TFHE Bootstrapping

I have some problem about polynomial multiplication in TFHE. Sicen I want to try realizate the bootstrapping and there is some problems about data. The coefficients of poly are 32 bits, and the answer of FFT is complex number(fixed point)(32 bits im and 32 bits re). Then I try to multiple two complex numbers. but I find I can not understand how to assure the data after mult is still 32 bits, I must have a complex number(64 bits im and 64 bits re) to store data, then when I do ifft, the coefficients of poly become 64 bits?

Hello @yyf,

Could you give us a bit more context on your issue.
Are you trying to modify tfhe-rs code or doing your own code?

Tried reasoning it this way ,looking for others clarification as well

Thank you very much, and can you give me your email, so I can ask for guidance to you.