// 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 bignum
import (
"fmt";
"testing";
)
const (
sa = "991";
sb = "2432902008176640000"; // 20!
sc = "933262154439441526816992388562667004907159682643816214685929"
"638952175999932299156089414639761565182862536979208272237582"
"51185210916864000000000000000000000000"; // 100!
sp = "170141183460469231731687303715884105727"; // prime
)
func natFromString(s string, base uint, slen *int) Natural {
x, _, len := NatFromString(s, base);
if slen != nil {
*slen = len
}
return x;
}
func intFromString(s string, base uint, slen *int) *Integer {
x, _, len := IntFromString(s, base);
if slen != nil {
*slen = len
}
return x;
}
func ratFromString(s string, base uint, slen *int) *Rational {
x, _, len := RatFromString(s, base);
if slen != nil {
*slen = len
}
return x;
}
var (
nat_zero = Nat(0);
nat_one = Nat(1);
nat_two = Nat(2);
a = natFromString(sa, 10, nil);
b = natFromString(sb, 10, nil);
c = natFromString(sc, 10, nil);
p = natFromString(sp, 10, nil);
int_zero = Int(0);
int_one = Int(1);
int_two = Int(2);
ip = intFromString(sp, 10, nil);
rat_zero = Rat(0, 1);
rat_half = Rat(1, 2);
rat_one = Rat(1, 1);
rat_two = Rat(2, 1);
)
var test_msg string
var tester *testing.T
func test(n uint, b bool) {
if !b {
tester.Fatalf("TEST failed: %s (%d)", test_msg, n)
}
}
func nat_eq(n uint, x, y Natural) {
if x.Cmp(y) != 0 {
tester.Fatalf("TEST failed: %s (%d)\nx = %v\ny = %v", test_msg, n, &x, &y)
}
}
func int_eq(n uint, x, y *Integer) {
if x.Cmp(y) != 0 {
tester.Fatalf("TEST failed: %s (%d)\nx = %v\ny = %v", test_msg, n, x, y)
}
}
func rat_eq(n uint, x, y *Rational) {
if x.Cmp(y) != 0 {
tester.Fatalf("TEST failed: %s (%d)\nx = %v\ny = %v", test_msg, n, x, y)
}
}
func TestNatConv(t *testing.T) {
tester = t;
test_msg = "NatConvA";
type entry1 struct {
x uint64;
s string;
}
tab := []entry1{
entry1{0, "0"},
entry1{255, "255"},
entry1{65535, "65535"},
entry1{4294967295, "4294967295"},
entry1{18446744073709551615, "18446744073709551615"},
};
for i, e := range tab {
test(100+uint(i), Nat(e.x).String() == e.s);
test(200+uint(i), natFromString(e.s, 0, nil).Value() == e.x);
}
test_msg = "NatConvB";
for i := uint(0); i < 100; i++ {
test(i, Nat(uint64(i)).String() == fmt.Sprintf("%d", i))
}
test_msg = "NatConvC";
z := uint64(7);
for i := uint(0); i <= 64; i++ {
test(i, Nat(z).Value() == z);
z <<= 1;
}
test_msg = "NatConvD";
nat_eq(0, a, Nat(991));
nat_eq(1, b, Fact(20));
nat_eq(2, c, Fact(100));
test(3, a.String() == sa);
test(4, b.String() == sb);
test(5, c.String() == sc);
test_msg = "NatConvE";
var slen int;
nat_eq(10, natFromString("0", 0, nil), nat_zero);
nat_eq(11, natFromString("123", 0, nil), Nat(123));
nat_eq(12, natFromString("077", 0, nil), Nat(7*8+7));
