run(`git config --get user.name`)
Keno Fischer
using Gadfly
using WWWClient
using DataFrames
const w = WWWClient
Warning: New definition
round(DataArray{T<:Number,N},Integer...) at /Users/kfischer/.julia/DataFrames/src/operators.jl:350
is ambiguous with:
round(AbstractArray{T<:Real,1},) at operators.jl:236.
To fix, define
round(DataArray{_<:Real,1},)
before the new definition.
Warning: New definition
round(DataArray{T<:Number,N},Integer...) at /Users/kfischer/.julia/DataFrames/src/operators.jl:350
is ambiguous with:
round(AbstractArray{T<:Real,2},) at operators.jl:237.
To fix, define
round(DataArray{_<:Real,2},)
before the new definition.
Warning: New definition
round(AbstractDataArray{T<:Number,N},Integer...) at /Users/kfischer/.julia/DataFrames/src/operators.jl:359
is ambiguous with:
round(AbstractArray{T<:Real,1},) at operators.jl:236.
To fix, define
round(AbstractDataArray{_<:Real,1},)
before the new definition.
Warning: New definition
round(AbstractDataArray{T<:Number,N},Integer...) at /Users/kfischer/.julia/DataFrames/src/operators.jl:359
is ambiguous with:
round(AbstractArray{T<:Real,2},) at operators.jl:237.
To fix, define
round(AbstractDataArray{_<:Real,2},)
before the new definition.
Warning: New definition
ceil(DataArray{T<:Number,N},Integer...) at /Users/kfischer/.julia/DataFrames/src/operators.jl:350
is ambiguous with:
ceil(AbstractArray{T<:Real,1},) at operators.jl:236.
To fix, define
ceil(DataArray{_<:Real,1},)
before the new definition.
Warning: New definition
ceil(DataArray{T<:Number,N},Integer...) at /Users/kfischer/.julia/DataFrames/src/operators.jl:350
is ambiguous with:
ceil(AbstractArray{T<:Real,2},) at operators.jl:237.
To fix, define
ceil(DataArray{_<:Real,2},)
before the new definition.
Warning: New definition
ceil(AbstractDataArray{T<:Number,N},Integer...) at /Users/kfischer/.julia/DataFrames/src/operators.jl:359
is ambiguous with:
ceil(AbstractArray{T<:Real,1},) at operators.jl:236.
To fix, define
ceil(AbstractDataArray{_<:Real,1},)
before the new definition.
Warning: New definition
ceil(AbstractDataArray{T<:Number,N},Integer...) at /Users/kfischer/.julia/DataFrames/src/operators.jl:359
is ambiguous with:
ceil(AbstractArray{T<:Real,2},) at operators.jl:237.
To fix, define
ceil(AbstractDataArray{_<:Real,2},)
before the new definition.
Warning: New definition
floor(DataArray{T<:Number,N},Integer...) at /Users/kfischer/.julia/DataFrames/src/operators.jl:350
is ambiguous with:
floor(AbstractArray{T<:Real,1},) at operators.jl:236.
To fix, define
floor(DataArray{_<:Real,1},)
before the new definition.
Warning: New definition
floor(DataArray{T<:Number,N},Integer...) at /Users/kfischer/.julia/DataFrames/src/operators.jl:350
is ambiguous with:
floor(AbstractArray{T<:Real,2},) at operators.jl:237.
To fix, define
floor(DataArray{_<:Real,2},)
before the new definition.
Warning: New definition
floor(AbstractDataArray{T<:Number,N},Integer...) at /Users/kfischer/.julia/DataFrames/src/operators.jl:359
is ambiguous with:
floor(AbstractArray{T<:Real,1},) at operators.jl:236.
To fix, define
floor(AbstractDataArray{_<:Real,1},)
before the new definition.
Warning: New definition
floor(AbstractDataArray{T<:Number,N},Integer...) at /Users/kfischer/.julia/DataFrames/src/operators.jl:359
is ambiguous with:
floor(AbstractArray{T<:Real,2},) at operators.jl:237.
To fix, define
floor(AbstractDataArray{_<:Real,2},)
before the new definition.
Warning: New definition
trunc(DataArray{T<:Number,N},Integer...) at /Users/kfischer/.julia/DataFrames/src/operators.jl:350
is ambiguous with:
trunc(AbstractArray{T<:Real,1},) at operators.jl:236.
To fix, define
trunc(DataArray{_<:Real,1},)
before the new definition.
Warning: New definition
trunc(DataArray{T<:Number,N},Integer...) at /Users/kfischer/.julia/DataFrames/src/operators.jl:350
is ambiguous with:
trunc(AbstractArray{T<:Real,2},) at operators.jl:237.
