X-Git-Url: http://demsky.eecs.uci.edu/git/?a=blobdiff_plain;f=lib%2FSupport%2FAPFloat.cpp;h=8713ede6a17c4d12190b35f8c7579c6d4106b5ac;hb=55804a089e7ac26d5a07a9ac38e5dcedad3f2754;hp=128fee4f01fe8fa2ba3d463684a6e62b15619c26;hpb=88f2d6c167a575e5d9c62ecb211ff4d825b09ed3;p=oota-llvm.git

diff --git a/lib/Support/APFloat.cpp b/lib/Support/APFloat.cpp
index 128fee4f01f..8713ede6a17 100644
--- a/lib/Support/APFloat.cpp
+++ b/lib/Support/APFloat.cpp
@@ -13,13 +13,25 @@
 //===----------------------------------------------------------------------===//
 
 #include "llvm/ADT/APFloat.h"
+#include "llvm/ADT/APSInt.h"
 #include "llvm/ADT/FoldingSet.h"
+#include "llvm/ADT/Hashing.h"
+#include "llvm/ADT/StringExtras.h"
+#include "llvm/ADT/StringRef.h"
+#include "llvm/Support/ErrorHandling.h"
 #include "llvm/Support/MathExtras.h"
 #include <cstring>
+#include <limits.h>
 
 using namespace llvm;
 
-#define convolve(lhs, rhs) ((lhs) * 4 + (rhs))
+/// 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.  */
@@ -32,36 +44,42 @@ namespace llvm {
   struct fltSemantics {
     /* The largest E such that 2^E is representable; this matches the
        definition of IEEE 754.  */
-    exponent_t maxExponent;
+    APFloat::ExponentType maxExponent;
 
     /* The smallest E such that 2^E is a normalized number; this
        matches the definition of IEEE 754.  */
-    exponent_t minExponent;
+    APFloat::ExponentType minExponent;
 
     /* Number of bits in the significand.  This includes the integer
        bit.  */
     unsigned int precision;
-
-    /* True if arithmetic is supported.  */
-    unsigned int arithmeticOK;
   };
 
-  const fltSemantics APFloat::IEEEsingle = { 127, -126, 24, true };
-  const fltSemantics APFloat::IEEEdouble = { 1023, -1022, 53, true };
-  const fltSemantics APFloat::IEEEquad = { 16383, -16382, 113, true };
-  const fltSemantics APFloat::x87DoubleExtended = { 16383, -16382, 64, true };
-  const fltSemantics APFloat::Bogus = { 0, 0, 0, true };
-
-  // The PowerPC format consists of two doubles.  It does not map cleanly
-  // onto the usual format above.  For now only storage of constants of
-  // this type is supported, no arithmetic.
-  const fltSemantics APFloat::PPCDoubleDouble = { 1023, -1022, 106, false };
+  const fltSemantics APFloat::IEEEhalf = { 15, -14, 11 };
+  const fltSemantics APFloat::IEEEsingle = { 127, -126, 24 };
+  const fltSemantics APFloat::IEEEdouble = { 1023, -1022, 53 };
+  const fltSemantics APFloat::IEEEquad = { 16383, -16382, 113 };
+  const fltSemantics APFloat::x87DoubleExtended = { 16383, -16382, 64 };
+  const fltSemantics APFloat::Bogus = { 0, 0, 0 };
+
+  /* The PowerPC format consists of two doubles.  It does not map cleanly
+     onto the usual format above.  It is approximated using twice the
+     mantissa bits.  Note that for exponents near the double minimum,
+     we no longer can represent the full 106 mantissa bits, so those
+     will be treated as denormal numbers.
+
+     FIXME: While this approximation is equivalent to what GCC uses for
+     compile-time arithmetic on PPC double-double numbers, it is not able
+     to represent all possible values held by a PPC double-double number,
+     for example: (long double) 1.0 + (long double) 0x1p-106
+     Should this be replaced by a full emulation of PPC double-double?  */
+  const fltSemantics APFloat::PPCDoubleDouble = { 1023, -1022 + 53, 53 + 53 };
 
   /* 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
@@ -75,489 +93,482 @@ namespace llvm {
                                                 / (351 * integerPartWidth));
 }
 
-/* Put a bunch of private, handy routines in an anonymous namespace.  */
-namespace {
-
-  static inline unsigned int
-  partCountForBits(unsigned int bits)
-  {
-    return ((bits) + integerPartWidth - 1) / integerPartWidth;
-  }
-
-  /* Returns 0U-9U.  Return values >= 10U are not digits.  */
-  static inline unsigned int
-  decDigitValue(unsigned int c)
-  {
-    return c - '0';
-  }
-
-  static unsigned int
-  hexDigitValue(unsigned int c)
-  {
-    unsigned int r;
+/* A bunch of private, handy routines.  */
 
-    r = c - '0';
-    if(r <= 9)
-      return r;
+static inline unsigned int
+partCountForBits(unsigned int bits)
+{
+  return ((bits) + integerPartWidth - 1) / integerPartWidth;
+}
 
-    r = c - 'A';
-    if(r <= 5)
-      return r + 10;
+/* Returns 0U-9U.  Return values >= 10U are not digits.  */
+static inline unsigned int
+decDigitValue(unsigned int c)
+{
+  return c - '0';
+}
 
-    r = c - 'a';
-    if(r <= 5)
-      return r + 10;
+/* Return the value of a decimal exponent of the form
+   [+-]ddddddd.
 
-    return -1U;
-  }
+   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;
 
-  static inline void
-  assertArithmeticOK(const llvm::fltSemantics &semantics) {
-    assert(semantics.arithmeticOK
-           && "Compile-time arithmetic does not support these semantics");
-  }
+  assert(p != end && "Exponent has no digits");
 
-  static inline bool
-  isArithmeticOk(const llvm::fltSemantics &semantics) {
-    return semantics.arithmeticOK;
+  isNegative = (*p == '-');
+  if (*p == '-' || *p == '+') {
+    p++;
+    assert(p != end && "Exponent has no digits");
   }
 
-  /* 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(const char *p)
-  {
-    bool isNegative;
-    unsigned int absExponent;
-    const unsigned int overlargeExponent = 24000;  /* FIXME.  */
+  absExponent = decDigitValue(*p++);
+  assert(absExponent < 10U && "Invalid character in exponent");
 
-    isNegative = (*p == '-');
-    if (*p == '-' || *p == '+')
-      p++;
+  for (; p != end; ++p) {
+    unsigned int value;
 
-    absExponent = decDigitValue(*p++);
-    assert (absExponent < 10U);
+    value = decDigitValue(*p);
+    assert(value < 10U && "Invalid character in exponent");
 
-    for (;;) {
-      unsigned int value;
+    value += absExponent * 10;
+    if (absExponent >= overlargeExponent) {
+      absExponent = overlargeExponent;
+      p = end;  /* outwit assert below */
+      break;
+    }
+    absExponent = value;
+  }
 
-      value = decDigitValue(*p);
-      if (value >= 10U)
-        break;
+  assert(p == end && "Invalid exponent in exponent");
 
-      p++;
-      value += absExponent * 10;
-      if (absExponent >= overlargeExponent) {
-        absExponent = overlargeExponent;
-        break;
-      }
-      absExponent = value;
-    }
+  if (isNegative)
+    return -(int) absExponent;
+  else
+    return (int) absExponent;
+}
 
-    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;
 
-  /* This is ugly and needs cleaning up, but I don't immediately see
-     how whilst remaining safe.  */
-  static int
-  totalExponent(const char *p, int exponentAdjustment)
-  {
-    int unsignedExponent;
-    bool negative, overflow;
-    int exponent;
+  assert(p != end && "Exponent has no digits");
 
-    /* Move past the exponent letter and sign to the digits.  */
+  negative = *p == '-';
+  if (*p == '-' || *p == '+') {
     p++;
-    negative = *p == '-';
-    if(*p == '-' || *p == '+')
-      p++;
-
-    unsignedExponent = 0;
-    overflow = false;
-    for(;;) {
-      unsigned int value;
+    assert(p != end && "Exponent has no digits");
+  }
 
-      value = decDigitValue(*p);
-      if(value >= 10U)
-        break;
+  unsignedExponent = 0;
+  overflow = false;
+  for (; p != end; ++p) {
+    unsigned int value;
 
-      p++;
-      unsignedExponent = unsignedExponent * 10 + value;
-      if(unsignedExponent > 65535)
-        overflow = true;
-    }
+    value = decDigitValue(*p);
+    assert(value < 10U && "Invalid character in exponent");
 
-    if(exponentAdjustment > 65535 || exponentAdjustment < -65536)
+    unsignedExponent = unsignedExponent * 10 + value;
+    if (unsignedExponent > 32767) {
       overflow = true;
-
-    if(!overflow) {
-      exponent = unsignedExponent;
-      if(negative)
-        exponent = -exponent;
-      exponent += exponentAdjustment;
-      if(exponent > 65535 || exponent < -65536)
-        overflow = true;
+      break;
     }
+  }
 
-    if(overflow)
-      exponent = negative ? -65536: 65535;
+  if (exponentAdjustment > 32767 || exponentAdjustment < -32768)
+    overflow = true;
 
-    return exponent;
+  if (!overflow) {
+    exponent = unsignedExponent;
+    if (negative)
+      exponent = -exponent;
+    exponent += exponentAdjustment;
+    if (exponent > 32767 || exponent < -32768)
+      overflow = true;
   }
 
-  static const char *
-  skipLeadingZeroesAndAnyDot(const char *p, const char **dot)
-  {
-    *dot = 0;
-    while(*p == '0')
-      p++;
+  if (overflow)
+    exponent = negative ? -32768: 32767;
 
-    if(*p == '.') {
-      *dot = p++;
-      while(*p == '0')
-        p++;
-    }
+  return exponent;
+}
 
-    return p;
-  }
+static StringRef::iterator
+skipLeadingZeroesAndAnyDot(StringRef::iterator begin, StringRef::iterator end,
+                           StringRef::iterator *dot)
+{
+  StringRef::iterator p = begin;
+  *dot = end;
+  while (*p == '0' && p != end)
+    p++;
 
-  /* Given a normal decimal floating point number of the form
+  if (*p == '.') {
+    *dot = p++;
 
-       dddd.dddd[eE][+-]ddd
+    assert(end - begin != 1 && "Significand has no digits");
 
-     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.
+    while (*p == '0' && p != end)
+      p++;
+  }
 
-     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;
-  };
+  return p;
+}
 
-  static void
-  interpretDecimal(const char *p, decimalInfo *D)
-  {
-    const char *dot;
+/* Given a normal decimal floating point number of the form
 
-    p = skipLeadingZeroesAndAnyDot (p, &dot);
+     dddd.dddd[eE][+-]ddd
 
-    D->firstSigDigit = p;
-    D->exponent = 0;
-    D->normalizedExponent = 0;
+   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.
 
-    for (;;) {
-      if (*p == '.') {
-        assert(dot == 0);
-        dot = p++;
-      }
-      if (decDigitValue(*p) >= 10U)
+   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;
-      p++;
     }
+    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");
 
-    /* If number is all zerooes accept any exponent.  */
-    if (p != D->firstSigDigit) {
-      if (*p == 'e' || *p == 'E')
-        D->exponent = readExponent(p + 1);
+    /* p points to the first non-digit in the string */
+    D->exponent = readExponent(p + 1, end);
 
-      /* Implied decimal point?  */
-      if (!dot)
-        dot = p;
+    /* Implied decimal point?  */
+    if (dot == end)
+      dot = p;
+  }
 
-      /* Drop insignificant trailing zeroes.  */
+  /* If number is all zeroes accept any exponent.  */
+  if (p != D->firstSigDigit) {
+    /* Drop insignificant trailing zeroes.  */
+    if (p != begin) {
       do
         do
           p--;
-        while (*p == '0');
-      while (*p == '.');
-
-      /* Adjust the exponents for any decimal point.  */
-      D->exponent += static_cast<exponent_t>((dot - p) - (dot > p));
-      D->normalizedExponent = (D->exponent +
-                static_cast<exponent_t>((p - D->firstSigDigit)
-                                        - (dot > D->firstSigDigit && dot < p)));
+        while (p != begin && *p == '0');
+      while (p != begin && *p == '.');
     }
 
-    D->lastSigDigit = 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)));
   }
 
-  /* 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(const char *p, unsigned int digitValue)
-  {
-    unsigned int hexDigit;
+  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;
+  /* 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 == '0')
-      p++;
+  /* Otherwise we need to find the first non-zero digit.  */
+  while (*p == '0')
+    p++;
 
-    hexDigit = hexDigitValue(*p);
+  assert(p != end && "Invalid trailing hexadecimal fraction!");
 
-    /* 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;
-  }
+  hexDigit = hexDigitValue(*p);
 
-  /* Return the fraction lost were a bignum truncated losing the least
-     significant BITS bits.  */
-  static lostFraction
-  lostFractionThroughTruncation(const integerPart *parts,
-                                unsigned int partCount,
-                                unsigned int bits)
-  {
-    unsigned int lsb;
+  /* 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;
+}
 
-    lsb = APInt::tcLSB(parts, partCount);
+/* Return the fraction lost were a bignum truncated losing the least
+   significant BITS bits.  */
+static lostFraction
+lostFractionThroughTruncation(const integerPart *parts,
+                              unsigned int partCount,
+                              unsigned int bits)
+{
+  unsigned int lsb;
 
-    /* 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 * integerPartWidth
-       && APInt::tcExtractBit(parts, bits - 1))
-      return lfMoreThanHalf;
+  lsb = APInt::tcLSB(parts, partCount);
 
-    return lfLessThanHalf;
-  }
+  /* 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 * integerPartWidth &&
+      APInt::tcExtractBit(parts, bits - 1))
+    return lfMoreThanHalf;
 
-  /* Shift DST right BITS bits noting lost fraction.  */
-  static lostFraction
-  shiftRight(integerPart *dst, unsigned int parts, unsigned int bits)
-  {
-    lostFraction lost_fraction;
+  return lfLessThanHalf;
+}
 
-    lost_fraction = lostFractionThroughTruncation(dst, parts, bits);
+/* Shift DST right BITS bits noting lost fraction.  */
+static lostFraction
+shiftRight(integerPart *dst, unsigned int parts, unsigned int bits)
+{
+  lostFraction lost_fraction;
 
-    APInt::tcShiftRight(dst, parts, bits);
+  lost_fraction = lostFractionThroughTruncation(dst, parts, bits);
 
-    return lost_fraction;
-  }
+  APInt::tcShiftRight(dst, parts, bits);
 
-  /* 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 lost_fraction;
+}
 
-    return moreSignificant;
+/* 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;
   }
 
-  /* 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.
+  return moreSignificant;
+}
 
-     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));
+/* 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.
 
