Introduction Julia features Concluding remarks The Julia Programming Language: A fresh approach to technical computing Tim Schoof 1/20 Introduction Julia features Concluding remarks Sharelatex1 A I Online LTEX editor A I Complete modern LTEX environment =) no installation needed I Collaborative real-time editing =) no version conflicts I Eternal history =) Go back to any point in time I Bibliography search, comments, chat, github integration, and more 1 sharelatex.com 2/20 Introduction Julia features Concluding remarks Zotero2 I Organize your bibliography I Share downloaded papers with the group I Download pdf and meta-data with a single click I Full text search in meta-data and pdfs 2 https://www.zotero.org/ 3/20 Introduction Julia features Concluding remarks History I Work started 2009 at UC Santa Barbara and MIT (by Stefan Karpinski, Viral Shah, Jeff Bezanson, Alan Edelman) I First public release 2012 I Julia Computing founded in 2015 (by inventors + Deepak Vinchhi and Keno Fischer) I 2017 Julia Computing raises $4.6M in seed funding 4/20 Introduction Julia features Concluding remarks Example 1: Calculate π with Monte Carlo I Choose M random points within a square (uniformly distributed) I Count points within enclosed circle, e.g., N I It follows N A π(d=2)2 ≈ = M A d2 N =) π ≈ 4 M I In picture π ≈ 3:15 5/20 Introduction Julia features Concluding remarks Example 1: Calculate π in C++ 1 #include <random> #include <iostream> 3 std::mt19937_64 rng; 5 std::uniform_real_distribution<double> distUReal; 7 using namespace std; 9 double calc_pi(int M) { int sum = 0; 11 double x; double y; 13 for (int i = 0; i < M; ++i) { 15 x = distUReal(rng); y = distUReal(rng); 17 sum += x*x + y*y < 1; } 19 return 4.0 * sum / M; } 21 int main() 23 { int M = pow(10,9); 25 cout << calc_pi(M) << endl; } 6/20 Introduction Julia features Concluding remarks Example 1: Calculate π in C++ #include <random> 2 #include <iostream> 4 std::mt19937_64 rng; std::uniform_real_distribution<double> distUReal; 6 using namespace std; 8 double calc_pi(int M) { 10 int sum = 0; I characterdouble count:x; 432 12 double y; I run time:for 19(int s i = 0; i < M; ++i) 14 { x = distUReal(rng); 16 y = distUReal(rng); sum += x*x + y*y < 1; 18 } return 4.0 * sum / M; 20 } 22 int main() { 24 int M = pow(10,9); cout << calc_pi(M) << endl; 26 } 6/20 Introduction Julia features Concluding remarks Example 1: Calculate π in Python from random import random 2 def calc_pi(M): 4 return 4*sum(random()**2 + random()**2 < 1 for i in range(M)) / M 6 print(calc_pi(10**9)) Much shorter due to high level code: I no type declarations necessary I predefined functions: sum,… I range based for loops: for elem in <iterable> I generator expressions: (f(elem) for elem in <iterable>) 7/20 Introduction Julia features Concluding remarks Example 1: Calculate π in Python from random import random 2 def calc_pi(M): 4 return 4*sum(random()**2 + random()**2 < 1 for i in range(M)) / M 6 print(calc_pi(10**9)) I character count: 135 I run time: 280 s Much shorter due to high level code: I no type declarations necessary I predefined functions: sum,… I range based for loops: for elem in <iterable> I generator expressions: (f(elem) for elem in <iterable>) 7/20 Introduction Julia features Concluding remarks Example 1: Calculate π in Julia calc_pi(M) = 4*sum(rand()^2 + rand()^2 < 1 for i=1:M) / M 2 println(calc_pi(10^9)) Even shorter syntax: I many important functions imported by default I inline function definitions: f(x) = 2x I ranges: start:stop and start:step:stop 8/20 Introduction Julia features Concluding remarks Example 1: Calculate π in Julia calc_pi(M) = 4*sum(rand()^2 + rand()^2 < 1 for i=1:M) / M 2 println(calc_pi(10^9)) I character count: 83 EvenI run shorter time: 7 syntax: s I many important functions imported by default I inline function definitions: f(x) = 2x I ranges: start:stop and start:step:stop 8/20 Introduction Julia features Concluding remarks Example 2: Micro benchmarks 9/20 Introduction Julia features Concluding remarks Example 2: Micro benchmarks 10/20 Introduction Julia features Concluding remarks Example 3: Celeste project I Locate and characterize light sources in the universe I Sloan Digital Sky Survey I 178 TB image data I 188 million stars and galaxies I 1.54 PFLOPS peak performance I 9300 nodes I 1.3 million threads on 650,000 KNL cores I <15 min runtime I Julia first language since C/C++/Fortran reaching >1PFLOPS 11/20 I only inferable Julia code is fast I type-unstable code has Python like performance (or even slower due to missing optimizations) I see also performance tips in manual! (https://docs.julialang.org/en/latest/manual/performance-tips/) I Aggrassive specialization on argument types I Language design focused on speed I avoids hard to optimize language features