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diff --git a/contrib/llvm-project/llvm/lib/Support/APFloat.cpp b/contrib/llvm-project/llvm/lib/Support/APFloat.cpp
new file mode 100644
index 000000000000..b79baf1834a7
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+++ b/contrib/llvm-project/llvm/lib/Support/APFloat.cpp
@@ -0,0 +1,4562 @@
+//===-- APFloat.cpp - Implement APFloat class -----------------------------===//
+//
+// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+// See https://llvm.org/LICENSE.txt for license information.
+// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+//
+//===----------------------------------------------------------------------===//
+//
+// This file implements a class to represent arbitrary precision floating
+// point values and provide a variety of arithmetic operations on them.
+//
+//===----------------------------------------------------------------------===//
+
+#include "llvm/ADT/APFloat.h"
+#include "llvm/ADT/APSInt.h"
+#include "llvm/ADT/ArrayRef.h"
+#include "llvm/ADT/FoldingSet.h"
+#include "llvm/ADT/Hashing.h"
+#include "llvm/ADT/StringExtras.h"
+#include "llvm/ADT/StringRef.h"
+#include "llvm/Config/llvm-config.h"
+#include "llvm/Support/Debug.h"
+#include "llvm/Support/ErrorHandling.h"
+#include "llvm/Support/MathExtras.h"
+#include "llvm/Support/raw_ostream.h"
+#include <cstring>
+#include <limits.h>
+
+#define APFLOAT_DISPATCH_ON_SEMANTICS(METHOD_CALL)                             \
+  do {                                                                         \
+    if (usesLayout<IEEEFloat>(getSemantics()))                                 \
+      return U.IEEE.METHOD_CALL;                                               \
+    if (usesLayout<DoubleAPFloat>(getSemantics()))                             \
+      return U.Double.METHOD_CALL;                                             \
+    llvm_unreachable("Unexpected semantics");                                  \
+  } while (false)
+
+using namespace llvm;
+
+/// A macro used to combine two fcCategory enums into one key which can be used
+/// in a switch statement to classify how the interaction of two APFloat's
+/// categories affects an operation.
+///
+/// TODO: If clang source code is ever allowed to use constexpr in its own
+/// codebase, change this into a static inline function.
+#define PackCategoriesIntoKey(_lhs, _rhs) ((_lhs) * 4 + (_rhs))
+
+/* Assumed in hexadecimal significand parsing, and conversion to
+   hexadecimal strings.  */
+static_assert(APFloatBase::integerPartWidth % 4 == 0, "Part width must be divisible by 4!");
+
+namespace llvm {
+  /* Represents floating point arithmetic semantics.  */
+  struct fltSemantics {
+    /* The largest E such that 2^E is representable; this matches the
+       definition of IEEE 754.  */
+    APFloatBase::ExponentType maxExponent;
+
+    /* The smallest E such that 2^E is a normalized number; this
+       matches the definition of IEEE 754.  */
+    APFloatBase::ExponentType minExponent;
+
+    /* Number of bits in the significand.  This includes the integer
+       bit.  */
+    unsigned int precision;
+
+    /* Number of bits actually used in the semantics. */
+    unsigned int sizeInBits;
+  };
+
+  static const fltSemantics semIEEEhalf = {15, -14, 11, 16};
+  static const fltSemantics semIEEEsingle = {127, -126, 24, 32};
+  static const fltSemantics semIEEEdouble = {1023, -1022, 53, 64};
+  static const fltSemantics semIEEEquad = {16383, -16382, 113, 128};
+  static const fltSemantics semX87DoubleExtended = {16383, -16382, 64, 80};
+  static const fltSemantics semBogus = {0, 0, 0, 0};
+
+  /* The IBM double-double semantics. Such a number consists of a pair of IEEE
+     64-bit doubles (Hi, Lo), where |Hi| > |Lo|, and if normal,
+     (double)(Hi + Lo) == Hi. The numeric value it's modeling is Hi + Lo.
+     Therefore it has two 53-bit mantissa parts that aren't necessarily adjacent
+     to each other, and two 11-bit exponents.
+
+     Note: we need to make the value different from semBogus as otherwise
+     an unsafe optimization may collapse both values to a single address,
+     and we heavily rely on them having distinct addresses.             */
+  static const fltSemantics semPPCDoubleDouble = {-1, 0, 0, 0};
+
+  /* These are legacy semantics for the fallback, inaccrurate implementation of
+     IBM double-double, if the accurate semPPCDoubleDouble doesn't handle the
+     operation. It's equivalent to having an IEEE number with consecutive 106
+     bits of mantissa and 11 bits of exponent.
+
+     It's not equivalent to IBM double-double. For example, a legit IBM
+     double-double, 1 + epsilon:
+
+       1 + epsilon = 1 + (1 >> 1076)
+
+     is not representable by a consecutive 106 bits of mantissa.
+
+     Currently, these semantics are used in the following way:
+
+       semPPCDoubleDouble -> (IEEEdouble, IEEEdouble) ->
+       (64-bit APInt, 64-bit APInt) -> (128-bit APInt) ->
+       semPPCDoubleDoubleLegacy -> IEEE operations
+
+     We use bitcastToAPInt() to get the bit representation (in APInt) of the
+     underlying IEEEdouble, then use the APInt constructor to construct the
+     legacy IEEE float.
+
+     TODO: Implement all operations in semPPCDoubleDouble, and delete these
+     semantics.  */
+  static const fltSemantics semPPCDoubleDoubleLegacy = {1023, -1022 + 53,
+                                                        53 + 53, 128};
+
+  const llvm::fltSemantics &APFloatBase::EnumToSemantics(Semantics S) {
+    switch (S) {
+    case S_IEEEhalf:
+      return IEEEhalf();
+    case S_IEEEsingle:
+      return IEEEsingle();
+    case S_IEEEdouble:
+      return IEEEdouble();
+    case S_x87DoubleExtended:
+      return x87DoubleExtended();
+    case S_IEEEquad:
+      return IEEEquad();
+    case S_PPCDoubleDouble:
+      return PPCDoubleDouble();
+    }
+    llvm_unreachable("Unrecognised floating semantics");
+  }
+
+  APFloatBase::Semantics
+  APFloatBase::SemanticsToEnum(const llvm::fltSemantics &Sem) {
+    if (&Sem == &llvm::APFloat::IEEEhalf())
+      return S_IEEEhalf;
+    else if (&Sem == &llvm::APFloat::IEEEsingle())
+      return S_IEEEsingle;
+    else if (&Sem == &llvm::APFloat::IEEEdouble())
+      return S_IEEEdouble;
+    else if (&Sem == &llvm::APFloat::x87DoubleExtended())
+      return S_x87DoubleExtended;
+    else if (&Sem == &llvm::APFloat::IEEEquad())
+      return S_IEEEquad;
+    else if (&Sem == &llvm::APFloat::PPCDoubleDouble())
+      return S_PPCDoubleDouble;
+    else
+      llvm_unreachable("Unknown floating semantics");
+  }
+
+  const fltSemantics &APFloatBase::IEEEhalf() {
+    return semIEEEhalf;
+  }
+  const fltSemantics &APFloatBase::IEEEsingle() {
+    return semIEEEsingle;
+  }
+  const fltSemantics &APFloatBase::IEEEdouble() {
+    return semIEEEdouble;
+  }
+  const fltSemantics &APFloatBase::IEEEquad() {
+    return semIEEEquad;
+  }
+  const fltSemantics &APFloatBase::x87DoubleExtended() {
+    return semX87DoubleExtended;
+  }
+  const fltSemantics &APFloatBase::Bogus() {
+    return semBogus;
+  }
+  const fltSemantics &APFloatBase::PPCDoubleDouble() {
+    return semPPCDoubleDouble;
+  }
+
+  /* A tight upper bound on number of parts required to hold the value
+     pow(5, power) is
+
+       power * 815 / (351 * integerPartWidth) + 1
+
+     However, whilst the result may require only this many parts,
+     because we are multiplying two values to get it, the
+     multiplication may require an extra part with the excess part
+     being zero (consider the trivial case of 1 * 1, tcFullMultiply
+     requires two parts to hold the single-part result).  So we add an
+     extra one to guarantee enough space whilst multiplying.  */
+  const unsigned int maxExponent = 16383;
+  const unsigned int maxPrecision = 113;
+  const unsigned int maxPowerOfFiveExponent = maxExponent + maxPrecision - 1;
+  const unsigned int maxPowerOfFiveParts = 2 + ((maxPowerOfFiveExponent * 815) / (351 * APFloatBase::integerPartWidth));
+
+  unsigned int APFloatBase::semanticsPrecision(const fltSemantics &semantics) {
+    return semantics.precision;
+  }
+  APFloatBase::ExponentType
+  APFloatBase::semanticsMaxExponent(const fltSemantics &semantics) {
+    return semantics.maxExponent;
+  }
+  APFloatBase::ExponentType
+  APFloatBase::semanticsMinExponent(const fltSemantics &semantics) {
+    return semantics.minExponent;
+  }
+  unsigned int APFloatBase::semanticsSizeInBits(const fltSemantics &semantics) {
+    return semantics.sizeInBits;
+  }
+
+  unsigned APFloatBase::getSizeInBits(const fltSemantics &Sem) {
+    return Sem.sizeInBits;
+}
+
+/* A bunch of private, handy routines.  */
+
+static inline unsigned int
+partCountForBits(unsigned int bits)
+{
+  return ((bits) + APFloatBase::integerPartWidth - 1) / APFloatBase::integerPartWidth;
+}
+
+/* Returns 0U-9U.  Return values >= 10U are not digits.  */
+static inline unsigned int
+decDigitValue(unsigned int c)
+{
+  return c - '0';
+}
+
+/* Return the value of a decimal exponent of the form
+   [+-]ddddddd.
