content/constants.article - blog - Git at Google

 Constants
 25 Aug 2014
 Tags: constants

 Rob Pike

 * Introduction

 Go is a statically typed language that does not permit operations that mix numeric types.
 You can't add a `float64` to an `int`, or even an `int32` to an `int`.
 Yet it is legal to write `1e6*time.Second` or `math.Exp(1)` or even `1<<('\t'+2.0)`.
 In Go, constants, unlike variables, behave pretty much like regular numbers.
 This post explains why that is and what it means.

 * Background: C

 In the early days of thinking about Go, we talked about a number of problems caused by the way C and its descendants let you mix and match numeric types.
 Many mysterious bugs, crashes, and portability problems are caused by expressions that combine integers of different sizes and "signedness".
 Although to a seasoned C programmer the result of a calculation like

 	unsigned int u = 1e9;
 	long signed int i = -1;
 	... i + u ...

 may be familiar, it isn't _a_priori_ obvious.
 How big is the result?
 What is its value?
 Is it signed or unsigned?

 Nasty bugs lurk here.

 C has a set of rules called "the usual arithmetic conversions" and it is an indicator of their subtlety that they have changed over the years (introducing yet more bugs, retroactively).

 When designing Go, we decided to avoid this minefield by mandating that there is _no_ mixing of numeric types.
 If you want to add `i` and `u`, you must be explicit about what you want the result to be.
 Given

 	var u uint
 	var i int

 you can write either `uint(i)+u` or `i+int(u)`, with both the meaning and type of the addition clearly expressed, but unlike in C you cannot write `i+u`.
 You can't even mix `int` and `int32`, even when `int` is a 32-bit type.

 This strictness eliminates a common cause of bugs and other failures.
 It is a vital property of Go.
 But it has a cost: it sometimes requires programmers to decorate their code with clumsy numeric conversions to express their meaning clearly.

 And what about constants?
 Given the declarations above, what would make it legal to write `i` `=` `0` or `u` `=` `0`?
 What is the _type_ of `0`?
 It would be unreasonable to require constants to have type conversions in simple contexts such as `i` `=` `int(0)`.

 We soon realized the answer lay in making numeric constants work differently from how they behave in other C-like languages.
 After much thinking and experimentation, we came up with a design that we believe feels right almost always, freeing the programmer from converting constants all the time yet being able to write things like `math.Sqrt(2)` without being chided by the compiler.

 In short, constants in Go just work, most of the time anyway.
 Let's see how that happens.

 * Terminology

 First, a quick definition.
 In Go, `const` is a keyword introducing a name for a scalar value such as `2` or `3.14159` or `"scrumptious"`.
 Such values, named or otherwise, are called _constants_ in Go.
 Constants can also be created by expressions built from constants, such as `2+3` or `2+3i` or `math.Pi/2` or `("go"+"pher")`.

 Some languages don't have constants, and others have a more general definition of constant or application of the word `const`.
 In C and C++, for instance, `const` is a type qualifier that can codify more intricate properties of more intricate values.

 But in Go, a constant is just a simple, unchanging value, and from here on we're talking only about Go.

 * String constants

 There are many kinds of numeric constants—integers, floats, runes, signed, unsigned, imaginary, complex—so let's start with a simpler form of constant: strings.
 String constants are easy to understand and provide a smaller space in which to explore the type issues of constants in Go.

 A string constant encloses some text between double quotes.
 (Go also has raw string literals, enclosed by backquotes ``````, but for the purpose of this discussion they have all the same properties.)
 Here is a string constant:

 	"Hello, 世界"

 (For much more detail about the representation and interpretation of strings, see [[https://blog.golang.org/strings][this blog post]].)

 What type does this string constant have?
 The obvious answer is `string`, but that is _wrong_.

 This is an _untyped_string_constant_, which is to say it is a constant textual value that does not yet have a fixed type.
 Yes, it's a string, but it's not a Go value of type `string`.
 It remains an untyped string constant even when given a name:

 	const hello = "Hello, 世界"

 After this declaration, `hello` is also an untyped string constant.
 An untyped constant is just a value, one not yet given a defined type that would force it to obey the strict rules that prevent combining differently typed values.

 It is this notion of an _untyped_ constant that makes it possible for us to use constants in Go with great freedom.