nat_eq(13, natFromString("0x1f", 0, nil), Nat(1*16+15));
nat_eq(14, natFromString("0x1fg", 0, &slen), Nat(1*16+15));
test(4, slen == 4);
test_msg = "NatConvF";
tmp := c.Mul(c);
for base := uint(2); base <= 16; base++ {
nat_eq(base, natFromString(tmp.ToString(base), base, nil), tmp)
}
test_msg = "NatConvG";
x := Nat(100);
y, _, _ := NatFromString(fmt.Sprintf("%b", &x), 2);
nat_eq(100, y, x);
}
func abs(x int64) uint64 {
if x < 0 {
x = -x
}
return uint64(x);
}
func TestIntConv(t *testing.T) {
tester = t;
test_msg = "IntConvA";
type entry2 struct {
x int64;
s string;
}
tab := []entry2{
entry2{0, "0"},
entry2{-128, "-128"},
entry2{127, "127"},
entry2{-32768, "-32768"},
entry2{32767, "32767"},
entry2{-2147483648, "-2147483648"},
entry2{2147483647, "2147483647"},
entry2{-9223372036854775808, "-9223372036854775808"},
entry2{9223372036854775807, "9223372036854775807"},
};
for i, e := range tab {
test(100+uint(i), Int(e.x).String() == e.s);
test(200+uint(i), intFromString(e.s, 0, nil).Value() == e.x);
test(300+uint(i), Int(e.x).Abs().Value() == abs(e.x));
}
test_msg = "IntConvB";
var slen int;
int_eq(0, intFromString("0", 0, nil), int_zero);
int_eq(1, intFromString("-0", 0, nil), int_zero);
int_eq(2, intFromString("123", 0, nil), Int(123));
int_eq(3, intFromString("-123", 0, nil), Int(-123));
int_eq(4, intFromString("077", 0, nil), Int(7*8+7));
int_eq(5, intFromString("-077", 0, nil), Int(-(7*8 + 7)));
int_eq(6, intFromString("0x1f", 0, nil), Int(1*16+15));
int_eq(7, intFromString("-0x1f", 0, &slen), Int(-(1*16 + 15)));
test(7, slen == 5);
int_eq(8, intFromString("+0x1f", 0, &slen), Int(+(1*16 + 15)));
test(8, slen == 5);
int_eq(9, intFromString("0x1fg", 0, &slen), Int(1*16+15));
test(9, slen == 4);
int_eq(10, intFromString("-0x1fg", 0, &slen), Int(-(1*16 + 15)));
test(10, slen == 5);
}
func TestRatConv(t *testing.T) {
tester = t;
test_msg = "RatConv";
var slen int;
rat_eq(0, ratFromString("0", 0, nil), rat_zero);
rat_eq(1, ratFromString("0/1", 0, nil), rat_zero);
rat_eq(2, ratFromString("0/01", 0, nil), rat_zero);
rat_eq(3, ratFromString("0x14/10", 0, &slen), rat_two);
test(4, slen == 7);
rat_eq(5, ratFromString("0.", 0, nil), rat_zero);
rat_eq(6, ratFromString("0.001f", 10, nil), Rat(1, 1000));
rat_eq(7, ratFromString(".1", 0, nil), Rat(1, 10));
rat_eq(8, ratFromString("10101.0101", 2, nil), Rat(0x155, 1<<4));
rat_eq(9, ratFromString("-0003.145926", 10, &slen), Rat(-3145926, 1000000));
test(10, slen == 12);
rat_eq(11, ratFromString("1e2", 0, nil), Rat(100, 1));
rat_eq(12, ratFromString("1e-2", 0, nil), Rat(1, 100));
rat_eq(13, ratFromString("1.1e2", 0, nil), Rat(110, 1));
rat_eq(14, ratFromString(".1e2x", 0, &slen), Rat(10, 1));
test(15, slen == 4);
}
func add(x, y Natural) Natural {
z1 := x.Add(y);
z2 := y.Add(x);
