def generate_scheme(self):
""" main scheme generation """
int_size = 3
frac_size = self.width - int_size
input_precision = hdl_precision_parser("FU%d.%d" %
(int_size, frac_size))
output_precision = hdl_precision_parser("FS%d.%d" %
(int_size, frac_size))
# declaring main input variable
var_x = self.implementation.add_input_signal("x", input_precision)
var_y = self.implementation.add_input_signal("y", input_precision)
var_z = self.implementation.add_input_signal("z", input_precision)
abstract_formulae = var_x
anchor = FixedPointPosition(abstract_formulae,
-3,
align=FixedPointPosition.FromPointToMSB,
tag="anchor")
comp = abstract_formulae > anchor
result = Select(comp, Conversion(var_x, precision=self.precision),
Conversion(var_y, precision=self.precision))
self.implementation.add_output_signal("result", result)
return [self.implementation]
def legalize_Select(optree):
""" legalize Select operation node by converting if and else inputs to
Select output format if the bit sizes do not match """
cond = optree.get_input(0)
op0 = optree.get_input(1)
op1 = optree.get_input(2)
precision = optree.get_precision()
if precision is None:
Log.report(Log.Error, "None precision for Select:\n{}", optree)
if op0.get_precision().get_bit_size() != precision.get_bit_size():
optree.set_input(
1,
Conversion(
op0,
precision = precision
)
)
if op1.get_precision().get_bit_size() != precision.get_bit_size():
optree.set_input(
2,
Conversion(
op1,
precision = optree.get_precision()
)
)
return optree
def legalize_invsqrt_seed(optree):
""" Legalize an InverseSquareRootSeed optree """
assert isinstance(optree, ReciprocalSquareRootSeed)
op_prec = optree.get_precision()
# input = 1.m_hi-m_lo * 2^e
# approx = 2^(-int(e/2)) * approx_insqrt(1.m_hi) * (e % 2 ? 1.0 : ~2**-0.5)
op_input = optree.get_input(0)
convert_back = False
approx_prec = ML_Binary32
if op_prec != approx_prec:
op_input = Conversion(op_input, precision=ML_Binary32)
convert_back = True
# TODO: fix integer precision selection
# as we are in a late code generation stage, every node's precision
# must be set
op_exp = ExponentExtraction(op_input,
tag="op_exp",
debug=debug_multi,
precision=ML_Int32)
neg_half_exp = Division(Negation(op_exp, precision=ML_Int32),
Constant(2, precision=ML_Int32),
precision=ML_Int32)
approx_exp = ExponentInsertion(neg_half_exp,
tag="approx_exp",
debug=debug_multi,
precision=approx_prec)
op_exp_parity = Modulo(op_exp,
Constant(2, precision=ML_Int32),
precision=ML_Int32)
approx_exp_correction = Select(Equal(op_exp_parity,
Constant(0, precision=ML_Int32)),
Constant(1.0, precision=approx_prec),
Select(Equal(
op_exp_parity,
Constant(-1, precision=ML_Int32)),
Constant(S2**0.5,
precision=approx_prec),
Constant(S2**-0.5,
precision=approx_prec),
precision=approx_prec),
precision=approx_prec,
tag="approx_exp_correction",
debug=debug_multi)
table_index = invsqrt_approx_table.get_index_function()(op_input)
table_index.set_attributes(tag="invsqrt_index", debug=debug_multi)
approx = Multiplication(TableLoad(invsqrt_approx_table,
table_index,
precision=approx_prec),
Multiplication(approx_exp_correction,
approx_exp,
precision=approx_prec),
tag="invsqrt_approx",
debug=debug_multi,
precision=approx_prec)
if approx_prec != op_prec:
return Conversion(approx, precision=op_prec)
else:
return approx
def sw_legalize_concatenation(node):
""" Legalize a RTL Concatenation node into a sub-graph
