 Descending boundary search

For a nonincreasing array, maintain indices $0\le a\le b\le n$ such that entries before $a$ exceed the target and entries from $b$ onward are at most the target. Probe the middle of the half-open interval. A value above the target advances $a$ past that index; otherwise set $b$ to that index. The interval length decreases geometrically. At termination the common boundary is the first possible match, so one guarded equality test decides presence even with duplicates.