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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 Float-to-string conversion functions.
+// It is closely following the corresponding implementation
+// in strconv/ftoa.go, but modified and simplified for Float.
+
+package big
+
+import (
+ "fmt"
+ "strconv"
+ "strings"
+)
+
+// Text converts the floating-point number x to a string according
+// to the given format and precision prec. The format is one of:
+//
+// 'e' -d.dddde±dd, decimal exponent, at least two (possibly 0) exponent digits
+// 'E' -d.ddddE±dd, decimal exponent, at least two (possibly 0) exponent digits
+// 'f' -ddddd.dddd, no exponent
+// 'g' like 'e' for large exponents, like 'f' otherwise
+// 'G' like 'E' for large exponents, like 'f' otherwise
+// 'b' -ddddddp±dd, binary exponent
+// 'p' -0x.dddp±dd, binary exponent, hexadecimal mantissa
+//
+// For the binary exponent formats, the mantissa is printed in normalized form:
+//
+// 'b' decimal integer mantissa using x.Prec() bits, or -0
+// 'p' hexadecimal fraction with 0.5 <= 0.mantissa < 1.0, or -0
+//
+// If format is a different character, Text returns a "%" followed by the
+// unrecognized format character.
+//
+// The precision prec controls the number of digits (excluding the exponent)
+// printed by the 'e', 'E', 'f', 'g', and 'G' formats. For 'e', 'E', and 'f'
+// it is the number of digits after the decimal point. For 'g' and 'G' it is
+// the total number of digits. A negative precision selects the smallest
+// number of digits necessary to identify the value x uniquely.
+// The prec value is ignored for the 'b' or 'p' format.
+//
+// BUG(gri) Float.Text does not accept negative precisions (issue #10991).
+func (x *Float) Text(format byte, prec int) string {
+ const extra = 10 // TODO(gri) determine a good/better value here
+ return string(x.Append(make([]byte, 0, prec+extra), format, prec))
+}
+
+// String formats x like x.Text('g', 10).
+func (x *Float) String() string {
+ return x.Text('g', 10)
+}
+
+// Append appends to buf the string form of the floating-point number x,
+// as generated by x.Text, and returns the extended buffer.
+func (x *Float) Append(buf []byte, fmt byte, prec int) []byte {
+ // sign
+ if x.neg {
+ buf = append(buf, '-')
+ }
+
+ // Inf
+ if x.form == inf {
+ if !x.neg {
+ buf = append(buf, '+')
+ }
+ return append(buf, "Inf"...)
+ }
+
+ // pick off easy formats
+ switch fmt {
+ case 'b':
+ return x.fmtB(buf)
+ case 'p':
+ return x.fmtP(buf)
+ }
+
+ // Algorithm:
+ // 1) convert Float to multiprecision decimal
+ // 2) round to desired precision
+ // 3) read digits out and format
+
+ // 1) convert Float to multiprecision decimal
+ var d decimal // == 0.0
+ if x.form == finite {
+ d.init(x.mant, int(x.exp)-x.mant.bitLen())
+ }
+
+ // 2) round to desired precision
+ shortest := false
+ if prec < 0 {
+ shortest = true
+ panic("unimplemented")
+ // TODO(gri) complete this
+ // roundShortest(&d, f.mant, int(f.exp))
+ // Precision for shortest representation mode.
+ switch fmt {
+ case 'e', 'E':
+ prec = len(d.mant) - 1
+ case 'f':
+ prec = max(len(d.mant)-d.exp, 0)
+ case 'g', 'G':
+ prec = len(d.mant)
+ }
+ } else {
+ // round appropriately
+ switch fmt {
+ case 'e', 'E':
+ // one digit before and number of digits after decimal point
+ d.round(1 + prec)
+ case 'f':
+ // number of digits before and after decimal point
+ d.round(d.exp + prec)
+ case 'g', 'G':
+ if prec == 0 {
+ prec = 1
+ }
+ d.round(prec)
+ }
+ }
+
+ // 3) read digits out and format
+ switch fmt {
+ case 'e', 'E':
+ return fmtE(buf, fmt, prec, d)
+ case 'f':
+ return fmtF(buf, prec, d)
+ case 'g', 'G':
+ // trim trailing fractional zeros in %e format
+ eprec := prec
+ if eprec > len(d.mant) && len(d.mant) >= d.exp {
+ eprec = len(d.mant)
+ }
+ // %e is used if the exponent from the conversion
+ // is less than -4 or greater than or equal to the precision.
