mirror of
https://github.com/gonum/gonum.git
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635 lines
12 KiB
Go
635 lines
12 KiB
Go
// Code generated by "go generate github.com/gonum/blas/native"; DO NOT EDIT.
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// Copyright ©2015 The gonum Authors. All rights reserved.
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// Use of this source code is governed by a BSD-style
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// license that can be found in the LICENSE file.
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package native
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import (
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math "gonum.org/v1/gonum/blas/native/internal/math32"
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"gonum.org/v1/gonum/blas"
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"gonum.org/v1/gonum/internal/asm/f32"
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)
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var _ blas.Float32Level1 = Implementation{}
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// Snrm2 computes the Euclidean norm of a vector,
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// sqrt(\sum_i x[i] * x[i]).
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// This function returns 0 if incX is negative.
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//
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// Float32 implementations are autogenerated and not directly tested.
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func (Implementation) Snrm2(n int, x []float32, incX int) float32 {
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if incX < 1 {
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if incX == 0 {
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panic(zeroIncX)
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}
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return 0
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}
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if incX > 0 && (n-1)*incX >= len(x) {
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panic(badX)
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}
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if n < 2 {
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if n == 1 {
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return math.Abs(x[0])
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}
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if n == 0 {
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return 0
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}
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if n < 1 {
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panic(negativeN)
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}
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}
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var (
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scale float32 = 0
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sumSquares float32 = 1
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)
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if incX == 1 {
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x = x[:n]
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for _, v := range x {
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if v == 0 {
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continue
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}
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absxi := math.Abs(v)
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if math.IsNaN(absxi) {
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return math.NaN()
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}
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if scale < absxi {
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sumSquares = 1 + sumSquares*(scale/absxi)*(scale/absxi)
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scale = absxi
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} else {
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sumSquares = sumSquares + (absxi/scale)*(absxi/scale)
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}
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}
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if math.IsInf(scale, 1) {
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return math.Inf(1)
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}
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return scale * math.Sqrt(sumSquares)
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}
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for ix := 0; ix < n*incX; ix += incX {
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val := x[ix]
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if val == 0 {
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continue
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}
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absxi := math.Abs(val)
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if math.IsNaN(absxi) {
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return math.NaN()
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}
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if scale < absxi {
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sumSquares = 1 + sumSquares*(scale/absxi)*(scale/absxi)
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scale = absxi
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} else {
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sumSquares = sumSquares + (absxi/scale)*(absxi/scale)
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}
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}
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if math.IsInf(scale, 1) {
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return math.Inf(1)
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}
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return scale * math.Sqrt(sumSquares)
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}
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// Sasum computes the sum of the absolute values of the elements of x.
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// \sum_i |x[i]|
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// Sasum returns 0 if incX is negative.
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//
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// Float32 implementations are autogenerated and not directly tested.
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func (Implementation) Sasum(n int, x []float32, incX int) float32 {
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var sum float32
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if n < 0 {
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panic(negativeN)
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}
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if incX < 1 {
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if incX == 0 {
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panic(zeroIncX)
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}
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return 0
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}
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if incX > 0 && (n-1)*incX >= len(x) {
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panic(badX)
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}
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if incX == 1 {
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x = x[:n]
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for _, v := range x {
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sum += math.Abs(v)
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}
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return sum
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}
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for i := 0; i < n; i++ {
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sum += math.Abs(x[i*incX])
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}
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return sum
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}
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// Isamax returns the index of an element of x with the largest absolute value.
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// If there are multiple such indices the earliest is returned.
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// Isamax returns -1 if n == 0.
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//
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// Float32 implementations are autogenerated and not directly tested.
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func (Implementation) Isamax(n int, x []float32, incX int) int {
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if incX < 1 {
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if incX == 0 {
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panic(zeroIncX)
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}
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return -1
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}
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if incX > 0 && (n-1)*incX >= len(x) {
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panic(badX)
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}
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if n < 2 {
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if n == 1 {
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return 0
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}
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if n == 0 {
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return -1 // Netlib returns invalid index when n == 0
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}
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if n < 1 {
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panic(negativeN)
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}
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}
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idx := 0
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max := math.Abs(x[0])
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if incX == 1 {
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for i, v := range x[:n] {
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absV := math.Abs(v)
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if absV > max {
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max = absV
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idx = i
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}
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}
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return idx
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}
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ix := incX
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for i := 1; i < n; i++ {
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v := x[ix]
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absV := math.Abs(v)
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if absV > max {
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max = absV
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idx = i
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}
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ix += incX
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}
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return idx
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}
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// Sswap exchanges the elements of two vectors.
