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_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 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_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):
# declaring target and instantiating optimization engine
precision_ptr = self.get_input_precision(0)
index_format = self.get_input_precision(2)
multi_elt_num = self.multi_elt_num
dst = self.implementation.add_input_variable("dst", precision_ptr)
src = self.implementation.add_input_variable("src", precision_ptr)
n = self.implementation.add_input_variable("len", index_format)
i = Variable("i", precision=index_format, var_type=Variable.Local)
CU0 = Constant(0, precision=index_format)
element_format = self.precision
self.function_list = []
if multi_elt_num > 1:
element_format = VECTOR_TYPE_MAP[self.precision][multi_elt_num]
elt_input = TableLoad(src, i, precision=element_format)
local_exp = Variable("local_exp",
precision=element_format,
var_type=Variable.Local)
if self.use_libm_function:
libm_fct_operator = FunctionOperator(self.use_libm_function,
arity=1)
libm_fct = FunctionObject(self.use_libm_function, [ML_Binary32],
ML_Binary32, libm_fct_operator)
if multi_elt_num > 1:
result_list = [
libm_fct(
VectorElementSelection(elt_input,
Constant(elt_id,
precision=ML_Integer),
precision=self.precision))
for elt_id in range(multi_elt_num)
]
result = VectorAssembling(*result_list,
precision=element_format)
else:
result = libm_fct(elt_input)
elt_result = ReferenceAssign(local_exp, result)
else:
if multi_elt_num > 1:
scalar_result = Variable("scalar_result",
precision=self.precision,
var_type=Variable.Local)
fct_ctor_args = self.function_ctor.get_default_args(
precision=self.precision,
libm_compliant=False,
)
meta_function = self.function_ctor(fct_ctor_args)
exponential_scheme = meta_function.generate_scheme()
# instanciating required passes for typing
pass_inst_abstract_prec = PassInstantiateAbstractPrecision(
self.processor)
pass_inst_prec = PassInstantiatePrecision(
self.processor, default_precision=None)
# exectuting format instanciation passes on optree
exponential_scheme = pass_inst_abstract_prec.execute_on_optree(
exponential_scheme)
exponential_scheme = pass_inst_prec.execute_on_optree(
exponential_scheme)
vectorizer = StaticVectorizer()
# extracting scalar argument from meta_exponential meta function
scalar_input = meta_function.implementation.arg_list[0]
# vectorize scalar scheme
vector_result, vec_arg_list, vector_scheme, scalar_callback, scalar_callback_fct = vectorize_function_scheme(
vectorizer,
self.get_main_code_object(), exponential_scheme,
element_format.get_scalar_format(), [scalar_input],
multi_elt_num)
elt_result = inline_function(vector_scheme, vector_result,
{vec_arg_list[0]: elt_input})
local_exp = vector_result
self.function_list.append(scalar_callback_fct)
libm_fct = scalar_callback
else:
scalar_input = elt_input
scalar_result = local_exp
elt_result = generate_inline_fct_scheme(
self.function_ctor, scalar_result, [scalar_input], {
"precision": self.precision,
"libm_compliant": False
})
CU1 = Constant(1, precision=index_format)
local_exp_init_value = Constant(0, precision=self.precision)
if multi_elt_num > 1:
local_exp_init_value = Constant([0] * multi_elt_num,
precision=element_format)
remain_n = Modulo(n, multi_elt_num, precision=index_format)
iter_n = n - remain_n
CU_ELTNUM = Constant(multi_elt_num, precision=index_format)
inc = i + CU_ELTNUM
else:
remain_n = None
iter_n = n
inc = i + CU1
# main loop processing multi_elt_num element(s) per iteration
main_loop = Loop(
