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263 lines
11 KiB
C
263 lines
11 KiB
C
#if !defined(OMT_H)
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#define OMT_H
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#ident "Copyright (c) 2008 Tokutek Inc. All rights reserved."
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// Order Maintenance Tree (OMT)
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//
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// Maintains a collection of totally ordered values, where each value has an integer weight.
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// The OMT is a mutable datatype.
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//
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// The Abstraction:
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//
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// An OMT is a vector of values, $V$, where $|V|$ is the length of the vector.
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// The vector is numbered from $0$ to $|V|-1$.
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// Each value has a weight. The weight of the $i$th element is denoted $w(V_i)$.
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//
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// We can create a new OMT, which is the empty vector.
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//
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// We can insert a new element $x$ into slot $i$, changing $V$ into $V'$ where
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// $|V'|=1+|V|$ and
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//
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// V'_j = V_j if $j<i$
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// x if $j=i$
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// V_{j-1} if $j>i$.
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//
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// We can specify $i$ using a kind of function instead of as an integer.
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// Let $b$ be a function mapping from values to nonzero integers, such that
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// the signum of $b$ is monotically increasing.
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// We can specify $i$ as the minimum integer such that $b(V_i)>0$.
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//
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// We look up a value using its index, or using a Heaviside function.
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// For lookups, we allow $b$ to be zero for some values, and again the signum of $b$ must be monotonically increasing.
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// When lookup up values, we can look up
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// $V_i$ where $i$ is the minimum integer such that $b(V_i)=0$. (With a special return code if no such value exists.)
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// (Rationale: Ordinarily we want $i$ to be unique. But for various reasons we want to allow multiple zeros, and we want the smallest $i$ in that case.)
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// $V_i$ where $i$ is the minimum integer such that $b(V_i)>0$. (Or an indication that no such value exists.)
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// $V_i$ where $i$ is the maximum integer such that $b(V_i)<0$. (Or an indication that no such value exists.)
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//
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// When looking up a value using a Heaviside function, we get the value and its index.
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//
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// We can also split an OMT into two OMTs, splitting the weight of the values evenly.
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// Find a value $j$ such that the values to the left of $j$ have about the same total weight as the values to the right of $j$.
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// The resulting two OMTs contain the values to the left of $j$ and the values to the right of $j$ respectively.
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// All of the values from the original OMT go into one of the new OMTs.
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// If the weights of the values don't split exactly evenly, then the implementation has the freedom to choose whether
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// the new left OMT or the new right OMT is larger.
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//
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// Performance:
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// Insertion and deletion should run with $O(\log |V|)$ time and $O(\log |V|)$ calls to the Heaviside function.
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// The memory required is O(|V|).
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//
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// The programming API:
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//typedef struct value *OMTVALUE; // A slight improvement over using void*.
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typedef struct omt *OMT;
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int toku_omt_create (OMT *omtp);
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// Effect: Create an empty OMT. Stores it in *omtp.
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// Requires: omtp != NULL
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// Returns:
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// 0 success
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// ENOMEM out of memory (and doesn't modify *omtp)
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// Performance: constant time.
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int toku_omt_create_from_sorted_array(OMT *omtp, OMTVALUE *values, u_int32_t numvalues);
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// Effect: Create a OMT containing values. The number of values is in numvalues.
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// Stores the new OMT in *omtp.
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// Requires: omtp != NULL
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// Requires: values != NULL
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// Requires: values is sorted
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// Returns:
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// 0 success
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// ENOMEM out of memory (and doesn't modify *omtp)
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// Performance: time=O(numvalues)
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// Rational: Normally to insert N values takes O(N lg N) amortized time.
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// If the N values are known in advance, are sorted, and
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// the structure is empty, we can batch insert them much faster.
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void toku_omt_destroy(OMT *omtp);
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// Effect: Destroy an OMT, freeing all its memory.
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// Does not free the OMTVALUEs stored in the OMT.
