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git-svn-id: https://llvm.org/svn/llvm-project/llvm/trunk@217295 91177308-0d34-0410-b5e6-96231b3b80d8
3909 lines
115 KiB
C++
3909 lines
115 KiB
C++
//===-- APFloat.cpp - Implement APFloat class -----------------------------===//
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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 implements 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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#include "llvm/ADT/APFloat.h"
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#include "llvm/ADT/APSInt.h"
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#include "llvm/ADT/FoldingSet.h"
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#include "llvm/ADT/Hashing.h"
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#include "llvm/ADT/StringExtras.h"
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#include "llvm/ADT/StringRef.h"
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#include "llvm/Support/ErrorHandling.h"
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#include "llvm/Support/MathExtras.h"
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#include <cstring>
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#include <limits.h>
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using namespace llvm;
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/// A macro used to combine two fcCategory enums into one key which can be used
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/// in a switch statement to classify how the interaction of two APFloat's
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/// categories affects an operation.
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///
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/// TODO: If clang source code is ever allowed to use constexpr in its own
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/// codebase, change this into a static inline function.
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#define PackCategoriesIntoKey(_lhs, _rhs) ((_lhs) * 4 + (_rhs))
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/* Assumed in hexadecimal significand parsing, and conversion to
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hexadecimal strings. */
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#define COMPILE_TIME_ASSERT(cond) extern int CTAssert[(cond) ? 1 : -1]
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COMPILE_TIME_ASSERT(integerPartWidth % 4 == 0);
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namespace llvm {
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/* Represents floating point arithmetic semantics. */
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struct fltSemantics {
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/* The largest E such that 2^E is representable; this matches the
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definition of IEEE 754. */
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APFloat::ExponentType maxExponent;
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/* The smallest E such that 2^E is a normalized number; this
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matches the definition of IEEE 754. */
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APFloat::ExponentType minExponent;
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/* Number of bits in the significand. This includes the integer
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bit. */
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unsigned int precision;
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};
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const fltSemantics APFloat::IEEEhalf = { 15, -14, 11 };
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const fltSemantics APFloat::IEEEsingle = { 127, -126, 24 };
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const fltSemantics APFloat::IEEEdouble = { 1023, -1022, 53 };
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const fltSemantics APFloat::IEEEquad = { 16383, -16382, 113 };
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const fltSemantics APFloat::x87DoubleExtended = { 16383, -16382, 64 };
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const fltSemantics APFloat::Bogus = { 0, 0, 0 };
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/* The PowerPC format consists of two doubles. It does not map cleanly
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onto the usual format above. It is approximated using twice the
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mantissa bits. Note that for exponents near the double minimum,
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we no longer can represent the full 106 mantissa bits, so those
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will be treated as denormal numbers.
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FIXME: While this approximation is equivalent to what GCC uses for
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compile-time arithmetic on PPC double-double numbers, it is not able
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to represent all possible values held by a PPC double-double number,
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for example: (long double) 1.0 + (long double) 0x1p-106
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Should this be replaced by a full emulation of PPC double-double? */
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const fltSemantics APFloat::PPCDoubleDouble = { 1023, -1022 + 53, 53 + 53 };
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/* A tight upper bound on number of parts required to hold the value
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pow(5, power) is
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power * 815 / (351 * integerPartWidth) + 1
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However, whilst the result may require only this many parts,
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because we are multiplying two values to get it, the
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multiplication may require an extra part with the excess part
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being zero (consider the trivial case of 1 * 1, tcFullMultiply
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requires two parts to hold the single-part result). So we add an
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extra one to guarantee enough space whilst multiplying. */
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const unsigned int maxExponent = 16383;
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const unsigned int maxPrecision = 113;
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const unsigned int maxPowerOfFiveExponent = maxExponent + maxPrecision - 1;
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const unsigned int maxPowerOfFiveParts = 2 + ((maxPowerOfFiveExponent * 815)
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/ (351 * integerPartWidth));
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}
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/* A bunch of private, handy routines. */
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static inline unsigned int
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partCountForBits(unsigned int bits)
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{
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return ((bits) + integerPartWidth - 1) / integerPartWidth;
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}
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/* Returns 0U-9U. Return values >= 10U are not digits. */
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static inline unsigned int
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decDigitValue(unsigned int c)
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{
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return c - '0';
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}
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/* Return the value of a decimal exponent of the form
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[+-]ddddddd.
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If the exponent overflows, returns a large exponent with the
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appropriate sign. */
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static int
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readExponent(StringRef::iterator begin, StringRef::iterator end)
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{
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bool isNegative;
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unsigned int absExponent;
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const unsigned int overlargeExponent = 24000; /* FIXME. */
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StringRef::iterator p = begin;
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assert(p != end && "Exponent has no digits");
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isNegative = (*p == '-');
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if (*p == '-' || *p == '+') {
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p++;
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assert(p != end && "Exponent has no digits");
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}
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absExponent = decDigitValue(*p++);
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assert(absExponent < 10U && "Invalid character in exponent");
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for (; p != end; ++p) {
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unsigned int value;
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value = decDigitValue(*p);
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assert(value < 10U && "Invalid character in exponent");
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value += absExponent * 10;
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if (absExponent >= overlargeExponent) {
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absExponent = overlargeExponent;
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p = end; /* outwit assert below */
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break;
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}
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absExponent = value;
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}
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assert(p == end && "Invalid exponent in exponent");
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if (isNegative)
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return -(int) absExponent;
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else
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return (int) absExponent;
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}
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/* This is ugly and needs cleaning up, but I don't immediately see
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how whilst remaining safe. */
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static int
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totalExponent(StringRef::iterator p, StringRef::iterator end,
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int exponentAdjustment)
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{
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int unsignedExponent;
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bool negative, overflow;
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int exponent = 0;
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assert(p != end && "Exponent has no digits");
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negative = *p == '-';
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if (*p == '-' || *p == '+') {
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p++;
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assert(p != end && "Exponent has no digits");
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}
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unsignedExponent = 0;
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overflow = false;
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for (; p != end; ++p) {
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unsigned int value;
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value = decDigitValue(*p);
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assert(value < 10U && "Invalid character in exponent");
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unsignedExponent = unsignedExponent * 10 + value;
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if (unsignedExponent > 32767) {
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overflow = true;
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break;
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}
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}
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if (exponentAdjustment > 32767 || exponentAdjustment < -32768)
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overflow = true;
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if (!overflow) {
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exponent = unsignedExponent;
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if (negative)
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exponent = -exponent;
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exponent += exponentAdjustment;
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if (exponent > 32767 || exponent < -32768)
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overflow = true;
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}
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if (overflow)
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exponent = negative ? -32768: 32767;
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return exponent;
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}
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static StringRef::iterator
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skipLeadingZeroesAndAnyDot(StringRef::iterator begin, StringRef::iterator end,
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StringRef::iterator *dot)
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{
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StringRef::iterator p = begin;
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*dot = end;
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while (p != end && *p == '0')
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p++;
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if (p != end && *p == '.') {
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*dot = p++;
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assert(end - begin != 1 && "Significand has no digits");
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while (p != end && *p == '0')
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p++;
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}
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return p;
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}
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/* Given a normal decimal floating point number of the form
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dddd.dddd[eE][+-]ddd
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where the decimal point and exponent are optional, fill out the
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structure D. Exponent is appropriate if the significand is
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treated as an integer, and normalizedExponent if the significand
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is taken to have the decimal point after a single leading
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non-zero digit.
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If the value is zero, V->firstSigDigit points to a non-digit, and
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the return exponent is zero.
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*/
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struct decimalInfo {
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const char *firstSigDigit;
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const char *lastSigDigit;
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int exponent;
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int normalizedExponent;
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};
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static void
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interpretDecimal(StringRef::iterator begin, StringRef::iterator end,
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decimalInfo *D)
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{
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StringRef::iterator dot = end;
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StringRef::iterator p = skipLeadingZeroesAndAnyDot (begin, end, &dot);
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D->firstSigDigit = p;
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D->exponent = 0;
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D->normalizedExponent = 0;
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for (; p != end; ++p) {
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if (*p == '.') {
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assert(dot == end && "String contains multiple dots");
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dot = p++;
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if (p == end)
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break;
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}
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if (decDigitValue(*p) >= 10U)
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break;
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}
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if (p != end) {
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assert((*p == 'e' || *p == 'E') && "Invalid character in significand");
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assert(p != begin && "Significand has no digits");
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assert((dot == end || p - begin != 1) && "Significand has no digits");
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/* p points to the first non-digit in the string */
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D->exponent = readExponent(p + 1, end);
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/* Implied decimal point? */
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if (dot == end)
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dot = p;
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}
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/* If number is all zeroes accept any exponent. */
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if (p != D->firstSigDigit) {
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/* Drop insignificant trailing zeroes. */
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if (p != begin) {
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do
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do
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p--;
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while (p != begin && *p == '0');
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while (p != begin && *p == '.');
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}
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/* Adjust the exponents for any decimal point. */
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D->exponent += static_cast<APFloat::ExponentType>((dot - p) - (dot > p));
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D->normalizedExponent = (D->exponent +
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static_cast<APFloat::ExponentType>((p - D->firstSigDigit)
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- (dot > D->firstSigDigit && dot < p)));
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}
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D->lastSigDigit = p;
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}
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/* Return the trailing fraction of a hexadecimal number.
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DIGITVALUE is the first hex digit of the fraction, P points to
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the next digit. */
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static lostFraction
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trailingHexadecimalFraction(StringRef::iterator p, StringRef::iterator end,
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unsigned int digitValue)
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{
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unsigned int hexDigit;
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/* If the first trailing digit isn't 0 or 8 we can work out the
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fraction immediately. */
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if (digitValue > 8)
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return lfMoreThanHalf;
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else if (digitValue < 8 && digitValue > 0)
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return lfLessThanHalf;
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// Otherwise we need to find the first non-zero digit.
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while (p != end && (*p == '0' || *p == '.'))
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p++;
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assert(p != end && "Invalid trailing hexadecimal fraction!");
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hexDigit = hexDigitValue(*p);
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/* If we ran off the end it is exactly zero or one-half, otherwise
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a little more. */
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if (hexDigit == -1U)
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return digitValue == 0 ? lfExactlyZero: lfExactlyHalf;
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else
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return digitValue == 0 ? lfLessThanHalf: lfMoreThanHalf;
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}
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/* Return the fraction lost were a bignum truncated losing the least
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significant BITS bits. */
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static lostFraction
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lostFractionThroughTruncation(const integerPart *parts,
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unsigned int partCount,
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unsigned int bits)
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{
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unsigned int lsb;
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lsb = APInt::tcLSB(parts, partCount);
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/* Note this is guaranteed true if bits == 0, or LSB == -1U. */
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if (bits <= lsb)
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return lfExactlyZero;
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if (bits == lsb + 1)
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return lfExactlyHalf;
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if (bits <= partCount * integerPartWidth &&
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APInt::tcExtractBit(parts, bits - 1))
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return lfMoreThanHalf;
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return lfLessThanHalf;
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}
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/* Shift DST right BITS bits noting lost fraction. */
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static lostFraction
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shiftRight(integerPart *dst, unsigned int parts, unsigned int bits)
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{
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lostFraction lost_fraction;
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lost_fraction = lostFractionThroughTruncation(dst, parts, bits);
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APInt::tcShiftRight(dst, parts, bits);
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return lost_fraction;
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}
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/* Combine the effect of two lost fractions. */
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static lostFraction
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combineLostFractions(lostFraction moreSignificant,
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lostFraction lessSignificant)
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{
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if (lessSignificant != lfExactlyZero) {
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if (moreSignificant == lfExactlyZero)
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moreSignificant = lfLessThanHalf;
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else if (moreSignificant == lfExactlyHalf)
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moreSignificant = lfMoreThanHalf;
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}
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return moreSignificant;
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}
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/* The error from the true value, in half-ulps, on multiplying two
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floating point numbers, which differ from the value they
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approximate by at most HUE1 and HUE2 half-ulps, is strictly less
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than the returned value.
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See "How to Read Floating Point Numbers Accurately" by William D
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Clinger. */
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static unsigned int
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HUerrBound(bool inexactMultiply, unsigned int HUerr1, unsigned int HUerr2)
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{
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assert(HUerr1 < 2 || HUerr2 < 2 || (HUerr1 + HUerr2 < 8));
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if (HUerr1 + HUerr2 == 0)
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return inexactMultiply * 2; /* <= inexactMultiply half-ulps. */
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else
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return inexactMultiply + 2 * (HUerr1 + HUerr2);
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}
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/* The number of ulps from the boundary (zero, or half if ISNEAREST)
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when the least significant BITS are truncated. BITS cannot be
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zero. */
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static integerPart
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ulpsFromBoundary(const integerPart *parts, unsigned int bits, bool isNearest)
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{
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unsigned int count, partBits;
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integerPart part, boundary;
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assert(bits != 0);
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bits--;
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count = bits / integerPartWidth;
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partBits = bits % integerPartWidth + 1;
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part = parts[count] & (~(integerPart) 0 >> (integerPartWidth - partBits));
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if (isNearest)
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boundary = (integerPart) 1 << (partBits - 1);
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else
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boundary = 0;
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if (count == 0) {
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if (part - boundary <= boundary - part)
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return part - boundary;
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else
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return boundary - part;
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}
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if (part == boundary) {
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while (--count)
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if (parts[count])
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return ~(integerPart) 0; /* A lot. */
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return parts[0];
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} else if (part == boundary - 1) {
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while (--count)
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if (~parts[count])
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return ~(integerPart) 0; /* A lot. */
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return -parts[0];
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}
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return ~(integerPart) 0; /* A lot. */
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}
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/* Place pow(5, power) in DST, and return the number of parts used.
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DST must be at least one part larger than size of the answer. */
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static unsigned int
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powerOf5(integerPart *dst, unsigned int power)
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{
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static const integerPart firstEightPowers[] = { 1, 5, 25, 125, 625, 3125,
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15625, 78125 };
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integerPart pow5s[maxPowerOfFiveParts * 2 + 5];
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pow5s[0] = 78125 * 5;
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unsigned int partsCount[16] = { 1 };
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integerPart scratch[maxPowerOfFiveParts], *p1, *p2, *pow5;
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unsigned int result;
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assert(power <= maxExponent);
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p1 = dst;
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p2 = scratch;
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*p1 = firstEightPowers[power & 7];
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power >>= 3;
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result = 1;
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pow5 = pow5s;
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for (unsigned int n = 0; power; power >>= 1, n++) {
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unsigned int pc;
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pc = partsCount[n];
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/* Calculate pow(5,pow(2,n+3)) if we haven't yet. */
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if (pc == 0) {
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pc = partsCount[n - 1];
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APInt::tcFullMultiply(pow5, pow5 - pc, pow5 - pc, pc, pc);
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pc *= 2;
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if (pow5[pc - 1] == 0)
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pc--;
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partsCount[n] = pc;
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}
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if (power & 1) {
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integerPart *tmp;
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APInt::tcFullMultiply(p2, p1, pow5, result, pc);
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result += pc;
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if (p2[result - 1] == 0)
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result--;
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/* Now result is in p1 with partsCount parts and p2 is scratch
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space. */
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tmp = p1, p1 = p2, p2 = tmp;
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}
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pow5 += pc;
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}
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if (p1 != dst)
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APInt::tcAssign(dst, p1, result);
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return result;
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}
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/* Zero at the end to avoid modular arithmetic when adding one; used
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when rounding up during hexadecimal output. */
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static const char hexDigitsLower[] = "0123456789abcdef0";
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static const char hexDigitsUpper[] = "0123456789ABCDEF0";
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static const char infinityL[] = "infinity";
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static const char infinityU[] = "INFINITY";
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static const char NaNL[] = "nan";
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static const char NaNU[] = "NAN";
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/* Write out an integerPart in hexadecimal, starting with the most
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significant nibble. Write out exactly COUNT hexdigits, return
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COUNT. */
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static unsigned int
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partAsHex (char *dst, integerPart part, unsigned int count,
|
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const char *hexDigitChars)
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{
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unsigned int result = count;
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assert(count != 0 && count <= integerPartWidth / 4);
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part >>= (integerPartWidth - 4 * count);
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while (count--) {
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dst[count] = hexDigitChars[part & 0xf];
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part >>= 4;
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}
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return result;
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}
|
|
|
|
/* Write out an unsigned decimal integer. */
|
|
static char *
|
|
writeUnsignedDecimal (char *dst, unsigned int n)
|
|
{
|
|
char buff[40], *p;
|
|
|
|
p = buff;
|
|
do
|
|
*p++ = '0' + n % 10;
|
|
while (n /= 10);
|
|
|
|
do
|
|
*dst++ = *--p;
|
|
while (p != buff);
|
|
|
|
return dst;
|
|
}
|
|
|
|
/* Write out a signed decimal integer. */
|
|
static char *
|
|
writeSignedDecimal (char *dst, int value)
|
|
{
|
|
if (value < 0) {
|
|
*dst++ = '-';
|
|
dst = writeUnsignedDecimal(dst, -(unsigned) value);
|
|
} else
|
|
dst = writeUnsignedDecimal(dst, value);
|
|
|
|
return dst;
|
|
}
|
|
|
|
/* Constructors. */
|
|
void
|
|
APFloat::initialize(const fltSemantics *ourSemantics)
|
|
{
|
|
unsigned int count;
|
|
|
|
semantics = ourSemantics;
|
|
count = partCount();
|
|
if (count > 1)
|
|
significand.parts = new integerPart[count];
|
|
}
|
|
|
|
void
|
|
APFloat::freeSignificand()
|
|
{
|
|
if (needsCleanup())
|
|
delete [] significand.parts;
|
|
}
|
|
|
|
void
|
|
APFloat::assign(const APFloat &rhs)
|
|
{
|
|
assert(semantics == rhs.semantics);
|
|
|
|
sign = rhs.sign;
|
|
category = rhs.category;
|
|
exponent = rhs.exponent;
|
|
if (isFiniteNonZero() || category == fcNaN)
|
|
copySignificand(rhs);
|
|
}
|
|
|
|
void
|
|
APFloat::copySignificand(const APFloat &rhs)
|
|
{
|
|
assert(isFiniteNonZero() || category == fcNaN);
|
|
assert(rhs.partCount() >= partCount());
|
|
|
|
APInt::tcAssign(significandParts(), rhs.significandParts(),
|
|
partCount());
|
|
}
|
|
|
|
/* Make this number a NaN, with an arbitrary but deterministic value
|
|
for the significand. If double or longer, this is a signalling NaN,
|
|
which may not be ideal. If float, this is QNaN(0). */
|
|
void APFloat::makeNaN(bool SNaN, bool Negative, const APInt *fill)
|
|
{
|
|
category = fcNaN;
|
|
sign = Negative;
|
|
|
|
integerPart *significand = significandParts();
|
|
unsigned numParts = partCount();
|
|
|
|
// Set the significand bits to the fill.