if z1.Cmp(z2) != 0 {
tester.Fatalf("addition not symmetric:\n\tx = %v\n\ty = %t", x, y)
}
return z1;
}
func sum(n uint64, scale Natural) Natural {
s := nat_zero;
for ; n > 0; n-- {
s = add(s, Nat(n).Mul(scale))
}
return s;
}
func TestNatAdd(t *testing.T) {
tester = t;
test_msg = "NatAddA";
nat_eq(0, add(nat_zero, nat_zero), nat_zero);
nat_eq(1, add(nat_zero, c), c);
test_msg = "NatAddB";
for i := uint64(0); i < 100; i++ {
t := Nat(i);
nat_eq(uint(i), sum(i, c), t.Mul(t).Add(t).Shr(1).Mul(c));
}
}
func mul(x, y Natural) Natural {
z1 := x.Mul(y);
z2 := y.Mul(x);
if z1.Cmp(z2) != 0 {
tester.Fatalf("multiplication not symmetric:\n\tx = %v\n\ty = %t", x, y)
}
if !x.IsZero() && z1.Div(x).Cmp(y) != 0 {
tester.Fatalf("multiplication/division not inverse (A):\n\tx = %v\n\ty = %t", x, y)
}
if !y.IsZero() && z1.Div(y).Cmp(x) != 0 {
tester.Fatalf("multiplication/division not inverse (B):\n\tx = %v\n\ty = %t", x, y)
}
return z1;
}
func TestNatSub(t *testing.T) {
tester = t;
test_msg = "NatSubA";
nat_eq(0, nat_zero.Sub(nat_zero), nat_zero);
nat_eq(1, c.Sub(nat_zero), c);
test_msg = "NatSubB";
for i := uint64(0); i < 100; i++ {
t := sum(i, c);
for j := uint64(0); j <= i; j++ {
t = t.Sub(mul(Nat(j), c))
}
nat_eq(uint(i), t, nat_zero);
}
}
func TestNatMul(t *testing.T) {
tester = t;
test_msg = "NatMulA";
nat_eq(0, mul(c, nat_zero), nat_zero);
nat_eq(1, mul(c, nat_one), c);
test_msg = "NatMulB";
nat_eq(0, b.Mul(MulRange(0, 100)), nat_zero);
nat_eq(1, b.Mul(MulRange(21, 100)), c);
test_msg = "NatMulC";
const n = 100;
p := b.Mul(c).Shl(n);
for i := uint(0); i < n; i++ {
nat_eq(i, mul(b.Shl(i), c.Shl(n-i)), p)
}
}
func TestNatDiv(t *testing.T) {
tester = t;
test_msg = "NatDivA";
nat_eq(0, c.Div(nat_one), c);
nat_eq(1, c.Div(Nat(100)), Fact(99));
nat_eq(2, b.Div(c), nat_zero);
nat_eq(4, nat_one.Shl(100).Div(nat_one.Shl(90)), nat_one.Shl(10));
nat_eq(5, c.Div(b), MulRange(21, 100));
test_msg = "NatDivB";
const n = 100;
p := Fact(n);
for i := uint(0); i < n; i++ {
nat_eq(100+i, p.Div(MulRange(1, i)), MulRange(i+1, n))
}
}
func TestIntQuoRem(t *testing.T) {
tester = t;
test_msg = "IntQuoRem";
type T struct {
x, y, q, r int64;
}
a := []T{
T{+8, +3, +2, +2},
T{+8, -3, -2, +2},
T{-8, +3, -2, -2},
T{-8, -3, +2, -2},
T{+1, +2, 0, +1},
T{+1, -2, 0, +1},
T{-1, +2, 0, -1},
T{-1, -2, 0, -1},
};
for i := uint(0); i < uint(len(a)); i++ {
e := &a[i];
x, y := Int(e.x).Mul(ip), Int(e.y).Mul(ip);
q, r := Int(e.q), Int(e.r).Mul(ip);
qq, rr := x.QuoRem(y);
int_eq(4*i+0, x.Quo(y), q);
int_eq(4*i+1, x.Rem(y), r);
int_eq(4*i+2, qq, q);
int_eq(4*i+3, rr, r);
}
}
func TestIntDivMod(t *testing.T) {
tester = t;
test_msg = "IntDivMod";
type T struct {
x, y, q, r int64;
}
a := []T{
T{+8, +3, +2, +2},
T{+8, -3, -2, +2},
T{-8, +3, -3, +1},
T{-8, -3, +3, +1},
