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Diffstat (limited to 'src/pkg/big/rat.go')
-rw-r--r-- | src/pkg/big/rat.go | 399 |
1 files changed, 0 insertions, 399 deletions
diff --git a/src/pkg/big/rat.go b/src/pkg/big/rat.go deleted file mode 100644 index b61cbb966..000000000 --- a/src/pkg/big/rat.go +++ /dev/null @@ -1,399 +0,0 @@ -// 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 -} |