Can the MSB (Most Significant Bit) be set in advance in CKKSRNS Bootstrapping?

Library Questions
1

Hi, I’m currently conducting calculations using CKKS Bootstrapping and evaluating performance. I’m interested in observing performance differences when defining the precision of decimal places in advance. For example, I have the number 5.7811581611561, and I want to see the differences when the most significant bit (MSB) is at positions 2, 4, 6, and 8. Does anyone know how to realize this? Thank you very much.

The input parameters sets I’m evaluating for my benchmark are as follows:

  • Rescaling Mode (FIXEDAUTO, FLEXIBLEAUTO, FLEXIBLEAUTOEXT)
  • Batchsize (8, 16, 32, 64, 128 bits)
  • ScaleModSize (49, 54, 59)
  • FirstModSize (50, 55, 60)
  • Ring Dimension (1024, 2048, 4096, 8192, 16384)
2

I am not sure I understand the question:

For example, I have the number 5.7811581611561, and I want to see the differences when the most significant bit (MSB) is at positions 2, 4, 6, and 8.

In general, the precision of CKKS bootstrapping depends on the message size (it is better to have the message in the range [-1,1] to get the best precision after bootstrapping). Internally the modular reduction is approximated using a sine wave, which works well for small values of the argument, where the sine wave is close to a linear function. Under the hood, OpenFHE scales down the message by 10 bits or so to get best modular reduction approximation.