Add function for machine precision number to avoid expensive calculat…

…ion in the Givens rotation algorithms. Remove subtype relation to AbstractMatrix and therefore also the now unnecessary ambiguity warning avoiding method definitions. Use @simd and @inbounds in methods for applying Givens rotations.

base/linalg/givens.jl

@@ -1,5 +1,4 @@
-immutable Givens{T} <: AbstractMatrix{T}
-    size::Int
+immutable Givens{T}
     i1::Int
     i2::Int
     c::T
@@ -11,14 +10,18 @@ type Rotation{T}
 end
 typealias AbstractRotation Union(Givens, Rotation)
 
+realmin2(::Type{Float32}) = reinterpret(Float32, 0x26000000)
+realmin2(::Type{Float64}) = reinterpret(Float64, 0x21a0000000000000)
+realmin2{T}(::Type{T}) = (twopar = 2one(T); twopar^itrunc(log(realmin(T)/eps(T))/log(twopar)/twopar))
+
 function givensAlgorithm{T<:FloatingPoint}(f::T, g::T)
     zeropar = zero(T)
     onepar = one(T)
     twopar = 2one(T)
 
     safmin = realmin(T)
     epspar = eps(T)
-    safmn2 = twopar^itrunc(log(safmin/epspar)/log(twopar)/twopar)
+    safmn2 = realmin2(T)
     safmx2 = onepar/safmn2
 
     if g == 0
@@ -84,7 +87,7 @@ function givensAlgorithm{T<:FloatingPoint}(f::Complex{T}, g::Complex{T})
     abs1(ff) = max(abs(real(ff)), abs(imag(ff)))
     safmin = realmin(T)
     epspar = eps(T)
-    safmn2 = twopar^itrunc(log(safmin/epspar)/log(twopar)/twopar)
+    safmn2 = realmin2(T)
     safmx2 = onepar/safmn2
     scalepar = max(abs1(f), abs1(g))
     fs = f
@@ -181,33 +184,25 @@ function givensAlgorithm{T<:FloatingPoint}(f::Complex{T}, g::Complex{T})
     return cs, sn, r
 end
 
-function givens{T}(f::T, g::T, i1::Integer, i2::Integer, size::Integer)
-    i2 <= size || error("indices cannot be larger than size Givens rotation matrix")
+function givens{T}(f::T, g::T, i1::Integer, i2::Integer)
     i1 < i2 || error("second index must be larger than the first")
-    h = givensAlgorithm(f, g)
-    Givens(size, i1, i2, convert(T, h[1]), convert(T, h[2]), convert(T, h[3]))
+    c, s, r = givensAlgorithm(f, g)
+    Givens(i1, i2, convert(T, c), convert(T, s), convert(T, r))
 end
 
 function givens{T}(A::AbstractMatrix{T}, i1::Integer, i2::Integer, col::Integer)
     i1 < i2 || error("second index must be larger than the first")
-    h = givensAlgorithm(A[i1,col], A[i2,col])
-    Givens(size(A, 1), i1, i2, convert(T, h[1]), convert(T, h[2]), convert(T, h[3]))
+    c, s, r = givensAlgorithm(A[i1,col], A[i2,col])
+    Givens(i1, i2, convert(T, c), convert(T, s), convert(T, r))
 end
 
-*{T}(G1::Givens{T}, G2::Givens{T}) = Rotation(push!(push!(Givens{T}[], G2), G1))
-*(G::Givens, B::BitArray{2}) = error("method not defined")
-*{TBf,TBi}(G::Givens, B::SparseMatrixCSC{TBf,TBi}) = error("method not defined")
-*(R::AbstractRotation, A::AbstractMatrix) = A_mul_B!(R, copy(A))
-
-A_mul_Bc(A::AbstractMatrix, R::Rotation) = A_mul_Bc!(copy(A), R)
-
 getindex(G::Givens, i::Integer, j::Integer) = i == j ? (i == G.i1 || i == G.i2 ? G.c : one(G.c)) : (i == G.i1 && j == G.i2 ? G.s : (i == G.i2 && j == G.i1 ? -G.s : zero(G.s)))
-size(G::Givens) = (G.size, G.size)
-size(G::Givens, i::Integer) = 1 <= i <= 2 ? G.size : 1
+
 A_mul_B!(G1::Givens, G2::Givens) = error("Operation not supported. Consider *")
 function A_mul_B!(G::Givens, A::AbstractMatrix)
     m, n = size(A)
-    for i = 1:n
+    G.i2 <= m || throw(DimensionMismatch("column indices for ratation are outside the matrix"))
+    @inbounds @simd for i = 1:n
         tmp = G.c*A[G.i1,i] + G.s*A[G.i2,i]
         A[G.i2,i] = G.c*A[G.i2,i] - conj(G.s)*A[G.i1,i]
         A[G.i1,i] = tmp
@@ -216,7 +211,8 @@ function A_mul_B!(G::Givens, A::AbstractMatrix)
 end
 function A_mul_Bc!(A::AbstractMatrix, G::Givens)
     m, n = size(A)
-    for i = 1:m
+    G.i2 <= n || throw(DimensionMismatch("column indices for ratation are outside the matrix"))
+    @inbounds @simd for i = 1:m
         tmp = G.c*A[i,G.i1] + conj(G.s)*A[i,G.i2]
         A[i,G.i2] = G.c*A[i,G.i2] - G.s*A[i,G.i1]
         A[i,G.i1] = tmp
@@ -228,14 +224,18 @@ function A_mul_B!(G::Givens, R::Rotation)
     return R
 end
 function A_mul_B!(R::Rotation, A::AbstractMatrix)
-    for i = 1:length(R.rotations)
+    @inbounds for i = 1:length(R.rotations)
         A_mul_B!(R.rotations[i], A)
     end
     return A
 end
 function A_mul_Bc!(A::AbstractMatrix, R::Rotation)
-    for i = 1:length(R.rotations)
+    @inbounds for i = 1:length(R.rotations)
         A_mul_Bc!(A, R.rotations[i])
     end
     return A
 end
+*{T}(G1::Givens{T}, G2::Givens{T}) = Rotation(push!(push!(Givens{T}[], G2), G1))
+*(R::AbstractRotation, A::AbstractMatrix) = A_mul_B!(R, copy(A))
+
+A_mul_Bc(A::AbstractMatrix, R::AbstractRotation) = A_mul_Bc!(copy(A), R)