go/src/lib/strconv/ftoa.go

// 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 "strconv"

// TODO: move elsewhere?
package type FloatInfo struct {
	mantbits uint;
	expbits uint;
	bias int;
}
package var float32info = FloatInfo{ 23, 8, -127 }
package var float64info = FloatInfo{ 52, 11, -1023 }

func FmtB(neg bool, mant uint64, exp int, flt *FloatInfo) string
func FmtE(neg bool, d *Decimal, prec int) string
func FmtF(neg bool, d *Decimal, prec int) string
func GenericFtoa(bits uint64, fmt byte, prec int, flt *FloatInfo) string
func Max(a, b int) int
func RoundShortest(d *Decimal, mant uint64, exp int, flt *FloatInfo)

func FloatSize() int {
	// Figure out whether float is float32 or float64.
	// 1e-35 is representable in both, but 1e-70
	// is too small for a float32.
	var f float = 1e-35;
	if f*f == 0 {
		return 32;
	}
	return 64;
}
export var floatsize = FloatSize()

export func ftoa32(f float32, fmt byte, prec int) string {
	return GenericFtoa(uint64(sys.float32bits(f)), fmt, prec, &float32info);
}

export func ftoa64(f float64, fmt byte, prec int) string {
	return GenericFtoa(sys.float64bits(f), fmt, prec, &float64info);
}

export func ftoa(f float, fmt byte, prec int) string {
	if floatsize == 32 {
		return ftoa32(float32(f), fmt, prec);
	}
	return ftoa64(float64(f), fmt, prec);
}

func GenericFtoa(bits uint64, fmt byte, prec int, flt *FloatInfo) string {
	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
		if mant != 0 {
			return "NaN";
		}
		if neg {
			return "-Inf";
		}
		return "+Inf";

	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(neg, mant, exp, flt);
	}

	// Create exact decimal representation.
	// The shift is exp - flt.mantbits because mant is a 1-bit integer
	// followed by a flt.mantbits fraction, and we are treating it as
	// a 1+flt.mantbits-bit integer.
	d := NewDecimal(mant).Shift(exp - int(flt.mantbits));

	// Round appropriately.
	// Negative precision means "only as much as needed to be exact."
	if prec < 0 {
		RoundShortest(d, mant, exp, flt);
		switch fmt {
		case 'e':
			prec = d.nd - 1;
		case 'f':
			prec = Max(d.nd - d.dp, 0);
		case 'g':
			prec = d.nd;
		}
	} else {
		switch fmt {
		case 'e':
			d.Round(prec+1);
		case 'f':
			d.Round(d.dp+prec);
		case 'g':
			if prec == 0 {
				prec = 1;
			}
			d.Round(prec);
		}
	}

	switch fmt {
	case 'e':
		return FmtE(neg, d, prec);
	case 'f':
		return FmtF(neg, d, prec);
	case 'g':
		// trailing zeros are removed.
		if prec > d.nd {
			prec = d.nd;
		}
		// %e is used if the exponent from the conversion
		// is less than -4 or greater than or equal to the precision.
		exp := d.dp - 1;
		if exp < -4 || exp >= prec {
			return FmtE(neg, d, prec - 1);
		}
		return FmtF(neg, d, Max(prec - d.dp, 0));
	}

	return "%" + string(fmt);
}

// Round d (= mant * 2^exp) to the shortest number of digits
// that will let the original floating point value be precisely
// reconstructed.  Size is original floating point size (64 or 32).
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;
	}

	// TODO: Unless exp == minexp, if the number of digits in d
	// is less than 17, it seems unlikely that it could not be
	// the shortest possible number already.  So maybe we can
	// bail out without doing the extra multiprecision math here.

	// Compute upper and lower such that any decimal number
	// between upper and lower (possibly inclusive)
	// will round to the original floating point number.

