def implement_test_case(self, io_map, input_values, output_signals, output_values, time_step):
""" Implement the test case check and assertion whose I/Os values
are described in input_values and output_values dict """
test_statement = Statement()
input_msg = ""
# Adding input setting
for input_tag in input_values:
input_signal = io_map[input_tag]
# FIXME: correct value generation depending on signal precision
input_value = input_values[input_tag]
test_statement.add(get_input_assign(input_signal, input_value))
input_msg += get_input_msg(input_tag, input_signal, input_value)
test_statement.add(Wait(time_step * (self.stage_num + 2)))
# Adding output value comparison
for output_tag in output_signals:
output_signal = output_signals[output_tag]
output_value = output_values[output_tag]
output_cst_value = Constant(output_value, precision=output_signal.get_precision())
value_msg = get_output_value_msg(output_signal, output_value)
test_pass_cond, check_statement = get_output_check_statement(output_signal, output_tag, output_cst_value)
test_statement.add(check_statement)
assert_statement = Assert(
test_pass_cond,
"\"unexpected value for inputs {input_msg}, output {output_tag}, expecting {value_msg}, got: \"".format(input_msg = input_msg, output_tag = output_tag, value_msg = value_msg),
severity = Assert.Failure
)
test_statement.add(assert_statement)
return test_statement
def test_ref_assign(self):
""" test behavior of StaticVectorizer on predicated ReferenceAssign """
va = Variable("a")
vb = Variable("b")
vc = Variable("c")
scheme = Statement(
ReferenceAssign(va, Constant(3)),
ConditionBlock(
(va > vb).modify_attributes(likely=True),
Statement(ReferenceAssign(vb, va),
ReferenceAssign(va, Constant(11)), Return(va)),
), ReferenceAssign(va, Constant(7)), Return(vb))
vectorized_path = StaticVectorizer().extract_vectorizable_path(
scheme, fallback_policy)
linearized_most_likely_path = instanciate_variable(
vectorized_path.linearized_optree,
vectorized_path.variable_mapping)
test_result = (isinstance(linearized_most_likely_path, Constant)
and linearized_most_likely_path.get_value() == 11)
if not test_result:
print("test UT_StaticVectorizer failure")
print("scheme: {}".format(scheme.get_str()))
print("linearized_most_likely_path: {}".format(
linearized_most_likely_path))
self.assertTrue(test_result)
def generate_embedded_testbench(self, tc_list, io_map, input_signals, output_signals, time_step, test_fname="test.input"):
""" Generate testbench with embedded input and output data """
self_component = self.implementation.get_component_object()
self_instance = self_component(io_map = io_map, tag = "tested_entity")
test_statement = Statement()
for index, (input_values, output_values) in enumerate(tc_list):
test_statement.add(
self.implement_test_case(io_map, input_values, output_signals, output_values, time_step, index=index)
)
reset_statement = self.get_reset_statement(io_map, time_step)
testbench = CodeEntity("testbench")
test_process = Process(
reset_statement,
test_statement,
# end of test
Assert(
Constant(0, precision = ML_Bool),
" \"end of test, no error encountered \"",
severity = Assert.Warning
),
# infinite end loop
WhileLoop(
Constant(1, precision=ML_Bool),
Statement(
Wait(time_step * (self.stage_num + 2)),
)
)
)
testbench_scheme = Statement(
self_instance,
test_process
)
if self.pipelined:
half_time_step = time_step / 2
assert (half_time_step * 2) == time_step
# adding clock process for pipelined bench
clk_process = Process(
Statement(
ReferenceAssign(
io_map["clk"],
Constant(1, precision = ML_StdLogic)
),
Wait(half_time_step),
ReferenceAssign(
io_map["clk"],
Constant(0, precision = ML_StdLogic)
),
Wait(half_time_step),
)
)
testbench_scheme.push(clk_process)
testbench.add_process(testbench_scheme)
return [testbench]
def externalize_call(self, optree, arg_list, tag = "foo", result_format = None):
# determining return format
return_format = optree.get_precision() if result_format is None else result_format
assert(not return_format is None and "external call result format must be defined")
# function_name = self.main_code_object.declare_free_function_name(tag)
function_name = self.name_factory.declare_free_function_name(tag)
ext_function = CodeFunction(function_name, output_format = return_format)
# creating argument copy
arg_map = {}
arg_index = 0
for arg in arg_list:
arg_tag = arg.get_tag(default = "arg_%d" % arg_index)
arg_index += 1
arg_map[arg] = ext_function.add_input_variable(arg_tag, arg.get_precision())
# copying optree while swapping argument for variables
optree_copy = optree.copy(copy_map = arg_map)
# instanciating external function scheme
if isinstance(optree, ML_ArithmeticOperation):
function_optree = Statement(Return(optree_copy))
else:
function_optree = Statement(optree_copy)
ext_function.set_scheme(function_optree)
self.name_factory.declare_function(function_name, ext_function.get_function_object())
return ext_function
def expand_sub_ndrange(var_range_list, kernel):
if len(var_range_list) == 0:
pre_expanded_kernel = expand_kernel_expr(kernel)
expanded_kernel, statement_list = extract_placeholder(
pre_expanded_kernel)
expanded_statement = Statement(*tuple(statement_list))
print("expand_ndrange: ", expanded_kernel, statement_list)
if not expanded_kernel is None:
# append expanded_kernel at the Statement's end once
# every PlaceHolder's dependency has been resolved
expanded_statement.add(expanded_kernel)
return expanded_statement
else:
var_range = var_range_list.pop(0)
scheme = Loop(
# init statement
ReferenceAssign(var_range.var_index, var_range.first_index),
# exit condition
var_range.var_index <= var_range.last_index,
# loop body
Statement(
expand_sub_ndrange(var_range_list, kernel),
# loop iterator increment
ReferenceAssign(var_range.var_index, var_range.var_index +
var_range.index_step)),
)
return scheme
def generate_function_from_optree(name_factory,
optree,
arg_list,
tag="foo",
result_format=None):
""" Function which transform a sub-graph @p optree whose inputs are @p arg_list
into a meta function
@param optree operation graph to be incorporated as function boday
@param arg_list list of @p optree's parameters to be used as function arguments
@param name_factory engine to generate unique function name and to register function
@param tag string to be used as seed to generate function name
@param result_format hint to indicate function's return format (if optree is not
an arithmetic operation (e.g. it already contains a Return node, then @p result_format
must be used to specify the funciton return format)
@return CodeFunction object containing the function implementation (plus the function
would have been declared into name_factory)
"""
