LichenDataStructure.Mesa
Last tweaked by Mike Spreitzer on February 2, 1988 11:57:11 am PST
DIRECTORY AbSets, Asserting, Basics, BasicTime, BiRels, CardHashTableThreaded, IntHashTable, RefTab, Rope, TextReplace;
LichenDataStructure: CEDAR DEFINITIONS
IMPORTS AbSets, BiRels, IntHashTable, RefTab
=
BEGIN OPEN Sets:AbSets;
nyet: ERROR --not yet implemented--;
Warning: SIGNAL [msg: ROPE, v1, v2, v3, v4, v5: REF ANYNIL];
Error: ERROR [msg: ROPE, v1, v2, v3, v4, v5: REF ANYNIL];
LNAT: TYPE ~ INT--[0 .. INT.LAST]--;
LORA: TYPE = LIST OF REF ANY;
LOLORA: TYPE = LIST OF LORA;
ROPE: TYPE = Rope.ROPE;
RopeList: TYPE = LIST OF ROPE;
LOR: TYPE ~ LIST OF ROPE;
LOLOR: TYPE ~ LIST OF LOR;
Assertions: TYPE = Asserting.Assertions;
Assertion: TYPE = Asserting.Assertion;
ColorTable: TYPE = CardHashTableThreaded.Table;
RopeMap: TYPE ~ TextReplace.RopeMap;
Time: TYPE ~ RECORD [BasicTime.GMT]; --so we can discriminate REFS to them; you can't discriminate REFS to opaque types, and BasicTime.GMT is opaque.
Set: TYPE ~ Sets.Set;
VarSet: TYPE ~ Sets.VarSet;
ConstSet: TYPE ~ Sets.ConstSet;
ConstFilter: TYPE ~ Sets.ConstFilter;
BiRel: TYPE ~ BiRels.BiRel;
VarBiRel: TYPE ~ BiRels.VarBiRel;
ConstBiRel: TYPE ~ BiRels.ConstBiRel;
Function: TYPE ~ BiRels.Function;
VarFunction: TYPE ~ BiRels.VarFunction;
UWFunction: TYPE ~ BiRels.UWFunction;
ConstFunction: TYPE ~ BiRels.ConstFunction;
InvFunction: TYPE ~ BiRels.InvFunction;
OneToOne: TYPE ~ BiRels.OneToOne;
VarOneToOne: TYPE ~ BiRels.VarOneToOne;
ConstOneToOne: TYPE ~ BiRels.ConstOneToOne;
IntFn: TYPE ~ BiRels.IntFn;
Permutation: TYPE ~ BiRels.Permutation;
AV: PROC [a: REF ANY] RETURNS [Sets.Value]
~ INLINE {RETURN [[ra: a]]};
IV: PROC [i: INT] RETURNS [Sets.Value]
~ INLINE {RETURN [[i: i]]};
RefTable: TYPE = RefTab.Ref;
CreateRefTable: PROC RETURNS [rt: RefTable]
= INLINE {rt ← RefTab.Create[]};
IntTable: TYPE = IntHashTable.Table;
CreateIntTable: PROC RETURNS [it: IntTable]
= INLINE {it ← IntHashTable.Create[]};
TList: TYPE ~ RECORD [head, tail: LORANIL];
Cat: PROC [a, b: TList] RETURNS [TList]
~ INLINE {IF a.head=NIL THEN RETURN [b] ELSE IF b.head=NIL THEN RETURN [a] ELSE {a.tail.rest ← b.head; RETURN [[a.head, b.tail]]}};
Prepend: PROC [l: TList, ra: REF ANY] RETURNS [l2: TList]
~ INLINE {l2.head ← CONS[ra, l.head]; l2.tail ← IF l.tail#NIL THEN l.tail ELSE l2.head};
Append: PROC [l: TList, ra: REF ANY] RETURNS [l2: TList]
~ INLINE {l2.tail ← LIST[ra]; IF l.head=NIL THEN l2.head ← l2.tail ELSE {l2.head ← l.head; l.tail.rest ← l2.tail}};
CopyTil: PROC [TList] RETURNS [TList];
Reln1Set: PROC [reln: REF ANY, assns: Assertions] RETURNS [Set];
TermsSet: PROC [reln: REF ANY, assns: Assertions] RETURNS [Set];
Reln2Reln: PROC [reln: REF ANY, assns: Assertions] RETURNS [BiRel];
GraphID: TYPE = {A, B, Unspecified};
RealGraphID: TYPE = GraphID[A .. B];
OtherGraph: ARRAY RealGraphID OF RealGraphID = [A: B, B: A];
graphIDToRope: GraphDescriptions;
GraphDescriptions: TYPE ~ ARRAY GraphID OF ROPE;
RealGraphDescriptions: TYPE ~ ARRAY RealGraphID OF ROPE;
Color: TYPE = INT;
