From 82ea33ea2ebeefdae7e41ecd6cf5dfa42a613f45 Mon Sep 17 00:00:00 2001
From: chriswaudby <cwaudby@gmail.com>
Date: Sun, 9 Jul 2023 16:50:55 +0100
Subject: [PATCH] Add rtol and norm to implement isapprox

---
 README.md   |  1 +
 src/base.jl | 18 ++++++++++++++++++
 2 files changed, 19 insertions(+)

diff --git a/README.md b/README.md
index 48ce3bf..0650278 100644
--- a/README.md
+++ b/README.md
@@ -20,6 +20,7 @@ Multicomplex numbers are a generalisation of complex numbers, recursively define
 ## TODO
 
 * FFT
+* The comparison `exp(0im1) == 1.` throws a TypeError
 
 
 ## useful links (notes to self for development)
diff --git a/src/base.jl b/src/base.jl
index 5d3533c..7d7487d 100644
--- a/src/base.jl
+++ b/src/base.jl
@@ -119,6 +119,20 @@ Base.widen(::Type{Multicomplex{T,N,C}}) where {T,N,C} = Multicomplex{widen(T),N,
 Base.float(::Type{Multicomplex{T,N,C}}) where {T<:AbstractFloat,N,C} = Multicomplex{T,N,C}
 Base.float(::Type{Multicomplex{T,N,C}}) where {T,N,C} = Multicomplex{float(T),N,C}
 
+Base.rtoldefault(::Type{Multicomplex{T,N,C}}) where {T,N,C} = Base.rtoldefault(T)
+Base.rtoldefault(::Multicomplex{T,N,C}) where {T,N,C} = Base.rtoldefault(T)
+function Base.rtoldefault(x::Union{T,Type{T}}, y::Union{S,Type{S}}, atol::Real) where {T<:Multicomplex,S<:Number}
+    rtol = max(Base.rtoldefault(T),Base.rtoldefault(real(S)))
+    return atol > 0 ? zero(rtol) : rtol
+end
+function Base.rtoldefault(x::Union{T,Type{T}}, y::Union{S,Type{S}}, atol::Real) where {T<:Number,S<:Multicomplex}
+    rtol = max(Base.rtoldefault(real(T)),Base.rtoldefault(S))
+    return atol > 0 ? zero(rtol) : rtol
+end
+function Base.rtoldefault(x::Union{T,Type{T}}, y::Union{S,Type{S}}, atol::Real) where {T<:Multicomplex,S<:Multicomplex}
+    rtol = max(Base.rtoldefault(T),Base.rtoldefault(S))
+    return atol > 0 ? zero(rtol) : rtol
+end
 
 ##############
 # Components #
@@ -158,6 +172,10 @@ Base.iszero(m::Multicomplex) = all(iszero.(m.value))
 Base.isone(m::Multicomplex) = isreal(m) && isone(m.value[1])
 
 
+"""Norm is sum of squares of components"""
+LinearAlgebra.norm(m::Multicomplex) = norm(m.value)
+
+
 ##########
 # Traits #
 ##########