Commit 5ac88f4a authored by Evan Shaw's avatar Evan Shaw Committed by Robert Griesemer

big: Add Rat type

Implementations are pretty rough and simple at this point, but it's a start.

R=gri
CC=golang-dev
https://golang.org/cl/1250043
parent e2b6022f
......@@ -7,8 +7,9 @@ include ../../Make.$(GOARCH)
TARG=big
GOFILES=\
arith.go\
nat.go\
int.go\
nat.go\
rat.go\
OFILES=\
arith_$(GOARCH).$O\
......
......@@ -10,6 +10,7 @@
// The following numeric types are supported:
//
// - Int signed integers
// - Rat rational numbers
//
// All methods on Int take the result as the receiver; if it is one
// of the operands it may be overwritten (and its memory reused).
......@@ -39,6 +40,7 @@ type nat []Word
var (
natOne = nat{1}
natTwo = nat{2}
natTen = nat{10}
)
......
// Copyright 2010 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.
// This file implements multi-precision rational numbers.
package big
import "strings"
// A Rat represents a quotient a/b of arbitrary precision. The zero value for
// a Rat, 0/0, is not a legal Rat.
type Rat struct {
a Int
b nat
}
// NewRat creates a new Rat with numerator a and denominator b.
func NewRat(a, b int64) *Rat {
return new(Rat).SetFrac64(a, b)
}
// SetFrac sets z to a/b and returns z.
func (z *Rat) SetFrac(a, b *Int) *Rat {
z.a.Set(a)
z.a.neg = a.neg != b.neg
z.b = z.b.set(b.abs)
return z.norm()
}
// SetFrac64 sets z to a/b and returns z.
func (z *Rat) SetFrac64(a, b int64) *Rat {
z.a.SetInt64(a)
if b < 0 {
z.b.setUint64(uint64(-b))
z.a.neg = !z.a.neg
return z.norm()
}
z.b = z.b.setUint64(uint64(b))
return z.norm()
}
// SetInt sets z to x (by making a copy of x) and returns z.
func (z *Rat) SetInt(x *Int) *Rat {
z.a.Set(x)
z.b = z.b.setWord(1)
return z
}
// SetInt64 sets z to x and returns z.
func (z *Rat) SetInt64(x int64) *Rat {
z.a.SetInt64(x)
z.b = z.b.setWord(1)
return z
}
// Num returns the numerator of z; it may be <= 0.
// The result is a reference to z's numerator; it
// may change if a new value is assigned to z.
func (z *Rat) Num() *Int {
return &z.a
}
// Demom returns the denominator of z; it is always > 0.
// The result is a reference to z's denominator; it
// may change if a new value is assigned to z.
func (z *Rat) Denom() *Int {
return &Int{false, z.b}
}
func gcd(x, y nat) nat {
// Euclidean algorithm.
var a, b nat
a = a.set(x)
b = b.set(y)
for len(b) != 0 {
var q, r nat
_, r = q.div(r, a, b)
a = b
b = r
}
return a
}
func (z *Rat) norm() *Rat {
f := gcd(z.a.abs, z.b)
if len(z.a.abs) == 0 {
// z == 0
z.a.neg = false // normalize sign
z.b = z.b.setWord(1)
return z
}
if f.cmp(natOne) != 0 {
z.a.abs, _ = z.a.abs.div(nil, z.a.abs, f)
z.b, _ = z.b.div(nil, z.b, f)
}
return z
}
func mulNat(x *Int, y nat) *Int {
var z Int
z.abs = z.abs.mul(x.abs, y)
z.neg = len(z.abs) > 0 && x.neg
return &z
}
// Cmp compares x and y and returns:
//
// -1 if x < y
// 0 if x == y
// +1 if x > y
//
func (x *Rat) Cmp(y *Rat) (r int) {
return mulNat(&x.a, y.b).Cmp(mulNat(&y.a, x.b))
}
// Add sets z to the sum x+y and returns z.
func (z *Rat) Add(x, y *Rat) *Rat {
a1 := mulNat(&x.a, y.b)
a2 := mulNat(&y.a, x.b)
z.a.Add(a1, a2)
z.b = z.b.mul(x.b, y.b)
return z.norm()
}
// Sub sets z to the difference x-y and returns z.
func (z *Rat) Sub(x, y *Rat) *Rat {
a1 := mulNat(&x.a, y.b)
a2 := mulNat(&y.a, x.b)
z.a.Sub(a1, a2)
z.b = z.b.mul(x.b, y.b)
return z.norm()
}
// Mul sets z to the product x*y and returns z.
func (z *Rat) Mul(x, y *Rat) *Rat {
z.a.Mul(&x.a, &y.a)
z.b = z.b.mul(x.b, y.b)
return z.norm()
}
// Quo sets z to the quotient x/y and returns z.