# determining return format
return_format = optree.get_precision(
) if result_format is None else result_format
assert (not return_format is None
and "external call result format must be defined")
function_name = name_factory.declare_free_function_name(tag)
ext_function = CodeFunction(function_name, output_format=return_format)
# creating argument copy
arg_map = {}
arg_index = 0
for arg in arg_list:
arg_tag = arg.get_tag(default="arg_%d" % arg_index)
arg_index += 1
arg_map[arg] = ext_function.add_input_variable(arg_tag,
arg.get_precision())
# extracting const table to make sure then are not duplicated
table_set = extract_tables(optree)
arg_map.update({table: table for table in table_set if table.const})
# copying optree while swapping argument for variables
optree_copy = optree.copy(copy_map=arg_map)
# instanciating external function scheme
if isinstance(optree, ML_ArithmeticOperation):
function_optree = Statement(Return(optree_copy))
else:
function_optree = Statement(optree_copy)
ext_function.set_scheme(function_optree)
name_factory.declare_function(function_name,
ext_function.get_function_object())
return ext_function
def generate_scheme(self):
# declaring function input variable
vx = self.implementation.add_input_variable("x", self.precision)
vy = self.implementation.add_input_variable("y", self.precision)
Cst0 = Constant(5, precision=self.precision)
Cst1 = Constant(7, precision=self.precision)
comp = Comparison(vx,
vy,
specifier=Comparison.Greater,
precision=ML_Bool,
tag="comp")
comp_eq = Comparison(vx,
vy,
specifier=Comparison.Equal,
precision=ML_Bool,
tag="comp_eq")
scheme = Statement(
ConditionBlock(
comp, Return(vy, precision=self.precision),
ConditionBlock(
comp_eq,
Return(vx + vy * Cst0 - Cst1, precision=self.precision))),
ConditionBlock(comp_eq, Return(Cst1 * vy,
precision=self.precision)),
Return(vx * vy, precision=self.precision))
return scheme
def ExpRaiseReturn(*args, **kwords):
kwords["arg_value"] = vx
kwords["function_name"] = self.function_name
if self.libm_compliant:
return RaiseReturn(*args, **kwords)
else:
return Statement()
def generate_test_wrapper(self, tensor_descriptors, input_tables,
output_tables):
auto_test = CodeFunction("test_wrapper", output_format=ML_Int32)
tested_function = self.implementation.get_function_object()
function_name = self.implementation.get_name()
failure_report_op = FunctionOperator("report_failure")
failure_report_function = FunctionObject("report_failure", [], ML_Void,
failure_report_op)
printf_success_op = FunctionOperator(
"printf",
arg_map={0: "\"test successful %s\\n\"" % function_name},
void_function=True,
require_header=["stdio.h"])
printf_success_function = FunctionObject("printf", [], ML_Void,
printf_success_op)
# accumulate element number
acc_num = Variable("acc_num",
precision=ML_Int64,
var_type=Variable.Local)
test_loop = self.get_tensor_test_wrapper(
tested_function, tensor_descriptors, input_tables, output_tables,
acc_num, self.generate_tensor_check_loop)
# common test scheme between scalar and vector functions
test_scheme = Statement(test_loop, printf_success_function(),
Return(Constant(0, precision=ML_Int32)))
auto_test.set_scheme(test_scheme)
return FunctionGroup([auto_test])
def simplify_condition_block(node):
assert isinstance(node, ConditionBlock)
cond = node.get_input(0)
if isinstance(cond, Constant):
if cond.get_value():
return Statement(
node.get_pre_statement(),
node.get_input(1)
)
elif len(node.inputs) >= 3:
return Statement(
node.get_pre_statement(),
node.get_input(2)
)
return None
def generate_scheme(self):
size_format = ML_Int32
# Matrix storage
in_storage = self.implementation.add_input_variable(
"buffer_in", ML_Pointer_Format(self.precision))
kernel_storage = self.implementation.add_input_variable(
"buffer_kernel", ML_Pointer_Format(self.precision))
out_storage = self.implementation.add_input_variable(
"buffer_out", ML_Pointer_Format(self.precision))
# Matrix sizes
w = self.implementation.add_input_variable("w", size_format)
h = self.implementation.add_input_variable("h", size_format)
# A is a (n x p) matrix in row-major
tIn = Tensor(in_storage,
TensorDescriptor([w, h], [1, w], self.precision))
# B is a (p x m) matrix in row-major
kernel_strides = [1]
for previous_dim in self.kernel_size[:-1]:
kernel_strides.append(previous_dim * kernel_strides[-1])
print("kernel_strides: {}".format(kernel_strides))
tKernel = Tensor(
kernel_storage,
TensorDescriptor(self.kernel_size, kernel_strides, self.precision))
# C is a (n x m) matrix in row-major
tOut = Tensor(out_storage,
TensorDescriptor([w, h], [1, w], self.precision))
index_format = ML_Int32
# main NDRange description
i = Variable("i", precision=index_format, var_type=Variable.Local)
j = Variable("j", precision=index_format, var_type=Variable.Local)
k_w = Variable("k_w", precision=index_format, var_type=Variable.Local)
k_h = Variable("k_h", precision=index_format, var_type=Variable.Local)
result = NDRange([IterRange(i, 0, w - 1),
IterRange(j, 0, h - 1)],
WriteAccessor(
tOut, [i, j],
Sum(Sum(Multiplication(
ReadAccessor(tIn, [i + k_w, j - k_h],
self.precision),
ReadAccessor(tKernel, [k_w, k_h],
self.precision)),
IterRange(k_w,
-(self.kernel_size[0] - 1) // 2,
(self.kernel_size[0] - 1) // 2),
precision=self.precision),
IterRange(k_h,
-(self.kernel_size[1] - 1) // 2,
(self.kernel_size[1] - 1) // 2),
precision=self.precision)))
mdl_scheme = expand_ndrange(result)
print("mdl_scheme:\n{}".format(mdl_scheme.get_str(depth=None)))
return Statement(mdl_scheme, Return())
def expand_kernel_expr(kernel, iterator_format=ML_Int32):
""" Expand a kernel expression into the corresponding MDL graph """
if isinstance(kernel, NDRange):
return expand_ndrange(kernel)
elif isinstance(kernel, Sum):
var_iter = kernel.index_iter_range.var_index
# TODO/FIXME to be uniquified
acc = Variable("acc",
var_type=Variable.Local,
precision=kernel.precision)
# TODO/FIXME implement proper acc init
if kernel.precision.is_vector_format():
C0 = Constant([0] * kernel.precision.get_vector_size(),
precision=kernel.precision)
else:
C0 = Constant(0, precision=kernel.precision)
scheme = Loop(
Statement(
ReferenceAssign(var_iter, kernel.index_iter_range.first_index),
ReferenceAssign(acc, C0)),
var_iter <= kernel.index_iter_range.last_index,
Statement(
ReferenceAssign(
acc,
Addition(acc,
expand_kernel_expr(kernel.elt_operation),
precision=kernel.precision)),
# loop iterator increment
ReferenceAssign(var_iter, var_iter +
kernel.index_iter_range.index_step)))
return PlaceHolder(acc, scheme)
elif isinstance(kernel, (ReadAccessor, WriteAccessor)):
return expand_accessor(kernel)
elif is_leaf_node(kernel):
return kernel
else:
# vanilla metalibm ops are left unmodified (except
# recursive expansion)
for index, op in enumerate(kernel.inputs):
