What is the maximum length in chars needed to represent any double value?

A correct source of information that goes into more detail than the IEEE-754 Specification are these lecture notes from UC Berkely on page 4, plus a little bit of DIY calculations. These lecture slides are also good for engineering students.

Recommended Buffer Sizes

| Single| Double | Extended | Quad  |
|:-----:|:------:|:--------:|:-----:|
|   16  |  24    |    30    |  45   |

These numbers are based on the following calculations:

Maximum Decimal Count of the Integral Portion

| Single| Double | Extended | Quad  |
|:-----:|:------:|:--------:|:-----:|
|   9   |   17   |    21    |  36   |

* Quantities listed in decimals.

Decimal counts are based on the formula: At most Ceiling(1 + NLog_10(2)) decimals, where N is the number of bits in the integral portion*.

Maximum Exponent Lengths

| Single| Double | Extended | Quad  |
|:-----:|:------:|:--------:|:-----:|
|   5   |   5    |     7    |   7   |
* Standard format is `e-123`.

Fastest Algorithm

The fastest algorithm for printing floating-point numbers is the Grisu2 algorithm detailed in the research paper Printing Floating-point Numbers Quickly and Accurately. The best benchmark I could find can be found here.

You can use snprintf() to check how many chars you need. snprintf() returns the number of chars needed to print whatever is passed to it.

/* NOT TESTED */
#include <stdio.h>
#include <stdlib.h>
int main(void) {
    char dummy[1];
    double value = 42.000042; /* or anything else */
    int siz;
    char *representation;
    siz = snprintf(dummy, sizeof dummy, "%f", value);
    printf("exact length needed to represent 'value' "
           "(without the '\\0' terminator) is %d.\n", siz);
    representation = malloc(siz + 1);
    if (representation) {
        sprintf(representation, "%f", value);
        /* use `representation` */
        free(representation);
    } else {
        /* no memory */
    }
    return 0;
}

Note: snprintf() is a C99 function. If a C89 compiler provides it as an extension, it may not do what the above program expects.

Edit: Changed the link to snprintf() to one that actually describes the functionality imposed by the C99 Standard; the description in the original link is wrong.
2013: Changed the link back to POSIX site which I prefer over the site of the first edit.

According to IEEE 754-1985, the longest notation for value represented by double type, i.e.:

-2.2250738585072020E-308

has 24 chars.

The standard header <float.h> in C, or <cfloat> in C++, contains several constants to do with the range and other metrics of the floating point types. One of these is DBL_MAX_10_EXP, the largest power-of-10 exponent needed to represent all double values. Since 1eN needs N+1 digits to represent, and there might be a negative sign as well, then the answer is

int max_digits = DBL_MAX_10_EXP + 2;

This assumes that the exponent is larger than the number of digits needed to represent the largest possible mantissa value; otherwise, there will also be a decimal point followed by more digits.

CORRECTION

The longest number is actually the smallest representable negative number: it needs enough digits to cover both the exponent and the mantissa. This value is -pow(2, DBL_MIN_EXP - DBL_MANT_DIG), where DBL_MIN_EXP is negative. It's fairly easy to see (and prove by induction) that -pow(2,-N) needs 3+N characters for a non-scientific decimal representation ("-0.", followed by N digits). So the answer is

int max_digits = 3 + DBL_MANT_DIG - DBL_MIN_EXP

For a 64-bit IEEE double, we have

DBL_MANT_DIG = 53
DBL_MIN_EXP = -1023
max_digits = 3 + 53 - (-1023) = 1079