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git-svn-id: https://llvm.org/svn/llvm-project/llvm/trunk@41203 91177308-0d34-0410-b5e6-96231b3b80d8
259 lines
9.4 KiB
C++
259 lines
9.4 KiB
C++
//== llvm/Support/APFloat.h - Arbitrary Precision Floating Point -*- C++ -*-==//
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//
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// The LLVM Compiler Infrastructure
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//
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// This file was developed by Neil Booth and is distributed under the
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// University of Illinois Open Source License. See LICENSE.TXT for details.
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//
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//===----------------------------------------------------------------------===//
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//
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// This file declares a class to represent arbitrary precision floating
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// point values and provide a variety of arithmetic operations on them.
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//
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//===----------------------------------------------------------------------===//
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/* A self-contained host- and target-independent arbitrary-precision
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floating-point software implementation using bignum integer
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arithmetic, as provided by static functions in the APInt class.
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The library will work with bignum integers whose parts are any
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unsigned type at least 16 bits wide. 64 bits is recommended.
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Written for clarity rather than speed, in particular with a view
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to use in the front-end of a cross compiler so that target
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arithmetic can be correctly performed on the host. Performance
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should nonetheless be reasonable, particularly for its intended
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use. It may be useful as a base implementation for a run-time
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library during development of a faster target-specific one.
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All 5 rounding modes in the IEEE-754R draft are handled correctly
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for all implemented operations. Currently implemented operations
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are add, subtract, multiply, divide, fused-multiply-add,
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conversion-to-float, conversion-to-integer and
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conversion-from-integer. New rounding modes (e.g. away from zero)
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can be added with three or four lines of code. The library reads
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and correctly rounds hexadecimal floating point numbers as per
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C99; syntax is required to have been validated by the caller.
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Conversion from decimal is not currently implemented.
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Four formats are built-in: IEEE single precision, double
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precision, quadruple precision, and x87 80-bit extended double
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(when operating with full extended precision). Adding a new
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format that obeys IEEE semantics only requires adding two lines of
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code: a declaration and definition of the format.
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All operations return the status of that operation as an exception
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bit-mask, so multiple operations can be done consecutively with
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their results or-ed together. The returned status can be useful
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for compiler diagnostics; e.g., inexact, underflow and overflow
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can be easily diagnosed on constant folding, and compiler
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optimizers can determine what exceptions would be raised by
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folding operations and optimize, or perhaps not optimize,
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accordingly.
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At present, underflow tininess is detected after rounding; it
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should be straight forward to add support for the before-rounding
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case too.
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Non-zero finite numbers are represented internally as a sign bit,
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a 16-bit signed exponent, and the significand as an array of
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integer parts. After normalization of a number of precision P the
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exponent is within the range of the format, and if the number is
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not denormal the P-th bit of the significand is set as an explicit
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integer bit. For denormals the most significant bit is shifted
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right so that the exponent is maintained at the format's minimum,
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so that the smallest denormal has just the least significant bit
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of the significand set. The sign of zeroes and infinities is
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significant; the exponent and significand of such numbers is
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indeterminate and meaningless. For QNaNs the sign bit, as well as
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the exponent and significand are indeterminate and meaningless.
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TODO
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====
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Some features that may or may not be worth adding:
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Conversions to and from decimal strings (hard).
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Conversions to hexadecimal string.
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Read and write IEEE-format in-memory representations.
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Optional ability to detect underflow tininess before rounding.
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New formats: x87 in single and double precision mode (IEEE apart
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from extended exponent range) and IBM two-double extended
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precision (hard).
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New operations: sqrt, copysign, nextafter, nexttoward.
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*/
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#ifndef LLVM_FLOAT_H
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#define LLVM_FLOAT_H
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// APInt contains static functions implementing bignum arithmetic.
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#include "llvm/ADT/APInt.h"
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namespace llvm {
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/* Exponents are stored as signed numbers. */
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typedef signed short exponent_t;
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struct fltSemantics;
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/* When bits of a floating point number are truncated, this enum is
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used to indicate what fraction of the LSB those bits represented.
