atof.go

/**
 *  Copyright 2014 Paul Querna
 *
 *  Licensed under the Apache License, Version 2.0 (the "License");
 *  you may not use this file except in compliance with the License.
 *  You may obtain a copy of the License at
 *
 *      http://www.apache.org/licenses/LICENSE-2.0
 *
 *  Unless required by applicable law or agreed to in writing, software
 *  distributed under the License is distributed on an "AS IS" BASIS,
 *  WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
 *  See the License for the specific language governing permissions and
 *  limitations under the License.
 *
 */

/* Portions of this file are on Go stdlib's strconv/atof.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.

package internal

// 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 // can change for testing

func equalIgnoreCase(s1 []byte, s2 []byte) bool {
	if len(s1) != len(s2) {
		return false
	}
	for i := 0; i < len(s1); i++ {
		c1 := s1[i]
		if 'A' <= c1 && c1 <= 'Z' {
			c1 += 'a' - 'A'
		}
		c2 := s2[i]
		if 'A' <= c2 && c2 <= 'Z' {
			c2 += 'a' - 'A'
		}
		if c1 != c2 {
			return false
		}
	}
	return true
}

func special(s []byte) (f float64, ok bool) {
	if len(s) == 0 {
		return
	}
	switch s[0] {
	default:
		return
	case '+':
		if equalIgnoreCase(s, []byte("+inf")) || equalIgnoreCase(s, []byte("+infinity")) {
			return math.Inf(1), true
		}
	case '-':
		if equalIgnoreCase(s, []byte("-inf")) || equalIgnoreCase(s, []byte("-infinity")) {
			return math.Inf(-1), true
		}
	case 'n', 'N':
		if equalIgnoreCase(s, []byte("nan")) {
			return math.NaN(), true
		}
	case 'i', 'I':
		if equalIgnoreCase(s, []byte("inf")) || equalIgnoreCase(s, []byte("infinity")) {
			return math.Inf(1), true
		}
	}
	return
}

func (b *decimal) set(s []byte) (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] == '.':
			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) && (s[i] == 'e' || 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'; i++ {
			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 mantissa and exponent from a float
// string representation. It sets ok to false if the number could
// not fit return types or is invalid.
func readFloat(s []byte) (mantissa uint64, exp int, neg, trunc, ok bool) {
	const uint64digits = 19
	i := 0

	// optional sign
	if i >= len(s) {
		return
	}
	switch {
	case s[i] == '+':
		i++
	case s[i] == '-':
		neg = true
		i++
	}

	// digits
	sawdot := false
	sawdigits := false
	nd := 0
	ndMant := 0
	dp := 0
	for ; i < len(s); i++ {
		switch c := s[i]; true {
		case c == '.':
			if sawdot {
				return
			}
			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 < uint64digits {
				mantissa *= 10
				mantissa += uint64(c - '0')
				ndMant++
			} else if s[i] != '0' {
				trunc = true
			}
			continue
		}
		break
	}
	if !sawdigits {
		return
	}
	if !sawdot {
		dp = 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) && (s[i] == 'e' || 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'; i++ {
			if e < 10000 {
				e = e*10 + int(s[i]) - '0'
			}
		}
		dp += e * esign
	}

	if i != len(s) {
		return
	}

	exp = dp - ndMant
	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
}

const fnParseFloat = "ParseFloat"

func atof32(s []byte) (f float32, err error) {
	if val, ok := special(s); ok {
		return float32(val), nil
	}

	if optimize {
		// Parse mantissa and exponent.
		mantissa, exp, neg, trunc, ok := readFloat(s)
		if ok {
			// Try pure floating-point arithmetic conversion.
			if !trunc {
				if f, ok := atof32exact(mantissa, exp, neg); ok {
					return f, nil
				}
			}
			// Try another fast path.
			ext := new(extFloat)
			if ok := ext.AssignDecimal(mantissa, exp, neg, trunc, &float32info); ok {
				b, ovf := ext.floatBits(&float32info)
				f = math.Float32frombits(uint32(b))
				if ovf {
					err = rangeError(fnParseFloat, string(s))
				}
				return f, err
			}
		}
	}
	var d decimal
	if !d.set(s) {
		return 0, syntaxError(fnParseFloat, string(s))
	}
	b, ovf := d.floatBits(&float32info)
	f = math.Float32frombits(uint32(b))
	if ovf {
		err = rangeError(fnParseFloat, string(s))
	}
	return f, err
}

