Added base/1 and unbase/1

[ghost]

Base conversion functions get re-implemented quite frequently, thus they deserve their own built-ins.

base/1 takes an operand x and converts the input to base x. Example usage:

14 | base(2)  -> [1, 1, 1, 0]

unbase/1 is the opposite of base/1: it takes an operand x and converts the input from base x. Example usage:

[1, 1, 1, 0] | unbase(2) -> 14

[coveralls]

Coverage increased (+0.4%) to 84.494% when pulling 0d872a8 on 2x-1:master into 80052e5 on stedolan:master.

[odnoletkov]

In my experience it is more convenient to work with this representation of numbers – array of base digits – when order of digits is reversed. So the lowest order digit is the first and highest is the last in the array:

14 | base(2)  -> [0, 1, 1, 1]

That way when implementing operations with multiple numbers same order digits match naturally, for example:

def bitwiseand($a; $b): [$a, $b] | transpose | map(if all(. > 0) then 1 else 0 end);

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For the names what do you think about tobase/1 and frombase/1? This follows convention set by other APIs in the standard library.

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Lastly, we need to document these in the manual.

[itchyny]

Lastly, we need to document these in the manual.

And tests, too.

[ghost]

@odnoletkov Sorry for the inactivity. These are all good suggestions, I'll be trying to fullfill them.

[ghost]

@itchyny Not sure where the tests are though - I'm relatively new to jq's source code.

[tst2005]

I think there is a bug in frombase.

-def frombase($a): reduce (.[] | reverse) as $i (0; . * $a + $i);
+def frombase($a): reduce (reverse | .[]) as $i (0; . * $a + $i);

[tst2005]

in tobase, there is an issue but only when the input value is 0.
jq -n '0|tobase(16)' shoule be [0] not []

-def tobase($a): [while(. > 0; (. / $a) | floor) % $a];
+def tobase($a): [while(. > 0; (. / $a) | floor) % $a]|if .==[] then [0] else . end;