Types

[jacob navia]

Hi people
I have been working again in my tutorial, and I have finished the
"types" chapter. If you feel like "jacob bashing" this is the
occasion! I am asking for criticisms, or for things I may have said
wrong. Keep in mind that this is a tutorial, and I donot want to
overwhelm the reader with little details.

-------------------------------------------------------------------------*

Types

A machine has no concept of type, everything is just a sequence of bits,
and any operation with those sequences can be done, even if it is not
meaningful at all, for example adding two addresses, or multiplying two
character strings.

A high level programming language however, enforces the concept of types
of data. Operations are allowed between compatible types and not between
any data whatsoever. It is possible to add two integers, or an integer
and a floating point number, and even an integer and a complex number.
It is not possible to add an integer to a function or to a character
string, the operation has no meaning for those types.

An operation implies always compatible types netween the operands.
In C, all data must be associated with a specific type before it can be
used. All variables must be declared to be of a known type before any
operation with them is attempted since to be able to generate code the
compiler must know the type of each operand.

C allows the programmer to define new types based on the previously
dfined ones. This means that the type system in C is static, i.e. known
at compile time, but extensible since you can add new types.

This is in contrast to dynamic typing, where no declarations are needed
since the language associates types and data during the run time.
Dynamic typing is much more flexible, but this flexibility has a price:
the run time system must constantly check the types of the operands for
each operation to see if they are compatible, what slows down the
program considerably.

In C there is absolutely no run time checking in most operations, since
the compiler is able to check everything during the compilation, what
accelerates execution of the program, and allows the compiler to
discover a lot of errors during the compilation instead of crashing at
run time when an operation with incompatible types is attempted.


What is a type?

A first tentative, definition for what a type is, could be “a type is a
definition of an algorithm for understanding a sequence of storage
bits”. It gives the meaning of the data stored in memory. If we say that
the object a is an int, it means that the bits stored at that location
are to be understood as a natural number that is built by consecutive
additions of powers of two. If we say that the type of a is a double, it
means that the bits are to be understood as the IEEE 754 standard
sequences of bits representing a double precision floating point value.
Functions have a type too. The type of a function is determined by the
type of its return value, and all its arguments. The type of a function
is its interface with the outside world: its inputs (arguments) and its
outputs (return value).

Types in C can be incomplete, i.e. they can exist as types but nothing
is known about them, neither their size nor their bit-layout. They are
useful for encapsulating data into entities that are known only to
certain parts of the program.

Each type can have an associated pointer type: for int we have int
pointer, for double we have double pointer, etc. We can have also
pointers that point to an unspecified object. They are written as void
*, i.e. pointers to void. Some types exist only as pointers: the
function pointer type has no object counterpart since a function object
doesn’t exist in C, only pointers to functions exist.

Types classification

This type classification is based on the classification published by
Plauger and Brody, slightly modified.
Types
1. Function types
1.1 Fully qualified function types. (Functions whose full prototype is
visible)
1.2 Assumed function types (Functions whose prototype is partly or not
visible)
1.2.1 Functions whose return value is visible but not their arguments
1.2.2 Functions where the return value and their arguments are unknown.
2. Incomplete types (Types not completely specified)
2.1 void
2.2 Incomplete struct types
2.3 Incomplete array types
2.4 Incomplete union types
3. Object types
3.1 Scalar types
3.1.1 Arithmetic types
3.1.1.1 Integer types
3.1.1.1.1 Specific integer types
3.1.1.1.1.1 char (signed/unsigned)
3.1.1.1.1.2 short (signed unsigned)
3.1.1.1.1.3 int (signed/unsigned)
3.1.1.1.1.4 long (signed/unsigned)
3.1.1.1.1.5 long long (signed/unsigned)
3.1.1.1.2 Bitfields (signed/unsigned)
3.1.1.1.3 Enumeration types
3.1.1.2 Floating types
3.1.1.2.1 float
3.1.1.2.2 double
3.1.1.2.3 long double
3.1.2 Pointer types
3.1.2.1 Pointer to function
3.1.2.2 Pointer to object types
3.1.2.3 Pointer to incomplete types
3.2 Non -scalar types
3.2.1 Struct types
3.2.2 Union types
3.2.3 Array types



Integer types

The language doesn’t specify exactly how big each integer type must be,
but it has some requirements as to the minimum size of the integer
types. The char type must be at least 8 bits, the int type must be at
least 16 bits, and the long type must be at least 32 bits. How big each
integer type actually is, is defined in the standard header limits.h.