|
|
if (!fill || fill->getNumWords() < numParts)
|
|
APInt::tcSet(significand, 0, numParts);
|
|
if (fill) {
|
|
APInt::tcAssign(significand, fill->getRawData(),
|
|
std::min(fill->getNumWords(), numParts));
|
|
|
|
// Zero out the excess bits of the significand.
|
|
unsigned bitsToPreserve = semantics->precision - 1;
|
|
unsigned part = bitsToPreserve / 64;
|
|
bitsToPreserve %= 64;
|
|
significand[part] &= ((1ULL << bitsToPreserve) - 1);
|
|
for (part++; part != numParts; ++part)
|
|
significand[part] = 0;
|
|
}
|
|
|
|
unsigned QNaNBit = semantics->precision - 2;
|
|
|
|
if (SNaN) {
|
|
// We always have to clear the QNaN bit to make it an SNaN.
|
|
APInt::tcClearBit(significand, QNaNBit);
|
|
|
|
// If there are no bits set in the payload, we have to set
|
|
// *something* to make it a NaN instead of an infinity;
|
|
// conventionally, this is the next bit down from the QNaN bit.
|
|
if (APInt::tcIsZero(significand, numParts))
|
|
APInt::tcSetBit(significand, QNaNBit - 1);
|
|
} else {
|
|
// We always have to set the QNaN bit to make it a QNaN.
|
|
APInt::tcSetBit(significand, QNaNBit);
|
|
}
|
|
|
|
// For x87 extended precision, we want to make a NaN, not a
|
|
// pseudo-NaN. Maybe we should expose the ability to make
|
|
// pseudo-NaNs?
|
|
if (semantics == &APFloat::x87DoubleExtended)
|
|
APInt::tcSetBit(significand, QNaNBit + 1);
|
|
}
|
|
|
|
APFloat APFloat::makeNaN(const fltSemantics &Sem, bool SNaN, bool Negative,
|
|
const APInt *fill) {
|
|
APFloat value(Sem, uninitialized);
|
|
value.makeNaN(SNaN, Negative, fill);
|
|
return value;
|
|
}
|
|
|
|
APFloat &
|
|
APFloat::operator=(const APFloat &rhs)
|
|
{
|
|
if (this != &rhs) {
|
|
if (semantics != rhs.semantics) {
|
|
freeSignificand();
|
|
initialize(rhs.semantics);
|
|
}
|
|
assign(rhs);
|
|
}
|
|
|
|
return *this;
|
|
}
|
|
|
|
APFloat &
|
|
APFloat::operator=(APFloat &&rhs) {
|
|
freeSignificand();
|
|
|
|
semantics = rhs.semantics;
|
|
significand = rhs.significand;
|
|
exponent = rhs.exponent;
|
|
category = rhs.category;
|
|
sign = rhs.sign;
|
|
|
|
rhs.semantics = &Bogus;
|
|
return *this;
|
|
}
|
|
|
|
bool
|
|
APFloat::isDenormal() const {
|
|
return isFiniteNonZero() && (exponent == semantics->minExponent) &&
|
|
(APInt::tcExtractBit(significandParts(),
|
|
semantics->precision - 1) == 0);
|
|
}
|
|
|
|
bool
|
|
APFloat::isSmallest() const {
|
|
// The smallest number by magnitude in our format will be the smallest
|
|
// denormal, i.e. the floating point number with exponent being minimum
|
|
// exponent and significand bitwise equal to 1 (i.e. with MSB equal to 0).
|
|
return isFiniteNonZero() && exponent == semantics->minExponent &&
|
|
significandMSB() == 0;
|
|
}
|
|
|
|
bool APFloat::isSignificandAllOnes() const {
|
|
// Test if the significand excluding the integral bit is all ones. This allows
|
|
// us to test for binade boundaries.
|
|
const integerPart *Parts = significandParts();
|
|
const unsigned PartCount = partCount();
|
|
for (unsigned i = 0; i < PartCount - 1; i++)
|
|
if (~Parts[i])
|
|
return false;
|
|
|
|
// Set the unused high bits to all ones when we compare.
|
|
const unsigned NumHighBits =
|
|
PartCount*integerPartWidth - semantics->precision + 1;
|
|
assert(NumHighBits <= integerPartWidth && "Can not have more high bits to "
|
|
"fill than integerPartWidth");
|
|
const integerPart HighBitFill =
|
|
~integerPart(0) << (integerPartWidth - NumHighBits);
|
|
if (~(Parts[PartCount - 1] | HighBitFill))
|
|
return false;
|
|
|
|
return true;
|
|
}
|
|
|
|
bool APFloat::isSignificandAllZeros() const {
|
|
// Test if the significand excluding the integral bit is all zeros. This
|
|
// allows us to test for binade boundaries.
|
|
const integerPart *Parts = significandParts();
|
|
const unsigned PartCount = partCount();
|
|
|
|
for (unsigned i = 0; i < PartCount - 1; i++)
|
|
if (Parts[i])
|
|
return false;
|
|
|
|
const unsigned NumHighBits =
|
|
PartCount*integerPartWidth - semantics->precision + 1;
|
|
assert(NumHighBits <= integerPartWidth && "Can not have more high bits to "
|
|
"clear than integerPartWidth");
|
|
const integerPart HighBitMask = ~integerPart(0) >> NumHighBits;
|
|
|
|
if (Parts[PartCount - 1] & HighBitMask)
|
|
return false;
|
|
|
|
return true;
|
|
}
|
|
|
|
bool
|
|
APFloat::isLargest() const {
|
|
// The largest number by magnitude in our format will be the floating point
|
|
// number with maximum exponent and with significand that is all ones.
|
|
return isFiniteNonZero() && exponent == semantics->maxExponent
|
|
&& isSignificandAllOnes();
|
|
}
|
|
|
|
bool
|
|
APFloat::bitwiseIsEqual(const APFloat &rhs) const {
|
|
if (this == &rhs)
|
|
return true;
|
|
if (semantics != rhs.semantics ||
|
|
category != rhs.category ||
|
|
sign != rhs.sign)
|
|
return false;
|
|
if (category==fcZero || category==fcInfinity)
|
|
return true;
|
|
else if (isFiniteNonZero() && exponent!=rhs.exponent)
|
|
return false;
|
|
else {
|
|
int i= partCount();
|
|
const integerPart* p=significandParts();
|
|
const integerPart* q=rhs.significandParts();
|
|
for (; i>0; i--, p++, q++) {
|
|
if (*p != *q)
|
|
return false;
|
|
}
|
|
return true;
|
|
}
|
|
}
|
|
|
|
APFloat::APFloat(const fltSemantics &ourSemantics, integerPart value) {
|
|
initialize(&ourSemantics);
|
|
sign = 0;
|
|
category = fcNormal;
|
|
zeroSignificand();
|
|
exponent = ourSemantics.precision - 1;
|
|
significandParts()[0] = value;
|
|
normalize(rmNearestTiesToEven, lfExactlyZero);
|
|
}
|
|
|
|
APFloat::APFloat(const fltSemantics &ourSemantics) {
|
|
initialize(&ourSemantics);
|
|
category = fcZero;
|
|
sign = false;
|
|
}
|
|
|
|
APFloat::APFloat(const fltSemantics &ourSemantics, uninitializedTag tag) {
|
|
// Allocates storage if necessary but does not initialize it.
|
|
initialize(&ourSemantics);
|
|
}
|
|
|
|
APFloat::APFloat(const fltSemantics &ourSemantics, StringRef text) {
|
|
initialize(&ourSemantics);
|
|
convertFromString(text, rmNearestTiesToEven);
|
|
}
|
|
|
|
APFloat::APFloat(const APFloat &rhs) {
|
|
initialize(rhs.semantics);
|
|
assign(rhs);
|
|
}
|
|
|
|
APFloat::APFloat(APFloat &&rhs) : semantics(&Bogus) {
|
|
*this = std::move(rhs);
|
|
}
|
|
|
|
APFloat::~APFloat()
|
|
{
|
|
freeSignificand();
|
|
}
|
|
|
|
// Profile - This method 'profiles' an APFloat for use with FoldingSet.
|
|
void APFloat::Profile(FoldingSetNodeID& ID) const {
|
|
ID.Add(bitcastToAPInt());
|
|
}
|
|
|
|
unsigned int
|
|
APFloat::partCount() const
|
|
{
|
|
return partCountForBits(semantics->precision + 1);
|
|
}
|
|
|
|
unsigned int
|
|
APFloat::semanticsPrecision(const fltSemantics &semantics)
|
|
{
|
|
return semantics.precision;
|
|
}
|
|
|
|
const integerPart *
|
|
APFloat::significandParts() const
|
|
{
|
|
return const_cast<APFloat *>(this)->significandParts();
|
|
}
|
|
|
|
integerPart *
|
|
APFloat::significandParts()
|
|
{
|
|
if (partCount() > 1)
|
|
return significand.parts;
|
|
else
|
|
return &significand.part;
|
|
}
|
|
|
|
void
|
|
APFloat::zeroSignificand()
|
|
{
|
|
APInt::tcSet(significandParts(), 0, partCount());
|
|
}
|
|
|
|
/* Increment an fcNormal floating point number's significand. */
|
|
void
|
|
APFloat::incrementSignificand()
|
|
{
|
|
integerPart carry;
|
|
|
|
carry = APInt::tcIncrement(significandParts(), partCount());
|
|
|
|
/* Our callers should never cause us to overflow. */
|
|
assert(carry == 0);
|
|
(void)carry;
|
|
}
|
|
|
|
/* Add the significand of the RHS. Returns the carry flag. */
|
|
integerPart
|
|
APFloat::addSignificand(const APFloat &rhs)
|
|
{
|
|
integerPart *parts;
|
|
|
|
parts = significandParts();
|
|
|
|
assert(semantics == rhs.semantics);
|
|
assert(exponent == rhs.exponent);
|
|
|
|
return APInt::tcAdd(parts, rhs.significandParts(), 0, partCount());
|
|
}
|
|
|
|
/* Subtract the significand of the RHS with a borrow flag. Returns
|
|
the borrow flag. */
|
|
integerPart
|
|
APFloat::subtractSignificand(const APFloat &rhs, integerPart borrow)
|
|
{
|
|
integerPart *parts;
|
|
|
|
parts = significandParts();
|
|
|
|
assert(semantics == rhs.semantics);
|
|
assert(exponent == rhs.exponent);
|
|
|
|
return APInt::tcSubtract(parts, rhs.significandParts(), borrow,
|
|
partCount());
|
|
}
|
|
|
|
/* Multiply the significand of the RHS. If ADDEND is non-NULL, add it
|
|
on to the full-precision result of the multiplication. Returns the
|
|
lost fraction. */
|
|
lostFraction
|
|
APFloat::multiplySignificand(const APFloat &rhs, const APFloat *addend)
|
|
{
|
|
unsigned int omsb; // One, not zero, based MSB.
|
|
unsigned int partsCount, newPartsCount, precision;
|
|
integerPart *lhsSignificand;
|
|
integerPart scratch[4];
|
|
integerPart *fullSignificand;
|
|
lostFraction lost_fraction;
|
|
bool ignored;
|
|
|
|
assert(semantics == rhs.semantics);
|
|
|
|
precision = semantics->precision;
|
|
newPartsCount = partCountForBits(precision * 2);
|
|
|
|
if (newPartsCount > 4)
|
|
fullSignificand = new integerPart[newPartsCount];
|
|
else
|
|
fullSignificand = scratch;
|
|
|
|
lhsSignificand = significandParts();
|
|
partsCount = partCount();
|
|
|
|
APInt::tcFullMultiply(fullSignificand, lhsSignificand,
|
|
rhs.significandParts(), partsCount, partsCount);
|
|
|
|
lost_fraction = lfExactlyZero;
|
|
omsb = APInt::tcMSB(fullSignificand, newPartsCount) + 1;
|
|
exponent += rhs.exponent;
|
|
|
|
// Assume the operands involved in the multiplication are single-precision
|
|
// FP, and the two multiplicants are:
|
|
// *this = a23 . a22 ... a0 * 2^e1
|
|
// rhs = b23 . b22 ... b0 * 2^e2
|
|
// the result of multiplication is:
|
|
// *this = c47 c46 . c45 ... c0 * 2^(e1+e2)
|
|
// Note that there are two significant bits at the left-hand side of the
|
|
// radix point. Move the radix point toward left by one bit, and adjust
|
|
// exponent accordingly.
|
|
exponent += 1;
|
|
|
|
if (addend) {
|
|
// The intermediate result of the multiplication has "2 * precision"
|
|
// signicant bit; adjust the addend to be consistent with mul result.
|
|
//
|
|
Significand savedSignificand = significand;
|
|
const fltSemantics *savedSemantics = semantics;
|
|
fltSemantics extendedSemantics;
|
|
opStatus status;
|
|
unsigned int extendedPrecision;
|
|
|
|
/* Normalize our MSB. */
|
|
extendedPrecision = 2 * precision;
|
|
if (omsb != extendedPrecision) {
|
|
assert(extendedPrecision > omsb);
|
|
APInt::tcShiftLeft(fullSignificand, newPartsCount,
|
|
extendedPrecision - omsb);
|
|
exponent -= extendedPrecision - omsb;
|
|
}
|
|
|
|
/* Create new semantics. */
|
|
extendedSemantics = *semantics;
|
|
extendedSemantics.precision = extendedPrecision;
|
|
|
|
if (newPartsCount == 1)
|
|
significand.part = fullSignificand[0];
|
|
else
|
|
significand.parts = fullSignificand;
|
|
semantics = &extendedSemantics;
|
|
|
|
APFloat extendedAddend(*addend);
|
|
status = extendedAddend.convert(extendedSemantics, rmTowardZero, &ignored);
|
|
assert(status == opOK);
|
|
(void)status;
|
|
lost_fraction = addOrSubtractSignificand(extendedAddend, false);
|
|
|
|
/* Restore our state. */
|
|
if (newPartsCount == 1)
|
|
fullSignificand[0] = significand.part;
|
|
significand = savedSignificand;
|
|
semantics = savedSemantics;
|
|
|
|
omsb = APInt::tcMSB(fullSignificand, newPartsCount) + 1;
|
|
}
|
|
|
|
// Convert the result having "2 * precision" significant-bits back to the one
|
|
// having "precision" significant-bits. First, move the radix point from
|
|
// poision "2*precision - 1" to "precision - 1". The exponent need to be
|
|
// adjusted by "2*precision - 1" - "precision - 1" = "precision".
|
|
exponent -= precision;
|
|
|
|
// In case MSB resides at the left-hand side of radix point, shift the
|
|
// mantissa right by some amount to make sure the MSB reside right before
|
|
// the radix point (i.e. "MSB . rest-significant-bits").
|
|
//
|
|
// Note that the result is not normalized when "omsb < precision". So, the
|
|
// caller needs to call APFloat::normalize() if normalized value is expected.
|
|
if (omsb > precision) {
|
|
unsigned int bits, significantParts;
|
|
lostFraction lf;
|
|
|
|
bits = omsb - precision;
|
|
significantParts = partCountForBits(omsb);
|
|
lf = shiftRight(fullSignificand, significantParts, bits);
|
|
lost_fraction = combineLostFractions(lf, lost_fraction);
|
|
exponent += bits;
|
|
}
|
|
|
|
APInt::tcAssign(lhsSignificand, fullSignificand, partsCount);
|
|
|
|
if (newPartsCount > 4)
|
|
delete [] fullSignificand;
|
|
|
|
return lost_fraction;
|
|
}
|
|
|
|
/* Multiply the significands of LHS and RHS to DST. */
|
|
lostFraction
|
|
APFloat::divideSignificand(const APFloat &rhs)
|
|
{
|
|
unsigned int bit, i, partsCount;
|
|
const integerPart *rhsSignificand;
|
|
integerPart *lhsSignificand, *dividend, *divisor;
|
|
integerPart scratch[4];
|
|
lostFraction lost_fraction;
|
|
|
|
assert(semantics == rhs.semantics);
|
|
|
|
lhsSignificand = significandParts();
|
|
rhsSignificand = rhs.significandParts();
|
|
partsCount = partCount();
|
|
|
|
if (partsCount > 2)
|
|
dividend = new integerPart[partsCount * 2];
|
|
else
|
|
dividend = scratch;
|
|
|
|
divisor = dividend + partsCount;
|
|
|
|
/* Copy the dividend and divisor as they will be modified in-place. */
|
|
for (i = 0; i < partsCount; i++) {
|
|
dividend[i] = lhsSignificand[i];
|
|
divisor[i] = rhsSignificand[i];
|
|
lhsSignificand[i] = 0;
|
|
}
|
|
|
|
exponent -= rhs.exponent;
|
|
|
|
unsigned int precision = semantics->precision;
|
|
|
|
/* Normalize the divisor. */
|
|
bit = precision - APInt::tcMSB(divisor, partsCount) - 1;
|
|
if (bit) {
|
|
exponent += bit;
|
|
APInt::tcShiftLeft(divisor, partsCount, bit);
|
|
}
|
|
|
|
/* Normalize the dividend. */
|
|
bit = precision - APInt::tcMSB(dividend, partsCount) - 1;
|
|
if (bit) {
|
|
exponent -= bit;
|
|
APInt::tcShiftLeft(dividend, partsCount, bit);
|
|
}
|
|
|
|
/* Ensure the dividend >= divisor initially for the loop below.
