mirror of
https://github.com/golang/go
synced 2024-10-04 02:31:22 -06:00
495 lines
10 KiB
Go
495 lines
10 KiB
Go
// Copyright 2009 The Go Authors. All rights reserved.
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// Use of this source code is governed by a BSD-style
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// license that can be found in the LICENSE file.
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// $G $D/$F.go && $L $F.$A && ./$A.out
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package main
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import Big "bignum"
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const (
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sa = "991";
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sb = "2432902008176640000"; // 20!
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sc = "933262154439441526816992388562667004907159682643816214685929"
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"638952175999932299156089414639761565182862536979208272237582"
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"51185210916864000000000000000000000000"; // 100!
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sp = "170141183460469231731687303715884105727"; // prime
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)
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func NatFromString(s string, base uint, slen *int) *Big.Natural {
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x, dummy := Big.NatFromString(s, base, slen);
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return x;
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}
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func IntFromString(s string, base uint, slen *int) *Big.Integer {
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x, dummy := Big.IntFromString(s, base, slen);
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return x;
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}
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func RatFromString(s string, base uint, slen *int) *Big.Rational {
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x, dummy := Big.RatFromString(s, base, slen);
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return x;
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}
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var (
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nat_zero = Big.Nat(0);
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nat_one = Big.Nat(1);
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nat_two = Big.Nat(2);
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a = NatFromString(sa, 10, nil);
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b = NatFromString(sb, 10, nil);
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c = NatFromString(sc, 10, nil);
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p = NatFromString(sp, 10, nil);
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int_zero = Big.Int(0);
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int_one = Big.Int(1);
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int_two = Big.Int(2);
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ip = IntFromString(sp, 10, nil);
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rat_zero = Big.Rat(0, 1);
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rat_half = Big.Rat(1, 2);
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rat_one = Big.Rat(1, 1);
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rat_two = Big.Rat(2, 1);
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)
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var test_msg string;
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func TEST(n uint, b bool) {
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if !b {
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println("TEST failed: ", test_msg, "(", n, ")");
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panic();
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}
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}
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func NAT_EQ(n uint, x, y *Big.Natural) {
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if x.Cmp(y) != 0 {
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println("TEST failed:", test_msg, "(", n, ")");
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println("x =", x.String(10));
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println("y =", y.String(10));
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panic();
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}
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}
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func INT_EQ(n uint, x, y *Big.Integer) {
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if x.Cmp(y) != 0 {
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println("TEST failed:", test_msg, "(", n, ")");
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println("x =", x.String(10));
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println("y =", y.String(10));
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panic();
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}
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}
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func RAT_EQ(n uint, x, y *Big.Rational) {
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if x.Cmp(y) != 0 {
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println("TEST failed:", test_msg, "(", n, ")");
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println("x =", x.String(10));
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println("y =", y.String(10));
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panic();
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}
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}
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func NatConv() {
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test_msg = "NatConvA";
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NAT_EQ(0, a, Big.Nat(991));
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NAT_EQ(1, b, Big.Fact(20));
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NAT_EQ(2, c, Big.Fact(100));
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TEST(3, a.String(10) == sa);
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TEST(4, b.String(10) == sb);
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TEST(5, c.String(10) == sc);
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test_msg = "NatConvB";
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var slen int;
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NAT_EQ(0, NatFromString("0", 0, nil), nat_zero);
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NAT_EQ(1, NatFromString("123", 0, nil), Big.Nat(123));
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NAT_EQ(2, NatFromString("077", 0, nil), Big.Nat(7*8 + 7));
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NAT_EQ(3, NatFromString("0x1f", 0, nil), Big.Nat(1*16 + 15));
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NAT_EQ(4, NatFromString("0x1fg", 0, &slen), Big.Nat(1*16 + 15));
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TEST(4, slen == 4);
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test_msg = "NatConvC";
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t := c.Mul(c);
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for base := uint(2); base <= 16; base++ {
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NAT_EQ(base, NatFromString(t.String(base), base, nil), t);
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}
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}
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func IntConv() {
