Source file src/go/constant/value.go

Documentation: go/constant

     1  // Copyright 2013 The Go Authors. All rights reserved.
     2  // Use of this source code is governed by a BSD-style
     3  // license that can be found in the LICENSE file.
     4  
     5  // Package constant implements Values representing untyped
     6  // Go constants and their corresponding operations.
     7  //
     8  // A special Unknown value may be used when a value
     9  // is unknown due to an error. Operations on unknown
    10  // values produce unknown values unless specified
    11  // otherwise.
    12  //
    13  package constant
    14  
    15  import (
    16  	"fmt"
    17  	"go/token"
    18  	"math"
    19  	"math/big"
    20  	"strconv"
    21  	"strings"
    22  	"sync"
    23  	"unicode/utf8"
    24  )
    25  
    26  // Kind specifies the kind of value represented by a Value.
    27  type Kind int
    28  
    29  const (
    30  	// unknown values
    31  	Unknown Kind = iota
    32  
    33  	// non-numeric values
    34  	Bool
    35  	String
    36  
    37  	// numeric values
    38  	Int
    39  	Float
    40  	Complex
    41  )
    42  
    43  // A Value represents the value of a Go constant.
    44  type Value interface {
    45  	// Kind returns the value kind.
    46  	Kind() Kind
    47  
    48  	// String returns a short, quoted (human-readable) form of the value.
    49  	// For numeric values, the result may be an approximation;
    50  	// for String values the result may be a shortened string.
    51  	// Use ExactString for a string representing a value exactly.
    52  	String() string
    53  
    54  	// ExactString returns an exact, quoted (human-readable) form of the value.
    55  	// If the Value is of Kind String, use StringVal to obtain the unquoted string.
    56  	ExactString() string
    57  
    58  	// Prevent external implementations.
    59  	implementsValue()
    60  }
    61  
    62  // ----------------------------------------------------------------------------
    63  // Implementations
    64  
    65  // Maximum supported mantissa precision.
    66  // The spec requires at least 256 bits; typical implementations use 512 bits.
    67  const prec = 512
    68  
    69  type (
    70  	unknownVal struct{}
    71  	boolVal    bool
    72  	stringVal  struct {
    73  		// Lazy value: either a string (l,r==nil) or an addition (l,r!=nil).
    74  		mu   sync.Mutex
    75  		s    string
    76  		l, r *stringVal
    77  	}
    78  	int64Val   int64                    // Int values representable as an int64
    79  	intVal     struct{ val *big.Int }   // Int values not representable as an int64
    80  	ratVal     struct{ val *big.Rat }   // Float values representable as a fraction
    81  	floatVal   struct{ val *big.Float } // Float values not representable as a fraction
    82  	complexVal struct{ re, im Value }
    83  )
    84  
    85  func (unknownVal) Kind() Kind { return Unknown }
    86  func (boolVal) Kind() Kind    { return Bool }
    87  func (*stringVal) Kind() Kind { return String }
    88  func (int64Val) Kind() Kind   { return Int }
    89  func (intVal) Kind() Kind     { return Int }
    90  func (ratVal) Kind() Kind     { return Float }
    91  func (floatVal) Kind() Kind   { return Float }
    92  func (complexVal) Kind() Kind { return Complex }
    93  
    94  func (unknownVal) String() string { return "unknown" }
    95  func (x boolVal) String() string  { return strconv.FormatBool(bool(x)) }
    96  
    97  // String returns a possibly shortened quoted form of the String value.
    98  func (x *stringVal) String() string {
    99  	const maxLen = 72 // a reasonable length
   100  	s := strconv.Quote(x.string())
   101  	if utf8.RuneCountInString(s) > maxLen {
   102  		// The string without the enclosing quotes is greater than maxLen-2 runes
   103  		// long. Remove the last 3 runes (including the closing '"') by keeping
   104  		// only the first maxLen-3 runes; then add "...".
   105  		i := 0
   106  		for n := 0; n < maxLen-3; n++ {
   107  			_, size := utf8.DecodeRuneInString(s[i:])
   108  			i += size
   109  		}
   110  		s = s[:i] + "..."
   111  	}
   112  	return s
   113  }
   114  
   115  // string constructs and returns the actual string literal value.
   116  // If x represents an addition, then it rewrites x to be a single
   117  // string, to speed future calls. This lazy construction avoids
   118  // building different string values for all subpieces of a large
   119  // concatenation. See golang.org/issue/23348.
   120  func (x *stringVal) string() string {
   121  	x.mu.Lock()
   122  	if x.l != nil {
   123  		x.s = strings.Join(reverse(x.appendReverse(nil)), "")
   124  		x.l = nil
   125  		x.r = nil
   126  	}
   127  	s := x.s
   128  	x.mu.Unlock()
   129  
   130  	return s
   131  }
   132  
   133  // reverse reverses x in place and returns it.
   134  func reverse(x []string) []string {
   135  	n := len(x)
   136  	for i := 0; i+i < n; i++ {
   137  		x[i], x[n-1-i] = x[n-1-i], x[i]
   138  	}
   139  	return x
   140  }
   141  
   142  // appendReverse appends to list all of x's subpieces, but in reverse,
   143  // and returns the result. Appending the reversal allows processing
   144  // the right side in a recursive call and the left side in a loop.
   145  // Because a chain like a + b + c + d + e is actually represented
   146  // as ((((a + b) + c) + d) + e), the left-side loop avoids deep recursion.
   147  // x must be locked.
   148  func (x *stringVal) appendReverse(list []string) []string {
   149  	y := x
   150  	for y.r != nil {
   151  		y.r.mu.Lock()
   152  		list = y.r.appendReverse(list)
   153  		y.r.mu.Unlock()
   154  
   155  		l := y.l
   156  		if y != x {
   157  			y.mu.Unlock()
   158  		}
   159  		l.mu.Lock()
   160  		y = l
   161  	}
   162  	s := y.s
   163  	if y != x {
   164  		y.mu.Unlock()
   165  	}
   166  	return append(list, s)
   167  }
   168  
   169  func (x int64Val) String() string { return strconv.FormatInt(int64(x), 10) }
   170  func (x intVal) String() string   { return x.val.String() }
   171  func (x ratVal) String() string   { return rtof(x).String() }
   172  
   173  // String returns returns a decimal approximation of the Float value.
