mirror of
https://github.com/golang/go
synced 2024-11-22 11:34:47 -07:00
619 lines
10 KiB
Go
Executable File
619 lines
10 KiB
Go
Executable File
// 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 Integer
|
|
|
|
const ValueLen = 1000;
|
|
type Word uint32
|
|
type Value *[ValueLen]Word
|
|
type IntegerImpl struct {
|
|
val Value
|
|
}
|
|
type Integer *IntegerImpl
|
|
|
|
export IntegerImpl, Integer
|
|
|
|
const N = 4;
|
|
const H = 1
|
|
const L = 28;
|
|
const M = 1 << L - 1;
|
|
|
|
|
|
// ----------------------------------------------------------------------------
|
|
// Support
|
|
|
|
// TODO What are we going to about asserts?
|
|
func ASSERT(p bool) {
|
|
if !p {
|
|
panic "ASSERT failed";
|
|
}
|
|
}
|
|
|
|
|
|
func CHECK(p bool) {
|
|
if !p {
|
|
panic "CHECK failed";
|
|
}
|
|
}
|
|
|
|
|
|
func UNIMPLEMENTED(s string) {
|
|
panic "UNIMPLEMENTED: ", s;
|
|
}
|
|
|
|
|
|
// ----------------------------------------------------------------------------
|
|
//
|
|
|
|
// TODO "len" is a reserved word at the moment - I think that's wrong
|
|
func len_(x Value) int {
|
|
l := int(x[0]);
|
|
if l < 0 { return -l; }
|
|
return l;
|
|
}
|
|
|
|
|
|
func set_len(x Value, len_ int) {
|
|
x[0] = Word(len_);
|
|
}
|
|
|
|
|
|
func alloc(len_ int) Value {
|
|
ASSERT(len_ >= 0);
|
|
z := new([ValueLen] Word);
|
|
set_len(z, len_);
|
|
return z;
|
|
}
|
|
|
|
|
|
func sign(x Value) bool {
|
|
return int(x[0]) < 0;
|
|
}
|
|
|
|
|
|
func zero(x Value) bool {
|
|
return x[0] == 0;
|
|
}
|
|
|
|
|
|
func neg(x Value) {
|
|
x[0] = Word(-int(x[0]));
|
|
}
|
|
|
|
|
|
// ----------------------------------------------------------------------------
|
|
// Unsigned ops
|
|
|
|
func make(x int) Value;
|
|
|
|
|
|
func Update(x Word) (z, c Word) {
|
|
// z = x & M;
|
|
// c = x >> L;
|
|
return x & M, x >> L;
|
|
}
|
|
|
|
|
|
func uadd(x, y Value) Value {
|
|
xl := len_(x);
|
|
yl := len_(y);
|
|
if xl < yl {
|
|
return uadd(y, x);
|
|
}
|
|
ASSERT(xl >= yl);
|
|
z := alloc(xl + 1);
|
|
|
|
i := 0;
|
|
c := Word(0);
|
|
for i < yl { z[i + H], c = Update(x[i + H] + y[i + H] + c); i++; }
|
|
for i < xl { z[i + H], c = Update(x[i + H] + c); i++; }
|
|
if c != 0 { z[i + H] = c; i++; }
|
|
set_len(z, i);
|
|
|
|
return z;
|
|
}
|
|
|
|
|
|
func usub(x, y Value) Value {
|
|
xl := len_(x);
|
|
yl := len_(y);
|
|
if xl < yl {
|
|
return uadd(y, x);
|
|
}
|
|
ASSERT(xl >= yl);
|
|
z := alloc(xl + 1);
|
|
|
|
i := 0;
|
|
c := Word(0);
|
|
for i < yl { z[i + H], c = Update(x[i + H] - y[i + H] + c); i++; }
|
|
for i < xl { z[i + H], c = Update(x[i + H] + c); i++; }
|
|
ASSERT(c == 0); // usub(x, y) must be called with x >= y
|
|
for i > 0 && z[i - 1 + H] == 0 { i--; }
|
|
set_len(z, i);
|
|
|
|
return z;
|
|
}
|
|
|
|
|
|
// Computes x = x*a + c (in place) for "small" a's.
|
|
func umul_add(x Value, a, c Word) Value {
|
|
CHECK(0 <= a && a < (1 << N));
|
|
CHECK(0 <= c && c < (1 << N));
|
|
if (zero(x) || a == 0) && c == 0 {
|
|
return make(0);
|
|
}
|
|
xl := len_(x);
|
|
|
|
z := alloc(xl + 1);
|
|
i := 0;
|
|
for i < xl { z[i + H], c = Update(x[i + H] * a + c); i++; }
|
|
if c != 0 { z[i + H] = c; i++; }
|
|
set_len(z, i);
|
|
|
|
return z;
|
|
}
|
|
|
|
|
|
// Computes x = x div d (in place) for "small" d's. Returns x mod d.
