1 files changed, 432 insertions, 0 deletions
diff --git a/libgo/go/math/big/rat.go b/libgo/go/math/big/rat.go
new file mode 100644
index 0000000..3a0add3
--- /dev/null
+++ b/libgo/go/math/big/rat.go
@@ -0,0 +1,432 @@
+// 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"
+	"errors"
+	"fmt"
+	"strings"
+)
+
+// A Rat represents a quotient a/b of arbitrary precision.
+// The zero value for a Rat represents the value 0.
+type Rat struct {
+	a Int
+	b nat // len(b) == 0 acts like b == 1
+}
+
+// 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.neg = a.neg != b.neg
+	babs := b.abs
+	if len(babs) == 0 {
+		panic("division by zero")
+	}
+	if &z.a == b || alias(z.a.abs, babs) {
+		babs = nat{}.set(babs) // make a copy
+	}
+	z.a.abs = z.a.abs.set(a.abs)
+	z.b = z.b.set(babs)
+	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 {
+		panic("division by zero")
+	}
+	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.make(0)
+	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.make(0)
+	return z
+}
+
+// Set sets z to x (by making a copy of x) and returns z.
+func (z *Rat) Set(x *Rat) *Rat {
+	if z != x {
+		z.a.Set(&x.a)
+		z.b = z.b.set(x.b)
+	}
+	return z
+}
+
+// Abs sets z to |x| (the absolute value of x) and returns z.
+func (z *Rat) Abs(x *Rat) *Rat {
+	z.Set(x)
+	z.a.neg = false
+	return z
+}
+
+// Neg sets z to -x and returns z.
+func (z *Rat) Neg(x *Rat) *Rat {
+	z.Set(x)
+	z.a.neg = len(z.a.abs) > 0 && !z.a.neg // 0 has no sign
+	return z
+}
+
+// Inv sets z to 1/x and returns z.
+func (z *Rat) Inv(x *Rat) *Rat {
+	if len(x.a.abs) == 0 {
+		panic("division by zero")
+	}
+	z.Set(x)
+	a := z.b
+	if len(a) == 0 {
+		a = a.setWord(1) // materialize numerator
+	}
+	b := z.a.abs
+	if b.cmp(natOne) == 0 {
+		b = b.make(0) // normalize denominator
+	}
+	z.a.abs, z.b = a, b // sign doesn't change
+	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) == 0 || x.b.cmp(natOne) == 0
+}
+
+// Num returns the numerator of x; it may be <= 0.
+// The result is a reference to x's numerator; it
+// may change if a new value is assigned to x.
+func (x *Rat) Num() *Int {
+	return &x.a
+}
+
+// Denom returns the denominator of x; it is always > 0.
+// The result is a reference to x's denominator; it
+// may change if a new value is assigned to x.
+func (x *Rat) Denom() *Int {
+	if len(x.b) == 0 {
+		return &Int{abs: nat{1}}
+	}
+	return &Int{abs: x.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 {
+	switch {
+	case len(z.a.abs) == 0:
+		// z == 0 - normalize sign and denominator
+		z.a.neg = false
+		z.b = z.b.make(0)
+	case len(z.b) == 0:
+		// z is normalized int - nothing to do
+	case z.b.cmp(natOne) == 0:
+		// z is int - normalize denominator
+		z.b = z.b.make(0)
+	default:
+		if f := gcd(z.a.abs, z.b); 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
+}
+
+// mulDenom sets z to the denominator product x*y (by taking into
+// account that 0 values for x or y must be interpreted as 1) and
+// returns z.
+func mulDenom(z, x, y nat) nat {
+	switch {
+	case len(x) == 0:
+		return z.set(y)
+	case len(y) == 0:
+		return z.set(x)
+	}
+	return z.mul(x, y)
+}
+
+// scaleDenom computes x*f.
+// If f == 0 (zero value of denominator), the result is (a copy of) x.
+func scaleDenom(x *Int, f nat) *Int {
+	var z Int
+	if len(f) == 0 {
+		return z.Set(x)
+	}
+	z.abs = z.abs.mul(x.abs, f)
+	z.neg = 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) int {
+	return scaleDenom(&x.a, y.b).Cmp(scaleDenom(&y.a, x.b))
+}
+
+// Add sets z to the sum x+y and returns z.
+func (z *Rat) Add(x, y *Rat) *Rat {
+	a1 := scaleDenom(&x.a, y.b)
+	a2 := scaleDenom(&y.a, x.b)
+	z.a.Add(a1, a2)
+	z.b = mulDenom(z.b, 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 := scaleDenom(&x.a, y.b)
+	a2 := scaleDenom(&y.a, x.b)
+	z.a.Sub(a1, a2)
+	z.b = mulDenom(z.b, 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 = mulDenom(z.b, 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 := scaleDenom(&x.a, y.b)
+	b := scaleDenom(&y.a, x.b)
+	z.a.abs = a.abs
+	z.b = b.abs
+	z.a.neg = a.neg != b.neg
+	return z.norm()
+}
+
+func ratTok(ch rune) 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 rune) error {
+	tok, err := s.Token(true, ratTok)
+	if err != nil {
+		return err
+	}
+	if strings.IndexRune("efgEFGv", ch) < 0 {
+		return errors.New("Rat.Scan: invalid verb")
+	}
+	if _, ok := z.SetString(string(tok)); !ok {
+		return errors.New("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 but the returned value is nil.
+func (z *Rat) SetString(s string) (*Rat, bool) {
+	if len(s) == 0 {
+		return nil, false
+	}
+
+	// check for a quotient
+	sep := strings.Index(s, "/")
+	if sep >= 0 {
+		if _, ok := z.a.SetString(s[0:sep], 10); !ok {
+			return nil, false
+		}
+		s = s[sep+1:]
+		var err error
+		if z.b, _, err = z.b.scan(strings.NewReader(s), 10); err != nil {
+			return nil, 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 nil, false
+		}
+		if _, ok := exp.SetString(s[e+1:], 10); !ok {
+			return nil, 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 nil, 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.make(0)
+	}
+
+	return z, true
+}
+
+// String returns a string representation of z in the form "a/b" (even if b == 1).
+func (z *Rat) String() string {
+	s := "/1"
+	if len(z.b) != 0 {
+		s = "/" + z.b.decimalString()
+	}
+	return z.a.String() + s
+}
+
+// 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
+	}
+	// z.b != 0
+
+	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, 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, errors.New("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) error {
+	if len(buf) == 0 {
+		return errors.New("Rat.GobDecode: no data")
+	}
+	b := buf[0]
+	if b>>1 != ratGobVersion {
+		return errors.New(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
+}