 So what, then, is a _typed_ string constant?
 It's one that's been given a type, like this:

 	const typedHello string = "Hello, 世界"

 Notice that the declaration of `typedHello` has an explicit `string` type before the equals sign.
 This means that `typedHello` has Go type `string`, and cannot be assigned to a Go variable of a different type.
 That is to say, this code works:

 .play -edit constants/string1.go /START/,/STOP/

 but this does not:

 .play -edit constants/string2.go /START/,/STOP/

 The variable `m` has type `MyString` and cannot be assigned a value of a different type.
 It can only be assigned values of type `MyString`, like this:

 .play -edit constants/string3.go /START/,/STOP/

 or by forcing the issue with a conversion, like this:

 .play -edit constants/string4.go /START/,/STOP/

 Returning to our _untyped_ string constant, it has the helpful property that, since it has no type, assigning it to a typed variable does not cause a type error.
 That is, we can write

 	m = "Hello, 世界"

 or

 	m = hello

 because, unlike the typed constants `typedHello` and `myStringHello`, the untyped constants `"Hello,`世界"` and `hello` _have_no_type_.
 Assigning them to a variable of any type compatible with strings works without error.

 These untyped string constants are strings, of course, so they can only be used where a string is allowed, but they do not have _type_ `string`.

 * Default type

 As a Go programmer, you have certainly seen many declarations like

 	str := "Hello, 世界"

 and by now you might be asking, "if the constant is untyped, how does `str` get a type in this variable declaration?"
 The answer is that an untyped constant has a default type, an implicit type that it transfers to a value if a type is needed where none is provided.
 For untyped string constants, that default type is obviously `string`, so

 	str := "Hello, 世界"

 or

 	var str = "Hello, 世界"

 means exactly the same as

 	var str string = "Hello, 世界"

 One way to think about untyped constants is that they live in a kind of ideal space of values, a space less restrictive than Go's full type system.
 But to do anything with them, we need to assign them to variables, and when that happens the _variable_ (not the constant itself) needs a type, and the constant can tell the variable what type it should have.
 In this example, `str` becomes a value of type `string` because the untyped string constant gives the declaration its default type, `string`.

 In such a declaration, a variable is declared with a type and initial value.
 Sometimes when we use a constant, however, the destination of the value is not so clear.
 For instance consider this statement:

 .play -edit constants/default1.go /START/,/STOP/

 The signature of `fmt.Printf` is

 	func Printf(format string, a ...interface{}) (n int, err error)

 which is to say its arguments (after the format string) are interface values.
 What happens when `fmt.Printf` is called with an untyped constant is that an interface value is created
 to pass as an argument, and the concrete type stored for that argument is the default type of the constant.
 This process is analogous to what we saw earlier when declaring an initialized value using an untyped string constant.

 You can see the result in this example, which uses the format `%v` to print the value and `%T` to print the type of the value being passed to `fmt.Printf`:

 .play -edit constants/default2.go /START/,/STOP/

 If the constant has a type, that goes into the interface, as this example shows:

 .play -edit constants/default3.go /START/,/STOP/

 (For more information about how interface values work, see the first sections of [[https://blog.golang.org/laws-of-reflection][this blog post]].)

 In summary, a typed constant obeys all the rules of typed values in Go.
 On the other hand, an untyped constant does not carry a Go type in the same way and can be mixed and matched more freely.
 It does, however, have a default type that is exposed when, and only when, no other type information is available.

 * Default type determined by syntax

 The default type of an untyped constant is determined by its syntax.
 For string constants, the only possible implicit type is `string`.
 For [[https://golang.org/ref/spec#Numeric_types][numeric constants]], the implicit type has more variety.
 Integer constants default to `int`, floating-point constants `float64`, rune constants to `rune` (an alias for `int32`), and imaginary constants to `complex128`.
 Here's our canonical print statement used repeatedly to show the default types in action:

 .play -edit constants/syntax.go /START/,/STOP/

 (Exercise: Explain the result for `'x'`.)

 * Booleans

 Everything we said about untyped string constants can be said for untyped boolean constants.
 The values `true` and `false` are untyped boolean constants that can be assigned to any boolean variable,
 but once given a type, boolean variables cannot be mixed:

 .play -edit constants/bool.go /START/,/STOP/

 Run the example and see what happens, then comment out the "Bad" line and run it again.
 The pattern here follows exactly that of string constants.

 * Floats

 Floating-point constants are just like boolean constants in most respects.
 Our standard example works as expected in translation:

 .play -edit constants/float1.go /START/,/STOP/

 One wrinkle is that there are _two_ floating-point types in Go: `float32` and `float64`.
 The default type for a floating-point constant is `float64`, although an untyped floating-point
 constant can be assigned to a `float32` value just fine:

 .play -edit constants/float2.go /START/,/STOP/

 Floating-point values are a good place to introduce the concept of overflow, or the range of values.

