src/math/big/floatconv.go - go - Git at Google

 // 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 string-to-Float conversion functions.

 package big

 import (
 	"fmt"
 	"io"
 	"strings"
 )

 var floatZero Float

 // SetString sets z to the value of s and returns z and a boolean indicating
 // success. s must be a floating-point number of the same format as accepted
 // by Parse, with base argument 0. The entire string (not just a prefix) must
 // be valid for success. If the operation failed, the value of z is undefined
 // but the returned value is nil.
 func (z *Float) SetString(s string) (*Float, bool) {
 	if f, _, err := z.Parse(s, 0); err == nil {
 		return f, true
 	}
 	return nil, false
 }

 // scan is like Parse but reads the longest possible prefix representing a valid
 // floating point number from an io.ByteScanner rather than a string. It serves
 // as the implementation of Parse. It does not recognize ±Inf and does not expect
 // EOF at the end.
 func (z *Float) scan(r io.ByteScanner, base int) (f *Float, b int, err error) {
 	prec := z.prec
 	if prec == 0 {
 		prec = 64
 	}

 	// A reasonable value in case of an error.
 	z.form = zero

 	// sign
 	z.neg, err = scanSign(r)
 	if err != nil {
 		return
 	}

 	// mantissa
 	var fcount int // fractional digit count; valid if <= 0
 	z.mant, b, fcount, err = z.mant.scan(r, base, true)
 	if err != nil {
 		return
 	}

 	// exponent
 	var exp int64
 	var ebase int
 	exp, ebase, err = scanExponent(r, true, base == 0)
 	if err != nil {
 		return
 	}

 	// special-case 0
 	if len(z.mant) == 0 {
 		z.prec = prec
 		z.acc = Exact
 		z.form = zero
 		f = z
 		return
 	}
 	// len(z.mant) > 0

 	// The mantissa may have a radix point (fcount <= 0) and there
 	// may be a nonzero exponent exp. The radix point amounts to a
 	// division by b**(-fcount). An exponent means multiplication by
 	// ebase**exp. Finally, mantissa normalization (shift left) requires
 	// a correcting multiplication by 2**(-shiftcount). Multiplications
 	// are commutative, so we can apply them in any order as long as there
 	// is no loss of precision. We only have powers of 2 and 10, and
 	// we split powers of 10 into the product of the same powers of
 	// 2 and 5. This reduces the size of the multiplication factor
 	// needed for base-10 exponents.

 	// normalize mantissa and determine initial exponent contributions
 	exp2 := int64(len(z.mant))*_W - fnorm(z.mant)
 	exp5 := int64(0)

 	// determine binary or decimal exponent contribution of radix point
 	if fcount < 0 {
 		// The mantissa has a radix point ddd.dddd; and
 		// -fcount is the number of digits to the right
 		// of '.'. Adjust relevant exponent accordingly.
 		d := int64(fcount)
 		switch b {
 		case 10:
 			exp5 = d
 			fallthrough // 10**e == 5**e * 2**e
 		case 2:
 			exp2 += d
 		case 8:
 			exp2 += d * 3 // octal digits are 3 bits each
 		case 16:
 			exp2 += d * 4 // hexadecimal digits are 4 bits each
 		default:
 			panic("unexpected mantissa base")
 		}
 		// fcount consumed - not needed anymore
 	}

 	// take actual exponent into account
 	switch ebase {
 	case 10:
 		exp5 += exp
 		fallthrough // see fallthrough above
 	case 2:
 		exp2 += exp
 	default:
 		panic("unexpected exponent base")
 	}
 	// exp consumed - not needed anymore

 	// apply 2**exp2
 	if MinExp <= exp2 && exp2 <= MaxExp {
 		z.prec = prec
 		z.form = finite
 		z.exp = int32(exp2)
 		f = z
 	} else {
 		err = fmt.Errorf("exponent overflow")
 		return
 	}

 	if exp5 == 0 {
 		// no decimal exponent contribution
 		z.round(0)
 		return
 	}
 	// exp5 != 0

