Merge tag 'upstream/1.4' into debian-experimental

* tag 'upstream/1.4':
  Imported Upstream version 1.4

1 files changed, 1625 insertions, 0 deletions

diff --git a/src/math/big/int_test.go b/src/math/big/int_test.go
new file mode 100644
index 000000000..6070cf325
--- /dev/null
+++ b/src/math/big/int_test.go
@@ -0,0 +1,1625 @@
+// 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.
+
+package big
+
+import (
+	"bytes"
+	"encoding/gob"
+	"encoding/hex"
+	"encoding/json"
+	"encoding/xml"
+	"fmt"
+	"math/rand"
+	"testing"
+	"testing/quick"
+)
+
+func isNormalized(x *Int) bool {
+	if len(x.abs) == 0 {
+		return !x.neg
+	}
+	// len(x.abs) > 0
+	return x.abs[len(x.abs)-1] != 0
+}
+
+type funZZ func(z, x, y *Int) *Int
+type argZZ struct {
+	z, x, y *Int
+}
+
+var sumZZ = []argZZ{
+	{NewInt(0), NewInt(0), NewInt(0)},
+	{NewInt(1), NewInt(1), NewInt(0)},
+	{NewInt(1111111110), NewInt(123456789), NewInt(987654321)},
+	{NewInt(-1), NewInt(-1), NewInt(0)},
+	{NewInt(864197532), NewInt(-123456789), NewInt(987654321)},
+	{NewInt(-1111111110), NewInt(-123456789), NewInt(-987654321)},
+}
+
+var prodZZ = []argZZ{
+	{NewInt(0), NewInt(0), NewInt(0)},
+	{NewInt(0), NewInt(1), NewInt(0)},
+	{NewInt(1), NewInt(1), NewInt(1)},
+	{NewInt(-991 * 991), NewInt(991), NewInt(-991)},
+	// TODO(gri) add larger products
+}
+
+func TestSignZ(t *testing.T) {
+	var zero Int
+	for _, a := range sumZZ {
+		s := a.z.Sign()
+		e := a.z.Cmp(&zero)
+		if s != e {
+			t.Errorf("got %d; want %d for z = %v", s, e, a.z)
+		}
+	}
+}
+
+func TestSetZ(t *testing.T) {
+	for _, a := range sumZZ {
+		var z Int
+		z.Set(a.z)
+		if !isNormalized(&z) {
+			t.Errorf("%v is not normalized", z)
+		}
+		if (&z).Cmp(a.z) != 0 {
+			t.Errorf("got z = %v; want %v", z, a.z)
+		}
+	}
+}
+
+func TestAbsZ(t *testing.T) {
+	var zero Int
+	for _, a := range sumZZ {
+		var z Int
+		z.Abs(a.z)
+		var e Int
+		e.Set(a.z)
+		if e.Cmp(&zero) < 0 {
+			e.Sub(&zero, &e)
+		}
+		if z.Cmp(&e) != 0 {
+			t.Errorf("got z = %v; want %v", z, e)
+		}
+	}
+}
+
+func testFunZZ(t *testing.T, msg string, f funZZ, a argZZ) {
+	var z Int
+	f(&z, a.x, a.y)
+	if !isNormalized(&z) {
+		t.Errorf("%s%v is not normalized", msg, z)
+	}
+	if (&z).Cmp(a.z) != 0 {
+		t.Errorf("%s%+v\n\tgot z = %v; want %v", msg, a, &z, a.z)
+	}
+}
+
+func TestSumZZ(t *testing.T) {
+	AddZZ := func(z, x, y *Int) *Int { return z.Add(x, y) }
+	SubZZ := func(z, x, y *Int) *Int { return z.Sub(x, y) }
+	for _, a := range sumZZ {
+		arg := a
+		testFunZZ(t, "AddZZ", AddZZ, arg)
+
+		arg = argZZ{a.z, a.y, a.x}
+		testFunZZ(t, "AddZZ symmetric", AddZZ, arg)
+
+		arg = argZZ{a.x, a.z, a.y}
+		testFunZZ(t, "SubZZ", SubZZ, arg)
+
+		arg = argZZ{a.y, a.z, a.x}
+		testFunZZ(t, "SubZZ symmetric", SubZZ, arg)
+	}
+}
+
+func TestProdZZ(t *testing.T) {
+	MulZZ := func(z, x, y *Int) *Int { return z.Mul(x, y) }
+	for _, a := range prodZZ {
+		arg := a
+		testFunZZ(t, "MulZZ", MulZZ, arg)
+
+		arg = argZZ{a.z, a.y, a.x}
+		testFunZZ(t, "MulZZ symmetric", MulZZ, arg)
+	}
+}
+
+// mulBytes returns x*y via grade school multiplication. Both inputs
+// and the result are assumed to be in big-endian representation (to
+// match the semantics of Int.Bytes and Int.SetBytes).
+func mulBytes(x, y []byte) []byte {
+	z := make([]byte, len(x)+len(y))
+
+	// multiply
+	k0 := len(z) - 1
+	for j := len(y) - 1; j >= 0; j-- {
+		d := int(y[j])
+		if d != 0 {
+			k := k0
+			carry := 0
+			for i := len(x) - 1; i >= 0; i-- {
+				t := int(z[k]) + int(x[i])*d + carry
+				z[k], carry = byte(t), t>>8
+				k--
+			}
+			z[k] = byte(carry)
+		}
+		k0--
+	}
+
+	// normalize (remove leading 0's)
+	i := 0
+	for i < len(z) && z[i] == 0 {
+		i++
+	}
+
+	return z[i:]
+}
+
+func checkMul(a, b []byte) bool {
+	var x, y, z1 Int
+	x.SetBytes(a)
+	y.SetBytes(b)
+	z1.Mul(&x, &y)
+
+	var z2 Int
+	z2.SetBytes(mulBytes(a, b))
+
+	return z1.Cmp(&z2) == 0
+}
+
+func TestMul(t *testing.T) {
+	if err := quick.Check(checkMul, nil); err != nil {
+		t.Error(err)
+	}
+}
+
+var mulRangesZ = []struct {
+	a, b int64
+	prod string
+}{
+	// entirely positive ranges are covered by mulRangesN
+	{-1, 1, "0"},
+	{-2, -1, "2"},
+	{-3, -2, "6"},
+	{-3, -1, "-6"},
+	{1, 3, "6"},
+	{-10, -10, "-10"},
+	{0, -1, "1"},                      // empty range
+	{-1, -100, "1"},                   // empty range
+	{-1, 1, "0"},                      // range includes 0
+	{-1e9, 0, "0"},                    // range includes 0
+	{-1e9, 1e9, "0"},                  // range includes 0
+	{-10, -1, "3628800"},              // 10!
+	{-20, -2, "-2432902008176640000"}, // -20!
+	{-99, -1,
+		"-933262154439441526816992388562667004907159682643816214685929" +
+			"638952175999932299156089414639761565182862536979208272237582" +
+			"511852109168640000000000000000000000", // -99!