func atof64(s []byte) (f float64, err error) {
	if val, ok := special(s); ok {
		return val, nil
	}

	if optimize {
		// Parse mantissa and exponent.
		mantissa, exp, neg, trunc, ok := readFloat(s)
		if ok {
			// Try pure floating-point arithmetic conversion.
			if !trunc {
				if f, ok := atof64exact(mantissa, exp, neg); ok {
					return f, nil
				}
			}
			// Try another fast path.
			ext := new(extFloat)
			if ok := ext.AssignDecimal(mantissa, exp, neg, trunc, &float64info); ok {
				b, ovf := ext.floatBits(&float64info)
				f = math.Float64frombits(b)
				if ovf {
					err = rangeError(fnParseFloat, string(s))
				}
				return f, err
			}
		}
	}
	var d decimal
	if !d.set(s) {
		return 0, syntaxError(fnParseFloat, string(s))
	}
	b, ovf := d.floatBits(&float64info)
	f = math.Float64frombits(b)
	if ovf {
		err = rangeError(fnParseFloat, string(s))
	}
	return f, 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.
//
// If s is well-formed and near a valid floating point number,
// ParseFloat returns the nearest floating point number rounded
// using IEEE754 unbiased rounding.
//
// 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.
func ParseFloat(s []byte, bitSize int) (f float64, err error) {
	if bitSize == 32 {
		f1, err1 := atof32(s)
		return float64(f1), err1
	}
	f1, err1 := atof64(s)
	return f1, err1
}

// oroginal: strconv/decimal.go, but not exported, and needed for PareFloat.

// 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.

// Multiprecision decimal numbers.
// For floating-point formatting only; not general purpose.
// Only operations are assign and (binary) left/right shift.
// Can do binary floating point in multiprecision decimal precisely
// because 2 divides 10; cannot do decimal floating point
// in multiprecision binary precisely.

type decimal struct {
	d     [800]byte // digits
	nd    int       // number of digits used
	dp    int       // decimal point
	neg   bool
	trunc bool // discarded nonzero digits beyond d[:nd]
}

func (a *decimal) String() string {
	n := 10 + a.nd
	if a.dp > 0 {
		n += a.dp
	}
	if a.dp < 0 {
		n += -a.dp
	}

	buf := make([]byte, n)
	w := 0
	switch {
	case a.nd == 0:
		return "0"

	case a.dp <= 0:
		// zeros fill space between decimal point and digits
		buf[w] = '0'
		w++
		buf[w] = '.'
		w++
		w += digitZero(buf[w : w+-a.dp])
		w += copy(buf[w:], a.d[0:a.nd])

	case a.dp < a.nd:
		// decimal point in middle of digits
		w += copy(buf[w:], a.d[0:a.dp])
		buf[w] = '.'
		w++
		w += copy(buf[w:], a.d[a.dp:a.nd])

	default:
		// zeros fill space between digits and decimal point
		w += copy(buf[w:], a.d[0:a.nd])
		w += digitZero(buf[w : w+a.dp-a.nd])
	}
	return string(buf[0:w])
}

func digitZero(dst []byte) int {
	for i := range dst {
		dst[i] = '0'
	}
	return len(dst)
}

// trim trailing zeros from number.
// (They are meaningless; the decimal point is tracked
// independent of the number of digits.)
func trim(a *decimal) {
	for a.nd > 0 && a.d[a.nd-1] == '0' {
		a.nd--
	}
	if a.nd == 0 {
		a.dp = 0
	}
}

// Assign v to a.
func (a *decimal) Assign(v uint64) {
	var buf [24]byte

	// Write reversed decimal in buf.
	n := 0
	for v > 0 {
		v1 := v / 10
		v -= 10 * v1
		buf[n] = byte(v + '0')
		n++
		v = v1
	}

