1 files changed, 326 insertions, 0 deletions
diff --git a/libgo/go/big/rat.go b/libgo/go/big/rat.go
new file mode 100644
index 0000000000..e70673a1cb
--- /dev/null
+++ b/libgo/go/big/rat.go
@@ -0,0 +1,326 @@
+// 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 {
+		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
+}
+
+
+// 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))
+}
+
+
+// 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
+}
+
+
+// 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 n int
+		if z.b, _, n = z.b.scan(s, 10); n != len(s) {
+			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.string(10)
+}
+
+
+// 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() {
+		return z.a.String()
+	}
+
+	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.string(10)
+	if z.a.neg {
+		s = "-" + s
+	}
+
+	if prec > 0 {
+		rs := r.string(10)
+		leadingZeros := prec - len(rs)
+		s += "." + strings.Repeat("0", leadingZeros) + rs
+	}
+
+	return s
+}