+	},
+}
+
+func TestMulRangeZ(t *testing.T) {
+	var tmp Int
+	// test entirely positive ranges
+	for i, r := range mulRangesN {
+		prod := tmp.MulRange(int64(r.a), int64(r.b)).String()
+		if prod != r.prod {
+			t.Errorf("#%da: got %s; want %s", i, prod, r.prod)
+		}
+	}
+	// test other ranges
+	for i, r := range mulRangesZ {
+		prod := tmp.MulRange(r.a, r.b).String()
+		if prod != r.prod {
+			t.Errorf("#%db: got %s; want %s", i, prod, r.prod)
+		}
+	}
+}
+
+var stringTests = []struct {
+	in   string
+	out  string
+	base int
+	val  int64
+	ok   bool
+}{
+	{in: "", ok: false},
+	{in: "a", ok: false},
+	{in: "z", ok: false},
+	{in: "+", ok: false},
+	{in: "-", ok: false},
+	{in: "0b", ok: false},
+	{in: "0x", ok: false},
+	{in: "2", base: 2, ok: false},
+	{in: "0b2", base: 0, ok: false},
+	{in: "08", ok: false},
+	{in: "8", base: 8, ok: false},
+	{in: "0xg", base: 0, ok: false},
+	{in: "g", base: 16, ok: false},
+	{"0", "0", 0, 0, true},
+	{"0", "0", 10, 0, true},
+	{"0", "0", 16, 0, true},
+	{"+0", "0", 0, 0, true},
+	{"-0", "0", 0, 0, true},
+	{"10", "10", 0, 10, true},
+	{"10", "10", 10, 10, true},
+	{"10", "10", 16, 16, true},
+	{"-10", "-10", 16, -16, true},
+	{"+10", "10", 16, 16, true},
+	{"0x10", "16", 0, 16, true},
+	{in: "0x10", base: 16, ok: false},
+	{"-0x10", "-16", 0, -16, true},
+	{"+0x10", "16", 0, 16, true},
+	{"00", "0", 0, 0, true},
+	{"0", "0", 8, 0, true},
+	{"07", "7", 0, 7, true},
+	{"7", "7", 8, 7, true},
+	{"023", "19", 0, 19, true},
+	{"23", "23", 8, 19, true},
+	{"cafebabe", "cafebabe", 16, 0xcafebabe, true},
+	{"0b0", "0", 0, 0, true},
+	{"-111", "-111", 2, -7, true},
+	{"-0b111", "-7", 0, -7, true},
+	{"0b1001010111", "599", 0, 0x257, true},
+	{"1001010111", "1001010111", 2, 0x257, true},
+}
+
+func format(base int) string {
+	switch base {
+	case 2:
+		return "%b"
+	case 8:
+		return "%o"
+	case 16:
+		return "%x"
+	}
+	return "%d"
+}
+
+func TestGetString(t *testing.T) {
+	z := new(Int)
+	for i, test := range stringTests {
+		if !test.ok {
+			continue
+		}
+		z.SetInt64(test.val)
+
+		if test.base == 10 {
+			s := z.String()
+			if s != test.out {
+				t.Errorf("#%da got %s; want %s", i, s, test.out)
+			}
+		}
+
+		s := fmt.Sprintf(format(test.base), z)
+		if s != test.out {
+			t.Errorf("#%db got %s; want %s", i, s, test.out)
+		}
+	}
+}
+
+func TestSetString(t *testing.T) {
+	tmp := new(Int)
+	for i, test := range stringTests {
+		// initialize to a non-zero value so that issues with parsing
+		// 0 are detected
+		tmp.SetInt64(1234567890)
+		n1, ok1 := new(Int).SetString(test.in, test.base)
+		n2, ok2 := tmp.SetString(test.in, test.base)
+		expected := NewInt(test.val)
+		if ok1 != test.ok || ok2 != test.ok {
+			t.Errorf("#%d (input '%s') ok incorrect (should be %t)", i, test.in, test.ok)
+			continue
+		}
+		if !ok1 {
+			if n1 != nil {
+				t.Errorf("#%d (input '%s') n1 != nil", i, test.in)
+			}
+			continue
+		}
+		if !ok2 {
+			if n2 != nil {
+				t.Errorf("#%d (input '%s') n2 != nil", i, test.in)
+			}
+			continue
+		}
+
+		if ok1 && !isNormalized(n1) {
+			t.Errorf("#%d (input '%s'): %v is not normalized", i, test.in, *n1)
+		}
+		if ok2 && !isNormalized(n2) {
+			t.Errorf("#%d (input '%s'): %v is not normalized", i, test.in, *n2)
+		}
+
+		if n1.Cmp(expected) != 0 {
+			t.Errorf("#%d (input '%s') got: %s want: %d", i, test.in, n1, test.val)
+		}
+		if n2.Cmp(expected) != 0 {
+			t.Errorf("#%d (input '%s') got: %s want: %d", i, test.in, n2, test.val)
+		}
+	}
+}
+
+var formatTests = []struct {
+	input  string
+	format string
+	output string
+}{
+	{"<nil>", "%x", "<nil>"},
+	{"<nil>", "%#x", "<nil>"},
+	{"<nil>", "%#y", "%!y(big.Int=<nil>)"},
+
+	{"10", "%b", "1010"},
+	{"10", "%o", "12"},
+	{"10", "%d", "10"},
+	{"10", "%v", "10"},
+	{"10", "%x", "a"},
+	{"10", "%X", "A"},
+	{"-10", "%X", "-A"},
+	{"10", "%y", "%!y(big.Int=10)"},
+	{"-10", "%y", "%!y(big.Int=-10)"},
+
+	{"10", "%#b", "1010"},
+	{"10", "%#o", "012"},
+	{"10", "%#d", "10"},
+	{"10", "%#v", "10"},
+	{"10", "%#x", "0xa"},
+	{"10", "%#X", "0XA"},
+	{"-10", "%#X", "-0XA"},
+	{"10", "%#y", "%!y(big.Int=10)"},
+	{"-10", "%#y", "%!y(big.Int=-10)"},
+
+	{"1234", "%d", "1234"},
+	{"1234", "%3d", "1234"},
+	{"1234", "%4d", "1234"},
+	{"-1234", "%d", "-1234"},
+	{"1234", "% 5d", " 1234"},
+	{"1234", "%+5d", "+1234"},
+	{"1234", "%-5d", "1234 "},
+	{"1234", "%x", "4d2"},
+	{"1234", "%X", "4D2"},
+	{"-1234", "%3x", "-4d2"},
+	{"-1234", "%4x", "-4d2"},
+	{"-1234", "%5x", " -4d2"},
+	{"-1234", "%-5x", "-4d2 "},
+	{"1234", "%03d", "1234"},
+	{"1234", "%04d", "1234"},
+	{"1234", "%05d", "01234"},
+	{"1234", "%06d", "001234"},
+	{"-1234", "%06d", "-01234"},
+	{"1234", "%+06d", "+01234"},
+	{"1234", "% 06d", " 01234"},
+	{"1234", "%-6d", "1234  "},
+	{"1234", "%-06d", "1234  "},
+	{"-1234", "%-06d", "-1234 "},
+
+	{"1234", "%.3d", "1234"},
+	{"1234", "%.4d", "1234"},
+	{"1234", "%.5d", "01234"},
+	{"1234", "%.6d", "001234"},
+	{"-1234", "%.3d", "-1234"},
+	{"-1234", "%.4d", "-1234"},
+	{"-1234", "%.5d", "-01234"},
+	{"-1234", "%.6d", "-001234"},
+
+	{"1234", "%8.3d", "    1234"},
+	{"1234", "%8.4d", "    1234"},
+	{"1234", "%8.5d", "   01234"},
+	{"1234", "%8.6d", "  001234"},
+	{"-1234", "%8.3d", "   -1234"},
+	{"-1234", "%8.4d", "   -1234"},
+	{"-1234", "%8.5d", "  -01234"},
+	{"-1234", "%8.6d", " -001234"},
+
+	{"1234", "%+8.3d", "   +1234"},
+	{"1234", "%+8.4d", "   +1234"},
+	{"1234", "%+8.5d", "  +01234"},
+	{"1234", "%+8.6d", " +001234"},
+	{"-1234", "%+8.3d", "   -1234"},
+	{"-1234", "%+8.4d", "   -1234"},
+	{"-1234", "%+8.5d", "  -01234"},
+	{"-1234", "%+8.6d", " -001234"},
+
+	{"1234", "% 8.3d", "    1234"},
+	{"1234", "% 8.4d", "    1234"},
+	{"1234", "% 8.5d", "   01234"},
+	{"1234", "% 8.6d", "  001234"},
+	{"-1234", "% 8.3d", "   -1234"},
+	{"-1234", "% 8.4d", "   -1234"},
+	{"-1234", "% 8.5d", "  -01234"},
