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Source file src/strconv/ftoa.go

Documentation: strconv

  // Copyright 2009 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.
  
  // Binary to decimal floating point conversion.
  // Algorithm:
  //   1) store mantissa in multiprecision decimal
  //   2) shift decimal by exponent
  //   3) read digits out & format
  
  package strconv
  
  import "math"
  
  // TODO: move elsewhere?
  type floatInfo struct {
  	mantbits uint
  	expbits  uint
  	bias     int
  }
  
  var float32info = floatInfo{23, 8, -127}
  var float64info = floatInfo{52, 11, -1023}
  
  // FormatFloat converts the floating-point number f to a string,
  // according to the format fmt and precision prec. It rounds the
  // result assuming that the original was obtained from a floating-point
  // value of bitSize bits (32 for float32, 64 for float64).
  //
  // The format fmt is one of
  // 'b' (-ddddp±ddd, a binary exponent),
  // 'e' (-d.dddde±dd, a decimal exponent),
  // 'E' (-d.ddddE±dd, a decimal exponent),
  // 'f' (-ddd.dddd, no exponent),
  // 'g' ('e' for large exponents, 'f' otherwise), or
  // 'G' ('E' for large exponents, 'f' otherwise).
  //
  // 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.
  // The special precision -1 uses the smallest number of digits
  // necessary such that ParseFloat will return f exactly.
  func FormatFloat(f float64, fmt byte, prec, bitSize int) string {
  	return string(genericFtoa(make([]byte, 0, max(prec+4, 24)), f, fmt, prec, bitSize))
  }
  
  // AppendFloat appends the string form of the floating-point number f,
  // as generated by FormatFloat, to dst and returns the extended buffer.
  func AppendFloat(dst []byte, f float64, fmt byte, prec, bitSize int) []byte {
  	return genericFtoa(dst, f, fmt, prec, bitSize)
  }
  
  func genericFtoa(dst []byte, val float64, fmt byte, prec, bitSize int) []byte {
  	var bits uint64
  	var flt *floatInfo
  	switch bitSize {
  	case 32:
  		bits = uint64(math.Float32bits(float32(val)))
  		flt = &float32info
  	case 64:
  		bits = math.Float64bits(val)
  		flt = &float64info
  	default:
  		panic("strconv: illegal AppendFloat/FormatFloat bitSize")
  	}
  
  	neg := bits>>(flt.expbits+flt.mantbits) != 0
  	exp := int(bits>>flt.mantbits) & (1<<flt.expbits - 1)
  	mant := bits & (uint64(1)<<flt.mantbits - 1)
  
  	switch exp {
  	case 1<<flt.expbits - 1:
  		// Inf, NaN
  		var s string
  		switch {
  		case mant != 0:
  			s = "NaN"
  		case neg:
  			s = "-Inf"
  		default:
  			s = "+Inf"
  		}
  		return append(dst, s...)
  
  	case 0:
  		// denormalized
  		exp++
  
  	default:
  		// add implicit top bit
  		mant |= uint64(1) << flt.mantbits
  	}
  	exp += flt.bias
  
  	// Pick off easy binary format.
  	if fmt == 'b' {
  		return fmtB(dst, neg, mant, exp, flt)
  	}
  
  	if !optimize {
  		return bigFtoa(dst, prec, fmt, neg, mant, exp, flt)
  	}
  
  	var digs decimalSlice
  	ok := false
  	// Negative precision means "only as much as needed to be exact."
  	shortest := prec < 0
  	if shortest {
  		// Try Grisu3 algorithm.
  		f := new(extFloat)
  		lower, upper := f.AssignComputeBounds(mant, exp, neg, flt)
  		var buf [32]byte
  		digs.d = buf[:]
  		ok = f.ShortestDecimal(&digs, &lower, &upper)
  		if !ok {
  			return bigFtoa(dst, prec, fmt, neg, mant, exp, flt)
  		}
  		// Precision for shortest representation mode.
  		switch fmt {
  		case 'e', 'E':
  			prec = max(digs.nd-1, 0)
  		case 'f':
  			prec = max(digs.nd-digs.dp, 0)
  		case 'g', 'G':
  			prec = digs.nd
  		}
  	} else if fmt != 'f' {
  		// Fixed number of digits.
  		digits := prec
  		switch fmt {
  		case 'e', 'E':
  			digits++
  		case 'g', 'G':
  			if prec == 0 {
  				prec = 1
  			}
  			digits = prec
  		}
  		if digits <= 15 {
  			// try fast algorithm when the number of digits is reasonable.
  			var buf [24]byte
  			digs.d = buf[:]
  			f := extFloat{mant, exp - int(flt.mantbits), neg}
  			ok = f.FixedDecimal(&digs, digits)
  		}
  	}
  	if !ok {
  		return bigFtoa(dst, prec, fmt, neg, mant, exp, flt)
  	}
  	return formatDigits(dst, shortest, neg, digs, prec, fmt)
  }
  
