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 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  			if r, ok := newRat().SetString(lit); ok {
   319  				return ratVal{r}
   320  			}
   321  		}
   322  		// otherwise use floats
   323  		return makeFloat(f)
   324  	}
   325  	return nil
   326  }
   327  
   328  // smallRat reports whether x would lead to "reasonably"-sized fraction
   329  // if converted to a *big.Rat.
   330  func smallRat(x *big.Float) bool {
   331  	if !x.IsInf() {
   332  		e := x.MantExp(nil)
   333  		return -maxExp < e && e < maxExp
   334  	}
   335  	return false
   336  }
   337  
   338  // ----------------------------------------------------------------------------
   339  // Factories
   340  
   341  // MakeUnknown returns the Unknown value.
   342  func MakeUnknown() Value { return unknownVal{} }
   343  
   344  // MakeBool returns the Bool value for b.
   345  func MakeBool(b bool) Value { return boolVal(b) }
   346  
   347  // MakeString returns the String value for s.
   348  func MakeString(s string) Value { return &stringVal{s: s} }
   349  
   350  // MakeInt64 returns the Int value for x.
   351  func MakeInt64(x int64) Value { return int64Val(x) }
   352  
   353  // MakeUint64 returns the Int value for x.
   354  func MakeUint64(x uint64) Value {
   355  	if x < 1<<63 {
   356  		return int64Val(int64(x))
   357  	}
   358  	return intVal{newInt().SetUint64(x)}
   359  }
   360  
   361  // MakeFloat64 returns the Float value for x.
   362  // If x is not finite, the result is an Unknown.
   363  func MakeFloat64(x float64) Value {
   364  	if math.IsInf(x, 0) || math.IsNaN(x) {
   365  		return unknownVal{}
   366  	}
   367  	// convert -0 to 0
   368  	if x == 0 {
   369  		return int64Val(0)
   370  	}
   371  	return ratVal{newRat().SetFloat64(x)}
   372  }
   373  
   374  // MakeFromLiteral returns the corresponding integer, floating-point,
   375  // imaginary, character, or string value for a Go literal string. The
   376  // tok value must be one of token.INT, token.FLOAT, token.IMAG,
   377  // token.CHAR, or token.STRING. The final argument must be zero.
   378  // If the literal string syntax is invalid, the result is an Unknown.
   379  func MakeFromLiteral(lit string, tok token.Token, zero uint) Value {
   380  	if zero != 0 {
   381  		panic("MakeFromLiteral called with non-zero last argument")
   382  	}
   383  
   384  	// TODO(gri) Remove stripSep and, for token.INT, 0o-octal handling
   385  	//           below once strconv and math/big can handle separators
   386  	//           and 0o-octals.
   387  
   388  	switch tok {
   389  	case token.INT:
   390  		// TODO(gri) remove 0o-special case once strconv and math/big can handle 0o-octals
   391  		lit = stripSep(lit)
   392  		if len(lit) >= 2 && lit[0] == '0' && (lit[1] == 'o' || lit[1] == 'O') {
   393  			lit = "0" + lit[2:]
   394  		}
   395  		if x, err := strconv.ParseInt(lit, 0, 64); err == nil {
   396  			return int64Val(x)
   397  		}
   398  		if x, ok := newInt().SetString(lit, 0); ok {
   399  			return intVal{x}
   400  		}
   401  
   402  	case token.FLOAT:
   403  		lit = stripSep(lit)
   404  		if x := makeFloatFromLiteral(lit); x != nil {
   405  			return x
   406  		}
   407  
   408  	case token.IMAG:
   409  		lit = stripSep(lit)
   410  		if n := len(lit); n > 0 && lit[n-1] == 'i' {
   411  			if im := makeFloatFromLiteral(lit[:n-1]); im != nil {
   412  				return makeComplex(int64Val(0), im)
   413  			}
   414  		}
   415  
   416  	case token.CHAR:
   417  		if n := len(lit); n >= 2 {
   418  			if code, _, _, err := strconv.UnquoteChar(lit[1:n-1], '\''); err == nil {
   419  				return MakeInt64(int64(code))
   420  			}
   421  		}
   422  
   423  	case token.STRING:
   424  		if s, err := strconv.Unquote(lit); err == nil {
   425  			return MakeString(s)
   426  		}
   427  
   428  	default:
   429  		panic(fmt.Sprintf("%v is not a valid token", tok))
   430  	}
   431  
   432  	return unknownVal{}
   433  }
   434  
   435  func stripSep(s string) string {
   436  	// avoid making a copy if there are no separators (common case)
   437  	i := 0
   438  	for i < len(s) && s[i] != '_' {
   439  		i++
   440  	}
   441  	if i == len(s) {
   442  		return s
   443  	}
   444  
   445  	// make a copy of s without separators
   446  	var buf []byte
   447  	for i := 0; i < len(s); i++ {
   448  		if c := s[i]; c != '_' {
   449  			buf = append(buf, c)
   450  		}
   451  	}
   452  	return string(buf)
   453  }
   454  
   455  // ----------------------------------------------------------------------------
   456  // Accessors
   457  //
   458  // For unknown arguments the result is the zero value for the respective
   459  // accessor type, except for Sign, where the result is 1.
