+++ /dev/null
-// 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
-export type IntegerImpl struct {
- val Value
-}
-export type Integer *IntegerImpl
-
-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, int(x[0])); // don't loose sign!
-
- 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++;
- }
- length := i;
- 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)[0:length];
-}
-
-
-// ----------------------------------------------------------------------------
-// Creation
-
-export func FromInt(v int) Integer {
- return new(IntegerImpl).Init(make(v));
-}
-
-
-export 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 {
- // do better then this
- d := x.sub(y);
- switch {
- case sign(d.val): return -1;
- case zero(d.val): return 0;
- default : return +1;
- }
- panic("UNREACHABLE");
-}
-
-
-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 func Fact(n int) Integer {
- return new(IntegerImpl).Init(fact(n));
-}
-
-
-func (x Integer) ToString() string {
- return tostring(x.val);
-}
-
-
-func (x Integer) ToInt() int {
- v := x.val;
- if len_(v) <= 1 {
- if zero(v) {
- return 0;
- }
- i := int(v[0 + H]);
- if sign(v) {
- i = -i; // incorrect for smallest int
- }
- return i;
- }
- panic("integer too large");
-}
+++ /dev/null
-// 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 main
-
-import Integer "integer"
-
-type Int Integer.Integer;
-
-const (
- sa = "991";
- sb = "2432902008176640000"; // 20!
- sc = "93326215443944152681699238856266700490715968264381621468592963895217599993229915608941463976156518286253697920827223758251185210916864000000000000000000000000"; // 100!
-)
-
-var (
- m, z, p,
- a, b, c,
- a_a, a_b, a_c, b_b, b_c, c_c, a_b_c
- Int
-)
-
-
-func CHECK(msg string, p bool) {
- if !p {
- panic("CHECK failed: ", msg, "\n");
- }
-}
-
-
-func Init() {
- m = Integer.FromInt(-1);
- z = Integer.FromInt(0);
- p = Integer.FromInt(1);
-
- a = Integer.FromString(sa);
- b = Integer.FromString(sb);
- c = Integer.FromString(sc);
-
- a_a = Integer.FromInt(991 + 991);
- a_b = Integer.FromString("2432902008176640991");
- a_c = Integer.FromString("93326215443944152681699238856266700490715968264381621468592963895217599993229915608941463976156518286253697920827223758251185210916864000000000000000000000991");
-}
-
-func N991() string { return "991" }
-
-func TestConv() {
- print("TestConv\n");
- CHECK("TC1", a.eql(Integer.FromInt(991)));
- CHECK("TC2", b.eql(Integer.Fact(20)));
- CHECK("TC3", c.eql(Integer.Fact(100)));
- CHECK("TC4", a.ToString() == sa);
- CHECK("TC5", b.ToString() == sb);
- CHECK("TC6", c.ToString() == sc);
-
- // also tested much via TestFact
-}
-
-
-func TestAdd() {
- print("TestAdd\n");
- CHECK("TA1", z.add(z).eql(z));
- CHECK("TA2", a.add(z).eql(a));
- CHECK("TA3", z.add(a).eql(a));
-
- CHECK("TA4", c.add(z).eql(c));
- CHECK("TA5", z.add(c).eql(c));
-
- CHECK("TA6", m.add(p).eql(z));
-
- CHECK("TA7", a.add(a).eql(a_a));
- CHECK("TA8", a.add(b).eql(a_b));
- CHECK("TA9", a.add(c).eql(a_c));
-
- // needs more
-}
-
-
-func TestSub() {
- print("TestSub\n");
- CHECK("TS1", z.sub(z).eql(z));
- CHECK("TS2", a.sub(z).eql(a));
- CHECK("TS3", z.sub(a).eql(a.neg()));
-
- CHECK("TS4", c.sub(z).eql(c));
- CHECK("TS5", z.sub(c).eql(c.neg()));
-
- CHECK("TS6", p.sub(m).eql(p.add(p)));
-
- CHECK("TS7", a.sub(a).eql(z));
-
- // needs more
-}
-
-
-func TestMul() {
- print("TestMul\n");
- // tested much via TestFact for now
-}
-
-
-func TestDiv() {
- print("TestDiv\n");
- // no div implemented yet
-}
-
-
-func TestMod() {
- print("TestMod\n");
- // no mod implemented yet
-}
-
-
-func TestFact() {
- print("TestFact\n");
- for n := 990; n < 1010; n++ {
- f := Integer.Fact(n);
- CHECK("TF", Integer.FromString(f.ToString()).eql(f));
- }
-}
-
-
-func main() {
- Init();
-
- TestConv();
- TestAdd();
- TestSub();
- TestMul();
- TestDiv();
- TestMod();
-
- TestFact();
-
- print("PASSED\n");
-}