Source file src/go/constant/value.go

     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  	"math/bits"
    21  	"strconv"
    22  	"strings"
    23  	"sync"
    24  	"unicode/utf8"
    25  )
    26  
    27  // Kind specifies the kind of value represented by a Value.
    28  type Kind int
    29  
    30  const (
    31  	// unknown values
    32  	Unknown Kind = iota
    33  
    34  	// non-numeric values
    35  	Bool
    36  	String
    37  
    38  	// numeric values
    39  	Int
    40  	Float
    41  	Complex
    42  )
    43  
    44  // A Value represents the value of a Go constant.
    45  type Value interface {
    46  	// Kind returns the value kind.
    47  	Kind() Kind
    48  
    49  	// String returns a short, quoted (human-readable) form of the value.
    50  	// For numeric values, the result may be an approximation;
    51  	// for String values the result may be a shortened string.
    52  	// Use ExactString for a string representing a value exactly.
    53  	String() string
    54  
    55  	// ExactString returns an exact, quoted (human-readable) form of the value.
    56  	// If the Value is of Kind String, use StringVal to obtain the unquoted string.
    57  	ExactString() string
    58  
    59  	// Prevent external implementations.
    60  	implementsValue()
    61  }
    62  
    63  // ----------------------------------------------------------------------------
    64  // Implementations
    65  
    66  // Maximum supported mantissa precision.
    67  // The spec requires at least 256 bits; typical implementations use 512 bits.
    68  const prec = 512
    69  
    70  // TODO(gri) Consider storing "error" information in an unknownVal so clients
    71  //           can provide better error messages. For instance, if a number is
    72  //           too large (incl. infinity), that could be recorded in unknownVal.
    73  //           See also #20583 and #42695 for use cases.
    74  
    75  // Representation of values:
    76  //
    77  // Values of Int and Float Kind have two different representations each: int64Val
    78  // and intVal, and ratVal and floatVal. When possible, the "smaller", respectively
    79  // more precise (for Floats) representation is chosen. However, once a Float value
    80  // is represented as a floatVal, any subsequent results remain floatVals (unless
    81  // explicitly converted); i.e., no attempt is made to convert a floatVal back into
    82  // a ratVal. The reasoning is that all representations but floatVal are mathematically
    83  // exact, but once that precision is lost (by moving to floatVal), moving back to
    84  // a different representation implies a precision that's not actually there.
    85  
    86  type (
    87  	unknownVal struct{}
    88  	boolVal    bool
    89  	stringVal  struct {
    90  		// Lazy value: either a string (l,r==nil) or an addition (l,r!=nil).
    91  		mu   sync.Mutex
    92  		s    string
    93  		l, r *stringVal
    94  	}
    95  	int64Val   int64                    // Int values representable as an int64
    96  	intVal     struct{ val *big.Int }   // Int values not representable as an int64
    97  	ratVal     struct{ val *big.Rat }   // Float values representable as a fraction
    98  	floatVal   struct{ val *big.Float } // Float values not representable as a fraction
    99  	complexVal struct{ re, im Value }
   100  )
   101  
   102  func (unknownVal) Kind() Kind { return Unknown }
   103  func (boolVal) Kind() Kind    { return Bool }
   104  func (*stringVal) Kind() Kind { return String }
   105  func (int64Val) Kind() Kind   { return Int }
   106  func (intVal) Kind() Kind     { return Int }
   107  func (ratVal) Kind() Kind     { return Float }
   108  func (floatVal) Kind() Kind   { return Float }
   109  func (complexVal) Kind() Kind { return Complex }
   110  
   111  func (unknownVal) String() string { return "unknown" }
   112  func (x boolVal) String() string  { return strconv.FormatBool(bool(x)) }
   113  
   114  // String returns a possibly shortened quoted form of the String value.
   115  func (x *stringVal) String() string {
   116  	const maxLen = 72 // a reasonable length
   117  	s := strconv.Quote(x.string())
   118  	if utf8.RuneCountInString(s) > maxLen {
   119  		// The string without the enclosing quotes is greater than maxLen-2 runes
   120  		// long. Remove the last 3 runes (including the closing '"') by keeping
   121  		// only the first maxLen-3 runes; then add "...".
   122  		i := 0
   123  		for n := 0; n < maxLen-3; n++ {
   124  			_, size := utf8.DecodeRuneInString(s[i:])
   125  			i += size
   126  		}
   127  		s = s[:i] + "..."
   128  	}
   129  	return s
   130  }
   131  
   132  // string constructs and returns the actual string literal value.
   133  // If x represents an addition, then it rewrites x to be a single
   134  // string, to speed future calls. This lazy construction avoids
   135  // building different string values for all subpieces of a large
   136  // concatenation. See golang.org/issue/23348.
   137  func (x *stringVal) string() string {
   138  	x.mu.Lock()
   139  	if x.l != nil {
   140  		x.s = strings.Join(reverse(x.appendReverse(nil)), "")
   141  		x.l = nil
   142  		x.r = nil
   143  	}
   144  	s := x.s
   145  	x.mu.Unlock()
   146  
   147  	return s
   148  }
   149  
   150  // reverse reverses x in place and returns it.
   151  func reverse(x []string) []string {
   152  	n := len(x)
   153  	for i := 0; i+i < n; i++ {
   154  		x[i], x[n-1-i] = x[n-1-i], x[i]
   155  	}
   156  	return x
   157  }
   158  
   159  // appendReverse appends to list all of x's subpieces, but in reverse,
   160  // and returns the result. Appending the reversal allows processing
   161  // the right side in a recursive call and the left side in a loop.
   162  // Because a chain like a + b + c + d + e is actually represented
   163  // as ((((a + b) + c) + d) + e), the left-side loop avoids deep recursion.
   164  // x must be locked.
   165  func (x *stringVal) appendReverse(list []string) []string {
   166  	y := x
   167  	for y.r != nil {
   168  		y.r.mu.Lock()
   169  		list = y.r.appendReverse(list)
   170  		y.r.mu.Unlock()
   171  
   172  		l := y.l
   173  		if y != x {
   174  			y.mu.Unlock()
   175  		}
   176  		l.mu.Lock()
   177  		y = l
   178  	}
   179  	s := y.s
   180  	if y != x {
   181  		y.mu.Unlock()
   182  	}
   183  	return append(list, s)
   184  }
   185  
   186  func (x int64Val) String() string { return strconv.FormatInt(int64(x), 10) }
   187  func (x intVal) String() string   { return x.val.String() }
   188  func (x ratVal) String() string   { return rtof(x).String() }
   189  
   190  // String returns a decimal approximation of the Float value.
