I think you're off by the 113 billion number and the year 2050. The U.N. estimates 11.2 billion around 2100. Also, current anthropology fossil research puts modern homo sapiens sapiens ("Homo sapiens" is a broad term that includes other extinct sapiens subspecies. The extra "sapiens' designates the modern man subspecies).
If you assume humans continue technological advancement a population of a trillion humans could easily be possible when Kardashev scale Type II level is reached.
I have an anthropology community I'll cross-post this to. You are welcome to join if this kind of thing interests you.