	// Reverse again to produce forward decimal in a.d.
	a.nd = 0
	for n--; n >= 0; n-- {
		a.d[a.nd] = buf[n]
		a.nd++
	}
	a.dp = a.nd
	trim(a)
}

// Maximum shift that we can do in one pass without overflow.
// Signed int has 31 bits, and we have to be able to accommodate 9<<k.
const maxShift = 27

// Binary shift right (* 2) by k bits.  k <= maxShift to avoid overflow.
func rightShift(a *decimal, k uint) {
	r := 0 // read pointer
	w := 0 // write pointer

	// Pick up enough leading digits to cover first shift.
	n := 0
	for ; n>>k == 0; r++ {
		if r >= a.nd {
			if n == 0 {
				// a == 0; shouldn't get here, but handle anyway.
				a.nd = 0
				return
			}
			for n>>k == 0 {
				n = n * 10
				r++
			}
			break
		}
		c := int(a.d[r])
		n = n*10 + c - '0'
	}
	a.dp -= r - 1

	// Pick up a digit, put down a digit.
	for ; r < a.nd; r++ {
		c := int(a.d[r])
		dig := n >> k
		n -= dig << k
		a.d[w] = byte(dig + '0')
		w++
		n = n*10 + c - '0'
	}

	// Put down extra digits.
	for n > 0 {
		dig := n >> k
		n -= dig << k
		if w < len(a.d) {
			a.d[w] = byte(dig + '0')
			w++
		} else if dig > 0 {
			a.trunc = true
		}
		n = n * 10
	}

	a.nd = w
	trim(a)
}

// Cheat sheet for left shift: table indexed by shift count giving
// number of new digits that will be introduced by that shift.
//
// For example, leftcheats[4] = {2, "625"}.  That means that
// if we are shifting by 4 (multiplying by 16), it will add 2 digits
// when the string prefix is "625" through "999", and one fewer digit
// if the string prefix is "000" through "624".
//
// Credit for this trick goes to Ken.

type leftCheat struct {
	delta  int    // number of new digits
	cutoff string //   minus one digit if original < a.
}

var leftcheats = []leftCheat{
	// Leading digits of 1/2^i = 5^i.
	// 5^23 is not an exact 64-bit floating point number,
	// so have to use bc for the math.
	/*
		seq 27 | sed 's/^/5^/' | bc |
		awk 'BEGIN{ print "\tleftCheat{ 0, \"\" }," }
		{
			log2 = log(2)/log(10)
			printf("\tleftCheat{ %d, \"%s\" },\t// * %d\n",
				int(log2*NR+1), $0, 2**NR)
		}'
	*/
	{0, ""},
	{1, "5"},                   // * 2
	{1, "25"},                  // * 4
	{1, "125"},                 // * 8
	{2, "625"},                 // * 16
	{2, "3125"},                // * 32
	{2, "15625"},               // * 64
	{3, "78125"},               // * 128
	{3, "390625"},              // * 256
	{3, "1953125"},             // * 512
	{4, "9765625"},             // * 1024
	{4, "48828125"},            // * 2048
	{4, "244140625"},           // * 4096
	{4, "1220703125"},          // * 8192
	{5, "6103515625"},          // * 16384
	{5, "30517578125"},         // * 32768
	{5, "152587890625"},        // * 65536
	{6, "762939453125"},        // * 131072
	{6, "3814697265625"},       // * 262144
	{6, "19073486328125"},      // * 524288
	{7, "95367431640625"},      // * 1048576
	{7, "476837158203125"},     // * 2097152
	{7, "2384185791015625"},    // * 4194304
	{7, "11920928955078125"},   // * 8388608
	{8, "59604644775390625"},   // * 16777216
	{8, "298023223876953125"},  // * 33554432
	{8, "1490116119384765625"}, // * 67108864
	{9, "7450580596923828125"}, // * 134217728
}