|
|
Incidentally, this means that the division loop below is
|
|
guaranteed to set the integer bit to one. */
|
|
if (APInt::tcCompare(dividend, divisor, partsCount) < 0) {
|
|
exponent--;
|
|
APInt::tcShiftLeft(dividend, partsCount, 1);
|
|
assert(APInt::tcCompare(dividend, divisor, partsCount) >= 0);
|
|
}
|
|
|
|
/* Long division. */
|
|
for (bit = precision; bit; bit -= 1) {
|
|
if (APInt::tcCompare(dividend, divisor, partsCount) >= 0) {
|
|
APInt::tcSubtract(dividend, divisor, 0, partsCount);
|
|
APInt::tcSetBit(lhsSignificand, bit - 1);
|
|
}
|
|
|
|
APInt::tcShiftLeft(dividend, partsCount, 1);
|
|
}
|
|
|
|
/* Figure out the lost fraction. */
|
|
int cmp = APInt::tcCompare(dividend, divisor, partsCount);
|
|
|
|
if (cmp > 0)
|
|
lost_fraction = lfMoreThanHalf;
|
|
else if (cmp == 0)
|
|
lost_fraction = lfExactlyHalf;
|
|
else if (APInt::tcIsZero(dividend, partsCount))
|
|
lost_fraction = lfExactlyZero;
|
|
else
|
|
lost_fraction = lfLessThanHalf;
|
|
|
|
if (partsCount > 2)
|
|
delete [] dividend;
|
|
|
|
return lost_fraction;
|
|
}
|
|
|
|
unsigned int
|
|
APFloat::significandMSB() const
|
|
{
|
|
return APInt::tcMSB(significandParts(), partCount());
|
|
}
|
|
|
|
unsigned int
|
|
APFloat::significandLSB() const
|
|
{
|
|
return APInt::tcLSB(significandParts(), partCount());
|
|
}
|
|
|
|
/* Note that a zero result is NOT normalized to fcZero. */
|
|
lostFraction
|
|
APFloat::shiftSignificandRight(unsigned int bits)
|
|
{
|
|
/* Our exponent should not overflow. */
|
|
assert((ExponentType) (exponent + bits) >= exponent);
|
|
|
|
exponent += bits;
|
|
|
|
return shiftRight(significandParts(), partCount(), bits);
|
|
}
|
|
|
|
/* Shift the significand left BITS bits, subtract BITS from its exponent. */
|
|
void
|
|
APFloat::shiftSignificandLeft(unsigned int bits)
|
|
{
|
|
assert(bits < semantics->precision);
|
|
|
|
if (bits) {
|
|
unsigned int partsCount = partCount();
|
|
|
|
APInt::tcShiftLeft(significandParts(), partsCount, bits);
|
|
exponent -= bits;
|
|
|
|
assert(!APInt::tcIsZero(significandParts(), partsCount));
|
|
}
|
|
}
|
|
|
|
APFloat::cmpResult
|
|
APFloat::compareAbsoluteValue(const APFloat &rhs) const
|
|
{
|
|
int compare;
|
|
|
|
assert(semantics == rhs.semantics);
|
|
assert(isFiniteNonZero());
|
|
assert(rhs.isFiniteNonZero());
|
|
|
|
compare = exponent - rhs.exponent;
|
|
|
|
/* If exponents are equal, do an unsigned bignum comparison of the
|
|
significands. */
|
|
if (compare == 0)
|
|
compare = APInt::tcCompare(significandParts(), rhs.significandParts(),
|
|
partCount());
|
|
|
|
if (compare > 0)
|
|
return cmpGreaterThan;
|
|
else if (compare < 0)
|
|
return cmpLessThan;
|
|
else
|
|
return cmpEqual;
|
|
}
|
|
|
|
/* Handle overflow. Sign is preserved. We either become infinity or
|
|
the largest finite number. */
|
|
APFloat::opStatus
|
|
APFloat::handleOverflow(roundingMode rounding_mode)
|
|
{
|
|
/* Infinity? */
|
|
if (rounding_mode == rmNearestTiesToEven ||
|
|
rounding_mode == rmNearestTiesToAway ||
|
|
(rounding_mode == rmTowardPositive && !sign) ||
|
|
(rounding_mode == rmTowardNegative && sign)) {
|
|
category = fcInfinity;
|
|
return (opStatus) (opOverflow | opInexact);
|
|
}
|
|
|
|
/* Otherwise we become the largest finite number. */
|
|
category = fcNormal;
|
|
exponent = semantics->maxExponent;
|
|
APInt::tcSetLeastSignificantBits(significandParts(), partCount(),
|
|
semantics->precision);
|
|
|
|
return opInexact;
|
|
}
|
|
|
|
/* Returns TRUE if, when truncating the current number, with BIT the
|
|
new LSB, with the given lost fraction and rounding mode, the result
|
|
would need to be rounded away from zero (i.e., by increasing the
|
|
signficand). This routine must work for fcZero of both signs, and
|
|
fcNormal numbers. */
|
|
bool
|
|
APFloat::roundAwayFromZero(roundingMode rounding_mode,
|
|
lostFraction lost_fraction,
|
|
unsigned int bit) const
|
|
{
|
|
/* NaNs and infinities should not have lost fractions. */
|
|
assert(isFiniteNonZero() || category == fcZero);
|
|
|
|
/* Current callers never pass this so we don't handle it. */
|
|
assert(lost_fraction != lfExactlyZero);
|
|
|
|
switch (rounding_mode) {
|
|
case rmNearestTiesToAway:
|
|
return lost_fraction == lfExactlyHalf || lost_fraction == lfMoreThanHalf;
|
|
|
|
case rmNearestTiesToEven:
|
|
if (lost_fraction == lfMoreThanHalf)
|
|
return true;
|
|
|
|
/* Our zeroes don't have a significand to test. */
|
|
if (lost_fraction == lfExactlyHalf && category != fcZero)
|
|
return APInt::tcExtractBit(significandParts(), bit);
|
|
|
|
return false;
|
|
|
|
case rmTowardZero:
|
|
return false;
|
|
|
|
case rmTowardPositive:
|
|
return sign == false;
|
|
|
|
case rmTowardNegative:
|
|
return sign == true;
|
|
}
|
|
llvm_unreachable("Invalid rounding mode found");
|
|
}
|
|
|
|
APFloat::opStatus
|
|
APFloat::normalize(roundingMode rounding_mode,
|
|
lostFraction lost_fraction)
|
|
{
|
|
unsigned int omsb; /* One, not zero, based MSB. */
|
|
int exponentChange;
|
|
|
|
if (!isFiniteNonZero())
|
|
return opOK;
|
|
|
|
/* Before rounding normalize the exponent of fcNormal numbers. */
|
|
omsb = significandMSB() + 1;
|
|
|
|
if (omsb) {
|
|
/* OMSB is numbered from 1. We want to place it in the integer
|
|
bit numbered PRECISION if possible, with a compensating change in
|
|
the exponent. */
|
|
exponentChange = omsb - semantics->precision;
|
|
|
|
/* If the resulting exponent is too high, overflow according to
|
|
the rounding mode. */
|
|
if (exponent + exponentChange > semantics->maxExponent)
|
|
return handleOverflow(rounding_mode);
|
|
|
|
/* Subnormal numbers have exponent minExponent, and their MSB
|
|
is forced based on that. */
|
|
if (exponent + exponentChange < semantics->minExponent)
|
|
exponentChange = semantics->minExponent - exponent;
|
|
|
|
/* Shifting left is easy as we don't lose precision. */
|
|
if (exponentChange < 0) {
|
|
assert(lost_fraction == lfExactlyZero);
|
|
|
|
shiftSignificandLeft(-exponentChange);
|
|
|
|
return opOK;
|
|
}
|
|
|
|
if (exponentChange > 0) {
|
|
lostFraction lf;
|
|
|
|
/* Shift right and capture any new lost fraction. */
|
|
lf = shiftSignificandRight(exponentChange);
|
|
|
|
lost_fraction = combineLostFractions(lf, lost_fraction);
|
|
|
|
/* Keep OMSB up-to-date. */
|
|
if (omsb > (unsigned) exponentChange)
|
|
omsb -= exponentChange;
|
|
else
|
|
omsb = 0;
|
|
}
|
|
}
|
|
|
|
/* Now round the number according to rounding_mode given the lost
|
|
fraction. */
|
|
|
|
/* As specified in IEEE 754, since we do not trap we do not report
|
|
underflow for exact results. */
|
|
if (lost_fraction == lfExactlyZero) {
|
|
/* Canonicalize zeroes. */
|
|
if (omsb == 0)
|
|
category = fcZero;
|
|
|
|
return opOK;
|
|
}
|
|
|
|
/* Increment the significand if we're rounding away from zero. */
|
|
if (roundAwayFromZero(rounding_mode, lost_fraction, 0)) {
|
|
if (omsb == 0)
|
|
exponent = semantics->minExponent;
|
|
|
|
incrementSignificand();
|
|
omsb = significandMSB() + 1;
|
|
|
|
/* Did the significand increment overflow? */
|
|
if (omsb == (unsigned) semantics->precision + 1) {
|
|
/* Renormalize by incrementing the exponent and shifting our
|
|
significand right one. However if we already have the
|
|
maximum exponent we overflow to infinity. */
|
|
if (exponent == semantics->maxExponent) {
|
|
category = fcInfinity;
|
|
|
|
return (opStatus) (opOverflow | opInexact);
|
|
}
|
|
|
|
shiftSignificandRight(1);
|
|
|
|
return opInexact;
|
|
}
|
|
}
|
|
|
|
/* The normal case - we were and are not denormal, and any
|
|
significand increment above didn't overflow. */
|
|
if (omsb == semantics->precision)
|
|
return opInexact;
|
|
|
|
/* We have a non-zero denormal. */
|
|
assert(omsb < semantics->precision);
|
|
|
|
/* Canonicalize zeroes. */
|
|
if (omsb == 0)
|
|
category = fcZero;
|
|
|
|
/* The fcZero case is a denormal that underflowed to zero. */
|
|
return (opStatus) (opUnderflow | opInexact);
|
|
}
|
|
|
|
APFloat::opStatus
|
|
APFloat::addOrSubtractSpecials(const APFloat &rhs, bool subtract)
|
|
{
|
|
switch (PackCategoriesIntoKey(category, rhs.category)) {
|
|
default:
|
|
llvm_unreachable(nullptr);
|
|
|
|
case PackCategoriesIntoKey(fcNaN, fcZero):
|
|
case PackCategoriesIntoKey(fcNaN, fcNormal):
|
|
case PackCategoriesIntoKey(fcNaN, fcInfinity):
|
|
case PackCategoriesIntoKey(fcNaN, fcNaN):
|
|
case PackCategoriesIntoKey(fcNormal, fcZero):
|
|
case PackCategoriesIntoKey(fcInfinity, fcNormal):
|
|
case PackCategoriesIntoKey(fcInfinity, fcZero):
|
|
return opOK;
|
|
|
|
case PackCategoriesIntoKey(fcZero, fcNaN):
|
|
case PackCategoriesIntoKey(fcNormal, fcNaN):
|
|
case PackCategoriesIntoKey(fcInfinity, fcNaN):
|
|
// We need to be sure to flip the sign here for subtraction because we
|
|
// don't have a separate negate operation so -NaN becomes 0 - NaN here.
|
|
sign = rhs.sign ^ subtract;
|
|
category = fcNaN;
|
|
copySignificand(rhs);
|
|
return opOK;
|
|
|
|
case PackCategoriesIntoKey(fcNormal, fcInfinity):
|
|
case PackCategoriesIntoKey(fcZero, fcInfinity):
|
|
category = fcInfinity;
|
|
sign = rhs.sign ^ subtract;
|
|
return opOK;
|
|
|
|
case PackCategoriesIntoKey(fcZero, fcNormal):
|
|
assign(rhs);
|
|
sign = rhs.sign ^ subtract;
|
|
return opOK;
|
|
|
|
case PackCategoriesIntoKey(fcZero, fcZero):
|
|
/* Sign depends on rounding mode; handled by caller. */
|
|
return opOK;
|
|
|
|
case PackCategoriesIntoKey(fcInfinity, fcInfinity):
|
|
/* Differently signed infinities can only be validly
|
|
subtracted. */
|
|
if (((sign ^ rhs.sign)!=0) != subtract) {
|
|
makeNaN();
|
|
return opInvalidOp;
|
|
}
|
|
|
|
return opOK;
|
|
|
|
case PackCategoriesIntoKey(fcNormal, fcNormal):
|
|
return opDivByZero;
|
|
}
|
|
}
|
|
|
|
/* Add or subtract two normal numbers. */
|
|
lostFraction
|
|
APFloat::addOrSubtractSignificand(const APFloat &rhs, bool subtract)
|
|
{
|
|
integerPart carry;
|
|
lostFraction lost_fraction;
|
|
int bits;
|
|
|
|
/* Determine if the operation on the absolute values is effectively
|
|
an addition or subtraction. */
|
|
subtract ^= (sign ^ rhs.sign) ? true : false;
|
|
|
|
/* Are we bigger exponent-wise than the RHS? */
|
|
bits = exponent - rhs.exponent;
|
|
|
|
/* Subtraction is more subtle than one might naively expect. */
|
|
if (subtract) {
|
|
APFloat temp_rhs(rhs);
|
|
bool reverse;
|
|
|
|
if (bits == 0) {
|
|
reverse = compareAbsoluteValue(temp_rhs) == cmpLessThan;
|
|
lost_fraction = lfExactlyZero;
|
|
} else if (bits > 0) {
|
|
lost_fraction = temp_rhs.shiftSignificandRight(bits - 1);
|
|
shiftSignificandLeft(1);
|
|
reverse = false;
|
|
} else {
|
|
lost_fraction = shiftSignificandRight(-bits - 1);
|
|
temp_rhs.shiftSignificandLeft(1);
|
|
reverse = true;
|
|
}
|
|
|
|
if (reverse) {
|
|
carry = temp_rhs.subtractSignificand
|
|
(*this, lost_fraction != lfExactlyZero);
|
|
copySignificand(temp_rhs);
|
|
sign = !sign;
|
|
} else {
|
|
carry = subtractSignificand
|
|
(temp_rhs, lost_fraction != lfExactlyZero);
|
|
}
|
|
|
|
/* Invert the lost fraction - it was on the RHS and
|
|
subtracted. */
|
|
if (lost_fraction == lfLessThanHalf)
|
|
lost_fraction = lfMoreThanHalf;
|
|
else if (lost_fraction == lfMoreThanHalf)
|
|
lost_fraction = lfLessThanHalf;
|
|
|
|
/* The code above is intended to ensure that no borrow is
|
|
necessary. */
|
|
assert(!carry);
|
|
(void)carry;
|
|
} else {
|
|
if (bits > 0) {
|
|
APFloat temp_rhs(rhs);
|
|
|
|
lost_fraction = temp_rhs.shiftSignificandRight(bits);
|
|
carry = addSignificand(temp_rhs);
|
|
} else {
|
|
lost_fraction = shiftSignificandRight(-bits);
|
|
carry = addSignificand(rhs);
|
|
}
|
|
|
|
/* We have a guard bit; generating a carry cannot happen. */
|
|
assert(!carry);
|
|
(void)carry;
|
|
}
|
|
|
|
return lost_fraction;
|
|
}
|
|
|
|
APFloat::opStatus
|
|
APFloat::multiplySpecials(const APFloat &rhs)
|
|
{
|
|
switch (PackCategoriesIntoKey(category, rhs.category)) {
|
|
default:
|
|
llvm_unreachable(nullptr);
|
|
|
|
case PackCategoriesIntoKey(fcNaN, fcZero):
|
|
case PackCategoriesIntoKey(fcNaN, fcNormal):
|
|
case PackCategoriesIntoKey(fcNaN, fcInfinity):
|
|
case PackCategoriesIntoKey(fcNaN, fcNaN):
|
|
sign = false;
|
|
return opOK;
|
|
|
|
case PackCategoriesIntoKey(fcZero, fcNaN):
|
|
case PackCategoriesIntoKey(fcNormal, fcNaN):
|
|
case PackCategoriesIntoKey(fcInfinity, fcNaN):
|
|
sign = false;
|
|
category = fcNaN;
|
|
copySignificand(rhs);
|
|
return opOK;
|
|
|
|
case PackCategoriesIntoKey(fcNormal, fcInfinity):
|
|
case PackCategoriesIntoKey(fcInfinity, fcNormal):
|
|
case PackCategoriesIntoKey(fcInfinity, fcInfinity):
|
|
category = fcInfinity;
|
|
return opOK;
|
|
|
|
case PackCategoriesIntoKey(fcZero, fcNormal):
|
|
case PackCategoriesIntoKey(fcNormal, fcZero):
|
|
case PackCategoriesIntoKey(fcZero, fcZero):
|
|
category = fcZero;
|
|
return opOK;
|
|
|
|
case PackCategoriesIntoKey(fcZero, fcInfinity):
|
|
case PackCategoriesIntoKey(fcInfinity, fcZero):
|
|
makeNaN();
|
|
return opInvalidOp;
|
|
|
|
case PackCategoriesIntoKey(fcNormal, fcNormal):
|
|
return opOK;
|
|
}
|
|
}
|
|
|
|
APFloat::opStatus
|
|
APFloat::divideSpecials(const APFloat &rhs)
|
|
{
|
|
switch (PackCategoriesIntoKey(category, rhs.category)) {
|
|
default:
|
|
llvm_unreachable(nullptr);
|
|
|
|
case PackCategoriesIntoKey(fcZero, fcNaN):
|
|
case PackCategoriesIntoKey(fcNormal, fcNaN):
|
|
case PackCategoriesIntoKey(fcInfinity, fcNaN):
|
|
category = fcNaN;
|
|
copySignificand(rhs);
|
|
case PackCategoriesIntoKey(fcNaN, fcZero):
|
|
case PackCategoriesIntoKey(fcNaN, fcNormal):
|
|
case PackCategoriesIntoKey(fcNaN, fcInfinity):
|
|
case PackCategoriesIntoKey(fcNaN, fcNaN):
|
|
sign = false;
|
|
case PackCategoriesIntoKey(fcInfinity, fcZero):
|
|
case PackCategoriesIntoKey(fcInfinity, fcNormal):
|
|
case PackCategoriesIntoKey(fcZero, fcInfinity):
|
|
case PackCategoriesIntoKey(fcZero, fcNormal):
|
|
return opOK;
|
|
|
|
case PackCategoriesIntoKey(fcNormal, fcInfinity):
|
|
category = fcZero;
|
|
return opOK;
|
|
|
|
case PackCategoriesIntoKey(fcNormal, fcZero):
|
|
category = fcInfinity;
|
|
return opDivByZero;
|
|
|
|
case PackCategoriesIntoKey(fcInfinity, fcInfinity):
|
|
case PackCategoriesIntoKey(fcZero, fcZero):
|
|
makeNaN();
|
|
return opInvalidOp;
|
|
|
|
case PackCategoriesIntoKey(fcNormal, fcNormal):
|
|
return opOK;
|
|
}
|
|
}
|
|
|
|
APFloat::opStatus
|
|
APFloat::modSpecials(const APFloat &rhs)
|
|
{
|
|
switch (PackCategoriesIntoKey(category, rhs.category)) {
|
|
default:
|
|
llvm_unreachable(nullptr);
|
|
|
|
case PackCategoriesIntoKey(fcNaN, fcZero):
|
|
case PackCategoriesIntoKey(fcNaN, fcNormal):
|
|
case PackCategoriesIntoKey(fcNaN, fcInfinity):
|
|
case PackCategoriesIntoKey(fcNaN, fcNaN):
|
|
case PackCategoriesIntoKey(fcZero, fcInfinity):
|
|
case PackCategoriesIntoKey(fcZero, fcNormal):
|
|
case PackCategoriesIntoKey(fcNormal, fcInfinity):
|
|
return opOK;
|
|
|
|
case PackCategoriesIntoKey(fcZero, fcNaN):
|
|
case PackCategoriesIntoKey(fcNormal, fcNaN):
|
|
case PackCategoriesIntoKey(fcInfinity, fcNaN):
|
|
