Intervals over a finite field. More...

#include <Intervals.h>

Classes
struct	Hash

Public Types
enum class	Type : std::uint8_t { TypeA = 0 , TypeB , TypeC , TypeF , Empty , Degenerate , Entire }

Public Member Functions
	Interval ()
	To satisfy the dataflow::ScalarLatticeValue requirements, this class must be default initializable.
UnreducedInterval	toUnreduced () const
	Convert to an UnreducedInterval.
UnreducedInterval	firstUnreduced () const
	Get the first side of the interval for TypeF intervals, otherwise just get the full interval as an UnreducedInterval (with toUnreduced).
UnreducedInterval	secondUnreduced () const
	Get the second side of the interval for TypeA, TypeB, and TypeC intervals.
Interval	join (const Interval &rhs) const
	Union.
Interval	intersect (const Interval &rhs) const
	Intersect.
Interval	difference (const Interval &other) const
	Computes and returns this - (this & other) if the operation produces a single interval.
Interval	operator- () const
Interval	operator~ () const
bool	isEmpty () const
bool	isNotEmpty () const
bool	isDegenerate () const
bool	isEntire () const
bool	isTypeA () const
bool	isTypeB () const
bool	isTypeC () const
bool	isTypeF () const
bool	isBoolFalse () const
bool	isBoolTrue () const
bool	isBoolEither () const
bool	isBoolean () const
template<Type... Types>
bool	is () const
bool	operator== (const Interval &rhs) const
const Field &	getField () const
llvm::DynamicAPInt	width () const
llvm::DynamicAPInt	lhs () const
llvm::DynamicAPInt	rhs () const
void	print (llvm::raw_ostream &os) const

Static Public Member Functions
static std::string_view	TypeName (Type t)
static Interval	Empty (const Field &f)
static Interval	Degenerate (const Field &f, const llvm::DynamicAPInt &val)
static Interval	False (const Field &f)
static Interval	True (const Field &f)
static Interval	Boolean (const Field &f)
static Interval	Entire (const Field &f)
static Interval	TypeA (const Field &f, const llvm::DynamicAPInt &a, const llvm::DynamicAPInt &b)
static Interval	TypeB (const Field &f, const llvm::DynamicAPInt &a, const llvm::DynamicAPInt &b)
static Interval	TypeC (const Field &f, const llvm::DynamicAPInt &a, const llvm::DynamicAPInt &b)
static Interval	TypeF (const Field &f, const llvm::DynamicAPInt &a, const llvm::DynamicAPInt &b)
template<std::pair< Type, Type >... Pairs>
static bool	areOneOf (const Interval &a, const Interval &b)

Static Public Attributes
static constexpr std::array< std::string_view, 7 >	TypeNames

Friends
Interval	operator+ (const Interval &lhs, const Interval &rhs)
Interval	operator- (const Interval &lhs, const Interval &rhs)
Interval	operator* (const Interval &lhs, const Interval &rhs)
Interval	operator% (const Interval &lhs, const Interval &rhs)
Interval	operator& (const Interval &lhs, const Interval &rhs)
Interval	operator\| (const Interval &lhs, const Interval &rhs)
	Perform a bitwise OR between the two intervals.
Interval	operator^ (const Interval &lhs, const Interval &rhs)
	Perform a bitwise XOR between the two intervals.
Interval	operator<< (const Interval &lhs, const Interval &rhs)
Interval	operator>> (const Interval &lhs, const Interval &rhs)
Interval	boolAnd (const Interval &lhs, const Interval &rhs)
Interval	boolOr (const Interval &lhs, const Interval &rhs)
Interval	boolXor (const Interval &lhs, const Interval &rhs)
Interval	boolNot (const Interval &iv)
llvm::raw_ostream &	operator<< (llvm::raw_ostream &os, const Interval &i)

Detailed Description

Intervals over a finite field.

