[R] rounding down with as.integer

[Mike Miller]

On Fri, 2 Jan 2015, Duncan Murdoch wrote:

> On 01/01/2015 10:05 PM, Mike Miller wrote:

>> This is how big those errors are:
>>
>>> 512*.Machine$double.eps
>> [1] 1.136868e-13
>>
>> Under other conditions you also were seeing errors of twice that, or 
>> 1024*.Machine$double.eps.  It might not be a coincidence that the 
>> largest number giving me an error was 1023.
>>
>>> 2^-43
>> [1] 1.136868e-13
>>
>>> .Machine$double.eps
>> [1] 2.220446e-16
>>
>>> 2^-52
>> [1] 2.220446e-16
>>
>> I guess the 52 comes from the IEEE floating point spec...
>>
>> http://en.wikipedia.org/wiki/Double-precision_floating-point_format#IEEE_754_double-precision_binary_floating-point_format:_binary64
>>
>> ...but why are we seeing errors so much bigger than the machine precision?
>
> You are multiplying by 1000.  That magnifies the error.
>
>> Why does it change at 2?
>
> Because (most) floating point numbers are stored as (1 + x) * 2^y, where 
> x is a number between 0 and 1, and y is an integer value between -1023 
> and 1023. The value of y changes at 2, and this means errors in x become 
> twice as big.  (The exceptions are 0, Inf, NaN, etc., as well as 
> "denormals", where y is -1024 and the format changes to x * 2^(y+1).)


That is a great explanation.  Thanks very much!

Mike