2 ms·

The precise value of double(0.1) is 0.1000000000000000055511151231257827021181583404541015625. That is precise, not an approximation. If you know of a program

The precise value of double(0.1) is 0.1000000000000000055511151231257827021181583404541015625. That is precise, not an approximation. If you know of a program in any of these languages that will print this value for "0.1" using built-in functionality, please let me know because I would love to know about it. Likewise the precise value of double(1e50) is 100000000000000007629769841091887003294964970946560. Anything else is an approximation of its true value. In another message you said that what's really important is that the string representation uniquely identifies the precise value. While that will help you reconstruct the value later, it does not help you understand why 0.1 + 0.2 != 0.3.

PaulAJ 13y ago
Haskell will tell you that toRational 0.1 = 3602879701896397 % 36028797018963968 toRational 1e50 = 100000000000000007629769841091887003294964970946560 % 1 Both of those values are precise, although I admit the first isn't really useful for human beings.
masida 13y ago
Python does it: >>> from decimal import Decimal >>> Decimal(0.1) Decimal('0.1000000000000000055511151231257827021181583404541015625') >>> Decimal(1e50) Decimal('100000000000000007629769841091887003294964970946560')
- haberman 13y ago
  Great to know, thanks!
StefanKarpinski 13y ago
It helps because 0.1 + 0.2 produces 0.30000000000000004 for 64-bit floats – so at least you can see that this value isn't the same as 0.3. In Ruby you just get two values that print the same yet aren't equal, which is way more confusing. I agree that printing the minimal number of digits required for reconstruction does not help with explaining why 0.1, 0.2 and 0.3 in 64-bit floats aren't the real values 1/10, 2/10 and 3/10.
StefanKarpinski 13y ago
The easiest way to see this exact value in Julia is to convert the Float64 value 0.1 to BigFloat and then print that: julia> big(0.1) 1.000000000000000055511151231257827021181583404541015625e-01 julia> big(1e50) 1.0000000000000000762976984109188700329496497094656e+50 Note that this is exactly why you don't normally want to construct BigFloats this way. Instead you want to do this: julia> BigFloat("0.1") 1.000000000000000000000000000000000000000000000000000000000000000000000000000002e-01 julia> BigFloat("1e50") 1e+50

PaulAJ 13y ago

Haskell will tell you that toRational 0.1 = 3602879701896397 % 36028797018963968 toRational 1e50 = 100000000000000007629769841091887003294964970946560 % 1 Both of those values are precise, although I admit the first isn't really useful for human beings.

masida 13y ago

Python does it: >>> from decimal import Decimal >>> Decimal(0.1) Decimal('0.1000000000000000055511151231257827021181583404541015625') >>> Decimal(1e50) Decimal('100000000000000007629769841091887003294964970946560')

haberman 13y ago
Great to know, thanks!

StefanKarpinski 13y ago

It helps because 0.1 + 0.2 produces 0.30000000000000004 for 64-bit floats – so at least you can see that this value isn't the same as 0.3. In Ruby you just get two values that print the same yet aren't equal, which is way more confusing. I agree that printing the minimal number of digits required for reconstruction does not help with explaining why 0.1, 0.2 and 0.3 in 64-bit floats aren't the real values 1/10, 2/10 and 3/10.

StefanKarpinski 13y ago

The easiest way to see this exact value in Julia is to convert the Float64 value 0.1 to BigFloat and then print that: julia> big(0.1) 1.000000000000000055511151231257827021181583404541015625e-01 julia> big(1e50) 1.0000000000000000762976984109188700329496497094656e+50 Note that this is exactly why you don't normally want to construct BigFloats this way. Instead you want to do this: julia> BigFloat("0.1") 1.000000000000000000000000000000000000000000000000000000000000000000000000000002e-01 julia> BigFloat("1e50") 1e+50