Why does Math.Exp give different results between 32-bit and 64-bit, with same input, same hardware

I am using .NET 2.0 with PlatformTarget x64 and x86. I am giving Math.Exp the same input number, and it returns different results in either platform.

MSDN says you can't rely on a literal/parsed Double to represent the same number between platforms, but I think my use of Int64BitsToDouble below avoids this problem and guarantees the same input to Math.Exp on both platforms.

My question is why are the results different? I would have thought that:

• the input is stored in the same way (double/64-bit precision)
• the FPU would do the same calculations regardless of processor's bitness
• the output is stored in the same way

I know I should not compare floating-point numbers after the 15/17th digit in general, but I am confused about the inconsistency here with what looks like the same operation on the same hardware.

Any one know what's going on under the hood?

double d = BitConverter.Int64BitsToDouble(-4648784593573222648L); // same as Double.Parse("-0.0068846153846153849") but with no concern about losing digits in conversion
Debug.Assert(d.ToString("G17") == "-0.0068846153846153849"
    &a开发者_JAVA技巧mp;& BitConverter.DoubleToInt64Bits(d) == -4648784593573222648L); // true on both 32 & 64 bit

double exp = Math.Exp(d);

Console.WriteLine("{0:G17} = {1}", exp, BitConverter.DoubleToInt64Bits(exp));
// 64-bit: 0.99313902928727449 = 4607120620669726947
// 32-bit: 0.9931390292872746  = 4607120620669726948

The results are consistent on both platforms with JIT turned on or off.

[Edit]

I'm not completely satisfied with the answers below so here are some more details from my searching.

http://www.manicai.net/comp/debugging/fpudiff/ says that:

So 32-bit is using the 80-bit FPU registers, 64-bit is using the 128-bit SSE registers.

And the CLI Standard says that doubles can be represented with higher precision if the hardware supports it:

[Rationale: This design allows the CLI to choose a platform-specific high-performance representation for floating-point numbers until they are placed in storage locations. For example, it might be able to leave floating-point variables in hardware registers that provide more precision than a user has requested. At the Partition I 69 same time, CIL generators can force operations to respect language-specific rules for representations through the use of conversion instructions. end rationale]

http://www.ecma-international.org/publications/files/ECMA-ST/Ecma-335.pdf (12.1.3 Handling of floating-point data types)

I think this is what is happening here, because the results different after Double's standard 15 digits of precision. The 64-bit Math.Exp result is more precise (it has an extra digit) because internally 64-bit .NET is using an FPU register with more precision than the FPU register used by 32-bit .NET.

Yes rounding errors, and it is effectively NOT the same hardware. The 32 bit version is targeting a different set of instructions and register sizes.

With the Double type you will get rounding errors, as fractions in binary get very large very quickly. It would possibly help if you used the Decimal type.