sign = false;
|
|
category = fcNaN;
|
|
copySignificand(rhs);
|
|
return opOK;
|
|
|
|
case PackCategoriesIntoKey(fcNormal, fcZero):
|
|
case PackCategoriesIntoKey(fcInfinity, fcZero):
|
|
case PackCategoriesIntoKey(fcInfinity, fcNormal):
|
|
case PackCategoriesIntoKey(fcInfinity, fcInfinity):
|
|
case PackCategoriesIntoKey(fcZero, fcZero):
|
|
makeNaN();
|
|
return opInvalidOp;
|
|
|
|
case PackCategoriesIntoKey(fcNormal, fcNormal):
|
|
return opOK;
|
|
}
|
|
}
|
|
|
|
/* Change sign. */
|
|
void
|
|
APFloat::changeSign()
|
|
{
|
|
/* Look mummy, this one's easy. */
|
|
sign = !sign;
|
|
}
|
|
|
|
void
|
|
APFloat::clearSign()
|
|
{
|
|
/* So is this one. */
|
|
sign = 0;
|
|
}
|
|
|
|
void
|
|
APFloat::copySign(const APFloat &rhs)
|
|
{
|
|
/* And this one. */
|
|
sign = rhs.sign;
|
|
}
|
|
|
|
/* Normalized addition or subtraction. */
|
|
APFloat::opStatus
|
|
APFloat::addOrSubtract(const APFloat &rhs, roundingMode rounding_mode,
|
|
bool subtract)
|
|
{
|
|
opStatus fs;
|
|
|
|
fs = addOrSubtractSpecials(rhs, subtract);
|
|
|
|
/* This return code means it was not a simple case. */
|
|
if (fs == opDivByZero) {
|
|
lostFraction lost_fraction;
|
|
|
|
lost_fraction = addOrSubtractSignificand(rhs, subtract);
|
|
fs = normalize(rounding_mode, lost_fraction);
|
|
|
|
/* Can only be zero if we lost no fraction. */
|
|
assert(category != fcZero || lost_fraction == lfExactlyZero);
|
|
}
|
|
|
|
/* If two numbers add (exactly) to zero, IEEE 754 decrees it is a
|
|
positive zero unless rounding to minus infinity, except that
|
|
adding two like-signed zeroes gives that zero. */
|
|
if (category == fcZero) {
|
|
if (rhs.category != fcZero || (sign == rhs.sign) == subtract)
|
|
sign = (rounding_mode == rmTowardNegative);
|
|
}
|
|
|
|
return fs;
|
|
}
|
|
|
|
/* Normalized addition. */
|
|
APFloat::opStatus
|
|
APFloat::add(const APFloat &rhs, roundingMode rounding_mode)
|
|
{
|
|
return addOrSubtract(rhs, rounding_mode, false);
|
|
}
|
|
|
|
/* Normalized subtraction. */
|
|
APFloat::opStatus
|
|
APFloat::subtract(const APFloat &rhs, roundingMode rounding_mode)
|
|
{
|
|
return addOrSubtract(rhs, rounding_mode, true);
|
|
}
|
|
|
|
/* Normalized multiply. */
|
|
APFloat::opStatus
|
|
APFloat::multiply(const APFloat &rhs, roundingMode rounding_mode)
|
|
{
|
|
opStatus fs;
|
|
|
|
sign ^= rhs.sign;
|
|
fs = multiplySpecials(rhs);
|
|
|
|
if (isFiniteNonZero()) {
|
|
lostFraction lost_fraction = multiplySignificand(rhs, nullptr);
|
|
fs = normalize(rounding_mode, lost_fraction);
|
|
if (lost_fraction != lfExactlyZero)
|
|
fs = (opStatus) (fs | opInexact);
|
|
}
|
|
|
|
return fs;
|
|
}
|
|
|
|
/* Normalized divide. */
|
|
APFloat::opStatus
|
|
APFloat::divide(const APFloat &rhs, roundingMode rounding_mode)
|
|
{
|
|
opStatus fs;
|
|
|
|
sign ^= rhs.sign;
|
|
fs = divideSpecials(rhs);
|
|
|
|
if (isFiniteNonZero()) {
|
|
lostFraction lost_fraction = divideSignificand(rhs);
|
|
fs = normalize(rounding_mode, lost_fraction);
|
|
if (lost_fraction != lfExactlyZero)
|
|
fs = (opStatus) (fs | opInexact);
|
|
}
|
|
|
|
return fs;
|
|
}
|
|
|
|
/* Normalized remainder. This is not currently correct in all cases. */
|
|
APFloat::opStatus
|
|
APFloat::remainder(const APFloat &rhs)
|
|
{
|
|
opStatus fs;
|
|
APFloat V = *this;
|
|
unsigned int origSign = sign;
|
|
|
|
fs = V.divide(rhs, rmNearestTiesToEven);
|
|
if (fs == opDivByZero)
|
|
return fs;
|
|
|
|
int parts = partCount();
|
|
integerPart *x = new integerPart[parts];
|
|
bool ignored;
|
|
fs = V.convertToInteger(x, parts * integerPartWidth, true,
|
|
rmNearestTiesToEven, &ignored);
|
|
if (fs==opInvalidOp)
|
|
return fs;
|
|
|
|
fs = V.convertFromZeroExtendedInteger(x, parts * integerPartWidth, true,
|
|
rmNearestTiesToEven);
|
|
assert(fs==opOK); // should always work
|
|
|
|
fs = V.multiply(rhs, rmNearestTiesToEven);
|
|
assert(fs==opOK || fs==opInexact); // should not overflow or underflow
|
|
|
|
fs = subtract(V, rmNearestTiesToEven);
|
|
assert(fs==opOK || fs==opInexact); // likewise
|
|
|
|
if (isZero())
|
|
sign = origSign; // IEEE754 requires this
|
|
delete[] x;
|
|
return fs;
|
|
}
|
|
|
|
/* Normalized llvm frem (C fmod).
|
|
This is not currently correct in all cases. */
|
|
APFloat::opStatus
|
|
APFloat::mod(const APFloat &rhs, roundingMode rounding_mode)
|
|
{
|
|
opStatus fs;
|
|
fs = modSpecials(rhs);
|
|
|
|
if (isFiniteNonZero() && rhs.isFiniteNonZero()) {
|
|
APFloat V = *this;
|
|
unsigned int origSign = sign;
|
|
|
|
fs = V.divide(rhs, rmNearestTiesToEven);
|
|
if (fs == opDivByZero)
|
|
return fs;
|
|
|
|
int parts = partCount();
|
|
integerPart *x = new integerPart[parts];
|
|
bool ignored;
|
|
fs = V.convertToInteger(x, parts * integerPartWidth, true,
|
|
rmTowardZero, &ignored);
|
|
if (fs==opInvalidOp)
|
|
return fs;
|
|
|
|
fs = V.convertFromZeroExtendedInteger(x, parts * integerPartWidth, true,
|
|
rmNearestTiesToEven);
|
|
assert(fs==opOK); // should always work
|
|
|
|
fs = V.multiply(rhs, rounding_mode);
|
|
assert(fs==opOK || fs==opInexact); // should not overflow or underflow
|
|
|
|
fs = subtract(V, rounding_mode);
|
|
assert(fs==opOK || fs==opInexact); // likewise
|
|
|
|
if (isZero())
|
|
sign = origSign; // IEEE754 requires this
|
|
delete[] x;
|
|
}
|
|
return fs;
|
|
}
|
|
|
|
/* Normalized fused-multiply-add. */
|
|
APFloat::opStatus
|
|
APFloat::fusedMultiplyAdd(const APFloat &multiplicand,
|
|
const APFloat &addend,
|
|
roundingMode rounding_mode)
|
|
{
|
|
opStatus fs;
|
|
|
|
/* Post-multiplication sign, before addition. */
|
|
sign ^= multiplicand.sign;
|
|
|
|
/* If and only if all arguments are normal do we need to do an
|
|
extended-precision calculation. */
|
|
if (isFiniteNonZero() &&
|
|
multiplicand.isFiniteNonZero() &&
|
|
addend.isFiniteNonZero()) {
|
|
lostFraction lost_fraction;
|
|
|
|
lost_fraction = multiplySignificand(multiplicand, &addend);
|
|
fs = normalize(rounding_mode, lost_fraction);
|
|
if (lost_fraction != lfExactlyZero)
|
|
fs = (opStatus) (fs | opInexact);
|
|
|
|
/* If two numbers add (exactly) to zero, IEEE 754 decrees it is a
|
|
positive zero unless rounding to minus infinity, except that
|
|
adding two like-signed zeroes gives that zero. */
|
|
if (category == fcZero && sign != addend.sign)
|
|
sign = (rounding_mode == rmTowardNegative);
|
|
} else {
|
|
fs = multiplySpecials(multiplicand);
|
|
|
|
/* FS can only be opOK or opInvalidOp. There is no more work
|
|
to do in the latter case. The IEEE-754R standard says it is
|
|
implementation-defined in this case whether, if ADDEND is a
|
|
quiet NaN, we raise invalid op; this implementation does so.
|
|
|
|
If we need to do the addition we can do so with normal
|
|
precision. */
|
|
if (fs == opOK)
|
|
fs = addOrSubtract(addend, rounding_mode, false);
|
|
}
|
|
|
|
return fs;
|
|
}
|
|
|
|
/* Rounding-mode corrrect round to integral value. */
|
|
APFloat::opStatus APFloat::roundToIntegral(roundingMode rounding_mode) {
|
|
opStatus fs;
|
|
|
|
// If the exponent is large enough, we know that this value is already
|
|
// integral, and the arithmetic below would potentially cause it to saturate
|
|
// to +/-Inf. Bail out early instead.
|
|
if (isFiniteNonZero() && exponent+1 >= (int)semanticsPrecision(*semantics))
|
|
return opOK;
|
|
|
|
// The algorithm here is quite simple: we add 2^(p-1), where p is the
|
|
// precision of our format, and then subtract it back off again. The choice
|
|
// of rounding modes for the addition/subtraction determines the rounding mode
|
|
// for our integral rounding as well.
|
|
// NOTE: When the input value is negative, we do subtraction followed by
|
|
// addition instead.
|
|
APInt IntegerConstant(NextPowerOf2(semanticsPrecision(*semantics)), 1);
|
|
IntegerConstant <<= semanticsPrecision(*semantics)-1;
|
|
APFloat MagicConstant(*semantics);
|
|
fs = MagicConstant.convertFromAPInt(IntegerConstant, false,
|
|
rmNearestTiesToEven);
|
|
MagicConstant.copySign(*this);
|
|
|
|
if (fs != opOK)
|
|
return fs;
|
|
|
|
// Preserve the input sign so that we can handle 0.0/-0.0 cases correctly.
|
|
bool inputSign = isNegative();
|
|
|
|
fs = add(MagicConstant, rounding_mode);
|
|
if (fs != opOK && fs != opInexact)
|
|
return fs;
|
|
|
|
fs = subtract(MagicConstant, rounding_mode);
|
|
|
|
// Restore the input sign.
|
|
if (inputSign != isNegative())
|
|
changeSign();
|
|
|
|
return fs;
|
|
}
|
|
|
|
|
|
/* Comparison requires normalized numbers. */
|
|
APFloat::cmpResult
|
|
APFloat::compare(const APFloat &rhs) const
|
|
{
|
|
cmpResult result;
|
|
|
|
assert(semantics == rhs.semantics);
|
|
|
|
switch (PackCategoriesIntoKey(category, rhs.category)) {
|
|
default:
|
|
llvm_unreachable(nullptr);
|
|
|
|
case PackCategoriesIntoKey(fcNaN, fcZero):
|
|
case PackCategoriesIntoKey(fcNaN, fcNormal):
|
|
case PackCategoriesIntoKey(fcNaN, fcInfinity):
|
|
case PackCategoriesIntoKey(fcNaN, fcNaN):
|
|
case PackCategoriesIntoKey(fcZero, fcNaN):
|
|
case PackCategoriesIntoKey(fcNormal, fcNaN):
|
|
case PackCategoriesIntoKey(fcInfinity, fcNaN):
|
|
return cmpUnordered;
|
|
|
|
case PackCategoriesIntoKey(fcInfinity, fcNormal):
|
|
case PackCategoriesIntoKey(fcInfinity, fcZero):
|
|
case PackCategoriesIntoKey(fcNormal, fcZero):
|
|
if (sign)
|
|
return cmpLessThan;
|
|
else
|
|
return cmpGreaterThan;
|
|
|
|
case PackCategoriesIntoKey(fcNormal, fcInfinity):
|
|
case PackCategoriesIntoKey(fcZero, fcInfinity):
|
|
case PackCategoriesIntoKey(fcZero, fcNormal):
|
|
if (rhs.sign)
|
|
return cmpGreaterThan;
|
|
else
|
|
return cmpLessThan;
|
|
|
|
case PackCategoriesIntoKey(fcInfinity, fcInfinity):
|
|
if (sign == rhs.sign)
|
|
return cmpEqual;
|
|
else if (sign)
|
|
return cmpLessThan;
|
|
else
|
|
return cmpGreaterThan;
|
|
|
|
case PackCategoriesIntoKey(fcZero, fcZero):
|
|
return cmpEqual;
|
|
|
|
case PackCategoriesIntoKey(fcNormal, fcNormal):
|
|
break;
|
|
}
|
|
|
|
/* Two normal numbers. Do they have the same sign? */
|
|
if (sign != rhs.sign) {
|
|
if (sign)
|
|
result = cmpLessThan;
|
|
else
|
|
result = cmpGreaterThan;
|
|
} else {
|
|
/* Compare absolute values; invert result if negative. */
|
|
result = compareAbsoluteValue(rhs);
|
|
|
|
if (sign) {
|
|
if (result == cmpLessThan)
|
|
result = cmpGreaterThan;
|
|
else if (result == cmpGreaterThan)
|
|
result = cmpLessThan;
|
|
}
|
|
}
|
|
|
|
return result;
|
|
}
|
|
|
|
/// APFloat::convert - convert a value of one floating point type to another.
|
|
/// The return value corresponds to the IEEE754 exceptions. *losesInfo
|
|
/// records whether the transformation lost information, i.e. whether
|
|
/// converting the result back to the original type will produce the
|
|
/// original value (this is almost the same as return value==fsOK, but there
|
|
/// are edge cases where this is not so).
|
|
|
|
APFloat::opStatus
|
|
APFloat::convert(const fltSemantics &toSemantics,
|
|
roundingMode rounding_mode, bool *losesInfo)
|
|
{
|
|
lostFraction lostFraction;
|
|
unsigned int newPartCount, oldPartCount;
|
|
opStatus fs;
|
|
int shift;
|
|
const fltSemantics &fromSemantics = *semantics;
|
|
|
|
lostFraction = lfExactlyZero;
|
|
newPartCount = partCountForBits(toSemantics.precision + 1);
|
|
oldPartCount = partCount();
|
|
shift = toSemantics.precision - fromSemantics.precision;
|
|
|
|
bool X86SpecialNan = false;
|
|
if (&fromSemantics == &APFloat::x87DoubleExtended &&
|
|
&toSemantics != &APFloat::x87DoubleExtended && category == fcNaN &&
|
|
(!(*significandParts() & 0x8000000000000000ULL) ||
|
|
!(*significandParts() & 0x4000000000000000ULL))) {
|
|
// x86 has some unusual NaNs which cannot be represented in any other
|
|
// format; note them here.
|
|
X86SpecialNan = true;
|
|
}
|
|
|
|
// If this is a truncation of a denormal number, and the target semantics
|
|
// has larger exponent range than the source semantics (this can happen
|
|
// when truncating from PowerPC double-double to double format), the
|
|
// right shift could lose result mantissa bits. Adjust exponent instead
|
|
// of performing excessive shift.
|
|
if (shift < 0 && isFiniteNonZero()) {
|
|
int exponentChange = significandMSB() + 1 - fromSemantics.precision;
|
|
if (exponent + exponentChange < toSemantics.minExponent)
|
|
exponentChange = toSemantics.minExponent - exponent;
|
|
if (exponentChange < shift)
|
|
exponentChange = shift;
|
|
if (exponentChange < 0) {
|
|
shift -= exponentChange;
|
|
exponent += exponentChange;
|
|
}
|
|
}
|
|
|
|
// If this is a truncation, perform the shift before we narrow the storage.
|
|
if (shift < 0 && (isFiniteNonZero() || category==fcNaN))
|
|
lostFraction = shiftRight(significandParts(), oldPartCount, -shift);
|
|
|
|
// Fix the storage so it can hold to new value.
|
|
if (newPartCount > oldPartCount) {
|
|
// The new type requires more storage; make it available.
|
|
integerPart *newParts;
|
|
newParts = new integerPart[newPartCount];
|
|
APInt::tcSet(newParts, 0, newPartCount);
|
|
if (isFiniteNonZero() || category==fcNaN)
|
|
APInt::tcAssign(newParts, significandParts(), oldPartCount);
|
|
freeSignificand();
|
|
significand.parts = newParts;
|
|
} else if (newPartCount == 1 && oldPartCount != 1) {
|
|
// Switch to built-in storage for a single part.
|
|
integerPart newPart = 0;
|
|
if (isFiniteNonZero() || category==fcNaN)
|
|
newPart = significandParts()[0];
|
|
freeSignificand();
|
|
significand.part = newPart;
|
|
}
|
|
|
|
// Now that we have the right storage, switch the semantics.
|
|
semantics = &toSemantics;
|
|
|
|
// If this is an extension, perform the shift now that the storage is
|
|
// available.
|
|
if (shift > 0 && (isFiniteNonZero() || category==fcNaN))
|
|
APInt::tcShiftLeft(significandParts(), newPartCount, shift);
|
|
|
|
if (isFiniteNonZero()) {
|
|
fs = normalize(rounding_mode, lostFraction);
|
|
*losesInfo = (fs != opOK);
|
|
} else if (category == fcNaN) {
|
|
*losesInfo = lostFraction != lfExactlyZero || X86SpecialNan;
|
|
|
|
// For x87 extended precision, we want to make a NaN, not a special NaN if
|
|
// the input wasn't special either.
|
|
if (!X86SpecialNan && semantics == &APFloat::x87DoubleExtended)
|
|
APInt::tcSetBit(significandParts(), semantics->precision - 1);
|
|
|
|
// gcc forces the Quiet bit on, which means (float)(double)(float_sNan)
|
|
// does not give you back the same bits. This is dubious, and we
|
|
// don't currently do it. You're really supposed to get
|
|
// an invalid operation signal at runtime, but nobody does that.
|
|
fs = opOK;
|
|
} else {
|
|
*losesInfo = false;
|
|
fs = opOK;
|
|
}
|
|
|
|
return fs;
|
|
}
|
|
|
|
/* Convert a floating point number to an integer according to the
|
|
rounding mode. If the rounded integer value is out of range this
|
|
returns an invalid operation exception and the contents of the
|
|
destination parts are unspecified. If the rounded value is in
|
|
range but the floating point number is not the exact integer, the C
|
|
standard doesn't require an inexact exception to be raised. IEEE
|
|
854 does require it so we do that.