Floating types

Floating types are discussed in more detail later. Here we will just
retain that they can represent integer and non integer quantities, and
in general, their dynamic range is bigger that integers of the same
size. They have two parts: a mantissa and an exponent.
As a result, there are some values that can’t be expressed in floating
point, for instance 1/3 or 1/10. This comes as a surprise for many
people, so it is better to underscore this fact here. More explanations
for this later on.
Floating point arithmetic is approximative, and many mathematical laws
that we take for granted like a+b is equal to b+a do not apply in many
cases to floating point math.

Compatible types

There are types that share the same underlying representation. For
instance, in lcc-win32 for the Intel platform, in 32 bits, long and int
are the same. They are compatible types for that version of lcc. In the
version of lcc-linux for 64 bits however, long is 64 bits and int is 32
bits, they are no longer compatible types, but long is now compatible
with the long long type.
Plauger and Brody give the following definition for when two types are
compatible types:
Both types are the same.
Both are pointer types, with the same type qualifiers, that point to
compatible types.
Both are array types whose elements have compatible types. If both
specify repetition counts, the repetition counts are equal.
Both are function types whose return types are compatible. If both
specify types for their parameters, both declare the same number of
parameters (including ellipses) and the types of corresponding
parameters are compatible. Otherwise, at least one does not specify
types for its parameters. If the other specifies types for its
parameters, it specifies only a fixed number of parameters and does not
specify parameters of type float or of any integer types that change
when promoted.
Both are structure, union, or enumeration types that are declared in
different translation units with the same member names. Structure
members are declared in the same order. Structure and union members
whose names match are declared with compatible types. Enumeration
constants whose names match have the same values.

Incomplete types

An incomplete type is missing some part of the declaration. For instance

struct SomeType;

We know now that “SomeType” is a struct, but since the contents aren’t
specified, we can’t use directly that type. The use of this is precisely
to avoid using the type: encapsulation. Many times you want to publish
some interface but you do not want people using the structure,
allocating a structure, or doing anything else but pass those structure
to your functions. In those situations, an opaque type is a good thing
to have.

Casting

The programmer can at any time change the type associated with a piece
of data by making a “cast” operation. For instance if you have:
float f = 67.8f;
you can do
double d = (double)f;
The “(double)” means that the type of data in f should be converted into
an equvalent data using the double representation. We will come back to
types when we speak again about casts later.

 

[jacob navia]

P.S. The difference between the classification of types as proposed by
Plauger and Brody and the classification there is that I think it is
important to differenciate function types, between functions with full
prototype

int fn(int,double);

"half prototype"

char *fn();

and no prototype at all.

 

[Richard Heathfield]

jacob navia said:

P.S. The difference between the classification of types as proposed by
Plauger and Brody and the classification there is that I think it is
important to differenciate function types, between functions with full
prototype

int fn(int,double);

"half prototype"

char *fn();

That isn't a half-prototype. It's a function declaration, and that's all it
is.

 

[jacob navia]

Richard Heathfield a écrit :

jacob navia said:




That isn't a half-prototype. It's a function declaration, and that's all it
is.

No, it is missing the number and types of the arguments.

I do not know if this classification in function types is correct, or it
would be better to add this to the "incomplete types" section.

 

[CBFalconer]

I have been working again in my tutorial, and I have finished the
"types" chapter. If you feel like "jacob bashing" this is the
occasion! I am asking for criticisms, or for things I may have said
wrong. Keep in mind that this is a tutorial, and I donot want to
overwhelm the reader with little details.

-----------------------------------------------------------------*

Types

A machine has no concept of type, everything is just a sequence of
bits, and any operation with those sequences can be done, even if
it is not meaningful at all, for example adding two addresses, or
multiplying two character strings.

Meet the Burroughs machines.

.... snip ...

In C there is absolutely no run time checking in most operations,
since the compiler is able to check everything during the
compilation, what accelerates execution of the program, and allows
the compiler to discover a lot of errors during the compilation
instead of crashing at run time when an operation with incompatible
types is attempted.

