Multiplying two numbers of the form x.xxxxxxe-x*10^xx is not working properly

Question

I am trying to evaluate the following example inside my code, but getting the wrong answer:

julia> -1.259237254330301e-29*10^29 
-9.930838679817422e-11

The answer is clearly wrong, -1.259237254330301 is expected. I got the right answer by

julia> -1.259237254330301e-29*1e29
-1.2592372543303008

anyone know the reason?

Possible duplicate of [Is floating point math broken?](https://stackoverflow.com/questions/588004/is-floating-point-math-broken) — Code-Apprentice, Jun 13 '18 at 14:00
This Q&A explains the perils of floating point arithmetic in general. — Code-Apprentice, Jun 13 '18 at 14:01
[Why does Julia use native machine integer arithmetic?](https://docs.julialang.org/en/latest/manual/faq/#Why-does-Julia-use-native-machine-integer-arithmetic?-1) — Gnimuc, Jun 13 '18 at 14:50
This is clearly not a duplicate of "Is floating point math broken?" — Simon Byrne, Jun 13 '18 at 16:28

score 8 · Accepted Answer · answered Jun 13 '18 at 14:28

Despite the rounding errors of Floats, the cause for the wrong result comes from the use of Integer Arithmetic with overflow in the Type: On a 64-Bit OS 10^29 overflows (in JULIA without an error).

64-Bit OS: 10^18 =  = 1000000000000000000  (64-Bit Integers can hold up to ~ 9,22x10^18)

while: 10^19 turns to: -8446744073709551616 which is wrong, due to overflowing.

If you choose a type capabale of holding the value the result is correct: eg.:

julia> -1.259237254330301e-29*Int128(10)^29
-1.2592372543303008

or:

julia> -1.259237254330301e-29*big(10)^29
-1.259237254330300936796903330938514872571882315563023692882767533667837970629477

Multiplying two numbers of the form x.xxxxxxe-x*10^xx is not working properly

1 Answers1