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# 2. Bit tables

## 2.1. Introduction

.readership: Any MPS developer.

.intro: This is the design of the Bit Tables module. A Bit Table is a linear array of bits. A Bit Table of length n is indexed using an integer from 0 up to (but not including) n. Each bit in a Bit Table can hold either the value 0 (aka `FALSE`) or 1 (aka `TRUE`). A variety of operations are provided including: set, reset, and retrieve, individual bits; set and reset a contiguous range of bits; search for a contiguous range of reset bits; making a “negative image” copy of a range.

## 2.2. History

.hist.0-3: The history for versions 0-3 is lost pending possible reconstruction. David Jones, 1997-03-04.

.hist.4: Prepared for review. Added full requirements section. Made notation more consistent throughout. Documented all functions. David Jones, 1999-04-29.

.hist.5: Converted from MMInfo database design document. Richard Brooksby, 2002-06-07.

.hist.6: Converted to reStructuredText. Gareth Rees, 2013-03-12.

## 2.3. Definitions

.def.set: Set

> Used as a verb meaning to assign the value 1 or `TRUE` to a bit. Used descriptively to denote a bit containing the value 1. Note 1 and `TRUE` are synonyms in MPS C code (see design.mps.type(0).bool.value).

.def.reset: Reset

> Used as a verb meaning to assign the value 0 or `FALSE` to a bit. Used descriptively to denote a bit containing the value 0. Note 0 and `FALSE` are synonyms in MPS C code (see design.mps.type(0).bool.value).

Note

Consider using “fill/empty” or “mark/clear” instead of “set/reset”, set/reset is probably a hangover from drj’s z80 hacking days – drj 1999-04-26

.def.bt: Bit Table

> A Bit Table is a mapping from [0, n) to {0,1} for some n, represented as a linear array of bits.

> ..def.bt.justify: They are called bit tables because a single bit is used to encode whether the image of a particular integer under the map is 0 or 1.

.def.range: Range

> A contiguous sequence of bits in a Bit Table. Ranges are typically specified as a base–limit pair where the range includes the position specified by the base, but excludes that specified by the limit. The mathematical interval notation for half-open intervals, [base, limit), is used.

## 2.4. Requirements

.req.bit: The storage for a Bit Table of n bits shall take no more than a small constant addition to the storage required for n bits. ..req.bit.why: This is so that clients can make some predictions about how much storage their algorithms use. A small constant is allowed over the minimal for two reasons: inevitable implementation overheads (such as only being able to allocate storage in multiples of 32 bits), extra storage for robustness or speed (such as signature and length fields).

.req.create: A means to create Bit Tables. .req.create.why: Obvious.

.req.destroy: A means to destroy Bit Tables. .req.destroy.why: Obvious.

.req.ops: The following operations shall be supported:

- .req.ops.get: Get. Get the value of a bit at a specified index.
- .req.ops.set: Set. Set a bit at a specified index.
- .req.ops.reset: Reset. Reset a bit at a specified index.

.req.ops.minimal.why: Get, Set, Reset, are the minimal operations. All possible mappings can be created and inspected using these operations.