+
+   If the exponent overflows, returns a large exponent with the
+   appropriate sign.  */
+static int
+readExponent(StringRef::iterator begin, StringRef::iterator end)
+{
+  bool isNegative;
+  unsigned int absExponent;
+  const unsigned int overlargeExponent = 24000;  /* FIXME.  */
+  StringRef::iterator p = begin;
+
+  // Treat no exponent as 0 to match binutils
+  if (p == end || ((*p == '-' || *p == '+') && (p + 1) == end)) {
+    return 0;
+  }
+
+  isNegative = (*p == '-');
+  if (*p == '-' || *p == '+') {
+    p++;
+    assert(p != end && "Exponent has no digits");
+  }
+
+  absExponent = decDigitValue(*p++);
+  assert(absExponent < 10U && "Invalid character in exponent");
+
+  for (; p != end; ++p) {
+    unsigned int value;
+
+    value = decDigitValue(*p);
+    assert(value < 10U && "Invalid character in exponent");
+
+    value += absExponent * 10;
+    if (absExponent >= overlargeExponent) {
+      absExponent = overlargeExponent;
+      p = end;  /* outwit assert below */
+      break;
+    }
+    absExponent = value;
+  }
+
+  assert(p == end && "Invalid exponent in exponent");
+
+  if (isNegative)
+    return -(int) absExponent;
+  else
+    return (int) absExponent;
+}
+
+/* This is ugly and needs cleaning up, but I don't immediately see
+   how whilst remaining safe.  */
+static int
+totalExponent(StringRef::iterator p, StringRef::iterator end,
+              int exponentAdjustment)
+{
+  int unsignedExponent;
+  bool negative, overflow;
+  int exponent = 0;
+
+  assert(p != end && "Exponent has no digits");
+
+  negative = *p == '-';
+  if (*p == '-' || *p == '+') {
+    p++;
+    assert(p != end && "Exponent has no digits");
+  }
+
+  unsignedExponent = 0;
+  overflow = false;
+  for (; p != end; ++p) {
+    unsigned int value;
+
+    value = decDigitValue(*p);
+    assert(value < 10U && "Invalid character in exponent");
+
+    unsignedExponent = unsignedExponent * 10 + value;
+    if (unsignedExponent > 32767) {
+      overflow = true;
+      break;
+    }
+  }
+
+  if (exponentAdjustment > 32767 || exponentAdjustment < -32768)
+    overflow = true;
+
+  if (!overflow) {
+    exponent = unsignedExponent;
+    if (negative)
+      exponent = -exponent;
+    exponent += exponentAdjustment;
+    if (exponent > 32767 || exponent < -32768)
+      overflow = true;
+  }
+
+  if (overflow)
+    exponent = negative ? -32768: 32767;
+
+  return exponent;
+}
+
+static StringRef::iterator
+skipLeadingZeroesAndAnyDot(StringRef::iterator begin, StringRef::iterator end,
+                           StringRef::iterator *dot)
+{
+  StringRef::iterator p = begin;
+  *dot = end;
+  while (p != end && *p == '0')
+    p++;
+
+  if (p != end && *p == '.') {
+    *dot = p++;
+
+    assert(end - begin != 1 && "Significand has no digits");
+
+    while (p != end && *p == '0')
+      p++;
+  }
+
+  return p;
+}
+
+/* Given a normal decimal floating point number of the form
+
+     dddd.dddd[eE][+-]ddd
+
+   where the decimal point and exponent are optional, fill out the
+   structure D.  Exponent is appropriate if the significand is
+   treated as an integer, and normalizedExponent if the significand
+   is taken to have the decimal point after a single leading
+   non-zero digit.
+
+   If the value is zero, V->firstSigDigit points to a non-digit, and
+   the return exponent is zero.
+*/
+struct decimalInfo {
+  const char *firstSigDigit;
+  const char *lastSigDigit;
+  int exponent;
+  int normalizedExponent;
+};
+
+static void
+interpretDecimal(StringRef::iterator begin, StringRef::iterator end,
+                 decimalInfo *D)
+{
+  StringRef::iterator dot = end;
+  StringRef::iterator p = skipLeadingZeroesAndAnyDot (begin, end, &dot);
+
+  D->firstSigDigit = p;
+  D->exponent = 0;
+  D->normalizedExponent = 0;
+
+  for (; p != end; ++p) {
+    if (*p == '.') {
+      assert(dot == end && "String contains multiple dots");
+      dot = p++;
+      if (p == end)
+        break;
+    }
+    if (decDigitValue(*p) >= 10U)
+      break;
+  }
+
+  if (p != end) {
+    assert((*p == 'e' || *p == 'E') && "Invalid character in significand");
+    assert(p != begin && "Significand has no digits");
+    assert((dot == end || p - begin != 1) && "Significand has no digits");
+
+    /* p points to the first non-digit in the string */
+    D->exponent = readExponent(p + 1, end);
+
+    /* Implied decimal point?  */
+    if (dot == end)
+      dot = p;
+  }
+
+  /* If number is all zeroes accept any exponent.  */
+  if (p != D->firstSigDigit) {
+    /* Drop insignificant trailing zeroes.  */
+    if (p != begin) {
+      do
+        do
+          p--;
+        while (p != begin && *p == '0');
+      while (p != begin && *p == '.');
+    }
+
+    /* Adjust the exponents for any decimal point.  */
+    D->exponent += static_cast<APFloat::ExponentType>((dot - p) - (dot > p));
+    D->normalizedExponent = (D->exponent +
+              static_cast<APFloat::ExponentType>((p - D->firstSigDigit)
+                                      - (dot > D->firstSigDigit && dot < p)));
+  }
+
+  D->lastSigDigit = p;
+}
+
+/* Return the trailing fraction of a hexadecimal number.
+   DIGITVALUE is the first hex digit of the fraction, P points to
+   the next digit.  */
+static lostFraction
+trailingHexadecimalFraction(StringRef::iterator p, StringRef::iterator end,
+                            unsigned int digitValue)
+{
+  unsigned int hexDigit;
+
+  /* If the first trailing digit isn't 0 or 8 we can work out the
+     fraction immediately.  */
+  if (digitValue > 8)
+    return lfMoreThanHalf;
+  else if (digitValue < 8 && digitValue > 0)
+    return lfLessThanHalf;
+
+  // Otherwise we need to find the first non-zero digit.
+  while (p != end && (*p == '0' || *p == '.'))
+    p++;
+
+  assert(p != end && "Invalid trailing hexadecimal fraction!");
+
+  hexDigit = hexDigitValue(*p);
+
+  /* If we ran off the end it is exactly zero or one-half, otherwise
+     a little more.  */
+  if (hexDigit == -1U)
+    return digitValue == 0 ? lfExactlyZero: lfExactlyHalf;
+  else
+    return digitValue == 0 ? lfLessThanHalf: lfMoreThanHalf;
+}
+
+/* Return the fraction lost were a bignum truncated losing the least
+   significant BITS bits.  */
+static lostFraction
+lostFractionThroughTruncation(const APFloatBase::integerPart *parts,
+                              unsigned int partCount,
+                              unsigned int bits)
+{
+  unsigned int lsb;
+
+  lsb = APInt::tcLSB(parts, partCount);
+
+  /* Note this is guaranteed true if bits == 0, or LSB == -1U.  */
+  if (bits <= lsb)
+    return lfExactlyZero;
+  if (bits == lsb + 1)
+    return lfExactlyHalf;
+  if (bits <= partCount * APFloatBase::integerPartWidth &&
+      APInt::tcExtractBit(parts, bits - 1))
+    return lfMoreThanHalf;
+
+  return lfLessThanHalf;
+}
+
+/* Shift DST right BITS bits noting lost fraction.  */
+static lostFraction
+shiftRight(APFloatBase::integerPart *dst, unsigned int parts, unsigned int bits)
+{
+  lostFraction lost_fraction;
+
+  lost_fraction = lostFractionThroughTruncation(dst, parts, bits);
+
+  APInt::tcShiftRight(dst, parts, bits);
+
+  return lost_fraction;
+}
+
+/* Combine the effect of two lost fractions.  */
+static lostFraction
+combineLostFractions(lostFraction moreSignificant,
+                     lostFraction lessSignificant)
+{
+  if (lessSignificant != lfExactlyZero) {
+    if (moreSignificant == lfExactlyZero)
+      moreSignificant = lfLessThanHalf;
+    else if (moreSignificant == lfExactlyHalf)
+      moreSignificant = lfMoreThanHalf;
+  }
+
+  return moreSignificant;
+}
+
+/* The error from the true value, in half-ulps, on multiplying two
+   floating point numbers, which differ from the value they
+   approximate by at most HUE1 and HUE2 half-ulps, is strictly less
+   than the returned value.
+
+   See "How to Read Floating Point Numbers Accurately" by William D
+   Clinger.  */
+static unsigned int
+HUerrBound(bool inexactMultiply, unsigned int HUerr1, unsigned int HUerr2)
+{
+  assert(HUerr1 < 2 || HUerr2 < 2 || (HUerr1 + HUerr2 < 8));
+
+  if (HUerr1 + HUerr2 == 0)
+    return inexactMultiply * 2;  /* <= inexactMultiply half-ulps.  */
+  else
+    return inexactMultiply + 2 * (HUerr1 + HUerr2);
+}
+
+/* The number of ulps from the boundary (zero, or half if ISNEAREST)
+   when the least significant BITS are truncated.  BITS cannot be
+   zero.  */
+static APFloatBase::integerPart
+ulpsFromBoundary(const APFloatBase::integerPart *parts, unsigned int bits,
+                 bool isNearest) {
+  unsigned int count, partBits;
+  APFloatBase::integerPart part, boundary;
+
+  assert(bits != 0);
+
+  bits--;
+  count = bits / APFloatBase::integerPartWidth;
+  partBits = bits % APFloatBase::integerPartWidth + 1;
+
+  part = parts[count] & (~(APFloatBase::integerPart) 0 >> (APFloatBase::integerPartWidth - partBits));
+
+  if (isNearest)
+    boundary = (APFloatBase::integerPart) 1 << (partBits - 1);
+  else
+    boundary = 0;
+
+  if (count == 0) {
+    if (part - boundary <= boundary - part)
+      return part - boundary;
+    else
+      return boundary - part;
+  }
+
+  if (part == boundary) {
+    while (--count)
+      if (parts[count])
+        return ~(APFloatBase::integerPart) 0; /* A lot.  */
+
+    return parts[0];
+  } else if (part == boundary - 1) {
+    while (--count)
+      if (~parts[count])
+        return ~(APFloatBase::integerPart) 0; /* A lot.  */
+
+    return -parts[0];
+  }
+
+  return ~(APFloatBase::integerPart) 0; /* A lot.  */
+}
+
+/* Place pow(5, power) in DST, and return the number of parts used.
