debye_1(x) = ccall((:gsl_sf_debye_1,:libgsl), Cdouble, (Cdouble,), x)debye_1(2), debye_1(3.7), and so on. (Even easier would be to use Jiahao Chen's GSL package for Julia, which has already created such wrappers for you.) This makes a vast array of existing C libraries accessible to you in Julia (along with Fortran libraries and other languages with C-accessible calling conventions).
In fact, you can even go the other way around, passing Julia routines to C, so that C code is calling Julia code in the form of callback functions. For example, a C library for numerical integration might expect you to pass the integrand as a function argument, which the library will then call to evaluate the integrand as many times as needed to estimate the integral. Callback functions are also natural for optimization, root-finding, and many other numerical tasks, as well as in many non-numerical problems. The purpose of this blog post is to illustrate the techniques for passing Julia functions as callbacks to C routines, which is straightforward and efficient but requires some lower-level understanding of how functions and other values are passed as arguments.
The code in this post requires Julia 0.2 (or a recent git facsimile thereof); the key features needed for callback functions (especially unsafe_pointer_to_objref) are not available in Julia 0.1.
qsortvoid qsort(void *base, size_t nmemb, size_t size,
int(*compare)(const void *a, const void *b));base argument is a pointer to an array of length nmemb, with elements of size bytes each. compare is a callback function which takes pointers to two elements a and b and returns an integer less/greater than zero if a should appear before/after b (or zero if any order is permitted). Now, suppose that we have a 1d array A of values in Julia that we want to sort using the qsort function (rather than Julia's built-in sort function). Before we worry about calling qsort and passing arguments, we need to write a comparison function that works for some arbitrary type T, e.g.
function mycompare{T}(a_::Ptr{T}, b_::Ptr{T})
a = unsafe_load(a_)
b = unsafe_load(b_)
return a < b ? cint(-1) : a > b ? cint(+1) : cint(0)
end
cint(n) = convert(Cint, n)unsafe_load to fetch the values pointed to by the arguments a_ and b_ (which is "unsafe" because it will crash if these are not valid pointers, but qsort will always pass valid pointers). Also, we have to be a little careful about return values: qsort expects a function returning a C int, so we must be sure to return Cint (the corresponding type in Julia) via a call to convert.
Now, how do we pass this to C? A function pointer in C is essentially just a pointer to the memory location of the machine code implementing that function, whereas a function value mycompare (of type Function) in Julia is quite different. Thanks to Julia's JIT compilation approach,a Julia function may not even be compiled until the first time it is called, and in general the same Julia function may be compiled into multiple machine-code instantiations, which are specialized for arguments of different types (e.g. different T in this case). So, you can imagine that mycompare must internally point to a rather complicated data structure (a jl_function_t in julia.h, if you are interested), which holds information about the argument types, the compiled versions (if any), and so on. In general, it must store a closure with information about the environment in which the function was defined; we will talk more about this below. In any case, it is a very different object than a simple pointer to machine code for one set of argument types. Fortunately, we can get the latter simply by calling a built-in Julia function called cfunction:
const mycompare_c = cfunction(mycompare, Cint, (Ptr{Cdouble}, Ptr{Cdouble}))cfunction three arguments: the function mycompare, the return type Cint, and a tuple of the argument types, in this case to sort an array of Cdouble (Float64) elements. Julia compiles a version of mycompare specialized for these argument types (if it has not done so already), and returns a Ptr{Void} holding the address of the machine code, exactly what we need to pass to qsort. We are now ready to call qsort on some sample data:
A = [1.3, -2.7, 4.4, 3.1]
ccall(:qsort, Void, (Ptr{Cdouble}, Csize_t, Csize_t, Ptr{Void}),
A, length(A), sizeof(eltype(A)), mycompare_c)A is changed to the sorted array [ -2.7, 1.3,
3.1, 4.4]. Note that Julia knows how to convert an array A::Vector{Cdouble} into a Ptr{Cdouble}, how to compute the sizeof a type in bytes (identical to C's sizeof operator), and so on. For fun, try inserting a println("mycompare($a,$b)") line into mycompare, which will allow you to see the comparisons that qsort is performing (and to verify that it is really calling the Julia function that you passed to it).
