LLVM  9.0.0svn
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llvm::ScaledNumber< DigitsT > Class Template Reference

Simple representation of a scaled number. More...

#include "llvm/Support/ScaledNumber.h"

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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. More...
 
bool isZero () const
 
bool isLargest () const
 
bool isOne () const
 
int32_t lg () const
 The log base 2, rounded. More...
 
int32_t lgFloor () const
 The log base 2, rounded towards INT32_MIN. More...
 
int32_t lgCeiling () const
 The log base 2, rounded towards INT32_MAX. More...
 
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. More...
 
raw_ostreamprint (raw_ostream &OS, unsigned Precision=DefaultPrecision) const
 Print a decimal representation. More...
 
void dump () const
 
ScaledNumberoperator+= (const ScaledNumber &X)
 
ScaledNumberoperator-= (const ScaledNumber &X)
 
ScaledNumberoperator*= (const ScaledNumber &X)
 
ScaledNumberoperator/= (const ScaledNumber &X)
 
ScaledNumberoperator<<= (int16_t Shift)
 
ScaledNumberoperator>>= (int16_t Shift)
 
uint64_t scale (uint64_t N) const
 Scale a large number accurately. More...
 
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
 
ScaledNumberinvert ()
 
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:

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

Definition at line 492 of file ScaledNumber.h.

Member Typedef Documentation

◆ DigitsType

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

Definition at line 495 of file ScaledNumber.h.

Constructor & Destructor Documentation

◆ ScaledNumber() [1/2]

template<class DigitsT>
llvm::ScaledNumber< DigitsT >::ScaledNumber ( )
default

◆ ScaledNumber() [2/2]

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

Definition at line 512 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 668 of file ScaledNumber.h.

◆ compareTo() [1/2]

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

Definition at line 671 of file ScaledNumber.h.

◆ compareTo() [2/2]

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

Definition at line 674 of file ScaledNumber.h.

Referenced by llvm::ScaledNumber< uint64_t >::compareTo().

◆ dump()

template<class DigitsT>
void llvm::ScaledNumber< DigitsT >::dump ( ) const
inline

Definition at line 606 of file ScaledNumber.h.

◆ get()

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

Definition at line 525 of file ScaledNumber.h.

Referenced by llvm::ScaledNumber< uint64_t >::invert().

◆ getDigits()

template<class DigitsT>
DigitsType llvm::ScaledNumber< DigitsT >::getDigits ( ) const
inline

Definition at line 534 of file ScaledNumber.h.

◆ getFraction()

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

Definition at line 529 of file ScaledNumber.h.

◆ getInverse()

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

Definition at line 526 of file ScaledNumber.h.

◆ getLargest()

template<class DigitsT>
static ScaledNumber llvm::ScaledNumber< DigitsT >::getLargest ( )
inlinestatic

Definition at line 522 of file ScaledNumber.h.

◆ getOne()

template<class DigitsT>
static ScaledNumber llvm::ScaledNumber< DigitsT >::getOne ( )
inlinestatic

Definition at line 521 of file ScaledNumber.h.

◆ getScale()

template<class DigitsT>
int16_t llvm::ScaledNumber< DigitsT >::getScale ( ) const
inline

Definition at line 533 of file ScaledNumber.h.

◆ getZero()

template<class DigitsT>
static ScaledNumber llvm::ScaledNumber< DigitsT >::getZero ( )
inlinestatic

Definition at line 520 of file ScaledNumber.h.

◆ inverse()

template<class DigitsT>
ScaledNumber llvm::ScaledNumber< DigitsT >::inverse ( ) const
inline

◆ invert()

template<class DigitsT>
ScaledNumber& llvm::ScaledNumber< DigitsT >::invert ( )
inline

Definition at line 676 of file ScaledNumber.h.

Referenced by llvm::ScaledNumber< uint64_t >::inverse().

◆ isLargest()

template<class DigitsT>
bool llvm::ScaledNumber< DigitsT >::isLargest ( ) const
inline

Definition at line 543 of file ScaledNumber.h.

Referenced by llvm::ScaledNumber< uint64_t >::inverse().

◆ isOne()

template<class DigitsT>
bool llvm::ScaledNumber< DigitsT >::isOne ( ) const
inline

Definition at line 544 of file ScaledNumber.h.

◆ isZero()

template<class DigitsT>
bool llvm::ScaledNumber< DigitsT >::isZero ( ) const
inline

◆ 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 553 of file ScaledNumber.h.

◆ 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 563 of file ScaledNumber.h.

◆ 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 558 of file ScaledNumber.h.

◆ operator!()

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

Definition at line 574 of file ScaledNumber.h.

◆ operator!=()

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

Definition at line 569 of file ScaledNumber.h.

◆ operator*=()

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

Definition at line 801 of file ScaledNumber.h.

Referenced by llvm::ScaledNumber< uint64_t >::toInt().

◆ operator+=()

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

Definition at line 608 of file ScaledNumber.h.

◆ operator-=()

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

Definition at line 616 of file ScaledNumber.h.

◆ operator/=()

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

Definition at line 818 of file ScaledNumber.h.

Referenced by llvm::ScaledNumber< uint64_t >::operator*=().

◆ operator<()

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

Definition at line 568 of file ScaledNumber.h.

◆ operator<<=()

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

Definition at line 623 of file ScaledNumber.h.

◆ operator<=()

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

Definition at line 571 of file ScaledNumber.h.

◆ operator==()

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

Definition at line 567 of file ScaledNumber.h.

◆ operator>()

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

Definition at line 570 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.

◆ operator>>=()

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

Definition at line 627 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 602 of file ScaledNumber.h.

◆ scale() [1/2]

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 770 of file ScaledNumber.h.

◆ scale() [2/2]

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

Definition at line 659 of file ScaledNumber.h.

◆ scaleByInverse() [1/2]

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

Definition at line 654 of file ScaledNumber.h.

◆ scaleByInverse() [2/2]

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

Definition at line 663 of file ScaledNumber.h.

◆ toInt()

template<class DigitsT >
template<class IntT >
IntT llvm::ScaledNumber< DigitsT >::toInt ( ) const

Convert to the given integer type.

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

Definition at line 780 of file ScaledNumber.h.

Referenced by convertFloatingToInteger().

◆ 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 595 of file ScaledNumber.h.


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