This was discussed on mailing list [1].

The bug seems to be that the conversion of an APFloat to a string (using the "natural precision") and then converting that back into an APFloat can result in a different value when not using ``APFloat::rmNearestTiesToEven``. 

In the implementation of ``APFloat::toString(...)`` you can
specify ``FormatPrecision`` as 0. The method comments state that this
will use the "natural precision" of the number. In the actual
implementation the comments say that when FormatPrecision is 0 that

```
// We use enough digits so the number can be round-tripped back to an
// APFloat. The formula comes from "How to Print Floating-Point Numbers
// Accurately" by Steele and White.
```

Based on the above comments I expected to be able to convert an
APFloat to a string and back again when ``FormatPrecision`` is set to
zero. However this does not seem to hold. Here's some example code
that demonstrates this.

```
#include "llvm/Support/raw_ostream.h"
#include "llvm/ADT/APFloat.h"
#include <string>

using namespace llvm;

std::string getString(APFloat f) {
  SmallVector<char,10> strRep;
  // FormatPrecision=0 means that the "natural precision" of the number is used
  f.toString(strRep,/*FormatPrecision=*/0, /*FormatMaxPadding=*/0);
  return std::string(strRep.begin(), strRep.end());
}

uint16_t getBits(APFloat f) {
  APInt bits = f.bitcastToAPInt();
  assert(bits.getActiveBits() <= 16);
  return (uint16_t) (bits.getZExtValue() & 0xffff);
}

int main(int argc, char** argv) {
  APFloat f(APFloat::IEEEhalf);
  APFloat newF(APFloat::IEEEhalf);
  f.convertFromString("0.3", APFloat::rmTowardZero);
  outs() << "f bits: 0x";
  outs().write_hex(getBits(f));
  outs() << "\n";
  assert(getBits(f) == 0x34cc);
  // Check that if we get the string using FormatPrecision=0
  // that this can be used to construct another APFloat of the
  // same value.
  std::string fAsString = getString(f);
  outs() << "f as string: \"" << fAsString << "\"\n";
  newF.convertFromString(fAsString, APFloat::rmTowardZero);
  outs() << "newF as string: \"" << getString(newF) << "\"\n";
  outs() << "newF bits: 0x";
  outs().write_hex(getBits(newF));
  outs() << "\n";
  // BUG This assert fails
  assert(getBits(newF) == 0x34cc);
  return 0;
}
```

The output I see is

```
f bits: 0x34cc
f as string: "2.998E-1"
newF as string: "2.9956E-1"
newF bits: 0x34cb
... Assertion `getBits(newF) == 0x34cc' failed.
```

As you can see when we create a new APFloat from the string we get a
slightly smaller number. I have observed that if I use
``APFloat::rmNearestTiesToEven`` when creating ``newF`` that I do get
an APFloat instance which has the same value as the original APFloat.


[1] http://lists.llvm.org/pipermail/llvm-dev/2015-August/089085.html