|
|
func umod(x Value, d Word) Word {
|
|
CHECK(0 < d && d < (1 << N));
|
|
xl := len_(x);
|
|
c := Word(0);
|
|
|
|
i := xl;
|
|
for i > 0 {
|
|
i--;
|
|
c = c << L + x[i + H];
|
|
|
|
q := c / d;
|
|
x[i + H] = q;
|
|
|
|
//x[i + H] = c / d; // BUG
|
|
|
|
c = c % d;
|
|
}
|
|
if xl > 0 && x[xl - 1 + H] == 0 {
|
|
set_len(x, xl - 1);
|
|
}
|
|
|
|
return c;
|
|
}
|
|
|
|
|
|
// Returns z = (x * y) div B, c = (x * y) mod B.
|
|
func umul1(x, y Word) (z Word, c Word) {
|
|
const L2 = (L + 1) >> 1;
|
|
const B2 = 1 << L2;
|
|
const M2 = B2 - 1;
|
|
|
|
x0 := x & M2;
|
|
x1 := x >> L2;
|
|
|
|
y0 := y & M2;
|
|
y1 := y >> L2;
|
|
|
|
z10 := x0*y0;
|
|
z21 := x1*y0 + x0*y1 + (z10 >> L2);
|
|
|
|
cc := x1*y1 + (z21 >> L2);
|
|
zz := ((z21 & M2) << L2) | (z10 & M2);
|
|
return zz, cc
|
|
}
|
|
|
|
|
|
func umul(x Value, y Value) Value {
|
|
if zero(x) || zero(y) {
|
|
return make(0);
|
|
}
|
|
xl := len_(x);
|
|
yl := len_(y);
|
|
if xl < yl {
|
|
return umul(y, x); // for speed
|
|
}
|
|
ASSERT(xl >= yl && yl > 0);
|
|
|
|
// initialize z
|
|
zl := xl + yl;
|
|
z := alloc(zl);
|
|
for i := 0; i < zl; i++ { z[i + H] = 0; }
|
|
|
|
k := 0;
|
|
for j := 0; j < yl; j++ {
|
|
d := y[j + H];
|
|
if d != 0 {
|
|
k = j;
|
|
c := Word(0);
|
|
for i := 0; i < xl; i++ {
|
|
// compute z[k + H] += x[i + H] * d + c;
|
|
t := z[k + H] + c;
|
|
var z1 Word;
|
|
z1, c = umul1(x[i + H], d);
|
|
t += z1;
|
|
z[k + H] = t & M;
|
|
c += t >> L;
|
|
k++;
|
|
}
|
|
if c != 0 {
|
|
z[k + H] = Word(c);
|
|
k++;
|
|
}
|
|
}
|
|
}
|
|
set_len(z, k);
|
|
|
|
return z;
|
|
}
|
|
|
|
|
|
func ucmp(x Value, y Value) int {
|
|
xl := len_(x);
|
|
yl := len_(y);
|
|
|
|
if xl != yl || xl == 0 {
|
|
return xl - yl;
|
|
}
|
|
|
|
i := xl - 1;
|
|
for i > 0 && x[i + H] == y[i + H] { i--; }
|
|
return int(x[i + H]) - int(y[i + H]);
|
|
}
|
|
|
|
|
|
func ulog(x Value) int {
|
|
xl := len_(x);
|
|
if xl == 0 { return 0; }
|
|
|
|
n := (xl - 1) * L;
|
|
for t := x[xl - 1 + H]; t != 0; t >>= 1 { n++ };
|
|
|
|
return n;
|
|
}
|
|
|
|
|
|
func make(x int) Value {
|
|
if x == 0 {
|
|
z := alloc(0);
|
|
set_len(z, 0);
|
|
return z;
|
|
}
|
|
|
|
if x == -x { // smallest int
|
|
z := alloc(2);
|
|
z[0 + H] = 0;
|
|
z[1 + H] = 1;
|
|
set_len(z, -2);
|
|
return z;
|
|
}
|
|
|
|
z := alloc(1);
|
|
if x < 0 {
|
|