+   DST must be at least one part larger than size of the answer.  */
+static unsigned int
+powerOf5(APFloatBase::integerPart *dst, unsigned int power) {
+  static const APFloatBase::integerPart firstEightPowers[] = { 1, 5, 25, 125, 625, 3125, 15625, 78125 };
+  APFloatBase::integerPart pow5s[maxPowerOfFiveParts * 2 + 5];
+  pow5s[0] = 78125 * 5;
+
+  unsigned int partsCount[16] = { 1 };
+  APFloatBase::integerPart scratch[maxPowerOfFiveParts], *p1, *p2, *pow5;
+  unsigned int result;
+  assert(power <= maxExponent);
+
+  p1 = dst;
+  p2 = scratch;
+
+  *p1 = firstEightPowers[power & 7];
+  power >>= 3;
+
+  result = 1;
+  pow5 = pow5s;
+
+  for (unsigned int n = 0; power; power >>= 1, n++) {
+    unsigned int pc;
+
+    pc = partsCount[n];
+
+    /* Calculate pow(5,pow(2,n+3)) if we haven't yet.  */
+    if (pc == 0) {
+      pc = partsCount[n - 1];
+      APInt::tcFullMultiply(pow5, pow5 - pc, pow5 - pc, pc, pc);
+      pc *= 2;
+      if (pow5[pc - 1] == 0)
+        pc--;
+      partsCount[n] = pc;
+    }
+
+    if (power & 1) {
+      APFloatBase::integerPart *tmp;
+
+      APInt::tcFullMultiply(p2, p1, pow5, result, pc);
+      result += pc;
+      if (p2[result - 1] == 0)
+        result--;
+
+      /* Now result is in p1 with partsCount parts and p2 is scratch
+         space.  */
+      tmp = p1;
+      p1 = p2;
+      p2 = tmp;
+    }
+
+    pow5 += pc;
+  }
+
+  if (p1 != dst)
+    APInt::tcAssign(dst, p1, result);
+
+  return result;
+}
+
+/* Zero at the end to avoid modular arithmetic when adding one; used
+   when rounding up during hexadecimal output.  */
+static const char hexDigitsLower[] = "0123456789abcdef0";
+static const char hexDigitsUpper[] = "0123456789ABCDEF0";
+static const char infinityL[] = "infinity";
+static const char infinityU[] = "INFINITY";
+static const char NaNL[] = "nan";
+static const char NaNU[] = "NAN";
+
+/* Write out an integerPart in hexadecimal, starting with the most
+   significant nibble.  Write out exactly COUNT hexdigits, return
+   COUNT.  */
+static unsigned int
+partAsHex (char *dst, APFloatBase::integerPart part, unsigned int count,
+           const char *hexDigitChars)
+{
+  unsigned int result = count;
+
+  assert(count != 0 && count <= APFloatBase::integerPartWidth / 4);
+
+  part >>= (APFloatBase::integerPartWidth - 4 * count);
+  while (count--) {
+    dst[count] = hexDigitChars[part & 0xf];
+    part >>= 4;
+  }
+
+  return result;
+}
+
+/* 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;
+}
+
+namespace detail {
+/* Constructors.  */
+void IEEEFloat::initialize(const fltSemantics *ourSemantics) {
+  unsigned int count;
+
+  semantics = ourSemantics;
+  count = partCount();
+  if (count > 1)
+    significand.parts = new integerPart[count];
+}
+
+void IEEEFloat::freeSignificand() {
+  if (needsCleanup())
+    delete [] significand.parts;
+}
+
+void IEEEFloat::assign(const IEEEFloat &rhs) {
+  assert(semantics == rhs.semantics);
+
+  sign = rhs.sign;
+  category = rhs.category;
+  exponent = rhs.exponent;
+  if (isFiniteNonZero() || category == fcNaN)
+    copySignificand(rhs);
+}
+
+void IEEEFloat::copySignificand(const IEEEFloat &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 IEEEFloat::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 == &semX87DoubleExtended)
+    APInt::tcSetBit(significand, QNaNBit + 1);
+}
+
+IEEEFloat &IEEEFloat::operator=(const IEEEFloat &rhs) {
+  if (this != &rhs) {
+    if (semantics != rhs.semantics) {
+      freeSignificand();
+      initialize(rhs.semantics);
+    }
+    assign(rhs);
+  }
+
+  return *this;
+}
+
+IEEEFloat &IEEEFloat::operator=(IEEEFloat &&rhs) {
+  freeSignificand();
+
+  semantics = rhs.semantics;
+  significand = rhs.significand;
+  exponent = rhs.exponent;
+  category = rhs.category;
+  sign = rhs.sign;
+
+  rhs.semantics = &semBogus;
+  return *this;
+}
+
+bool IEEEFloat::isDenormal() const {
+  return isFiniteNonZero() && (exponent == semantics->minExponent) &&
+         (APInt::tcExtractBit(significandParts(),
+                              semantics->precision - 1) == 0);
+}
+
+bool IEEEFloat::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 IEEEFloat::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 IEEEFloat::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 IEEEFloat::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 IEEEFloat::isInteger() const {
+  // This could be made more efficient; I'm going for obviously correct.
+  if (!isFinite()) return false;
+  IEEEFloat truncated = *this;
+  truncated.roundToIntegral(rmTowardZero);
+  return compare(truncated) == cmpEqual;
+}
+
+bool IEEEFloat::bitwiseIsEqual(const IEEEFloat &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;
+
+  if (isFiniteNonZero() && exponent != rhs.exponent)
+    return false;
+
+  return std::equal(significandParts(), significandParts() + partCount(),
+                    rhs.significandParts());
+}
+
+IEEEFloat::IEEEFloat(const fltSemantics &ourSemantics, integerPart value) {
+  initialize(&ourSemantics);
+  sign = 0;
+  category = fcNormal;
+  zeroSignificand();
+  exponent = ourSemantics.precision - 1;
+  significandParts()[0] = value;
+  normalize(rmNearestTiesToEven, lfExactlyZero);
+}
+
+IEEEFloat::IEEEFloat(const fltSemantics &ourSemantics) {
+  initialize(&ourSemantics);
+  category = fcZero;
+  sign = false;
+}
+
+// Delegate to the previous constructor, because later copy constructor may
+// actually inspects category, which can't be garbage.
+IEEEFloat::IEEEFloat(const fltSemantics &ourSemantics, uninitializedTag tag)
+    : IEEEFloat(ourSemantics) {}
+
+IEEEFloat::IEEEFloat(const IEEEFloat &rhs) {
+  initialize(rhs.semantics);
+  assign(rhs);
+}
+
+IEEEFloat::IEEEFloat(IEEEFloat &&rhs) : semantics(&semBogus) {
+  *this = std::move(rhs);
+}
+
+IEEEFloat::~IEEEFloat() { freeSignificand(); }
+
+unsigned int IEEEFloat::partCount() const {
+  return partCountForBits(semantics->precision + 1);
+}
+
+const IEEEFloat::integerPart *IEEEFloat::significandParts() const {
+  return const_cast<IEEEFloat *>(this)->significandParts();
+}
+
+IEEEFloat::integerPart *IEEEFloat::significandParts() {
+  if (partCount() > 1)
+    return significand.parts;
+  else
+    return &significand.part;
+}
+
+void IEEEFloat::zeroSignificand() {
+  APInt::tcSet(significandParts(), 0, partCount());
+}
+
+/* Increment an fcNormal floating point number's significand.  */
+void IEEEFloat::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.  */
+IEEEFloat::integerPart IEEEFloat::addSignificand(const IEEEFloat &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.  */
+IEEEFloat::integerPart IEEEFloat::subtractSignificand(const IEEEFloat &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 IEEEFloat::multiplySignificand(const IEEEFloat &rhs,
+                                            const IEEEFloat *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;
+
+  // Allocate space for twice as many bits as the original significand, plus one
+  // extra bit for the addition to overflow into.
+  newPartsCount = partCountForBits(precision * 2 + 1);
+
+  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 = c48 c47 c46 . c45 ... c0 * 2^(e1+e2)
+  // Note that there are three significant bits at the left-hand side of the
+  // radix point: two for the multiplication, and an overflow bit for the
+  // addition (that will always be zero at this point). Move the radix point
+  // toward left by two bits, and adjust exponent accordingly.
+  exponent += 2;
+
+  if (addend && addend->isNonZero()) {
+    // 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 to one below the top bit to allow for overflow.
+    extendedPrecision = 2 * precision + 1;
+    if (omsb != extendedPrecision - 1) {
+      assert(extendedPrecision > omsb);
+      APInt::tcShiftLeft(fullSignificand, newPartsCount,
+                         (extendedPrecision - 1) - omsb);
+      exponent -= (extendedPrecision - 1) - omsb;
+    }
+
+    /* Create new semantics.  */
+    extendedSemantics = *semantics;
+    extendedSemantics.precision = extendedPrecision;
+
+    if (newPartsCount == 1)
+      significand.part = fullSignificand[0];
+    else
+      significand.parts = fullSignificand;
+    semantics = &extendedSemantics;
+
+    IEEEFloat extendedAddend(*addend);
+    status = extendedAddend.convert(extendedSemantics, rmTowardZero, &ignored);
+    assert(status == opOK);
+    (void)status;
+
+    // Shift the significand of the addend right by one bit. This guarantees
+    // that the high bit of the significand is zero (same as fullSignificand),
+    // so the addition will overflow (if it does overflow at all) into the top bit.