   174  func (x floatVal) String() string {
   175  	f := x.val
   176  
   177  	// Don't try to convert infinities (will not terminate).
   178  	if f.IsInf() {
   179  		return f.String()
   180  	}
   181  
   182  	// Use exact fmt formatting if in float64 range (common case):
   183  	// proceed if f doesn't underflow to 0 or overflow to inf.
   184  	if x, _ := f.Float64(); f.Sign() == 0 == (x == 0) && !math.IsInf(x, 0) {
   185  		return fmt.Sprintf("%.6g", x)
   186  	}
   187  
   188  	// Out of float64 range. Do approximate manual to decimal
   189  	// conversion to avoid precise but possibly slow Float
   190  	// formatting.
   191  	// f = mant * 2**exp
   192  	var mant big.Float
   193  	exp := f.MantExp(&mant) // 0.5 <= |mant| < 1.0
   194  
   195  	// approximate float64 mantissa m and decimal exponent d
   196  	// f ~ m * 10**d
   197  	m, _ := mant.Float64()                     // 0.5 <= |m| < 1.0
   198  	d := float64(exp) * (math.Ln2 / math.Ln10) // log_10(2)
   199  
   200  	// adjust m for truncated (integer) decimal exponent e
   201  	e := int64(d)
   202  	m *= math.Pow(10, d-float64(e))
   203  
   204  	// ensure 1 <= |m| < 10
   205  	switch am := math.Abs(m); {
   206  	case am < 1-0.5e-6:
   207  		// The %.6g format below rounds m to 5 digits after the
   208  		// decimal point. Make sure that m*10 < 10 even after
   209  		// rounding up: m*10 + 0.5e-5 < 10 => m < 1 - 0.5e6.
   210  		m *= 10
   211  		e--
   212  	case am >= 10:
   213  		m /= 10
   214  		e++
   215  	}
   216  
   217  	return fmt.Sprintf("%.6ge%+d", m, e)
   218  }
   219  
   220  func (x complexVal) String() string { return fmt.Sprintf("(%s + %si)", x.re, x.im) }
   221  
   222  func (x unknownVal) ExactString() string { return x.String() }
   223  func (x boolVal) ExactString() string    { return x.String() }
   224  func (x *stringVal) ExactString() string { return strconv.Quote(x.string()) }
   225  func (x int64Val) ExactString() string   { return x.String() }
   226  func (x intVal) ExactString() string     { return x.String() }
   227  
   228  func (x ratVal) ExactString() string {
   229  	r := x.val
   230  	if r.IsInt() {
   231  		return r.Num().String()
   232  	}
   233  	return r.String()
   234  }
   235  
   236  func (x floatVal) ExactString() string { return x.val.Text('p', 0) }
   237  
   238  func (x complexVal) ExactString() string {
   239  	return fmt.Sprintf("(%s + %si)", x.re.ExactString(), x.im.ExactString())
   240  }
   241  
   242  func (unknownVal) implementsValue() {}
   243  func (boolVal) implementsValue()    {}
   244  func (*stringVal) implementsValue() {}
   245  func (int64Val) implementsValue()   {}
   246  func (ratVal) implementsValue()     {}
   247  func (intVal) implementsValue()     {}
   248  func (floatVal) implementsValue()   {}
   249  func (complexVal) implementsValue() {}
   250  
   251  func newInt() *big.Int     { return new(big.Int) }
   252  func newRat() *big.Rat     { return new(big.Rat) }
   253  func newFloat() *big.Float { return new(big.Float).SetPrec(prec) }
   254  
   255  func i64toi(x int64Val) intVal   { return intVal{newInt().SetInt64(int64(x))} }
   256  func i64tor(x int64Val) ratVal   { return ratVal{newRat().SetInt64(int64(x))} }
   257  func i64tof(x int64Val) floatVal { return floatVal{newFloat().SetInt64(int64(x))} }
   258  func itor(x intVal) ratVal       { return ratVal{newRat().SetInt(x.val)} }
   259  func itof(x intVal) floatVal     { return floatVal{newFloat().SetInt(x.val)} }
   260  
   261  func rtof(x ratVal) floatVal {
   262  	a := newFloat().SetInt(x.val.Num())
   263  	b := newFloat().SetInt(x.val.Denom())
   264  	return floatVal{a.Quo(a, b)}
   265  }
   266  
   267  func vtoc(x Value) complexVal { return complexVal{x, int64Val(0)} }
   268  
   269  func makeInt(x *big.Int) Value {
   270  	if x.IsInt64() {
   271  		return int64Val(x.Int64())
   272  	}
   273  	return intVal{x}
   274  }
   275  
   276  // Permit fractions with component sizes up to maxExp
   277  // before switching to using floating-point numbers.
   278  const maxExp = 4 << 10
   279  
   280  func makeRat(x *big.Rat) Value {
   281  	a := x.Num()
   282  	b := x.Denom()
   283  	if a.BitLen() < maxExp && b.BitLen() < maxExp {
   284  		// ok to remain fraction
   285  		return ratVal{x}
   286  	}
   287  	// components too large => switch to float
   288  	fa := newFloat().SetInt(a)
   289  	fb := newFloat().SetInt(b)
   290  	return floatVal{fa.Quo(fa, fb)}
   291  }
   292  
   293  var floatVal0 = floatVal{newFloat()}
   294  
   295  func makeFloat(x *big.Float) Value {
   296  	// convert -0
   297  	if x.Sign() == 0 {
   298  		return floatVal0
   299  	}
   300  	return floatVal{x}
   301  }
   302  
   303  func makeComplex(re, im Value) Value {
   304  	return complexVal{re, im}
   305  }
   306  
   307  func makeFloatFromLiteral(lit string) Value {
   308  	if f, ok := newFloat().SetString(lit); ok {
   309  		if smallRat(f) {
   310  			// ok to use rationals
   311  			if f.Sign() == 0 {
   312  				// Issue 20228: If the float underflowed to zero, parse just "0".
