Functions for BFloat16

Project.toml

@@ -5,3 +5,4 @@ version = "0.1.0"
 
 [deps]
 LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
+Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"

src/bfloat16.jl

@@ -1,10 +1,9 @@
 import Base: isfinite, isnan, precision, iszero,
     sign_mask, exponent_mask, exponent_one, exponent_half,
     significand_mask,
-    +, -, *, /
+    +, -, *, /, ^
 
 primitive type BFloat16 <: AbstractFloat 16 end
-BFloat16(x::Integer) = convert(BFloat16, convert(Float32, x))
 
 # Floating point property queries
 for f in (:sign_mask, :exponent_mask, :exponent_one,
@@ -46,21 +45,38 @@ function BFloat16(x::Float32)
     return reinterpret(BFloat16, (h >> 16) % UInt16)
 end
 
+# Conversion from Float64
+function BFloat16(x::Float64)
+	BFloat16(Float32(x))
+end
+
+# Conversion from Integer
+function BFloat16(x::Integer)
+	convert(BFloat16, convert(Float32, x))
+end
+
 # Expansion to Float32
 function Base.Float32(x::BFloat16)
     reinterpret(Float32, UInt32(reinterpret(UInt16, x)) << 16)
 end
 
+# Expansion to Float64
+function Base.Float64(x::BFloat16)
+    Float64(Float32(x))
+end
+
 # Truncation to integer types
 Base.unsafe_trunc(T::Type{<:Integer}, x::BFloat16) = unsafe_trunc(T, Float32(x))
 
 # Basic arithmetic
-for f in (:+, :-, :*, :/)
-    @eval ($f)(a::BFloat16, b::BFloat16) = BFloat16($(f)(Float32(a), Float32(b)))
+for f in (:+, :-, :*, :/, :^)
+    @eval ($f)(x::BFloat16, y::BFloat16) = BFloat16($(f)(Float32(x), Float32(y)))
 end
 -(x::BFloat16) = reinterpret(BFloat16, reinterpret(UInt16, x) ⊻ sign_mask(BFloat16))
+abs(x::BFloat16) = reinterpret(BFloat16, reinterpret(UInt16, x) & 0x7fff)
+Base.sqrt(x::BFloat16) = BFloat16(sqrt(Float32(x)))
 
-# Floating point comparisoin
+# Floating point comparison
 function Base.:(==)(x::BFloat16, y::BFloat16)
     ix = reinterpret(UInt16, x)
     iy = reinterpret(UInt16, y)
@@ -75,11 +91,31 @@ function Base.:(==)(x::BFloat16, y::BFloat16)
     return ix == iy
 end
 
+function Base.:(<)(x::BFloat16, y::BFloat16)
+	return Float32(x) < Float32(y)
+end
+
+function Base.:(<=)(x::BFloat16, y::BFloat16)
+	return Float32(x) <= Float32(y)
+end
+
+function Base.:(>)(x::BFloat16, y::BFloat16)
+	return Float32(x) > Float32(y)
+end
+
+function Base.:(>=)(x::BFloat16, y::BFloat16)
+	return Float32(x) >= Float32(y)
+end
+
 Base.widen(::Type{BFloat16}) = Float32
 Base.promote_rule(::Type{Float32}, ::Type{BFloat16}) = Float32
+Base.promote_rule(::Type{Float64}, ::Type{BFloat16}) = Float64
+for t in (Int8, Int16, Int32, Int64, Int128, UInt8, UInt16, UInt32, UInt64, UInt128)
+    @eval Base.promote_rule(::Type{BFloat16}, ::Type{$t}) = BFloat16
+end
 
 # Wide multiplication
-Base.widemul(a::BFloat16, b::BFloat16) = Float32(a) * Float32(b)
+Base.widemul(x::BFloat16, y::BFloat16) = Float32(x) * Float32(y)
 
 # Showing
 function Base.show(io::IO, x::BFloat16)

test/runtests.jl

@@ -0,0 +1,19 @@
+using Test, BFloat16s
+
+@test BFloat16(1)   <  BFloat16(2)
+@test BFloat16(1f0) <  BFloat16(2f0)
+@test BFloat16(1.0) <  BFloat16(2.0)
+@test BFloat16(1)   <= BFloat16(2)
+@test BFloat16(1f0) <= BFloat16(2f0)
+@test BFloat16(1.0) <= BFloat16(2.0)
+@test BFloat16(2)   >  BFloat16(1)
+@test BFloat16(2f0) >  BFloat16(1f0)
+@test BFloat16(2)   >= BFloat16(1)
+@test BFloat16(2f0) >= BFloat16(1f0)
+@test BFloat16(2.0) >= BFloat16(1.0)
+
+@test abs(BFloat16(-10)) == BFloat16(10)
+@test Float32(BFloat16(10)) == 1f1
+@test Float64(BFloat16(10)) == 10.0
+@test BFloat16(2) ^ BFloat16(4) == BFloat16(16)
+@test sqrt(BFloat16(4f0)) == BFloat16(2f0)