z[0 + H] = Word(-x);
|
|
set_len(z, -1);
|
|
} else {
|
|
z[0 + H] = Word(x);
|
|
set_len(z, 1);
|
|
}
|
|
|
|
return z;
|
|
}
|
|
|
|
|
|
func make_from_string(s string) Value {
|
|
// skip sign, if any
|
|
i := 0;
|
|
if len(s) > 0 && (s[i] == '-' || s[i] == '+') {
|
|
i = 1;
|
|
}
|
|
|
|
// read digits
|
|
x := make(0);
|
|
for i < len(s) && '0' <= s[i] && s[i] <= '9' {
|
|
x = umul_add(x, 10, Word(s[i] - '0'));
|
|
i++;
|
|
}
|
|
|
|
// read sign
|
|
if len(s) > 0 && s[0] == '-' {
|
|
neg(x);
|
|
}
|
|
|
|
return x;
|
|
}
|
|
|
|
|
|
// ----------------------------------------------------------------------------
|
|
// Creation
|
|
|
|
|
|
func (x Integer) Init(val Value) Integer {
|
|
x.val = val;
|
|
return x;
|
|
}
|
|
|
|
|
|
// ----------------------------------------------------------------------------
|
|
// Signed ops
|
|
|
|
func add(x Value, y Value) Value {
|
|
var z Value;
|
|
if sign(x) == sign(y) {
|
|
// x + y == x + y
|
|
// (-x) + (-y) == -(x + y)
|
|
z = uadd(x, y);
|
|
} else {
|
|
// x + (-y) == x - y == -(y - x)
|
|
// (-x) + y == y - x == -(x - y)
|
|
if ucmp(x, y) >= 0 {
|
|
z = usub(x, y);
|
|
} else {
|
|
z = usub(y, x);
|
|
neg(z);
|
|
}
|
|
}
|
|
if sign(x) {
|
|
neg(z);
|
|
}
|
|
return z;
|
|
}
|
|
|
|
|
|
func sub(x Value, y Value) Value {
|
|
var z Value;
|
|
if sign(x) != sign(y) {
|
|
// x - (-y) == x + y
|
|
// (-x) - y == -(x + y)
|
|
z = uadd(x, y);
|
|
} else {
|
|
// x - y == x - y == -(y - x)
|
|
// (-x) - (-y) == y - x == -(x - y)
|
|
if ucmp(x, y) >= 0 {
|
|
z = usub(x, y);
|
|
} else {
|
|
z = usub(y, x);
|
|
neg(z);
|
|
}
|
|
}
|
|
if sign(x) {
|
|
neg(z);
|
|
}
|
|
return z;
|
|
}
|
|
|
|
|
|
func mul(x Value, y Value) Value {
|
|
// x * y == x * y
|
|
// x * (-y) == -(x * y)
|
|
// (-x) * y == -(x * y)
|
|
// (-x) * (-y) == x * y
|
|
z := umul(x, y);
|
|
if sign(x) != sign(y) {
|
|
neg(z);
|
|
}
|
|
return z;
|
|
}
|
|
|
|
|
|
func mul_range(a, b int) Value {
|
|
if a > b { return make(1) };
|
|
if a == b { return make(a) };
|
|
if a + 1 == b { return mul(make(a), make(b)) };
|
|
m := (a + b) >> 1;
|
|
ASSERT(a <= m && m < b);
|
|
return mul(mul_range(a, m), mul_range(m + 1, b));
|
|
}
|
|
|
|
|
|
func fact(n int) Value {
|
|
return mul_range(2, n);
|
|
}
|
|
|
|
|
|
// Returns a copy of x with space for one extra digit.