noColor: Color = LAST[Color];
someColor: Color = 87654321H;
FilterColor: PROC [color: Color] RETURNS [filtered: Color] = INLINE {
filtered ← IF color # noColor THEN color ELSE someColor};
Design: TYPE = REF DesignPrivate;
DesignPrivate: TYPE = RECORD [
cellTypes: VarSet--of CellType--,
other: Assertions ← NIL,
allKnown: BOOLFALSE];
nameReln: ATOM; --relative to narrowest enclosing scope
Describe: PROC [subject: REF ANY, relativeTo: REF ANYNIL, nameGen: NameGenerator ← NIL] RETURNS [ROPE];
SteppyDescribe: PROC [subject: REF ANY, relativeTo: REF ANYNIL, nameGen: NameGenerator ← NIL] RETURNS [SteppyName];
NameGenerator: TYPE = REF NameGeneratorPrivate;
NameGeneratorPrivate: TYPE = RECORD [
GenerateName: PROC [data, subject: REF ANY] RETURNS [ROPE],
data: REF ANYNIL
];
EnumerateCellTypes: PROC [design: Design, Consume: PROC [CellType]];
CellClass: TYPE = REF CellClassPrivate;
CellClassPrivate: TYPE = RECORD [
DefinePrivates: PROC [CellType]
];
CellType: TYPE = REF CellTypePrivate;
CellTypePrivate: TYPE = RECORD [
class: CellClass,
designs: VarSet--of Design--,
inheritNames: BOOL --inherit names into me now, or later?--,
publicKnown, privateKnown: BOOLFALSE,
wasntNormalized: BOOLFALSE, --Leftover
port: Port ← NIL,
asUnorganized: Unorganized ← NIL,
asArray: Array ← NIL,
firstInstance, lastInstance: CellInstance ← NIL,
firstArray, lastArray: CellType ← NIL,
useCount: INT ← 0 --#instances + #arrays--,
otherPublic, otherPrivate: Assertions ← NIL,
color: Color ← noColor];
EnumeratePorts: PROC [cellType: CellType, Consume: PROC [Port]];
ScanPorts: PROC [cellType: CellType, Consume: PROC [Port] RETURNS [subs, sibs: BOOLTRUE]];
EnumerateInstances: PROC [cellType: CellType, Consume: PROC [CellInstance], mirror: BOOL];
EnumerateArrays: PROC [cellType: CellType, Consume: PROC [CellType]];
partsByNameKey: ATOM;
private CellType b VarFunction(ROPE b Vertex)
PortList: TYPE = LIST OF Port;
Port: TYPE = REF PortPrivate;
PortPrivate: TYPE = RECORD [
next, prev: Port,
firstChild, lastChild: Port,
parent: REF ANY--UNION [Port, CellType]--,
wire: Wire ← NIL,
names: ListData,
other: Assertions ← NIL,
color: Color ← noColor];
PortCCT: PROC [port: Port] RETURNS [containingCT: CellType];
PortSeqSize: PROC [Port] RETURNS [LNAT--number of leaves--];
FirstChildPort: PROC [port: Port] RETURNS [child: Port]
= INLINE {child ← port.firstChild};
NextChildPort: PROC [child: Port] RETURNS [sibling: Port]
= INLINE {sibling ← child.next};
EnumeratePort: PROC [port: Port, Consume: PROC [Port] RETURNS [doKids, moreSibs: BOOLTRUE]] RETURNS [didKids, moreSibs: BOOL];
PortIndex: PROC [child: Port] RETURNS [index: INT];
SubPort: PROC [parent: Port, index: INT] RETURNS [child: Port];
PortNames: PROC [port: Port] RETURNS [Set]
~ INLINE {RETURN [[listClass, AV[port.names]]]};
SteppyName: TYPE ~ RECORD [
steps: NameStepList,
grade: SteppyNameGrade];
SteppyNameList: TYPE ~ LIST OF SteppyName;
NameStepList: TYPE ~ LIST OF NameStep --most significant first--;
NameStep: TYPE ~ REF ANY --actually UNION [ROPE, REF INT]--;