+	{"-1234", "% 8.6d", " -001234"},
+
+	{"1234", "%.3x", "4d2"},
+	{"1234", "%.4x", "04d2"},
+	{"1234", "%.5x", "004d2"},
+	{"1234", "%.6x", "0004d2"},
+	{"-1234", "%.3x", "-4d2"},
+	{"-1234", "%.4x", "-04d2"},
+	{"-1234", "%.5x", "-004d2"},
+	{"-1234", "%.6x", "-0004d2"},
+
+	{"1234", "%8.3x", "     4d2"},
+	{"1234", "%8.4x", "    04d2"},
+	{"1234", "%8.5x", "   004d2"},
+	{"1234", "%8.6x", "  0004d2"},
+	{"-1234", "%8.3x", "    -4d2"},
+	{"-1234", "%8.4x", "   -04d2"},
+	{"-1234", "%8.5x", "  -004d2"},
+	{"-1234", "%8.6x", " -0004d2"},
+
+	{"1234", "%+8.3x", "    +4d2"},
+	{"1234", "%+8.4x", "   +04d2"},
+	{"1234", "%+8.5x", "  +004d2"},
+	{"1234", "%+8.6x", " +0004d2"},
+	{"-1234", "%+8.3x", "    -4d2"},
+	{"-1234", "%+8.4x", "   -04d2"},
+	{"-1234", "%+8.5x", "  -004d2"},
+	{"-1234", "%+8.6x", " -0004d2"},
+
+	{"1234", "% 8.3x", "     4d2"},
+	{"1234", "% 8.4x", "    04d2"},
+	{"1234", "% 8.5x", "   004d2"},
+	{"1234", "% 8.6x", "  0004d2"},
+	{"1234", "% 8.7x", " 00004d2"},
+	{"1234", "% 8.8x", " 000004d2"},
+	{"-1234", "% 8.3x", "    -4d2"},
+	{"-1234", "% 8.4x", "   -04d2"},
+	{"-1234", "% 8.5x", "  -004d2"},
+	{"-1234", "% 8.6x", " -0004d2"},
+	{"-1234", "% 8.7x", "-00004d2"},
+	{"-1234", "% 8.8x", "-000004d2"},
+
+	{"1234", "%-8.3d", "1234    "},
+	{"1234", "%-8.4d", "1234    "},
+	{"1234", "%-8.5d", "01234   "},
+	{"1234", "%-8.6d", "001234  "},
+	{"1234", "%-8.7d", "0001234 "},
+	{"1234", "%-8.8d", "00001234"},
+	{"-1234", "%-8.3d", "-1234   "},
+	{"-1234", "%-8.4d", "-1234   "},
+	{"-1234", "%-8.5d", "-01234  "},
+	{"-1234", "%-8.6d", "-001234 "},
+	{"-1234", "%-8.7d", "-0001234"},
+	{"-1234", "%-8.8d", "-00001234"},
+
+	{"16777215", "%b", "111111111111111111111111"}, // 2**24 - 1
+
+	{"0", "%.d", ""},
+	{"0", "%.0d", ""},
+	{"0", "%3.d", ""},
+}
+
+func TestFormat(t *testing.T) {
+	for i, test := range formatTests {
+		var x *Int
+		if test.input != "<nil>" {
+			var ok bool
+			x, ok = new(Int).SetString(test.input, 0)
+			if !ok {
+				t.Errorf("#%d failed reading input %s", i, test.input)
+			}
+		}
+		output := fmt.Sprintf(test.format, x)
+		if output != test.output {
+			t.Errorf("#%d got %q; want %q, {%q, %q, %q}", i, output, test.output, test.input, test.format, test.output)
+		}
+	}
+}
+
+var scanTests = []struct {
+	input     string
+	format    string
+	output    string
+	remaining int
+}{
+	{"1010", "%b", "10", 0},
+	{"0b1010", "%v", "10", 0},
+	{"12", "%o", "10", 0},
+	{"012", "%v", "10", 0},
+	{"10", "%d", "10", 0},
+	{"10", "%v", "10", 0},
+	{"a", "%x", "10", 0},
+	{"0xa", "%v", "10", 0},
+	{"A", "%X", "10", 0},
+	{"-A", "%X", "-10", 0},
+	{"+0b1011001", "%v", "89", 0},
+	{"0xA", "%v", "10", 0},
+	{"0 ", "%v", "0", 1},
+	{"2+3", "%v", "2", 2},
+	{"0XABC 12", "%v", "2748", 3},
+}
+
+func TestScan(t *testing.T) {
+	var buf bytes.Buffer
+	for i, test := range scanTests {
+		x := new(Int)
+		buf.Reset()
+		buf.WriteString(test.input)
+		if _, err := fmt.Fscanf(&buf, test.format, x); err != nil {
+			t.Errorf("#%d error: %s", i, err)
+		}
+		if x.String() != test.output {
+			t.Errorf("#%d got %s; want %s", i, x.String(), test.output)
+		}
+		if buf.Len() != test.remaining {
+			t.Errorf("#%d got %d bytes remaining; want %d", i, buf.Len(), test.remaining)
+		}
+	}
+}
+
+// Examples from the Go Language Spec, section "Arithmetic operators"
+var divisionSignsTests = []struct {
+	x, y int64
+	q, r int64 // T-division
+	d, m int64 // Euclidian division
+}{
+	{5, 3, 1, 2, 1, 2},
+	{-5, 3, -1, -2, -2, 1},
+	{5, -3, -1, 2, -1, 2},
+	{-5, -3, 1, -2, 2, 1},
+	{1, 2, 0, 1, 0, 1},
+	{8, 4, 2, 0, 2, 0},
+}
+
+func TestDivisionSigns(t *testing.T) {
+	for i, test := range divisionSignsTests {
+		x := NewInt(test.x)
+		y := NewInt(test.y)
+		q := NewInt(test.q)
+		r := NewInt(test.r)
+		d := NewInt(test.d)
+		m := NewInt(test.m)
+
+		q1 := new(Int).Quo(x, y)
+		r1 := new(Int).Rem(x, y)
+		if !isNormalized(q1) {
+			t.Errorf("#%d Quo: %v is not normalized", i, *q1)
+		}
+		if !isNormalized(r1) {
+			t.Errorf("#%d Rem: %v is not normalized", i, *r1)
+		}
+		if q1.Cmp(q) != 0 || r1.Cmp(r) != 0 {
+			t.Errorf("#%d QuoRem: got (%s, %s), want (%s, %s)", i, q1, r1, q, r)
+		}
+
+		q2, r2 := new(Int).QuoRem(x, y, new(Int))
+		if !isNormalized(q2) {
+			t.Errorf("#%d Quo: %v is not normalized", i, *q2)
+		}
+		if !isNormalized(r2) {
+			t.Errorf("#%d Rem: %v is not normalized", i, *r2)
+		}
+		if q2.Cmp(q) != 0 || r2.Cmp(r) != 0 {
+			t.Errorf("#%d QuoRem: got (%s, %s), want (%s, %s)", i, q2, r2, q, r)
+		}
+
+		d1 := new(Int).Div(x, y)
+		m1 := new(Int).Mod(x, y)
+		if !isNormalized(d1) {
+			t.Errorf("#%d Div: %v is not normalized", i, *d1)
+		}
+		if !isNormalized(m1) {
+			t.Errorf("#%d Mod: %v is not normalized", i, *m1)
+		}
+		if d1.Cmp(d) != 0 || m1.Cmp(m) != 0 {
+			t.Errorf("#%d DivMod: got (%s, %s), want (%s, %s)", i, d1, m1, d, m)
+		}
+
+		d2, m2 := new(Int).DivMod(x, y, new(Int))
+		if !isNormalized(d2) {
+			t.Errorf("#%d Div: %v is not normalized", i, *d2)
+		}
+		if !isNormalized(m2) {
+			t.Errorf("#%d Mod: %v is not normalized", i, *m2)
+		}
+		if d2.Cmp(d) != 0 || m2.Cmp(m) != 0 {
+			t.Errorf("#%d DivMod: got (%s, %s), want (%s, %s)", i, d2, m2, d, m)
+		}
+	}
+}
+
+func checkSetBytes(b []byte) bool {
+	hex1 := hex.EncodeToString(new(Int).SetBytes(b).Bytes())
+	hex2 := hex.EncodeToString(b)
+
+	for len(hex1) < len(hex2) {
+		hex1 = "0" + hex1
+	}
+
+	for len(hex1) > len(hex2) {
+		hex2 = "0" + hex2
+	}
+
+	return hex1 == hex2
+}
+
+func TestSetBytes(t *testing.T) {
+	if err := quick.Check(checkSetBytes, nil); err != nil {
+		t.Error(err)
+	}
+}
+
+func checkBytes(b []byte) bool {
+	b2 := new(Int).SetBytes(b).Bytes()
+	return bytes.Equal(b, b2)
+}
+
+func TestBytes(t *testing.T) {
+	if err := quick.Check(checkSetBytes, nil); err != nil {
+		t.Error(err)
+	}
+}
+
