| // Copyright 2015 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 rat-to-string conversion functions. |
| |
| package big |
| |
| import ( |
| "errors" |
| "fmt" |
| "io" |
| "strconv" |
| "strings" |
| ) |
| |
| func ratTok(ch rune) bool { |
| return strings.ContainsRune("+-/0123456789.eE", ch) |
| } |
| |
| // 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.ContainsRune("efgEFGv", ch) { |
| 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 |
| } |
| // len(s) > 0 |
| |
| // parse fraction a/b, if any |
| if sep := strings.Index(s, "/"); sep >= 0 { |
| if _, ok := z.a.SetString(s[:sep], 0); !ok { |
| return nil, false |
| } |
| s = s[sep+1:] |
| var err error |
| if z.b.abs, _, _, err = z.b.abs.scan(strings.NewReader(s), 0, false); err != nil { |
| return nil, false |
| } |
| if len(z.b.abs) == 0 { |
| return nil, false |
| } |
| return z.norm(), true |
| } |
| |
| // parse floating-point number |
| r := strings.NewReader(s) |
| |
| // sign |
| neg, err := scanSign(r) |
| if err != nil { |
| return nil, false |
| } |
| |
| // mantissa |
| var ecorr int |
| z.a.abs, _, ecorr, err = z.a.abs.scan(r, 10, true) |
| if err != nil { |
| return nil, false |
| } |
| |
| // exponent |
| var exp int64 |
| exp, _, err = scanExponent(r, false) |
| if err != nil { |
| return nil, false |
| } |
| |
| // there should be no unread characters left |
| if _, err = r.ReadByte(); err != io.EOF { |
| return nil, false |
| } |
| |
| // correct exponent |
| if ecorr < 0 { |
| exp += int64(ecorr) |
| } |
| |
| // compute exponent power |
| expabs := exp |
| if expabs < 0 { |
| expabs = -expabs |
| } |
| powTen := nat(nil).expNN(natTen, nat(nil).setWord(Word(expabs)), nil) |
| |
| // complete fraction |
| if exp < 0 { |
| z.b.abs = powTen |
| z.norm() |
| } else { |
| z.a.abs = z.a.abs.mul(z.a.abs, powTen) |
| z.b.abs = z.b.abs[:0] |
| } |
| |
| z.a.neg = neg && len(z.a.abs) > 0 // 0 has no sign |
| |
| return z, true |
| } |
| |
| // scanExponent scans the longest possible prefix of r representing a decimal |
| // ('e', 'E') or binary ('p') exponent, if any. It returns the exponent, the |
| // exponent base (10 or 2), or a read or syntax error, if any. |
| // |
| // exponent = ( "E" | "e" | "p" ) [ sign ] digits . |
| // sign = "+" | "-" . |
| // digits = digit { digit } . |
| // digit = "0" ... "9" . |
| // |
| // A binary exponent is only permitted if binExpOk is set. |
| func scanExponent(r io.ByteScanner, binExpOk bool) (exp int64, base int, err error) { |
| base = 10 |
| |
| var ch byte |
| if ch, err = r.ReadByte(); err != nil { |
| if err == io.EOF { |
| err = nil // no exponent; same as e0 |
| } |
| return |
| } |
| |
| switch ch { |
| case 'e', 'E': |
| // ok |
| case 'p': |
| if binExpOk { |
| base = 2 |
| break // ok |
| } |
| fallthrough // binary exponent not permitted |
| default: |
| r.UnreadByte() |
| return // no exponent; same as e0 |
| } |
| |
| var neg bool |
| if neg, err = scanSign(r); err != nil { |
| return |
| } |
| |
| var digits []byte |
| if neg { |
| digits = append(digits, '-') |
| } |
| |
| // no need to use nat.scan for exponent digits |
| // since we only care about int64 values - the |
| // from-scratch scan is easy enough and faster |
| for i := 0; ; i++ { |
| if ch, err = r.ReadByte(); err != nil { |
| if err != io.EOF || i == 0 { |
| return |
| } |
| err = nil |
| break // i > 0 |
| } |
| if ch < '0' || '9' < ch { |
| if i == 0 { |
| r.UnreadByte() |
| err = fmt.Errorf("invalid exponent (missing digits)") |
| return |
| } |
| break // i > 0 |
| } |
| digits = append(digits, byte(ch)) |
| } |
| // i > 0 => we have at least one digit |
| |
| exp, err = strconv.ParseInt(string(digits), 10, 64) |
| return |
| } |
| |
| // String returns a string representation of x in the form "a/b" (even if b == 1). |
| func (x *Rat) String() string { |
| var buf []byte |
| buf = x.a.Append(buf, 10) |
| buf = append(buf, '/') |
| if len(x.b.abs) != 0 { |
| buf = x.b.Append(buf, 10) |
| } else { |
| buf = append(buf, '1') |
| } |
| return string(buf) |
| } |
| |
| // RatString returns a string representation of x in the form "a/b" if b != 1, |
| // and in the form "a" if b == 1. |
| func (x *Rat) RatString() string { |
| if x.IsInt() { |
| return x.a.String() |
| } |
| return x.String() |
| } |
| |
| // FloatString returns a string representation of x in decimal form with prec |
| // digits of precision after the decimal point. The last digit is rounded to |
| // nearest, with halves rounded away from zero. |
| func (x *Rat) FloatString(prec int) string { |
| var buf []byte |
| |
| if x.IsInt() { |
| buf = x.a.Append(buf, 10) |
| if prec > 0 { |
| buf = append(buf, '.') |
| for i := prec; i > 0; i-- { |
| buf = append(buf, '0') |
| } |
| } |
| return string(buf) |
| } |
| // x.b.abs != 0 |
| |
| q, r := nat(nil).div(nat(nil), x.a.abs, x.b.abs) |
| |
| p := natOne |
| if prec > 0 { |
| p = nat(nil).expNN(natTen, nat(nil).setUint64(uint64(prec)), nil) |
| } |
| |
| r = r.mul(r, p) |
| r, r2 := r.div(nat(nil), r, x.b.abs) |
| |
| // see if we need to round up |
| r2 = r2.add(r2, r2) |
| if x.b.abs.cmp(r2) <= 0 { |
| r = r.add(r, natOne) |
| if r.cmp(p) >= 0 { |
| q = nat(nil).add(q, natOne) |
| r = nat(nil).sub(r, p) |
| } |
| } |
| |
| if x.a.neg { |
| buf = append(buf, '-') |
| } |
| buf = append(buf, q.utoa(10)...) // itoa ignores sign if q == 0 |
| |
| if prec > 0 { |
| buf = append(buf, '.') |
| rs := r.utoa(10) |
| for i := prec - len(rs); i > 0; i-- { |
| buf = append(buf, '0') |
| } |
| buf = append(buf, rs...) |
| } |
| |
| return string(buf) |
| } |