Not necessarily. Signed integer overflow always results in
undefined behaviour, for example.

 

[jacob navia]

CBFalconer a écrit :

Meet the Burroughs machines.

... snip ...



Not necessarily. Signed integer overflow always results in
undefined behaviour, for example.

Yes, you are right, and lcc-win32 provides a way to check this at run
time. I will add a few sentences concerning this possibility, and the
runtime errors that can appear in C during the runtime in the primitive
types.

This means, as you notice, signed int overflow but also floating
point errors, bad pointer values, and other types of errors.

 

[Chris Torek]

... Keep in mind that this is a tutorial, and I donot want to
overwhelm the reader with little details.

It is OK to gloss over details, but if you are going to do so, I
think you should note where this has occurred. (Maybe mark parts
with footnotes, marginal notes, some of those typographic "dingbats"
as they are called, or some other technique.)

-------------------------------------------------------------------------*
Types

A machine has no concept of type,

This is a huge overstatement. Not only is it not strictly true
(there are machines with "typed RAM", although they are no longer
in common use and they can make C compilers difficult or even
impossible), it is also highly misleading: a typical modern machine
still applies a type to every operation, it is just that you get
to choose the type each time you do the operation. For instance:

mulf rResult, rInput1, rInput2

could treat the two inputs as 32-bit floating-point numbers, while:

mull rResult, rInput1, rInput2

would treat the two inputs as 32-bit integer values. And of course,
on many machines including the x86, "floating-point" numbers are
handled very differently from "integer" numbers: you cannot quite
stick a full FP number into an integer register (since there are
no 80-bit integer registers), although using SSE/MMX extensions,
you can sometimes do vice versa.

A lot of machines also have "semi-typed" registers: address vs
data, for instance (see the 680x0; and even the x86 does this, to
a lesser extent: computational results commonly go in %eax,
occasionally in %edx, rarely in %esi, etc.).

everything is just a sequence of bits,
and any operation with those sequences can be done, even if it is not
meaningful at all, for example adding two addresses, or multiplying two
character strings.

I think it is worth re-phrasing this paragraph. Maybe even just make
the opening sentence something like "Machines don't enforce consistency
of types. Everything is just a sequence of bits, ..."

A high level programming language however, enforces the concept of types
of data. Operations are allowed between compatible types and not between
any data whatsoever. It is possible to add two integers, or an integer
and a floating point number, and even an integer and a complex number.
It is not possible to add an integer to a function or to a character
string, the operation has no meaning for those types.

(This glosses over some stuff, e.g., many "high level" languages *do*
allow you to add an integer to a character string.)

A first tentative, definition for what a type is, could be 0x93a type is a
definition of an algorithm for understanding a sequence of storage
bits0x94.

(These 0x93/0x94 characters are rather annoying Microsoft-isms. They
are not just non-ASCII, they are even non-ISO-8851. This definition
seems good though. There are other Microsoft characters that snuck
into the posting, too, I just noticed these first. I have no comments
on the rest of this)

 

[Chris Torek]

I disagree that a type is a "definition of an algorithm". To me, it is
a specification of the meaning of the bits of a variable. I don't
associate such specifications directly with algorithms.

That might be a better "first, tentative definition" for a type,
as it is the actual definition of a concrete type. But given a
specification, one can derive an algorithm ... and it depends
on whether one wants to start with the concrete or the abstract.

(An abstract type is sort of "more algorithm, less specification",
as it were. With a concrete type, you not only have the raw bits,
but also everything you need to know to find the value given the
bits. With an abstract type, you have at least some, but not
necessarily all, the bits -- some set of bits that provide a sort
of handle to the underlying value, at least[%] -- and only as much
information as the type-provider chooses to provide to find values,
along with a separate set of operations upon bit-sets to produce
new bit-sets.)

[% Consider an abstract type where the value is simply a pointer to
the "real" value, e.g., "struct incomplete *p".]

 

[Thad Smith]

I am asking for criticisms, or for things I may have said
wrong. Keep in mind that this is a tutorial, and I donot want to
overwhelm the reader with little details.

First suggestion: correct spelling errors before asking for criticisms.

A high level programming language however, enforces the concept of types
of data.

I would say that high-level programming languages implement the concept
of types of data. "Enforcing a concept" doesn't make sense.

