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// Copyright ©2015 The Gonum Authors. All rights reserved.
// Use of this source code is governed by a BSD-style
// license that can be found in the LICENSE file.
package gonum
import "gonum.org/v1/gonum/lapack"
// Implementation is the native Go implementation of LAPACK routines. It
// is built on top of calls to the return of blas64.Implementation(), so while
// this code is in pure Go, the underlying BLAS implementation may not be.
type Implementation struct{}
var _ lapack.Float64 = Implementation{}
func abs(a int) int {
if a < 0 {
return -a
}
return a
}
const (
// dlamchE is the machine epsilon. For IEEE this is 2^{-53}.
dlamchE = 0x1p-53
// dlamchB is the radix of the machine (the base of the number system).
dlamchB = 2
// dlamchP is base * eps.
dlamchP = dlamchB * dlamchE
// dlamchS is the "safe minimum", that is, the lowest number such that
// 1/dlamchS does not overflow, or also the smallest normal number.
// For IEEE this is 2^{-1022}.
dlamchS = 0x1p-1022
// Blue's scaling constants
//
// An n-vector x is well-scaled if
// dtsml ≤ |xᵢ| ≤ dtbig for 0 ≤ i < n and n ≤ 1/dlamchP,
// where
// dtsml = 2^ceil((expmin-1)/2) = 2^ceil((-1021-1)/2) = 2^{-511} = 1.4916681462400413e-154
// dtbig = 2^floor((expmax-digits+1)/2) = 2^floor((1024-53+1)/2) = 2^{486} = 1.997919072202235e+146
// If any xᵢ is not well-scaled, then multiplying small values by dssml and
// large values by dsbig avoids underflow or overflow when computing the sum
// of squares \sum_0^{n-1} (xᵢ)².
// dssml = 2^{-floor((expmin-digits)/2)} = 2^{-floor((-1021-53)/2)} = 2^537 = 4.4989137945431964e+161
// dsbig = 2^{-ceil((expmax+digits-1)/2)} = 2^{-ceil((1024+53-1)/2)} = 2^{-538} = 1.1113793747425387e-162
//
// References:
// - Anderson E. (2017)
// Algorithm 978: Safe Scaling in the Level 1 BLAS
// ACM Trans Math Softw 44:1--28
// https://doi.org/10.1145/3061665
// - Blue, James L. (1978)
// A Portable Fortran Program to Find the Euclidean Norm of a Vector
// ACM Trans Math Softw 4:15--23
// https://doi.org/10.1145/355769.355771
dtsml = 0x1p-511
dtbig = 0x1p486
dssml = 0x1p537
dsbig = 0x1p-538
)
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