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 versions) and return all-bits-one (0xFFFF or 0xFFFFFFFF) if the sum overflows.

Target is x86 and ARM using gcc (4.1.2) and Visual Studio (for simulation only, so a fallback implementation is OK there).

Answer 1

uint32_t saturate_add32(uint32_t a, uint32_t b)
{
    uint32_t sum = a + b;
    if ((sum < a) || (sum < b))
        return ~((uint32_t)0);
    else
        return sum;
} /* saturate_add32 */

uint16_t saturate_add16(uint16_t a, uint16_t b)
{
    uint16_t sum = a + b;
    if ((sum < a) || (sum < b))
        return ~((uint16_t)0);
    else
        return sum;
} /* saturate_add16 */

Edit: Now that you've posted your version, I'm not sure mine is any cleaner/better/more efficient/more studly.

Answer 2

The current implementation we are using is:

#define sadd16(a, b)  (uint16_t)( ((uint32_t)(a)+(uint32_t)(b)) > 0xffff ? 0xffff : ((a)+(b)))
#define sadd32(a, b)  (uint32_t)( ((uint64_t)(a)+(uint64_t)(b)) > 0xffffffff ? 0xffffffff : ((a)+(b)))

Answer 3

I suppose, the best way for x86 is to use inline assembler to check overflow flag after addition. Something like:

add eax, ebx
jno @@1
or eax, 0FFFFFFFFh
@@1:
.......

It's not very portable, but IMHO the most efficient way.

Answer 4

In ARM you may already have saturated arithmetic built-in. The ARMv5 DSP-extensions can saturate registers to any bit-length. Also on ARM saturation is usually cheap because you can excute most instructions conditional.

ARMv6 even has saturated addition, subtraction and all the other stuff for 32 bits and packed numbers.

On the x86 you get saturated arithmetic either via MMX or SSE.

All this needs assembler, so it's not what you've asked for.

There are C-tricks to do saturated arithmetic as well. This little code does saturated addition on four bytes of a dword. It's based on the idea to calculate 32 half-adders in parallel, e.g. adding numbers without carry overflow.

This is done first. Then the carries are calculated, added and replaced with a mask if the addition would overflow.

uint32_t SatAddUnsigned8(uint32_t x, uint32_t y) 
{
  uint32_t signmask = 0x80808080;
  uint32_t t0 = (y ^ x) & signmask;
  uint32_t t1 = (y & x) & signmask;
  x &= ~signmask;
  y &= ~signmask;
  x += y;
  t1 |= t0 & x;
  t1 = (t1 << 1) - (t1 >> 7);
  return (x ^ t0) | t1;
}

You can get the same for 16 bits (or any kind of bit-field) by changing the signmask constant and the shifts at the bottom like this:

uint32_t SatAddUnsigned16(uint32_t x, uint32_t y) 
{
  uint32_t signmask = 0x80008000;
  uint32_t t0 = (y ^ x) & signmask;
  uint32_t t1 = (y & x) & signmask;
  x &= ~signmask;
  y &= ~signmask;
  x += y;
  t1 |= t0 & x;
  t1 = (t1 << 1) - (t1 >> 15);
  return (x ^ t0) | t1;
}

uint32_t SatAddUnsigned32 (uint32_t x, uint32_t y)
{
  uint32_t signmask = 0x80000000;
  uint32_t t0 = (y ^ x) & signmask;
  uint32_t t1 = (y & x) & signmask;
  x &= ~signmask;
  y &= ~signmask;
  x += y;
  t1 |= t0 & x;
  t1 = (t1 << 1) - (t1 >> 31);
  return (x ^ t0) | t1;
}

Above code does the same for 16 and 32 bit values.

If you don't need the feature that the functions add and saturate multiple values in parallel just mask out the bits you need. On ARM you also want to change the signmask constant because ARM can't load all possible 32 bit constants in a single cycle.

Edit: The parallel versions are most likely slower than the straight forward methods, but they are faster if you have to saturate more than one value at a time.

Answer 5

In IA32 without conditional jumps:

unsigned add (unsigned a, unsigned 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
}

Skizz

Answer 6

I'm not sure if this is faster than Skizz's solution (always profile), but here's an alternative no-branch assembly solution. Note that this requires the conditional move (CMOV) instruction, which I'm not sure is available on your target.

uint32_t sadd32(uint32_t a, uint32_t b)
{
    __asm
    {
     movl eax, a
     addl eax, b
     movl edx, 0xffffffff
     cmovc eax, edx
    }
}

Answer 7

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 8

If you care about performance, you really want to do this sort of stuff in SIMD, where x86 has native saturating arithmetic.

Because of this lack of saturating arithmetic in scalar math, one can get cases in which operations done on 4-variable-wide SIMD is more than 4 times faster than the equivalent C (and correspondingly true with 8-variable-wide SIMD):

sub8x8_dct8_c: 1332 clocks
sub8x8_dct8_mmx: 182 clocks
sub8x8_dct8_sse2: 127 clocks

Answer 9

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 10

You probably want portable C code here, which your compiler will turn into proper ARM assembly. ARM has conditional moves, and these can be conditional on overflow. The algorithm then becomes add, and conditionally set the destination to unsigned(-1) if overflow was detected.

In code:

uint16_t add16(uint16_t a, uint16_t b) { uint16_t c = a + b; if (c<a) /* Can only happen due to overflow */ { c = uint16_t(-1); } return c; }

Note that this differs from the other algorithms in that it corrects overflow, instead of relying on another calculation to detect overflow.

Answer 11

Zero branch solution:

uint32_t sadd32(uint32_t a, uint32_t b)
{
    uint64_t s = (uint64_t)a+b;
    return -(s>>32) | (uint32_t)s;
}

A good compiler will optimize this to avoid doing any actual 64-bit arithmetic (s>>32 will merely be the carry flag, and -(s>>32) is the result of sbb %eax,%eax).

In x86 asm (AT&T syntax, a and b in eax and ebx, result in eax):

add %eax,%ebx
sbb %eax,%eax
or %ebx,%eax

8- and 16-bit versions should be obvious. Signed version might require a bit more work.