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// x[i], y[i] = y[i], x[i] for all i
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//
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// Float32 implementations are autogenerated and not directly tested.
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func (Implementation) Sswap(n int, x []float32, incX int, y []float32, incY int) {
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if incX == 0 {
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panic(zeroIncX)
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}
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if incY == 0 {
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panic(zeroIncY)
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}
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if n < 1 {
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if n == 0 {
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return
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}
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panic(negativeN)
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}
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if (incX > 0 && (n-1)*incX >= len(x)) || (incX < 0 && (1-n)*incX >= len(x)) {
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panic(badX)
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}
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if (incY > 0 && (n-1)*incY >= len(y)) || (incY < 0 && (1-n)*incY >= len(y)) {
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panic(badY)
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}
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if incX == 1 && incY == 1 {
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x = x[:n]
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for i, v := range x {
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x[i], y[i] = y[i], v
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}
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return
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}
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var ix, iy int
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if incX < 0 {
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ix = (-n + 1) * incX
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}
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if incY < 0 {
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iy = (-n + 1) * incY
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}
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for i := 0; i < n; i++ {
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x[ix], y[iy] = y[iy], x[ix]
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ix += incX
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iy += incY
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}
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}
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// Scopy copies the elements of x into the elements of y.
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// y[i] = x[i] for all i
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//
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// Float32 implementations are autogenerated and not directly tested.
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func (Implementation) Scopy(n int, x []float32, incX int, y []float32, incY int) {
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if incX == 0 {
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panic(zeroIncX)
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}
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if incY == 0 {
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panic(zeroIncY)
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}
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if n < 1 {
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if n == 0 {
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return
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}
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panic(negativeN)
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}
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if (incX > 0 && (n-1)*incX >= len(x)) || (incX < 0 && (1-n)*incX >= len(x)) {
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panic(badX)
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}
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if (incY > 0 && (n-1)*incY >= len(y)) || (incY < 0 && (1-n)*incY >= len(y)) {
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panic(badY)
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}
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if incX == 1 && incY == 1 {
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copy(y[:n], x[:n])
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return
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}
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var ix, iy int
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if incX < 0 {
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ix = (-n + 1) * incX
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}
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if incY < 0 {
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iy = (-n + 1) * incY
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}
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for i := 0; i < n; i++ {
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y[iy] = x[ix]
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ix += incX
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iy += incY
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}
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}
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// Saxpy adds alpha times x to y
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// y[i] += alpha * x[i] for all i
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//
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// Float32 implementations are autogenerated and not directly tested.
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func (Implementation) Saxpy(n int, alpha float32, x []float32, incX int, y []float32, incY int) {
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if incX == 0 {
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panic(zeroIncX)
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}
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if incY == 0 {
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panic(zeroIncY)
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}
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if n < 1 {
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if n == 0 {
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return
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}
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panic(negativeN)
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}
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if (incX > 0 && (n-1)*incX >= len(x)) || (incX < 0 && (1-n)*incX >= len(x)) {
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panic(badX)
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}
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if (incY > 0 && (n-1)*incY >= len(y)) || (incY < 0 && (1-n)*incY >= len(y)) {
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panic(badY)
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}
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if alpha == 0 {
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return
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}
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if incX == 1 && incY == 1 {
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if len(x) < n {
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panic(badLenX)
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}
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if len(y) < n {
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panic(badLenY)
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}
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f32.AxpyUnitaryTo(y, alpha, x[:n], y)
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return
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}
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var ix, iy int
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if incX < 0 {
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ix = (-n + 1) * incX
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}
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if incY < 0 {
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iy = (-n + 1) * incY
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}
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if ix >= len(x) || ix+(n-1)*incX >= len(x) {
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panic(badLenX)
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}
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if iy >= len(y) || iy+(n-1)*incY >= len(y) {
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panic(badLenY)
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}
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f32.AxpyInc(alpha, x, y, uintptr(n), uintptr(incX), uintptr(incY), uintptr(ix), uintptr(iy))
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}
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// Srotg computes the plane rotation
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// _ _ _ _ _ _
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// | c s | | a | | r |
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// | -s c | * | b | = | 0 |
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// ‾ ‾ ‾ ‾ ‾ ‾
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// where
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// r = ±√(a^2 + b^2)
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// c = a/r, the cosine of the plane rotation
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// s = b/r, the sine of the plane rotation
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//
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// NOTE: There is a discrepancy between the refence implementation and the BLAS
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// technical manual regarding the sign for r when a or b are zero.
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// Srotg agrees with the definition in the manual and other
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// common BLAS implementations.
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//
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// Float32 implementations are autogenerated and not directly tested.