   313  				// Otherwise, lit might contain a value with a large negative exponent,
   314  				// such as -6e-1886451601. As a float, that will underflow to 0,
   315  				// but it'll take forever to parse as a Rat.
   316  				lit = "0"
   317  			}
   318  			r, _ := newRat().SetString(lit)
   319  			return ratVal{r}
   320  		}
   321  		// otherwise use floats
   322  		return makeFloat(f)
   323  	}
   324  	return nil
   325  }
   326  
   327  // smallRat reports whether x would lead to "reasonably"-sized fraction
   328  // if converted to a *big.Rat.
   329  func smallRat(x *big.Float) bool {
   330  	if !x.IsInf() {
   331  		e := x.MantExp(nil)
   332  		return -maxExp < e && e < maxExp
   333  	}
   334  	return false
   335  }
   336  
   337  // ----------------------------------------------------------------------------
   338  // Factories
   339  
   340  // MakeUnknown returns the Unknown value.
   341  func MakeUnknown() Value { return unknownVal{} }
   342  
   343  // MakeBool returns the Bool value for b.
   344  func MakeBool(b bool) Value { return boolVal(b) }
   345  
   346  // MakeString returns the String value for s.
   347  func MakeString(s string) Value { return &stringVal{s: s} }
   348  
   349  // MakeInt64 returns the Int value for x.
   350  func MakeInt64(x int64) Value { return int64Val(x) }
   351  
   352  // MakeUint64 returns the Int value for x.
   353  func MakeUint64(x uint64) Value {
   354  	if x < 1<<63 {
   355  		return int64Val(int64(x))
   356  	}
   357  	return intVal{newInt().SetUint64(x)}
   358  }
   359  
   360  // MakeFloat64 returns the Float value for x.
   361  // If x is not finite, the result is an Unknown.
   362  func MakeFloat64(x float64) Value {
   363  	if math.IsInf(x, 0) || math.IsNaN(x) {
   364  		return unknownVal{}
   365  	}
   366  	// convert -0 to 0
   367  	if x == 0 {
   368  		return int64Val(0)
   369  	}
   370  	return ratVal{newRat().SetFloat64(x)}
   371  }
   372  
   373  // MakeFromLiteral returns the corresponding integer, floating-point,
   374  // imaginary, character, or string value for a Go literal string. The
   375  // tok value must be one of token.INT, token.FLOAT, token.IMAG,
   376  // token.CHAR, or token.STRING. The final argument must be zero.
   377  // If the literal string syntax is invalid, the result is an Unknown.
   378  func MakeFromLiteral(lit string, tok token.Token, zero uint) Value {
   379  	if zero != 0 {
   380  		panic("MakeFromLiteral called with non-zero last argument")
   381  	}
   382  
   383  	switch tok {
   384  	case token.INT:
   385  		if x, err := strconv.ParseInt(lit, 0, 64); err == nil {
   386  			return int64Val(x)
   387  		}
   388  		if x, ok := newInt().SetString(lit, 0); ok {
   389  			return intVal{x}
   390  		}
   391  
   392  	case token.FLOAT:
   393  		if x := makeFloatFromLiteral(lit); x != nil {
   394  			return x
   395  		}
   396  
   397  	case token.IMAG:
   398  		if n := len(lit); n > 0 && lit[n-1] == 'i' {
   399  			if im := makeFloatFromLiteral(lit[:n-1]); im != nil {
   400  				return makeComplex(int64Val(0), im)
   401  			}
   402  		}
   403  
   404  	case token.CHAR:
   405  		if n := len(lit); n >= 2 {
   406  			if code, _, _, err := strconv.UnquoteChar(lit[1:n-1], '\''); err == nil {
   407  				return MakeInt64(int64(code))
   408  			}
   409  		}
   410  
   411  	case token.STRING:
   412  		if s, err := strconv.Unquote(lit); err == nil {
   413  			return MakeString(s)
   414  		}
   415  
   416  	default:
   417  		panic(fmt.Sprintf("%v is not a valid token", tok))
   418  	}
   419  
   420  	return unknownVal{}
   421  }
   422  
   423  // ----------------------------------------------------------------------------
   424  // Accessors
   425  //
   426  // For unknown arguments the result is the zero value for the respective
   427  // accessor type, except for Sign, where the result is 1.
   428  
   429  // BoolVal returns the Go boolean value of x, which must be a Bool or an Unknown.
   430  // If x is Unknown, the result is false.
   431  func BoolVal(x Value) bool {
   432  	switch x := x.(type) {
   433  	case boolVal:
   434  		return bool(x)
   435  	case unknownVal:
   436  		return false
   437  	default:
   438  		panic(fmt.Sprintf("%v not a Bool", x))
   439  	}
   440  }
   441  
   442  // StringVal returns the Go string value of x, which must be a String or an Unknown.
   443  // If x is Unknown, the result is "".
   444  func StringVal(x Value) string {
   445  	switch x := x.(type) {
   446  	case *stringVal:
   447  		return x.string()
   448  	case unknownVal:
   449  		return ""
   450  	default:
   451  		panic(fmt.Sprintf("%v not a String", x))
   452  	}
   453  }
   454  
   455  // Int64Val returns the Go int64 value of x and whether the result is exact;
   456  // x must be an Int or an Unknown. If the result is not exact, its value is undefined.
   457  // If x is Unknown, the result is (0, false).
