Simple representation of a scaled number. More...

#include "llvm/Support/ScaledNumber.h"

Inheritance diagram for llvm::ScaledNumber< DigitsT >:

Public Types
typedef DigitsT	DigitsType

Public Member Functions
	ScaledNumber ()=default

constexpr	ScaledNumber (DigitsType Digits, int16_t Scale)

int16_t	getScale () const

DigitsType	getDigits () const

template<class IntT >
IntT	toInt () const
	Convert to the given integer type.

bool	isZero () const

bool	isLargest () const

bool	isOne () const

int32_t	lg () const
	The log base 2, rounded.

int32_t	lgFloor () const
	The log base 2, rounded towards INT32_MIN.

int32_t	lgCeiling () const
	The log base 2, rounded towards INT32_MAX.

bool	operator== (const ScaledNumber &X) const

bool	operator< (const ScaledNumber &X) const

bool	operator!= (const ScaledNumber &X) const

bool	operator> (const ScaledNumber &X) const

bool	operator<= (const ScaledNumber &X) const

bool	operator>= (const ScaledNumber &X) const

bool	operator! () const

std::string	toString (unsigned Precision=DefaultPrecision)
	Convert to a decimal representation in a string.

raw_ostream &	print (raw_ostream &OS, unsigned Precision=DefaultPrecision) const
	Print a decimal representation.

void	dump () const

ScaledNumber &	operator+= (const ScaledNumber &X)

ScaledNumber &	operator-= (const ScaledNumber &X)

ScaledNumber &	operator*= (const ScaledNumber &X)

ScaledNumber &	operator/= (const ScaledNumber &X)

ScaledNumber &	operator<<= (int16_t Shift)

ScaledNumber &	operator>>= (int16_t Shift)

uint64_t	scale (uint64_t N) const
	Scale a large number accurately.

uint64_t	scaleByInverse (uint64_t N) const

int64_t	scale (int64_t N) const

int64_t	scaleByInverse (int64_t N) const

int	compare (const ScaledNumber &X) const

int	compareTo (uint64_t N) const

int	compareTo (int64_t N) const

ScaledNumber &	invert ()

ScaledNumber	inverse () const

Static Public Member Functions
static ScaledNumber	getZero ()

static ScaledNumber	getOne ()

static ScaledNumber	getLargest ()

static ScaledNumber	get (uint64_t N)

static ScaledNumber	getInverse (uint64_t N)

static ScaledNumber	getFraction (DigitsType N, DigitsType D)

Detailed Description

template<class DigitsT>
class llvm::ScaledNumber< DigitsT >

Simple representation of a scaled number.

ScaledNumber is a number represented by digits and a scale. It uses simple saturation arithmetic and every operation is well-defined for every value. It's somewhat similar in behaviour to a soft-float, but is not a replacement for one. If you're doing numerics, look at APFloat instead. Nevertheless, we've found these semantics useful for modelling certain cost metrics.

The number is split into a signed scale and unsigned digits. The number represented is getDigits()*2^getScale(). In this way, the digits are much like the mantissa in the x87 long double, but there is no canonical form so the same number can be represented by many bit representations.

ScaledNumber is templated on the underlying integer type for digits, which is expected to be unsigned.

Unlike APFloat, ScaledNumber does not model architecture floating point behaviour – while this might make it a little faster and easier to reason about, it certainly makes it more dangerous for general numerics.

ScaledNumber is totally ordered. However, there is no canonical form, so there are multiple representations of most scalars. E.g.:

ScaledNumber(8u, 0) == ScaledNumber(4u, 1)
ScaledNumber(4u, 1) == ScaledNumber(2u, 2)
ScaledNumber(2u, 2) == ScaledNumber(1u, 3)

ScaledNumber implements most arithmetic operations. Precision is kept where possible. Uses simple saturation arithmetic, so that operations saturate to 0.0 or getLargest() rather than under or overflowing. It has some extra arithmetic for unit inversion. 0.0/0.0 is defined to be 0.0. Any other division by 0.0 is defined to be getLargest().

