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

[Mark H Harris]

On 5/11/14 12:05 PM, Alain Ketterlin wrote:
>> Julia is Matlab and  R, Python, Lisp, Scheme; all rolled together on
>> steroids. Its amazing as a dynamic language, and its fast, like
>> lightning fast as well as multiprocessing (parallel processing) at its
>> core. Its astounding, really.
>
> Hmmm...
>
>> Its number concept is unified,
>
> What exactly is unified? There is no implicit promotion between
> primitive types and BigInt/Float.


The built-in math functions (extensive, by the way) just work, and they 
work consistently the way you might expect across types. Consider sqrt():

 > julia> sqrt(-1+0im)
 > 0.0 + 1.0im

 > julia> sqrt(complex(-1))
 > 0.0 + 1.0im

 > julia> sqrt(2)
 > 1.4142135623730951

 >julia> sqrt(2.0)
 > 1.4142135623730951

 > julia> sqrt(BigFloat(2.0))
 >1.414213562373095048801688724209698078569671875376948073176679737990732478462102
 >e+00 with 256 bits of precision

 >julia> with_bigfloat_precision(1024) do
 >         sqrt(BigFloat(2.0))
 >       end
 >1.414213562373095048801688724209698078569671875376948073176679737990732478462107
 >03885038753432764157273501384623091229702492483605585073721264412149709993583141
 >32226659275055927557999505011527820605714701095599716059702745345968620147285174
 >18640889198609552329230484308714321450839762603627995251407989687253402e+00 >with 1024 bits of precision


You'll notice that I did not need to import anything to use sqrt(), and 
sqrt() takes all types and does something meaningful with them.

The following code will produce over 100,000 digits of π (pi) in less 
than 2 seconds on a low-end processor, like my mac mini dual core 2Ghz:

 >julia> prec=524288
 >524288

 >julia> with_bigfloat_precision(prec) do
 >         println(atan(BigFloat(1)/5)*16 - atan(BigFloat(1)/239)*4)
 >       end

The scientific and transcendental functions (built-ins) just work. The 
coder sets the precision in floating point bits, and the functions just 
work --- at that precision. Nothing needs to be imported, and special 
functions are not necessary. The maths are unified, and they are fast; 
yet, the coder has the flexibility and ease of python coding, with a 
very useful repl.

But, like lisp, Julia's internal structures are lists, so, it can create 
and modify its own code on-the-fly. Unicode characters above code point 
\u00A0 can be used as symbols, and constants ARE their unicode characters:

 >julia> sin(π/4)
 > 0.7071067811865475

 >julia> cos(π/4)
 > 0.7071067811865476

 >julia> sin(BigFloat(π/4))
 > 7.0710678118654750275194295621751674626154323953749278952436611913748
 > 20215180412e-01 with 256 bits of precision


marcus