327 lines
6.2 KiB
Go
327 lines
6.2 KiB
Go
// Copyright 2010 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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// This file implements multi-precision rational numbers.
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package big
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import "strings"
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// A Rat represents a quotient a/b of arbitrary precision. The zero value for
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// a Rat, 0/0, is not a legal Rat.
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type Rat struct {
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a Int
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b nat
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}
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// NewRat creates a new Rat with numerator a and denominator b.
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func NewRat(a, b int64) *Rat {
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return new(Rat).SetFrac64(a, b)
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}
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// SetFrac sets z to a/b and returns z.
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func (z *Rat) SetFrac(a, b *Int) *Rat {
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z.a.Set(a)
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z.a.neg = a.neg != b.neg
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z.b = z.b.set(b.abs)
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return z.norm()
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}
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// SetFrac64 sets z to a/b and returns z.
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func (z *Rat) SetFrac64(a, b int64) *Rat {
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z.a.SetInt64(a)
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if b < 0 {
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b = -b
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z.a.neg = !z.a.neg
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}
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z.b = z.b.setUint64(uint64(b))
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return z.norm()
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}
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// SetInt sets z to x (by making a copy of x) and returns z.
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func (z *Rat) SetInt(x *Int) *Rat {
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z.a.Set(x)
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z.b = z.b.setWord(1)
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return z
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}
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// SetInt64 sets z to x and returns z.
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func (z *Rat) SetInt64(x int64) *Rat {
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z.a.SetInt64(x)
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z.b = z.b.setWord(1)
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return z
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}
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// Sign returns:
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//
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// -1 if x < 0
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// 0 if x == 0
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// +1 if x > 0
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//
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func (x *Rat) Sign() int {
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return x.a.Sign()
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}
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// IsInt returns true if the denominator of x is 1.
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func (x *Rat) IsInt() bool {
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return len(x.b) == 1 && x.b[0] == 1
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}
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// Num returns the numerator of z; it may be <= 0.
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// The result is a reference to z's numerator; it
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// may change if a new value is assigned to z.
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func (z *Rat) Num() *Int {
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return &z.a
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}
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// Demom returns the denominator of z; it is always > 0.
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// The result is a reference to z's denominator; it
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// may change if a new value is assigned to z.
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func (z *Rat) Denom() *Int {
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return &Int{false, z.b}
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}
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func gcd(x, y nat) nat {
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// Euclidean algorithm.
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var a, b nat
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a = a.set(x)
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b = b.set(y)
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for len(b) != 0 {
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var q, r nat
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_, r = q.div(r, a, b)
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a = b
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b = r
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}
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return a
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}
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func (z *Rat) norm() *Rat {
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f := gcd(z.a.abs, z.b)
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if len(z.a.abs) == 0 {
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// z == 0
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z.a.neg = false // normalize sign
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z.b = z.b.setWord(1)
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return z
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}
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if f.cmp(natOne) != 0 {
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z.a.abs, _ = z.a.abs.div(nil, z.a.abs, f)
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z.b, _ = z.b.div(nil, z.b, f)
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}
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return z
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}
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func mulNat(x *Int, y nat) *Int {
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var z Int
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z.abs = z.abs.mul(x.abs, y)
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z.neg = len(z.abs) > 0 && x.neg
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return &z
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}
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// Cmp compares x and y and returns:
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//
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// -1 if x < y
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// 0 if x == y
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// +1 if x > y
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//
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func (x *Rat) Cmp(y *Rat) (r int) {
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return mulNat(&x.a, y.b).Cmp(mulNat(&y.a, x.b))
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}
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// Abs sets z to |x| (the absolute value of x) and returns z.
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func (z *Rat) Abs(x *Rat) *Rat {
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z.a.Abs(&x.a)
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z.b = z.b.set(x.b)
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return z
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}
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// Add sets z to the sum x+y and returns z.
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func (z *Rat) Add(x, y *Rat) *Rat {
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a1 := mulNat(&x.a, y.b)
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a2 := mulNat(&y.a, x.b)
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z.a.Add(a1, a2)
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z.b = z.b.mul(x.b, y.b)
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return z.norm()
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}
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// Sub sets z to the difference x-y and returns z.
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func (z *Rat) Sub(x, y *Rat) *Rat {
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a1 := mulNat(&x.a, y.b)
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a2 := mulNat(&y.a, x.b)
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z.a.Sub(a1, a2)
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z.b = z.b.mul(x.b, y.b)
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return z.norm()
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}
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// Mul sets z to the product x*y and returns z.