-    if (HUerr1 + HUerr2 == 0)
-      return inexactMultiply * 2;  /* <= inexactMultiply half-ulps.  */
-    else
-      return inexactMultiply + 2 * (HUerr1 + HUerr2);
-  }
+   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));
 
-  /* The number of ulps from the boundary (zero, or half if ISNEAREST)
-     when the least significant BITS are truncated.  BITS cannot be
-     zero.  */
-  static integerPart
-  ulpsFromBoundary(const integerPart *parts, unsigned int bits, bool isNearest)
-  {
-    unsigned int count, partBits;
-    integerPart part, boundary;
+  if (HUerr1 + HUerr2 == 0)
+    return inexactMultiply * 2;  /* <= inexactMultiply half-ulps.  */
+  else
+    return inexactMultiply + 2 * (HUerr1 + HUerr2);
+}
 
-    assert (bits != 0);
+/* The number of ulps from the boundary (zero, or half if ISNEAREST)
+   when the least significant BITS are truncated.  BITS cannot be
+   zero.  */
+static integerPart
+ulpsFromBoundary(const integerPart *parts, unsigned int bits, bool isNearest)
+{
+  unsigned int count, partBits;
+  integerPart part, boundary;
 
-    bits--;
-    count = bits / integerPartWidth;
-    partBits = bits % integerPartWidth + 1;
+  assert(bits != 0);
 
-    part = parts[count] & (~(integerPart) 0 >> (integerPartWidth - partBits));
+  bits--;
+  count = bits / integerPartWidth;
+  partBits = bits % integerPartWidth + 1;
 
-    if (isNearest)
-      boundary = (integerPart) 1 << (partBits - 1);
-    else
-      boundary = 0;
+  part = parts[count] & (~(integerPart) 0 >> (integerPartWidth - partBits));
 
-    if (count == 0) {
-      if (part - boundary <= boundary - part)
-        return part - boundary;
-      else
-        return boundary - part;
-    }
+  if (isNearest)
+    boundary = (integerPart) 1 << (partBits - 1);
+  else
+    boundary = 0;
 
-    if (part == boundary) {
-      while (--count)
-        if (parts[count])
-          return ~(integerPart) 0; /* A lot.  */
+  if (count == 0) {
+    if (part - boundary <= boundary - part)
+      return part - boundary;
+    else
+      return boundary - part;
+  }
 
-      return parts[0];
-    } else if (part == boundary - 1) {
-      while (--count)
-        if (~parts[count])
-          return ~(integerPart) 0; /* A lot.  */
+  if (part == boundary) {
+    while (--count)
+      if (parts[count])
+        return ~(integerPart) 0; /* A lot.  */
 
-      return -parts[0];
-    }
+    return parts[0];
+  } else if (part == boundary - 1) {
+    while (--count)
+      if (~parts[count])
+        return ~(integerPart) 0; /* A lot.  */
 
-    return ~(integerPart) 0; /* A lot.  */
+    return -parts[0];
   }
 
-  /* 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(integerPart *dst, unsigned int power)
-  {
-    static const integerPart firstEightPowers[] = { 1, 5, 25, 125, 625, 3125,
-                                                    15625, 78125 };
-    static integerPart pow5s[maxPowerOfFiveParts * 2 + 5] = { 78125 * 5 };
-    static unsigned int partsCount[16] = { 1 };
-
-    integerPart scratch[maxPowerOfFiveParts], *p1, *p2, *pow5;
-    unsigned int result;
+  return ~(integerPart) 0; /* A lot.  */
+}
 
-    assert(power <= maxExponent);
+/* 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(integerPart *dst, unsigned int power)
+{
+  static const integerPart firstEightPowers[] = { 1, 5, 25, 125, 625, 3125,
+                                                  15625, 78125 };
+  integerPart pow5s[maxPowerOfFiveParts * 2 + 5];
+  pow5s[0] = 78125 * 5;
 
-    p1 = dst;
-    p2 = scratch;
+  unsigned int partsCount[16] = { 1 };
+  integerPart scratch[maxPowerOfFiveParts], *p1, *p2, *pow5;
+  unsigned int result;
+  assert(power <= maxExponent);
 
-    *p1 = firstEightPowers[power & 7];
-    power >>= 3;
+  p1 = dst;
+  p2 = scratch;
 
-    result = 1;
-    pow5 = pow5s;
+  *p1 = firstEightPowers[power & 7];
+  power >>= 3;
 
-    for (unsigned int n = 0; power; power >>= 1, n++) {
-      unsigned int pc;
+  result = 1;
+  pow5 = pow5s;
 
-      pc = partsCount[n];
+  for (unsigned int n = 0; power; power >>= 1, n++) {
+    unsigned int pc;
 
-      /* 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;
-      }
+    pc = partsCount[n];
 
-      if (power & 1) {
-        integerPart *tmp;
+    /* 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;
+    }
 
-        APInt::tcFullMultiply(p2, p1, pow5, result, pc);
-        result += pc;
-        if (p2[result - 1] == 0)
-          result--;
+    if (power & 1) {
+      integerPart *tmp;
 
-        /* Now result is in p1 with partsCount parts and p2 is scratch
-           space.  */
-        tmp = p1, p1 = p2, p2 = tmp;
-      }
+      APInt::tcFullMultiply(p2, p1, pow5, result, pc);
+      result += pc;
+      if (p2[result - 1] == 0)
+        result--;
 
-      pow5 += pc;
+      /* Now result is in p1 with partsCount parts and p2 is scratch
+         space.  */
+      tmp = p1, p1 = p2, p2 = tmp;
     }
 
-    if (p1 != dst)
-      APInt::tcAssign(dst, p1, result);
-
-    return result;
+    pow5 += pc;
   }
 
-  /* 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";
+  if (p1 != dst)
+    APInt::tcAssign(dst, p1, result);
 
-  /* 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, integerPart part, unsigned int count,
-             const char *hexDigitChars)
-  {
-    unsigned int result = count;
+  return result;
+}
 
-    assert (count != 0 && count <= integerPartWidth / 4);
+/* 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";
 
-    part >>= (integerPartWidth - 4 * count);
-    while (count--) {
-      dst[count] = hexDigitChars[part & 0xf];
-      part >>= 4;
-    }
+/* 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, integerPart part, unsigned int count,
+           const char *hexDigitChars)
+{
+  unsigned int result = count;
+
+  assert(count != 0 && count <= integerPartWidth / 4);
 
-    return result;
+  part >>= (integerPartWidth - 4 * count);
+  while (count--) {
+    dst[count] = hexDigitChars[part & 0xf];
+    part >>= 4;
   }
 
-  /* Write out an unsigned decimal integer.  */
-  static char *
-  writeUnsignedDecimal (char *dst, unsigned int n)
-  {
-    char buff[40], *p;
+  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);
+  p = buff;
+  do
+    *p++ = '0' + n % 10;
+  while (n /= 10);
 
-    do
-      *dst++ = *--p;
-    while (p != buff);
+  do
+    *dst++ = *--p;
+  while (p != buff);
 
-    return dst;
-  }
+  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);
+/* 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;
-  }
+  return dst;
 }
 
 /* Constructors.  */
@@ -568,14 +579,14 @@ APFloat::initialize(const fltSemantics *ourSemantics)
 
   semantics = ourSemantics;
   count = partCount();
-  if(count > 1)
+  if (count > 1)
     significand.parts = new integerPart[count];
 }
 
 void
 APFloat::freeSignificand()
 {
-  if(partCount() > 1)
+  if (needsCleanup())
     delete [] significand.parts;
 }
 
@@ -587,16 +598,14 @@ APFloat::assign(const APFloat &rhs)
   sign = rhs.sign;
   category = rhs.category;
   exponent = rhs.exponent;
-  sign2 = rhs.sign2;
-  exponent2 = rhs.exponent2;
-  if(category == fcNormal || category == fcNaN)
+  if (isFiniteNonZero() || category == fcNaN)
     copySignificand(rhs);
 }
 
 void
 APFloat::copySignificand(const APFloat &rhs)
 {
-  assert(category == fcNormal || category == fcNaN);
+  assert(isFiniteNonZero() || category == fcNaN);
   assert(rhs.partCount() >= partCount());
 
   APInt::tcAssign(significandParts(), rhs.significandParts(),
@@ -604,19 +613,67 @@ APFloat::copySignificand(const APFloat &rhs)
 }
 
 /* Make this number a NaN, with an arbitrary but deterministic value
-   for the significand.  */
-void
-APFloat::makeNaN(void)
+   for the significand.  If double or longer, this is a signalling NaN,
+   which may not be ideal.  If float, this is QNaN(0).  */
+void APFloat::makeNaN(bool SNaN, bool Negative, const APInt *fill)
 {
   category = fcNaN;
-  APInt::tcSet(significandParts(), ~0U, partCount());
+  sign = Negative;
+
+  integerPart *significand = significandParts();
+  unsigned numParts = partCount();
+
+  // Set the significand bits to the fill.
+  if (!fill || fill->getNumWords() < numParts)
+    APInt::tcSet(significand, 0, numParts);
+  if (fill) {
+    APInt::tcAssign(significand, fill->getRawData(),
+                    std::min(fill->getNumWords(), numParts));
+
+    // Zero out the excess bits of the significand.
+    unsigned bitsToPreserve = semantics->precision - 1;
+    unsigned part = bitsToPreserve / 64;
+    bitsToPreserve %= 64;
+    significand[part] &= ((1ULL << bitsToPreserve) - 1);
+    for (part++; part != numParts; ++part)
+      significand[part] = 0;
+  }
+
+  unsigned QNaNBit = semantics->precision - 2;
+
+  if (SNaN) {
+    // We always have to clear the QNaN bit to make it an SNaN.
+    APInt::tcClearBit(significand, QNaNBit);
+
+    // If there are no bits set in the payload, we have to set
+    // *something* to make it a NaN instead of an infinity;
+    // conventionally, this is the next bit down from the QNaN bit.
+    if (APInt::tcIsZero(significand, numParts))
+      APInt::tcSetBit(significand, QNaNBit - 1);
+  } else {
+    // We always have to set the QNaN bit to make it a QNaN.
+    APInt::tcSetBit(significand, QNaNBit);
+  }
+
+  // For x87 extended precision, we want to make a NaN, not a
+  // pseudo-NaN.  Maybe we should expose the ability to make
+  // pseudo-NaNs?
+  if (semantics == &APFloat::x87DoubleExtended)
+    APInt::tcSetBit(significand, QNaNBit + 1);
+}
+
+APFloat APFloat::makeNaN(const fltSemantics &Sem, bool SNaN, bool Negative,
+                         const APInt *fill) {
+  APFloat value(Sem, uninitialized);
+  value.makeNaN(SNaN, Negative, fill);
+  return value;
 }
 
 APFloat &
 APFloat::operator=(const APFloat &rhs)
 {
-  if(this != &rhs) {
-    if(semantics != rhs.semantics) {
+  if (this != &rhs) {
+    if (semantics != rhs.semantics) {
       freeSignificand();
       initialize(rhs.semantics);
     }
@@ -626,6 +683,74 @@ APFloat::operator=(const APFloat &rhs)
   return *this;
 }
 
+bool
+APFloat::isDenormal() const {
+  return isFiniteNonZero() && (exponent == semantics->minExponent) &&
+         (APInt::tcExtractBit(significandParts(), 
+                              semantics->precision - 1) == 0);
+}
+
+bool
+APFloat::isSmallest() const {
+  // The smallest number by magnitude in our format will be the smallest
+  // denormal, i.e. the floating point number with exponent being minimum
+  // exponent and significand bitwise equal to 1 (i.e. with MSB equal to 0).
+  return isFiniteNonZero() && exponent == semantics->minExponent &&
+    significandMSB() == 0;
+}
+
+bool APFloat::isSignificandAllOnes() const {
+  // Test if the significand excluding the integral bit is all ones. This allows
+  // us to test for binade boundaries.
+  const integerPart *Parts = significandParts();
+  const unsigned PartCount = partCount();
+  for (unsigned i = 0; i < PartCount - 1; i++)
+    if (~Parts[i])
+      return false;
+
+  // Set the unused high bits to all ones when we compare.
+  const unsigned NumHighBits =
+    PartCount*integerPartWidth - semantics->precision + 1;
+  assert(NumHighBits <= integerPartWidth && "Can not have more high bits to "
+         "fill than integerPartWidth");
+  const integerPart HighBitFill =
+    ~integerPart(0) << (integerPartWidth - NumHighBits);
+  if (~(Parts[PartCount - 1] | HighBitFill))
+    return false;
+
+  return true;
+}
+
+bool APFloat::isSignificandAllZeros() const {
+  // Test if the significand excluding the integral bit is all zeros. This
+  // allows us to test for binade boundaries.
+  const integerPart *Parts = significandParts();
+  const unsigned PartCount = partCount();
+
+  for (unsigned i = 0; i < PartCount - 1; i++)
+    if (Parts[i])
+      return false;
+
+  const unsigned NumHighBits =
+    PartCount*integerPartWidth - semantics->precision + 1;
+  assert(NumHighBits <= integerPartWidth && "Can not have more high bits to "
+         "clear than integerPartWidth");
+  const integerPart HighBitMask = ~integerPart(0) >> NumHighBits;
+
+  if (Parts[PartCount - 1] & HighBitMask)
+    return false;
+
+  return true;
+}
+
+bool
+APFloat::isLargest() const {
+  // The largest number by magnitude in our format will be the floating point
+  // number with maximum exponent and with significand that is all ones.
+  return isFiniteNonZero() && exponent == semantics->maxExponent
+    && isSignificandAllOnes();
+}
+
 bool
 APFloat::bitwiseIsEqual(const APFloat &rhs) const {
   if (this == &rhs)
@@ -634,15 +759,9 @@ APFloat::bitwiseIsEqual(const APFloat &rhs) const {
       category != rhs.category ||
       sign != rhs.sign)
     return false;
-  if (semantics==(const llvm::fltSemantics*)&PPCDoubleDouble &&
-      sign2 != rhs.sign2)
-    return false;
   if (category==fcZero || category==fcInfinity)
     return true;
-  else if (category==fcNormal && exponent!=rhs.exponent)
-    return false;
-  else if (semantics==(const llvm::fltSemantics*)&PPCDoubleDouble &&
-           exponent2!=rhs.exponent2)
+  else if (isFiniteNonZero() && exponent!=rhs.exponent)
     return false;
   else {
     int i= partCount();
@@ -656,9 +775,7 @@ APFloat::bitwiseIsEqual(const APFloat &rhs) const {
   }
 }
 
-APFloat::APFloat(const fltSemantics &ourSemantics, integerPart value)
-{
-  assertArithmeticOK(ourSemantics);
+APFloat::APFloat(const fltSemantics &ourSemantics, integerPart value) {
   initialize(&ourSemantics);
   sign = 0;
   zeroSignificand();
@@ -667,28 +784,23 @@ APFloat::APFloat(const fltSemantics &ourSemantics, integerPart value)
   normalize(rmNearestTiesToEven, lfExactlyZero);
 }
 
-APFloat::APFloat(const fltSemantics &ourSemantics,
-                 fltCategory ourCategory, bool negative)
-{
-  assertArithmeticOK(ourSemantics);
+APFloat::APFloat(const fltSemantics &ourSemantics) {
   initialize(&ourSemantics);
-  category = ourCategory;
-  sign = negative;
-  if(category == fcNormal)
-    category = fcZero;
-  else if (ourCategory == fcNaN)
-    makeNaN();
+  category = fcZero;
+  sign = false;
 }
 
