.  In
     518             :      this case we reset to either ghost_best or ghost_deepest beginning
     519             :      from our prev vote blk.
     520             : 
     521             :      We must reset to a block beginning from our prev vote fork to
     522             :      ensure votes get a chance to propagate.  Because in order for votes
     523             :      to land, someone needs to build a block on that fork.
     524             : 
     525             :      We reset to ghost_best or ghost_deepest depending on whether our
     526             :      prev vote is valid.  When it's invalid we use ghost_deepest instead
     527             :      of ghost_best, because ghost_best won't be able to return a valid
     528             :      block beginning from our prev_vote because by definition the entire
     529             :      subtree will be invalid.
     530             : 
     531             :      When our prev vote fork is not a duplicate, we want to propagate
     532             :      votes that might allow others to switch to our fork.  In addition,
     533             :      if our prev vote fork is a duplicate, we want to propagate votes
     534             :      that might "duplicate confirm" that block (reach 52% of stake).
     535             : 
     536             :      See top-level documentation in fd_tower.h for more details on vote
     537             :      propagation. */
     538             : 
     539           0 :   else {
     540             : 
     541             :     /* Case 5a: failed switch check, duplicate.
     542             : 
     543             :       https://github.com/anza-xyz/agave/blob/v2.3.7/core/src/consensus/heaviest_subtree_fork_choice.rs#L1187 */
     544             : 
     545           0 :     if( FD_UNLIKELY( invalid_ancestor ) ) {
     546           0 :       flags     = fd_uchar_set_bit( flags, FD_TOWER_FLAG_SWITCH_FAIL );
     547           0 :       reset_blk = fd_ghost_deepest( ghost, prev_vote_blk );
     548           0 :     }
     549             : 
     550             :     /* Case 5b: failed switch check, non-duplicate.
     551             : 
     552             :       https://github.com/anza-xyz/agave/blob/v2.3.7/core/src/consensus/fork_choice.rs#L200 */
     553             : 
     554           0 :     else {
     555           0 :       flags     = fd_uchar_set_bit( flags, FD_TOWER_FLAG_SWITCH_FAIL );
     556           0 :       reset_blk = fd_ghost_best( ghost, prev_vote_blk );
     557           0 :     }
     558           0 :   }
     559             : 
     560             :   /* If there is a block to vote for, there are a few additional checks
     561             :      to make sure we can actually vote for it.
     562             : 
     563             :      Specifically, we need to make sure we're not locked out, pass the
     564             :      threshold check and that our previous leader block has propagated
     565             :      (reached the prop threshold according to fd_notar).
     566             : 
     567             :      https://github.com/firedancer-io/agave/blob/master/core/src/consensus/fork_choice.rs#L382-L385
     568             : 
     569             :      Agave uses the total stake on the fork being threshold checked
     570             :      (vote_blk) for determining whether it meets the stake threshold. */
     571             : 
     572           0 :   if( FD_LIKELY( vote_blk ) ) {
     573           0 :     if     ( FD_UNLIKELY( !lockout_check( tower, forks, vote_blk->slot ) ) ) {
     574           0 :       flags    = fd_uchar_set_bit( flags, FD_TOWER_FLAG_LOCKOUT_FAIL );
     575           0 :       vote_blk = NULL;
     576           0 :     }
     577           0 :     else if( FD_UNLIKELY( !threshold_check( tower, accts, vote_blk->total_stake, vote_blk->slot ) ) ) {
     578           0 :       flags    = fd_uchar_set_bit( flags, FD_TOWER_FLAG_THRESHOLD_FAIL );
     579           0 :       vote_blk = NULL;
     580           0 :     }
     581           0 :     else if( FD_UNLIKELY( !propagated_check( notar, vote_blk->slot ) ) ) {
     582           0 :       flags    = fd_uchar_set_bit( flags, FD_TOWER_FLAG_PROPAGATED_FAIL );
     583           0 :       vote_blk = NULL;
     584           0 :     }
     585           0 :   }
     586             : 
     587           0 :   FD_TEST( reset_blk ); /* always a reset_blk */
     588           0 :   fd_tower_out_t out = {
     589           0 :     .flags          = flags,
     590           0 :     .reset_slot     = reset_blk->slot,
     591           0 :     .reset_block_id = reset_blk->id,
     592           0 :     .vote_slot      = ULONG_MAX,
     593           0 :     .root_slot      = ULONG_MAX
     594           0 :   };
     595             : 
     596             :   /* Finally, if our vote passed all the checks, we actually push the
     597             :      vote onto the tower. */
     598             : 
     599           0 :   if( FD_LIKELY( vote_blk ) ) {
     600           0 :     out.vote_slot     = vote_blk->slot;
     601           0 :     out.vote_block_id = vote_blk->id;
     602           0 :     out.root_slot     = push_vote( tower, vote_blk->slot );
     603             : 
     604             :     /* Query our tower fork for this slot we're voting for.  Note this
     605             :        can never be NULL because we record tower forks as we replay, and
     606             :        we should never be voting on something we haven't replayed. */
     607             : 
     608           0 :     fd_tower_forks_t * fork = fd_forks_query( forks, vote_blk->slot );
     609           0 :     fork->voted             = 1;
     610           0 :     fork->voted_block_id    = vote_blk->id;
     611             : 
     612             :     /* Query the root slot's block id from tower forks.  This block id
     613             :        may not necessarily be confirmed, because confirmation requires
     614             :        votes on the block itself (vs. block and its descendants).