new_op = expand_kernel_expr(op)
kernel.set_input(index, new_op)
return kernel
def generate_scheme(self):
var = self.implementation.add_input_variable("x", self.precision)
var_y = self.implementation.add_input_variable("y", self.precision)
var_z = self.implementation.add_input_variable("z", self.precision)
mult = Multiplication(var, var_z, precision=self.precision)
add = Addition(var_y, mult, precision=self.precision)
test_program = Statement(
add,
Return(add)
)
return test_program
def generate_scheme(self):
vx = self.implementation.add_input_variable("x", FIXED_FORMAT)
# declaring specific interval for input variable <x>
vx.set_interval(Interval(-1, 1))
acc_format = ML_Custom_FixedPoint_Format(6, 58, False)
c = Constant(2, precision=acc_format, tag="C2")
ivx = vx
add_ivx = Addition(
c,
Multiplication(ivx, ivx, precision=acc_format, tag="mul"),
precision=acc_format,
tag="add"
)
result = add_ivx
input_mapping = {ivx: ivx.get_precision().round_sollya_object(0.125)}
error_eval_map = runtime_error_eval.generate_error_eval_graph(result, input_mapping)
# dummy scheme to make functionnal code generation
scheme = Statement()
for node in error_eval_map:
scheme.add(error_eval_map[node])
scheme.add(Return(result))
return scheme
def generate_tensor_check_loop(self, tensor_descriptors, input_tables,
output_tables):
# unpack tensor descriptors tuple
(input_tensor_descriptor_list,
output_tensor_descriptor_list) = tensor_descriptors
# internal array iterator index
vj = Variable("j", precision=ML_UInt32, var_type=Variable.Local)
printf_error_detail_function = self.get_printf_error_detail_fct(
output_tensor_descriptor_list[0])
NUM_INPUT_ARRAY = len(input_tables)
# generate the expected table for the whole multi-array
expected_tables = self.generate_expected_table(tensor_descriptors,
input_tables)
# global statement to list all checks
check_statement = Statement()
# implement check for each output tensor
for out_id, out_td in enumerate(output_tensor_descriptor_list):
# expected values for the (vj)-th entry of the sub-array
expected_values = [
TableLoad(expected_tables[out_id], vj, i)
for i in range(self.accuracy.get_num_output_value())
]
# local result for the (vj)-th entry of the sub-array
local_result = TableLoad(output_tables[out_id], vj)
array_len = out_td.get_bounding_size()
if self.break_error:
return_statement_break = Statement(
printf_error_detail_function(*((vj, ) + (local_result, ))),
self.accuracy.get_output_print_call(
self.function_name, output_values))
else:
return_statement_break = Statement(
printf_error_detail_function(*((vj, ) + (local_result, ))),
self.accuracy.get_output_print_call(
self.function_name, expected_values),
Return(Constant(1, precision=ML_Int32)))
check_array_loop = Loop(
ReferenceAssign(vj, 0), vj < array_len,
Statement(
ConditionBlock(
self.accuracy.get_output_check_test(
local_result, expected_values),
return_statement_break),
ReferenceAssign(vj, vj + 1),
))
check_statement.add(check_array_loop)
return check_statement
def generate_scalar_scheme(self, vx, vy):
div = Division(vx, vy, precision=self.precision)
div_if = Trunc(div, precision=self.precision)
rem = Variable("rem",
var_type=Variable.Local,
precision=self.precision)
qi = Variable("qi", var_type=Variable.Local, precision=self.precision)
qi_bound = Constant(S2**self.precision.get_mantissa_size())
init_rem = FusedMultiplyAdd(-div_if, vy, vx)
# factorizing 1 / vy to save time
# NOTES: it makes rem / vy approximate
# shared_rcp = Division(1, vy, precision=self.precision)
iterative_fmod = Loop(
Statement(
ReferenceAssign(rem, init_rem),
ReferenceAssign(qi, div_if),
),
Abs(qi) > qi_bound,
Statement(
ReferenceAssign(
qi,
#Trunc(shared_rcp * rem, precision=self.precision)
Trunc(rem / vy, precision=self.precision)),
ReferenceAssign(rem, FMA(-qi, vy, rem))))
scheme = Statement(
rem,
# shared_rcp,
iterative_fmod,
ConditionBlock(
# if rem's sign and vx sign mismatch
(rem * vx < 0.0).modify_attributes(tag="update_cond",
debug=debug_multi),
Return(rem + vy),
Return(rem),
))
return scheme
def generate_scheme(self):
size_format = ML_Int32
# Matrix storage
A_storage = self.implementation.add_input_variable("buffer_a", ML_Pointer_Format(self.precision))
B_storage = self.implementation.add_input_variable("buffer_b", ML_Pointer_Format(self.precision))
C_storage = self.implementation.add_input_variable("buffer_c", ML_Pointer_Format(self.precision))
# Matrix sizes
n = self.implementation.add_input_variable("n", size_format)
m = self.implementation.add_input_variable("m", size_format)
p = self.implementation.add_input_variable("p", size_format)
# A is a (n x p) matrix in row-major
tA = Tensor(A_storage, TensorDescriptor([p, n], [1, p], self.precision))
# B is a (p x m) matrix in row-major
tB = Tensor(B_storage, TensorDescriptor([m, p], [1, m], self.precision))
# C is a (n x m) matrix in row-major
tC = Tensor(C_storage, TensorDescriptor([m, n], [1, m], self.precision))
index_format = ML_Int32
#
i = Variable("i", precision=index_format, var_type=Variable.Local)
j = Variable("j", precision=index_format, var_type=Variable.Local)
k = Variable("k", precision=index_format, var_type=Variable.Local)
result = NDRange(
[IterRange(j, 0, m-1), IterRange(i, 0, n -1)],
WriteAccessor(
tC, [j, i],
Sum(
Multiplication(
ReadAccessor(tA, [k, i], self.precision),
ReadAccessor(tB, [j, k], self.precision),
precision=self.precision),
IterRange(k, 0, p - 1),
precision=self.precision)))
#mdl_scheme = expand_ndrange(exchange_loop_order(tile_ndrange(result, {j: 2, i: 2}), [1, 0]))
if self.vectorize:
mdl_scheme = expand_ndrange(vectorize_ndrange(result, j, 4))
else:
mdl_scheme = expand_ndrange(exchange_loop_order(tile_ndrange(result, {j: 2, i: 2}), [1, 0]))
print("mdl_scheme:\n{}".format(mdl_scheme.get_str(depth=None, display_precision=True)))
return Statement(
mdl_scheme,
Return()
)
def instanciate_graph(self,
op_graph,
memoization_map=None,
expand_div=False):
""" instanciate function graph, replacing FunctionCall node
by expanded function implementation """
memoization_map = memoization_map or {}
statement = Statement()
def rec_instanciate(node):
""" recursive internal function for function graph instanciation """
new_node = None
if node in memoization_map:
return memoization_map[node]
elif isinstance(node, FunctionCall):
# recursively going through the input graph of FunctionCall for
# instanciation
for arg_index in range(node.get_function_object().arity):
input_node = rec_instanciate(node.get_input(arg_index))
if not input_node is None:
node.set_input(arg_index, input_node)
result_var, fct_scheme = instanciate_fct_call(
node, self.precision)
statement.add(
result_var