An operation implies always compatible types netween the operands.

An operation requires compatible operand types.

C allows the programmer to define new types based on the previously
dfined ones. This means that the type system in C is static, i.e. known
at compile time, but extensible since you can add new types.

This means that although the type system in C is static (known at
compile time), it is also extensible, since you can add new types.

This is in contrast to dynamic typing, where no declarations are needed
since the language associates types and data during the run time.
Dynamic typing is much more flexible, but this flexibility has a price:
the run time system must constantly check the types of the operands for
each operation to see if they are compatible, what slows down the
program considerably.

.... each operation to see if they are compatible, and perform
conversions if needed, which significantly slows execution.

A first tentative, definition for what a type is, could be “a type is a
definition of an algorithm for understanding a sequence of storage
bits”.

I disagree that a type is a "definition of an algorithm". To me, it is
a specification of the meaning of the bits of a variable. I don't
associate such specifications directly with algorithms.

If we say that the type of a is a double, it
means that the bits are to be understood as the IEEE 754 standard
sequences of bits representing a double precision floating point value.

This is not universally true. How about

If a variable type is double, it means that the variable contains a
sign, mantissa, and exponent used to approximate a real number. The
IEEE 754 standard specifies floating point formats that are used by a
majority of current computers.

Floating point arithmetic is approximative, and many mathematical laws

approximate

that we take for granted like a+b is equal to b+a do not apply in many
cases to floating point math.

That is a poor example. There may be some arithmetic units for which
addition is not commutative, but I am not aware of any (excluding result
carry-over with additional precision). Consider "(a+b)+c is equal to
a+(b+c)".

There are types that share the same underlying representation. For That's fine.
instance, in lcc-win32 for the Intel platform, in 32 bits, long and int
are the same. They are compatible types for that version of lcc.

The precision of the wording should be improved. Are the types "the
same" or "compatible"? These are different concepts.

I can't speak for lcc-win32, but in Standard C, I think, different
integer types, even if the same size, are not compatible. Conversions
apply, even if they result in no code being generated.

 

[Guest]

Richard Heathfield a écrit :

No, it is missing the number and types of the arguments.

Right. So it's just a function declaration that is not a prototype.
There's no such thing as a "half-prototype".

I do not know if this classification in function types is correct, or it
would be better to add this to the "incomplete types" section.

A function type cannot ever be an incomplete type.

 

[Guest]

That is a poor example. There may be some arithmetic units for which
addition is not commutative, but I am not aware of any (excluding result
carry-over with additional precision).

Isn't that enough?

Consider "(a+b)+c is equal to
a+(b+c)".

That does not apply to integer or pointer arithmetic either.

 

[Keith Thompson]

Isn't that enough?


That does not apply to integer or pointer arithmetic either.

It's different, though. Integer and pointer arithmetic are
associative *unless* an intermediate result is undefined, I think. In
floating-point arithmetic, it's possible that (a+b)+c and a+(b+c) have
different values without overflow.

 

[Richard Bos]

Types

A machine has no concept of type, everything is just a sequence of bits,
and any operation with those sequences can be done, even if it is not
meaningful at all, for example adding two addresses, or multiplying two
character strings.

Great way to start... never heard of address register, floating point
registers, and integer registers?

A high level programming language however, enforces the concept of types
of data. Operations are allowed between compatible types and not between
any data whatsoever. It is possible to add two integers, or an integer
and a floating point number, and even an integer and a complex number.
It is not possible to add an integer to a function or to a character
string, the operation has no meaning for those types.

This is a run on sentence, run on sentences are just as wrong in French
as in English so you should have known better, you are unfortunately not
the only person to make such mistakes so don't feel too bad, replace the
last comma with a full stop.

An operation implies always compatible types netween the operands.

Not necessarily. See casts. And for some operations, the compatibility
needs to run only one way.

This is in contrast to dynamic typing, where no declarations are needed
since the language associates types and data during the run time.
Dynamic typing is much more flexible, but this flexibility has a price:
the run time system must constantly check the types of the operands for
each operation to see if they are compatible, what slows down the
program considerably.

_Which_ slows down the program. And that's not the only problem; it also
leads to more run-time errors and fewer compile-time errors.

In C there is absolutely no run time checking in most operations, since
the compiler is able to check everything during the compilation, what
accelerates execution of the program,
_Which_.

