R not calculating large cubes correctly?

Question

There's been some news lately about the discovery of three cubes that sum to 42. Namely, Andrew Sutherland and Andrew Booker discovered that (-80538738812075974)^3 + 80435758145817515^3 + 12602123297335631^3=42 (https://math.mit.edu/~drew/)

I was tinkering with this a bit, and I'm not getting 42 in R.

I do get it in other places (WolframAlpha), but R gives me this:

> (-80538738812075974)^3 + 80435758145817515^3 + 12602123297335631^3
[1] 1.992544e+35

Any idea what I'm doing wrong? Is it a limitation with large numbers in R? Or am I (very probably) just doing something dumb?

slava-kohut · Answer 1 · 2019-09-11T18:38:23.877

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UPDATE

As pointed out by @MrFlick, this is a well-known floating point arithmetic issue. R stores large numbers in your example as double precision numbers.

Also, be aware of integer overflow. See a related discussion here. Note that base R will not throw an error (just a warning) when integer overflow occurs.The bit64 package may help sometimes, but won't do the job in your case the accuracy it provides is still not enough.

edited Sep 11 '19 at 18:38

answered Sep 11 '19 at 17:57

slava-kohut

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Actually R doesn't treat very large numbers like that as integers. R will store that as a "numeric" value which is in this case would be a double floating point number (see `typeof(80538738812075974)`). So there is no integer overflow error message here. R will throw a integer overflow warning if you actually use integers (see `2e9L + 2e9L`). This is really more about the [well known problems with floating point arithmetic](https://stackoverflow.com/questions/9508518/why-are-these-numbers-not-equal) which is shared with most modern programming languages. – MrFlick Sep 11 '19 at 18:24
@MrFlick thanks for your comment. I edited my post and acknowledged your contribution. – slava-kohut Sep 11 '19 at 18:34

GKi · Answer 2 · 2019-09-12T08:46:21.697

If you want to calculate with large (integer) numbers in R you can use the gmp library like:

library(gmp)
as.bigz("-80538738812075974")^3 + as.bigz("80435758145817515")^3 + as.bigz("12602123297335631")^3
#[1] 42

#or even better use also Integer in the exponent:
as.bigz("-80538738812075974")^3L + as.bigz("80435758145817515")^3L + as.bigz("12602123297335631")^3L

As @mrflick pointed already out you are using numeric - double. So the calculated result is approximately right. When using Integer you get warnings and R will convert it to numeric:

(-80538738812075974L)^3L + 80435758145817515L^3L + 12602123297335631L^3L
#[1] 1.992544e+35
#Warning messages:
#1: non-integer value 80538738812075974L qualified with L; using numeric value 
#2: non-integer value 80435758145817515L qualified with L; using numeric value 
#3: non-integer value 12602123297335631L qualified with L; using numeric value

Note that you have to give a string to as.bigz. When writing a number R will treat it as double or convert, as above, large integer numbers, to double and might lose precision.

R not calculating large cubes correctly?

2 Answers2