 Numeric constants live in an arbitrary-precision numeric space; they are just regular numbers.
 But when they are assigned to a variable the value must be able to fit in the destination.
 We can declare a constant with a very large value:

 .code constants/float3.go /Huge/

 —that's just a number, after all—but we can't assign it or even print it. This statement won't even compile:

 .play -edit constants/float3.go /Println/

 The error is, "constant 1.00000e+1000 overflows float64", which is true.
 But `Huge` might be useful: we can use it in expressions with other constants and use the value of those expressions if the result
 can be represented in the range of a `float64`.
 The statement,

 .play -edit constants/float4.go /Println/

 prints `10`, as one would expect.

 In a related way, floating-point constants may have very high precision, so that arithmetic involving them is more accurate.
 The constants defined in the [[https://golang.org/pkg/math][math]] package are given with many more digits than are
 available in a `float64`. Here is the definition of `math.Pi`:

 	Pi	= 3.14159265358979323846264338327950288419716939937510582097494459

 When that value is assigned to a variable, some of the precision will be lost; the assignment will create the `float64` (or `float32`)
 value closest to the high-precision value. This snippet

 .play -edit constants/float5.go /START/,/STOP/

 prints `3.141592653589793`.

 Having so many digits available means that calculations like `Pi/2` or other more intricate evaluations can carry more precision
 until the result is assigned, making calculations involving constants easier to write without losing precision.
 It also means that there is no occasion in which the floating-point corner cases like infinities,
 soft underflows, and `NaNs` arise in constant expressions.
 (Division by a constant zero is a compile-time error, and when everything is a number there's no such thing as "not a number".)

 * Complex numbers

 Complex constants behave a lot like floating-point constants.
 Here's a version of our now-familiar litany translated into complex numbers:

 .play -edit constants/complex1.go /START/,/STOP/

 The default type of a complex number is `complex128`, the larger-precision version composed of two `float64` values.

 For clarity in our example, we wrote out the full expression `(0.0+1.0i)`, but this value can be shortened to `0.0+1.0i`,
 `1.0i` or even `1i`.

 Let's play a trick.
 We know that in Go, a numeric constant is just a number.
 What if that number is a complex number with no imaginary part, that is, a real?
 Here's one:

 .code constants/complex2.go /const Two/

 That's an untyped complex constant.
 Even though it has no imaginary part, the _syntax_ of the expression defines it to have default type `complex128`.
 Therefore, if we use it to declare a variable, the default type will be `complex128`. The snippet

 .play -edit constants/complex2.go /START/,/STOP/

 prints `complex128:` `(2+0i)`.
 But numerically, `Two` can be stored in a scalar floating-point number, a `float64` or `float32`, with no loss of information.
 Thus we can assign `Two` to a `float64`, either in an initialization or an assignment, without problems:

 .play -edit constants/complex3.go /START/,/STOP/

 The output is `2` `and` `2`.
 Even though `Two` is a complex constant, it can be assigned to scalar floating-point variables.
 This ability for a constant to "cross" types like this will prove useful.

 * Integers

 At last we come to integers.
 They have more moving parts—[[https://golang.org/ref/spec#Numeric_types][many sizes, signed or unsigned, and more]]—but they play by the same rules.
 For the last time, here is our familiar example, using just `int` this time:

 .play -edit constants/int1.go /START/,/STOP/

 The same example could be built for any of the integer types, which are:

 	int int8 int16 int32 int64
 	uint uint8 uint16 uint32 uint64
 	uintptr

 (plus the aliases `byte` for `uint8` and `rune` for `int32`).
 That's a lot, but the pattern in the way constants work should be familiar enough by now that you can see how things will play out.

 As mentioned above, integers come in a couple of forms and each form has its own default type: `int` for simple constants like `123` or `0xFF` or `-14`
 and `rune` for quoted characters like 'a', '世' or '\r'.

 No constant form has as its default type an unsigned integer type.
 However, the flexibility of untyped constants means we can initialize unsigned integer variables using simple constants as long as we are clear about the type.
 It's analogous to how we can initialize a `float64` using a complex number with zero imaginary part.
 Here are several different ways to initialize a `uint`; all are equivalent, but all must mention the type explicitly for the result to be unsigned.

 	var u uint = 17
 	var u = uint(17)
 	u := uint(17)

 Similarly to the range issue mentioned in the section on floating-point values, not all integer values can fit in all integer types.
 There are two problems that might arise: the value might be too large, or it might be a negative value being assigned to an unsigned integer type.
 For instance, `int8` has range -128 through 127, so constants outside of that range can never be assigned to a variable of type `int8`:

 .play -edit constants/int2.go /var/

 Similarly, `uint8`, also known as `byte`, has range 0 through 255, so a large or negative constant cannot be assigned to a `uint8`:

 .play -edit constants/int3.go /var/

 This type-checking can catch mistakes like this one:

 .play -edit constants/int4.go /START/,/STOP/

 If the compiler complains about your use of a constant, it's likely a real bug like this.

