1 files changed, 704 insertions, 0 deletions
diff --git a/src/strconv/atof.go b/src/strconv/atof.go
new file mode 100644
index 0000000..57556c7
--- /dev/null
+++ b/src/strconv/atof.go
@@ -0,0 +1,704 @@
+// 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.
+
+package strconv
+
+// decimal to binary floating point conversion.
+// Algorithm:
+//   1) Store input in multiprecision decimal.
+//   2) Multiply/divide decimal by powers of two until in range [0.5, 1)
+//   3) Multiply by 2^precision and round to get mantissa.
+
+import "math"
+
+var optimize = true // set to false to force slow-path conversions for testing
+
+// commonPrefixLenIgnoreCase returns the length of the common
+// prefix of s and prefix, with the character case of s ignored.
+// The prefix argument must be all lower-case.
+func commonPrefixLenIgnoreCase(s, prefix string) int {
+	n := len(prefix)
+	if n > len(s) {
+		n = len(s)
+	}
+	for i := 0; i < n; i++ {
+		c := s[i]
+		if 'A' <= c && c <= 'Z' {
+			c += 'a' - 'A'
+		}
+		if c != prefix[i] {
+			return i
+		}
+	}
+	return n
+}
+
+// special returns the floating-point value for the special,
+// possibly signed floating-point representations inf, infinity,
+// and NaN. The result is ok if a prefix of s contains one
+// of these representations and n is the length of that prefix.
+// The character case is ignored.
+func special(s string) (f float64, n int, ok bool) {
+	if len(s) == 0 {
+		return 0, 0, false
+	}
+	sign := 1
+	nsign := 0
+	switch s[0] {
+	case '+', '-':
+		if s[0] == '-' {
+			sign = -1
+		}
+		nsign = 1
+		s = s[1:]
+		fallthrough
+	case 'i', 'I':
+		n := commonPrefixLenIgnoreCase(s, "infinity")
+		// Anything longer than "inf" is ok, but if we
+		// don't have "infinity", only consume "inf".
+		if 3 < n && n < 8 {
+			n = 3
+		}
+		if n == 3 || n == 8 {
+			return math.Inf(sign), nsign + n, true
+		}
+	case 'n', 'N':
+		if commonPrefixLenIgnoreCase(s, "nan") == 3 {
+			return math.NaN(), 3, true
+		}
+	}
+	return 0, 0, false
+}
+
+func (b *decimal) set(s string) (ok bool) {
+	i := 0
+	b.neg = false
+	b.trunc = false
+
+	// optional sign
+	if i >= len(s) {
+		return
+	}
+	switch {
+	case s[i] == '+':
+		i++
+	case s[i] == '-':
+		b.neg = true
+		i++
+	}
+
+	// digits
+	sawdot := false
+	sawdigits := false
+	for ; i < len(s); i++ {
+		switch {
+		case s[i] == '_':
+			// readFloat already checked underscores
+			continue
+		case s[i] == '.':
+			if sawdot {
+				return
+			}
+			sawdot = true
+			b.dp = b.nd
+			continue
+
+		case '0' <= s[i] && s[i] <= '9':
+			sawdigits = true
+			if s[i] == '0' && b.nd == 0 { // ignore leading zeros
+				b.dp--
+				continue
+			}
+			if b.nd < len(b.d) {
+				b.d[b.nd] = s[i]
+				b.nd++
+			} else if s[i] != '0' {
+				b.trunc = true
+			}
+			continue
+		}
+		break
+	}
+	if !sawdigits {
+		return
+	}
+	if !sawdot {
+		b.dp = b.nd
+	}
+
+	// optional exponent moves decimal point.
+	// if we read a very large, very long number,
+	// just be sure to move the decimal point by
+	// a lot (say, 100000).  it doesn't matter if it's
+	// not the exact number.
+	if i < len(s) && lower(s[i]) == 'e' {
+		i++
+		if i >= len(s) {
+			return
+		}
+		esign := 1
+		if s[i] == '+' {
+			i++
+		} else if s[i] == '-' {
+			i++
+			esign = -1
+		}
+		if i >= len(s) || s[i] < '0' || s[i] > '9' {
+			return
+		}
+		e := 0
+		for ; i < len(s) && ('0' <= s[i] && s[i] <= '9' || s[i] == '_'); i++ {
+			if s[i] == '_' {
+				// readFloat already checked underscores
+				continue
+			}
+			if e < 10000 {
+				e = e*10 + int(s[i]) - '0'
+			}
+		}
+		b.dp += e * esign
+	}
+
+	if i != len(s) {
+		return
+	}
+
+	ok = true
+	return
+}
+
+// readFloat reads a decimal or hexadecimal mantissa and exponent from a float
+// string representation in s; the number may be followed by other characters.