SteppyNameGrade: TYPE ~ RECORD [
global: BOOL,
nonsubs: NATURAL,
gend: BOOL,
subs: NATURAL];
noGrade: SteppyNameGrade ~ [FALSE, 0, FALSE, 0];
noName: SteppyName ~ [NIL, noGrade];
noNameVal: Sets.Value ~ [NIL, LOOPHOLE[noGrade]];
SNCat: PROC [a, b: SteppyName] RETURNS [SteppyName];
SNPrepend: PROC [ns: NameStep, sn: SteppyName] RETURNS [SteppyName];
SNAppend: PROC [sn: SteppyName, ns: NameStep] RETURNS [SteppyName];
SnV: PROC [sn: SteppyName] RETURNS [Sets.Value]
~ INLINE {RETURN [[ra: sn.steps, i: LOOPHOLE[sn.grade]]]};
VSn: PROC [v: Sets.Value] RETURNS [SteppyName]
~ INLINE {RETURN [[steps: NARROW[v.ra], grade: LOOPHOLE[v.i]]]};
LSn: PROC [NameStepList] RETURNS [SteppyName];
nameStepSpace, steppyNameSpace: Sets.Space;
SteppyNameEqual: PROC [n1, n2: SteppyName, clip1, clip2: NameStepList ← NIL] RETURNS [BOOL];
portToInternalWire: READONLY UWFunction--port of an Unorganized CellType b its internal wire--;
Unorganized: TYPE = REF UnorganizedPrivate;
UnorganizedPrivate: TYPE = RECORD [
internalWire: Wire ← NIL,
containedInstances: VarSet--of CellInstance--,
mirror: CellInstance ← NIL --the outside world, as seen from the inside
AM1: A mirror is not entered in containedInstances.
AM2: A mirror is not counted as an instance of its type.
AM3: mirror.type = mirror.container
];
Vertex: TYPE = REF VertexPrivate;
VertexPrivate: TYPE = RECORD [
containingCT: CellType,
QNext: Vertex ← notInQ,
colorNext, equiv: Vertex ← NIL,
firstEdge, lastEdge: Edge ← NIL,
The connections to/from cells.
AI1: The edges are in the following order: first, the cellward ones, if any, in any order, then the wireward ones, ordered by port.
names: ListData,
other: Assertions ← NIL,
oldColor, curColor: Color ← noColor,
graph: GraphID ← Unspecified,
unique, suspect: BOOLFALSE,
variant: SELECT class: VertexClass FROM
cell => [
type: CellType ← NIL,
nextInstance, prevInstance: CellInstance ← NIL
],
intermediate => [
port: Port
],
wire => [
containingWire: Wire ← NIL,
next, prev: Wire ← NIL, --Siblings
firstChild, lastChild: Wire ← NIL
],
ENDCASE];
VertexClass: TYPE = {cell, intermediate, wire};
CellInstance: TYPE = REF cell VertexPrivate;
Intermediary: TYPE = REF intermediate VertexPrivate;
Wire: TYPE = REF wire VertexPrivate;
VertexNames: PROC [v: Vertex] RETURNS [Set]
~ INLINE {RETURN [[listClass, AV[v.names]]]};
WireIndex: PROC [parent, child: Wire] RETURNS [index: INT];
SubWire: PROC [parent: Wire, index: INT] RETURNS [child: Wire];
WireSeqSize: PROC [Wire] RETURNS [LNAT];
EnumeratePortAndWire: PROC [port: Port, wire: Wire, Consume: PROC [Port, Wire]];
EnumerateWire: PROC [wire: Wire, Consume: PROC [Wire] RETURNS [doKids, moreSibs: BOOLTRUE]] RETURNS [didKids, moreSibs: BOOL];
FirstChildWire: PROC [parent: Wire] RETURNS [child: Wire]
= INLINE {child ← parent.firstChild};
NextChildWire: PROC [child: Wire] RETURNS [sibling: Wire]
= INLINE {sibling ← child.next};
Edge: TYPE = REF EdgePrivate;
EdgePrivate: TYPE = RECORD [
sides: ARRAY GraphDirection OF RECORD [v: Vertex, next, prev: Edge],
