about 816 in his Computus. An English translation of Dicuil's account is available.

Occasionally it is necessary to compute large triangular numbers where the standard formula t = n*(n+1)/2 would suffer integer overflow before the final division by 2. For example, = 210 < 256, so will fit into an 8-bit byte, but not the intermediate product 420. This can be solved by dividing either or by 2 before the multiplication, whichever is even. This does not require a conditional branch if implemented as t = (n|1) * ((n+1)/2). If n is odd, the binary OR operation n|1 has no effect, so this is equivalent to t = n * ((n+1)/2) and thus correct. If n is even, setting the low bit with n|1 is the same as adding 1, while the 1 added before the division is truncated away, so this is equivalent to t = (n+1) * (n/2) and also correct.