quoted

+     const size_t num = ctx->num % POLY1305_BLOCK_SIZE;

0 <= ctx->num < POLY1305_BLOCK_SIZE, so no need to mod by POLY1305_BLOCK_SIZE.

quoted

+     size_t num = ctx->num % POLY1305_BLOCK_SIZE;

Same here.

I know, but I was having a hard time convincing gcc-8 of that
invariant, and it was warning me. Perhaps this is something they
fixed, though, between 8.1 and 8.2 though. I'll check back and adjust
accordingly.