   458  func Int64Val(x Value) (int64, bool) {
   459  	switch x := x.(type) {
   460  	case int64Val:
   461  		return int64(x), true
   462  	case intVal:
   463  		return x.val.Int64(), false // not an int64Val and thus not exact
   464  	case unknownVal:
   465  		return 0, false
   466  	default:
   467  		panic(fmt.Sprintf("%v not an Int", x))
   468  	}
   469  }
   470  
   471  // Uint64Val returns the Go uint64 value of x and whether the result is exact;
   472  // x must be an Int or an Unknown. If the result is not exact, its value is undefined.
   473  // If x is Unknown, the result is (0, false).
   474  func Uint64Val(x Value) (uint64, bool) {
   475  	switch x := x.(type) {
   476  	case int64Val:
   477  		return uint64(x), x >= 0
   478  	case intVal:
   479  		return x.val.Uint64(), x.val.IsUint64()
   480  	case unknownVal:
   481  		return 0, false
   482  	default:
   483  		panic(fmt.Sprintf("%v not an Int", x))
   484  	}
   485  }
   486  
   487  // Float32Val is like Float64Val but for float32 instead of float64.
   488  func Float32Val(x Value) (float32, bool) {
   489  	switch x := x.(type) {
   490  	case int64Val:
   491  		f := float32(x)
   492  		return f, int64Val(f) == x
   493  	case intVal:
   494  		f, acc := newFloat().SetInt(x.val).Float32()
   495  		return f, acc == big.Exact
   496  	case ratVal:
   497  		return x.val.Float32()
   498  	case floatVal:
   499  		f, acc := x.val.Float32()
   500  		return f, acc == big.Exact
   501  	case unknownVal:
   502  		return 0, false
   503  	default:
   504  		panic(fmt.Sprintf("%v not a Float", x))
   505  	}
   506  }
   507  
   508  // Float64Val returns the nearest Go float64 value of x and whether the result is exact;
   509  // x must be numeric or an Unknown, but not Complex. For values too small (too close to 0)
   510  // to represent as float64, Float64Val silently underflows to 0. The result sign always
   511  // matches the sign of x, even for 0.
   512  // If x is Unknown, the result is (0, false).
   513  func Float64Val(x Value) (float64, bool) {
   514  	switch x := x.(type) {
   515  	case int64Val:
   516  		f := float64(int64(x))
   517  		return f, int64Val(f) == x
   518  	case intVal:
   519  		f, acc := newFloat().SetInt(x.val).Float64()
   520  		return f, acc == big.Exact
   521  	case ratVal:
   522  		return x.val.Float64()
   523  	case floatVal:
   524  		f, acc := x.val.Float64()
   525  		return f, acc == big.Exact
   526  	case unknownVal:
   527  		return 0, false
   528  	default:
   529  		panic(fmt.Sprintf("%v not a Float", x))
   530  	}
   531  }
   532  
   533  // BitLen returns the number of bits required to represent
   534  // the absolute value x in binary representation; x must be an Int or an Unknown.
   535  // If x is Unknown, the result is 0.
   536  func BitLen(x Value) int {
   537  	switch x := x.(type) {
   538  	case int64Val:
   539  		return i64toi(x).val.BitLen()
   540  	case intVal:
   541  		return x.val.BitLen()
   542  	case unknownVal:
   543  		return 0
   544  	default:
   545  		panic(fmt.Sprintf("%v not an Int", x))
   546  	}
   547  }
   548  
   549  // Sign returns -1, 0, or 1 depending on whether x < 0, x == 0, or x > 0;
   550  // x must be numeric or Unknown. For complex values x, the sign is 0 if x == 0,
   551  // otherwise it is != 0. If x is Unknown, the result is 1.
   552  func Sign(x Value) int {
   553  	switch x := x.(type) {
   554  	case int64Val:
   555  		switch {
   556  		case x < 0:
   557  			return -1
   558  		case x > 0:
   559  			return 1
   560  		}
   561  		return 0
   562  	case intVal:
   563  		return x.val.Sign()
   564  	case ratVal:
   565  		return x.val.Sign()
   566  	case floatVal:
   567  		return x.val.Sign()
   568  	case complexVal:
   569  		return Sign(x.re) | Sign(x.im)
   570  	case unknownVal:
   571  		return 1 // avoid spurious division by zero errors
   572  	default:
   573  		panic(fmt.Sprintf("%v not numeric", x))
   574  	}
   575  }
   576  
   577  // ----------------------------------------------------------------------------
   578  // Support for assembling/disassembling numeric values
   579  
   580  const (
   581  	// Compute the size of a Word in bytes.
   582  	_m       = ^big.Word(0)
   583  	_log     = _m>>8&1 + _m>>16&1 + _m>>32&1
   584  	wordSize = 1 << _log
   585  )
   586  
   587  // Bytes returns the bytes for the absolute value of x in little-
   588  // endian binary representation; x must be an Int.
   589  func Bytes(x Value) []byte {
   590  	var t intVal
   591  	switch x := x.(type) {
   592  	case int64Val:
   593  		t = i64toi(x)
   594  	case intVal:
   595  		t = x
   596  	default:
   597  		panic(fmt.Sprintf("%v not an Int", x))
   598  	}
   599  
   600  	words := t.val.Bits()
   601  	bytes := make([]byte, len(words)*wordSize)
   602  
   603  	i := 0
   604  	for _, w := range words {
   605  		for j := 0; j < wordSize; j++ {
   606  			bytes[i] = byte(w)
   607  			w >>= 8
   608  			i++
   609  		}
   610  	}
   611  	// remove leading 0's
   612  	for i > 0 && bytes[i-1] == 0 {
   613  		i--
   614  	}
   615  
   616  	return bytes[:i]
   617  }
   618  
   619  // MakeFromBytes returns the Int value given the bytes of its little-endian
   620  // binary representation. An empty byte slice argument represents 0.