What is a type?

A first tentative, definition for what a type is, could be “a type is a

A first, tentative, definition. And don't use that kind of quote mark on
Usenet - it's OK (indeed, better) if it goes into a web page.

definition of an algorithm for understanding a sequence of storage
bits”.

An unusual, but not a bad definition of type.

Each type can have an associated pointer type:

s/can have/has/.

for int we have int
pointer, for double we have double pointer, etc. We can have also
pointers that point to an unspecified object. They are written as void
*, i.e. pointers to void.

Bad line break. Break this before "void *".

Some types exist only as pointers: the function pointer type has no
object counterpart since a function object doesn’t exist in C, only
pointers to functions exist.

A function object doesn't exist (because it's a contradiction in terms),
but that doesn't mean that a function type doesn't. See 6.2.5.

Types classification

This type classification is based on the classification published by
Plauger and Brody, slightly modified.
Types
1. Function types
1.1 Fully qualified function types. (Functions whose full prototype is
visible)
1.2 Assumed function types (Functions whose prototype is partly or not
visible)
1.2.1 Functions whose return value is visible but not their arguments
1.2.2 Functions where the return value and their arguments are unknown.

You're missing variadic functions, which fall in between 1.1 and 1.2.1.

2. Incomplete types (Types not completely specified)
2.1 void
2.2 Incomplete struct types
2.3 Incomplete array types
2.4 Incomplete union types

Better keep struct and union together - not necessarily under the same
item, but not separated by array.

3. Object types
3.1 Scalar types
3.1.1 Arithmetic types
3.1.1.1 Integer types
3.1.1.1.1 Specific integer types
3.1.1.1.1.1 char (signed/unsigned)
3.1.1.1.1.2 short (signed unsigned)
3.1.1.1.1.3 int (signed/unsigned)
3.1.1.1.1.4 long (signed/unsigned)
3.1.1.1.1.5 long long (signed/unsigned)

Don't use 8-space tabs. This indentation is ridiculous.

If you mention long long, you need to mention intN_t, intmax_t, and so
forth...

3.1.1.1.2 Bitfields (signed/unsigned)
3.1.1.1.3 Enumeration types
3.1.1.2 Floating types
3.1.1.2.1 float
3.1.1.2.2 double
3.1.1.2.3 long double

....and complex types.

You also need to mention that these, including long long, are C99 only.

3.1.2 Pointer types
3.1.2.1 Pointer to function
3.1.2.2 Pointer to object types
3.1.2.3 Pointer to incomplete types
3.2 Non -scalar types
3.2.1 Struct types
3.2.2 Union types
3.2.3 Array types

This is better than 2.2-2.4 above, but at the very least be consistent.

Integer types

The language doesn’t specify exactly how big each integer type must be,
but it has some requirements as to the minimum size of the integer
types.

Wrong. It has requirements as to the minimum _values_ it can hold. This
necessarily does translate to a minimum bit size, but it pays to be
precise.

The char type must be at least 8 bits, the int type must be at
least 16 bits, and the long type must be at least 32 bits. How big each
integer type actually is, is defined in the standard header limits.h.

Floating types

Floating types are discussed in more detail later. Here we will just
retain that they can represent integer and non integer quantities, and
in general, their dynamic range is bigger that integers of the same
size.

This is highly misleading unless you define "dynamic range" and mention
that it means that a 4-byte float can't represent all values that a
4-byte int can, as much as the opposite.

They have two parts: a mantissa and an exponent.

And this is just subtly wrong. You missed one bit.

Floating point arithmetic is approximative,

Usually, but...

and many mathematical laws that we take for granted like a+b is
equal to b+a do not apply in many cases to floating point math.

....this shouldn't be true. Floating point addition _is_ commutative; it
isn't associative.

Plauger and Brody give the following definition for when two types are
compatible types:

Use the Standard instead. I _think_ what you have here is equivalent,
but check.

Incomplete types

An incomplete type is missing some part of the declaration.

No. Check the Standard: an incomplete type is an object type which does
not have the necessary information to determine its size. This does not
mean that anything need be missing; the information may simply not
exist. In particular, void is an incomplete type which cannot be
completed.

Casting

The programmer can at any time change the type associated with a piece
of data by making a “cast” operation.

s/making/using/, and see below.

