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math/big: accept non-decimal floats with Rat.SetString

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This fixes an old oversight. Rat.SetString already permitted
fractions a/b where both a and b could independently specify
a base prefix. With this CL, it now also accepts non-decimal
floating-point numbers.

Fixes #29799.

Change-Id: I9cc65666a5cebb00f0202da2e4fc5654a02e3234
Reviewed-on: https://go-review.googlesource.com/c/go/+/168237
Reviewed-by: Emmanuel Odeke <emm.odeke@gmail.com>
This commit is contained in:
Robert Griesemer 2019-03-18 16:10:07 -07:00
parent a591fd08dd
commit e4ba40030f
4 changed files with 133 additions and 38 deletions
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14
src/math/big/floatconv.go
View File

@ -70,8 +70,8 @@ func (z *Float) scan(r io.ByteScanner, base int) (f *Float, b int, err error) {
}
// len(z.mant) > 0
// The mantissa may have a decimal point (fcount <= 0) and there
// may be a nonzero exponent exp. The decimal point amounts to a
// 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
@ -85,11 +85,11 @@ func (z *Float) scan(r io.ByteScanner, base int) (f *Float, b int, err error) {
exp2 := int64(len(z.mant))*_W - fnorm(z.mant)
exp5 := int64(0)
// determine binary or decimal exponent contribution of decimal point
// determine binary or decimal exponent contribution of radix point
if fcount < 0 {
// The mantissa has a "decimal" point ddd.dddd; and
// -fcount is the number of digits to the right of '.'.
// Adjust relevant exponent accordingly.
// 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:
@ -111,7 +111,7 @@ func (z *Float) scan(r io.ByteScanner, base int) (f *Float, b int, err error) {
switch ebase {
case 10:
exp5 += exp
fallthrough
fallthrough // see fallthrough above
case 2:
exp2 += exp
default:

7
src/math/big/nat.go
View File

@ -35,9 +35,10 @@ import (
type nat []Word
var (
natOne = nat{1}
natTwo = nat{2}
natTen = nat{10}
natOne = nat{1}
natTwo = nat{2}
natFive = nat{5}
natTen = nat{10}
)
func (z nat) clear() {

