c++ exp function different results under x64 on i7-3770 and i7-4790

Question

When I execute a simple x64 application with the following code, I get different results on Windows PCs with a i7-3770 and i7-4790 CPU.

#include <cmath>
#include <iostream>
#include <limits>

void main()
{
  double val = exp(-10.240990982718174);
  std::cout.precision(std::numeric_limits<double>::max_digits10);
  std::cout << val;
}

Result on i7-3770:

3.5677476354876406e-05

Result on i7-4790:

3.5677476354876413e-05

When I modify the code to call

unsigned int control_word;
_controlfp_s(&control_word, _RC_UP, MCW_RC);

before the exp function call, both CPUs deliver the same results.

My questions:

• Does anyone have an idea for the reason of the differences between the i7-3770 and i7-4790?
• Is there a way to set the floating point precision or consistency in a Visual Studio 2015/2017 C++ project for the whole project and not only for the following function call? The "Floating Point Model" setting (/fp) does not have any influence on the results here.

Wary

According to ttmath.org/online_calculator the first 20 or so digits should be 0.000035677476354876 393107 (I've added a space to show where the digits start to diverge). The first result is slightly closer. – Dennard

Not relevant to the question but main returns int, not void – Registered

There is almost certainly an Evil DLL getting injected into your process that changes the control word. Do note that _RC_UP is not the default, it is _RC_NEAR. So whatever machine you consider the "good" one is actually the troublemaker. Hunting for that DLL can keep you busy for a while. It is the kind of problem that a disk format tends to solve a lot quicker, especially when it isn't you that has to do it. – Specialty

I am aware that this is not the default behavior. But this is the only possiblity I currently found which gives me the same results on both CPU types. Furthermore I tried this on more PCs with different CPUs and I have got the impression that all PCs with Ivy Bridge and prior CPUs deliver the same results (3.5677476354876406e-05) and all Haswell and later CPUs deliver also the same results (3.5677476354876413e-05). Could it be possible, that beginning with Haswell rounding of double precision values under x64 has changed. – Wary

Possible duplicate of Math precision requirements of C and C++ standard – Torticollis

complex functions like sin, cos, exp are not required to be properly rounded by IEEE-754. Those values differ by only 1ULP which is normal. See sin(45) and cos(45) giving different results – Torticollis

and void main() is prohibited in C++ and C although it's allowed in free-standing C implementations – Torticollis

another possible duplicate: exp precision between Mac OS and Windows – Torticollis

Answer 1

I did some further investigations and I found out the following facts:

• the problem does also occur on Windows with a different compiler (Intel)
• on a linux system both values are equal

I also posted this question to the Visual Studio Community. I got the information, that Haswell and newer CPUs use FMA3. You can disable this feature with _set_FMA3_enable(0) at the beginning of the program. When I do this, the results are the same.

Wary

This is documented here learn.microsoft.com/en-us/cpp/c-runtime-library/reference/… "By default, on X64 platforms, the CRT startup code detects whether the CPU supports FMA3 instructions, and enables or disables the FMA3 implementations in the library." – Iceblink

Answer 2

Assuming that double is coded using IEEE-754, and using this decimal to binary converter, you can see that:

3.5677476354876406e-05 is represented in hexa as 0x3F02B48CC0D0ABA8 3.5677476354876413e-05 is represented in hexa as 0x3F02B48CC0D0ABA9

which differ only in the last bit, probably due round error.

Registered