This page documents library components that are all basically just implementations of mathematical functions or algorithms that don't fit in any of the other pages of the dlib documentation. So this includes things like checksums, cryptographic hashes, sorting, etc.
This implementation is done using an array of unsigned shorts. It is also reference counted. For further details see the above link. Also note that kernel_2 should be faster in almost every case so you should really just use that version of the bigint object.
kernel_1a is a typedef for bigint_kernel_1 kernel_1a_c is a typedef for kernel_1a that checks its preconditions.
This implementation is basically the same as kernel_1 except it uses the Fast Fourier Transform to perform multiplications much faster.
kernel_2a is a typedef for bigint_kernel_2 kernel_2a_c is a typedef for kernel_2a that checks its preconditions.
An Introduction to the Kalman Filter by Greg Welch and Gary Bishop