     615             : 
     616             :        So if we have a confirmed block id, we return that.  Otherwise
     617             :        we return our own vote block id for that slot, which we assume
     618             :        is the cluster converged on by the time we're rooting it.
     619             : 
     620             :        The only way it is possible for us to root the wrong version of
     621             :        a block (ie. not the one the cluster confirmed) is if there is
     622             :        mass equivocation (>2/3 of threshold check stake has voted for
     623             :        two versions of a block).  This exceeds the equivocation safety
     624             :        threshold and we would eventually detect this via a bank hash
     625             :        mismatch and error out. */
     626             : 
     627           0 :     if( FD_LIKELY( out.root_slot!=ULONG_MAX ) ) {
     628           0 :       fd_tower_forks_t * root_fork = fd_forks_query( forks, out.root_slot );
     629           0 :       out.root_block_id            = *fd_ptr_if( root_fork->confirmed, &root_fork->confirmed_block_id, &root_fork->voted_block_id );
     630           0 :     }
     631           0 :   }
     632             : 
     633             : # if LOGGING
     634             :   FD_LOG_NOTICE(( "[%s] code: %d. reset_slot: %lu. vote_slot: %lu. root_slot: %lu.", __func__, out.code, out.reset_slot, out.vote_slot, out.root_slot ));
     635             : # endif
     636             : 
     637           0 :   return out;
     638           0 : }
     639             : 
     640             : void
     641             : fd_tower_reconcile( fd_tower_t  * tower,
     642             :                     ulong         root,
     643           0 :                     uchar const * vote_account_data ) {
     644           0 :   ulong on_chain_vote = fd_voter_vote_slot( vote_account_data );
     645           0 :   ulong on_chain_root = fd_voter_root_slot( vote_account_data );
     646             : 
     647           0 :   fd_tower_vote_t const * last_vote      = fd_tower_peek_tail_const( tower );
     648           0 :   ulong                   last_vote_slot = last_vote ? last_vote->slot : ULONG_MAX;
     649             : 
     650           0 :   if( FD_UNLIKELY( ( on_chain_vote==ULONG_MAX && last_vote_slot==ULONG_MAX ) ) ) return;
     651           0 :   if( FD_LIKELY  ( ( on_chain_vote!=ULONG_MAX && last_vote_slot!=ULONG_MAX
     652           0 :                      && on_chain_vote <= last_vote_slot                    ) ) ) return;
     653             : 
     654             :   /* At this point our local tower is too old, and we need to replace it
     655             :      with our on-chain tower.  However, it's possible our local root is
     656             :      newer than the on-chain root (even though the tower is older).  The
     657             :      most likely reason this happens is because we just booted from a
     658             :      snapshot and the snapshot slot > on-chain root.