+// readFloat reports the number of bytes consumed (i), and whether the number
+// is valid (ok).
+func readFloat(s string) (mantissa uint64, exp int, neg, trunc, hex bool, i int, ok bool) {
+	underscores := false
+
+	// optional sign
+	if i >= len(s) {
+		return
+	}
+	switch {
+	case s[i] == '+':
+		i++
+	case s[i] == '-':
+		neg = true
+		i++
+	}
+
+	// digits
+	base := uint64(10)
+	maxMantDigits := 19 // 10^19 fits in uint64
+	expChar := byte('e')
+	if i+2 < len(s) && s[i] == '0' && lower(s[i+1]) == 'x' {
+		base = 16
+		maxMantDigits = 16 // 16^16 fits in uint64
+		i += 2
+		expChar = 'p'
+		hex = true
+	}
+	sawdot := false
+	sawdigits := false
+	nd := 0
+	ndMant := 0
+	dp := 0
+loop:
+	for ; i < len(s); i++ {
+		switch c := s[i]; true {
+		case c == '_':
+			underscores = true
+			continue
+
+		case c == '.':
+			if sawdot {
+				break loop
+			}
+			sawdot = true
+			dp = nd
+			continue
+
+		case '0' <= c && c <= '9':
+			sawdigits = true
+			if c == '0' && nd == 0 { // ignore leading zeros
+				dp--
+				continue
+			}
+			nd++
+			if ndMant < maxMantDigits {
+				mantissa *= base
+				mantissa += uint64(c - '0')
+				ndMant++
+			} else if c != '0' {
+				trunc = true
+			}
+			continue
+
+		case base == 16 && 'a' <= lower(c) && lower(c) <= 'f':
+			sawdigits = true
+			nd++
+			if ndMant < maxMantDigits {
+				mantissa *= 16
+				mantissa += uint64(lower(c) - 'a' + 10)
+				ndMant++
+			} else {
+				trunc = true
+			}
+			continue
+		}
+		break
+	}
+	if !sawdigits {
+		return
+	}
+	if !sawdot {
+		dp = nd
+	}
+
+	if base == 16 {
+		dp *= 4
+		ndMant *= 4
+	}
+
+	// optional exponent moves decimal point.
+	// if we read a very large, very long number,
+	// just be sure to move the decimal point by
+	// a lot (say, 100000).  it doesn't matter if it's
+	// not the exact number.
+	if i < len(s) && lower(s[i]) == expChar {
+		i++
+		if i >= len(s) {
+			return
+		}
+		esign := 1
+		if s[i] == '+' {
+			i++
+		} else if s[i] == '-' {
+			i++
+			esign = -1
+		}
+		if i >= len(s) || s[i] < '0' || s[i] > '9' {
+			return
+		}
+		e := 0
+		for ; i < len(s) && ('0' <= s[i] && s[i] <= '9' || s[i] == '_'); i++ {
+			if s[i] == '_' {
+				underscores = true
+				continue
+			}
+			if e < 10000 {
+				e = e*10 + int(s[i]) - '0'
+			}
+		}
+		dp += e * esign
+	} else if base == 16 {
+		// Must have exponent.
+		return
+	}
+
+	if mantissa != 0 {
+		exp = dp - ndMant
+	}
+
+	if underscores && !underscoreOK(s[:i]) {
+		return
+	}
+
+	ok = true
+	return
+}
+
+// decimal power of ten to binary power of two.
+var powtab = []int{1, 3, 6, 9, 13, 16, 19, 23, 26}
+
+func (d *decimal) floatBits(flt *floatInfo) (b uint64, overflow bool) {
+	var exp int
+	var mant uint64
+
+	// Zero is always a special case.
+	if d.nd == 0 {
+		mant = 0
+		exp = flt.bias
+		goto out
+	}
+
+	// Obvious overflow/underflow.
+	// These bounds are for 64-bit floats.