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It essentially combines the roles of guard and sticky bits. */
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enum lostFraction { // Example of truncated bits:
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lfExactlyZero, // 000000
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lfLessThanHalf, // 0xxxxx x's not all zero
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lfExactlyHalf, // 100000
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lfMoreThanHalf // 1xxxxx x's not all zero
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};
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class APFloat {
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public:
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/* We support the following floating point semantics. */
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static const fltSemantics IEEEsingle;
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static const fltSemantics IEEEdouble;
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static const fltSemantics IEEEquad;
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static const fltSemantics x87DoubleExtended;
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static unsigned int semanticsPrecision(const fltSemantics &);
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/* Floating point numbers have a four-state comparison relation. */
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enum cmpResult {
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cmpLessThan,
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cmpEqual,
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cmpGreaterThan,
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cmpUnordered
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};
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/* IEEE-754R gives five rounding modes. */
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enum roundingMode {
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rmNearestTiesToEven,
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rmTowardPositive,
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rmTowardNegative,
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rmTowardZero,
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rmNearestTiesToAway
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};
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/* Operation status. opUnderflow or opOverflow are always returned
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or-ed with opInexact. */
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enum opStatus {
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opOK = 0x00,
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opInvalidOp = 0x01,
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opDivByZero = 0x02,
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opOverflow = 0x04,
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opUnderflow = 0x08,
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opInexact = 0x10
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};
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/* Category of internally-represented number. */
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enum fltCategory {
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fcInfinity,
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fcQNaN,
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fcNormal,
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fcZero
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};
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/* Constructors. */
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APFloat(const fltSemantics &, const char *);
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APFloat(const fltSemantics &, integerPart);
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APFloat(const fltSemantics &, fltCategory, bool negative);
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APFloat(const APFloat &);
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~APFloat();
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/* Arithmetic. */
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opStatus add(const APFloat &, roundingMode);
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opStatus subtract(const APFloat &, roundingMode);
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opStatus multiply(const APFloat &, roundingMode);
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opStatus divide(const APFloat &, roundingMode);
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opStatus fusedMultiplyAdd(const APFloat &, const APFloat &, roundingMode);
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void changeSign();
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/* Conversions. */
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opStatus convert(const fltSemantics &, roundingMode);
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opStatus convertToInteger(integerPart *, unsigned int, bool,
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roundingMode) const;
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opStatus convertFromInteger(const integerPart *, unsigned int, bool,
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roundingMode);
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opStatus convertFromString(const char *, roundingMode);
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/* Comparison with another floating point number. */
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cmpResult compare(const APFloat &) const;
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/* Simple queries. */
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fltCategory getCategory() const { return category; }
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const fltSemantics &getSemantics() const { return *semantics; }
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bool isZero() const { return category == fcZero; }
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bool isNonZero() const { return category != fcZero; }
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bool isNegative() const { return sign; }
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APFloat& operator=(const APFloat &);
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private:
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/* Trivial queries. */
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integerPart *significandParts();
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const integerPart *significandParts() const;
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unsigned int partCount() const;
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/* Significand operations. */
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integerPart addSignificand(const APFloat &);
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integerPart subtractSignificand(const APFloat &, integerPart);
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lostFraction addOrSubtractSignificand(const APFloat &, bool subtract);
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lostFraction multiplySignificand(const APFloat &, const APFloat *);
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lostFraction divideSignificand(const APFloat &);
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void incrementSignificand();
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void initialize(const fltSemantics *);
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void shiftSignificandLeft(unsigned int);
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lostFraction shiftSignificandRight(unsigned int);
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unsigned int significandLSB() const;
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unsigned int significandMSB() const;
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void zeroSignificand();
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/* Arithmetic on special values. */
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opStatus addOrSubtractSpecials(const APFloat &, bool subtract);
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opStatus divideSpecials(const APFloat &);
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opStatus multiplySpecials(const APFloat &);
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/* Miscellany. */
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opStatus normalize(roundingMode, lostFraction);
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opStatus addOrSubtract(const APFloat &, roundingMode, bool subtract);
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cmpResult compareAbsoluteValue(const APFloat &) const;
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opStatus handleOverflow(roundingMode);
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bool roundAwayFromZero(roundingMode, lostFraction);
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opStatus convertFromUnsignedInteger(integerPart *, unsigned int,
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roundingMode);
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lostFraction combineLostFractions(lostFraction, lostFraction);
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opStatus convertFromHexadecimalString(const char *, roundingMode);
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void assign(const APFloat &);
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void copySignificand(const APFloat &);
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void freeSignificand();
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/* What kind of semantics does this value obey? */
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const fltSemantics *semantics;
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/* Significand - the fraction with an explicit integer bit. Must be
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at least one bit wider than the target precision. */
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union Significand
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{
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integerPart part;
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integerPart *parts;
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} significand;
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/* The exponent - a signed number. */
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exponent_t exponent;
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/* What kind of floating point number this is. */
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fltCategory category: 2;
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/* The sign bit of this number. */
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unsigned int sign: 1;
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};
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} /* namespace llvm */
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#endif /* LLVM_FLOAT_H */
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