// If y == 0, a division-by-zero run-time panic occurs.
func (z *Rat) Quo(x, y *Rat) *Rat {
if len(y.a.abs) == 0 {
panic("division by zero")
}
z.a.abs = z.a.abs.mul(x.a.abs, y.b)
z.b = z.b.mul(x.b, y.a.abs)
z.a.neg = x.a.neg != y.a.neg
return z.norm()
}
// Neg sets z to -x (by making a copy of x if necessary) and returns z.
func (z *Rat) Neg(x *Rat) *Rat {
z.a.Neg(&x.a)
z.b = z.b.set(x.b)
return z
}
// Set sets z to x (by making a copy of x if necessary) and returns z.
func (z *Rat) Set(x *Rat) *Rat {
z.a.Set(&x.a)
z.b = z.b.set(x.b)
return z
}
// SetString sets z to the value of s and returns z and a boolean indicating
// success. s can be given as a fraction "a/b" or as a decimal number "a.b".
// If the operation failed, the value of z is undefined.
func (z *Rat) SetString(s string) (*Rat, bool) {
if len(s) == 0 {
return z, false
}
// Check for a decimal point
sep := strings.Index(s, ".")
if sep < 0 {
// Check for a quotient
sep = strings.Index(s, "/")
if sep < 0 {
// Just read in the string as an integer
if _, ok := z.a.SetString(s, 10); !ok {
return z, false
}
z.b = z.b.setWord(1)
return z, true
}
if _, ok := z.a.SetString(s[0:sep], 10); !ok {
return z, false
}
s = s[sep+1:]
var n int
if z.b, _, n = z.b.scan(s, 10); n != len(s) {
return z, false
}
return z.norm(), true
}
s = s[0:sep] + s[sep+1:]
if _, ok := z.a.SetString(s, 10); !ok {
return z, false
}
z.b = z.b.expNN(natTen, nat{Word(len(s) - sep)}, nil)
return z.norm(), true
}
// String returns a string representation of z in the form "a/b".
func (z *Rat) String() string {
s := z.a.String()
if len(z.b) == 1 && z.b[0] == 1 {
return s
}
return s + "/" + z.b.string(10)
}
// FloatString returns a string representation of z in decimal form with prec
// digits of precision after the decimal point and the last digit rounded.
func (z *Rat) FloatString(prec int) string {
q, r := nat{}.div(nat{}, z.a.abs, z.b)
s := ""
if z.a.neg {
s = "-"
}
s += q.string(10)
if len(z.b) == 1 && z.b[0] == 1 {
return s
}
p := nat{}.expNN(natTen, nat{Word(prec)}, nil)
r = r.mul(r, p)
r, r2 := r.div(nat{}, r, z.b)
// See if we need to round up
r2 = r2.mul(r2, natTwo)
if z.b.cmp(r2) <= 0 {
r = r.add(r, natOne)
}
rs := r.string(10)
leadingZeros := prec - len(rs)
s += "." + strings.Repeat("0", leadingZeros) + rs
s = strings.TrimRight(s, "0")
return s
}
// Copyright 2010 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 big
import "testing"
type setStringTest struct {
in, out string
}
var setStringTests = []setStringTest{
setStringTest{"0", "0"},
setStringTest{"1", "1"},
setStringTest{"-1", "-1"},
setStringTest{"2/4", "1/2"},
setStringTest{".25", "1/4"},
setStringTest{"-1/5", "-1/5"},
}
func TestRatSetString(t *testing.T) {
for i, test := range setStringTests {
x, _ := new(Rat).SetString(test.in)
if x.String() != test.out {
t.Errorf("#%d got %s want %s", i, x.String(), test.out)
}
}
}
type floatStringTest struct {
in string
prec int
out string
}
var floatStringTests = []floatStringTest{
floatStringTest{"0", 0, "0"},
floatStringTest{"0", 4, "0"},
floatStringTest{"1", 0, "1"},
floatStringTest{"1", 2, "1"},
floatStringTest{"-1", 0, "-1"},
floatStringTest{".25", 2, "0.25"},
floatStringTest{".25", 1, "0.3"},
floatStringTest{"-1/3", 3, "-0.333"},
floatStringTest{"-2/3", 4, "-0.6667"},
}
func TestFloatString(t *testing.T) {
for i, test := range floatStringTests {
x, _ := new(Rat).SetString(test.in)
if x.FloatString(test.prec) != test.out {
t.Errorf("#%d got %s want %s", i, x.FloatString(test.prec), test.out)
}
}
}
type ratCmpTest struct {
rat1, rat2 string
out int
}
var ratCmpTests = []ratCmpTest{
ratCmpTest{"0", "0/1", 0},
ratCmpTest{"1/1", "1", 0},
ratCmpTest{"-1", "-2/2", 0},
ratCmpTest{"1", "0", 1},
ratCmpTest{"0/1", "1/1", -1},
