Unit scaling: human readable Quantity units

Question

Consider some calculation yielding Quantity[x,"B"] as output ("B" interpreted as byte).

1. Is there a way to automatically convert this to the unit "GB" or "MB" or "TB" etc as the case may be. i.e. instead of checking y in x<2^(10 y), is there some inbuilt way of doing this?

Consider now the quantity Quantity[x,"s"]. ("s" interpreted as second).

Depending on x, the human readable unit may be micro seconds to days. This again has the same solution structure as the file-size case mentioned earlier. Only the base unit is different.

2. Say one implements the explicit solution mentioned in 1. If one wants to modify the function to now accommodate time based Quantitys too, one needs to know whether the input arg is of "data" category or "time" category. Are there meta categories for units in Mathematica? e.g. "KB,MB,GB,TB"->data, "s,h,year,days"->"time"

I did try CommonUnits, but it didn't work.

Answer 1

The relevant built-in here seems to be UnitConvert[Quantity[...],"Conventional"] at least to the extent that one's interpretation of "human-readable" is "Conventional".

For time this seems to reasonably align

Table[UnitConvert[Quantity[2^k, "Seconds"], "Conventional"], {k, 4, 24, 2}] // N

while for data "Conventional" seems to be somewhat "less human" as it insists on using bits for scaled units.

Table[UnitConvert[Quantity[2^k, "Bytes"], "Conventional"], {k, 5, 20, 5}]

Answer 2

This question is very much subject to taste. Here is a few ideas that may be tailored to the users' tastes. I happened to use time units for my example.

v1=Quantity[1,"Exaseconds"]
v2=Quantity[1,"Millenia"]
v3=Quantity[0.123000456,"seconds"];
unitList={"Eons","Megayears","Millenia","Years","Months","Days","Hours","Seconds","Milliseconds","Microseconds","Nanoseconds"}
human[quantity_Quantity,units_List]:= Block[
{result},
result=UnitConvert[quantity,MixedUnit[units]];
result=Evaluate[Select[{result[[1,1]],result[[2,1]]}\[Transpose],#[[1]]!=0&]\[Transpose]];
Quantity[MixedMagnitude[result[[1]]],MixedUnit[result[[2]]]]
]
human[v1,unitList]
human[v2,unitList]
human[v3,unitList]
approximate[quantity_Quantity,units_List]:= Block[
{result},
result=UnitConvert[quantity,MixedUnit[units]];
result=Evaluate[First[Select[{result[[1,1]],result[[2,1]]}\[Transpose],#[[1]]!=0&]]\[Transpose]];
Quantity@@result
]
approximate[v1,unitList]
approximate[v2,unitList]
approximate[v3,unitList]

1Es
1millennium
{Eons,Megayears,Millenia,Years,Months,Days,Hours,Seconds,Milliseconds,Microseconds,Nanoseconds}
31\[ThinSpace]eons709\[ThinSpace]Myr791\[ThinSpace]millennia458\[ThinSpace]yr2\[ThinSpace]mo25\[ThinSpace]days17\[ThinSpace]h2800\[ThinSpace]s
1millennium
123\[ThinSpace]ms456.\[ThinSpace]ns
31eons
1millennium
123ms

Here is a potentially useful utility function:

makeUnits = Function[base, (StringJoin[#1, base] & ) /@ 
    {"quetta", "ronna", "yotta", "zetta", "exa", "peta", 
     "tera", "giga", "mega", "kilo", "", "milli", "micro", 
     "nano", "pico", "femto", "atto", "zepto", "yocto", 
     "ronto", "quecto"}]

{quettajoule,ronnajoule,yottajoule,zettajoule,exajoule,petajoule,terajoule,gigajoule,megajoule,kilojoule,joule,millijoule,microjoule,nanojoule,picojoule,femtojoule,attojoule,zeptojoule,yoctojoule,rontojoule,quectojoule}

human[Quantity[1,"eV"],unitList]
160\[ThinSpace]zJ217\[ThinSpace]yJ663\[ThinSpace]rJ400\[ThinSpace]qJ
human[Quantity[1,"kWh"],unitList]
3\[ThinSpace]MJ600\[ThinSpace]kJ
human[Quantity[1,"BTU"],unitList]
1\[ThinSpace]kJ55\[ThinSpace]J55\[ThinSpace]mJ852\[ThinSpace]\[Mu]J620\[ThinSpace]nJ