-APFloat::APFloat(const fltSemantics &ourSemantics, const char *text)
-{
-  assertArithmeticOK(ourSemantics);
+APFloat::APFloat(const fltSemantics &ourSemantics, uninitializedTag tag) {
+  // Allocates storage if necessary but does not initialize it.
+  initialize(&ourSemantics);
+}
+
+APFloat::APFloat(const fltSemantics &ourSemantics, StringRef text) {
   initialize(&ourSemantics);
   convertFromString(text, rmNearestTiesToEven);
 }
 
-APFloat::APFloat(const APFloat &rhs)
-{
+APFloat::APFloat(const APFloat &rhs) {
   initialize(rhs.semantics);
   assign(rhs);
 }
@@ -724,9 +836,7 @@ APFloat::significandParts() const
 integerPart *
 APFloat::significandParts()
 {
-  assert(category == fcNormal || category == fcNaN);
-
-  if(partCount() > 1)
+  if (partCount() > 1)
     return significand.parts;
   else
     return &significand.part;
@@ -749,6 +859,7 @@ APFloat::incrementSignificand()
 
   /* Our callers should never cause us to overflow.  */
   assert(carry == 0);
+  (void)carry;
 }
 
 /* Add the significand of the RHS.  Returns the carry flag.  */
@@ -800,7 +911,7 @@ APFloat::multiplySignificand(const APFloat &rhs, const APFloat *addend)
   precision = semantics->precision;
   newPartsCount = partCountForBits(precision * 2);
 
-  if(newPartsCount > 4)
+  if (newPartsCount > 4)
     fullSignificand = new integerPart[newPartsCount];
   else
     fullSignificand = scratch;
@@ -815,7 +926,21 @@ APFloat::multiplySignificand(const APFloat &rhs, const APFloat *addend)
   omsb = APInt::tcMSB(fullSignificand, newPartsCount) + 1;
   exponent += rhs.exponent;
 
-  if(addend) {
+  // Assume the operands involved in the multiplication are single-precision
+  // FP, and the two multiplicants are:
+  //   *this = a23 . a22 ... a0 * 2^e1
+  //     rhs = b23 . b22 ... b0 * 2^e2
+  // the result of multiplication is:
+  //   *this = c47 c46 . c45 ... c0 * 2^(e1+e2)
+  // Note that there are two significant bits at the left-hand side of the 
+  // radix point. Move the radix point toward left by one bit, and adjust
+  // exponent accordingly.
+  exponent += 1;
+
+  if (addend) {
+    // The intermediate result of the multiplication has "2 * precision" 
+    // signicant bit; adjust the addend to be consistent with mul result.
+    //
     Significand savedSignificand = significand;
     const fltSemantics *savedSemantics = semantics;
     fltSemantics extendedSemantics;
@@ -823,19 +948,19 @@ APFloat::multiplySignificand(const APFloat &rhs, const APFloat *addend)
     unsigned int extendedPrecision;
 
     /* Normalize our MSB.  */
-    extendedPrecision = precision + precision - 1;
-    if(omsb != extendedPrecision)
-      {
-        APInt::tcShiftLeft(fullSignificand, newPartsCount,
-                           extendedPrecision - omsb);
-        exponent -= extendedPrecision - omsb;
-      }
+    extendedPrecision = 2 * precision;
+    if (omsb != extendedPrecision) {
+      assert(extendedPrecision > omsb);
+      APInt::tcShiftLeft(fullSignificand, newPartsCount,
+                         extendedPrecision - omsb);
+      exponent -= extendedPrecision - omsb;
+    }
 
     /* Create new semantics.  */
     extendedSemantics = *semantics;
     extendedSemantics.precision = extendedPrecision;
 
-    if(newPartsCount == 1)
+    if (newPartsCount == 1)
       significand.part = fullSignificand[0];
     else
       significand.parts = fullSignificand;
@@ -844,10 +969,11 @@ APFloat::multiplySignificand(const APFloat &rhs, const APFloat *addend)
     APFloat extendedAddend(*addend);
     status = extendedAddend.convert(extendedSemantics, rmTowardZero, &ignored);
     assert(status == opOK);
+    (void)status;
     lost_fraction = addOrSubtractSignificand(extendedAddend, false);
 
     /* Restore our state.  */
-    if(newPartsCount == 1)
+    if (newPartsCount == 1)
       fullSignificand[0] = significand.part;
     significand = savedSignificand;
     semantics = savedSemantics;
@@ -855,9 +981,19 @@ APFloat::multiplySignificand(const APFloat &rhs, const APFloat *addend)
     omsb = APInt::tcMSB(fullSignificand, newPartsCount) + 1;
   }
 
-  exponent -= (precision - 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;
 
-  if(omsb > precision) {
+  // In case MSB resides at the left-hand side of radix point, shift the
+  // mantissa right by some amount to make sure the MSB reside right before
+  // the radix point (i.e. "MSB . rest-significant-bits").
+  //
+  // Note that the result is not normalized when "omsb < precision". So, the
+  // caller needs to call APFloat::normalize() if normalized value is expected.
+  if (omsb > precision) {
     unsigned int bits, significantParts;
     lostFraction lf;
 
@@ -870,7 +1006,7 @@ APFloat::multiplySignificand(const APFloat &rhs, const APFloat *addend)
 
   APInt::tcAssign(lhsSignificand, fullSignificand, partsCount);
 
-  if(newPartsCount > 4)
+  if (newPartsCount > 4)
     delete [] fullSignificand;
 
   return lost_fraction;
@@ -892,7 +1028,7 @@ APFloat::divideSignificand(const APFloat &rhs)
   rhsSignificand = rhs.significandParts();
   partsCount = partCount();
 
-  if(partsCount > 2)
+  if (partsCount > 2)
     dividend = new integerPart[partsCount * 2];
   else
     dividend = scratch;
@@ -900,7 +1036,7 @@ APFloat::divideSignificand(const APFloat &rhs)
   divisor = dividend + partsCount;
 
   /* Copy the dividend and divisor as they will be modified in-place.  */
-  for(i = 0; i < partsCount; i++) {
+  for (i = 0; i < partsCount; i++) {
     dividend[i] = lhsSignificand[i];
     divisor[i] = rhsSignificand[i];
     lhsSignificand[i] = 0;
@@ -912,14 +1048,14 @@ APFloat::divideSignificand(const APFloat &rhs)
 
   /* Normalize the divisor.  */
   bit = precision - APInt::tcMSB(divisor, partsCount) - 1;
-  if(bit) {
+  if (bit) {
     exponent += bit;
     APInt::tcShiftLeft(divisor, partsCount, bit);
   }
 
   /* Normalize the dividend.  */
   bit = precision - APInt::tcMSB(dividend, partsCount) - 1;
-  if(bit) {
+  if (bit) {
     exponent -= bit;
     APInt::tcShiftLeft(dividend, partsCount, bit);
   }
@@ -927,15 +1063,15 @@ APFloat::divideSignificand(const APFloat &rhs)
   /* 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) {
+  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) {
+  for (bit = precision; bit; bit -= 1) {
+    if (APInt::tcCompare(dividend, divisor, partsCount) >= 0) {
       APInt::tcSubtract(dividend, divisor, 0, partsCount);
       APInt::tcSetBit(lhsSignificand, bit - 1);
     }
@@ -946,16 +1082,16 @@ APFloat::divideSignificand(const APFloat &rhs)
   /* Figure out the lost fraction.  */
   int cmp = APInt::tcCompare(dividend, divisor, partsCount);
 
-  if(cmp > 0)
+  if (cmp > 0)
     lost_fraction = lfMoreThanHalf;
-  else if(cmp == 0)
+  else if (cmp == 0)
     lost_fraction = lfExactlyHalf;
-  else if(APInt::tcIsZero(dividend, partsCount))
+  else if (APInt::tcIsZero(dividend, partsCount))
     lost_fraction = lfExactlyZero;
   else
     lost_fraction = lfLessThanHalf;
 
-  if(partsCount > 2)
+  if (partsCount > 2)
     delete [] dividend;
 
   return lost_fraction;
@@ -978,7 +1114,7 @@ lostFraction
 APFloat::shiftSignificandRight(unsigned int bits)
 {
   /* Our exponent should not overflow.  */
-  assert((exponent_t) (exponent + bits) >= exponent);
+  assert((ExponentType) (exponent + bits) >= exponent);
 
   exponent += bits;
 
@@ -991,7 +1127,7 @@ APFloat::shiftSignificandLeft(unsigned int bits)
 {
   assert(bits < semantics->precision);
 
-  if(bits) {
+  if (bits) {
     unsigned int partsCount = partCount();
 
     APInt::tcShiftLeft(significandParts(), partsCount, bits);
@@ -1007,20 +1143,20 @@ APFloat::compareAbsoluteValue(const APFloat &rhs) const
   int compare;
 
   assert(semantics == rhs.semantics);
-  assert(category == fcNormal);
-  assert(rhs.category == fcNormal);
+  assert(isFiniteNonZero());
+  assert(rhs.isFiniteNonZero());
 
   compare = exponent - rhs.exponent;
 
   /* If exponents are equal, do an unsigned bignum comparison of the
      significands.  */
-  if(compare == 0)
+  if (compare == 0)
     compare = APInt::tcCompare(significandParts(), rhs.significandParts(),
                                partCount());
 
-  if(compare > 0)
+  if (compare > 0)
     return cmpGreaterThan;
-  else if(compare < 0)
+  else if (compare < 0)
     return cmpLessThan;
   else
     return cmpEqual;
@@ -1032,14 +1168,13 @@ APFloat::opStatus
 APFloat::handleOverflow(roundingMode rounding_mode)
 {
   /* Infinity?  */
-  if(rounding_mode == rmNearestTiesToEven
-     || rounding_mode == rmNearestTiesToAway
-     || (rounding_mode == rmTowardPositive && !sign)
-     || (rounding_mode == rmTowardNegative && sign))
-    {
-      category = fcInfinity;
-      return (opStatus) (opOverflow | opInexact);
-    }
+  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;
@@ -1061,24 +1196,21 @@ APFloat::roundAwayFromZero(roundingMode rounding_mode,
                            unsigned int bit) const
 {
   /* NaNs and infinities should not have lost fractions.  */
-  assert(category == fcNormal || category == fcZero);
+  assert(isFiniteNonZero() || category == fcZero);
 
   /* Current callers never pass this so we don't handle it.  */
   assert(lost_fraction != lfExactlyZero);
 
-  switch(rounding_mode) {
-  default:
-    assert(0);
-
+  switch (rounding_mode) {
   case rmNearestTiesToAway:
     return lost_fraction == lfExactlyHalf || lost_fraction == lfMoreThanHalf;
 
   case rmNearestTiesToEven:
-    if(lost_fraction == lfMoreThanHalf)
+    if (lost_fraction == lfMoreThanHalf)
       return true;
 
     /* Our zeroes don't have a significand to test.  */
-    if(lost_fraction == lfExactlyHalf && category != fcZero)
+    if (lost_fraction == lfExactlyHalf && category != fcZero)
       return APInt::tcExtractBit(significandParts(), bit);
 
     return false;
@@ -1092,6 +1224,7 @@ APFloat::roundAwayFromZero(roundingMode rounding_mode,
   case rmTowardNegative:
     return sign == true;
   }
+  llvm_unreachable("Invalid rounding mode found");
 }
 
 APFloat::opStatus
@@ -1101,30 +1234,30 @@ APFloat::normalize(roundingMode rounding_mode,
   unsigned int omsb;                /* One, not zero, based MSB.  */
   int exponentChange;
 
-  if(category != fcNormal)
+  if (!isFiniteNonZero())
     return opOK;
 
   /* Before rounding normalize the exponent of fcNormal numbers.  */
   omsb = significandMSB() + 1;
 
-  if(omsb) {
+  if (omsb) {
     /* OMSB is numbered from 1.  We want to place it in the integer
-       bit numbered PRECISON if possible, with a compensating change in
+       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)
+    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)
+    if (exponent + exponentChange < semantics->minExponent)
       exponentChange = semantics->minExponent - exponent;
 
     /* Shifting left is easy as we don't lose precision.  */
-    if(exponentChange < 0) {
+    if (exponentChange < 0) {
       assert(lost_fraction == lfExactlyZero);
 
       shiftSignificandLeft(-exponentChange);
@@ -1132,7 +1265,7 @@ APFloat::normalize(roundingMode rounding_mode,
       return opOK;
     }
 
-    if(exponentChange > 0) {
+    if (exponentChange > 0) {
       lostFraction lf;
 
       /* Shift right and capture any new lost fraction.  */
@@ -1141,7 +1274,7 @@ APFloat::normalize(roundingMode rounding_mode,
       lost_fraction = combineLostFractions(lf, lost_fraction);
 
       /* Keep OMSB up-to-date.  */
-      if(omsb > (unsigned) exponentChange)
+      if (omsb > (unsigned) exponentChange)
         omsb -= exponentChange;
       else
         omsb = 0;
@@ -1153,28 +1286,28 @@ APFloat::normalize(roundingMode rounding_mode,
 
   /* As specified in IEEE 754, since we do not trap we do not report
      underflow for exact results.  */
-  if(lost_fraction == lfExactlyZero) {
+  if (lost_fraction == lfExactlyZero) {
     /* Canonicalize zeroes.  */
-    if(omsb == 0)
+    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)
+  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) {
+    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) {
+      if (exponent == semantics->maxExponent) {
         category = fcInfinity;
 
         return (opStatus) (opOverflow | opInexact);
@@ -1188,14 +1321,14 @@ APFloat::normalize(roundingMode rounding_mode,
 
   /* The normal case - we were and are not denormal, and any
      significand increment above didn't overflow.  */
-  if(omsb == semantics->precision)
+  if (omsb == semantics->precision)
     return opInexact;
 
   /* We have a non-zero denormal.  */
   assert(omsb < semantics->precision);
 
   /* Canonicalize zeroes.  */
-  if(omsb == 0)
+  if (omsb == 0)
     category = fcZero;
 
   /* The fcZero case is a denormal that underflowed to zero.  */
@@ -1205,52 +1338,52 @@ APFloat::normalize(roundingMode rounding_mode,
 APFloat::opStatus
 APFloat::addOrSubtractSpecials(const APFloat &rhs, bool subtract)
 {
-  switch(convolve(category, rhs.category)) {
+  switch (PackCategoriesIntoKey(category, rhs.category)) {
   default:
-    assert(0);
-
-  case convolve(fcNaN, fcZero):
-  case convolve(fcNaN, fcNormal):
-  case convolve(fcNaN, fcInfinity):
-  case convolve(fcNaN, fcNaN):
-  case convolve(fcNormal, fcZero):
-  case convolve(fcInfinity, fcNormal):
-  case convolve(fcInfinity, fcZero):
+    llvm_unreachable(0);
+
+  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 convolve(fcZero, fcNaN):
-  case convolve(fcNormal, fcNaN):
-  case convolve(fcInfinity, fcNaN):
+  case PackCategoriesIntoKey(fcZero, fcNaN):
+  case PackCategoriesIntoKey(fcNormal, fcNaN):
+  case PackCategoriesIntoKey(fcInfinity, fcNaN):
     category = fcNaN;
     copySignificand(rhs);
     return opOK;
 
