internal/asm/{c64,c128}: add stubs for kernels needed by cmplxs package

internal/asm/c128/asm_test.go

@@ -0,0 +1,121 @@
+// 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 c128_test
+
+import (
+	"math"
+	"math/cmplx"
+	"testing"
+
+	"golang.org/x/exp/rand"
+
+	"gonum.org/v1/gonum/floats"
+)
+
+const (
+	msgVal   = "%v: unexpected value at %v Got: %v Expected: %v"
+	msgGuard = "%v: Guard violated in %s vector %v %v"
+)
+
+var (
+	nan = math.NaN()
+
+	cnan = cmplx.NaN()
+	cinf = cmplx.Inf()
+)
+
+// TODO(kortschak): Harmonise the situation in asm/{f32,f64} and their sinks.
+const testLen = 1e5
+
+var x = make([]complex128, testLen)
+
+// guardVector copies the source vector (vec) into a new slice with guards.
+// Guards guarded[:gdLn] and guarded[len-gdLn:] will be filled with sigil value gdVal.
+func guardVector(vec []complex128, gdVal complex128, gdLn int) (guarded []complex128) {
+	guarded = make([]complex128, len(vec)+gdLn*2)
+	copy(guarded[gdLn:], vec)
+	for i := 0; i < gdLn; i++ {
+		guarded[i] = gdVal
+		guarded[len(guarded)-1-i] = gdVal
+	}
+	return guarded
+}
+
+// isValidGuard will test for violated guards, generated by guardVector.
+func isValidGuard(vec []complex128, gdVal complex128, gdLn int) bool {
+	for i := 0; i < gdLn; i++ {
+		if !sameCmplx(vec[i], gdVal) || !sameCmplx(vec[len(vec)-1-i], gdVal) {
+			return false
+		}
+	}
+	return true
+}
+
+// guardIncVector copies the source vector (vec) into a new incremented slice with guards.
+// End guards will be length gdLen.
+// Internal and end guards will be filled with sigil value gdVal.
+func guardIncVector(vec []complex128, gdVal complex128, inc, gdLen int) (guarded []complex128) {
+	if inc < 0 {
+		inc = -inc
+	}
+	inrLen := len(vec) * inc
+	guarded = make([]complex128, inrLen+gdLen*2)
+	for i := range guarded {
+		guarded[i] = gdVal
+	}
+	for i, v := range vec {
+		guarded[gdLen+i*inc] = v
+	}
+	return guarded
+}
+
+// checkValidIncGuard will test for violated guards, generated by guardIncVector
+func checkValidIncGuard(t *testing.T, vec []complex128, gdVal complex128, inc, gdLen int) {
+	srcLn := len(vec) - 2*gdLen
+	for i := range vec {
+		switch {
+		case sameCmplx(vec[i], gdVal):
+			// Correct value
+		case (i-gdLen)%inc == 0 && (i-gdLen)/inc < len(vec):
+			// Ignore input values
+		case i < gdLen:
+			t.Errorf("Front guard violated at %d %v", i, vec[:gdLen])
+		case i > gdLen+srcLn:
+			t.Errorf("Back guard violated at %d %v", i-gdLen-srcLn, vec[gdLen+srcLn:])
+		default:
+			t.Errorf("Internal guard violated at %d %v", i-gdLen, vec[gdLen:gdLen+srcLn])
+		}
+	}
+}
+
+// same tests for nan-aware equality.
+func same(a, b float64) bool {
+	return a == b || (math.IsNaN(a) && math.IsNaN(b))
+}
+
+// sameApprox tests for nan-aware equality within tolerance.
+func sameApprox(a, b, tol float64) bool {
+	return same(a, b) || floats.EqualWithinAbsOrRel(a, b, tol, tol)
+}
+
+// sameCmplx tests for nan-aware equality.
+func sameCmplx(a, b complex128) bool {
+	return a == b || (cmplx.IsNaN(a) && cmplx.IsNaN(b))
+}
+
+var ( // Offset sets for testing alignment handling in Unitary assembly functions.
