// valString returns the string representation for the value v.
// Setting floatFmt forces an integer value to be formatted in
// normalized floating-point format.
// TODO(gri) Move this code into package exact.
func valString(v exact.Value, floatFmt bool) string {
	switch v.Kind() {
	case exact.Int:
		if floatFmt {
			return floatString(v)
		}
	case exact.Float:
		return floatString(v)
	case exact.Complex:
		re := exact.Real(v)
		im := exact.Imag(v)
		var s string
		if exact.Sign(re) != 0 {
			s = floatString(re)
			if exact.Sign(im) >= 0 {
				s += " + "
			} else {
				s += " - "
				im = exact.UnaryOp(token.SUB, im, 0) // negate im
			}
		}
		// im != 0, otherwise v would be exact.Int or exact.Float
		return s + floatString(im) + "i"
	}
	return v.String()
}

// floatString returns the string representation for a
// numeric value v in normalized floating-point format.
func floatString(v exact.Value) string {
	if exact.Sign(v) == 0 {
		return "0.0"
	}
	// x != 0

	// convert |v| into a big.Rat x
	x := new(big.Rat).SetFrac(absInt(exact.Num(v)), absInt(exact.Denom(v)))

	// normalize x and determine exponent e
	// (This is not very efficient, but also not speed-critical.)
	var e int
	for x.Cmp(ten) >= 0 {
		x.Quo(x, ten)
		e++
	}
	for x.Cmp(one) < 0 {
		x.Mul(x, ten)
		e--
	}

	// TODO(gri) Values such as 1/2 are easier to read in form 0.5
	// rather than 5.0e-1. Similarly, 1.0e1 is easier to read as
	// 10.0. Fine-tune best exponent range for readability.

	s := x.FloatString(100) // good-enough precision

	// trim trailing 0's
	i := len(s)
	for i > 0 && s[i-1] == '0' {
		i--
	}
	s = s[:i]

	// add a 0 if the number ends in decimal point
	if len(s) > 0 && s[len(s)-1] == '.' {
		s += "0"
	}

	// add exponent and sign
	if e != 0 {
		s += fmt.Sprintf("e%+d", e)
	}
	if exact.Sign(v) < 0 {
		s = "-" + s
	}

	// TODO(gri) If v is a "small" fraction (i.e., numerator and denominator
	// are just a small number of decimal digits), add the exact fraction as
	// a comment. For instance: 3.3333...e-1 /* = 1/3 */

	return s
}

func (p *exporter) float(x exact.Value) {
	sign := exact.Sign(x)
	p.int(sign)
	if sign == 0 {
		return
	}

	p.ufloat(x)
}

func (p *exporter) fraction(x exact.Value) {
	sign := exact.Sign(x)
	p.int(sign)
	if sign == 0 {
		return
	}

	p.ufloat(exact.Num(x))
	p.ufloat(exact.Denom(x))
}

// index checks an index expression for validity.
// If max >= 0, it is the upper bound for index.
// If index is valid and the result i >= 0, then i is the constant value of index.
func (check *Checker) index(index ast.Expr, max int64) (i int64, valid bool) {
	var x operand
	check.expr(&x, index)
	if x.mode == invalid {
		return
	}

	// an untyped constant must be representable as Int
	check.convertUntyped(&x, Typ[Int])
	if x.mode == invalid {
		return
	}

	// the index must be of integer type
	if !isInteger(x.typ) {
		check.invalidArg(x.pos(), "index %s must be integer", &x)
		return
	}

	// a constant index i must be in bounds
	if x.mode == constant {
		if exact.Sign(x.val) < 0 {
			check.invalidArg(x.pos(), "index %s must not be negative", &x)
			return
		}
		i, valid = exact.Int64Val(x.val)
		if !valid || max >= 0 && i >= max {
			check.errorf(x.pos(), "index %s is out of bounds", &x)
			return i, false
		}
		// 0 <= i [ && i < max ]
		return i, true
	}

	return -1, true
}

func (check *Checker) binary(x *operand, lhs, rhs ast.Expr, op token.Token) {
	var y operand

	check.expr(x, lhs)
	check.expr(&y, rhs)

	if x.mode == invalid {
		return
	}
	if y.mode == invalid {
		x.mode = invalid
		x.expr = y.expr
		return
	}

	if isShift(op) {
		check.shift(x, &y, op)
		return
	}

	check.convertUntyped(x, y.typ)
	if x.mode == invalid {
		return
	}
	check.convertUntyped(&y, x.typ)
	if y.mode == invalid {
		x.mode = invalid
		return
	}

	if isComparison(op) {
		check.comparison(x, &y, op)
		return
	}

	if !Identical(x.typ, y.typ) {
		// only report an error if we have valid types
		// (otherwise we had an error reported elsewhere already)
		if x.typ != Typ[Invalid] && y.typ != Typ[Invalid] {
			check.invalidOp(x.pos(), "mismatched types %s and %s", x.typ, y.typ)
		}
		x.mode = invalid
		return
	}

	if !check.op(binaryOpPredicates, x, op) {
		x.mode = invalid
		return
	}

	if (op == token.QUO || op == token.REM) && (x.mode == constant || isInteger(x.typ)) && y.mode == constant && exact.Sign(y.val) == 0 {
		check.invalidOp(y.pos(), "division by zero")
		x.mode = invalid
		return
	}

	if x.mode == constant && y.mode == constant {
		typ := x.typ.Underlying().(*Basic)
		// force integer division of integer operands
		if op == token.QUO && isInteger(typ) {
			op = token.QUO_ASSIGN
		}
		x.val = exact.BinaryOp(x.val, op, y.val)
		// Typed constants must be representable in
		// their type after each constant operation.
		if isTyped(typ) {
			check.representable(x, typ)
		}
		return
	}

	x.mode = value
	// x.typ is unchanged
}

func (check *Checker) shift(x, y *operand, op token.Token) {
	untypedx := isUntyped(x.typ)