   621  func MakeFromBytes(bytes []byte) Value {
   622  	words := make([]big.Word, (len(bytes)+(wordSize-1))/wordSize)
   623  
   624  	i := 0
   625  	var w big.Word
   626  	var s uint
   627  	for _, b := range bytes {
   628  		w |= big.Word(b) << s
   629  		if s += 8; s == wordSize*8 {
   630  			words[i] = w
   631  			i++
   632  			w = 0
   633  			s = 0
   634  		}
   635  	}
   636  	// store last word
   637  	if i < len(words) {
   638  		words[i] = w
   639  		i++
   640  	}
   641  	// remove leading 0's
   642  	for i > 0 && words[i-1] == 0 {
   643  		i--
   644  	}
   645  
   646  	return makeInt(newInt().SetBits(words[:i]))
   647  }
   648  
   649  // Num returns the numerator of x; x must be Int, Float, or Unknown.
   650  // If x is Unknown, or if it is too large or small to represent as a
   651  // fraction, the result is Unknown. Otherwise the result is an Int
   652  // with the same sign as x.
   653  func Num(x Value) Value {
   654  	switch x := x.(type) {
   655  	case int64Val, intVal:
   656  		return x
   657  	case ratVal:
   658  		return makeInt(x.val.Num())
   659  	case floatVal:
   660  		if smallRat(x.val) {
   661  			r, _ := x.val.Rat(nil)
   662  			return makeInt(r.Num())
   663  		}
   664  	case unknownVal:
   665  		break
   666  	default:
   667  		panic(fmt.Sprintf("%v not Int or Float", x))
   668  	}
   669  	return unknownVal{}
   670  }
   671  
   672  // Denom returns the denominator of x; x must be Int, Float, or Unknown.
   673  // If x is Unknown, or if it is too large or small to represent as a
   674  // fraction, the result is Unknown. Otherwise the result is an Int >= 1.
   675  func Denom(x Value) Value {
   676  	switch x := x.(type) {
   677  	case int64Val, intVal:
   678  		return int64Val(1)
   679  	case ratVal:
   680  		return makeInt(x.val.Denom())
   681  	case floatVal:
   682  		if smallRat(x.val) {
   683  			r, _ := x.val.Rat(nil)
   684  			return makeInt(r.Denom())
   685  		}
   686  	case unknownVal:
   687  		break
   688  	default:
   689  		panic(fmt.Sprintf("%v not Int or Float", x))
   690  	}
   691  	return unknownVal{}
   692  }
   693  
   694  // MakeImag returns the Complex value x*i;
   695  // x must be Int, Float, or Unknown.
   696  // If x is Unknown, the result is Unknown.
   697  func MakeImag(x Value) Value {
   698  	switch x.(type) {
   699  	case unknownVal:
   700  		return x
   701  	case int64Val, intVal, ratVal, floatVal:
   702  		return makeComplex(int64Val(0), x)
   703  	default:
   704  		panic(fmt.Sprintf("%v not Int or Float", x))
   705  	}
   706  }
   707  
   708  // Real returns the real part of x, which must be a numeric or unknown value.
   709  // If x is Unknown, the result is Unknown.
   710  func Real(x Value) Value {
   711  	switch x := x.(type) {
   712  	case unknownVal, int64Val, intVal, ratVal, floatVal:
   713  		return x
   714  	case complexVal:
   715  		return x.re
   716  	default:
   717  		panic(fmt.Sprintf("%v not numeric", x))
   718  	}
   719  }
   720  
   721  // Imag returns the imaginary part of x, which must be a numeric or unknown value.
   722  // If x is Unknown, the result is Unknown.
   723  func Imag(x Value) Value {
   724  	switch x := x.(type) {
   725  	case unknownVal:
   726  		return x
   727  	case int64Val, intVal, ratVal, floatVal:
   728  		return int64Val(0)
   729  	case complexVal:
   730  		return x.im
   731  	default:
   732  		panic(fmt.Sprintf("%v not numeric", x))
   733  	}
   734  }
   735  
   736  // ----------------------------------------------------------------------------
   737  // Numeric conversions
   738  
   739  // ToInt converts x to an Int value if x is representable as an Int.
   740  // Otherwise it returns an Unknown.
   741  func ToInt(x Value) Value {
   742  	switch x := x.(type) {
   743  	case int64Val, intVal:
   744  		return x
   745  
   746  	case ratVal:
   747  		if x.val.IsInt() {
   748  			return makeInt(x.val.Num())
   749  		}
   750  
   751  	case floatVal:
   752  		// avoid creation of huge integers
   753  		// (Existing tests require permitting exponents of at least 1024;
   754  		// allow any value that would also be permissible as a fraction.)
   755  		if smallRat(x.val) {
   756  			i := newInt()
   757  			if _, acc := x.val.Int(i); acc == big.Exact {
   758  				return makeInt(i)
   759  			}
   760  
   761  			// If we can get an integer by rounding up or down,
   762  			// assume x is not an integer because of rounding
   763  			// errors in prior computations.
   764  
   765  			const delta = 4 // a small number of bits > 0
   766  			var t big.Float
   767  			t.SetPrec(prec - delta)
   768  
   769  			// try rounding down a little
   770  			t.SetMode(big.ToZero)
   771  			t.Set(x.val)
   772  			if _, acc := t.Int(i); acc == big.Exact {
   773  				return makeInt(i)
   774  			}
   775  
   776  			// try rounding up a little
   777  			t.SetMode(big.AwayFromZero)
   778  			t.Set(x.val)
   779  			if _, acc := t.Int(i); acc == big.Exact {
   780  				return makeInt(i)
   781  			}
   782  		}
   783  
   784  	case complexVal:
   785  		if re := ToFloat(x); re.Kind() == Float {
   786  			return ToInt(re)
   787  		}
   788  	}
   789  
   790  	return unknownVal{}
   791  }
   792  
   793  // ToFloat converts x to a Float value if x is representable as a Float.
   794  // Otherwise it returns an Unknown.