- .req.ops.set.range: SetRange. Set a range of bits. .req.ops.set.range.why: It’s expected that clients will often want to set a range of bits; providing this operation allows the implementation of the BT module to make the operation efficient.
- .req.ops.reset.range: ResetRange. Reset a range of bits. .req.ops.reset.range.why: as for SetRange, see .req.ops.set.range.why.
- .req.ops.test.range.set: IsSetRange. Test whether a range of bits are all set. .req.ops.test.range.set.why: Mostly for checking. For example, often clients will know that a range they are about to reset is currently all set, they can use this operation to assert that fact.
- .req.ops.test.range.reset: IsResetRange. Test whether a range of bits are all reset. .req.ops.test.range.reset.why: As for IsSetRange, see .req.ops.test.range.set.why.
- .req.ops.find: Find a range (which we’ll denote [i, j)) of at least L reset bits that lies in a specified subrange of the entire Bit Table. Various find operations are required according to the (additional) properties of the required range:
  - .req.ops.find.short.low: FindShortResetRange. Of all candidate ranges, find the range with least j (find the leftmost range that has at least L reset bits and return just enough of that). .req.ops.find.short.low.why: Required by client and VM arenas to allocate segments. The arenas implement definite placement policies (such as lowest addressed segment first) so they need the lowest (or highest) range that will do. It’s not currently useful to allocate segments larger than the requested size, so finding a short range is sufficient.
  - .req.ops.find.short.high: FindShortResetRangeHigh. Of all candidate ranges, find the range with greatest i (find the rightmost range that has at least L reset bits and return just enough of that). .req.ops.find.short.high.why: Required by arenas to implement a specific segment placement policy (highest addressed segment first).
  - .req.ops.find.long.low: FindLongResetRange. Of all candidate ranges, identify the ranges with least i and of those find the one with greatest j (find the leftmost range that has at least L reset bits and return all of it). .req.ops.find.long.low.why: Required by the mark and sweep Pool Classes (AMS, AWL, LO) for allocating objects (filling a buffer). It’s more efficient to fill a buffer with as much memory as is conveniently possible. There’s no strong reason to find the lowest range but it’s bound to have some beneficial (small) cache effect and makes the algorithm more predictable.
  - .req.ops.find.long.high: FindLongResetRangeHigh. Provided, but not required, see .non-req.ops.find.long.high.
- .req.ops.copy: Copy a range of bits from one Bit Table to another Bit Table. Various copy operations are required:
  - .req.ops.copy.simple: Copy a range of bits from one Bit Table to the same position in another Bit Table. .req.ops.copy.why: Required to support copying of the tables for the “low” segment during segment merging and splitting, for pools using tables (for example, `PoolClassAMS`).
  - .req.ops.copy.offset: Copy a range of bits from one Bit Table to an offset position in another Bit Table. .req.ops.copy.why: Required to support copying of the tables for the “high” segment during segment merging and splitting, for pools which support this (currently none, as of 2000-01-17).
  - .req.ops.copy.invert: Copy a range of bits from one Bit Table to the same position in another Bit Table inverting all the bits in the target copy. .req.ops.copy.invert.why: Required by colour manipulation code in `PoolClassAMS` and `PoolClassLO`.

.req.speed: Operations shall take no more than a few memory operations per bit manipulated. .req.speed.why: Any slower would be gratuitous.

.req.speed.fast: The following operations shall be very fast:

- .req.speed.fast.find.short: FindShortResRange (the operation used to meet .req.ops.find.short.low) FindShortResRangeHigh (the operation used to meet .req.ops.find.short.high).

  .req.speed.fast.find.short.why: These two are used by the client arena (design.mps.arena.client) and the VM arena (design.mps.arena.vm) for finding segments in page tables. The operation will be used sufficiently often that its speed will noticeably affect the overall speed of the MPS. They will be called with a length equal to the number of pages in a segment. Typical values of this length depend on the pool classes used and their configuration, but we can expect length to be small (1 to 16) usually. We can expect the Bit Table to be populated densely where it is populated at all, that is set bits will tend to be clustered together in subranges.

- .req.speed.fast.find.long: FindLongResRange (the operation used to meet .req.ops.find.long.low)

  .req.speed.fast.find.long.why: Used in the allocator for `PoolClassAWL` (design.mps.poolawl(1)), `PoolClassAMS` (design.mps.poolams(2)), `PoolClassEPVM` (design.mps.poolepvm(0)). Of these AWL and EPVM have speed requirements. For AWL the length of range to be found will be the length of a Dylan table in words. According to mail.tony.1999-05-05.11-36(0), only <entry-vector> objects are allocated in AWL (though not all <entry-vector> objects are allocated in AWL), and the mean length of an <entry-vector> object is 486 Words. No data for EPVM alas.

.req.speed.fast.other.why: We might expect mark and sweep pools to make use of Bit Tables, the MPS has general requirements to support efficient mark and sweep pools, so that imposes general speed requirements on Bit Tables.

## 2.5. Non requirements

The following are not requirements but the current design could support them with little modification or does support them. Often they used to be requirements, but are no longer, or were added speculatively or experimentally but aren’t currently used.