Based on the Picus implementation. An interval may be:

Empty
Entire (meaning any value across the entire field)
Degenerate (meaning it contains a single value)
Or Type A–F. For these types, refer to the below notes:

A range [a, b] can be split into 2 categories:

Internal: a <= b
External: a > b – equivalent to [a, p-1] U [0, b]

Internal range can be further split into 3 categories: (A) a, b < p/2. E.g., [10, 12] (B) a, b > p/2. OR: a, b \in {-p/2, 0}. E.g., [p-4, p-2] === [-4, -2] (C) a < p/2, b > p/2. E.g., [p/2 - 5, p/2 + 5]

External range can be further split into 3 categories: (D) a, b < p/2. OR: a \in {-p, -p/2}, b \in {0, p/2}. E.g., [12, 10] === [-p+12, 10] (E) a, b > p/2. OR: a \in {-p/2, 0} , b \in {p/2, p}. E.g., [p-2, p-4] === [-2, p-4] (F) a > p/2, b < p/2. OR: a \in {-p/2, 0} , b \in {0, p/2}. E.g., [p/2 + 5, p/2 - 5] === [-p/2 + 5, p/2 - 5]

<-------------------------------------------------------------> -p -p/2 0 p/2 p [ A ] [ A ] [ B ] [ B ] [ C ] [ C ] F ] [ F ] [ F <------------------------------------------------------------->

D ] [ D ] [ D E ] [ E ] [ E

For the sake of simplicity, let's just not care about D and E, which covers at least half of the field, and potentially more.

Now, there are 4 choose 2 possible non-self interactions:

A acts on B:

intersection: impossible
union: C or F

A acts on C:

intersection: A
union: C

A acts on F:

intersection: A
union: F

B acts on C

intersection: B
union: C

B acts on F:

intersection: B
union: F

C acts on F:

intersection: A, B, C, F

E.g. [p/2 - 10, p/2 + 10] intersects [-p/2 + 2, p/2 - 2]

= ((-p/2 - 10, -p/2 + 10) intersects (-p/2 + 2, p/2 - 2)) union (( p/2 - 10, p/2 + 10) intersects (-p/2 + 2, p/2 - 2))

= (-p/2 + 2, -p/2 + 10) union (p/2 - 10, p/2 - 2)
union: don't care for now, we can revisit this later.

Definition at line 206 of file Intervals.h.

Member Enumeration Documentation

◆ Type

enum class llzk::Interval::Type : std::uint8_t

strong

Enumerator
TypeA
TypeB
TypeC
TypeF
Empty
Degenerate
Entire

Definition at line 208 of file Intervals.h.

Constructor & Destructor Documentation

◆ Interval()

llzk::Interval::Interval ( )

inline

To satisfy the dataflow::ScalarLatticeValue requirements, this class must be default initializable.

The default interval is the full range of values.

Definition at line 249 of file Intervals.h.

Member Function Documentation

◆ areOneOf()

template<std::pair< Type, Type >... Pairs>

bool llzk::Interval::areOneOf	(	const Interval &	a,
		const Interval &	b )

inlinestatic

Definition at line 263 of file Intervals.h.

◆ Boolean()

Interval llzk::Interval::Boolean ( const Field & f )

inlinestatic

Definition at line 227 of file Intervals.h.

◆ Degenerate()

Interval llzk::Interval::Degenerate	(	const Field &	f,
		const llvm::DynamicAPInt &	val )

inlinestatic

Definition at line 219 of file Intervals.h.

◆ difference()

Interval llzk::Interval::difference ( const Interval & other ) const

Computes and returns this - (this & other) if the operation produces a single interval.

Note that this is an interval difference, not a subtraction operation like the operator- below.

For example, given *this = [1, 10] and other = [5, 11], this function would return [1, 4], as this & other (the intersection) = [5, 10], so [1, 10] - [5, 10] = [1, 4].

For example, given *this = [1, 10] and other = [5, 6], this function should return [1, 4] and [7, 10], but we don't support having multiple disjoint intervals, so this is returned as-is.

Definition at line 388 of file Intervals.cpp.

◆ Empty()

Interval llzk::Interval::Empty ( const Field & f )

inlinestatic

Definition at line 217 of file Intervals.h.

◆ Entire()

Interval llzk::Interval::Entire ( const Field & f )

inlinestatic

Definition at line 229 of file Intervals.h.

◆ False()

Interval llzk::Interval::False ( const Field & f )

inlinestatic

Definition at line 223 of file Intervals.h.

◆ firstUnreduced()

UnreducedInterval llzk::Interval::firstUnreduced ( ) const

Get the first side of the interval for TypeF intervals, otherwise just get the full interval as an UnreducedInterval (with toUnreduced).

Definition at line 245 of file Intervals.cpp.

◆ getField()

const Field & llzk::Interval::getField ( ) const

inline

Definition at line 334 of file Intervals.h.

◆ intersect()

Interval llzk::Interval::intersect ( const Interval & rhs ) const

Intersect.

Definition at line 315 of file Intervals.cpp.