port: Port --what the wireward vertex is connected to
];
GraphDirection: TYPE = {cellward, wireward};
OppositeDirection: ARRAY GraphDirection OF GraphDirection = [cellward: wireward, wireward: cellward];
notInQ: Vertex --don't look:-- = NIL --you looked!--;
endOfQ: Vertex;
SideFor: PROC [e: Edge, v: Vertex] RETURNS [side: GraphDirection]
~ INLINE {RETURN [SELECT v FROM e.sides[cellward].v => cellward, e.sides[wireward].v => wireward, ENDCASE => ERROR]};
EnumerateImmediateEdges: PROC [v: Vertex, Consume: PROC [Port, Vertex, Edge], filter: ARRAY GraphDirection OF BOOLALL[TRUE], order: Order ← any];
the Port is the wireward one.
ScanImmediateEdges: PROC [v: Vertex, Test: PROC [Port, Vertex, Edge] RETURNS [BOOL], filter: ARRAY GraphDirection OF BOOLALL[TRUE], order: Order ← any] RETURNS [BOOL];
EnumerateImmediateConnections: PROC [v: Vertex, Consume: PROC [Port, Vertex], filter: ARRAY GraphDirection OF BOOLALL[TRUE], order: Order ← any];
EnumerateTransitiveConnections: PROC [v: Vertex, Consume: PROC [Port, Vertex]];
EnumerateTopEdges: PROC [ci: CellInstance, Consume: PROC [Port, Wire, Edge]];
EnumerateTopConnections: PROC [ci: CellInstance, Consume: PROC [Port, Wire]];
EnumerateNeighboringVertices: PROC [v: Vertex, Consume: PROC [Vertex], filter: ARRAY GraphDirection OF BOOLALL[TRUE]];
FindImmediateConnection: PROC [cellward: Vertex, port: Port, hint: Order ← any] RETURNS [w: Vertex];
FindImmediateEdge: PROC [cellward: Vertex, port: Port, hint: Order ← any] RETURNS [w: Vertex, e: Edge];
FindTransitiveConnection: PROC [cellward: Vertex, from, to: Port] RETURNS [v: Vertex];
FindCellConnection: PROC [ci: CellInstance, port: Port] RETURNS [v: Vertex]
~ INLINE {RETURN FindTransitiveConnection[ci, ci.type.port, port]};
FindTopEdge: PROC [ci: CellInstance, port: Port] RETURNS [v: Vertex, e: Edge];
ImParent: PROC [im: Intermediary] RETURNS [v: Vertex];
EnumeratePortsForWire: PROC [w: Wire, Consume: PROC [Port--of container of w--]];
EnumerateParts: PROC [ct: CellType, Consume: PROC [Vertex], mirrorToo: BOOL];
ScanParts: PROC [ct: CellType, Test: Sets.Tester, filter: PartFilter, mirrorToo: BOOL] RETURNS [Sets.MaybeValue];
PartFilter: TYPE ~ PACKED ARRAY VertexClass OF BOOL;
Order: TYPE = {forward, backward, any};
Array: TYPE = REF ArrayPrivate;
ArrayPrivate: TYPE = RECORD [
eltType: CellType ← NIL,
nextArray, prevArray: CellType ← NIL,
size2: Size2 ← ALL[1],
size: NATURAL,
basePeriod: Nat2 ← ALL[1],
buildPhase: {buildingStatrep, statrepFixed} ← buildingStatrep,
dumrep: DumRep ← NIL,
statrep: StatRep ← NIL
];
DumRep: TYPE ~ REF DumRepPrivate;
DumRepPrivate: TYPE ~ RECORD [
topWires: Set--of TopDumbWire--,
epToTopWire: Function--elt port b RefSeq(CompositeArrayIndex b TopDumbWire)--,
apToWire: Function--array port b DumbWire--
];
DumbWire: TYPE ~ REF DumbWirePrivate;
DumbWireKind: TYPE ~ {top, child};
DumbWirePrivate: TYPE ~ RECORD [
children: Function--port b ChildDumbWire--,
variant: SELECT kind: DumbWireKind FROM
top => [eps: Function--elt port b BoolSeq(CompositeArrayIndex b member)--],