   460  
   461  // BoolVal returns the Go boolean value of x, which must be a Bool or an Unknown.
   462  // If x is Unknown, the result is false.
   463  func BoolVal(x Value) bool {
   464  	switch x := x.(type) {
   465  	case boolVal:
   466  		return bool(x)
   467  	case unknownVal:
   468  		return false
   469  	default:
   470  		panic(fmt.Sprintf("%v not a Bool", x))
   471  	}
   472  }
   473  
   474  // StringVal returns the Go string value of x, which must be a String or an Unknown.
   475  // If x is Unknown, the result is "".
   476  func StringVal(x Value) string {
   477  	switch x := x.(type) {
   478  	case *stringVal:
   479  		return x.string()
   480  	case unknownVal:
   481  		return ""
   482  	default:
   483  		panic(fmt.Sprintf("%v not a String", x))
   484  	}
   485  }
   486  
   487  // Int64Val returns the Go int64 value of x and whether the result is exact;
   488  // x must be an Int or an Unknown. If the result is not exact, its value is undefined.
   489  // If x is Unknown, the result is (0, false).
   490  func Int64Val(x Value) (int64, bool) {
   491  	switch x := x.(type) {
   492  	case int64Val:
   493  		return int64(x), true
   494  	case intVal:
   495  		return x.val.Int64(), false // not an int64Val and thus not exact
   496  	case unknownVal:
   497  		return 0, false
   498  	default:
   499  		panic(fmt.Sprintf("%v not an Int", x))
   500  	}
   501  }
   502  
   503  // Uint64Val returns the Go uint64 value of x and whether the result is exact;
   504  // x must be an Int or an Unknown. If the result is not exact, its value is undefined.
   505  // If x is Unknown, the result is (0, false).
   506  func Uint64Val(x Value) (uint64, bool) {
   507  	switch x := x.(type) {
   508  	case int64Val:
   509  		return uint64(x), x >= 0
   510  	case intVal:
   511  		return x.val.Uint64(), x.val.IsUint64()
   512  	case unknownVal:
   513  		return 0, false
   514  	default:
   515  		panic(fmt.Sprintf("%v not an Int", x))
   516  	}
   517  }
   518  
   519  // Float32Val is like Float64Val but for float32 instead of float64.
   520  func Float32Val(x Value) (float32, bool) {
   521  	switch x := x.(type) {
   522  	case int64Val:
   523  		f := float32(x)
   524  		return f, int64Val(f) == x
   525  	case intVal:
   526  		f, acc := newFloat().SetInt(x.val).Float32()
   527  		return f, acc == big.Exact
   528  	case ratVal:
   529  		return x.val.Float32()
   530  	case floatVal:
   531  		f, acc := x.val.Float32()
   532  		return f, acc == big.Exact
   533  	case unknownVal:
   534  		return 0, false
   535  	default:
   536  		panic(fmt.Sprintf("%v not a Float", x))
   537  	}
   538  }
   539  
   540  // Float64Val returns the nearest Go float64 value of x and whether the result is exact;
   541  // x must be numeric or an Unknown, but not Complex. For values too small (too close to 0)
   542  // to represent as float64, Float64Val silently underflows to 0. The result sign always
   543  // matches the sign of x, even for 0.
   544  // If x is Unknown, the result is (0, false).
   545  func Float64Val(x Value) (float64, bool) {
   546  	switch x := x.(type) {
   547  	case int64Val:
   548  		f := float64(int64(x))
   549  		return f, int64Val(f) == x
   550  	case intVal:
   551  		f, acc := newFloat().SetInt(x.val).Float64()
   552  		return f, acc == big.Exact
   553  	case ratVal:
   554  		return x.val.Float64()
   555  	case floatVal:
   556  		f, acc := x.val.Float64()
   557  		return f, acc == big.Exact
   558  	case unknownVal:
   559  		return 0, false
   560  	default:
   561  		panic(fmt.Sprintf("%v not a Float", x))
   562  	}
   563  }
   564  
   565  // Val returns the underlying value for a given constant. Since it returns an
   566  // interface, it is up to the caller to type assert the result to the expected
   567  // type. The possible dynamic return types are:
   568  //
   569  //    x Kind             type of result
   570  //    -----------------------------------------
   571  //    Bool               bool
   572  //    String             string
   573  //    Int                int64 or *big.Int
   574  //    Float              *big.Float or *big.Rat
   575  //    everything else    nil
   576  //
   577  func Val(x Value) interface{} {
   578  	switch x := x.(type) {
   579  	case boolVal:
   580  		return bool(x)
   581  	case *stringVal:
   582  		return x.string()
   583  	case int64Val:
   584  		return int64(x)
   585  	case intVal:
   586  		return x.val
   587  	case ratVal:
   588  		return x.val
   589  	case floatVal:
   590  		return x.val
   591  	default:
   592  		return nil
   593  	}
   594  }
   595  
   596  // Make returns the Value for x.
