''' Use llvmlite to create executable functions from SymPy expressions This module requires llvmlite (https://github.com/numba/llvmlite). ''' import ctypes from sympy.external import import_module from sympy.printing.printer import Printer from sympy.core.singleton import S from sympy.tensor.indexed import IndexedBase from sympy.utilities.decorator import doctest_depends_on llvmlite = import_module('llvmlite') if llvmlite: ll = import_module('llvmlite.ir').ir llvm = import_module('llvmlite.binding').binding llvm.initialize() llvm.initialize_native_target() llvm.initialize_native_asmprinter() __doctest_requires__ = {('llvm_callable'): ['llvmlite']} class LLVMJitPrinter(Printer): '''Convert expressions to LLVM IR''' def __init__(self, module, builder, fn, *args, **kwargs): self.func_arg_map = kwargs.pop("func_arg_map", {}) if not llvmlite: raise ImportError("llvmlite is required for LLVMJITPrinter") super().__init__(*args, **kwargs) self.fp_type = ll.DoubleType() self.module = module self.builder = builder self.fn = fn self.ext_fn = {} # keep track of wrappers to external functions self.tmp_var = {} def _add_tmp_var(self, name, value): self.tmp_var[name] = value def _print_Number(self, n): return ll.Constant(self.fp_type, float(n)) def _print_Integer(self, expr): return ll.Constant(self.fp_type, float(expr.p)) def _print_Symbol(self, s): val = self.tmp_var.get(s) if not val: # look up parameter with name s val = self.func_arg_map.get(s) if not val: raise LookupError("Symbol not found: %s" % s) return val def _print_Pow(self, expr): base0 = self._print(expr.base) if expr.exp == S.NegativeOne: return self.builder.fdiv(ll.Constant(self.fp_type, 1.0), base0) if expr.exp == S.Half: fn = self.ext_fn.get("sqrt") if not fn: fn_type = ll.FunctionType(self.fp_type, [self.fp_type]) fn = ll.Function(self.module, fn_type, "sqrt") self.ext_fn["sqrt"] = fn return self.builder.call(fn, [base0], "sqrt") if expr.exp == 2: return self.builder.fmul(base0, base0) exp0 = self._print(expr.exp) fn = self.ext_fn.get("pow") if not fn: fn_type = ll.FunctionType(self.fp_type, [self.fp_type, self.fp_type]) fn = ll.Function(self.module, fn_type, "pow") self.ext_fn["pow"] = fn return self.builder.call(fn, [base0, exp0], "pow") def _print_Mul(self, expr): nodes = [self._print(a) for a in expr.args] e = nodes[0] for node in nodes[1:]: e = self.builder.fmul(e, node) return e def _print_Add(self, expr): nodes = [self._print(a) for a in expr.args] e = nodes[0] for node in nodes[1:]: e = self.builder.fadd(e, node) return e # TODO - assumes all called functions take one double precision argument. # Should have a list of math library functions to validate this. def _print_Function(self, expr): name = expr.func.__name__ e0 = self._print(expr.args[0]) fn = self.ext_fn.get(name) if not fn: fn_type = ll.FunctionType(self.fp_type, [self.fp_type]) fn = ll.Function(self.module, fn_type, name) self.ext_fn[name] = fn return self.builder.call(fn, [e0], name) def emptyPrinter(self, expr): raise TypeError("Unsupported type for LLVM JIT conversion: %s" % type(expr)) # Used when parameters are passed by array. Often used in callbacks to # handle a variable number of parameters. class LLVMJitCallbackPrinter(LLVMJitPrinter): def __init__(self, *args, **kwargs): super().__init__(*args, **kwargs) def _print_Indexed(self, expr): array, idx = self.func_arg_map[expr.base] offset = int(expr.indices[0].evalf()) array_ptr = self.builder.gep(array, [ll.Constant(ll.IntType(32), offset)]) fp_array_ptr = self.builder.bitcast(array_ptr, ll.PointerType(self.fp_type)) value = self.builder.load(fp_array_ptr) return value def _print_Symbol(self, s): val = self.tmp_var.get(s) if val: return val array, idx = self.func_arg_map.get(s, [None, 0]) if not array: raise LookupError("Symbol not found: %s" % s) array_ptr = self.builder.gep(array, [ll.Constant(ll.IntType(32), idx)]) fp_array_ptr = self.builder.bitcast(array_ptr, ll.PointerType(self.fp_type)) value = self.builder.load(fp_array_ptr) return value # ensure lifetime of the execution engine persists (else call to compiled # function will seg fault) exe_engines = [] # ensure names for generated functions are unique link_names = set() current_link_suffix = 0 class LLVMJitCode: def __init__(self, signature): self.signature = signature self.fp_type = ll.DoubleType() self.module = ll.Module('mod1') self.fn = None self.llvm_arg_types = [] self.llvm_ret_type = self.fp_type self.param_dict = {} # map symbol name to LLVM function argument self.link_name = '' def _from_ctype(self, ctype): if