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Improve accuracy of NR-based fp_sqrt with better initial estimation and using one more bit internally. More reliable early termination. Good enough until better method is completed.

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git-svn-id: svn://svn.rockbox.org/rockbox/trunk@26681 a1c6a512-1295-4272-9138-f99709370657
This commit is contained in:
Michael Sevakis 2010-06-08 04:51:00 +00:00
parent 88f4a24c3a
commit 67277f1688
1 changed files with 24 additions and 17 deletions
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41
apps/fixedpoint.c
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@ -152,29 +152,36 @@ long fp_sincos(unsigned long phase, long *cos)
* @return Square root of argument in same fixed point format as input.
*
* This routine has been modified to run longer for greater precision,
* but cuts calculation short if the answer is reached sooner. In
* general, the closer x is to 1, the quicker the calculation.
* but cuts calculation short if the answer is reached sooner.
*/
long fp_sqrt(long x, unsigned int fracbits)
{
long b = x/2 + BIT_N(fracbits); /* initial approximation */
long c;
unsigned n;
const unsigned iterations = 8;
for (n = 0; n < iterations; ++n)
{
c = fp_div(x, b, fracbits);
if (c == b) break;
b = (b + c)/2;
}
unsigned long xfp, b;
int n = 8; /* iteration limit (should terminate earlier) */
return b;
if (x <= 0)
return 0; /* no sqrt(neg), or just sqrt(0) = 0 */
/* Increase working precision by one bit */
xfp = x << 1;
fracbits++;
/* Get the midpoint between fracbits index and the highest bit index */
b = ((sizeof(xfp)*8-1) - __builtin_clzl(xfp) + fracbits) >> 1;
b = BIT_N(b);
do
{
unsigned long c = b;
b = (fp_div(xfp, b, fracbits) + b) >> 1;
if (c == b) break;
}
while (n-- > 0);
return b >> 1;
}
/* Accurate int sqrt with only elementary operations. (the above
* routine fails badly without enough iterations, more iterations
* than this requires -- [give that one a FIXME]).
/* Accurate int sqrt with only elementary operations.
* Snagged from:
* http://www.devmaster.net/articles/fixed-point-optimizations/ */
unsigned long isqrt(unsigned long x)