 	// apply 5**exp5
 	p := new(Float).SetPrec(z.Prec() + 64) // use more bits for p -- TODO(gri) what is the right number?
 	if exp5 < 0 {
 		z.Quo(z, p.pow5(uint64(-exp5)))
 	} else {
 		z.Mul(z, p.pow5(uint64(exp5)))
 	}

 	return
 }

 // These powers of 5 fit into a uint64.
 //
 //	for p, q := uint64(0), uint64(1); p < q; p, q = q, q*5 {
 //		fmt.Println(q)
 //	}
 var pow5tab = [...]uint64{
 	1,
 	5,
 	25,
 	125,
 	625,
 	3125,
 	15625,
 	78125,
 	390625,
 	1953125,
 	9765625,
 	48828125,
 	244140625,
 	1220703125,
 	6103515625,
 	30517578125,
 	152587890625,
 	762939453125,
 	3814697265625,
 	19073486328125,
 	95367431640625,
 	476837158203125,
 	2384185791015625,
 	11920928955078125,
 	59604644775390625,
 	298023223876953125,
 	1490116119384765625,
 	7450580596923828125,
 }

 // pow5 sets z to 5**n and returns z.
 // n must not be negative.
 func (z *Float) pow5(n uint64) *Float {
 	const m = uint64(len(pow5tab) - 1)
 	if n <= m {
 		return z.SetUint64(pow5tab[n])
 	}
 	// n > m

 	z.SetUint64(pow5tab[m])
 	n -= m

 	// use more bits for f than for z
 	// TODO(gri) what is the right number?
 	f := new(Float).SetPrec(z.Prec() + 64).SetUint64(5)

 	for n > 0 {
 		if n&1 != 0 {
 			z.Mul(z, f)
 		}
 		f.Mul(f, f)
 		n >>= 1
 	}

 	return z
 }

 // Parse parses s which must contain a text representation of a floating-
 // point number with a mantissa in the given conversion base (the exponent
 // is always a decimal number), or a string representing an infinite value.
 //
 // For base 0, an underscore character “_” may appear between a base
 // prefix and an adjacent digit, and between successive digits; such
 // underscores do not change the value of the number, or the returned
 // digit count. Incorrect placement of underscores is reported as an
 // error if there are no other errors. If base != 0, underscores are
 // not recognized and thus terminate scanning like any other character
 // that is not a valid radix point or digit.
 //
 // It sets z to the (possibly rounded) value of the corresponding floating-
 // point value, and returns z, the actual base b, and an error err, if any.
 // The entire string (not just a prefix) must be consumed for success.
 // If z's precision is 0, it is changed to 64 before rounding takes effect.
 // The number must be of the form:
 //
 //	number    = [ sign ] ( float | "inf" | "Inf" ) .
 //	sign      = "+" | "-" .
 //	float     = ( mantissa | prefix pmantissa ) [ exponent ] .
 //	prefix    = "0" [ "b" | "B" | "o" | "O" | "x" | "X" ] .
 //	mantissa  = digits "." [ digits ] | digits | "." digits .
 //	pmantissa = [ "_" ] digits "." [ digits ] | [ "_" ] digits | "." digits .
 //	exponent  = ( "e" | "E" | "p" | "P" ) [ sign ] digits .
 //	digits    = digit { [ "_" ] digit } .
 //	digit     = "0" ... "9" | "a" ... "z" | "A" ... "Z" .
 //
 // The base argument must be 0, 2, 8, 10, or 16. Providing an invalid base
 // argument will lead to a run-time panic.
 //
 // For base 0, the number prefix determines the actual base: A prefix of
 // “0b” or “0B” selects base 2, “0o” or “0O” selects base 8, and
 // “0x” or “0X” selects base 16. Otherwise, the actual base is 10 and
 // no prefix is accepted. The octal prefix "0" is not supported (a leading
 // "0" is simply considered a "0").
 //
 // A "p" or "P" exponent indicates a base 2 (rather than base 10) exponent;
 // for instance, "0x1.fffffffffffffp1023" (using base 0) represents the
 // maximum float64 value. For hexadecimal mantissae, the exponent character
 // must be one of 'p' or 'P', if present (an "e" or "E" exponent indicator
 // cannot be distinguished from a mantissa digit).
 //
 // The returned *Float f is nil and the value of z is valid but not
 // defined if an error is reported.
 func (z *Float) Parse(s string, base int) (f *Float, b int, err error) {
 	// scan doesn't handle ±Inf
 	if len(s) == 3 && (s == "Inf" || s == "inf") {
 		f = z.SetInf(false)
 		return
 	}
 	if len(s) == 4 && (s[0] == '+' || s[0] == '-') && (s[1:] == "Inf" || s[1:] == "inf") {
 		f = z.SetInf(s[0] == '-')
 		return
 	}