+    lost_fraction = extendedAddend.shiftSignificandRight(1);
+    assert(lost_fraction == lfExactlyZero &&
+           "Lost precision while shifting addend for fused-multiply-add.");
+
+    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 + 1;
+
+  // 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 IEEEFloat::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 IEEEFloat::divideSignificand(const IEEEFloat &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 IEEEFloat::significandMSB() const {
+  return APInt::tcMSB(significandParts(), partCount());
+}
+
+unsigned int IEEEFloat::significandLSB() const {
+  return APInt::tcLSB(significandParts(), partCount());
+}
+
+/* Note that a zero result is NOT normalized to fcZero.  */
+lostFraction IEEEFloat::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 IEEEFloat::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));
+  }
+}
+
+IEEEFloat::cmpResult
+IEEEFloat::compareAbsoluteValue(const IEEEFloat &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.  */
+IEEEFloat::opStatus IEEEFloat::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 IEEEFloat::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;
+
+  case rmTowardNegative:
+    return sign;
+  }
+  llvm_unreachable("Invalid rounding mode found");
+}
+
+IEEEFloat::opStatus IEEEFloat::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);
+}
+
+IEEEFloat::opStatus IEEEFloat::addOrSubtractSpecials(const IEEEFloat &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 IEEEFloat::addOrSubtractSignificand(const IEEEFloat &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 ^= static_cast<bool>(sign ^ rhs.sign);
+
+  /* Are we bigger exponent-wise than the RHS?  */
+  bits = exponent - rhs.exponent;
+
+  /* Subtraction is more subtle than one might naively expect.  */
+  if (subtract) {
+    IEEEFloat 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) {
+      IEEEFloat 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;
+}
+
+IEEEFloat::opStatus IEEEFloat::multiplySpecials(const IEEEFloat &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;
+  }
+}
+
+IEEEFloat::opStatus IEEEFloat::divideSpecials(const IEEEFloat &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);
+    LLVM_FALLTHROUGH;
+  case PackCategoriesIntoKey(fcNaN, fcZero):
+  case PackCategoriesIntoKey(fcNaN, fcNormal):
+  case PackCategoriesIntoKey(fcNaN, fcInfinity):
+  case PackCategoriesIntoKey(fcNaN, fcNaN):
+    sign = false;
+    LLVM_FALLTHROUGH;
+  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;
+  }
+}
+
+IEEEFloat::opStatus IEEEFloat::modSpecials(const IEEEFloat &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 IEEEFloat::changeSign() {
+  /* Look mummy, this one's easy.  */
+  sign = !sign;
+}
+
+/* Normalized addition or subtraction.  */
+IEEEFloat::opStatus IEEEFloat::addOrSubtract(const IEEEFloat &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.  */
+IEEEFloat::opStatus IEEEFloat::add(const IEEEFloat &rhs,
+                                   roundingMode rounding_mode) {
+  return addOrSubtract(rhs, rounding_mode, false);
+}
+
+/* Normalized subtraction.  */
+IEEEFloat::opStatus IEEEFloat::subtract(const IEEEFloat &rhs,
+                                        roundingMode rounding_mode) {
+  return addOrSubtract(rhs, rounding_mode, true);
+}
+
+/* Normalized multiply.  */
+IEEEFloat::opStatus IEEEFloat::multiply(const IEEEFloat &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.  */
+IEEEFloat::opStatus IEEEFloat::divide(const IEEEFloat &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.  */
+IEEEFloat::opStatus IEEEFloat::remainder(const IEEEFloat &rhs) {
+  opStatus fs;
+  IEEEFloat 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(makeMutableArrayRef(x, parts),
+                          parts * integerPartWidth, true, rmNearestTiesToEven,
+                          &ignored);
+  if (fs == opInvalidOp) {
+    delete[] x;
+    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). */
+IEEEFloat::opStatus IEEEFloat::mod(const IEEEFloat &rhs) {
+  opStatus fs;
+  fs = modSpecials(rhs);
+  unsigned int origSign = sign;
+
+  while (isFiniteNonZero() && rhs.isFiniteNonZero() &&
+         compareAbsoluteValue(rhs) != cmpLessThan) {
+    IEEEFloat V = scalbn(rhs, ilogb(*this) - ilogb(rhs), rmNearestTiesToEven);
+    if (compareAbsoluteValue(V) == cmpLessThan)
+      V = scalbn(V, -1, rmNearestTiesToEven);
+    V.sign = sign;
+
+    fs = subtract(V, rmNearestTiesToEven);
+    assert(fs==opOK);
+  }
+  if (isZero())
+    sign = origSign; // fmod requires this
+  return fs;
+}
+
+/* Normalized fused-multiply-add.  */
+IEEEFloat::opStatus IEEEFloat::fusedMultiplyAdd(const IEEEFloat &multiplicand,
+                                                const IEEEFloat &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.isFinite()) {
+    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 && !(fs & opUnderflow) && 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.  */
+IEEEFloat::opStatus IEEEFloat::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;
+  IEEEFloat MagicConstant(*semantics);
+  fs = MagicConstant.convertFromAPInt(IntegerConstant, false,
+                                      rmNearestTiesToEven);
+  MagicConstant.sign = sign;
+
+  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.  */
+IEEEFloat::cmpResult IEEEFloat::compare(const IEEEFloat &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;
+}
+
+/// IEEEFloat::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).
+
+IEEEFloat::opStatus IEEEFloat::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 == &semX87DoubleExtended &&
+      &toSemantics != &semX87DoubleExtended && 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 == &semX87DoubleExtended)
+      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.  */
+IEEEFloat::opStatus IEEEFloat::convertToSignExtendedInteger(
+    MutableArrayRef<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);
+  assert(dstPartsCount <= parts.size() && "Integer too big");
+
+  if (category == fcZero) {
+    APInt::tcSet(parts.data(), 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.data(), 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.data(), dstPartsCount, src, bits, truncatedBits);
+    } else {
+      /* We want at least as many bits as are available.  */
+      APInt::tcExtract(parts.data(), dstPartsCount, src, semantics->precision,
+                       0);
+      APInt::tcShiftLeft(parts.data(), 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.data(), dstPartsCount))
+        return opInvalidOp;     /* Overflow.  */
+    }
+  } else {
+    lost_fraction = lfExactlyZero;
+  }
+
+  /* Step 3: check if we fit in the destination.  */
+  unsigned int omsb = APInt::tcMSB(parts.data(), 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.data(), dstPartsCount) + 1 != omsb)
+        return opInvalidOp;
+
+      /* This case can happen because of rounding.  */
+      if (omsb > width)
+        return opInvalidOp;
+    }
+
+    APInt::tcNegate (parts.data(), 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.
+*/
+IEEEFloat::opStatus
+IEEEFloat::convertToInteger(MutableArrayRef<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);
+    assert(dstPartsCount <= parts.size() && "Integer too big");
+
+    if (category == fcNaN)
+      bits = 0;
+    else if (sign)
+      bits = isSigned;
+    else
+      bits = width - isSigned;
+
+    APInt::tcSetLeastSignificantBits(parts.data(), dstPartsCount, bits);
+    if (sign && isSigned)
+      APInt::tcShiftLeft(parts.data(), dstPartsCount, width - 1);
+  }
+
+  return fs;
+}
+
+/* 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.  */
+IEEEFloat::opStatus IEEEFloat::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);
+}
+
+IEEEFloat::opStatus IEEEFloat::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.  */
+IEEEFloat::opStatus
+IEEEFloat::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?  */
+IEEEFloat::opStatus
+IEEEFloat::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);
+}
+
+IEEEFloat::opStatus
+IEEEFloat::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);
+}
+
+IEEEFloat::opStatus
+IEEEFloat::roundSignificandWithExponent(const integerPart *decSigParts,
+                                        unsigned sigPartCount, int exp,
+                                        roundingMode rounding_mode) {
+  unsigned int parts, pow5PartCount;
+  fltSemantics calcSemantics = { 32767, -32767, 0, 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;
+
+    IEEEFloat decSig(calcSemantics, uninitialized);
+    decSig.makeZero(sign);
+    IEEEFloat 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);
+    }
+  }
+}
+
+IEEEFloat::opStatus
+IEEEFloat::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 IEEEFloat::convertFromStringSpecials(StringRef str) {
+  if (str.equals("inf") || str.equals("INFINITY") || str.equals("+Inf")) {
+    makeInf(false);
+    return true;
+  }
+
+  if (str.equals("-inf") || str.equals("-INFINITY") || str.equals("-Inf")) {
+    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;
+}
+
+IEEEFloat::opStatus IEEEFloat::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 IEEEFloat::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 *IEEEFloat::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 hash_value(const IEEEFloat &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 IEEEFloat::convertF80LongDoubleAPFloatToAPInt() const {
+  assert(semantics == (const llvm::fltSemantics*)&semX87DoubleExtended);
+  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 IEEEFloat::convertPPCDoubleDoubleAPFloatToAPInt() const {
+  assert(semantics == (const llvm::fltSemantics *)&semPPCDoubleDoubleLegacy);
+  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 = semIEEEdouble.minExponent;
+  IEEEFloat extended(*this);
+  fs = extended.convert(extendedSemantics, rmNearestTiesToEven, &losesInfo);
+  assert(fs == opOK && !losesInfo);
+  (void)fs;
+
+  IEEEFloat u(extended);
+  fs = u.convert(semIEEEdouble, 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;
+
+    IEEEFloat v(extended);
+    v.subtract(u, rmNearestTiesToEven);
+    fs = v.convert(semIEEEdouble, rmNearestTiesToEven, &losesInfo);
+    assert(fs == opOK && !losesInfo);
+    (void)fs;
+    words[1] = *v.convertDoubleAPFloatToAPInt().getRawData();
+  } else {
+    words[1] = 0;
+  }
+
+  return APInt(128, words);
+}
+
+APInt IEEEFloat::convertQuadrupleAPFloatToAPInt() const {
+  assert(semantics == (const llvm::fltSemantics*)&semIEEEquad);
+  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 IEEEFloat::convertDoubleAPFloatToAPInt() const {
+  assert(semantics == (const llvm::fltSemantics*)&semIEEEdouble);
+  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 IEEEFloat::convertFloatAPFloatToAPInt() const {
+  assert(semantics == (const llvm::fltSemantics*)&semIEEEsingle);
+  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 IEEEFloat::convertHalfAPFloatToAPInt() const {
+  assert(semantics == (const llvm::fltSemantics*)&semIEEEhalf);
+  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 IEEEFloat::bitcastToAPInt() const {
+  if (semantics == (const llvm::fltSemantics*)&semIEEEhalf)
+    return convertHalfAPFloatToAPInt();
+
+  if (semantics == (const llvm::fltSemantics*)&semIEEEsingle)
+    return convertFloatAPFloatToAPInt();
+
+  if (semantics == (const llvm::fltSemantics*)&semIEEEdouble)
+    return convertDoubleAPFloatToAPInt();
+
+  if (semantics == (const llvm::fltSemantics*)&semIEEEquad)
+    return convertQuadrupleAPFloatToAPInt();
+
+  if (semantics == (const llvm::fltSemantics *)&semPPCDoubleDoubleLegacy)
+    return convertPPCDoubleDoubleAPFloatToAPInt();
+
+  assert(semantics == (const llvm::fltSemantics*)&semX87DoubleExtended &&
+         "unknown format!");
+  return convertF80LongDoubleAPFloatToAPInt();
+}
+
+float IEEEFloat::convertToFloat() const {
+  assert(semantics == (const llvm::fltSemantics*)&semIEEEsingle &&
+         "Float semantics are not IEEEsingle");
+  APInt api = bitcastToAPInt();
+  return api.bitsToFloat();
+}
+
+double IEEEFloat::convertToDouble() const {
+  assert(semantics == (const llvm::fltSemantics*)&semIEEEdouble &&
+         "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 nor all 1's, integer bit 0 ("unnormal")
+///  exponent = 0, integer bit 1 ("pseudodenormal")
+/// At the moment, the first three are treated as NaNs, the last one as Normal.