T{+1, +2, 0, +1},
T{+1, -2, 0, +1},
T{-1, +2, -1, +1},
T{-1, -2, +1, +1},
};
for i := uint(0); i < uint(len(a)); i++ {
e := &a[i];
x, y := Int(e.x).Mul(ip), Int(e.y).Mul(ip);
q, r := Int(e.q), Int(e.r).Mul(ip);
qq, rr := x.DivMod(y);
int_eq(4*i+0, x.Div(y), q);
int_eq(4*i+1, x.Mod(y), r);
int_eq(4*i+2, qq, q);
int_eq(4*i+3, rr, r);
}
}
func TestNatMod(t *testing.T) {
tester = t;
test_msg = "NatModA";
for i := uint(0); ; i++ {
d := nat_one.Shl(i);
if d.Cmp(c) < 0 {
nat_eq(i, c.Add(d).Mod(c), d)
} else {
nat_eq(i, c.Add(d).Div(c), nat_two);
nat_eq(i, c.Add(d).Mod(c), d.Sub(c));
break;
}
}
}
func TestNatShift(t *testing.T) {
tester = t;
test_msg = "NatShift1L";
test(0, b.Shl(0).Cmp(b) == 0);
test(1, c.Shl(1).Cmp(c) > 0);
test_msg = "NatShift1R";
test(3, b.Shr(0).Cmp(b) == 0);
test(4, c.Shr(1).Cmp(c) < 0);
test_msg = "NatShift2";
for i := uint(0); i < 100; i++ {
test(i, c.Shl(i).Shr(i).Cmp(c) == 0)
}
test_msg = "NatShift3L";
{
const m = 3;
p := b;
f := Nat(1 << m);
for i := uint(0); i < 100; i++ {
nat_eq(i, b.Shl(i*m), p);
p = mul(p, f);
}
}
test_msg = "NatShift3R";
{
p := c;
for i := uint(0); !p.IsZero(); i++ {
nat_eq(i, c.Shr(i), p);
p = p.Shr(1);
}
}
}
func TestIntShift(t *testing.T) {
tester = t;
test_msg = "IntShift1L";
test(0, ip.Shl(0).Cmp(ip) == 0);
test(1, ip.Shl(1).Cmp(ip) > 0);
test_msg = "IntShift1R";
test(0, ip.Shr(0).Cmp(ip) == 0);
test(1, ip.Shr(1).Cmp(ip) < 0);
test_msg = "IntShift2";
for i := uint(0); i < 100; i++ {
test(i, ip.Shl(i).Shr(i).Cmp(ip) == 0)
}
test_msg = "IntShift3L";
{
const m = 3;
p := ip;
f := Int(1 << m);
for i := uint(0); i < 100; i++ {
int_eq(i, ip.Shl(i*m), p);
p = p.Mul(f);
}
}
test_msg = "IntShift3R";
{
p := ip;
for i := uint(0); p.IsPos(); i++ {
int_eq(i, ip.Shr(i), p);
p = p.Shr(1);
}
}
test_msg = "IntShift4R";
int_eq(0, Int(-43).Shr(1), Int(-43>>1));
int_eq(0, Int(-1024).Shr(100), Int(-1));
int_eq(1, ip.Neg().Shr(10), ip.Neg().Div(Int(1).Shl(10)));
}
func TestNatBitOps(t *testing.T) {
tester = t;
x := uint64(0xf08e6f56bd8c3941);
y := uint64(0x3984ef67834bc);
bx := Nat(x);
by := Nat(y);
test_msg = "NatAnd";
bz := Nat(x & y);
for i := uint(0); i < 100; i++ {
nat_eq(i, bx.Shl(i).And(by.Shl(i)), bz.Shl(i))
}
test_msg = "NatAndNot";
bz = Nat(x &^ y);
for i := uint(0); i < 100; i++ {
nat_eq(i, bx.Shl(i).AndNot(by.Shl(i)), bz.Shl(i))
}
test_msg = "NatOr";
bz = Nat(x | y);
for i := uint(0); i < 100; i++ {
nat_eq(i, bx.Shl(i).Or(by.Shl(i)), bz.Shl(i))
}
test_msg = "NatXor";
bz = Nat(x ^ y);
for i := uint(0); i < 100; i++ {
nat_eq(i, bx.Shl(i).Xor(by.Shl(i)), bz.Shl(i))
}
}
func TestIntBitOps1(t *testing.T) {
tester = t;
test_msg = "IntBitOps1";
type T struct {
x, y int64;
}
a := []T{
T{+7, +3},
T{+7, -3},
T{-7, +3},
T{-7, -3},
};
for i := uint(0); i < uint(len(a)); i++ {