   191  func (x floatVal) String() string {
   192  	f := x.val
   193  
   194  	// Don't try to convert infinities (will not terminate).
   195  	if f.IsInf() {
   196  		return f.String()
   197  	}
   198  
   199  	// Use exact fmt formatting if in float64 range (common case):
   200  	// proceed if f doesn't underflow to 0 or overflow to inf.
   201  	if x, _ := f.Float64(); f.Sign() == 0 == (x == 0) && !math.IsInf(x, 0) {
   202  		return fmt.Sprintf("%.6g", x)
   203  	}
   204  
   205  	// Out of float64 range. Do approximate manual to decimal
   206  	// conversion to avoid precise but possibly slow Float
   207  	// formatting.
   208  	// f = mant * 2**exp
   209  	var mant big.Float
   210  	exp := f.MantExp(&mant) // 0.5 <= |mant| < 1.0
   211  
   212  	// approximate float64 mantissa m and decimal exponent d
   213  	// f ~ m * 10**d
   214  	m, _ := mant.Float64()                     // 0.5 <= |m| < 1.0
   215  	d := float64(exp) * (math.Ln2 / math.Ln10) // log_10(2)
   216  
   217  	// adjust m for truncated (integer) decimal exponent e
   218  	e := int64(d)
   219  	m *= math.Pow(10, d-float64(e))
   220  
   221  	// ensure 1 <= |m| < 10
   222  	switch am := math.Abs(m); {
   223  	case am < 1-0.5e-6:
   224  		// The %.6g format below rounds m to 5 digits after the
   225  		// decimal point. Make sure that m*10 < 10 even after
   226  		// rounding up: m*10 + 0.5e-5 < 10 => m < 1 - 0.5e6.
   227  		m *= 10
   228  		e--
   229  	case am >= 10:
   230  		m /= 10
   231  		e++
   232  	}
   233  
   234  	return fmt.Sprintf("%.6ge%+d", m, e)
   235  }
   236  
   237  func (x complexVal) String() string { return fmt.Sprintf("(%s + %si)", x.re, x.im) }
   238  
   239  func (x unknownVal) ExactString() string { return x.String() }
   240  func (x boolVal) ExactString() string    { return x.String() }
   241  func (x *stringVal) ExactString() string { return strconv.Quote(x.string()) }
   242  func (x int64Val) ExactString() string   { return x.String() }
   243  func (x intVal) ExactString() string     { return x.String() }
   244  
   245  func (x ratVal) ExactString() string {
   246  	r := x.val
   247  	if r.IsInt() {
   248  		return r.Num().String()
   249  	}
   250  	return r.String()
   251  }
   252  
   253  func (x floatVal) ExactString() string { return x.val.Text('p', 0) }
   254  
   255  func (x complexVal) ExactString() string {
   256  	return fmt.Sprintf("(%s + %si)", x.re.ExactString(), x.im.ExactString())
   257  }
   258  
   259  func (unknownVal) implementsValue() {}
   260  func (boolVal) implementsValue()    {}
   261  func (*stringVal) implementsValue() {}
   262  func (int64Val) implementsValue()   {}
   263  func (ratVal) implementsValue()     {}
   264  func (intVal) implementsValue()     {}
   265  func (floatVal) implementsValue()   {}
   266  func (complexVal) implementsValue() {}
   267  
   268  func newInt() *big.Int     { return new(big.Int) }
   269  func newRat() *big.Rat     { return new(big.Rat) }
   270  func newFloat() *big.Float { return new(big.Float).SetPrec(prec) }
   271  
   272  func i64toi(x int64Val) intVal   { return intVal{newInt().SetInt64(int64(x))} }
   273  func i64tor(x int64Val) ratVal   { return ratVal{newRat().SetInt64(int64(x))} }
   274  func i64tof(x int64Val) floatVal { return floatVal{newFloat().SetInt64(int64(x))} }
   275  func itor(x intVal) ratVal       { return ratVal{newRat().SetInt(x.val)} }
   276  func itof(x intVal) floatVal     { return floatVal{newFloat().SetInt(x.val)} }
   277  func rtof(x ratVal) floatVal     { return floatVal{newFloat().SetRat(x.val)} }
   278  func vtoc(x Value) complexVal    { return complexVal{x, int64Val(0)} }
   279  
   280  func makeInt(x *big.Int) Value {
   281  	if x.IsInt64() {
   282  		return int64Val(x.Int64())
   283  	}
   284  	return intVal{x}
   285  }
   286  
   287  func makeRat(x *big.Rat) Value {
   288  	a := x.Num()
   289  	b := x.Denom()
   290  	if smallInt(a) && smallInt(b) {
   291  		// ok to remain fraction
   292  		return ratVal{x}
   293  	}
   294  	// components too large => switch to float
   295  	return floatVal{newFloat().SetRat(x)}
   296  }
   297  
   298  var floatVal0 = floatVal{newFloat()}
   299  
   300  func makeFloat(x *big.Float) Value {
   301  	// convert -0
   302  	if x.Sign() == 0 {
   303  		return floatVal0
   304  	}
   305  	if x.IsInf() {
   306  		return unknownVal{}
   307  	}
   308  	// No attempt is made to "go back" to ratVal, even if possible,
   309  	// to avoid providing the illusion of a mathematically exact
   310  	// representation.
   311  	return floatVal{x}
   312  }
   313  
   314  func makeComplex(re, im Value) Value {
   315  	if re.Kind() == Unknown || im.Kind() == Unknown {
   316  		return unknownVal{}
   317  	}
   318  	return complexVal{re, im}
   319  }
   320  
   321  func makeFloatFromLiteral(lit string) Value {
   322  	if f, ok := newFloat().SetString(lit); ok {
   323  		if smallFloat(f) {
   324  			// ok to use rationals
   325  			if f.Sign() == 0 {
   326  				// Issue 20228: If the float underflowed to zero, parse just "0".
