Large 1D FFT fails with multiple of a prime number.

[Julianis]

One of our client reported an error on a specific size 1D FFT.
After some investigations we found out the issue was related to the size of the data.

We do 1D FFT, complex numbers in float (single precision), in place configuration (DFTI_INPLACE), and the we link mkl_sequential_dll.lib.

When the number of complex is 205'213'539, the DftiComputeForward() function returns an error code DFTI_INCONSISTENT_CONFIGURATION (3).

We did some tests to pinpoint the problem:

300M points, success
205'212'539, failure (this value is a multiple of 7, 7x29'316'077)
200'000'033 (prime number > 200M), success
100M, success
33'000'001 (prime number > 33M), success
2*33'000'001, success
34'000'009 (prime number > 34M), success
2*34'000'009, failure
3*50'000'017 (prime number > 50M), failure

It seems the FFT implementation has 2 paths, radix or non radix:
- the non radix path (when we use a prime number) can do the calculations on whatever size
- the radix path (when we use a multiple of prime number) seems to have a limit around radix * 33M

The errors have been reproduced with MKL 2022.1 and 2024.0.
Latest version didn't solve the issue unfortunately.

I understand the radix path can have limitations to the number of elements, but in this case, I would expect a fallback to the non radix path instead of failing.

[Gennady_F_Intel]

Could you try to link against ILP64 mode? Check how to do that with MKL Linker Adviser.

--Gennady

[Julianis]

Sorry I didn't specify it, but we are already linking against mkl_intel_ilp64_dll.lib.

To be specific we link against:

mkl_core_dll.lib
mkl_intel_ilp64_dll.lib
mkl_intel_thread_dll.lib

Regards

[Gennady_F_Intel]

Then please build the reproducer which will help us to check this case on our end.

[Julianis]

I modified the basic_sp_complex_dft_1d.c sample to reproduce the problem.

[Gennady_F_Intel]

We reproduced the behavior and will investigate the reason. The status would be updated here.

--Gennady

[Gennady_F_Intel]

I have to confirmed that this is the real issue. We are planning to fix it the nearest update which we are planning to release the next eom. I will keep you informed when it happen.

--Gennady

[Julianis]

Great, thanks for the support !

[Gennady_F_Intel]

Juilian,

Could you give us all problem sizes where do you see the problem beyond of those you already shared?

We fixed the problem and need to check all cases where do you see the problem.

--Gennady

[Julianis]

Hello,

sorry for the late answer, I was on vacation.

I identified the following dimensions which reproduce the issue:

int N = 1*34'000'009; // OK
//int N = 2*34'000'009; // FAILS
//int N = 3*34'000'009; // FAILS
//int N = 7*34'000'009; // FAILS
//int N = 11*34'000'009; // FAILS
//int N = 13*34'000'009; // FAILS
//int N = 17*34'000'009; // FAILS
//int N = 19*34'000'009; // FAILS
//int N = 23*34'000'009; // FAILS
//int N = 29*34'000'009; // FAILS
// i guess the issue is the following
//int N = {prime number}*34'000'009; // FAILS

Regards

[Gennady_F_Intel]

thanks for the update. 

[Gennady_F_Intel · Accepted solution]

The fix of the problem available into the latest MKL 2024 u1 which has been released this week and available to download.

here is the log I captured while linking the case against MKL 2024 u1 and while using Verbose mode :

Intel(R) oneAPI Math Kernel Library Version 2024.1-Product Build 20240215 for Intel(R) 64 architecture applications

Example basic_sp_complex_dft_1d

Forward and backward single-precision complex in-place 1D FFTs

Configuration parameters:

 DFTI_PRECISION   = DFTI_SINGLE

 DFTI_FORWARD_DOMAIN = DFTI_COMPLEX

 DFTI_DIMENSION   = 1

 DFTI_LENGTHS    = {205213539}

Create DFTI descriptor

Commit DFTI descriptor

Allocate input array

Initialize input for forward transform

Compute forward transform

MKL_VERBOSE oneMKL 2024.0 Update 1 Product build 20240215 for Intel(R) 64 architecture Intel(R) Advanced Vector Extensions 512 (Intel(R) AVX-512) enabled processors, Lnx 2.40GHz sequential

MKL_VERBOSE FFT(scfi205213539,tLim:1,desc:0x55bf372031c0) 35.78s CNR:OFF Dyn:1 FastMM:1

...DftiComputeForward returns 0 Verify the result of forward FFT

 Verify the result, errthr = 1.65e-05

 Verified, maximum error was 4.52e-07

Initialize input for backward transform

Compute backward transform

MKL_VERBOSE FFT(scbi205213539,tLim:1,desc:0x55bf372031c0) 32.04s CNR:OFF Dyn:1 FastMM:1

Verify the result of backward FFT

[Julianis]

I confirm the problem is fixed with the latest mkl version.

Thank you