Seminar Fortran and Julia

Modern Fortran & JuliaArquiteturas Avancadas de Computadores

Krissia de Zawadzki

Instituto de Fısica de Sao Carlos - Universidade de Sao Paulo

10 de junho 2014

Krissia de Zawadzki Modern Fortran & Julia 1 / 38

Motivation Modern Fortran Julia Programming with Julia Example of Julia code Summary

Outline

1 Motivation

2 Modern Fortran

3 Julia

4 Programming with Julia

5 Example of Julia code

6 Summary



Motivation



Motivation

MODERN FORTRAN

3 multi-paradigm:structured imperative, generic

3 typing discipline: strong, static,manifest

3 modern: 90, 95, 2003, 2008

3 John Backus, 1957

JULIA

3 multi-paradigm:multiple-dispatch, proceduralfunctional, meta

3 typing discipline: dynamic withoptional type annotations, andtype inference

3 J. Bezanson, S. Karpinski,V.B.Shah, A. Edelman, 2012



Motivation



Fortran - a historical review

FORTRAN

FORmula TRANslator

1953 - John Backus: alternative to assemblylanguage on IBM-704 mainframe

1954 - IBM Mathematical FormulaTranslating System

1956 - 1st FORTRAN manual

1957 - 1st FORTRAN compiler

”Much of my work has come frombeing lazy. I didn’t like writing

programs, and so, when I was workingon the IBM 701, writing programs for

computing missile trajectories, Istarted work on a programming systemto make it easier to write programs.”

John Backus




3 scientific computing

3 high-level programming language

3 reduced number of statements

3 compilers able to generate faster andefficient codes




FORTRAN versions

3 FORTRAN, I, II, IBM1401, IV

3 66 → ANSI industry-standard

3 77 → structured programming,character-based data

3 90 → array, modular and genericprogramming

3 95 → high performance Fortran

3 2003 → object-oriented programming

3 2008 → concurrent programming



Fortran features

Fortran features

Character set and layout

Letters (A to Z and a to z) and digits (0 to 9)

names : started with letters, up to 31 letters, digits and underscores

case-sensitive

special characters = +− */(), .′ :!”%$;<>?, space

any character allowed in comments

tab and form-feed not allowed, no other positioning options

lines - sequences of 132 characters

comments with !



Fortran features

Fortran features

fortran code

START

SPECIFICATIONS

EXECUTION

END

machineinstructions

executableprogram

run!

compiler

linker

OS



Early Fortran versions


Statements:

3 DIMENSION and EQUIVALENCE statements

3 assignment statements

3 arithmetic IF

3 IF for exceptions

3 GOTO, ASSIGN

3 DO loops

3 FORMAT, READ, READ INPUT TAPE, WRITE, WRITE OUTPUTTAPE, PRINT, and PUNCH

3 READ TAPE, READ DRUM, WRITE TAPE, and WRITE DRUM

3 END FILE, REWIND, and BACKSPACE

3 PAUSE, STOP, and CONTINUE

3 FREQUENCY statement





FORTRAN II - 1958

3 SUBROUTINE, FUNCTION and END

3 CALL and RETURN

3 COMMON

7 recursion not allowed in subroutines (arch without support forstacks)