+func checkQuo(x, y []byte) bool {
+	u := new(Int).SetBytes(x)
+	v := new(Int).SetBytes(y)
+
+	if len(v.abs) == 0 {
+		return true
+	}
+
+	r := new(Int)
+	q, r := new(Int).QuoRem(u, v, r)
+
+	if r.Cmp(v) >= 0 {
+		return false
+	}
+
+	uprime := new(Int).Set(q)
+	uprime.Mul(uprime, v)
+	uprime.Add(uprime, r)
+
+	return uprime.Cmp(u) == 0
+}
+
+var quoTests = []struct {
+	x, y string
+	q, r string
+}{
+	{
+		"476217953993950760840509444250624797097991362735329973741718102894495832294430498335824897858659711275234906400899559094370964723884706254265559534144986498357",
+		"9353930466774385905609975137998169297361893554149986716853295022578535724979483772383667534691121982974895531435241089241440253066816724367338287092081996",
+		"50911",
+		"1",
+	},
+	{
+		"11510768301994997771168",
+		"1328165573307167369775",
+		"8",
+		"885443715537658812968",
+	},
+}
+
+func TestQuo(t *testing.T) {
+	if err := quick.Check(checkQuo, nil); err != nil {
+		t.Error(err)
+	}
+
+	for i, test := range quoTests {
+		x, _ := new(Int).SetString(test.x, 10)
+		y, _ := new(Int).SetString(test.y, 10)
+		expectedQ, _ := new(Int).SetString(test.q, 10)
+		expectedR, _ := new(Int).SetString(test.r, 10)
+
+		r := new(Int)
+		q, r := new(Int).QuoRem(x, y, r)
+
+		if q.Cmp(expectedQ) != 0 || r.Cmp(expectedR) != 0 {
+			t.Errorf("#%d got (%s, %s) want (%s, %s)", i, q, r, expectedQ, expectedR)
+		}
+	}
+}
+
+func TestQuoStepD6(t *testing.T) {
+	// See Knuth, Volume 2, section 4.3.1, exercise 21. This code exercises
+	// a code path which only triggers 1 in 10^{-19} cases.
+
+	u := &Int{false, nat{0, 0, 1 + 1<<(_W-1), _M ^ (1 << (_W - 1))}}
+	v := &Int{false, nat{5, 2 + 1<<(_W-1), 1 << (_W - 1)}}
+
+	r := new(Int)
+	q, r := new(Int).QuoRem(u, v, r)
+	const expectedQ64 = "18446744073709551613"
+	const expectedR64 = "3138550867693340382088035895064302439801311770021610913807"
+	const expectedQ32 = "4294967293"
+	const expectedR32 = "39614081266355540837921718287"
+	if q.String() != expectedQ64 && q.String() != expectedQ32 ||
+		r.String() != expectedR64 && r.String() != expectedR32 {
+		t.Errorf("got (%s, %s) want (%s, %s) or (%s, %s)", q, r, expectedQ64, expectedR64, expectedQ32, expectedR32)
+	}
+}
+
+var bitLenTests = []struct {
+	in  string
+	out int
+}{
+	{"-1", 1},
+	{"0", 0},
+	{"1", 1},
+	{"2", 2},
+	{"4", 3},
+	{"0xabc", 12},
+	{"0x8000", 16},
+	{"0x80000000", 32},
+	{"0x800000000000", 48},
+	{"0x8000000000000000", 64},
+	{"0x80000000000000000000", 80},
+	{"-0x4000000000000000000000", 87},
+}
+
+func TestBitLen(t *testing.T) {
+	for i, test := range bitLenTests {
+		x, ok := new(Int).SetString(test.in, 0)
+		if !ok {
+			t.Errorf("#%d test input invalid: %s", i, test.in)
+			continue
+		}
+
+		if n := x.BitLen(); n != test.out {
+			t.Errorf("#%d got %d want %d", i, n, test.out)
+		}
+	}
+}
+
+var expTests = []struct {
+	x, y, m string
+	out     string
+}{
+	// y <= 0
+	{"0", "0", "", "1"},
+	{"1", "0", "", "1"},
+	{"-10", "0", "", "1"},
+	{"1234", "-1", "", "1"},
+
+	// m == 1
+	{"0", "0", "1", "0"},
+	{"1", "0", "1", "0"},
+	{"-10", "0", "1", "0"},
+	{"1234", "-1", "1", "0"},
+
+	// misc
+	{"5", "-7", "", "1"},
+	{"-5", "-7", "", "1"},
+	{"5", "0", "", "1"},
+	{"-5", "0", "", "1"},
+	{"5", "1", "", "5"},
+	{"-5", "1", "", "-5"},
+	{"-5", "1", "7", "2"},
+	{"-2", "3", "2", "0"},
+	{"5", "2", "", "25"},
+	{"1", "65537", "2", "1"},
+	{"0x8000000000000000", "2", "", "0x40000000000000000000000000000000"},
+	{"0x8000000000000000", "2", "6719", "4944"},
+	{"0x8000000000000000", "3", "6719", "5447"},
+	{"0x8000000000000000", "1000", "6719", "1603"},
+	{"0x8000000000000000", "1000000", "6719", "3199"},
+	{"0x8000000000000000", "-1000000", "6719", "1"},
+	{
+		"2938462938472983472983659726349017249287491026512746239764525612965293865296239471239874193284792387498274256129746192347",
+		"298472983472983471903246121093472394872319615612417471234712061",
+		"29834729834729834729347290846729561262544958723956495615629569234729836259263598127342374289365912465901365498236492183464",
+		"23537740700184054162508175125554701713153216681790245129157191391322321508055833908509185839069455749219131480588829346291",
+	},
+	// test case for issue 8822
+	{
+		"-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
+		"0xB08FFB20760FFED58FADA86DFEF71AD72AA0FA763219618FE022C197E54708BB1191C66470250FCE8879487507CEE41381CA4D932F81C2B3F1AB20B539D50DCD",
+		"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
+		"21484252197776302499639938883777710321993113097987201050501182909581359357618579566746556372589385361683610524730509041328855066514963385522570894839035884713051640171474186548713546686476761306436434146475140156284389181808675016576845833340494848283681088886584219750554408060556769486628029028720727393293111678826356480455433909233520504112074401376133077150471237549474149190242010469539006449596611576612573955754349042329130631128234637924786466585703488460540228477440853493392086251021228087076124706778899179648655221663765993962724699135217212118535057766739392069738618682722216712319320435674779146070442",
+	},
+}
+
+func TestExp(t *testing.T) {
+	for i, test := range expTests {
+		x, ok1 := new(Int).SetString(test.x, 0)
+		y, ok2 := new(Int).SetString(test.y, 0)
+		out, ok3 := new(Int).SetString(test.out, 0)
+
+		var ok4 bool
+		var m *Int
+
+		if len(test.m) == 0 {
+			m, ok4 = nil, true
+		} else {
+			m, ok4 = new(Int).SetString(test.m, 0)
+		}
+
+		if !ok1 || !ok2 || !ok3 || !ok4 {
+			t.Errorf("#%d: error in input", i)
+			continue
+		}
+
+		z1 := new(Int).Exp(x, y, m)
+		if !isNormalized(z1) {
+			t.Errorf("#%d: %v is not normalized", i, *z1)
+		}
+		if z1.Cmp(out) != 0 {
+			t.Errorf("#%d: got %s want %s", i, z1, out)
+		}
+
+		if m == nil {
+			// The result should be the same as for m == 0;
+			// specifically, there should be no div-zero panic.