   327  				// Otherwise, lit might contain a value with a large negative exponent,
   328  				// such as -6e-1886451601. As a float, that will underflow to 0,
   329  				// but it'll take forever to parse as a Rat.
   330  				lit = "0"
   331  			}
   332  			if r, ok := newRat().SetString(lit); ok {
   333  				return ratVal{r}
   334  			}
   335  		}
   336  		// otherwise use floats
   337  		return makeFloat(f)
   338  	}
   339  	return nil
   340  }
   341  
   342  // Permit fractions with component sizes up to maxExp
   343  // before switching to using floating-point numbers.
   344  const maxExp = 4 << 10
   345  
   346  // smallInt reports whether x would lead to "reasonably"-sized fraction
   347  // if converted to a *big.Rat.
   348  func smallInt(x *big.Int) bool {
   349  	return x.BitLen() < maxExp
   350  }
   351  
   352  // smallFloat64 reports whether x would lead to "reasonably"-sized fraction
   353  // if converted to a *big.Rat.
   354  func smallFloat64(x float64) bool {
   355  	if math.IsInf(x, 0) {
   356  		return false
   357  	}
   358  	_, e := math.Frexp(x)
   359  	return -maxExp < e && e < maxExp
   360  }
   361  
   362  // smallFloat reports whether x would lead to "reasonably"-sized fraction
   363  // if converted to a *big.Rat.
   364  func smallFloat(x *big.Float) bool {
   365  	if x.IsInf() {
   366  		return false
   367  	}
   368  	e := x.MantExp(nil)
   369  	return -maxExp < e && e < maxExp
   370  }
   371  
   372  // ----------------------------------------------------------------------------
   373  // Factories
   374  
   375  // MakeUnknown returns the Unknown value.
   376  func MakeUnknown() Value { return unknownVal{} }
   377  
   378  // MakeBool returns the Bool value for b.
   379  func MakeBool(b bool) Value { return boolVal(b) }
   380  
   381  // MakeString returns the String value for s.
   382  func MakeString(s string) Value { return &stringVal{s: s} }
   383  
   384  // MakeInt64 returns the Int value for x.
   385  func MakeInt64(x int64) Value { return int64Val(x) }
   386  
   387  // MakeUint64 returns the Int value for x.
   388  func MakeUint64(x uint64) Value {
   389  	if x < 1<<63 {
   390  		return int64Val(int64(x))
   391  	}
   392  	return intVal{newInt().SetUint64(x)}
   393  }
   394  
   395  // MakeFloat64 returns the Float value for x.
   396  // If x is -0.0, the result is 0.0.
   397  // If x is not finite, the result is an Unknown.
   398  func MakeFloat64(x float64) Value {
   399  	if math.IsInf(x, 0) || math.IsNaN(x) {
   400  		return unknownVal{}
   401  	}
   402  	if smallFloat64(x) {
   403  		return ratVal{newRat().SetFloat64(x + 0)} // convert -0 to 0
   404  	}
   405  	return floatVal{newFloat().SetFloat64(x + 0)}
   406  }
   407  
   408  // MakeFromLiteral returns the corresponding integer, floating-point,
   409  // imaginary, character, or string value for a Go literal string. The
   410  // tok value must be one of token.INT, token.FLOAT, token.IMAG,
   411  // token.CHAR, or token.STRING. The final argument must be zero.
   412  // If the literal string syntax is invalid, the result is an Unknown.
   413  func MakeFromLiteral(lit string, tok token.Token, zero uint) Value {
   414  	if zero != 0 {
   415  		panic("MakeFromLiteral called with non-zero last argument")
   416  	}
   417  
   418  	switch tok {
   419  	case token.INT:
   420  		if x, err := strconv.ParseInt(lit, 0, 64); err == nil {
   421  			return int64Val(x)
   422  		}
   423  		if x, ok := newInt().SetString(lit, 0); ok {
   424  			return intVal{x}
   425  		}
   426  
   427  	case token.FLOAT:
   428  		if x := makeFloatFromLiteral(lit); x != nil {
   429  			return x
   430  		}
   431  
   432  	case token.IMAG:
   433  		if n := len(lit); n > 0 && lit[n-1] == 'i' {
   434  			if im := makeFloatFromLiteral(lit[:n-1]); im != nil {
   435  				return makeComplex(int64Val(0), im)
   436  			}
   437  		}
   438  
   439  	case token.CHAR:
   440  		if n := len(lit); n >= 2 {
   441  			if code, _, _, err := strconv.UnquoteChar(lit[1:n-1], '\''); err == nil {
   442  				return MakeInt64(int64(code))
   443  			}
   444  		}
   445  
   446  	case token.STRING:
   447  		if s, err := strconv.Unquote(lit); err == nil {
   448  			return MakeString(s)
   449  		}
   450  
   451  	default:
   452  		panic(fmt.Sprintf("%v is not a valid token", tok))
   453  	}
   454  
   455  	return unknownVal{}
   456  }
   457  
   458  // ----------------------------------------------------------------------------
   459  // Accessors
   460  //
   461  // For unknown arguments the result is the zero value for the respective
   462  // accessor type, except for Sign, where the result is 1.
   463  
   464  // BoolVal returns the Go boolean value of x, which must be a Bool or an Unknown.
   465  // If x is Unknown, the result is false.
   466  func BoolVal(x Value) bool {
   467  	switch x := x.(type) {
   468  	case boolVal:
   469  		return bool(x)
   470  	case unknownVal:
   471  		return false
   472  	default:
   473  		panic(fmt.Sprintf("%v not a Bool", x))
   474  	}
   475  }
   476  
   477  // StringVal returns the Go string value of x, which must be a String or an Unknown.
   478  // If x is Unknown, the result is "".
   479  func StringVal(x Value) string {
   480  	switch x := x.(type) {
   481  	case *stringVal:
   482  		return x.string()
   483  	case unknownVal:
   484  		return ""
   485  	default:
   486  		panic(fmt.Sprintf("%v not a String", x))
   487  	}
   488  }
   489  
   490  // Int64Val returns the Go int64 value of x and whether the result is exact;
   491  // x must be an Int or an Unknown. If the result is not exact, its value is undefined.
   492  // If x is Unknown, the result is (0, false).