   597  //
   598  //    type of x        result Kind
   599  //    ----------------------------
   600  //    bool             Bool
   601  //    string           String
   602  //    int64            Int
   603  //    *big.Int         Int
   604  //    *big.Float       Float
   605  //    *big.Rat         Float
   606  //    anything else    Unknown
   607  //
   608  func Make(x interface{}) Value {
   609  	switch x := x.(type) {
   610  	case bool:
   611  		return boolVal(x)
   612  	case string:
   613  		return &stringVal{s: x}
   614  	case int64:
   615  		return int64Val(x)
   616  	case *big.Int:
   617  		return intVal{x}
   618  	case *big.Rat:
   619  		return ratVal{x}
   620  	case *big.Float:
   621  		return floatVal{x}
   622  	default:
   623  		return unknownVal{}
   624  	}
   625  }
   626  
   627  // BitLen returns the number of bits required to represent
   628  // the absolute value x in binary representation; x must be an Int or an Unknown.
   629  // If x is Unknown, the result is 0.
   630  func BitLen(x Value) int {
   631  	switch x := x.(type) {
   632  	case int64Val:
   633  		return i64toi(x).val.BitLen()
   634  	case intVal:
   635  		return x.val.BitLen()
   636  	case unknownVal:
   637  		return 0
   638  	default:
   639  		panic(fmt.Sprintf("%v not an Int", x))
   640  	}
   641  }
   642  
   643  // Sign returns -1, 0, or 1 depending on whether x < 0, x == 0, or x > 0;
   644  // x must be numeric or Unknown. For complex values x, the sign is 0 if x == 0,
   645  // otherwise it is != 0. If x is Unknown, the result is 1.
   646  func Sign(x Value) int {
   647  	switch x := x.(type) {
   648  	case int64Val:
   649  		switch {
   650  		case x < 0:
   651  			return -1
   652  		case x > 0:
   653  			return 1
   654  		}
   655  		return 0
   656  	case intVal:
   657  		return x.val.Sign()
   658  	case ratVal:
   659  		return x.val.Sign()
   660  	case floatVal:
   661  		return x.val.Sign()
   662  	case complexVal:
   663  		return Sign(x.re) | Sign(x.im)
   664  	case unknownVal:
   665  		return 1 // avoid spurious division by zero errors
   666  	default:
   667  		panic(fmt.Sprintf("%v not numeric", x))
   668  	}
   669  }
   670  
   671  // ----------------------------------------------------------------------------
   672  // Support for assembling/disassembling numeric values
   673  
   674  const (
   675  	// Compute the size of a Word in bytes.
   676  	_m       = ^big.Word(0)
   677  	_log     = _m>>8&1 + _m>>16&1 + _m>>32&1
   678  	wordSize = 1 << _log
   679  )
   680  
   681  // Bytes returns the bytes for the absolute value of x in little-
   682  // endian binary representation; x must be an Int.
   683  func Bytes(x Value) []byte {
   684  	var t intVal
   685  	switch x := x.(type) {
   686  	case int64Val:
   687  		t = i64toi(x)
   688  	case intVal:
   689  		t = x
   690  	default:
   691  		panic(fmt.Sprintf("%v not an Int", x))
   692  	}
   693  
   694  	words := t.val.Bits()
   695  	bytes := make([]byte, len(words)*wordSize)
   696  
   697  	i := 0
   698  	for _, w := range words {
   699  		for j := 0; j < wordSize; j++ {
   700  			bytes[i] = byte(w)
   701  			w >>= 8
   702  			i++
   703  		}
   704  	}
   705  	// remove leading 0's
   706  	for i > 0 && bytes[i-1] == 0 {
   707  		i--
   708  	}
   709  
   710  	return bytes[:i]
   711  }
   712  
   713  // MakeFromBytes returns the Int value given the bytes of its little-endian
   714  // binary representation. An empty byte slice argument represents 0.
