Added AbstractFloat for Quaternion Type

stdlib/LinearAlgebra/src/generic.jl

@@ -273,40 +273,40 @@ diag(A::AbstractVector) = throw(ArgumentError("use diagm instead of diag to cons
 # special cases of norm; note that they don't need to handle isempty(x)
 function generic_normMinusInf(x)
  (v, s) = iterate(x)::Tuple
- minabs = norm(float(v))
+ minabs = norm(v)
  while true
  y = iterate(x, s)
  y === nothing && break
  (v, s) = y
- vnorm = norm(float(v))
+ vnorm = norm(v)
  minabs = ifelse(isnan(minabs) | (minabs < vnorm), minabs, vnorm)
  end
  return float(minabs)
 end
 
 function generic_normInf(x)
  (v, s) = iterate(x)::Tuple
- maxabs = norm(float(v))
+ maxabs = norm(v)
  while true
  y = iterate(x, s)
  y === nothing && break
  (v, s) = y
- vnorm = norm(float(v))
+ vnorm = norm(v)
  maxabs = ifelse(isnan(maxabs) | (maxabs > vnorm), maxabs, vnorm)
  end
  return float(maxabs)
 end
 
 function generic_norm1(x)
  (v, s) = iterate(x)::Tuple
- av = float(norm(float(v)))
+ av = float(norm(v))
  T = typeof(av)
  sum::promote_type(Float64, T) = av
  while true
  y = iterate(x, s)
  y === nothing && break
  (v, s) = y
- sum += norm(float(v))
+ sum += norm(v)
  end
  return convert(T, sum)
 end
@@ -331,12 +331,12 @@ function generic_norm2(x)
  end
  return convert(T, sqrt(sum))
  else
- sum = abs2(norm(float(v))/maxabs)
+ sum = abs2(norm(v)/maxabs)
  while true
  y = iterate(x, s)
  y === nothing && break
  (v, s) = y
- sum += (norm(float(v))/maxabs)^2
+ sum += (norm(v)/maxabs)^2
  end
  return convert(T, maxabs*sqrt(sum))
  end
@@ -355,21 +355,21 @@ function generic_normp(x, p)
  end
  spp::promote_type(Float64, T) = p
  if -1 <= p <= 1 || (isfinite(length(x)*maxabs^spp) && maxabs^spp != 0) # scaling not necessary
- sum::promote_type(Float64, T) = norm(float(v))^spp
+ sum::promote_type(Float64, T) = norm(v)^spp
  while true
  y = iterate(x, s)
  y === nothing && break
  (v, s) = y
- sum += norm(float(v))^spp
+ sum += norm(v)^spp
  end
  return convert(T, sum^inv(spp))
  else # rescaling
- sum = (norm(float(v))/maxabs)^spp
+ sum = (norm(v)/maxabs)^spp
  while true
  y = iterate(x, s)
  y == nothing && break
  (v, s) = y
- sum += (norm(float(v))/maxabs)^spp
+ sum += (norm(v)/maxabs)^spp
  end
  return convert(T, maxabs*sum^inv(spp))
  end
@@ -487,7 +487,7 @@ julia> norm(-2, Inf)
 2
 ```
 """
-@inline norm(x::Number, p::Real=2) = p == 0 ? (x==0 ? zero(abs(x)) : oneunit(abs(x))) : abs(x)
+@inline norm(x::Number, p::Real=2) = p == 0 ? (x==0 ? zero(abs(float(x))) : oneunit(abs(float(x)))) : abs(float(x))
 norm(::Missing, p::Real=2) = missing
 
 # special cases of opnorm

test/testhelpers/Quaternions.jl

@@ -12,6 +12,7 @@ struct Quaternion{T<:Real} <: Number
 end
 Quaternion(s::Real, v1::Real, v2::Real, v3::Real) = Quaternion(promote(s, v1, v2, v3)...)
 Base.abs2(q::Quaternion) = q.s*q.s + q.v1*q.v1 + q.v2*q.v2 + q.v3*q.v3
+Base.AbstractFloat(q::Quaternion) = Quaternion(float(q.s), float(q.v1), float(q.v2), float(q.v3))
 Base.abs(q::Quaternion) = sqrt(abs2(q))
 Base.real(::Type{Quaternion{T}}) where {T} = T
 Base.conj(q::Quaternion) = Quaternion(q.s, -q.v1, -q.v2, -q.v3)