 * An exercise: The largest unsigned int

 Here is an informative little exercise.
 How do we express a constant representing the largest value that fits in a `uint`?
 If we were talking about `uint32` rather than `uint`, we could write

 	const MaxUint32 = 1<<32 - 1

 but we want `uint`, not `uint32`.
 The `int` and `uint` types have equal unspecified numbers of bits, either 32 or 64.
 Since the number of bits available depends on the architecture, we can't just write down a single value.

 Fans of [[http://en.wikipedia.org/wiki/Two's_complement][two's-complement arithmetic]],
 which Go's integers are defined to use, know that the representation of `-1` has all its bits set to 1,
 so the bit pattern of `-1` is internally the same as that of the
 largest unsigned integer.
 We therefore might think we could write

 .play -edit constants/exercise1.go /const/

 but that is illegal because -1 cannot be represented by an unsigned variable; `-1` is not in the range of unsigned values.
 A conversion won't help either, for the same reason:

 .play -edit constants/exercise2.go /const/

 Even though at run-time a value of -1 can be converted to an unsigned integer, the rules
 for constant [[https://golang.org/ref/spec#Conversions][conversions]] forbid this kind of coercion at compile time.
 That is to say, this works:

 .play -edit constants/exercise3.go /START/,/STOP/

 but only because `v` is a variable; if we made `v` a constant, even an untyped constant, we'd be back in forbidden territory:

 .play -edit constants/exercise4.go /START/,/STOP/

 We return to our previous approach, but instead of `-1` we try `^0`, the bitwise negation of an arbitrary number of zero bits.
 But that fails too, for a similar reason:
 In the space of numeric values,
 `^0` represents an infinite number of ones, so we lose information if we assign that to any fixed-size integer:

 .play -edit constants/exercise5.go /const/

 How then do we represent the largest unsigned integer as a constant?

 The key is to constrain the operation to the number of bits in a `uint` and avoiding
 values, such as negative numbers, that are not representable in a `uint`.
 The simplest `uint` value is the typed constant `uint(0)`.
 If `uints` have 32 or 64 bits, `uint(0)` has 32 or 64 zero bits accordingly.
 If we invert each of those bits, we'll get the correct number of one bits, which is the largest `uint` value.

 Therefore we don't flip the bits of the untyped constant `0`, we flip the bits of the typed constant `uint(0)`.
 Here, then, is our constant:

 .play -edit constants/exercise6.go /START/,/STOP/

 Whatever the number of bits it takes to represent a `uint` in the current execution environment
 (on the [[https://blog.golang.org/playground][playground]], it's 32),
 this constant correctly represents the largest value a variable of type `uint` can hold.

 If you understand the analysis that got us to this result, you understand all the important points about constants in Go.

 * Numbers

 The concept of untyped constants in Go means that all the numeric constants, whether integer, floating-point, complex, or even character values,
 live in a kind of unified space.
 It's when we bring them to the computational world of variables, assignments, and operations that the actual types matter.
 But as long as we stay in the world of numeric constants, we can mix and match values as we like.
 All these constants have numeric value 1:

 	1
 	1.000
 	1e3-99.0*10-9
 	'\x01'
 	'\u0001'
 	'b' - 'a'
 	1.0+3i-3.0i

 Therefore, although they have different implicit default types, written as untyped constants they can be assigned to a variable of any integer type:

 .play -edit constants/numbers1.go /START/,/STOP/

 The output from this snippet is: `1`1`1`1`1`(1+0i)`1`.

 You can even do nutty stuff like

 .play -edit constants/numbers2.go /START/,/STOP/

 which yields 145.5, which is pointless except to prove a point.

 But the real point of these rules is flexibility.
 That flexibility means that, despite the fact that in Go it is illegal in the same expression to mix floating-point and integer variables,
 or even `int` and `int32` variables, it is fine to write

 	sqrt2 := math.Sqrt(2)

 or

 	const millisecond = time.Second/1e3

 or

 	bigBufferWithHeader := make([]byte, 512+1e6)

 and have the results mean what you expect.

