def legalize_fixed_point_subselection(optree,
input_prec_solver=default_prec_solver):
""" Legalize a SubSignalSelection on a fixed-point node """
sub_input = optree.get_input(0)
inf_index = evaluate_cst_graph(optree.get_inf_index(),
input_prec_solver=input_prec_solver)
sup_index = evaluate_cst_graph(optree.get_sup_index(),
input_prec_solver=input_prec_solver)
assert not inf_index is None and not sup_index is None
input_format = ML_StdLogicVectorFormat(
sub_input.get_precision().get_bit_size())
output_format = ML_StdLogicVectorFormat(sup_index - inf_index + 1)
subselect = SubSignalSelection(TypeCast(sub_input, precision=input_format),
inf_index,
sup_index,
precision=output_format)
result = TypeCast(
subselect,
precision=optree.get_precision(),
)
# TypeCast may be simplified during code generation so attributes
# may also be forwarded to previous node
forward_attributes(optree, subselect)
forward_attributes(optree, result)
return result
def raw_fp_field_extraction(optree):
""" generate an operation sub-graph to extract the fp field
(mantissa without implicit digit) of a fp node """
size = optree.get_precision().get_base_format().get_bit_size()
field_size = optree.get_precision().get_base_format().get_field_size()
return TypeCast(SubSignalSelection(
TypeCast(optree, precision=ML_StdLogicVectorFormat(size)), 0,
field_size - 1),
precision=fixed_point(field_size, 0, signed=False))
def mantissa_extraction_modifier_from_fields(op,
field_op,
exp_is_zero,
tag="mant_extr"):
""" Legalizing a MantissaExtraction node into a sub-graph
of basic operation, assuming <field_op> bitfield and <exp_is_zero> flag
are already available """
op_precision = op.get_precision().get_base_format()
implicit_digit = Select(
exp_is_zero,
Constant(0, precision=ML_StdLogic),
Constant(1, precision=ML_StdLogic),
precision=ML_StdLogic,
tag=tag + "_implicit_digit",
)
result = Concatenation(
implicit_digit,
TypeCast(field_op,
precision=ML_StdLogicVectorFormat(
op_precision.get_field_size())),
precision=ML_StdLogicVectorFormat(op_precision.get_mantissa_size()),
)
return result
def get_output_check_statement(output_signal, output_tag, output_value):
""" Generate output value check statement """
test_pass_cond = Comparison(
output_signal,
output_value,
specifier=Comparison.Equal,
precision=ML_Bool
)
check_statement = ConditionBlock(
LogicalNot(
test_pass_cond,
precision = ML_Bool
),
Report(
Concatenation(
" result for {}: ".format(output_tag),
Conversion(
output_signal if output_signal.get_precision() is ML_StdLogic else
TypeCast(
output_signal,
precision=ML_StdLogicVectorFormat(
output_signal.get_precision().get_bit_size()
)
),
precision = ML_String
),
precision = ML_String
)
)
)
return test_pass_cond, check_statement
def signal_str_conversion(optree, op_format):
""" converision of @p optree from op_format to ML_String """
return Conversion(
optree if op_format is ML_StdLogic else
TypeCast(
optree,
precision=ML_StdLogicVectorFormat(
op_format.get_bit_size()
)
),
precision=ML_String
)
def comp_3to2(a, b, c):
""" 3 digits to 2 digits compressor """
s = BitLogicXor(a,
BitLogicXor(b, c, precision=ML_StdLogic),
precision=ML_StdLogic)
c = BitLogicOr(BitLogicAnd(a, b, precision=ML_StdLogic),
BitLogicOr(BitLogicAnd(a, c, precision=ML_StdLogic),
BitLogicAnd(c, b, precision=ML_StdLogic),
precision=ML_StdLogic),
precision=ML_StdLogic)
return c, s