   715  func MakeFromBytes(bytes []byte) Value {
   716  	words := make([]big.Word, (len(bytes)+(wordSize-1))/wordSize)
   717  
   718  	i := 0
   719  	var w big.Word
   720  	var s uint
   721  	for _, b := range bytes {
   722  		w |= big.Word(b) << s
   723  		if s += 8; s == wordSize*8 {
   724  			words[i] = w
   725  			i++
   726  			w = 0
   727  			s = 0
   728  		}
   729  	}
   730  	// store last word
   731  	if i < len(words) {
   732  		words[i] = w
   733  		i++
   734  	}
   735  	// remove leading 0's
   736  	for i > 0 && words[i-1] == 0 {
   737  		i--
   738  	}
   739  
   740  	return makeInt(newInt().SetBits(words[:i]))
   741  }
   742  
   743  // Num returns the numerator of x; x must be Int, Float, or Unknown.
   744  // If x is Unknown, or if it is too large or small to represent as a
   745  // fraction, the result is Unknown. Otherwise the result is an Int
   746  // with the same sign as x.
   747  func Num(x Value) Value {
   748  	switch x := x.(type) {
   749  	case int64Val, intVal:
   750  		return x
   751  	case ratVal:
   752  		return makeInt(x.val.Num())
   753  	case floatVal:
   754  		if smallRat(x.val) {
   755  			r, _ := x.val.Rat(nil)
   756  			return makeInt(r.Num())
   757  		}
   758  	case unknownVal:
   759  		break
   760  	default:
   761  		panic(fmt.Sprintf("%v not Int or Float", x))
   762  	}
   763  	return unknownVal{}
   764  }
   765  
   766  // Denom returns the denominator of x; x must be Int, Float, or Unknown.
   767  // If x is Unknown, or if it is too large or small to represent as a
   768  // fraction, the result is Unknown. Otherwise the result is an Int >= 1.
   769  func Denom(x Value) Value {
   770  	switch x := x.(type) {
   771  	case int64Val, intVal:
   772  		return int64Val(1)
   773  	case ratVal:
   774  		return makeInt(x.val.Denom())
   775  	case floatVal:
   776  		if smallRat(x.val) {
   777  			r, _ := x.val.Rat(nil)
   778  			return makeInt(r.Denom())
   779  		}
   780  	case unknownVal:
   781  		break
   782  	default:
   783  		panic(fmt.Sprintf("%v not Int or Float", x))
   784  	}
   785  	return unknownVal{}
   786  }
   787  
   788  // MakeImag returns the Complex value x*i;
   789  // x must be Int, Float, or Unknown.
   790  // If x is Unknown, the result is Unknown.
   791  func MakeImag(x Value) Value {
   792  	switch x.(type) {
   793  	case unknownVal:
   794  		return x
   795  	case int64Val, intVal, ratVal, floatVal:
   796  		return makeComplex(int64Val(0), x)
   797  	default:
   798  		panic(fmt.Sprintf("%v not Int or Float", x))
   799  	}
   800  }
   801  
   802  // Real returns the real part of x, which must be a numeric or unknown value.
   803  // If x is Unknown, the result is Unknown.
   804  func Real(x Value) Value {
   805  	switch x := x.(type) {
   806  	case unknownVal, int64Val, intVal, ratVal, floatVal:
   807  		return x
   808  	case complexVal:
   809  		return x.re
   810  	default:
   811  		panic(fmt.Sprintf("%v not numeric", x))
   812  	}
   813  }
   814  
   815  // Imag returns the imaginary part of x, which must be a numeric or unknown value.
   816  // If x is Unknown, the result is Unknown.
   817  func Imag(x Value) Value {
   818  	switch x := x.(type) {
   819  	case unknownVal:
   820  		return x
   821  	case int64Val, intVal, ratVal, floatVal:
   822  		return int64Val(0)
   823  	case complexVal:
   824  		return x.im
   825  	default:
   826  		panic(fmt.Sprintf("%v not numeric", x))
   827  	}
   828  }
   829  
   830  // ----------------------------------------------------------------------------
   831  // Numeric conversions
   832  
   833  // ToInt converts x to an Int value if x is representable as an Int.
   834  // Otherwise it returns an Unknown.
   835  func ToInt(x Value) Value {
   836  	switch x := x.(type) {
   837  	case int64Val, intVal:
   838  		return x
   839  
   840  	case ratVal:
   841  		if x.val.IsInt() {
   842  			return makeInt(x.val.Num())
   843  		}
   844  
   845  	case floatVal:
   846  		// avoid creation of huge integers
   847  		// (Existing tests require permitting exponents of at least 1024;
   848  		// allow any value that would also be permissible as a fraction.)
   849  		if smallRat(x.val) {
   850  			i := newInt()
   851  			if _, acc := x.val.Int(i); acc == big.Exact {
   852  				return makeInt(i)
   853  			}
   854  
   855  			// If we can get an integer by rounding up or down,
   856  			// assume x is not an integer because of rounding
   857  			// errors in prior computations.