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test_msg = "IntConv";
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var slen int;
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INT_EQ(0, IntFromString("0", 0, nil), int_zero);
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INT_EQ(1, IntFromString("-0", 0, nil), int_zero);
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INT_EQ(2, IntFromString("123", 0, nil), Big.Int(123));
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INT_EQ(3, IntFromString("-123", 0, nil), Big.Int(-123));
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INT_EQ(4, IntFromString("077", 0, nil), Big.Int(7*8 + 7));
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INT_EQ(5, IntFromString("-077", 0, nil), Big.Int(-(7*8 + 7)));
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INT_EQ(6, IntFromString("0x1f", 0, nil), Big.Int(1*16 + 15));
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INT_EQ(7, IntFromString("-0x1f", 0, nil), Big.Int(-(1*16 + 15)));
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INT_EQ(8, IntFromString("0x1fg", 0, &slen), Big.Int(1*16 + 15));
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INT_EQ(9, IntFromString("-0x1fg", 0, &slen), Big.Int(-(1*16 + 15)));
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TEST(10, slen == 5);
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}
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func RatConv() {
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test_msg = "RatConv";
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var slen int;
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RAT_EQ(0, RatFromString("0", 0, nil), rat_zero);
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RAT_EQ(1, RatFromString("0/1", 0, nil), rat_zero);
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RAT_EQ(2, RatFromString("0/01", 0, nil), rat_zero);
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RAT_EQ(3, RatFromString("0x14/10", 0, &slen), rat_two);
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TEST(4, slen == 7);
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RAT_EQ(5, RatFromString("0.", 0, nil), rat_zero);
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RAT_EQ(6, RatFromString("0.001f", 10, nil), Big.Rat(1, 1000));
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RAT_EQ(7, RatFromString("10101.0101", 2, nil), Big.Rat(0x155, 1<<4));
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RAT_EQ(8, RatFromString("-0003.145926", 10, &slen), Big.Rat(-3145926, 1000000));
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TEST(9, slen == 12);
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}
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func Add(x, y *Big.Natural) *Big.Natural {
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z1 := x.Add(y);
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z2 := y.Add(x);
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if z1.Cmp(z2) != 0 {
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println("addition not symmetric");
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println("x =", x.String(10));
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println("y =", y.String(10));
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panic();
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}
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return z1;
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}
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func Sum(n uint, scale *Big.Natural) *Big.Natural {
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s := nat_zero;
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for ; n > 0; n-- {
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s = Add(s, Big.Nat(n).Mul(scale));
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}
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return s;
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}
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func NatAdd() {
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test_msg = "NatAddA";
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NAT_EQ(0, Add(nat_zero, nat_zero), nat_zero);
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NAT_EQ(1, Add(nat_zero, c), c);
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test_msg = "NatAddB";
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for i := uint(0); i < 100; i++ {
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t := Big.Nat(i);
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NAT_EQ(i, Sum(i, c), t.Mul(t).Add(t).Shr(1).Mul(c));
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}
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}
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func Mul(x, y *Big.Natural) *Big.Natural {
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z1 := x.Mul(y);
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z2 := y.Mul(x);
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if z1.Cmp(z2) != 0 {
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println("multiplication not symmetric");
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println("x =", x.String(10));
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println("y =", y.String(10));
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panic();
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}
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if !x.IsZero() && z1.Div(x).Cmp(y) != 0 {
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println("multiplication/division not inverse (A)");
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println("x =", x.String(10));
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println("y =", y.String(10));
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panic();
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}
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if !y.IsZero() && z1.Div(y).Cmp(x) != 0 {
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println("multiplication/division not inverse (B)");
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println("x =", x.String(10));
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println("y =", y.String(10));
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panic();
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}
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return z1;
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}
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func NatSub() {
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test_msg = "NatSubA";
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NAT_EQ(0, nat_zero.Sub(nat_zero), nat_zero);
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NAT_EQ(1, c.Sub(nat_zero), c);
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test_msg = "NatSubB";
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for i := uint(0); i < 100; i++ {
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t := Sum(i, c);
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for j := uint(0); j <= i; j++ {
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t = t.Sub(Mul(Big.Nat(j), c));
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}
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NAT_EQ(i, t, nat_zero);
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}
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}
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func NatMul() {
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test_msg = "NatMulA";
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NAT_EQ(0, Mul(c, nat_zero), nat_zero);
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NAT_EQ(1, Mul(c, nat_one), c);
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test_msg = "NatMulB";