+			m = &Int{abs: nat{}} // m != nil && len(m.abs) == 0
+			z2 := new(Int).Exp(x, y, m)
+			if z2.Cmp(z1) != 0 {
+				t.Errorf("#%d: got %s want %s", i, z2, z1)
+			}
+		}
+	}
+}
+
+func checkGcd(aBytes, bBytes []byte) bool {
+	x := new(Int)
+	y := new(Int)
+	a := new(Int).SetBytes(aBytes)
+	b := new(Int).SetBytes(bBytes)
+
+	d := new(Int).GCD(x, y, a, b)
+	x.Mul(x, a)
+	y.Mul(y, b)
+	x.Add(x, y)
+
+	return x.Cmp(d) == 0
+}
+
+var gcdTests = []struct {
+	d, x, y, a, b string
+}{
+	// a <= 0 || b <= 0
+	{"0", "0", "0", "0", "0"},
+	{"0", "0", "0", "0", "7"},
+	{"0", "0", "0", "11", "0"},
+	{"0", "0", "0", "-77", "35"},
+	{"0", "0", "0", "64515", "-24310"},
+	{"0", "0", "0", "-64515", "-24310"},
+
+	{"1", "-9", "47", "120", "23"},
+	{"7", "1", "-2", "77", "35"},
+	{"935", "-3", "8", "64515", "24310"},
+	{"935000000000000000", "-3", "8", "64515000000000000000", "24310000000000000000"},
+	{"1", "-221", "22059940471369027483332068679400581064239780177629666810348940098015901108344", "98920366548084643601728869055592650835572950932266967461790948584315647051443", "991"},
+
+	// test early exit (after one Euclidean iteration) in binaryGCD
+	{"1", "", "", "1", "98920366548084643601728869055592650835572950932266967461790948584315647051443"},
+}
+
+func testGcd(t *testing.T, d, x, y, a, b *Int) {
+	var X *Int
+	if x != nil {
+		X = new(Int)
+	}
+	var Y *Int
+	if y != nil {
+		Y = new(Int)
+	}
+
+	D := new(Int).GCD(X, Y, a, b)
+	if D.Cmp(d) != 0 {
+		t.Errorf("GCD(%s, %s): got d = %s, want %s", a, b, D, d)
+	}
+	if x != nil && X.Cmp(x) != 0 {
+		t.Errorf("GCD(%s, %s): got x = %s, want %s", a, b, X, x)
+	}
+	if y != nil && Y.Cmp(y) != 0 {
+		t.Errorf("GCD(%s, %s): got y = %s, want %s", a, b, Y, y)
+	}
+
+	// binaryGCD requires a > 0 && b > 0
+	if a.Sign() <= 0 || b.Sign() <= 0 {
+		return
+	}
+
+	D.binaryGCD(a, b)
+	if D.Cmp(d) != 0 {
+		t.Errorf("binaryGcd(%s, %s): got d = %s, want %s", a, b, D, d)
+	}
+}
+
+func TestGcd(t *testing.T) {
+	for _, test := range gcdTests {
+		d, _ := new(Int).SetString(test.d, 0)
+		x, _ := new(Int).SetString(test.x, 0)
+		y, _ := new(Int).SetString(test.y, 0)
+		a, _ := new(Int).SetString(test.a, 0)
+		b, _ := new(Int).SetString(test.b, 0)
+
+		testGcd(t, d, nil, nil, a, b)
+		testGcd(t, d, x, nil, a, b)
+		testGcd(t, d, nil, y, a, b)
+		testGcd(t, d, x, y, a, b)
+	}
+
+	quick.Check(checkGcd, nil)
+}
+
+var primes = []string{
+	"2",
+	"3",
+	"5",
+	"7",
+	"11",
+
+	"13756265695458089029",
+	"13496181268022124907",
+	"10953742525620032441",
+	"17908251027575790097",
+
+	// http://code.google.com/p/go/issues/detail?id=638
+	"18699199384836356663",
+
+	"98920366548084643601728869055592650835572950932266967461790948584315647051443",
+	"94560208308847015747498523884063394671606671904944666360068158221458669711639",
+
+	// http://primes.utm.edu/lists/small/small3.html
+	"449417999055441493994709297093108513015373787049558499205492347871729927573118262811508386655998299074566974373711472560655026288668094291699357843464363003144674940345912431129144354948751003607115263071543163",
+	"230975859993204150666423538988557839555560243929065415434980904258310530753006723857139742334640122533598517597674807096648905501653461687601339782814316124971547968912893214002992086353183070342498989426570593",
+	"5521712099665906221540423207019333379125265462121169655563495403888449493493629943498064604536961775110765377745550377067893607246020694972959780839151452457728855382113555867743022746090187341871655890805971735385789993",
+	"203956878356401977405765866929034577280193993314348263094772646453283062722701277632936616063144088173312372882677123879538709400158306567338328279154499698366071906766440037074217117805690872792848149112022286332144876183376326512083574821647933992961249917319836219304274280243803104015000563790123",
+}
+
+var composites = []string{
+	"21284175091214687912771199898307297748211672914763848041968395774954376176754",
+	"6084766654921918907427900243509372380954290099172559290432744450051395395951",
+	"84594350493221918389213352992032324280367711247940675652888030554255915464401",
+	"82793403787388584738507275144194252681",
+}
+
+func TestProbablyPrime(t *testing.T) {
+	nreps := 20
+	if testing.Short() {
+		nreps = 1
+	}
+	for i, s := range primes {
+		p, _ := new(Int).SetString(s, 10)
+		if !p.ProbablyPrime(nreps) {
+			t.Errorf("#%d prime found to be non-prime (%s)", i, s)
+		}
+	}
+
+	for i, s := range composites {
+		c, _ := new(Int).SetString(s, 10)
+		if c.ProbablyPrime(nreps) {
+			t.Errorf("#%d composite found to be prime (%s)", i, s)
+		}
+		if testing.Short() {
+			break
+		}
+	}
+}
+
+type intShiftTest struct {
+	in    string
+	shift uint
+	out   string
+}
+
+var rshTests = []intShiftTest{
+	{"0", 0, "0"},
+	{"-0", 0, "0"},
+	{"0", 1, "0"},
+	{"0", 2, "0"},
+	{"1", 0, "1"},
+	{"1", 1, "0"},
+	{"1", 2, "0"},
+	{"2", 0, "2"},
+	{"2", 1, "1"},
+	{"-1", 0, "-1"},
+	{"-1", 1, "-1"},
+	{"-1", 10, "-1"},
+	{"-100", 2, "-25"},
+	{"-100", 3, "-13"},
+	{"-100", 100, "-1"},
+	{"4294967296", 0, "4294967296"},
+	{"4294967296", 1, "2147483648"},
+	{"4294967296", 2, "1073741824"},
+	{"18446744073709551616", 0, "18446744073709551616"},
+	{"18446744073709551616", 1, "9223372036854775808"},
+	{"18446744073709551616", 2, "4611686018427387904"},
