0.1 is a number that can be exactly represented by a Float16, or Float32, or a Float64. (at least according to how we print them) But not it would seem (at least according to printing) by a BigFloat. julia> parse(Float64, "0.1") 0.1 julia> parse(Float32, "0.1") 0.1f0 julia> parse(Float16, "0.1"…

[image] oxinabox: 0.1 is a number that can be exactly represented by a Float16 , or Float32 , or a Float64 . As Jeffrey pointed out, this assumption is wrong. Another way to see it: julia> @printf "%.20f" 0.1f0 0.10000000149011611938 julia> @printf "%.50f" 0.1 0.1000000000000000055511151231…

You can also prove by hand that 1/10 is an (infinitely) repeating decimal in base-2, which is why it can’t be represented exactly by binary floating-point with any finite precision: c# - Are there numbers that are not representable in base 10 but can be represented in base 2? - Software Engineering …

How does the show method know that we want to see 0.1 and not the real value that’s stored?

It’s for the same reason that 0.1 + 0.2 != 0.3 ( https://0.30000000000000004.com ) [image] roflmaostc: How does the show method know that we want to see 0.1 and not the real value that’s stored? Julia prints the shortest value that uniquely identifies the float in question when parsed back. Th…

Is it that we don’t use Ryu for BigFloat but instead use some inferior algorithm?

BigFloat is really a wrapper around the MPFR library, which has its own printing algorithm.

And for fun julia> bitstring(3) "0000000000000000000000000000000000000000000000000000000000000011" julia> bitstring(1.0) "0011111111110000000000000000000000000000000000000000000000000000" julia> bitstring(0.1) "0011111110111001100110011001100110011001100110011001100110011010"

BigFloats are binary floating point and it CANNOT exactly represent 0.1 because it is base-2 instead of base-10

I think part of the confusion is that the Julia expression 0.1 is a Float64 close, but not equal to 1//10. So Float64(0.1) is really the same thing as 0.1. I try always to be careful to distinguish 0.1 and 1/10 = 0.1 which are different (Julia left and common number right.) This also implies that a…

Are BigFloats unable to exactly represent 0.1?

General Usage

John_Gibson June 2, 2021, 11:05am 13

Topic		Replies	Views
BigFloat converted to string returns different number? Numerics numbers , bigfloat	8	619	August 28, 2022
Promotion to BigFloat -- no zero padding General Usage bigfloat	8	788	August 9, 2021
Printing exact decimal representations Numerics float , bigfloat	2	542	August 30, 2023
Rounding BigFloat to 3 significant digits New to Julia numbers , float , bigfloat	9	1607	December 6, 2022
Converting Float32 values back to Float64 without introducing nonzero digits at the end? General Usage	2	804	May 3, 2024

Are BigFloats unable to exactly represent 0.1?

Related topics