To fix, define
trunc(DataArray{_<:Real,2},)
before the new definition.
Warning: New definition
trunc(AbstractDataArray{T<:Number,N},Integer...) at /Users/kfischer/.julia/DataFrames/src/operators.jl:359
is ambiguous with:
trunc(AbstractArray{T<:Real,1},) at operators.jl:236.
To fix, define
trunc(AbstractDataArray{_<:Real,1},)
before the new definition.
Warning: New definition
trunc(AbstractDataArray{T<:Number,N},Integer...) at /Users/kfischer/.julia/DataFrames/src/operators.jl:359
is ambiguous with:
trunc(AbstractArray{T<:Real,2},) at operators.jl:237.
To fix, define
trunc(AbstractDataArray{_<:Real,2},)
before the new definition.
Warning: New definition
formatter(
Array{T,N},Date{C<:Calendar}...)
is ambiguous with:
formatter(Array{T,N},FloatingPoint...).
To fix, define
formatter(Array{T,N},)
before the new definition.
Warning: New definition
|(SynchronousStepCollection,Any) at /Users/kfischer/.julia/BinDeps/src/BinDeps.jl:283
is ambiguous with:
|(Any,NAtype) at /Users/kfischer/.julia/DataFrames/src/operators.jl:385.
To fix, define
|(SynchronousStepCollection,NAtype)
before the new definition.
Warning: New definition
|(Any,SynchronousStepCollection) at /Users/kfischer/.julia/BinDeps/src/BinDeps.jl:286
is ambiguous with:
|(NAtype,Any) at /Users/kfischer/.julia/DataFrames/src/operators.jl:385.
To fix, define
|(NAtype,SynchronousStepCollection)
before the new definition.
WARNING: BinDeps.find_library is deprecated, use Base.find_library instead.
WARNING: add_library_mapping is deprecated, use push!(DL_LOAD_PATH,"/path/to/search") instead.
Warning: New definition
+(AbstractArray{T1<:Union(AbstractCalendarDuration,CalendarTime),N},AbstractArray{T2<:Union(AbstractCalendarDuration,CalendarTime),N}) at operators.jl:253
is ambiguous with:
+(DataArray{T,N},AbstractArray{T,N}) at /Users/kfischer/.julia/DataFrames/src/operators.jl:201.
To fix, define
+(DataArray{T1<:Union(AbstractCalendarDuration,CalendarTime),N},AbstractArray{T2<:Union(AbstractCalendarDuration,CalendarTime),N})
before the new definition.
Warning: New definition
+(AbstractArray{T1<:Union(AbstractCalendarDuration,CalendarTime),N},AbstractArray{T2<:Union(AbstractCalendarDuration,CalendarTime),N}) at operators.jl:253
is ambiguous with:
+(AbstractDataArray{T,N},AbstractArray{T,N}) at /Users/kfischer/.julia/DataFrames/src/operators.jl:220.
To fix, define
+(AbstractDataArray{T1<:Union(AbstractCalendarDuration,CalendarTime),N},AbstractArray{T2<:Union(AbstractCalendarDuration,CalendarTime),N})
before the new definition.
Warning: New definition
+(AbstractArray{T1<:Union(AbstractCalendarDuration,CalendarTime),N},AbstractArray{T2<:Union(AbstractCalendarDuration,CalendarTime),N}) at operators.jl:253
is ambiguous with:
+(AbstractArray{T,N},DataArray{T,N}) at /Users/kfischer/.julia/DataFrames/src/operators.jl:201.
To fix, define
+(AbstractArray{T1<:Union(AbstractCalendarDuration,CalendarTime),N},DataArray{T2<:Union(AbstractCalendarDuration,CalendarTime),N})
before the new definition.
Warning: New definition
+(AbstractArray{T1<:Union(AbstractCalendarDuration,CalendarTime),N},AbstractArray{T2<:Union(AbstractCalendarDuration,CalendarTime),N}) at operators.jl:253
is ambiguous with:
+(AbstractArray{T,N},AbstractDataArray{T,N}) at /Users/kfischer/.julia/DataFrames/src/operators.jl:220.
To fix, define
+(AbstractArray{T1<:Union(AbstractCalendarDuration,CalendarTime),N},AbstractDataArray{T2<:Union(AbstractCalendarDuration,CalendarTime),N})
before the new definition.
Warning: New definition
-(AbstractArray{T1<:Union(AbstractCalendarDuration,CalendarTime),N},AbstractArray{T2<:Union(AbstractCalendarDuration,CalendarTime),N}) at operators.jl:253
is ambiguous with:
-(DataArray{T,N},AbstractArray{T,N}) at /Users/kfischer/.julia/DataFrames/src/operators.jl:201.