FORTRAN III - 1958

3 inline assembly code

7 codes 704 FORTRAN and FORTRAN II, FORTRAN III unportablefrom machine

7 never released





IBM 1401 FORTRAN

3 program in memory

3 executable form not machine language - early Pascal code

FORTRAN IV - 1961

3 no machine-dependent features

3 + LOGICAL data type and boolean expressions

3 important educational tool

3 WATFIV simplifying compile and link



FORTRAN 66

FORTRAN 66

3 American Standard Fortran

3 Main, SUBROUTINE, FUNCTION and BLOCK DATA prog.units

3 INTEGER, REAL, DOUBLE PRECISION, COMPLEX andLOGICAL

3 COMMON, DIMENSION, and EQUIVALENCE statements

3 GOTO, assigned GOTO, and computed GOTO statements

3 Logical IF and arithmetic (three-way) IF statements

3 READ, WRITE, BACKSPACE, REWIND, and ENDFILEstatements for sequential I/O

3 FORMAT statement

3 CALL, RETURN, PAUSE, and STOP statements

3 Identifiers of up to six characters in length

3 Comment lines



FORTRAN 77

FORTRAN 77

3 Block IF- END IF - ELSE - ELSE IF

3 DO loop: negative increments, zero tripcounts

3 OPEN, CLOSE, and INQUIRE statements-I/O capability and direct access file

3 IMPLICIT statement

3 CHARACTER data type

3 PARAMETER - constants

3 SAVE - persistent local vars

3 LGE, LGT, LLE, LLT - lexical comparision ofstrings

3 Holletith constants and date

3 Overindexing of array

3 extended range



Fortran 90

Fortran 90

3 free form source code - columns

1 to 6 no longer special

3 implicit none - check all variables

declared with explicit type

3 modules - partioning the code in

small units

3 internal routines - compiles

check the correctness of args

3 no need for GOTO - replaced by exit

3 recursive routines

3 allocate and deallocate - changing size of arrays

3 array operations supported in arithmetic expressions

and can be automatic

3 derived types - used the same way of basic tpes

3 overboarding - extend the language operators to

derived types

3 optional args in funcs and subroutines - args in

arbitrary order

3 kinds -determining the characteristics of basic types

3 select/case - you can use a name for all control

structures

3 enhancements of I/O system - program can read or

write a part of a record in one statement and the rest

in another one



Fortran 95

Fortran 95

3 High Performance Fortran

3 null() to initialize pointers explicity

3 allocatable variables without save attribute -automatically deallocated

3 technical reports

3 pure - more opportunities of optimization - orelemental - work on individual elements ofarrays - routines

3 forall statement - enhance capabilities of arrayoperations



Fortran 2003

Fortran 2003

3 Object-oriented programming

3 procedures( funcs orsubroutines) - get passed to thevariables of a specific types

3 derived types can be extendedinto new types

3 select statement in polymorphic variables(classes)

3 abstract interfaces

3 procedure pointers as ordinary variavles

3 intrinsic modules - rounding mode, fpexceptions, interfacing to C, different callingand naming conventions

3 Memory management enhanced: lenght ofcharacter strings by allocate; arrays can bereallocated to correct size; allocations ofmemory from one variable to anothermovealloc

3 stream access to files - read and writeformatted binary files

3 standard access to system environmentvariables



Fortran 2008

Fortran 2008

3 coarrays - data avaliable on various copies

3 contiguous arrays

3 blocs - end blocks : local scope

3 submodules and import - very large source files

3 exit statement can be used to jump to the endof if or select blocks

3 do concurrent statement - the code can be runin parallel (thread concept)

3 internal procedures now passed as actual args- access to varables in the routine that containthem

3 new standard functions - Bessel functions andbit inquiry functions



Modern Fortran features

Modern Fortran features

Modern style

Free format, attributes

implicit none

do, exit, cycle, case

single and double precision

Dynamic data types

allocatable arrays

structures, derived types

Module-oriented programming

internal subprograms

private, public, protected

contains

use

Optional arguments & intent

FORmula TRANSlation

array syntax, where and forallstatements

extended & user-definedoperators

Functions: elemental, inquiry,mathematical

Improvements

Fortran pointers

command line arguments

Environment variables

Interoperability with C

3 performance considerations

3 objected-oriented programming



Performance

Comparison of Data StructuresImplementations

3 what is the performancepenalty of using Fortran 90data abstraction features?

3 test problem solves Maxwell’sEquations using the Yee-scheme

3 style loops and data structures:different in f77 and f90



Introduction

Introduction to Julia

3 2012, influenced by MATLAB, Scheme,Lisp, C, Fortran, Wolfram, Python,Perl, R, Ruby

3 high-level dynamic programminglanguage

3 parametric types

3 parallel and distributed computing

3 direct calling of C,Fortran and Pythonlibraries

3 libraries forfloating-point, linearalgebra, random numbergeneration, FFT andregular expressionmatching



Introduction

Introduction to Julia



Julia features

Julia Features

3 Multiple dispatch

3 Dynamic type system

3 Good performance

3 Built-in package manager

3 Lisp-like macros and metaprogramming facilities

3 PyCall package - call python function

3 Call C functions directly

3 shell-like capabilities for managing other process

3 paralellism and distributed computation

3 Coroutines: lightweight ”green”threading

3 user types as fast as built-ins

3 other types - generation, extensible conversions, etc are efficient

3 Unicode support not limited to UTF-8

3 MIT licensed : free and open source



High Performance JIT Compiler

High Performance JIT Compiler

LLVM-based just-in-time

3 compilation during the execution

3 ahead of time compilation (AOT) and

interpretation

3 optimized to the CPU and OS

3 statistics about the program - rearrange

and recompile for optimal performance

3 global code and cache use optimizations

3 performance often matches C!