of operation compatible with software implementation """
assert len(node.inputs) == 2
lhs = node.get_input(0)
rhs = node.get_input(1)
return BitLogicOr(BitLogicLeftShift(Conversion(
lhs, precision=node.get_precision()),
rhs.get_precision().get_bit_size(),
precision=node.get_precision()),
Conversion(rhs, precision=node.get_precision()),
precision=node.get_precision())
def legalize_reciprocal_seed(optree):
""" Legalize an ReciprocalSeed optree """
assert isinstance(optree, ReciprocalSeed)
op_prec = optree.get_precision()
initial_prec = op_prec
back_convert = False
op_input = optree.get_input(0)
INV_APPROX_TABLE_FORMAT = generic_inv_approx_table.get_storage_precision()
if op_prec != INV_APPROX_TABLE_FORMAT:
op_input = Conversion(op_input, precision=INV_APPROX_TABLE_FORMAT)
op_prec = INV_APPROX_TABLE_FORMAT
back_convert = True
# input = 1.m_hi-m_lo * 2^e
# approx = 2^(-int(e/2)) * approx_insqrt(1.m_hi) * (e % 2 ? 1.0 : ~2**-0.5)
# TODO: fix integer precision selection
# as we are in a late code generation stage, every node's precision
# must be set
int_prec = op_prec.get_integer_format()
op_sign = CopySign(op_input,
Constant(1.0, precision=op_prec),
precision=op_prec)
op_exp = ExponentExtraction(op_input,
tag="op_exp",
debug=debug_multi,
precision=int_prec)
neg_exp = Negation(op_exp, precision=int_prec)
approx_exp = ExponentInsertion(neg_exp,
tag="approx_exp",
debug=debug_multi,
precision=op_prec)
table_index = generic_inv_approx_table.get_index_function()(op_input)
table_index.set_attributes(tag="inv_index", debug=debug_multi)
approx = Multiplication(TableLoad(generic_inv_approx_table,
table_index,
precision=op_prec),
Multiplication(approx_exp,
op_sign,
precision=op_prec),
tag="inv_approx",
debug=debug_multi,
precision=op_prec)
if back_convert:
return Conversion(approx, precision=initial_prec)
else:
return approx
def propagate_format_to_input(new_format, optree, input_index_list):
""" Propgate new_format to @p optree's input whose index is listed in
@p input_index_list """
for op_index in input_index_list:
op_input = optree.get_input(op_index)
if op_input.get_precision() is None:
op_input.set_precision(new_format)
index_list = does_node_propagate_format(op_input)
propagate_format_to_input(new_format, op_input, index_list)
elif not test_format_equality(new_format, op_input.get_precision()):
if is_constant(op_input):
if not is_fixed_point(new_format):
Log.report(
Log.Error,
"format {} during propagation to input {} of {} is not a fixed-point format",
new_format, op_input, optree)
elif format_does_fit(op_input, new_format):
Log.report(
Log.Info,
"Simplify Constant Conversion {} to larger Constant: {}",
op_input.get_str(display_precision=True)
if Log.is_level_enabled(Log.Info) else "",
str(new_format))
new_input = op_input.copy()
new_input.set_precision(new_format)
optree.set_input(op_index, new_input)
else:
Log.report(
Log.Error,
"Constant is about to be reduced to a too constrained format: {}",
op_input.get_str(display_precision=True)
if Log.is_level_enabled(Log.Error) else "")
else:
new_input = Conversion(op_input, precision=new_format)
optree.set_input(op_index, new_input)
def generate_scheme(self):
""" main scheme generation """
Log.report(Log.Info,
"input_precision is {}".format(self.input_precision))
Log.report(Log.Info,
"output_precision is {}".format(self.output_precision))