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NAT_EQ(0, b.Mul(Big.MulRange(0, 100)), nat_zero);
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NAT_EQ(1, b.Mul(Big.MulRange(21, 100)), c);
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test_msg = "NatMulC";
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const n = 100;
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p := b.Mul(c).Shl(n);
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for i := uint(0); i < n; i++ {
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NAT_EQ(i, Mul(b.Shl(i), c.Shl(n-i)), p);
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}
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}
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func NatDiv() {
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test_msg = "NatDivA";
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NAT_EQ(0, c.Div(nat_one), c);
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NAT_EQ(1, c.Div(Big.Nat(100)), Big.Fact(99));
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NAT_EQ(2, b.Div(c), nat_zero);
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NAT_EQ(4, nat_one.Shl(100).Div(nat_one.Shl(90)), nat_one.Shl(10));
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NAT_EQ(5, c.Div(b), Big.MulRange(21, 100));
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test_msg = "NatDivB";
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const n = 100;
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p := Big.Fact(n);
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for i := uint(0); i < n; i++ {
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NAT_EQ(i, p.Div(Big.MulRange(1, i)), Big.MulRange(i+1, n));
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}
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}
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func IntQuoRem() {
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test_msg = "IntQuoRem";
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type T struct { x, y, q, r int };
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a := []T{
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T{+8, +3, +2, +2},
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T{+8, -3, -2, +2},
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T{-8, +3, -2, -2},
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T{-8, -3, +2, -2},
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T{+1, +2, 0, +1},
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T{+1, -2, 0, +1},
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T{-1, +2, 0, -1},
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T{-1, -2, 0, -1},
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};
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for i := uint(0); i < len(a); i++ {
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e := &a[i];
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x, y := Big.Int(e.x).Mul(ip), Big.Int(e.y).Mul(ip);
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q, r := Big.Int(e.q), Big.Int(e.r).Mul(ip);
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qq, rr := x.QuoRem(y);
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INT_EQ(4*i+0, x.Quo(y), q);
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INT_EQ(4*i+1, x.Rem(y), r);
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INT_EQ(4*i+2, qq, q);
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INT_EQ(4*i+3, rr, r);
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}
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}
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func IntDivMod() {
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test_msg = "IntDivMod";
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type T struct { x, y, q, r int };
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a := []T{
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T{+8, +3, +2, +2},
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T{+8, -3, -2, +2},
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T{-8, +3, -3, +1},
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T{-8, -3, +3, +1},
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T{+1, +2, 0, +1},
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T{+1, -2, 0, +1},
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T{-1, +2, -1, +1},
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T{-1, -2, +1, +1},
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};
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for i := uint(0); i < len(a); i++ {
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e := &a[i];
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x, y := Big.Int(e.x).Mul(ip), Big.Int(e.y).Mul(ip);
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q, r := Big.Int(e.q), Big.Int(e.r).Mul(ip);
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qq, rr := x.DivMod(y);
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INT_EQ(4*i+0, x.Div(y), q);
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INT_EQ(4*i+1, x.Mod(y), r);
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INT_EQ(4*i+2, qq, q);
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INT_EQ(4*i+3, rr, r);
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}
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}
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func NatMod() {
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test_msg = "NatModA";
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for i := uint(0); ; i++ {
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d := nat_one.Shl(i);
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if d.Cmp(c) < 0 {
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NAT_EQ(i, c.Add(d).Mod(c), d);
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} else {
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NAT_EQ(i, c.Add(d).Div(c), nat_two);
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NAT_EQ(i, c.Add(d).Mod(c), d.Sub(c));
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break;
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}
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}
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}
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func NatShift() {
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test_msg = "NatShift1L";
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TEST(0, b.Shl(0).Cmp(b) == 0);
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TEST(1, c.Shl(1).Cmp(c) > 0);
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test_msg = "NatShift1R";
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TEST(0, b.Shr(0).Cmp(b) == 0);
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TEST(1, c.Shr(1).Cmp(c) < 0);
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test_msg = "NatShift2";
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for i := uint(0); i < 100; i++ {
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TEST(i, c.Shl(i).Shr(i).Cmp(c) == 0);
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}
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test_msg = "NatShift3L";
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{ const m = 3;
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p := b;
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f := Big.Nat(1<<m);
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for i := uint(0); i < 100; i++ {
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NAT_EQ(i, b.Shl(i*m), p);
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p = Mul(p, f);
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}
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}
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test_msg = "NatShift3R";