-  case convolve(fcNormal, fcInfinity):
-  case convolve(fcZero, fcInfinity):
+  case PackCategoriesIntoKey(fcNormal, fcInfinity):
+  case PackCategoriesIntoKey(fcZero, fcInfinity):
     category = fcInfinity;
     sign = rhs.sign ^ subtract;
     return opOK;
 
-  case convolve(fcZero, fcNormal):
+  case PackCategoriesIntoKey(fcZero, fcNormal):
     assign(rhs);
     sign = rhs.sign ^ subtract;
     return opOK;
 
-  case convolve(fcZero, fcZero):
+  case PackCategoriesIntoKey(fcZero, fcZero):
     /* Sign depends on rounding mode; handled by caller.  */
     return opOK;
 
-  case convolve(fcInfinity, fcInfinity):
+  case PackCategoriesIntoKey(fcInfinity, fcInfinity):
     /* Differently signed infinities can only be validly
        subtracted.  */
-    if((sign ^ rhs.sign) != subtract) {
+    if (((sign ^ rhs.sign)!=0) != subtract) {
       makeNaN();
       return opInvalidOp;
     }
 
     return opOK;
 
-  case convolve(fcNormal, fcNormal):
+  case PackCategoriesIntoKey(fcNormal, fcNormal):
     return opDivByZero;
   }
 }
@@ -1271,7 +1404,7 @@ APFloat::addOrSubtractSignificand(const APFloat &rhs, bool subtract)
   bits = exponent - rhs.exponent;
 
   /* Subtraction is more subtle than one might naively expect.  */
-  if(subtract) {
+  if (subtract) {
     APFloat temp_rhs(rhs);
     bool reverse;
 
@@ -1300,16 +1433,17 @@ APFloat::addOrSubtractSignificand(const APFloat &rhs, bool subtract)
 
     /* Invert the lost fraction - it was on the RHS and
        subtracted.  */
-    if(lost_fraction == lfLessThanHalf)
+    if (lost_fraction == lfLessThanHalf)
       lost_fraction = lfMoreThanHalf;
-    else if(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) {
+    if (bits > 0) {
       APFloat temp_rhs(rhs);
 
       lost_fraction = temp_rhs.shiftSignificandRight(bits);
@@ -1321,6 +1455,7 @@ APFloat::addOrSubtractSignificand(const APFloat &rhs, bool subtract)
 
     /* We have a guard bit; generating a carry cannot happen.  */
     assert(!carry);
+    (void)carry;
   }
 
   return lost_fraction;
@@ -1329,41 +1464,41 @@ APFloat::addOrSubtractSignificand(const APFloat &rhs, bool subtract)
 APFloat::opStatus
 APFloat::multiplySpecials(const APFloat &rhs)
 {
-  switch(convolve(category, rhs.category)) {
+  switch (PackCategoriesIntoKey(category, rhs.category)) {
   default:
-    assert(0);
+    llvm_unreachable(0);
 
-  case convolve(fcNaN, fcZero):
-  case convolve(fcNaN, fcNormal):
-  case convolve(fcNaN, fcInfinity):
-  case convolve(fcNaN, fcNaN):
+  case PackCategoriesIntoKey(fcNaN, fcZero):
+  case PackCategoriesIntoKey(fcNaN, fcNormal):
+  case PackCategoriesIntoKey(fcNaN, fcInfinity):
+  case PackCategoriesIntoKey(fcNaN, fcNaN):
     return opOK;
 
-  case convolve(fcZero, fcNaN):
-  case convolve(fcNormal, fcNaN):
-  case convolve(fcInfinity, fcNaN):
+  case PackCategoriesIntoKey(fcZero, fcNaN):
+  case PackCategoriesIntoKey(fcNormal, fcNaN):
+  case PackCategoriesIntoKey(fcInfinity, fcNaN):
     category = fcNaN;
     copySignificand(rhs);
     return opOK;
 
-  case convolve(fcNormal, fcInfinity):
-  case convolve(fcInfinity, fcNormal):
-  case convolve(fcInfinity, fcInfinity):
+  case PackCategoriesIntoKey(fcNormal, fcInfinity):
+  case PackCategoriesIntoKey(fcInfinity, fcNormal):
+  case PackCategoriesIntoKey(fcInfinity, fcInfinity):
     category = fcInfinity;
     return opOK;
 
-  case convolve(fcZero, fcNormal):
-  case convolve(fcNormal, fcZero):
-  case convolve(fcZero, fcZero):
+  case PackCategoriesIntoKey(fcZero, fcNormal):
+  case PackCategoriesIntoKey(fcNormal, fcZero):
+  case PackCategoriesIntoKey(fcZero, fcZero):
     category = fcZero;
     return opOK;
 
-  case convolve(fcZero, fcInfinity):
-  case convolve(fcInfinity, fcZero):
+  case PackCategoriesIntoKey(fcZero, fcInfinity):
+  case PackCategoriesIntoKey(fcInfinity, fcZero):
     makeNaN();
     return opInvalidOp;
 
-  case convolve(fcNormal, fcNormal):
+  case PackCategoriesIntoKey(fcNormal, fcNormal):
     return opOK;
   }
 }
@@ -1371,41 +1506,77 @@ APFloat::multiplySpecials(const APFloat &rhs)
 APFloat::opStatus
 APFloat::divideSpecials(const APFloat &rhs)
 {
-  switch(convolve(category, rhs.category)) {
+  switch (PackCategoriesIntoKey(category, rhs.category)) {
   default:
-    assert(0);
-
-  case convolve(fcNaN, fcZero):
-  case convolve(fcNaN, fcNormal):
-  case convolve(fcNaN, fcInfinity):
-  case convolve(fcNaN, fcNaN):
-  case convolve(fcInfinity, fcZero):
-  case convolve(fcInfinity, fcNormal):
-  case convolve(fcZero, fcInfinity):
-  case convolve(fcZero, fcNormal):
+    llvm_unreachable(0);
+
+  case PackCategoriesIntoKey(fcNaN, fcZero):
+  case PackCategoriesIntoKey(fcNaN, fcNormal):
+  case PackCategoriesIntoKey(fcNaN, fcInfinity):
+  case PackCategoriesIntoKey(fcNaN, fcNaN):
+  case PackCategoriesIntoKey(fcInfinity, fcZero):
+  case PackCategoriesIntoKey(fcInfinity, fcNormal):
+  case PackCategoriesIntoKey(fcZero, fcInfinity):
+  case PackCategoriesIntoKey(fcZero, fcNormal):
     return opOK;
 
-  case convolve(fcZero, fcNaN):
-  case convolve(fcNormal, fcNaN):
-  case convolve(fcInfinity, fcNaN):
+  case PackCategoriesIntoKey(fcZero, fcNaN):
+  case PackCategoriesIntoKey(fcNormal, fcNaN):
+  case PackCategoriesIntoKey(fcInfinity, fcNaN):
     category = fcNaN;
     copySignificand(rhs);
     return opOK;
 
-  case convolve(fcNormal, fcInfinity):
+  case PackCategoriesIntoKey(fcNormal, fcInfinity):
     category = fcZero;
     return opOK;
 
-  case convolve(fcNormal, fcZero):
+  case PackCategoriesIntoKey(fcNormal, fcZero):
     category = fcInfinity;
     return opDivByZero;
 
-  case convolve(fcInfinity, fcInfinity):
-  case convolve(fcZero, fcZero):
+  case PackCategoriesIntoKey(fcInfinity, fcInfinity):
+  case PackCategoriesIntoKey(fcZero, fcZero):
+    makeNaN();
+    return opInvalidOp;
+
+  case PackCategoriesIntoKey(fcNormal, fcNormal):
+    return opOK;
+  }
+}
+
+APFloat::opStatus
+APFloat::modSpecials(const APFloat &rhs)
+{
+  switch (PackCategoriesIntoKey(category, rhs.category)) {
+  default:
+    llvm_unreachable(0);
+
+  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):
+    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 convolve(fcNormal, fcNormal):
+  case PackCategoriesIntoKey(fcNormal, fcNormal):
     return opOK;
   }
 }
@@ -1439,12 +1610,10 @@ APFloat::addOrSubtract(const APFloat &rhs, roundingMode rounding_mode,
 {
   opStatus fs;
 
-  assertArithmeticOK(*semantics);
-
   fs = addOrSubtractSpecials(rhs, subtract);
 
   /* This return code means it was not a simple case.  */
-  if(fs == opDivByZero) {
+  if (fs == opDivByZero) {
     lostFraction lost_fraction;
 
     lost_fraction = addOrSubtractSignificand(rhs, subtract);
@@ -1457,8 +1626,8 @@ APFloat::addOrSubtract(const APFloat &rhs, roundingMode rounding_mode,
   /* 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)
+  if (category == fcZero) {
+    if (rhs.category != fcZero || (sign == rhs.sign) == subtract)
       sign = (rounding_mode == rmTowardNegative);
   }
 
@@ -1485,14 +1654,13 @@ APFloat::multiply(const APFloat &rhs, roundingMode rounding_mode)
 {
   opStatus fs;
 
-  assertArithmeticOK(*semantics);
   sign ^= rhs.sign;
   fs = multiplySpecials(rhs);
 
-  if(category == fcNormal) {
+  if (isFiniteNonZero()) {
     lostFraction lost_fraction = multiplySignificand(rhs, 0);
     fs = normalize(rounding_mode, lost_fraction);
-    if(lost_fraction != lfExactlyZero)
+    if (lost_fraction != lfExactlyZero)
       fs = (opStatus) (fs | opInexact);
   }
 
@@ -1505,29 +1673,27 @@ APFloat::divide(const APFloat &rhs, roundingMode rounding_mode)
 {
   opStatus fs;
 
-  assertArithmeticOK(*semantics);
   sign ^= rhs.sign;
   fs = divideSpecials(rhs);
 
-  if(category == fcNormal) {
+  if (isFiniteNonZero()) {
     lostFraction lost_fraction = divideSignificand(rhs);
     fs = normalize(rounding_mode, lost_fraction);
-    if(lost_fraction != lfExactlyZero)
+    if (lost_fraction != lfExactlyZero)
       fs = (opStatus) (fs | opInexact);
   }
 
   return fs;
 }
 
-/* Normalized remainder.  This is not currently doing TRT.  */
+/* Normalized remainder.  This is not currently correct in all cases.  */
 APFloat::opStatus
-APFloat::mod(const APFloat &rhs, roundingMode rounding_mode)
+APFloat::remainder(const APFloat &rhs)
 {
   opStatus fs;
   APFloat V = *this;
   unsigned int origSign = sign;
 
-  assertArithmeticOK(*semantics);
   fs = V.divide(rhs, rmNearestTiesToEven);
   if (fs == opDivByZero)
     return fs;
@@ -1544,10 +1710,10 @@ APFloat::mod(const APFloat &rhs, roundingMode rounding_mode)
                                         rmNearestTiesToEven);
   assert(fs==opOK);   // should always work
 
-  fs = V.multiply(rhs, rounding_mode);
+  fs = V.multiply(rhs, rmNearestTiesToEven);
   assert(fs==opOK || fs==opInexact);   // should not overflow or underflow
 
-  fs = subtract(V, rounding_mode);
+  fs = subtract(V, rmNearestTiesToEven);
   assert(fs==opOK || fs==opInexact);   // likewise
 
   if (isZero())
@@ -1556,6 +1722,47 @@ APFloat::mod(const APFloat &rhs, roundingMode rounding_mode)
   return fs;
 }
 
+/* Normalized llvm frem (C fmod).
+   This is not currently correct in all cases.  */
+APFloat::opStatus
+APFloat::mod(const APFloat &rhs, roundingMode rounding_mode)
+{
+  opStatus fs;
+  fs = modSpecials(rhs);
+
+  if (isFiniteNonZero() && rhs.isFiniteNonZero()) {
+    APFloat V = *this;
+    unsigned int origSign = sign;
+
+    fs = V.divide(rhs, rmNearestTiesToEven);
+    if (fs == opDivByZero)
+      return fs;
+
+    int parts = partCount();
+    integerPart *x = new integerPart[parts];
+    bool ignored;
+    fs = V.convertToInteger(x, parts * integerPartWidth, true,
+                            rmTowardZero, &ignored);
+    if (fs==opInvalidOp)
+      return fs;
+
+    fs = V.convertFromZeroExtendedInteger(x, parts * integerPartWidth, true,
+                                          rmNearestTiesToEven);
+    assert(fs==opOK);   // should always work
+
+    fs = V.multiply(rhs, rounding_mode);
+    assert(fs==opOK || fs==opInexact);   // should not overflow or underflow
+
+    fs = subtract(V, rounding_mode);
+    assert(fs==opOK || fs==opInexact);   // likewise
+
+    if (isZero())
+      sign = origSign;    // IEEE754 requires this
+    delete[] x;
+  }
+  return fs;
+}
+
 /* Normalized fused-multiply-add.  */
 APFloat::opStatus
 APFloat::fusedMultiplyAdd(const APFloat &multiplicand,
@@ -1564,27 +1771,25 @@ APFloat::fusedMultiplyAdd(const APFloat &multiplicand,
 {
   opStatus fs;
 
-  assertArithmeticOK(*semantics);
-
   /* 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(category == fcNormal
-     && multiplicand.category == fcNormal
-     && addend.category == fcNormal) {
+  if (isFiniteNonZero() &&
+      multiplicand.isFiniteNonZero() &&
+      addend.isFiniteNonZero()) {
     lostFraction lost_fraction;
 
     lost_fraction = multiplySignificand(multiplicand, &addend);
     fs = normalize(rounding_mode, lost_fraction);
-    if(lost_fraction != lfExactlyZero)
+    if (lost_fraction != lfExactlyZero)
       fs = (opStatus) (fs | opInexact);
 
     /* If two numbers add (exactly) to zero, IEEE 754 decrees it is a
        positive zero unless rounding to minus infinity, except that
        adding two like-signed zeroes gives that zero.  */
-    if(category == fcZero && sign != addend.sign)
+    if (category == fcZero && sign != addend.sign)
       sign = (rounding_mode == rmTowardNegative);
   } else {
     fs = multiplySpecials(multiplicand);
@@ -1596,69 +1801,111 @@ APFloat::fusedMultiplyAdd(const APFloat &multiplicand,
 