To fix, define
-(DataArray{T1<:Union(AbstractCalendarDuration,CalendarTime),N},AbstractArray{T2<:Union(AbstractCalendarDuration,CalendarTime),N})
before the new definition.
Warning: New definition
-(AbstractArray{T1<:Union(AbstractCalendarDuration,CalendarTime),N},AbstractArray{T2<:Union(AbstractCalendarDuration,CalendarTime),N}) at operators.jl:253
is ambiguous with:
-(AbstractDataArray{T,N},AbstractArray{T,N}) at /Users/kfischer/.julia/DataFrames/src/operators.jl:220.
To fix, define
-(AbstractDataArray{T1<:Union(AbstractCalendarDuration,CalendarTime),N},AbstractArray{T2<:Union(AbstractCalendarDuration,CalendarTime),N})
before the new definition.
Warning: New definition
*(Any,AbstractCalendarDuration) at /Users/kfischer/.julia/Calendar/src/Calendar.jl:341
is ambiguous with:
*(MeasureNil,Any) at /Users/kfischer/.julia/Compose/src/measure.jl:32.
To fix, define
*(MeasureNil,AbstractCalendarDuration)
before the new definition.
Warning: New definition
-(AbstractArray{T1<:CalendarTime,N},AbstractArray{T2<:CalendarTime,N}) at operators.jl:253
is ambiguous with:
-(DataArray{T,N},AbstractArray{T,N}) at /Users/kfischer/.julia/DataFrames/src/operators.jl:201.
To fix, define
-(DataArray{T1<:CalendarTime,N},AbstractArray{T2<:CalendarTime,N})
before the new definition.
Warning: New definition
-(AbstractArray{T1<:CalendarTime,N},AbstractArray{T2<:CalendarTime,N}) at operators.jl:253
is ambiguous with:
-(AbstractDataArray{T,N},AbstractArray{T,N}) at /Users/kfischer/.julia/DataFrames/src/operators.jl:220.
To fix, define
-(AbstractDataArray{T1<:CalendarTime,N},AbstractArray{T2<:CalendarTime,N})
before the new definition.
WWWClient
function DataFrames.to_io(x::URI)
x = IOBuffer(WWWClient.get(x).data)
x,nb_available(x)
end
to_io (generic function with 2 methods)
benchmarks = readtable(URI("http://julialang.org/benchmarks.csv");header=false,colnames=["Language","Benchmark","Time"])
benchmarks = join(benchmarks, subset(benchmarks, :(Language .== "c")),
on="Benchmark", kind=:outer)
within!(benchmarks, :(Time ./= Time_1));
# Some cosmetic adjustments. Not essential to the plot, so let's skip them for the sake of space
# Reorder factors
benchmarks["Language"] = PooledDataArray(benchmarks["Language"])
benchmarks["Language"] = reorder(benchmarks["Language"], benchmarks["Time"])
benchmarks["Benchmark"] = PooledDataArray(benchmarks["Benchmark"])
benchmarks["Benchmark"] = reorder(benchmarks["Benchmark"], benchmarks["Time"])
# Capitalize
capitalize(str) = string(uppercase(str[1]) , str[2:end])
benchmarks["Language"] = set_levels(benchmarks["Language"],
Dict{Any, Any}(benchmarks["Language"],
[capitalize(l)
for l in benchmarks["Language"]]))
benchmarks = subset(benchmarks, :(Language .!= "C"))
set_default_plot_size(8inch,8inch/golden);
p = plot(benchmarks, x="Language", y="Time", color="Benchmark", Scale.y_log10,
Guide.ylabel("time relative to C"), Guide.xlabel("smaller is better"))
convert
convert (generic function with 464 methods)
+
+ (generic function with 188 methods)
@which convert(Float64,1)
@which 1.0 + 2
convert(::Type{Float64},x::Int64) at float.jl:21
+(x::Number,y::Number) at promotion.jl:148
f(a::Any, b) = "fallback"
f(a::Number, b::Number) = "a and b are both numbers"
f(a::Number, b) = "a is a number"
f(a, b::Number) = "b is a number"
