Wolfram Language at a compilers LAB college class​
​By Prof. Daniel Carvalho​
​@danielscarvalho - https://twitter.com/danielscarvalho​
​Nov 2021
Classes notes
LAB: Languages & Workshop
◼
  • C
    • ◼
  • Lua
    • ◼
  • Elixir
    • ◼
  • JavaScript
    • ◼
  • Java
    • ◼
  • Python
    • ◼
  • Wolfram Language - THIS LAB
    • ◼
  • Wolfram Cloud - www.wolframcloud.com
    • ◼
  • Mathematica (Local)
    • ◼
  • Wolfram Notebook Interface (GUI)
    • ◼
  • Assembly
    • ◼
  • NASM - https://www.nasm.us/
    • ◼
  • LLVM

    • Compiler Design
    Symbolic and numerical processing
    Interpreted and compiled process
    Programming Languages float point issue (error)

    Wolfram notebook user interface (GUI) provides an environment for exploratory computation, ideal for research and scientists. Jupyter Notebook is inspired by Wolfram notebook (1988), not otherwise.
    Float point at Wolfram Language
    In[]:=
    .1+.2
    Out[]=
    0.3
    Testing float point operation at some popular programming languages on Linux environment, command line interface (CLI):
    ​
    - Python
    - NodeJs - JavaScript
    - JShell - Java
    How those languages represent a float point number, 32 bits or 64 bits
    ​​https://en.wikipedia.org/wiki/IEEE_754-1985
    What Every Programmer Should Know About Floating-Point Arithmetic
    ​https://floating-point-gui.de/
    Wolfram Language symbolic and numerical processing
    By default (language kernel) the interpreted code give symbolic result, everything is an computable expression
    In[]:=
    1/2*20/7
    Out[]=
    10
    7
    You can ask for the numerical value
    In[]:=
    N[10/7]
    Out[]=
    1.42857
    In[]:=
    10./7
    Out[]=
    1.42857
    But it has an arbitrary precision, not limited by machine float point limitations
    In[]:=
    N[10/7,200]*2
    Out[]=
    2.8571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571429
    In the notebook GUI, you can run code in other programming languages installed
    〉
    In[]:=
    1/2*20/7
    Out[]=
    1.42857
    Wolfram Language symbolic computation:
    In[]:=
    1/2*20/7/x
    Out[]=
    10
    7x
    Other languages such as Python, gives and error, it do not know what to do with a symbolic value. The kernel is numeric...
    〉
    In[]:=
    1/2*20/7 /x
    Out[]=
    Failure
    