   493  func Int64Val(x Value) (int64, bool) {
   494  	switch x := x.(type) {
   495  	case int64Val:
   496  		return int64(x), true
   497  	case intVal:
   498  		return x.val.Int64(), false // not an int64Val and thus not exact
   499  	case unknownVal:
   500  		return 0, false
   501  	default:
   502  		panic(fmt.Sprintf("%v not an Int", x))
   503  	}
   504  }
   505  
   506  // Uint64Val returns the Go uint64 value of x and whether the result is exact;
   507  // x must be an Int or an Unknown. If the result is not exact, its value is undefined.
   508  // If x is Unknown, the result is (0, false).
   509  func Uint64Val(x Value) (uint64, bool) {
   510  	switch x := x.(type) {
   511  	case int64Val:
   512  		return uint64(x), x >= 0
   513  	case intVal:
   514  		return x.val.Uint64(), x.val.IsUint64()
   515  	case unknownVal:
   516  		return 0, false
   517  	default:
   518  		panic(fmt.Sprintf("%v not an Int", x))
   519  	}
   520  }
   521  
   522  // Float32Val is like Float64Val but for float32 instead of float64.
   523  func Float32Val(x Value) (float32, bool) {
   524  	switch x := x.(type) {
   525  	case int64Val:
   526  		f := float32(x)
   527  		return f, int64Val(f) == x
   528  	case intVal:
   529  		f, acc := newFloat().SetInt(x.val).Float32()
   530  		return f, acc == big.Exact
   531  	case ratVal:
   532  		return x.val.Float32()
   533  	case floatVal:
   534  		f, acc := x.val.Float32()
   535  		return f, acc == big.Exact
   536  	case unknownVal:
   537  		return 0, false
   538  	default:
   539  		panic(fmt.Sprintf("%v not a Float", x))
   540  	}
   541  }
   542  
   543  // Float64Val returns the nearest Go float64 value of x and whether the result is exact;
   544  // x must be numeric or an Unknown, but not Complex. For values too small (too close to 0)
   545  // to represent as float64, Float64Val silently underflows to 0. The result sign always
   546  // matches the sign of x, even for 0.
   547  // If x is Unknown, the result is (0, false).
   548  func Float64Val(x Value) (float64, bool) {
   549  	switch x := x.(type) {
   550  	case int64Val:
   551  		f := float64(int64(x))
   552  		return f, int64Val(f) == x
   553  	case intVal:
   554  		f, acc := newFloat().SetInt(x.val).Float64()
   555  		return f, acc == big.Exact
   556  	case ratVal:
   557  		return x.val.Float64()
   558  	case floatVal:
   559  		f, acc := x.val.Float64()
   560  		return f, acc == big.Exact
   561  	case unknownVal:
   562  		return 0, false
   563  	default:
   564  		panic(fmt.Sprintf("%v not a Float", x))
   565  	}
   566  }
   567  
   568  // Val returns the underlying value for a given constant. Since it returns an
   569  // interface, it is up to the caller to type assert the result to the expected
   570  // type. The possible dynamic return types are:
   571  //
   572  //    x Kind             type of result
   573  //    -----------------------------------------
   574  //    Bool               bool
   575  //    String             string
   576  //    Int                int64 or *big.Int
   577  //    Float              *big.Float or *big.Rat
   578  //    everything else    nil
   579  //
   580  func Val(x Value) interface{} {
   581  	switch x := x.(type) {
   582  	case boolVal:
   583  		return bool(x)
   584  	case *stringVal:
   585  		return x.string()
   586  	case int64Val:
   587  		return int64(x)
   588  	case intVal:
   589  		return x.val
   590  	case ratVal:
   591  		return x.val
   592  	case floatVal:
   593  		return x.val
   594  	default:
   595  		return nil
   596  	}
   597  }
   598  
   599  // Make returns the Value for x.
   600  //
   601  //    type of x        result Kind
   602  //    ----------------------------
   603  //    bool             Bool
   604  //    string           String
   605  //    int64            Int
   606  //    *big.Int         Int
   607  //    *big.Float       Float
   608  //    *big.Rat         Float
   609  //    anything else    Unknown
   610  //
   611  func Make(x interface{}) Value {
   612  	switch x := x.(type) {
   613  	case bool:
   614  		return boolVal(x)
   615  	case string:
   616  		return &stringVal{s: x}
   617  	case int64:
   618  		return int64Val(x)
   619  	case *big.Int:
   620  		return makeInt(x)
   621  	case *big.Rat:
   622  		return makeRat(x)
   623  	case *big.Float:
   624  		return makeFloat(x)
   625  	default:
   626  		return unknownVal{}
   627  	}
   628  }
   629  
   630  // BitLen returns the number of bits required to represent
   631  // the absolute value x in binary representation; x must be an Int or an Unknown.
   632  // If x is Unknown, the result is 0.
   633  func BitLen(x Value) int {
   634  	switch x := x.(type) {
   635  	case int64Val:
   636  		u := uint64(x)
   637  		if x < 0 {
   638  			u = uint64(-x)
   639  		}
   640  		return 64 - bits.LeadingZeros64(u)
   641  	case intVal:
   642  		return x.val.BitLen()
   643  	case unknownVal:
   644  		return 0
   645  	default:
   646  		panic(fmt.Sprintf("%v not an Int", x))
   647  	}
   648  }
   649  
   650  // Sign returns -1, 0, or 1 depending on whether x < 0, x == 0, or x > 0;
   651  // x must be numeric or Unknown. For complex values x, the sign is 0 if x == 0,
   652  // otherwise it is != 0. If x is Unknown, the result is 1.
   653  func Sign(x Value) int {
   654  	switch x := x.(type) {
   655  	case int64Val:
   656  		switch {
   657  		case x < 0:
   658  			return -1
   659  		case x > 0:
   660  			return 1
   661  		}
   662  		return 0
   663  	case intVal:
   664  		return x.val.Sign()
   665  	case ratVal:
   666  		return x.val.Sign()
   667  	case floatVal:
   668  		return x.val.Sign()
   669  	case complexVal:
   670  		return Sign(x.re) | Sign(x.im)
   671  	case unknownVal:
   672  		return 1 // avoid spurious division by zero errors
   673  	default:
   674  		panic(fmt.Sprintf("%v not numeric", x))
   675  	}
   676  }
   677  
   678  // ----------------------------------------------------------------------------
   679  // Support for assembling/disassembling numeric values
   680  
   681  const (
   682  	// Compute the size of a Word in bytes.