+	align1 = []int{0, 1}
+)
+
+func randomSlice(n, inc int) []complex128 {
+	if inc < 0 {
+		inc = -inc
+	}
+	x := make([]complex128, (n-1)*inc+1)
+	for i := range x {
+		x[i] = complex(rand.Float64(), rand.Float64())
+	}
+	return x
+}

internal/asm/c128/l2norm_test.go

@@ -0,0 +1,153 @@
+// Copyright ©2019 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 c128_test
+
+import (
+	"fmt"
+	"math"
+	"math/cmplx"
+	"testing"
+
+	. "gonum.org/v1/gonum/internal/asm/c128"
+)
+
+// nanwith copied from floats package
+func nanwith(payload uint64) complex128 {
+	const (
+		nanBits = 0x7ff8000000000000
+		nanMask = 0xfff8000000000000
+	)
+	nan := math.Float64frombits(nanBits | (payload &^ nanMask))
+	return complex(nan, nan)
+}
+
+func TestL2NormUnitary(t *testing.T) {
+	const tol = 1e-15
+
+	var src_gd complex128 = 1
+	for j, v := range []struct {
+		want float64
+		x    []complex128
+	}{
+		{want: 0, x: []complex128{}},
+		{want: 2, x: []complex128{2}},
+		{want: 2, x: []complex128{2i}},
+		{want: math.Sqrt(8), x: []complex128{2 + 2i}},
+		{want: 3.7416573867739413, x: []complex128{1, 2, 3}},
+		{want: 3.7416573867739413, x: []complex128{-1, -2, -3}},
+		{want: 3.7416573867739413, x: []complex128{1i, 2i, 3i}},
+		{want: 3.7416573867739413, x: []complex128{-1i, -2i, -3i}},
+		{want: math.Sqrt(28), x: []complex128{1 + 1i, 2 + 2i, 3 + 3i}},
+		{want: math.Sqrt(28), x: []complex128{-1 - 1i, -2 - 2i, -3 - 3i}},
+		{want: nan, x: []complex128{cnan}},
+		{want: nan, x: []complex128{1, cinf, 3, nanwith(25), 5}},
+		{want: 17.88854381999832, x: []complex128{8, -8, 8, -8, 8}},
+		{want: 2.23606797749979, x: []complex128{0, 1, 0, -1, 0, 1, 0, -1, 0, 1}},
+		{want: 17.88854381999832, x: []complex128{8i, -8i, 8i, -8i, 8i}},
+		{want: 2.23606797749979, x: []complex128{0, 1i, 0, -1i, 0, 1i, 0, -1i, 0, 1i}},
+		{want: math.Sqrt(640), x: []complex128{8 + 8i, -8 - 8i, 8 + 8i, -8 - 8i, 8 + 8i}},
+		{want: math.Sqrt(10), x: []complex128{0, 1 + 1i, 0, -1 - 1i, 0, 1 + 1i, 0, -1 - 1i, 0, 1 + 1i}},
+	} {
+		g_ln := 4 + j%2
+		v.x = guardVector(v.x, src_gd, g_ln)
+		src := v.x[g_ln : len(v.x)-g_ln]
+		ret := L2NormUnitary(src)
+		if !sameApprox(ret, v.want, tol) {
+			t.Errorf("Test %d L2Norm error Got: %f Expected: %f", j, ret, v.want)
+		}
+		if !isValidGuard(v.x, src_gd, g_ln) {
+			t.Errorf("Test %d Guard violated in src vector %v %v", j, v.x[:g_ln], v.x[len(v.x)-g_ln:])
+		}
+	}
+}
+
+func TestL2DistanceUnitary(t *testing.T) {
+	const tol = 1e-15
+
+	var src_gd complex128 = 1
+	for j, v := range []struct {
+		want float64
+		x, y []complex128
+	}{
+		{want: 0, x: []complex128{}, y: []complex128{}},
+		{want: 2, x: []complex128{3}, y: []complex128{1}},
+		{want: 2, x: []complex128{3i}, y: []complex128{1i}},
+		{want: 3.7416573867739413, x: []complex128{2, 4, 6}, y: []complex128{1, 2, 3}},
+		{want: 3.7416573867739413, x: []complex128{1, 2, 3}, y: []complex128{2, 4, 6}},
