From 67a0774144dde4ac0098c8fc47663d2e0ea526f1 Mon Sep 17 00:00:00 2001
From: Yuto Horikawa <hyrodium@gmail.com>
Date: Sat, 10 Sep 2022 16:42:41 +0900
Subject: [PATCH] Faster knotvector addition (#279)

* improve KnotVector addition speed

* add comments

* faster *(::Integer, ::KnotVector)

* remove unnecessary copy
---
 src/_EmptyKnotVector.jl |  5 +++++
 src/_KnotVector.jl      | 44 +++++++++++++++++++++++++++++++++++++----
 2 files changed, 45 insertions(+), 4 deletions(-)

diff --git a/src/_EmptyKnotVector.jl b/src/_EmptyKnotVector.jl
index ab78b7296..364ee38f5 100644
--- a/src/_EmptyKnotVector.jl
+++ b/src/_EmptyKnotVector.jl
@@ -45,6 +45,11 @@ Base.:+(::EmptyKnotVector{T1}, ::EmptyKnotVector{T2}) where {T1<:Real, T2<:Real}
 # + swap
 Base.:+(k1::EmptyKnotVector, k2::AbstractKnotVector) = k2 + k1
 
+function Base.:*(m::Integer, k::EmptyKnotVector) where T
+    m < 0 && throw(DomainError(m, "The number to be multiplied must be non-negative."))
+    return k
+end
+
 function Base.show(io::IO, ::T) where T<:EmptyKnotVector
     print(io, "$(T)()")
 end
diff --git a/src/_KnotVector.jl b/src/_KnotVector.jl
index 79cf7242c..1380286e9 100644
--- a/src/_KnotVector.jl
+++ b/src/_KnotVector.jl
@@ -84,7 +84,33 @@ julia> k1 + k2
 KnotVector([1, 2, 3, 4, 5, 5, 8])
 ```
 """
-Base.:+(k1::KnotVector{T}, k2::KnotVector{T}) where T = unsafe_knotvector(T,sort!(vcat(k1.vector,k2.vector)))
+function Base.:+(k1::KnotVector{T}, k2::KnotVector{T}) where T
+    v1, v2 = k1.vector, k2.vector
+    n1, n2 = length(v1), length(v2)
+    iszero(n1) && return k2
+    iszero(n2) && return k1
+    n = n1 + n2
+    v = Vector{T}(undef, n)
+    i1 = i2 = 1
+    for i in 1:n
+        if isless(v1[i1], v2[i2])
+            v[i] = v1[i1]
+            i1 += 1
+            if i1 > n1
+                v[i+1:n] = view(v2, i2:n2)
+                break
+            end
+        else
+            v[i] = v2[i2]
+            i2 += 1
+            if i2 > n2
+                v[i+1:n] = view(v1, i1:n1)
+                break
+            end
+        end
+    end
+    return BasicBSpline.unsafe_knotvector(T,v)
+end
 Base.:+(k1::AbstractKnotVector, k2::AbstractKnotVector) = +(promote(k1,k2)...)
 
 @doc raw"""
@@ -106,15 +132,25 @@ julia> 2 * k
 KnotVector([1, 1, 2, 2, 2, 2, 5, 5])
 ```
 """
-function Base.:*(m::Integer, k::AbstractKnotVector)
+function Base.:*(m::Integer, k::KnotVector{T}) where T
     if m == 0
         return zero(k)
-    elseif m > 0
-        return sum(k for _ in 1:m)
+    elseif m == 1
+        return k
+    elseif m > 1
+        n = length(k)
+        v = Vector{T}(undef, m*n)
+        for i in 1:m
+            v[i:m:m*(n-1)+i] .= k.vector
+        end
+        return BasicBSpline.unsafe_knotvector(T,v)
     else
         throw(DomainError(m, "The number to be multiplied must be non-negative."))
     end
 end
+function Base.:*(m::Integer, k::AbstractKnotVector) where T
+    return m*KnotVector(k)
+end
 Base.:*(k::AbstractKnotVector, m::Integer) = m*k
 
 Base.in(r::Real, k::AbstractKnotVector) = in(r, _vec(k))