As a convenience for modifying the exponent, left and right shifting are both implemented, and both interpret negative shifts as positive shifts in the opposite direction.

Scales are limited to the range accepted by x87 long double. This makes it trivial to add functionality to convert to APFloat (this is already relied on for the implementation of printing).

Possible (and conflicting) future directions:

Turn this into a wrapper around APFloat.
Share the algorithm implementations with APFloat.
Allow ScaledNumber to represent a signed number.

Definition at line 493 of file ScaledNumber.h.

Member Typedef Documentation

◆ DigitsType

template<class DigitsT >

typedef DigitsT llvm::ScaledNumber< DigitsT >::DigitsType

Definition at line 498 of file ScaledNumber.h.

Constructor & Destructor Documentation

◆ ScaledNumber() [1/2]

template<class DigitsT >

llvm::ScaledNumber< DigitsT >::ScaledNumber ( )

default

Referenced by llvm::ScaledNumber< DigitsT >::getLargest(), llvm::ScaledNumber< DigitsT >::getOne(), llvm::ScaledNumber< DigitsT >::getZero(), and llvm::ScaledNumber< DigitsT >::inverse().

◆ ScaledNumber() [2/2]

template<class DigitsT >

constexpr llvm::ScaledNumber< DigitsT >::ScaledNumber	(	DigitsType	Digits,
		int16_t	Scale
	)

inlineconstexpr

Definition at line 513 of file ScaledNumber.h.

Member Function Documentation

◆ compare()

template<class DigitsT >

int llvm::ScaledNumber< DigitsT >::compare ( const ScaledNumber< DigitsT > & X ) const

inline

Definition at line 669 of file ScaledNumber.h.

References llvm::ScaledNumbers::compare(), and X.

Referenced by llvm::ScaledNumber< DigitsT >::operator!=(), llvm::ScaledNumber< DigitsT >::operator<(), llvm::ScaledNumber< DigitsT >::operator<=(), llvm::ScaledNumber< DigitsT >::operator==(), llvm::ScaledNumber< DigitsT >::operator>(), and llvm::ScaledNumber< DigitsT >::operator>=().

◆ compareTo() [1/2]

template<class DigitsT >

int llvm::ScaledNumber< DigitsT >::compareTo ( int64_t N ) const

inline

Definition at line 675 of file ScaledNumber.h.

References llvm::ScaledNumber< DigitsT >::compareTo(), and N.

Referenced by llvm::ScaledNumber< DigitsT >::compareTo().

◆ compareTo() [2/2]

template<class DigitsT >

int llvm::ScaledNumber< DigitsT >::compareTo ( uint64_t N ) const

inline

Definition at line 672 of file ScaledNumber.h.

References N.

◆ dump()

template<class DigitsT >

void llvm::ScaledNumber< DigitsT >::dump ( ) const

inline

Definition at line 607 of file ScaledNumber.h.

References llvm::ScaledNumberBase::dump().

◆ get()

template<class DigitsT >

static ScaledNumber llvm::ScaledNumber< DigitsT >::get ( uint64_t N )

inlinestatic

Definition at line 526 of file ScaledNumber.h.

References N.

Referenced by llvm::ScaledNumber< DigitsT >::getInverse(), and llvm::ScaledNumber< DigitsT >::invert().

◆ getDigits()

template<class DigitsT >

DigitsType llvm::ScaledNumber< DigitsT >::getDigits ( ) const

inline

Definition at line 535 of file ScaledNumber.h.

◆ getFraction()

template<class DigitsT >

static ScaledNumber llvm::ScaledNumber< DigitsT >::getFraction	(	DigitsType	N,
		DigitsType	D
	)

inlinestatic

Definition at line 530 of file ScaledNumber.h.

References D, and N.

◆ getInverse()

template<class DigitsT >

static ScaledNumber llvm::ScaledNumber< DigitsT >::getInverse ( uint64_t N )

inlinestatic

Definition at line 527 of file ScaledNumber.h.

References llvm::ScaledNumber< DigitsT >::get(), llvm::ScaledNumber< DigitsT >::invert(), and N.