+		{want: 3.7416573867739413, x: []complex128{2i, 4i, 6i}, y: []complex128{1i, 2i, 3i}},
+		{want: 3.7416573867739413, x: []complex128{1i, 2i, 3i}, y: []complex128{2i, 4i, 6i}},
+		{want: math.Sqrt(28), x: []complex128{2 + 2i, 4 + 4i, 6 + 6i}, y: []complex128{1 + 1i, 2 + 2i, 3 + 3i}},
+		{want: math.Sqrt(28), x: []complex128{1 + 1i, 2 + 2i, 3 + 3i}, y: []complex128{2 + 2i, 4 + 4i, 6 + 6i}},
+		{want: nan, x: []complex128{cnan}, y: []complex128{0}},
+		{want: 17.88854381999832, x: []complex128{9, -9, 9, -9, 9}, y: []complex128{1, -1, 1, -1, 1}},
+		{want: 2.23606797749979, x: []complex128{0, 1, 0, -1, 0, 1, 0, -1, 0, 1}, y: []complex128{0, 2, 0, -2, 0, 2, 0, -2, 0, 2}},
+		{want: 17.88854381999832, x: []complex128{9i, -9i, 9i, -9i, 9i}, y: []complex128{1i, -1i, 1i, -1i, 1i}},
+		{want: 2.23606797749979, x: []complex128{0, 1i, 0, -1i, 0, 1i, 0, -1i, 0, 1i}, y: []complex128{0, 2i, 0, -2i, 0, 2i, 0, -2i, 0, 2i}},
+		{want: math.Sqrt(640), x: []complex128{9 + 9i, -9 - 9i, 9 + 9i, -9 - 9i, 9 + 9i}, y: []complex128{1 + 1i, -1 - 1i, 1 + 1i, -1 - 1i, 1 + 1i}},
+		{want: math.Sqrt(10), x: []complex128{0, 1 + 1i, 0, -1 - 1i, 0, 1 + 1i, 0, -1 - 1i, 0, 1 + 1i}, y: []complex128{0, 2 + 2i, 0, -2 - 2i, 0, 2 + 2i, 0, -2 - 2i, 0, 2 + 2i}},
+	} {
+		g_ln := 4 + j%2
+		v.x = guardVector(v.x, src_gd, g_ln)
+		v.y = guardVector(v.y, src_gd, g_ln)
+		srcX := v.x[g_ln : len(v.x)-g_ln]
+		srcY := v.y[g_ln : len(v.y)-g_ln]
+		ret := L2DistanceUnitary(srcX, srcY)
+		if !sameApprox(ret, v.want, tol) {
+			t.Errorf("Test %d L2Distance error Got: %f Expected: %f", j, ret, v.want)
+		}
+		if !isValidGuard(v.x, src_gd, g_ln) {
+			t.Errorf("Test %d Guard violated in src vector %v %v", j, v.x[:g_ln], v.x[len(v.x)-g_ln:])
+		}
+	}
+}
+
+func BenchmarkL2NormNetlib(b *testing.B) {
+	netlib := func(x []complex128) (sum float64) {
+		var scale float64
+		sumSquares := 1.0
+		for _, v := range x {
+			if v == 0 {
+				continue
+			}
+			absxi := cmplx.Abs(v)
+			if math.IsNaN(absxi) {
+				return math.NaN()
+			}
+			if scale < absxi {
+				s := scale / absxi
+				sumSquares = 1 + sumSquares*s*s
+				scale = absxi
+			} else {
+				s := absxi / scale
+				sumSquares += s * s
+			}
+		}
+		if math.IsInf(scale, 1) {
+			return math.Inf(1)
+		}
+		return scale * math.Sqrt(sumSquares)
+	}
+
+	tests := []struct {
+		name string
+		f    func(x []complex128) float64
+	}{
+		{"L2NormUnitaryNetlib", netlib},
+		{"L2NormUnitary", L2NormUnitary},
+	}
+	x[0] = randomSlice(1, 1)[0] // replace the leading zero (edge case)
+	for _, test := range tests {
+		for _, ln := range []uintptr{1, 3, 10, 30, 1e2, 3e2, 1e3, 3e3, 1e4, 3e4, 1e5} {
+			b.Run(fmt.Sprintf("%s-%d", test.name, ln), func(b *testing.B) {
+				b.SetBytes(int64(64 * ln))
+				x := x[:ln]
+				b.ResetTimer()
+				for i := 0; i < b.N; i++ {
+					test.f(x)
+				}
+			})
+		}
+	}
+}