ratCmpTest{"-5/1434770811533343057144", "-5/1434770811533343057145", -1},
ratCmpTest{"49832350382626108453/8964749413", "49832350382626108454/8964749413", -1},
ratCmpTest{"-37414950961700930/7204075375675961", "37414950961700930/7204075375675961", -1},
ratCmpTest{"37414950961700930/7204075375675961", "74829901923401860/14408150751351922", 0},
}
func TestRatCmp(t *testing.T) {
for i, test := range ratCmpTests {
x, _ := new(Rat).SetString(test.rat1)
y, _ := new(Rat).SetString(test.rat2)
out := x.Cmp(y)
if out != test.out {
t.Errorf("#%d got out = %v; want %v", i, out, test.out)
}
}
}
type ratBinFun func(z, x, y *Rat) *Rat
type ratBinArg struct {
x string
y string
out string
}
func testRatBin(t *testing.T, f ratBinFun, a []ratBinArg) {
for i, test := range a {
x, _ := NewRat(0, 1).SetString(test.x)
y, _ := NewRat(0, 1).SetString(test.y)
expected, _ := NewRat(0, 1).SetString(test.out)
out := f(NewRat(0, 1), x, y)
if out.Cmp(expected) != 0 {
t.Errorf("#%d got %s want %s", i, out, expected)
}
}
}
var ratAddTests = []ratBinArg{
ratBinArg{"0", "0", "0"},
ratBinArg{"0", "1", "1"},
ratBinArg{"-1", "0", "-1"},
ratBinArg{"-1", "1", "0"},
ratBinArg{"1", "1", "2"},
ratBinArg{"1/2", "1/2", "1"},
ratBinArg{"1/4", "1/3", "7/12"},
ratBinArg{"2/5", "-14/3", "-64/15"},
ratBinArg{"4707/49292519774798173060", "-3367/70976135186689855734", "84058377121001851123459/1749296273614329067191168098769082663020"},
ratBinArg{"-61204110018146728334/3", "-31052192278051565633/2", "-215564796870448153567/6"},
}
func TestRatAdd(t *testing.T) {
testRatBin(t, (*Rat).Add, ratAddTests)
}
var ratSubTests = []ratBinArg{
ratBinArg{"0", "0", "0"},
ratBinArg{"0", "1", "-1"},
ratBinArg{"-1", "0", "-1"},
ratBinArg{"-1", "1", "-2"},
ratBinArg{"1", "1", "0"},
ratBinArg{"1/2", "1/3", "1/6"},
ratBinArg{"1/4", "1/3", "-1/12"},
ratBinArg{"2/5", "-14/3", "76/15"},
ratBinArg{"4707/49292519774798173060", "-3367/70976135186689855734", "250026291202747299816479/1749296273614329067191168098769082663020"},
ratBinArg{"-27/133467566250814981", "-18/31750379913563777419", "-854857841473707320655/4237645934602118692642972629634714039"},
ratBinArg{"27674141753240653/30123979153216", "-19948846211000086/637313996471", "618575745270541348005638912139/19198433543745179392300736"},
}
func TestRatSub(t *testing.T) {
testRatBin(t, (*Rat).Sub, ratSubTests)
}
var ratMulTests = []ratBinArg{
ratBinArg{"0", "0", "0"},
ratBinArg{"0", "1", "0"},
ratBinArg{"-1", "0", "0"},
ratBinArg{"-1", "1", "-1"},
ratBinArg{"1", "1", "1"},
ratBinArg{"1/2", "1/2", "1/4"},
ratBinArg{"1/4", "1/3", "1/12"},
ratBinArg{"2/5", "-14/3", "-28/15"},
ratBinArg{"-3/26206484091896184128", "5/2848423294177090248", "-5/24882386581946146755650075889827061248"},
ratBinArg{"26946729/330400702820", "41563965/225583428284", "224002580204097/14906584649915733312176"},
ratBinArg{"-8259900599013409474/7", "-84829337473700364773/56707961321161574960", "350340947706464153265156004876107029701/198477864624065512360"},
}
func TestRatMul(t *testing.T) {
testRatBin(t, (*Rat).Mul, ratMulTests)
}
var ratQuoTests = []ratBinArg{
ratBinArg{"0", "1", "0"},
ratBinArg{"0", "-1", "0"},
ratBinArg{"-1", "1", "-1"},
ratBinArg{"1", "1", "1"},
ratBinArg{"1/2", "1/2", "1"},
ratBinArg{"1/4", "1/3", "3/4"},
ratBinArg{"2/5", "-14/3", "-3/35"},
ratBinArg{"808/45524274987585732633", "29/712593081308", "575775209696864/1320203974639986246357"},
ratBinArg{"8967230/3296219033", "6269770/1992362624741777", "1786597389946320496771/2066653520653241"},
ratBinArg{"-3784609207827/3426986245", "9381566963714/9633539", "-36459180403360509753/32150500941194292113930"},
}
func TestRatQuo(t *testing.T) {
testRatBin(t, (*Rat).Quo, ratQuoTests)
}
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