child => [parent: DumbWire, port: Port],
ENDCASE];
TopDumbWire: TYPE ~ REF DumbWirePrivate[top];
ChildDumbWire: TYPE ~ REF DumbWirePrivate[child];
StatRep: TYPE ~ REF StatRepPrivate;
StatRepPrivate: TYPE ~ RECORD [
edges: Set--of StatEdge--,
portEdge: ARRAY BOOL OF InvFunction--elt port ← StatEdge--,
apToPAI: Function--array port b PortAtIndex--
];
StatEdge: TYPE ~ REF StatEdgePrivate;
StatEdgePrivate: TYPE ~ RECORD [
vs: ARRAY BOOL OF StatVertex,
d: Int2];
StatVertex: TYPE ~ REF StatVertexPrivate;
StatVertexPrivate: TYPE ~ RECORD [port: Port, phase: Nat2];
PortAtIndex: TYPE ~ REF PortAtIndexPrivate;
PortAtIndexPrivate: TYPE ~ RECORD [port: Port, ai: ArrayIndex];
Dim--ension--: TYPE = {Foo, Bar};
OtherDim: ARRAY Dim OF Dim = [Foo: Bar, Bar: Foo];
Size2: TYPE = ARRAY Dim OF NATURAL;
Range: TYPE = RECORD [min, maxPlusOne: INT];
Range2: TYPE = ARRAY Dim OF Range;
Int2: TYPE = ARRAY Dim OF INT;
Nat2: TYPE = ARRAY Dim OF NATURAL;
Bool2: TYPE ~ ARRAY Dim OF BOOL;
ArrayIndex: TYPE = Int2;
PhaseIndex: TYPE ~ Int2;
CompositeArrayIndex: TYPE ~ NATURAL;
CompositePhaseIndex: TYPE ~ NATURAL;
nullAI: ArrayIndex ~ ALL[INT.FIRST];
PackedArrayIndex: TYPE [SIZE[INT]];
ListData: TYPE ~ RECORD [REF ANY];
noListData: ListData ~ [NIL];
listClass: Sets.SetClass;
CreateSteppyNames: PROC [names: SteppyNameList ← NIL] RETURNS [ListData];
Setify: PROC [l: ListData] RETURNS [Set] ~ INLINE {RETURN [[listClass, AV[l]]]};
SteppyNameGradeCompare: PROC [g1, g2: SteppyNameGrade] RETURNS [Basics.Comparison];
SteppyNamePartsCompare: PROC [l1, l2: NameStepList] RETURNS [Basics.Comparison];
Seq: TYPE ~ BiRels.Sequence;
CreateSeq: PROC [len: NATURAL ← 0, oneToOne, dense, domainFixed: BOOLFALSE] RETURNS [Seq]
~ INLINE {RETURN [BiRels.CreateVector[bounds: [0, len-1], val: Sets.noValue, oneToOne: oneToOne, dense: dense, domainFixed: domainFixed]]};
RefSeq: TYPE = REF RefSequence;
RefSequence: TYPE = RECORD [
elts: SEQUENCE length: NATURAL OF REF ANY];
CreateRefSeq: PROC [len: NATURAL] RETURNS [rs: RefSeq]
= INLINE {rs ← NEW [RefSequence[len]]};
VarRefSeq: TYPE = REF VarRefSequence;
VarRefSequence: TYPE = RECORD [
length: NATURAL,
refs: RefSeq];
CreateVarRefSeq: PROC [size: NATURAL ← 12] RETURNS [vrs: VarRefSeq]
= INLINE {vrs ← NEW [VarRefSequence ← [0, CreateRefSeq[size]]]};
VarRefSeqAppend: PROC [vrs: VarRefSeq, value: REF ANY];
Int2Seq: TYPE ~ REF Int2Sequence;
Int2Sequence: TYPE ~ RECORD [elts: SEQUENCE length: NATURAL OF Int2];
CreateInt2Seq: PROC [len: NATURAL, init: Int2] RETURNS [Int2Seq];
BoolSeq: TYPE = REF BoolSequence;
BoolSequence: TYPE = RECORD [elts: PACKED SEQUENCE length: NATURAL OF BOOL];
CreateBoolSeq: PROC [len: NATURAL, b0: BOOLFALSE] RETURNS [bs: BoolSeq]
= INLINE {bs ← NEW [BoolSequence[len]]; FOR i: NATURAL IN [0 .. len) DO bs[i] ← b0 ENDLOOP};
CopyBoolSeq: PROC [bs: BoolSeq] RETURNS [copy: BoolSeq]
~ INLINE {copy ← CreateBoolSeq[bs.length]; FOR i: NATURAL IN [0 .. copy.length) DO copy[i] ← bs[i] ENDLOOP};
NewInt: PROC [i: INT] RETURNS [REF INT];
Treat the result as a REF READONLY INT, or you'll be sorry!