- .non-req.ops.test.range.same: RangesSame. Test whether two ranges that occupy the same positions in different Bit Tables are the same. This used to be required by `PoolClassAMS`, but is no longer. Currently (1999-05-04) the functionality still exists.
- .non-req.ops.find.long.high: FindLongResetRangeHigh. (see .req.ops.find) Of all candidate ranges, identify the ranges with greatest j and of those find the one with least i (find the rightmost range that has at least L reset bits and return all of it). Provided for symmetry but only currently used by the BT tests and `cbstest.c`.

## 2.6. Background

.background: Originally Bit Tables were used and implemented by `PoolClassLO` (design.mps.poollo). It was decided to lift them out into a separate module when designing the Pool to manage Dylan Weak Tables which is also a mark and sweep pool and will make use of Bit Tables (see design.mps.poolawl). .background.analysis: analysis.mps.bt(0) contains some of the analysis of the design decisions that were and were not made in this document.

## 2.7. Clients

.clients: Bit Tables are used throughout the MPS but the important uses are in the client and VM arenas (design.mps.arena.client(0) and design.mps.arena.vm(1)) a bit table is used to record whether each page is free or not; several pool classes (`PoolClassLO`, `PoolClassEPVM`, `PoolClassAMS`) use bit tables to record which locations are free and also to store colour.

## 2.8. Overview

.over: Mostly, the design is as simple as possible. The significant complications are iteration (see .iteration below) and searching (see .fun.find-res-range below) because both of these are required to be fast.

## 2.9. Interface

`typedef Word *BT;`

.if.representation.abstract: A Bit Table is represented by the type `BT`.

.if.declare: The module declares a type `BT` and a prototype for each of the functions below. The type is declared in impl.h.mpmtypes, the prototypes are declared in impl.h.mpm. Some of the functions are in fact implemented as macros in the usual way (doc.mps.ref-man.if-conv(0).macro.std).

.if.general.index: Many of the functions specified below take indexes. If otherwise unspecified an index must be in the interval [0, n) (note, up to, but not including, n) where n is the number of bits in the relevant Bit Table (as passed to the `BTCreate()` function).

.if.general.range: Where a range is specified by two indexes (base and limit), the index base, which specifies the beginning of the range, must be in the interval [0, n), and the index limit, which specifies the end of the range, must be in the interval [1, n] (note can be n), and base must be strictly less than limit (empty ranges are not allowed). Sometimes i and j are used instead of base and limit.

Res `BTCreate`(BT *btReturn, Arena arena, Count n)

.if.create: Attempts to create a table of length `n` in the arena control pool, putting the table in `*btReturn`. Returns `ResOK` if and only if the table is created OK. The initial values of the bits in the table are undefined (so the client should probably call `BTResRange()` on the entire range before using the `BT`). Meets .req.create.

void `BTDestroy`(BT t, Arena arena, Count n)

.if.destroy: Destroys the table `t`, which must have been created with `BTCreate()`. The value of argument `n` must be same as the value of the argument passed to `BTCreate()`. Meets mps:ref:.req.destroy.

size_t `BTSize`(Count n)

.if.size: `BTSize(n)` returns the number of bytes needed for a Bit Table of `n` bits. `BTSize()` is a macro, but `(BTSize)(n)` will assert if `n` exceeds COUNT_MAX - MPS_WORD_WIDTH + 1`. This is used by clients that allocate storage for the `BT` themselves. Before `BTCreate()` and `BTDestroy()` were implemented that was the only way to allocate a Bit Table, but is now deprecated.

int `BTGet`(BT t, Index i)

.if.get: `BTGet(t, i)` returns the `i`-th bit of the table `t` (that is, the image of `i` under the mapping). Meets .req.ops.get.

void `BTSet`(BT t, Index i)

.if.set: `BTSet(t, i)` sets the `i`-th bit of the table `t` (to 1). `BTGet(t, i)` will now return 1. Meets .req.ops.set.

void `BTRes`(BT t, Index i)