a = TypeCast(a, precision=fixed_point(1, 0, signed=False))
b = TypeCast(b, precision=fixed_point(1, 0, signed=False))
c = TypeCast(c, precision=fixed_point(1, 0, signed=False))
full = TypeCast(Conversion(a + b + c,
precision=fixed_point(2, 0, signed=False)),
precision=ML_StdLogicVectorFormat(2))
carry = BitSelection(full, 1)
digit = BitSelection(full, 0)
return carry, digit
def generate_bitfield_extraction(target_format, input_node, lo_index,
hi_index):
shift = lo_index
mask_size = hi_index - lo_index + 1
input_format = input_node.get_precision().get_base_format()
if is_fixed_point(input_format) and is_fixed_point(target_format):
frac_size = target_format.get_frac_size()
int_size = input_format.get_bit_size() - frac_size
cast_format = ML_Custom_FixedPoint_Format(int_size,
frac_size,
signed=False)
else:
cast_format = None
# 1st step: shifting the input node the right amount
shifted_node = input_node if shift == 0 else BitLogicRightShift(
input_node,
Constant(shift, precision=ML_Int32),
precision=input_format)
raw_format = ML_Custom_FixedPoint_Format(input_format.get_bit_size(),
0,
signed=False)
# 2nd step: masking the input node
# TODO/FIXME: check thast mask does not overflow or wrap-around
masked_node = BitLogicAnd(TypeCast(shifted_node, precision=raw_format),
Constant((2**mask_size - 1),
precision=raw_format),
precision=raw_format)
if not cast_format is None:
casted_node = TypeCast(masked_node, precision=cast_format)
else:
casted_node = masked_node
converted_node = Conversion(casted_node, precision=target_format)
return converted_node
def generate_field_extraction(optree, precision, lo_index, hi_index):
""" extract bit-field optree[lo_index:hi_index-1] and cast to precision """
if optree.precision != precision:
optree = TypeCast(optree, precision=precision)
result = optree
if lo_index != 0:
result = BitLogicRightShift(optree,
Constant(vectorize_cst(
lo_index, precision),
precision=precision),
precision=precision)
if (hi_index - lo_index + 1) != precision.get_bit_size():
mask = Constant(vectorize_cst(2**(hi_index - lo_index + 1) - 1,
precision),
precision=precision)
result = BitLogicAnd(result, mask, precision=precision)
return result
def get_index_node(self, vx):
assert vx.precision is self.precision
int_precision = vx.precision.get_integer_format()
index_size = self.exp_bits + self.field_bits
# building an index mask from the index_size
index_mask = Constant(2**index_size - 1, precision=int_precision)
shift_amount = Constant(vx.get_precision().get_field_size() -
self.field_bits,
precision=int_precision)
exp_offset = Constant(self.precision.get_integer_coding(
S2**self.low_exp_value),
precision=int_precision)
return BitLogicAnd(BitLogicRightShift(Subtraction(
TypeCast(vx, precision=int_precision),
exp_offset,
precision=int_precision),
shift_amount,
precision=int_precision),
index_mask,
precision=int_precision)
def legalize_vector_reduction_test(optree):
""" Legalize a vector test (e.g. IsMaskNotAnyZero) to a sub-graph
of basic operations """
op_input = optree.get_input(0)
vector_size = op_input.get_precision().get_vector_size()
conv_format = {
2: v2int32,
4: v4int32,
8: v8int32,
}[vector_size]
cast_format = {
2: ML_Int64,
4: ML_Int128,
8: ML_Int256,
}[vector_size]
return Comparison(TypeCast(Conversion(op_input, precision=conv_format),
precision=cast_format),
Constant(0, precision=cast_format),
specifier=Comparison.Equal,
precision=ML_Bool)
