A self-contained host- and target-independent arbitrary-precision floating-point software implementation. More...

#include "llvm/ADT/APFloat.h"

Inheritance diagram for llvm::APFloatBase:

Collaboration diagram for llvm::APFloatBase:

Public Types
enum	cmpResult { cmpLessThan, cmpEqual, cmpGreaterThan, cmpUnordered }
	IEEE-754R 5.11: Floating Point Comparison Relations. More...

enum	roundingMode { rmNearestTiesToEven, rmTowardPositive, rmTowardNegative, rmTowardZero, rmNearestTiesToAway }
	IEEE-754R 4.3: Rounding-direction attributes. More...

enum	opStatus { opOK = 0x00, opInvalidOp = 0x01, opDivByZero = 0x02, opOverflow = 0x04, opUnderflow = 0x08, opInexact = 0x10 }
	IEEE-754R 7: Default exception handling. More...

enum	fltCategory { fcInfinity, fcNaN, fcNormal, fcZero }
	Category of internally-represented number. More...

enum	uninitializedTag { uninitialized }
	Convenience enum used to construct an uninitialized APFloat. More...

enum	IlogbErrorKinds { IEK_Zero = INT_MIN + 1, IEK_NaN = INT_MIN, IEK_Inf = INT_MAX }
	Enumeration of `ilogb` error results. More...

typedef APInt::WordType	integerPart

typedef signed short	ExponentType
	A signed type to represent a floating point numbers unbiased exponent. More...

Static Public Member Functions
static unsigned int	semanticsPrecision (const fltSemantics &)

static ExponentType	semanticsMinExponent (const fltSemantics &)

static ExponentType	semanticsMaxExponent (const fltSemantics &)

static unsigned int	semanticsSizeInBits (const fltSemantics &)

static unsigned	getSizeInBits (const fltSemantics &Sem)
	Returns the size of the floating point number (in bits) in the given semantics. More...

Floating Point Semantics.
static const fltSemantics &	IEEEhalf () LLVM_READNONE

static const fltSemantics &	IEEEsingle () LLVM_READNONE

static const fltSemantics &	IEEEdouble () LLVM_READNONE

static const fltSemantics &	IEEEquad () LLVM_READNONE

static const fltSemantics &	PPCDoubleDouble () LLVM_READNONE

static const fltSemantics &	x87DoubleExtended () LLVM_READNONE

static const fltSemantics &	Bogus () LLVM_READNONE
	A Pseudo fltsemantic used to construct APFloats that cannot conflict with anything real. More...

Static Public Attributes
static const unsigned	integerPartWidth = APInt::APINT_BITS_PER_WORD

Detailed Description

A self-contained host- and target-independent arbitrary-precision floating-point software implementation.

APFloat uses bignum integer arithmetic as provided by static functions in the APInt class. The library will work with bignum integers whose parts are any unsigned type at least 16 bits wide, but 64 bits is recommended.

Written for clarity rather than speed, in particular with a view to use in the front-end of a cross compiler so that target arithmetic can be correctly performed on the host. Performance should nonetheless be reasonable, particularly for its intended use. It may be useful as a base implementation for a run-time library during development of a faster target-specific one.

All 5 rounding modes in the IEEE-754R draft are handled correctly for all implemented operations. Currently implemented operations are add, subtract, multiply, divide, fused-multiply-add, conversion-to-float, conversion-to-integer and conversion-from-integer. New rounding modes (e.g. away from zero) can be added with three or four lines of code.

Four formats are built-in: IEEE single precision, double precision, quadruple precision, and x87 80-bit extended double (when operating with full extended precision). Adding a new format that obeys IEEE semantics only requires adding two lines of code: a declaration and definition of the format.

All operations return the status of that operation as an exception bit-mask, so multiple operations can be done consecutively with their results or-ed together. The returned status can be useful for compiler diagnostics; e.g., inexact, underflow and overflow can be easily diagnosed on constant folding, and compiler optimizers can determine what exceptions would be raised by folding operations and optimize, or perhaps not optimize, accordingly.

At present, underflow tininess is detected after rounding; it should be straight forward to add support for the before-rounding case too.

The library reads hexadecimal floating point numbers as per C99, and correctly rounds if necessary according to the specified rounding mode. Syntax is required to have been validated by the caller. It also converts floating point numbers to hexadecimal text as per the C99 a and A conversions. The output precision (or alternatively the natural minimal precision) can be specified; if the requested precision is less than the natural precision the output is correctly rounded for the specified rounding mode.

It also reads decimal floating point numbers and correctly rounds according to the specified rounding mode.

Conversion to decimal text is not currently implemented.

Non-zero finite numbers are represented internally as a sign bit, a 16-bit signed exponent, and the significand as an array of integer parts. After normalization of a number of precision P the exponent is within the range of the format, and if the number is not denormal the P-th bit of the significand is set as an explicit integer bit. For denormals the most significant bit is shifted right so that the exponent is maintained at the format's minimum, so that the smallest denormal has just the least significant bit of the significand set. The sign of zeroes and infinities is significant; the exponent and significand of such numbers is not stored, but has a known implicit (deterministic) value: 0 for the significands, 0 for zero exponent, all 1 bits for infinity exponent. For NaNs the sign and significand are deterministic, although not really meaningful, and preserved in non-conversion operations. The exponent is implicitly all 1 bits.

APFloat does not provide any exception handling beyond default exception handling. We represent Signaling NaNs via IEEE-754R 2008 6.2.1 should clause by encoding Signaling NaNs with the first bit of its trailing significand as 0.