     659             : 
     660             :      So we need to filter out the stale votes < snapshot slot.  This
     661             :      mirrors the Agave logic:
     662             :      https://github.com/firedancer-io/agave/blob/master/core/src/replay_stage.rs#L3690-L3719 */
     663             : 
     664           0 :   if( FD_LIKELY( on_chain_root == ULONG_MAX || root > on_chain_root ) ) {
     665           0 :     fd_tower_remove_all( tower );
     666           0 :     fd_voter_t const * voter = (fd_voter_t const *)fd_type_pun_const( vote_account_data );
     667           0 :     uint               kind  = fd_uint_load_4_fast( vote_account_data ); /* skip node_pubkey */
     668           0 :     for( ulong i=0; i<voter->votes_cnt; i++ ) {
     669           0 :       if( FD_LIKELY( kind==FD_VOTER_V3 ) ) fd_tower_push_tail( tower, (fd_tower_t){ .slot = voter->votes_v3[i].slot, .conf = voter->votes_v3[i].conf } );
     670           0 :       if( FD_LIKELY( kind==FD_VOTER_V2 ) ) fd_tower_push_tail( tower, (fd_tower_t){ .slot = voter->votes_v2[i].slot, .conf = voter->votes_v2[i].conf } );
     671           0 :     }
     672             : 
     673             :     /* Fast forward our tower to tower_root by retaining only votes >
     674             :        local tower root. */
     675             : 
     676           0 :     while( FD_LIKELY( !fd_tower_empty( tower ) ) ) {
     677           0 :       fd_tower_t const * vote = fd_tower_peek_head_const( tower );
     678           0 :       if( FD_LIKELY( vote->slot > root ) ) break;
     679           0 :       fd_tower_pop_head( tower );
     680           0 :     }
     681           0 :   }
     682           0 : }
     683             : 
     684             : void
     685             : fd_tower_from_vote_acc( fd_tower_t   * tower,
     686          39 :                         uchar  const * vote_acc ) {
     687          39 :   fd_voter_t const * voter = (fd_voter_t const *)fd_type_pun_const( vote_acc );
     688          39 :   uint               kind  = fd_uint_load_4_fast( vote_acc ); /* skip node_pubkey */
     689          78 :   for( ulong i=0; i<voter->votes_cnt; i++ ) {
     690          39 :     if( FD_LIKELY( kind==FD_VOTER_V3 ) ) fd_tower_push_tail( tower, (fd_tower_t){ .slot = voter->votes_v3[i].slot, .conf = voter->votes_v3[i].conf } );
     691          39 :     if( FD_LIKELY( kind==FD_VOTER_V2 ) ) fd_tower_push_tail( tower, (fd_tower_t){ .slot = voter->votes_v2[i].slot, .conf = voter->votes_v2[i].conf } );
     692          39 :   }
     693          39 : }
     694             : 
     695             : void
     696             : fd_tower_to_vote_txn( fd_tower_t const *    tower,
     697             :                       ulong                 root,
     698             :                       fd_lockout_offset_t * lockouts_scratch,
     699             :                       fd_hash_t const *     bank_hash,
     700             :                       fd_hash_t const *     recent_blockhash,
     701             :                       fd_pubkey_t const *   validator_identity,
     702             :                       fd_pubkey_t const *   vote_authority,
     703             :                       fd_pubkey_t const *   vote_acc,
     704           0 :                       fd_txn_p_t *          vote_txn ) {
     705             : 
     706           0 :   fd_compact_vote_state_update_t tower_sync;
     707           0 :   tower_sync.root          = fd_ulong_if( root == ULONG_MAX, 0UL, root );
     708           0 :   tower_sync.lockouts_len  = (ushort)fd_tower_cnt( tower );
     709           0 :   tower_sync.lockouts      = lockouts_scratch;
     710           0 :   tower_sync.timestamp     = fd_log_wallclock() / (long)1e9; /* seconds */
     711           0 :   tower_sync.has_timestamp = 1;
     712             : 
     713           0 :   ulong prev = tower_sync.root;
     714           0 :   ulong i    = 0UL;
     715           0 :   for( fd_tower_iter_t iter = fd_tower_iter_init( tower       );
     716           0 :                              !fd_tower_iter_done( tower, iter );
     717           0 :                        iter = fd_tower_iter_next( tower, iter ) ) {
     718           0 :     fd_tower_t const * vote                   = fd_tower_iter_ele_const( tower, iter );