FloorDiv: PROC [num, den: INT] RETURNS [INT] ~ INLINE {
IF den<0 THEN {num ← -num; den ← -den};
RETURN [IF num>=0 THEN (num/den) ELSE ((num-den+1)/den)]};
CeilDiv: PROC [num, den: INT] RETURNS [INT] ~ INLINE {
IF den<0 THEN {num ← -num; den ← -den};
RETURN [IF num>=0 THEN ((num+den-1)/den) ELSE (num/den)]};
ConsInt2: PROC [d1: Dim, x1, x2: INT] RETURNS [x: Int2]
= INLINE {x[d1] ← x1; x[OtherDim[d1]] ← x2};
Int2Neg: PROC [a: Int2] RETURNS [Int2]
~ INLINE {RETURN [[Foo: -a[Foo], Bar: -a[Bar]]]};
Int2Add: PROC [a, b: Int2] RETURNS [Int2]
= INLINE {RETURN [[Foo: a[Foo]+b[Foo], Bar: a[Bar]+b[Bar]]]};
Int2Sub: PROC [a, b: Int2] RETURNS [Int2]
= INLINE {RETURN [[Foo: a[Foo]-b[Foo], Bar: a[Bar]-b[Bar]]]};
Int2SubN: PROC [a, b: Int2] RETURNS [Nat2]
= INLINE {RETURN [[Foo: a[Foo]-b[Foo], Bar: a[Bar]-b[Bar]]]};
Int2InRange: PROC [i: Int2, r: Range2] RETURNS [in: BOOL]
= INLINE {in ← i[Foo] IN [r[Foo].min .. r[Foo].maxPlusOne) AND i[Bar] IN [r[Bar].min .. r[Bar].maxPlusOne)};
Int2Tweak: PROC [i: Int2, d: Dim, D: INT] RETURNS [j: Int2]
= INLINE {j ← i; j[d] ← j[d] + D};
Int2Mul: PROC [i: Int2, t, f: Nat2] RETURNS [m: Int2]
~ INLINE {RETURN [[Foo: i[Foo]*t[Foo]+f[Foo], Bar: i[Bar]*t[Bar]+f[Bar]]]};
Int2Scale: PROC [a: Int2, b: INT] RETURNS [Int2]
= INLINE {RETURN [[Foo: a[Foo]*b, Bar: a[Bar]*b]]};
Int2Dot: PROC [a, b: Int2] RETURNS [INT]
~ INLINE {RETURN [a[Foo]*b[Foo]+a[Bar]*b[Bar]]};
Int2Cross: PROC [a, b: Int2] RETURNS [INT]
~ INLINE {RETURN [a[Foo]*b[Bar]-a[Bar]*b[Foo]]};
Int2Mod: PROC [a: Int2, mod: Nat2] RETURNS [Nat2]
~ INLINE {RETURN [[
Foo: ((a[Foo] MOD mod[Foo])+mod[Foo]) MOD mod[Foo],
Bar: ((a[Bar] MOD mod[Bar])+mod[Bar]) MOD mod[Bar]]]};
ConsNat2: PROC [d1: Dim, x1, x2: NATURAL] RETURNS [x: Nat2]
= INLINE {x[d1] ← x1; x[OtherDim[d1]] ← x2};
WidenNat2: PROC [x: Nat2] RETURNS [Int2]
~ INLINE {RETURN [[Foo: x[Foo], Bar: x[Bar]]]};
NarrowInt2: PROC [x: Int2] RETURNS [Nat2]
~ INLINE {RETURN [[Foo: x[Foo], Bar: x[Bar]]]};
Nat2Add: PROC [a, b: Nat2] RETURNS [Nat2]
= INLINE {RETURN [[Foo: a[Foo]+b[Foo], Bar: a[Bar]+b[Bar]]]};
Nat2Sub: PROC [a, b: Nat2] RETURNS [Nat2]
= INLINE {RETURN [[Foo: a[Foo]-b[Foo], Bar: a[Bar]-b[Bar]]]};