# declaring main input variable
var_x = self.implementation.add_input_signal("x", self.input_precision)
var_y = self.implementation.add_input_signal("y", self.input_precision)
var_x.set_attributes(debug=debug_fixed)
var_y.set_attributes(debug=debug_fixed)
self.implementation.start_new_stage()
add = var_x + var_y
self.implementation.start_new_stage()
sub = add - var_y
self.implementation.start_new_stage()
pre_result = sub - var_x
self.implementation.start_new_stage()
post_result = pre_result + var_x
result = Conversion(pre_result, precision=self.output_precision)
self.implementation.add_output_signal("vr_out", result)
return [self.implementation]
def generate_dummy_scheme(self):
Log.report(
Log.Info,
"generating MultArray with output precision {precision}".format(
precision=self.precision))
acc = None
a_inputs = {}
b_inputs = {}
stage_map = self.instanciate_inputs()
stage_index_list = sorted(stage_map.keys())
for stage_id in stage_index_list:
# synchronizing pipeline stage
if stage_id is None:
pass
else:
while stage_id > self.implementation.get_current_stage():
self.implementation.start_new_stage()
operation_list = stage_map[stage_id]
for ctor, operand_list in operation_list:
new_term = ctor(*tuple(operand_list))
if acc is None:
acc = new_term
else:
acc = Addition(acc, new_term)
result = Conversion(acc, precision=self.precision)
self.implementation.add_output_signal("result_o", result)
return [self.implementation]
def generate_scheme(self):
""" main scheme generation """
Log.report(Log.Info, "width parameter is {}".format(self.width))
int_size = 3
frac_size = self.width - int_size
input_precision = fixed_point(int_size, frac_size)
output_precision = fixed_point(int_size, frac_size)
# declaring main input variable
var_x = self.implementation.add_input_signal("x", input_precision)
var_y = self.implementation.add_input_signal("y", input_precision)
var_x.set_attributes(debug = debug_fixed)
var_y.set_attributes(debug = debug_fixed)
sub = var_x - var_y
c = Constant(0)
self.implementation.start_new_stage()
#pre_result = Select(
# c > sub,
# c,
# sub
#)
pre_result = Max(0, sub)
self.implementation.start_new_stage()
result = Conversion(pre_result + var_x, precision=output_precision)
self.implementation.add_output_signal("vr_out", result)
return [self.implementation]
def generate_scheme(self):
""" main scheme generation """
Log.report(Log.Info, "width parameter is {}".format(self.width))
int_size = 3
frac_size = self.width - int_size
input_precision = fixed_point(int_size, frac_size)
output_precision = fixed_point(int_size, frac_size)
# declaring main input variable
var_x = self.implementation.add_input_signal("x", input_precision)
var_y = self.implementation.add_input_signal("y", input_precision)
var_x.set_attributes(debug = debug_fixed)
var_y.set_attributes(debug = debug_fixed)
test = (var_x > 1)
test.set_attributes(tag = "test", debug = debug_std)
large_add = (var_x + var_y)
pre_result = Select(
test,
1,
large_add,
tag = "pre_result",
debug = debug_fixed
)
result = Conversion(pre_result, precision=output_precision)
self.implementation.add_output_signal("vr_out", result)
return [self.implementation]
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 legalize_integer_nearest(optree):
""" transform a NearestInteger node floating-point to integer
into a sequence of floating-point NearestInteger and Conversion.