For instance if you have:
float f = 67.8f;
you can do
double d = (double)f;
The “(double)” means that the type of data in f should be converted into
an equvalent data using the double representation.

Wrong, wrong, wrongity-wrong. The data in f should be left alone. The
_expression_ evaluates to the _value_ of f converted to that type. Not
the data, i.e. the bytes; purely the value.
(Oh, and: "equivalent". Use a spill chucker.)

Do we get credit in the final document?

Richard

 

[Guest]

It's different, though. Integer and pointer arithmetic are
associative *unless* an intermediate result is undefined, I think.

unsigned a = UINT_MAX;
unsigned b = UINT_MAX;
unsigned long c = 1;

Now, there is no undefined behaviour in either (a + b) + c or a + (b +
c), but it's still possible for those to give different results.

In
floating-point arithmetic, it's possible that (a+b)+c and a+(b+c) have
different values without overflow.

Technically, there is no overflow in my example, but I get your point.

 

[jacob navia]

It is OK to gloss over details, but if you are going to do so, I
think you should note where this has occurred. (Maybe mark parts
with footnotes, marginal notes, some of those typographic "dingbats"
as they are called, or some other technique.)




This is a huge overstatement. Not only is it not strictly true
(there are machines with "typed RAM", although they are no longer
in common use and they can make C compilers difficult or even
impossible), it is also highly misleading: a typical modern machine
still applies a type to every operation, it is just that you get
to choose the type each time you do the operation. For instance:

mulf rResult, rInput1, rInput2

could treat the two inputs as 32-bit floating-point numbers, while:

mull rResult, rInput1, rInput2

would treat the two inputs as 32-bit integer values. And of course,
on many machines including the x86, "floating-point" numbers are
handled very differently from "integer" numbers: you cannot quite
stick a full FP number into an integer register (since there are
no 80-bit integer registers), although using SSE/MMX extensions,
you can sometimes do vice versa.

A lot of machines also have "semi-typed" registers: address vs
data, for instance (see the 680x0; and even the x86 does this, to
a lesser extent: computational results commonly go in %eax,
occasionally in %edx, rarely in %esi, etc.).




I think it is worth re-phrasing this paragraph. Maybe even just make
the opening sentence something like "Machines don't enforce consistency
of types. Everything is just a sequence of bits, ..."

Yes, thanks. My intent was to say exactly that (there are no enforced
types) but I did not say it explicitely. Obviously a floating point add
assumes some structure in the bits at the input addresses, as an integer
add, etc.

(This glosses over some stuff, e.g., many "high level" languages *do*
allow you to add an integer to a character string.)

Adding an integer to a character string? What would be the result of THAT?

Or maybe you mean
"9" + "1" --> "91"

 

[Ian Collins]

Adding an integer to a character string? What would be the result of THAT?

Or maybe you mean
"9" + "1" --> "91"

More likely "string"+1, which is legal in several languages.

 

[Guest]

More likely "string"+1, which is legal in several languages.

The meaning of "string"+1 is inconsistent between languages, though. In
Perl, its result is 1. In JavaScript, the result is "string1". It's
also legal C, and equivalent to "tring".

 

[jacob navia]

Right. So it's just a function declaration that is not a prototype.
There's no such thing as a "half-prototype".




A function type cannot ever be an incomplete type.

Incomplete in the sense that the number and types of the function
arguments are unknown, as in an incomplete declaration the number and
types of the structure/union members are unknown.

There are two kinds:

1) Function declarations that are not prototypes, to use your terminology.
2) Completely implicit declaration where the compiler assumes:

int fn();

 

[jacob navia]

The meaning of "string"+1 is inconsistent between languages, though. In
Perl, its result is 1. In JavaScript, the result is "string1". It's
also legal C, and equivalent to "tring".

But this is not adding 1 to a character string!

It means (in C) adding 1 to the ADDRESS of the start of the string,
what is completely another matter!

 

[Richard Heathfield]

jacob navia said:

Incomplete in the sense that the number and types of the function
arguments are unknown,

That's not what "incomplete types" means in C, though. In C, there are three
kinds of types - object types, function types, and incomplete types. If
it's a function type, it simply can't be an incomplete type. See 3.1.2.5 of
C89 or 6.2.5 of C99.