Nat2Mul: PROC [a, b: Nat2] RETURNS [Nat2]
= INLINE {RETURN [[Foo: a[Foo]*b[Foo], Bar: a[Bar]*b[Bar]]]};
Nat2Div: PROC [a, b: Nat2] RETURNS [Nat2]
= INLINE {RETURN [[Foo: a[Foo]/b[Foo], Bar: a[Bar]/b[Bar]]]};
Nat2AddMod: PROC [a: Nat2, b: Int2, mod: Nat2] RETURNS [Nat2]
~ INLINE {RETURN [[
Foo: (a[Foo]+b[Foo]+mod[Foo]) MOD mod[Foo],
Bar: (a[Bar]+b[Bar]+mod[Bar]) MOD mod[Bar]]]};
Nat2Tweak: PROC [i: Nat2, d: Dim, D: INT] RETURNS [j: Nat2]
= INLINE {j ← i; j[d] ← j[d] + D};
Nat2Area: PROC [x: Nat2] RETURNS [NATURAL]
= INLINE {RETURN [x[Foo] * x[Bar]]};
RangeOff: PROC [r: Range, D: INT] RETURNS [Range]
= INLINE {RETURN[[min: r.min+D, maxPlusOne: r.maxPlusOne+D]]};
RangeOffClip: PROC [r: Range, D: INT] RETURNS [Range]
= INLINE {RETURN[[min: MAX[r.min+D, 0], maxPlusOne: r.maxPlusOne+D]]};
ShaveRange2Top1: PROC [r: Range2, d: Dim] RETURNS [sr: Range2]
= INLINE {sr ← r; sr[d].min ← MIN[sr[d].min, sr[d].maxPlusOne ← sr[d].maxPlusOne - 1]};
ConsRange2: PROC [d1: Dim, x1, x2: Range] RETURNS [x: Range2]
= INLINE {x[d1] ← x1; x[OtherDim[d1]] ← x2};
Range2Empty: PROC [r: Range2] RETURNS [BOOL]
= INLINE {RETURN [r[Foo].maxPlusOne<=r[Foo].min OR r[Bar].maxPlusOne<=r[Bar].min]};
Range2IsSingleton: PROC [r: Range2] RETURNS [BOOL]
= INLINE {RETURN [r[Foo].maxPlusOne=r[Foo].min+1 AND r[Bar].maxPlusOne=r[Bar].min+1]};
Range2Min: PROC [r2: Range2] RETURNS [Int2]
= INLINE {RETURN[[Foo: r2[Foo].min, Bar: r2[Bar].min]]};
Range2MinN: PROC [r2: Range2] RETURNS [Nat2]
= INLINE {RETURN[[Foo: r2[Foo].min, Bar: r2[Bar].min]]};
Range2Off: PROC [r: Range2, D: Int2] RETURNS [Range2]
= INLINE {RETURN[[Foo: RangeOff[r[Foo], D[Foo]], Bar: RangeOff[r[Bar], D[Bar]]]]};
Range2OffClip: PROC [r: Range2, D: Int2] RETURNS [Range2]
= INLINE {RETURN[[Foo: RangeOffClip[r[Foo], D[Foo]], Bar: RangeOffClip[r[Bar], D[Bar]]]]};
Range2Included: PROC [sub, in: Range2] RETURNS [BOOL]
~ INLINE {RETURN [RangeIncluded[sub[Foo], in[Foo]] AND RangeIncluded[sub[Bar], in[Bar]]]};
RangeIncluded: PROC [sub, in: Range] RETURNS [BOOL]
~ INLINE {RETURN [sub.min>=in.min AND sub.maxPlusOne<=in.maxPlusOne]};
Range2Intersection: PROC [a, b: Range2] RETURNS [Range2]
= INLINE {RETURN [[
Foo: [