        If we need to do the addition we can do so with normal
        precision.  */
-    if(fs == opOK)
+    if (fs == opOK)
       fs = addOrSubtract(addend, rounding_mode, false);
   }
 
   return fs;
 }
 
+/* Rounding-mode corrrect round to integral value.  */
+APFloat::opStatus APFloat::roundToIntegral(roundingMode rounding_mode) {
+  opStatus fs;
+
+  // If the exponent is large enough, we know that this value is already
+  // integral, and the arithmetic below would potentially cause it to saturate
+  // to +/-Inf.  Bail out early instead.
+  if (isFiniteNonZero() && exponent+1 >= (int)semanticsPrecision(*semantics))
+    return opOK;
+
+  // The algorithm here is quite simple: we add 2^(p-1), where p is the
+  // precision of our format, and then subtract it back off again.  The choice
+  // of rounding modes for the addition/subtraction determines the rounding mode
+  // for our integral rounding as well.
+  // NOTE: When the input value is negative, we do subtraction followed by
+  // addition instead.
+  APInt IntegerConstant(NextPowerOf2(semanticsPrecision(*semantics)), 1);
+  IntegerConstant <<= semanticsPrecision(*semantics)-1;
+  APFloat MagicConstant(*semantics);
+  fs = MagicConstant.convertFromAPInt(IntegerConstant, false,
+                                      rmNearestTiesToEven);
+  MagicConstant.copySign(*this);
+
+  if (fs != opOK)
+    return fs;
+
+  // Preserve the input sign so that we can handle 0.0/-0.0 cases correctly.
+  bool inputSign = isNegative();
+
+  fs = add(MagicConstant, rounding_mode);
+  if (fs != opOK && fs != opInexact)
+    return fs;
+
+  fs = subtract(MagicConstant, rounding_mode);
+
+  // Restore the input sign.
+  if (inputSign != isNegative())
+    changeSign();
+
+  return fs;
+}
+
+
 /* Comparison requires normalized numbers.  */
 APFloat::cmpResult
 APFloat::compare(const APFloat &rhs) const
 {
   cmpResult result;
 
-  assertArithmeticOK(*semantics);
   assert(semantics == rhs.semantics);
 
-  switch(convolve(category, rhs.category)) {
+  switch (PackCategoriesIntoKey(category, rhs.category)) {
   default:
-    assert(0);
-
-  case convolve(fcNaN, fcZero):
-  case convolve(fcNaN, fcNormal):
-  case convolve(fcNaN, fcInfinity):
-  case convolve(fcNaN, fcNaN):
-  case convolve(fcZero, fcNaN):
-  case convolve(fcNormal, fcNaN):
-  case convolve(fcInfinity, fcNaN):
+    llvm_unreachable(0);
+
+  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 convolve(fcInfinity, fcNormal):
-  case convolve(fcInfinity, fcZero):
-  case convolve(fcNormal, fcZero):
-    if(sign)
+  case PackCategoriesIntoKey(fcInfinity, fcNormal):
+  case PackCategoriesIntoKey(fcInfinity, fcZero):
+  case PackCategoriesIntoKey(fcNormal, fcZero):
+    if (sign)
       return cmpLessThan;
     else
       return cmpGreaterThan;
 
-  case convolve(fcNormal, fcInfinity):
-  case convolve(fcZero, fcInfinity):
-  case convolve(fcZero, fcNormal):
-    if(rhs.sign)
+  case PackCategoriesIntoKey(fcNormal, fcInfinity):
+  case PackCategoriesIntoKey(fcZero, fcInfinity):
+  case PackCategoriesIntoKey(fcZero, fcNormal):
+    if (rhs.sign)
       return cmpGreaterThan;
     else
       return cmpLessThan;
 
-  case convolve(fcInfinity, fcInfinity):
-    if(sign == rhs.sign)
+  case PackCategoriesIntoKey(fcInfinity, fcInfinity):
+    if (sign == rhs.sign)
       return cmpEqual;
-    else if(sign)
+    else if (sign)
       return cmpLessThan;
     else
       return cmpGreaterThan;
 
-  case convolve(fcZero, fcZero):
+  case PackCategoriesIntoKey(fcZero, fcZero):
     return cmpEqual;
 
-  case convolve(fcNormal, fcNormal):
+  case PackCategoriesIntoKey(fcNormal, fcNormal):
     break;
   }
 
   /* Two normal numbers.  Do they have the same sign?  */
-  if(sign != rhs.sign) {
-    if(sign)
+  if (sign != rhs.sign) {
+    if (sign)
       result = cmpLessThan;
     else
       result = cmpGreaterThan;
@@ -1666,10 +1913,10 @@ APFloat::compare(const APFloat &rhs) const
     /* Compare absolute values; invert result if negative.  */
     result = compareAbsoluteValue(rhs);
 
-    if(sign) {
-      if(result == cmpLessThan)
+    if (sign) {
+      if (result == cmpLessThan)
         result = cmpGreaterThan;
-      else if(result == cmpGreaterThan)
+      else if (result == cmpGreaterThan)
         result = cmpLessThan;
     }
   }
@@ -1691,82 +1938,74 @@ APFloat::convert(const fltSemantics &toSemantics,
   lostFraction lostFraction;
   unsigned int newPartCount, oldPartCount;
   opStatus fs;
+  int shift;
+  const fltSemantics &fromSemantics = *semantics;
 
-  assertArithmeticOK(*semantics);
-  assertArithmeticOK(toSemantics);
   lostFraction = lfExactlyZero;
   newPartCount = partCountForBits(toSemantics.precision + 1);
   oldPartCount = partCount();
+  shift = toSemantics.precision - fromSemantics.precision;
 
-  /* Handle storage complications.  If our new form is wider,
-     re-allocate our bit pattern into wider storage.  If it is
-     narrower, we ignore the excess parts, but if narrowing to a
-     single part we need to free the old storage.
-     Be careful not to reference significandParts for zeroes
-     and infinities, since it aborts.  */
+  bool X86SpecialNan = false;
+  if (&fromSemantics == &APFloat::x87DoubleExtended &&
+      &toSemantics != &APFloat::x87DoubleExtended && category == fcNaN &&
+      (!(*significandParts() & 0x8000000000000000ULL) ||
+       !(*significandParts() & 0x4000000000000000ULL))) {
+    // x86 has some unusual NaNs which cannot be represented in any other
+    // format; note them here.
+    X86SpecialNan = true;
+  }
+
+  // If this is a truncation, 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 (category==fcNormal || category==fcNaN)
+    if (isFiniteNonZero() || category==fcNaN)
       APInt::tcAssign(newParts, significandParts(), oldPartCount);
     freeSignificand();
     significand.parts = newParts;
-  } else if (newPartCount < oldPartCount) {
-    /* Capture any lost fraction through truncation of parts so we get
-       correct rounding whilst normalizing.  */
-    if (category==fcNormal)
-      lostFraction = lostFractionThroughTruncation
-        (significandParts(), oldPartCount, toSemantics.precision);
-    if (newPartCount == 1) {
-        integerPart newPart = 0;
-        if (category==fcNormal || category==fcNaN)
-          newPart = significandParts()[0];
-        freeSignificand();
-        significand.part = newPart;
-    }
+  } 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;
   }
 
-  if(category == fcNormal) {
-    /* Re-interpret our bit-pattern.  */
-    exponent += toSemantics.precision - semantics->precision;
-    semantics = &toSemantics;
+  // 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) {
-    int shift = toSemantics.precision - semantics->precision;
-    // Do this now so significandParts gets the right answer
-    const fltSemantics *oldSemantics = semantics;
-    semantics = &toSemantics;
-    *losesInfo = false;
-    // No normalization here, just truncate
-    if (shift>0)
-      APInt::tcShiftLeft(significandParts(), newPartCount, shift);
-    else if (shift < 0) {
-      unsigned ushift = -shift;
-      // Figure out if we are losing information.  This happens
-      // if are shifting out something other than 0s, or if the x87 long
-      // double input did not have its integer bit set (pseudo-NaN), or if the
-      // x87 long double input did not have its QNan bit set (because the x87
-      // hardware sets this bit when converting a lower-precision NaN to
-      // x87 long double).
-      if (APInt::tcLSB(significandParts(), newPartCount) < ushift)
-        *losesInfo = true;
-      if (oldSemantics == &APFloat::x87DoubleExtended && 
-          (!(*significandParts() & 0x8000000000000000ULL) ||
-           !(*significandParts() & 0x4000000000000000ULL)))
-        *losesInfo = true;
-      APInt::tcShiftRight(significandParts(), newPartCount, ushift);
-    }
+    *losesInfo = lostFraction != lfExactlyZero || X86SpecialNan;
+
+    // For x87 extended precision, we want to make a NaN, not a special NaN if
+    // the input wasn't special either.
+    if (!X86SpecialNan && semantics == &APFloat::x87DoubleExtended)
+      APInt::tcSetBit(significandParts(), semantics->precision - 1);
+
     // gcc forces the Quiet bit on, which means (float)(double)(float_sNan)
     // does not give you back the same bits.  This is dubious, and we
     // don't currently do it.  You're really supposed to get
     // an invalid operation signal at runtime, but nobody does that.
     fs = opOK;
   } else {
-    semantics = &toSemantics;
-    fs = opOK;
     *losesInfo = false;
+    fs = opOK;
   }
 
   return fs;
@@ -1792,18 +2031,15 @@ APFloat::convertToSignExtendedInteger(integerPart *parts, unsigned int width,
   const integerPart *src;
   unsigned int dstPartsCount, truncatedBits;
 
-  if (!isArithmeticOk(*semantics))
-    return opInvalidOp;
-
   *isExact = false;
 
   /* Handle the three special cases first.  */
-  if(category == fcInfinity || category == fcNaN)
+  if (category == fcInfinity || category == fcNaN)
     return opInvalidOp;
 
   dstPartsCount = partCountForBits(width);
 
-  if(category == fcZero) {
+  if (category == fcZero) {
     APInt::tcSet(parts, 0, dstPartsCount);
     // Negative zero can't be represented as an int.
     *isExact = !sign;
@@ -1817,7 +2053,9 @@ APFloat::convertToSignExtendedInteger(integerPart *parts, unsigned int width,
   if (exponent < 0) {
     /* Our absolute value is less than one; truncate everything.  */
     APInt::tcSet(parts, 0, dstPartsCount);
-    truncatedBits = semantics->precision;
+    /* 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.  */
@@ -1844,8 +2082,8 @@ APFloat::convertToSignExtendedInteger(integerPart *parts, unsigned int width,
   if (truncatedBits) {
     lost_fraction = lostFractionThroughTruncation(src, partCount(),
                                                   truncatedBits);
-    if (lost_fraction != lfExactlyZero
-        && roundAwayFromZero(rounding_mode, lost_fraction, truncatedBits)) {
+    if (lost_fraction != lfExactlyZero &&
+        roundAwayFromZero(rounding_mode, lost_fraction, truncatedBits)) {
       if (APInt::tcIncrement(parts, dstPartsCount))
         return opInvalidOp;     /* Overflow.  */
     }
@@ -1902,7 +2140,7 @@ APFloat::convertToInteger(integerPart *parts, unsigned int width,
 {
   opStatus fs;
 
-  fs = convertToSignExtendedInteger(parts, width, isSigned, rounding_mode, 
+  fs = convertToSignExtendedInteger(parts, width, isSigned, rounding_mode,
                                     isExact);
 
   if (fs == opInvalidOp) {
@@ -1925,6 +2163,23 @@ APFloat::convertToInteger(integerPart *parts, unsigned int width,
   return fs;
 }
 
+/* Same as convertToInteger(integerPart*, ...), except the result is returned in
+   an APSInt, whose initial bit-width and signed-ness are used to determine the
+   precision of the conversion.
+ */
+APFloat::opStatus
+APFloat::convertToInteger(APSInt &result,
+                          roundingMode rounding_mode, bool *isExact) const
+{
+  unsigned bitWidth = result.getBitWidth();
+  SmallVector<uint64_t, 4> parts(result.getNumWords());
+  opStatus status = convertToInteger(
+    parts.data(), bitWidth, result.isSigned(), rounding_mode, isExact);
+  // Keeps the original signed-ness.
+  result = APInt(bitWidth, parts);
+  return status;
+}
+
 /* Convert an unsigned integer SRC to a floating point number,
    rounding according to ROUNDING_MODE.  The sign of the floating
    point number is not modified.  */
@@ -1937,14 +2192,13 @@ APFloat::convertFromUnsignedParts(const integerPart *src,
   integerPart *dst;
   lostFraction lost_fraction;
 
-  assertArithmeticOK(*semantics);
   category = fcNormal;
   omsb = APInt::tcMSB(src, srcCount) + 1;
   dst = significandParts();
   dstCount = partCount();
   precision = semantics->precision;
 
-  /* We want the most significant PRECISON bits of SRC.  There may not
+  /* 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;
@@ -1988,9 +2242,8 @@ APFloat::convertFromSignExtendedInteger(const integerPart *src,
 {
   opStatus status;
 
-  assertArithmeticOK(*semantics);
-  if (isSigned
-      && APInt::tcExtractBit(src, srcCount * integerPartWidth - 1)) {
+  if (isSigned &&
+      APInt::tcExtractBit(src, srcCount * integerPartWidth - 1)) {
     integerPart *copy;
 
     /* If we're signed and negative negate a copy.  */
@@ -2015,10 +2268,10 @@ APFloat::convertFromZeroExtendedInteger(const integerPart *parts,
                                         roundingMode rounding_mode)
 {
   unsigned int partCount = partCountForBits(width);
-  APInt api = APInt(width, partCount, parts);
+  APInt api = APInt(width, makeArrayRef(parts, partCount));
 
   sign = false;
-  if(isSigned && APInt::tcExtractBit(parts, width - 1)) {
+  if (isSigned && APInt::tcExtractBit(parts, width - 1)) {
     sign = true;
     api = -api;
   }
@@ -2027,13 +2280,12 @@ APFloat::convertFromZeroExtendedInteger(const integerPart *parts,
 }
 
 APFloat::opStatus
-APFloat::convertFromHexadecimalString(const char *p,
-                                      roundingMode rounding_mode)
+APFloat::convertFromHexadecimalString(StringRef s, roundingMode rounding_mode)
 {
-  lostFraction lost_fraction;
+  lostFraction lost_fraction = lfExactlyZero;
   integerPart *significand;
   unsigned int bitPos, partsCount;
-  const char *dot, *firstSignificantDigit;
+  StringRef::iterator dot, firstSignificantDigit;
 
   zeroSignificand();
   exponent = 0;
@@ -2044,53 +2296,64 @@ APFloat::convertFromHexadecimalString(const char *p,
   bitPos = partsCount * integerPartWidth;
 
   /* Skip leading zeroes and any (hexa)decimal point.  */
-  p = skipLeadingZeroesAndAnyDot(p, &dot);
+  StringRef::iterator begin = s.begin();
+  StringRef::iterator end = s.end();
+  StringRef::iterator p = skipLeadingZeroesAndAnyDot(begin, end, &dot);
   firstSignificantDigit = p;
 
-  for(;;) {
+  for (; p != end;) {
     integerPart hex_value;
 
-    if(*p == '.') {
-      assert(dot == 0);
+    if (*p == '.') {
+      assert(dot == end && "String contains multiple dots");
       dot = p++;
+      if (p == end) {
+        break;
+      }
     }
 
     hex_value = hexDigitValue(*p);
-    if(hex_value == -1U) {
-      lost_fraction = lfExactlyZero;
+    if (hex_value == -1U) {
       break;
     }
 
     p++;
 
-    /* Store the number whilst 4-bit nibbles remain.  */
-    if(bitPos) {
-      bitPos -= 4;
-      hex_value <<= bitPos % integerPartWidth;
-      significand[bitPos / integerPartWidth] |= hex_value;
-    } else {
-      lost_fraction = trailingHexadecimalFraction(p, hex_value);
-      while(hexDigitValue(*p) != -1U)
-        p++;
+    if (p == end) {
       break;
+    } else {
+      /* Store the number whilst 4-bit nibbles remain.  */
+      if (bitPos) {
+        bitPos -= 4;
+        hex_value <<= bitPos % integerPartWidth;
+        significand[bitPos / integerPartWidth] |= hex_value;
+      } else {
+        lost_fraction = trailingHexadecimalFraction(p, end, hex_value);
+        while (p != end && hexDigitValue(*p) != -1U)
+          p++;
+        break;
+      }
     }
   }
 