+	// Will have to change if we want to support 80-bit floats in the future.
+	if d.dp > 310 {
+		goto overflow
+	}
+	if d.dp < -330 {
+		// zero
+		mant = 0
+		exp = flt.bias
+		goto out
+	}
+
+	// Scale by powers of two until in range [0.5, 1.0)
+	exp = 0
+	for d.dp > 0 {
+		var n int
+		if d.dp >= len(powtab) {
+			n = 27
+		} else {
+			n = powtab[d.dp]
+		}
+		d.Shift(-n)
+		exp += n
+	}
+	for d.dp < 0 || d.dp == 0 && d.d[0] < '5' {
+		var n int
+		if -d.dp >= len(powtab) {
+			n = 27
+		} else {
+			n = powtab[-d.dp]
+		}
+		d.Shift(n)
+		exp -= n
+	}
+
+	// Our range is [0.5,1) but floating point range is [1,2).
+	exp--
+
+	// Minimum representable exponent is flt.bias+1.
+	// If the exponent is smaller, move it up and
+	// adjust d accordingly.
+	if exp < flt.bias+1 {
+		n := flt.bias + 1 - exp
+		d.Shift(-n)
+		exp += n
+	}
+
+	if exp-flt.bias >= 1<<flt.expbits-1 {
+		goto overflow
+	}
+
+	// Extract 1+flt.mantbits bits.
+	d.Shift(int(1 + flt.mantbits))
+	mant = d.RoundedInteger()
+
+	// Rounding might have added a bit; shift down.
+	if mant == 2<<flt.mantbits {
+		mant >>= 1
+		exp++
+		if exp-flt.bias >= 1<<flt.expbits-1 {
+			goto overflow
+		}
+	}
+
+	// Denormalized?
+	if mant&(1<<flt.mantbits) == 0 {
+		exp = flt.bias
+	}
+	goto out
+
+overflow:
+	// ±Inf
+	mant = 0
+	exp = 1<<flt.expbits - 1 + flt.bias
+	overflow = true
+
+out:
+	// Assemble bits.
+	bits := mant & (uint64(1)<<flt.mantbits - 1)
+	bits |= uint64((exp-flt.bias)&(1<<flt.expbits-1)) << flt.mantbits
+	if d.neg {
+		bits |= 1 << flt.mantbits << flt.expbits
+	}
+	return bits, overflow
+}
+
+// Exact powers of 10.
+var float64pow10 = []float64{
+	1e0, 1e1, 1e2, 1e3, 1e4, 1e5, 1e6, 1e7, 1e8, 1e9,
+	1e10, 1e11, 1e12, 1e13, 1e14, 1e15, 1e16, 1e17, 1e18, 1e19,
+	1e20, 1e21, 1e22,
+}
+var float32pow10 = []float32{1e0, 1e1, 1e2, 1e3, 1e4, 1e5, 1e6, 1e7, 1e8, 1e9, 1e10}
+
+// If possible to convert decimal representation to 64-bit float f exactly,
+// entirely in floating-point math, do so, avoiding the expense of decimalToFloatBits.
+// Three common cases:
+//	value is exact integer
+//	value is exact integer * exact power of ten
+//	value is exact integer / exact power of ten
+// These all produce potentially inexact but correctly rounded answers.
+func atof64exact(mantissa uint64, exp int, neg bool) (f float64, ok bool) {
+	if mantissa>>float64info.mantbits != 0 {
+		return
+	}
+	f = float64(mantissa)
+	if neg {
+		f = -f
+	}
+	switch {
+	case exp == 0:
+		// an integer.
+		return f, true
+	// Exact integers are <= 10^15.
+	// Exact powers of ten are <= 10^22.
+	case exp > 0 && exp <= 15+22: // int * 10^k
+		// If exponent is big but number of digits is not,
+		// can move a few zeros into the integer part.
+		if exp > 22 {
+			f *= float64pow10[exp-22]
+			exp = 22
+		}
+		if f > 1e15 || f < -1e15 {
+			// the exponent was really too large.
+			return
+		}
+		return f * float64pow10[exp], true
+	case exp < 0 && exp >= -22: // int / 10^k
+		return f / float64pow10[-exp], true
+	}
+	return
+}
+
+// If possible to compute mantissa*10^exp to 32-bit float f exactly,
+// entirely in floating-point math, do so, avoiding the machinery above.