) # making sure result var is declared previously
statement.add(fct_scheme)
new_node = result_var
new_node.set_interval(node.get_interval())
elif isinstance(node, Division) and expand_div:
new_node = FUNCTION_OBJECT_MAPPING["div"](node.get_input(0),
node.get_input(1))
new_node.set_attributes(precision=node.get_precision(),
interval=node.get_interval())
new_node = rec_instanciate(new_node)
elif is_leaf_node(node):
# unmodified
new_node = None
else:
for index, op in enumerate(node.get_inputs()):
new_op = rec_instanciate(op)
if not new_op is None:
node.set_input(index, new_op)
statement.add(node)
memoization_map[node] = new_node
return new_node
final_node = rec_instanciate(op_graph) or op_graph
return final_node, statement
def generate_scheme(self):
# declare a new input parameters vx whose tag is "x" and
# whose format is single precision
vx = self.implementation.add_input_variable("x", self.get_input_precision(0))
# declare a new input parameters vy whose tag is "y" and
# whose format is single precision
vy = self.implementation.add_input_variable("x", self.get_input_precision(0))
# declare main operation graph for the meta-function:
# a single Statement containing a single return statement which
# the addition of the two inputs variable in single-precision
main_scheme = Statement(
Return(vx + vy, precision=ML_Binary32)
)
return main_scheme
def generate_pipeline_stage(entity):
""" Process a entity to generate pipeline stages required """
retiming_map = {}
retime_map = RetimeMap()
output_assign_list = entity.implementation.get_output_assign()
for output in output_assign_list:
Log.report(
Log.Verbose,
"generating pipeline from output %s " % (output.get_str(depth=1)))
retime_op(output, retime_map)
process_statement = Statement()
# adding stage forward process
clk = entity.get_clk_input()
clock_statement = Statement()
for stage_id in sorted(retime_map.stage_forward.keys()):
stage_statement = Statement(*tuple(
assign for assign in retime_map.stage_forward[stage_id]))
clock_statement.add(stage_statement)
# To meet simulation / synthesis tools, we build
# a single if clock predicate block which contains all
# the stage register allocation
clock_block = ConditionBlock(
LogicalAnd(Event(clk, precision=ML_Bool),
Comparison(clk,
Constant(1, precision=ML_StdLogic),
specifier=Comparison.Equal,
precision=ML_Bool),
precision=ML_Bool), clock_statement)
process_statement.add(clock_block)
pipeline_process = Process(process_statement, sensibility_list=[clk])
for op in retime_map.pre_statement:
pipeline_process.add_to_pre_statement(op)
entity.implementation.add_process(pipeline_process)
stage_num = len(retime_map.stage_forward.keys())
#print "there are %d pipeline stages" % (stage_num)
return stage_num
def get_tensor_test_wrapper(self,
tested_function,
tensor_descriptors,
input_tables,
output_tables,
acc_num,
post_statement_generator,
NUM_INPUT_ARRAY=1):
""" generate a test loop for multi-array tests
@param test_num number of elementary array tests to be executed
@param tested_function FunctionObject to be tested
@param table_size_offset_array ML_NewTable object containing
(table-size, offset) pairs for multi-array testing
@param input_table ML_NewTable containing multi-array test inputs
@param output_table ML_NewTable containing multi-array test outputs
@param post_statement_generator is generator used to generate
a statement executed at the end of the test of one of the
arrays of the multi-test. It expects 6 arguments:
(input_tables, output_array, table_size_offset_array,
array_offset, array_len, test_id)
@param printf_function FunctionObject to print error case
"""
array_len = Variable("len",
precision=ML_UInt32,
var_type=Variable.Local)
def pointer_add(table_addr, offset):
pointer_format = table_addr.get_precision_as_pointer_format()
return Addition(table_addr, offset, precision=pointer_format)
array_inputs = tuple(input_tables[in_id]
for in_id in range(NUM_INPUT_ARRAY))
function_call = tested_function(*(self.get_ordered_arg_tuple(
tensor_descriptors, input_tables, output_tables)))
post_statement = post_statement_generator(tensor_descriptors,
input_tables, output_tables)
test_statement = Statement(
function_call,
post_statement,
)
return test_statement
def generate_emulate(self, result_ternary, result, mpfr_x, mpfr_rnd):
""" generate the emulation code for ML_Log2 functions
mpfr_x is a mpfr_t variable which should have the right precision
mpfr_rnd is the rounding mode
"""
emulate_func_name = "mpfr_exp"
emulate_func_op = FunctionOperator(emulate_func_name,
arg_map={
0: FO_Arg(0),
1: FO_Arg(1),
2: FO_Arg(2)
},
require_header=["mpfr.h"])
emulate_func = FunctionObject(emulate_func_name,
[ML_Mpfr_t, ML_Mpfr_t, ML_Int32],
ML_Int32, emulate_func_op)
mpfr_call = Statement(
ReferenceAssign(result_ternary,
emulate_func(result, mpfr_x, mpfr_rnd)))
return mpfr_call
def vectorize_function_scheme(vectorizer,
name_factory,
scalar_scheme,
scalar_output_format,
scalar_arg_list,
vector_size,
sub_vector_size=None):
""" Use a vectorization engine @p vectorizer to vectorize the sub-graph @p
scalar_scheme, that is transforming and inputs and outputs from scalar
to vectors and performing required internal path duplication """
sub_vector_size = vector_size if sub_vector_size is None else sub_vector_size
vec_arg_list, vector_scheme, vector_mask = \
vectorizer.vectorize_scheme(scalar_scheme, scalar_arg_list,
vector_size, sub_vector_size)
vector_output_format = vectorize_format(scalar_output_format, vector_size)
vec_res = Variable("vec_res",
precision=vector_output_format,
var_type=Variable.Local)
vector_mask.set_attributes(tag="vector_mask", debug=debug_multi)
callback_name = "scalar_callback"
scalar_callback_fct = generate_function_from_optree(
name_factory, scalar_scheme, scalar_arg_list, callback_name,
scalar_output_format)
scalar_callback = scalar_callback_fct.get_function_object()
if no_scalar_fallback_required(vector_mask):
function_scheme = Statement(
Return(vector_scheme, precision=vector_output_format))
function_scheme = generate_c_vector_wrapper(vector_size, vec_arg_list,
vector_scheme, vector_mask,
vec_res, scalar_callback)
return vec_res, vec_arg_list, function_scheme, scalar_callback, scalar_callback_fct
def convert_bit_heap_to_fixed_point(current_bit_heap, signed=False):
# final propagating sum
op_index = 0
op_list = []
op_statement = Statement()
while current_bit_heap.max_count() > 0:
op_size = current_bit_heap.max_index - current_bit_heap.min_index + 1
op_format = ML_StdLogicVectorFormat(op_size)
op_reduce = Signal("op_%d" % op_index,
precision=op_format,
var_type=Variable.Local)
offset_index = current_bit_heap.min_index
for index in range(current_bit_heap.min_index,
current_bit_heap.max_index + 1):
