blob: d8c69b8b283e0baa876ad17a6fe2a4f9642074e5 [file] [log] [blame]
// 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"
)
var floatZero Float
// 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 [Float.Parse], with base argument 0. 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 *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, base == 0)
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 radix point (fcount <= 0) and there
// may be a nonzero exponent exp. The radix 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, and
// we split powers of 10 into the product of the same powers of
// 2 and 5. This reduces the size of the multiplication factor
// needed for base-10 exponents.
// normalize mantissa and determine initial exponent contributions
exp2 := int64(len(z.mant))*_W - fnorm(z.mant)
exp5 := int64(0)
// determine binary or decimal exponent contribution of radix point
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 b {
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 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 exp5 == 0 {
// no decimal exponent contribution
z.round(0)
return
}
// exp5 != 0
// apply 5**exp5
p := new(Float).SetPrec(z.Prec() + 64) // use more bits for p -- TODO(gri) what is the right number?
if exp5 < 0 {
z.Quo(z, p.pow5(uint64(-exp5)))
} else {
z.Mul(z, p.pow5(uint64(exp5)))
}
return
}
// These powers of 5 fit into a uint64.
//
// for p, q := uint64(0), uint64(1); p < q; p, q = q, q*5 {
// fmt.Println(q)
// }
var pow5tab = [...]uint64{
1,
5,
25,
125,
625,
3125,
15625,
78125,
390625,
1953125,
9765625,
48828125,
244140625,
1220703125,
6103515625,
30517578125,
152587890625,
762939453125,
3814697265625,
19073486328125,
95367431640625,
476837158203125,
2384185791015625,
11920928955078125,
59604644775390625,
298023223876953125,
1490116119384765625,
7450580596923828125,
}
// pow5 sets z to 5**n and returns z.
// n must not be negative.
func (z *Float) pow5(n uint64) *Float {
const m = uint64(len(pow5tab) - 1)
if n <= m {
return z.SetUint64(pow5tab[n])
}
// n > m
z.SetUint64(pow5tab[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).SetUint64(5)
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.
//
// For base 0, an underscore character “_” may appear between a base
// prefix and an adjacent digit, and between successive digits; such
// underscores do not change the value of the number, or the returned
// digit count. Incorrect placement of underscores is reported as an
// error if there are no other errors. If base != 0, underscores are
// not recognized and thus terminate scanning like any other character
// that is not a valid radix point or digit.
//
// 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.
// The entire string (not just a prefix) must be consumed for success.
// If z's precision is 0, it is changed to 64 before rounding takes effect.
// The number must be of the form:
//
// number = [ sign ] ( float | "inf" | "Inf" ) .
// sign = "+" | "-" .
// float = ( mantissa | prefix pmantissa ) [ exponent ] .
// prefix = "0" [ "b" | "B" | "o" | "O" | "x" | "X" ] .
// mantissa = digits "." [ digits ] | digits | "." digits .
// pmantissa = [ "_" ] digits "." [ digits ] | [ "_" ] digits | "." digits .
// exponent = ( "e" | "E" | "p" | "P" ) [ sign ] digits .
// digits = digit { [ "_" ] digit } .
// digit = "0" ... "9" | "a" ... "z" | "A" ... "Z" .
//
// The base argument must be 0, 2, 8, 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
// “0b” or “0B” selects base 2, “0o” or “0O” selects base 8, and
// “0x” or “0X” selects base 16. 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" or "P" exponent indicates a base 2 (rather than base 10) exponent;
// for instance, "0x1.fffffffffffffp1023" (using base 0) represents the
// maximum float64 value. For hexadecimal mantissae, the exponent character
// must be one of 'p' or 'P', 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)
}
var _ fmt.Scanner = (*Float)(nil) // *Float must implement fmt.Scanner
// Scan is a support routine for [fmt.Scanner]; it sets z to the value of
// the scanned number. It accepts formats whose verbs are supported by
// [fmt.Scan] for floating point values, which are:
// 'b' (binary), 'e', 'E', 'f', 'F', 'g' and 'G'.
// Scan doesn't handle ±Inf.
func (z *Float) Scan(s fmt.ScanState, ch rune) error {
s.SkipSpace()
_, _, err := z.scan(byteReader{s}, 0)
return err
}