+func atof32exact(mantissa uint64, exp int, neg bool) (f float32, ok bool) {
+	if mantissa>>float32info.mantbits != 0 {
+		return
+	}
+	f = float32(mantissa)
+	if neg {
+		f = -f
+	}
+	switch {
+	case exp == 0:
+		return f, true
+	// Exact integers are <= 10^7.
+	// Exact powers of ten are <= 10^10.
+	case exp > 0 && exp <= 7+10: // int * 10^k
+		// If exponent is big but number of digits is not,
+		// can move a few zeros into the integer part.
+		if exp > 10 {
+			f *= float32pow10[exp-10]
+			exp = 10
+		}
+		if f > 1e7 || f < -1e7 {
+			// the exponent was really too large.
+			return
+		}
+		return f * float32pow10[exp], true
+	case exp < 0 && exp >= -10: // int / 10^k
+		return f / float32pow10[-exp], true
+	}
+	return
+}
+
+// atofHex converts the hex floating-point string s
+// to a rounded float32 or float64 value (depending on flt==&float32info or flt==&float64info)
+// and returns it as a float64.
+// The string s has already been parsed into a mantissa, exponent, and sign (neg==true for negative).
+// If trunc is true, trailing non-zero bits have been omitted from the mantissa.
+func atofHex(s string, flt *floatInfo, mantissa uint64, exp int, neg, trunc bool) (float64, error) {
+	maxExp := 1<<flt.expbits + flt.bias - 2
+	minExp := flt.bias + 1
+	exp += int(flt.mantbits) // mantissa now implicitly divided by 2^mantbits.
+
+	// Shift mantissa and exponent to bring representation into float range.
+	// Eventually we want a mantissa with a leading 1-bit followed by mantbits other bits.
+	// For rounding, we need two more, where the bottom bit represents
+	// whether that bit or any later bit was non-zero.
+	// (If the mantissa has already lost non-zero bits, trunc is true,
+	// and we OR in a 1 below after shifting left appropriately.)
+	for mantissa != 0 && mantissa>>(flt.mantbits+2) == 0 {
+		mantissa <<= 1
+		exp--
+	}
+	if trunc {
+		mantissa |= 1
+	}
+	for mantissa>>(1+flt.mantbits+2) != 0 {
+		mantissa = mantissa>>1 | mantissa&1
+		exp++
+	}
+
+	// If exponent is too negative,
+	// denormalize in hopes of making it representable.
+	// (The -2 is for the rounding bits.)
+	for mantissa > 1 && exp < minExp-2 {
+		mantissa = mantissa>>1 | mantissa&1
+		exp++
+	}
+
+	// Round using two bottom bits.
+	round := mantissa & 3
+	mantissa >>= 2
+	round |= mantissa & 1 // round to even (round up if mantissa is odd)
+	exp += 2
+	if round == 3 {
+		mantissa++
+		if mantissa == 1<<(1+flt.mantbits) {
+			mantissa >>= 1
+			exp++
+		}
+	}
+
+	if mantissa>>flt.mantbits == 0 { // Denormal or zero.
+		exp = flt.bias
+	}
+	var err error
+	if exp > maxExp { // infinity and range error
+		mantissa = 1 << flt.mantbits
+		exp = maxExp + 1
+		err = rangeError(fnParseFloat, s)
+	}
+
+	bits := mantissa & (1<<flt.mantbits - 1)
+	bits |= uint64((exp-flt.bias)&(1<<flt.expbits-1)) << flt.mantbits
+	if neg {
+		bits |= 1 << flt.mantbits << flt.expbits
+	}
+	if flt == &float32info {
+		return float64(math.Float32frombits(uint32(bits))), err
+	}
+	return math.Float64frombits(bits), err
+}
+
+const fnParseFloat = "ParseFloat"
+
+func atof32(s string) (f float32, n int, err error) {
+	if val, n, ok := special(s); ok {
+		return float32(val), n, nil
+	}
+
+	mantissa, exp, neg, trunc, hex, n, ok := readFloat(s)
+	if !ok {
+		return 0, n, syntaxError(fnParseFloat, s)
+	}
+
+	if hex {
+		f, err := atofHex(s[:n], &float32info, mantissa, exp, neg, trunc)
+		return float32(f), n, err
+	}
+
+	if optimize {
+		// Try pure floating-point arithmetic conversion, and if that fails,
+		// the Eisel-Lemire algorithm.