f(a::Integer, b::Integer) = "a and b are both integers"
f (generic function with 5 methods)
f(1.5,2)
"a and b are both numbers"
f(1,"bar")
"a is a number"
f(1,2)
"a and b are both integers"
f("foo",[1,2])
"fallback"
methods(f)
# 5 methods for generic function "f": f(a::Integer,b::Integer) at In[8]:5 f(a::Number,b::Number) at In[8]:2 f(a::Number,b) at In[8]:3 f(a,b::Number) at In[8]:4 f(a,b) at In[8]:1
f{T<:Number}(a::T, b::T) = "a and b are both $(T)s"
f{T<:Number}(a::Vector{T}, b::Vector{T}) = "a and b are both vectors of $(T)s"
f (generic function with 7 methods)
f(big(1.5),big(1.0)) #Two BigFloats
f([1.0,2.0],[3.0,4.0]) #Two Array{Float64,1}
f([1,2],[3.,4]) #One Array{Int64,1} & One Array{Float64,1}
"fallback"
f(1,2) #Still more specific
"a and b are both integers"
import Base.LinAlg.det
function det{T}(A::AbstractArray{T,2})
n = size(A)[1]
n == size(A)[2] || error("Only square matrices allowed")
n == 2 && return A[1,1]*A[2,2] - A[1,2]*A[2,1]
s = zero(T)
for i = 1:n
s += (-one(T))^(i-1)*A[1,i]*(det(hcat(A[2:end,1:(i-1)],A[2:end,(i+1):end])))
end
s
end
det (generic function with 17 methods)
methods(det)
# 17 methods for generic function "det":
det(A::Triangular{T<:Number}) at linalg/triangular.jl:63
det(W::Woodbury{T}) at linalg/woodbury.jl:84
det(A::Tridiagonal{T}) at linalg/tridiag.jl:357
det(D::Diagonal{T}) at linalg/diagonal.jl:80
det{T<:Union(Float32,Complex{Float64},Complex{Float32},Float64)}(A::AbstractArray{T<:Union(Float32,Complex{Float64},Complex{Float32},Float64),2}) at linalg/dense.jl:416
det(x::Number) at linalg/dense.jl:419
det{T}(C::Cholesky{T}) at linalg/factorization.jl:44
det{T}(C::CholeskyPivoted{T}) at linalg/factorization.jl:122
det{T}(A::LU{T}) at linalg/factorization.jl:186
det(A::Eigen{T,V}) at linalg/factorization.jl:533
det{T}(lu::LUTridiagonal{T}) at linalg/tridiag.jl:353
det{Tv<:Float64,Ti<:Int32}(lu::UmfpackLU{Tv<:Float64,Ti<:Int32}) at linalg/umfpack.jl:189
det{Tv<:Complex{Float64},Ti<:Int32}(lu::UmfpackLU{Tv<:Complex{Float64},Ti<:Int32}) at linalg/umfpack.jl:197
det{Tv<:Float64,Ti<:Int64}(lu::UmfpackLU{Tv<:Float64,Ti<:Int64}) at linalg/umfpack.jl:189
det{Tv<:Complex{Float64},Ti<:Int64}(lu::UmfpackLU{Tv<:Complex{Float64},Ti<:Int64}) at linalg/umfpack.jl:197
det(L::CholmodFactor{Tv<:Union(Float32,Complex{Float64},Complex{Float32},Float64),Ti<:Union(Int64,Int32)}) at linalg/cholmod.jl:1039
det{T}(A::AbstractArray{T,2}) at In[17]:3
# This code is taken 1:1 from boot.jl
baremodule FakeMain
abstract Number
abstract Real <: Number
abstract FloatingPoint <: Real
abstract Integer <: Real
abstract Signed <: Integer
abstract Unsigned <: Integer
bitstype 16 Float16 <: FloatingPoint
bitstype 32 Float32 <: FloatingPoint
bitstype 64 Float64 <: FloatingPoint
bitstype 8 Bool <: Integer
bitstype 32 Char <: Integer
bitstype 8 Int8 <: Signed
bitstype 8 Uint8 <: Unsigned
bitstype 16 Int16 <: Signed
bitstype 16 Uint16 <: Unsigned
bitstype 32 Int32 <: Signed
bitstype 32 Uint32 <: Unsigned
bitstype 64 Int64 <: Signed
bitstype 64 Uint64 <: Unsigned
bitstype 128 Int128 <: Signed
bitstype 128 Uint128 <: Unsigned
end
+(x::Number, y::Number) = +(promote(x,y)...)
*(x::Number, y::Number) = *(promote(x,y)...)
-(x::Number, y::Number) = -(promote(x,y)...)
/(x::Number, y::Number) = /(promote(x,y)...)