◆ getLargest()

template<class DigitsT >

static ScaledNumber llvm::ScaledNumber< DigitsT >::getLargest ( )

inlinestatic

Definition at line 523 of file ScaledNumber.h.

References llvm::ScaledNumbers::MaxScale, and llvm::ScaledNumber< DigitsT >::ScaledNumber().

Referenced by llvm::ScaledNumber< DigitsT >::isLargest(), and llvm::ScaledNumber< DigitsT >::operator+=().

◆ getOne()

template<class DigitsT >

static ScaledNumber llvm::ScaledNumber< DigitsT >::getOne ( )

inlinestatic

Definition at line 522 of file ScaledNumber.h.

References llvm::ScaledNumber< DigitsT >::ScaledNumber().

◆ getScale()

template<class DigitsT >

int16_t llvm::ScaledNumber< DigitsT >::getScale ( ) const

inline

Definition at line 534 of file ScaledNumber.h.

◆ getZero()

template<class DigitsT >

static ScaledNumber llvm::ScaledNumber< DigitsT >::getZero ( )

inlinestatic

Definition at line 521 of file ScaledNumber.h.

References llvm::ScaledNumber< DigitsT >::ScaledNumber().

◆ inverse()

template<class DigitsT >

ScaledNumber llvm::ScaledNumber< DigitsT >::inverse ( ) const

inline

Definition at line 678 of file ScaledNumber.h.

References llvm::ScaledNumber< DigitsT >::ScaledNumber().

Referenced by llvm::BlockFrequencyInfoImplBase::computeLoopScale(), and llvm::ScaledNumber< DigitsT >::scaleByInverse().

◆ invert()

template<class DigitsT >

ScaledNumber & llvm::ScaledNumber< DigitsT >::invert ( )

inline

Definition at line 677 of file ScaledNumber.h.

References llvm::ScaledNumber< DigitsT >::get().

Referenced by llvm::ScaledNumber< DigitsT >::getInverse().

◆ isLargest()

template<class DigitsT >

bool llvm::ScaledNumber< DigitsT >::isLargest ( ) const

inline

Definition at line 544 of file ScaledNumber.h.

References llvm::ScaledNumber< DigitsT >::getLargest().

◆ isOne()

template<class DigitsT >

bool llvm::ScaledNumber< DigitsT >::isOne ( ) const

inline

Definition at line 545 of file ScaledNumber.h.

◆ isZero()

template<class DigitsT >

bool llvm::ScaledNumber< DigitsT >::isZero ( ) const

inline

Definition at line 543 of file ScaledNumber.h.

Referenced by llvm::ScaledNumber< DigitsT >::operator!().

◆ lg()

template<class DigitsT >

int32_t llvm::ScaledNumber< DigitsT >::lg ( ) const

inline

The log base 2, rounded.

Get the lg of the scalar. lg 0 is defined to be INT32_MIN.

Definition at line 554 of file ScaledNumber.h.

References llvm::ScaledNumbers::getLg().

◆ lgCeiling()

template<class DigitsT >

int32_t llvm::ScaledNumber< DigitsT >::lgCeiling ( ) const

inline

The log base 2, rounded towards INT32_MAX.

Get the lg ceiling. lg 0 is defined to be INT32_MIN.

Definition at line 564 of file ScaledNumber.h.

References llvm::ScaledNumbers::getLgCeiling().

◆ lgFloor()

template<class DigitsT >

int32_t llvm::ScaledNumber< DigitsT >::lgFloor ( ) const

inline

The log base 2, rounded towards INT32_MIN.

Get the lg floor. lg 0 is defined to be INT32_MIN.

Definition at line 559 of file ScaledNumber.h.

References llvm::ScaledNumbers::getLgFloor().

◆ operator!()

template<class DigitsT >

bool llvm::ScaledNumber< DigitsT >::operator! ( ) const

inline

Definition at line 575 of file ScaledNumber.h.

References llvm::ScaledNumber< DigitsT >::isZero().