   858  
   859  			const delta = 4 // a small number of bits > 0
   860  			var t big.Float
   861  			t.SetPrec(prec - delta)
   862  
   863  			// try rounding down a little
   864  			t.SetMode(big.ToZero)
   865  			t.Set(x.val)
   866  			if _, acc := t.Int(i); acc == big.Exact {
   867  				return makeInt(i)
   868  			}
   869  
   870  			// try rounding up a little
   871  			t.SetMode(big.AwayFromZero)
   872  			t.Set(x.val)
   873  			if _, acc := t.Int(i); acc == big.Exact {
   874  				return makeInt(i)
   875  			}
   876  		}
   877  
   878  	case complexVal:
   879  		if re := ToFloat(x); re.Kind() == Float {
   880  			return ToInt(re)
   881  		}
   882  	}
   883  
   884  	return unknownVal{}
   885  }
   886  
   887  // ToFloat converts x to a Float value if x is representable as a Float.
   888  // Otherwise it returns an Unknown.
   889  func ToFloat(x Value) Value {
   890  	switch x := x.(type) {
   891  	case int64Val:
   892  		return i64tof(x)
   893  	case intVal:
   894  		return itof(x)
   895  	case ratVal, floatVal:
   896  		return x
   897  	case complexVal:
   898  		if im := ToInt(x.im); im.Kind() == Int && Sign(im) == 0 {
   899  			// imaginary component is 0
   900  			return ToFloat(x.re)
   901  		}
   902  	}
   903  	return unknownVal{}
   904  }
   905  
   906  // ToComplex converts x to a Complex value if x is representable as a Complex.
   907  // Otherwise it returns an Unknown.
   908  func ToComplex(x Value) Value {
   909  	switch x := x.(type) {
   910  	case int64Val:
   911  		return vtoc(i64tof(x))
   912  	case intVal:
   913  		return vtoc(itof(x))
   914  	case ratVal:
   915  		return vtoc(x)
   916  	case floatVal:
   917  		return vtoc(x)
   918  	case complexVal:
   919  		return x
   920  	}
   921  	return unknownVal{}
   922  }
   923  
   924  // ----------------------------------------------------------------------------
   925  // Operations
   926  
   927  // is32bit reports whether x can be represented using 32 bits.
   928  func is32bit(x int64) bool {
   929  	const s = 32
   930  	return -1<<(s-1) <= x && x <= 1<<(s-1)-1
   931  }
   932  
   933  // is63bit reports whether x can be represented using 63 bits.
   934  func is63bit(x int64) bool {
   935  	const s = 63
   936  	return -1<<(s-1) <= x && x <= 1<<(s-1)-1
   937  }
   938  
   939  // UnaryOp returns the result of the unary expression op y.
   940  // The operation must be defined for the operand.
   941  // If prec > 0 it specifies the ^ (xor) result size in bits.
   942  // If y is Unknown, the result is Unknown.
   943  //
   944  func UnaryOp(op token.Token, y Value, prec uint) Value {
   945  	switch op {
   946  	case token.ADD:
   947  		switch y.(type) {
   948  		case unknownVal, int64Val, intVal, ratVal, floatVal, complexVal:
   949  			return y
   950  		}
   951  
   952  	case token.SUB:
   953  		switch y := y.(type) {
   954  		case unknownVal:
   955  			return y
   956  		case int64Val:
   957  			if z := -y; z != y {
   958  				return z // no overflow
   959  			}
   960  			return makeInt(newInt().Neg(big.NewInt(int64(y))))
   961  		case intVal:
   962  			return makeInt(newInt().Neg(y.val))
   963  		case ratVal:
   964  			return makeRat(newRat().Neg(y.val))
   965  		case floatVal:
   966  			return makeFloat(newFloat().Neg(y.val))
   967  		case complexVal:
   968  			re := UnaryOp(token.SUB, y.re, 0)
   969  			im := UnaryOp(token.SUB, y.im, 0)
   970  			return makeComplex(re, im)
   971  		}
   972  
   973  	case token.XOR:
   974  		z := newInt()
   975  		switch y := y.(type) {
   976  		case unknownVal:
   977  			return y
   978  		case int64Val:
   979  			z.Not(big.NewInt(int64(y)))
   980  		case intVal:
   981  			z.Not(y.val)
   982  		default:
   983  			goto Error
   984  		}
   985  		// For unsigned types, the result will be negative and
   986  		// thus "too large": We must limit the result precision
   987  		// to the type's precision.
