I was originally thinking of making a lookup table, but thought of this along the way.

Thanks for that - I still haven't worked my way through it properly.
It seems to work fine now that I've changed:

long long smallest_invalid = last_set << 52;
to
long long smallest_invalid = last_set << 53;
[download]

Without that change, the following values (for example) wrongly reported "NOPE":

1844674407366955264,
1844674407366955776,
1844674407366956288,
1844674407366956800,
1844674407366957312,
1844674407366957824,
1844674407366958336,
1844674407366958848,
1844674407366959360,
1844674407366959872,
1844674407366960384,
1844674407366960896,
1844674407366961408,
1844674407366961920,
1844674407366962432,
1844674407366962944,
1844674407366963456,
1844674407366963968,
1844674407366964480,
1844674407366964992
[download]

In the following XS adaptation it's taking over twice as long as uv_fits_double3.

use warnings;
use Benchmark;

use Inline C => Config =>
  BUILD_NOISY => 1;

use Inline C => <<'EOC';

int uv_fits_double3(SV * x, ...) {
  dXSARGS;
  int i, count = 0;
  UV arg;

  for(i = 0; i < items; i++) {
    arg = SvUV(ST(i));
    if(arg) {
      while(!(arg & 1)) arg >>= 1;
      if(arg < 9007199254740993) count++;
    }
  }
  return count;
}

int uv_fits_double_bitfiddle(SV * t, ...) {
    dXSARGS;
    int i, count = 0;

  for(i = 0; i < items; i++) {
    /* First we need to identify the lowest bit set */
    IV neg_t    = -(SvIV(ST(i)));
    IV last_set = SvUV(ST(i)) & neg_t;

    /* Shift it left 53 bits to get location of lowest invalid bit    
+     *
     * NOTE: If smallest invalid bit is far enough left, then this wil
+l    *
     * turn into 0 making the invalid bits also 0, which happens to be
+ OK! */
    IV smallest_invalid = last_set << 53;

    UV valid_bits = smallest_invalid - 1;
    UV invalid_bits = ~valid_bits;

    /* It's a 'valid' number unless one of the upper-order invalid bit
+s are set */
    if(!(SvUV(ST(i)) & invalid_bits)) count++;
  }
  return count;
}

EOC

@in = (1844674407366955161 .. 1844674407378955161);
# @in = (9007199248740992 .. 9007199260740992);
# @in = (184467436737095 .. 184467448737095);
# @in = (184463440737 .. 184475440737);

die "wrong size" unless @in == 12000001;

timethese (1, {
'uv_fits_double3'    =>       '$count1 = uv_fits_double3(@in);',
'uv_fits_double_bitfiddle' => '$count2 = uv_fits_double_bitfiddle(@in)
+;',
});

print "$count1 $count2\n";

die "Error in at least one of the XSubs" unless $count1 == $count2;
__END__
[download]

Benchmarking results on my Windows 7 machine with perl-5.30.0 are:

Benchmark: timing 1 iterations of uv_fits_double3, uv_fits_double_bitf
+iddle...
uv_fits_double3:  0 wallclock secs ( 0.44 usr +  0.00 sys =  0.44 CPU)
+ @  2.29/s (n=1)
            (warning: too few iterations for a reliable count)
uv_fits_double_bitfiddle:  1 wallclock secs ( 0.94 usr +  0.00 sys =  
+0.94 CPU) @  1.07/s (n=1)
            (warning: too few iterations for a reliable count)
12000001 12000001
[download]

Can you see room for significant improvement in performance of uv_fits_double_bitfiddle ?

Thanks for another interesting approach !!

Cheers,
Rob

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