Difference between revisions of "Larry's PseudoCode for Emulating Division"
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LarryP's division pseudoCode, attempting to follow the Wikipedia Newton-Raphson algorithm: | LarryP's division pseudoCode, attempting to follow the Wikipedia Newton-Raphson algorithm: | ||
| + | Please don't make changes without discussing with me. | ||
| + | Instead please make a separate copy. | ||
| + | |||
| + | 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. | 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. | ||
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//suspect there are some overflow checks that NEED to be added. | //suspect there are some overflow checks that NEED to be added. | ||
| − | if (isNaR(n) || isNar(d)) {return NaR, NaR} | + | if (isNaR(n) || isNar(d)) {return NaR, NaR} // Handle NaR inputs |
| − | if (isNone(n) || isNone(d)) {return None, None} | + | if (isNone(n) || isNone(d)) {return None, None} // Handle NaR inputs |
| − | if (0 == d) {return NaR, NaR} | + | if (0 == d) {return NaR, NaR} // Handle zero divisor |
/* '''How do we determine what width the arguments are?''' | /* '''How do we determine what width the arguments are?''' | ||
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d = widen(d); | d = widen(d); | ||
| + | |||
n = widen(n); // This assumes d and n are same width. MUST FIX LATER! | 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 | d = (d << lzd + 1); // I'm essentially putting the binary point at the mid-width | ||
| + | |||
n = (n << lzd + 1); // of the widened input args. | n = (n << lzd + 1); // of the widened input args. | ||
| + | |||
// I want to try following the Wikipedia N-R algorithm, | // I want to try following the Wikipedia N-R algorithm, | ||
// including the suggested scaling. | // including the suggested scaling. | ||
| − | // | + | // S'''till looking for genAsm examples of width-aware code.''' |
// Now have an implicit binary point at the midpoint of our width | // Now have an implicit binary point at the midpoint of our width | ||
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x = rdivu(d) * n; // Initialize via rdiv*. Assumes that rdivu is better than | x = rdivu(d) * n; // Initialize via rdiv*. Assumes that rdivu is better than | ||
| − | |||
| − | + | // approximating X0 as = (48/17) - (32/17)*d | |
//******************************************************************** | //******************************************************************** | ||
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// Repeat above 4 calcs a TDB (and width-dependent!) number of times | // Repeat above 4 calcs a TDB (and width-dependent!) number of times | ||
//********************************************************************* | //********************************************************************* | ||
| + | |||
q = n * x; | q = n * x; | ||
| + | |||
q = q >> 1; // undo the "floating point style" scaling to be in the lower half word | 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 | q = narrow(q); // force result back to same width as starting args | ||
return q; | return q; | ||
| − | // OPTIONALLY calc and return remainder, | + | // OPTIONALLY calc and return remainder, BUT DON'T FORGET the scaling |
Revision as of 17:03, 21 April 2015
LarryP's division pseudoCode, attempting to follow the Wikipedia Newton-Raphson algorithm:
Please don't make changes without discussing with me. Instead please make a separate copy.
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