+	{"18446744073709551616", 64, "1"},
+	{"340282366920938463463374607431768211456", 64, "18446744073709551616"},
+	{"340282366920938463463374607431768211456", 128, "1"},
+}
+
+func TestRsh(t *testing.T) {
+	for i, test := range rshTests {
+		in, _ := new(Int).SetString(test.in, 10)
+		expected, _ := new(Int).SetString(test.out, 10)
+		out := new(Int).Rsh(in, test.shift)
+
+		if !isNormalized(out) {
+			t.Errorf("#%d: %v is not normalized", i, *out)
+		}
+		if out.Cmp(expected) != 0 {
+			t.Errorf("#%d: got %s want %s", i, out, expected)
+		}
+	}
+}
+
+func TestRshSelf(t *testing.T) {
+	for i, test := range rshTests {
+		z, _ := new(Int).SetString(test.in, 10)
+		expected, _ := new(Int).SetString(test.out, 10)
+		z.Rsh(z, test.shift)
+
+		if !isNormalized(z) {
+			t.Errorf("#%d: %v is not normalized", i, *z)
+		}
+		if z.Cmp(expected) != 0 {
+			t.Errorf("#%d: got %s want %s", i, z, expected)
+		}
+	}
+}
+
+var lshTests = []intShiftTest{
+	{"0", 0, "0"},
+	{"0", 1, "0"},
+	{"0", 2, "0"},
+	{"1", 0, "1"},
+	{"1", 1, "2"},
+	{"1", 2, "4"},
+	{"2", 0, "2"},
+	{"2", 1, "4"},
+	{"2", 2, "8"},
+	{"-87", 1, "-174"},
+	{"4294967296", 0, "4294967296"},
+	{"4294967296", 1, "8589934592"},
+	{"4294967296", 2, "17179869184"},
+	{"18446744073709551616", 0, "18446744073709551616"},
+	{"9223372036854775808", 1, "18446744073709551616"},
+	{"4611686018427387904", 2, "18446744073709551616"},
+	{"1", 64, "18446744073709551616"},
+	{"18446744073709551616", 64, "340282366920938463463374607431768211456"},
+	{"1", 128, "340282366920938463463374607431768211456"},
+}
+
+func TestLsh(t *testing.T) {
+	for i, test := range lshTests {
+		in, _ := new(Int).SetString(test.in, 10)
+		expected, _ := new(Int).SetString(test.out, 10)
+		out := new(Int).Lsh(in, test.shift)
+
+		if !isNormalized(out) {
+			t.Errorf("#%d: %v is not normalized", i, *out)
+		}
+		if out.Cmp(expected) != 0 {
+			t.Errorf("#%d: got %s want %s", i, out, expected)
+		}
+	}
+}
+
+func TestLshSelf(t *testing.T) {
+	for i, test := range lshTests {
+		z, _ := new(Int).SetString(test.in, 10)
+		expected, _ := new(Int).SetString(test.out, 10)
+		z.Lsh(z, test.shift)
+
+		if !isNormalized(z) {
+			t.Errorf("#%d: %v is not normalized", i, *z)
+		}
+		if z.Cmp(expected) != 0 {
+			t.Errorf("#%d: got %s want %s", i, z, expected)
+		}
+	}
+}
+
+func TestLshRsh(t *testing.T) {
+	for i, test := range rshTests {
+		in, _ := new(Int).SetString(test.in, 10)
+		out := new(Int).Lsh(in, test.shift)
+		out = out.Rsh(out, test.shift)
+
+		if !isNormalized(out) {
+			t.Errorf("#%d: %v is not normalized", i, *out)
+		}
+		if in.Cmp(out) != 0 {
+			t.Errorf("#%d: got %s want %s", i, out, in)
+		}
+	}
+	for i, test := range lshTests {
+		in, _ := new(Int).SetString(test.in, 10)
+		out := new(Int).Lsh(in, test.shift)
+		out.Rsh(out, test.shift)
+
+		if !isNormalized(out) {
+			t.Errorf("#%d: %v is not normalized", i, *out)
+		}
+		if in.Cmp(out) != 0 {
+			t.Errorf("#%d: got %s want %s", i, out, in)
+		}
+	}
+}
+
+var int64Tests = []int64{
+	0,
+	1,
+	-1,
+	4294967295,
+	-4294967295,
+	4294967296,
+	-4294967296,
+	9223372036854775807,
+	-9223372036854775807,
+	-9223372036854775808,
+}
+
+func TestInt64(t *testing.T) {
+	for i, testVal := range int64Tests {
+		in := NewInt(testVal)
+		out := in.Int64()
+
+		if out != testVal {
+			t.Errorf("#%d got %d want %d", i, out, testVal)
+		}
+	}
+}
+
+var uint64Tests = []uint64{
+	0,
+	1,
+	4294967295,
+	4294967296,
+	8589934591,
+	8589934592,
+	9223372036854775807,
+	9223372036854775808,
+	18446744073709551615, // 1<<64 - 1
+}
+
+func TestUint64(t *testing.T) {
+	in := new(Int)
+	for i, testVal := range uint64Tests {
+		in.SetUint64(testVal)
+		out := in.Uint64()
+
+		if out != testVal {
+			t.Errorf("#%d got %d want %d", i, out, testVal)
+		}
+
+		str := fmt.Sprint(testVal)
+		strOut := in.String()
+		if strOut != str {
+			t.Errorf("#%d.String got %s want %s", i, strOut, str)
+		}
+	}
+}
+
+var bitwiseTests = []struct {
+	x, y                 string
+	and, or, xor, andNot string
+}{
+	{"0x00", "0x00", "0x00", "0x00", "0x00", "0x00"},
+	{"0x00", "0x01", "0x00", "0x01", "0x01", "0x00"},
+	{"0x01", "0x00", "0x00", "0x01", "0x01", "0x01"},
+	{"-0x01", "0x00", "0x00", "-0x01", "-0x01", "-0x01"},
+	{"-0xaf", "-0x50", "-0xf0", "-0x0f", "0xe1", "0x41"},
+	{"0x00", "-0x01", "0x00", "-0x01", "-0x01", "0x00"},
+	{"0x01", "0x01", "0x01", "0x01", "0x00", "0x00"},
+	{"-0x01", "-0x01", "-0x01", "-0x01", "0x00", "0x00"},
+	{"0x07", "0x08", "0x00", "0x0f", "0x0f", "0x07"},
+	{"0x05", "0x0f", "0x05", "0x0f", "0x0a", "0x00"},
+	{"0x013ff6", "0x9a4e", "0x1a46", "0x01bffe", "0x01a5b8", "0x0125b0"},
+	{"-0x013ff6", "0x9a4e", "0x800a", "-0x0125b2", "-0x01a5bc", "-0x01c000"},
+	{"-0x013ff6", "-0x9a4e", "-0x01bffe", "-0x1a46", "0x01a5b8", "0x8008"},
+	{
+		"0x1000009dc6e3d9822cba04129bcbe3401",
+		"0xb9bd7d543685789d57cb918e833af352559021483cdb05cc21fd",
+		"0x1000001186210100001000009048c2001",
+		"0xb9bd7d543685789d57cb918e8bfeff7fddb2ebe87dfbbdfe35fd",
+		"0xb9bd7d543685789d57ca918e8ae69d6fcdb2eae87df2b97215fc",
+		"0x8c40c2d8822caa04120b8321400",
+	},
+	{
+		"0x1000009dc6e3d9822cba04129bcbe3401",
+		"-0xb9bd7d543685789d57cb918e833af352559021483cdb05cc21fd",
+		"0x8c40c2d8822caa04120b8321401",
+		"-0xb9bd7d543685789d57ca918e82229142459020483cd2014001fd",
