BigFloat wrong

Specific Domains Numerics
1

Why BigFloat(10^(1/4) is wrong?
julia> BigFloat(10^(1/4))
1.778279410038922758729995621251873672008514404296875

exact: 1.77827941003892280122542119519…

Thanks

2

Perhaps you want to convert before the operation:

julia> BigFloat(10)^(1/4)
1.778279410038922801225421195192684844735790526402255358011830722776301881539489
3

To elaborate more on the previous answer, when x is a Float64, BigFloat(x) doesn’t give you extra precision compared to the original x, it just represents x, which has 53 bits of precision, as a BigFloat. To construct a BigFloat you want either to start from an integer (like in the example above) or use the big"..." string literal

4

Oh, Thanks. What you mean with “convert”?

5

Try:

julia> 10^(1/BigFloat(4))
1.778279410038922801225421195192684844735790526402255358011830722776301881539489

You must make sure that already the first operation, the division is done with high accuracy.

6

BigFloat(10) will convert 10::Int to a BigFloat.

The key point is that ^ already happens with BigFloats, which can be achieved by either argument being one.

7

It’s often more convenient to just write big(n) to get either a BigFloat or a BigInt depending on the argument type:

julia> big(10)^(1/4)
1.778279410038922801225421195192684844735790526402255358011830722776301881539489

julia> 10^(1/big(4))
1.778279410038922801225421195192684844735790526402255358011830722776301881539489

Note that for 1/4 these are the same because 1/4 is exactly representable in binary but for other fractions, as @ufechner7 pointed out, you’ll want to make sure the division is done in high precision by doing the latter version. Here’s an example where they differ:

julia> big(10)^(1/5)
1.584893192461113525718041298089470305609734784375671350368393872884966550887179

julia> 10^(1/big(5))
1.584893192461113485202101373391507013269442133825039068316296812316656863668456
4 Likes
8

Thank You for this tip.
Sincerely

Albert Gächter