out_index = index - offset_index
bit_list = current_bit_heap.pop_bits(index, 1)
if len(bit_list) == 0:
op_statement.push(
ReferenceAssign(BitSelection(op_reduce, out_index),
Constant(0, precision=ML_StdLogic)))
else:
assert len(bit_list) == 1
op_statement.push(
ReferenceAssign(BitSelection(op_reduce, out_index),
bit_list[0]))
op_precision = fixed_point(op_size + offset_index,
-offset_index,
signed=signed)
op_list.append(
PlaceHolder(TypeCast(op_reduce, precision=op_precision),
op_statement))
op_index += 1
return op_list, op_statement
def generate_scheme(self):
# declaring target and instantiating optimization engine
vx = self.implementation.add_input_variable("x", self.precision)
Log.set_dump_stdout(True)
Log.report(Log.Info,
"\033[33;1m generating implementation scheme \033[0m")
if self.debug_flag:
Log.report(Log.Info, "\033[31;1m debug has been enabled \033[0;m")
# local overloading of RaiseReturn operation
def ExpRaiseReturn(*args, **kwords):
kwords["arg_value"] = vx
kwords["function_name"] = self.function_name
if self.libm_compliant:
return RaiseReturn(*args, precision=self.precision, **kwords)
else:
return Return(kwords["return_value"], precision=self.precision)
test_nan_or_inf = Test(vx,
specifier=Test.IsInfOrNaN,
likely=False,
debug=debug_multi,
tag="nan_or_inf")
test_nan = Test(vx,
specifier=Test.IsNaN,
debug=debug_multi,
tag="is_nan_test")
test_positive = Comparison(vx,
0,
specifier=Comparison.GreaterOrEqual,
debug=debug_multi,
tag="inf_sign")
test_signaling_nan = Test(vx,
specifier=Test.IsSignalingNaN,
debug=debug_multi,
tag="is_signaling_nan")
return_snan = Statement(
ExpRaiseReturn(ML_FPE_Invalid,
return_value=FP_QNaN(self.precision)))
# return in case of infinity input
infty_return = Statement(
ConditionBlock(
test_positive,
Return(FP_PlusInfty(self.precision), precision=self.precision),
Return(FP_PlusZero(self.precision), precision=self.precision)))
# return in case of specific value input (NaN or inf)
specific_return = ConditionBlock(
test_nan,
ConditionBlock(
test_signaling_nan, return_snan,
Return(FP_QNaN(self.precision), precision=self.precision)),
infty_return)
# return in case of standard (non-special) input
# exclusion of early overflow and underflow cases
precision_emax = self.precision.get_emax()
precision_max_value = S2 * S2**precision_emax
exp_overflow_bound = sollya.ceil(log(precision_max_value))
early_overflow_test = Comparison(vx,
exp_overflow_bound,
likely=False,
specifier=Comparison.Greater)
early_overflow_return = Statement(
ClearException() if self.libm_compliant else Statement(),
ExpRaiseReturn(ML_FPE_Inexact,
ML_FPE_Overflow,
return_value=FP_PlusInfty(self.precision)))
precision_emin = self.precision.get_emin_subnormal()
precision_min_value = S2**precision_emin
exp_underflow_bound = floor(log(precision_min_value))
early_underflow_test = Comparison(vx,
exp_underflow_bound,
likely=False,
specifier=Comparison.Less)
early_underflow_return = Statement(
ClearException() if self.libm_compliant else Statement(),
ExpRaiseReturn(ML_FPE_Inexact,
ML_FPE_Underflow,
return_value=FP_PlusZero(self.precision)))
# constant computation
invlog2 = self.precision.round_sollya_object(1 / log(2), sollya.RN)
interval_vx = Interval(exp_underflow_bound, exp_overflow_bound)
interval_fk = interval_vx * invlog2
interval_k = Interval(floor(inf(interval_fk)),
sollya.ceil(sup(interval_fk)))
log2_hi_precision = self.precision.get_field_size() - (
sollya.ceil(log2(sup(abs(interval_k)))) + 2)
Log.report(Log.Info, "log2_hi_precision: %d" % log2_hi_precision)
invlog2_cst = Constant(invlog2, precision=self.precision)
log2_hi = round(log(2), log2_hi_precision, sollya.RN)
log2_lo = self.precision.round_sollya_object(
log(2) - log2_hi, sollya.RN)
# argument reduction
unround_k = vx * invlog2
unround_k.set_attributes(tag="unround_k", debug=debug_multi)
k = NearestInteger(unround_k,
precision=self.precision,
debug=debug_multi)
ik = NearestInteger(unround_k,
precision=self.precision.get_integer_format(),
debug=debug_multi,
tag="ik")
ik.set_tag("ik")
k.set_tag("k")
exact_pre_mul = (k * log2_hi)
exact_pre_mul.set_attributes(exact=True)
exact_hi_part = vx - exact_pre_mul
exact_hi_part.set_attributes(exact=True,
tag="exact_hi",
debug=debug_multi,
prevent_optimization=True)
exact_lo_part = -k * log2_lo
exact_lo_part.set_attributes(tag="exact_lo",
debug=debug_multi,
prevent_optimization=True)
r = exact_hi_part + exact_lo_part
r.set_tag("r")
r.set_attributes(debug=debug_multi)
approx_interval = Interval(-log(2) / 2, log(2) / 2)
approx_interval_half = approx_interval / 2
approx_interval_split = [
Interval(-log(2) / 2, inf(approx_interval_half)),
approx_interval_half,
Interval(sup(approx_interval_half),
log(2) / 2)
]
# TODO: should be computed automatically
exact_hi_interval = approx_interval
exact_lo_interval = -interval_k * log2_lo
opt_r = self.optimise_scheme(r, copy={})
tag_map = {}
self.opt_engine.register_nodes_by_tag(opt_r, tag_map)
cg_eval_error_copy_map = {
vx:
Variable("x", precision=self.precision, interval=interval_vx),
tag_map["k"]:
Variable("k", interval=interval_k, precision=self.precision)
}
#try:
if is_gappa_installed():
eval_error = self.gappa_engine.get_eval_error_v2(
self.opt_engine,
opt_r,
cg_eval_error_copy_map,
gappa_filename="red_arg.g")
else:
eval_error = 0.0
Log.report(Log.Warning,
"gappa is not installed in this environnement")
Log.report(Log.Info, "eval error: %s" % eval_error)
local_ulp = sup(ulp(sollya.exp(approx_interval), self.precision))
# FIXME refactor error_goal from accuracy
Log.report(Log.Info, "accuracy: %s" % self.accuracy)
if isinstance(self.accuracy, ML_Faithful):
error_goal = local_ulp
elif isinstance(self.accuracy, ML_CorrectlyRounded):
error_goal = S2**-1 * local_ulp
elif isinstance(self.accuracy, ML_DegradedAccuracyAbsolute):
error_goal = self.accuracy.goal
elif isinstance(self.accuracy, ML_DegradedAccuracyRelative):
error_goal = self.accuracy.goal
else:
Log.report(Log.Error, "unknown accuracy: %s" % self.accuracy)
# error_goal = local_ulp #S2**-(self.precision.get_field_size()+1)
error_goal_approx = S2**-1 * error_goal
Log.report(Log.Info,
"\033[33;1m building mathematical polynomial \033[0m\n")
poly_degree = max(
sup(
guessdegree(
expm1(sollya.x) / sollya.x, approx_interval,
error_goal_approx)) - 1, 2)
init_poly_degree = poly_degree
error_function = lambda p, f, ai, mod, t: dirtyinfnorm(f - p, ai)
polynomial_scheme_builder = PolynomialSchemeEvaluator.generate_estrin_scheme
#polynomial_scheme_builder = PolynomialSchemeEvaluator.generate_horner_scheme
while 1:
Log.report(Log.Info, "attempting poly degree: %d" % poly_degree)
precision_list = [1] + [self.precision] * (poly_degree)
poly_object, poly_approx_error = Polynomial.build_from_approximation_with_error(