     719           0 :     tower_sync.lockouts[i].offset             = vote->slot - prev;
     720           0 :     tower_sync.lockouts[i].confirmation_count = (uchar)vote->conf;
     721           0 :     prev                                      = vote->slot;
     722           0 :     i++;
     723           0 :   }
     724           0 :   memcpy( tower_sync.hash.uc, bank_hash, sizeof(fd_hash_t) );
     725             : 
     726           0 :   uchar * txn_out = vote_txn->payload;
     727           0 :   uchar * txn_meta_out = vote_txn->_;
     728             : 
     729           0 :   int same_addr = !memcmp( validator_identity, vote_authority, sizeof(fd_pubkey_t) );
     730           0 :   if( FD_LIKELY( same_addr ) ) {
     731             : 
     732             :     /* 0: validator identity
     733             :        1: vote account address
     734             :        2: vote program */
     735             : 
     736           0 :     fd_txn_accounts_t votes;
     737           0 :     votes.signature_cnt         = 1;
     738           0 :     votes.readonly_signed_cnt   = 0;
     739           0 :     votes.readonly_unsigned_cnt = 1;
     740           0 :     votes.acct_cnt              = 3;
     741           0 :     votes.signers_w             = validator_identity;
     742           0 :     votes.signers_r             = NULL;
     743           0 :     votes.non_signers_w         = vote_acc;
     744           0 :     votes.non_signers_r         = &fd_solana_vote_program_id;
     745           0 :     FD_TEST( fd_txn_base_generate( txn_meta_out, txn_out, votes.signature_cnt, &votes, recent_blockhash->uc ) );
     746             : 
     747           0 :   } else {
     748             : 
     749             :     /* 0: validator identity
     750             :        1: vote authority
     751             :        2: vote account address
     752             :        3: vote program */
     753             : 
     754           0 :     fd_txn_accounts_t votes;
     755           0 :     votes.signature_cnt         = 2;
     756           0 :     votes.readonly_signed_cnt   = 1;
     757           0 :     votes.readonly_unsigned_cnt = 1;
     758           0 :     votes.acct_cnt              = 4;
     759           0 :     votes.signers_w             = validator_identity;
     760           0 :     votes.signers_r             = vote_authority;
     761           0 :     votes.non_signers_w         = vote_acc;
     762           0 :     votes.non_signers_r         = &fd_solana_vote_program_id;
     763           0 :     FD_TEST( fd_txn_base_generate( txn_meta_out, txn_out, votes.signature_cnt, &votes, recent_blockhash->uc ) );
     764           0 :   }
     765             : 
     766             :   /* Add the vote instruction to the transaction. */
     767             : 
     768           0 :   fd_vote_instruction_t vote_ix;
     769           0 :   uchar                 vote_ix_buf[FD_TXN_MTU];
     770           0 :   vote_ix.discriminant                    = fd_vote_instruction_enum_compact_update_vote_state;
     771           0 :   vote_ix.inner.compact_update_vote_state = tower_sync;
     772           0 :   fd_bincode_encode_ctx_t encode = { .data = vote_ix_buf, .dataend = ( vote_ix_buf + FD_TXN_MTU ) };
     773           0 :   fd_vote_instruction_encode( &vote_ix, &encode );
     774           0 :   uchar program_id;
     775           0 :   uchar ix_accs[2];
     776           0 :   if( FD_LIKELY( same_addr ) ) {
     777           0 :     ix_accs[0] = 1; /* vote account address */
     778           0 :     ix_accs[1] = 0; /* vote authority */
     779           0 :     program_id = 2; /* vote program */
     780           0 :   } else {
     781           0 :     ix_accs[0] = 2; /* vote account address */
     782           0 :     ix_accs[1] = 1; /* vote authority */
     783           0 :     program_id = 3; /* vote program */
     784           0 :   }
     785           0 :   ushort vote_ix_sz = (ushort)fd_vote_instruction_size( &vote_ix );
     786           0 :   vote_txn->payload_sz = fd_txn_add_instr( txn_meta_out, txn_out, program_id, ix_accs, 2, vote_ix_buf, vote_ix_sz );
     787           0 : }
     788             : 
     789             : int
     790           0 : fd_tower_verify( fd_tower_t const * tower ) {
     791           0 :   if( FD_UNLIKELY( fd_tower_cnt( tower )>=FD_TOWER_VOTE_MAX ) ) {
