mirror of
https://github.com/golang/go
synced 2024-11-25 09:27:57 -07:00
619 lines
10 KiB
Go
Executable File
619 lines
10 KiB
Go
Executable File
// 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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package Integer
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const ValueLen = 1000;
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type Word uint32
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type Value *[ValueLen]Word
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type IntegerImpl struct {
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val Value
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}
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type Integer *IntegerImpl
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export IntegerImpl, Integer
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const N = 4;
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const H = 1
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const L = 28;
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const M = 1 << L - 1;
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// ----------------------------------------------------------------------------
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// Support
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// TODO What are we going to about asserts?
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func ASSERT(p bool) {
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if !p {
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panic "ASSERT failed";
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}
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}
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func CHECK(p bool) {
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if !p {
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panic "CHECK failed";
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}
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}
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func UNIMPLEMENTED(s string) {
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panic "UNIMPLEMENTED: ", s;
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}
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// ----------------------------------------------------------------------------
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//
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// TODO "len" is a reserved word at the moment - I think that's wrong
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func len_(x Value) int {
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l := int(x[0]);
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if l < 0 { return -l; }
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return l;
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}
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func set_len(x Value, len_ int) {
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x[0] = Word(len_);
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}
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func alloc(len_ int) Value {
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ASSERT(len_ >= 0);
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z := new([ValueLen] Word);
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set_len(z, len_);
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return z;
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}
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func sign(x Value) bool {
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return int(x[0]) < 0;
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}
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func zero(x Value) bool {
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return x[0] == 0;
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}
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func neg(x Value) {
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x[0] = Word(-int(x[0]));
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}
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// ----------------------------------------------------------------------------
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// Unsigned ops
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func make(x int) Value;
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func Update(x Word) (z, c Word) {
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// z = x & M;
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// c = x >> L;
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return x & M, x >> L;
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}
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func uadd(x, y Value) Value {
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xl := len_(x);
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yl := len_(y);
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if xl < yl {
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return uadd(y, x);
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}
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ASSERT(xl >= yl);
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z := alloc(xl + 1);
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i := 0;
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c := Word(0);
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for i < yl { z[i + H], c = Update(x[i + H] + y[i + H] + c); i++; }
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for i < xl { z[i + H], c = Update(x[i + H] + c); i++; }
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if c != 0 { z[i + H] = c; i++; }
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set_len(z, i);
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return z;
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}
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func usub(x, y Value) Value {
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xl := len_(x);
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yl := len_(y);
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if xl < yl {
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return uadd(y, x);
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}
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ASSERT(xl >= yl);
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z := alloc(xl + 1);
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i := 0;
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c := Word(0);
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for i < yl { z[i + H], c = Update(x[i + H] - y[i + H] + c); i++; }
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for i < xl { z[i + H], c = Update(x[i + H] + c); i++; }
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ASSERT(c == 0); // usub(x, y) must be called with x >= y
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for i > 0 && z[i - 1 + H] == 0 { i--; }
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set_len(z, i);
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return z;
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}
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// Computes x = x*a + c (in place) for "small" a's.
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func umul_add(x Value, a, c Word) Value {
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CHECK(0 <= a && a < (1 << N));
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CHECK(0 <= c && c < (1 << N));
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if (zero(x) || a == 0) && c == 0 {
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return make(0);
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}
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xl := len_(x);
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z := alloc(xl + 1);
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i := 0;
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for i < xl { z[i + H], c = Update(x[i + H] * a + c); i++; }
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if c != 0 { z[i + H] = c; i++; }
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set_len(z, i);
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return z;
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}
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// Computes x = x div d (in place) for "small" d's. Returns x mod d.
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func umod(x Value, d Word) Word {
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CHECK(0 < d && d < (1 << N));
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xl := len_(x);
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c := Word(0);
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i := xl;
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for i > 0 {
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i--;
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c = c << L + x[i + H];
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q := c / d;
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x[i + H] = q;
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//x[i + H] = c / d; // BUG
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c = c % d;
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}
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if xl > 0 && x[xl - 1 + H] == 0 {
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set_len(x, xl - 1);
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}
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return c;
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}
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// Returns z = (x * y) div B, c = (x * y) mod B.