   683  	_m       = ^big.Word(0)
   684  	_log     = _m>>8&1 + _m>>16&1 + _m>>32&1
   685  	wordSize = 1 << _log
   686  )
   687  
   688  // Bytes returns the bytes for the absolute value of x in little-
   689  // endian binary representation; x must be an Int.
   690  func Bytes(x Value) []byte {
   691  	var t intVal
   692  	switch x := x.(type) {
   693  	case int64Val:
   694  		t = i64toi(x)
   695  	case intVal:
   696  		t = x
   697  	default:
   698  		panic(fmt.Sprintf("%v not an Int", x))
   699  	}
   700  
   701  	words := t.val.Bits()
   702  	bytes := make([]byte, len(words)*wordSize)
   703  
   704  	i := 0
   705  	for _, w := range words {
   706  		for j := 0; j < wordSize; j++ {
   707  			bytes[i] = byte(w)
   708  			w >>= 8
   709  			i++
   710  		}
   711  	}
   712  	// remove leading 0's
   713  	for i > 0 && bytes[i-1] == 0 {
   714  		i--
   715  	}
   716  
   717  	return bytes[:i]
   718  }
   719  
   720  // MakeFromBytes returns the Int value given the bytes of its little-endian
   721  // binary representation. An empty byte slice argument represents 0.
   722  func MakeFromBytes(bytes []byte) Value {
   723  	words := make([]big.Word, (len(bytes)+(wordSize-1))/wordSize)
   724  
   725  	i := 0
   726  	var w big.Word
   727  	var s uint
   728  	for _, b := range bytes {
   729  		w |= big.Word(b) << s
   730  		if s += 8; s == wordSize*8 {
   731  			words[i] = w
   732  			i++
   733  			w = 0
   734  			s = 0
   735  		}
   736  	}
   737  	// store last word
   738  	if i < len(words) {
   739  		words[i] = w
   740  		i++
   741  	}
   742  	// remove leading 0's
   743  	for i > 0 && words[i-1] == 0 {
   744  		i--
   745  	}
   746  
   747  	return makeInt(newInt().SetBits(words[:i]))
   748  }
   749  
   750  // Num returns the numerator of x; x must be Int, Float, or Unknown.
   751  // If x is Unknown, or if it is too large or small to represent as a
   752  // fraction, the result is Unknown. Otherwise the result is an Int
   753  // with the same sign as x.
   754  func Num(x Value) Value {
   755  	switch x := x.(type) {
   756  	case int64Val, intVal:
   757  		return x
   758  	case ratVal:
   759  		return makeInt(x.val.Num())
   760  	case floatVal:
   761  		if smallFloat(x.val) {
   762  			r, _ := x.val.Rat(nil)
   763  			return makeInt(r.Num())
   764  		}
   765  	case unknownVal:
   766  		break
   767  	default:
   768  		panic(fmt.Sprintf("%v not Int or Float", x))
   769  	}
   770  	return unknownVal{}
   771  }
   772  
   773  // Denom returns the denominator of x; x must be Int, Float, or Unknown.
   774  // If x is Unknown, or if it is too large or small to represent as a
   775  // fraction, the result is Unknown. Otherwise the result is an Int >= 1.
   776  func Denom(x Value) Value {
   777  	switch x := x.(type) {
   778  	case int64Val, intVal:
   779  		return int64Val(1)
   780  	case ratVal:
   781  		return makeInt(x.val.Denom())
   782  	case floatVal:
   783  		if smallFloat(x.val) {
   784  			r, _ := x.val.Rat(nil)
   785  			return makeInt(r.Denom())
   786  		}
   787  	case unknownVal:
   788  		break
   789  	default:
   790  		panic(fmt.Sprintf("%v not Int or Float", x))
   791  	}
   792  	return unknownVal{}
   793  }
   794  
   795  // MakeImag returns the Complex value x*i;
   796  // x must be Int, Float, or Unknown.
   797  // If x is Unknown, the result is Unknown.
   798  func MakeImag(x Value) Value {
   799  	switch x.(type) {
   800  	case unknownVal:
   801  		return x
   802  	case int64Val, intVal, ratVal, floatVal:
   803  		return makeComplex(int64Val(0), x)
   804  	default:
   805  		panic(fmt.Sprintf("%v not Int or Float", x))
   806  	}
   807  }
   808  
   809  // Real returns the real part of x, which must be a numeric or unknown value.
   810  // If x is Unknown, the result is Unknown.
   811  func Real(x Value) Value {
   812  	switch x := x.(type) {
   813  	case unknownVal, int64Val, intVal, ratVal, floatVal:
   814  		return x
   815  	case complexVal:
   816  		return x.re
   817  	default:
   818  		panic(fmt.Sprintf("%v not numeric", x))
   819  	}
   820  }
   821  
   822  // Imag returns the imaginary part of x, which must be a numeric or unknown value.
   823  // If x is Unknown, the result is Unknown.
   824  func Imag(x Value) Value {
   825  	switch x := x.(type) {
   826  	case unknownVal:
   827  		return x
   828  	case int64Val, intVal, ratVal, floatVal:
   829  		return int64Val(0)
   830  	case complexVal:
   831  		return x.im
   832  	default:
   833  		panic(fmt.Sprintf("%v not numeric", x))
   834  	}
   835  }
   836  
   837  // ----------------------------------------------------------------------------
   838  // Numeric conversions
   839  
   840  // ToInt converts x to an Int value if x is representable as an Int.
   841  // Otherwise it returns an Unknown.
   842  func ToInt(x Value) Value {
   843  	switch x := x.(type) {
   844  	case int64Val, intVal:
   845  		return x
   846  
   847  	case ratVal:
   848  		if x.val.IsInt() {
   849  			return makeInt(x.val.Num())
   850  		}
   851  
   852  	case floatVal:
   853  		// avoid creation of huge integers
   854  		// (Existing tests require permitting exponents of at least 1024;
   855  		// allow any value that would also be permissible as a fraction.)
   856  		if smallFloat(x.val) {
   857  			i := newInt()
   858  			if _, acc := x.val.Int(i); acc == big.Exact {
   859  				return makeInt(i)
   860  			}
   861  
   862  			// If we can get an integer by rounding up or down,
   863  			// assume x is not an integer because of rounding
   864  			// errors in prior computations.