     792           0 :     FD_LOG_WARNING(( "[%s] invariant violation: cnt %lu >= FD_TOWER_VOTE_MAX %lu", __func__, fd_tower_cnt( tower ), (ulong)FD_TOWER_VOTE_MAX ));
     793           0 :     return -1;
     794           0 :   }
     795             : 
     796           0 :   fd_tower_t const * prev = NULL;
     797           0 :   for( fd_tower_iter_t iter = fd_tower_iter_init( tower       );
     798           0 :                                    !fd_tower_iter_done( tower, iter );
     799           0 :                              iter = fd_tower_iter_next( tower, iter ) ) {
     800           0 :     fd_tower_t const * vote = fd_tower_iter_ele_const( tower, iter );
     801           0 :     if( FD_UNLIKELY( prev && ( vote->slot < prev->slot || vote->conf < prev->conf ) ) ) {
     802           0 :       FD_LOG_WARNING(( "[%s] invariant violation: vote (slot:%lu conf:%lu) prev (slot:%lu conf:%lu)", __func__, vote->slot, vote->conf, prev->slot, prev->conf ));
     803           0 :       return -1;
     804           0 :     }
     805           0 :     prev = vote;
     806           0 :   }
     807           0 :   return 0;
     808           0 : }
     809             : 
     810             : #include <stdio.h>
     811             : 
     812             : void
     813           0 : fd_tower_print( fd_tower_t const * tower, ulong root ) {
     814           0 :   FD_LOG_NOTICE( ( "\n\n[Tower]" ) );
     815             : 
     816           0 :   if( FD_UNLIKELY( fd_tower_empty( tower ) ) ) return;
     817             : 
     818           0 :   ulong max_slot = 0;
     819             : 
     820             :   /* Determine spacing. */
     821             : 
     822           0 :   for( fd_tower_iter_t iter = fd_tower_iter_init_rev( tower       );
     823           0 :                              !fd_tower_iter_done_rev( tower, iter );
     824           0 :                        iter = fd_tower_iter_prev    ( tower, iter ) ) {
     825             : 
     826           0 :     max_slot = fd_ulong_max( max_slot, fd_tower_iter_ele_const( tower, iter )->slot );
     827           0 :   }
     828             : 
     829             :   /* Calculate the number of digits in the maximum slot value. */
     830             : 
     831           0 :   int           digit_cnt = 0;
     832           0 :   unsigned long rem       = max_slot;
     833           0 :   do {
     834           0 :     rem /= 10;
     835           0 :     ++digit_cnt;
     836           0 :   } while( rem > 0 );
     837             : 
     838             :   /* Print the column headers. */
     839             : 
     840           0 :   printf( "slot%*s | %s\n", digit_cnt - (int)strlen("slot"), "", "confirmation count" );
     841             : 
     842             :   /* Print the divider line. */
     843             : 
     844           0 :   for( int i = 0; i < digit_cnt; i++ ) {
     845           0 :     printf( "-" );
     846           0 :   }
     847           0 :   printf( " | " );
     848           0 :   for( ulong i = 0; i < strlen( "confirmation count" ); i++ ) {
     849           0 :     printf( "-" );
     850           0 :   }
     851           0 :   printf( "\n" );
     852             : 
     853             :   /* Print each vote as a table. */
     854             : 
     855           0 :   for( fd_tower_iter_t iter = fd_tower_iter_init_rev( tower       );
     856           0 :                              !fd_tower_iter_done_rev( tower, iter );
     857           0 :                        iter = fd_tower_iter_prev    ( tower, iter ) ) {
     858             : 
     859           0 :     fd_tower_t const * vote = fd_tower_iter_ele_const( tower, iter );
     860           0 :     printf( "%*lu | %lu\n", digit_cnt, vote->slot, vote->conf );
     861           0 :     max_slot = fd_ulong_max( max_slot, fd_tower_iter_ele_const( tower, iter )->slot );
     862           0 :   }
     863           0 :   if( FD_UNLIKELY( root==ULONG_MAX ) ) {
     864           0 :     printf( "%*s | root\n", digit_cnt, "NULL" );
     865           0 :   } else {
     866           0 :     printf( "%*lu | root\n", digit_cnt, root );
     867           0 :   }
     868             :   printf( "\n" );
     869           0 : }

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