+ // If precision was the shortest possible, use eprec = 6 for
+ // this decision.
+ if shortest {
+ eprec = 6
+ }
+ exp := d.exp - 1
+ if exp < -4 || exp >= eprec {
+ if prec > len(d.mant) {
+ prec = len(d.mant)
+ }
+ return fmtE(buf, fmt+'e'-'g', prec-1, d)
+ }
+ if prec > d.exp {
+ prec = len(d.mant)
+ }
+ return fmtF(buf, max(prec-d.exp, 0), d)
+ }
+
+ // unknown format
+ if x.neg {
+ buf = buf[:len(buf)-1] // sign was added prematurely - remove it again
+ }
+ return append(buf, '%', fmt)
+}
+
+// %e: d.ddddde±dd
+func fmtE(buf []byte, fmt byte, prec int, d decimal) []byte {
+ // first digit
+ ch := byte('0')
+ if len(d.mant) > 0 {
+ ch = d.mant[0]
+ }
+ buf = append(buf, ch)
+
+ // .moredigits
+ if prec > 0 {
+ buf = append(buf, '.')
+ i := 1
+ m := min(len(d.mant), prec+1)
+ if i < m {
+ buf = append(buf, d.mant[i:m]...)
+ i = m
+ }
+ for ; i <= prec; i++ {
+ buf = append(buf, '0')
+ }
+ }
+
+ // e±
+ buf = append(buf, fmt)
+ var exp int64
+ if len(d.mant) > 0 {
+ exp = int64(d.exp) - 1 // -1 because first digit was printed before '.'
+ }
+ if exp < 0 {
+ ch = '-'
+ exp = -exp
+ } else {
+ ch = '+'
+ }
+ buf = append(buf, ch)
+
+ // dd...d
+ if exp < 10 {
+ buf = append(buf, '0') // at least 2 exponent digits
+ }
+ return strconv.AppendInt(buf, exp, 10)
+}
+
+// %f: ddddddd.ddddd
+func fmtF(buf []byte, prec int, d decimal) []byte {
+ // integer, padded with zeros as needed
+ if d.exp > 0 {
+ m := min(len(d.mant), d.exp)
+ buf = append(buf, d.mant[:m]...)
+ for ; m < d.exp; m++ {
+ buf = append(buf, '0')
+ }
+ } else {
+ buf = append(buf, '0')
+ }
+
+ // fraction
+ if prec > 0 {
+ buf = append(buf, '.')
+ for i := 0; i < prec; i++ {
+ ch := byte('0')
+ if j := d.exp + i; 0 <= j && j < len(d.mant) {
+ ch = d.mant[j]
+ }
+ buf = append(buf, ch)
+ }
+ }
+
+ return buf
+}
+
+// fmtB appends the string of x in the format mantissa "p" exponent
+// with a decimal mantissa and a binary exponent, or 0" if x is zero,
+// and returns the extended buffer.
+// The mantissa is normalized such that is uses x.Prec() bits in binary
+// representation.
+// The sign of x is ignored, and x must not be an Inf.
+func (x *Float) fmtB(buf []byte) []byte {
+ if x.form == zero {
+ return append(buf, '0')
+ }
+
+ if debugFloat && x.form != finite {
+ panic("non-finite float")
+ }
+ // x != 0
+
+ // adjust mantissa to use exactly x.prec bits
+ m := x.mant
+ switch w := uint32(len(x.mant)) * _W; {
+ case w < x.prec:
+ m = nat(nil).shl(m, uint(x.prec-w))
+ case w > x.prec:
+ m = nat(nil).shr(m, uint(w-x.prec))
+ }
+
+ buf = append(buf, m.decimalString()...)
