Fortran (Was: The "does Python have variables?" debate)

[Mark H Harris]

On 5/11/14 11:10 PM, Mark H Harris wrote:
> On 5/11/14 10:10 PM, Dave Angel wrote:
>> On 05/11/2014 02:54 PM, Mark H Harris wrote:
>>
>>>
>>>  >julia> sin(BigFloat(π/4))
>>>  > 7.0710678118654750275194295621751674626154323953749278952436611913748
>>>  > 20215180412e-01 with 256 bits of precision
>>>
>>
>> That answer doesn't seem to come anywhere near 256 bits of precision.
>>
>> Using Python 3.2,
>>
>>  >>>
>> x=70710678118654750275194295621751674626154323953749278952436611913748
>>  >>> x*x
>> 4999999999999999693838300213161705693483516931249926767981110058185818806614907837502621065882204197129973479350206261627418690991407504
>>
>>
>>
>> Not that this is surprising, but it does make a terrible ad for how
>> great Julia is.
>>
>
> Dave, you get the golden egg!  I expected D'Aprano to catch it first!
>
> Yes, BigFloat does the same dumb thing Python's Decimal does.  π/4 is
> not a BigFloat, and BigFloat simply makes the 16 digit float into a 256
> bit float, the sin of which will only be 16 digits accurate (more or less).
>
> It has nothing to do with the language (Python vs. Julia) it has to do
> with the way the BigFloat is formed.  So let's fix it by forming the π
> constant as a BigFloat constant:
>
>  >julia> n = BigFloat(1)
>  >1e+00 with 256 bits of precision
>
>  >julia> π = atan(n/5)*16 - atan(n/239)*4
>  >3.141592653589793238462643383279502884197169399375105820974944592307816406286198e+00 >with 256 bits of precision
>
>  >julia> S = sin(π/4)
>  >7.07106781186547524400844362104849039284835937688474036588339868995366239231051e-01 >with 256 bits of precision
>
>  >julia> S * S
>  >4.999999999999999999999999999999999999999999999999999999999999999999999999999957e-01 >with 256 bits of precision


Having said that, the accuracy was not my point; in the first place.  My 
point is that the sin() function is built-in, takes standard floats (32 
bit, 64 bit, 128 bit) and BigFloats of arbitrary precision (and does 
something meaningful with it).  Let's take a look at Python Deciaml:

 >>> =================== RESTART ===============
 >>> from decimal import *          (first I have to import)
 >>> from math import *          (than I have to import again)
 >>> π
Traceback (most recent call last):
   File "<pyshell#13>", line 1, in <module>
     π
NameError: name 'π' is not defined     (whoops, don't know π )
 >>> π=4*atan(1)                  (let's create it)
 >>> sin(Decimal(π/4))
0.7071067811865475                   (whoops sin doesn't do Decimals)
 >>> from pdeclib import sin      (let's get a sin that does do Decimals)
 >>> sin(Decimal(π/4))
Decimal('0.707106781186547502751942956217516746261543')
 >>> S=sin(Decimal(π/4))       (Whoops has the same problem as BigFloat)
 >>> S**2
Decimal('0.499999999999999969383830021316170569348351')
 >>>

Now let's fix it:

 >>>
 >>> from pdeclib import d
 >>> n=d(1)
 >>> from pdeclib import *
 >>> n=d(1)
 >>> π=atan(n/5)*16 - atan(n/239)*4
 >>> S=sin(π/4)
 >>> S**2
 > Decimal('0.500000000000000000000000000000000000000000')
 >>>


Also not bad,  but slower.    ;-)


marcus