expm1(sollya.x),
poly_degree,
precision_list,
approx_interval,
sollya.absolute,
error_function=error_function)
Log.report(Log.Info, "polynomial: %s " % poly_object)
sub_poly = poly_object.sub_poly(start_index=2)
Log.report(Log.Info, "polynomial: %s " % sub_poly)
Log.report(Log.Info, "poly approx error: %s" % poly_approx_error)
Log.report(
Log.Info,
"\033[33;1m generating polynomial evaluation scheme \033[0m")
pre_poly = polynomial_scheme_builder(
poly_object, r, unified_precision=self.precision)
pre_poly.set_attributes(tag="pre_poly", debug=debug_multi)
pre_sub_poly = polynomial_scheme_builder(
sub_poly, r, unified_precision=self.precision)
pre_sub_poly.set_attributes(tag="pre_sub_poly", debug=debug_multi)
poly = 1 + (exact_hi_part + (exact_lo_part + pre_sub_poly))
poly.set_tag("poly")
# optimizing poly before evaluation error computation
#opt_poly = self.opt_engine.optimization_process(poly, self.precision, fuse_fma = fuse_fma)
#opt_sub_poly = self.opt_engine.optimization_process(pre_sub_poly, self.precision, fuse_fma = fuse_fma)
opt_poly = self.optimise_scheme(poly)
opt_sub_poly = self.optimise_scheme(pre_sub_poly)
# evaluating error of the polynomial approximation
r_gappa_var = Variable("r",
precision=self.precision,
interval=approx_interval)
exact_hi_gappa_var = Variable("exact_hi",
precision=self.precision,
interval=exact_hi_interval)
exact_lo_gappa_var = Variable("exact_lo",
precision=self.precision,
interval=exact_lo_interval)
vx_gappa_var = Variable("x",
precision=self.precision,
interval=interval_vx)
k_gappa_var = Variable("k",
interval=interval_k,
precision=self.precision)
#print "exact_hi interval: ", exact_hi_interval
sub_poly_error_copy_map = {
#r.get_handle().get_node(): r_gappa_var,
#vx.get_handle().get_node(): vx_gappa_var,
exact_hi_part.get_handle().get_node():
exact_hi_gappa_var,
exact_lo_part.get_handle().get_node():
exact_lo_gappa_var,
#k.get_handle().get_node(): k_gappa_var,
}
poly_error_copy_map = {
exact_hi_part.get_handle().get_node(): exact_hi_gappa_var,
exact_lo_part.get_handle().get_node(): exact_lo_gappa_var,
}
if is_gappa_installed():
sub_poly_eval_error = -1.0
sub_poly_eval_error = self.gappa_engine.get_eval_error_v2(
self.opt_engine,
opt_sub_poly,
sub_poly_error_copy_map,
gappa_filename="%s_gappa_sub_poly.g" % self.function_name)
dichotomy_map = [
{
exact_hi_part.get_handle().get_node():
approx_interval_split[0],
},
{
exact_hi_part.get_handle().get_node():
approx_interval_split[1],
},
{
exact_hi_part.get_handle().get_node():
approx_interval_split[2],
},
]
poly_eval_error_dico = self.gappa_engine.get_eval_error_v3(
self.opt_engine,
opt_poly,
poly_error_copy_map,
gappa_filename="gappa_poly.g",
dichotomy=dichotomy_map)
poly_eval_error = max(
[sup(abs(err)) for err in poly_eval_error_dico])
else:
poly_eval_error = 0.0
sub_poly_eval_error = 0.0
Log.report(Log.Warning,
"gappa is not installed in this environnement")
Log.report(Log.Info, "stopping autonomous degree research")
# incrementing polynomial degree to counteract initial decrementation effect
poly_degree += 1
break
Log.report(Log.Info, "poly evaluation error: %s" % poly_eval_error)
Log.report(Log.Info,
"sub poly evaluation error: %s" % sub_poly_eval_error)
global_poly_error = None
global_rel_poly_error = None
for case_index in range(3):
poly_error = poly_approx_error + poly_eval_error_dico[
case_index]
rel_poly_error = sup(
abs(poly_error /
sollya.exp(approx_interval_split[case_index])))
if global_rel_poly_error == None or rel_poly_error > global_rel_poly_error:
global_rel_poly_error = rel_poly_error
global_poly_error = poly_error
flag = error_goal > global_rel_poly_error
if flag:
break
else:
poly_degree += 1
late_overflow_test = Comparison(ik,
self.precision.get_emax(),
specifier=Comparison.Greater,
likely=False,
debug=debug_multi,
tag="late_overflow_test")
overflow_exp_offset = (self.precision.get_emax() -
self.precision.get_field_size() / 2)
diff_k = Subtraction(
ik,
Constant(overflow_exp_offset,
precision=self.precision.get_integer_format()),
precision=self.precision.get_integer_format(),
debug=debug_multi,
tag="diff_k",
)
late_overflow_result = (ExponentInsertion(
diff_k, precision=self.precision) * poly) * ExponentInsertion(
overflow_exp_offset, precision=self.precision)
late_overflow_result.set_attributes(silent=False,
tag="late_overflow_result",
debug=debug_multi,
precision=self.precision)
late_overflow_return = ConditionBlock(
Test(late_overflow_result, specifier=Test.IsInfty, likely=False),
ExpRaiseReturn(ML_FPE_Overflow,
return_value=FP_PlusInfty(self.precision)),
Return(late_overflow_result, precision=self.precision))
late_underflow_test = Comparison(k,
self.precision.get_emin_normal(),
specifier=Comparison.LessOrEqual,
likely=False)
underflow_exp_offset = 2 * self.precision.get_field_size()
corrected_exp = Addition(
ik,
Constant(underflow_exp_offset,
precision=self.precision.get_integer_format()),
precision=self.precision.get_integer_format(),
tag="corrected_exp")
late_underflow_result = (
ExponentInsertion(corrected_exp, precision=self.precision) *
poly) * ExponentInsertion(-underflow_exp_offset,
precision=self.precision)
late_underflow_result.set_attributes(debug=debug_multi,
tag="late_underflow_result",
silent=False)
test_subnormal = Test(late_underflow_result,
specifier=Test.IsSubnormal)
late_underflow_return = Statement(
ConditionBlock(
test_subnormal,
ExpRaiseReturn(ML_FPE_Underflow,
return_value=late_underflow_result)),
Return(late_underflow_result, precision=self.precision))
twok = ExponentInsertion(ik,
tag="exp_ik",
debug=debug_multi,
precision=self.precision)
#std_result = twok * ((1 + exact_hi_part * pre_poly) + exact_lo_part * pre_poly)
std_result = twok * poly
std_result.set_attributes(tag="std_result", debug=debug_multi)
result_scheme = ConditionBlock(
late_overflow_test, late_overflow_return,
ConditionBlock(late_underflow_test, late_underflow_return,
Return(std_result, precision=self.precision)))
std_return = ConditionBlock(
early_overflow_test, early_overflow_return,
ConditionBlock(early_underflow_test, early_underflow_return,
result_scheme))
# main scheme
Log.report(Log.Info, "\033[33;1m MDL scheme \033[0m")
scheme = ConditionBlock(
test_nan_or_inf,
Statement(ClearException() if self.libm_compliant else Statement(),
specific_return), std_return)
return scheme
def generate_auto_test(self,
test_num=10,
test_range=Interval(-1.0, 1.0),
debug=False,
time_step=10):
""" time_step: duration of a stage (in ns) """
# instanciating tested component
# map of input_tag -> input_signal and output_tag -> output_signal
io_map = {}
# map of input_tag -> input_signal, excludind commodity signals
# (e.g. clock and reset)
input_signals = {}