◆ operator!=()

template<class DigitsT >

bool llvm::ScaledNumber< DigitsT >::operator!= ( const ScaledNumber< DigitsT > & X ) const

inline

Definition at line 570 of file ScaledNumber.h.

References llvm::ScaledNumber< DigitsT >::compare(), and X.

◆ operator*=()

template<class DigitsT >

ScaledNumber< DigitsT > & llvm::ScaledNumber< DigitsT >::operator*= ( const ScaledNumber< DigitsT > & X )

Definition at line 801 of file ScaledNumber.h.

References isZero(), and X.

◆ operator+=()

template<class DigitsT >

ScaledNumber & llvm::ScaledNumber< DigitsT >::operator+= ( const ScaledNumber< DigitsT > & X )

inline

Definition at line 609 of file ScaledNumber.h.

References llvm::ScaledNumber< DigitsT >::getLargest(), llvm::ScaledNumbers::getSum(), llvm::ScaledNumbers::MaxScale, and X.

◆ operator-=()

template<class DigitsT >

ScaledNumber & llvm::ScaledNumber< DigitsT >::operator-= ( const ScaledNumber< DigitsT > & X )

inline

Definition at line 617 of file ScaledNumber.h.

References llvm::ScaledNumbers::getDifference(), and X.

◆ operator/=()

template<class DigitsT >

ScaledNumber< DigitsT > & llvm::ScaledNumber< DigitsT >::operator/= ( const ScaledNumber< DigitsT > & X )

Definition at line 818 of file ScaledNumber.h.

References isZero(), and X.

◆ operator<()

template<class DigitsT >

bool llvm::ScaledNumber< DigitsT >::operator< ( const ScaledNumber< DigitsT > & X ) const

inline

Definition at line 569 of file ScaledNumber.h.

References llvm::ScaledNumber< DigitsT >::compare(), and X.

◆ operator<<=()

template<class DigitsT >

ScaledNumber & llvm::ScaledNumber< DigitsT >::operator<<= ( int16_t Shift )

inline

Definition at line 624 of file ScaledNumber.h.

◆ operator<=()

template<class DigitsT >

bool llvm::ScaledNumber< DigitsT >::operator<= ( const ScaledNumber< DigitsT > & X ) const

inline

Definition at line 572 of file ScaledNumber.h.

References llvm::ScaledNumber< DigitsT >::compare(), and X.

◆ operator==()

template<class DigitsT >

bool llvm::ScaledNumber< DigitsT >::operator== ( const ScaledNumber< DigitsT > & X ) const

inline

Definition at line 568 of file ScaledNumber.h.

References llvm::ScaledNumber< DigitsT >::compare(), and X.

◆ operator>()

template<class DigitsT >

bool llvm::ScaledNumber< DigitsT >::operator> ( const ScaledNumber< DigitsT > & X ) const

inline

Definition at line 571 of file ScaledNumber.h.

References llvm::ScaledNumber< DigitsT >::compare(), and X.

◆ operator>=()

template<class DigitsT >

bool llvm::ScaledNumber< DigitsT >::operator>= ( const ScaledNumber< DigitsT > & X ) const

inline

Definition at line 573 of file ScaledNumber.h.

References llvm::ScaledNumber< DigitsT >::compare(), and X.

◆ operator>>=()

template<class DigitsT >

ScaledNumber & llvm::ScaledNumber< DigitsT >::operator>>= ( int16_t Shift )

inline

Definition at line 628 of file ScaledNumber.h.

◆ print()

template<class DigitsT >

raw_ostream & llvm::ScaledNumber< DigitsT >::print	(	raw_ostream &	OS,
		unsigned	Precision = `DefaultPrecision`
	)		const

inline

Print a decimal representation.

Print a string. See toString for documentation.

Definition at line 603 of file ScaledNumber.h.

References OS, and llvm::ScaledNumberBase::print().

◆ scale() [1/2]

template<class DigitsT >

int64_t llvm::ScaledNumber< DigitsT >::scale ( int64_t N ) const

inline

Definition at line 660 of file ScaledNumber.h.