def generate_exp_insertion(optree, result_precision):
""" generate the expanded version of ExponentInsertion
with @p optree as input and assuming @p result_precision
as output precision """
if result_precision.is_vector_format():
scalar_format = optree.precision.get_scalar_format()
vector_size = optree.precision.get_vector_size()
bias_cst = [-result_precision.get_scalar_format().get_bias()
] * vector_size
shift_cst = [result_precision.get_scalar_format().get_field_size()
] * vector_size
else:
scalar_format = optree.precision
bias_cst = -result_precision.get_bias()
shift_cst = result_precision.get_field_size()
assert is_std_integer_format(scalar_format)
biased_exponent = Addition(optree,
Constant(bias_cst, precision=optree.precision),
precision=optree.precision)
result = BitLogicLeftShift(biased_exponent,
Constant(shift_cst, precision=optree.precision),
precision=optree.precision)
return TypeCast(result, precision=result_precision)
def mantissa_extraction_modifier(optree):
""" Legalizing a MantissaExtraction node into a sub-graph
of basic operation """
init_stage = optree.attributes.get_dyn_attribute("init_stage")
op = optree.get_input(0)
tag = optree.get_tag() or "mant_extr"
op_precision = op.get_precision().get_base_format()
exp_prec = ML_StdLogicVectorFormat(op_precision.get_exponent_size())
field_prec = ML_StdLogicVectorFormat(op_precision.get_field_size())
exp_op = RawExponentExtraction(op,
precision=exp_prec,
init_stage=init_stage,
tag=tag + "_exp_extr")
field_op = SubSignalSelection(TypeCast(
op,
precision=op.get_precision().get_support_format(),
init_stage=init_stage,
tag=tag + "_field_cast"),
0,
op_precision.get_field_size() - 1,
precision=field_prec,
init_stage=init_stage,
tag=tag + "_field")
exp_is_zero = Comparison(exp_op,
Constant(op_precision.get_zero_exponent_value(),
precision=exp_prec,
init_stage=init_stage),
precision=ML_Bool,
specifier=Comparison.Equal,
init_stage=init_stage)
result = mantissa_extraction_modifier_from_fields(op, field_op,
exp_is_zero)
forward_attributes(optree, result)
return result
def legalizer(exp_insertion_node):
optree = exp_insertion_node.get_input(0)
if result_precision.is_vector_format():
scalar_format = optree.precision.get_scalar_format()
vector_size = optree.precision.get_vector_size()
bias_cst = [-result_precision.get_scalar_format().get_bias()
] * vector_size
shift_cst = [
result_precision.get_scalar_format().get_field_size()
] * vector_size
else:
scalar_format = optree.precision
bias_cst = -result_precision.get_bias()
shift_cst = result_precision.get_field_size()
assert is_std_integer_format(scalar_format)
biased_exponent = Addition(optree,
Constant(bias_cst,
precision=optree.precision),
precision=optree.precision)
result = BitLogicLeftShift(biased_exponent,
Constant(shift_cst,
precision=optree.precision),
precision=optree.precision)
return TypeCast(result, precision=result_precision)
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_exp_insertion(optree, result_precision):
""" generate the expanded version of ExponentInsertion
with @p optree as input and assuming @p result_precision
as output precision """
if result_precision.is_vector_format():
scalar_format = optree.precision.get_scalar_format()
vector_size = optree.precision.get_vector_size()
# determine the working format (for expression)
work_format = VECTOR_TYPE_MAP[result_precision.get_scalar_format().