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{ p := c;
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for i := uint(0); !p.IsZero(); i++ {
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NAT_EQ(i, c.Shr(i), p);
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p = p.Shr(1);
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}
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}
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}
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func IntShift() {
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test_msg = "IntShift1L";
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TEST(0, ip.Shl(0).Cmp(ip) == 0);
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TEST(1, ip.Shl(1).Cmp(ip) > 0);
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test_msg = "IntShift1R";
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TEST(0, ip.Shr(0).Cmp(ip) == 0);
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TEST(1, ip.Shr(1).Cmp(ip) < 0);
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test_msg = "IntShift2";
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for i := uint(0); i < 100; i++ {
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TEST(i, ip.Shl(i).Shr(i).Cmp(ip) == 0);
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}
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test_msg = "IntShift3L";
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{ const m = 3;
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p := ip;
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f := Big.Int(1<<m);
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for i := uint(0); i < 100; i++ {
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INT_EQ(i, ip.Shl(i*m), p);
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p = p.Mul(f);
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}
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}
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test_msg = "IntShift3R";
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{ p := ip;
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for i := uint(0); p.IsPos(); i++ {
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INT_EQ(i, ip.Shr(i), p);
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p = p.Shr(1);
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}
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}
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test_msg = "IntShift4R";
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//INT_EQ(0, Big.Int(-43).Shr(1), Big.Int(-43 >> 1));
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//INT_EQ(1, ip.Neg().Shr(10), ip.Neg().Div(Big.Int(1).Shl(10)));
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}
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func NatCmp() {
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test_msg = "NatCmp";
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TEST(0, a.Cmp(a) == 0);
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TEST(1, a.Cmp(b) < 0);
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TEST(2, b.Cmp(a) > 0);
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TEST(3, a.Cmp(c) < 0);
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d := c.Add(b);
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TEST(4, c.Cmp(d) < 0);
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TEST(5, d.Cmp(c) > 0);
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}
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func NatLog2() {
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test_msg = "NatLog2A";
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TEST(0, nat_one.Log2() == 0);
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TEST(1, nat_two.Log2() == 1);
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TEST(2, Big.Nat(3).Log2() == 1);
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TEST(3, Big.Nat(4).Log2() == 2);
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test_msg = "NatLog2B";
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for i := uint(0); i < 100; i++ {
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TEST(i, nat_one.Shl(i).Log2() == i);
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}
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}
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func NatGcd() {
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test_msg = "NatGcdA";
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f := Big.Nat(99991);
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NAT_EQ(0, b.Mul(f).Gcd(c.Mul(f)), Big.MulRange(1, 20).Mul(f));
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}
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func NatPow() {
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test_msg = "NatPowA";
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NAT_EQ(0, nat_two.Pow(0), nat_one);
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test_msg = "NatPowB";
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for i := uint(0); i < 100; i++ {
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NAT_EQ(i, nat_two.Pow(i), nat_one.Shl(i));
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}
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}
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func NatPop() {
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test_msg = "NatPopA";
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TEST(0, nat_zero.Pop() == 0);
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TEST(1, nat_one.Pop() == 1);
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TEST(2, Big.Nat(10).Pop() == 2);
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TEST(3, Big.Nat(30).Pop() == 4);
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TEST(4, Big.Nat(0x1248f).Shl(33).Pop() == 8);
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test_msg = "NatPopB";
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for i := uint(0); i < 100; i++ {
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TEST(i, nat_one.Shl(i).Sub(nat_one).Pop() == i);
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}
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}
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func main() {
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// Naturals
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NatConv();
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NatAdd();
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NatSub();
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NatMul();
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NatDiv();
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NatMod();
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NatShift();
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NatCmp();
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NatLog2();
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NatGcd();
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NatPow();
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NatPop();
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// Integers
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// TODO add more tests
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IntConv();
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IntQuoRem();
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IntDivMod();
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IntShift();
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|
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// Rationals
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// TODO add more tests
|
|
RatConv();
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|
}
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