From 73df946d56c74384511a194dd01dbe099584fd1a Mon Sep 17 00:00:00 2001
From: Daniel Baumann <daniel.baumann@progress-linux.org>
Date: Sun, 28 Apr 2024 15:14:23 +0200
Subject: Adding upstream version 1.16.10.

Signed-off-by: Daniel Baumann <daniel.baumann@progress-linux.org>
---
 src/math/big/hilbert_test.go | 160 +++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 160 insertions(+)
 create mode 100644 src/math/big/hilbert_test.go

(limited to 'src/math/big/hilbert_test.go')

diff --git a/src/math/big/hilbert_test.go b/src/math/big/hilbert_test.go
new file mode 100644
index 0000000..1a84341
--- /dev/null
+++ b/src/math/big/hilbert_test.go
@@ -0,0 +1,160 @@
+// Copyright 2009 The Go Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+// A little test program and benchmark for rational arithmetics.
+// Computes a Hilbert matrix, its inverse, multiplies them
+// and verifies that the product is the identity matrix.
+
+package big
+
+import (
+	"fmt"
+	"testing"
+)
+
+type matrix struct {
+	n, m int
+	a    []*Rat
+}
+
+func (a *matrix) at(i, j int) *Rat {
+	if !(0 <= i && i < a.n && 0 <= j && j < a.m) {
+		panic("index out of range")
+	}
+	return a.a[i*a.m+j]
+}
+
+func (a *matrix) set(i, j int, x *Rat) {
+	if !(0 <= i && i < a.n && 0 <= j && j < a.m) {
+		panic("index out of range")
+	}
+	a.a[i*a.m+j] = x
+}
+
+func newMatrix(n, m int) *matrix {
+	if !(0 <= n && 0 <= m) {
+		panic("illegal matrix")
+	}
+	a := new(matrix)
+	a.n = n
+	a.m = m
+	a.a = make([]*Rat, n*m)
+	return a
+}
+
+func newUnit(n int) *matrix {
+	a := newMatrix(n, n)
+	for i := 0; i < n; i++ {
+		for j := 0; j < n; j++ {
+			x := NewRat(0, 1)
+			if i == j {
+				x.SetInt64(1)
+			}
+			a.set(i, j, x)
+		}
+	}
+	return a
+}
+
+func newHilbert(n int) *matrix {
+	a := newMatrix(n, n)
+	for i := 0; i < n; i++ {
+		for j := 0; j < n; j++ {
+			a.set(i, j, NewRat(1, int64(i+j+1)))
+		}
+	}
+	return a
+}
+
+func newInverseHilbert(n int) *matrix {
+	a := newMatrix(n, n)
+	for i := 0; i < n; i++ {
+		for j := 0; j < n; j++ {
+			x1 := new(Rat).SetInt64(int64(i + j + 1))
+			x2 := new(Rat).SetInt(new(Int).Binomial(int64(n+i), int64(n-j-1)))
+			x3 := new(Rat).SetInt(new(Int).Binomial(int64(n+j), int64(n-i-1)))
+			x4 := new(Rat).SetInt(new(Int).Binomial(int64(i+j), int64(i)))
+
+			x1.Mul(x1, x2)
+			x1.Mul(x1, x3)
+			x1.Mul(x1, x4)
+			x1.Mul(x1, x4)
+
+			if (i+j)&1 != 0 {
+				x1.Neg(x1)
+			}
+
+			a.set(i, j, x1)
+		}
+	}
+	return a
+}
+
+func (a *matrix) mul(b *matrix) *matrix {
+	if a.m != b.n {
+		panic("illegal matrix multiply")
+	}
+	c := newMatrix(a.n, b.m)
+	for i := 0; i < c.n; i++ {
+		for j := 0; j < c.m; j++ {
+			x := NewRat(0, 1)
+			for k := 0; k < a.m; k++ {
+				x.Add(x, new(Rat).Mul(a.at(i, k), b.at(k, j)))
+			}
+			c.set(i, j, x)
+		}
+	}
+	return c
+}
+
+func (a *matrix) eql(b *matrix) bool {
+	if a.n != b.n || a.m != b.m {
+		return false
+	}
+	for i := 0; i < a.n; i++ {
+		for j := 0; j < a.m; j++ {
+			if a.at(i, j).Cmp(b.at(i, j)) != 0 {
+				return false
+			}
+		}
+	}
+	return true
+}
+
+func (a *matrix) String() string {
+	s := ""
+	for i := 0; i < a.n; i++ {
+		for j := 0; j < a.m; j++ {
+			s += fmt.Sprintf("\t%s", a.at(i, j))
+		}
+		s += "\n"
+	}
+	return s
+}
+
+func doHilbert(t *testing.T, n int) {
+	a := newHilbert(n)
+	b := newInverseHilbert(n)
+	I := newUnit(n)
+	ab := a.mul(b)
+	if !ab.eql(I) {
+		if t == nil {
+			panic("Hilbert failed")
+		}
+		t.Errorf("a   = %s\n", a)
+		t.Errorf("b   = %s\n", b)
+		t.Errorf("a*b = %s\n", ab)
+		t.Errorf("I   = %s\n", I)
+	}
+}
+
+func TestHilbert(t *testing.T) {
+	doHilbert(t, 10)
+}
+
+func BenchmarkHilbert(b *testing.B) {
+	for i := 0; i < b.N; i++ {
+		doHilbert(nil, 10)
+	}
+}
-- 
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