 Because in Go, numeric constants work as you expect: like numbers.
	Constants
	25 Aug 2014
	Tags: constants

	Rob Pike

	* Introduction

	Go is a statically typed language that does not permit operations that mix numeric types.
	You can't add a `float64` to an `int`, or even an `int32` to an `int`.
	Yet it is legal to write `1e6*time.Second` or `math.Exp(1)` or even `1<<('\t'+2.0)`.
	In Go, constants, unlike variables, behave pretty much like regular numbers.
	This post explains why that is and what it means.

	* Background: C

	In the early days of thinking about Go, we talked about a number of problems caused by the way C and its descendants let you mix and match numeric types.
	Many mysterious bugs, crashes, and portability problems are caused by expressions that combine integers of different sizes and "signedness".
	Although to a seasoned C programmer the result of a calculation like

	unsigned int u = 1e9;
	long signed int i = -1;
	... i + u ...

	may be familiar, it isn't _a_priori_ obvious.
	How big is the result?
	What is its value?
	Is it signed or unsigned?

	Nasty bugs lurk here.

	C has a set of rules called "the usual arithmetic conversions" and it is an indicator of their subtlety that they have changed over the years (introducing yet more bugs, retroactively).

	When designing Go, we decided to avoid this minefield by mandating that there is _no_ mixing of numeric types.
	If you want to add `i` and `u`, you must be explicit about what you want the result to be.
	Given

	var u uint
	var i int

	you can write either `uint(i)+u` or `i+int(u)`, with both the meaning and type of the addition clearly expressed, but unlike in C you cannot write `i+u`.
	You can't even mix `int` and `int32`, even when `int` is a 32-bit type.

	This strictness eliminates a common cause of bugs and other failures.
	It is a vital property of Go.
	But it has a cost: it sometimes requires programmers to decorate their code with clumsy numeric conversions to express their meaning clearly.

	And what about constants?
	Given the declarations above, what would make it legal to write `i` `=` `0` or `u` `=` `0`?
	What is the _type_ of `0`?
	It would be unreasonable to require constants to have type conversions in simple contexts such as `i` `=` `int(0)`.

	We soon realized the answer lay in making numeric constants work differently from how they behave in other C-like languages.
	After much thinking and experimentation, we came up with a design that we believe feels right almost always, freeing the programmer from converting constants all the time yet being able to write things like `math.Sqrt(2)` without being chided by the compiler.

	In short, constants in Go just work, most of the time anyway.
	Let's see how that happens.

	* Terminology

	First, a quick definition.
	In Go, `const` is a keyword introducing a name for a scalar value such as `2` or `3.14159` or `"scrumptious"`.
	Such values, named or otherwise, are called _constants_ in Go.
	Constants can also be created by expressions built from constants, such as `2+3` or `2+3i` or `math.Pi/2` or `("go"+"pher")`.

	Some languages don't have constants, and others have a more general definition of constant or application of the word `const`.
	In C and C++, for instance, `const` is a type qualifier that can codify more intricate properties of more intricate values.

	But in Go, a constant is just a simple, unchanging value, and from here on we're talking only about Go.

	* String constants

	There are many kinds of numeric constants—integers, floats, runes, signed, unsigned, imaginary, complex—so let's start with a simpler form of constant: strings.
	String constants are easy to understand and provide a smaller space in which to explore the type issues of constants in Go.

	A string constant encloses some text between double quotes.
	(Go also has raw string literals, enclosed by backquotes ``````, but for the purpose of this discussion they have all the same properties.)
	Here is a string constant:

	"Hello, 世界"

	(For much more detail about the representation and interpretation of strings, see [[https://blog.golang.org/strings][this blog post]].)

	What type does this string constant have?
	The obvious answer is `string`, but that is _wrong_.

	This is an _untyped_string_constant_, which is to say it is a constant textual value that does not yet have a fixed type.
	Yes, it's a string, but it's not a Go value of type `string`.
	It remains an untyped string constant even when given a name:

	const hello = "Hello, 世界"

	After this declaration, `hello` is also an untyped string constant.
	An untyped constant is just a value, one not yet given a defined type that would force it to obey the strict rules that prevent combining differently typed values.

	It is this notion of an _untyped_ constant that makes it possible for us to use constants in Go with great freedom.