cfunction doesn't always work. For example, suppose we tried to declare our comparison function inline, via:
mycomp = cfunction((a_,b_) -> unsafe_load(a_) < unsafe_load(b_) ?
cint(-1) : cint(+1),
Cint, (Ptr{Cdouble}, Ptr{Cdouble}))ERROR: function is not yet c-callable. In general, cfunction only works for "top-level" functions: named functions defined in the top-level (global or module) scope, but not anonymous (args -> value) functions and not functions defined within other functions ("nested" functions). The reason for this stems from one important concept in computer science: a closure.
To understand the need for closures, and the difficulty they pose for callback functions, suppose that we wanted to provide a nicer interface for qsort, one which permitted the user to simply pass a lessthan function returning true or false while hiding all of the low-level business with pointers, Cint, and so on. We might like to do something of the form:
function qsort!{T}(A::Vector{T}, lessthan::Function)
function mycompare(a_::Ptr{T}, b_::Ptr{T})
a = unsafe_load(a_)
b = unsafe_load(b_)
return lessthan(a, b) ? cint(-1) : cint(+1)
end
mycompare_c = cfunction(mycompare, Cint, (Ptr{T}, Ptr{T}))
ccall(:qsort, Void, (Ptr{T}, Csize_t, Csize_t, Ptr{Void}),
A, length(A), sizeof(T), mycompare_c)
A
endqsort!([1.3, -2.7, 4.4, 3.1], <) to sort in ascending order using the built-in < comparison, or any other comparison function we wanted. Unfortunately cfunction will again barf when you try to call qsort!, and it is no longer so difficult to understand why. Notice that the nested mycompare function is no longer self-contained: it uses the variable lessthan from the surrounding scope. This is a common pattern for nested functions and anonymous functions: often, they are parameterized by local variables in the environment where the function is defined. Technically, the ability to have this kind of dependency is provided by lexical scoping in a programming language like Julia, and is typical of any language in which functions are "first-class" objects. In order to support lexical scoping, a Julia Function object needs to internally carry around a pointer to the variables in the enclosing environment, and this encapsulation is called a closure.
In contrast, a C function pointer is not a closure. It doesn't enclose a pointer to the environment in which the function was defined, or anything else for that matter; it is just the address of a stream of instructions. This makes it hard, in C, to write functions to transform other functions (higher-order functions) or to parameterize functions by local variables. This apparently leaves us with two options, neither of which is especially attractive:
We could store lessthan in a global variable, and reference that from a top-level mycompare function. (This is the traditional solution for C programmers calling qsort with parameterized comparison functions.) The problem with this strategy is that it is not re-entrant: it prevents us from calling qsort! recursively (e.g. if the comparison function itself needs to do a sort, for some complicated datastructure), or from calling qsort! from multiple threads (when a future Julia version supports shared-memory parallelism). Still, this is better than nothing.
Every time qsort! is called, Julia could JIT-compile a new version of mycompare, which hard-codes the reference to the lessthan argument passed on that call. This is technically possible and has been implemented in some languages (e.g. reportedly GNU Guile and Lua do something like this). However, this strategy comes at a price: it requires that callbacks be recompiled every time a parameter in them changes, which is not true of the global-variable strategy. Anyway, it is not implemented yet in Julia.
Fortunately, there is often a third option, because C programmers long ago recognized these limitations of function pointers, and devised a workaround: most modern C callback interfaces allow arbitrary data to be passed through to the callback via a "pass-through" (or "thunk") pointer parameter. As explained in the next section, we can exploit this technique in Julia to pass a "true" closure as a callback.
qsort interface is nowadays considered rather antiquated. Years ago, it was supplemented on BSD-Unix systems, and eventually in GNU libc, by a function called qsort_r that solves the problem of passing parameters to the callback in a re-entrant way. This is how the BSD (e.g. MacOS) qsort_r function is defined:
void qsort_r(void *base, size_t nmemb, size_t size, void *thunk,
int (*compare)(void *thunk, const void *a, const void *b));qsort, there is an extra thunk parameter, and this is passed through to the compare function as its first argument. In this way, you can pass a pointer to arbitrary data through to your callback, and we can exploit this to pass a closure through for an arbitrary Julia callback.