ReferenceAssign(i, CU0),
i < iter_n,
Statement(ReferenceAssign(local_exp, local_exp_init_value),
elt_result,
TableStore(local_exp, dst, i, precision=ML_Void),
ReferenceAssign(i, inc)),
)
# epilog to process remaining item (when the length is not a multiple
# of multi_elt_num)
if not remain_n is None:
# TODO/FIXME: try alternative method for processing epilog
# by using full vector length and mask
epilog_loop = Loop(
Statement(), i < n,
Statement(
TableStore(libm_fct(
TableLoad(src, i, precision=self.precision)),
dst,
i,
precision=ML_Void),
ReferenceAssign(i, i + CU1),
))
main_loop = Statement(main_loop, epilog_loop)
return main_loop
def generate_scheme(self):
# declaring target and instantiating optimization engine
precision_ptr = self.get_input_precision(0)
index_format = self.get_input_precision(2)
dst = self.implementation.add_input_variable("dst", precision_ptr)
src = self.implementation.add_input_variable("src", precision_ptr)
n = self.implementation.add_input_variable("len", index_format)
i = Variable("i", precision=index_format, var_type=Variable.Local)
CU1 = Constant(1, precision=index_format)
CU0 = Constant(0, precision=index_format)
inc = i + CU1
elt_input = TableLoad(src, i, precision=self.precision)
local_exp = Variable("local_exp",
precision=self.precision,
var_type=Variable.Local)
if self.use_libm_function:
libm_exp_operator = FunctionOperator("expf", arity=1)
libm_exp = FunctionObject("expf", [ML_Binary32], ML_Binary32,
libm_exp_operator)
elt_result = ReferenceAssign(local_exp, libm_exp(elt_input))
else:
exponential_args = ML_Exponential.get_default_args(
precision=self.precision,
libm_compliant=False,
debug=False,
)
meta_exponential = ML_Exponential(exponential_args)
exponential_scheme = meta_exponential.generate_scheme()
elt_result = inline_function(
exponential_scheme,
local_exp,
{meta_exponential.implementation.arg_list[0]: elt_input},
)
elt_acc = Variable("elt_acc",
precision=self.precision,
var_type=Variable.Local)
exp_loop = Loop(
ReferenceAssign(i, CU0),
i < n,
Statement(ReferenceAssign(local_exp, 0), elt_result,
TableStore(local_exp, dst, i, precision=ML_Void),
ReferenceAssign(elt_acc, elt_acc + local_exp),
ReferenceAssign(i, i + CU1)),
)
sum_rcp = Division(1,
elt_acc,
precision=self.precision,
tag="sum_rcp",
debug=debug_multi)
div_loop = Loop(
ReferenceAssign(i, CU0),
i < n,
Statement(
TableStore(Multiplication(
TableLoad(dst, i, precision=self.precision), sum_rcp),
dst,
i,
precision=ML_Void), ReferenceAssign(i, inc)),
)
main_scheme = Statement(ReferenceAssign(elt_acc, 0), exp_loop, sum_rcp,
div_loop)
return main_scheme
def generate_bench(self, processor, test_num=1000, unroll_factor=10):
""" generate performance bench for self.op_class """
initial_inputs = [
Constant(random.uniform(inf(self.init_interval),
sup(self.init_interval)),
precision=precision)
for i, precision in enumerate(self.input_precisions)
]
var_inputs = [
Variable("var_%d" % i,
precision=FormatAttributeWrapper(precision, ["volatile"]),
var_type=Variable.Local)
for i, precision in enumerate(self.input_precisions)
]
printf_timing_op = FunctionOperator(
"printf",
arg_map={
0: "\"%s[%s] %%lld elts computed "\
"in %%lld cycles =>\\n %%.3f CPE \\n\"" %
(
self.bench_name,
self.output_precision.get_display_format()
),
1: FO_Arg(0),
2: FO_Arg(1),
3: FO_Arg(2),
4: FO_Arg(3)
}, void_function=True
)
printf_timing_function = FunctionObject(
"printf", [self.output_precision, ML_Int64, ML_Int64, ML_Binary64],
ML_Void, printf_timing_op)
timer = Variable("timer", precision=ML_Int64, var_type=Variable.Local)