	// d = mant << (exp - mantbits)
	// Next highest floating point number is mant+1 << exp-mantbits.
	// Our upper bound is halfway inbetween, mant*2+1 << exp-mantbits-1.
	upper := NewDecimal(mant*2+1).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 inbetween, mantlo*2+1 << explo-mantbits-1.
	minexp := flt.bias + 1;	// minimum possible exponent
	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 := NewDecimal(mantlo*2+1).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++ {
		var l, m, u byte;	// lower, middle, upper digits
		if i < lower.nd {
			l = lower.d[i];
		} else {
			l = '0';
		}
		m = d.d[i];
		if i < upper.nd {
			u = upper.d[i];
		} else {
			u = '0';
		}

		// Okay to round down (truncate) if lower has a different digit
		// or if lower is inclusive and is exactly the result of rounding down.
		okdown := l != m || (inclusive && l == m && 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 || 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;
		}
	}
}

// %e: -d.ddddde±dd
func FmtE(neg bool, d *Decimal, prec int) string {
	buf := new([]byte, 3+Max(prec, 0)+30);	// "-0." + prec digits + exp
	w := 0;	// write index

	// sign
	if neg {
		buf[w] = '-';
		w++;
	}

	// first digit
	if d.nd == 0 {
		buf[w] = '0';
	} else {
		buf[w] = d.d[0];
	}
	w++;

	// .moredigits
	if prec > 0 {
		buf[w] = '.';
		w++;
		for i := 0; i < prec; i++ {
			if 1+i < d.nd {
				buf[w] = d.d[1+i];
			} else {
				buf[w] = '0';
			}
			w++;
		}
	}

	// e±
	buf[w] = 'e';
	w++;
	exp := d.dp - 1;
	if d.nd == 0 {	// special case: 0 has exponent 0
		exp = 0;
	}
	if exp < 0 {
		buf[w] = '-';
		exp = -exp;
	} else {
		buf[w] = '+';
	}
	w++;

	// dddd
	// count digits
	n := 0;
	for e := exp; e > 0; e /= 10 {
		n++;
	}
	// leading zeros
	for i := n; i < 2; i++ {
		buf[w] = '0';
		w++;
	}
	// digits
	w += n;
	n = 0;
	for e := exp; e > 0; e /= 10 {
		n++;
		buf[w-n] = byte(e%10 + '0');
	}

	return string(buf[0:w]);
}

// %f: -ddddddd.ddddd
func FmtF(neg bool, d *Decimal, prec int) string {
	buf := new([]byte, 1+Max(d.dp, 1)+1+Max(prec, 0));
	w := 0;

	// sign
	if neg {
		buf[w] = '-';
		w++;
	}

	// integer, padded with zeros as needed.
	if d.dp > 0 {
		var i int;
		for i = 0; i < d.dp && i < d.nd; i++ {
			buf[w] = d.d[i];
			w++;
		}
		for ; i < d.dp; i++ {
			buf[w] = '0';
			w++;
		}
	} else {
		buf[w] = '0';
		w++;
	}

	// fraction
	if prec > 0 {
		buf[w] = '.';
		w++;
		for i := 0; i < prec; i++ {
			if d.dp+i < 0 || d.dp+i >= d.nd {
				buf[w] = '0';
			} else {
				buf[w] = d.d[d.dp+i];
			}
			w++;
		}
	}

	return string(buf[0:w]);
}

// %b: -ddddddddp+ddd
func FmtB(neg bool, mant uint64, exp int, flt *FloatInfo) string {
	var buf [50]byte;
	w := len(buf);
	exp -= int(flt.mantbits);
	esign := byte('+');
	if exp < 0 {
		esign = '-';
		exp = -exp;
	}
	n := 0;
	for exp > 0 || n < 1 {
		n++;
		w--;
		buf[w] = byte(exp%10 + '0');
		exp /= 10
	}
	w--;
	buf[w] = esign;
	w--;
	buf[w] = 'p';
	n = 0;
	for mant > 0 || n < 1 {
		n++;
		w--;
		buf[w] = byte(mant%10 + '0');
		mant /= 10;
	}
	if neg {
		w--;
		buf[w] = '-';
	}
	return string((&buf)[w:len(buf)]);
}

func Max(a, b int) int {
	if a > b {
		return a;
	}
	return b;
}