 	r := strings.NewReader(s)
 	if f, b, err = z.scan(r, base); err != nil {
 		return
 	}

 	// entire string must have been consumed
 	if ch, err2 := r.ReadByte(); err2 == nil {
 		err = fmt.Errorf("expected end of string, found %q", ch)
 	} else if err2 != io.EOF {
 		err = err2
 	}

 	return
 }

 // ParseFloat is like f.Parse(s, base) with f set to the given precision
 // and rounding mode.
 func ParseFloat(s string, base int, prec uint, mode RoundingMode) (f *Float, b int, err error) {
 	return new(Float).SetPrec(prec).SetMode(mode).Parse(s, base)
 }

 var _ fmt.Scanner = (*Float)(nil) // *Float must implement fmt.Scanner

 // Scan is a support routine for fmt.Scanner; it sets z to the value of
 // the scanned number. It accepts formats whose verbs are supported by
 // fmt.Scan for floating point values, which are:
 // 'b' (binary), 'e', 'E', 'f', 'F', 'g' and 'G'.
 // Scan doesn't handle ±Inf.
 func (z *Float) Scan(s fmt.ScanState, ch rune) error {
 	s.SkipSpace()
 	_, _, err := z.scan(byteReader{s}, 0)
 	return err
 }
	// 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 string-to-Float conversion functions.

	package big

	import (
	"fmt"
	"io"
	"strings"
	)

	var floatZero Float

	// SetString sets z to the value of s and returns z and a boolean indicating
	// success. s must be a floating-point number of the same format as accepted
	// by Parse, with base argument 0. The entire string (not just a prefix) must
	// be valid for success. If the operation failed, the value of z is undefined
	// but the returned value is nil.
	func (z Float) SetString(s string) (Float, bool) {
	if f, _, err := z.Parse(s, 0); err == nil {
	return f, true
	}
	return nil, false
	}

	// scan is like Parse but reads the longest possible prefix representing a valid
	// floating point number from an io.ByteScanner rather than a string. It serves
	// as the implementation of Parse. It does not recognize ±Inf and does not expect
	// EOF at the end.
	func (z Float) scan(r io.ByteScanner, base int) (f Float, b int, err error) {
	prec := z.prec
	if prec == 0 {
	prec = 64
	}

	// A reasonable value in case of an error.
	z.form = zero

	// sign
	z.neg, err = scanSign(r)
	if err != nil {
	return
	}

	// mantissa
	var fcount int // fractional digit count; valid if <= 0
	z.mant, b, fcount, err = z.mant.scan(r, base, true)
	if err != nil {
	return
	}

	// exponent
	var exp int64
	var ebase int
	exp, ebase, err = scanExponent(r, true, base == 0)
	if err != nil {
	return
	}

	// special-case 0
	if len(z.mant) == 0 {
	z.prec = prec
	z.acc = Exact
	z.form = zero
	f = z
	return
	}
	// len(z.mant) > 0

	// The mantissa may have a radix point (fcount <= 0) and there
	// may be a nonzero exponent exp. The radix point amounts to a
	// division by b**(-fcount). An exponent means multiplication by
	// ebase**exp. Finally, mantissa normalization (shift left) requires
	// a correcting multiplication by 2**(-shiftcount). Multiplications
	// are commutative, so we can apply them in any order as long as there
	// is no loss of precision. We only have powers of 2 and 10, and
	// we split powers of 10 into the product of the same powers of
	// 2 and 5. This reduces the size of the multiplication factor
	// needed for base-10 exponents.