+void IEEEFloat::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;
+  uint8_t myintegerbit = mysignificand >> 63;
+
+  initialize(&semX87DoubleExtended);
+  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) ||
+             (myexponent != 0x7fff && myexponent != 0 && myintegerbit == 0)) {
+    // 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 IEEEFloat::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(semPPCDoubleDoubleLegacy, rmNearestTiesToEven, &losesInfo);
+  assert(fs == opOK && !losesInfo);
+  (void)fs;
+
+  // Unless we have a special case, add in second double.
+  if (isFiniteNonZero()) {
+    IEEEFloat v(semIEEEdouble, APInt(64, i2));
+    fs = v.convert(semPPCDoubleDoubleLegacy, rmNearestTiesToEven, &losesInfo);
+    assert(fs == opOK && !losesInfo);
+    (void)fs;
+
+    add(v, rmNearestTiesToEven);
+  }
+}
+
+void IEEEFloat::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(&semIEEEquad);
+  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 IEEEFloat::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(&semIEEEdouble);
+  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 IEEEFloat::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(&semIEEEsingle);
+  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 IEEEFloat::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(&semIEEEhalf);
+  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 IEEEFloat::initFromAPInt(const fltSemantics *Sem, const APInt &api) {
+  if (Sem == &semIEEEhalf)
+    return initFromHalfAPInt(api);
+  if (Sem == &semIEEEsingle)
+    return initFromFloatAPInt(api);
+  if (Sem == &semIEEEdouble)
+    return initFromDoubleAPInt(api);
+  if (Sem == &semX87DoubleExtended)
+    return initFromF80LongDoubleAPInt(api);
+  if (Sem == &semIEEEquad)
+    return initFromQuadrupleAPInt(api);
+  if (Sem == &semPPCDoubleDoubleLegacy)
+    return initFromPPCDoubleDoubleAPInt(api);
+
+  llvm_unreachable(nullptr);
+}
+
+/// Make this number the largest magnitude normal number in the given
+/// semantics.
+void IEEEFloat::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 IEEEFloat::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());
+}
+
+void IEEEFloat::makeSmallestNormalized(bool Negative) {
+  // We want (in interchange format):
+  //   sign = {Negative}
+  //   exponent = 0..0
+  //   significand = 10..0
+
+  category = fcNormal;
+  zeroSignificand();
+  sign = Negative;
+  exponent = semantics->minExponent;
+  significandParts()[partCountForBits(semantics->precision) - 1] |=
+      (((integerPart)1) << ((semantics->precision - 1) % integerPartWidth));
+}
+
+IEEEFloat::IEEEFloat(const fltSemantics &Sem, const APInt &API) {
+  initFromAPInt(&Sem, API);
+}
+
+IEEEFloat::IEEEFloat(float f) {
+  initFromAPInt(&semIEEEsingle, APInt::floatToBits(f));
+}
+
+IEEEFloat::IEEEFloat(double d) {
+  initFromAPInt(&semIEEEdouble, 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 IEEEFloat::toString(SmallVectorImpl<char> &Str, unsigned FormatPrecision,
+                         unsigned FormatMaxPadding, bool TruncateZero) 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) {
+      if (TruncateZero)
+        append(Str, "0.0E+0");
+      else {
+        append(Str, "0.0");
+        if (FormatPrecision > 1)
+          Str.append(FormatPrecision - 1, '0');
+        append(Str, "e+00");
+      }
+    } 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.lshrInPlace(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 && TruncateZero)
+      Str.push_back('0');
+    else
+      for (unsigned I = 1; I != NDigits; ++I)
+        Str.push_back(buffer[NDigits-1-I]);
+    // Fill with zeros up to FormatPrecision.
+    if (!TruncateZero && FormatPrecision > NDigits - 1)
+      Str.append(FormatPrecision - NDigits + 1, '0');
+    // For !TruncateZero we use lower 'e'.
+    Str.push_back(TruncateZero ? 'E' : '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);
+    // Exponent always at least two digits if we do not truncate zeros.
+    if (!TruncateZero && expbuf.size() < 2)
+      expbuf.push_back('0');
+    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 IEEEFloat::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.
+  IEEEFloat 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 = APFloat(reciprocal, *semantics);
+
+  return true;
+}
+
+bool IEEEFloat::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.
+IEEEFloat::opStatus IEEEFloat::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 IEEEFloat::makeInf(bool Negative) {
+  category = fcInfinity;
+  sign = Negative;
+  exponent = semantics->maxExponent + 1;
+  APInt::tcSet(significandParts(), 0, partCount());
+}
+
+void IEEEFloat::makeZero(bool Negative) {
+  category = fcZero;
+  sign = Negative;
+  exponent = semantics->minExponent-1;
+  APInt::tcSet(significandParts(), 0, partCount());
+}
+
+void IEEEFloat::makeQuiet() {
+  assert(isNaN());
+  APInt::tcSetBit(significandParts(), semantics->precision - 2);
+}
+
+int ilogb(const IEEEFloat &Arg) {
+  if (Arg.isNaN())
+    return IEEEFloat::IEK_NaN;
+  if (Arg.isZero())
+    return IEEEFloat::IEK_Zero;
+  if (Arg.isInfinity())
+    return IEEEFloat::IEK_Inf;
+  if (!Arg.isDenormal())
+    return Arg.exponent;
+
+  IEEEFloat Normalized(Arg);
+  int SignificandBits = Arg.getSemantics().precision - 1;
+
+  Normalized.exponent += SignificandBits;
+  Normalized.normalize(IEEEFloat::rmNearestTiesToEven, lfExactlyZero);
+  return Normalized.exponent - SignificandBits;
+}
+
+IEEEFloat scalbn(IEEEFloat X, int Exp, IEEEFloat::roundingMode RoundingMode) {
+  auto MaxExp = X.getSemantics().maxExponent;
+  auto MinExp = X.getSemantics().minExponent;
+
+  // If Exp is wildly out-of-scale, simply adding it to X.exponent will
+  // overflow; clamp it to a safe range before adding, but ensure that the range
+  // is large enough that the clamp does not change the result. The range we
+  // need to support is the difference between the largest possible exponent and
+  // the normalized exponent of half the smallest denormal.
+
+  int SignificandBits = X.getSemantics().precision - 1;
+  int MaxIncrement = MaxExp - (MinExp - SignificandBits) + 1;
+
+  // Clamp to one past the range ends to let normalize handle overlflow.
+  X.exponent += std::min(std::max(Exp, -MaxIncrement - 1), MaxIncrement);
+  X.normalize(RoundingMode, lfExactlyZero);
+  if (X.isNaN())
+    X.makeQuiet();
+  return X;
+}
+
+IEEEFloat frexp(const IEEEFloat &Val, int &Exp, IEEEFloat::roundingMode RM) {
+  Exp = ilogb(Val);
+
+  // Quiet signalling nans.
+  if (Exp == IEEEFloat::IEK_NaN) {
+    IEEEFloat Quiet(Val);
+    Quiet.makeQuiet();
+    return Quiet;
+  }
+
+  if (Exp == IEEEFloat::IEK_Inf)
+    return Val;
+
+  // 1 is added because frexp is defined to return a normalized fraction in
+  // +/-[0.5, 1.0), rather than the usual +/-[1.0, 2.0).