void_function_op = FunctionOperator("(void)",
arity=1,
void_function=True)
void_function = FunctionObject("(void)", [self.output_precision],
ML_Void, void_function_op)
# initialization of operation inputs
init_assign = metaop.Statement()
for var_input, init_value in zip(var_inputs, initial_inputs):
init_assign.push(ReferenceAssign(var_input, init_value))
# test loop
loop_i = Variable("i", precision=ML_Int64, var_type=Variable.Local)
test_num_cst = Constant(test_num / unroll_factor,
precision=ML_Int64,
tag="test_num")
# Goal build a chain of dependant operation to measure
# elementary operation latency
local_inputs = tuple(var_inputs)
local_result = self.op_class(*local_inputs,
precision=self.output_precision,
unbreakable=True)
for i in range(unroll_factor - 1):
local_inputs = tuple([local_result] + var_inputs[1:])
local_result = self.op_class(*local_inputs,
precision=self.output_precision,
unbreakable=True)
# renormalisation
local_result = self.renorm_function(local_result)
# variable assignation to build dependency chain
var_assign = Statement()
var_assign.push(ReferenceAssign(var_inputs[0], local_result))
final_value = var_inputs[0]
# loop increment value
loop_increment = 1
test_loop = Loop(
ReferenceAssign(loop_i, Constant(0, precision=ML_Int32)),
loop_i < test_num_cst,
Statement(var_assign,
ReferenceAssign(loop_i, loop_i + loop_increment)),
)
# bench scheme
test_scheme = Statement(
ReferenceAssign(timer, processor.get_current_timestamp()),
init_assign,
test_loop,
ReferenceAssign(
timer,
Subtraction(processor.get_current_timestamp(),
timer,
precision=ML_Int64)),
# prevent intermediary variable simplification
void_function(final_value),
printf_timing_function(
final_value, Constant(test_num, precision=ML_Int64), timer,
Division(Conversion(timer, precision=ML_Binary64),
Constant(test_num, precision=ML_Binary64),
precision=ML_Binary64))
# ,Return(Constant(0, precision = ML_Int32))
)
return test_scheme
def generate_bench_wrapper(self,
test_num=1,
loop_num=100000,
test_ranges=[Interval(-1.0, 1.0)],
debug=False):
# interval where the array lenght is chosen from (randomly)
index_range = self.test_index_range
auto_test = CodeFunction("bench_wrapper", output_format=ML_Binary64)
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)
printf_success_function = FunctionObject("printf", [], ML_Void,
printf_success_op)
output_precision = FormatAttributeWrapper(self.precision, ["volatile"])
test_total = test_num
# number of arrays expected as inputs for tested_function
NUM_INPUT_ARRAY = 1
# position of the input array in tested_function operands (generally
# equals to 1 as to 0-th input is often the destination array)
INPUT_INDEX_OFFSET = 1
# concatenating standard test array at the beginning of randomly
# generated array
TABLE_SIZE_VALUES = [
len(std_table) for std_table in self.standard_test_cases
] + [
random.randrange(index_range[0], index_range[1] + 1)
for i in range(test_num)
]
OFFSET_VALUES = [sum(TABLE_SIZE_VALUES[:i]) for i in range(test_total)]
table_size_offset_array = generate_2d_table(
test_total,
2,
ML_UInt32,
self.uniquify_name("table_size_array"),
value_gen=(lambda row_id:
(TABLE_SIZE_VALUES[row_id], OFFSET_VALUES[row_id])))
INPUT_ARRAY_SIZE = sum(TABLE_SIZE_VALUES)
# TODO/FIXME: implement proper input range depending on input index
# assuming a single input array
input_precisions = [self.get_input_precision(1).get_data_precision()]
rng_map = [
get_precision_rng(precision, inf(test_range), sup(test_range))
for precision, test_range in zip(input_precisions, test_ranges)