	// The lhs must be of integer type or be representable
	// as an integer; otherwise the shift has no chance.
	if !isInteger(x.typ) && (!untypedx || !representableConst(x.val, nil, UntypedInt, nil)) {
		check.invalidOp(x.pos(), "shifted operand %s must be integer", x)
		x.mode = invalid
		return
	}

	// spec: "The right operand in a shift expression must have unsigned
	// integer type or be an untyped constant that can be converted to
	// unsigned integer type."
	switch {
	case isInteger(y.typ) && isUnsigned(y.typ):
		// nothing to do
	case isUntyped(y.typ):
		check.convertUntyped(y, Typ[UntypedInt])
		if y.mode == invalid {
			x.mode = invalid
			return
		}
	default:
		check.invalidOp(y.pos(), "shift count %s must be unsigned integer", y)
		x.mode = invalid
		return
	}

	if x.mode == constant {
		if y.mode == constant {
			// rhs must be within reasonable bounds
			const stupidShift = 1023 - 1 + 52 // so we can express smallestFloat64
			s, ok := exact.Uint64Val(y.val)
			if !ok || s > stupidShift {
				check.invalidOp(y.pos(), "stupid shift count %s", y)
				x.mode = invalid
				return
			}
			// The lhs is representable as an integer but may not be an integer
			// (e.g., 2.0, an untyped float) - this can only happen for untyped
			// non-integer numeric constants. Correct the type so that the shift
			// result is of integer type.
			if !isInteger(x.typ) {
				x.typ = Typ[UntypedInt]
			}
			x.val = exact.Shift(x.val, op, uint(s))
			return
		}

		// non-constant shift with constant lhs
		if untypedx {
			// spec: "If the left operand of a non-constant shift
			// expression is an untyped constant, the type of the
			// constant is what it would be if the shift expression
			// were replaced by its left operand alone.".
			//
			// Delay operand checking until we know the final type:
			// The lhs expression must be in the untyped map, mark
			// the entry as lhs shift operand.
			info, found := check.untyped[x.expr]
			assert(found)
			info.isLhs = true
			check.untyped[x.expr] = info
			// keep x's type
			x.mode = value
			return
		}
	}

	// constant rhs must be >= 0
	if y.mode == constant && exact.Sign(y.val) < 0 {
		check.invalidOp(y.pos(), "shift count %s must not be negative", y)
	}

	// non-constant shift - lhs must be an integer
	if !isInteger(x.typ) {
		check.invalidOp(x.pos(), "shifted operand %s must be integer", x)
		x.mode = invalid
		return
	}

	x.mode = value
}

// representableConst reports whether x can be represented as
// value of the given basic type kind and for the configuration
// provided (only needed for int/uint sizes).
//
// If rounded != nil, *rounded is set to the rounded value of x for
// representable floating-point values; it is left alone otherwise.
// It is ok to provide the addressof the first argument for rounded.
func representableConst(x exact.Value, conf *Config, as BasicKind, rounded *exact.Value) bool {
	switch x.Kind() {
	case exact.Unknown:
		return true

	case exact.Bool:
		return as == Bool || as == UntypedBool

	case exact.Int:
		if x, ok := exact.Int64Val(x); ok {
			switch as {
			case Int:
				var s = uint(conf.sizeof(Typ[as])) * 8
				return int64(-1)<<(s-1) <= x && x <= int64(1)<<(s-1)-1
			case Int8:
				const s = 8
				return -1<<(s-1) <= x && x <= 1<<(s-1)-1
			case Int16:
				const s = 16
				return -1<<(s-1) <= x && x <= 1<<(s-1)-1
			case Int32:
				const s = 32
				return -1<<(s-1) <= x && x <= 1<<(s-1)-1
			case Int64:
				return true
			case Uint, Uintptr:
				if s := uint(conf.sizeof(Typ[as])) * 8; s < 64 {
					return 0 <= x && x <= int64(1)<<s-1
				}
				return 0 <= x
			case Uint8:
				const s = 8
				return 0 <= x && x <= 1<<s-1
			case Uint16:
				const s = 16
				return 0 <= x && x <= 1<<s-1
			case Uint32:
				const s = 32
				return 0 <= x && x <= 1<<s-1
			case Uint64:
				return 0 <= x
			case Float32, Float64, Complex64, Complex128,
				UntypedInt, UntypedFloat, UntypedComplex:
				return true
			}
		}

		n := exact.BitLen(x)
		switch as {
		case Uint, Uintptr:
			var s = uint(conf.sizeof(Typ[as])) * 8
			return exact.Sign(x) >= 0 && n <= int(s)
		case Uint64:
			return exact.Sign(x) >= 0 && n <= 64
		case Float32, Complex64:
			if rounded == nil {
				return fitsFloat32(x)
			}
			r := roundFloat32(x)
			if r != nil {
				*rounded = r
				return true
			}
		case Float64, Complex128:
			if rounded == nil {
				return fitsFloat64(x)
			}
			r := roundFloat64(x)
			if r != nil {
				*rounded = r
				return true
			}
		case UntypedInt, UntypedFloat, UntypedComplex:
			return true
		}

	case exact.Float:
		switch as {
		case Float32, Complex64:
			if rounded == nil {
				return fitsFloat32(x)
			}
			r := roundFloat32(x)
			if r != nil {
				*rounded = r
				return true
			}
		case Float64, Complex128:
			if rounded == nil {
				return fitsFloat64(x)
			}
			r := roundFloat64(x)
			if r != nil {
//.........这里部分代码省略.........