Conversion to branchless of consecutive if statements

Question

I'm stuck there trying to figure out how to convert the last two "if" statements of the following code to a branchless state.

int u, x, y;
x = rand() % 100 - 50;
y = rand() % 100 - 50;

u = rand() % 4;
if ( y > x) u = 5;
if (-y > x) u = 4;

Or, in case the above turns out to be too difficult, you can consider them as:

if (x > 0) u = 5;
if (y > 0) u = 4;

I think that what gets me is the fact that those don't have an else catcher. If it was the case I could have probably adapted a variation of a branchless abs (or max / min ) function.

The rand() functions you see aren't part of the real code. I added them like this just to hint at the expected ranges that the variables x , y and u can possibly have at the time the two branches happen.

Assembly machine code is allowed for the purpose.

EDIT:

After a bit of braingrinding I managed to put together a working branchless version:

int u, x, y;
x = rand() % 100 - 50;
y = rand() % 100 - 50;

u = rand() % 4;
u += (4-u)*((unsigned int)(x+y) >> 31);
u += (5-u)*((unsigned int)(x-y) >> 31);

Unfortunately, due to the integer arithmetic involved, the original version with if statements turns out to be faster by a 30% range.

Compiler knows where the party is at.

Answer 1

[All: this answer was written with the assumption that the calls on rand() were part of the problem. I offer improvement below under that assumption. OP belatedly clarifies he only used rand to tell us ranges (and presumably distribution) of the values of x and y. Unclear if he meant for the value for u, too. Anyway, enjoy my improved answer to the problem he didn't really pose].

I think you'd be better off recoding this as:

int u, x, y;
x = rand() % 100 - 50;
y = rand() % 100 - 50;

if ( y > x) u = 5;
else if (-y > x) u = 4;
else u = rand() % 4;

This calls the last rand only 1/4 as often as OP's original code. Since I assume rand (and the divides) are much more expensive than compare-and-branch, this would be a significant savings.

If your rand generator produces a lot of truly random bits (eg 16) on each call as it should, you can call it just once (I've assumed rand is more expensive than divide, YMMV):

int u, x, y, t;
t = rand() ;
u = t % 4;
t = t >> 2;
x = t % 100 - 50;
y = ( t / 100 ) %100 - 50;

if ( y > x) u = 5;
else if (-y > x) u = 4;

I think that the rand function in the MS C library is not good enough for this if you want really random values. I had to code my own; turned out faster anyway.

You might also get rid of the divide, by using multiplication by a reciprocal (untested):

int u, x, y;
unsigned int t;
unsigned long t2;
t = rand() ;
u = t % 4;

{ // Compute value of x * 2^32 in a long by multiplying.
  // The (unsigned int) term below should be folded into a single constant at compile time.
  // The remaining multiply can be done by one machine instruction
  // (typically 32bits * 32bits --> 64bits) widely found in processors.
  // The "4" has the same effect as the t = t >> 2 in the previous version
  t2 = ( t * ((unsigned int)1./(4.*100.)*(1<<32));
}
x = (t2>>32)-50; // take the upper word (if compiler won't, do this in assembler)
{ // compute y from the fractional remainder of the above multiply,
  // which is sitting in the lower 32 bits of the t2 product
  y = ( t2 mod (1<<32) ) * (unsigned int)(100.*(1<<32));
}

if ( y > x) u = 5;
else if (-y > x) u = 4;

If your compiler won't produce the "right" instructions, it should be straightforward to write assembly code to do this.

Answer 2

Some tricks using arrays indices, they may be quite fast if the compiler/CPU has one-step instructions to convert comparison results to 0-1 values (eg x86's "sete" and similar).

int ycpx[3];

/* ... */
ycpx[0] = 4;
ycpx[1] = u;
ycpx[2] = 5;
u = ycpx[1 - (-y <= x) + (y > x)];

Alternate form

int v1[2];
int v2[2];

/* ... */
v1[0] = u;
v1[1] = 5;
v2[1] = 4;
v2[0] = v1[y > x];
u = v2[-y > x];

Almost unreadable...

NOTE: In both cases the initialization of array elements containing 4 and 5 may be included in declaration and arrays may be made static if reentrancy is not a problem for you.