   988  		if prec > 0 {
   989  			z.AndNot(z, newInt().Lsh(big.NewInt(-1), prec)) // z &^= (-1)<<prec
   990  		}
   991  		return makeInt(z)
   992  
   993  	case token.NOT:
   994  		switch y := y.(type) {
   995  		case unknownVal:
   996  			return y
   997  		case boolVal:
   998  			return !y
   999  		}
  1000  	}
  1001  
  1002  Error:
  1003  	panic(fmt.Sprintf("invalid unary operation %s%v", op, y))
  1004  }
  1005  
  1006  func ord(x Value) int {
  1007  	switch x.(type) {
  1008  	default:
  1009  		// force invalid value into "x position" in match
  1010  		// (don't panic here so that callers can provide a better error message)
  1011  		return -1
  1012  	case unknownVal:
  1013  		return 0
  1014  	case boolVal, *stringVal:
  1015  		return 1
  1016  	case int64Val:
  1017  		return 2
  1018  	case intVal:
  1019  		return 3
  1020  	case ratVal:
  1021  		return 4
  1022  	case floatVal:
  1023  		return 5
  1024  	case complexVal:
  1025  		return 6
  1026  	}
  1027  }
  1028  
  1029  // match returns the matching representation (same type) with the
  1030  // smallest complexity for two values x and y. If one of them is
  1031  // numeric, both of them must be numeric. If one of them is Unknown
  1032  // or invalid (say, nil) both results are that value.
  1033  //
  1034  func match(x, y Value) (_, _ Value) {
  1035  	if ord(x) > ord(y) {
  1036  		y, x = match(y, x)
  1037  		return x, y
  1038  	}
  1039  	// ord(x) <= ord(y)
  1040  
  1041  	switch x := x.(type) {
  1042  	case boolVal, *stringVal, complexVal:
  1043  		return x, y
  1044  
  1045  	case int64Val:
  1046  		switch y := y.(type) {
  1047  		case int64Val:
  1048  			return x, y
  1049  		case intVal:
  1050  			return i64toi(x), y
  1051  		case ratVal:
  1052  			return i64tor(x), y
  1053  		case floatVal:
  1054  			return i64tof(x), y
  1055  		case complexVal:
  1056  			return vtoc(x), y
  1057  		}
  1058  
  1059  	case intVal:
  1060  		switch y := y.(type) {
  1061  		case intVal:
  1062  			return x, y
  1063  		case ratVal:
  1064  			return itor(x), y
  1065  		case floatVal:
  1066  			return itof(x), y
  1067  		case complexVal:
  1068  			return vtoc(x), y
  1069  		}
  1070  
  1071  	case ratVal:
  1072  		switch y := y.(type) {
  1073  		case ratVal:
  1074  			return x, y
  1075  		case floatVal:
  1076  			return rtof(x), y
  1077  		case complexVal:
  1078  			return vtoc(x), y
  1079  		}
  1080  
  1081  	case floatVal:
  1082  		switch y := y.(type) {
  1083  		case floatVal:
  1084  			return x, y
  1085  		case complexVal:
  1086  			return vtoc(x), y
  1087  		}
  1088  	}
  1089  
  1090  	// force unknown and invalid values into "x position" in callers of match
  1091  	// (don't panic here so that callers can provide a better error message)
  1092  	return x, x
  1093  }
  1094  
  1095  // BinaryOp returns the result of the binary expression x op y.
  1096  // The operation must be defined for the operands. If one of the
  1097  // operands is Unknown, the result is Unknown.
  1098  // BinaryOp doesn't handle comparisons or shifts; use Compare
  1099  // or Shift instead.
  1100  //
  1101  // To force integer division of Int operands, use op == token.QUO_ASSIGN
  1102  // instead of token.QUO; the result is guaranteed to be Int in this case.
  1103  // Division by zero leads to a run-time panic.