+		"-0xb9bd7d543685789d57ca918e8ae69d6fcdb2eae87df2b97215fe",
+		"0x1000001186210100001000009048c2000",
+	},
+	{
+		"-0x1000009dc6e3d9822cba04129bcbe3401",
+		"-0xb9bd7d543685789d57cb918e833af352559021483cdb05cc21fd",
+		"-0xb9bd7d543685789d57cb918e8bfeff7fddb2ebe87dfbbdfe35fd",
+		"-0x1000001186210100001000009048c2001",
+		"0xb9bd7d543685789d57ca918e8ae69d6fcdb2eae87df2b97215fc",
+		"0xb9bd7d543685789d57ca918e82229142459020483cd2014001fc",
+	},
+}
+
+type bitFun func(z, x, y *Int) *Int
+
+func testBitFun(t *testing.T, msg string, f bitFun, x, y *Int, exp string) {
+	expected := new(Int)
+	expected.SetString(exp, 0)
+
+	out := f(new(Int), x, y)
+	if out.Cmp(expected) != 0 {
+		t.Errorf("%s: got %s want %s", msg, out, expected)
+	}
+}
+
+func testBitFunSelf(t *testing.T, msg string, f bitFun, x, y *Int, exp string) {
+	self := new(Int)
+	self.Set(x)
+	expected := new(Int)
+	expected.SetString(exp, 0)
+
+	self = f(self, self, y)
+	if self.Cmp(expected) != 0 {
+		t.Errorf("%s: got %s want %s", msg, self, expected)
+	}
+}
+
+func altBit(x *Int, i int) uint {
+	z := new(Int).Rsh(x, uint(i))
+	z = z.And(z, NewInt(1))
+	if z.Cmp(new(Int)) != 0 {
+		return 1
+	}
+	return 0
+}
+
+func altSetBit(z *Int, x *Int, i int, b uint) *Int {
+	one := NewInt(1)
+	m := one.Lsh(one, uint(i))
+	switch b {
+	case 1:
+		return z.Or(x, m)
+	case 0:
+		return z.AndNot(x, m)
+	}
+	panic("set bit is not 0 or 1")
+}
+
+func testBitset(t *testing.T, x *Int) {
+	n := x.BitLen()
+	z := new(Int).Set(x)
+	z1 := new(Int).Set(x)
+	for i := 0; i < n+10; i++ {
+		old := z.Bit(i)
+		old1 := altBit(z1, i)
+		if old != old1 {
+			t.Errorf("bitset: inconsistent value for Bit(%s, %d), got %v want %v", z1, i, old, old1)
+		}
+		z := new(Int).SetBit(z, i, 1)
+		z1 := altSetBit(new(Int), z1, i, 1)
+		if z.Bit(i) == 0 {
+			t.Errorf("bitset: bit %d of %s got 0 want 1", i, x)
+		}
+		if z.Cmp(z1) != 0 {
+			t.Errorf("bitset: inconsistent value after SetBit 1, got %s want %s", z, z1)
+		}
+		z.SetBit(z, i, 0)
+		altSetBit(z1, z1, i, 0)
+		if z.Bit(i) != 0 {
+			t.Errorf("bitset: bit %d of %s got 1 want 0", i, x)
+		}
+		if z.Cmp(z1) != 0 {
+			t.Errorf("bitset: inconsistent value after SetBit 0, got %s want %s", z, z1)
+		}
+		altSetBit(z1, z1, i, old)
+		z.SetBit(z, i, old)
+		if z.Cmp(z1) != 0 {
+			t.Errorf("bitset: inconsistent value after SetBit old, got %s want %s", z, z1)
+		}
+	}
+	if z.Cmp(x) != 0 {
+		t.Errorf("bitset: got %s want %s", z, x)
+	}
+}
+
+var bitsetTests = []struct {
+	x string
+	i int
+	b uint
+}{
+	{"0", 0, 0},
+	{"0", 200, 0},
+	{"1", 0, 1},
+	{"1", 1, 0},
+	{"-1", 0, 1},
+	{"-1", 200, 1},
+	{"0x2000000000000000000000000000", 108, 0},
+	{"0x2000000000000000000000000000", 109, 1},
+	{"0x2000000000000000000000000000", 110, 0},
+	{"-0x2000000000000000000000000001", 108, 1},
+	{"-0x2000000000000000000000000001", 109, 0},
+	{"-0x2000000000000000000000000001", 110, 1},
+}
+
+func TestBitSet(t *testing.T) {
+	for _, test := range bitwiseTests {
+		x := new(Int)
+		x.SetString(test.x, 0)
+		testBitset(t, x)
+		x = new(Int)
+		x.SetString(test.y, 0)
+		testBitset(t, x)
+	}
+	for i, test := range bitsetTests {
+		x := new(Int)
+		x.SetString(test.x, 0)
+		b := x.Bit(test.i)
+		if b != test.b {
+			t.Errorf("#%d got %v want %v", i, b, test.b)
+		}
+	}
+	z := NewInt(1)
+	z.SetBit(NewInt(0), 2, 1)
+	if z.Cmp(NewInt(4)) != 0 {
+		t.Errorf("destination leaked into result; got %s want 4", z)
+	}
+}
+
+func BenchmarkBitset(b *testing.B) {
+	z := new(Int)
+	z.SetBit(z, 512, 1)
+	b.ResetTimer()
+	b.StartTimer()
+	for i := b.N - 1; i >= 0; i-- {
+		z.SetBit(z, i&512, 1)
+	}
+}
+
+func BenchmarkBitsetNeg(b *testing.B) {
+	z := NewInt(-1)
+	z.SetBit(z, 512, 0)
+	b.ResetTimer()
+	b.StartTimer()
+	for i := b.N - 1; i >= 0; i-- {
+		z.SetBit(z, i&512, 0)
+	}
+}
+
+func BenchmarkBitsetOrig(b *testing.B) {
+	z := new(Int)
+	altSetBit(z, z, 512, 1)
+	b.ResetTimer()
+	b.StartTimer()
+	for i := b.N - 1; i >= 0; i-- {
+		altSetBit(z, z, i&512, 1)
+	}
+}
+
+func BenchmarkBitsetNegOrig(b *testing.B) {
+	z := NewInt(-1)
+	altSetBit(z, z, 512, 0)
+	b.ResetTimer()
+	b.StartTimer()
+	for i := b.N - 1; i >= 0; i-- {
+		altSetBit(z, z, i&512, 0)
+	}
+}
+
+func TestBitwise(t *testing.T) {
+	x := new(Int)
+	y := new(Int)
+	for _, test := range bitwiseTests {
+		x.SetString(test.x, 0)
+		y.SetString(test.y, 0)
+
+		testBitFun(t, "and", (*Int).And, x, y, test.and)
+		testBitFunSelf(t, "and", (*Int).And, x, y, test.and)
+		testBitFun(t, "andNot", (*Int).AndNot, x, y, test.andNot)
+		testBitFunSelf(t, "andNot", (*Int).AndNot, x, y, test.andNot)
+		testBitFun(t, "or", (*Int).Or, x, y, test.or)
+		testBitFunSelf(t, "or", (*Int).Or, x, y, test.or)
+		testBitFun(t, "xor", (*Int).Xor, x, y, test.xor)
+		testBitFunSelf(t, "xor", (*Int).Xor, x, y, test.xor)
+	}
+}
+
+var notTests = []struct {
+	in  string
+	out string
+}{
+	{"0", "-1"},
+	{"1", "-2"},
+	{"7", "-8"},
+	{"0", "-1"},
+	{"-81910", "81909"},
+	{
+		"298472983472983471903246121093472394872319615612417471234712061",
+		"-298472983472983471903246121093472394872319615612417471234712062",
+	},
+}
+
+func TestNot(t *testing.T) {
+	in := new(Int)
+	out := new(Int)
+	expected := new(Int)
+	for i, test := range notTests {
+		in.SetString(test.in, 10)
+		expected.SetString(test.out, 10)
+		out = out.Not(in)