Julia packages

Julia packages

3 219 avaliable packages!

3 mature package ecosystem

3 easy install -Pkg.add(”mypackage”)

PyCall, PyPlot, PySide, SymPy

Calculus, Cartesian, Elliptic,

Polynomial, TimeSeries

RdRand, RandomMatrices

BioSeq, ChemicalKinetics,

GeneticAlgorithms, Phylogenetics

MarketTechnicals

Clustering, DecisionTree,

DimensionalityReduction,

SortingAlgorithms

TextAnalysis



Parallel and cloud computing with Julia

Parallel and cloud computing with Julia

3 worker processes - key building blocks for

distributed computation

3 message-passing ”one-side”!= from MPI

3 remote references and remote calls

3 data management

3 code editing and sharing, data exploration

and visualization

3 networks and streams



Getting started

Getting started



Integer types

Integer types



Float types

Float types



Math operations

Math operations



Strings

Strings



Functions

Functions



Control Flow

Control Flow



Parallel Julia - beginners

Parallel Julia - beginners



Parallel Julia - beginners: adding vectors

Parallel Julia - beginners: adding vectors



Laplace equation

Example of Julia code - laplace equation

Laplace Equation ∇2𝜙 = 0 bondary conditions!

𝜙(𝑥−Δ𝑥, 𝑦)− 2𝜙(𝑥, 𝑦) + 𝜙(𝑥+Δ𝑥, 𝑦)

Δ𝑥+

𝜙(𝑥, 𝑦 −Δ𝑦)− 2𝜙(𝑥, 𝑦) + 𝜙(𝑥, 𝑦 +Δ𝑦)

Δ𝑦= 0

𝜙𝑖𝑗 =𝜙𝑖−1,𝑗 + 𝜙𝑖+1,𝑗 + 𝜙𝑖,𝑗−1 + 𝜙𝑖,𝑗+1

4



Julia code

Example of Julia code

Julia code: solve lap.jl



Julia code


C code: laplace.c



Tests - bondary conditions:1


𝑚[0, 0 : 𝑁 ] = 𝑚[𝑁, 0 : 𝑁 ] = −1 and 𝑚[0 : 𝑁, 0] = 𝑚[0 : 𝑁,𝑁 ] = 1





𝑚[0, 𝑁/3 : 2𝑁/3] = 𝑚[𝑁,𝑁/3 : 2𝑁/3] = −1; 𝑚[𝑁/3 : 2𝑁/3, 0] = 𝑚[𝑁/3 : 2𝑁/3, 𝑁 ] = 1





𝑚[0, 0 : 𝑁 ] = −1; 𝑚[𝑁, 0 : 𝑁 ] = 0; 𝑚[0 : 𝑁, 0] = 1 and 𝑚[0 : 𝑁,𝑁 ] = 2



Summary

3 Programming languages develop basically with applications demand

3 Fortran has released the high-level programming paradigm in 60’sand since then has been continuosly updated in order to serve newscientific applications

3 Current trends: New languages integrating high performance withgraphics potential and parallelism

3 Julia is the bet of enthusiastic programmers! It combines highperformance with easy syntax and offers a variety of scientificpackages!



References

3 Markus, Arjen; Modern Fortran in Practice; Cambridge UniversityPress

3 http://people.ds.cam.ac.uk/nmm1/Fortran/index.html

3 /www.tacc.utexas.edu/documents/13601/162125/fortran class.pdf

3 http://julialang.org/

3 https://github.com/JuliaLang/julia/issues/273

3 http://learnxinyminutes.com/docs/julia/



Julia around the world

Julia around the world


Parallel Linear Algebra with Julia


Two parallel tiled LA algoritms:

Cholesky decomposition

𝐴 symmetric positive matrix →lower-triangular matrix 𝐿: 𝐿𝐿′ = 𝐴

QR decomposition

𝐴 being 𝑚× 𝑛 matrix, with 𝑚 ≥ 𝑛 →𝑚×𝑚 unitary matrix 𝑄 and 𝑚× 𝑛 upper

triangular matrix 𝑅 : 𝑄𝑅 = 𝐴




2 processors, 16 tilesKrissia de Zawadzki Modern Fortran & Julia 3 / 3

Software

Seminar Fortran and Julia