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// 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"
        "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", z, msg)
        }
        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.Compare(b, b2) == 0
}

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
}{
        {"5", "0", "", "1"},
        {"-5", "0", "", "-1"},
        {"5", "1", "", "5"},
        {"-5", "1", "", "-5"},
        {"-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"},
        {
                "2938462938472983472983659726349017249287491026512746239764525612965293865296239471239874193284792387498274256129746192347",
                "298472983472983471903246121093472394872319615612417471234712061",
                "29834729834729834729347290846729561262544958723956495615629569234729836259263598127342374289365912465901365498236492183464",
                "23537740700184054162508175125554701713153216681790245129157191391322321508055833908509185839069455749219131480588829346291",
        },
}

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
                }

                z := y.Exp(x, y, m)
                if !isNormalized(z) {
                        t.Errorf("#%d: %v is not normalized", i, *z)
                }
                if z.Cmp(out) != 0 {
                        t.Errorf("#%d: got %s want %s", i, z, out)
                }
        }
}

func checkGcd(aBytes, bBytes []byte) bool {
        a := new(Int).SetBytes(aBytes)
        b := new(Int).SetBytes(bBytes)

        x := new(Int)
        y := new(Int)
        d := new(Int)

        d.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 {
        a, b    int64
        d, x, y int64
}{
        {120, 23, 1, -9, 47},
}

func TestGcd(t *testing.T) {
        for i, test := range gcdTests {
                a := NewInt(test.a)
                b := NewInt(test.b)

                x := new(Int)
                y := new(Int)
                d := new(Int)

                expectedX := NewInt(test.x)
                expectedY := NewInt(test.y)
                expectedD := NewInt(test.d)

                d.GCD(x, y, a, b)

                if expectedX.Cmp(x) != 0 ||
                        expectedY.Cmp(y) != 0 ||
                        expectedD.Cmp(d) != 0 {
                        t.Errorf("#%d got (%s %s %s) want (%s %s %s)", i, x, y, d, expectedX, expectedY, expectedD)
                }
        }

        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 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
        prime   string
}{
        {"1", "7"},
        {"1", "13"},
        {"239487239847", "2410312426921032588552076022197566074856950548502459942654116941958108831682612228890093858261341614673227141477904012196503648957050582631942730706805009223062734745341073406696246014589361659774041027169249453200378729434170325843778659198143763193776859869524088940195577346119843545301547043747207749969763750084308926339295559968882457872412993810129130294592999947926365264059284647209730384947211681434464714438488520940127459844288859336526896320919633919"},
}

func TestModInverse(t *testing.T) {
        var element, prime Int
        one := NewInt(1)
        for i, test := range modInverseTests {
                (&element).SetString(test.element, 10)
                (&prime).SetString(test.prime, 10)
                inverse := new(Int).ModInverse(&element, &prime)
                inverse.Mul(inverse, &element)
                inverse.Mod(inverse, &prime)
                if inverse.Cmp(one) != 0 {
                        t.Errorf("#%d: failed (e·e^(-1)=%s)", i, inverse)
                }
        }
}

// used by TestIntGobEncoding and TestRatGobEncoding
var gobEncodingTests = []string{
        "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 i, test := range gobEncodingTests {
                for j := 0; j < 2; j++ {
                        medium.Reset() // empty buffer for each test case (in case of failures)
                        stest := test
                        if j != 0 {
                                // negative numbers
                                stest = "-" + test
                        }
                        var tx Int
                        tx.SetString(stest, 10)
                        if err := enc.Encode(&tx); err != nil {
                                t.Errorf("#%d%c: encoding failed: %s", i, 'a'+j, err)
                        }
                        var rx Int
                        if err := dec.Decode(&rx); err != nil {
                                t.Errorf("#%d%c: decoding failed: %s", i, 'a'+j, err)
                        }
                        if rx.Cmp(&tx) != 0 {
                                t.Errorf("#%d%c: transmission failed: got %s want %s", i, 'a'+j, &rx, &tx)
                        }
                }
        }
}

func TestIssue2607(t *testing.T) {
        // This code sequence used to hang.
        n := NewInt(10)
        n.Rand(rand.New(rand.NewSource(9)), n)
}