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446 lines
18 KiB
C++
446 lines
18 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 is distributed under the University of Illinois Open Source
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// 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. It uses 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, but 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.
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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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The library reads hexadecimal floating point numbers as per C99,
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and correctly rounds if necessary according to the specified
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rounding mode. Syntax is required to have been validated by the
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caller. It also converts floating point numbers to hexadecimal
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text as per the C99 %a and %A conversions. The output precision
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(or alternatively the natural minimal precision) can be specified;
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if the requested precision is less than the natural precision the
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output is correctly rounded for the specified rounding mode.
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It also reads decimal floating point numbers and correctly rounds
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according to the specified rounding mode.
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Conversion to decimal text is not currently implemented.
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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 not
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stored, but has a known implicit (deterministic) value: 0 for the
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significands, 0 for zero exponent, all 1 bits for infinity
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exponent. For NaNs the sign and significand are deterministic,
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although not really meaningful, and preserved in non-conversion
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operations. The exponent is implicitly all 1 bits.
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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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Binary to decimal conversion (hard).
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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) (hard).
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New operations: sqrt, IEEE remainder, C90 fmod, nextafter,
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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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class StringRef;
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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 IEEEhalf;
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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 PPCDoubleDouble;
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static const fltSemantics x87DoubleExtended;
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/* And this pseudo, used to construct APFloats that cannot
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conflict with anything real. */
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static const fltSemantics Bogus;
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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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fcNaN,
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fcNormal,
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fcZero
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};
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enum uninitializedTag {
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uninitialized
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};
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// Constructors.
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APFloat(const fltSemantics &); // Default construct to 0.0
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APFloat(const fltSemantics &, StringRef);
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APFloat(const fltSemantics &, integerPart);
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APFloat(const fltSemantics &, fltCategory, bool negative);
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APFloat(const fltSemantics &, uninitializedTag);
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explicit APFloat(double d);
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explicit APFloat(float f);
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explicit APFloat(const APInt &, bool isIEEE = false);
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APFloat(const APFloat &);
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~APFloat();
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// Convenience "constructors"
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static APFloat getZero(const fltSemantics &Sem, bool Negative = false) {
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return APFloat(Sem, fcZero, Negative);
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}
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static APFloat getInf(const fltSemantics &Sem, bool Negative = false) {
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return APFloat(Sem, fcInfinity, Negative);
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}
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/// getNaN - Factory for QNaN values.
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///
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/// \param Negative - True iff the NaN generated should be negative.
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/// \param type - The unspecified fill bits for creating the NaN, 0 by
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/// default. The value is truncated as necessary.
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static APFloat getNaN(const fltSemantics &Sem, bool Negative = false,
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unsigned type = 0) {
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if (type) {
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APInt fill(64, type);
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return getQNaN(Sem, Negative, &fill);
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} else {
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return getQNaN(Sem, Negative, 0);
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}
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}
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/// getQNan - Factory for QNaN values.
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static APFloat getQNaN(const fltSemantics &Sem,
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bool Negative = false,
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const APInt *payload = 0) {
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return makeNaN(Sem, false, Negative, payload);
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}
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/// getSNan - Factory for SNaN values.
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static APFloat getSNaN(const fltSemantics &Sem,
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bool Negative = false,
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const APInt *payload = 0) {
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return makeNaN(Sem, true, Negative, payload);
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}
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/// getLargest - Returns the largest finite number in the given
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/// semantics.
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///
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/// \param Negative - True iff the number should be negative
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static APFloat getLargest(const fltSemantics &Sem, bool Negative = false);
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/// getSmallest - Returns the smallest (by magnitude) finite number
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/// in the given semantics. Might be denormalized, which implies a
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/// relative loss of precision.
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///
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/// \param Negative - True iff the number should be negative
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static APFloat getSmallest(const fltSemantics &Sem, bool Negative = false);
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/// getSmallestNormalized - Returns the smallest (by magnitude)
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/// normalized finite number in the given semantics.
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///
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/// \param Negative - True iff the number should be negative
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static APFloat getSmallestNormalized(const fltSemantics &Sem,
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bool Negative = false);
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/// Profile - Used to insert APFloat objects, or objects that contain
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/// APFloat objects, into FoldingSets.
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void Profile(FoldingSetNodeID& NID) const;
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/// @brief Used by the Bitcode serializer to emit APInts to Bitcode.
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void Emit(Serializer& S) const;
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/// @brief Used by the Bitcode deserializer to deserialize APInts.