References llvm::ScaledNumberBase::joinSigned(), N, llvm::ScaledNumber< DigitsT >::scale(), llvm::ScaledNumberBase::splitSigned(), and Unsigned.

◆ scale() [2/2]

template<class DigitsT >

uint64_t llvm::ScaledNumber< DigitsT >::scale ( uint64_t N ) const

Scale a large number accurately.

Scale N (multiply it by this). Uses full precision multiplication, even if Width is smaller than 64, so information is not lost.

Definition at line 771 of file ScaledNumber.h.

References llvm::get(), N, and llvm::ScaledNumber< DigitsT >::scale().

Referenced by llvm::ScaledNumber< DigitsT >::scale(), and llvm::ScaledNumber< DigitsT >::scaleByInverse().

◆ scaleByInverse() [1/2]

template<class DigitsT >

int64_t llvm::ScaledNumber< DigitsT >::scaleByInverse ( int64_t N ) const

inline

Definition at line 664 of file ScaledNumber.h.

References llvm::ScaledNumberBase::joinSigned(), N, llvm::ScaledNumber< DigitsT >::scaleByInverse(), llvm::ScaledNumberBase::splitSigned(), and Unsigned.

◆ scaleByInverse() [2/2]

template<class DigitsT >

uint64_t llvm::ScaledNumber< DigitsT >::scaleByInverse ( uint64_t N ) const

inline

Definition at line 655 of file ScaledNumber.h.

References llvm::ScaledNumber< DigitsT >::inverse(), N, and llvm::ScaledNumber< DigitsT >::scale().

Referenced by llvm::ScaledNumber< DigitsT >::scaleByInverse().

◆ toInt()

template<class DigitsT >

template<class IntT >

IntT llvm::ScaledNumber< DigitsT >::toInt

Convert to the given integer type.

Convert to IntT using simple saturating arithmetic, truncating if necessary.

Definition at line 781 of file ScaledNumber.h.

References assert(), and N.

◆ toString()

template<class DigitsT >

std::string llvm::ScaledNumber< DigitsT >::toString ( unsigned Precision = DefaultPrecision )

inline

Convert to a decimal representation in a string.

Convert to a string. Uses scientific notation for very large/small numbers. Scientific notation is used roughly for numbers outside of the range 2^-64 through 2^64.

Precision indicates the number of decimal digits of precision to use; 0 requests the maximum available.

As a special case to make debugging easier, if the number is small enough to convert without scientific notation and has more than Precision digits before the decimal place, it's printed accurately to the first digit past zero. E.g., assuming 10 digits of precision:

98765432198.7654... => 98765432198.8
 8765432198.7654... =>  8765432198.8
  765432198.7654... =>   765432198.8
   65432198.7654... =>    65432198.77
    5432198.7654... =>     5432198.765

Definition at line 596 of file ScaledNumber.h.

References llvm::ScaledNumberBase::toString().

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

include/llvm/Support/ScaledNumber.h

Public Types

Public Member Functions

Static Public Member Functions

Detailed Description

Member Typedef Documentation

◆ DigitsType

Constructor & Destructor Documentation

◆ ScaledNumber() [1/2]

◆ ScaledNumber() [2/2]

Member Function Documentation

◆ compare()

◆ compareTo() [1/2]

◆ compareTo() [2/2]

◆ dump()

◆ get()

◆ getDigits()

◆ getFraction()

◆ getInverse()

◆ getLargest()

◆ getOne()

◆ getScale()

◆ getZero()

◆ inverse()

◆ invert()

◆ isLargest()

◆ isOne()

◆ isZero()

◆ lg()

◆ lgCeiling()

◆ lgFloor()

◆ operator!()

◆ operator!=()

◆ operator*=()

◆ operator+=()

◆ operator-=()

◆ operator/=()

◆ operator<()

◆ operator<<=()

◆ operator<=()

◆ operator==()

◆ operator>()

◆ operator>=()

◆ operator>>=()

◆ print()

◆ scale() [1/2]

◆ scale() [2/2]

◆ scaleByInverse() [1/2]

◆ scaleByInverse() [2/2]

◆ toInt()

◆ toString()