   795  func ToFloat(x Value) Value {
   796  	switch x := x.(type) {
   797  	case int64Val:
   798  		return i64tof(x)
   799  	case intVal:
   800  		return itof(x)
   801  	case ratVal, floatVal:
   802  		return x
   803  	case complexVal:
   804  		if im := ToInt(x.im); im.Kind() == Int && Sign(im) == 0 {
   805  			// imaginary component is 0
   806  			return ToFloat(x.re)
   807  		}
   808  	}
   809  	return unknownVal{}
   810  }
   811  
   812  // ToComplex converts x to a Complex value if x is representable as a Complex.
   813  // Otherwise it returns an Unknown.
   814  func ToComplex(x Value) Value {
   815  	switch x := x.(type) {
   816  	case int64Val:
   817  		return vtoc(i64tof(x))
   818  	case intVal:
   819  		return vtoc(itof(x))
   820  	case ratVal:
   821  		return vtoc(x)
   822  	case floatVal:
   823  		return vtoc(x)
   824  	case complexVal:
   825  		return x
   826  	}
   827  	return unknownVal{}
   828  }
   829  
   830  // ----------------------------------------------------------------------------
   831  // Operations
   832  
   833  // is32bit reports whether x can be represented using 32 bits.
   834  func is32bit(x int64) bool {
   835  	const s = 32
   836  	return -1<<(s-1) <= x && x <= 1<<(s-1)-1
   837  }
   838  
   839  // is63bit reports whether x can be represented using 63 bits.
   840  func is63bit(x int64) bool {
   841  	const s = 63
   842  	return -1<<(s-1) <= x && x <= 1<<(s-1)-1
   843  }
   844  
   845  // UnaryOp returns the result of the unary expression op y.
   846  // The operation must be defined for the operand.
   847  // If prec > 0 it specifies the ^ (xor) result size in bits.
   848  // If y is Unknown, the result is Unknown.
   849  //
   850  func UnaryOp(op token.Token, y Value, prec uint) Value {
   851  	switch op {
   852  	case token.ADD:
   853  		switch y.(type) {
   854  		case unknownVal, int64Val, intVal, ratVal, floatVal, complexVal:
   855  			return y
   856  		}
   857  
   858  	case token.SUB:
   859  		switch y := y.(type) {
   860  		case unknownVal:
   861  			return y
   862  		case int64Val:
   863  			if z := -y; z != y {
   864  				return z // no overflow
   865  			}
   866  			return makeInt(newInt().Neg(big.NewInt(int64(y))))
   867  		case intVal:
   868  			return makeInt(newInt().Neg(y.val))
   869  		case ratVal:
   870  			return makeRat(newRat().Neg(y.val))
   871  		case floatVal:
   872  			return makeFloat(newFloat().Neg(y.val))
   873  		case complexVal:
   874  			re := UnaryOp(token.SUB, y.re, 0)
   875  			im := UnaryOp(token.SUB, y.im, 0)
   876  			return makeComplex(re, im)
   877  		}
   878  
   879  	case token.XOR:
   880  		z := newInt()
   881  		switch y := y.(type) {
   882  		case unknownVal:
   883  			return y
   884  		case int64Val:
   885  			z.Not(big.NewInt(int64(y)))
   886  		case intVal:
   887  			z.Not(y.val)
   888  		default:
   889  			goto Error
   890  		}
   891  		// For unsigned types, the result will be negative and
   892  		// thus "too large": We must limit the result precision
   893  		// to the type's precision.
   894  		if prec > 0 {
   895  			z.AndNot(z, newInt().Lsh(big.NewInt(-1), prec)) // z &^= (-1)<<prec
   896  		}
   897  		return makeInt(z)
   898  
   899  	case token.NOT:
   900  		switch y := y.(type) {
   901  		case unknownVal:
   902  			return y
   903  		case boolVal:
   904  			return !y
   905  		}
   906  	}
   907  
   908  Error:
   909  	panic(fmt.Sprintf("invalid unary operation %s%v", op, y))
   910  }
   911  
   912  func ord(x Value) int {
   913  	switch x.(type) {
   914  	default:
   915  		// force invalid value into "x position" in match
   916  		// (don't panic here so that callers can provide a better error message)
   917  		return -1
   918  	case unknownVal:
   919  		return 0
   920  	case boolVal, *stringVal:
   921  		return 1
   922  	case int64Val:
   923  		return 2
   924  	case intVal:
   925  		return 3
   926  	case ratVal:
   927  		return 4
   928  	case floatVal:
   929  		return 5
   930  	case complexVal:
   931  		return 6
   932  	}
   933  }
   934  
   935  // match returns the matching representation (same type) with the
   936  // smallest complexity for two values x and y. If one of them is
   937  // numeric, both of them must be numeric. If one of them is Unknown
   938  // or invalid (say, nil) both results are that value.
   939  //
   940  func match(x, y Value) (_, _ Value) {
   941  	if ord(x) > ord(y) {
   942  		y, x = match(y, x)
   943  		return x, y
   944  	}
   945  	// ord(x) <= ord(y)
   946  
   947  	switch x := x.(type) {
   948  	case boolVal, *stringVal, complexVal:
   949  		return x, y
   950  
   951  	case int64Val:
   952  		switch y := y.(type) {
   953  		case int64Val:
   954  			return x, y
   955  		case intVal:
   956  			return i64toi(x), y
   957  		case ratVal:
   958  			return i64tor(x), y
   959  		case floatVal:
   960  			return i64tof(x), y
   961  		case complexVal:
   962  			return vtoc(x), y
   963  		}
   964  
   965  	case intVal:
   966  		switch y := y.(type) {
   967  		case intVal:
   968  			return x, y
   969  		case ratVal:
   970  			return itor(x), y
   971  		case floatVal:
   972  			return itof(x), y
   973  		case complexVal:
   974  			return vtoc(x), y
   975  		}
   976  
   977  	case ratVal:
   978  		switch y := y.(type) {
   979  		case ratVal:
   980  			return x, y
   981  		case floatVal:
   982  			return rtof(x), y
   983  		case complexVal:
   984  			return vtoc(x), y
   985  		}
   986  
   987  	case floatVal:
   988  		switch y := y.(type) {
   989  		case floatVal:
   990  			return x, y
   991  		case complexVal:
   992  			return vtoc(x), y
   993  		}
   994  	}
   995  
   996  	// force unknown and invalid values into "x position" in callers of match
   997  	// (don't panic here so that callers can provide a better error message)
   998  	return x, x
   999  }
  1000  
  1001  // BinaryOp returns the result of the binary expression x op y.