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func (z *Rat) Mul(x, y *Rat) *Rat {
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z.a.Mul(&x.a, &y.a)
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z.b = z.b.mul(x.b, y.b)
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return z.norm()
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}
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// Quo sets z to the quotient x/y and returns z.
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// If y == 0, a division-by-zero run-time panic occurs.
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func (z *Rat) Quo(x, y *Rat) *Rat {
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if len(y.a.abs) == 0 {
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panic("division by zero")
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}
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a := mulNat(&x.a, y.b)
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b := mulNat(&y.a, x.b)
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z.a.abs = a.abs
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z.b = b.abs
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z.a.neg = a.neg != b.neg
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return z.norm()
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}
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// Neg sets z to -x (by making a copy of x if necessary) and returns z.
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func (z *Rat) Neg(x *Rat) *Rat {
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z.a.Neg(&x.a)
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z.b = z.b.set(x.b)
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return z
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}
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// Set sets z to x (by making a copy of x if necessary) and returns z.
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func (z *Rat) Set(x *Rat) *Rat {
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z.a.Set(&x.a)
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z.b = z.b.set(x.b)
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return z
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}
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// SetString sets z to the value of s and returns z and a boolean indicating
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// success. s can be given as a fraction "a/b" or as a floating-point number
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// optionally followed by an exponent. If the operation failed, the value of z
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// is undefined.
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func (z *Rat) SetString(s string) (*Rat, bool) {
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if len(s) == 0 {
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return z, false
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}
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// check for a quotient
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sep := strings.Index(s, "/")
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if sep >= 0 {
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if _, ok := z.a.SetString(s[0:sep], 10); !ok {
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return z, false
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}
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s = s[sep+1:]
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var n int
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if z.b, _, n = z.b.scan(s, 10); n != len(s) {
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return z, false
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}
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return z.norm(), true
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}
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// check for a decimal point
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sep = strings.Index(s, ".")
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// check for an exponent
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e := strings.IndexAny(s, "eE")
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var exp Int
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if e >= 0 {
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if e < sep {
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// The E must come after the decimal point.
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return z, false
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}
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if _, ok := exp.SetString(s[e+1:], 10); !ok {
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return z, false
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}
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s = s[0:e]
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}
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if sep >= 0 {
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s = s[0:sep] + s[sep+1:]
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exp.Sub(&exp, NewInt(int64(len(s)-sep)))
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}
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if _, ok := z.a.SetString(s, 10); !ok {
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return z, false
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}
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powTen := nat{}.expNN(natTen, exp.abs, nil)
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if exp.neg {
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z.b = powTen
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z.norm()
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} else {
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z.a.abs = z.a.abs.mul(z.a.abs, powTen)
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z.b = z.b.setWord(1)
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}
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return z, true
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}
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// String returns a string representation of z in the form "a/b" (even if b == 1).
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func (z *Rat) String() string {
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return z.a.String() + "/" + z.b.string(10)
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}
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// RatString returns a string representation of z in the form "a/b" if b != 1,
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// and in the form "a" if b == 1.
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func (z *Rat) RatString() string {
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if z.IsInt() {
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return z.a.String()
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}
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return z.String()
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}
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// FloatString returns a string representation of z in decimal form with prec
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// digits of precision after the decimal point and the last digit rounded.
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func (z *Rat) FloatString(prec int) string {
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if z.IsInt() {
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return z.a.String()
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}
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q, r := nat{}.div(nat{}, z.a.abs, z.b)
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p := natOne
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if prec > 0 {
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p = nat{}.expNN(natTen, nat{}.setUint64(uint64(prec)), nil)
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}
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r = r.mul(r, p)
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r, r2 := r.div(nat{}, r, z.b)
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// see if we need to round up
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r2 = r2.add(r2, r2)
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if z.b.cmp(r2) <= 0 {
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r = r.add(r, natOne)
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if r.cmp(p) >= 0 {
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q = nat{}.add(q, natOne)
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r = nat{}.sub(r, p)
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}
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}
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s := q.string(10)
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if z.a.neg {
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s = "-" + s
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}
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if prec > 0 {
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rs := r.string(10)
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leadingZeros := prec - len(rs)
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s += "." + strings.Repeat("0", leadingZeros) + rs
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}
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return s
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}
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