+		if out.Cmp(expected) != 0 {
+			t.Errorf("#%d: got %s want %s", i, out, expected)
+		}
+		out = out.Not(out)
+		if out.Cmp(in) != 0 {
+			t.Errorf("#%d: got %s want %s", i, out, in)
+		}
+	}
+}
+
+var modInverseTests = []struct {
+	element string
+	modulus string
+}{
+	{"1234567", "458948883992"},
+	{"239487239847", "2410312426921032588552076022197566074856950548502459942654116941958108831682612228890093858261341614673227141477904012196503648957050582631942730706805009223062734745341073406696246014589361659774041027169249453200378729434170325843778659198143763193776859869524088940195577346119843545301547043747207749969763750084308926339295559968882457872412993810129130294592999947926365264059284647209730384947211681434464714438488520940127459844288859336526896320919633919"},
+}
+
+func TestModInverse(t *testing.T) {
+	var element, modulus, gcd, inverse Int
+	one := NewInt(1)
+	for i, test := range modInverseTests {
+		(&element).SetString(test.element, 10)
+		(&modulus).SetString(test.modulus, 10)
+		(&inverse).ModInverse(&element, &modulus)
+		(&inverse).Mul(&inverse, &element)
+		(&inverse).Mod(&inverse, &modulus)
+		if (&inverse).Cmp(one) != 0 {
+			t.Errorf("#%d: failed (e·e^(-1)=%s)", i, &inverse)
+		}
+	}
+	// exhaustive test for small values
+	for n := 2; n < 100; n++ {
+		(&modulus).SetInt64(int64(n))
+		for x := 1; x < n; x++ {
+			(&element).SetInt64(int64(x))
+			(&gcd).GCD(nil, nil, &element, &modulus)
+			if (&gcd).Cmp(one) != 0 {
+				continue
+			}
+			(&inverse).ModInverse(&element, &modulus)
+			(&inverse).Mul(&inverse, &element)
+			(&inverse).Mod(&inverse, &modulus)
+			if (&inverse).Cmp(one) != 0 {
+				t.Errorf("ModInverse(%d,%d)*%d%%%d=%d, not 1", &element, &modulus, &element, &modulus, &inverse)
+			}
+		}
+	}
+}
+
+var encodingTests = []string{
+	"-539345864568634858364538753846587364875430589374589",
+	"-678645873",
+	"-100",
+	"-2",
+	"-1",
+	"0",
+	"1",
+	"2",
+	"10",
+	"42",
+	"1234567890",
+	"298472983472983471903246121093472394872319615612417471234712061",
+}
+
+func TestIntGobEncoding(t *testing.T) {
+	var medium bytes.Buffer
+	enc := gob.NewEncoder(&medium)
+	dec := gob.NewDecoder(&medium)
+	for _, test := range encodingTests {
+		medium.Reset() // empty buffer for each test case (in case of failures)
+		var tx Int
+		tx.SetString(test, 10)
+		if err := enc.Encode(&tx); err != nil {
+			t.Errorf("encoding of %s failed: %s", &tx, err)
+		}
+		var rx Int
+		if err := dec.Decode(&rx); err != nil {
+			t.Errorf("decoding of %s failed: %s", &tx, err)
+		}
+		if rx.Cmp(&tx) != 0 {
+			t.Errorf("transmission of %s failed: got %s want %s", &tx, &rx, &tx)
+		}
+	}
+}
+
+// Sending a nil Int pointer (inside a slice) on a round trip through gob should yield a zero.
+// TODO: top-level nils.
+func TestGobEncodingNilIntInSlice(t *testing.T) {
+	buf := new(bytes.Buffer)
+	enc := gob.NewEncoder(buf)
+	dec := gob.NewDecoder(buf)
+
+	var in = make([]*Int, 1)
+	err := enc.Encode(&in)
+	if err != nil {
+		t.Errorf("gob encode failed: %q", err)
+	}
+	var out []*Int
+	err = dec.Decode(&out)
+	if err != nil {
+		t.Fatalf("gob decode failed: %q", err)
+	}
+	if len(out) != 1 {
+		t.Fatalf("wrong len; want 1 got %d", len(out))
+	}
+	var zero Int
+	if out[0].Cmp(&zero) != 0 {
+		t.Errorf("transmission of (*Int)(nill) failed: got %s want 0", out)
+	}
+}
+
+func TestIntJSONEncoding(t *testing.T) {
+	for _, test := range encodingTests {
+		var tx Int
+		tx.SetString(test, 10)
+		b, err := json.Marshal(&tx)
+		if err != nil {
+			t.Errorf("marshaling of %s failed: %s", &tx, err)
+		}
+		var rx Int
+		if err := json.Unmarshal(b, &rx); err != nil {
+			t.Errorf("unmarshaling of %s failed: %s", &tx, err)
+		}
+		if rx.Cmp(&tx) != 0 {
+			t.Errorf("JSON encoding of %s failed: got %s want %s", &tx, &rx, &tx)
+		}
+	}
+}
+
+var intVals = []string{
+	"-141592653589793238462643383279502884197169399375105820974944592307816406286",
+	"-1415926535897932384626433832795028841971",
+	"-141592653589793",
+	"-1",
+	"0",
+	"1",
+	"141592653589793",
+	"1415926535897932384626433832795028841971",
+	"141592653589793238462643383279502884197169399375105820974944592307816406286",
+}
+
+func TestIntJSONEncodingTextMarshaller(t *testing.T) {
+	for _, num := range intVals {
+		var tx Int
+		tx.SetString(num, 0)
+		b, err := json.Marshal(&tx)
+		if err != nil {
+			t.Errorf("marshaling of %s failed: %s", &tx, err)
+			continue
+		}
+		var rx Int
+		if err := json.Unmarshal(b, &rx); err != nil {
+			t.Errorf("unmarshaling of %s failed: %s", &tx, err)
+			continue
+		}
+		if rx.Cmp(&tx) != 0 {
+			t.Errorf("JSON encoding of %s failed: got %s want %s", &tx, &rx, &tx)
+		}
+	}
+}
+
+func TestIntXMLEncodingTextMarshaller(t *testing.T) {
+	for _, num := range intVals {
+		var tx Int
+		tx.SetString(num, 0)
+		b, err := xml.Marshal(&tx)
+		if err != nil {
+			t.Errorf("marshaling of %s failed: %s", &tx, err)
+			continue
+		}
+		var rx Int
+		if err := xml.Unmarshal(b, &rx); err != nil {
+			t.Errorf("unmarshaling of %s failed: %s", &tx, err)
+			continue
+		}
+		if rx.Cmp(&tx) != 0 {
+			t.Errorf("XML encoding of %s failed: got %s want %s", &tx, &rx, &tx)
+		}
+	}
+}
+
+func TestIssue2607(t *testing.T) {
+	// This code sequence used to hang.
+	n := NewInt(10)
+	n.Rand(rand.New(rand.NewSource(9)), n)
+}