All we need is a way to convert a Julia Function into an opaque Ptr{Void} so that we can pass it through to our callback, and then a way to convert the opaque pointer back into a Function. The former is automatic if we simply declare the ccall argument as type Any (which passes the argument as an opaque Julia object pointer), and the latter is accomplished by the built-in function unsafe_pointer_to_objref. (Technically, we could use type Function or an explicit call to pointer_from_objref instead of Any.) Using these, we can now define a working high-level qsort! function that takes an arbitrary lessthan comparison-function argument:
function qsort!_compare{T}(lessthan_::Ptr{Void}, a_::Ptr{T}, b_::Ptr{T})
a = unsafe_load(a_)
b = unsafe_load(b_)
lessthan = unsafe_pointer_to_objref(lessthan_)::Function
return lessthan(a, b) ? cint(-1) : cint(+1)
end
function qsort!{T}(A::Vector{T}, lessthan::Function=<)
compare_c = cfunction(qsort!_compare, Cint, (Ptr{Void}, Ptr{T}, Ptr{T}))
ccall(:qsort_r, Void, (Ptr{T}, Csize_t, Csize_t, Any, Ptr{Void}),
A, length(A), sizeof(T), lessthan, compare_c)
return A
endqsort!_compare is a top-level function, so cfunction has no problem with it, and it will only be compiled once per type T to be sorted (rather than once per call to qsort! or per lessthan function). We use the explicit ::Function assertion to tell the compiler that we will only pass Function pointers in lessthan_. Note that we gave the lessthan argument a default value of < (default arguments being a recent feature added to Julia).
We can now do qsort!([1.3, -2.7, 4.4, 3.1]) and it will return the array sorted in ascending order, or qsort!([1.3, -2.7,
4.4, 3.1], >) to sort in descending order.
qsort_r is not portableqsort_r function is not portable. The above example won't work on Windows, since the Windows C library doesn't define qsort_r (instead, it has a function called qsort_s, which of course uses an argument order incompatible with both the BSD and GNU qsort_r functions). Worse, it will crash on GNU/Linux systems, which do provide qsort_r but with an incompatible calling convention. And as a result it is difficult to use qsort_r in a way that does not crash either on GNU/Linux or BSD (e.g. MacOS) systems. This is how glibc's qsort_r is defined:
void qsort_r(void *base, size_t nmemb, size_t size,
int (*compare)(const void *a, const void *b, void *thunk),
void *thunk);thunk argument is moved, both in qsort_r itself and in the comparison function. So, the corresponding qsort! Julia code on GNU/Linux systems should be:
function qsort!_compare{T}(a_::Ptr{T}, b_::Ptr{T}, lessthan_::Ptr{Void})
a = unsafe_load(a_)
b = unsafe_load(b_)
lessthan = unsafe_pointer_to_objref(lessthan_)::Function
return lessthan(a, b) ? cint(-1) : cint(+1)
end
function qsort!{T}(A::Vector{T}, lessthan::Function=<)
compare_c = cfunction(qsort!_compare, Cint, (Ptr{T}, Ptr{T}, Ptr{Void}))
ccall(:qsort_r, Void, (Ptr{T}, Csize_t, Csize_t, Ptr{Void}, Any),
A, length(A), sizeof(T), compare_c, lessthan)
return A
endqsort_r from Julia, you could use the above definitions if OS_NAME == :Linux and the BSD definitions otherwise, with a third version using qsort_s on Windows, but fortunately there is not much need as Julia comes with its own perfectly adequate sort and sort! routines.