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// Those values may be freed before or after calling toku_omt_destroy.
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// Also sets *omtp=NULL.
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// Requires: omtp != NULL
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// Requires: *omtp != NULL
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// Rationale: The usage is to do something like
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// toku_omt_destroy(&s->omt);
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// and now s->omt will have a NULL pointer instead of a dangling freed pointer.
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// Rationale: Returns no values since free() cannot fail.
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// Rationale: Does not free the OMTVALUEs to reduce complexity.
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// Performance: time=O(toku_omt_size(*omtp))
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u_int32_t toku_omt_size(OMT V);
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// Effect: return |V|.
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// Requires: V != NULL
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// Performance: time=O(1)
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int toku_omt_iterate(OMT omt, int (*f)(OMTVALUE, u_int32_t, void*), void*v);
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// Effect: Iterate over the values of the omt, from left to right, calling f on each value.
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// The second argument passed to f is the index of the value.
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// The third argument passed to f is v.
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// The indices run from 0 (inclusive) to toku_omt_size(omt) (exclusive).
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// Requires: omt != NULL
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// Requires: f != NULL
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// Returns:
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// If f ever returns nonzero, then the iteration stops, and the value returned by f is returned by toku_omt_iterate.
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// If f always returns zero, then toku_omt_iterate returns 0.
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// Requires: Don't modify omt while running. (E.g., f may not insert or delete values form omt.)
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// Performance: time=O(i+\log N) where i is the number of times f is called, and N is the number of elements in omt.
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// Rational: Although the functional iterator requires defining another function (as opposed to C++ style iterator), it is much easier to read.
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int toku_omt_insert_at(OMT omt, OMTVALUE value, u_int32_t index);
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// Effect: Increases indexes of all items at slot >= index by 1.
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// Insert value into the position at index.
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//
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// Returns:
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// 0 success
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// ERANGE if index>toku_omt_size(omt)
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// ENOMEM
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// On error, omt is unchanged.
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// Performance: time=O(\log N) amortized time.
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// Rationale: Some future implementation may be O(\log N) worst-case time, but O(\log N) amortized is good enough for now.
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int toku_omt_set_at (OMT omt, OMTVALUE value, u_int32_t index);
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// Effect: Replaces the item at index with value.
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// Returns:
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// 0 success
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// ERANGE if index>=toku_omt_size(omt)
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// On error, omt i sunchanged.
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// Performance: time=O(\log N)
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// Rationale: The BRT needs to be able to replace a value with another copy of the same value (allocated in a different location)
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int toku_omt_insert(OMT omt, OMTVALUE value, int(*h)(OMTVALUE, void*v), void *v, u_int32_t *index);
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// Effect: Insert value into the OMT.
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// If there is some i such that $h(V_i, v)=0$ then returns DB_KEYEXIST.
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// Otherwise, let i be the minimum value such that $h(V_i, v)>0$.
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// If no such i exists, then let i be |V|
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// Then this has the same effect as
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// omt_insert_at(tree, value, i);
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// If index!=NULL then i is stored in *index
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// Requires: The signum of h must be monotonically increasing.
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// Returns:
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// 0 success
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// DB_KEYEXIST the key is present (h was equal to zero for some value)
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// ENOMEM
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// On nonzero return, omt is unchanged.
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// On nonzero non-DB_KEYEXIST return, *index is unchanged.
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// Performance: time=O(\log N) amortized.
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// Rationale: Some future implementation may be O(\log N) worst-case time, but O(\log N) amortized is good enough for now.
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int toku_omt_delete_at(OMT omt, u_int32_t index);
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// Effect: Delete the item in slot index.
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// Decreases indexes of all items at slot >= index by 1.
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// Returns
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// 0 success
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// ERANGE if index>=toku_omt_size(omt)
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// On error, omt is unchanged.
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// Rationale: To delete an item, first find its index using toku_omt_find, then delete it.
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// Performance: time=O(\log N) amortized.