   865  
   866  			const delta = 4 // a small number of bits > 0
   867  			var t big.Float
   868  			t.SetPrec(prec - delta)
   869  
   870  			// try rounding down a little
   871  			t.SetMode(big.ToZero)
   872  			t.Set(x.val)
   873  			if _, acc := t.Int(i); acc == big.Exact {
   874  				return makeInt(i)
   875  			}
   876  
   877  			// try rounding up a little
   878  			t.SetMode(big.AwayFromZero)
   879  			t.Set(x.val)
   880  			if _, acc := t.Int(i); acc == big.Exact {
   881  				return makeInt(i)
   882  			}
   883  		}
   884  
   885  	case complexVal:
   886  		if re := ToFloat(x); re.Kind() == Float {
   887  			return ToInt(re)
   888  		}
   889  	}
   890  
   891  	return unknownVal{}
   892  }
   893  
   894  // ToFloat converts x to a Float value if x is representable as a Float.
   895  // Otherwise it returns an Unknown.
   896  func ToFloat(x Value) Value {
   897  	switch x := x.(type) {
   898  	case int64Val:
   899  		return i64tor(x) // x is always a small int
   900  	case intVal:
   901  		if smallInt(x.val) {
   902  			return itor(x)
   903  		}
   904  		return itof(x)
   905  	case ratVal, floatVal:
   906  		return x
   907  	case complexVal:
   908  		if Sign(x.im) == 0 {
   909  			return ToFloat(x.re)
   910  		}
   911  	}
   912  	return unknownVal{}
   913  }
   914  
   915  // ToComplex converts x to a Complex value if x is representable as a Complex.
   916  // Otherwise it returns an Unknown.
   917  func ToComplex(x Value) Value {
   918  	switch x := x.(type) {
   919  	case int64Val, intVal, ratVal, floatVal:
   920  		return vtoc(x)
   921  	case complexVal:
   922  		return x
   923  	}
   924  	return unknownVal{}
   925  }
   926  
   927  // ----------------------------------------------------------------------------
   928  // Operations
   929  
   930  // is32bit reports whether x can be represented using 32 bits.
   931  func is32bit(x int64) bool {
   932  	const s = 32
   933  	return -1<<(s-1) <= x && x <= 1<<(s-1)-1
   934  }
   935  
   936  // is63bit reports whether x can be represented using 63 bits.
   937  func is63bit(x int64) bool {
   938  	const s = 63
   939  	return -1<<(s-1) <= x && x <= 1<<(s-1)-1
   940  }
   941  
   942  // UnaryOp returns the result of the unary expression op y.
   943  // The operation must be defined for the operand.
   944  // If prec > 0 it specifies the ^ (xor) result size in bits.
   945  // If y is Unknown, the result is Unknown.
   946  //
   947  func UnaryOp(op token.Token, y Value, prec uint) Value {
   948  	switch op {
   949  	case token.ADD:
   950  		switch y.(type) {
   951  		case unknownVal, int64Val, intVal, ratVal, floatVal, complexVal:
   952  			return y
   953  		}
   954  
   955  	case token.SUB:
   956  		switch y := y.(type) {
   957  		case unknownVal:
   958  			return y
   959  		case int64Val:
   960  			if z := -y; z != y {
   961  				return z // no overflow
   962  			}
   963  			return makeInt(newInt().Neg(big.NewInt(int64(y))))
   964  		case intVal:
   965  			return makeInt(newInt().Neg(y.val))
   966  		case ratVal:
   967  			return makeRat(newRat().Neg(y.val))
   968  		case floatVal:
   969  			return makeFloat(newFloat().Neg(y.val))
   970  		case complexVal:
   971  			re := UnaryOp(token.SUB, y.re, 0)
   972  			im := UnaryOp(token.SUB, y.im, 0)
   973  			return makeComplex(re, im)
   974  		}
   975  
   976  	case token.XOR:
   977  		z := newInt()
   978  		switch y := y.(type) {
   979  		case unknownVal:
   980  			return y
   981  		case int64Val:
   982  			z.Not(big.NewInt(int64(y)))
   983  		case intVal:
   984  			z.Not(y.val)
   985  		default:
   986  			goto Error
   987  		}
   988  		// For unsigned types, the result will be negative and
   989  		// thus "too large": We must limit the result precision
   990  		// to the type's precision.
   991  		if prec > 0 {
   992  			z.AndNot(z, newInt().Lsh(big.NewInt(-1), prec)) // z &^= (-1)<<prec
   993  		}
   994  		return makeInt(z)
   995  
   996  	case token.NOT:
   997  		switch y := y.(type) {
   998  		case unknownVal:
   999  			return y
  1000  		case boolVal:
  1001  			return !y
  1002  		}
  1003  	}
  1004  
  1005  Error:
  1006  	panic(fmt.Sprintf("invalid unary operation %s%v", op, y))
  1007  }
  1008  
  1009  func ord(x Value) int {
  1010  	switch x.(type) {
  1011  	default:
  1012  		// force invalid value into "x position" in match
  1013  		// (don't panic here so that callers can provide a better error message)
  1014  		return -1
  1015  	case unknownVal:
  1016  		return 0
  1017  	case boolVal, *stringVal:
  1018  		return 1
  1019  	case int64Val:
  1020  		return 2
  1021  	case intVal:
  1022  		return 3
  1023  	case ratVal:
  1024  		return 4
  1025  	case floatVal:
  1026  		return 5
  1027  	case complexVal:
  1028  		return 6
  1029  	}
  1030  }
  1031  
  1032  // match returns the matching representation (same type) with the
  1033  // smallest complexity for two values x and y. If one of them is
  1034  // numeric, both of them must be numeric. If one of them is Unknown
  1035  // or invalid (say, nil) both results are that value.
  1036  //
  1037  func match(x, y Value) (_, _ Value) {
  1038  	switch ox, oy := ord(x), ord(y); {
  1039  	case ox < oy:
  1040  		x, y = match0(x, y)
  1041  	case ox > oy:
  1042  		y, x = match0(y, x)
  1043  	}
  1044  	return x, y
  1045  }
  1046  
  1047  // match0 must only be called by match.