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func umul1(x, y Word) (z Word, c Word) {
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const L2 = (L + 1) >> 1;
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const B2 = 1 << L2;
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const M2 = B2 - 1;
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x0 := x & M2;
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x1 := x >> L2;
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y0 := y & M2;
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y1 := y >> L2;
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z10 := x0*y0;
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z21 := x1*y0 + x0*y1 + (z10 >> L2);
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cc := x1*y1 + (z21 >> L2);
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zz := ((z21 & M2) << L2) | (z10 & M2);
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return zz, cc
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}
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func umul(x Value, y Value) Value {
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if zero(x) || zero(y) {
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return make(0);
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}
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xl := len_(x);
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yl := len_(y);
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if xl < yl {
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return umul(y, x); // for speed
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}
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ASSERT(xl >= yl && yl > 0);
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// initialize z
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zl := xl + yl;
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z := alloc(zl);
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for i := 0; i < zl; i++ { z[i + H] = 0; }
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k := 0;
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for j := 0; j < yl; j++ {
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d := y[j + H];
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if d != 0 {
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k = j;
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c := Word(0);
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for i := 0; i < xl; i++ {
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// compute z[k + H] += x[i + H] * d + c;
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t := z[k + H] + c;
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var z1 Word;
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z1, c = umul1(x[i + H], d);
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t += z1;
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z[k + H] = t & M;
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c += t >> L;
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k++;
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}
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if c != 0 {
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z[k + H] = Word(c);
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k++;
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}
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}
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}
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set_len(z, k);
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return z;
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}
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func ucmp(x Value, y Value) int {
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xl := len_(x);
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yl := len_(y);
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if xl != yl || xl == 0 {
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return xl - yl;
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}
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i := xl - 1;
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for i > 0 && x[i + H] == y[i + H] { i--; }
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return int(x[i + H]) - int(y[i + H]);
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}
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func ulog(x Value) int {
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xl := len_(x);
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if xl == 0 { return 0; }
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n := (xl - 1) * L;
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for t := x[xl - 1 + H]; t != 0; t >>= 1 { n++ };
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return n;
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}
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func make(x int) Value {
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if x == 0 {
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z := alloc(0);
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set_len(z, 0);
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return z;
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}
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if x == -x { // smallest int
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z := alloc(2);
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z[0 + H] = 0;
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z[1 + H] = 1;
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set_len(z, -2);
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return z;
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}
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z := alloc(1);
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if x < 0 {
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z[0 + H] = Word(-x);
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set_len(z, -1);
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} else {
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z[0 + H] = Word(x);
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set_len(z, 1);
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}
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return z;
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}
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func make_from_string(s string) Value {
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// skip sign, if any
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i := 0;
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if len(s) > 0 && (s[i] == '-' || s[i] == '+') {
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i = 1;
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}
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// read digits
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x := make(0);
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for i < len(s) && '0' <= s[i] && s[i] <= '9' {
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x = umul_add(x, 10, Word(s[i] - '0'));
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i++;
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}
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// read sign
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if len(s) > 0 && s[0] == '-' {
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neg(x);
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}
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return x;
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}
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// ----------------------------------------------------------------------------
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// Creation
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func (x Integer) Init(val Value) Integer {
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x.val = val;
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return x;
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}
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// ----------------------------------------------------------------------------
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// Signed ops
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func add(x Value, y Value) Value {
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var z Value;
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if sign(x) == sign(y) {
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// x + y == x + y
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// (-x) + (-y) == -(x + y)
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z = uadd(x, y);
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} else {
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// x + (-y) == x - y == -(y - x)
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// (-x) + y == y - x == -(x - y)
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if ucmp(x, y) >= 0 {
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z = usub(x, y);
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} else {
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z = usub(y, x);
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neg(z);
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}
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}
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if sign(x) {
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neg(z);
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}
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return z;
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}
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func sub(x Value, y Value) Value {
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var z Value;
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if sign(x) != sign(y) {
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// x - (-y) == x + y
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// (-x) - y == -(x + y)
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z = uadd(x, y);
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} else {
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// x - y == x - y == -(y - x)
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// (-x) - (-y) == y - x == -(x - y)
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if ucmp(x, y) >= 0 {
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z = usub(x, y);
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} else {
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z = usub(y, x);
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neg(z);
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}
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}
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if sign(x) {
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neg(z);
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}
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return z;
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}
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func mul(x Value, y Value) Value {
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// x * y == x * y
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// x * (-y) == -(x * y)
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// (-x) * y == -(x * y)
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// (-x) * (-y) == x * y
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z := umul(x, y);
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if sign(x) != sign(y) {
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neg(z);
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}
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return z;
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}
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func mul_range(a, b int) Value {
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if a > b { return make(1) };
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if a == b { return make(a) };
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if a + 1 == b { return mul(make(a), make(b)) };
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m := (a + b) >> 1;
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ASSERT(a <= m && m < b);
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return mul(mul_range(a, m), mul_range(m + 1, b));
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}
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func fact(n int) Value {
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return mul_range(2, n);
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}
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// Returns a copy of x with space for one extra digit.
