From f6bf5ba60d06d98ffe094dc78ea7128374506338 Mon Sep 17 00:00:00 2001
From: Sander Schobers <sander@schobers.eu>
Date: Sat, 21 Dec 2019 12:53:57 +0100
Subject: [PATCH] Added helper methods for big ints.

---
 ints/big.go        | 13 ++++++
 ints/big_test.go   | 17 ++++++++
 ints/bignumbers.go | 98 ++++++++++++++++++++++++++++++++++++++++++++++
 3 files changed, 128 insertions(+)
 create mode 100644 ints/big.go
 create mode 100644 ints/big_test.go
 create mode 100644 ints/bignumbers.go

diff --git a/ints/big.go b/ints/big.go
new file mode 100644
index 0000000..ef361e7
--- /dev/null
+++ b/ints/big.go
@@ -0,0 +1,13 @@
+package ints
+
+import "math/big"
+
+func CopyBig(i *big.Int) *big.Int { return (&big.Int{}).Set(i) }
+
+func DivBig(x, y *big.Int) *big.Int { return x.Div(x, y) }
+
+func MulBig(x, y *big.Int) *big.Int { return x.Mul(x, y) }
+
+func PowTenBig(p int) *big.Int { return Big.PowTen(p) }
+
+func RepunitBig(k int) *big.Int { return Big.Repunit(k) }
diff --git a/ints/big_test.go b/ints/big_test.go
new file mode 100644
index 0000000..bff5779
--- /dev/null
+++ b/ints/big_test.go
@@ -0,0 +1,17 @@
+package ints
+
+import (
+	"testing"
+)
+
+func BenchmarkIntsSmallRepunit(b *testing.B) {
+	for i := 0; i < b.N; i++ {
+		Big.Repunit(1234)
+	}
+}
+
+func BenchmarkIntsLargeRepunit(b *testing.B) {
+	for i := 0; i < b.N; i++ {
+		Big.Repunit(1234567)
+	}
+}
diff --git a/ints/bignumbers.go b/ints/bignumbers.go
new file mode 100644
index 0000000..c764961
--- /dev/null
+++ b/ints/bignumbers.go
@@ -0,0 +1,98 @@
+package ints
+
+import "math/big"
+
+type BigNumbers struct {
+	Zero       *big.Int
+	One        *big.Int
+	Two        *big.Int
+	Nine       *big.Int
+	Ten        *big.Int
+	Thousand   *big.Int
+	Million    *big.Int
+	Ten10      *big.Int
+	Ten30      *big.Int
+	Ten100     *big.Int
+	Ten300     *big.Int
+	Ten1000    *big.Int
+	Ten3000    *big.Int
+	Ten10000   *big.Int
+	Ten30000   *big.Int
+	Ten100000  *big.Int
+	Ten300000  *big.Int
+	Ten1000000 *big.Int
+}
+
+var Big *BigNumbers = NewBigNumbers()
+
+func NewBigNumbers() *BigNumbers {
+	ten := big.NewInt(10)
+	thousand := big.NewInt(1000)
+	million := big.NewInt(1000000)
+	ten10 := MulBig(MulBig(MulBig(big.NewInt(1), million), thousand), ten)
+	ten30 := MulBig(MulBig(MulBig(big.NewInt(1), ten10), ten10), ten10)
+	ten100 := MulBig(MulBig(MulBig(MulBig(big.NewInt(1), ten30), ten30), ten30), ten10)
+	ten300 := MulBig(MulBig(MulBig(big.NewInt(1), ten100), ten100), ten100)
+	ten1000 := MulBig(MulBig(MulBig(MulBig(big.NewInt(1), ten300), ten300), ten300), ten100)
+	ten3000 := MulBig(MulBig(MulBig(big.NewInt(1), ten1000), ten1000), ten1000)
+	ten10000 := MulBig(MulBig(MulBig(MulBig(big.NewInt(1), ten3000), ten3000), ten3000), ten1000)
+	ten30000 := MulBig(MulBig(MulBig(big.NewInt(1), ten10000), ten10000), ten10000)
+	ten100000 := MulBig(MulBig(MulBig(MulBig(big.NewInt(1), ten30000), ten30000), ten30000), ten10000)
+	ten300000 := MulBig(MulBig(MulBig(big.NewInt(1), ten100000), ten100000), ten100000)
+	ten1000000 := MulBig(MulBig(MulBig(MulBig(big.NewInt(1), ten300000), ten300000), ten300000), ten100000)
+	return &BigNumbers{
+		Zero:       big.NewInt(0),
+		One:        big.NewInt(1),
+		Two:        big.NewInt(2),
+		Nine:       big.NewInt(9),
+		Ten:        ten,
+		Thousand:   thousand,
+		Million:    million,
+		Ten10:      ten10,
+		Ten30:      ten30,
+		Ten100:     ten100,
+		Ten300:     ten300,
+		Ten1000:    ten1000,
+		Ten3000:    ten3000,
+		Ten10000:   ten10000,
+		Ten30000:   ten30000,
+		Ten100000:  ten100000,
+		Ten300000:  ten300000,
+		Ten1000000: ten1000000,
+	}
+}
+
+func (n *BigNumbers) Repunit(k int) *big.Int {
+	rep := n.PowTen(k)
+	return rep.Sub(rep, n.One).Div(rep, n.Nine)
+}
+
+func (n *BigNumbers) PowTen(p int) *big.Int {
+	result := big.NewInt(1)
+	pow := func(n int, one, three *big.Int) {
+		for n >= 3 {
+			result.Mul(result, three)
+			n -= 3
+		}
+		for n >= 1 {
+			result.Mul(result, one)
+			n--
+		}
+	}
+	mul := func(n int, one, three *big.Int) int {
+		mod := n % 10
+		pow(mod, one, three)
+		return n / 10
+	}
+	p = mul(p, n.Ten, n.Thousand)
+	p = mul(p, n.Ten10, n.Ten30)
+	p = mul(p, n.Ten100, n.Ten300)
+	p = mul(p, n.Ten1000, n.Ten3000)
+	p = mul(p, n.Ten10000, n.Ten30000)
+	p = mul(p, n.Ten100000, n.Ten300000)
+	for p > 0 {
+		result.Mul(result, n.Ten1000000)
+		p--
+	}
+	return result
+}