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Source file src/math/big/ftoa.go

  // 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 (
  	"bytes"
  	"fmt"
  	"strconv"
  )
  
  // 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 decimal digits necessary to identify the value x uniquely using
  // x.Prec() mantissa bits.
  // The prec value is ignored for the 'b' or 'p' format.
  func (x *Float) Text(format byte, prec int) string {
  	cap := 10 // TODO(gri) determine a good/better value here
  	if prec > 0 {
  		cap += prec
  	}
  	return string(x.Append(make([]byte, 0, cap), format, prec))
  }
  
  // String formats x like x.Text('g', 10).
  // (String must be called explicitly, Float.Format does not support %s verb.)
  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 {
  		// x != 0
  		d.init(x.mant, int(x.exp)-x.mant.bitLen())
  	}
  
  	// 2) round to desired precision
  	shortest := false
  	if prec < 0 {
  		shortest = true
  		roundShortest(&d, x)
  		// 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)
  }
  
  func roundShortest(d *decimal, x *Float) {
  	// if the mantissa is zero, the number is zero - stop now
  	if len(d.mant) == 0 {
  		return
  	}
  
  	// Approach: All numbers in the interval [x - 1/2ulp, x + 1/2ulp]
  	// (possibly exclusive) round to x for the given precision of x.
  	// Compute the lower and upper bound in decimal form and find the
  	// shortest decimal number d such that lower <= d <= upper.
  
  	// TODO(gri) strconv/ftoa.do describes a shortcut in some cases.
  	// See if we can use it (in adjusted form) here as well.
  
  	// 1) Compute normalized mantissa mant and exponent exp for x such
  	// that the lsb of mant corresponds to 1/2 ulp for the precision of
  	// x (i.e., for mant we want x.prec + 1 bits).
  	mant := nat(nil).set(x.mant)
  	exp := int(x.exp) - mant.bitLen()
  	s := mant.bitLen() - int(x.prec+1)
  	switch {
  	case s < 0:
  		mant = mant.shl(mant, uint(-s))
  	case s > 0:
  		mant = mant.shr(mant, uint(+s))
  	}
  	exp += s
  	// x = mant * 2**exp with lsb(mant) == 1/2 ulp of x.prec
  
  	// 2) Compute lower bound by subtracting 1/2 ulp.
  	var lower decimal
  	var tmp nat
  	lower.init(tmp.sub(mant, natOne), exp)
  
  	// 3) Compute upper bound by adding 1/2 ulp.
  	var upper decimal
  	upper.init(tmp.add(mant, natOne), exp)
  
  	// The upper and lower bounds are possible outputs only if
  	// the original mantissa is even, so that ToNearestEven rounding
  	// would round to the original mantissa and not the neighbors.
  	inclusive := mant[0]&2 == 0 // test bit 1 since original mantissa was shifted by 1
  
  	// Now we can figure out the minimum number of digits required.
  	// Walk along until d has distinguished itself from upper and lower.
  	for i, m := range d.mant {
  		l := lower.at(i)
  		u := upper.at(i)
  
  		// Okay to round down (truncate) if lower has a different digit
  		// or if lower is inclusive and is exactly the result of rounding
  		// down (i.e., and we have reached the final digit of lower).
  		okdown := l != m || inclusive && i+1 == len(lower.mant)
  
  		// Okay to round up if upper has a different digit and either upper
  		// is inclusive or upper is bigger than the result of rounding up.
  		okup := m != u && (inclusive || m+1 < u || i+1 < len(upper.mant))
  
  		// If it's okay to do either, then round to the nearest one.
  		// If it's okay to do only one, do it.
  		switch {
  		case okdown && okup:
  			d.round(i + 1)
  			return
  		case okdown:
  			d.roundDown(i + 1)
  			return
  		case okup:
  			d.roundUp(i + 1)
  			return
  		}
  	}
  }
  
  // %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++ {
  			buf = append(buf, d.at(d.exp+i))
  		}
  	}
  
  	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.utoa(10)...)
  	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,
  // and 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, bytes.TrimRight(m.utoa(16), "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
  }
  
  var _ fmt.Formatter = &floatZero // *Float must implement fmt.Formatter
  
  // Format implements fmt.Formatter. It accepts all the regular
  // formats for floating-point numbers ('b', 'e', 'E', 'f', 'F',
  // 'g', 'G') as well as 'p' and 'v'. See (*Float).Text for the
  // interpretation of '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 flags
  // '+' and ' ' for sign control, '0' for space or zero padding,
  // and '-' for left or right justification. See the fmt package
  // for details.
  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 {
  			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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