  1048  // Invariant: ord(x) < ord(y)
  1049  func match0(x, y Value) (_, _ Value) {
  1050  	// Prefer to return the original x and y arguments when possible,
  1051  	// to avoid unnecessary heap allocations.
  1052  
  1053  	switch y.(type) {
  1054  	case intVal:
  1055  		switch x1 := x.(type) {
  1056  		case int64Val:
  1057  			return i64toi(x1), y
  1058  		}
  1059  	case ratVal:
  1060  		switch x1 := x.(type) {
  1061  		case int64Val:
  1062  			return i64tor(x1), y
  1063  		case intVal:
  1064  			return itor(x1), y
  1065  		}
  1066  	case floatVal:
  1067  		switch x1 := x.(type) {
  1068  		case int64Val:
  1069  			return i64tof(x1), y
  1070  		case intVal:
  1071  			return itof(x1), y
  1072  		case ratVal:
  1073  			return rtof(x1), y
  1074  		}
  1075  	case complexVal:
  1076  		return vtoc(x), y
  1077  	}
  1078  
  1079  	// force unknown and invalid values into "x position" in callers of match
  1080  	// (don't panic here so that callers can provide a better error message)
  1081  	return x, x
  1082  }
  1083  
  1084  // BinaryOp returns the result of the binary expression x op y.
  1085  // The operation must be defined for the operands. If one of the
  1086  // operands is Unknown, the result is Unknown.
  1087  // BinaryOp doesn't handle comparisons or shifts; use Compare
  1088  // or Shift instead.
  1089  //
  1090  // To force integer division of Int operands, use op == token.QUO_ASSIGN
  1091  // instead of token.QUO; the result is guaranteed to be Int in this case.
  1092  // Division by zero leads to a run-time panic.
  1093  //
  1094  func BinaryOp(x_ Value, op token.Token, y_ Value) Value {
  1095  	x, y := match(x_, y_)
  1096  
  1097  	switch x := x.(type) {
  1098  	case unknownVal:
  1099  		return x
  1100  
  1101  	case boolVal:
  1102  		y := y.(boolVal)
  1103  		switch op {
  1104  		case token.LAND:
  1105  			return x && y
  1106  		case token.LOR:
  1107  			return x || y
  1108  		}
  1109  
  1110  	case int64Val:
  1111  		a := int64(x)
  1112  		b := int64(y.(int64Val))
  1113  		var c int64
  1114  		switch op {
  1115  		case token.ADD:
  1116  			if !is63bit(a) || !is63bit(b) {
  1117  				return makeInt(newInt().Add(big.NewInt(a), big.NewInt(b)))
  1118  			}
  1119  			c = a + b
  1120  		case token.SUB:
  1121  			if !is63bit(a) || !is63bit(b) {
  1122  				return makeInt(newInt().Sub(big.NewInt(a), big.NewInt(b)))
  1123  			}
  1124  			c = a - b
  1125  		case token.MUL:
  1126  			if !is32bit(a) || !is32bit(b) {
  1127  				return makeInt(newInt().Mul(big.NewInt(a), big.NewInt(b)))
  1128  			}
  1129  			c = a * b
  1130  		case token.QUO:
  1131  			return makeRat(big.NewRat(a, b))
  1132  		case token.QUO_ASSIGN: // force integer division
  1133  			c = a / b
  1134  		case token.REM:
  1135  			c = a % b
  1136  		case token.AND:
  1137  			c = a & b
  1138  		case token.OR:
  1139  			c = a | b
  1140  		case token.XOR:
  1141  			c = a ^ b
  1142  		case token.AND_NOT:
  1143  			c = a &^ b
  1144  		default:
  1145  			goto Error
  1146  		}
  1147  		return int64Val(c)
  1148  
  1149  	case intVal:
  1150  		a := x.val
  1151  		b := y.(intVal).val
  1152  		c := newInt()
  1153  		switch op {
  1154  		case token.ADD:
  1155  			c.Add(a, b)
  1156  		case token.SUB:
  1157  			c.Sub(a, b)
  1158  		case token.MUL:
  1159  			c.Mul(a, b)
  1160  		case token.QUO:
  1161  			return makeRat(newRat().SetFrac(a, b))
  1162  		case token.QUO_ASSIGN: // force integer division
  1163  			c.Quo(a, b)
  1164  		case token.REM:
  1165  			c.Rem(a, b)
  1166  		case token.AND:
  1167  			c.And(a, b)
  1168  		case token.OR:
  1169  			c.Or(a, b)
  1170  		case token.XOR:
  1171  			c.Xor(a, b)
  1172  		case token.AND_NOT:
  1173  			c.AndNot(a, b)
  1174  		default:
  1175  			goto Error
  1176  		}
  1177  		return makeInt(c)
  1178  
  1179  	case ratVal:
  1180  		a := x.val
  1181  		b := y.(ratVal).val
  1182  		c := newRat()
  1183  		switch op {
  1184  		case token.ADD:
  1185  			c.Add(a, b)
  1186  		case token.SUB:
  1187  			c.Sub(a, b)
  1188  		case token.MUL:
  1189  			c.Mul(a, b)
  1190  		case token.QUO:
  1191  			c.Quo(a, b)
  1192  		default:
  1193  			goto Error
  1194  		}
  1195  		return makeRat(c)
  1196  
  1197  	case floatVal:
  1198  		a := x.val
  1199  		b := y.(floatVal).val
  1200  		c := newFloat()
  1201  		switch op {
  1202  		case token.ADD:
  1203  			c.Add(a, b)
  1204  		case token.SUB:
  1205  			c.Sub(a, b)
  1206  		case token.MUL:
  1207  			c.Mul(a, b)
  1208  		case token.QUO:
  1209  			c.Quo(a, b)
  1210  		default:
  1211  			goto Error
  1212  		}
  1213  		return makeFloat(c)
  1214  
  1215  	case complexVal:
  1216  		y := y.(complexVal)
  1217  		a, b := x.re, x.im
  1218  		c, d := y.re, y.im
  1219  		var re, im Value
  1220  		switch op {
  1221  		case token.ADD:
  1222  			// (a+c) + i(b+d)
  1223  			re = add(a, c)
  1224  			im = add(b, d)