This conversion is lossy """
op_input = optree.get_input(0)
int_precision = {
v4float32: v4int32,
ML_Binary32: ML_Int32
}[optree.get_precision()]
return Conversion(NearestInteger(op_input, precision=int_precision),
precision=optree.get_precision())
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 simplify_inverse(optree, processor):
dummy_var = Variable("dummy_var_seed", precision = optree.get_precision())
dummy_div_seed = DivisionSeed(dummy_var, precision = optree.get_precision())
inv_approx_table = processor.get_recursive_implementation(dummy_div_seed, language = None, table_getter = lambda self: self.approx_table_map)
seed_input = optree.inputs[0]
c0 = Constant(0, precision = ML_Int32)
if optree.get_precision() == inv_approx_table.get_storage_precision():
return TableLoad(inv_approx_table, inv_approx_table.get_index_function()(seed_input), c0, precision = optree.get_precision())
else:
return Conversion(TableLoad(inv_approx_table, inv_approx_table.get_index_function()(seed_input), c0, precision = inv_approx_table.get_storage_precision()), precision = optree.get_precision())
def insert_conversion_when_required(op_input, final_precision):
""" Generate a conversion of op_input to format final_precision if required
:param op_input: input operation node
:type op_input: ML_Operation
:param final_precision: target format
:type final_precision: ML_Format
:return: op_input converted to final_precision if required
:rtype: ML_Operation """
# assert not final_precision is None
if op_input.get_precision() != final_precision:
return Conversion(op_input, precision=final_precision)
else:
return op_input
def generate_scheme(self):
# declaring function input variable
vx = self.implementation.add_input_variable("x", self.get_input_precision(0))
bf16_params = ML_NewTable(dimensions=[self.table_size], storage_precision=BFloat16)
for i in range(self.table_size):
bf16_params[i] = 1.1**i
conv_vx = Conversion(TableLoad(bf16_params, vx), precision=ML_Binary32, tag="conv_vx", debug=debug_multi)
result = conv_vx
scheme = Return(result, precision=self.precision, debug=debug_multi)
return scheme
def generate_scheme(self):
""" main scheme generation """
Log.report(Log.Info, "width parameter is {}".format(self.width))
int_size = 3
frac_size = self.width - int_size
input_precision = fixed_point(int_size, frac_size)
output_precision = fixed_point(int_size, frac_size)
# declaring main input variable
var_x = self.implementation.add_input_signal("x", input_precision)
var_y = self.implementation.add_input_signal("y", input_precision)
var_x.set_attributes(debug=debug_fixed)
var_y.set_attributes(debug=debug_fixed)
test = (var_x > 1)
test.set_attributes(tag="test", debug=debug_std)
sub = var_x - var_y
c = Constant(0)
pre_result_select = Select(c > sub,
Select(c < var_y,
sub,
Select(LogicalAnd(
c > var_x,
c < var_y,
tag="last_lev_cond"),
var_x,
c,
tag="last_lev_sel"),
tag="pre_select"),
var_y,
tag="pre_result_select")
pre_result = Max(0, var_x - var_y, tag="pre_result")
result = Conversion(Addition(pre_result, pre_result_select, tag="add"),
precision=output_precision)
self.implementation.add_output_signal("vr_out", result)
return [self.implementation]
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 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_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 generate_scalar_scheme(self, vx, n):
# fixing inputs' node tag
vx.set_attributes(tag="x")
n.set_attributes(tag="n")
int_precision = self.precision.get_integer_format()
# assuming x = m.2^e (m in [1, 2[)
# n, positive or null integers
#
# rootn(x, n) = x^(1/n)
# = exp(1/n * log(x))
# = 2^(1/n * log2(x))
# = 2^(1/n * (log2(m) + e))
#
# approximation log2(m)
# retrieving processor inverse approximation table
dummy_var = Variable("dummy", precision=self.precision)
dummy_div_seed = ReciprocalSeed(dummy_var, precision=self.precision)
inv_approx_table = self.processor.get_recursive_implementation(
dummy_div_seed,