    Message:
    name 'x' is not defined
    Tag:
    PythonError
    
    Wolfram Language compiled:
    Defining a symbolic function
    In[]:=
    F[v_]:=v/Sqrt[v]
    In[]:=
    F[10]
    Out[]=
    10
    In[]:=
    F[1]
    Out[]=
    1
    Request the numerical response
    In[]:=
    N[F[133],100]
    Out[]=
    11.53256259467079588935418323881787250058306885124138683332787807613527144147488257205290252967436635
    Now set the function to return just numerical result
    In[]:=
    FN[v_]:=N[v/Sqrt[v]]
    In[]:=
    FN[133]
    Out[]=
    11.5326
    Some tests, lets do it together, with functional programming:
    In[]:=
    Range[10]
    Out[]=
    {1,2,3,4,5,6,7,8,9,10}
    In[]:=
    Map[Z,Range[10]]
    Out[]=
    {Z[1],Z[2],Z[3],Z[4],Z[5],Z[6],Z[7],Z[8],Z[9],Z[10]}
    In[]:=
    Z/@Range[10]
    Out[]=
    {Z[1],Z[2],Z[3],Z[4],Z[5],Z[6],Z[7],Z[8],Z[9],Z[10]}
    In[]:=
    F/@Range[100]
    Out[]=
    1,
    2
    ,
    3
    ,2,
    5
    ,
    6
    ,
    7
    ,2
    2
    ,3,
    10
    ,
    11
    ,2
    3
    ,
    13
    ,
    14
    ,
    15
    ,4,
    17
    ,3
    2
    ,
    19
    ,2
    5
    ,
    21
    ,
    22
    ,
    23
    ,2
    6
    ,5,
    26
    ,3
    3
    ,2
    7
    ,
    29
    ,
    30
    ,
    31
    ,4
    2
    ,
    33
    ,
    34
    ,
    35
    ,6,
    37
    ,
    38
    ,
    39
    ,2
    10
    ,
    41
    ,
    42
    ,
    43
    ,2
    11
    ,3
    5
    ,
    46
    ,
    47
    ,4
    3
    ,7,5
    2
    ,
    51
    ,2
    13
    ,
    53
    ,3
    6
    ,
    55
    ,2
    14
    ,
    57
    ,
    58
    ,
    59
    ,2
    15
    ,
    61
    ,
    62
    ,3
    7
    ,8,
    65
    ,
    66
    ,
    67
    ,2
    17
    ,
    69
    ,
    70
    ,
    71
    ,6
    2
    ,
    73
    ,
    74
    ,5
    3
    ,2
    19
    ,
    77
    ,
    78
    ,
    79
    ,4
    5
    ,9,
    82
    ,
    83
    ,2
    21
    ,
    85
    ,
    86
    ,
    87
    ,2
    22
    ,
    89
    ,3
    10
    ,
    91
    ,2
    23
    ,
    93
    ,
    94
    ,
    95
    ,4
    6
    ,
    97
    ,7
    2
    ,3
    11
    ,10
    In[]:=
    FN/@Range[100]
    Out[]=
    {1.,1.41421,1.73205,2.,2.23607,2.44949,2.64575,2.82843,3.,3.16228,3.31662,3.4641,3.60555,3.74166,3.87298,4.,4.12311,4.24264,4.3589,4.47214,4.58258,4.69042,4.79583,4.89898,5.,5.09902,5.19615,5.2915,5.38516,5.47723,5.56776,5.65685,5.74456,5.83095,5.91608,6.,6.08276,6.16441,6.245,6.32456,6.40312,6.48074,6.55744,6.63325,6.7082,6.78233,6.85565,6.9282,7.,7.07107,7.14143,7.2111,7.28011,7.34847,7.4162,7.48331,7.54983,7.61577,7.68115,7.74597,7.81025,7.87401,7.93725,8.,8.06226,8.12404,8.18535,8.24621,8.30662,8.3666,8.42615,8.48528,8.544,8.60233,8.66025,8.7178,8.77496,8.83176,8.88819,8.94427,9.,9.05539,9.11043,9.16515,9.21954,9.27362,9.32738,9.38083,9.43398,9.48683,9.53939,9.59166,9.64365,9.69536,9.74679,9.79796,9.84886,9.89949,9.94987,10.}
    In[]:=
    ?Timing
    Out[]=
    Symbol
    Timing[expr] evaluates expr​, and returns a list of the time in seconds used, together with the result obtained.
    Now lest define the same function, but now compiled (and numeric)
    We can set the target language
    Test
    Compare compiled X interpreted timing
    The symbolic operations are expressions, check with FullForm

    Wolfram Language (Basics)

    Wolfram Cloud: www.wolframcloud.com
    Lets do it together, step by step:
    NLP - Natural Language Processing, asking Wolfram|Alpha, in plain English
    GEO Processing:
    Wolfram Language
    ​
    - Functional
    - Numerical
    - Symbolic
    - Curated Data
    - Algorithms (functions ready to go)
    Computable expressions everywhere:
    More AI with Wolfram|Alpha
    Code generation:
    Curated data:
    Try numerical computation and 2D and 3D visualization, in just on line of code:
    Integrated with Wolfram Cloud, share on the WEB is easy:
    Easy interactivity:

    Image Processing and AI

    Let do it together, step by step.
    As all is an expression, you can just past an image in the source code... the image is an expression too:
    Here we can see the image as a computable expression:

    IA, ML

    Wolfram Language is largely used in science, enterprise P&D, research, education, data science, startups, AI & ML, prototyping etc...
    WL can call other programming languages, and it can be called by other programing languages, data bases, works on Windows, Linux, Mac, etc... it is friendly
    ​
    Speed up Wolfram Language:
    ​
    - CPU Kernels (Local)
    - GPU - CUDA (Local at your gaming PC)
    - Compile - LLVM
    - Cluster at AWS (HPC) - Cloud
    - GridMathematica (Network)
    ​
    Very high level programming language, designed to communicate clearly with real people.
    ​
    To learn more: https://www.wolfram.com/wolfram-u/

    Benchmark Java vs C

    Next class (LAB)
    JIT - Just In Time compiler (JRE)
    https://github.com/danielscarvalho/FTT-Benchmark-Java-vs.-C
    NASM - Assembly
    GCC - C
    Can Java be faster than C??