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func (Implementation) Srotg(a, b float32) (c, s, r, z float32) {
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if b == 0 && a == 0 {
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return 1, 0, a, 0
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}
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absA := math.Abs(a)
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absB := math.Abs(b)
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aGTb := absA > absB
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r = math.Hypot(a, b)
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if aGTb {
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r = math.Copysign(r, a)
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} else {
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r = math.Copysign(r, b)
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}
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c = a / r
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s = b / r
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if aGTb {
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z = s
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} else if c != 0 { // r == 0 case handled above
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z = 1 / c
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} else {
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z = 1
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}
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return
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}
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// Srotmg computes the modified Givens rotation. See
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// http://www.netlib.org/lapack/explore-html/df/deb/drotmg_8f.html
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// for more details.
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//
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// Float32 implementations are autogenerated and not directly tested.
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func (Implementation) Srotmg(d1, d2, x1, y1 float32) (p blas.SrotmParams, rd1, rd2, rx1 float32) {
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var p1, p2, q1, q2, u float32
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const (
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gam = 4096.0
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gamsq = 16777216.0
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rgamsq = 5.9604645e-8
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)
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if d1 < 0 {
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p.Flag = blas.Rescaling
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return
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}
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p2 = d2 * y1
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if p2 == 0 {
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p.Flag = blas.Identity
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rd1 = d1
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rd2 = d2
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rx1 = x1
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return
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}
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p1 = d1 * x1
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q2 = p2 * y1
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q1 = p1 * x1
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absQ1 := math.Abs(q1)
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absQ2 := math.Abs(q2)
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if absQ1 < absQ2 && q2 < 0 {
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p.Flag = blas.Rescaling
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return
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}
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if d1 == 0 {
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p.Flag = blas.Diagonal
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p.H[0] = p1 / p2
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p.H[3] = x1 / y1
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u = 1 + p.H[0]*p.H[3]
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rd1, rd2 = d2/u, d1/u
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rx1 = y1 / u
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return
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}
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// Now we know that d1 != 0, and d2 != 0. If d2 == 0, it would be caught
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// when p2 == 0, and if d1 == 0, then it is caught above
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if absQ1 > absQ2 {
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p.H[1] = -y1 / x1
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p.H[2] = p2 / p1
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u = 1 - p.H[2]*p.H[1]
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rd1 = d1
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rd2 = d2
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rx1 = x1
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p.Flag = blas.OffDiagonal
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// u must be greater than zero because |q1| > |q2|, so check from netlib
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// is unnecessary
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// This is left in for ease of comparison with complex routines
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//if u > 0 {
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rd1 /= u
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rd2 /= u
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rx1 *= u
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//}
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} else {
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p.Flag = blas.Diagonal
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p.H[0] = p1 / p2
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p.H[3] = x1 / y1
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u = 1 + p.H[0]*p.H[3]
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rd1 = d2 / u
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rd2 = d1 / u
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rx1 = y1 * u
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}
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for rd1 <= rgamsq || rd1 >= gamsq {
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if p.Flag == blas.OffDiagonal {
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p.H[0] = 1
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p.H[3] = 1
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p.Flag = blas.Rescaling
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} else if p.Flag == blas.Diagonal {
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p.H[1] = -1
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p.H[2] = 1
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p.Flag = blas.Rescaling
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}
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if rd1 <= rgamsq {
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rd1 *= gam * gam
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rx1 /= gam
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p.H[0] /= gam
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p.H[2] /= gam
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} else {
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rd1 /= gam * gam
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rx1 *= gam
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p.H[0] *= gam
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p.H[2] *= gam
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}
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}
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for math.Abs(rd2) <= rgamsq || math.Abs(rd2) >= gamsq {
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if p.Flag == blas.OffDiagonal {
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p.H[0] = 1
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p.H[3] = 1
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p.Flag = blas.Rescaling
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} else if p.Flag == blas.Diagonal {
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p.H[1] = -1
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p.H[2] = 1
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p.Flag = blas.Rescaling
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}
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if math.Abs(rd2) <= rgamsq {
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rd2 *= gam * gam
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p.H[1] /= gam
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p.H[3] /= gam
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} else {
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rd2 /= gam * gam
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p.H[1] *= gam
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p.H[3] *= gam
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}
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}
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return
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}
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// Srot applies a plane transformation.
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// x[i] = c * x[i] + s * y[i]
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// y[i] = c * y[i] - s * x[i]
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//
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// Float32 implementations are autogenerated and not directly tested.