	So what, then, is a _typed_ string constant?
	It's one that's been given a type, like this:

	const typedHello string = "Hello, 世界"

	Notice that the declaration of `typedHello` has an explicit `string` type before the equals sign.
	This means that `typedHello` has Go type `string`, and cannot be assigned to a Go variable of a different type.
	That is to say, this code works:

	.play -edit constants/string1.go /START/,/STOP/

	but this does not:

	.play -edit constants/string2.go /START/,/STOP/

	The variable `m` has type `MyString` and cannot be assigned a value of a different type.
	It can only be assigned values of type `MyString`, like this:

	.play -edit constants/string3.go /START/,/STOP/

	or by forcing the issue with a conversion, like this:

	.play -edit constants/string4.go /START/,/STOP/

	Returning to our _untyped_ string constant, it has the helpful property that, since it has no type, assigning it to a typed variable does not cause a type error.
	That is, we can write

	m = "Hello, 世界"

	or

	m = hello

	because, unlike the typed constants `typedHello` and `myStringHello`, the untyped constants `"Hello,`世界"` and `hello` _have_no_type_.
	Assigning them to a variable of any type compatible with strings works without error.

	These untyped string constants are strings, of course, so they can only be used where a string is allowed, but they do not have _type_ `string`.

	* Default type

	As a Go programmer, you have certainly seen many declarations like

	str := "Hello, 世界"

	and by now you might be asking, "if the constant is untyped, how does `str` get a type in this variable declaration?"
	The answer is that an untyped constant has a default type, an implicit type that it transfers to a value if a type is needed where none is provided.
	For untyped string constants, that default type is obviously `string`, so

	str := "Hello, 世界"

	or

	var str = "Hello, 世界"

	means exactly the same as

	var str string = "Hello, 世界"

	One way to think about untyped constants is that they live in a kind of ideal space of values, a space less restrictive than Go's full type system.
	But to do anything with them, we need to assign them to variables, and when that happens the _variable_ (not the constant itself) needs a type, and the constant can tell the variable what type it should have.
	In this example, `str` becomes a value of type `string` because the untyped string constant gives the declaration its default type, `string`.

	In such a declaration, a variable is declared with a type and initial value.
	Sometimes when we use a constant, however, the destination of the value is not so clear.
	For instance consider this statement:

	.play -edit constants/default1.go /START/,/STOP/

	The signature of `fmt.Printf` is

	func Printf(format string, a ...interface{}) (n int, err error)

	which is to say its arguments (after the format string) are interface values.
	What happens when `fmt.Printf` is called with an untyped constant is that an interface value is created
	to pass as an argument, and the concrete type stored for that argument is the default type of the constant.
	This process is analogous to what we saw earlier when declaring an initialized value using an untyped string constant.

	You can see the result in this example, which uses the format `%v` to print the value and `%T` to print the type of the value being passed to `fmt.Printf`:

	.play -edit constants/default2.go /START/,/STOP/

	If the constant has a type, that goes into the interface, as this example shows:

	.play -edit constants/default3.go /START/,/STOP/

	(For more information about how interface values work, see the first sections of [[https://blog.golang.org/laws-of-reflection][this blog post]].)

	In summary, a typed constant obeys all the rules of typed values in Go.
	On the other hand, an untyped constant does not carry a Go type in the same way and can be mixed and matched more freely.
	It does, however, have a default type that is exposed when, and only when, no other type information is available.

	* Default type determined by syntax

	The default type of an untyped constant is determined by its syntax.
	For string constants, the only possible implicit type is `string`.
	For [[https://golang.org/ref/spec#Numeric_types][numeric constants]], the implicit type has more variety.
	Integer constants default to `int`, floating-point constants `float64`, rune constants to `rune` (an alias for `int32`), and imaginary constants to `complex128`.
	Here's our canonical print statement used repeatedly to show the default types in action:

	.play -edit constants/syntax.go /START/,/STOP/

	(Exercise: Explain the result for `'x'`.)

	* Booleans

	Everything we said about untyped string constants can be said for untyped boolean constants.
	The values `true` and `false` are untyped boolean constants that can be assigned to any boolean variable,
	but once given a type, boolean variables cannot be mixed:

	.play -edit constants/bool.go /START/,/STOP/

	Run the example and see what happens, then comment out the "Bad" line and run it again.
	The pattern here follows exactly that of string constants.

	* Floats

	Floating-point constants are just like boolean constants in most respects.
	Our standard example works as expected in translation:

	.play -edit constants/float1.go /START/,/STOP/

	One wrinkle is that there are _two_ floating-point types in Go: `float32` and `float64`.
	The default type for a floating-point constant is `float64`, although an untyped floating-point
	constant can be assigned to a `float32` value just fine:

	.play -edit constants/float2.go /START/,/STOP/

	Floating-point values are a good place to introduce the concept of overflow, or the range of values.