   /* Hex floats require an exponent but not a hexadecimal point.  */
-  assert(*p == 'p' || *p == 'P');
+  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) {
+  if (p != firstSignificantDigit) {
     int expAdjustment;
 
     /* Implicit hexadecimal point?  */
-    if(!dot)
+    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)
+    if (expAdjustment < 0)
       expAdjustment++;
     expAdjustment = expAdjustment * 4 - 1;
 
@@ -2100,7 +2363,7 @@ APFloat::convertFromHexadecimalString(const char *p,
     expAdjustment -= partsCount * integerPartWidth;
 
     /* Adjust for the given exponent.  */
-    exponent = totalExponent(p, expAdjustment);
+    exponent = totalExponent(p + 1, end, expAdjustment);
   }
 
   return normalize(rounding_mode, lost_fraction);
@@ -2112,12 +2375,12 @@ APFloat::roundSignificandWithExponent(const integerPart *decSigParts,
                                       roundingMode rounding_mode)
 {
   unsigned int parts, pow5PartCount;
-  fltSemantics calcSemantics = { 32767, -32767, 0, true };
+  fltSemantics calcSemantics = { 32767, -32767, 0 };
   integerPart pow5Parts[maxPowerOfFiveParts];
   bool isNearest;
 
-  isNearest = (rounding_mode == rmNearestTiesToEven
-               || rounding_mode == rmNearestTiesToAway);
+  isNearest = (rounding_mode == rmNearestTiesToEven ||
+               rounding_mode == rmNearestTiesToAway);
 
   parts = partCountForBits(semantics->precision + 11);
 
@@ -2132,8 +2395,8 @@ APFloat::roundSignificandWithExponent(const integerPart *decSigParts,
     excessPrecision = calcSemantics.precision - semantics->precision;
     truncatedBits = excessPrecision;
 
-    APFloat decSig(calcSemantics, fcZero, sign);
-    APFloat pow5(calcSemantics, fcZero, false);
+    APFloat decSig = APFloat::getZero(calcSemantics, sign);
+    APFloat pow5(calcSemantics);
 
     sigStatus = decSig.convertFromUnsignedParts(decSigParts, sigPartCount,
                                                 rmNearestTiesToEven);
@@ -2165,8 +2428,8 @@ APFloat::roundSignificandWithExponent(const integerPart *decSigParts,
 
     /* Both multiplySignificand and divideSignificand return the
        result with the integer bit set.  */
-    assert (APInt::tcExtractBit
-            (decSig.significandParts(), calcSemantics.precision - 1) == 1);
+    assert(APInt::tcExtractBit
+           (decSig.significandParts(), calcSemantics.precision - 1) == 1);
 
     HUerr = HUerrBound(calcLostFraction != lfExactlyZero, sigStatus != opOK,
                        powHUerr);
@@ -2192,13 +2455,14 @@ APFloat::roundSignificandWithExponent(const integerPart *decSigParts,
 }
 
 APFloat::opStatus
-APFloat::convertFromDecimalString(const char *p, roundingMode rounding_mode)
+APFloat::convertFromDecimalString(StringRef str, roundingMode rounding_mode)
 {
   decimalInfo D;
   opStatus fs;
 
   /* Scan the text.  */
-  interpretDecimal(p, &D);
+  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
@@ -2217,14 +2481,34 @@ APFloat::convertFromDecimalString(const char *p, roundingMode rounding_mode)
            42039/12655 < L < 28738/8651  [ numerator <= 65536 ]
   */
 
-  if (decDigitValue(*D.firstSigDigit) >= 10U) {
+  // 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;
-  } else if ((D.normalizedExponent + 1) * 28738
-             <= 8651 * (semantics->minExponent - (int) semantics->precision)) {
+
+  /* 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.  */
     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.  */
@@ -2253,10 +2537,14 @@ APFloat::convertFromDecimalString(const char *p, roundingMode rounding_mode)
       multiplier = 1;
 
       do {
-        if (*p == '.')
+        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
@@ -2283,21 +2571,57 @@ APFloat::convertFromDecimalString(const char *p, roundingMode rounding_mode)
   return fs;
 }
 
-APFloat::opStatus
-APFloat::convertFromString(const char *p, roundingMode rounding_mode)
-{
-  assertArithmeticOK(*semantics);
-
-  /* Handle a leading minus sign.  */
-  if(*p == '-')
-    sign = 1, p++;
-  else
-    sign = 0;
+bool
+APFloat::convertFromStringSpecials(StringRef str) {
+  if (str.equals("inf") || str.equals("INFINITY")) {
+    makeInf(false);
+    return true;
+  }
 
-  if(p[0] == '0' && (p[1] == 'x' || p[1] == 'X'))
-    return convertFromHexadecimalString(p + 2, rounding_mode);
-  else
-    return convertFromDecimalString(p, rounding_mode);
+  if (str.equals("-inf") || str.equals("-INFINITY")) {
+    makeInf(true);
+    return true;
+  }
+
+  if (str.equals("nan") || str.equals("NaN")) {
+    makeNaN(false, false);
+    return true;
+  }
+
+  if (str.equals("-nan") || str.equals("-NaN")) {
+    makeNaN(false, true);
+    return true;
+  }
+
+  return false;
+}
+
+APFloat::opStatus
+APFloat::convertFromString(StringRef str, roundingMode rounding_mode)
+{
+  assert(!str.empty() && "Invalid string length");
+
+  // Handle special cases.
+  if (convertFromStringSpecials(str))
+    return opOK;
+
+  /* Handle a leading minus sign.  */
+  StringRef::iterator p = str.begin();
+  size_t slen = str.size();
+  sign = *p == '-' ? 1 : 0;
+  if (*p == '-' || *p == '+') {
+    p++;
+    slen--;
+    assert(slen && "String has no digits");
+  }
+
+  if (slen >= 2 && p[0] == '0' && (p[1] == 'x' || p[1] == 'X')) {
+    assert(slen - 2 && "Invalid string");
+    return convertFromHexadecimalString(StringRef(p + 2, slen - 2),
+                                        rounding_mode);
+  }
+
+  return convertFromDecimalString(StringRef(p, slen), rounding_mode);
 }
 
 /* Write out a hexadecimal representation of the floating point value
@@ -2330,8 +2654,6 @@ APFloat::convertToHexString(char *dst, unsigned int hexDigits,
 {
   char *p;
 
-  assertArithmeticOK(*semantics);
-
   p = dst;
   if (sign)
     *dst++ = '-';
@@ -2456,7 +2778,7 @@ APFloat::convertNormalToHexString(char *dst, unsigned int hexDigits,
       q--;
       *q = hexDigitChars[hexDigitValue (*q) + 1];
     } while (*q == '0');
-    assert (q >= p);
+    assert(q >= p);
   } else {
     /* Add trailing zeroes.  */
     memset (dst, '0', outputDigits);
@@ -2478,21 +2800,19 @@ APFloat::convertNormalToHexString(char *dst, unsigned int hexDigits,
   return writeSignedDecimal (dst, exponent);
 }
 
-// For good performance it is desirable for different APFloats
-// to produce different integers.
-uint32_t
-APFloat::getHashValue() const
-{
-  if (category==fcZero) return sign<<8 | semantics->precision ;
-  else if (category==fcInfinity) return sign<<9 | semantics->precision;
-  else if (category==fcNaN) return 1<<10 | semantics->precision;
-  else {
-    uint32_t hash = sign<<11 | semantics->precision | exponent<<12;
-    const integerPart* p = significandParts();
-    for (int i=partCount(); i>0; i--, p++)
-      hash ^= ((uint32_t)*p) ^ (uint32_t)((*p)>>32);
-    return hash;
-  }
+hash_code llvm::hash_value(const APFloat &Arg) {
+  if (!Arg.isFiniteNonZero())
+    return hash_combine((uint8_t)Arg.category,
+                        // NaN has no sign, fix it at zero.
+                        Arg.isNaN() ? (uint8_t)0 : (uint8_t)Arg.sign,
+                        Arg.semantics->precision);
+
+  // Normal floats need their exponent and significand hashed.
+  return hash_combine((uint8_t)Arg.category, (uint8_t)Arg.sign,
+                      Arg.semantics->precision, Arg.exponent,
+                      hash_combine_range(
+                        Arg.significandParts(),
+                        Arg.significandParts() + Arg.partCount()));
 }
 
 // Conversion from APFloat to/from host float/double.  It may eventually be
@@ -2508,11 +2828,11 @@ APInt
 APFloat::convertF80LongDoubleAPFloatToAPInt() const
 {
   assert(semantics == (const llvm::fltSemantics*)&x87DoubleExtended);
-  assert (partCount()==2);
+  assert(partCount()==2);
 
   uint64_t myexponent, mysignificand;
 
-  if (category==fcNormal) {
+  if (isFiniteNonZero()) {
     myexponent = exponent+16383; //bias
     mysignificand = significandParts()[0];
     if (myexponent==1 && !(mysignificand & 0x8000000000000000ULL))
@@ -2530,67 +2850,108 @@ APFloat::convertF80LongDoubleAPFloatToAPInt() const
   }
 
   uint64_t words[2];
-  words[0] =  ((uint64_t)(sign & 1) << 63) |
-              ((myexponent & 0x7fffLL) <<  48) |
-              ((mysignificand >>16) & 0xffffffffffffLL);
-  words[1] = mysignificand & 0xffff;
-  return APInt(80, 2, words);
+  words[0] = mysignificand;
+  words[1] =  ((uint64_t)(sign & 1) << 15) |
+              (myexponent & 0x7fffLL);
+  return APInt(80, words);
 }
 
 APInt
 APFloat::convertPPCDoubleDoubleAPFloatToAPInt() const
 {
   assert(semantics == (const llvm::fltSemantics*)&PPCDoubleDouble);
-  assert (partCount()==2);
+  assert(partCount()==2);
 
-  uint64_t myexponent, mysignificand, myexponent2, mysignificand2;
+  uint64_t words[2];
+  opStatus fs;
+  bool losesInfo;
+
+  // Convert number to double.  To avoid spurious underflows, we re-
+  // normalize against the "double" minExponent first, and only *then*
+  // truncate the mantissa.  The result of that second conversion
+  // may be inexact, but should never underflow.
+  // Declare fltSemantics before APFloat that uses it (and
+  // saves pointer to it) to ensure correct destruction order.
+  fltSemantics extendedSemantics = *semantics;
+  extendedSemantics.minExponent = IEEEdouble.minExponent;
+  APFloat extended(*this);
+  fs = extended.convert(extendedSemantics, rmNearestTiesToEven, &losesInfo);
+  assert(fs == opOK && !losesInfo);
+  (void)fs;
+
+  APFloat u(extended);
+  fs = u.convert(IEEEdouble, rmNearestTiesToEven, &losesInfo);
+  assert(fs == opOK || fs == opInexact);
+  (void)fs;
+  words[0] = *u.convertDoubleAPFloatToAPInt().getRawData();
+
+  // If conversion was exact or resulted in a special case, we're done;
+  // just set the second double to zero.  Otherwise, re-convert back to
+  // the extended format and compute the difference.  This now should
+  // convert exactly to double.
+  if (u.isFiniteNonZero() && losesInfo) {
+    fs = u.convert(extendedSemantics, rmNearestTiesToEven, &losesInfo);
+    assert(fs == opOK && !losesInfo);
+    (void)fs;
+
+    APFloat v(extended);
+    v.subtract(u, rmNearestTiesToEven);
+    fs = v.convert(IEEEdouble, rmNearestTiesToEven, &losesInfo);
+    assert(fs == opOK && !losesInfo);
+    (void)fs;
+    words[1] = *v.convertDoubleAPFloatToAPInt().getRawData();
+  } else {
+    words[1] = 0;
+  }
+
+  return APInt(128, words);
+}
+
+APInt
+APFloat::convertQuadrupleAPFloatToAPInt() const
+{
+  assert(semantics == (const llvm::fltSemantics*)&IEEEquad);
+  assert(partCount()==2);
+
+  uint64_t myexponent, mysignificand, mysignificand2;
 
-  if (category==fcNormal) {
-    myexponent = exponent + 1023; //bias
-    myexponent2 = exponent2 + 1023;
+  if (isFiniteNonZero()) {
+    myexponent = exponent+16383; //bias
     mysignificand = significandParts()[0];
     mysignificand2 = significandParts()[1];
-    if (myexponent==1 && !(mysignificand & 0x10000000000000LL))
+    if (myexponent==1 && !(mysignificand2 & 0x1000000000000LL))
       myexponent = 0;   // denormal
-    if (myexponent2==1 && !(mysignificand2 & 0x10000000000000LL))
-      myexponent2 = 0;   // denormal
   } else if (category==fcZero) {
     myexponent = 0;
-    mysignificand = 0;
-    myexponent2 = 0;
-    mysignificand2 = 0;
+    mysignificand = mysignificand2 = 0;
   } else if (category==fcInfinity) {
-    myexponent = 0x7ff;
-    myexponent2 = 0;
-    mysignificand = 0;
-    mysignificand2 = 0;
+    myexponent = 0x7fff;
+    mysignificand = mysignificand2 = 0;
   } else {
-    assert(category == fcNaN && "Unknown category");
-    myexponent = 0x7ff;
+    assert(category == fcNaN && "Unknown category!");
+    myexponent = 0x7fff;
     mysignificand = significandParts()[0];
-    myexponent2 = exponent2;
     mysignificand2 = significandParts()[1];
   }
 
   uint64_t words[2];
-  words[0] =  ((uint64_t)(sign & 1) << 63) |
-              ((myexponent & 0x7ff) <<  52) |
-              (mysignificand & 0xfffffffffffffLL);
-  words[1] =  ((uint64_t)(sign2 & 1) << 63) |
-              ((myexponent2 & 0x7ff) <<  52) |
-              (mysignificand2 & 0xfffffffffffffLL);
-  return APInt(128, 2, words);
+  words[0] = mysignificand;
+  words[1] = ((uint64_t)(sign & 1) << 63) |
+             ((myexponent & 0x7fff) << 48) |
+             (mysignificand2 & 0xffffffffffffLL);
+
+  return APInt(128, words);
 }
 
 APInt
 APFloat::convertDoubleAPFloatToAPInt() const
 {
   assert(semantics == (const llvm::fltSemantics*)&IEEEdouble);
-  assert (partCount()==1);
+  assert(partCount()==1);
 
   uint64_t myexponent, mysignificand;
 
-  if (category==fcNormal) {
+  if (isFiniteNonZero()) {
     myexponent = exponent+1023; //bias
     mysignificand = *significandParts();
     if (myexponent==1 && !(mysignificand & 0x10000000000000LL))
@@ -2616,11 +2977,11 @@ APInt
 APFloat::convertFloatAPFloatToAPInt() const
 {
   assert(semantics == (const llvm::fltSemantics*)&IEEEsingle);
-  assert (partCount()==1);
+  assert(partCount()==1);
 
   uint32_t myexponent, mysignificand;
 