◆ is()

template<Type... Types>

bool llzk::Interval::is ( ) const

inline

Definition at line 328 of file Intervals.h.

◆ isBoolean()

bool llzk::Interval::isBoolean ( ) const

inline

Definition at line 326 of file Intervals.h.

◆ isBoolEither()

bool llzk::Interval::isBoolEither ( ) const

inline

Definition at line 325 of file Intervals.h.

◆ isBoolFalse()

bool llzk::Interval::isBoolFalse ( ) const

inline

Definition at line 323 of file Intervals.h.

◆ isBoolTrue()

bool llzk::Interval::isBoolTrue ( ) const

inline

Definition at line 324 of file Intervals.h.

◆ isDegenerate()

bool llzk::Interval::isDegenerate ( ) const

inline

Definition at line 316 of file Intervals.h.

◆ isEmpty()

bool llzk::Interval::isEmpty ( ) const

inline

Definition at line 314 of file Intervals.h.

◆ isEntire()

bool llzk::Interval::isEntire ( ) const

inline

Definition at line 317 of file Intervals.h.

◆ isNotEmpty()

bool llzk::Interval::isNotEmpty ( ) const

inline

Definition at line 315 of file Intervals.h.

◆ isTypeA()

bool llzk::Interval::isTypeA ( ) const

inline

Definition at line 318 of file Intervals.h.

◆ isTypeB()

bool llzk::Interval::isTypeB ( ) const

inline

Definition at line 319 of file Intervals.h.

◆ isTypeC()

bool llzk::Interval::isTypeC ( ) const

inline

Definition at line 320 of file Intervals.h.

◆ isTypeF()

bool llzk::Interval::isTypeF ( ) const

inline

Definition at line 321 of file Intervals.h.

◆ join()

Interval llzk::Interval::join ( const Interval & rhs ) const

Union.

Definition at line 257 of file Intervals.cpp.

◆ lhs()

llvm::DynamicAPInt llzk::Interval::lhs ( ) const

inline

Definition at line 338 of file Intervals.h.

◆ operator-()

Interval llzk::Interval::operator- ( ) const

Definition at line 450 of file Intervals.cpp.

◆ operator==()

bool llzk::Interval::operator== ( const Interval & rhs ) const

inline

Definition at line 330 of file Intervals.h.

◆ operator~()

Interval llzk::Interval::operator~ ( ) const

Definition at line 452 of file Intervals.cpp.

◆ print()

void llzk::Interval::print ( llvm::raw_ostream & os ) const

Definition at line 797 of file Intervals.cpp.

◆ rhs()

llvm::DynamicAPInt llzk::Interval::rhs ( ) const

inline

Definition at line 339 of file Intervals.h.

◆ secondUnreduced()

UnreducedInterval llzk::Interval::secondUnreduced ( ) const

Get the second side of the interval for TypeA, TypeB, and TypeC intervals.

Using this function is an error for all other interval types.

Definition at line 252 of file Intervals.cpp.

◆ toUnreduced()

UnreducedInterval llzk::Interval::toUnreduced ( ) const

Convert to an UnreducedInterval.

Definition at line 233 of file Intervals.cpp.

◆ True()

Interval llzk::Interval::True ( const Field & f )

inlinestatic

Definition at line 225 of file Intervals.h.

◆ TypeA()

Interval llzk::Interval::TypeA	(	const Field &	f,
		const llvm::DynamicAPInt &	a,
		const llvm::DynamicAPInt &	b )

inlinestatic

Definition at line 231 of file Intervals.h.

◆ TypeB()

Interval llzk::Interval::TypeB	(	const Field &	f,
		const llvm::DynamicAPInt &	a,
		const llvm::DynamicAPInt &	b )

inlinestatic

Definition at line 235 of file Intervals.h.

◆ TypeC()

Interval llzk::Interval::TypeC	(	const Field &	f,
		const llvm::DynamicAPInt &	a,
		const llvm::DynamicAPInt &	b )

inlinestatic

Definition at line 239 of file Intervals.h.

◆ TypeF()

Interval llzk::Interval::TypeF	(	const Field &	f,
		const llvm::DynamicAPInt &	a,
		const llvm::DynamicAPInt &	b )

inlinestatic

Definition at line 243 of file Intervals.h.

◆ TypeName()

std::string_view llzk::Interval::TypeName ( Type t )

inlinestatic

Definition at line 213 of file Intervals.h.

◆ width()

DynamicAPInt llzk::Interval::width ( ) const

Definition at line 710 of file Intervals.cpp.