  1002  // The operation must be defined for the operands. If one of the
  1003  // operands is Unknown, the result is Unknown.
  1004  // BinaryOp doesn't handle comparisons or shifts; use Compare
  1005  // or Shift instead.
  1006  //
  1007  // To force integer division of Int operands, use op == token.QUO_ASSIGN
  1008  // instead of token.QUO; the result is guaranteed to be Int in this case.
  1009  // Division by zero leads to a run-time panic.
  1010  //
  1011  func BinaryOp(x_ Value, op token.Token, y_ Value) Value {
  1012  	x, y := match(x_, y_)
  1013  
  1014  	switch x := x.(type) {
  1015  	case unknownVal:
  1016  		return x
  1017  
  1018  	case boolVal:
  1019  		y := y.(boolVal)
  1020  		switch op {
  1021  		case token.LAND:
  1022  			return x && y
  1023  		case token.LOR:
  1024  			return x || y
  1025  		}
  1026  
  1027  	case int64Val:
  1028  		a := int64(x)
  1029  		b := int64(y.(int64Val))
  1030  		var c int64
  1031  		switch op {
  1032  		case token.ADD:
  1033  			if !is63bit(a) || !is63bit(b) {
  1034  				return makeInt(newInt().Add(big.NewInt(a), big.NewInt(b)))
  1035  			}
  1036  			c = a + b
  1037  		case token.SUB:
  1038  			if !is63bit(a) || !is63bit(b) {
  1039  				return makeInt(newInt().Sub(big.NewInt(a), big.NewInt(b)))
  1040  			}
  1041  			c = a - b
  1042  		case token.MUL:
  1043  			if !is32bit(a) || !is32bit(b) {
  1044  				return makeInt(newInt().Mul(big.NewInt(a), big.NewInt(b)))
  1045  			}
  1046  			c = a * b
  1047  		case token.QUO:
  1048  			return makeRat(big.NewRat(a, b))
  1049  		case token.QUO_ASSIGN: // force integer division
  1050  			c = a / b
  1051  		case token.REM:
  1052  			c = a % b
  1053  		case token.AND:
  1054  			c = a & b
  1055  		case token.OR:
  1056  			c = a | b
  1057  		case token.XOR:
  1058  			c = a ^ b
  1059  		case token.AND_NOT:
  1060  			c = a &^ b
  1061  		default:
  1062  			goto Error
  1063  		}
  1064  		return int64Val(c)
  1065  
  1066  	case intVal:
  1067  		a := x.val
  1068  		b := y.(intVal).val
  1069  		c := newInt()
  1070  		switch op {
  1071  		case token.ADD:
  1072  			c.Add(a, b)
  1073  		case token.SUB:
  1074  			c.Sub(a, b)
  1075  		case token.MUL:
  1076  			c.Mul(a, b)
  1077  		case token.QUO:
  1078  			return makeRat(newRat().SetFrac(a, b))
  1079  		case token.QUO_ASSIGN: // force integer division
  1080  			c.Quo(a, b)
  1081  		case token.REM:
  1082  			c.Rem(a, b)
  1083  		case token.AND:
  1084  			c.And(a, b)
  1085  		case token.OR:
  1086  			c.Or(a, b)
  1087  		case token.XOR:
  1088  			c.Xor(a, b)
  1089  		case token.AND_NOT:
  1090  			c.AndNot(a, b)
  1091  		default:
  1092  			goto Error
  1093  		}
  1094  		return makeInt(c)
  1095  
  1096  	case ratVal:
  1097  		a := x.val
  1098  		b := y.(ratVal).val
  1099  		c := newRat()
  1100  		switch op {
  1101  		case token.ADD:
  1102  			c.Add(a, b)
  1103  		case token.SUB:
  1104  			c.Sub(a, b)
  1105  		case token.MUL:
  1106  			c.Mul(a, b)
  1107  		case token.QUO:
  1108  			c.Quo(a, b)
  1109  		default:
  1110  			goto Error
  1111  		}
  1112  		return makeRat(c)
  1113  
  1114  	case floatVal:
  1115  		a := x.val
  1116  		b := y.(floatVal).val
  1117  		c := newFloat()
  1118  		switch op {
  1119  		case token.ADD:
  1120  			c.Add(a, b)
  1121  		case token.SUB:
  1122  			c.Sub(a, b)
  1123  		case token.MUL:
  1124  			c.Mul(a, b)
  1125  		case token.QUO:
  1126  			c.Quo(a, b)
  1127  		default:
  1128  			goto Error
  1129  		}
  1130  		return makeFloat(c)
  1131  
  1132  	case complexVal:
  1133  		y := y.(complexVal)
  1134  		a, b := x.re, x.im
  1135  		c, d := y.re, y.im
  1136  		var re, im Value
  1137  		switch op {
  1138  		case token.ADD:
  1139  			// (a+c) + i(b+d)
  1140  			re = add(a, c)
  1141  			im = add(b, d)
  1142  		case token.SUB:
  1143  			// (a-c) + i(b-d)
  1144  			re = sub(a, c)
  1145  			im = sub(b, d)
  1146  		case token.MUL:
  1147  			// (ac-bd) + i(bc+ad)
  1148  			ac := mul(a, c)
  1149  			bd := mul(b, d)
  1150  			bc := mul(b, c)
  1151  			ad := mul(a, d)
  1152  			re = sub(ac, bd)
  1153  			im = add(bc, ad)
  1154  		case token.QUO:
  1155  			// (ac+bd)/s + i(bc-ad)/s, with s = cc + dd
  1156  			ac := mul(a, c)
  1157  			bd := mul(b, d)
  1158  			bc := mul(b, c)
  1159  			ad := mul(a, d)
  1160  			cc := mul(c, c)
  1161  			dd := mul(d, d)
  1162  			s := add(cc, dd)
  1163  			re = add(ac, bd)
  1164  			re = quo(re, s)
  1165  			im = sub(bc, ad)
  1166  			im = quo(im, s)
  1167  		default:
  1168  			goto Error
  1169  		}
  1170  		return makeComplex(re, im)
  1171  
  1172  	case *stringVal:
  1173  		if op == token.ADD {
  1174  			return &stringVal{l: x, r: y.(*stringVal)}
  1175  		}
  1176  	}
  1177  
  1178  Error:
  1179  	panic(fmt.Sprintf("invalid binary operation %v %s %v", x_, op, y_))
  1180  }
  1181  
  1182  func add(x, y Value) Value { return BinaryOp(x, token.ADD, y) }
  1183  func sub(x, y Value) Value { return BinaryOp(x, token.SUB, y) }
  1184  func mul(x, y Value) Value { return BinaryOp(x, token.MUL, y) }
  1185  func quo(x, y Value) Value { return BinaryOp(x, token.QUO, y) }
  1186  
  1187  // Shift returns the result of the shift expression x op s
  1188  // with op == token.SHL or token.SHR (<< or >>). x must be
  1189  // an Int or an Unknown. If x is Unknown, the result is x.
