How to do unsigned saturating addition in C?

Question

What is the best (cleanest, most efficient) way to write saturating addition in C?

The function or macro should add two unsigned inputs (need both 16- and 32-bit ver

Answer 1

//function-like macro to add signed vals, 
//then test for overlow and clamp to max if required
#define SATURATE_ADD(a,b,val)  ( {\
if( (a>=0) && (b>=0) )\
{\
    val = a + b;\
    if (val < 0) {val=0x7fffffff;}\
}\
else if( (a<=0) && (b<=0) )\
{\
    val = a + b;\
    if (val > 0) {val=-1*0x7fffffff;}\
}\
else\
{\
    val = a + b;\
}\
})

I did a quick test and seems to work, but not extensively bashed it yet! This works with SIGNED 32 bit. op : the editor used on the web page does not let me post a macro ie its not understanding non-indented syntax etc!

Answer 2

The best performance will usually involve inline assembly (as some have already stated).

But for portable C, these functions only involve one comparison and no type-casting (and thus I believe optimal):

unsigned saturate_add_uint(unsigned x, unsigned y)
{
    if (y > UINT_MAX - x) return UINT_MAX;
    return x + y;
}

unsigned short saturate_add_ushort(unsigned short x, unsigned short y)
{
    if (y > USHRT_MAX - x) return USHRT_MAX;
    return x + y;
}

As macros, they become:

SATURATE_ADD_UINT(x, y) (((y)>UINT_MAX-(x)) ? UINT_MAX : ((x)+(y)))
SATURATE_ADD_USHORT(x, y) (((y)>SHRT_MAX-(x)) ? USHRT_MAX : ((x)+(y)))

I leave versions for 'unsigned long' and 'unsigned long long' as an exercise to the reader. ;-)

Answer 3

Saturation arithmetic is not standard for C, but it's often implemented via compiler intrinsics, so the most efficient way will not be the cleanest. You must add #ifdef blocks to select the proper way. MSalters's answer is the fastest for x86 architecture. For ARM you need to use __qadd16 function (ARM compiler) of _arm_qadd16 (Microsoft Visual Studio) for 16 bit version and __qadd for 32-bit version. They'll be automatically translated to one ARM instruction.

Links:

• __qadd16
• _arm_qadd16
• __qadd

Answer 4

In plain C:

uint16_t sadd16(uint16_t a, uint16_t b) {
  return (a > 0xFFFF - b) ? 0xFFFF : a + b;
}
     
uint32_t sadd32(uint32_t a, uint32_t b) {
  return (a > 0xFFFFFFFF - b) ? 0xFFFFFFFF : a + b;
}

which is almost macro-ized and directly conveys the meaning.

Answer 5

In IA32 without conditional jumps:

uint32_t sadd32(uint32_t a, uint32_t b)
{
#if defined IA32
  __asm
  {
    mov eax,a
    xor edx,edx
    add eax,b
    setnc dl
    dec edx
    or eax,edx
  }
#elif defined ARM
  // ARM code
#else
  // non-IA32/ARM way, copy from above
#endif
}

Answer 6

An alternative to the branch free x86 asm solution is (AT&T syntax, a and b in eax and ebx, result in eax):

add %eax,%ebx
sbb $0,%ebx