	// normalize mantissa and determine initial exponent contributions
	exp2 := int64(len(z.mant))*_W - fnorm(z.mant)
	exp5 := int64(0)

	// determine binary or decimal exponent contribution of radix point
	if fcount < 0 {
	// The mantissa has a radix point ddd.dddd; and
	// -fcount is the number of digits to the right
	// of '.'. Adjust relevant exponent accordingly.
	d := int64(fcount)
	switch b {
	case 10:
	exp5 = d
	fallthrough // 10e == 5e * 2**e
	case 2:
	exp2 += d
	case 8:
	exp2 += d * 3 // octal digits are 3 bits each
	case 16:
	exp2 += d * 4 // hexadecimal digits are 4 bits each
	default:
	panic("unexpected mantissa base")
	}
	// fcount consumed - not needed anymore
	}

	// take actual exponent into account
	switch ebase {
	case 10:
	exp5 += exp
	fallthrough // see fallthrough above
	case 2:
	exp2 += exp
	default:
	panic("unexpected exponent base")
	}
	// exp consumed - not needed anymore

	// apply 2**exp2
	if MinExp <= exp2 && exp2 <= MaxExp {
	z.prec = prec
	z.form = finite
	z.exp = int32(exp2)
	f = z
	} else {
	err = fmt.Errorf("exponent overflow")
	return
	}

	if exp5 == 0 {
	// no decimal exponent contribution
	z.round(0)
	return
	}
	// exp5 != 0

	// apply 5**exp5
	p := new(Float).SetPrec(z.Prec() + 64) // use more bits for p -- TODO(gri) what is the right number?
	if exp5 < 0 {
	z.Quo(z, p.pow5(uint64(-exp5)))
	} else {
	z.Mul(z, p.pow5(uint64(exp5)))
	}

	return
	}

	// These powers of 5 fit into a uint64.
	//
	// for p, q := uint64(0), uint64(1); p < q; p, q = q, q*5 {
	// fmt.Println(q)
	// }
	var pow5tab = [...]uint64{
	1,
	5,
	25,
	125,
	625,
	3125,
	15625,
	78125,
	390625,
	1953125,
	9765625,
	48828125,
	244140625,
	1220703125,
	6103515625,
	30517578125,
	152587890625,
	762939453125,
	3814697265625,
	19073486328125,
	95367431640625,
	476837158203125,
	2384185791015625,
	11920928955078125,
	59604644775390625,
	298023223876953125,
	1490116119384765625,
	7450580596923828125,
	}

	// pow5 sets z to 5**n and returns z.
	// n must not be negative.
	func (z Float) pow5(n uint64) Float {
	const m = uint64(len(pow5tab) - 1)
	if n <= m {
	return z.SetUint64(pow5tab[n])
	}
	// n > m

	z.SetUint64(pow5tab[m])
	n -= m

	// use more bits for f than for z
	// TODO(gri) what is the right number?
	f := new(Float).SetPrec(z.Prec() + 64).SetUint64(5)