  1190  //
  1191  func Shift(x Value, op token.Token, s uint) Value {
  1192  	switch x := x.(type) {
  1193  	case unknownVal:
  1194  		return x
  1195  
  1196  	case int64Val:
  1197  		if s == 0 {
  1198  			return x
  1199  		}
  1200  		switch op {
  1201  		case token.SHL:
  1202  			z := i64toi(x).val
  1203  			return makeInt(z.Lsh(z, s))
  1204  		case token.SHR:
  1205  			return x >> s
  1206  		}
  1207  
  1208  	case intVal:
  1209  		if s == 0 {
  1210  			return x
  1211  		}
  1212  		z := newInt()
  1213  		switch op {
  1214  		case token.SHL:
  1215  			return makeInt(z.Lsh(x.val, s))
  1216  		case token.SHR:
  1217  			return makeInt(z.Rsh(x.val, s))
  1218  		}
  1219  	}
  1220  
  1221  	panic(fmt.Sprintf("invalid shift %v %s %d", x, op, s))
  1222  }
  1223  
  1224  func cmpZero(x int, op token.Token) bool {
  1225  	switch op {
  1226  	case token.EQL:
  1227  		return x == 0
  1228  	case token.NEQ:
  1229  		return x != 0
  1230  	case token.LSS:
  1231  		return x < 0
  1232  	case token.LEQ:
  1233  		return x <= 0
  1234  	case token.GTR:
  1235  		return x > 0
  1236  	case token.GEQ:
  1237  		return x >= 0
  1238  	}
  1239  	panic(fmt.Sprintf("invalid comparison %v %s 0", x, op))
  1240  }
  1241  
  1242  // Compare returns the result of the comparison x op y.
  1243  // The comparison must be defined for the operands.
  1244  // If one of the operands is Unknown, the result is
  1245  // false.
  1246  //
  1247  func Compare(x_ Value, op token.Token, y_ Value) bool {
  1248  	x, y := match(x_, y_)
  1249  
  1250  	switch x := x.(type) {
  1251  	case unknownVal:
  1252  		return false
  1253  
  1254  	case boolVal:
  1255  		y := y.(boolVal)
  1256  		switch op {
  1257  		case token.EQL:
  1258  			return x == y
  1259  		case token.NEQ:
  1260  			return x != y
  1261  		}
  1262  
  1263  	case int64Val:
  1264  		y := y.(int64Val)
  1265  		switch op {
  1266  		case token.EQL:
  1267  			return x == y
  1268  		case token.NEQ:
  1269  			return x != y
  1270  		case token.LSS:
  1271  			return x < y
  1272  		case token.LEQ:
  1273  			return x <= y
  1274  		case token.GTR:
  1275  			return x > y
  1276  		case token.GEQ:
  1277  			return x >= y
  1278  		}
  1279  
  1280  	case intVal:
  1281  		return cmpZero(x.val.Cmp(y.(intVal).val), op)
  1282  
  1283  	case ratVal:
  1284  		return cmpZero(x.val.Cmp(y.(ratVal).val), op)
  1285  
  1286  	case floatVal:
  1287  		return cmpZero(x.val.Cmp(y.(floatVal).val), op)
  1288  
  1289  	case complexVal:
  1290  		y := y.(complexVal)
  1291  		re := Compare(x.re, token.EQL, y.re)
  1292  		im := Compare(x.im, token.EQL, y.im)
  1293  		switch op {
  1294  		case token.EQL:
  1295  			return re && im
  1296  		case token.NEQ:
  1297  			return !re || !im
  1298  		}
  1299  
  1300  	case *stringVal:
  1301  		xs := x.string()
  1302  		ys := y.(*stringVal).string()
  1303  		switch op {
  1304  		case token.EQL:
  1305  			return xs == ys
  1306  		case token.NEQ:
  1307  			return xs != ys
  1308  		case token.LSS:
  1309  			return xs < ys
  1310  		case token.LEQ:
  1311  			return xs <= ys
  1312  		case token.GTR:
  1313  			return xs > ys
  1314  		case token.GEQ:
  1315  			return xs >= ys
  1316  		}
  1317  	}
  1318  
  1319  	panic(fmt.Sprintf("invalid comparison %v %s %v", x_, op, y_))
  1320  }
  1321  

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