ctype == ctypes.c_int: return ll.IntType(32) if ctype == ctypes.c_double: return self.fp_type if ctype == ctypes.POINTER(ctypes.c_double): return ll.PointerType(self.fp_type) if ctype == ctypes.c_void_p: return ll.PointerType(ll.IntType(32)) if ctype == ctypes.py_object: return ll.PointerType(ll.IntType(32)) print("Unhandled ctype = %s" % str(ctype)) def _create_args(self, func_args): """Create types for function arguments""" self.llvm_ret_type = self._from_ctype(self.signature.ret_type) self.llvm_arg_types = \ [self._from_ctype(a) for a in self.signature.arg_ctypes] def _create_function_base(self): """Create function with name and type signature""" global link_names, current_link_suffix default_link_name = 'jit_func' current_link_suffix += 1 self.link_name = default_link_name + str(current_link_suffix) link_names.add(self.link_name) fn_type = ll.FunctionType(self.llvm_ret_type, self.llvm_arg_types) self.fn = ll.Function(self.module, fn_type, name=self.link_name) def _create_param_dict(self, func_args): """Mapping of symbolic values to function arguments""" for i, a in enumerate(func_args): self.fn.args[i].name = str(a) self.param_dict[a] = self.fn.args[i] def _create_function(self, expr): """Create function body and return LLVM IR""" bb_entry = self.fn.append_basic_block('entry') builder = ll.IRBuilder(bb_entry) lj = LLVMJitPrinter(self.module, builder, self.fn, func_arg_map=self.param_dict) ret = self._convert_expr(lj, expr) lj.builder.ret(self._wrap_return(lj, ret)) strmod = str(self.module) return strmod def _wrap_return(self, lj, vals): # Return a single double if there is one return value, # else return a tuple of doubles. # Don't wrap return value in this case if self.signature.ret_type == ctypes.c_double: return vals[0] # Use this instead of a real PyObject* void_ptr = ll.PointerType(ll.IntType(32)) # Create a wrapped double: PyObject* PyFloat_FromDouble(double v) wrap_type = ll.FunctionType(void_ptr, [self.fp_type]) wrap_fn = ll.Function(lj.module, wrap_type, "PyFloat_FromDouble") wrapped_vals = [lj.builder.call(wrap_fn, [v]) for v in vals] if len(vals) == 1: final_val = wrapped_vals[0] else: # Create a tuple: PyObject* PyTuple_Pack(Py_ssize_t n, ...) # This should be Py_ssize_t tuple_arg_types = [ll.IntType(32)] tuple_arg_types.extend([void_ptr]*len(vals)) tuple_type = ll.FunctionType(void_ptr, tuple_arg_types) tuple_fn = ll.Function(lj.module, tuple_type, "PyTuple_Pack") tuple_args = [ll.Constant(ll.IntType(32), len(wrapped_vals))] tuple_args.extend(wrapped_vals) final_val = lj.builder.call(tuple_fn, tuple_args) return final_val def _convert_expr(self, lj, expr): try: # Match CSE return data structure. if len(expr) == 2: tmp_exprs = expr[0] final_exprs = expr[1] if len(final_exprs) != 1 and self.signature.ret_type == ctypes.c_double: raise NotImplementedError("Return of multiple expressions not supported for this callback") for name, e in tmp_exprs: val = lj._print(e) lj._add_tmp_var(name, val) except TypeError: final_exprs = [expr] vals = [lj._print(e) for e in final_exprs] return vals def _compile_function(self, strmod): global exe_engines llmod = llvm.parse_assembly(strmod) pmb = llvm.create_pass_manager_builder() pmb.opt_level = 2 pass_manager = llvm.create_module_pass_manager() pmb.populate(pass_manager) pass_manager.run(llmod) target_machine = \ llvm.Target.from_default_triple().create_target_machine() exe_eng = llvm.create_mcjit_compiler(llmod, target_machine) exe_eng.finalize_object() exe_engines.append(exe_eng) if False: print("Assembly") print(target_machine.emit_assembly(llmod)) fptr = exe_eng.get_function_address(self.link_name) return fptr class LLVMJitCodeCallback(LLVMJitCode): def __init__(self, signature): super().__init__(signature) def _create_param_dict(self, func_args): for i, a in enumerate(func_args): if isinstance(a, IndexedBase): self.param_dict[a] = (self.fn.args[i], i) self.fn.args[i].name = str(a) else: self.param_dict[a] = (self.fn.args[self.signature.input_arg], i) def _create_function(self, expr): """Create function body and return LLVM IR""" bb_entry = self.fn.append_basic_block('entry') builder = ll.IRBuilder(bb_entry) lj = LLVMJitCallbackPrinter(self.module, builder, self.fn, func_arg_map=self.param_dict) ret = self._convert_expr(lj, expr) if self.signature.ret_arg: output_fp_ptr = builder.bitcast(self.fn.args[self.signature.ret_arg], ll.PointerType(self.fp_type)) for i, val in enumerate(ret): index = ll.Constant(ll.IntType(32), i) output_array_ptr = builder.gep(output_fp_ptr, [index]) builder.store(val, output_array_ptr) builder.ret(ll.Constant(ll.IntType(32), 