get_integer_format()][vector_size]
bias_cst = [-result_precision.get_scalar_format().get_bias()
] * vector_size
shift_cst = [result_precision.get_scalar_format().get_field_size()
] * vector_size
else:
scalar_format = optree.precision
work_format = result_precision.get_integer_format()
bias_cst = -result_precision.get_bias()
shift_cst = result_precision.get_field_size()
if not is_std_integer_format(scalar_format):
Log.report(
Log.Error,
"{} should be a std integer format in generate_exp_insertion {} with precision {}",
scalar_format, optree, result_precision)
assert is_std_integer_format(scalar_format)
biased_exponent = Addition(Conversion(optree, precision=work_format) if
not optree.precision is work_format else optree,
Constant(bias_cst, precision=work_format),
precision=work_format)
result = BitLogicLeftShift(biased_exponent,
Constant(
shift_cst,
precision=work_format,
),
precision=work_format)
return TypeCast(result, precision=result_precision)
def generic_atan2_generate(self, _vx, vy=None):
""" if vy is None, compute atan(_vx), else compute atan2(vy / vx) """
if vy is None:
# approximation
# if abs_vx <= 1.0 then atan(abx_vx) is directly approximated
# if abs_vx > 1.0 then atan(abs_vx) = pi/2 - atan(1 / abs_vx)
#
# for vx >= 0, atan(vx) = atan(abs_vx)
#
# for vx < 0, atan(vx) = -atan(abs_vx) for vx < 0
# = -pi/2 + atan(1 / abs_vx)
vx = _vx
sign_cond = vx < 0
abs_vx = Select(vx < 0, -vx, vx, tag="abs_vx", debug=debug_multi)
bound_cond = abs_vx > 1
inv_abs_vx = 1 / abs_vx
# condition to select subtraction
cond = LogicalOr(LogicalAnd(vx < 0, LogicalNot(bound_cond)),
vx > 1,
tag="cond",
debug=debug_multi)
# reduced argument
red_vx = Select(bound_cond,
inv_abs_vx,
abs_vx,
tag="red_vx",
debug=debug_multi)
offset = None
else:
# bound_cond is True iff Abs(vy / _vx) > 1.0
bound_cond = Abs(vy) > Abs(_vx)
bound_cond.set_attributes(tag="bound_cond", debug=debug_multi)
# vx and vy are of opposite signs
#sign_cond = (_vx * vy) < 0
# using cast to int(signed) and bitwise xor
# to determine if _vx and vy are of opposite sign rapidly
fast_sign_cond = BitLogicXor(
TypeCast(_vx, precision=self.precision.get_integer_format()),
TypeCast(vy, precision=self.precision.get_integer_format()),
precision=self.precision.get_integer_format()) < 0
# sign_cond = (_vx * vy) < 0
sign_cond = fast_sign_cond
sign_cond.set_attributes(tag="sign_cond", debug=debug_multi)
# condition to select subtraction
# TODO: could be accelerated if LogicalXor existed
slow_cond = LogicalOr(
LogicalAnd(sign_cond,
LogicalNot(bound_cond)), # 1 < (vy / _vx) < 0
LogicalAnd(bound_cond,
LogicalNot(sign_cond)), # (vy / _vx) > 1
tag="cond",
debug=debug_multi)
cond = slow_cond
numerator = Select(bound_cond,
_vx,
vy,
tag="numerator",
debug=debug_multi)
denominator = Select(bound_cond,
vy,
_vx,
tag="denominator",
debug=debug_multi)
# reduced argument
red_vx = Abs(numerator) / Abs(denominator)
red_vx.set_attributes(tag="red_vx", debug=debug_multi)
offset = Select(
_vx > 0,
Constant(0, precision=self.precision),
# vx < 0
Select(
sign_cond,
# vy > 0
Constant(sollya.pi, precision=self.precision),
Constant(-sollya.pi, precision=self.precision),
precision=self.precision),
precision=self.precision,
tag="offset")
approx_fct = sollya.atan(sollya.x)
if self.method == "piecewise":
sign_vx = Select(cond,
-1,
1,
precision=self.precision,
tag="sign_vx",
debug=debug_multi)
cst_sign = Select(sign_cond,
-1,
1,
precision=self.precision,
tag="cst_sign",
debug=debug_multi)
cst = cst_sign * Select(
bound_cond, sollya.pi / 2, 0, precision=self.precision)
cst.set_attributes(tag="cst", debug=debug_multi)
bound_low = 0.0
bound_high = 1.0
num_intervals = self.num_sub_intervals
error_threshold = S2**-(self.precision.get_mantissa_size() + 8)
approx, eval_error = piecewise_approximation(
approx_fct,
red_vx,