  // bigFtoa uses multiprecision computations to format a float.
  func bigFtoa(dst []byte, prec int, fmt byte, neg bool, mant uint64, exp int, flt *floatInfo) []byte {
  	d := new(decimal)
  	d.Assign(mant)
  	d.Shift(exp - int(flt.mantbits))
  	var digs decimalSlice
  	shortest := prec < 0
  	if shortest {
  		roundShortest(d, mant, exp, flt)
  		digs = decimalSlice{d: d.d[:], nd: d.nd, dp: d.dp}
  		// Precision for shortest representation mode.
  		switch fmt {
  		case 'e', 'E':
  			prec = digs.nd - 1
  		case 'f':
  			prec = max(digs.nd-digs.dp, 0)
  		case 'g', 'G':
  			prec = digs.nd
  		}
  	} else {
  		// Round appropriately.
  		switch fmt {
  		case 'e', 'E':
  			d.Round(prec + 1)
  		case 'f':
  			d.Round(d.dp + prec)
  		case 'g', 'G':
  			if prec == 0 {
  				prec = 1
  			}
  			d.Round(prec)
  		}
  		digs = decimalSlice{d: d.d[:], nd: d.nd, dp: d.dp}
  	}
  	return formatDigits(dst, shortest, neg, digs, prec, fmt)
  }
  
  func formatDigits(dst []byte, shortest bool, neg bool, digs decimalSlice, prec int, fmt byte) []byte {
  	switch fmt {
  	case 'e', 'E':
  		return fmtE(dst, neg, digs, prec, fmt)
  	case 'f':
  		return fmtF(dst, neg, digs, prec)
  	case 'g', 'G':
  		// trailing fractional zeros in 'e' form will be trimmed.
  		eprec := prec
  		if eprec > digs.nd && digs.nd >= digs.dp {
  			eprec = digs.nd
  		}
  		// %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 precision 6 for this decision.
  		if shortest {
  			eprec = 6
  		}
  		exp := digs.dp - 1
  		if exp < -4 || exp >= eprec {
  			if prec > digs.nd {
  				prec = digs.nd
  			}
  			return fmtE(dst, neg, digs, prec-1, fmt+'e'-'g')
  		}
  		if prec > digs.dp {
  			prec = digs.nd
  		}
  		return fmtF(dst, neg, digs, max(prec-digs.dp, 0))
  	}
  
  	// unknown format
  	return append(dst, '%', fmt)
  }
  
  // roundShortest rounds d (= mant * 2^exp) to the shortest number of digits
  // that will let the original floating point value be precisely reconstructed.
  func roundShortest(d *decimal, mant uint64, exp int, flt *floatInfo) {
  	// If mantissa is zero, the number is zero; stop now.
  	if mant == 0 {
  		d.nd = 0
  		return
  	}
  
  	// Compute upper and lower such that any decimal number
  	// between upper and lower (possibly inclusive)
  	// will round to the original floating point number.
  
  	// We may see at once that the number is already shortest.
  	//
  	// Suppose d is not denormal, so that 2^exp <= d < 10^dp.
  	// The closest shorter number is at least 10^(dp-nd) away.
  	// The lower/upper bounds computed below are at distance
  	// at most 2^(exp-mantbits).
  	//
  	// So the number is already shortest if 10^(dp-nd) > 2^(exp-mantbits),
  	// or equivalently log2(10)*(dp-nd) > exp-mantbits.
  	// It is true if 332/100*(dp-nd) >= exp-mantbits (log2(10) > 3.32).
  	minexp := flt.bias + 1 // minimum possible exponent
  	if exp > minexp && 332*(d.dp-d.nd) >= 100*(exp-int(flt.mantbits)) {
  		// The number is already shortest.
  		return
  	}
  
  	// d = mant << (exp - mantbits)
  	// Next highest floating point number is mant+1 << exp-mantbits.
  	// Our upper bound is halfway between, mant*2+1 << exp-mantbits-1.
  	upper := new(decimal)
  	upper.Assign(mant*2 + 1)
  	upper.Shift(exp - int(flt.mantbits) - 1)
  