# map of output_tag -> output_signal
output_signals = {}
# excluding clock and reset signals from argument list
# reduced_arg_list = [input_port for input_port in self.implementation.get_arg_list() if not input_port.get_tag() in ["clk", "reset"]]
reduced_arg_list = self.implementation.get_arg_list()
for input_port in reduced_arg_list:
input_tag = input_port.get_tag()
input_signal = Signal(input_tag + "_i",
precision=input_port.get_precision(),
var_type=Signal.Local)
io_map[input_tag] = input_signal
if not input_tag in ["clk", "reset"]:
input_signals[input_tag] = input_signal
for output_port in self.implementation.get_output_port():
output_tag = output_port.get_tag()
output_signal = Signal(output_tag + "_o",
precision=output_port.get_precision(),
var_type=Signal.Local)
io_map[output_tag] = output_signal
output_signals[output_tag] = output_signal
# building list of test cases
tc_list = []
self_component = self.implementation.get_component_object()
self_instance = self_component(io_map=io_map, tag="tested_entity")
test_statement = Statement()
# initializing random test case generator
self.init_test_generator()
# Appending standard test cases if required
if self.auto_test_std:
tc_list += self.standard_test_cases
for i in range(test_num):
input_values = self.generate_test_case(input_signals, io_map, i,
test_range)
tc_list.append((input_values, None))
def compute_results(tc):
""" update test case with output values if required """
input_values, output_values = tc
if output_values is None:
return input_values, self.numeric_emulate(input_values)
else:
return tc
# filling output values
tc_list = [compute_results(tc) for tc in tc_list]
for input_values, output_values in tc_list:
test_statement.add(
self.implement_test_case(io_map, input_values, output_signals,
output_values, time_step))
testbench = CodeEntity("testbench")
test_process = Process(
test_statement,
# end of test
Assert(Constant(0, precision=ML_Bool),
" \"end of test, no error encountered \"",
severity=Assert.Failure))
testbench_scheme = Statement(self_instance, test_process)
if self.pipelined:
half_time_step = time_step / 2
assert (half_time_step * 2) == time_step
# adding clock process for pipelined bench
clk_process = Process(
Statement(
ReferenceAssign(io_map["clk"],
Constant(1, precision=ML_StdLogic)),
Wait(half_time_step),
ReferenceAssign(io_map["clk"],
Constant(0, precision=ML_StdLogic)),
Wait(half_time_step),
))
testbench_scheme.push(clk_process)
testbench.add_process(testbench_scheme)
return [testbench]
def __init__(self, *args, **kw):
Statement.__init__(self, *args, **kw)
# indicate that the current basic block is final (end with
# a Return like statement)
self.final = False
def generate_scheme(self):
# declaring CodeFunction and retrieving input variable
vx = self.implementation.add_input_variable("x", self.precision)
table_size_log = self.table_size_log
integer_size = 31
integer_precision = ML_Int32
max_bound = sup(abs(self.input_intervals[0]))
max_bound_log = int(ceil(log2(max_bound)))
Log.report(Log.Info, "max_bound_log=%s " % max_bound_log)
scaling_power = integer_size - max_bound_log
Log.report(Log.Info, "scaling power: %s " % scaling_power)
storage_precision = ML_Custom_FixedPoint_Format(1, 30, signed=True)
Log.report(Log.Info, "tabulating cosine and sine")
# cosine and sine fused table
fused_table = ML_NewTable(
dimensions=[2**table_size_log, 2],
storage_precision=storage_precision,
tag="fast_lib_shared_table") # self.uniquify_name("cossin_table"))
# filling table
for i in range(2**table_size_log):
local_x = i / S2**table_size_log * S2**max_bound_log
cos_local = cos(
local_x
) # nearestint(cos(local_x) * S2**storage_precision.get_frac_size())
sin_local = sin(
local_x
) # nearestint(sin(local_x) * S2**storage_precision.get_frac_size())
fused_table[i][0] = cos_local
fused_table[i][1] = sin_local
# argument reduction evaluation scheme
# scaling_factor = Constant(S2**scaling_power, precision = self.precision)
red_vx_precision = ML_Custom_FixedPoint_Format(31 - scaling_power,
scaling_power,
signed=True)
Log.report(
Log.Verbose, "red_vx_precision.get_c_bit_size()=%d" %
red_vx_precision.get_c_bit_size())
# red_vx = NearestInteger(vx * scaling_factor, precision = integer_precision)
red_vx = Conversion(vx,
precision=red_vx_precision,
tag="red_vx",
debug=debug_fixed32)
computation_precision = red_vx_precision # self.precision
output_precision = self.get_output_precision()
Log.report(Log.Info,
"computation_precision is %s" % computation_precision)
Log.report(Log.Info, "storage_precision is %s" % storage_precision)
Log.report(Log.Info, "output_precision is %s" % output_precision)
hi_mask_value = 2**32 - 2**(32 - table_size_log - 1)
hi_mask = Constant(hi_mask_value, precision=ML_Int32)
Log.report(Log.Info, "hi_mask=0x%x" % hi_mask_value)
red_vx_hi_int = BitLogicAnd(TypeCast(red_vx, precision=ML_Int32),
hi_mask,
precision=ML_Int32,
tag="red_vx_hi_int",
debug=debugd)
red_vx_hi = TypeCast(red_vx_hi_int,
precision=red_vx_precision,
tag="red_vx_hi",
debug=debug_fixed32)
red_vx_lo = red_vx - red_vx_hi
red_vx_lo.set_attributes(precision=red_vx_precision,
tag="red_vx_lo",
debug=debug_fixed32)
table_index = BitLogicRightShift(TypeCast(red_vx, precision=ML_Int32),
scaling_power -
(table_size_log - max_bound_log),
precision=ML_Int32,
tag="table_index",
debug=debugd)
tabulated_cos = TableLoad(fused_table,
table_index,
0,
tag="tab_cos",
precision=storage_precision,
debug=debug_fixed32)
tabulated_sin = TableLoad(fused_table,
table_index,
1,
tag="tab_sin",
precision=storage_precision,
debug=debug_fixed32)
error_function = lambda p, f, ai, mod, t: dirtyinfnorm(f - p, ai)
Log.report(Log.Info, "building polynomial approximation for cosine")
# cosine polynomial approximation
poly_interval = Interval(0, S2**(max_bound_log - table_size_log))
Log.report(Log.Info, "poly_interval=%s " % poly_interval)
cos_poly_degree = 2 # int(sup(guessdegree(cos(x), poly_interval, accuracy_goal)))
Log.report(Log.Verbose, "cosine polynomial approximation")
cos_poly_object, cos_approx_error = Polynomial.build_from_approximation_with_error(
cos(sollya.x), [0, 2],
[0] + [computation_precision.get_bit_size()],
poly_interval,
sollya.absolute,
error_function=error_function)
#cos_eval_scheme = PolynomialSchemeEvaluator.generate_horner_scheme(cos_poly_object, red_vx_lo, unified_precision = computation_precision)
Log.report(Log.Info, "cos_approx_error=%e" % cos_approx_error)
cos_coeff_list = cos_poly_object.get_ordered_coeff_list()
coeff_C0 = cos_coeff_list[0][1]
coeff_C2 = Constant(cos_coeff_list[1][1],
precision=ML_Custom_FixedPoint_Format(-1,
32,
signed=True))
Log.report(Log.Info, "building polynomial approximation for sine")
