The reason for asking, is that this occurs in real life with CRT calculation of RSA decryption/signing. In CRT RSA, there's the need to calculate subtraction, and it's known negative numbers could occur, especially with multi-prime cases.
While RSA would eventually phase out when moderately-sized quantum computers are available, before QCs can reach that scale, scaling RSA parameters (especially towards using more primes) may be more feasible than rushing to adopt post-quantum schemes in the short term, therefore, it's still a bit relevant.
While it's easy to to do modular arithmetic in variable-time, it seems very difficult do it in constant-time and with limited space for holding working variables.
Q1: Is there a way to implement efficient constant-time modular arithmetic for signed two's-comlement integers in constant time?
Additional Q2 for refuting the use of such implementation: Is there alternative methods for computing CRT RSA decryption/signing that uses no more (or even less) number of working variables? (these "working variables" are big integers).