|
|
|
|
Note that for conversions to integer type the C standard requires
|
|
round-to-zero to always be used. */
|
|
APFloat::opStatus
|
|
APFloat::convertToSignExtendedInteger(integerPart *parts, unsigned int width,
|
|
bool isSigned,
|
|
roundingMode rounding_mode,
|
|
bool *isExact) const
|
|
{
|
|
lostFraction lost_fraction;
|
|
const integerPart *src;
|
|
unsigned int dstPartsCount, truncatedBits;
|
|
|
|
*isExact = false;
|
|
|
|
/* Handle the three special cases first. */
|
|
if (category == fcInfinity || category == fcNaN)
|
|
return opInvalidOp;
|
|
|
|
dstPartsCount = partCountForBits(width);
|
|
|
|
if (category == fcZero) {
|
|
APInt::tcSet(parts, 0, dstPartsCount);
|
|
// Negative zero can't be represented as an int.
|
|
*isExact = !sign;
|
|
return opOK;
|
|
}
|
|
|
|
src = significandParts();
|
|
|
|
/* Step 1: place our absolute value, with any fraction truncated, in
|
|
the destination. */
|
|
if (exponent < 0) {
|
|
/* Our absolute value is less than one; truncate everything. */
|
|
APInt::tcSet(parts, 0, dstPartsCount);
|
|
/* For exponent -1 the integer bit represents .5, look at that.
|
|
For smaller exponents leftmost truncated bit is 0. */
|
|
truncatedBits = semantics->precision -1U - exponent;
|
|
} else {
|
|
/* We want the most significant (exponent + 1) bits; the rest are
|
|
truncated. */
|
|
unsigned int bits = exponent + 1U;
|
|
|
|
/* Hopelessly large in magnitude? */
|
|
if (bits > width)
|
|
return opInvalidOp;
|
|
|
|
if (bits < semantics->precision) {
|
|
/* We truncate (semantics->precision - bits) bits. */
|
|
truncatedBits = semantics->precision - bits;
|
|
APInt::tcExtract(parts, dstPartsCount, src, bits, truncatedBits);
|
|
} else {
|
|
/* We want at least as many bits as are available. */
|
|
APInt::tcExtract(parts, dstPartsCount, src, semantics->precision, 0);
|
|
APInt::tcShiftLeft(parts, dstPartsCount, bits - semantics->precision);
|
|
truncatedBits = 0;
|
|
}
|
|
}
|
|
|
|
/* Step 2: work out any lost fraction, and increment the absolute
|
|
value if we would round away from zero. */
|
|
if (truncatedBits) {
|
|
lost_fraction = lostFractionThroughTruncation(src, partCount(),
|
|
truncatedBits);
|
|
if (lost_fraction != lfExactlyZero &&
|
|
roundAwayFromZero(rounding_mode, lost_fraction, truncatedBits)) {
|
|
if (APInt::tcIncrement(parts, dstPartsCount))
|
|
return opInvalidOp; /* Overflow. */
|
|
}
|
|
} else {
|
|
lost_fraction = lfExactlyZero;
|
|
}
|
|
|
|
/* Step 3: check if we fit in the destination. */
|
|
unsigned int omsb = APInt::tcMSB(parts, dstPartsCount) + 1;
|
|
|
|
if (sign) {
|
|
if (!isSigned) {
|
|
/* Negative numbers cannot be represented as unsigned. */
|
|
if (omsb != 0)
|
|
return opInvalidOp;
|
|
} else {
|
|
/* It takes omsb bits to represent the unsigned integer value.
|
|
We lose a bit for the sign, but care is needed as the
|
|
maximally negative integer is a special case. */
|
|
if (omsb == width && APInt::tcLSB(parts, dstPartsCount) + 1 != omsb)
|
|
return opInvalidOp;
|
|
|
|
/* This case can happen because of rounding. */
|
|
if (omsb > width)
|
|
return opInvalidOp;
|
|
}
|
|
|
|
APInt::tcNegate (parts, dstPartsCount);
|
|
} else {
|
|
if (omsb >= width + !isSigned)
|
|
return opInvalidOp;
|
|
}
|
|
|
|
if (lost_fraction == lfExactlyZero) {
|
|
*isExact = true;
|
|
return opOK;
|
|
} else
|
|
return opInexact;
|
|
}
|
|
|
|
/* Same as convertToSignExtendedInteger, except we provide
|
|
deterministic values in case of an invalid operation exception,
|
|
namely zero for NaNs and the minimal or maximal value respectively
|
|
for underflow or overflow.
|
|
The *isExact output tells whether the result is exact, in the sense
|
|
that converting it back to the original floating point type produces
|
|
the original value. This is almost equivalent to result==opOK,
|
|
except for negative zeroes.
|
|
*/
|
|
APFloat::opStatus
|
|
APFloat::convertToInteger(integerPart *parts, unsigned int width,
|
|
bool isSigned,
|
|
roundingMode rounding_mode, bool *isExact) const
|
|
{
|
|
opStatus fs;
|
|
|
|
fs = convertToSignExtendedInteger(parts, width, isSigned, rounding_mode,
|
|
isExact);
|
|
|
|
if (fs == opInvalidOp) {
|
|
unsigned int bits, dstPartsCount;
|
|
|
|
dstPartsCount = partCountForBits(width);
|
|
|
|
if (category == fcNaN)
|
|
bits = 0;
|
|
else if (sign)
|
|
bits = isSigned;
|
|
else
|
|
bits = width - isSigned;
|
|
|
|
APInt::tcSetLeastSignificantBits(parts, dstPartsCount, bits);
|
|
if (sign && isSigned)
|
|
APInt::tcShiftLeft(parts, dstPartsCount, width - 1);
|
|
}
|
|
|
|
return fs;
|
|
}
|
|
|
|
/* Same as convertToInteger(integerPart*, ...), except the result is returned in
|
|
an APSInt, whose initial bit-width and signed-ness are used to determine the
|
|
precision of the conversion.
|
|
*/
|
|
APFloat::opStatus
|
|
APFloat::convertToInteger(APSInt &result,
|
|
roundingMode rounding_mode, bool *isExact) const
|
|
{
|
|
unsigned bitWidth = result.getBitWidth();
|
|
SmallVector<uint64_t, 4> parts(result.getNumWords());
|
|
opStatus status = convertToInteger(
|
|
parts.data(), bitWidth, result.isSigned(), rounding_mode, isExact);
|
|
// Keeps the original signed-ness.
|
|
result = APInt(bitWidth, parts);
|
|
return status;
|
|
}
|
|
|
|
/* Convert an unsigned integer SRC to a floating point number,
|
|
rounding according to ROUNDING_MODE. The sign of the floating
|
|
point number is not modified. */
|
|
APFloat::opStatus
|
|
APFloat::convertFromUnsignedParts(const integerPart *src,
|
|
unsigned int srcCount,
|
|
roundingMode rounding_mode)
|
|
{
|
|
unsigned int omsb, precision, dstCount;
|
|
integerPart *dst;
|
|
lostFraction lost_fraction;
|
|
|
|
category = fcNormal;
|
|
omsb = APInt::tcMSB(src, srcCount) + 1;
|
|
dst = significandParts();
|
|
dstCount = partCount();
|
|
precision = semantics->precision;
|
|
|
|
/* We want the most significant PRECISION bits of SRC. There may not
|
|
be that many; extract what we can. */
|
|
if (precision <= omsb) {
|
|
exponent = omsb - 1;
|
|
lost_fraction = lostFractionThroughTruncation(src, srcCount,
|
|
omsb - precision);
|
|
APInt::tcExtract(dst, dstCount, src, precision, omsb - precision);
|
|
} else {
|
|
exponent = precision - 1;
|
|
lost_fraction = lfExactlyZero;
|
|
APInt::tcExtract(dst, dstCount, src, omsb, 0);
|
|
}
|
|
|
|
return normalize(rounding_mode, lost_fraction);
|
|
}
|
|
|
|
APFloat::opStatus
|
|
APFloat::convertFromAPInt(const APInt &Val,
|
|
bool isSigned,
|
|
roundingMode rounding_mode)
|
|
{
|
|
unsigned int partCount = Val.getNumWords();
|
|
APInt api = Val;
|
|
|
|
sign = false;
|
|
if (isSigned && api.isNegative()) {
|
|
sign = true;
|
|
api = -api;
|
|
}
|
|
|
|
return convertFromUnsignedParts(api.getRawData(), partCount, rounding_mode);
|
|
}
|
|
|
|
/* Convert a two's complement integer SRC to a floating point number,
|
|
rounding according to ROUNDING_MODE. ISSIGNED is true if the
|
|
integer is signed, in which case it must be sign-extended. */
|
|
APFloat::opStatus
|
|
APFloat::convertFromSignExtendedInteger(const integerPart *src,
|
|
unsigned int srcCount,
|
|
bool isSigned,
|
|
roundingMode rounding_mode)
|
|
{
|
|
opStatus status;
|
|
|
|
if (isSigned &&
|
|
APInt::tcExtractBit(src, srcCount * integerPartWidth - 1)) {
|
|
integerPart *copy;
|
|
|
|
/* If we're signed and negative negate a copy. */
|
|
sign = true;
|
|
copy = new integerPart[srcCount];
|
|
APInt::tcAssign(copy, src, srcCount);
|
|
APInt::tcNegate(copy, srcCount);
|
|
status = convertFromUnsignedParts(copy, srcCount, rounding_mode);
|
|
delete [] copy;
|
|
} else {
|
|
sign = false;
|
|
status = convertFromUnsignedParts(src, srcCount, rounding_mode);
|
|
}
|
|
|
|
return status;
|
|
}
|
|
|
|
/* FIXME: should this just take a const APInt reference? */
|
|
APFloat::opStatus
|
|
APFloat::convertFromZeroExtendedInteger(const integerPart *parts,
|
|
unsigned int width, bool isSigned,
|
|
roundingMode rounding_mode)
|
|
{
|
|
unsigned int partCount = partCountForBits(width);
|
|
APInt api = APInt(width, makeArrayRef(parts, partCount));
|
|
|
|
sign = false;
|
|
if (isSigned && APInt::tcExtractBit(parts, width - 1)) {
|
|
sign = true;
|
|
api = -api;
|
|
}
|
|
|
|
return convertFromUnsignedParts(api.getRawData(), partCount, rounding_mode);
|
|
}
|
|
|
|
APFloat::opStatus
|
|
APFloat::convertFromHexadecimalString(StringRef s, roundingMode rounding_mode)
|
|
{
|
|
lostFraction lost_fraction = lfExactlyZero;
|
|
|
|
category = fcNormal;
|
|
zeroSignificand();
|
|
exponent = 0;
|
|
|
|
integerPart *significand = significandParts();
|
|
unsigned partsCount = partCount();
|
|
unsigned bitPos = partsCount * integerPartWidth;
|
|
bool computedTrailingFraction = false;
|
|
|
|
// Skip leading zeroes and any (hexa)decimal point.
|
|
StringRef::iterator begin = s.begin();
|
|
StringRef::iterator end = s.end();
|
|
StringRef::iterator dot;
|
|
StringRef::iterator p = skipLeadingZeroesAndAnyDot(begin, end, &dot);
|
|
StringRef::iterator firstSignificantDigit = p;
|
|
|
|
while (p != end) {
|
|
integerPart hex_value;
|
|
|
|
if (*p == '.') {
|
|
assert(dot == end && "String contains multiple dots");
|
|
dot = p++;
|
|
continue;
|
|
}
|
|
|
|
hex_value = hexDigitValue(*p);
|
|
if (hex_value == -1U)
|
|
break;
|
|
|
|
p++;
|
|
|
|
// Store the number while we have space.
|
|
if (bitPos) {
|
|
bitPos -= 4;
|
|
hex_value <<= bitPos % integerPartWidth;
|
|
significand[bitPos / integerPartWidth] |= hex_value;
|
|
} else if (!computedTrailingFraction) {
|
|
lost_fraction = trailingHexadecimalFraction(p, end, hex_value);
|
|
computedTrailingFraction = true;
|
|
}
|
|
}
|
|
|
|
/* Hex floats require an exponent but not a hexadecimal point. */
|
|
assert(p != end && "Hex strings require an exponent");
|
|
assert((*p == 'p' || *p == 'P') && "Invalid character in significand");
|
|
assert(p != begin && "Significand has no digits");
|
|
assert((dot == end || p - begin != 1) && "Significand has no digits");
|
|
|
|
/* Ignore the exponent if we are zero. */
|
|
if (p != firstSignificantDigit) {
|
|
int expAdjustment;
|
|
|
|
/* Implicit hexadecimal point? */
|
|
if (dot == end)
|
|
dot = p;
|
|
|
|
/* Calculate the exponent adjustment implicit in the number of
|
|
significant digits. */
|
|
expAdjustment = static_cast<int>(dot - firstSignificantDigit);
|
|
if (expAdjustment < 0)
|
|
expAdjustment++;
|
|
expAdjustment = expAdjustment * 4 - 1;
|
|
|
|
/* Adjust for writing the significand starting at the most
|
|
significant nibble. */
|
|
expAdjustment += semantics->precision;
|
|
expAdjustment -= partsCount * integerPartWidth;
|
|
|
|
/* Adjust for the given exponent. */
|
|
exponent = totalExponent(p + 1, end, expAdjustment);
|
|
}
|
|
|
|
return normalize(rounding_mode, lost_fraction);
|
|
}
|
|
|
|
APFloat::opStatus
|
|
APFloat::roundSignificandWithExponent(const integerPart *decSigParts,
|
|
unsigned sigPartCount, int exp,
|
|
roundingMode rounding_mode)
|
|
{
|
|
unsigned int parts, pow5PartCount;
|
|
fltSemantics calcSemantics = { 32767, -32767, 0 };
|
|
integerPart pow5Parts[maxPowerOfFiveParts];
|
|
bool isNearest;
|
|
|
|
isNearest = (rounding_mode == rmNearestTiesToEven ||
|
|
rounding_mode == rmNearestTiesToAway);
|
|
|
|
parts = partCountForBits(semantics->precision + 11);
|
|
|
|
/* Calculate pow(5, abs(exp)). */
|
|
pow5PartCount = powerOf5(pow5Parts, exp >= 0 ? exp: -exp);
|
|
|
|
for (;; parts *= 2) {
|
|
opStatus sigStatus, powStatus;
|
|
unsigned int excessPrecision, truncatedBits;
|
|
|
|
calcSemantics.precision = parts * integerPartWidth - 1;
|
|
excessPrecision = calcSemantics.precision - semantics->precision;
|
|
truncatedBits = excessPrecision;
|
|
|
|
APFloat decSig = APFloat::getZero(calcSemantics, sign);
|
|
APFloat pow5(calcSemantics);
|
|
|
|
sigStatus = decSig.convertFromUnsignedParts(decSigParts, sigPartCount,
|
|
rmNearestTiesToEven);
|
|
powStatus = pow5.convertFromUnsignedParts(pow5Parts, pow5PartCount,
|
|
rmNearestTiesToEven);
|
|
/* Add exp, as 10^n = 5^n * 2^n. */
|
|
decSig.exponent += exp;
|
|
|
|
lostFraction calcLostFraction;
|
|
integerPart HUerr, HUdistance;
|
|
unsigned int powHUerr;
|
|
|
|
if (exp >= 0) {
|
|
/* multiplySignificand leaves the precision-th bit set to 1. */
|
|
calcLostFraction = decSig.multiplySignificand(pow5, nullptr);
|
|
powHUerr = powStatus != opOK;
|
|
} else {
|
|
calcLostFraction = decSig.divideSignificand(pow5);
|
|
/* Denormal numbers have less precision. */
|
|
if (decSig.exponent < semantics->minExponent) {
|
|
excessPrecision += (semantics->minExponent - decSig.exponent);
|
|
truncatedBits = excessPrecision;
|
|
if (excessPrecision > calcSemantics.precision)
|
|
excessPrecision = calcSemantics.precision;
|
|
}
|
|
/* Extra half-ulp lost in reciprocal of exponent. */
|
|
powHUerr = (powStatus == opOK && calcLostFraction == lfExactlyZero) ? 0:2;
|
|
}
|
|
|
|
/* Both multiplySignificand and divideSignificand return the
|
|
result with the integer bit set. */
|
|
assert(APInt::tcExtractBit
|
|
(decSig.significandParts(), calcSemantics.precision - 1) == 1);
|
|
|
|
HUerr = HUerrBound(calcLostFraction != lfExactlyZero, sigStatus != opOK,
|
|
powHUerr);
|
|
HUdistance = 2 * ulpsFromBoundary(decSig.significandParts(),
|
|
excessPrecision, isNearest);
|
|
|
|
/* Are we guaranteed to round correctly if we truncate? */
|
|
if (HUdistance >= HUerr) {
|
|
APInt::tcExtract(significandParts(), partCount(), decSig.significandParts(),
|
|
calcSemantics.precision - excessPrecision,
|
|
excessPrecision);
|
|
/* Take the exponent of decSig. If we tcExtract-ed less bits
|
|
above we must adjust our exponent to compensate for the
|
|
implicit right shift. */
|
|
exponent = (decSig.exponent + semantics->precision
|
|
- (calcSemantics.precision - excessPrecision));
|
|
calcLostFraction = lostFractionThroughTruncation(decSig.significandParts(),
|
|
decSig.partCount(),
|
|
truncatedBits);
|
|
return normalize(rounding_mode, calcLostFraction);
|
|
}
|
|
}
|
|
}
|
|
|
|
APFloat::opStatus
|
|
APFloat::convertFromDecimalString(StringRef str, roundingMode rounding_mode)
|
|
{
|
|
decimalInfo D;
|
|
opStatus fs;
|
|
|
|
/* Scan the text. */
|
|
StringRef::iterator p = str.begin();
|
|
interpretDecimal(p, str.end(), &D);
|
|
|
|
/* Handle the quick cases. First the case of no significant digits,
|
|
i.e. zero, and then exponents that are obviously too large or too
|
|
small. Writing L for log 10 / log 2, a number d.ddddd*10^exp
|
|
definitely overflows if
|
|
|
|
(exp - 1) * L >= maxExponent
|
|
|
|
and definitely underflows to zero where
|
|
|
|
(exp + 1) * L <= minExponent - precision
|
|
|
|
With integer arithmetic the tightest bounds for L are
|
|
|
|
93/28 < L < 196/59 [ numerator <= 256 ]
|
|
42039/12655 < L < 28738/8651 [ numerator <= 65536 ]
|
|
*/
|
|
|
|
// Test if we have a zero number allowing for strings with no null terminators
|
|
// and zero decimals with non-zero exponents.