+		if !trunc {
+			if f, ok := atof32exact(mantissa, exp, neg); ok {
+				return f, n, nil
+			}
+		}
+		f, ok := eiselLemire32(mantissa, exp, neg)
+		if ok {
+			if !trunc {
+				return f, n, nil
+			}
+			// Even if the mantissa was truncated, we may
+			// have found the correct result. Confirm by
+			// converting the upper mantissa bound.
+			fUp, ok := eiselLemire32(mantissa+1, exp, neg)
+			if ok && f == fUp {
+				return f, n, nil
+			}
+		}
+	}
+
+	// Slow fallback.
+	var d decimal
+	if !d.set(s[:n]) {
+		return 0, n, syntaxError(fnParseFloat, s)
+	}
+	b, ovf := d.floatBits(&float32info)
+	f = math.Float32frombits(uint32(b))
+	if ovf {
+		err = rangeError(fnParseFloat, s)
+	}
+	return f, n, err
+}
+
+func atof64(s string) (f float64, n int, err error) {
+	if val, n, ok := special(s); ok {
+		return val, n, nil
+	}
+
+	mantissa, exp, neg, trunc, hex, n, ok := readFloat(s)
+	if !ok {
+		return 0, n, syntaxError(fnParseFloat, s)
+	}
+
+	if hex {
+		f, err := atofHex(s[:n], &float64info, mantissa, exp, neg, trunc)
+		return f, n, err
+	}
+
+	if optimize {
+		// Try pure floating-point arithmetic conversion, and if that fails,
+		// the Eisel-Lemire algorithm.
+		if !trunc {
+			if f, ok := atof64exact(mantissa, exp, neg); ok {
+				return f, n, nil
+			}
+		}
+		f, ok := eiselLemire64(mantissa, exp, neg)
+		if ok {
+			if !trunc {
+				return f, n, nil
+			}
+			// Even if the mantissa was truncated, we may
+			// have found the correct result. Confirm by
+			// converting the upper mantissa bound.
+			fUp, ok := eiselLemire64(mantissa+1, exp, neg)
+			if ok && f == fUp {
+				return f, n, nil
+			}
+		}
+	}
+
+	// Slow fallback.
+	var d decimal
+	if !d.set(s[:n]) {
+		return 0, n, syntaxError(fnParseFloat, s)
+	}
+	b, ovf := d.floatBits(&float64info)
+	f = math.Float64frombits(b)
+	if ovf {
+		err = rangeError(fnParseFloat, s)
+	}
+	return f, n, err
+}
+
+// ParseFloat converts the string s to a floating-point number
+// with the precision specified by bitSize: 32 for float32, or 64 for float64.
+// When bitSize=32, the result still has type float64, but it will be
+// convertible to float32 without changing its value.
+//
+// ParseFloat accepts decimal and hexadecimal floating-point number syntax.
+// If s is well-formed and near a valid floating-point number,
+// ParseFloat returns the nearest floating-point number rounded
+// using IEEE754 unbiased rounding.
+// (Parsing a hexadecimal floating-point value only rounds when
+// there are more bits in the hexadecimal representation than
+// will fit in the mantissa.)
+//
+// The errors that ParseFloat returns have concrete type *NumError
+// and include err.Num = s.
+//
+// If s is not syntactically well-formed, ParseFloat returns err.Err = ErrSyntax.
+//
+// If s is syntactically well-formed but is more than 1/2 ULP
+// away from the largest floating point number of the given size,
+// ParseFloat returns f = ±Inf, err.Err = ErrRange.
+//
+// ParseFloat recognizes the strings "NaN", and the (possibly signed) strings "Inf" and "Infinity"
+// as their respective special floating point values. It ignores case when matching.
+func ParseFloat(s string, bitSize int) (float64, error) {
+	f, n, err := parseFloatPrefix(s, bitSize)
+	if n != len(s) && (err == nil || err.(*NumError).Err != ErrSyntax) {
+		return 0, syntaxError(fnParseFloat, s)
+	}
+	return f, err
+}
+
+func parseFloatPrefix(s string, bitSize int) (float64, int, error) {
+	if bitSize == 32 {
+		f, n, err := atof32(s)
+		return float64(f), n, err
+	}
+	return atof64(s)
+}