]
# generated table of inputs
input_tables = [
generate_1d_table(
INPUT_ARRAY_SIZE,
self.get_input_precision(INPUT_INDEX_OFFSET +
table_id).get_data_precision(),
self.uniquify_name("input_table_arg%d" % table_id),
value_gen=(
lambda _: input_precisions[table_id].round_sollya_object(
rng_map[table_id].get_new_value(), sollya.RN)))
for table_id in range(NUM_INPUT_ARRAY)
]
# generate output_array
output_array = generate_1d_table(
INPUT_ARRAY_SIZE,
output_precision,
self.uniquify_name("output_array"),
#value_gen=(lambda _: FP_QNaN(self.precision))
value_gen=(lambda _: None),
const=False,
empty=True)
# accumulate element number
acc_num = Variable("acc_num",
precision=ML_Int64,
var_type=Variable.Local)
def empty_post_statement_gen(input_tables, output_array,
table_size_offset_array, array_offset,
array_len, test_id):
return Statement()
test_loop = self.get_array_test_wrapper(test_total, tested_function,
table_size_offset_array,
input_tables, output_array,
acc_num,
empty_post_statement_gen)
timer = Variable("timer", precision=ML_Int64, var_type=Variable.Local)
printf_timing_op = FunctionOperator(
"printf",
arg_map={
0:
"\"%s %%\"PRIi64\" elts computed in %%\"PRIi64\" nanoseconds => %%.3f CPE \\n\""
% function_name,
1:
FO_Arg(0),
2:
FO_Arg(1),
3:
FO_Arg(2)
},
void_function=True)
printf_timing_function = FunctionObject(
"printf", [ML_Int64, ML_Int64, ML_Binary64], ML_Void,
printf_timing_op)
vj = Variable("j", precision=ML_Int32, var_type=Variable.Local)
loop_num_cst = Constant(loop_num, precision=ML_Int32, tag="loop_num")
loop_increment = 1
# bench measure of clock per element
cpe_measure = Division(
Conversion(timer, precision=ML_Binary64),
Conversion(acc_num, precision=ML_Binary64),
precision=ML_Binary64,
tag="cpe_measure",
)
# common test scheme between scalar and vector functions
test_scheme = Statement(
self.processor.get_init_timestamp(),
ReferenceAssign(timer, self.processor.get_current_timestamp()),
ReferenceAssign(acc_num, 0),
Loop(
ReferenceAssign(vj, Constant(0, precision=ML_Int32)),
vj < loop_num_cst,
Statement(test_loop, ReferenceAssign(vj,
vj + loop_increment))),
ReferenceAssign(
timer,
Subtraction(self.processor.get_current_timestamp(),
timer,
precision=ML_Int64)),
printf_timing_function(
Conversion(acc_num, precision=ML_Int64),
timer,
cpe_measure,
),
Return(cpe_measure),
# Return(Constant(0, precision = ML_Int32))
)
auto_test.set_scheme(test_scheme)
return FunctionGroup([auto_test])
def get_array_test_wrapper(self,
test_num,
tested_function,
table_size_offset_array,
input_tables,
output_array,
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
"""
test_id = Variable("test_id",
precision=ML_Int32,
var_type=Variable.Local)
test_num_cst = Constant(test_num, precision=ML_Int32, tag="test_num")
array_len = Variable("len",
precision=ML_UInt32,
var_type=Variable.Local)
array_offset = TableLoad(table_size_offset_array, test_id, 1)
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(
pointer_add(input_tables[in_id], array_offset)
for in_id in range(NUM_INPUT_ARRAY))
function_call = tested_function(
*((pointer_add(output_array, array_offset), ) + array_inputs +
(array_len, )))
post_statement = post_statement_generator(input_tables, output_array,
table_size_offset_array,
array_offset, array_len,
test_id)
loop_increment = 1
test_loop = Loop(
ReferenceAssign(test_id, Constant(0, precision=ML_Int32)),
test_id < test_num_cst,
Statement(
ReferenceAssign(array_len,
TableLoad(table_size_offset_array, test_id,
0)),
function_call,
post_statement,