	for n > 0 {
	if n&1 != 0 {
	z.Mul(z, f)
	}
	f.Mul(f, f)
	n >>= 1
	}

	return z
	}

	// Parse parses s which must contain a text representation of a floating-
	// point number with a mantissa in the given conversion base (the exponent
	// is always a decimal number), or a string representing an infinite value.
	//
	// For base 0, an underscore character “_” may appear between a base
	// prefix and an adjacent digit, and between successive digits; such
	// underscores do not change the value of the number, or the returned
	// digit count. Incorrect placement of underscores is reported as an
	// error if there are no other errors. If base != 0, underscores are
	// not recognized and thus terminate scanning like any other character
	// that is not a valid radix point or digit.
	//
	// It sets z to the (possibly rounded) value of the corresponding floating-
	// point value, and returns z, the actual base b, and an error err, if any.
	// The entire string (not just a prefix) must be consumed for success.
	// If z's precision is 0, it is changed to 64 before rounding takes effect.
	// The number must be of the form:
	//
	// number = [ sign ] ( float \| "inf" \| "Inf" ) .
	// sign = "+" \| "-" .
	// float = ( mantissa \| prefix pmantissa ) [ exponent ] .
	// prefix = "0" [ "b" \| "B" \| "o" \| "O" \| "x" \| "X" ] .
	// mantissa = digits "." [ digits ] \| digits \| "." digits .
	// pmantissa = [ "_" ] digits "." [ digits ] \| [ "_" ] digits \| "." digits .
	// exponent = ( "e" \| "E" \| "p" \| "P" ) [ sign ] digits .
	// digits = digit { [ "_" ] digit } .
	// digit = "0" ... "9" \| "a" ... "z" \| "A" ... "Z" .
	//
	// The base argument must be 0, 2, 8, 10, or 16. Providing an invalid base
	// argument will lead to a run-time panic.
	//
	// For base 0, the number prefix determines the actual base: A prefix of
	// “0b” or “0B” selects base 2, “0o” or “0O” selects base 8, and
	// “0x” or “0X” selects base 16. Otherwise, the actual base is 10 and
	// no prefix is accepted. The octal prefix "0" is not supported (a leading
	// "0" is simply considered a "0").
	//
	// A "p" or "P" exponent indicates a base 2 (rather than base 10) exponent;
	// for instance, "0x1.fffffffffffffp1023" (using base 0) represents the
	// maximum float64 value. For hexadecimal mantissae, the exponent character
	// must be one of 'p' or 'P', if present (an "e" or "E" exponent indicator
	// cannot be distinguished from a mantissa digit).
	//
	// The returned *Float f is nil and the value of z is valid but not
	// defined if an error is reported.
	func (z Float) Parse(s string, base int) (f Float, b int, err error) {
	// scan doesn't handle ±Inf
	if len(s) == 3 && (s == "Inf" \|\| s == "inf") {
	f = z.SetInf(false)
	return
	}
	if len(s) == 4 && (s[0] == '+' \|\| s[0] == '-') && (s[1:] == "Inf" \|\| s[1:] == "inf") {
	f = z.SetInf(s[0] == '-')
	return
	}

	r := strings.NewReader(s)
	if f, b, err = z.scan(r, base); err != nil {
	return
	}

	// entire string must have been consumed
	if ch, err2 := r.ReadByte(); err2 == nil {
	err = fmt.Errorf("expected end of string, found %q", ch)
	} else if err2 != io.EOF {
	err = err2
	}

	return
	}

	// ParseFloat is like f.Parse(s, base) with f set to the given precision
	// and rounding mode.
	func ParseFloat(s string, base int, prec uint, mode RoundingMode) (f *Float, b int, err error) {
	return new(Float).SetPrec(prec).SetMode(mode).Parse(s, base)
	}

	var _ fmt.Scanner = (Float)(nil) // Float must implement fmt.Scanner

	// Scan is a support routine for fmt.Scanner; it sets z to the value of
	// the scanned number. It accepts formats whose verbs are supported by
	// fmt.Scan for floating point values, which are:
	// 'b' (binary), 'e', 'E', 'f', 'F', 'g' and 'G'.
	// Scan doesn't handle ±Inf.
	func (z *Float) Scan(s fmt.ScanState, ch rune) error {
	s.SkipSpace()
	_, _, err := z.scan(byteReader{s}, 0)
	return err
	}