+  Exp = Exp == IEEEFloat::IEK_Zero ? 0 : Exp + 1;
+  return scalbn(Val, -Exp, RM);
+}
+
+DoubleAPFloat::DoubleAPFloat(const fltSemantics &S)
+    : Semantics(&S),
+      Floats(new APFloat[2]{APFloat(semIEEEdouble), APFloat(semIEEEdouble)}) {
+  assert(Semantics == &semPPCDoubleDouble);
+}
+
+DoubleAPFloat::DoubleAPFloat(const fltSemantics &S, uninitializedTag)
+    : Semantics(&S),
+      Floats(new APFloat[2]{APFloat(semIEEEdouble, uninitialized),
+                            APFloat(semIEEEdouble, uninitialized)}) {
+  assert(Semantics == &semPPCDoubleDouble);
+}
+
+DoubleAPFloat::DoubleAPFloat(const fltSemantics &S, integerPart I)
+    : Semantics(&S), Floats(new APFloat[2]{APFloat(semIEEEdouble, I),
+                                           APFloat(semIEEEdouble)}) {
+  assert(Semantics == &semPPCDoubleDouble);
+}
+
+DoubleAPFloat::DoubleAPFloat(const fltSemantics &S, const APInt &I)
+    : Semantics(&S),
+      Floats(new APFloat[2]{
+          APFloat(semIEEEdouble, APInt(64, I.getRawData()[0])),
+          APFloat(semIEEEdouble, APInt(64, I.getRawData()[1]))}) {
+  assert(Semantics == &semPPCDoubleDouble);
+}
+
+DoubleAPFloat::DoubleAPFloat(const fltSemantics &S, APFloat &&First,
+                             APFloat &&Second)
+    : Semantics(&S),
+      Floats(new APFloat[2]{std::move(First), std::move(Second)}) {
+  assert(Semantics == &semPPCDoubleDouble);
+  assert(&Floats[0].getSemantics() == &semIEEEdouble);
+  assert(&Floats[1].getSemantics() == &semIEEEdouble);
+}
+
+DoubleAPFloat::DoubleAPFloat(const DoubleAPFloat &RHS)
+    : Semantics(RHS.Semantics),
+      Floats(RHS.Floats ? new APFloat[2]{APFloat(RHS.Floats[0]),
+                                         APFloat(RHS.Floats[1])}
+                        : nullptr) {
+  assert(Semantics == &semPPCDoubleDouble);
+}
+
+DoubleAPFloat::DoubleAPFloat(DoubleAPFloat &&RHS)
+    : Semantics(RHS.Semantics), Floats(std::move(RHS.Floats)) {
+  RHS.Semantics = &semBogus;
+  assert(Semantics == &semPPCDoubleDouble);
+}
+
+DoubleAPFloat &DoubleAPFloat::operator=(const DoubleAPFloat &RHS) {
+  if (Semantics == RHS.Semantics && RHS.Floats) {
+    Floats[0] = RHS.Floats[0];
+    Floats[1] = RHS.Floats[1];
+  } else if (this != &RHS) {
+    this->~DoubleAPFloat();
+    new (this) DoubleAPFloat(RHS);
+  }
+  return *this;
+}
+
+// Implement addition, subtraction, multiplication and division based on:
+// "Software for Doubled-Precision Floating-Point Computations",
+// by Seppo Linnainmaa, ACM TOMS vol 7 no 3, September 1981, pages 272-283.
+APFloat::opStatus DoubleAPFloat::addImpl(const APFloat &a, const APFloat &aa,
+                                         const APFloat &c, const APFloat &cc,
+                                         roundingMode RM) {
+  int Status = opOK;
+  APFloat z = a;
+  Status |= z.add(c, RM);
+  if (!z.isFinite()) {
+    if (!z.isInfinity()) {
+      Floats[0] = std::move(z);
+      Floats[1].makeZero(/* Neg = */ false);
+      return (opStatus)Status;
+    }
+    Status = opOK;
+    auto AComparedToC = a.compareAbsoluteValue(c);
+    z = cc;
+    Status |= z.add(aa, RM);
+    if (AComparedToC == APFloat::cmpGreaterThan) {
+      // z = cc + aa + c + a;
+      Status |= z.add(c, RM);
+      Status |= z.add(a, RM);
+    } else {
+      // z = cc + aa + a + c;
+      Status |= z.add(a, RM);
+      Status |= z.add(c, RM);
+    }
+    if (!z.isFinite()) {
+      Floats[0] = std::move(z);
+      Floats[1].makeZero(/* Neg = */ false);
+      return (opStatus)Status;
+    }
+    Floats[0] = z;
+    APFloat zz = aa;
+    Status |= zz.add(cc, RM);
+    if (AComparedToC == APFloat::cmpGreaterThan) {
+      // Floats[1] = a - z + c + zz;
+      Floats[1] = a;
+      Status |= Floats[1].subtract(z, RM);
+      Status |= Floats[1].add(c, RM);
+      Status |= Floats[1].add(zz, RM);
+    } else {
+      // Floats[1] = c - z + a + zz;
+      Floats[1] = c;
+      Status |= Floats[1].subtract(z, RM);
+      Status |= Floats[1].add(a, RM);
+      Status |= Floats[1].add(zz, RM);
+    }
+  } else {
+    // q = a - z;
+    APFloat q = a;
+    Status |= q.subtract(z, RM);
+
+    // zz = q + c + (a - (q + z)) + aa + cc;
+    // Compute a - (q + z) as -((q + z) - a) to avoid temporary copies.
+    auto zz = q;
+    Status |= zz.add(c, RM);
+    Status |= q.add(z, RM);
+    Status |= q.subtract(a, RM);
+    q.changeSign();
+    Status |= zz.add(q, RM);
+    Status |= zz.add(aa, RM);
+    Status |= zz.add(cc, RM);
+    if (zz.isZero() && !zz.isNegative()) {
+      Floats[0] = std::move(z);
+      Floats[1].makeZero(/* Neg = */ false);
+      return opOK;
+    }
+    Floats[0] = z;
+    Status |= Floats[0].add(zz, RM);
+    if (!Floats[0].isFinite()) {
+      Floats[1].makeZero(/* Neg = */ false);
+      return (opStatus)Status;
+    }
+    Floats[1] = std::move(z);
+    Status |= Floats[1].subtract(Floats[0], RM);
+    Status |= Floats[1].add(zz, RM);
+  }
+  return (opStatus)Status;
+}
+
+APFloat::opStatus DoubleAPFloat::addWithSpecial(const DoubleAPFloat &LHS,
+                                                const DoubleAPFloat &RHS,
+                                                DoubleAPFloat &Out,
+                                                roundingMode RM) {
+  if (LHS.getCategory() == fcNaN) {
+    Out = LHS;
+    return opOK;
+  }
+  if (RHS.getCategory() == fcNaN) {
+    Out = RHS;
+    return opOK;
+  }
+  if (LHS.getCategory() == fcZero) {
+    Out = RHS;
+    return opOK;
+  }
+  if (RHS.getCategory() == fcZero) {
+    Out = LHS;
+    return opOK;
+  }
+  if (LHS.getCategory() == fcInfinity && RHS.getCategory() == fcInfinity &&
+      LHS.isNegative() != RHS.isNegative()) {
+    Out.makeNaN(false, Out.isNegative(), nullptr);
+    return opInvalidOp;
+  }
+  if (LHS.getCategory() == fcInfinity) {
+    Out = LHS;
+    return opOK;
+  }
+  if (RHS.getCategory() == fcInfinity) {
+    Out = RHS;
+    return opOK;
+  }
+  assert(LHS.getCategory() == fcNormal && RHS.getCategory() == fcNormal);
+
+  APFloat A(LHS.Floats[0]), AA(LHS.Floats[1]), C(RHS.Floats[0]),
+      CC(RHS.Floats[1]);
+  assert(&A.getSemantics() == &semIEEEdouble);
+  assert(&AA.getSemantics() == &semIEEEdouble);
+  assert(&C.getSemantics() == &semIEEEdouble);
+  assert(&CC.getSemantics() == &semIEEEdouble);
+  assert(&Out.Floats[0].getSemantics() == &semIEEEdouble);
+  assert(&Out.Floats[1].getSemantics() == &semIEEEdouble);
+  return Out.addImpl(A, AA, C, CC, RM);
+}
+
+APFloat::opStatus DoubleAPFloat::add(const DoubleAPFloat &RHS,
+                                     roundingMode RM) {
+  return addWithSpecial(*this, RHS, *this, RM);
+}
+
+APFloat::opStatus DoubleAPFloat::subtract(const DoubleAPFloat &RHS,
+                                          roundingMode RM) {
+  changeSign();
+  auto Ret = add(RHS, RM);
+  changeSign();
+  return Ret;
+}
+
+APFloat::opStatus DoubleAPFloat::multiply(const DoubleAPFloat &RHS,
+                                          APFloat::roundingMode RM) {
+  const auto &LHS = *this;
+  auto &Out = *this;
+  /* Interesting observation: For special categories, finding the lowest
+     common ancestor of the following layered graph gives the correct
+     return category:
+
+        NaN
+       /   \
+     Zero  Inf
+       \   /
+       Normal
+
+     e.g. NaN * NaN = NaN
+          Zero * Inf = NaN
+          Normal * Zero = Zero
+          Normal * Inf = Inf
+  */
+  if (LHS.getCategory() == fcNaN) {
+    Out = LHS;
+    return opOK;
+  }
+  if (RHS.getCategory() == fcNaN) {
+    Out = RHS;
+    return opOK;
+  }
+  if ((LHS.getCategory() == fcZero && RHS.getCategory() == fcInfinity) ||
+      (LHS.getCategory() == fcInfinity && RHS.getCategory() == fcZero)) {
+    Out.makeNaN(false, false, nullptr);
+    return opOK;
+  }
+  if (LHS.getCategory() == fcZero || LHS.getCategory() == fcInfinity) {
+    Out = LHS;
+    return opOK;
+  }
+  if (RHS.getCategory() == fcZero || RHS.getCategory() == fcInfinity) {
+    Out = RHS;
+    return opOK;
+  }
+  assert(LHS.getCategory() == fcNormal && RHS.getCategory() == fcNormal &&
+         "Special cases not handled exhaustively");
+
+  int Status = opOK;
+  APFloat A = Floats[0], B = Floats[1], C = RHS.Floats[0], D = RHS.Floats[1];
+  // t = a * c
+  APFloat T = A;
+  Status |= T.multiply(C, RM);
+  if (!T.isFiniteNonZero()) {
+    Floats[0] = T;
+    Floats[1].makeZero(/* Neg = */ false);
+    return (opStatus)Status;
+  }
+
+  // tau = fmsub(a, c, t), that is -fmadd(-a, c, t).