	Numeric constants live in an arbitrary-precision numeric space; they are just regular numbers.
	But when they are assigned to a variable the value must be able to fit in the destination.
	We can declare a constant with a very large value:

	.code constants/float3.go /Huge/

	—that's just a number, after all—but we can't assign it or even print it. This statement won't even compile:

	.play -edit constants/float3.go /Println/

	The error is, "constant 1.00000e+1000 overflows float64", which is true.
	But `Huge` might be useful: we can use it in expressions with other constants and use the value of those expressions if the result
	can be represented in the range of a `float64`.
	The statement,

	.play -edit constants/float4.go /Println/

	prints `10`, as one would expect.

	In a related way, floating-point constants may have very high precision, so that arithmetic involving them is more accurate.
	The constants defined in the [[https://golang.org/pkg/math][math]] package are given with many more digits than are
	available in a `float64`. Here is the definition of `math.Pi`:

	Pi = 3.14159265358979323846264338327950288419716939937510582097494459

	When that value is assigned to a variable, some of the precision will be lost; the assignment will create the `float64` (or `float32`)
	value closest to the high-precision value. This snippet

	.play -edit constants/float5.go /START/,/STOP/

	prints `3.141592653589793`.

	Having so many digits available means that calculations like `Pi/2` or other more intricate evaluations can carry more precision
	until the result is assigned, making calculations involving constants easier to write without losing precision.
	It also means that there is no occasion in which the floating-point corner cases like infinities,
	soft underflows, and `NaNs` arise in constant expressions.
	(Division by a constant zero is a compile-time error, and when everything is a number there's no such thing as "not a number".)

	* Complex numbers

	Complex constants behave a lot like floating-point constants.
	Here's a version of our now-familiar litany translated into complex numbers:

	.play -edit constants/complex1.go /START/,/STOP/

	The default type of a complex number is `complex128`, the larger-precision version composed of two `float64` values.

	For clarity in our example, we wrote out the full expression `(0.0+1.0i)`, but this value can be shortened to `0.0+1.0i`,
	`1.0i` or even `1i`.

	Let's play a trick.
	We know that in Go, a numeric constant is just a number.
	What if that number is a complex number with no imaginary part, that is, a real?
	Here's one:

	.code constants/complex2.go /const Two/

	That's an untyped complex constant.
	Even though it has no imaginary part, the _syntax_ of the expression defines it to have default type `complex128`.
	Therefore, if we use it to declare a variable, the default type will be `complex128`. The snippet

	.play -edit constants/complex2.go /START/,/STOP/

	prints `complex128:` `(2+0i)`.
	But numerically, `Two` can be stored in a scalar floating-point number, a `float64` or `float32`, with no loss of information.
	Thus we can assign `Two` to a `float64`, either in an initialization or an assignment, without problems:

	.play -edit constants/complex3.go /START/,/STOP/

	The output is `2` `and` `2`.
	Even though `Two` is a complex constant, it can be assigned to scalar floating-point variables.
	This ability for a constant to "cross" types like this will prove useful.

	* Integers

	At last we come to integers.
	They have more moving parts—[[https://golang.org/ref/spec#Numeric_types][many sizes, signed or unsigned, and more]]—but they play by the same rules.
	For the last time, here is our familiar example, using just `int` this time:

	.play -edit constants/int1.go /START/,/STOP/

	The same example could be built for any of the integer types, which are:

	int int8 int16 int32 int64
	uint uint8 uint16 uint32 uint64
	uintptr

	(plus the aliases `byte` for `uint8` and `rune` for `int32`).
	That's a lot, but the pattern in the way constants work should be familiar enough by now that you can see how things will play out.

	As mentioned above, integers come in a couple of forms and each form has its own default type: `int` for simple constants like `123` or `0xFF` or `-14`
	and `rune` for quoted characters like 'a', '世' or '\r'.

	No constant form has as its default type an unsigned integer type.
	However, the flexibility of untyped constants means we can initialize unsigned integer variables using simple constants as long as we are clear about the type.
	It's analogous to how we can initialize a `float64` using a complex number with zero imaginary part.
	Here are several different ways to initialize a `uint`; all are equivalent, but all must mention the type explicitly for the result to be unsigned.

	var u uint = 17
	var u = uint(17)
	u := uint(17)

	Similarly to the range issue mentioned in the section on floating-point values, not all integer values can fit in all integer types.
	There are two problems that might arise: the value might be too large, or it might be a negative value being assigned to an unsigned integer type.
	For instance, `int8` has range -128 through 127, so constants outside of that range can never be assigned to a variable of type `int8`:

	.play -edit constants/int2.go /var/

	Similarly, `uint8`, also known as `byte`, has range 0 through 255, so a large or negative constant cannot be assigned to a `uint8`:

	.play -edit constants/int3.go /var/

	This type-checking can catch mistakes like this one:

	.play -edit constants/int4.go /START/,/STOP/

	If the compiler complains about your use of a constant, it's likely a real bug like this.