Like most modern C libraries accepting callbacks, GSL uses a void* pass-through parameter to allow arbitrary data to be passed through to the callback routine, and we can use that to support arbitrary closures in Julia. Unlike qsort_r, however, GSL wraps both the C function pointer and the pass-through pointer in a data structure called gsl_function:
struct {
double (*function)(double x, void *params);
void *params;
} gsl_function;GSL_Function type in Julia that mirrors this C type, and with a constructor GSL_Function(f::Function) that creates a wrapper around an arbitrary Julia function f:
function gsl_function_wrap(x::Cdouble, params::Ptr{Void})
f = unsafe_pointer_to_objref(params)::Function
convert(Cdouble, f(x))::Cdouble
end
const gsl_function_wrap_c = cfunction(gsl_function_wrap,
Cdouble, (Cdouble, Ptr{Void}))
type GSL_Function
func::Ptr{Void}
params::Any
GSL_Function(f::Function) = new(gsl_function_wrap_c, f)
endconvert the return value of f to a Cdouble (in case the caller's code returns some other numeric type for some x, such as an Int). Moreover, we need to explicitly assert (::Cdouble) that the result of the convert was a Cdouble. As with the qsort example, this is because cfunction only works if Julia can guarantee that gsl_function_wrap returns the specified Cdouble type, and Julia cannot infer the return type of convert since it does not know the return type of f(x).
Given the above definitions, it is a simple matter to pass this to the GSL adaptive-integration routines in a wrapper function gsl_integration_qag:
function gsl_integration_qag(f::Function, a::Real, b::Real, epsrel::Real=1e-12,
maxintervals::Integer=10^7)
s = ccall((:gsl_integration_workspace_alloc,:libgsl), Ptr{Void}, (Csize_t,),
maxintervals)
result = Array(Cdouble,1)
abserr = Array(Cdouble,1)
ccall((:gsl_integration_qag,:libgsl), Cint,
(Ptr{GSL_Function}, Cdouble,Cdouble, Cdouble, Csize_t, Cint, Ptr{Void},
Ptr{Cdouble}, Ptr{Cdouble}),
&GSL_Function(f), a, b, epsrel, maxintervals, 1, s, result, abserr)
ccall((:gsl_integration_workspace_free,:libgsl), Void, (Ptr{Void},), s)
return (result[1], abserr[1])
end&GSL_Function(f) passes a pointer to a GSL_Function "struct" containing a pointer to gsl_function_wrap_c and f, corresponding to the gsl_function* argument in C. The return value is a tuple of the estimated integral and an estimated error.
For example, gsl_integration_qag(cos, 0, 1) returns (0.8414709848078965,9.34220461887732e-15), which computes the correct integral sin(1) to machine precision.
Function into C. Whenever one passes pointers to Julia data into C code, one has to ensure that the Julia data is not garbage-collected until the C code is done with it, and functions are no exception to this rule. An anonymous function that is no longer referred to by any Julia variable may be garbage collected, at which point any C pointers to it become invalid.
This sounds scary, but in practice you don't need to worry about it very often, because Julia guarantees that ccall arguments won't be garbage-collected until the ccall exits. So, in all of the above examples, we are safe: the Function only needs to live as long as the ccall.
The only danger arises when you pass a function pointer to C and the C code saves the pointer in some data structure which it will use in a later ccall. In that case, you are responsible for ensuring that the Function variable lives (is referred to by some Julia variable) as long as the C code might need it.
