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// 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)
}
var ratZero Rat
var _ fmt.Scanner = &ratZero // *Rat must implement fmt.Scanner
// 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 (possibly signed) fraction "a/b", or as a
// floating-point number optionally followed by an exponent.
// If a fraction is provided, both the dividend and the divisor may be a
// decimal integer or independently use a prefix of ``0b'', ``0'' or ``0o'',
// or ``0x'' (or their upper-case variants) to denote a binary, octal, or
// hexadecimal integer, respectively. The divisor may not be signed.
// If a floating-point number is provided, it may be in decimal form or
// use any of the same prefixes as above but for ``0'' to denote a non-decimal
// mantissa. A leading ``0'' is considered a decimal leading 0; it does not
// indicate octal representation in this case.
// An optional base-10 ``e'' or base-2 ``p'' (or their upper-case variants)
// exponent may be provided as well, except for hexadecimal floats which
// only accept an (optional) ``p'' exponent (because an ``e'' or ``E'' cannot
// be distinguished from a mantissa digit). If the exponent's absolute value
// is too large, the operation may fail.
// The entire string, not just a prefix, must be valid for success. 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
}
r := strings.NewReader(s[sep+1:])
var err error
if z.b.abs, _, _, err = z.b.abs.scan(r, 0, false); err != nil {
return nil, false
}
// entire string must have been consumed
if _, err = r.ReadByte(); err != io.EOF {
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 base int
var fcount int // fractional digit count; valid if <= 0
z.a.abs, base, fcount, err = z.a.abs.scan(r, 0, true)
if err != nil {
return nil, false
}
// exponent
var exp int64
var ebase int
exp, ebase, err = scanExponent(r, true, true)
if err != nil {
return nil, false
}
// there should be no unread characters left
if _, err = r.ReadByte(); err != io.EOF {
return nil, false
}
// special-case 0 (see also issue #16176)
if len(z.a.abs) == 0 {
return z, true
}
// len(z.a.abs) > 0
// The mantissa may have a radix point (fcount <= 0) and there
// may be a nonzero exponent exp. The radix point amounts to a
// division by base**(-fcount), which equals a multiplication by
// base**fcount. An exponent means multiplication by ebase**exp.
// Multiplications are commutative, so we can apply them in any
// order. We only have powers of 2 and 10, and we split powers
// of 10 into the product of the same powers of 2 and 5. This
// may reduce the size of shift/multiplication factors or
// divisors required to create the final fraction, depending
// on the actual floating-point value.
// determine binary or decimal exponent contribution of radix point
var exp2, exp5 int64
if fcount < 0 {
// The mantissa has a radix point ddd.dddd; and
// -fcount is the number of digits to the right
// of '.'. Adjust relevant exponent accordingly.
d := int64(fcount)
switch base {
case 10:
exp5 = d
fallthrough // 10**e == 5**e * 2**e
case 2:
exp2 = d
case 8:
exp2 = d * 3 // octal digits are 3 bits each
case 16:
exp2 = d * 4 // hexadecimal digits are 4 bits each
default:
panic("unexpected mantissa base")
}
// fcount consumed - not needed anymore
}
// take actual exponent into account
switch ebase {
case 10:
exp5 += exp
fallthrough // see fallthrough above
case 2:
exp2 += exp
default:
panic("unexpected exponent base")
}
// exp consumed - not needed anymore
// apply exp5 contributions
// (start with exp5 so the numbers to multiply are smaller)
if exp5 != 0 {
n := exp5
if n < 0 {
n = -n
}
if n > 1e6 {
return nil, false // avoid excessively large exponents
}
pow5 := z.b.abs.expNN(natFive, nat(nil).setWord(Word(n)), nil) // use underlying array of z.b.abs
if exp5 > 0 {
z.a.abs = z.a.abs.mul(z.a.abs, pow5)
z.b.abs = z.b.abs.setWord(1)
} else {
z.b.abs = pow5
}
} else {
z.b.abs = z.b.abs.setWord(1)
}
// apply exp2 contributions
if exp2 < -1e7 || exp2 > 1e7 {
return nil, false // avoid excessively large exponents
}
if exp2 > 0 {
z.a.abs = z.a.abs.shl(z.a.abs, uint(exp2))
} else if exp2 < 0 {
z.b.abs = z.b.abs.shl(z.b.abs, uint(-exp2))
}
z.a.neg = neg && len(z.a.abs) > 0 // 0 has no sign
return z.norm(), true
}
// scanExponent scans the longest possible prefix of r representing a base 10
// (``e'', ``E'') or a base 2 (``p'', ``P'') exponent, if any. It returns the
// exponent, the exponent base (10 or 2), or a read or syntax error, if any.
//
// If sepOk is set, an underscore character ``_'' may appear between successive
// exponent digits; such underscores do not change the value of the exponent.
// Incorrect placement of underscores is reported as an error if there are no
// other errors. If sepOk is not set, underscores are not recognized and thus
// terminate scanning like any other character that is not a valid digit.
//
// exponent = ( "e" | "E" | "p" | "P" ) [ sign ] digits .
// sign = "+" | "-" .
// digits = digit { [ '_' ] digit } .
// digit = "0" ... "9" .
//
// A base 2 exponent is only permitted if base2ok is set.
func scanExponent(r io.ByteScanner, base2ok, sepOk bool) (exp int64, base int, err error) {
// one char look-ahead
ch, err := r.ReadByte()
if err != nil {
if err == io.EOF {
err = nil
}
return 0, 10, err
}
// exponent char
switch ch {
case 'e', 'E':
base = 10
case 'p', 'P':
if base2ok {
base = 2
break // ok
}
fallthrough // binary exponent not permitted
default:
r.UnreadByte() // ch does not belong to exponent anymore
return 0, 10, nil
}
// sign
var digits []byte
ch, err = r.ReadByte()
if err == nil && (ch == '+' || ch == '-') {
if ch == '-' {
digits = append(digits, '-')
}
ch, err = r.ReadByte()
}
// prev encodes the previously seen char: it is one
// of '_', '0' (a digit), or '.' (anything else). A
// valid separator '_' may only occur after a digit.
prev := '.'
invalSep := false
// exponent value
hasDigits := false
for err == nil {
if '0' <= ch && ch <= '9' {
digits = append(digits, ch)
prev = '0'
hasDigits = true
} else if ch == '_' && sepOk {
if prev != '0' {
invalSep = true
}
prev = '_'
} else {
r.UnreadByte() // ch does not belong to number anymore
break
}
ch, err = r.ReadByte()
}
if err == io.EOF {
err = nil
}
if err == nil && !hasDigits {
err = errNoDigits
}
if err == nil {
exp, err = strconv.ParseInt(string(digits), 10, 64)
}
// other errors take precedence over invalid separators
if err == nil && (invalSep || prev == '_') {
err = errInvalSep
}
return
}
// String returns a string representation of x in the form "a/b" (even if b == 1).
func (x *Rat) String() string {
return string(x.marshal())
}
// marshal implements String returning a slice of bytes
func (x *Rat) marshal() []byte {
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 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 radix 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)
}