|
|
//
|
|
// We computed firstSigDigit by ignoring all zeros and dots. Thus if
|
|
// D->firstSigDigit equals str.end(), every digit must be a zero and there can
|
|
// be at most one dot. On the other hand, if we have a zero with a non-zero
|
|
// exponent, then we know that D.firstSigDigit will be non-numeric.
|
|
if (D.firstSigDigit == str.end() || decDigitValue(*D.firstSigDigit) >= 10U) {
|
|
category = fcZero;
|
|
fs = opOK;
|
|
|
|
/* Check whether the normalized exponent is high enough to overflow
|
|
max during the log-rebasing in the max-exponent check below. */
|
|
} else if (D.normalizedExponent - 1 > INT_MAX / 42039) {
|
|
fs = handleOverflow(rounding_mode);
|
|
|
|
/* If it wasn't, then it also wasn't high enough to overflow max
|
|
during the log-rebasing in the min-exponent check. Check that it
|
|
won't overflow min in either check, then perform the min-exponent
|
|
check. */
|
|
} else if (D.normalizedExponent - 1 < INT_MIN / 42039 ||
|
|
(D.normalizedExponent + 1) * 28738 <=
|
|
8651 * (semantics->minExponent - (int) semantics->precision)) {
|
|
/* Underflow to zero and round. */
|
|
category = fcNormal;
|
|
zeroSignificand();
|
|
fs = normalize(rounding_mode, lfLessThanHalf);
|
|
|
|
/* We can finally safely perform the max-exponent check. */
|
|
} else if ((D.normalizedExponent - 1) * 42039
|
|
>= 12655 * semantics->maxExponent) {
|
|
/* Overflow and round. */
|
|
fs = handleOverflow(rounding_mode);
|
|
} else {
|
|
integerPart *decSignificand;
|
|
unsigned int partCount;
|
|
|
|
/* A tight upper bound on number of bits required to hold an
|
|
N-digit decimal integer is N * 196 / 59. Allocate enough space
|
|
to hold the full significand, and an extra part required by
|
|
tcMultiplyPart. */
|
|
partCount = static_cast<unsigned int>(D.lastSigDigit - D.firstSigDigit) + 1;
|
|
partCount = partCountForBits(1 + 196 * partCount / 59);
|
|
decSignificand = new integerPart[partCount + 1];
|
|
partCount = 0;
|
|
|
|
/* Convert to binary efficiently - we do almost all multiplication
|
|
in an integerPart. When this would overflow do we do a single
|
|
bignum multiplication, and then revert again to multiplication
|
|
in an integerPart. */
|
|
do {
|
|
integerPart decValue, val, multiplier;
|
|
|
|
val = 0;
|
|
multiplier = 1;
|
|
|
|
do {
|
|
if (*p == '.') {
|
|
p++;
|
|
if (p == str.end()) {
|
|
break;
|
|
}
|
|
}
|
|
decValue = decDigitValue(*p++);
|
|
assert(decValue < 10U && "Invalid character in significand");
|
|
multiplier *= 10;
|
|
val = val * 10 + decValue;
|
|
/* The maximum number that can be multiplied by ten with any
|
|
digit added without overflowing an integerPart. */
|
|
} while (p <= D.lastSigDigit && multiplier <= (~ (integerPart) 0 - 9) / 10);
|
|
|
|
/* Multiply out the current part. */
|
|
APInt::tcMultiplyPart(decSignificand, decSignificand, multiplier, val,
|
|
partCount, partCount + 1, false);
|
|
|
|
/* If we used another part (likely but not guaranteed), increase
|
|
the count. */
|
|
if (decSignificand[partCount])
|
|
partCount++;
|
|
} while (p <= D.lastSigDigit);
|
|
|
|
category = fcNormal;
|
|
fs = roundSignificandWithExponent(decSignificand, partCount,
|
|
D.exponent, rounding_mode);
|
|
|
|
delete [] decSignificand;
|
|
}
|
|
|
|
return fs;
|
|
}
|
|
|
|
bool
|
|
APFloat::convertFromStringSpecials(StringRef str) {
|
|
if (str.equals("inf") || str.equals("INFINITY")) {
|
|
makeInf(false);
|
|
return true;
|
|
}
|
|
|
|
if (str.equals("-inf") || str.equals("-INFINITY")) {
|
|
makeInf(true);
|
|
return true;
|
|
}
|
|
|
|
if (str.equals("nan") || str.equals("NaN")) {
|
|
makeNaN(false, false);
|
|
return true;
|
|
}
|
|
|
|
if (str.equals("-nan") || str.equals("-NaN")) {
|
|
makeNaN(false, true);
|
|
return true;
|
|
}
|
|
|
|
return false;
|
|
}
|
|
|
|
APFloat::opStatus
|
|
APFloat::convertFromString(StringRef str, roundingMode rounding_mode)
|
|
{
|
|
assert(!str.empty() && "Invalid string length");
|
|
|
|
// Handle special cases.
|
|
if (convertFromStringSpecials(str))
|
|
return opOK;
|
|
|
|
/* Handle a leading minus sign. */
|
|
StringRef::iterator p = str.begin();
|
|
size_t slen = str.size();
|
|
sign = *p == '-' ? 1 : 0;
|
|
if (*p == '-' || *p == '+') {
|
|
p++;
|
|
slen--;
|
|
assert(slen && "String has no digits");
|
|
}
|
|
|
|
if (slen >= 2 && p[0] == '0' && (p[1] == 'x' || p[1] == 'X')) {
|
|
assert(slen - 2 && "Invalid string");
|
|
return convertFromHexadecimalString(StringRef(p + 2, slen - 2),
|
|
rounding_mode);
|
|
}
|
|
|
|
return convertFromDecimalString(StringRef(p, slen), rounding_mode);
|
|
}
|
|
|
|
/* Write out a hexadecimal representation of the floating point value
|
|
to DST, which must be of sufficient size, in the C99 form
|
|
[-]0xh.hhhhp[+-]d. Return the number of characters written,
|
|
excluding the terminating NUL.
|
|
|
|
If UPPERCASE, the output is in upper case, otherwise in lower case.
|
|
|
|
HEXDIGITS digits appear altogether, rounding the value if
|
|
necessary. If HEXDIGITS is 0, the minimal precision to display the
|
|
number precisely is used instead. If nothing would appear after
|
|
the decimal point it is suppressed.
|
|
|
|
The decimal exponent is always printed and has at least one digit.
|
|
Zero values display an exponent of zero. Infinities and NaNs
|
|
appear as "infinity" or "nan" respectively.
|
|
|
|
The above rules are as specified by C99. There is ambiguity about
|
|
what the leading hexadecimal digit should be. This implementation
|
|
uses whatever is necessary so that the exponent is displayed as
|
|
stored. This implies the exponent will fall within the IEEE format
|
|
range, and the leading hexadecimal digit will be 0 (for denormals),
|
|
1 (normal numbers) or 2 (normal numbers rounded-away-from-zero with
|
|
any other digits zero).
|
|
*/
|
|
unsigned int
|
|
APFloat::convertToHexString(char *dst, unsigned int hexDigits,
|
|
bool upperCase, roundingMode rounding_mode) const
|
|
{
|
|
char *p;
|
|
|
|
p = dst;
|
|
if (sign)
|
|
*dst++ = '-';
|
|
|
|
switch (category) {
|
|
case fcInfinity:
|
|
memcpy (dst, upperCase ? infinityU: infinityL, sizeof infinityU - 1);
|
|
dst += sizeof infinityL - 1;
|
|
break;
|
|
|
|
case fcNaN:
|
|
memcpy (dst, upperCase ? NaNU: NaNL, sizeof NaNU - 1);
|
|
dst += sizeof NaNU - 1;
|
|
break;
|
|
|
|
case fcZero:
|
|
*dst++ = '0';
|
|
*dst++ = upperCase ? 'X': 'x';
|
|
*dst++ = '0';
|
|
if (hexDigits > 1) {
|
|
*dst++ = '.';
|
|
memset (dst, '0', hexDigits - 1);
|
|
dst += hexDigits - 1;
|
|
}
|
|
*dst++ = upperCase ? 'P': 'p';
|
|
*dst++ = '0';
|
|
break;
|
|
|
|
case fcNormal:
|
|
dst = convertNormalToHexString (dst, hexDigits, upperCase, rounding_mode);
|
|
break;
|
|
}
|
|
|
|
*dst = 0;
|
|
|
|
return static_cast<unsigned int>(dst - p);
|
|
}
|
|
|
|
/* Does the hard work of outputting the correctly rounded hexadecimal
|
|
form of a normal floating point number with the specified number of
|
|
hexadecimal digits. If HEXDIGITS is zero the minimum number of
|
|
digits necessary to print the value precisely is output. */
|
|
char *
|
|
APFloat::convertNormalToHexString(char *dst, unsigned int hexDigits,
|
|
bool upperCase,
|
|
roundingMode rounding_mode) const
|
|
{
|
|
unsigned int count, valueBits, shift, partsCount, outputDigits;
|
|
const char *hexDigitChars;
|
|
const integerPart *significand;
|
|
char *p;
|
|
bool roundUp;
|
|
|
|
*dst++ = '0';
|
|
*dst++ = upperCase ? 'X': 'x';
|
|
|
|
roundUp = false;
|
|
hexDigitChars = upperCase ? hexDigitsUpper: hexDigitsLower;
|
|
|
|
significand = significandParts();
|
|
partsCount = partCount();
|
|
|
|
/* +3 because the first digit only uses the single integer bit, so
|
|
we have 3 virtual zero most-significant-bits. */
|
|
valueBits = semantics->precision + 3;
|
|
shift = integerPartWidth - valueBits % integerPartWidth;
|
|
|
|
/* The natural number of digits required ignoring trailing
|
|
insignificant zeroes. */
|
|
outputDigits = (valueBits - significandLSB () + 3) / 4;
|
|
|
|
/* hexDigits of zero means use the required number for the
|
|
precision. Otherwise, see if we are truncating. If we are,
|
|
find out if we need to round away from zero. */
|
|
if (hexDigits) {
|
|
if (hexDigits < outputDigits) {
|
|
/* We are dropping non-zero bits, so need to check how to round.
|
|
"bits" is the number of dropped bits. */
|
|
unsigned int bits;
|
|
lostFraction fraction;
|
|
|
|
bits = valueBits - hexDigits * 4;
|
|
fraction = lostFractionThroughTruncation (significand, partsCount, bits);
|
|
roundUp = roundAwayFromZero(rounding_mode, fraction, bits);
|
|
}
|
|
outputDigits = hexDigits;
|
|
}
|
|
|
|
/* Write the digits consecutively, and start writing in the location
|
|
of the hexadecimal point. We move the most significant digit
|
|
left and add the hexadecimal point later. */
|
|
p = ++dst;
|
|
|
|
count = (valueBits + integerPartWidth - 1) / integerPartWidth;
|
|
|
|
while (outputDigits && count) {
|
|
integerPart part;
|
|
|
|
/* Put the most significant integerPartWidth bits in "part". */
|
|
if (--count == partsCount)
|
|
part = 0; /* An imaginary higher zero part. */
|
|
else
|
|
part = significand[count] << shift;
|
|
|
|
if (count && shift)
|
|
part |= significand[count - 1] >> (integerPartWidth - shift);
|
|
|
|
/* Convert as much of "part" to hexdigits as we can. */
|
|
unsigned int curDigits = integerPartWidth / 4;
|
|
|
|
if (curDigits > outputDigits)
|
|
curDigits = outputDigits;
|
|
dst += partAsHex (dst, part, curDigits, hexDigitChars);
|
|
outputDigits -= curDigits;
|
|
}
|
|
|
|
if (roundUp) {
|
|
char *q = dst;
|
|
|
|
/* Note that hexDigitChars has a trailing '0'. */
|
|
do {
|
|
q--;
|
|
*q = hexDigitChars[hexDigitValue (*q) + 1];
|
|
} while (*q == '0');
|
|
assert(q >= p);
|
|
} else {
|
|
/* Add trailing zeroes. */
|
|
memset (dst, '0', outputDigits);
|
|
dst += outputDigits;
|
|
}
|
|
|
|
/* Move the most significant digit to before the point, and if there
|
|
is something after the decimal point add it. This must come
|
|
after rounding above. */
|
|
p[-1] = p[0];
|
|
if (dst -1 == p)
|
|
dst--;
|
|
else
|
|
p[0] = '.';
|
|
|
|
/* Finally output the exponent. */
|
|
*dst++ = upperCase ? 'P': 'p';
|
|
|
|
return writeSignedDecimal (dst, exponent);
|
|
}
|
|
|
|
hash_code llvm::hash_value(const APFloat &Arg) {
|
|
if (!Arg.isFiniteNonZero())
|
|
return hash_combine((uint8_t)Arg.category,
|
|
// NaN has no sign, fix it at zero.
|
|
Arg.isNaN() ? (uint8_t)0 : (uint8_t)Arg.sign,
|
|
Arg.semantics->precision);
|
|
|
|
// Normal floats need their exponent and significand hashed.
|
|
return hash_combine((uint8_t)Arg.category, (uint8_t)Arg.sign,
|
|
Arg.semantics->precision, Arg.exponent,
|
|
hash_combine_range(
|
|
Arg.significandParts(),
|
|
Arg.significandParts() + Arg.partCount()));
|
|
}
|
|
|
|
// Conversion from APFloat to/from host float/double. It may eventually be
|
|
// possible to eliminate these and have everybody deal with APFloats, but that
|
|
// will take a while. This approach will not easily extend to long double.
|
|
// Current implementation requires integerPartWidth==64, which is correct at
|
|
// the moment but could be made more general.
|
|
|
|
// Denormals have exponent minExponent in APFloat, but minExponent-1 in
|
|
// the actual IEEE respresentations. We compensate for that here.
|
|
|
|
APInt
|
|
APFloat::convertF80LongDoubleAPFloatToAPInt() const
|
|
{
|
|
assert(semantics == (const llvm::fltSemantics*)&x87DoubleExtended);
|
|
assert(partCount()==2);
|
|
|
|
uint64_t myexponent, mysignificand;
|
|
|
|
if (isFiniteNonZero()) {
|
|
myexponent = exponent+16383; //bias
|
|
mysignificand = significandParts()[0];
|
|
if (myexponent==1 && !(mysignificand & 0x8000000000000000ULL))
|
|
myexponent = 0; // denormal
|
|
} else if (category==fcZero) {
|
|
myexponent = 0;
|
|
mysignificand = 0;
|
|
} else if (category==fcInfinity) {
|
|
myexponent = 0x7fff;
|
|
mysignificand = 0x8000000000000000ULL;
|
|
} else {
|
|
assert(category == fcNaN && "Unknown category");
|
|
myexponent = 0x7fff;
|
|
mysignificand = significandParts()[0];
|
|
}
|
|
|
|
uint64_t words[2];
|
|
words[0] = mysignificand;
|
|
words[1] = ((uint64_t)(sign & 1) << 15) |
|
|
(myexponent & 0x7fffLL);
|
|
return APInt(80, words);
|
|
}
|
|
|
|
APInt
|
|
APFloat::convertPPCDoubleDoubleAPFloatToAPInt() const
|
|
{
|
|
assert(semantics == (const llvm::fltSemantics*)&PPCDoubleDouble);
|
|
assert(partCount()==2);
|
|
|
|
uint64_t words[2];
|
|
opStatus fs;
|
|
bool losesInfo;
|
|
|
|
// Convert number to double. To avoid spurious underflows, we re-
|
|
// normalize against the "double" minExponent first, and only *then*
|
|
// truncate the mantissa. The result of that second conversion
|
|
// may be inexact, but should never underflow.
|
|
// Declare fltSemantics before APFloat that uses it (and
|
|
// saves pointer to it) to ensure correct destruction order.
|
|
fltSemantics extendedSemantics = *semantics;
|
|
extendedSemantics.minExponent = IEEEdouble.minExponent;
|
|
APFloat extended(*this);
|
|
fs = extended.convert(extendedSemantics, rmNearestTiesToEven, &losesInfo);
|
|
assert(fs == opOK && !losesInfo);
|
|
(void)fs;
|
|
|
|
APFloat u(extended);
|
|
fs = u.convert(IEEEdouble, rmNearestTiesToEven, &losesInfo);
|
|
assert(fs == opOK || fs == opInexact);
|
|
(void)fs;
|
|
words[0] = *u.convertDoubleAPFloatToAPInt().getRawData();
|
|
|
|
// If conversion was exact or resulted in a special case, we're done;
|
|
// just set the second double to zero. Otherwise, re-convert back to
|
|
// the extended format and compute the difference. This now should
|
|
// convert exactly to double.