self.precision,
bound_low=bound_low,
bound_high=bound_high,
max_degree=None,
num_intervals=num_intervals,
error_threshold=error_threshold,
odd=True)
result = cst + sign_vx * approx
result.set_attributes(tag="result",
precision=self.precision,
debug=debug_multi)
elif self.method == "single":
approx_interval = Interval(0, 1.0)
# determining the degree of the polynomial approximation
poly_degree_range = sollya.guessdegree(
approx_fct / sollya.x, approx_interval,
S2**-(self.precision.get_field_size() + 2))
poly_degree = int(sollya.sup(poly_degree_range)) + 4
Log.report(Log.Info, "poly_degree={}".format(poly_degree))
# arctan is an odd function, so only odd coefficient must be non-zero
poly_degree_list = list(range(1, poly_degree + 1, 2))
poly_object, poly_error = Polynomial.build_from_approximation_with_error(
approx_fct, poly_degree_list,
[1] + [self.precision.get_sollya_object()] *
(len(poly_degree_list) - 1), approx_interval)
odd_predicate = lambda index, _: ((index - 1) % 4 != 0)
even_predicate = lambda index, _: (index != 1 and
(index - 1) % 4 == 0)
poly_odd_object = poly_object.sub_poly_cond(odd_predicate,
offset=1)
poly_even_object = poly_object.sub_poly_cond(even_predicate,
offset=1)
sollya.settings.display = sollya.hexadecimal
Log.report(Log.Info, "poly_error: {}".format(poly_error))
Log.report(Log.Info, "poly_odd: {}".format(poly_odd_object))
Log.report(Log.Info, "poly_even: {}".format(poly_even_object))
poly_odd = PolynomialSchemeEvaluator.generate_horner_scheme(
poly_odd_object, abs_vx)
poly_odd.set_attributes(tag="poly_odd", debug=debug_multi)
poly_even = PolynomialSchemeEvaluator.generate_horner_scheme(
poly_even_object, abs_vx)
poly_even.set_attributes(tag="poly_even", debug=debug_multi)
exact_sum = poly_odd + poly_even
exact_sum.set_attributes(tag="exact_sum", debug=debug_multi)
# poly_even should be (1 + poly_even)
result = vx + vx * exact_sum
result.set_attributes(tag="result",
precision=self.precision,
debug=debug_multi)
else:
raise NotImplementedError
if not offset is None:
result = result + offset
std_scheme = Statement(Return(result))
scheme = std_scheme
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:
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(
ReferenceAssign(
input_signal,
Constant(input_value,
precision=input_signal.get_precision())))
value_msg = input_signal.get_precision().get_cst(
input_value, language=VHDL_Code).replace('"', "'")
value_msg += " / " + hex(input_signal.get_precision(
).get_base_format().get_integer_coding(input_value))
input_msg += " {}={} ".format(input_tag, value_msg)
test_statement.add(Wait(time_step * self.stage_num))
# Adding output value comparison
for output_tag in output_signals:
output_signal = output_signals[output_tag]
output_value = Constant(
output_values[output_tag],
precision=output_signal.get_precision())
output_precision = output_signal.get_precision()
expected_dec = output_precision.get_cst(
output_values[output_tag],
language=VHDL_Code).replace('"', "'")
expected_hex = " / " + hex(
output_precision.get_base_format().get_integer_coding(
output_values[output_tag]))
value_msg = "{} / {}".format(expected_dec, expected_hex)
test_pass_cond = Comparison(output_signal,
output_value,
specifier=Comparison.Equal,
precision=ML_Bool)
test_statement.add(
ConditionBlock(
LogicalNot(test_pass_cond, precision=ML_Bool),
Report(
Concatenation(
" result for {}: ".format(output_tag),
Conversion(TypeCast(
output_signal,
precision=ML_StdLogicVectorFormat(
output_signal.get_precision(
).get_bit_size())),
precision=ML_String),
precision=ML_String))))
test_statement.add(
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))
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 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
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