  1225  		case token.SUB:
  1226  			// (a-c) + i(b-d)
  1227  			re = sub(a, c)
  1228  			im = sub(b, d)
  1229  		case token.MUL:
  1230  			// (ac-bd) + i(bc+ad)
  1231  			ac := mul(a, c)
  1232  			bd := mul(b, d)
  1233  			bc := mul(b, c)
  1234  			ad := mul(a, d)
  1235  			re = sub(ac, bd)
  1236  			im = add(bc, ad)
  1237  		case token.QUO:
  1238  			// (ac+bd)/s + i(bc-ad)/s, with s = cc + dd
  1239  			ac := mul(a, c)
  1240  			bd := mul(b, d)
  1241  			bc := mul(b, c)
  1242  			ad := mul(a, d)
  1243  			cc := mul(c, c)
  1244  			dd := mul(d, d)
  1245  			s := add(cc, dd)
  1246  			re = add(ac, bd)
  1247  			re = quo(re, s)
  1248  			im = sub(bc, ad)
  1249  			im = quo(im, s)
  1250  		default:
  1251  			goto Error
  1252  		}
  1253  		return makeComplex(re, im)
  1254  
  1255  	case *stringVal:
  1256  		if op == token.ADD {
  1257  			return &stringVal{l: x, r: y.(*stringVal)}
  1258  		}
  1259  	}
  1260  
  1261  Error:
  1262  	panic(fmt.Sprintf("invalid binary operation %v %s %v", x_, op, y_))
  1263  }
  1264  
  1265  func add(x, y Value) Value { return BinaryOp(x, token.ADD, y) }
  1266  func sub(x, y Value) Value { return BinaryOp(x, token.SUB, y) }
  1267  func mul(x, y Value) Value { return BinaryOp(x, token.MUL, y) }
  1268  func quo(x, y Value) Value { return BinaryOp(x, token.QUO, y) }
  1269  
  1270  // Shift returns the result of the shift expression x op s
  1271  // with op == token.SHL or token.SHR (<< or >>). x must be
  1272  // an Int or an Unknown. If x is Unknown, the result is x.
  1273  //
  1274  func Shift(x Value, op token.Token, s uint) Value {
  1275  	switch x := x.(type) {
  1276  	case unknownVal:
  1277  		return x
  1278  
  1279  	case int64Val:
  1280  		if s == 0 {
  1281  			return x
  1282  		}
  1283  		switch op {
  1284  		case token.SHL:
  1285  			z := i64toi(x).val
  1286  			return makeInt(z.Lsh(z, s))
  1287  		case token.SHR:
  1288  			return x >> s
  1289  		}
  1290  
  1291  	case intVal:
  1292  		if s == 0 {
  1293  			return x
  1294  		}
  1295  		z := newInt()
  1296  		switch op {
  1297  		case token.SHL:
  1298  			return makeInt(z.Lsh(x.val, s))
  1299  		case token.SHR:
  1300  			return makeInt(z.Rsh(x.val, s))
  1301  		}
  1302  	}
  1303  
  1304  	panic(fmt.Sprintf("invalid shift %v %s %d", x, op, s))
  1305  }
  1306  
  1307  func cmpZero(x int, op token.Token) bool {
  1308  	switch op {
  1309  	case token.EQL:
  1310  		return x == 0
  1311  	case token.NEQ:
  1312  		return x != 0
  1313  	case token.LSS:
  1314  		return x < 0
  1315  	case token.LEQ:
  1316  		return x <= 0
  1317  	case token.GTR:
  1318  		return x > 0
  1319  	case token.GEQ:
  1320  		return x >= 0
  1321  	}
  1322  	panic(fmt.Sprintf("invalid comparison %v %s 0", x, op))
  1323  }
  1324  
  1325  // Compare returns the result of the comparison x op y.
  1326  // The comparison must be defined for the operands.
  1327  // If one of the operands is Unknown, the result is
  1328  // false.
  1329  //
  1330  func Compare(x_ Value, op token.Token, y_ Value) bool {
  1331  	x, y := match(x_, y_)
  1332  
  1333  	switch x := x.(type) {
  1334  	case unknownVal:
  1335  		return false
  1336  
  1337  	case boolVal:
  1338  		y := y.(boolVal)
  1339  		switch op {
  1340  		case token.EQL:
  1341  			return x == y
  1342  		case token.NEQ:
  1343  			return x != y
  1344  		}
  1345  
  1346  	case int64Val:
  1347  		y := y.(int64Val)
  1348  		switch op {
  1349  		case token.EQL:
  1350  			return x == y
  1351  		case token.NEQ:
  1352  			return x != y
  1353  		case token.LSS:
  1354  			return x < y
  1355  		case token.LEQ:
  1356  			return x <= y
  1357  		case token.GTR:
  1358  			return x > y
  1359  		case token.GEQ:
  1360  			return x >= y
  1361  		}
  1362  
  1363  	case intVal:
  1364  		return cmpZero(x.val.Cmp(y.(intVal).val), op)
  1365  
  1366  	case ratVal:
  1367  		return cmpZero(x.val.Cmp(y.(ratVal).val), op)
  1368  
  1369  	case floatVal:
  1370  		return cmpZero(x.val.Cmp(y.(floatVal).val), op)
  1371  
  1372  	case complexVal:
  1373  		y := y.(complexVal)
  1374  		re := Compare(x.re, token.EQL, y.re)
  1375  		im := Compare(x.im, token.EQL, y.im)
  1376  		switch op {
  1377  		case token.EQL:
  1378  			return re && im
  1379  		case token.NEQ:
  1380  			return !re || !im
  1381  		}
  1382  
  1383  	case *stringVal:
  1384  		xs := x.string()
  1385  		ys := y.(*stringVal).string()
  1386  		switch op {
  1387  		case token.EQL:
  1388  			return xs == ys
  1389  		case token.NEQ:
  1390  			return xs != ys
  1391  		case token.LSS:
  1392  			return xs < ys
  1393  		case token.LEQ:
  1394  			return xs <= ys
  1395  		case token.GTR:
  1396  			return xs > ys
  1397  		case token.GEQ:
  1398  			return xs >= ys
  1399  		}
  1400  	}
  1401  
  1402  	panic(fmt.Sprintf("invalid comparison %v %s %v", x_, op, y_))
  1403  }
  1404  

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