simplify norm computations. (#43190)

* simplify norm computations.

stdlib/LinearAlgebra/src/generic.jl

@@ -449,45 +449,11 @@ diag(A::AbstractVector) = throw(ArgumentError("use diagm instead of diag to cons
 # Dot products and norms
 
 # 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(v)
-    while true
-        y = iterate(x, s)
-        y === nothing && break
-        (v, s) = y
-        vnorm = norm(v)
-        minabs = ifelse(isnan(minabs) | (minabs < vnorm), minabs, vnorm)
-    end
-    return float(minabs)
-end
+generic_normMinusInf(x) = float(mapreduce(norm, min, x))
 
-function generic_normInf(x)
-    (v, s) = iterate(x)::Tuple
-    maxabs = norm(v)
-    while true
-        y = iterate(x, s)
-        y === nothing && break
-        (v, s) = y
-        vnorm = norm(v)
-        maxabs = ifelse(isnan(maxabs) | (maxabs > vnorm), maxabs, vnorm)
-    end
-    return float(maxabs)
-end
+generic_normInf(x) = float(mapreduce(norm, max, x))
 
-function generic_norm1(x)
-    (v, s) = iterate(x)::Tuple
-    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(v)
-    end
-    return convert(T, sum)
-end
+generic_norm1(x) = mapreduce(float ∘ norm, +, x)
 
 # faster computation of norm(x)^2, avoiding overflow for integers
 norm_sqr(x) = norm(x)^2