  	// d = mant << (exp - mantbits)
  	// Next lowest floating point number is mant-1 << exp-mantbits,
  	// unless mant-1 drops the significant bit and exp is not the minimum exp,
  	// in which case the next lowest is mant*2-1 << exp-mantbits-1.
  	// Either way, call it mantlo << explo-mantbits.
  	// Our lower bound is halfway between, mantlo*2+1 << explo-mantbits-1.
  	var mantlo uint64
  	var explo int
  	if mant > 1<<flt.mantbits || exp == minexp {
  		mantlo = mant - 1
  		explo = exp
  	} else {
  		mantlo = mant*2 - 1
  		explo = exp - 1
  	}
  	lower := new(decimal)
  	lower.Assign(mantlo*2 + 1)
  	lower.Shift(explo - int(flt.mantbits) - 1)
  
  	// The upper and lower bounds are possible outputs only if
  	// the original mantissa is even, so that IEEE round-to-even
  	// would round to the original mantissa and not the neighbors.
  	inclusive := mant%2 == 0
  
  	// Now we can figure out the minimum number of digits required.
  	// Walk along until d has distinguished itself from upper and lower.
  	for i := 0; i < d.nd; i++ {
  		l := byte('0') // lower digit
  		if i < lower.nd {
  			l = lower.d[i]
  		}
  		m := d.d[i]    // middle digit
  		u := byte('0') // upper digit
  		if i < upper.nd {
  			u = upper.d[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 == lower.nd
  
  		// 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 < upper.nd)
  
  		// 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
  		}
  	}
  }
  
  type decimalSlice struct {
  	d      []byte
  	nd, dp int
  	neg    bool
  }
  
  // %e: -d.ddddde±dd
  func fmtE(dst []byte, neg bool, d decimalSlice, prec int, fmt byte) []byte {
  	// sign
  	if neg {
  		dst = append(dst, '-')
  	}
  
  	// first digit
  	ch := byte('0')
  	if d.nd != 0 {
  		ch = d.d[0]
  	}
  	dst = append(dst, ch)
  
  	// .moredigits
  	if prec > 0 {
  		dst = append(dst, '.')
  		i := 1
  		m := min(d.nd, prec+1)
  		if i < m {
  			dst = append(dst, d.d[i:m]...)
  			i = m
  		}
  		for ; i <= prec; i++ {
  			dst = append(dst, '0')
  		}
  	}
  
  	// e±
  	dst = append(dst, fmt)
  	exp := d.dp - 1
  	if d.nd == 0 { // special case: 0 has exponent 0
  		exp = 0
  	}
  	if exp < 0 {
  		ch = '-'
  		exp = -exp
  	} else {
  		ch = '+'
  	}
  	dst = append(dst, ch)
  
  	// dd or ddd
  	switch {
  	case exp < 10:
  		dst = append(dst, '0', byte(exp)+'0')
  	case exp < 100:
  		dst = append(dst, byte(exp/10)+'0', byte(exp%10)+'0')
  	default:
  		dst = append(dst, byte(exp/100)+'0', byte(exp/10)%10+'0', byte(exp%10)+'0')
  	}
  
  	return dst
  }
  
  // %f: -ddddddd.ddddd
  func fmtF(dst []byte, neg bool, d decimalSlice, prec int) []byte {
  	// sign
  	if neg {
  		dst = append(dst, '-')
  	}
  
  	// integer, padded with zeros as needed.
  	if d.dp > 0 {
  		m := min(d.nd, d.dp)
  		dst = append(dst, d.d[:m]...)
  		for ; m < d.dp; m++ {
  			dst = append(dst, '0')
  		}
  	} else {
  		dst = append(dst, '0')
  	}
  
  	// fraction
  	if prec > 0 {
  		dst = append(dst, '.')
  		for i := 0; i < prec; i++ {
  			ch := byte('0')
  			if j := d.dp + i; 0 <= j && j < d.nd {
  				ch = d.d[j]
  			}
  			dst = append(dst, ch)
  		}
  	}
  
  	return dst
  }
  
  // %b: -ddddddddp±ddd
  func fmtB(dst []byte, neg bool, mant uint64, exp int, flt *floatInfo) []byte {
  	// sign
  	if neg {
  		dst = append(dst, '-')
  	}
  
  	// mantissa
  	dst, _ = formatBits(dst, mant, 10, false, true)
  
  	// p
  	dst = append(dst, 'p')
  
  	// ±exponent
  	exp -= int(flt.mantbits)
  	if exp >= 0 {
  		dst = append(dst, '+')
  	}
  	dst, _ = formatBits(dst, uint64(exp), 10, exp < 0, true)
  
  	return dst
  }
  
  func min(a, b int) int {
  	if a < b {
  		return a
  	}
  	return b
  }
  
  func max(a, b int) int {
  	if a > b {
  		return a
  	}
  	return b
  }
  

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