e.g., dictionary semantics for objects and scopes I machine integers (overflow!) I driven by LLVM’s possibilities from the start I “Type-stable” standard library Introduction Julia features Concluding remarks How is that possible? I Just-In-Time (JIT) compilation to native machine code 12/20 4 julia> @time f(1) # first call with an Int 0.001466 seconds (244 allocations: 17.041 KiB) 6 2 julia> @time f(1) # second call with an Int 8 0.000003 seconds (4 allocations: 160 bytes) 2 10 julia> @time f(2) # Only the type matters, not the value 12 0.000003 seconds (4 allocations: 160 bytes) 4 14 julia> @time f(1.0) # First call with a Float64 16 0.004278 seconds (215 allocations: 13.104 KiB) 2.0 18 julia> @time f(1.0) 20 0.000003 seconds (5 allocations: 176 bytes) 2.0 22 julia> @time f(2.0) 24 0.000003 seconds (5 allocations: 176 bytes) 4.0 Introduction Julia features Concluding remarks Just-in-time (JIT) Compilation A new function is compiled on first use for each combination of argument types3: julia> f(x) = 2x 2 f (generic function with 1 method) 3 except for functions and types by default 13/20 11 julia> @time f(2) # Only the type matters, not the value 0.000003 seconds (4 allocations: 160 bytes) 13 4 15 julia> @time f(1.0) # First call with a Float64 0.004278 seconds (215 allocations: 13.104 KiB) 17 2.0 19 julia> @time f(1.0) 0.000003 seconds (5 allocations: 176 bytes) 21 2.0 23 julia> @time f(2.0) 0.000003 seconds (5 allocations: 176 bytes) 25 4.0 Introduction Julia features Concluding remarks Just-in-time (JIT) Compilation A new function is compiled on first use for each combination of argument types3: 1 julia> f(x) = 2x f (generic function with 1 method) 3 julia> @time f(1) # first call with an Int 5 0.001466 seconds (244 allocations: 17.041 KiB) 2 7 julia> @time f(1) # second call with an Int 0.000003 seconds (4 allocations: 160 bytes) 9 2 3 except for functions and types by default 13/20 15 julia> @time f(1.0) # First call with a Float64 0.004278 seconds (215 allocations: 13.104 KiB) 17 2.0 19 julia> @time f(1.0) 0.000003 seconds (5 allocations: 176 bytes) 21 2.0 23 julia> @time f(2.0) 0.000003 seconds (5 allocations: 176 bytes) 25 4.0 Introduction Julia features Concluding remarks Just-in-time (JIT) Compilation A new function is compiled on first use for each combination of argument types3: 1 julia> f(x) = 2x f (generic function with 1 method) 3 julia> @time f(1) # first call with an Int 5 0.001466 seconds (244 allocations: 17.041 KiB) 2 7 julia> @time f(1) # second call with an Int 0.000003 seconds (4 allocations: 160 bytes) 9 2 11 julia> @time f(2) # Only the type matters, not the value 0.000003 seconds (4 allocations: 160 bytes) 13 4 3 except for functions and types by default 13/20 Introduction Julia features Concluding remarks Just-in-time (JIT) Compilation A new function is compiled on first use for each combination of argument types3: 1 julia> f(x) = 2x f (generic function with 1 method) 3 julia> @time f(1) # first call with an Int 5 0.001466 seconds (244 allocations: 17.041 KiB) 2 7 julia> @time f(1) # second call with an Int 0.000003 seconds (4 allocations: 160 bytes) 9 2 11 julia> @time f(2) # Only the type matters, not the value 0.000003 seconds (4 allocations: 160 bytes) 13 4 15 julia> @time f(1.0) # First call with a Float64 0.004278 seconds (215 allocations: 13.104 KiB) 17 2.0 19 julia> @time f(1.0) 0.000003 seconds (5 allocations: 176 bytes) 21 2.0 23 julia> @time f(2.0) 0.000003 seconds (5 allocations: 176 bytes) 25 4.0 3 except for functions and types by default 13/20 Introduction Julia features Concluding remarks Machine code Julia compiles to native machine code very similar to C++ 1 julia> @code_native f(1) .text 3 Filename: REPL[1] pushq %rbp 5 movq %rsp, %rbp Source line: 1 7 leaq (%rdi,%rdi), %rax popq %rbp 9 retq nopw (%rax,%rax) 11 julia> @code_native f(1.0) 13 .text Filename: REPL[1] 15 pushq %rbp movq %rsp, %rbp 17 Source line: 1 vaddsd %xmm0, %xmm0, %xmm0 19 popq %rbp retq 21 nopw (%rax,%rax) 14/20 I only inferable Julia code is fast I type-unstable code has Python like performance (or even slower due to missing optimizations) I see also performance tips in manual! (https://docs.julialang.org/en/latest/manual/performance-tips/) I Language design focused on speed I avoids hard to optimize language features e.g., dictionary semantics for objects and scopes I machine integers (overflow!) I driven by LLVM’s possibilities from the start I “Type-stable” standard library Introduction Julia features Concluding remarks How is that possible? I Just-In-Time (JIT) compilation to native machine code I Aggrassive specialization on argument types 15/20 I only inferable Julia code is fast I type-unstable code has Python like performance (or even slower due to missing optimizations) I see also performance