BIT TABLES
                             design.mps.bt
                               draft doc
                             drj 1997-03-04

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 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.


HISTORY

.history.0-3: The history for versions 0-3 is lost pending possible 
reconstruction.

.history.4: Prepared for review.  Added full requirements section.  Made 
notation more consistent throughout.  Documented all functions.  drj 1999-04-29


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).

[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.


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 (e.g. 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.


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.




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.


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.


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.


INTERFACE

.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, base, which specifies the beginning of 
the range, must be in the interval [0,n), 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.

.if.create:
Res BTCreate(BT *btReturn, Arena arena, Count n)

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.

.if.destroy:
void BTDestroy(BT t, Arena arena, Count n);

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


.if.size:
size_t BTSize(Count n);

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.

.if.get:
int BTGet(BT t, Index i);

BTGet(t, i) returns the ith bit of the table t (i.e. the image of i under the 
mapping).  Meets .req.ops.get.

.if.set:
void BTSet(BT t, Index i);

BTSet(t, i) sets the ith bit of the table t (to 1).  BTGet(t, i) will now 
return 1.  Meets .req.ops.set.

.if.res:
void BTRes(BT t, Index i);

BTRes(t, i) resets the ith bit of the table t (to 0).  BTGet(t, i) will now 
return 0.  Meets .req.ops.res.

.if.set-range:
void BTSetRange(BT t, Index base, Index limit);

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.

.if.res-range:
void BTResRange(BT t, Index base, Index limit);

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.

.if.test.range.set:
Bool BTIsSetRange(BT bt, Index base, Index limit);

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

.if.test.range.reset:
Bool BTIsResRange(BT bt, Index base, Index limit);

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

.if.test.range.same: 
Bool BTRangesSame(BT BTx, BT BTy, Index base, Index limit);

returns TRUE if BTGet(BTx,i) equals BTGet(BTy,i) for i in [base, limit), and 
false otherwise.  Meets .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);

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, 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).

.if.find-short-res-range:
Bool BTFindShortResRange(Index *baseReturn, Index *limitReturn,
                         BT bt,
                         Index searchBase, Index searchLimit,
                         Count length);

BTFindShortResRange(&base, &limit, table, searchBase, searchLimit, length) 
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).

.if.find-short-res-range-high:
Bool BTFindShortResRangeHigh(Index *baseReturn, Index *limitReturn,
                             BT bt,
                             Index searchBase, Index searchLimit,
                             Count length);

BTFindShortResRangeHigh(&base, &limit, table, searchBase, searchLimit, length) 
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.

.if.find-long-res-range:
Bool BTFindLongResRange(Index *baseReturn, Index *limitReturn,
                        BT bt,
                        Index searchBase, Index searchLimit,
                        Count length);

BTFindLongResRange(&base, &limit, table, searchBase, searchLimit, length) 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).

.if.find-long-res-range-high:
Bool BTFindLongResRangeHigh(Index *baseReturn, Index *limitReturn,
                            BT bt,
                            Index searchBase, Index searchLimit,
                            Count length);

BTFindLongResRangeHigh(&base, &limit, table, searchBase, searchLimit, length) 
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).

.if.copy-range:
extern void BTCopyRange(BT fromBT, BT toBT, Index base, Index limit);

overwrites the ith bit of toBT with the ith bit of fromBT, for all i in [base, 
limit).  Meets .req.ops.copy.simple.

.if.copy-offset-range:
extern void BTCopyOffsetRange(BT fromBT, BT toBT, Index fromBase, Index 
fromLimit, Index toBase, Index toLimit);

overwrites the ith bit of toBT with the jth bit of fromBT, for all i in [toBase,
toLimit) and corresponding j in [fromBase, fromLimit).  Each of these 2 
ranges must be the same size. This might be significantly less efficient than 
BTCopyRange. Meets .req.ops.copy.offset.

.if.copy-invert-range:
extern void BTCopyInvertRange(BT fromBT, BT toBT, Index base, Index limit);

overwrites the ith bit of toBT with the inverse of the ith bit of fromBT, for 
all i in [base, limit).  Meets .req.ops.copy.invert.


DETAILED DESIGN


DataStructures

.datastructure: Bit Tables will be represented as (a pointer to) an array of 
Words.  A plain array is used instead of the more usual design convention of 
implementing an ADT as a structure with a signature etc (see 
guide.impl.c.adt(0)).  .datastructure.words.justify: Words are used as these 
will probably map to the object that can be most efficiently accessed on any 
particular platform.  .datastructure.non-adt.justify: The usual ADT conventions 
are not followed because a) The initial design (drj) was lazy, b) 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 ADT style.


Functions

.fun.size: BTSize.
Since Bit Tables are an array of Words, 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); }

.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 & 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, word_action).
  
  base, 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 macro must not use 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 & 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 parameter (wordIndex) where wordIndex is 
the index of the whole-word in the array.  The macro must not use break or 
continue because it will be called from within a loop from the expansion of 
ACT_ON_RANGE.

.iteration.exit: The code in the single_action, bits_action, and word_action 
macros is allowed to use 'return' or 'goto' to terminate the iteration early.  
This is used by the test (.fun.test.*) 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 ORed into the relevant word 
(thereby setting a single bit).  For BTRes the mask is inverted and ANDed 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 
& 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, 
BTFindResRangeHigh.   BTFindResRange and BTFindResRangeHigh both have the 
following prototype (with a different name obviously):

Bool BTFindResRange(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* maxLength is equal 
to minLength when passed; for BTFindLong* maxLength is equal to the maximum 
possible range (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 (reference please?) is used (it's 
particularly easy 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 & ACT_ON_RANGE_HIGH macros 
using of '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
e.g. lookup tables.

.fun.find-res-range.improve.lookup: When testing a candidate run,
examine multiple bits at once (e.g. 8), using lookup tables for (e.g)
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.


TESTING

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

.test.btcv: MMsrc!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: MMsrc!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: MMsrc!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.