// Is the leading prefix of b lexicographically less than s?
func prefixIsLessThan(b []byte, s string) bool {
	for i := 0; i < len(s); i++ {
		if i >= len(b) {
			return true
		}
		if b[i] != s[i] {
			return b[i] < s[i]
		}
	}
	return false
}

// Binary shift left (/ 2) by k bits.  k <= maxShift to avoid overflow.
func leftShift(a *decimal, k uint) {
	delta := leftcheats[k].delta
	if prefixIsLessThan(a.d[0:a.nd], leftcheats[k].cutoff) {
		delta--
	}

	r := a.nd         // read index
	w := a.nd + delta // write index
	n := 0

	// Pick up a digit, put down a digit.
	for r--; r >= 0; r-- {
		n += (int(a.d[r]) - '0') << k
		quo := n / 10
		rem := n - 10*quo
		w--
		if w < len(a.d) {
			a.d[w] = byte(rem + '0')
		} else if rem != 0 {
			a.trunc = true
		}
		n = quo
	}

	// Put down extra digits.
	for n > 0 {
		quo := n / 10
		rem := n - 10*quo
		w--
		if w < len(a.d) {
			a.d[w] = byte(rem + '0')
		} else if rem != 0 {
			a.trunc = true
		}
		n = quo
	}

	a.nd += delta
	if a.nd >= len(a.d) {
		a.nd = len(a.d)
	}
	a.dp += delta
	trim(a)
}

// Binary shift left (k > 0) or right (k < 0).
func (a *decimal) Shift(k int) {
	switch {
	case a.nd == 0:
		// nothing to do: a == 0
	case k > 0:
		for k > maxShift {
			leftShift(a, maxShift)
			k -= maxShift
		}
		leftShift(a, uint(k))
	case k < 0:
		for k < -maxShift {
			rightShift(a, maxShift)
			k += maxShift
		}
		rightShift(a, uint(-k))
	}
}

// If we chop a at nd digits, should we round up?
func shouldRoundUp(a *decimal, nd int) bool {
	if nd < 0 || nd >= a.nd {
		return false
	}
	if a.d[nd] == '5' && nd+1 == a.nd { // exactly halfway - round to even
		// if we truncated, a little higher than what's recorded - always round up
		if a.trunc {
			return true
		}
		return nd > 0 && (a.d[nd-1]-'0')%2 != 0
	}
	// not halfway - digit tells all
	return a.d[nd] >= '5'
}

// Round a to nd digits (or fewer).
// If nd is zero, it means we're rounding
// just to the left of the digits, as in
// 0.09 -> 0.1.
func (a *decimal) Round(nd int) {
	if nd < 0 || nd >= a.nd {
		return
	}
	if shouldRoundUp(a, nd) {
		a.RoundUp(nd)
	} else {
		a.RoundDown(nd)
	}
}

// Round a down to nd digits (or fewer).
func (a *decimal) RoundDown(nd int) {
	if nd < 0 || nd >= a.nd {
		return
	}
	a.nd = nd
	trim(a)
}

// Round a up to nd digits (or fewer).
func (a *decimal) RoundUp(nd int) {
	if nd < 0 || nd >= a.nd {
		return
	}

	// round up
	for i := nd - 1; i >= 0; i-- {
		c := a.d[i]
		if c < '9' { // can stop after this digit
			a.d[i]++
			a.nd = i + 1
			return
		}
	}

	// Number is all 9s.
	// Change to single 1 with adjusted decimal point.
	a.d[0] = '1'
	a.nd = 1
	a.dp++
}

// Extract integer part, rounded appropriately.
// No guarantees about overflow.
func (a *decimal) RoundedInteger() uint64 {
	if a.dp > 20 {
		return 0xFFFFFFFFFFFFFFFF
	}
	var i int
	n := uint64(0)
	for i = 0; i < a.dp && i < a.nd; i++ {
		n = n*10 + uint64(a.d[i]-'0')
	}
	for ; i < a.dp; i++ {
		n *= 10
	}
	if shouldRoundUp(a, a.dp) {
		n++
	}
	return n
}