Warning: Method definition +(Number,Number) in module Base at promotion.jl:148 overwritten in module Main at In[20]:1. Warning: Method definition *(Number,Number) in module Base at promotion.jl:149 overwritten in module Main at In[20]:2. Warning: Method definition -(Number,Number) in module Base at promotion.jl:150 overwritten in module Main at In[20]:3. Warning: Method definition /(Number,Number)
/ (generic function with 79 methods)
baremodule FakeBase
promote_type{T,S}(::Type{T}, ::Type{S}) =
promote_result(T, S, promote_rule(T,S), promote_rule(S,T))
promote_rule(T, S) = None
promote_result(t,s,T,S) = typejoin(T,S)
# If no promote_rule is defined, both directions give None. In that
# case use typejoin on the original types instead.
promote_result{T,S}(::Type{T},::Type{S},::Type{None},::Type{None}) = typejoin(T, S)
end
module ModInts
export ModInt
import Base: -, +, *, convert, promote_rule, show, showcompact
immutable ModInt{n} <: Integer
k::Int
ModInt(k) = new(k % n)
end
-{n}(a::ModInt{n}) = ModInt{n}(-a.k)
+{n}(a::ModInt{n}, b::ModInt{n}) = ModInt{n}(a.k+b.k)
-{n}(a::ModInt{n}, b::ModInt{n}) = ModInt{n}(a.k-b.k)
*{n}(a::ModInt{n}, b::ModInt{n}) = ModInt{n}(a.k*b.k)
convert{n}(::Type{ModInt{n}}, i::Int) = ModInt{n}(i)
promote_rule{n}(::Type{ModInt{n}}, ::Type{Int}) = ModInt{n}
show{n}(io::IO, k::ModInt{n}) = print(io, "$(k.k) mod $n")
showcompact(io::IO, k::ModInt) = print(io, k.k)
end # module
using ModInts
a = ModInt{11}(11119)
9 mod 11
b = ModInt{11}(12345)
3 mod 11
a+b
1 mod 11
a*b
5 mod 11
n = 8
A = map(ModInt{11}, rand(1:100,n,n))
8x8 Array{ModInt{11},2}:
10 1 1 3 1 9 7 0
2 4 9 3 4 3 10 4
4 0 0 0 10 1 10 1
10 9 5 7 2 5 7 0
6 2 10 0 9 4 10 4
0 9 6 2 3 4 1 2
8 6 10 10 1 7 4 5
9 0 7 1 5 4 1 10
A^2 + A + 4
8x8 Array{ModInt{11},2}:
3 6 8 6 1 2 4 0
9 5 10 2 10 10 2 2
10 9 1 9 5 5 8 8
4 4 2 10 2 1 4 10
9 2 5 8 8 7 6 6
0 5 3 1 3 6 0 5
8 1 0 9 7 10 2 10
5 8 3 1 0 8 4 0
Theorem: Every Matrix satisfies its own characteristic polynomial.
Let's Check
using Polynomial
in module Base at promotion.jl:151 overwritten in module Main at In[20]:4.
Warning: New definition
promote_rule(Type{Poly{T}},Type{T}) at /Users/kfischer/.julia/Polynomial/src/Polynomial.jl:19
is ambiguous with:
promote_rule(Type{T},Type{NAtype}) at /Users/kfischer/.julia/DataFrames/src/natype.jl:32.
To fix, define
promote_rule(Type{Poly{T}},Type{NAtype})
using Polynomial
λ = Poly(ModInt{11}[0,1])
p=det(A-map(x->λ*x,eye(ModInt{11},n,n)))
Poly(-7 mod 11 + 10 mod 11x^2 + -1 mod 11x^3 + -7 mod 11x^4 + 9 mod 11x^5 + -8 mod 11x^6 + -4 mod 11x^7 + x^8)
papply(p,A)
8x8 Array{ModInt{11},2}:
0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0
import Base: promote_rule, convert, show, one, zero
immutable Face <: Number
v::Bool
end
+(x::Face,y::Face) = Face(x.v$y.v)
*(x::Face,y::Face) = Face(x.v&y.v)
-(x::Face,y::Face) = x+y
-(x::Face) = x
one(::Type{Face}) = ☺
zero(::Type{Face}) = ☹
Base.show(io::IO,f::Face) = print(io,f.v?'☺':'☹')
Base.convert(::Type{Face},x) = Face(convert(Bool,x))
Base.convert(::Type{Bool},x::Face) = x.v
const ☺ = Face(true)
const ☹ = Face(false)
☹
n=8
A=map(Face,randbool(n,n))
8x8 Array{Face,2}:
☹ ☹ ☹ ☹ ☹ ☺ ☹ ☹
☺ ☺ ☹ ☹ ☹ ☺ ☺ ☹
☹ ☹ ☹ ☹ ☹ ☹ ☹ ☹
☺ ☹ ☹ ☹ ☺ ☺ ☹ ☺
☹ ☹ ☺ ☺ ☹ ☹ ☹ ☺
☺ ☺ ☺ ☺ ☺ ☹ ☹ ☺
☹ ☺ ☹ ☺ ☹ ☹ ☺ ☺
☺ ☺ ☺ ☹ ☹ ☹ ☹ ☺
using Polynomial
λ = Poly([☹,☺])
λI = map(x->λ*x,eye(Face,n,n))
p=det(A-λI)
Poly(x^3 + x^5 + x^7 + x^8)
papply(p,A)
8x8 Array{Face,2}:
☹ ☹ ☹ ☹ ☹ ☹ ☹ ☹
☹ ☹ ☹ ☹ ☹ ☹ ☹ ☹
☹ ☹ ☹ ☹ ☹ ☹ ☹ ☹
☹ ☹ ☹ ☹ ☹ ☹ ☹ ☹
☹ ☹ ☹ ☹ ☹ ☹ ☹ ☹
☹ ☹ ☹ ☹ ☹ ☹ ☹ ☹
☹ ☹ ☹ ☹ ☹ ☹ ☹ ☹
☹ ☹ ☹ ☹ ☹ ☹ ☹ ☹
a = ModInt{11}(11119)
9 mod 11
b = ModInt{11}(12345)
3 mod 11
a+b
1 mod 11
code_llvm(+,(ModInt{11},ModInt{11}))
before the new definition.
