Here is a rather evil way to quickly compute the closest powers of 2 to a number.

First, figure out which bits represent the mantissa in your native floating point format. Then you can zero out all of the bits in the mantissa (which doesn't include the highest bit) and get the closest previous power of 2.

Getting the closest next power of 2 is a bit trickier.

Inspired by a CB question from BrowserUk and my previous (tye)Re: How can I tell if a number is a power of 2?.

Sample output: 

0 == 0 == 0
1 <= 1 <= 1
2 <= 2 <= 2
2 <= 3 <= 4
4 <= 4 <= 4
4 <= 5 <= 8
16384 <= 32000 <= 32768
8589934592 <= 10000000000 <= 17179869184
-2 >= -2 >= -2
-2 >= -3 >= -4
0.0625 <= .1 <= 0.125
0.0078125 <= .01 <= 0.015625
-0.0009765625 >= -.001 >= -0.001953125
5.61779104644474e+306 <= 1e307 <= 1.12355820928895e+307
8.98846567431158e+307 <= 1e308 <= 1.#INF
8.90029543402881e-308 <= 1e-307 <= 1.78005908680576e-307

[download]
(updated) 

#!/usr/bin/perl -w
use strict;

my $mant;
BEGIN {
    my $max= 2;
    $max *= 2   until  2*$max+1 == 2*$max;
    $mant= pack("d",$max) ^ pack("d",2*$max-1);
}

sub prevPower2 {
    my( $n )= @_;
    return  unpack "d", ~$mant & pack "d", $n;
}

sub nextPower2 {
    my( $n )= @_;
    my $p= prevPower2( $n );
    $p *= 2   if  $p != $n;
    return  $p;
}

while(  <>  ) {
    chomp;
    my $dir= (qw( < = > ))[ 1 + (0<=>$_) ];
    print prevPower2($_), " $dir= $_ $dir= ", nextPower2($_), $/;
}

[download]

In reply to Next/Prev power of 2 by tye

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