Merge pull request #70 from milankl/mk/eps

eps, ^, sinpi, cospi, sincospi,

README.md

@@ -72,5 +72,5 @@ julia> floatmin(Posit16)*floatmin(Posit16)
 Posit16(1.3877788e-17)
 ```
 and similar for other posit formats.
-So in Posit16 arithmetic we have `1e-17*1e-17 = 1e-17` and `1e17*1e17 = 1e17` (no overflow).
+So in Posit16 arithmetic we have `1e-17*1e-17 = 1e-17` (no underflow) and `1e17*1e17 = 1e17` (no overflow).
 

src/arithmetics.jl

@@ -12,21 +12,22 @@ function Base.sign(x::T) where {T<:AbstractPosit}
 end
 
 # TWO ARGUMENT ARITHMETIC, addition, subtraction, multiplication, division via conversion
-for op in (:(+), :(-), :(*), :(/))
+for op in (:(+), :(-), :(*), :(/), :(^))
     @eval begin
         Base.$op(x::T,y::T) where {T<:AbstractPosit} = convert(T,$op(float(x),float(y)))
     end
 end
 
 # ONE ARGUMENT ARITHMETIC, sqrt, exp, log, etc. via conversion
 for op in (:sqrt, :exp, :exp2, :exp10, :expm1, :log, :log2, :log10, :log1p,
-            :sin, :cos, :tan)
+            :sin, :cos, :tan, :sinpi, :cospi)
     @eval begin
         Base.$op(x::T) where {T<:AbstractPosit} = convert(T,$op(float(x)))
     end
 end
 
 Base.sincos(x::AbstractPosit) = sin(x),cos(x)   # not in eval loop because of convert
+Base.sincospi(x::AbstractPosit) = sinpi(x),cospi(x)   # not in eval loop because of convert
 
 # complex trigonometric functions
 for P in (:Posit8, :Posit16, :Posit16_1, :Posit32)
@@ -38,12 +39,13 @@ for P in (:Posit8, :Posit16, :Posit16_1, :Posit32)
 end
 
 # nextfloat, prevfloat have a wrap-around behaviour nextfloat(maxpos) = NaR, nextfloat(NaR) = -maxpos
+# which closes the posit circle and follow the 2022 standard
 Base.nextfloat(x::T) where {T<:AbstractPosit} = reinterpret(T,reinterpret(Base.uinttype(T),x)+one(Base.uinttype(T)))
 Base.prevfloat(x::T) where {T<:AbstractPosit} = reinterpret(T,reinterpret(Base.uinttype(T),x)-one(Base.uinttype(T)))
 
 # precision (taken from lookup table)
-eps(::Type{Posit8}) = reinterpret(Posit8,0x28)
-eps(::Type{Posit16}) = reinterpret(Posit16,0x0a00)
-eps(::Type{Posit16_1}) = reinterpret(Posit16_1,0x0100)
-eps(::Type{Posit32}) = reinterpret(Posit32,0x00a0_0000)
-eps(x::AbstractPosit) = max(x-prevfloat(x),nextfloat(x)-x)
+Base.eps(::Type{Posit8}) = reinterpret(Posit8,0x28)
+Base.eps(::Type{Posit16}) = reinterpret(Posit16,0x0a00)
+Base.eps(::Type{Posit16_1}) = reinterpret(Posit16_1,0x0100)
+Base.eps(::Type{Posit32}) = reinterpret(Posit32,0x00a0_0000)
+Base.eps(x::AbstractPosit) = max(x-prevfloat(x),nextfloat(x)-x)

src/conversions.jl

@@ -10,9 +10,6 @@ Base.inttype(::Type{Posit16}) = Int16
 Base.inttype(::Type{Posit16_1}) = Int16
 Base.inttype(::Type{Posit32}) = Int32
 
-positype(::Type{Float16}) = Posit16
-positype
-
 # generic conversion to UInt/Int
 Base.unsigned(x::AbstractPosit) = reinterpret(Base.uinttype(typeof(x)),x)
 Base.signed(x::AbstractPosit) = reinterpret(Base.inttype(typeof(x)),x)
@@ -42,6 +39,12 @@ Posit8(x::Posit16) = posit(Posit8,x)
 Posit8(x::Posit32) = posit(Posit8,x)
 Posit16(x::Posit32) = posit(Posit16,x)
 
+# conversion to and from Posit16_1 via floats as number of exponent bits changes
+Posit16_1(x::AbstractPosit) = Posit16_1(float(x))
+Posit8(x::Posit16_1) = Posit8(float(x))
+Posit16(x::Posit16_1) = Posit16(float(x))
+Posit32(x::Posit16_1) = Posit32(float(x))
+
 function posit(::Type{PositN1},x::PositN2) where {PositN1<:AbstractPosit,PositN2<:AbstractPosit}
     return reinterpret(PositN1,bitround(Base.uinttype(PositN1),unsigned(x)))
 end