	* An exercise: The largest unsigned int

	Here is an informative little exercise.
	How do we express a constant representing the largest value that fits in a `uint`?
	If we were talking about `uint32` rather than `uint`, we could write

	const MaxUint32 = 1<<32 - 1

	but we want `uint`, not `uint32`.
	The `int` and `uint` types have equal unspecified numbers of bits, either 32 or 64.
	Since the number of bits available depends on the architecture, we can't just write down a single value.

	Fans of [[http://en.wikipedia.org/wiki/Two's_complement][two's-complement arithmetic]],
	which Go's integers are defined to use, know that the representation of `-1` has all its bits set to 1,
	so the bit pattern of `-1` is internally the same as that of the
	largest unsigned integer.
	We therefore might think we could write

	.play -edit constants/exercise1.go /const/

	but that is illegal because -1 cannot be represented by an unsigned variable; `-1` is not in the range of unsigned values.
	A conversion won't help either, for the same reason:

	.play -edit constants/exercise2.go /const/

	Even though at run-time a value of -1 can be converted to an unsigned integer, the rules
	for constant [[https://golang.org/ref/spec#Conversions][conversions]] forbid this kind of coercion at compile time.
	That is to say, this works:

	.play -edit constants/exercise3.go /START/,/STOP/

	but only because `v` is a variable; if we made `v` a constant, even an untyped constant, we'd be back in forbidden territory:

	.play -edit constants/exercise4.go /START/,/STOP/

	We return to our previous approach, but instead of `-1` we try `^0`, the bitwise negation of an arbitrary number of zero bits.
	But that fails too, for a similar reason:
	In the space of numeric values,
	`^0` represents an infinite number of ones, so we lose information if we assign that to any fixed-size integer:

	.play -edit constants/exercise5.go /const/

	How then do we represent the largest unsigned integer as a constant?

	The key is to constrain the operation to the number of bits in a `uint` and avoiding
	values, such as negative numbers, that are not representable in a `uint`.
	The simplest `uint` value is the typed constant `uint(0)`.
	If `uints` have 32 or 64 bits, `uint(0)` has 32 or 64 zero bits accordingly.
	If we invert each of those bits, we'll get the correct number of one bits, which is the largest `uint` value.

	Therefore we don't flip the bits of the untyped constant `0`, we flip the bits of the typed constant `uint(0)`.
	Here, then, is our constant:

	.play -edit constants/exercise6.go /START/,/STOP/

	Whatever the number of bits it takes to represent a `uint` in the current execution environment
	(on the [[https://blog.golang.org/playground][playground]], it's 32),
	this constant correctly represents the largest value a variable of type `uint` can hold.

	If you understand the analysis that got us to this result, you understand all the important points about constants in Go.

	* Numbers

	The concept of untyped constants in Go means that all the numeric constants, whether integer, floating-point, complex, or even character values,
	live in a kind of unified space.
	It's when we bring them to the computational world of variables, assignments, and operations that the actual types matter.
	But as long as we stay in the world of numeric constants, we can mix and match values as we like.
	All these constants have numeric value 1:

	1
	1.000
	1e3-99.0*10-9
	'\x01'
	'\u0001'
	'b' - 'a'
	1.0+3i-3.0i

	Therefore, although they have different implicit default types, written as untyped constants they can be assigned to a variable of any integer type:

	.play -edit constants/numbers1.go /START/,/STOP/

	The output from this snippet is: `1`1`1`1`1`(1+0i)`1`.

	You can even do nutty stuff like

	.play -edit constants/numbers2.go /START/,/STOP/

	which yields 145.5, which is pointless except to prove a point.

	But the real point of these rules is flexibility.
	That flexibility means that, despite the fact that in Go it is illegal in the same expression to mix floating-point and integer variables,
	or even `int` and `int32` variables, it is fine to write

	sqrt2 := math.Sqrt(2)

	or

	const millisecond = time.Second/1e3

	or

	bigBufferWithHeader := make([]byte, 512+1e6)

	and have the results mean what you expect.

	Because in Go, numeric constants work as you expect: like numbers.