; Function Attrs: sspreq
define %ModInt @"julia_+6067"(%ModInt, %ModInt) #2 {
top:
%2 = extractvalue %ModInt %0, 0, !dbg !27934
%3 = extractvalue %ModInt %1, 0, !dbg !27934
%4 = add i64 %3, %2, !dbg !27934
%5 = srem i64 %4, 11, !dbg !27934
%6 = insertvalue %ModInt undef, i64 %5, 0, !dbg !27934, !julia_type !27939
ret %ModInt %6, !dbg !27934
}
code_native(+, (ModInt{11},ModInt{11}))
.section __TEXT,__text,regular,pure_instructions Filename: In[22] Source line: 11 push rbp mov rbp, rsp sub rsp, 16 mov rcx, rdi Source line: 11 movabs rdi, 4348774360 mov rax, qword ptr [rdi] mov qword ptr [rbp - 8], rax add rcx, rsi movabs rdx, 3353953467947191203 mov rax, rcx imul rdx mov rax, qword ptr [rdi] cmp rax, qword ptr [rbp - 8] jne 29 mov rax, rdx shr rax, 63 sar rdx add rdx, rax imul rax, rdx, 11 sub rcx, rax mov rax, rcx add rsp, 16 pop rbp ret movabs rax, 140735631254601 call rax
poly = :(A^3+2A-1)
:(-(+(^(A,3),*(2,A)),1))
ex = :(evaluate_a_polynomial(A) = $poly)
:(evaluate_a_polynomial(A) = -(+(^(A,3),*(2,A)),1))
dump(ex)
Expr
head: Symbol =
args: Array(Any,(2,))
1: Expr
head: Symbol call
args: Array(Any,(2,))
1: Symbol evaluate_a_polynomial
2: Symbol A
typ: Any
2: Expr
head: Symbol call
args: Array(Any,(3,))
1: Symbol -
2: Expr
head: Symbol call
args: Array(Any,(3,))
typ: Any
3: Int64 1
typ: Any
typ: Any
eval(ex)
evaluate_a_polynomial (generic function with 1 method)
evaluate_a_polynomial |> methods
# 1 method for generic function "evaluate_a_polynomial": evaluate_a_polynomial(A)
typeof(A)
Array{Face,2}
typeof(a)
ModInt{11} (constructor with 1 method)
code_lowered(evaluate_a_polynomial,(typeof(A),))
1-element Array{Any,1}:
:($(Expr(:lambda, {:A}, {{},{{:A,:Any,0}},{}}, quote
return -(+(^(A,3),*(2,A)),1)
end)))
code_lowered(evaluate_a_polynomial,(typeof(a),))
1-element Array{Any,1}:
:($(Expr(:lambda, {:A}, {{},{{:A,:Any,0}},{}}, quote
return -(+(^(A,3),*(2,A)),1)
end)))
evaluate_a_polynomial(x::typeof(a)) = 14x^6+3x^2+2x+3
evaluate_a_polynomial (generic function with 2 methods)
code_lowered(evaluate_a_polynomial,(typeof(a),))
1-element Array{Any,1}:
:($(Expr(:lambda, {:x}, {{},{{:x,:Any,0}},{}}, quote # In[50], line 1:
return +(*(14,^(x,6)),*(3,^(x,2)),*(2,x),3)
end)))
function a_more_complicated_function(A)
if sum(sum(A)) > 0
return :ok
else
return 0
end
end
a_more_complicated_function (generic function with 1 method)
code_lowered(a_more_complicated_function,(typeof(A),))
1-element Array{Any,1}:
:($(Expr(:lambda, {:A}, {{},{{:A,:Any,0}},{}}, quote # In[52], line 2:
unless >(sum(sum(A)),0) goto 0 # line 3:
return :ok
goto 1
0: # In[52], line 5:
return 0
1:
end)))
code_typed(evaluate_a_polynomial,(typeof(A),))
1-element Array{Any,1}:
:($(Expr(:lambda, {:A}, {{},{{:A,Array{Face,2},0}},{}}, quote
return -(+(^(A::Array{Face,2},3)::Array{Face,2},.*(2,A::Array{Face,2})::None)::None,1)::None
end)))
