/big/rat.go
https://code.google.com/p/algogo/ · Go · 371 lines · 267 code · 44 blank · 60 comment · 48 complexity · 7bce3e25a89f6bfdff156dcd9f748b05 MD5 · raw file
- // 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 (
- "encoding/binary"
- "fmt"
- "os"
- "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 {
- b = -b
- z.a.neg = !z.a.neg
- }
- 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
- }
- // Sign returns:
- //
- // -1 if x < 0
- // 0 if x == 0
- // +1 if x > 0
- //
- func (x *Rat) Sign() int {
- return x.a.Sign()
- }
- // IsInt returns true if the denominator of x is 1.
- func (x *Rat) IsInt() bool {
- return len(x.b) == 1 && x.b[0] == 1
- }
- // 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
- }
- // Denom 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))
- }
- // Abs sets z to |x| (the absolute value of x) and returns z.
- func (z *Rat) Abs(x *Rat) *Rat {
- z.a.Abs(&x.a)
- z.b = z.b.set(x.b)
- return z
- }
- // 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")
- }
- a := mulNat(&x.a, y.b)
- b := mulNat(&y.a, x.b)
- z.a.abs = a.abs
- z.b = b.abs
- z.a.neg = a.neg != b.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
- }
- func ratTok(ch int) bool {
- return strings.IndexRune("+-/0123456789.eE", ch) >= 0
- }
- // Scan is a support routine for fmt.Scanner. It accepts the formats
- // 'e', 'E', 'f', 'F', 'g', 'G', and 'v'. All formats are equivalent.
- func (z *Rat) Scan(s fmt.ScanState, ch int) os.Error {
- tok, err := s.Token(true, ratTok)
- if err != nil {
- return err
- }
- if strings.IndexRune("efgEFGv", ch) < 0 {
- return os.NewError("Rat.Scan: invalid verb")
- }
- if _, ok := z.SetString(string(tok)); !ok {
- return os.NewError("Rat.Scan: invalid syntax")
- }
- return nil
- }
- // 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 floating-point number
- // optionally followed by an exponent. 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 quotient
- sep := strings.Index(s, "/")
- if sep >= 0 {
- if _, ok := z.a.SetString(s[0:sep], 10); !ok {
- return z, false
- }
- s = s[sep+1:]
- var err os.Error
- if z.b, _, err = z.b.scan(strings.NewReader(s), 10); err != nil {
- return z, false
- }
- return z.norm(), true
- }
- // check for a decimal point
- sep = strings.Index(s, ".")
- // check for an exponent
- e := strings.IndexAny(s, "eE")
- var exp Int
- if e >= 0 {
- if e < sep {
- // The E must come after the decimal point.
- return z, false
- }
- if _, ok := exp.SetString(s[e+1:], 10); !ok {
- return z, false
- }
- s = s[0:e]
- }
- if sep >= 0 {
- s = s[0:sep] + s[sep+1:]
- exp.Sub(&exp, NewInt(int64(len(s)-sep)))
- }
- if _, ok := z.a.SetString(s, 10); !ok {
- return z, false
- }
- powTen := nat{}.expNN(natTen, exp.abs, nil)
- if exp.neg {
- z.b = powTen
- z.norm()
- } else {
- z.a.abs = z.a.abs.mul(z.a.abs, powTen)
- z.b = z.b.setWord(1)
- }
- return z, true
- }
- // String returns a string representation of z in the form "a/b" (even if b == 1).
- func (z *Rat) String() string {
- return z.a.String() + "/" + z.b.decimalString()
- }
- // RatString returns a string representation of z in the form "a/b" if b != 1,
- // and in the form "a" if b == 1.
- func (z *Rat) RatString() string {
- if z.IsInt() {
- return z.a.String()
- }
- return z.String()
- }
- // 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 {
- if z.IsInt() {
- s := z.a.String()
- if prec > 0 {
- s += "." + strings.Repeat("0", prec)
- }
- return s
- }
- q, r := nat{}.div(nat{}, z.a.abs, z.b)
- p := natOne
- if prec > 0 {
- p = nat{}.expNN(natTen, nat{}.setUint64(uint64(prec)), nil)
- }
- r = r.mul(r, p)
- r, r2 := r.div(nat{}, r, z.b)
- // see if we need to round up
- r2 = r2.add(r2, r2)
- if z.b.cmp(r2) <= 0 {
- r = r.add(r, natOne)
- if r.cmp(p) >= 0 {
- q = nat{}.add(q, natOne)
- r = nat{}.sub(r, p)
- }
- }
- s := q.decimalString()
- if z.a.neg {
- s = "-" + s
- }
- if prec > 0 {
- rs := r.decimalString()
- leadingZeros := prec - len(rs)
- s += "." + strings.Repeat("0", leadingZeros) + rs
- }
- return s
- }
- // Gob codec version. Permits backward-compatible changes to the encoding.
- const ratGobVersion byte = 1
- // GobEncode implements the gob.GobEncoder interface.
- func (z *Rat) GobEncode() ([]byte, os.Error) {
- buf := make([]byte, 1+4+(len(z.a.abs)+len(z.b))*_S) // extra bytes for version and sign bit (1), and numerator length (4)
- i := z.b.bytes(buf)
- j := z.a.abs.bytes(buf[0:i])
- n := i - j
- if int(uint32(n)) != n {
- // this should never happen
- return nil, os.NewError("Rat.GobEncode: numerator too large")
- }
- binary.BigEndian.PutUint32(buf[j-4:j], uint32(n))
- j -= 1 + 4
- b := ratGobVersion << 1 // make space for sign bit
- if z.a.neg {
- b |= 1
- }
- buf[j] = b
- return buf[j:], nil
- }
- // GobDecode implements the gob.GobDecoder interface.
- func (z *Rat) GobDecode(buf []byte) os.Error {
- if len(buf) == 0 {
- return os.NewError("Rat.GobDecode: no data")
- }
- b := buf[0]
- if b>>1 != ratGobVersion {
- return os.NewError(fmt.Sprintf("Rat.GobDecode: encoding version %d not supported", b>>1))
- }
- const j = 1 + 4
- i := j + binary.BigEndian.Uint32(buf[j-4:j])
- z.a.neg = b&1 != 0
- z.a.abs = z.a.abs.setBytes(buf[j:i])
- z.b = z.b.setBytes(buf[i:])
- return nil
- }