1 files changed, 302 insertions, 0 deletions
diff --git a/src/math/big/floatconv.go b/src/math/big/floatconv.go
new file mode 100644
index 0000000..d8c69b8
--- /dev/null
+++ b/src/math/big/floatconv.go
@@ -0,0 +1,302 @@
+// 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 [Float.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
+}