.if.res: `BTRes(t, i)` resets the `i`-th bit of the table `t` (to 0). `BTGet(t, i)` will now return 0. Meets .req.ops.res.

void `BTSetRange`(BT t, Index base, Index limit)

.if.set-range: `BTSetRange(t, base, limit)` sets the range of bits [`base`, `limit`) in the table `t`. `BTGet(t, x)` will now return 1 for `base` ≤ `x` < `limit`. Meets .req.ops.range.set.

void `BTResRange`(BT t, Index base, Index limit)

.if.res-range: `BTResRange(t, base, limit)` resets the range of bits [`base`, `limit`) in the table `t`. `BTGet(t, x)` will now return 0 for `base` ≤ `x` < `limit`. Meets .req.ops.range.res.

Bool `BTIsSetRange`(BT bt, Index base, Index limit)

.if.test.range.set: Returns `TRUE` if all the bits in the range [`base`, `limit`) are set, `FALSE` otherwise. Meets .req.ops.test.range.set.

Bool `BTIsResRange`(BT bt, Index base, Index limit)

.if.test.range.reset: Returns `TRUE` if all the bits in the range [`base`, `limit`) are reset, `FALSE` otherwise. Meets .req.ops.test.range.reset.

`Bool BTRangesSame(BT BTx, BT BTy, Index base, Index limit);`

.if.test.range.same: returns `TRUE` if `BTGet(BTx,i)` equals `BTGet(BTy,i)` for `i` in [`base`, `limit`), and `FALSE` otherwise. Meets .non-req.ops.test.range.same.

.if.find.general: There are four functions (below) to find reset ranges. All the functions have the same prototype (for symmetry):

    Bool find(Index *baseReturn, Index *limitReturn,
              BT bt,
              Index searchBase, Index searchLimit,
              Count length);

where `bt` is the Bit Table in which to search. `searchBase` and `searchLimit` specify a subset of the Bit Table to use, the functions will only find ranges that are subsets of [`searchBase`, `searchLimit`) (when set, `*baseReturn` will never be less than `searchBase` and `*limitReturn` will never be greater than `searchLimit`). `searchBase` and `searchLimit` specify a range that must conform to the general range requirements for a range [i, j), as per .if.general.range modified appropriately. `length` is the number of contiguous reset bits to find; it must not be bigger than `searchLimit - searchBase` (that would be silly). If a suitable range cannot be found the function returns `FALSE` (0) and leaves `*baseReturn` and `*limitReturn` untouched. If a suitable range is found then the function returns the range’s base in `*baseReturn` and its limit in `*limitReturn` and returns `TRUE` (1).

Bool `BTFindShortResRange`(Index *baseReturn, Index *limitReturn, BT bt, Index searchBase, Index searchLimit, Count length)

.if.find-short-res-range: Finds a range of reset bits in the table, starting at `searchBase` and working upwards. This function is intended to meet .req.ops.find.short.low so it will find the leftmost range that will do, and never finds a range longer than the requested length (the intention is that it will not waste time looking).

Bool `BTFindShortResRangeHigh`(Index *baseReturn, Index *limitReturn, BT bt, Index searchBase, Index searchLimit, Count length)

.if.find-short-res-range-high: Finds a range of reset bits in the table, starting at `searchLimit` and working downwards. This function is intended to meet .req.ops.find.short.high so it will find the rightmost range that will do, and never finds a range longer than the requested length.

Bool `BTFindLongResRange`(Index *baseReturn, Index *limitReturn, BT bt, Index searchBase, Index searchLimit, Count length)

.if.find-long-res-range: Finds a range of reset bits in the table, starting at `searchBase` and working upwards. This function is intended to meet .req.ops.find.long.low so it will find the leftmost range that will do and returns all of that range (which can be longer than the requested length).