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static APFloat ReadVal(Deserializer& D);
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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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/* IEEE remainder. */
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opStatus remainder(const APFloat &);
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/* C fmod, or llvm frem. */
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opStatus mod(const APFloat &, roundingMode);
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opStatus fusedMultiplyAdd(const APFloat &, const APFloat &, roundingMode);
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/* Sign operations. */
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void changeSign();
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void clearSign();
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void copySign(const APFloat &);
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/* Conversions. */
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opStatus convert(const fltSemantics &, roundingMode, bool *);
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opStatus convertToInteger(integerPart *, unsigned int, bool,
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roundingMode, bool *) const;
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opStatus convertFromAPInt(const APInt &,
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bool, roundingMode);
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opStatus convertFromSignExtendedInteger(const integerPart *, unsigned int,
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bool, roundingMode);
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opStatus convertFromZeroExtendedInteger(const integerPart *, unsigned int,
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bool, roundingMode);
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opStatus convertFromString(StringRef, roundingMode);
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APInt bitcastToAPInt() const;
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double convertToDouble() const;
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float convertToFloat() const;
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/* The definition of equality is not straightforward for floating point,
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so we won't use operator==. Use one of the following, or write
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whatever it is you really mean. */
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// bool operator==(const APFloat &) const; // DO NOT IMPLEMENT
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/* IEEE comparison with another floating point number (NaNs
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compare unordered, 0==-0). */
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cmpResult compare(const APFloat &) const;
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/* Bitwise comparison for equality (QNaNs compare equal, 0!=-0). */
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bool bitwiseIsEqual(const APFloat &) const;
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/* Write out a hexadecimal representation of the floating point
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value to DST, which must be of sufficient size, in the C99 form
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[-]0xh.hhhhp[+-]d. Return the number of characters written,
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excluding the terminating NUL. */
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unsigned int convertToHexString(char *dst, unsigned int hexDigits,
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bool upperCase, roundingMode) 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 isNaN() const { return category == fcNaN; }
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bool isInfinity() const { return category == fcInfinity; }
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bool isNegative() const { return sign; }
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bool isPosZero() const { return isZero() && !isNegative(); }
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bool isNegZero() const { return isZero() && isNegative(); }
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APFloat& operator=(const APFloat &);
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/* Return an arbitrary integer value usable for hashing. */
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uint32_t getHashValue() const;
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/// Converts this value into a decimal string.
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///
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/// \param FormatPrecision The maximum number of digits of
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/// precision to output. If there are fewer digits available,
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/// zero padding will not be used unless the value is
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/// integral and small enough to be expressed in
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/// FormatPrecision digits. 0 means to use the natural
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/// precision of the number.
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/// \param FormatMaxPadding The maximum number of zeros to
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/// consider inserting before falling back to scientific
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/// notation. 0 means to always use scientific notation.
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///
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/// Number Precision MaxPadding Result
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/// ------ --------- ---------- ------
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/// 1.01E+4 5 2 10100
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/// 1.01E+4 4 2 1.01E+4
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/// 1.01E+4 5 1 1.01E+4
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/// 1.01E-2 5 2 0.0101
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/// 1.01E-2 4 2 0.0101
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/// 1.01E-2 4 1 1.01E-2
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void toString(SmallVectorImpl<char> &Str,
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unsigned FormatPrecision = 0,
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unsigned FormatMaxPadding = 3) const;
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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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opStatus modSpecials(const APFloat &);
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/* Miscellany. */
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static APFloat makeNaN(const fltSemantics &Sem, bool SNaN, bool Negative,
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const APInt *fill);
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void makeNaN(bool SNaN = false, bool Neg = false, const APInt *fill = 0);
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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, unsigned int) const;
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opStatus convertToSignExtendedInteger(integerPart *, unsigned int, bool,
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roundingMode, bool *) const;
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opStatus convertFromUnsignedParts(const integerPart *, unsigned int,
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roundingMode);
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opStatus convertFromHexadecimalString(StringRef, roundingMode);
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opStatus convertFromDecimalString(StringRef, roundingMode);
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char *convertNormalToHexString(char *, unsigned int, bool,
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roundingMode) const;
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opStatus roundSignificandWithExponent(const integerPart *, unsigned int,
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int, roundingMode);
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APInt convertHalfAPFloatToAPInt() const;
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APInt convertFloatAPFloatToAPInt() const;
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APInt convertDoubleAPFloatToAPInt() const;
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APInt convertQuadrupleAPFloatToAPInt() const;
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APInt convertF80LongDoubleAPFloatToAPInt() const;
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APInt convertPPCDoubleDoubleAPFloatToAPInt() const;
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void initFromAPInt(const APInt& api, bool isIEEE = false);
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void initFromHalfAPInt(const APInt& api);
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void initFromFloatAPInt(const APInt& api);
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void initFromDoubleAPInt(const APInt& api);
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void initFromQuadrupleAPInt(const APInt &api);
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void initFromF80LongDoubleAPInt(const APInt& api);
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void initFromPPCDoubleDoubleAPInt(const APInt& api);
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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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/* Only 2 bits are required, but VisualStudio incorrectly sign extends
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it. Using the extra bit keeps it from failing under VisualStudio */
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fltCategory category: 3;
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/* The sign bit of this number. */
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unsigned int sign: 1;
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/* For PPCDoubleDouble, we have a second exponent and sign (the second
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significand is appended to the first one, although it would be wrong to
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regard these as a single number for arithmetic purposes). These fields
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are not meaningful for any other type. */
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exponent_t exponent2 : 11;
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unsigned int sign2: 1;
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};
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} /* namespace llvm */
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#endif /* LLVM_FLOAT_H */
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