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7dee51f491
go/test/bignum_test.go
Robert Griesemer 66c6b13b03 - implemented String() and Format functionality in Bignum 
- added a test

R=r
OCL=18687
CL=18687
2008-11-06 12:13:52 -08:00

501 lines
10 KiB
Go
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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.
// $G $D/$F.go && $L $F.$A && ./$A.out
package main
import Big "bignum"
import Fmt "fmt"
const (
sa = "991";
sb = "2432902008176640000"; // 20!
sc = "933262154439441526816992388562667004907159682643816214685929"
"638952175999932299156089414639761565182862536979208272237582"
"51185210916864000000000000000000000000"; // 100!
sp = "170141183460469231731687303715884105727"; // prime
)
func NatFromString(s string, base uint, slen *int) *Big.Natural {
x, dummy := Big.NatFromString(s, base, slen);
return x;
}
func IntFromString(s string, base uint, slen *int) *Big.Integer {
x, dummy := Big.IntFromString(s, base, slen);
return x;
}
func RatFromString(s string, base uint, slen *int) *Big.Rational {
x, dummy := Big.RatFromString(s, base, slen);
return x;
}
var (
nat_zero = Big.Nat(0);
nat_one = Big.Nat(1);
nat_two = Big.Nat(2);
a = NatFromString(sa, 10, nil);
b = NatFromString(sb, 10, nil);
c = NatFromString(sc, 10, nil);
p = NatFromString(sp, 10, nil);
int_zero = Big.Int(0);
int_one = Big.Int(1);
int_two = Big.Int(2);
ip = IntFromString(sp, 10, nil);
rat_zero = Big.Rat(0, 1);
rat_half = Big.Rat(1, 2);
rat_one = Big.Rat(1, 1);
rat_two = Big.Rat(2, 1);
)
var test_msg string;
func TEST(n uint, b bool) {
if !b {
println("TEST failed: ", test_msg, "(", n, ")");
panic();
}
}
func NAT_EQ(n uint, x, y *Big.Natural) {
if x.Cmp(y) != 0 {
println("TEST failed:", test_msg, "(", n, ")");
println("x =", x.String());
println("y =", y.String());
panic();
}
}
func INT_EQ(n uint, x, y *Big.Integer) {
if x.Cmp(y) != 0 {
println("TEST failed:", test_msg, "(", n, ")");
println("x =", x.String());
println("y =", y.String());
panic();
}
}
func RAT_EQ(n uint, x, y *Big.Rational) {
if x.Cmp(y) != 0 {
println("TEST failed:", test_msg, "(", n, ")");
println("x =", x.String());
println("y =", y.String());
panic();
}
}
func NatConv() {
test_msg = "NatConvA";
NAT_EQ(0, a, Big.Nat(991));
NAT_EQ(1, b, Big.Fact(20));
NAT_EQ(2, c, Big.Fact(100));
TEST(3, a.String() == sa);
TEST(4, b.String() == sb);
TEST(5, c.String() == sc);
test_msg = "NatConvB";
var slen int;
NAT_EQ(0, NatFromString("0", 0, nil), nat_zero);
NAT_EQ(1, NatFromString("123", 0, nil), Big.Nat(123));
NAT_EQ(2, NatFromString("077", 0, nil), Big.Nat(7*8 + 7));
NAT_EQ(3, NatFromString("0x1f", 0, nil), Big.Nat(1*16 + 15));
NAT_EQ(4, NatFromString("0x1fg", 0, &slen), Big.Nat(1*16 + 15));
TEST(4, slen == 4);
test_msg = "NatConvC";
t := c.Mul(c);
for base := uint(2); base <= 16; base++ {
NAT_EQ(base, NatFromString(t.ToString(base), base, nil), t);
}
test_msg = "NatConvD";
x := Big.Nat(100);
y, b := Big.NatFromString(Fmt.sprintf("%b", x), 2, nil);
NAT_EQ(0, y, x);
}
func IntConv() {
test_msg = "IntConv";
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), Big.Int(123));
INT_EQ(3, IntFromString("-123", 0, nil), Big.Int(-123));
INT_EQ(4, IntFromString("077", 0, nil), Big.Int(7*8 + 7));
INT_EQ(5, IntFromString("-077", 0, nil), Big.Int(-(7*8 + 7)));
INT_EQ(6, IntFromString("0x1f", 0, nil), Big.Int(1*16 + 15));
INT_EQ(7, IntFromString("-0x1f", 0, nil), Big.Int(-(1*16 + 15)));
INT_EQ(8, IntFromString("0x1fg", 0, &slen), Big.Int(1*16 + 15));
INT_EQ(9, IntFromString("-0x1fg", 0, &slen), Big.Int(-(1*16 + 15)));
TEST(10, slen == 5);
}
func RatConv() {
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), Big.Rat(1, 1000));
RAT_EQ(7, RatFromString("10101.0101", 2, nil), Big.Rat(0x155, 1<<4));
RAT_EQ(8, RatFromString("-0003.145926", 10, &slen), Big.Rat(-3145926, 1000000));
TEST(9, slen == 12);
}
func Add(x, y *Big.Natural) *Big.Natural {
z1 := x.Add(y);
z2 := y.Add(x);
if z1.Cmp(z2) != 0 {