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func copy(x Value) Value {
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xl := len_(x);
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z := alloc(xl + 1); // add space for one extra digit
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for i := 0; i < xl; i++ { z[i + H] = x[i + H]; }
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set_len(z, xl);
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return z;
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}
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func tostring(x Value) string {
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// allocate string
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// approx. length: 1 char for 3 bits
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n := ulog(x)/3 + 3; // +1 (round up) +1 (sign) +1 (0 termination)
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//s := new([]byte, n);
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s := new([100000]byte);
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// convert
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z := copy(x);
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i := 0;
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for i == 0 || !zero(z) {
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s[i] = byte(umod(z, 10) + '0');
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i++;
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};
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if sign(x) {
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s[i] = '-';
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i++;
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}
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length := i;
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ASSERT(0 < i && i < n);
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// reverse in place
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i--;
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for j := 0; j < i; j++ {
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t := s[j];
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s[j] = s[i];
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s[i] = t;
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i--;
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}
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return string(s)[0:length];
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}
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// ----------------------------------------------------------------------------
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// Creation
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export FromInt
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func FromInt(v int) Integer {
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return new(IntegerImpl).Init(make(v));
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}
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export FromString
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func FromString(s string) Integer {
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return new(IntegerImpl).Init(make_from_string(s));
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}
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// ----------------------------------------------------------------------------
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// Arithmetic ops
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func (x Integer) neg () Integer {
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if (zero(x.val)) {
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return new(IntegerImpl).Init(make(0));
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}
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z := copy(x.val);
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neg(z);
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return new(IntegerImpl).Init(z);
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}
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func (x Integer) add (y Integer) Integer {
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return new(IntegerImpl).Init(add(x.val, y.val));
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}
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func (x Integer) sub (y Integer) Integer {
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return new(IntegerImpl).Init(sub(x.val, y.val));
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}
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func (x Integer) mul (y Integer) Integer {
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return new(IntegerImpl).Init(mul(x.val, y.val));
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}
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func (x Integer) quo (y Integer) Integer {
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UNIMPLEMENTED("quo");
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return nil;
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}
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func (x Integer) rem (y Integer) Integer {
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UNIMPLEMENTED("rem");
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return nil;
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}
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func (x Integer) div (y Integer) Integer {
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UNIMPLEMENTED("div");
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return nil;
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}
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func (x Integer) mod (y Integer) Integer {
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UNIMPLEMENTED("mod");
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return nil;
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}
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// ----------------------------------------------------------------------------
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// Arithmetic shifts
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func (x Integer) shl (s uint) Integer {
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UNIMPLEMENTED("shl");
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return nil;
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}
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func (x Integer) shr (s uint) Integer {
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UNIMPLEMENTED("shr");
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return nil;
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}
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// ----------------------------------------------------------------------------
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// Logical ops
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func (x Integer) inv () Integer {
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UNIMPLEMENTED("inv");
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return nil;
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}
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func (x Integer) and (y Integer) Integer {
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UNIMPLEMENTED("and");
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return nil;
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}
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func (x Integer) or (y Integer) Integer {
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UNIMPLEMENTED("or");
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return nil;
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}
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func (x Integer) xor (y Integer) Integer {
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UNIMPLEMENTED("xor");
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return nil;
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}
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// ----------------------------------------------------------------------------
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// Comparisons
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func (x Integer) cmp (y Integer) int {
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return 0;
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}
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func (x Integer) eql (y Integer) bool {
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return x.cmp(y) == 0;
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}
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func (x Integer) neq (y Integer) bool {
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return x.cmp(y) != 0;
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}
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func (x Integer) lss (y Integer) bool {
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return x.cmp(y) < 0;
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}
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func (x Integer) leq (y Integer) bool {
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return x.cmp(y) <= 0;
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}
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func (x Integer) gtr (y Integer) bool {
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return x.cmp(y) > 0;
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}
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func (x Integer) geq (y Integer) bool {
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return x.cmp(y) >= 0;
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}
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// ----------------------------------------------------------------------------
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// Specials
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export Fact
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func Fact(n int) Integer {
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return new(IntegerImpl).Init(fact(n));
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}
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func (x Integer) ToString() string {
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return tostring(x.val);
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}
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