0)) # return success else: lj.builder.ret(self._wrap_return(lj, ret)) strmod = str(self.module) return strmod class CodeSignature: def __init__(self, ret_type): self.ret_type = ret_type self.arg_ctypes = [] # Input argument array element index self.input_arg = 0 # For the case output value is referenced through a parameter rather # than the return value self.ret_arg = None def _llvm_jit_code(args, expr, signature, callback_type): """Create a native code function from a SymPy expression""" if callback_type is None: jit = LLVMJitCode(signature) else: jit = LLVMJitCodeCallback(signature) jit._create_args(args) jit._create_function_base() jit._create_param_dict(args) strmod = jit._create_function(expr) if False: print("LLVM IR") print(strmod) fptr = jit._compile_function(strmod) return fptr @doctest_depends_on(modules=('llvmlite', 'scipy')) def llvm_callable(args, expr, callback_type=None): '''Compile function from a SymPy expression Expressions are evaluated using double precision arithmetic. Some single argument math functions (exp, sin, cos, etc.) are supported in expressions. Parameters ========== args : List of Symbol Arguments to the generated function. Usually the free symbols in the expression. Currently each one is assumed to convert to a double precision scalar. expr : Expr, or (Replacements, Expr) as returned from 'cse' Expression to compile. callback_type : string Create function with signature appropriate to use as a callback. Currently supported: 'scipy.integrate' 'scipy.integrate.test' 'cubature' Returns ======= Compiled function that can evaluate the expression. Examples ======== >>> import sympy.printing.llvmjitcode as jit >>> from sympy.abc import a >>> e = a*a + a + 1 >>> e1 = jit.llvm_callable([a], e) >>> e.subs(a, 1.1) # Evaluate via substitution 3.31000000000000 >>> e1(1.1) # Evaluate using JIT-compiled code 3.3100000000000005 Callbacks for integration functions can be JIT compiled. >>> import sympy.printing.llvmjitcode as jit >>> from sympy.abc import a >>> from sympy import integrate >>> from scipy.integrate import quad >>> e = a*a >>> e1 = jit.llvm_callable([a], e, callback_type='scipy.integrate') >>> integrate(e, (a, 0.0, 2.0)) 2.66666666666667 >>> quad(e1, 0.0, 2.0)[0] 2.66666666666667 The 'cubature' callback is for the Python wrapper around the cubature package ( https://github.com/saullocastro/cubature ) and ( http://ab-initio.mit.edu/wiki/index.php/Cubature ) There are two signatures for the SciPy integration callbacks. The first ('scipy.integrate') is the function to be passed to the integration routine, and will pass the signature checks. The second ('scipy.integrate.test') is only useful for directly calling the function using ctypes variables. It will not pass the signature checks for scipy.integrate. The return value from the cse module can also be compiled. This can improve the performance of the compiled function. If multiple expressions are given to cse, the compiled function returns a tuple. The 'cubature' callback handles multiple expressions (set `fdim` to match in the integration call.) >>> import sympy.printing.llvmjitcode as jit >>> from sympy import cse >>> from sympy.abc import x,y >>> e1 = x*x + y*y >>> e2 = 4*(x*x + y*y) + 8.0 >>> after_cse = cse([e1,e2]) >>> after_cse ([(x0, x**2), (x1, y**2)], [x0 + x1, 4*x0 + 4*x1 + 8.0]) >>> j1 = jit.llvm_callable([x,y], after_cse) # doctest: +SKIP >>> j1(1.0, 2.0) # doctest: +SKIP (5.0, 28.0) ''' if not llvmlite: raise ImportError("llvmlite is required for llvmjitcode") signature = CodeSignature(ctypes.py_object) arg_ctypes = [] if callback_type is None: for _ in args: arg_ctype = ctypes.c_double arg_ctypes.append(arg_ctype) elif callback_type in ('scipy.integrate', 'scipy.integrate.test'): signature.ret_type = ctypes.c_double arg_ctypes = [ctypes.c_int, ctypes.POINTER(ctypes.c_double)] arg_ctypes_formal = [ctypes.c_int, ctypes.c_double] signature.input_arg = 1 elif callback_type == 'cubature': arg_ctypes = [ctypes.c_int, ctypes.POINTER(ctypes.c_double), ctypes.c_void_p, ctypes.c_int, ctypes.POINTER(ctypes.c_double) ] signature.ret_type = ctypes.c_int signature.input_arg = 1 signature.ret_arg = 4 else: raise ValueError("Unknown callback type: %s" % callback_type) signature.arg_ctypes = arg_ctypes fptr = _llvm_jit_code(args, expr, signature, callback_type) if callback_type and callback_type == 'scipy.integrate': arg_ctypes = arg_ctypes_formal cfunc = ctypes.CFUNCTYPE(signature.ret_type, *arg_ctypes)(fptr) return cfunc