Bool `BTFindLongResRangeHigh`(Index *baseReturn, Index *limitReturn, BT bt, Index searchBase, Index searchLimit, Count length)

.if.find-long-res-range-high: Finds a range of reset bits in the table, starting at `searchLimit` and working downwards. This function is intended to meet .req.ops.find.long.high so it will find the rightmost range that will do and returns all that range (which can be longer than the requested length).

void `BTCopyRange`(BT fromBT, BT toBT, Index base, Index limit)

.if.copy-range: Overwrites the `i`-th bit of `toBT` with the `i`-th bit of `fromBT`, for all `i` in [`base`, `limit`). Meets .req.ops.copy.simple.

void `BTCopyOffsetRange`(BT fromBT, BT toBT, Index fromBase, Index fromLimit, Index toBase, Index toLimit)

.if.copy-offset-range: Overwrites the `i`-th bit of `toBT` with the `j`-th bit of `fromBT`, for all `i` in [`toBase`, `toLimit`) and corresponding `j` in [`fromBase`, `fromLimit`). Each of these ranges must be the same size. This might be significantly less efficient than `BTCopyRange()`. Meets .req.ops.copy.offset.

void `BTCopyInvertRange`(BT fromBT, BT toBT, Index base, Index limit)

.if.copy-invert-range: Overwrites the `i`-th bit of `toBT` with the inverse of the `i`-th bit of `fromBT`, for all `i` in [`base`, `limit`). Meets .req.ops.copy.invert.

## 2.10. Detailed design

### 2.10.1. Data structures

.datastructure: Bit Tables will be represented as (a pointer to) an array of `Word`. A plain array is used instead of the more usual design convention of implementing an abstract data type as a structure with a signature (see guide.impl.c.adt(0)). .datastructure.words.justify: The type `Word` is used as it will probably map to the object that can be most efficiently accessed on any particular platform. .datastructure.non-adt.justify: The usual abstract data type convention was not followed because (i) The initial design (drj) was lazy, (ii) Bit Tables are more likely to come in convenient powers of two with the extra one or two words overhead. However, the loss of checking is severe. Perhaps it would be better to use the usual abstract data type style.

### 2.10.2. Functions

.fun.size: `BTSize()`. Since a Bit Table is an array of `Word`, the size of a Bit Table of n bits is simply the number of words that it takes to store n bits times the number of bytes in a word. This is ceiling(n/MPS_WORD_WIDTH)*sizeof(Word). .fun.size.justify: Since there can be at most MPS_WORD_WIDTH - 1 unused bits in the entire table, this satisfies .req.bit.

.index: The designs for the following functions use a decomposition of a bit-index, `i`, into two parts, `iw`, `ib`.

- .index.word: `iw` is the “word-index” which is the index into the word array of the word that contains the bit referred to by the bit-index. `iw = i / MPS_WORD_WIDTH`. Since `MPS_WORD_WIDTH` is a power of two, this is the same as `iw = i >> MPS_WORD_SHIFT`. The latter expression is used in the code. .index.word.justify: The compiler is more likely to generate good code without the divide.
- .index.sub-word: `ib` is the “sub-word-index” which is the index of the bit referred to by the bit-index in the above word. `ib = i % MPS_WORD_WIDTH`. Since `MPS_WORD_WIDTH` is a power of two, this is the same as `ib = i & ~((Word)-1<<MPS_WORD_SHIFT)`. The latter expression is used in the code. .index.sub-word.justify: The compiler is more likely to generate good code without the modulus.

.index.justify.dubious: The above justifications are dubious; gcc 2.7.2 (with -O2) running on a sparc (zaphod) produces identical code for the following two functions:

    unsigned long f(unsigned long i) {
        return i/32 + i%32;
    }

    unsigned long g(unsigned long i) {
       return (i>>5) + (i&31);
    }

`ACT_ON_RANGE`(Index base, Index limit, single_action, bits_action, word_action)

`ACT_ON_RANGE_HIGH`(Index base, Index limit, single_action, bits_action, word_action)

.iteration: Many of the following functions involve iteration over ranges in a Bit Table. This is performed on whole words rather than individual bits, whenever possible (to improve speed). This is implemented internally by the macros `ACT_ON_RANGE()` and `ACT_ON_RANGE_HIGH()` for iterating over the range forwards and backwards respectively. These macros do not form part of the interface of the module, but are used extensively in the implementation. The macros are often used even when speed is not an issue because it simplifies the implementation and makes it more uniform. The iteration macros take the parameters `base`, `limit`, `single_action`, `bits_action`, and `word_action`:

