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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 string-to-Float conversion functions.
package big
import (
"fmt"
"io"
"strings"
)
// SetString sets z to the value of s and returns z and a boolean indicating
// success. s must be a floating-point number of the same format as accepted
// by Parse, with base argument 0.
func (z *Float) SetString(s string) (*Float, bool) {
if f, _, err := z.Parse(s, 0); err == nil {
return f, true
}
return nil, false
}
// scan is like Parse but reads the longest possible prefix representing a valid
// floating point number from an io.ByteScanner rather than a string. It serves
// as the implementation of Parse. It does not recognize ±Inf and does not expect
// EOF at the end.
func (z *Float) scan(r io.ByteScanner, base int) (f *Float, b int, err error) {
prec := z.prec
if prec == 0 {
prec = 64
}
// A reasonable value in case of an error.
z.form = zero
// sign
z.neg, err = scanSign(r)
if err != nil {
return
}
// mantissa
var fcount int // fractional digit count; valid if <= 0
z.mant, b, fcount, err = z.mant.scan(r, base, true)
if err != nil {
return
}
// exponent
var exp int64
var ebase int
exp, ebase, err = scanExponent(r, true)
if err != nil {
return
}
// special-case 0
if len(z.mant) == 0 {
z.prec = prec
z.acc = Exact
z.form = zero
f = z
return
}
// len(z.mant) > 0
// The mantissa may have a decimal point (fcount <= 0) and there
// may be a nonzero exponent exp. The decimal point amounts to a
// division by b**(-fcount). An exponent means multiplication by
// ebase**exp. Finally, mantissa normalization (shift left) requires
// a correcting multiplication by 2**(-shiftcount). Multiplications
// are commutative, so we can apply them in any order as long as there
// is no loss of precision. We only have powers of 2 and 10; keep
// track via separate exponents exp2 and exp10.
// normalize mantissa and get initial binary exponent
var exp2 = int64(len(z.mant))*_W - fnorm(z.mant)
// determine binary or decimal exponent contribution of decimal point
var exp10 int64
if fcount < 0 {
// The mantissa has a "decimal" point ddd.dddd; and
// -fcount is the number of digits to the right of '.'.
// Adjust relevant exponent accodingly.
switch b {
case 16:
fcount *= 4 // hexadecimal digits are 4 bits each
fallthrough
case 2:
exp2 += int64(fcount)
default: // b == 10
exp10 = int64(fcount)
}
// we don't need fcount anymore
}
// take actual exponent into account
if ebase == 2 {
exp2 += exp
} else { // ebase == 10
exp10 += exp
}
// we don't need exp anymore
// apply 2**exp2
if MinExp <= exp2 && exp2 <= MaxExp {
z.prec = prec
z.form = finite
z.exp = int32(exp2)
f = z
} else {
err = fmt.Errorf("exponent overflow")
return
}
if exp10 == 0 {
// no decimal exponent to consider
z.round(0)
return
}
// exp10 != 0
// apply 10**exp10
p := new(Float).SetPrec(z.Prec() + 64) // use more bits for p -- TODO(gri) what is the right number?
if exp10 < 0 {
z.uquo(z, p.pow10(-exp10))
} else {
z.umul(z, p.pow10(exp10))
}
return
}
// These powers of 10 can be represented exactly as a float64.
var pow10tab = [...]float64{
1e0, 1e1, 1e2, 1e3, 1e4, 1e5, 1e6, 1e7, 1e8, 1e9,
1e10, 1e11, 1e12, 1e13, 1e14, 1e15, 1e16, 1e17, 1e18, 1e19,
}
// pow10 sets z to 10**n and returns z.
// n must not be negative.
func (z *Float) pow10(n int64) *Float {
if n < 0 {
panic("pow10 called with negative argument")
}
const m = int64(len(pow10tab) - 1)
if n <= m {
return z.SetFloat64(pow10tab[n])
}
// n > m
z.SetFloat64(pow10tab[m])
n -= m
// use more bits for f than for z
// TODO(gri) what is the right number?
f := new(Float).SetPrec(z.Prec() + 64).SetInt64(10)
for n > 0 {
if n&1 != 0 {
z.Mul(z, f)
}
f.Mul(f, f)
n >>= 1
}
return z
}
// Parse parses s which must contain a text representation of a floating-
// point number with a mantissa in the given conversion base (the exponent
// is always a decimal number), or a string representing an infinite value.
//
// It sets z to the (possibly rounded) value of the corresponding floating-
// point value, and returns z, the actual base b, and an error err, if any.
// If z's precision is 0, it is changed to 64 before rounding takes effect.
// The number must be of the form:
//
// number = [ sign ] [ prefix ] mantissa [ exponent ] | infinity .
// sign = "+" | "-" .
// prefix = "0" ( "x" | "X" | "b" | "B" ) .
// mantissa = digits | digits "." [ digits ] | "." digits .
// exponent = ( "E" | "e" | "p" ) [ sign ] digits .
// digits = digit { digit } .
// digit = "0" ... "9" | "a" ... "z" | "A" ... "Z" .
// infinity = [ sign ] ( "inf" | "Inf" ) .
//
// The base argument must be 0, 2, 10, or 16. Providing an invalid base
// argument will lead to a run-time panic.
//
// For base 0, the number prefix determines the actual base: A prefix of
// "0x" or "0X" selects base 16, and a "0b" or "0B" prefix selects
// base 2; otherwise, the actual base is 10 and no prefix is accepted.
// The octal prefix "0" is not supported (a leading "0" is simply
// considered a "0").
//
// A "p" exponent indicates a binary (rather then decimal) exponent;
// for instance "0x1.fffffffffffffp1023" (using base 0) represents the
// maximum float64 value. For hexadecimal mantissae, the exponent must
// be binary, if present (an "e" or "E" exponent indicator cannot be
// distinguished from a mantissa digit).
//
// The returned *Float f is nil and the value of z is valid but not
// defined if an error is reported.
//
func (z *Float) Parse(s string, base int) (f *Float, b int, err error) {
// scan doesn't handle ±Inf
if len(s) == 3 && (s == "Inf" || s == "inf") {
f = z.SetInf(false)
return
}
if len(s) == 4 && (s[0] == '+' || s[0] == '-') && (s[1:] == "Inf" || s[1:] == "inf") {
f = z.SetInf(s[0] == '-')
return
}
r := strings.NewReader(s)
if f, b, err = z.scan(r, base); err != nil {
return
}
// entire string must have been consumed
if ch, err2 := r.ReadByte(); err2 == nil {
err = fmt.Errorf("expected end of string, found %q", ch)
} else if err2 != io.EOF {
err = err2
}
return
}
// ParseFloat is like f.Parse(s, base) with f set to the given precision
// and rounding mode.
func ParseFloat(s string, base int, prec uint, mode RoundingMode) (f *Float, b int, err error) {
return new(Float).SetPrec(prec).SetMode(mode).Parse(s, base)
}