305 lines
8.4 KiB
Go
305 lines
8.4 KiB
Go
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// Copyright 2015 The Go Authors. All rights reserved.
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// Use of this source code is governed by a BSD-style
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// license that can be found in the LICENSE file.
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// This file implements string-to-Float conversion functions.
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package big
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import (
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"fmt"
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"io"
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"strings"
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)
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var floatZero Float
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// SetString sets z to the value of s and returns z and a boolean indicating
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// success. s must be a floating-point number of the same format as accepted
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// by Parse, with base argument 0. The entire string (not just a prefix) must
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// be valid for success. If the operation failed, the value of z is undefined
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// but the returned value is nil.
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func (z *Float) SetString(s string) (*Float, bool) {
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if f, _, err := z.Parse(s, 0); err == nil {
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return f, true
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}
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return nil, false
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}
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// scan is like Parse but reads the longest possible prefix representing a valid
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// floating point number from an io.ByteScanner rather than a string. It serves
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// as the implementation of Parse. It does not recognize ±Inf and does not expect
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// EOF at the end.
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func (z *Float) scan(r io.ByteScanner, base int) (f *Float, b int, err error) {
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prec := z.prec
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if prec == 0 {
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prec = 64
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}
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// A reasonable value in case of an error.
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z.form = zero
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// sign
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z.neg, err = scanSign(r)
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if err != nil {
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return
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}
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// mantissa
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var fcount int // fractional digit count; valid if <= 0
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z.mant, b, fcount, err = z.mant.scan(r, base, true)
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if err != nil {
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return
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}
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// exponent
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var exp int64
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var ebase int
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exp, ebase, err = scanExponent(r, true, base == 0)
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if err != nil {
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return
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}
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// special-case 0
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if len(z.mant) == 0 {
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z.prec = prec
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z.acc = Exact
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z.form = zero
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f = z
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return
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}
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// len(z.mant) > 0
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// The mantissa may have a radix point (fcount <= 0) and there
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// may be a nonzero exponent exp. The radix point amounts to a
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// division by b**(-fcount). An exponent means multiplication by
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// ebase**exp. Finally, mantissa normalization (shift left) requires
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// a correcting multiplication by 2**(-shiftcount). Multiplications
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// are commutative, so we can apply them in any order as long as there
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// is no loss of precision. We only have powers of 2 and 10, and
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// we split powers of 10 into the product of the same powers of
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// 2 and 5. This reduces the size of the multiplication factor
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// needed for base-10 exponents.
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// normalize mantissa and determine initial exponent contributions
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exp2 := int64(len(z.mant))*_W - fnorm(z.mant)
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exp5 := int64(0)
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// determine binary or decimal exponent contribution of radix point
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if fcount < 0 {
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// The mantissa has a radix point ddd.dddd; and
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// -fcount is the number of digits to the right
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// of '.'. Adjust relevant exponent accordingly.
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d := int64(fcount)
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switch b {
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case 10:
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exp5 = d
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fallthrough // 10**e == 5**e * 2**e
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case 2:
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exp2 += d
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case 8:
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exp2 += d * 3 // octal digits are 3 bits each
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case 16:
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exp2 += d * 4 // hexadecimal digits are 4 bits each
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default:
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panic("unexpected mantissa base")
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}
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// fcount consumed - not needed anymore
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}
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// take actual exponent into account
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switch ebase {
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case 10:
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exp5 += exp
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fallthrough // see fallthrough above
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case 2:
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exp2 += exp
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default:
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panic("unexpected exponent base")
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}
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// exp consumed - not needed anymore
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// apply 2**exp2
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if MinExp <= exp2 && exp2 <= MaxExp {
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z.prec = prec
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z.form = finite
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z.exp = int32(exp2)
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f = z
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} else {
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err = fmt.Errorf("exponent overflow")
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return
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}
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if exp5 == 0 {
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// no decimal exponent contribution
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z.round(0)
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return
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}
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// exp5 != 0
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// apply 5**exp5
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p := new(Float).SetPrec(z.Prec() + 64) // use more bits for p -- TODO(gri) what is the right number?
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if exp5 < 0 {
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z.Quo(z, p.pow5(uint64(-exp5)))
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} else {
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z.Mul(z, p.pow5(uint64(exp5)))
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}
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return
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}
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// These powers of 5 fit into a uint64.
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//
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// for p, q := uint64(0), uint64(1); p < q; p, q = q, q*5 {
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// fmt.Println(q)
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// }
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//
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var pow5tab = [...]uint64{
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1,
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5,
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25,
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125,
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625,
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3125,
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15625,
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78125,
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390625,
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1953125,
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9765625,
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48828125,
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244140625,
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1220703125,
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6103515625,
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30517578125,
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152587890625,
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762939453125,
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3814697265625,
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19073486328125,
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95367431640625,
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476837158203125,
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2384185791015625,
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11920928955078125,
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59604644775390625,
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298023223876953125,
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1490116119384765625,
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7450580596923828125,
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}
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// pow5 sets z to 5**n and returns z.
