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" && 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.