e := &a[i];
int_eq(4*i+0, Int(e.x).And(Int(e.y)), Int(e.x&e.y));
int_eq(4*i+1, Int(e.x).AndNot(Int(e.y)), Int(e.x&^e.y));
int_eq(4*i+2, Int(e.x).Or(Int(e.y)), Int(e.x|e.y));
int_eq(4*i+3, Int(e.x).Xor(Int(e.y)), Int(e.x^e.y));
}
}
func TestIntBitOps2(t *testing.T) {
tester = t;
test_msg = "IntNot";
int_eq(0, Int(-2).Not(), Int(1));
int_eq(0, Int(-1).Not(), Int(0));
int_eq(0, Int(0).Not(), Int(-1));
int_eq(0, Int(1).Not(), Int(-2));
int_eq(0, Int(2).Not(), Int(-3));
test_msg = "IntAnd";
for x := int64(-15); x < 5; x++ {
bx := Int(x);
for y := int64(-5); y < 15; y++ {
by := Int(y);
for i := uint(50); i < 70; i++ { // shift across 64bit boundary
int_eq(i, bx.Shl(i).And(by.Shl(i)), Int(x&y).Shl(i))
}
}
}
test_msg = "IntAndNot";
for x := int64(-15); x < 5; x++ {
bx := Int(x);
for y := int64(-5); y < 15; y++ {
by := Int(y);
for i := uint(50); i < 70; i++ { // shift across 64bit boundary
int_eq(2*i+0, bx.Shl(i).AndNot(by.Shl(i)), Int(x&^y).Shl(i));
int_eq(2*i+1, bx.Shl(i).And(by.Shl(i).Not()), Int(x&^y).Shl(i));
}
}
}
test_msg = "IntOr";
for x := int64(-15); x < 5; x++ {
bx := Int(x);
for y := int64(-5); y < 15; y++ {
by := Int(y);
for i := uint(50); i < 70; i++ { // shift across 64bit boundary
int_eq(i, bx.Shl(i).Or(by.Shl(i)), Int(x|y).Shl(i))
}
}
}
test_msg = "IntXor";
for x := int64(-15); x < 5; x++ {
bx := Int(x);
for y := int64(-5); y < 15; y++ {
by := Int(y);
for i := uint(50); i < 70; i++ { // shift across 64bit boundary
int_eq(i, bx.Shl(i).Xor(by.Shl(i)), Int(x^y).Shl(i))
}
}
}
}
func TestNatCmp(t *testing.T) {
tester = t;
test_msg = "NatCmp";
test(0, a.Cmp(a) == 0);
test(1, a.Cmp(b) < 0);
test(2, b.Cmp(a) > 0);
test(3, a.Cmp(c) < 0);
d := c.Add(b);
test(4, c.Cmp(d) < 0);
test(5, d.Cmp(c) > 0);
}
func TestNatLog2(t *testing.T) {
tester = t;
test_msg = "NatLog2A";
test(0, nat_one.Log2() == 0);
test(1, nat_two.Log2() == 1);
test(2, Nat(3).Log2() == 1);
test(3, Nat(4).Log2() == 2);
test_msg = "NatLog2B";
for i := uint(0); i < 100; i++ {
test(i, nat_one.Shl(i).Log2() == i)
}
}
func TestNatGcd(t *testing.T) {
tester = t;
test_msg = "NatGcdA";
f := Nat(99991);
nat_eq(0, b.Mul(f).Gcd(c.Mul(f)), MulRange(1, 20).Mul(f));
}
func TestNatPow(t *testing.T) {
tester = t;
test_msg = "NatPowA";
nat_eq(0, nat_two.Pow(0), nat_one);
test_msg = "NatPowB";
for i := uint(0); i < 100; i++ {
nat_eq(i, nat_two.Pow(i), nat_one.Shl(i))
}
}
func TestNatPop(t *testing.T) {
tester = t;
test_msg = "NatPopA";
test(0, nat_zero.Pop() == 0);
test(1, nat_one.Pop() == 1);
test(2, Nat(10).Pop() == 2);
test(3, Nat(30).Pop() == 4);
test(4, Nat(0x1248f).Shl(33).Pop() == 8);
test_msg = "NatPopB";
for i := uint(0); i < 100; i++ {
test(i, nat_one.Shl(i).Sub(nat_one).Pop() == i)
}
}
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