For example, in the GSL one-dimensional minimization interface, you don't simply pass your objective function to a minimization routine and wait until it is minimized. Instead, you call a GSL routine to create a "minimizer object", store your function pointer in this object, call routines to iterate the minimization, and then deallocate the minimizer when you are done. The Julia function must not be garbage-collected until this process is complete. The easiest way to ensure this is to create a Julia wrapper type around the minimizer object that stores an explicit reference to the Julia function, like this:
type GSL_Minimizer
m::Ptr{Void} # the gsl_min_fminimizer pointer
f::Any # explicit reference to objective, to prevent garbage-collection
function GSL_Minimizer(t)
m = ccall((:gsl_min_fminimizer_alloc,:libgsl), Ptr{Void}, (Ptr{Void},), t)
p = new(m, nothing)
finalizer(p, p -> ccall((:gsl_min_fminimizer_free,:libgsl),
Void, (Ptr{Void},), p.m))
p
end
endgsl_min_fminimizer object of type t, with a placeholder f to store a reference to the objective function (once it is set below), including a finalizer to deallocate the GSL object when the GSL_Minimizer is garbage-collected. The parameter t is used to specify the minimization algorithm, which could default to Brent's algorithm via:
const gsl_brent = unsafe_load(cglobal((:gsl_min_fminimizer_brent,:libgsl), Ptr{Void}))
GSL_Minimizer() = GSL_Minimizer(gsl_brent)cglobal yields a pointer to the gsl_min_fminimizer_brent global variable in GSL, which we then dereference to get the actual pointer via unsafe_load.)
Then, when we set the function to minimize (the "objective"), we store an extra reference to it in the GSL_Minimizer to prevent garbage-collection for the lifetime of the GSL_Minimizer, again using the GSL_Function type defined above to wrap the callback:
function gsl_minimizer_set!(m::GSL_Minimizer, f, x0, xmin, xmax)
ccall((:gsl_min_fminimizer_set,:libgsl), Cint,
(Ptr{Void}, Ptr{GSL_Function}, Cdouble, Cdouble, Cdouble),
m.m, &GSL_Function(f), x0, xmin, xmax)
m.f = f
m
endx, objective value, or bounds on the minimum, which are convenient to wrap:
gsl_minimizer_iterate!(m::GSL_Minimizer) =
ccall((:gsl_min_fminimizer_iterate,:libgsl), Cint, (Ptr{Void},), m.m)
gsl_minimizer_x(m::GSL_Minimizer) =
ccall((:gsl_min_fminimizer_x_minimum,:libgsl), Cdouble, (Ptr{Void},), m.m)
gsl_minimizer_f(m::GSL_Minimizer) =
ccall((:gsl_min_fminimizer_f_minimum,:libgsl), Cdouble, (Ptr{Void},), m.m)
gsl_minimizer_xmin(m::GSL_Minimizer) =
ccall((:gsl_min_fminimizer_x_lower,:libgsl), Cdouble, (Ptr{Void},), m.m)
gsl_minimizer_xmax(m::GSL_Minimizer) =
ccall((:gsl_min_fminimizer_x_upper,:libgsl), Cdouble, (Ptr{Void},), m.m)sin(x) in the interval [-3,1], with a starting guess -1, via:
m = GSL_Minimizer()
gsl_minimizer_set!(m, sin, -1, -3, 1)
while gsl_minimizer_xmax(m) - gsl_minimizer_xmin(m) > 1e-6
println("iterating at x = $(gsl_minimizer_x(m))")
gsl_minimizer_iterate!(m)
end
println("found minimum $(gsl_minimizer_f(m)) at x = $(gsl_minimizer_x(m))")found minimum -1.0 at x =
-1.5707963269964016, which is the correct minimum (−π/2) to about 10 digits.
At this point, I will shamelessly plug my own NLopt package for Julia, which wraps around my free/open-source NLopt library to provide many more optimization algorithms than GSL, with perhaps a nicer interface. However, the techniques used to pass callback functions to NLopt are actually quite similar to those used for GSL.
An even more complicated version of these techniques can be found in the PyCall package to call Python from Julia. In order to pass a Julia function to Python, we again use cfunction on a wrapper function that handles the type conversions and so on, and pass the actual Julia closure through via a pass-through pointer. But in that case, the pass-through pointer consists of a Python object that has been created with a new type that allows it to wrap a Julia object, and garbage-collection is deferred by storing the Julia object in a global dictionary of saved objects (removing it via the Python destructor of the new type). That is all somewhat tricky stuff and beyond the scope of this blog post; I only mention it to illustrate the fact that it is possible to implement quite complex inter-language calling behaviors purely in Julia by building on the above techniques.