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func (Implementation) Srot(n int, x []float32, incX int, y []float32, incY int, c float32, s float32) {
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if incX == 0 {
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panic(zeroIncX)
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}
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if incY == 0 {
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panic(zeroIncY)
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}
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if n < 1 {
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if n == 0 {
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return
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}
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panic(negativeN)
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}
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if (incX > 0 && (n-1)*incX >= len(x)) || (incX < 0 && (1-n)*incX >= len(x)) {
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panic(badX)
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}
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if (incY > 0 && (n-1)*incY >= len(y)) || (incY < 0 && (1-n)*incY >= len(y)) {
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panic(badY)
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}
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if incX == 1 && incY == 1 {
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x = x[:n]
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for i, vx := range x {
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vy := y[i]
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x[i], y[i] = c*vx+s*vy, c*vy-s*vx
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}
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return
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}
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var ix, iy int
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if incX < 0 {
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ix = (-n + 1) * incX
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}
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if incY < 0 {
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iy = (-n + 1) * incY
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}
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for i := 0; i < n; i++ {
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vx := x[ix]
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vy := y[iy]
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x[ix], y[iy] = c*vx+s*vy, c*vy-s*vx
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ix += incX
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iy += incY
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}
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}
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// Srotm applies the modified Givens rotation to the 2×n matrix.
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||
//
|
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// Float32 implementations are autogenerated and not directly tested.
|
||
func (Implementation) Srotm(n int, x []float32, incX int, y []float32, incY int, p blas.SrotmParams) {
|
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if incX == 0 {
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panic(zeroIncX)
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}
|
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if incY == 0 {
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panic(zeroIncY)
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}
|
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if n <= 0 {
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if n == 0 {
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return
|
||
}
|
||
panic(negativeN)
|
||
}
|
||
if (incX > 0 && (n-1)*incX >= len(x)) || (incX < 0 && (1-n)*incX >= len(x)) {
|
||
panic(badX)
|
||
}
|
||
if (incY > 0 && (n-1)*incY >= len(y)) || (incY < 0 && (1-n)*incY >= len(y)) {
|
||
panic(badY)
|
||
}
|
||
|
||
var h11, h12, h21, h22 float32
|
||
var ix, iy int
|
||
switch p.Flag {
|
||
case blas.Identity:
|
||
return
|
||
case blas.Rescaling:
|
||
h11 = p.H[0]
|
||
h12 = p.H[2]
|
||
h21 = p.H[1]
|
||
h22 = p.H[3]
|
||
case blas.OffDiagonal:
|
||
h11 = 1
|
||
h12 = p.H[2]
|
||
h21 = p.H[1]
|
||
h22 = 1
|
||
case blas.Diagonal:
|
||
h11 = p.H[0]
|
||
h12 = 1
|
||
h21 = -1
|
||
h22 = p.H[3]
|
||
}
|
||
if incX < 0 {
|
||
ix = (-n + 1) * incX
|
||
}
|
||
if incY < 0 {
|
||
iy = (-n + 1) * incY
|
||
}
|
||
if incX == 1 && incY == 1 {
|
||
x = x[:n]
|
||
for i, vx := range x {
|
||
vy := y[i]
|
||
x[i], y[i] = vx*h11+vy*h12, vx*h21+vy*h22
|
||
}
|
||
return
|
||
}
|
||
for i := 0; i < n; i++ {
|
||
vx := x[ix]
|
||
vy := y[iy]
|
||
x[ix], y[iy] = vx*h11+vy*h12, vx*h21+vy*h22
|
||
ix += incX
|
||
iy += incY
|
||
}
|
||
return
|
||
}
|
||
|
||
// Sscal scales x by alpha.
|
||
// x[i] *= alpha
|
||
// Sscal has no effect if incX < 0.
|
||
//
|
||
// Float32 implementations are autogenerated and not directly tested.
|
||
func (Implementation) Sscal(n int, alpha float32, x []float32, incX int) {
|
||
if incX < 1 {
|
||
if incX == 0 {
|
||
panic(zeroIncX)
|
||
}
|
||
return
|
||
}
|
||
if (n-1)*incX >= len(x) {
|
||
panic(badX)
|
||
}
|
||
if n < 1 {
|
||
if n == 0 {
|
||
return
|
||
}
|
||
panic(negativeN)
|
||
}
|
||
if alpha == 0 {
|
||
if incX == 1 {
|
||
x = x[:n]
|
||
for i := range x {
|
||
x[i] = 0
|
||
}
|
||
return
|
||
}
|
||
for ix := 0; ix < n*incX; ix += incX {
|
||
x[ix] = 0
|
||
}
|
||
return
|
||
}
|
||
if incX == 1 {
|
||
f32.ScalUnitary(alpha, x[:n])
|
||
return
|
||
}
|
||
for ix := 0; ix < n*incX; ix += incX {
|
||
x[ix] *= alpha
|
||
}
|
||
}
|