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int toku_omt_fetch (OMT V, u_int32_t i, OMTVALUE *v);
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// Effect: Set *v=V_i
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// Requires: v != NULL
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// Returns
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// 0 success
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// ERANGE if index>=toku_omt_size(omt)
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// On nonzero return, *v is unchanged.
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// Performance: time=O(\log N)
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int toku_omt_find_zero(OMT V, int (*h)(OMTVALUE, void*extra), void*extra, OMTVALUE *value, u_int32_t *index);
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// Effect: Find the smallest i such that h(V_i, extra)>=0
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// If there is such an i and h(V_i,extra)==0 then set *index=i and return 0.
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// If there is such an i and h(V_i,extra)>0 then set *index=i and return DB_NOTFOUND.
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// If there is no such i then set *index=toku_omt_size(V) and return DB_NOTFOUND.
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// Requires: index!=NULL
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int toku_omt_find(OMT V, int (*h)(OMTVALUE, void*extra), void*extra, int direction, OMTVALUE *value, u_int32_t *index);
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/* Effect:
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If direction >0 then find the smallest i such that h(V_i,extra)>0.
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If direction <0 then find the largest i such that h(V_i,extra)<0.
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(Direction may not be equal to zero.)
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If value!=NULL then store V_i in *value
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If index!=NULL then store i in *index.
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Requires: The signum of h is monotically increasing.
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Returns
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0 success
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DB_NOTFOUND no such value is found.
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On nonzero return, *value and *index are unchanged.
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Performance: time=O(\log N)
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Rationale:
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Here's how to use the find function to find various things
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Cases for find:
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find first value: ( h(v)=+1, direction=+1 )
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find last value ( h(v)=-1, direction=-1 )
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find first X ( h(v)=(v< x) ? -1 : 1 direction=+1 )
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find last X ( h(v)=(v<=x) ? -1 : 1 direction=-1 )
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find X or successor to X ( same as find first X. )
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Rationale: To help understand heaviside functions and behavor of find:
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There are 7 kinds of heaviside functions.
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The signus of the h must be monotonically increasing.
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Given a function of the following form, A is the element
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returned for direction>0, B is the element returned
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for direction<0, C is the element returned for
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direction==0 (see find_zero) (with a return of 0), and D is the element
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returned for direction==0 (see find_zero) with a return of DB_NOTFOUND.
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If any of A, B, or C are not found, then asking for the
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associated direction will return DB_NOTFOUND.
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See find_zero for more information.
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Let the following represent the signus of the heaviside function.
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-...-
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A
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D
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+...+
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B
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D
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0...0
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C
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-...-0...0
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AC
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0...0+...+
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C B
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-...-+...+
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AB
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D
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-...-0...0+...+
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AC B
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*/
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int toku_omt_split_at(OMT omt, OMT *newomt, u_int32_t index);
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// Effect: Create a new OMT, storing it in *newomt.
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// The values to the right of index (starting at index) are moved to *newomt.
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// Requires: omt != NULL
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// Requires: newomt != NULL
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// Returns
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// 0 success,
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// ERANGE if index > toku_omt_size(omt)
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// ENOMEM
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// On nonzero return, omt and *newomt are unmodified.
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// Performance: time=O(n)
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// Rationale: We don't need a split-evenly operation. We need to split items so that their total sizes
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// are even, and other similar splitting criteria. It's easy to split evenly by calling toku_omt_size(), and dividing by two.
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int toku_omt_merge(OMT leftomt, OMT rightomt, OMT *newomt);
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// Effect: Appends leftomt and rightomt to produce a new omt.
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// Sets *newomt to the new omt.
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// On success, leftomt and rightomt destroyed,.
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// Returns 0 on success
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// ENOMEM on out of memory.
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// On error, nothing is modified.
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// Performance: time=O(n) is acceptable, but one can imagine implementations that are O(\log n) worst-case.
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#endif /* #ifndef OMT_H */
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