Multiplying very large hex numbers and printing them in C

Question

I want to multiply 2 very big hex numbers and print them out like for example:

28B2D48D74212E4F x 6734B42C025D5CF7 = 1068547cd3052bbe5688de35695b1239

Since I expected it to be a very big number I used unsigned long long int type:

unsigned long long int x = 0x28B2D48D74212E4F;   
unsigned long long int y = 0x6734B42C025D5CF7;

and print the multiplication like this:

fprintf(stdout, "%llx\n",  x*y);

What I get is exactly the half of the expected result:

5688de35695b1239

Why does it truncate it to exactly the half? Is there something bigger than unsigned long long?

Your `unsigned long long int` is obviously a 64bit number. Check again the `ULLONG_MAX`, you probably got it wrong. — Martin Heralecký, Dec 21 '19 at 23:27
*" tried to see if the output is bigger than ULLONG_MAX"* - how did you do that? The output is a lot larger than the max size of `unsigned long long` on any system I know of, you cannot compare against it, since it overflows on the arithmetic — UnholySheep, Dec 21 '19 at 23:27
Are you expecting `unsigned long long` to be 128 bits on your platform? Which platform would that be? — Steve Friedl, Dec 21 '19 at 23:27
Some compilers offer a 128-bit `uintmax_t`; or things like `__uint128` — M.M, Dec 21 '19 at 23:28
@SteveFriedl I expect to get `1068547cd3052bbe5688de35695b1239` as my output — cheshire, Dec 21 '19 at 23:31
Platform - linux, windows, armv7h, alpha? 32bit, 64bit? Gcc may have `__uint128` on your platform, you can print it as two 64-bit words. — KamilCuk, Dec 21 '19 at 23:35
@KamilCuk linux, 64 bit. How would I print it as two 64-bit words? — cheshire, Dec 21 '19 at 23:38

score 1 · Accepted Answer · answered Dec 21 '19 at 23:43

The response you're looking for won't fit in a 64-bit unsigned long long, which is the normal size on a 64-bit platform; any excess during multiply is overflow and dropped.

Newer versions of GCC do support 128-bit integers on 64-bit machines with __int128 (and unsigned __int128), and this works:

unsigned long long int x = 0x28B2D48D74212E4FULL;
unsigned long long int y = 0x6734B42C025D5CF7ULL;
unsigned __int128 xy = x * (unsigned __int128)y;

Note that you have to cast one of x or y to the wider type so the multiplication is done in 128 bits; otherwise that promotion to 128 is not done until after the (truncated) 64-bit multiply.

The problem is, as far as I can tell, printf() doesn't have a way to do this easily, so you're going to have to roll your own a bit.

Some reasonable discussion here: how to print __uint128_t number using gcc?

But this worked for me on:

gcc (GCC) 4.8.5 20150623 (Red Hat 4.8.5-39)

#include <stdio.h>

int main()
{
unsigned long long int x = 0x28B2D48D74212E4F;
unsigned long long int y = 0x6734B42C025D5CF7;
unsigned __int128 xy = x * (unsigned __int128)y;

    printf("Result = %016llx%016llx\n",
        (unsigned long long)( xy >> 64),
        (unsigned long long)( xy & 0xFFFFFFFFFFFFFFFFULL));

    return 0;

The casts inside the printf are important: otherwise the shifting/masking are done in 128-bit scalars, and those 128 bits pushed onto the stack, but then each %llx expects 64 bits.

Note that this is all entirely dependent on the underlying platform and is not portable; there's surely a way to use various #ifdefs and sizeofs to make it more general, but there's probably no super awesome way to make this work everywhere.

Note: `LL` in `0xFFFFFFFFFFFFFFFFULL` is OK, but not needed. `U` is not _needed_ either here as a hex constant, but still good to use for _unsigned_ constants. — chux - Reinstate Monica, Dec 22 '19 at 00:05
@chux-ReinstateMonica in fact the whole `&` operation is redundant, they could just put `(unsigned long long)xy`. Which I would even say is an improvement as you can't miscount the F's — M.M, Dec 22 '19 at 00:55
actually I take back my last comment, it's possible that `unsigned long long` is also 128-bit. Maybe using `UINT64_MAX` as the mask would be smart; or using `uint64_t` in the first place — M.M, Dec 22 '19 at 00:57

Multiplying very large hex numbers and printing them in C

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