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// n must not be negative.
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func (z *Float) pow5(n uint64) *Float {
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const m = uint64(len(pow5tab) - 1)
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if n <= m {
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return z.SetUint64(pow5tab[n])
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}
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// n > m
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z.SetUint64(pow5tab[m])
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n -= m
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// use more bits for f than for z
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// TODO(gri) what is the right number?
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f := new(Float).SetPrec(z.Prec() + 64).SetUint64(5)
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for n > 0 {
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if n&1 != 0 {
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z.Mul(z, f)
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}
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f.Mul(f, f)
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n >>= 1
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}
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return z
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}
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// Parse parses s which must contain a text representation of a floating-
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// point number with a mantissa in the given conversion base (the exponent
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// is always a decimal number), or a string representing an infinite value.
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//
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// For base 0, an underscore character ``_'' may appear between a base
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// prefix and an adjacent digit, and between successive digits; such
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// underscores do not change the value of the number, or the returned
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// digit count. Incorrect placement of underscores is reported as an
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// error if there are no other errors. If base != 0, underscores are
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// not recognized and thus terminate scanning like any other character
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// that is not a valid radix point or digit.
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//
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// It sets z to the (possibly rounded) value of the corresponding floating-
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// point value, and returns z, the actual base b, and an error err, if any.
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// The entire string (not just a prefix) must be consumed for success.
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// If z's precision is 0, it is changed to 64 before rounding takes effect.
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// The number must be of the form:
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//
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// number = [ sign ] ( float | "inf" | "Inf" ) .
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// sign = "+" | "-" .
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// float = ( mantissa | prefix pmantissa ) [ exponent ] .
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// prefix = "0" [ "b" | "B" | "o" | "O" | "x" | "X" ] .
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// mantissa = digits "." [ digits ] | digits | "." digits .
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// pmantissa = [ "_" ] digits "." [ digits ] | [ "_" ] digits | "." digits .
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// exponent = ( "e" | "E" | "p" | "P" ) [ sign ] digits .
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// digits = digit { [ "_" ] digit } .
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// digit = "0" ... "9" | "a" ... "z" | "A" ... "Z" .
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//
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// The base argument must be 0, 2, 8, 10, or 16. Providing an invalid base
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// argument will lead to a run-time panic.
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//
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// For base 0, the number prefix determines the actual base: A prefix of
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// ``0b'' or ``0B'' selects base 2, ``0o'' or ``0O'' selects base 8, and
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// ``0x'' or ``0X'' selects base 16. Otherwise, the actual base is 10 and
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// no prefix is accepted. The octal prefix "0" is not supported (a leading
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// "0" is simply considered a "0").
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//
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// A "p" or "P" exponent indicates a base 2 (rather then base 10) exponent;
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// for instance, "0x1.fffffffffffffp1023" (using base 0) represents the
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// maximum float64 value. For hexadecimal mantissae, the exponent character
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// must be one of 'p' or 'P', if present (an "e" or "E" exponent indicator
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// cannot be distinguished from a mantissa digit).
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//
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// The returned *Float f is nil and the value of z is valid but not
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// defined if an error is reported.
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//
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func (z *Float) Parse(s string, base int) (f *Float, b int, err error) {
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// scan doesn't handle ±Inf
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if len(s) == 3 && (s == "Inf" || s == "inf") {
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f = z.SetInf(false)
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return
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}
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if len(s) == 4 && (s[0] == '+' || s[0] == '-') && (s[1:] == "Inf" || s[1:] == "inf") {
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f = z.SetInf(s[0] == '-')
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return
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}
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r := strings.NewReader(s)
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if f, b, err = z.scan(r, base); err != nil {
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return
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}
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// entire string must have been consumed
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if ch, err2 := r.ReadByte(); err2 == nil {
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err = fmt.Errorf("expected end of string, found %q", ch)
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} else if err2 != io.EOF {
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err = err2
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}
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return
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}
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// ParseFloat is like f.Parse(s, base) with f set to the given precision
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// and rounding mode.
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func ParseFloat(s string, base int, prec uint, mode RoundingMode) (f *Float, b int, err error) {
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return new(Float).SetPrec(prec).SetMode(mode).Parse(s, base)
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}
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var _ fmt.Scanner = (*Float)(nil) // *Float must implement fmt.Scanner
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// Scan is a support routine for fmt.Scanner; it sets z to the value of
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// the scanned number. It accepts formats whose verbs are supported by
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// fmt.Scan for floating point values, which are:
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// 'b' (binary), 'e', 'E', 'f', 'F', 'g' and 'G'.
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// Scan doesn't handle ±Inf.
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func (z *Float) Scan(s fmt.ScanState, ch rune) error {
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s.SkipSpace()
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_, _, err := z.scan(byteReader{s}, 0)
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return err
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}
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