diff --git a/Project.toml b/Project.toml
index de04aeb..15e4b3e 100644
--- a/Project.toml
+++ b/Project.toml
@@ -1,6 +1,6 @@
 name = "BFloat16s"
 uuid = "ab4f0b2a-ad5b-11e8-123f-65d77653426b"
-authors = ["Keno Fischer <keno@alumni.harvard.edu>"]
+authors = ["Keno Fischer <keno@alumni.harvard.edu>", "Jeffrey Sarnoff <jeffrey.sarnoff@gmail.com>"]
 version = "0.5.1"
 
 [deps]
diff --git a/README.md b/README.md
index 1177cce..7cf0f50 100644
--- a/README.md
+++ b/README.md
@@ -36,34 +36,27 @@ a method for `BFloat16` although it should. In this case, please raise an issue
 close the gap in support compared to other low-precision types like `Float16`. The usage
 of `BFloat16` should be as smooth as the following example, solving a linear equation system
 
-```julia
-julia> A = randn(BFloat16,3,3)
-3×3 Matrix{BFloat16}:
-  1.46875   -1.20312   -1.0
-  0.257812  -0.671875  -0.929688
- -0.410156  -1.75      -0.0162354
-
-julia> b = randn(BFloat16,3)
-3-element Vector{BFloat16}:
- -0.26367188
- -0.14160156
-  0.77734375
-
-julia> A\b
-3-element Vector{BFloat16}:
- -0.24902344
- -0.38671875
-  0.36328125
+This package exports the BFloat16 data type. This datatype should behave
+just like any builtin floating point type (e.g. you can construct it from
+other floating point types - e.g. `BFloat16(1.0)`). Many predicates, 
+conversion, structural and mathematical functions are supported:
+```
+ Int16, Int32, Int64, Float16, Float32, Float64, +, -, *, /, ^, ==, <, <=, >=, >, !=, inv,
+ isfinite, isnan, precision, iszero, eps, typemin, typemax, floatmin, floatmax,
+ sign_mask, exponent_mask, significand_mask, exponent_bits, significand_bits, exponent_bias,
+ signbit, exponent, significand, frexp, ldexp, exponent_one, exponent_half,
+ exp, exp2, exp10, expm1, log, log2, log10, log1p,
+ sin, cos, tan, csc, sec, cot, asin, acos, atan, acsc, asec, acot,
+ sinh, cosh, tanh, csch, sech, coth, asinh, acosh, atanh, acsch, asech, acoth,
+ round, trunc, floor, ceil, abs, abs2, sqrt, cbrt, clamp, hypot, bitstring
 ```
 
-## `LowPrecArray` for mixed-precision Float32/BFloat16 matrix multiplications
+In addition, this package provides the `LowPrecArray` type. This array is 
+supposed to emulate the kind of matmul operation that TPUs do well
+(BFloat16 multiply with Float32 accumulate). Broadcasts and scalar operations
+are peformed in Float32 (as they would be on a TPU) while matrix multiplies
+are performed in BFloat16 with Float32 accumulates, e.g.
 
-In addition, this package provides the `LowPrecArray` type.
-This array is supposed to emulate the kind
-of matrix multiplications that TPUs do well (BFloat16 multiply with Float32
-accumulate). Broadcasts and scalar operations are peformed in Float32 (as
-they would be on a TPU) while matrix multiplies are performed in BFloat16 with
-Float32 accumulates, e.g.
 
 ```julia
 julia> A = LowPrecArray(rand(Float32, 5, 5))
diff --git a/src/bfloat16.jl b/src/bfloat16.jl
index 0b3e8e0..1b234a2 100644
--- a/src/bfloat16.jl
+++ b/src/bfloat16.jl
@@ -13,6 +13,7 @@ import Base: isfinite, isnan, precision, iszero, eps,
     asin, acos, atan, acsc, asec, acot,
     sinh, cosh, tanh, csch, sech, coth,
     asinh, acosh, atanh, acsch, asech, acoth,
+    clamp, hypot,
     bitstring, isinteger
 
 import Printf
@@ -222,6 +223,13 @@ else
     end
 end
 
+# accept Irrational
+BFloat16s.BFloat16(x::Irrational) = BFloat16(Float32(x))
+
+# Truncation to integer types
+Base.unsafe_trunc(T::Type{<:Integer}, x::BFloat16) = unsafe_trunc(T, Float32(x))
+Base.trunc(::Type{T}, x::BFloat16) where {T<:Integer} = trunc(T, Float32(x))
+
 # BigFloat conversion
 BFloat16(x::BigFloat) = BFloat16(Float32(x))
 Base.BigFloat(x::BFloat16) = BigFloat(Float32(x))
@@ -424,3 +432,10 @@ for F in (:abs, :abs2, :sqrt, :cbrt,
      Base.$F(x::BFloat16) = BFloat16($F(Float32(x)))
   end
 end
+
+Base.atan(y::BFloat16, x::BFloat16) = BFloat16(atan(Float32(y), Float32(x)))
+Base.hypot(x::BFloat16, y::BFloat16) = BFloat16(hypot(Float32(x), Float32(y)))
+Base.hypot(x::BFloat16, y::BFloat16, z::BFloat16) = BFloat16(hypot(Float32(x), Float32(y), Float32(z)))
+Base.clamp(x::BFloat16, lo::BFloat16, hi::BFloat16) = BFloat16(clamp(Float32(x), Float32(lo), Float32(hi)))
+
+Base.bitstring(x::BFloat16) = bitstring(reinterpret(UInt16, x))