// Copyright ©2025 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 mathext

import (
	"math"
	"math/cmplx"
	"testing"

	"gonum.org/v1/gonum/cmplxs/cscalar"
)

func TestDiLogValues(t *testing.T) {
	t.Parallel()
	const tol = 1e-12

	for _, test := range []struct {
		in, want complex128
	}{
		// Reference values were generated using Python's scipy.special.spence
		// (where Li2(z) = spence(1 - z)) and verified with a computer algebra system.

		// well known values
		{in: 0, want: 0},
		{in: 1, want: math.Pi * math.Pi / 6},
		{in: -1, want: -math.Pi * math.Pi / 12},
		{in: 0.5, want: math.Pi*math.Pi/12 - math.Ln2*math.Ln2/2},
		{in: 2, want: complex(math.Pi*math.Pi/4, -math.Pi*math.Ln2)},

		// abs(z) < 0.5
		{in: 0.1 + 0.1i, want: 0.099751196798713 + 0.105220383905600i},
		{in: -0.3 + 0.39i, want: -0.306174046754339 + 0.337550668621259i},
		{in: 0.001 - 0.49i, want: -0.055831393285929 - 0.478156430372353i},

		// 0.5 < abs(z) < 1
		{in: -0.9999 + 0.001i, want: -0.8223978143206974 + 0.0006931664732411i},
		{in: 0.5 + 0.7i, want: 0.359364350522653 + 0.856767712327590i},
		{in: complex(math.Pi/4, -math.Pi/7), want: 0.828086461155377 - 0.739345385309341i},
		{in: -0.8 - 0.0001i, want: -0.679781588954542 - 0.000073473333084i},

		// abs(z) > 1
		{in: -1.1 + 0.1i, want: -0.8917388814454027 + 0.0674285967726009i},
		{in: 5 + 0i, want: 1.783719161266631 - 5.056198322111862i},
		{in: -10 + 0i, want: -4.198277886858104 + 0i},
		{in: 1000 + 10000i, want: -42.71073756884990 + 15.39396088869304i},
		{in: -1791.91931 + 0.5i, want: -29.70223568904652 + 0.00209038439188i},
	} {
		got := Li2(test.in)
		diff := cmplx.Abs(got - test.want)
		if cmplx.Abs(test.want) != 0 {
			if !cscalar.EqualWithinRel(got, test.want, tol) {
				t.Errorf("Li2(%g) relative error %g exceeds tol %g", test.in, diff/cmplx.Abs(test.want), tol)
			}
		} else if !cscalar.EqualWithinAbs(got, test.want, tol) {
			t.Errorf("Li2(%g) abs error %g exceeds tol %g", test.in, diff, tol)
		}
	}
}

func TestDiLogProperties(t *testing.T) {
	t.Parallel()
	const tol = 1e-12

	// Duplication formula: Li2(z^2) = 2*(Li2(z) + Li2(-z))
	for i, z := range []complex128{
		0.1 + 0.1i,
		-0.3 + 0.4i,
		0.5,
		200,
	} {
		lhs := Li2(z * z)
		rhs := 2 * (Li2(z) + Li2(-z))
		if !cscalar.EqualWithinAbs(lhs, rhs, tol) {
			t.Errorf("duplication formula failed for case %d, z=%v: got %v want %v", i, z, lhs, rhs)
		}
	}

	// Conjugation symmetry: Li2(conj(z)) == conj(Li2(z))
	// Valid for all z not on the branch cut (real z > 1).
	for i, z := range []complex128{
		0.3 + 0.5i,
		-0.8 + 0.1i,
		2 + 0.7i,
	} {
		lhs := Li2(cmplx.Conj(z))
		rhs := cmplx.Conj(Li2(z))
		if !cscalar.EqualWithinAbs(lhs, rhs, tol) {
			t.Errorf("conjugation symmetry failed for case %d, z=%v: got %v want %v", i, z, lhs, rhs)
		}
	}
}