println("addition not symmetric");
println("x =", x.String());
println("y =", y.String());
panic();
}
return z1;
}
func Sum(n uint, scale *Big.Natural) *Big.Natural {
s := nat_zero;
for ; n > 0; n-- {
s = Add(s, Big.Nat(n).Mul(scale));
}
return s;
}
func NatAdd() {
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 := uint(0); i < 100; i++ {
t := Big.Nat(i);
NAT_EQ(i, Sum(i, c), t.Mul(t).Add(t).Shr(1).Mul(c));
}
}
func Mul(x, y *Big.Natural) *Big.Natural {
z1 := x.Mul(y);
z2 := y.Mul(x);
if z1.Cmp(z2) != 0 {
println("multiplication not symmetric");
println("x =", x.String());
println("y =", y.String());
panic();
}
if !x.IsZero() && z1.Div(x).Cmp(y) != 0 {
println("multiplication/division not inverse (A)");
println("x =", x.String());
println("y =", y.String());
panic();
}
if !y.IsZero() && z1.Div(y).Cmp(x) != 0 {
println("multiplication/division not inverse (B)");
println("x =", x.String());
println("y =", y.String());
panic();
}
return z1;
}
func NatSub() {
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 := uint(0); i < 100; i++ {
t := Sum(i, c);
for j := uint(0); j <= i; j++ {
t = t.Sub(Mul(Big.Nat(j), c));
}
NAT_EQ(i, t, nat_zero);
}
}
func NatMul() {
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(Big.MulRange(0, 100)), nat_zero);
NAT_EQ(1, b.Mul(Big.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 NatDiv() {
test_msg = "NatDivA";
NAT_EQ(0, c.Div(nat_one), c);
NAT_EQ(1, c.Div(Big.Nat(100)), Big.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), Big.MulRange(21, 100));
test_msg = "NatDivB";
const n = 100;
p := Big.Fact(n);
for i := uint(0); i < n; i++ {
NAT_EQ(i, p.Div(Big.MulRange(1, i)), Big.MulRange(i+1, n));
}
}
func IntQuoRem() {
test_msg = "IntQuoRem";
type T struct { x, y, q, r int };
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 < len(a); i++ {
e := &a[i];
x, y := Big.Int(e.x).Mul(ip), Big.Int(e.y).Mul(ip);
q, r := Big.Int(e.q), Big.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 IntDivMod() {
test_msg = "IntDivMod";
type T struct { x, y, q, r int };
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 < len(a); i++ {
e := &a[i];
x, y := Big.Int(e.x).Mul(ip), Big.Int(e.y).Mul(ip);
q, r := Big.Int(e.q), Big.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 NatMod() {
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 NatShift() {
test_msg = "NatShift1L";
TEST(0, b.Shl(0).Cmp(b) == 0);
TEST(1, c.Shl(1).Cmp(c) > 0);
test_msg = "NatShift1R";
TEST(0, b.Shr(0).Cmp(b) == 0);
TEST(1, 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 := Big.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 IntShift() {
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 := Big.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, Big.Int(-43).Shr(1), Big.Int(-43 >> 1));
//INT_EQ(1, ip.Neg().Shr(10), ip.Neg().Div(Big.Int(1).Shl(10)));
}
func NatCmp() {
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 NatLog2() {
test_msg = "NatLog2A";
TEST(0, nat_one.Log2() == 0);
TEST(1, nat_two.Log2() == 1);
TEST(2, Big.Nat(3).Log2() == 1);
TEST(3, Big.Nat(4).Log2() == 2);
test_msg = "NatLog2B";
for i := uint(0); i < 100; i++ {
TEST(i, nat_one.Shl(i).Log2() == i);
}
}
func NatGcd() {
test_msg = "NatGcdA";
f := Big.Nat(99991);
NAT_EQ(0, b.Mul(f).Gcd(c.Mul(f)), Big.MulRange(1, 20).Mul(f));
}
func NatPow() {
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 NatPop() {
test_msg = "NatPopA";
TEST(0, nat_zero.Pop() == 0);
TEST(1, nat_one.Pop() == 1);
TEST(2, Big.Nat(10).Pop() == 2);
TEST(3, Big.Nat(30).Pop() == 4);
TEST(4, Big.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);
}
}
func main() {
// Naturals
NatConv();
NatAdd();
NatSub();
NatMul();
NatDiv();
NatMod();
NatShift();
NatCmp();
NatLog2();
NatGcd();
NatPow();
NatPop();
// Integers
// TODO add more tests
IntConv();
IntQuoRem();
IntDivMod();
IntShift();
// Rationals
// TODO add more tests
RatConv();
}
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