|
|
if (u.isFiniteNonZero() && losesInfo) {
|
|
fs = u.convert(extendedSemantics, rmNearestTiesToEven, &losesInfo);
|
|
assert(fs == opOK && !losesInfo);
|
|
(void)fs;
|
|
|
|
APFloat v(extended);
|
|
v.subtract(u, rmNearestTiesToEven);
|
|
fs = v.convert(IEEEdouble, rmNearestTiesToEven, &losesInfo);
|
|
assert(fs == opOK && !losesInfo);
|
|
(void)fs;
|
|
words[1] = *v.convertDoubleAPFloatToAPInt().getRawData();
|
|
} else {
|
|
words[1] = 0;
|
|
}
|
|
|
|
return APInt(128, words);
|
|
}
|
|
|
|
APInt
|
|
APFloat::convertQuadrupleAPFloatToAPInt() const
|
|
{
|
|
assert(semantics == (const llvm::fltSemantics*)&IEEEquad);
|
|
assert(partCount()==2);
|
|
|
|
uint64_t myexponent, mysignificand, mysignificand2;
|
|
|
|
if (isFiniteNonZero()) {
|
|
myexponent = exponent+16383; //bias
|
|
mysignificand = significandParts()[0];
|
|
mysignificand2 = significandParts()[1];
|
|
if (myexponent==1 && !(mysignificand2 & 0x1000000000000LL))
|
|
myexponent = 0; // denormal
|
|
} else if (category==fcZero) {
|
|
myexponent = 0;
|
|
mysignificand = mysignificand2 = 0;
|
|
} else if (category==fcInfinity) {
|
|
myexponent = 0x7fff;
|
|
mysignificand = mysignificand2 = 0;
|
|
} else {
|
|
assert(category == fcNaN && "Unknown category!");
|
|
myexponent = 0x7fff;
|
|
mysignificand = significandParts()[0];
|
|
mysignificand2 = significandParts()[1];
|
|
}
|
|
|
|
uint64_t words[2];
|
|
words[0] = mysignificand;
|
|
words[1] = ((uint64_t)(sign & 1) << 63) |
|
|
((myexponent & 0x7fff) << 48) |
|
|
(mysignificand2 & 0xffffffffffffLL);
|
|
|
|
return APInt(128, words);
|
|
}
|
|
|
|
APInt
|
|
APFloat::convertDoubleAPFloatToAPInt() const
|
|
{
|
|
assert(semantics == (const llvm::fltSemantics*)&IEEEdouble);
|
|
assert(partCount()==1);
|
|
|
|
uint64_t myexponent, mysignificand;
|
|
|
|
if (isFiniteNonZero()) {
|
|
myexponent = exponent+1023; //bias
|
|
mysignificand = *significandParts();
|
|
if (myexponent==1 && !(mysignificand & 0x10000000000000LL))
|
|
myexponent = 0; // denormal
|
|
} else if (category==fcZero) {
|
|
myexponent = 0;
|
|
mysignificand = 0;
|
|
} else if (category==fcInfinity) {
|
|
myexponent = 0x7ff;
|
|
mysignificand = 0;
|
|
} else {
|
|
assert(category == fcNaN && "Unknown category!");
|
|
myexponent = 0x7ff;
|
|
mysignificand = *significandParts();
|
|
}
|
|
|
|
return APInt(64, ((((uint64_t)(sign & 1) << 63) |
|
|
((myexponent & 0x7ff) << 52) |
|
|
(mysignificand & 0xfffffffffffffLL))));
|
|
}
|
|
|
|
APInt
|
|
APFloat::convertFloatAPFloatToAPInt() const
|
|
{
|
|
assert(semantics == (const llvm::fltSemantics*)&IEEEsingle);
|
|
assert(partCount()==1);
|
|
|
|
uint32_t myexponent, mysignificand;
|
|
|
|
if (isFiniteNonZero()) {
|
|
myexponent = exponent+127; //bias
|
|
mysignificand = (uint32_t)*significandParts();
|
|
if (myexponent == 1 && !(mysignificand & 0x800000))
|
|
myexponent = 0; // denormal
|
|
} else if (category==fcZero) {
|
|
myexponent = 0;
|
|
mysignificand = 0;
|
|
} else if (category==fcInfinity) {
|
|
myexponent = 0xff;
|
|
mysignificand = 0;
|
|
} else {
|
|
assert(category == fcNaN && "Unknown category!");
|
|
myexponent = 0xff;
|
|
mysignificand = (uint32_t)*significandParts();
|
|
}
|
|
|
|
return APInt(32, (((sign&1) << 31) | ((myexponent&0xff) << 23) |
|
|
(mysignificand & 0x7fffff)));
|
|
}
|
|
|
|
APInt
|
|
APFloat::convertHalfAPFloatToAPInt() const
|
|
{
|
|
assert(semantics == (const llvm::fltSemantics*)&IEEEhalf);
|
|
assert(partCount()==1);
|
|
|
|
uint32_t myexponent, mysignificand;
|
|
|
|
if (isFiniteNonZero()) {
|
|
myexponent = exponent+15; //bias
|
|
mysignificand = (uint32_t)*significandParts();
|
|
if (myexponent == 1 && !(mysignificand & 0x400))
|
|
myexponent = 0; // denormal
|
|
} else if (category==fcZero) {
|
|
myexponent = 0;
|
|
mysignificand = 0;
|
|
} else if (category==fcInfinity) {
|
|
myexponent = 0x1f;
|
|
mysignificand = 0;
|
|
} else {
|
|
assert(category == fcNaN && "Unknown category!");
|
|
myexponent = 0x1f;
|
|
mysignificand = (uint32_t)*significandParts();
|
|
}
|
|
|
|
return APInt(16, (((sign&1) << 15) | ((myexponent&0x1f) << 10) |
|
|
(mysignificand & 0x3ff)));
|
|
}
|
|
|
|
// This function creates an APInt that is just a bit map of the floating
|
|
// point constant as it would appear in memory. It is not a conversion,
|
|
// and treating the result as a normal integer is unlikely to be useful.
|
|
|
|
APInt
|
|
APFloat::bitcastToAPInt() const
|
|
{
|
|
if (semantics == (const llvm::fltSemantics*)&IEEEhalf)
|
|
return convertHalfAPFloatToAPInt();
|
|
|
|
if (semantics == (const llvm::fltSemantics*)&IEEEsingle)
|
|
return convertFloatAPFloatToAPInt();
|
|
|
|
if (semantics == (const llvm::fltSemantics*)&IEEEdouble)
|
|
return convertDoubleAPFloatToAPInt();
|
|
|
|
if (semantics == (const llvm::fltSemantics*)&IEEEquad)
|
|
return convertQuadrupleAPFloatToAPInt();
|
|
|
|
if (semantics == (const llvm::fltSemantics*)&PPCDoubleDouble)
|
|
return convertPPCDoubleDoubleAPFloatToAPInt();
|
|
|
|
assert(semantics == (const llvm::fltSemantics*)&x87DoubleExtended &&
|
|
"unknown format!");
|
|
return convertF80LongDoubleAPFloatToAPInt();
|
|
}
|
|
|
|
float
|
|
APFloat::convertToFloat() const
|
|
{
|
|
assert(semantics == (const llvm::fltSemantics*)&IEEEsingle &&
|
|
"Float semantics are not IEEEsingle");
|
|
APInt api = bitcastToAPInt();
|
|
return api.bitsToFloat();
|
|
}
|
|
|
|
double
|
|
APFloat::convertToDouble() const
|
|
{
|
|
assert(semantics == (const llvm::fltSemantics*)&IEEEdouble &&
|
|
"Float semantics are not IEEEdouble");
|
|
APInt api = bitcastToAPInt();
|
|
return api.bitsToDouble();
|
|
}
|
|
|
|
/// Integer bit is explicit in this format. Intel hardware (387 and later)
|
|
/// does not support these bit patterns:
|
|
/// exponent = all 1's, integer bit 0, significand 0 ("pseudoinfinity")
|
|
/// exponent = all 1's, integer bit 0, significand nonzero ("pseudoNaN")
|
|
/// exponent = 0, integer bit 1 ("pseudodenormal")
|
|
/// exponent!=0 nor all 1's, integer bit 0 ("unnormal")
|
|
/// At the moment, the first two are treated as NaNs, the second two as Normal.
|
|
void
|
|
APFloat::initFromF80LongDoubleAPInt(const APInt &api)
|
|
{
|
|
assert(api.getBitWidth()==80);
|
|
uint64_t i1 = api.getRawData()[0];
|
|
uint64_t i2 = api.getRawData()[1];
|
|
uint64_t myexponent = (i2 & 0x7fff);
|
|
uint64_t mysignificand = i1;
|
|
|
|
initialize(&APFloat::x87DoubleExtended);
|
|
assert(partCount()==2);
|
|
|
|
sign = static_cast<unsigned int>(i2>>15);
|
|
if (myexponent==0 && mysignificand==0) {
|
|
// exponent, significand meaningless
|
|
category = fcZero;
|
|
} else if (myexponent==0x7fff && mysignificand==0x8000000000000000ULL) {
|
|
// exponent, significand meaningless
|
|
category = fcInfinity;
|
|
} else if (myexponent==0x7fff && mysignificand!=0x8000000000000000ULL) {
|
|
// exponent meaningless
|
|
category = fcNaN;
|
|
significandParts()[0] = mysignificand;
|
|
significandParts()[1] = 0;
|
|
} else {
|
|
category = fcNormal;
|
|
exponent = myexponent - 16383;
|
|
significandParts()[0] = mysignificand;
|
|
significandParts()[1] = 0;
|
|
if (myexponent==0) // denormal
|
|
exponent = -16382;
|
|
}
|
|
}
|
|
|
|
void
|
|
APFloat::initFromPPCDoubleDoubleAPInt(const APInt &api)
|
|
{
|
|
assert(api.getBitWidth()==128);
|
|
uint64_t i1 = api.getRawData()[0];
|
|
uint64_t i2 = api.getRawData()[1];
|
|
opStatus fs;
|
|
bool losesInfo;
|
|
|
|
// Get the first double and convert to our format.
|
|
initFromDoubleAPInt(APInt(64, i1));
|
|
fs = convert(PPCDoubleDouble, rmNearestTiesToEven, &losesInfo);
|
|
assert(fs == opOK && !losesInfo);
|
|
(void)fs;
|
|
|
|
// Unless we have a special case, add in second double.
|
|
if (isFiniteNonZero()) {
|
|
APFloat v(IEEEdouble, APInt(64, i2));
|
|
fs = v.convert(PPCDoubleDouble, rmNearestTiesToEven, &losesInfo);
|
|
assert(fs == opOK && !losesInfo);
|
|
(void)fs;
|
|
|
|
add(v, rmNearestTiesToEven);
|
|
}
|
|
}
|
|
|
|
void
|
|
APFloat::initFromQuadrupleAPInt(const APInt &api)
|
|
{
|
|
assert(api.getBitWidth()==128);
|
|
uint64_t i1 = api.getRawData()[0];
|
|
uint64_t i2 = api.getRawData()[1];
|
|
uint64_t myexponent = (i2 >> 48) & 0x7fff;
|
|
uint64_t mysignificand = i1;
|
|
uint64_t mysignificand2 = i2 & 0xffffffffffffLL;
|
|
|
|
initialize(&APFloat::IEEEquad);
|
|
assert(partCount()==2);
|
|
|
|
sign = static_cast<unsigned int>(i2>>63);
|
|
if (myexponent==0 &&
|
|
(mysignificand==0 && mysignificand2==0)) {
|
|
// exponent, significand meaningless
|
|
category = fcZero;
|
|
} else if (myexponent==0x7fff &&
|
|
(mysignificand==0 && mysignificand2==0)) {
|
|
// exponent, significand meaningless
|
|
category = fcInfinity;
|
|
} else if (myexponent==0x7fff &&
|
|
(mysignificand!=0 || mysignificand2 !=0)) {
|
|
// exponent meaningless
|
|
category = fcNaN;
|
|
significandParts()[0] = mysignificand;
|
|
significandParts()[1] = mysignificand2;
|
|
} else {
|
|
category = fcNormal;
|
|
exponent = myexponent - 16383;
|
|
significandParts()[0] = mysignificand;
|
|
significandParts()[1] = mysignificand2;
|
|
if (myexponent==0) // denormal
|
|
exponent = -16382;
|
|
else
|
|
significandParts()[1] |= 0x1000000000000LL; // integer bit
|
|
}
|
|
}
|
|
|
|
void
|
|
APFloat::initFromDoubleAPInt(const APInt &api)
|
|
{
|
|
assert(api.getBitWidth()==64);
|
|
uint64_t i = *api.getRawData();
|
|
uint64_t myexponent = (i >> 52) & 0x7ff;
|
|
uint64_t mysignificand = i & 0xfffffffffffffLL;
|
|
|
|
initialize(&APFloat::IEEEdouble);
|
|
assert(partCount()==1);
|
|
|
|
sign = static_cast<unsigned int>(i>>63);
|
|
if (myexponent==0 && mysignificand==0) {
|
|
// exponent, significand meaningless
|
|
category = fcZero;
|
|
} else if (myexponent==0x7ff && mysignificand==0) {
|
|
// exponent, significand meaningless
|
|
category = fcInfinity;
|
|
} else if (myexponent==0x7ff && mysignificand!=0) {
|
|
// exponent meaningless
|
|
category = fcNaN;
|
|
*significandParts() = mysignificand;
|
|
} else {
|
|
category = fcNormal;
|
|
exponent = myexponent - 1023;
|
|
*significandParts() = mysignificand;
|
|
if (myexponent==0) // denormal
|
|
exponent = -1022;
|
|
else
|
|
*significandParts() |= 0x10000000000000LL; // integer bit
|
|
}
|
|
}
|
|
|
|
void
|
|
APFloat::initFromFloatAPInt(const APInt & api)
|
|
{
|
|
assert(api.getBitWidth()==32);
|
|
uint32_t i = (uint32_t)*api.getRawData();
|
|
uint32_t myexponent = (i >> 23) & 0xff;
|
|
uint32_t mysignificand = i & 0x7fffff;
|
|
|
|
initialize(&APFloat::IEEEsingle);
|
|
assert(partCount()==1);
|
|
|
|
sign = i >> 31;
|
|
if (myexponent==0 && mysignificand==0) {
|
|
// exponent, significand meaningless
|
|
category = fcZero;
|
|
} else if (myexponent==0xff && mysignificand==0) {
|
|
// exponent, significand meaningless
|
|
category = fcInfinity;
|
|
} else if (myexponent==0xff && mysignificand!=0) {
|
|
// sign, exponent, significand meaningless
|
|
category = fcNaN;
|
|
*significandParts() = mysignificand;
|
|
} else {
|
|
category = fcNormal;
|
|
exponent = myexponent - 127; //bias
|
|
*significandParts() = mysignificand;
|
|
if (myexponent==0) // denormal
|
|
exponent = -126;
|
|
else
|
|
*significandParts() |= 0x800000; // integer bit
|
|
}
|
|
}
|
|
|
|
void
|
|
APFloat::initFromHalfAPInt(const APInt & api)
|
|
{
|
|
assert(api.getBitWidth()==16);
|
|
uint32_t i = (uint32_t)*api.getRawData();
|
|
uint32_t myexponent = (i >> 10) & 0x1f;
|
|
uint32_t mysignificand = i & 0x3ff;
|
|
|
|
initialize(&APFloat::IEEEhalf);
|
|
assert(partCount()==1);
|
|
|
|
sign = i >> 15;
|
|
if (myexponent==0 && mysignificand==0) {
|
|
// exponent, significand meaningless
|
|
category = fcZero;
|
|
} else if (myexponent==0x1f && mysignificand==0) {
|
|
// exponent, significand meaningless
|
|
category = fcInfinity;
|
|
} else if (myexponent==0x1f && mysignificand!=0) {
|
|
// sign, exponent, significand meaningless
|
|
category = fcNaN;
|
|
*significandParts() = mysignificand;
|
|
} else {
|
|
category = fcNormal;
|
|
exponent = myexponent - 15; //bias
|
|
*significandParts() = mysignificand;
|
|
if (myexponent==0) // denormal
|
|
exponent = -14;
|
|
else
|
|
*significandParts() |= 0x400; // integer bit
|
|
}
|
|
}
|
|
|
|
/// Treat api as containing the bits of a floating point number. Currently
|
|
/// we infer the floating point type from the size of the APInt. The
|
|
/// isIEEE argument distinguishes between PPC128 and IEEE128 (not meaningful
|
|
/// when the size is anything else).
|
|
void
|
|
APFloat::initFromAPInt(const fltSemantics* Sem, const APInt& api)
|
|
{
|
|
if (Sem == &IEEEhalf)
|
|
return initFromHalfAPInt(api);
|
|
if (Sem == &IEEEsingle)
|
|
return initFromFloatAPInt(api);
|
|
if (Sem == &IEEEdouble)
|
|
return initFromDoubleAPInt(api);
|
|
if (Sem == &x87DoubleExtended)
|
|
return initFromF80LongDoubleAPInt(api);
|
|
if (Sem == &IEEEquad)
|
|
return initFromQuadrupleAPInt(api);
|
|
if (Sem == &PPCDoubleDouble)
|
|
return initFromPPCDoubleDoubleAPInt(api);
|
|
|
|
llvm_unreachable(nullptr);
|
|
}
|
|
|
|
APFloat
|
|
APFloat::getAllOnesValue(unsigned BitWidth, bool isIEEE)
|
|
{
|
|
switch (BitWidth) {
|
|
case 16:
|
|
return APFloat(IEEEhalf, APInt::getAllOnesValue(BitWidth));
|
|
case 32:
|
|
return APFloat(IEEEsingle, APInt::getAllOnesValue(BitWidth));
|
|
case 64:
|
|
return APFloat(IEEEdouble, APInt::getAllOnesValue(BitWidth));
|
|
case 80:
|
|
return APFloat(x87DoubleExtended, APInt::getAllOnesValue(BitWidth));
|
|
case 128:
|
|
if (isIEEE)
|
|
return APFloat(IEEEquad, APInt::getAllOnesValue(BitWidth));
|
|
return APFloat(PPCDoubleDouble, APInt::getAllOnesValue(BitWidth));
|
|
default:
|
|
llvm_unreachable("Unknown floating bit width");
|
|
}
|
|
}
|
|
|
|
/// Make this number the largest magnitude normal number in the given
|
|
/// semantics.
|
|
void APFloat::makeLargest(bool Negative) {
|
|
// We want (in interchange format):
|
|
// sign = {Negative}
|
|
// exponent = 1..10
|
|
// significand = 1..1
|
|
category = fcNormal;
|
|
sign = Negative;
|
|
exponent = semantics->maxExponent;
|
|
|
|
// Use memset to set all but the highest integerPart to all ones.
|
|
integerPart *significand = significandParts();
|
|
unsigned PartCount = partCount();
|
|
memset(significand, 0xFF, sizeof(integerPart)*(PartCount - 1));
|
|
|
|
// Set the high integerPart especially setting all unused top bits for
|
|
// internal consistency.
|
|
const unsigned NumUnusedHighBits =
|
|
PartCount*integerPartWidth - semantics->precision;
|
|
significand[PartCount - 1] = (NumUnusedHighBits < integerPartWidth)
|
|
? (~integerPart(0) >> NumUnusedHighBits)
|
|
: 0;
|
|
}
|
|
|
|
/// Make this number the smallest magnitude denormal number in the given
|
|
/// semantics.
|
|
void APFloat::makeSmallest(bool Negative) {
|
|
// We want (in interchange format):
|
|
// sign = {Negative}
|
|
// exponent = 0..0
|
|
// significand = 0..01
|
|
category = fcNormal;
|
|
sign = Negative;
|
|
exponent = semantics->minExponent;
|
|
APInt::tcSet(significandParts(), 1, partCount());
|
|
}
|
|
|
|
|
|
APFloat APFloat::getLargest(const fltSemantics &Sem, bool Negative) {
|
|
// We want (in interchange format):
|
|
// sign = {Negative}
|
|
// exponent = 1..10
|
|
// significand = 1..1
|
|
APFloat Val(Sem, uninitialized);
|
|
Val.makeLargest(Negative);
|
|
return Val;
|
|
}
|
|
|
|
APFloat APFloat::getSmallest(const fltSemantics &Sem, bool Negative) {
|
|
// We want (in interchange format):
|
|
// sign = {Negative}
|
|
// exponent = 0..0
|
|
// significand = 0..01
|
|
APFloat Val(Sem, uninitialized);
|
|
Val.makeSmallest(Negative);
|
|
return Val;
|
|
}
|
|
|
|
APFloat APFloat::getSmallestNormalized(const fltSemantics &Sem, bool Negative) {
|
|
APFloat Val(Sem, uninitialized);
|
|
|
|
// We want (in interchange format):
|
|
// sign = {Negative}
|
|
// exponent = 0..0
|
|
// significand = 10..0
|
|
|
|
Val.category = fcNormal;
|
|
Val.zeroSignificand();
|
|
Val.sign = Negative;
|
|
Val.exponent = Sem.minExponent;
|
|
Val.significandParts()[partCountForBits(Sem.precision)-1] |=
|
|
(((integerPart) 1) << ((Sem.precision - 1) % integerPartWidth));
|
|
|
|
return Val;
|
|
}
|
|
|
|
APFloat::APFloat(const fltSemantics &Sem, const APInt &API) {
|
|
initFromAPInt(&Sem, API);
|
|
}
|
|
|
|
APFloat::APFloat(float f) {
|
|
initFromAPInt(&IEEEsingle, APInt::floatToBits(f));
|
|
}
|
|
|
|
APFloat::APFloat(double d) {
|
|
initFromAPInt(&IEEEdouble, APInt::doubleToBits(d));
|
|
}
|
|
|
|
namespace {
|
|
void append(SmallVectorImpl<char> &Buffer, StringRef Str) {
|
|
Buffer.append(Str.begin(), Str.end());
|
|
}
|
|
|
|
/// Removes data from the given significand until it is no more
|
|
/// precise than is required for the desired precision.