+  APFloat Tau = A;
+  T.changeSign();
+  Status |= Tau.fusedMultiplyAdd(C, T, RM);
+  T.changeSign();
+  {
+    // v = a * d
+    APFloat V = A;
+    Status |= V.multiply(D, RM);
+    // w = b * c
+    APFloat W = B;
+    Status |= W.multiply(C, RM);
+    Status |= V.add(W, RM);
+    // tau += v + w
+    Status |= Tau.add(V, RM);
+  }
+  // u = t + tau
+  APFloat U = T;
+  Status |= U.add(Tau, RM);
+
+  Floats[0] = U;
+  if (!U.isFinite()) {
+    Floats[1].makeZero(/* Neg = */ false);
+  } else {
+    // Floats[1] = (t - u) + tau
+    Status |= T.subtract(U, RM);
+    Status |= T.add(Tau, RM);
+    Floats[1] = T;
+  }
+  return (opStatus)Status;
+}
+
+APFloat::opStatus DoubleAPFloat::divide(const DoubleAPFloat &RHS,
+                                        APFloat::roundingMode RM) {
+  assert(Semantics == &semPPCDoubleDouble && "Unexpected Semantics");
+  APFloat Tmp(semPPCDoubleDoubleLegacy, bitcastToAPInt());
+  auto Ret =
+      Tmp.divide(APFloat(semPPCDoubleDoubleLegacy, RHS.bitcastToAPInt()), RM);
+  *this = DoubleAPFloat(semPPCDoubleDouble, Tmp.bitcastToAPInt());
+  return Ret;
+}
+
+APFloat::opStatus DoubleAPFloat::remainder(const DoubleAPFloat &RHS) {
+  assert(Semantics == &semPPCDoubleDouble && "Unexpected Semantics");
+  APFloat Tmp(semPPCDoubleDoubleLegacy, bitcastToAPInt());
+  auto Ret =
+      Tmp.remainder(APFloat(semPPCDoubleDoubleLegacy, RHS.bitcastToAPInt()));
+  *this = DoubleAPFloat(semPPCDoubleDouble, Tmp.bitcastToAPInt());
+  return Ret;
+}
+
+APFloat::opStatus DoubleAPFloat::mod(const DoubleAPFloat &RHS) {
+  assert(Semantics == &semPPCDoubleDouble && "Unexpected Semantics");
+  APFloat Tmp(semPPCDoubleDoubleLegacy, bitcastToAPInt());
+  auto Ret = Tmp.mod(APFloat(semPPCDoubleDoubleLegacy, RHS.bitcastToAPInt()));
+  *this = DoubleAPFloat(semPPCDoubleDouble, Tmp.bitcastToAPInt());
+  return Ret;
+}
+
+APFloat::opStatus
+DoubleAPFloat::fusedMultiplyAdd(const DoubleAPFloat &Multiplicand,
+                                const DoubleAPFloat &Addend,
+                                APFloat::roundingMode RM) {
+  assert(Semantics == &semPPCDoubleDouble && "Unexpected Semantics");
+  APFloat Tmp(semPPCDoubleDoubleLegacy, bitcastToAPInt());
+  auto Ret = Tmp.fusedMultiplyAdd(
+      APFloat(semPPCDoubleDoubleLegacy, Multiplicand.bitcastToAPInt()),
+      APFloat(semPPCDoubleDoubleLegacy, Addend.bitcastToAPInt()), RM);
+  *this = DoubleAPFloat(semPPCDoubleDouble, Tmp.bitcastToAPInt());
+  return Ret;
+}
+
+APFloat::opStatus DoubleAPFloat::roundToIntegral(APFloat::roundingMode RM) {
+  assert(Semantics == &semPPCDoubleDouble && "Unexpected Semantics");
+  APFloat Tmp(semPPCDoubleDoubleLegacy, bitcastToAPInt());
+  auto Ret = Tmp.roundToIntegral(RM);
+  *this = DoubleAPFloat(semPPCDoubleDouble, Tmp.bitcastToAPInt());
+  return Ret;
+}
+
+void DoubleAPFloat::changeSign() {
+  Floats[0].changeSign();
+  Floats[1].changeSign();
+}
+
+APFloat::cmpResult
+DoubleAPFloat::compareAbsoluteValue(const DoubleAPFloat &RHS) const {
+  auto Result = Floats[0].compareAbsoluteValue(RHS.Floats[0]);
+  if (Result != cmpEqual)
+    return Result;
+  Result = Floats[1].compareAbsoluteValue(RHS.Floats[1]);
+  if (Result == cmpLessThan || Result == cmpGreaterThan) {
+    auto Against = Floats[0].isNegative() ^ Floats[1].isNegative();
+    auto RHSAgainst = RHS.Floats[0].isNegative() ^ RHS.Floats[1].isNegative();
+    if (Against && !RHSAgainst)
+      return cmpLessThan;
+    if (!Against && RHSAgainst)
+      return cmpGreaterThan;
+    if (!Against && !RHSAgainst)
+      return Result;
+    if (Against && RHSAgainst)
+      return (cmpResult)(cmpLessThan + cmpGreaterThan - Result);
+  }
+  return Result;
+}
+
+APFloat::fltCategory DoubleAPFloat::getCategory() const {
+  return Floats[0].getCategory();
+}
+
+bool DoubleAPFloat::isNegative() const { return Floats[0].isNegative(); }
+
+void DoubleAPFloat::makeInf(bool Neg) {
+  Floats[0].makeInf(Neg);
+  Floats[1].makeZero(/* Neg = */ false);
+}
+
+void DoubleAPFloat::makeZero(bool Neg) {
+  Floats[0].makeZero(Neg);
+  Floats[1].makeZero(/* Neg = */ false);
+}
+
+void DoubleAPFloat::makeLargest(bool Neg) {
+  assert(Semantics == &semPPCDoubleDouble && "Unexpected Semantics");
+  Floats[0] = APFloat(semIEEEdouble, APInt(64, 0x7fefffffffffffffull));
+  Floats[1] = APFloat(semIEEEdouble, APInt(64, 0x7c8ffffffffffffeull));
+  if (Neg)
+    changeSign();
+}
+
+void DoubleAPFloat::makeSmallest(bool Neg) {
+  assert(Semantics == &semPPCDoubleDouble && "Unexpected Semantics");
+  Floats[0].makeSmallest(Neg);
+  Floats[1].makeZero(/* Neg = */ false);
+}
+
+void DoubleAPFloat::makeSmallestNormalized(bool Neg) {
+  assert(Semantics == &semPPCDoubleDouble && "Unexpected Semantics");
+  Floats[0] = APFloat(semIEEEdouble, APInt(64, 0x0360000000000000ull));
+  if (Neg)
+    Floats[0].changeSign();
+  Floats[1].makeZero(/* Neg = */ false);
+}
+
+void DoubleAPFloat::makeNaN(bool SNaN, bool Neg, const APInt *fill) {
+  Floats[0].makeNaN(SNaN, Neg, fill);
+  Floats[1].makeZero(/* Neg = */ false);
+}
+
+APFloat::cmpResult DoubleAPFloat::compare(const DoubleAPFloat &RHS) const {
+  auto Result = Floats[0].compare(RHS.Floats[0]);
+  // |Float[0]| > |Float[1]|
+  if (Result == APFloat::cmpEqual)
+    return Floats[1].compare(RHS.Floats[1]);
+  return Result;
+}
+
+bool DoubleAPFloat::bitwiseIsEqual(const DoubleAPFloat &RHS) const {
+  return Floats[0].bitwiseIsEqual(RHS.Floats[0]) &&
+         Floats[1].bitwiseIsEqual(RHS.Floats[1]);
+}
+
+hash_code hash_value(const DoubleAPFloat &Arg) {
+  if (Arg.Floats)
+    return hash_combine(hash_value(Arg.Floats[0]), hash_value(Arg.Floats[1]));
+  return hash_combine(Arg.Semantics);
+}
+
+APInt DoubleAPFloat::bitcastToAPInt() const {
+  assert(Semantics == &semPPCDoubleDouble && "Unexpected Semantics");
+  uint64_t Data[] = {
+      Floats[0].bitcastToAPInt().getRawData()[0],
+      Floats[1].bitcastToAPInt().getRawData()[0],
+  };
+  return APInt(128, 2, Data);
+}
+
+APFloat::opStatus DoubleAPFloat::convertFromString(StringRef S,
+                                                   roundingMode RM) {
+  assert(Semantics == &semPPCDoubleDouble && "Unexpected Semantics");
+  APFloat Tmp(semPPCDoubleDoubleLegacy);
+  auto Ret = Tmp.convertFromString(S, RM);
+  *this = DoubleAPFloat(semPPCDoubleDouble, Tmp.bitcastToAPInt());
+  return Ret;
+}
+
+APFloat::opStatus DoubleAPFloat::next(bool nextDown) {
+  assert(Semantics == &semPPCDoubleDouble && "Unexpected Semantics");
+  APFloat Tmp(semPPCDoubleDoubleLegacy, bitcastToAPInt());
+  auto Ret = Tmp.next(nextDown);
+  *this = DoubleAPFloat(semPPCDoubleDouble, Tmp.bitcastToAPInt());
+  return Ret;
+}
+
+APFloat::opStatus
+DoubleAPFloat::convertToInteger(MutableArrayRef<integerPart> Input,
+                                unsigned int Width, bool IsSigned,
+                                roundingMode RM, bool *IsExact) const {
+  assert(Semantics == &semPPCDoubleDouble && "Unexpected Semantics");
+  return APFloat(semPPCDoubleDoubleLegacy, bitcastToAPInt())
+      .convertToInteger(Input, Width, IsSigned, RM, IsExact);
+}
+
+APFloat::opStatus DoubleAPFloat::convertFromAPInt(const APInt &Input,
+                                                  bool IsSigned,
+                                                  roundingMode RM) {
+  assert(Semantics == &semPPCDoubleDouble && "Unexpected Semantics");
+  APFloat Tmp(semPPCDoubleDoubleLegacy);
+  auto Ret = Tmp.convertFromAPInt(Input, IsSigned, RM);
+  *this = DoubleAPFloat(semPPCDoubleDouble, Tmp.bitcastToAPInt());
+  return Ret;
+}
+
+APFloat::opStatus
+DoubleAPFloat::convertFromSignExtendedInteger(const integerPart *Input,
+                                              unsigned int InputSize,
+                                              bool IsSigned, roundingMode RM) {
+  assert(Semantics == &semPPCDoubleDouble && "Unexpected Semantics");
+  APFloat Tmp(semPPCDoubleDoubleLegacy);
+  auto Ret = Tmp.convertFromSignExtendedInteger(Input, InputSize, IsSigned, RM);
+  *this = DoubleAPFloat(semPPCDoubleDouble, Tmp.bitcastToAPInt());
+  return Ret;
+}
+
+APFloat::opStatus
+DoubleAPFloat::convertFromZeroExtendedInteger(const integerPart *Input,
+                                              unsigned int InputSize,
+                                              bool IsSigned, roundingMode RM) {
+  assert(Semantics == &semPPCDoubleDouble && "Unexpected Semantics");
+  APFloat Tmp(semPPCDoubleDoubleLegacy);
+  auto Ret = Tmp.convertFromZeroExtendedInteger(Input, InputSize, IsSigned, RM);
+  *this = DoubleAPFloat(semPPCDoubleDouble, Tmp.bitcastToAPInt());
+  return Ret;
+}
+
+unsigned int DoubleAPFloat::convertToHexString(char *DST,
+                                               unsigned int HexDigits,
+                                               bool UpperCase,
+                                               roundingMode RM) const {
+  assert(Semantics == &semPPCDoubleDouble && "Unexpected Semantics");
+  return APFloat(semPPCDoubleDoubleLegacy, bitcastToAPInt())
+      .convertToHexString(DST, HexDigits, UpperCase, RM);
+}
+
+bool DoubleAPFloat::isDenormal() const {
+  return getCategory() == fcNormal &&
+         (Floats[0].isDenormal() || Floats[1].isDenormal() ||
+          // (double)(Hi + Lo) == Hi defines a normal number.