foo(A) = a_more_complicated_function(det(evaluate_a_polynomial(A)))
code_typed(foo,(typeof(A),))
1-element Array{Any,1}:
:($(Expr(:lambda, {:A}, {{},{{:A,Array{Face,2},0}},{}}, quote # In[55], line 1:
return a_more_complicated_function(det(-(+(^(A::Array{Face,2},3)::Array{Face,2},.*(2,A::Array{Face,2})::None)::None,1)::None)::None)::None
end)))
code_llvm(evaluate_a_polynomial,(typeof(a),))
; Function Attrs: sspreq
define %ModInt @julia_evaluate_a_polynomial(%ModInt) #2 {
top:
%1 = call %ModInt @julia_power_by_squaring6226(%ModInt %0, i64 6), !dbg !28559, !julia_type !28564
%2 = extractvalue %ModInt %1, 0, !dbg !28559
%3 = mul i64 %2, 3, !dbg !28559
%4 = srem i64 %3, 11, !dbg !28559
%5 = call %ModInt @julia_power_by_squaring6226(%ModInt %0, i64 2), !dbg !28559, !julia_type !28564
%6 = extractvalue %ModInt %5, 0, !dbg !28559
%7 = mul i64 %6, 3, !dbg !28559
%8 = srem i64 %7, 11, !dbg !28559
%9 = add i64 %8, %4, !dbg !28559
%10 = srem i64 %9, 11, !dbg !28559
%11 = extractvalue %ModInt %0, 0, !dbg !28559
%12 = shl i64 %11, 1, !dbg !28559
%13 = srem i64 %12, 11, !dbg !28559
%14 = add i64 %13, %10, !dbg !28559
%15 = srem i64 %14, 11, !dbg !28559
%16 = add i64 %15, 3, !dbg !28559
%17 = srem i64 %16, 11, !dbg !28559
%18 = insertvalue %ModInt undef, i64 %17, 0, !dbg !28559, !julia_type !28564
ret %ModInt %18, !dbg !28559
}
code_llvm(evaluate_a_polynomial,(typeof(A),))
; Function Attrs: sspreq
define %jl_value_t* @julia_evaluate_a_polynomial6230(%jl_value_t*, %jl_value_t**, i32) #2 {
top:
%3 = alloca [4 x %jl_value_t*], align 8
%.sub = getelementptr inbounds [4 x %jl_value_t*]* %3, i64 0, i64 0
%4 = getelementptr [4 x %jl_value_t*]* %3, i64 0, i64 2, !dbg !28571
store %jl_value_t* inttoptr (i64 4 to %jl_value_t*), %jl_value_t** %.sub, align 8
%5 = load %jl_value_t*** @jl_pgcstack, align 8, !dbg !28571
%6 = getelementptr [4 x %jl_value_t*]* %3, i64 0, i64 1, !dbg !28571
%.c = bitcast %jl_value_t** %5 to %jl_value_t*, !dbg !28571
store %jl_value_t* %.c, %jl_value_t** %6, align 8, !dbg !28571
store %jl_value_t** %.sub, %jl_value_t*** @jl_pgcstack, align 8, !dbg !28571
store %jl_value_t* null, %jl_value_t** %4, align 8
%7 = getelementptr [4 x %jl_value_t*]* %3, i64 0, i64 3
store %jl_value_t* null, %jl_value_t** %7, align 8
%8 = load %jl_value_t** %1, align 8, !dbg !28571
%9 = call %jl_value_t* @"julia_^6025"(%jl_value_t* %8, i64 3), !dbg !28571
store %jl_value_t* %9, %jl_value_t** %4, align 8, !dbg !28571
call void @"julia_.*6231"(i64 2, %jl_value_t* %8), !dbg !28571
store %jl_value_t* inttoptr (i64 140620606479776 to %jl_value_t*), %jl_value_t** %7, align 8, !dbg !28571
%10 = call %jl_value_t* @jl_apply_generic(%jl_value_t* inttoptr (i64 140620629152784 to %jl_value_t*), %jl_value_t** %4, i32 2), !dbg !28571
store %jl_value_t* %10, %jl_value_t** %4, align 8, !dbg !28571
store %jl_value_t* inttoptr (i64 140620605942320 to %jl_value_t*), %jl_value_t** %7, align 8, !dbg !28571