|
|
func copy(x Value) Value {
|
|
xl := len_(x);
|
|
|
|
z := alloc(xl + 1); // add space for one extra digit
|
|
for i := 0; i < xl; i++ { z[i + H] = x[i + H]; }
|
|
set_len(z, xl);
|
|
|
|
return z;
|
|
}
|
|
|
|
|
|
func tostring(x Value) string {
|
|
// allocate string
|
|
// approx. length: 1 char for 3 bits
|
|
n := ulog(x)/3 + 3; // +1 (round up) +1 (sign) +1 (0 termination)
|
|
//s := new([]byte, n);
|
|
s := new([100000]byte);
|
|
|
|
// convert
|
|
z := copy(x);
|
|
i := 0;
|
|
for i == 0 || !zero(z) {
|
|
s[i] = byte(umod(z, 10) + '0');
|
|
i++;
|
|
};
|
|
if sign(x) {
|
|
s[i] = '-';
|
|
i++;
|
|
}
|
|
s[i] = 0;
|
|
ASSERT(0 < i && i < n);
|
|
|
|
// reverse in place
|
|
i--;
|
|
for j := 0; j < i; j++ {
|
|
t := s[j];
|
|
s[j] = s[i];
|
|
s[i] = t;
|
|
i--;
|
|
}
|
|
|
|
return string(s);
|
|
}
|
|
|
|
|
|
// ----------------------------------------------------------------------------
|
|
// Creation
|
|
|
|
export FromInt
|
|
func FromInt(v int) Integer {
|
|
return new(IntegerImpl).Init(make(v));
|
|
}
|
|
|
|
|
|
export FromString
|
|
func FromString(s string) Integer {
|
|
return new(IntegerImpl).Init(make_from_string(s));
|
|
}
|
|
|
|
|
|
// ----------------------------------------------------------------------------
|
|
// Arithmetic ops
|
|
|
|
func (x Integer) neg () Integer {
|
|
if (zero(x.val)) {
|
|
return new(IntegerImpl).Init(make(0));
|
|
}
|
|
|
|
z := copy(x.val);
|
|
neg(z);
|
|
return new(IntegerImpl).Init(z);
|
|
}
|
|
|
|
|
|
func (x Integer) add (y Integer) Integer {
|
|
return new(IntegerImpl).Init(add(x.val, y.val));
|
|
}
|
|
|
|
|
|
func (x Integer) sub (y Integer) Integer {
|
|
return new(IntegerImpl).Init(sub(x.val, y.val));
|
|
}
|
|
|
|
|
|
func (x Integer) mul (y Integer) Integer {
|
|
return new(IntegerImpl).Init(mul(x.val, y.val));
|
|
}
|
|
|
|
|
|
func (x Integer) quo (y Integer) Integer {
|
|
UNIMPLEMENTED("quo");
|
|
return nil;
|
|
}
|
|
|
|
|
|
func (x Integer) rem (y Integer) Integer {
|
|
UNIMPLEMENTED("rem");
|
|
return nil;
|
|
}
|
|
|
|
|
|
func (x Integer) div (y Integer) Integer {
|
|
UNIMPLEMENTED("div");
|
|
return nil;
|
|
}
|
|
|
|
|
|
func (x Integer) mod (y Integer) Integer {
|
|
UNIMPLEMENTED("mod");
|
|
return nil;
|
|
}
|
|
|
|
|
|
// ----------------------------------------------------------------------------
|
|
// Arithmetic shifts
|
|
|
|
func (x Integer) shl (s uint) Integer {
|
|
UNIMPLEMENTED("shl");
|
|
return nil;
|
|
}
|
|
|
|
|
|
func (x Integer) shr (s uint) Integer {
|
|
UNIMPLEMENTED("shr");
|
|
return nil;
|
|
}
|
|
|
|
|
|
// ----------------------------------------------------------------------------
|
|
// Logical ops
|
|
|
|
func (x Integer) inv () Integer {
|
|
UNIMPLEMENTED("inv");
|
|
return nil;
|
|
}
|
|
|
|
|
|
func (x Integer) and (y Integer) Integer {
|
|
UNIMPLEMENTED("and");
|
|
return nil;
|
|
}
|
|
|
|
|
|
func (x Integer) or (y Integer) Integer {
|
|
UNIMPLEMENTED("or");
|
|
return nil;
|
|
}
|
|
|
|
|
|
func (x Integer) xor (y Integer) Integer {
|
|
UNIMPLEMENTED("xor");
|
|
return nil;
|
|
}
|
|
|
|
|
|
// ----------------------------------------------------------------------------
|
|
// Comparisons
|
|
|
|
func (x Integer) cmp (y Integer) int {
|
|
return 0;
|
|
}
|
|
|
|
|
|
func (x Integer) eql (y Integer) bool {
|
|
return x.cmp(y) == 0;
|
|
}
|
|
|
|
|
|
func (x Integer) neq (y Integer) bool {
|
|
return x.cmp(y) != 0;
|
|
}
|
|
|
|
|
|
func (x Integer) lss (y Integer) bool {
|
|
return x.cmp(y) < 0;
|
|
}
|
|
|
|
|
|
func (x Integer) leq (y Integer) bool {
|
|
return x.cmp(y) <= 0;
|
|
}
|
|
|
|
|
|
func (x Integer) gtr (y Integer) bool {
|
|
return x.cmp(y) > 0;
|
|
}
|
|
|
|
|
|
func (x Integer) geq (y Integer) bool {
|
|
return x.cmp(y) >= 0;
|
|
}
|
|
|
|
|
|
// ----------------------------------------------------------------------------
|
|
// Specials
|
|
|
|
export Fact
|
|
func Fact(n int) Integer {
|
|
return new(IntegerImpl).Init(fact(n));
|
|
}
|
|
|
|
|
|
func (x Integer) ToString() string {
|
|
return tostring(x.val);
|
|
}
|
|
|