  1104  //
  1105  func BinaryOp(x_ Value, op token.Token, y_ Value) Value {
  1106  	x, y := match(x_, y_)
  1107  
  1108  	switch x := x.(type) {
  1109  	case unknownVal:
  1110  		return x
  1111  
  1112  	case boolVal:
  1113  		y := y.(boolVal)
  1114  		switch op {
  1115  		case token.LAND:
  1116  			return x && y
  1117  		case token.LOR:
  1118  			return x || y
  1119  		}
  1120  
  1121  	case int64Val:
  1122  		a := int64(x)
  1123  		b := int64(y.(int64Val))
  1124  		var c int64
  1125  		switch op {
  1126  		case token.ADD:
  1127  			if !is63bit(a) || !is63bit(b) {
  1128  				return makeInt(newInt().Add(big.NewInt(a), big.NewInt(b)))
  1129  			}
  1130  			c = a + b
  1131  		case token.SUB:
  1132  			if !is63bit(a) || !is63bit(b) {
  1133  				return makeInt(newInt().Sub(big.NewInt(a), big.NewInt(b)))
  1134  			}
  1135  			c = a - b
  1136  		case token.MUL:
  1137  			if !is32bit(a) || !is32bit(b) {
  1138  				return makeInt(newInt().Mul(big.NewInt(a), big.NewInt(b)))
  1139  			}
  1140  			c = a * b
  1141  		case token.QUO:
  1142  			return makeRat(big.NewRat(a, b))
  1143  		case token.QUO_ASSIGN: // force integer division
  1144  			c = a / b
  1145  		case token.REM:
  1146  			c = a % b
  1147  		case token.AND:
  1148  			c = a & b
  1149  		case token.OR:
  1150  			c = a | b
  1151  		case token.XOR:
  1152  			c = a ^ b
  1153  		case token.AND_NOT:
  1154  			c = a &^ b
  1155  		default:
  1156  			goto Error
  1157  		}
  1158  		return int64Val(c)
  1159  
  1160  	case intVal:
  1161  		a := x.val
  1162  		b := y.(intVal).val
  1163  		c := newInt()
  1164  		switch op {
  1165  		case token.ADD:
  1166  			c.Add(a, b)
  1167  		case token.SUB:
  1168  			c.Sub(a, b)
  1169  		case token.MUL:
  1170  			c.Mul(a, b)
  1171  		case token.QUO:
  1172  			return makeRat(newRat().SetFrac(a, b))
  1173  		case token.QUO_ASSIGN: // force integer division
  1174  			c.Quo(a, b)
  1175  		case token.REM:
  1176  			c.Rem(a, b)
  1177  		case token.AND:
  1178  			c.And(a, b)
  1179  		case token.OR:
  1180  			c.Or(a, b)
  1181  		case token.XOR:
  1182  			c.Xor(a, b)
  1183  		case token.AND_NOT:
  1184  			c.AndNot(a, b)
  1185  		default:
  1186  			goto Error
  1187  		}
  1188  		return makeInt(c)
  1189  
  1190  	case ratVal:
  1191  		a := x.val
  1192  		b := y.(ratVal).val
  1193  		c := newRat()
  1194  		switch op {
  1195  		case token.ADD:
  1196  			c.Add(a, b)
  1197  		case token.SUB:
  1198  			c.Sub(a, b)
  1199  		case token.MUL:
  1200  			c.Mul(a, b)
  1201  		case token.QUO:
  1202  			c.Quo(a, b)
  1203  		default:
  1204  			goto Error
  1205  		}
  1206  		return makeRat(c)
  1207  
  1208  	case floatVal:
  1209  		a := x.val
  1210  		b := y.(floatVal).val
  1211  		c := newFloat()
  1212  		switch op {
  1213  		case token.ADD:
  1214  			c.Add(a, b)
  1215  		case token.SUB:
  1216  			c.Sub(a, b)
  1217  		case token.MUL:
  1218  			c.Mul(a, b)
  1219  		case token.QUO:
  1220  			c.Quo(a, b)
  1221  		default:
  1222  			goto Error
  1223  		}
  1224  		return makeFloat(c)
  1225  
  1226  	case complexVal:
  1227  		y := y.(complexVal)
  1228  		a, b := x.re, x.im
  1229  		c, d := y.re, y.im
  1230  		var re, im Value
  1231  		switch op {
  1232  		case token.ADD:
  1233  			// (a+c) + i(b+d)
  1234  			re = add(a, c)
  1235  			im = add(b, d)
  1236  		case token.SUB:
  1237  			// (a-c) + i(b-d)
  1238  			re = sub(a, c)
  1239  			im = sub(b, d)
  1240  		case token.MUL:
  1241  			// (ac-bd) + i(bc+ad)
  1242  			ac := mul(a, c)
  1243  			bd := mul(b, d)
  1244  			bc := mul(b, c)
  1245  			ad := mul(a, d)
  1246  			re = sub(ac, bd)
  1247  			im = add(bc, ad)
  1248  		case token.QUO:
  1249  			// (ac+bd)/s + i(bc-ad)/s, with s = cc + dd
  1250  			ac := mul(a, c)
  1251  			bd := mul(b, d)
  1252  			bc := mul(b, c)
  1253  			ad := mul(a, d)
  1254  			cc := mul(c, c)
  1255  			dd := mul(d, d)
  1256  			s := add(cc, dd)
  1257  			re = add(ac, bd)
  1258  			re = quo(re, s)
  1259  			im = sub(bc, ad)
  1260  			im = quo(im, s)
  1261  		default:
  1262  			goto Error
  1263  		}
  1264  		return makeComplex(re, im)
  1265  
  1266  	case *stringVal:
  1267  		if op == token.ADD {
  1268  			return &stringVal{l: x, r: y.(*stringVal)}
  1269  		}
  1270  	}
  1271  
  1272  Error:
  1273  	panic(fmt.Sprintf("invalid binary operation %v %s %v", x_, op, y_))
  1274  }
  1275  
  1276  func add(x, y Value) Value { return BinaryOp(x, token.ADD, y) }
  1277  func sub(x, y Value) Value { return BinaryOp(x, token.SUB, y) }
  1278  func mul(x, y Value) Value { return BinaryOp(x, token.MUL, y) }
  1279  func quo(x, y Value) Value { return BinaryOp(x, token.QUO, y) }
  1280  
  1281  // Shift returns the result of the shift expression x op s
  1282  // with op == token.SHL or token.SHR (<< or >>). x must be
  1283  // an Int or an Unknown. If x is Unknown, the result is x.