- `base` and `limit` are of type `Index` and define the range of the iteration.
- `single_action` is the name of a macro which will be used for iterating over bits in the table individually. This macro must take a single `Index` parameter corresponding to the index for the bit. The expansion of the macro must not contain `break` or `continue` because it will be called from within a loop from the expansion of `ACT_ON_RANGE()`.
- `bits_action` is the name of a macro which will be used for iterating over part-words. This macro must take parameters `wordIndex`, `base`, `limit` where `wordIndex` is the index into the array of words, and `base` and `limit` define a range of bits within the indexed word.
- `word_action` is the name of a macro which will be used for iterating over whole-words. This macro must take the single parameter `wordIndex` which is the index of the whole-word in the array. The expansion of the macro must not contain `break` or `continue` because it will be called from within a loop from the expansion of `ACT_ON_RANGE()`.

.iteration.exit: The expansion of the `single_action`, `bits_action`, and `word_action` macros is allowed to contain `return` or `goto` to terminate the iteration early. This is used by the test (.fun.test.range.set) and find (.fun.find) operations.

.iteration.small: If the range is sufficiently small only the `single_action` macro will be used, as this is more efficient in practice. The choice of what constitutes a small range is made entirely on the basis of experimental performance results (and currently, 1999-04-27, a “small range” is 6 bits or fewer. See change.mps.epcore.brisling.160181 for some justification). Otherwise (for a bigger range) `bits_action` is used on the part words at either end of the range (or the whole of the range it if it fits in a single word), and `word_action` is used on the words that comprise the inner portion of the range.

The implementation of `ACT_ON_RANGE()` (and `ACT_ON_RANGE_HIGH()`) is simple enough. It decides which macros it should invoke and invokes them. `single_action` and `word_action` are invoked inside loops.

.fun.get: `BTGet()`. The bit-index will be converted in the usual way, see .index. The relevant `Word` will be read out of the Bit Table and shifted right by the sub-`Word` index (this brings the relevant bit down to the least significant bit of the `Word`), the `Word` will then be masked with 1, producing the answer.

.fun.set: `BTSet()`.

.fun.res: `BTRes()`.

In both `BTSet()` and `BTRes()` a mask is constructed by shifting 1 left by the sub-word-index (see .index). For `BTSet()` the mask is or-ed into the relevant word (thereby setting a single bit). For `BTRes()` the mask is inverted and and-ed into the relevant word (thereby resetting a single bit).

.fun.set-range: `BTSetRange()`. `ACT_ON_RANGE()` (see .iteration above) is used with macros that set a single bit (using `BTSet()`), set a range of bits in a word, and set a whole word.

.fun.res-range: `BTResRange()` This is implemented similarly to `BTSetRange()` (.fun.set-range) except using `BTRes()` and reverse bit-masking logic.

.fun.test.range.set: `BTIsSetRange()`. `ACT_ON_RANGE()` (see .iteration above) is used with macros that test whether all the relevant bits are set; if some of the relevant bits are not set then `return FALSE` is used to terminate the iteration early and return from the `BTIsSetRange()` function. If the iteration completes then `TRUE` is returned.

.fun.test.range.reset: `BTIsResRange()`. As for `BTIsSetRange()` (.fun.test.range.set above) but testing whether the bits are reset.

.fun.test.range.same: `BTRangesSame()`. As for `BTIsSetRange()` (.fun.test.range.set above) but testing whether corresponding ranges in the two Bit Tables are the same. Note there are no speed requirements, but `ACT_ON_RANGE()` is used for simplicity and uniformity.

.fun.find: The four external find functions (`BTFindShortResRange()`, `BTFindShortResRangeHigh()`, `BTFindLongResRange()`, `BTFindLongResRangeHigh()`) simply call through to one of the two internal functions: `BTFindResRange()` and `BTFindResRangeHigh()`.

