Optional arguments: simple case

Optional arguments: simple case#

Work In Progress

This page is a draft

Let’s see how the tricks introduced in the previous chapter can be used to simulate optional arguments with a default value.

Definition

Optional arguments is a language feature that allows the caller of a function not to provide certain arguments, in which case a default value is used, chosen by the callee.

Here is an example in C++:

uint64_t fibonacci(uint8_t n, uint64_t f0 = 0, uint64_t f1 = 1)
{
	switch (n)
	{
	case 0: return f0;
	case 1: return f1;
	default: return fibonacci(n - 1, f1, f0 + f1);
	}
}

This allows having the expected interface with a single argument, while also allowing the caller to choose the first two terms of the sequence.

The caller may then write:

// Starting with 0 1
fibonacci(7); // 13
fibonacci(7, 0); // 13
fibonacci(7, 0, 1); // 13

// Starting with 1 1
fibonacci(6, 1); // 13
fibonacci(6, 1, 1); // 13

// Historical sequence
fibonacci(5, 1, 2); // 13

// Custom sequence
fibonacci(5, 5, 10); // 40

We are going to demonstrate how to achieve a similar interface in C.

Single optional argument#

Let’s start with a simpler example: the factorial of an integer.

Why is there a second argument to factorial ?

The most straightforward implementation looks like:

unsigned long factorial(unsigned char n)
{
	if (n <= 1)
		return 1;
	return n * factorial(n - 1);
}

And in fact, it is all you need, because your compiler will most likely optimize it to a loop with constant memory usage. But to please your computer science professor we’ll write an implementation with explicit tail call optimization.

How it is usually done in C#
static // Tell the compiler this function will not be called outside this compilation unit, so it won't create a symbol for it and just inline it
unsigned long factorial_aux(unsigned char n, unsigned long accumulator)
{
	if (n <= 1)
		return accumulator;
	__attribute__((musttail)) // We can even ask the compiler to issue an error if tail recursion isn't possible
	return factorial_aux(n - 1, n * accumulator);
}

unsigned long factorial(unsigned char n)
{
	return factorial_aux(n, 1);
}

What you can see is that the factorial function is just a wrapper to provide a default value. Which is perfectly fine as the auxillary function will be inlined inside, but let’s act like it’s an unforgivable faux pas. Using obscure preprocessor tricks to solve non-existant problems is what we are here for anyway.

Also, if you really care about performance, just use a lookup-table: there’s only 20 factorial values that can fit on 64 bits

A first attempt is to replace the wrapper function with a wrapper macro that has the same name:

in factorial.h#
unsigned long factorial(unsigned char n, unsigned long);

#define factorial(N) factorial(N, 1)
in factorial.c#
unsigned long factorial(unsigned char n, unsigned long accumulator)
{
	if (n <= 1)
		return accumulator;
	__attribute__((musttail))
	return factorial(n - 1, n * accumulator);
}
user code#
#include <factorial.h>

int main()
{
	unsigned long x = factorial(10);
}

This works because:

  • in the header, the function declaration is not affected by the macro as the latter is defined after.

  • macros cannot be recursive, so once factorial(10) is replaced by factorial(10, 1), no further expansion is performed

  • factorial.c does not include factorial.h, so it is not affected by the macro

 1#include <stdio.h> // printf
 2
 3#define eval(x) printf("%s = %lu\n", #x, x)
 4
 5unsigned long _factorial(unsigned short n, unsigned long accumulator)
 6{
 7    if (n == 1)
 8        return accumulator;
 9    __attribute__((musttail)) return _factorial(n - 1, accumulator * n);
10}
11
12#define FACTORIAL_(N, ACC, ...) _factorial(N, ACC)
13#define FACTORIAL(N, ...)       FACTORIAL_(N, ##__VA_ARGS__, 1)
14
15int main()
16{
17    eval(FACTORIAL(5));
18    eval(FACTORIAL(10));
19    eval(FACTORIAL(12));
20}

 1#include <stdio.h> // printf
 2
 3#define eval(x) printf("%s = %lu\n", #x, x)
 4
 5unsigned long _factorial(unsigned short n, unsigned long accumulator)
 6{
 7    if (n == 1)
 8        return accumulator;
 9    __attribute__((musttail)) return _factorial(n - 1, accumulator * n);
10}
11
12#define FACTORIAL_(N, ACC, ...) _factorial(N, ACC)
13#define FACTORIAL(N, ...)       FACTORIAL_(N, ##__VA_ARGS__, 1)
14
15int main()
16{
17    eval(FACTORIAL(5));
18    eval(FACTORIAL(10));
19    eval(FACTORIAL(12));
20}

unsigned long _factorial(unsigned short n, unsigned long accumulator)
{
    if (n == 1)
        return accumulator;
    __attribute__((musttail)) return _factorial(n - 1, accumulator * n);
}

int main()
{
    printf("%s = %lu\n", "FACTORIAL(5)", _factorial(5, 1));
    printf("%s = %lu\n", "FACTORIAL(10)", _factorial(10, 1));
    printf("%s = %lu\n", "FACTORIAL(12)", _factorial(12, 1));
}

FACTORIAL(5) = 120
FACTORIAL(10) = 3628800
FACTORIAL(12) = 479001600

 1#include <sys/types.h> // uint*_t
 2
 3#include <inttypes.h> // PRI*
 4#include <stdio.h>    // printf
 5
 6#define FIBONACCI(N, A, B, ...) fibonacci(N, A, B)
 7#define fibonacci(N, ...)       FIBONACCI(N, ##__VA_ARGS__, 1, 1)
 8
 9uint64_t fibonacci(uint16_t n, uint64_t f0, uint64_t f1)
10{
11    switch (n)
12    {
13    case 0: return f0;
14    case 1: return f1;
15    default: return fibonacci(n - 1, f1, f0 + f1);
16    }
17}
18
19int main()
20{
21    printf("%" PRIu64 "\n", fibonacci(6));
22    printf("%" PRIu64 "\n", fibonacci(7, 0, 1));
23    printf("%" PRIu64 "\n", fibonacci(5, 1, 2));
24}

 1#include <sys/types.h> // uint*_t
 2
 3#include <inttypes.h> // PRI*
 4#include <stdio.h>    // printf
 5
 6#define FIBONACCI(N, A, B, ...) fibonacci(N, A, B)
 7#define fibonacci(N, ...)       FIBONACCI(N, ##__VA_ARGS__, 1, 1)
 8
 9uint64_t fibonacci(uint16_t n, uint64_t f0, uint64_t f1)
10{
11    switch (n)
12    {
13    case 0: return f0;
14    case 1: return f1;
15    default: return fibonacci(n - 1, f1, f0 + f1);
16    }
17}
18
19int main()
20{
21    printf("%" PRIu64 "\n", fibonacci(6));
22    printf("%" PRIu64 "\n", fibonacci(7, 0, 1));
23    printf("%" PRIu64 "\n", fibonacci(5, 1, 2));
24}

uint64_t fibonacci(uint16_t n, uint64_t f0, uint64_t f1)
{
    switch (n)
    {
    case 0: return f0;
    case 1: return f1;
    default: return fibonacci(n - 1, f1, f0 + f1);
    }
}

int main()
{
    printf("%"
           "l"
           "u"
           "\n",
           fibonacci(6, 1, 1));
    printf("%"
           "l"
           "u"
           "\n",
           fibonacci(7, 0, 1));
    printf("%"
           "l"
           "u"
           "\n",
           fibonacci(5, 1, 2));
}

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