-  if (category==fcNormal) {
+  if (isFiniteNonZero()) {
     myexponent = exponent+127; //bias
     mysignificand = (uint32_t)*significandParts();
     if (myexponent == 1 && !(mysignificand & 0x800000))
@@ -2641,6 +3002,35 @@ APFloat::convertFloatAPFloatToAPInt() const
                     (mysignificand & 0x7fffff)));
 }
 
+APInt
+APFloat::convertHalfAPFloatToAPInt() const
+{
+  assert(semantics == (const llvm::fltSemantics*)&IEEEhalf);
+  assert(partCount()==1);
+
+  uint32_t myexponent, mysignificand;
+
+  if (isFiniteNonZero()) {
+    myexponent = exponent+15; //bias
+    mysignificand = (uint32_t)*significandParts();
+    if (myexponent == 1 && !(mysignificand & 0x400))
+      myexponent = 0;   // denormal
+  } else if (category==fcZero) {
+    myexponent = 0;
+    mysignificand = 0;
+  } else if (category==fcInfinity) {
+    myexponent = 0x1f;
+    mysignificand = 0;
+  } else {
+    assert(category == fcNaN && "Unknown category!");
+    myexponent = 0x1f;
+    mysignificand = (uint32_t)*significandParts();
+  }
+
+  return APInt(16, (((sign&1) << 15) | ((myexponent&0x1f) << 10) |
+                    (mysignificand & 0x3ff)));
+}
+
 // This function creates an APInt that is just a bit map of the floating
 // point constant as it would appear in memory.  It is not a conversion,
 // and treating the result as a normal integer is unlikely to be useful.
@@ -2648,12 +3038,18 @@ APFloat::convertFloatAPFloatToAPInt() const
 APInt
 APFloat::bitcastToAPInt() const
 {
+  if (semantics == (const llvm::fltSemantics*)&IEEEhalf)
+    return convertHalfAPFloatToAPInt();
+
   if (semantics == (const llvm::fltSemantics*)&IEEEsingle)
     return convertFloatAPFloatToAPInt();
-  
+
   if (semantics == (const llvm::fltSemantics*)&IEEEdouble)
     return convertDoubleAPFloatToAPInt();
 
+  if (semantics == (const llvm::fltSemantics*)&IEEEquad)
+    return convertQuadrupleAPFloatToAPInt();
+
   if (semantics == (const llvm::fltSemantics*)&PPCDoubleDouble)
     return convertPPCDoubleDoubleAPFloatToAPInt();
 
@@ -2665,7 +3061,8 @@ APFloat::bitcastToAPInt() const
 float
 APFloat::convertToFloat() const
 {
-  assert(semantics == (const llvm::fltSemantics*)&IEEEsingle);
+  assert(semantics == (const llvm::fltSemantics*)&IEEEsingle &&
+         "Float semantics are not IEEEsingle");
   APInt api = bitcastToAPInt();
   return api.bitsToFloat();
 }
@@ -2673,7 +3070,8 @@ APFloat::convertToFloat() const
 double
 APFloat::convertToDouble() const
 {
-  assert(semantics == (const llvm::fltSemantics*)&IEEEdouble);
+  assert(semantics == (const llvm::fltSemantics*)&IEEEdouble &&
+         "Float semantics are not IEEEdouble");
   APInt api = bitcastToAPInt();
   return api.bitsToDouble();
 }
@@ -2691,14 +3089,13 @@ APFloat::initFromF80LongDoubleAPInt(const APInt &api)
   assert(api.getBitWidth()==80);
   uint64_t i1 = api.getRawData()[0];
   uint64_t i2 = api.getRawData()[1];
-  uint64_t myexponent = (i1 >> 48) & 0x7fff;
-  uint64_t mysignificand = ((i1 << 16) &  0xffffffffffff0000ULL) |
-                          (i2 & 0xffff);
+  uint64_t myexponent = (i2 & 0x7fff);
+  uint64_t mysignificand = i1;
 
   initialize(&APFloat::x87DoubleExtended);
   assert(partCount()==2);
 
-  sign = static_cast<unsigned int>(i1>>63);
+  sign = static_cast<unsigned int>(i2>>15);
   if (myexponent==0 && mysignificand==0) {
     // exponent, significand meaningless
     category = fcZero;
@@ -2726,47 +3123,63 @@ APFloat::initFromPPCDoubleDoubleAPInt(const APInt &api)
   assert(api.getBitWidth()==128);
   uint64_t i1 = api.getRawData()[0];
   uint64_t i2 = api.getRawData()[1];
-  uint64_t myexponent = (i1 >> 52) & 0x7ff;
-  uint64_t mysignificand = i1 & 0xfffffffffffffLL;
-  uint64_t myexponent2 = (i2 >> 52) & 0x7ff;
-  uint64_t mysignificand2 = i2 & 0xfffffffffffffLL;
+  opStatus fs;
+  bool losesInfo;
+
+  // Get the first double and convert to our format.
+  initFromDoubleAPInt(APInt(64, i1));
+  fs = convert(PPCDoubleDouble, rmNearestTiesToEven, &losesInfo);
+  assert(fs == opOK && !losesInfo);
+  (void)fs;
+
+  // Unless we have a special case, add in second double.
+  if (isFiniteNonZero()) {
+    APFloat v(IEEEdouble, APInt(64, i2));
+    fs = v.convert(PPCDoubleDouble, rmNearestTiesToEven, &losesInfo);
+    assert(fs == opOK && !losesInfo);
+    (void)fs;
+
+    add(v, rmNearestTiesToEven);
+  }
+}
 
-  initialize(&APFloat::PPCDoubleDouble);
+void
+APFloat::initFromQuadrupleAPInt(const APInt &api)
+{
+  assert(api.getBitWidth()==128);
+  uint64_t i1 = api.getRawData()[0];
+  uint64_t i2 = api.getRawData()[1];
+  uint64_t myexponent = (i2 >> 48) & 0x7fff;
+  uint64_t mysignificand  = i1;
+  uint64_t mysignificand2 = i2 & 0xffffffffffffLL;
+
+  initialize(&APFloat::IEEEquad);
   assert(partCount()==2);
 
-  sign = static_cast<unsigned int>(i1>>63);
-  sign2 = static_cast<unsigned int>(i2>>63);
-  if (myexponent==0 && mysignificand==0) {
+  sign = static_cast<unsigned int>(i2>>63);
+  if (myexponent==0 &&
+      (mysignificand==0 && mysignificand2==0)) {
     // exponent, significand meaningless
-    // exponent2 and significand2 are required to be 0; we don't check
     category = fcZero;
-  } else if (myexponent==0x7ff && mysignificand==0) {
+  } else if (myexponent==0x7fff &&
+             (mysignificand==0 && mysignificand2==0)) {
     // exponent, significand meaningless
-    // exponent2 and significand2 are required to be 0; we don't check
     category = fcInfinity;
-  } else if (myexponent==0x7ff && mysignificand!=0) {
-    // exponent meaningless.  So is the whole second word, but keep it 
-    // for determinism.
+  } else if (myexponent==0x7fff &&
+             (mysignificand!=0 || mysignificand2 !=0)) {
+    // exponent meaningless
     category = fcNaN;
-    exponent2 = myexponent2;
     significandParts()[0] = mysignificand;
     significandParts()[1] = mysignificand2;
   } else {
     category = fcNormal;
-    // Note there is no category2; the second word is treated as if it is
-    // fcNormal, although it might be something else considered by itself.
-    exponent = myexponent - 1023;
-    exponent2 = myexponent2 - 1023;
+    exponent = myexponent - 16383;
     significandParts()[0] = mysignificand;
     significandParts()[1] = mysignificand2;
     if (myexponent==0)          // denormal
-      exponent = -1022;
-    else
-      significandParts()[0] |= 0x10000000000000LL;  // integer bit
-    if (myexponent2==0) 
-      exponent2 = -1022;
+      exponent = -16382;
     else
-      significandParts()[1] |= 0x10000000000000LL;  // integer bit
+      significandParts()[1] |= 0x1000000000000LL;  // integer bit
   }
 }
 
@@ -2836,38 +3249,623 @@ APFloat::initFromFloatAPInt(const APInt & api)
   }
 }
 
+void
+APFloat::initFromHalfAPInt(const APInt & api)
+{
+  assert(api.getBitWidth()==16);
+  uint32_t i = (uint32_t)*api.getRawData();
+  uint32_t myexponent = (i >> 10) & 0x1f;
+  uint32_t mysignificand = i & 0x3ff;
+
+  initialize(&APFloat::IEEEhalf);
+  assert(partCount()==1);
+
+  sign = i >> 15;
+  if (myexponent==0 && mysignificand==0) {
+    // exponent, significand meaningless
+    category = fcZero;
+  } else if (myexponent==0x1f && mysignificand==0) {
+    // exponent, significand meaningless
+    category = fcInfinity;
+  } else if (myexponent==0x1f && mysignificand!=0) {
+    // sign, exponent, significand meaningless
+    category = fcNaN;
+    *significandParts() = mysignificand;
+  } else {
+    category = fcNormal;
+    exponent = myexponent - 15;  //bias
+    *significandParts() = mysignificand;
+    if (myexponent==0)    // denormal
+      exponent = -14;
+    else
+      *significandParts() |= 0x400; // integer bit
+  }
+}
+
 /// Treat api as containing the bits of a floating point number.  Currently
 /// we infer the floating point type from the size of the APInt.  The
 /// isIEEE argument distinguishes between PPC128 and IEEE128 (not meaningful
 /// when the size is anything else).
 void
-APFloat::initFromAPInt(const APInt& api, bool isIEEE)
+APFloat::initFromAPInt(const fltSemantics* Sem, const APInt& api)
 {
-  if (api.getBitWidth() == 32)
+  if (Sem == &IEEEhalf)
+    return initFromHalfAPInt(api);
+  if (Sem == &IEEEsingle)
     return initFromFloatAPInt(api);
-  else if (api.getBitWidth()==64)
+  if (Sem == &IEEEdouble)
     return initFromDoubleAPInt(api);
-  else if (api.getBitWidth()==80)
+  if (Sem == &x87DoubleExtended)
     return initFromF80LongDoubleAPInt(api);
-  else if (api.getBitWidth()==128 && !isIEEE)
+  if (Sem == &IEEEquad)
+    return initFromQuadrupleAPInt(api);
+  if (Sem == &PPCDoubleDouble)
     return initFromPPCDoubleDoubleAPInt(api);
-  else
-    assert(0);
+
+  llvm_unreachable(0);
+}
+
+APFloat
+APFloat::getAllOnesValue(unsigned BitWidth, bool isIEEE)
+{
+  switch (BitWidth) {
+  case 16:
+    return APFloat(IEEEhalf, APInt::getAllOnesValue(BitWidth));
+  case 32:
+    return APFloat(IEEEsingle, APInt::getAllOnesValue(BitWidth));
+  case 64:
+    return APFloat(IEEEdouble, APInt::getAllOnesValue(BitWidth));
+  case 80:
+    return APFloat(x87DoubleExtended, APInt::getAllOnesValue(BitWidth));
+  case 128:
+    if (isIEEE)
+      return APFloat(IEEEquad, APInt::getAllOnesValue(BitWidth));
+    return APFloat(PPCDoubleDouble, APInt::getAllOnesValue(BitWidth));
+  default:
+    llvm_unreachable("Unknown floating bit width");
+  }
 }
 
-APFloat::APFloat(const APInt& api, bool isIEEE)
-{
-  initFromAPInt(api, isIEEE);
+/// Make this number the largest magnitude normal number in the given
+/// semantics.
+void APFloat::makeLargest(bool Negative) {
+  // We want (in interchange format):
+  //   sign = {Negative}
+  //   exponent = 1..10
+  //   significand = 1..1
+  category = fcNormal;
+  sign = Negative;
+  exponent = semantics->maxExponent;
+
+  // Use memset to set all but the highest integerPart to all ones.
+  integerPart *significand = significandParts();
+  unsigned PartCount = partCount();
+  memset(significand, 0xFF, sizeof(integerPart)*(PartCount - 1));
+
+  // Set the high integerPart especially setting all unused top bits for
+  // internal consistency.
+  const unsigned NumUnusedHighBits =
+    PartCount*integerPartWidth - semantics->precision;
+  significand[PartCount - 1] = ~integerPart(0) >> NumUnusedHighBits;
+}
+
+/// Make this number the smallest magnitude denormal number in the given
+/// semantics.
+void APFloat::makeSmallest(bool Negative) {
+  // We want (in interchange format):
+  //   sign = {Negative}
+  //   exponent = 0..0
+  //   significand = 0..01
+  category = fcNormal;
+  sign = Negative;
+  exponent = semantics->minExponent;
+  APInt::tcSet(significandParts(), 1, partCount());
 }
 
-APFloat::APFloat(float f)
-{
-  APInt api = APInt(32, 0);
-  initFromAPInt(api.floatToBits(f));
+
+APFloat APFloat::getLargest(const fltSemantics &Sem, bool Negative) {
+  // We want (in interchange format):
+  //   sign = {Negative}
+  //   exponent = 1..10
+  //   significand = 1..1
+  APFloat Val(Sem, uninitialized);
+  Val.makeLargest(Negative);
+  return Val;
 }
 
