I'm just curious about the result of the following multiplication :
(* 2.14 5.0) ==> 10.700001
Why this remaining '1' at the end of the result ? Thank you !
Asked
Active
Viewed 42 times
1
-
2.14 isn't exact in base 2 float. It's `10.0*01000111101011100001` with the part after * repeating infinitely. A float has 65 base2 so you only get `10.001000111101011100001010001111010111000010100011110101110000101` which is the source of the error. You can write it as a ratio `(* 214/100 5) ; ==> 107/10`. You have this in base 10 too. eg `1/3` is `0,*3` and if you use a limited significant digits you end up with a lower value than it really is. [DEC64](http://dec64.com/) as a numeric type in our programming languages would have fixed this. – Sylwester Jan 21 '18 at 21:22
-
A double float only has 54 bits of precision (53 explicit), I suspect you were a column out on your keyboard. A single float (typical for `single-float` and default CL float type) has 24 bits of precision (23 explicit). – Dan Robertson Jan 21 '18 at 22:55
-
1Try also `(* (/ 214 100) 5)` for comparison – coredump Jan 22 '18 at 10:37