124
src/math/big/ratconv.go
View File

@ -38,10 +38,22 @@ func (z *Rat) Scan(s fmt.ScanState, ch rune) error {
}
// SetString sets z to the value of s and returns z and a boolean indicating
// success. s can be given as a fraction "a/b" or as a decimal floating-point
// number optionally followed by an exponent. 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.
// success. s can be given as a (possibly signed) fraction "a/b", or as a
// floating-point number optionally followed by an exponent.
// If a fraction is provided, both the dividend and the divisor may be a
// decimal integer or independently use a prefix of ``0b'', ``0'' or ``0o'',
// or ``0x'' (or their upper-case variants) to denote a binary, octal, or
// hexadecimal integer, respectively. The divisor may not be signed.
// If a floating-point number is provided, it may be in decimal form or
// use any of the same prefixes as above but for ``0'' to denote a non-decimal
// mantissa. A leading ``0'' is considered a decimal leading 0; it does not
// indicate octal representation in this case.
// An optional base-10 ``e'' or base-2 ``p'' (or their upper-case variants)
// exponent may be provided as well, except for hexadecimal floats which
// only accept an (optional) ``p'' exponent (because an ``e'' or ``E'' cannot
// be distinguished from a mantissa digit).
// 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 *Rat) SetString(s string) (*Rat, bool) {
if len(s) == 0 {
return nil, false
@ -78,16 +90,17 @@ func (z *Rat) SetString(s string) (*Rat, bool) {
}
// mantissa
// TODO(gri) allow other bases besides 10 for mantissa and exponent? (issue #29799)
var ecorr int
z.a.abs, _, ecorr, err = z.a.abs.scan(r, 10, true)
var base int
var fcount int // fractional digit count; valid if <= 0
z.a.abs, base, fcount, err = z.a.abs.scan(r, 0, true)
if err != nil {
return nil, false
}
// exponent
var exp int64
exp, _, err = scanExponent(r, false, false)
var ebase int
exp, ebase, err = scanExponent(r, true, true)
if err != nil {
return nil, false
}
@ -103,30 +116,91 @@ func (z *Rat) SetString(s string) (*Rat, bool) {
}
// len(z.a.abs) > 0
// correct exponent
if ecorr < 0 {
exp += int64(ecorr)
// 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 base**(-fcount), which equals a multiplication by
// base**fcount. An exponent means multiplication by ebase**exp.
// Multiplications are commutative, so we can apply them in any
// order. 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
// may reduce the the size of shift/multiplication factors or
// divisors required to create the final fraction, depending
// on the actual floating-point value.
// determine binary or decimal exponent contribution of radix point
var exp2, exp5 int64
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 base {
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
}
// compute exponent power
expabs := exp
if expabs < 0 {
expabs = -expabs
// take actual exponent into account
switch ebase {
case 10:
exp5 += exp
fallthrough // see fallthrough above
case 2:
exp2 += exp
default:
panic("unexpected exponent base")
}
powTen := nat(nil).expNN(natTen, nat(nil).setWord(Word(expabs)), nil)
// exp consumed - not needed anymore
// complete fraction
if exp < 0 {
z.b.abs = powTen
z.norm()
} else {
z.a.abs = z.a.abs.mul(z.a.abs, powTen)
z.b.abs = z.b.abs[:0]
// compute pow5 if needed
pow5 := z.b.abs
if exp5 != 0 {
n := exp5
if n < 0 {
n = -n
}
pow5 = pow5.expNN(natFive, nat(nil).setWord(Word(n)), nil)
}
// apply dividend contributions of exponents
// (start with exp5 so the numbers to multiply are smaller)
if exp5 > 0 {
z.a.abs = z.a.abs.mul(z.a.abs, pow5)
exp5 = 0
}
if exp2 > 0 {
if int64(uint(exp2)) != exp2 {
panic("exponent too large")
}
z.a.abs = z.a.abs.shl(z.a.abs, uint(exp2))
exp2 = 0
}
// apply divisor contributions of exponents
z.b.abs = z.b.abs.setWord(1)
if exp5 < 0 {
z.b.abs = pow5
}
if exp2 < 0 {
if int64(uint(-exp2)) != -exp2 {
panic("exponent too large")
}
z.b.abs = z.b.abs.shl(z.b.abs, uint(-exp2))
}
z.a.neg = neg && len(z.a.abs) > 0 // 0 has no sign
return z, true
return z.norm(), true
}
// scanExponent scans the longest possible prefix of r representing a base 10
@ -250,7 +324,7 @@ func (x *Rat) RatString() string {
}
// FloatString returns a string representation of x in decimal form with prec
// digits of precision after the decimal point. The last digit is rounded to
// digits of precision after the radix point. The last digit is rounded to
// nearest, with halves rounded away from zero.
func (x *Rat) FloatString(prec int) string {
var buf []byte

26
src/math/big/ratconv_test.go
View File

@ -135,29 +135,49 @@ var setStringTests = []StringTest{
var setStringTests2 = []StringTest{
// invalid
{in: "4/3x"},
{in: "0/-1"},
{in: "-1/-1"},
// invalid with separators
// (smoke tests only - a comprehensive set of tests is in natconv_test.go)
{in: "10_/1"},
{in: "_10/1"},
{in: "1/1__0"},
{in: "1_000.0"}, // floats are base 10 which doesn't permit separators; see also issue #29799
// valid
{"0b1000/3", "8/3", true},
{"0B1000/0x8", "1", true},
{"-010/1", "-8", true},
{"-010.", "-10", true},
{"-010/1", "-8", true}, // 0-prefix indicates octal in this case
{"-010.0", "-10", true},
{"-0o10/1", "-8", true},
{"0x10/1", "16", true},
{"0x10/0x20", "1/2", true},
{"0010", "10", true}, // 0-prefix is ignored in this case (not a fraction)
{"0x10.0", "16", true},
{"0x1.8", "3/2", true},
{"0X1.8p4", "24", true},
{"0x1.1E2", "2289/2048", true}, // E is part of hex mantissa, not exponent
{"0b1.1E2", "150", true},
{"0B1.1P3", "12", true},
{"0o10e-2", "2/25", true},
{"0O10p-3", "1", true},
// valid with separators
// (smoke tests only - a comprehensive set of tests is in natconv_test.go)
{"0b_1000/3", "8/3", true},
{"0B_10_00/0x8", "1", true},
{"0xdead/0B1101_1110_1010_1101", "1", true},
{"0B1101_1110_1010_1101/0XD_E_A_D", "1", true},
{"1_000.0", "1000", true},
{"0x_10.0", "16", true},
{"0x1_0.0", "16", true},
{"0x1.8_0", "3/2", true},
{"0X1.8p0_4", "24", true},
{"0b1.1_0E2", "150", true},
{"0o1_0e-2", "2/25", true},
{"0O_10p-3", "1", true},
}
func TestRatSetString(t *testing.T) {