  We present the results of a survey for stellar and substellar companions to
82 young stars in the nearby OB association Upper Scorpius. This survey used
nonredundant aperture-mask interferometry to achieve typical contrast limits of
DeltaK~5-6 at the diffraction limit, revealing 12 new binary companions that
lay below the detection limits of traditional high-resolution imaging; we also
summarize a complementary snapshot imaging survey that discovered 7 directly
resolved companions. The overall frequency of binary companions (~35+5/-4% at
separations of 6-435 AU) appears to be equivalent to field stars of similar
mass, but companions could be more common among lower-mass stars than for the
field. The companion mass function has statistically significant differences
compared to several suggested mass functions for the field, and we suggest an
alternate log-normal parameterization of the mass-function. Our survey limits
encompass the entire brown dwarf mass range, but we only detected a single
companion that might be a brown dwarf; this deficit resembles the so-called
``brown dwarf desert'' that has been observed by radial-velocity planet
searches. Finally, our survey's deep detection limits extend into the top of
the planetary mass function, reaching 8-12 MJup for half of our sample. We have
not identified any planetary companions at high confidence (>99.5%), but we
have identified four candidate companions at lower confidence (>97.5%) that
merit additional followup to confirm or disprove their existence.