|
|
void AdjustToPrecision(APInt &significand,
|
|
int &exp, unsigned FormatPrecision) {
|
|
unsigned bits = significand.getActiveBits();
|
|
|
|
// 196/59 is a very slight overestimate of lg_2(10).
|
|
unsigned bitsRequired = (FormatPrecision * 196 + 58) / 59;
|
|
|
|
if (bits <= bitsRequired) return;
|
|
|
|
unsigned tensRemovable = (bits - bitsRequired) * 59 / 196;
|
|
if (!tensRemovable) return;
|
|
|
|
exp += tensRemovable;
|
|
|
|
APInt divisor(significand.getBitWidth(), 1);
|
|
APInt powten(significand.getBitWidth(), 10);
|
|
while (true) {
|
|
if (tensRemovable & 1)
|
|
divisor *= powten;
|
|
tensRemovable >>= 1;
|
|
if (!tensRemovable) break;
|
|
powten *= powten;
|
|
}
|
|
|
|
significand = significand.udiv(divisor);
|
|
|
|
// Truncate the significand down to its active bit count.
|
|
significand = significand.trunc(significand.getActiveBits());
|
|
}
|
|
|
|
|
|
void AdjustToPrecision(SmallVectorImpl<char> &buffer,
|
|
int &exp, unsigned FormatPrecision) {
|
|
unsigned N = buffer.size();
|
|
if (N <= FormatPrecision) return;
|
|
|
|
// The most significant figures are the last ones in the buffer.
|
|
unsigned FirstSignificant = N - FormatPrecision;
|
|
|
|
// Round.
|
|
// FIXME: this probably shouldn't use 'round half up'.
|
|
|
|
// Rounding down is just a truncation, except we also want to drop
|
|
// trailing zeros from the new result.
|
|
if (buffer[FirstSignificant - 1] < '5') {
|
|
while (FirstSignificant < N && buffer[FirstSignificant] == '0')
|
|
FirstSignificant++;
|
|
|
|
exp += FirstSignificant;
|
|
buffer.erase(&buffer[0], &buffer[FirstSignificant]);
|
|
return;
|
|
}
|
|
|
|
// Rounding up requires a decimal add-with-carry. If we continue
|
|
// the carry, the newly-introduced zeros will just be truncated.
|
|
for (unsigned I = FirstSignificant; I != N; ++I) {
|
|
if (buffer[I] == '9') {
|
|
FirstSignificant++;
|
|
} else {
|
|
buffer[I]++;
|
|
break;
|
|
}
|
|
}
|
|
|
|
// If we carried through, we have exactly one digit of precision.
|
|
if (FirstSignificant == N) {
|
|
exp += FirstSignificant;
|
|
buffer.clear();
|
|
buffer.push_back('1');
|
|
return;
|
|
}
|
|
|
|
exp += FirstSignificant;
|
|
buffer.erase(&buffer[0], &buffer[FirstSignificant]);
|
|
}
|
|
}
|
|
|
|
void APFloat::toString(SmallVectorImpl<char> &Str,
|
|
unsigned FormatPrecision,
|
|
unsigned FormatMaxPadding) const {
|
|
switch (category) {
|
|
case fcInfinity:
|
|
if (isNegative())
|
|
return append(Str, "-Inf");
|
|
else
|
|
return append(Str, "+Inf");
|
|
|
|
case fcNaN: return append(Str, "NaN");
|
|
|
|
case fcZero:
|
|
if (isNegative())
|
|
Str.push_back('-');
|
|
|
|
if (!FormatMaxPadding)
|
|
append(Str, "0.0E+0");
|
|
else
|
|
Str.push_back('0');
|
|
return;
|
|
|
|
case fcNormal:
|
|
break;
|
|
}
|
|
|
|
if (isNegative())
|
|
Str.push_back('-');
|
|
|
|
// Decompose the number into an APInt and an exponent.
|
|
int exp = exponent - ((int) semantics->precision - 1);
|
|
APInt significand(semantics->precision,
|
|
makeArrayRef(significandParts(),
|
|
partCountForBits(semantics->precision)));
|
|
|
|
// Set FormatPrecision if zero. We want to do this before we
|
|
// truncate trailing zeros, as those are part of the precision.
|
|
if (!FormatPrecision) {
|
|
// We use enough digits so the number can be round-tripped back to an
|
|
// APFloat. The formula comes from "How to Print Floating-Point Numbers
|
|
// Accurately" by Steele and White.
|
|
// FIXME: Using a formula based purely on the precision is conservative;
|
|
// we can print fewer digits depending on the actual value being printed.
|
|
|
|
// FormatPrecision = 2 + floor(significandBits / lg_2(10))
|
|
FormatPrecision = 2 + semantics->precision * 59 / 196;
|
|
}
|
|
|
|
// Ignore trailing binary zeros.
|
|
int trailingZeros = significand.countTrailingZeros();
|
|
exp += trailingZeros;
|
|
significand = significand.lshr(trailingZeros);
|
|
|
|
// Change the exponent from 2^e to 10^e.
|
|
if (exp == 0) {
|
|
// Nothing to do.
|
|
} else if (exp > 0) {
|
|
// Just shift left.
|
|
significand = significand.zext(semantics->precision + exp);
|
|
significand <<= exp;
|
|
exp = 0;
|
|
} else { /* exp < 0 */
|
|
int texp = -exp;
|
|
|
|
// We transform this using the identity:
|
|
// (N)(2^-e) == (N)(5^e)(10^-e)
|
|
// This means we have to multiply N (the significand) by 5^e.
|
|
// To avoid overflow, we have to operate on numbers large
|
|
// enough to store N * 5^e:
|
|
// log2(N * 5^e) == log2(N) + e * log2(5)
|
|
// <= semantics->precision + e * 137 / 59
|
|
// (log_2(5) ~ 2.321928 < 2.322034 ~ 137/59)
|
|
|
|
unsigned precision = semantics->precision + (137 * texp + 136) / 59;
|
|
|
|
// Multiply significand by 5^e.
|
|
// N * 5^0101 == N * 5^(1*1) * 5^(0*2) * 5^(1*4) * 5^(0*8)
|
|
significand = significand.zext(precision);
|
|
APInt five_to_the_i(precision, 5);
|
|
while (true) {
|
|
if (texp & 1) significand *= five_to_the_i;
|
|
|
|
texp >>= 1;
|
|
if (!texp) break;
|
|
five_to_the_i *= five_to_the_i;
|
|
}
|
|
}
|
|
|
|
AdjustToPrecision(significand, exp, FormatPrecision);
|
|
|
|
SmallVector<char, 256> buffer;
|
|
|
|
// Fill the buffer.
|
|
unsigned precision = significand.getBitWidth();
|
|
APInt ten(precision, 10);
|
|
APInt digit(precision, 0);
|
|
|
|
bool inTrail = true;
|
|
while (significand != 0) {
|
|
// digit <- significand % 10
|
|
// significand <- significand / 10
|
|
APInt::udivrem(significand, ten, significand, digit);
|
|
|
|
unsigned d = digit.getZExtValue();
|
|
|
|
// Drop trailing zeros.
|
|
if (inTrail && !d) exp++;
|
|
else {
|
|
buffer.push_back((char) ('0' + d));
|
|
inTrail = false;
|
|
}
|
|
}
|
|
|
|
assert(!buffer.empty() && "no characters in buffer!");
|
|
|
|
// Drop down to FormatPrecision.
|
|
// TODO: don't do more precise calculations above than are required.
|
|
AdjustToPrecision(buffer, exp, FormatPrecision);
|
|
|
|
unsigned NDigits = buffer.size();
|
|
|
|
// Check whether we should use scientific notation.
|
|
bool FormatScientific;
|
|
if (!FormatMaxPadding)
|
|
FormatScientific = true;
|
|
else {
|
|
if (exp >= 0) {
|
|
// 765e3 --> 765000
|
|
// ^^^
|
|
// But we shouldn't make the number look more precise than it is.
|
|
FormatScientific = ((unsigned) exp > FormatMaxPadding ||
|
|
NDigits + (unsigned) exp > FormatPrecision);
|
|
} else {
|
|
// Power of the most significant digit.
|
|
int MSD = exp + (int) (NDigits - 1);
|
|
if (MSD >= 0) {
|
|
// 765e-2 == 7.65
|
|
FormatScientific = false;
|
|
} else {
|
|
// 765e-5 == 0.00765
|
|
// ^ ^^
|
|
FormatScientific = ((unsigned) -MSD) > FormatMaxPadding;
|
|
}
|
|
}
|
|
}
|
|
|
|
// Scientific formatting is pretty straightforward.
|
|
if (FormatScientific) {
|
|
exp += (NDigits - 1);
|
|
|
|
Str.push_back(buffer[NDigits-1]);
|
|
Str.push_back('.');
|
|
if (NDigits == 1)
|
|
Str.push_back('0');
|
|
else
|
|
for (unsigned I = 1; I != NDigits; ++I)
|
|
Str.push_back(buffer[NDigits-1-I]);
|
|
Str.push_back('E');
|
|
|
|
Str.push_back(exp >= 0 ? '+' : '-');
|
|
if (exp < 0) exp = -exp;
|
|
SmallVector<char, 6> expbuf;
|
|
do {
|
|
expbuf.push_back((char) ('0' + (exp % 10)));
|
|
exp /= 10;
|
|
} while (exp);
|
|
for (unsigned I = 0, E = expbuf.size(); I != E; ++I)
|
|
Str.push_back(expbuf[E-1-I]);
|
|
return;
|
|
}
|
|
|
|
// Non-scientific, positive exponents.
|
|
if (exp >= 0) {
|
|
for (unsigned I = 0; I != NDigits; ++I)
|
|
Str.push_back(buffer[NDigits-1-I]);
|
|
for (unsigned I = 0; I != (unsigned) exp; ++I)
|
|
Str.push_back('0');
|
|
return;
|
|
}
|
|
|
|
// Non-scientific, negative exponents.
|
|
|
|
// The number of digits to the left of the decimal point.
|
|
int NWholeDigits = exp + (int) NDigits;
|
|
|
|
unsigned I = 0;
|
|
if (NWholeDigits > 0) {
|
|
for (; I != (unsigned) NWholeDigits; ++I)
|
|
Str.push_back(buffer[NDigits-I-1]);
|
|
Str.push_back('.');
|
|
} else {
|
|
unsigned NZeros = 1 + (unsigned) -NWholeDigits;
|
|
|
|
Str.push_back('0');
|
|
Str.push_back('.');
|
|
for (unsigned Z = 1; Z != NZeros; ++Z)
|
|
Str.push_back('0');
|
|
}
|
|
|
|
for (; I != NDigits; ++I)
|
|
Str.push_back(buffer[NDigits-I-1]);
|
|
}
|
|
|
|
bool APFloat::getExactInverse(APFloat *inv) const {
|
|
// Special floats and denormals have no exact inverse.
|
|
if (!isFiniteNonZero())
|
|
return false;
|
|
|
|
// Check that the number is a power of two by making sure that only the
|
|
// integer bit is set in the significand.
|
|
if (significandLSB() != semantics->precision - 1)
|
|
return false;
|
|
|
|
// Get the inverse.
|
|
APFloat reciprocal(*semantics, 1ULL);
|
|
if (reciprocal.divide(*this, rmNearestTiesToEven) != opOK)
|
|
return false;
|
|
|
|
// Avoid multiplication with a denormal, it is not safe on all platforms and
|
|
// may be slower than a normal division.
|
|
if (reciprocal.isDenormal())
|
|
return false;
|
|
|
|
assert(reciprocal.isFiniteNonZero() &&
|
|
reciprocal.significandLSB() == reciprocal.semantics->precision - 1);
|
|
|
|
if (inv)
|
|
*inv = reciprocal;
|
|
|
|
return true;
|
|
}
|
|
|
|
bool APFloat::isSignaling() const {
|
|
if (!isNaN())
|
|
return false;
|
|
|
|
// IEEE-754R 2008 6.2.1: A signaling NaN bit string should be encoded with the
|
|
// first bit of the trailing significand being 0.
|
|
return !APInt::tcExtractBit(significandParts(), semantics->precision - 2);
|
|
}
|
|
|
|
/// IEEE-754R 2008 5.3.1: nextUp/nextDown.
|
|
///
|
|
/// *NOTE* since nextDown(x) = -nextUp(-x), we only implement nextUp with
|
|
/// appropriate sign switching before/after the computation.
|
|
APFloat::opStatus APFloat::next(bool nextDown) {
|
|
// If we are performing nextDown, swap sign so we have -x.
|
|
if (nextDown)
|
|
changeSign();
|
|
|
|
// Compute nextUp(x)
|
|
opStatus result = opOK;
|
|
|
|
// Handle each float category separately.
|
|
switch (category) {
|
|
case fcInfinity:
|
|
// nextUp(+inf) = +inf
|
|
if (!isNegative())
|
|
break;
|
|
// nextUp(-inf) = -getLargest()
|
|
makeLargest(true);
|
|
break;
|
|
case fcNaN:
|
|
// IEEE-754R 2008 6.2 Par 2: nextUp(sNaN) = qNaN. Set Invalid flag.
|
|
// IEEE-754R 2008 6.2: nextUp(qNaN) = qNaN. Must be identity so we do not
|
|
// change the payload.
|
|
if (isSignaling()) {
|
|
result = opInvalidOp;
|
|
// For consistency, propagate the sign of the sNaN to the qNaN.
|
|
makeNaN(false, isNegative(), nullptr);
|
|
}
|
|
break;
|
|
case fcZero:
|
|
// nextUp(pm 0) = +getSmallest()
|
|
makeSmallest(false);
|
|
break;
|
|
case fcNormal:
|
|
// nextUp(-getSmallest()) = -0
|
|
if (isSmallest() && isNegative()) {
|
|
APInt::tcSet(significandParts(), 0, partCount());
|
|
category = fcZero;
|
|
exponent = 0;
|
|
break;
|
|
}
|
|
|
|
// nextUp(getLargest()) == INFINITY
|
|
if (isLargest() && !isNegative()) {
|
|
APInt::tcSet(significandParts(), 0, partCount());
|
|
category = fcInfinity;
|
|
exponent = semantics->maxExponent + 1;
|
|
break;
|
|
}
|
|
|
|
// nextUp(normal) == normal + inc.
|
|
if (isNegative()) {
|
|
// If we are negative, we need to decrement the significand.
|
|
|
|
// We only cross a binade boundary that requires adjusting the exponent
|
|
// if:
|
|
// 1. exponent != semantics->minExponent. This implies we are not in the
|
|
// smallest binade or are dealing with denormals.
|
|
// 2. Our significand excluding the integral bit is all zeros.
|
|
bool WillCrossBinadeBoundary =
|
|
exponent != semantics->minExponent && isSignificandAllZeros();
|
|
|
|
// Decrement the significand.
|
|
//
|
|
// We always do this since:
|
|
// 1. If we are dealing with a non-binade decrement, by definition we
|
|
// just decrement the significand.
|
|
// 2. If we are dealing with a normal -> normal binade decrement, since
|
|
// we have an explicit integral bit the fact that all bits but the
|
|
// integral bit are zero implies that subtracting one will yield a
|
|
// significand with 0 integral bit and 1 in all other spots. Thus we
|
|
// must just adjust the exponent and set the integral bit to 1.
|
|
// 3. If we are dealing with a normal -> denormal binade decrement,
|
|
// since we set the integral bit to 0 when we represent denormals, we
|
|
// just decrement the significand.
|
|
integerPart *Parts = significandParts();
|
|
APInt::tcDecrement(Parts, partCount());
|
|
|
|
if (WillCrossBinadeBoundary) {
|
|
// Our result is a normal number. Do the following:
|
|
// 1. Set the integral bit to 1.
|
|
// 2. Decrement the exponent.
|
|
APInt::tcSetBit(Parts, semantics->precision - 1);
|
|
exponent--;
|
|
}
|
|
} else {
|
|
// If we are positive, we need to increment the significand.
|
|
|
|
// We only cross a binade boundary that requires adjusting the exponent if
|
|
// the input is not a denormal and all of said input's significand bits
|
|
// are set. If all of said conditions are true: clear the significand, set
|
|
// the integral bit to 1, and increment the exponent. If we have a
|
|
// denormal always increment since moving denormals and the numbers in the
|
|
// smallest normal binade have the same exponent in our representation.
|
|
bool WillCrossBinadeBoundary = !isDenormal() && isSignificandAllOnes();
|
|
|
|
if (WillCrossBinadeBoundary) {
|
|
integerPart *Parts = significandParts();
|
|
APInt::tcSet(Parts, 0, partCount());
|
|
APInt::tcSetBit(Parts, semantics->precision - 1);
|
|
assert(exponent != semantics->maxExponent &&
|
|
"We can not increment an exponent beyond the maxExponent allowed"
|
|
" by the given floating point semantics.");
|
|
exponent++;
|
|
} else {
|
|
incrementSignificand();
|
|
}
|
|
}
|
|
break;
|
|
}
|
|
|
|
// If we are performing nextDown, swap sign so we have -nextUp(-x)
|
|
if (nextDown)
|
|
changeSign();
|
|
|
|
return result;
|
|
}
|
|
|
|
void
|
|
APFloat::makeInf(bool Negative) {
|
|
category = fcInfinity;
|
|
sign = Negative;
|
|
exponent = semantics->maxExponent + 1;
|
|
APInt::tcSet(significandParts(), 0, partCount());
|
|
}
|
|
|
|
void
|
|
APFloat::makeZero(bool Negative) {
|
|
category = fcZero;
|
|
sign = Negative;
|
|
exponent = semantics->minExponent-1;
|
|
APInt::tcSet(significandParts(), 0, partCount());
|
|
}
|