# sine polynomial approximation
sin_poly_degree = 2 # int(sup(guessdegree(sin(x)/x, poly_interval, accuracy_goal)))
Log.report(Log.Info, "sine poly degree: %e" % sin_poly_degree)
Log.report(Log.Verbose, "sine polynomial approximation")
sin_poly_object, sin_approx_error = Polynomial.build_from_approximation_with_error(
sin(sollya.x) / sollya.x, [0, 2], [0] +
[computation_precision.get_bit_size()] * (sin_poly_degree + 1),
poly_interval,
sollya.absolute,
error_function=error_function)
sin_coeff_list = sin_poly_object.get_ordered_coeff_list()
coeff_S0 = sin_coeff_list[0][1]
coeff_S2 = Constant(sin_coeff_list[1][1],
precision=ML_Custom_FixedPoint_Format(-1,
32,
signed=True))
# scheme selection between sine and cosine
if self.cos_output:
scheme = self.generate_cos_scheme(computation_precision,
tabulated_cos, tabulated_sin,
coeff_S2, coeff_C2, red_vx_lo)
else:
scheme = self.generate_sin_scheme(computation_precision,
tabulated_cos, tabulated_sin,
coeff_S2, coeff_C2, red_vx_lo)
result = Conversion(scheme, precision=self.get_output_precision())
Log.report(
Log.Verbose, "result operation tree :\n %s " % result.get_str(
display_precision=True, depth=None, memoization_map={}))
scheme = Statement(Return(result))
return scheme
def generate_pipeline_stage(entity,
reset=False,
recirculate=False,
one_process_per_stage=True):
""" Process a entity to generate pipeline stages required """
retiming_map = {}
retime_map = RetimeMap()
output_assign_list = entity.implementation.get_output_assign()
for output in output_assign_list:
Log.report(Log.Verbose, "generating pipeline from output {} ", output)
retime_op(output, retime_map)
for recirculate_stage in entity.recirculate_signal_map:
recirculate_ctrl = entity.recirculate_signal_map[recirculate_stage]
Log.report(Log.Verbose,
"generating pipeline from recirculation control signal {}",
recirculate_ctrl)
retime_op(recirculate_ctrl, retime_map)
process_statement = Statement()
# adding stage forward process
clk = entity.get_clk_input()
clock_statement = Statement()
# handle towards the first clock Process (in generation order)
# which must be the one whose pre_statement is filled with
# signal required to be generated outside the processes
first_process = False
for stage_id in sorted(retime_map.stage_forward.keys()):
stage_statement = Statement(*tuple(
assign for assign in retime_map.stage_forward[stage_id]))
if reset:
reset_statement = Statement()
for assign in retime_map.stage_forward[stage_id]:
target = assign.get_input(0)
reset_value = Constant(0, precision=target.get_precision())
reset_statement.push(ReferenceAssign(target, reset_value))
if recirculate:
# inserting recirculation condition
recirculate_signal = entity.get_recirculate_signal(stage_id)
stage_statement = ConditionBlock(
Comparison(
recirculate_signal,
Constant(0,
precision=recirculate_signal.get_precision()),
specifier=Comparison.Equal,
precision=ML_Bool), stage_statement)
stage_statement = ConditionBlock(
Comparison(entity.reset_signal,
Constant(1, precision=ML_StdLogic),
specifier=Comparison.Equal,
precision=ML_Bool), reset_statement,
stage_statement)
# To meet simulation / synthesis tools, we build
# a single if clock predicate block per stage
clock_block = ConditionBlock(
LogicalAnd(Event(clk, precision=ML_Bool),
Comparison(clk,
Constant(1, precision=ML_StdLogic),
specifier=Comparison.Equal,
precision=ML_Bool),
precision=ML_Bool), stage_statement)
if one_process_per_stage:
clock_process = Process(clock_block, sensibility_list=[clk])
entity.implementation.add_process(clock_process)
first_process = first_process or clock_process
else:
clock_statement.add(clock_block)
if one_process_per_stage:
pass
else:
process_statement.add(clock_statement)
pipeline_process = Process(process_statement, sensibility_list=[clk])
entity.implementation.add_process(pipeline_process)
first_process = pipeline_process
# statement that gather signals which must be pre-computed
for op in retime_map.pre_statement:
first_process.add_to_pre_statement(op)
stage_num = len(retime_map.stage_forward.keys())
#print "there are %d pipeline stages" % (stage_num)
return stage_num
def generate_scheme(self):
# declaring function input variable
v_x = [
self.implementation.add_input_variable(
"x%d" % index, self.get_input_precision(index))
for index in range(self.arity)
]
double_format = {
ML_Binary32: ML_SingleSingle,
ML_Binary64: ML_DoubleDouble
}[self.precision]
# testing Add211
exact_add = Addition(v_x[0],
v_x[1],
precision=double_format,
tag="exact_add")
# testing Mul211
exact_mul = Multiplication(v_x[0],
v_x[1],
precision=double_format,
tag="exact_mul")
# testing Sub211
exact_sub = Subtraction(v_x[1],
v_x[0],
precision=double_format,
tag="exact_sub")
# testing Add222
multi_add = Addition(exact_add,
exact_sub,
precision=double_format,
tag="multi_add")
# testing Mul222
multi_mul = Multiplication(multi_add,
exact_mul,
precision=double_format,
tag="multi_mul")
# testing Add221 and Add212 and Sub222
multi_sub = Subtraction(Addition(exact_sub,
v_x[1],
precision=double_format,
tag="add221"),
Addition(v_x[0],
multi_mul,
precision=double_format,
tag="add212"),
precision=double_format,
tag="sub222")
# testing Mul212 and Mul221
mul212 = Multiplication(multi_sub,
v_x[0],
precision=double_format,
tag="mul212")
mul221 = Multiplication(exact_mul,
v_x[1],
precision=double_format,
tag="mul221")
# testing Sub221 and Sub212
sub221 = Subtraction(mul212,
mul221.hi,
precision=double_format,
tag="sub221")
sub212 = Subtraction(sub221,
mul212.lo,
precision=double_format,
tag="sub212")
# testing FMA2111
fma2111 = FMA(sub221.lo,
sub212.hi,
mul221.hi,
precision=double_format,
tag="fma2111")
# testing FMA2112
fma2112 = FMA(fma2111.lo,
fma2111.hi,
fma2111,
precision=double_format,
tag="fma2112")
# testing FMA2212
fma2212 = FMA(fma2112,
fma2112.hi,
fma2112,
precision=double_format,
tag="fma2212")
# testing FMA2122
fma2122 = FMA(fma2212.lo,
fma2212,
fma2212,
precision=double_format,
tag="fma2122")
# testing FMA22222
fma2222 = FMA(fma2122,
fma2212,
fma2111,
precision=double_format,
tag="fma2222")
# testing Add122
add122 = Addition(fma2222,
fma2222,
precision=self.precision,
tag="add122")
# testing Add112
add112 = Addition(add122,
fma2222,
precision=self.precision,
tag="add112")
# testing Add121
add121 = Addition(fma2222,
add112,
precision=self.precision,
tag="add121")
# testing subnormalization
multi_subnormalize = SpecificOperation(
Addition(add121, add112, precision=double_format),
Constant(3, precision=self.precision.get_integer_format()),
specifier=SpecificOperation.Subnormalize,
precision=double_format,
tag="multi_subnormalize")
result = Conversion(multi_subnormalize, precision=self.precision)
scheme = Statement(Return(result))
return scheme