-APFloat::APFloat(double d)
-{
-  APInt api = APInt(64, 0);
-  initFromAPInt(api.doubleToBits(d));
+APFloat APFloat::getSmallest(const fltSemantics &Sem, bool Negative) {
+  // We want (in interchange format):
+  //   sign = {Negative}
+  //   exponent = 0..0
+  //   significand = 0..01
+  APFloat Val(Sem, uninitialized);
+  Val.makeSmallest(Negative);
+  return Val;
+}
+
+APFloat APFloat::getSmallestNormalized(const fltSemantics &Sem, bool Negative) {
+  APFloat Val(Sem, uninitialized);
+
+  // We want (in interchange format):
+  //   sign = {Negative}
+  //   exponent = 0..0
+  //   significand = 10..0
+
+  Val.zeroSignificand();
+  Val.sign = Negative;
+  Val.exponent = Sem.minExponent;
+  Val.significandParts()[partCountForBits(Sem.precision)-1] |=
+    (((integerPart) 1) << ((Sem.precision - 1) % integerPartWidth));
+
+  return Val;
+}
+
+APFloat::APFloat(const fltSemantics &Sem, const APInt &API) {
+  initFromAPInt(&Sem, API);
+}
+
+APFloat::APFloat(float f) {
+  initFromAPInt(&IEEEsingle, APInt::floatToBits(f));
+}
+
+APFloat::APFloat(double d) {
+  initFromAPInt(&IEEEdouble, APInt::doubleToBits(d));
+}
+
+namespace {
+  void append(SmallVectorImpl<char> &Buffer, StringRef Str) {
+    Buffer.append(Str.begin(), Str.end());
+  }
+
+  /// Removes data from the given significand until it is no more
+  /// precise than is required for the desired precision.
+  void AdjustToPrecision(APInt &significand,
+                         int &exp, unsigned FormatPrecision) {
+    unsigned bits = significand.getActiveBits();
+
+    // 196/59 is a very slight overestimate of lg_2(10).
+    unsigned bitsRequired = (FormatPrecision * 196 + 58) / 59;
+
+    if (bits <= bitsRequired) return;
+
+    unsigned tensRemovable = (bits - bitsRequired) * 59 / 196;
+    if (!tensRemovable) return;
+
+    exp += tensRemovable;
+
+    APInt divisor(significand.getBitWidth(), 1);
+    APInt powten(significand.getBitWidth(), 10);
+    while (true) {
+      if (tensRemovable & 1)
+        divisor *= powten;
+      tensRemovable >>= 1;
+      if (!tensRemovable) break;
+      powten *= powten;
+    }
+
+    significand = significand.udiv(divisor);
+
+    // Truncate the significand down to its active bit count.
+    significand = significand.trunc(significand.getActiveBits());
+  }
+
+
+  void AdjustToPrecision(SmallVectorImpl<char> &buffer,
+                         int &exp, unsigned FormatPrecision) {
+    unsigned N = buffer.size();
+    if (N <= FormatPrecision) return;
+
+    // The most significant figures are the last ones in the buffer.
+    unsigned FirstSignificant = N - FormatPrecision;
+
+    // Round.
+    // FIXME: this probably shouldn't use 'round half up'.
+
+    // Rounding down is just a truncation, except we also want to drop
+    // trailing zeros from the new result.
+    if (buffer[FirstSignificant - 1] < '5') {
+      while (FirstSignificant < N && buffer[FirstSignificant] == '0')
+        FirstSignificant++;
+
+      exp += FirstSignificant;
+      buffer.erase(&buffer[0], &buffer[FirstSignificant]);
+      return;
+    }
+
+    // Rounding up requires a decimal add-with-carry.  If we continue
+    // the carry, the newly-introduced zeros will just be truncated.
+    for (unsigned I = FirstSignificant; I != N; ++I) {
+      if (buffer[I] == '9') {
+        FirstSignificant++;
+      } else {
+        buffer[I]++;
+        break;
+      }
+    }
+
+    // If we carried through, we have exactly one digit of precision.
+    if (FirstSignificant == N) {
+      exp += FirstSignificant;
+      buffer.clear();
+      buffer.push_back('1');
+      return;
+    }
+
+    exp += FirstSignificant;
+    buffer.erase(&buffer[0], &buffer[FirstSignificant]);
+  }
+}
+
+void APFloat::toString(SmallVectorImpl<char> &Str,
+                       unsigned FormatPrecision,
+                       unsigned FormatMaxPadding) const {
+  switch (category) {
+  case fcInfinity:
+    if (isNegative())
+      return append(Str, "-Inf");
+    else
+      return append(Str, "+Inf");
+
+  case fcNaN: return append(Str, "NaN");
+
+  case fcZero:
+    if (isNegative())
+      Str.push_back('-');
+
+    if (!FormatMaxPadding)
+      append(Str, "0.0E+0");
+    else
+      Str.push_back('0');
+    return;
+
+  case fcNormal:
+    break;
+  }
+
+  if (isNegative())
+    Str.push_back('-');
+
+  // Decompose the number into an APInt and an exponent.
+  int exp = exponent - ((int) semantics->precision - 1);
+  APInt significand(semantics->precision,
+                    makeArrayRef(significandParts(),
+                                 partCountForBits(semantics->precision)));
+
+  // Set FormatPrecision if zero.  We want to do this before we
+  // truncate trailing zeros, as those are part of the precision.
+  if (!FormatPrecision) {
+    // It's an interesting question whether to use the nominal
+    // precision or the active precision here for denormals.
+
+    // FormatPrecision = ceil(significandBits / lg_2(10))
+    FormatPrecision = (semantics->precision * 59 + 195) / 196;
+  }
+
+  // Ignore trailing binary zeros.
+  int trailingZeros = significand.countTrailingZeros();
+  exp += trailingZeros;
+  significand = significand.lshr(trailingZeros);
+
+  // Change the exponent from 2^e to 10^e.
+  if (exp == 0) {
+    // Nothing to do.
+  } else if (exp > 0) {
+    // Just shift left.
+    significand = significand.zext(semantics->precision + exp);
+    significand <<= exp;
+    exp = 0;
+  } else { /* exp < 0 */
+    int texp = -exp;
+
+    // We transform this using the identity:
+    //   (N)(2^-e) == (N)(5^e)(10^-e)
+    // This means we have to multiply N (the significand) by 5^e.
+    // To avoid overflow, we have to operate on numbers large
+    // enough to store N * 5^e:
+    //   log2(N * 5^e) == log2(N) + e * log2(5)
+    //                 <= semantics->precision + e * 137 / 59
+    //   (log_2(5) ~ 2.321928 < 2.322034 ~ 137/59)
+
+    unsigned precision = semantics->precision + (137 * texp + 136) / 59;
+
+    // Multiply significand by 5^e.
+    //   N * 5^0101 == N * 5^(1*1) * 5^(0*2) * 5^(1*4) * 5^(0*8)
+    significand = significand.zext(precision);
+    APInt five_to_the_i(precision, 5);
+    while (true) {
+      if (texp & 1) significand *= five_to_the_i;
+
+      texp >>= 1;
+      if (!texp) break;
+      five_to_the_i *= five_to_the_i;
+    }
+  }
+
+  AdjustToPrecision(significand, exp, FormatPrecision);
+
+  SmallVector<char, 256> buffer;
+
+  // Fill the buffer.
+  unsigned precision = significand.getBitWidth();
+  APInt ten(precision, 10);
+  APInt digit(precision, 0);
+
+  bool inTrail = true;
+  while (significand != 0) {
+    // digit <- significand % 10
+    // significand <- significand / 10
+    APInt::udivrem(significand, ten, significand, digit);
+
+    unsigned d = digit.getZExtValue();
+
+    // Drop trailing zeros.
+    if (inTrail && !d) exp++;
+    else {
+      buffer.push_back((char) ('0' + d));
+      inTrail = false;
+    }
+  }
+
+  assert(!buffer.empty() && "no characters in buffer!");
+
+  // Drop down to FormatPrecision.
+  // TODO: don't do more precise calculations above than are required.
+  AdjustToPrecision(buffer, exp, FormatPrecision);
+
+  unsigned NDigits = buffer.size();
+
+  // Check whether we should use scientific notation.
+  bool FormatScientific;
+  if (!FormatMaxPadding)
+    FormatScientific = true;
+  else {
+    if (exp >= 0) {
+      // 765e3 --> 765000
+      //              ^^^
+      // But we shouldn't make the number look more precise than it is.
+      FormatScientific = ((unsigned) exp > FormatMaxPadding ||
+                          NDigits + (unsigned) exp > FormatPrecision);
+    } else {
+      // Power of the most significant digit.
+      int MSD = exp + (int) (NDigits - 1);
+      if (MSD >= 0) {
+        // 765e-2 == 7.65
+        FormatScientific = false;
+      } else {
+        // 765e-5 == 0.00765
+        //           ^ ^^
+        FormatScientific = ((unsigned) -MSD) > FormatMaxPadding;
+      }
+    }
+  }
+
+  // Scientific formatting is pretty straightforward.
+  if (FormatScientific) {
+    exp += (NDigits - 1);
+
+    Str.push_back(buffer[NDigits-1]);
+    Str.push_back('.');
+    if (NDigits == 1)
+      Str.push_back('0');
+    else
+      for (unsigned I = 1; I != NDigits; ++I)
+        Str.push_back(buffer[NDigits-1-I]);
+    Str.push_back('E');
+
+    Str.push_back(exp >= 0 ? '+' : '-');
+    if (exp < 0) exp = -exp;
+    SmallVector<char, 6> expbuf;
+    do {
+      expbuf.push_back((char) ('0' + (exp % 10)));
+      exp /= 10;
+    } while (exp);
+    for (unsigned I = 0, E = expbuf.size(); I != E; ++I)
+      Str.push_back(expbuf[E-1-I]);
+    return;
+  }
+
+  // Non-scientific, positive exponents.
+  if (exp >= 0) {
+    for (unsigned I = 0; I != NDigits; ++I)
+      Str.push_back(buffer[NDigits-1-I]);
+    for (unsigned I = 0; I != (unsigned) exp; ++I)
+      Str.push_back('0');
+    return;
+  }
+
+  // Non-scientific, negative exponents.
+
+  // The number of digits to the left of the decimal point.
+  int NWholeDigits = exp + (int) NDigits;
+
+  unsigned I = 0;
+  if (NWholeDigits > 0) {
+    for (; I != (unsigned) NWholeDigits; ++I)
+      Str.push_back(buffer[NDigits-I-1]);
+    Str.push_back('.');
+  } else {
+    unsigned NZeros = 1 + (unsigned) -NWholeDigits;
+
+    Str.push_back('0');
+    Str.push_back('.');
+    for (unsigned Z = 1; Z != NZeros; ++Z)
+      Str.push_back('0');
+  }
+
+  for (; I != NDigits; ++I)
+    Str.push_back(buffer[NDigits-I-1]);
+}
+
+bool APFloat::getExactInverse(APFloat *inv) const {
+  // Special floats and denormals have no exact inverse.
+  if (!isFiniteNonZero())
+    return false;
+
+  // Check that the number is a power of two by making sure that only the
+  // integer bit is set in the significand.
+  if (significandLSB() != semantics->precision - 1)
+    return false;
+
+  // Get the inverse.
+  APFloat reciprocal(*semantics, 1ULL);
+  if (reciprocal.divide(*this, rmNearestTiesToEven) != opOK)
+    return false;
+
+  // Avoid multiplication with a denormal, it is not safe on all platforms and
+  // may be slower than a normal division.
+  if (reciprocal.isDenormal())
+    return false;
+
+  assert(reciprocal.isFiniteNonZero() &&
+         reciprocal.significandLSB() == reciprocal.semantics->precision - 1);
+
+  if (inv)
+    *inv = reciprocal;
+
+  return true;
+}
+
+bool APFloat::isSignaling() const {
+  if (!isNaN())
+    return false;
+
+  // IEEE-754R 2008 6.2.1: A signaling NaN bit string should be encoded with the
+  // first bit of the trailing significand being 0.
+  return !APInt::tcExtractBit(significandParts(), semantics->precision - 2);
+}
+
+/// IEEE-754R 2008 5.3.1: nextUp/nextDown.
+///
+/// *NOTE* since nextDown(x) = -nextUp(-x), we only implement nextUp with
+/// appropriate sign switching before/after the computation.
+APFloat::opStatus APFloat::next(bool nextDown) {
+  // If we are performing nextDown, swap sign so we have -x.
+  if (nextDown)
+    changeSign();
+
+  // Compute nextUp(x)
+  opStatus result = opOK;
+
+  // Handle each float category separately.
+  switch (category) {
+  case fcInfinity:
+    // nextUp(+inf) = +inf
+    if (!isNegative())
+      break;
+    // nextUp(-inf) = -getLargest()
+    makeLargest(true);
+    break;
+  case fcNaN:
+    // IEEE-754R 2008 6.2 Par 2: nextUp(sNaN) = qNaN. Set Invalid flag.
+    // IEEE-754R 2008 6.2: nextUp(qNaN) = qNaN. Must be identity so we do not
+    //                     change the payload.
+    if (isSignaling()) {
+      result = opInvalidOp;
+      // For consistency, propogate the sign of the sNaN to the qNaN.
+      makeNaN(false, isNegative(), 0);
+    }
+    break;
+  case fcZero:
+    // nextUp(pm 0) = +getSmallest()
+    makeSmallest(false);
+    break;
+  case fcNormal:
+    // nextUp(-getSmallest()) = -0
+    if (isSmallest() && isNegative()) {
+      APInt::tcSet(significandParts(), 0, partCount());
+      category = fcZero;
+      exponent = 0;
+      break;
+    }
+
+    // nextUp(getLargest()) == INFINITY
+    if (isLargest() && !isNegative()) {
+      APInt::tcSet(significandParts(), 0, partCount());
+      category = fcInfinity;
+      exponent = semantics->maxExponent + 1;
+      break;
+    }
+
+    // nextUp(normal) == normal + inc.
+    if (isNegative()) {
+      // If we are negative, we need to decrement the significand.
+
+      // We only cross a binade boundary that requires adjusting the exponent
+      // if:
+      //   1. exponent != semantics->minExponent. This implies we are not in the
+      //   smallest binade or are dealing with denormals.
+      //   2. Our significand excluding the integral bit is all zeros.
+      bool WillCrossBinadeBoundary =
+        exponent != semantics->minExponent && isSignificandAllZeros();
+
+      // Decrement the significand.
+      //
+      // We always do this since:
+      //   1. If we are dealing with a non binade decrement, by definition we
+      //   just decrement the significand.
+      //   2. If we are dealing with a normal -> normal binade decrement, since
+      //   we have an explicit integral bit the fact that all bits but the
+      //   integral bit are zero implies that subtracting one will yield a
+      //   significand with 0 integral bit and 1 in all other spots. Thus we
+      //   must just adjust the exponent and set the integral bit to 1.
+      //   3. If we are dealing with a normal -> denormal binade decrement,
+      //   since we set the integral bit to 0 when we represent denormals, we
+      //   just decrement the significand.
+      integerPart *Parts = significandParts();
+      APInt::tcDecrement(Parts, partCount());
+
+      if (WillCrossBinadeBoundary) {
+        // Our result is a normal number. Do the following:
+        // 1. Set the integral bit to 1.
+        // 2. Decrement the exponent.
+        APInt::tcSetBit(Parts, semantics->precision - 1);
+        exponent--;
+      }
+    } else {
+      // If we are positive, we need to increment the significand.
+
+      // We only cross a binade boundary that requires adjusting the exponent if
+      // the input is not a denormal and all of said input's significand bits
+      // are set. If all of said conditions are true: clear the significand, set
+      // the integral bit to 1, and increment the exponent. If we have a
+      // denormal always increment since moving denormals and the numbers in the
+      // smallest normal binade have the same exponent in our representation.
+      bool WillCrossBinadeBoundary = !isDenormal() && isSignificandAllOnes();
+
+      if (WillCrossBinadeBoundary) {
+        integerPart *Parts = significandParts();
+        APInt::tcSet(Parts, 0, partCount());
+        APInt::tcSetBit(Parts, semantics->precision - 1);
+        assert(exponent != semantics->maxExponent &&
+               "We can not increment an exponent beyond the maxExponent allowed"
+               " by the given floating point semantics.");
+        exponent++;
+      } else {
+        incrementSignificand();
+      }
+    }
+    break;
+  }
+
+  // If we are performing nextDown, swap sign so we have -nextUp(-x)
+  if (nextDown)
+    changeSign();
+
+  return result;
+}
+
+void
+APFloat::makeInf(bool Negative) {
+  category = fcInfinity;
+  sign = Negative;
+  exponent = semantics->maxExponent + 1;
+  APInt::tcSet(significandParts(), 0, partCount());
+}
+
+void
+APFloat::makeZero(bool Negative) {
+  category = fcZero;
+  sign = Negative;
+  exponent = semantics->minExponent-1;
+  APInt::tcSet(significandParts(), 0, partCount());  
 }