◆ boolAnd

Interval boolAnd	(	const Interval &	lhs,
		const Interval &	rhs )

friend

Definition at line 723 of file Intervals.cpp.

◆ boolNot

Interval boolNot ( const Interval & iv )

friend

Definition at line 783 of file Intervals.cpp.

◆ boolOr

Interval boolOr	(	const Interval &	lhs,
		const Interval &	rhs )

friend

Definition at line 740 of file Intervals.cpp.

◆ boolXor

Interval boolXor	(	const Interval &	lhs,
		const Interval &	rhs )

friend

Definition at line 757 of file Intervals.cpp.

◆ operator%

Interval operator%	(	const Interval &	lhs,
		const Interval &	rhs )

friend

Definition at line 595 of file Intervals.cpp.

◆ operator&

Interval operator&	(	const Interval &	lhs,
		const Interval &	rhs )

friend

Definition at line 628 of file Intervals.cpp.

◆ operator*

Interval operator*	(	const Interval &	lhs,
		const Interval &	rhs )

friend

Definition at line 469 of file Intervals.cpp.

◆ operator+

Interval operator+	(	const Interval &	lhs,
		const Interval &	rhs )

friend

Definition at line 456 of file Intervals.cpp.

◆ operator-

Interval operator-	(	const Interval &	lhs,
		const Interval &	rhs )

friend

Definition at line 467 of file Intervals.cpp.

◆ operator<< [1/2]

Interval operator<<	(	const Interval &	lhs,
		const Interval &	rhs )

friend

Definition at line 679 of file Intervals.cpp.

◆ operator<< [2/2]

llvm::raw_ostream & operator<<	(	llvm::raw_ostream &	os,
		const Interval &	i )

friend

Definition at line 351 of file Intervals.h.

◆ operator>>

Interval operator>>	(	const Interval &	lhs,
		const Interval &	rhs )

friend

Definition at line 695 of file Intervals.cpp.

◆ operator^

Interval operator^	(	const Interval &	lhs,
		const Interval &	rhs )

friend

Perform a bitwise XOR between the two intervals.

This over-approximates for non-degenerate intervals on non-identity cases.

Definition at line 661 of file Intervals.cpp.

◆ operator|

Interval operator\|	(	const Interval &	lhs,
		const Interval &	rhs )

friend

Perform a bitwise OR between the two intervals.

This over-approximates for non-degenerate intervals on non-identity cases.

Definition at line 643 of file Intervals.cpp.

Member Data Documentation

◆ TypeNames

std::array<std::string_view, 7> llzk::Interval::TypeNames

staticconstexpr

Initial value:

= {"TypeA", "TypeB", "TypeC",
                                                                "TypeF", "Empty", "Degenerate",
                                                                "Entire"}

Definition at line 209 of file Intervals.h.

The documentation for this class was generated from the following files:

include/llzk/Analysis/Intervals.h
lib/Analysis/Intervals.cpp

Classes

Public Types

Public Member Functions

Static Public Member Functions

Static Public Attributes

Friends

Detailed Description

Member Enumeration Documentation

◆ Type

Constructor & Destructor Documentation

◆ Interval()

Member Function Documentation

◆ areOneOf()

◆ Boolean()

◆ Degenerate()

◆ difference()

◆ Empty()

◆ Entire()

◆ False()

◆ firstUnreduced()

◆ getField()

◆ intersect()

◆ is()

◆ isBoolean()

◆ isBoolEither()

◆ isBoolFalse()

◆ isBoolTrue()

◆ isDegenerate()

◆ isEmpty()

◆ isEntire()

◆ isNotEmpty()

◆ isTypeA()

◆ isTypeB()

◆ isTypeC()

◆ isTypeF()

◆ join()

◆ lhs()

◆ operator-()

◆ operator==()

◆ operator~()

◆ print()

◆ rhs()

◆ secondUnreduced()

◆ toUnreduced()

◆ True()

◆ TypeA()

◆ TypeB()

◆ TypeC()

◆ TypeF()

◆ TypeName()

◆ width()

Friends And Related Symbol Documentation

◆ boolAnd

◆ boolNot

◆ boolOr

◆ boolXor

◆ operator%

◆ operator&

◆ operator*

◆ operator+

◆ operator-

◆ operator<< [1/2]

◆ operator<< [2/2]

◆ operator>>

◆ operator^

◆ operator|

Member Data Documentation

◆ TypeNames