ReferenceAssign(
acc_num, acc_num +
Conversion(array_len, precision=acc_num.precision)),
ReferenceAssign(test_id, test_id + loop_increment),
),
)
test_statement = Statement()
# adding functional test_loop to test statement
test_statement.add(test_loop)
return test_statement
def generate_array_check_loop(self, input_tables, output_array,
table_size_offset_array, array_offset,
array_len, test_id):
# internal array iterator index
vj = Variable("j", precision=ML_UInt32, var_type=Variable.Local)
printf_input_function = self.get_printf_input_function()
printf_error_template = "printf(\"max %s error is %s \\n\", %s)" % (
self.function_name,
self.precision.get_display_format().format_string,
self.precision.get_display_format().pre_process_fct("{0}"))
printf_error_op = TemplateOperatorFormat(printf_error_template,
arity=1,
void_function=True,
require_header=["stdio.h"])
printf_error_function = FunctionObject("printf", [self.precision],
ML_Void, printf_error_op)
printf_max_op = FunctionOperator(
"printf",
arg_map={
0:
"\"max %s error is reached at input number %s \\n \"" %
(self.function_name, "%d"),
1:
FO_Arg(0)
},
void_function=True,
require_header=["stdio.h"])
printf_max_function = FunctionObject("printf", [self.precision],
ML_Void, printf_max_op)
NUM_INPUT_ARRAY = len(input_tables)
# generate the expected table for the whole multi-array
expected_table = self.generate_expected_table(input_tables,
table_size_offset_array)
# inputs for the (vj)-th entry of the sub-arrat
local_inputs = tuple(
TableLoad(input_tables[in_id], array_offset + vj)
for in_id in range(NUM_INPUT_ARRAY))
# expected values for the (vj)-th entry of the sub-arrat
expected_values = [
TableLoad(expected_table, array_offset + vj, i)
for i in range(self.accuracy.get_num_output_value())
]
# local result for the (vj)-th entry of the sub-arrat
local_result = TableLoad(output_array, array_offset + vj)
if self.break_error:
return_statement_break = Statement(
printf_input_function(*((vj, ) + local_inputs +
(local_result, ))),
self.accuracy.get_output_print_call(self.function_name,
output_values))
else:
return_statement_break = Statement(
printf_input_function(*((vj, ) + local_inputs +
(local_result, ))),
self.accuracy.get_output_print_call(self.function_name,
expected_values),
Return(Constant(1, precision=ML_Int32)))
# loop implementation to check sub-array array_offset
# results validity
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),
))
return check_array_loop
def generate_scheme(self):
int_precision = self.precision.get_integer_format()
# We wish to compute vx / vy
vx = self.implementation.add_input_variable("x", self.precision, interval=self.input_intervals[0])
vy = self.implementation.add_input_variable("y", self.precision, interval=self.input_intervals[1])
if self.mode is FULL_MODE:
quo = self.implementation.add_input_variable("quo", ML_Pointer_Format(int_precision))
i = Variable("i", precision=int_precision, var_type=Variable.Local)
q = Variable("q", precision=int_precision, var_type=Variable.Local)
CI = lambda v: Constant(v, precision=int_precision)
CF = lambda v: Constant(v, precision=self.precision)
vx_subnormal = Test(vx, specifier=Test.IsSubnormal, tag="vx_subnormal")
vy_subnormal = Test(vy, specifier=Test.IsSubnormal, tag="vy_subnormal")
DELTA_EXP = self.precision.get_mantissa_size()
scale_factor = Constant(2.0**DELTA_EXP, precision=self.precision)
inv_scale_factor = Constant(2.0**-DELTA_EXP, precision=self.precision)
normalized_vx = Select(vx_subnormal, vx * scale_factor, vx, tag="scaled_vx")