+ buf = append(buf, 'p')
+ e := int64(x.exp) - int64(x.prec)
+ if e >= 0 {
+ buf = append(buf, '+')
+ }
+ return strconv.AppendInt(buf, e, 10)
+}
+
+// fmtP appends the string of x in the format 0x." mantissa "p" exponent
+// with a hexadecimal mantissa and a binary exponent, or 0" if x is zero,
+// ad returns the extended buffer.
+// The mantissa is normalized such that 0.5 <= 0.mantissa < 1.0.
+// The sign of x is ignored, and x must not be an Inf.
+func (x *Float) fmtP(buf []byte) []byte {
+ if x.form == zero {
+ return append(buf, '0')
+ }
+
+ if debugFloat && x.form != finite {
+ panic("non-finite float")
+ }
+ // x != 0
+
+ // remove trailing 0 words early
+ // (no need to convert to hex 0's and trim later)
+ m := x.mant
+ i := 0
+ for i < len(m) && m[i] == 0 {
+ i++
+ }
+ m = m[i:]
+
+ buf = append(buf, "0x."...)
+ buf = append(buf, strings.TrimRight(m.hexString(), "0")...)
+ buf = append(buf, 'p')
+ if x.exp >= 0 {
+ buf = append(buf, '+')
+ }
+ return strconv.AppendInt(buf, int64(x.exp), 10)
+}
+
+func min(x, y int) int {
+ if x < y {
+ return x
+ }
+ return y
+}
+
+// Format implements fmt.Formatter. It accepts all the regular
+// formats for floating-point numbers ('e', 'E', 'f', 'F', 'g',
+// 'G') as well as 'b', 'p', and 'v'. See (*Float).Text for the
+// interpretation of 'b' and 'p'. The 'v' format is handled like
+// 'g'.
+// Format also supports specification of the minimum precision
+// in digits, the output field width, as well as the format verbs
+// '+' and ' ' for sign control, '0' for space or zero padding,
+// and '-' for left or right justification. See the fmt package
+// for details.
+//
+// BUG(gri) A missing precision for the 'g' format, or a negative
+// (via '*') precision is not yet supported. Instead the
+// default precision (6) is used in that case (issue #10991).
+func (x *Float) Format(s fmt.State, format rune) {
+ prec, hasPrec := s.Precision()
+ if !hasPrec {
+ prec = 6 // default precision for 'e', 'f'
+ }
+
+ switch format {
+ case 'e', 'E', 'f', 'b', 'p':
+ // nothing to do
+ case 'F':
+ // (*Float).Text doesn't support 'F'; handle like 'f'
+ format = 'f'
+ case 'v':
+ // handle like 'g'
+ format = 'g'
+ fallthrough
+ case 'g', 'G':
+ if !hasPrec {
+ // TODO(gri) uncomment once (*Float).Text handles prec < 0
+ // prec = -1 // default precision for 'g', 'G'
+ }
+ default:
+ fmt.Fprintf(s, "%%!%c(*big.Float=%s)", format, x.String())
+ return
+ }
+ var buf []byte
+ buf = x.Append(buf, byte(format), prec)
+ if len(buf) == 0 {
+ buf = []byte("?") // should never happen, but don't crash
+ }
+ // len(buf) > 0
+
+ var sign string
+ switch {
+ case buf[0] == '-':
+ sign = "-"
+ buf = buf[1:]
+ case buf[0] == '+':
+ // +Inf
+ sign = "+"
+ if s.Flag(' ') {
+ sign = " "
+ }
+ buf = buf[1:]
+ case s.Flag('+'):
+ sign = "+"
+ case s.Flag(' '):
+ sign = " "
+ }
+
+ var padding int
+ if width, hasWidth := s.Width(); hasWidth && width > len(sign)+len(buf) {
+ padding = width - len(sign) - len(buf)
+ }
+
+ switch {
+ case s.Flag('0') && !x.IsInf():
+ // 0-padding on left
+ writeMultiple(s, sign, 1)
+ writeMultiple(s, "0", padding)
+ s.Write(buf)
+ case s.Flag('-'):
+ // padding on right
+ writeMultiple(s, sign, 1)
+ s.Write(buf)
+ writeMultiple(s, " ", padding)
+ default:
+ // padding on left
+ writeMultiple(s, " ", padding)
+ writeMultiple(s, sign, 1)
+ s.Write(buf)
+ }
+}
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