min: MAX[a[Foo].min, b[Foo].min],
maxPlusOne: MIN[a[Foo].maxPlusOne, b[Foo].maxPlusOne]],
Bar: [
min: MAX[a[Bar].min, b[Bar].min],
maxPlusOne: MIN[a[Bar].maxPlusOne, b[Bar].maxPlusOne]]]]};
RangeArea: PROC [r: Range2] RETURNS [area: NATURAL]
= INLINE {area ← RangeLength[r[Foo]] * RangeLength[r[Bar]]};
RangeShape: PROC [r: Range2] RETURNS [shape: Nat2]
= INLINE {shape ← [RangeLength[r[Foo]], RangeLength[r[Bar]]]};
SizeRange: PROC [size: Nat2] RETURNS [r: Range2]
= INLINE {r ← [[0, size[Foo]], [0, size[Bar]]]};
RangeLength: PROC [r: Range] RETURNS [length: NATURAL]
= INLINE {length ← r.maxPlusOne - r.min};
Int2sRange: PROC [a, b: Int2] RETURNS [r: Range2]
~ INLINE {RETURN [[
Foo: [MIN[a[Foo], b[Foo]], MAX[a[Foo], b[Foo]]+1],
Bar: [MIN[a[Bar], b[Bar]], MAX[a[Bar], b[Bar]]+1]]]};
Range2Mbb: PROC [a, b: Range2] RETURNS [Range2]
~ INLINE {RETURN [[Foo: RangeMbb[a[Foo], b[Foo]], Bar: RangeMbb[a[Bar], b[Bar]]]]};
RangeMbb: PROC [a, b: Range] RETURNS [Range]
~ INLINE {RETURN [[min: MIN[a.min, b.min], maxPlusOne: MAX[a.maxPlusOne, b.maxPlusOne]]]};
Range2sIntersect: PROC [r1, r2: Range2] RETURNS [BOOL]
= INLINE {RETURN [RangesIntersect[r1[Foo], r2[Foo]] AND RangesIntersect[r1[Bar], r2[Bar]]]};
RangesIntersect: PROC [r1, r2: Range] RETURNS [BOOL]
= INLINE {RETURN [
(r1.min IN [r2.min .. r2.maxPlusOne) AND r1.maxPlusOne > r1.min) OR
(r2.min IN [r1.min .. r1.maxPlusOne) AND r2.maxPlusOne > r2.min)]};
Range2Div: PROC [r: Range2, t, f: Nat2] RETURNS [rr: Range2];
Range1Div: PROC [r: Range, t, f: NATURAL] RETURNS [rr: Range];
The range of i such that i*t+f is in r.
Range2MulA: PROC [r: Range2, t, f: Nat2] RETURNS [rr: Range2];
Range1MulA: PROC [r: Range, t, f: NATURAL] RETURNS [rr: Range];
rr.maxPlusOne-1 has given phase.
Range2MulB: PROC [r: Range2, t, f: Nat2] RETURNS [rr: Range2];
Range1MulB: PROC [r: Range, t, f: NATURAL] RETURNS [rr: Range];
rr.maxPlusOne has given phase.
Range2RoundA: PROC [r: Range2, t, f: Nat2] RETURNS [rr: Range2];
Range2RoundB: PROC [r: Range2, t, f: Nat2] RETURNS [rr: Range2];
FmtRange: PROC [r: Range] RETURNS [asRope: ROPE];
BeRope: PROC [r: ROPE] RETURNS [r2: ROPE] = INLINE {r2 ← r}--stupid goddam anachronism--;
END.