Removing requirement for promotions from 0,1 in lufact (#22146)

* Removing requirement for promotions from 0,1

* Using iszero() and added test

* Tidy up spaces, tabs etc

Author: arghhhh

base/linalg/generic.jl

@@ -957,7 +957,7 @@ true
 function istriu(A::AbstractMatrix)
     m, n = size(A)
     for j = 1:min(n,m-1), i = j+1:m
-        if A[i,j] != 0
+        if !iszero(A[i,j])
             return false
         end
     end
@@ -992,7 +992,7 @@ true
 function istril(A::AbstractMatrix)
     m, n = size(A)
     for j = 2:n, i = 1:min(j-1,m)
-        if A[i,j] != 0
+        if !iszero(A[i,j])
             return false
         end
     end

base/linalg/lu.jl

@@ -39,7 +39,7 @@ function generic_lufact!(A::StridedMatrix{T}, ::Type{Val{Pivot}} = Val{true}) wh
             # find index max
             kp = k
             if Pivot
-                amax = real(zero(T))
+                amax = abs(zero(T))
                 for i = k:m
                     absi = abs(A[i,k])
                     if absi > amax
@@ -49,7 +49,7 @@ function generic_lufact!(A::StridedMatrix{T}, ::Type{Val{Pivot}} = Val{true}) wh
                 end
             end
             ipiv[k] = kp
-            if A[kp,k] != 0
+            if !iszero(A[kp,k])
                 if k != kp
                     # Interchange
                     for i = 1:n

test/linalg/generic.jl

@@ -310,3 +310,33 @@ end
 @test [[1, 2], [3, 4]] ≈ [[1.0-eps(), 2.0+eps()], [3.0+2eps(), 4.0-1e8eps()]]
 @test [[1, 2], [3, 4]] ≉ [[1.0-eps(), 2.0+eps()], [3.0+2eps(), 4.0-1e9eps()]]
 @test [[1,2, [3,4]], 5.0, [6im, [7.0, 8.0]]] ≈ [[1,2, [3,4]], 5.0, [6im, [7.0, 8.0]]]
+
+# Issue 22042
+# Minimal modulo number type - but not subtyping Number
+struct ModInt{n}
+    k
+    ModInt{n}(k) where {n} = new(mod(k,n))
+end
+
+Base.:+(a::ModInt{n}, b::ModInt{n}) where {n} = ModInt{n}(a.k + b.k)
+Base.:-(a::ModInt{n}, b::ModInt{n}) where {n} = ModInt{n}(a.k - b.k)
+Base.:*(a::ModInt{n}, b::ModInt{n}) where {n} = ModInt{n}(a.k * b.k)
+Base.:-(a::ModInt{n}) where {n} = ModInt{n}(-a.k)
+Base.inv(a::ModInt{n}) where {n} = ModInt{n}(invmod(a.k, n))
+Base.:/(a::ModInt{n}, b::ModInt{n}) where {n} = a*inv(b)
+
+Base.zero(::Type{ModInt{n}}) where {n} = ModInt{n}(0)
+Base.zero(::ModInt{n}) where {n} = ModInt{n}(0)
+Base.one(::Type{ModInt{n}}) where {n} = ModInt{n}(1)
+Base.one(::ModInt{n}) where {n} = ModInt{n}(1)
+
+# Needed for pivoting:
+Base.abs(a::ModInt{n}) where {n} = a
+Base.:<(a::ModInt{n}, b::ModInt{n}) where {n} = a.k < b.k
+Base.transpose(a::ModInt{n}) where {n} = a  # see Issue 20978
+
+A = [ ModInt{2}(1) ModInt{2}(0) ; ModInt{2}(1) ModInt{2}(1) ]
+b = [ ModInt{2}(1), ModInt{2}(0) ]
+
+@test A*(A\b) == b
+@test_nowarn lufact( A, Val{true} )