  We present a novel application of the machine learning / artificial
intelligence method called boosted decision trees to estimate physical
quantities on field programmable gate arrays (FPGA). The software package
fwXmachina features a new architecture called parallel decision paths that
allows for deep decision trees with arbitrary number of input variables. It
also features a new optimization scheme to use different numbers of bits for
each input variable, which produces optimal physics results and ultraefficient
FPGA resource utilization. Problems in high energy physics of proton collisions
at the Large Hadron Collider (LHC) are considered. Estimation of missing
transverse momentum (ETmiss) at the first level trigger system at the High
Luminosity LHC (HL-LHC) experiments, with a simplified detector modeled by
Delphes, is used to benchmark and characterize the firmware performance. The
firmware implementation with a maximum depth of up to 10 using eight input
variables of 16-bit precision gives a latency value of O(10) ns, independent of
the clock speed, and O(0.1)% of the available FPGA resources without using
digital signal processors.