normalized_vy = Select(vy_subnormal, vy * scale_factor, vy, tag="scaled_vy")
real_ex = ExponentExtraction(vx, tag="real_ex", precision=int_precision)
real_ey = ExponentExtraction(vy, tag="real_ey", precision=int_precision)
# if real_e<x/y> is +1023 then it may Overflow in -real_ex for ExponentInsertion
# which only supports downto -1022 before falling into subnormal numbers (which are
# not supported by ExponentInsertion)
real_ex_h0 = real_ex / 2
real_ex_h1 = real_ex - real_ex_h0
real_ey_h0 = real_ey / 2
real_ey_h1 = real_ey - real_ey_h0
EI = lambda v: ExponentInsertion(v, precision=self.precision)
mx = Abs((vx * EI(-real_ex_h0)) * EI(-real_ex_h1), tag="mx")
my = Abs((vy * EI(-real_ey_h0)) * EI(-real_ey_h1), tag="pre_my")
# scale_ey is used to regain the unscaling of mx in the first loop
# if real_ey >= real_ex, the first loop is never executed
# so a different scaling is required
mx_unscaling = Select(real_ey < real_ex, real_ey, real_ex)
ey_half0 = (mx_unscaling) / 2
ey_half1 = (mx_unscaling) - ey_half0
scale_ey_half0 = ExponentInsertion(ey_half0, precision=self.precision, tag="scale_ey_half0")
scale_ey_half1 = ExponentInsertion(ey_half1, precision=self.precision, tag="scale_ey_half1")
# if only vy is subnormal we want to normalize it
#normal_cond = LogicalAnd(vy_subnormal, LogicalNot(vx_subnormal))
normal_cond = vy_subnormal #LogicalAnd(vy_subnormal, LogicalNot(vx_subnormal))
my = Select(normal_cond, Abs(MantissaExtraction(vy * scale_factor)), my, tag="my")
# vx / vy = vx * 2^-ex * 2^(ex-ey) / (vy * 2^-ey)
# vx % vy
post_mx = Variable("post_mx", precision=self.precision, var_type=Variable.Local)
# scaling for half comparison
VY_SCALING = Select(vy_subnormal, 1.0, 0.5, precision=self.precision)
VX_SCALING = Select(vy_subnormal, 2.0, 1.0, precision=self.precision)
def LogicalXor(a, b):
return LogicalOr(LogicalAnd(a, LogicalNot(b)), LogicalAnd(LogicalNot(a), b))
rem_sign = Select(vx < 0, CF(-1), CF(1), precision=self.precision, tag="rem_sign")
quo_sign = Select(LogicalXor(vx <0, vy < 0), CI(-1), CI(1), precision=int_precision, tag="quo_sign")
loop_watchdog = Variable("loop_watchdog", precision=ML_Int32, var_type=Variable.Local)
loop = Statement(
real_ex, real_ey, mx, my, loop_watchdog,
ReferenceAssign(loop_watchdog, 5000),
ReferenceAssign(q, CI(0)),
Loop(
ReferenceAssign(i, CI(0)), i < (real_ex - real_ey),
Statement(
ReferenceAssign(i, i+CI(1)),
ReferenceAssign(q, ((q << 1) + Select(mx >= my, CI(1), CI(0))).modify_attributes(tag="step1_q")),
ReferenceAssign(mx, (CF(2) * (mx - Select(mx >= my, my, CF(0)))).modify_attributes(tag="step1_mx")),
# loop watchdog
ReferenceAssign(loop_watchdog, loop_watchdog - 1),
ConditionBlock(loop_watchdog < 0, Return(-1)),
),
),
# unscaling remainder
ReferenceAssign(mx, ((mx * scale_ey_half0) * scale_ey_half1).modify_attributes(tag="scaled_rem")),
ReferenceAssign(my, ((my * scale_ey_half0) * scale_ey_half1).modify_attributes(tag="scaled_rem_my")),
Loop(
Statement(), (my > Abs(vy)),
Statement(
ReferenceAssign(q, ((q << 1) + Select(mx >= Abs(my), CI(1), CI(0))).modify_attributes(tag="step2_q")),
ReferenceAssign(mx, (mx - Select(mx >= Abs(my), Abs(my), CF(0))).modify_attributes(tag="step2_mx")),
ReferenceAssign(my, (my * 0.5).modify_attributes(tag="step2_my")),
# loop watchdog
ReferenceAssign(loop_watchdog, loop_watchdog - 1),
ConditionBlock(loop_watchdog < 0, Return(-1)),
),
),
ReferenceAssign(q, q << 1),
Loop(
ReferenceAssign(i, CI(0)), mx > Abs(vy),
Statement(
ReferenceAssign(q, (q + Select(mx > Abs(vy), CI(1), CI(0))).modify_attributes(tag="step3_q")),
