Larry's PseudoCode for Emulating Division

LarryP's division pseudoCode, attempting to follow the Wikipedia Newton-Raphson algorithm:

Non Millcomputing folks, please don't make changes to my pseudocode, at least not yet. Instead please make a separate sibling file in the Wiki.

I'm fighting the Wiki's formatting; probably best to view the source, rather than the Wikified version.

Some rough pseudocode follows. Note, I'm defaulting to the variable names used in the Wikipedia Newton-Raphson division algorithm, but lower-cased wherever possible.

Function (OK, really more of a macro for expansion)

divu(n,d) --> q, r

// For now, assume both n and d are // (a) unsigned, // (b) the same width and // (c) are less than 128 bits.

// Unless otherwise specified, all math operations are non-widening versions. //suspect there are some overflow checks that NEED to be added.

if (isNaR(n) || isNar(d)) {return NaR, NaR} // Handle NaR inputs

if (isNone(n) || isNone(d)) {return None, None} // Handle NaR inputs

if (0 == d) {return NaR, NaR} // Handle zero divisor

/* How do we determine what width the arguments are?

*
* The width matters, especially when either of the inputs 
* is already at max width (128 bits!!) 
*
* For now, I'm assuming BOTH input args are a width were we can apply widen, 
* and get a result that's 
* the same number of elements as the input.  This is bogus, but is a starting point.
*/

lzd = countlz(d);

if (MAX_INT_BITS == width(d)|| MAX_INT_BITS == width(n)) GOTO another algorithm

d = widen(d);

n = widen(n); // This assumes d and n are same width. MUST FIX LATER!

d = (d << lzd + 1); // I'm essentially putting the binary point at the mid-width

n = (n << lzd + 1); // of the widened input args.

// I want to try following the Wikipedia N-R algorithm, // including the suggested scaling. // Still looking for genAsm examples of width-aware code.

// Now have an implicit binary point at the midpoint of our width // And D is in the interval [1 -- 2) (can be 1, can't be 2 // with respect to our implicit binary point

x = rdivu(d) * n; // Initialize via rdiv*. Assumes that rdivu is better than

                       // approximating X0 as = (48/17) - (32/17)*d 

//********************************************************************

// X := X + X × (1 - D' × X), done without fused multiply-adds :-(

// we want NON-WIDENING multiplied here, I believe.

t1 = d * x; t2 = (1 << (half_our_width)) - t1; // How do we determine our width?

t3 = x * t2; x = x + t3;

// Repeat above 4 calcs a TDB (and width-dependent!) number of times //*********************************************************************

q = n * x;

q = q >> 1; // undo the "floating point style" scaling to be in the lower half word

q = narrow(q); // force result back to same width as starting args

return q;

// OPTIONALLY calc and return remainder, BUT DON'T FORGET the scaling