%11 = call %jl_value_t* @jl_apply_generic(%jl_value_t* inttoptr (i64 140620629567872 to %jl_value_t*), %jl_value_t** %4, i32 2), !dbg !28571
%12 = load %jl_value_t** %6, align 8, !dbg !28571
%13 = getelementptr inbounds %jl_value_t* %12, i64 0, i32 0, !dbg !28571
store %jl_value_t** %13, %jl_value_t*** @jl_pgcstack, align 8, !dbg !28571
ret %jl_value_t* %11, !dbg !28571
}
code_native(evaluate_a_polynomial,(typeof(A),))
.section __TEXT,__text,regular,pure_instructions Filename: no file Source line: 0 push rbp mov rbp, rsp push r15 push r14 push r12 push rbx sub rsp, 48 movabs r14, 4348774360 mov rax, qword ptr [r14] mov qword ptr [rbp - 40], rax mov qword ptr [rbp - 72], 4 Source line: 0 movabs r15, 4348775232 mov rax, qword ptr [r15] mov qword ptr [rbp - 64], rax lea rax, qword ptr [rbp - 72] mov qword ptr [r15], rax vxorps xmm0, xmm0, xmm0 vmovups xmmword ptr [rbp - 56], xmm0 movabs rax, 4380607552 mov rbx, qword ptr [rsi] mov rdi, rbx mov esi, 3 call rax movabs rcx, 4380609184 mov qword ptr [rbp - 56], rax mov edi, 2 mov rsi, rbx call rcx lea rbx, qword ptr [rbp - 56] movabs r12, 4318407168 movabs rax, 140620606479776 mov qword ptr [rbp - 48], rax movabs rdi, 140620629152784 mov rsi, rbx mov edx, 2 call r12 movabs rcx, 140620605942320 mov qword ptr [rbp - 56], rax mov qword ptr [rbp - 48], rcx movabs rdi, 140620629567872 mov rsi, rbx mov edx, 2 call r12 mov rcx, qword ptr [rbp - 64] mov qword ptr [r15], rcx mov rcx, qword ptr [r14] cmp rcx, qword ptr [rbp - 40] jne 13 add rsp, 48 pop rbx pop r12 pop r14 pop r15 pop rbp ret movabs rax, 140735631254601 call rax
pid() = ccall(:getpid, Int32, ())
pid (generic function with 1 method)
pid()
46441
code_llvm(pid,())
; Function Attrs: sspreq
define i32 @julia_pid6253() #2 {
top:
%0 = call i32 @getpid(), !dbg !28644
ret i32 %0, !dbg !28644
}
import Base.llvmcall
simd(x::NTuple{4,Int64}) = llvmcall(
"""
%3 = add <4 x i64> %1, %0
ret <4 x i64> %3
""",NTuple{4,Int64},(NTuple{4,Int64},NTuple{4,Int64}),(1,2,3,4),x)
simd (generic function with 1 method)
simd((2,3,4,5))
(3,5,7,9)
code_llvm(simd,(NTuple{4,Int64},))
; Function Attrs: sspreq
define <4 x i64> @julia_simd6273(<4 x i64>) #2 {
top:
%1 = add <4 x i64> %0, <i64 1, i64 2, i64 3, i64 4>
ret <4 x i64> %1, !dbg !28729
}
code_native(simd,(NTuple{4,Int64},))
.section __TEXT,__text,regular,pure_instructions Filename: In[62] Source line: 2 push rbp mov rbp, rsp sub rsp, 16 movabs rax, 4348774360 mov rcx, qword ptr [rax] mov qword ptr [rbp - 8], rcx movabs rcx, 4624115088 vpaddq xmm1, xmm0, xmmword ptr [rcx] mov rax, qword ptr [rax] cmp rax, qword ptr [rbp - 8] jne 32 vextractf128 xmm0, ymm0, 1 movabs rax, 4624115072 vpaddq xmm0, xmm0, xmmword ptr [rax] vinsertf128 ymm0, ymm1, xmm0, 1 Source line: 2 add rsp, 16 pop rbp ret movabs rax, 140735631254601 vzeroupper call rax