ReferenceAssign(mx, (mx - Select(mx > Abs(vy), Abs(vy), CF(0))).modify_attributes(tag="step3_mx")),
# loop watchdog
ReferenceAssign(loop_watchdog, loop_watchdog - 1),
ConditionBlock(loop_watchdog < 0, Return(-1)),
),
),
ReferenceAssign(q, q + Select(mx >= Abs(vy), CI(1), CI(0))),
ReferenceAssign(mx, (mx - Select(mx >= Abs(vy), Abs(vy), CF(0))).modify_attributes(tag="pre_half_mx")),
ConditionBlock(
# actual comparison is mx > | abs(vy * 0.5) | to avoid rounding effect when
# vy is subnormal we mulitply both side by 2.0**60
((mx * VX_SCALING) > Abs(vy * VY_SCALING)).modify_attributes(tag="half_test"),
Statement(
ReferenceAssign(q, q + CI(1)),
ReferenceAssign(mx, (mx - Abs(vy)))
)
),
ConditionBlock(
# if the remainder is exactly half the dividend
# we need to make sure the quotient is even
LogicalAnd(
Equal(mx * VX_SCALING, Abs(vy * VY_SCALING)),
Equal(Modulo(q, CI(2)), CI(1)),
),
Statement(
ReferenceAssign(q, q + CI(1)),
ReferenceAssign(mx, (mx - Abs(vy)))
)
),
ReferenceAssign(mx, rem_sign * mx),
ReferenceAssign(q,
Modulo(TypeCast(q, precision=self.precision.get_unsigned_integer_format()), Constant(2**self.quotient_size, precision=self.precision.get_unsigned_integer_format()), tag="mod_q")
),
ReferenceAssign(q, quo_sign * q),
)
# NOTES: Warning QuotientReturn must always preceeds RemainderReturn
if self.mode is QUOTIENT_MODE:
#
QuotientReturn = Return
RemainderReturn = lambda _: Statement()
elif self.mode is REMAINDER_MODE:
QuotientReturn = lambda _: Statement()
RemainderReturn = Return
elif self.mode is FULL_MODE:
QuotientReturn = lambda v: ReferenceAssign(Dereference(quo, precision=int_precision), v)
RemainderReturn = Return
else:
raise NotImplemented
# quotient invalid value
QUO_INVALID_VALUE = 0
mod_scheme = Statement(
# x or y is NaN, a NaN is returned
ConditionBlock(
LogicalOr(Test(vx, specifier=Test.IsNaN), Test(vy, specifier=Test.IsNaN)),
Statement(
QuotientReturn(QUO_INVALID_VALUE),
RemainderReturn(FP_QNaN(self.precision))
),
),
#
ConditionBlock(
Test(vy, specifier=Test.IsZero),
Statement(
QuotientReturn(QUO_INVALID_VALUE),
RemainderReturn(FP_QNaN(self.precision))
),
),
ConditionBlock(
Test(vx, specifier=Test.IsZero),
Statement(
QuotientReturn(0),
RemainderReturn(vx)
),
),
ConditionBlock(
Test(vx, specifier=Test.IsInfty),
Statement(
QuotientReturn(QUO_INVALID_VALUE),
RemainderReturn(FP_QNaN(self.precision))
)
),
ConditionBlock(
Test(vy, specifier=Test.IsInfty),
Statement(
QuotientReturn(0),
RemainderReturn(vx),
)
),
ConditionBlock(
Abs(vx) < Abs(vy * 0.5),
Statement(
QuotientReturn(0),
RemainderReturn(vx),
)
),
ConditionBlock(
Equal(vx, vy),
Statement(
QuotientReturn(1),
# 0 with the same sign as x
RemainderReturn(vx - vx),
),
),
ConditionBlock(
Equal(vx, -vy),
Statement(
# quotient is -1
QuotientReturn(-1),
# 0 with the same sign as x
RemainderReturn(vx - vx),
),
),
loop,
QuotientReturn(q),
RemainderReturn(mx),
)
quo_scheme = Statement(
# x or y is NaN, a NaN is returned
ConditionBlock(
LogicalOr(Test(vx, specifier=Test.IsNaN), Test(vy, specifier=Test.IsNaN)),
Return(QUO_INVALID_VALUE),
),
#
ConditionBlock(
Test(vy, specifier=Test.IsZero),
Return(QUO_INVALID_VALUE),
),
ConditionBlock(
Test(vx, specifier=Test.IsZero),
Return(0),
),
ConditionBlock(
Test(vx, specifier=Test.IsInfty),
Return(QUO_INVALID_VALUE),
),
ConditionBlock(
Test(vy, specifier=Test.IsInfty),
Return(QUO_INVALID_VALUE),
),
ConditionBlock(
Abs(vx) < Abs(vy * 0.5),
Return(0),
),
ConditionBlock(
Equal(vx, vy),
Return(1),
),
ConditionBlock(
Equal(vx, -vy),
Return(-1),
),
loop,
Return(q),
)
return mod_scheme