  1284  //
  1285  func Shift(x Value, op token.Token, s uint) Value {
  1286  	switch x := x.(type) {
  1287  	case unknownVal:
  1288  		return x
  1289  
  1290  	case int64Val:
  1291  		if s == 0 {
  1292  			return x
  1293  		}
  1294  		switch op {
  1295  		case token.SHL:
  1296  			z := i64toi(x).val
  1297  			return makeInt(z.Lsh(z, s))
  1298  		case token.SHR:
  1299  			return x >> s
  1300  		}
  1301  
  1302  	case intVal:
  1303  		if s == 0 {
  1304  			return x
  1305  		}
  1306  		z := newInt()
  1307  		switch op {
  1308  		case token.SHL:
  1309  			return makeInt(z.Lsh(x.val, s))
  1310  		case token.SHR:
  1311  			return makeInt(z.Rsh(x.val, s))
  1312  		}
  1313  	}
  1314  
  1315  	panic(fmt.Sprintf("invalid shift %v %s %d", x, op, s))
  1316  }
  1317  
  1318  func cmpZero(x int, op token.Token) bool {
  1319  	switch op {
  1320  	case token.EQL:
  1321  		return x == 0
  1322  	case token.NEQ:
  1323  		return x != 0
  1324  	case token.LSS:
  1325  		return x < 0
  1326  	case token.LEQ:
  1327  		return x <= 0
  1328  	case token.GTR:
  1329  		return x > 0
  1330  	case token.GEQ:
  1331  		return x >= 0
  1332  	}
  1333  	panic(fmt.Sprintf("invalid comparison %v %s 0", x, op))
  1334  }
  1335  
  1336  // Compare returns the result of the comparison x op y.
  1337  // The comparison must be defined for the operands.
  1338  // If one of the operands is Unknown, the result is
  1339  // false.
  1340  //
  1341  func Compare(x_ Value, op token.Token, y_ Value) bool {
  1342  	x, y := match(x_, y_)
  1343  
  1344  	switch x := x.(type) {
  1345  	case unknownVal:
  1346  		return false
  1347  
  1348  	case boolVal:
  1349  		y := y.(boolVal)
  1350  		switch op {
  1351  		case token.EQL:
  1352  			return x == y
  1353  		case token.NEQ:
  1354  			return x != y
  1355  		}
  1356  
  1357  	case int64Val:
  1358  		y := y.(int64Val)
  1359  		switch op {
  1360  		case token.EQL:
  1361  			return x == y
  1362  		case token.NEQ:
  1363  			return x != y
  1364  		case token.LSS:
  1365  			return x < y
  1366  		case token.LEQ:
  1367  			return x <= y
  1368  		case token.GTR:
  1369  			return x > y
  1370  		case token.GEQ:
  1371  			return x >= y
  1372  		}
  1373  
  1374  	case intVal:
  1375  		return cmpZero(x.val.Cmp(y.(intVal).val), op)
  1376  
  1377  	case ratVal:
  1378  		return cmpZero(x.val.Cmp(y.(ratVal).val), op)
  1379  
  1380  	case floatVal:
  1381  		return cmpZero(x.val.Cmp(y.(floatVal).val), op)
  1382  
  1383  	case complexVal:
  1384  		y := y.(complexVal)
  1385  		re := Compare(x.re, token.EQL, y.re)
  1386  		im := Compare(x.im, token.EQL, y.im)
  1387  		switch op {
  1388  		case token.EQL:
  1389  			return re && im
  1390  		case token.NEQ:
  1391  			return !re || !im
  1392  		}
  1393  
  1394  	case *stringVal:
  1395  		xs := x.string()
  1396  		ys := y.(*stringVal).string()
  1397  		switch op {
  1398  		case token.EQL:
  1399  			return xs == ys
  1400  		case token.NEQ:
  1401  			return xs != ys
  1402  		case token.LSS:
  1403  			return xs < ys
  1404  		case token.LEQ:
  1405  			return xs <= ys
  1406  		case token.GTR:
  1407  			return xs > ys
  1408  		case token.GEQ:
  1409  			return xs >= ys
  1410  		}
  1411  	}
  1412  
  1413  	panic(fmt.Sprintf("invalid comparison %v %s %v", x_, op, y_))
  1414  }
  1415  

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