Bool `BTFindResRange`(Index *baseReturn, Index *limitReturn, BT bt, Index searchBase, Index searchLimit, Count minLength, Count maxLength)

Bool `BTFindResRangeHigh`(Index *baseReturn, Index *limitReturn, BT bt, Index searchBase, Index searchLimit, Count minLength, Count maxLength)

There are two length parameters, one specifying the minimum length of the range to be found, the other the maximum length. For `BTFindShort()` and `BTFindShortHigh()`, `maxLength` is equal to `minLength` when passed; for `BTFindLong()` and `BTFindLongHigh()`, `maxLength` is equal to the maximum possible range, namely ``searchLimit - searchBase`.

.fun.find-res-range: `BTFindResRange()`. Iterate within the search boundaries, identifying candidate ranges by searching for a reset bit. The Boyer–Moore algorithm is used (it’s particularly easy to implement when there are only two symbols, 0 and 1, in the alphabet). For each candidate range, iterate backwards over the bits from the end of the range towards the beginning. If a set bit is found, this candidate has failed and a new candidate range is selected. If when scanning for the set bit a range of reset bits was found before finding the set bit, then this (small) range of reset bits is used as the start of the next candidate. Additionally the end of this small range of reset bits (the end of the failed candidate range) is remembered so that we don’t have to iterate over this range again. But if no reset bits were found in the candidate range, then iterate again (starting from the end of the failed candidate) to look for one. If during the backwards search no set bit is found, then we have found a sufficiently large range of reset bits; now extend the valid range as far as possible up to the maximum length by iterating forwards up to the maximum limit looking for a set bit. The iterations make use of the `ACT_ON_RANGE()` and `ACT_ON_RANGE_HIGH()` macros, which can use `goto` to effect an early termination of the iteration when a set/reset (as appropriate) bit is found. The macro `ACTION_FIND_SET_BIT()` is used in the iterations. It efficiently finds the first (that is, with lowest index or weight) set bit in a word or subword.

.fun.find-res-range.improve: Various other performance improvements have been suggested in the past, including some from request.epcore.170534. Here is a list of potential improvements which all sound plausible, but which have not led to performance improvements in practice:

- .fun.find-res-range.improve.step.partial: When the top index in a candidate range fails, skip partial words as well as whole words, using, for example, lookup tables.
- .fun.find-res-range.improve.lookup: When testing a candidate run, examine multiple bits at once (for example, 8), using lookup tables for (for example) index of first set bit, index of last set bit, number of reset bits, length of maximum run of reset bits.

.fun.find-res-range-high: `BTFindResRangeHigh()`. Exactly the same algorithm as in `BTFindResRange()` (see .fun.find-res-range above), but moving over the table in the opposite direction.

.fun.copy-simple-range: `BTCopyRange()`. Uses `ACT_ON_RANGE()` (see .iteration above) with the obvious implementation. Should be fast.

.fun.copy-offset-range: `BTCopyOffsetRange()`. Uses a simple iteration loop, reading bits with `BTGet()` and setting them with `BTSet()`. Doesn’t use `ACT_ON_RANGE()` because the two ranges will not, in general, be similarly word-aligned.

.fun.copy-invert-range: `BTCopyInvertRange()`. Uses `ACT_ON_RANGE()` (see .iteration above) with the obvious implementation. Should be fast—although there are no speed requirements.

## 2.11. Testing

.test: The following tests are available or have been used during development.

.test.btcv: `btcv.c`. This is supposed to be a coverage test, intended to execute all of the module’s code in at least some minimal way.

.test.cbstest: `cbstest.c`. This was written as a test of the `CBS` module (design.mps.cbs(2)). It compares the functional operation of a `CBS` with that of a `BT` so is a good functional test of either module.

.test.mmqa.120: MMQA_test_function!210.c. This is used because it has a fair amount of segment allocation and freeing so exercises the arena code that uses Bit Tables.

.test.bttest: `bttest.c`. This is an interactive test that can be used to exercise some of the `BT` functionality by hand.

.test.dylan: It is possible to modify Dylan so that it uses Bit Tables more extensively. See change.mps.epcore.brisling.160181 TEST1 and TEST2.

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