+          Floats[0].compare(Floats[0] + Floats[1]) != cmpEqual);
+}
+
+bool DoubleAPFloat::isSmallest() const {
+  if (getCategory() != fcNormal)
+    return false;
+  DoubleAPFloat Tmp(*this);
+  Tmp.makeSmallest(this->isNegative());
+  return Tmp.compare(*this) == cmpEqual;
+}
+
+bool DoubleAPFloat::isLargest() const {
+  if (getCategory() != fcNormal)
+    return false;
+  DoubleAPFloat Tmp(*this);
+  Tmp.makeLargest(this->isNegative());
+  return Tmp.compare(*this) == cmpEqual;
+}
+
+bool DoubleAPFloat::isInteger() const {
+  assert(Semantics == &semPPCDoubleDouble && "Unexpected Semantics");
+  return Floats[0].isInteger() && Floats[1].isInteger();
+}
+
+void DoubleAPFloat::toString(SmallVectorImpl<char> &Str,
+                             unsigned FormatPrecision,
+                             unsigned FormatMaxPadding,
+                             bool TruncateZero) const {
+  assert(Semantics == &semPPCDoubleDouble && "Unexpected Semantics");
+  APFloat(semPPCDoubleDoubleLegacy, bitcastToAPInt())
+      .toString(Str, FormatPrecision, FormatMaxPadding, TruncateZero);
+}
+
+bool DoubleAPFloat::getExactInverse(APFloat *inv) const {
+  assert(Semantics == &semPPCDoubleDouble && "Unexpected Semantics");
+  APFloat Tmp(semPPCDoubleDoubleLegacy, bitcastToAPInt());
+  if (!inv)
+    return Tmp.getExactInverse(nullptr);
+  APFloat Inv(semPPCDoubleDoubleLegacy);
+  auto Ret = Tmp.getExactInverse(&Inv);
+  *inv = APFloat(semPPCDoubleDouble, Inv.bitcastToAPInt());
+  return Ret;
+}
+
+DoubleAPFloat scalbn(DoubleAPFloat Arg, int Exp, APFloat::roundingMode RM) {
+  assert(Arg.Semantics == &semPPCDoubleDouble && "Unexpected Semantics");
+  return DoubleAPFloat(semPPCDoubleDouble, scalbn(Arg.Floats[0], Exp, RM),
+                       scalbn(Arg.Floats[1], Exp, RM));
+}
+
+DoubleAPFloat frexp(const DoubleAPFloat &Arg, int &Exp,
+                    APFloat::roundingMode RM) {
+  assert(Arg.Semantics == &semPPCDoubleDouble && "Unexpected Semantics");
+  APFloat First = frexp(Arg.Floats[0], Exp, RM);
+  APFloat Second = Arg.Floats[1];
+  if (Arg.getCategory() == APFloat::fcNormal)
+    Second = scalbn(Second, -Exp, RM);
+  return DoubleAPFloat(semPPCDoubleDouble, std::move(First), std::move(Second));
+}
+
+} // End detail namespace
+
+APFloat::Storage::Storage(IEEEFloat F, const fltSemantics &Semantics) {
+  if (usesLayout<IEEEFloat>(Semantics)) {
+    new (&IEEE) IEEEFloat(std::move(F));
+    return;
+  }
+  if (usesLayout<DoubleAPFloat>(Semantics)) {
+    const fltSemantics& S = F.getSemantics();
+    new (&Double)
+        DoubleAPFloat(Semantics, APFloat(std::move(F), S),
+                      APFloat(semIEEEdouble));
+    return;
+  }
+  llvm_unreachable("Unexpected semantics");
+}
+
+APFloat::opStatus APFloat::convertFromString(StringRef Str, roundingMode RM) {
+  APFLOAT_DISPATCH_ON_SEMANTICS(convertFromString(Str, RM));
+}
+
+hash_code hash_value(const APFloat &Arg) {
+  if (APFloat::usesLayout<detail::IEEEFloat>(Arg.getSemantics()))
+    return hash_value(Arg.U.IEEE);
+  if (APFloat::usesLayout<detail::DoubleAPFloat>(Arg.getSemantics()))
+    return hash_value(Arg.U.Double);
+  llvm_unreachable("Unexpected semantics");
+}
+
+APFloat::APFloat(const fltSemantics &Semantics, StringRef S)
+    : APFloat(Semantics) {
+  convertFromString(S, rmNearestTiesToEven);
+}
+
+APFloat::opStatus APFloat::convert(const fltSemantics &ToSemantics,
+                                   roundingMode RM, bool *losesInfo) {
+  if (&getSemantics() == &ToSemantics) {
+    *losesInfo = false;
+    return opOK;
+  }
+  if (usesLayout<IEEEFloat>(getSemantics()) &&
+      usesLayout<IEEEFloat>(ToSemantics))
+    return U.IEEE.convert(ToSemantics, RM, losesInfo);
+  if (usesLayout<IEEEFloat>(getSemantics()) &&
+      usesLayout<DoubleAPFloat>(ToSemantics)) {
+    assert(&ToSemantics == &semPPCDoubleDouble);
+    auto Ret = U.IEEE.convert(semPPCDoubleDoubleLegacy, RM, losesInfo);
+    *this = APFloat(ToSemantics, U.IEEE.bitcastToAPInt());
+    return Ret;
+  }
+  if (usesLayout<DoubleAPFloat>(getSemantics()) &&
+      usesLayout<IEEEFloat>(ToSemantics)) {
+    auto Ret = getIEEE().convert(ToSemantics, RM, losesInfo);
+    *this = APFloat(std::move(getIEEE()), ToSemantics);
+    return Ret;
+  }
+  llvm_unreachable("Unexpected semantics");
+}
+
+APFloat APFloat::getAllOnesValue(unsigned BitWidth, bool isIEEE) {
+  if (isIEEE) {
+    switch (BitWidth) {
+    case 16:
+      return APFloat(semIEEEhalf, APInt::getAllOnesValue(BitWidth));
+    case 32:
+      return APFloat(semIEEEsingle, APInt::getAllOnesValue(BitWidth));
+    case 64:
+      return APFloat(semIEEEdouble, APInt::getAllOnesValue(BitWidth));
+    case 80:
+      return APFloat(semX87DoubleExtended, APInt::getAllOnesValue(BitWidth));
+    case 128:
+      return APFloat(semIEEEquad, APInt::getAllOnesValue(BitWidth));
+    default:
+      llvm_unreachable("Unknown floating bit width");
+    }
+  } else {
+    assert(BitWidth == 128);
+    return APFloat(semPPCDoubleDouble, APInt::getAllOnesValue(BitWidth));
+  }
+}
+
+void APFloat::print(raw_ostream &OS) const {
+  SmallVector<char, 16> Buffer;
+  toString(Buffer);
+  OS << Buffer << "\n";
+}
+
+#if !defined(NDEBUG) || defined(LLVM_ENABLE_DUMP)
+LLVM_DUMP_METHOD void APFloat::dump() const { print(dbgs()); }
+#endif
+
+void APFloat::Profile(FoldingSetNodeID &NID) const {
+  NID.Add(bitcastToAPInt());
+}
+
+/* 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, bitWidth, result.isSigned(),
+                                     rounding_mode, isExact);
+  // Keeps the original signed-ness.
+  result = APInt(bitWidth, parts);
+  return status;
+}
+
+} // End llvm namespace
+
+#undef APFLOAT_DISPATCH_ON_SEMANTICS