language=None,
table_getter=lambda self: self.approx_table_map)
log_f = sollya.log(sollya.x) # /sollya.log(self.basis)
use_reciprocal = False
# non-scaled vx used to compute vx^1
unmodified_vx = vx
is_subnormal = Test(vx, specifier=Test.IsSubnormal, tag="is_subnormal")
exp_correction_factor = self.precision.get_mantissa_size()
mantissa_factor = Constant(2**exp_correction_factor,
tag="mantissa_factor")
vx = Select(is_subnormal, vx * mantissa_factor, vx, tag="corrected_vx")
m = MantissaExtraction(vx, tag="m", precision=self.precision)
e = ExponentExtraction(vx, tag="e", precision=int_precision)
e = Select(is_subnormal,
e - exp_correction_factor,
e,
tag="corrected_e")
ml_log_args = ML_GenericLog.get_default_args(precision=self.precision,
basis=2)
ml_log = ML_GenericLog(ml_log_args)
log_table, log_table_tho, table_index_range = ml_log.generate_log_table(
log_f, inv_approx_table)
log_approx = ml_log.generate_reduced_log_split(
Abs(m, precision=self.precision), log_f, inv_approx_table,
log_table)
# floating-point version of n
n_f = Conversion(n, precision=self.precision, tag="n_f")
inv_n = Division(Constant(1, precision=self.precision), n_f)
log_approx = Select(Equal(vx, 0), FP_MinusInfty(self.precision),
log_approx)
log_approx.set_attributes(tag="log_approx", debug=debug_multi)
if use_reciprocal:
r = Multiplication(log_approx, inv_n, tag="r", debug=debug_multi)
else:
r = Division(log_approx, n_f, tag="r", debug=debug_multi)
# e_n ~ e / n
e_f = Conversion(e, precision=self.precision, tag="e_f")
if use_reciprocal:
e_n = Multiplication(e_f, inv_n, tag="e_n")
else:
e_n = Division(e_f, n_f, tag="e_n")
error_e_n = FMA(e_n, -n_f, e_f, tag="error_e_n")
e_n_int = NearestInteger(e_n, precision=self.precision, tag="e_n_int")
pre_e_n_frac = e_n - e_n_int
pre_e_n_frac.set_attributes(tag="pre_e_n_frac")
e_n_frac = pre_e_n_frac + error_e_n * inv_n
e_n_frac.set_attributes(tag="e_n_frac")
ml_exp2_args = ML_Exp2.get_default_args(precision=self.precision)
ml_exp2 = ML_Exp2(ml_exp2_args)
exp2_r = ml_exp2.generate_scalar_scheme(r, inline_select=True)
exp2_r.set_attributes(tag="exp2_r", debug=debug_multi)
exp2_e_n_frac = ml_exp2.generate_scalar_scheme(e_n_frac,
inline_select=True)
exp2_e_n_frac.set_attributes(tag="exp2_e_n_frac", debug=debug_multi)
exp2_e_n_int = ExponentInsertion(Conversion(e_n_int,
precision=int_precision),
precision=self.precision,
tag="exp2_e_n_int")
n_is_even = Equal(Modulo(n, 2), 0, tag="n_is_even", debug=debug_multi)
n_is_odd = LogicalNot(n_is_even, tag="n_is_odd")
result_sign = Select(
n_is_odd, CopySign(vx, Constant(1.0, precision=self.precision)), 1)
# managing n == -1
if self.expand_div:
ml_division_args = ML_Division.get_default_args(
precision=self.precision, input_formats=[self.precision] * 2)
ml_division = ML_Division(ml_division_args)
self.division_implementation = ml_division.implementation
self.division_implementation.set_scheme(
ml_division.generate_scheme())
ml_division_fct = self.division_implementation.get_function_object(
)
else:
ml_division_fct = Division
# manage n=1 separately to avoid catastrophic propagation of errors
# between log2 and exp2 to eventually compute the identity function
# test-case #3
result = ConditionBlock(
LogicalOr(LogicalOr(Test(vx, specifier=Test.IsNaN), Equal(n, 0)),
LogicalAnd(n_is_even, vx < 0)),
Return(FP_QNaN(self.precision)),
Statement(
ConditionBlock(
Equal(n, -1, tag="n_is_mone"),
#Return(Division(Constant(1, precision=self.precision), unmodified_vx, tag="div_res", precision=self.precision)),
Return(
ml_division_fct(Constant(1, precision=self.precision),
unmodified_vx,
tag="div_res",
precision=self.precision)),
),
ConditionBlock(
# rootn( ±inf, n) is +∞ for even n< 0.
Test(vx, specifier=Test.IsInfty),
Statement(
ConditionBlock(
n < 0,
#LogicalAnd(n_is_odd, n < 0),
Return(
Select(Test(vx,
specifier=Test.IsPositiveInfty),
Constant(FP_PlusZero(self.precision),
precision=self.precision),
Constant(FP_MinusZero(self.precision),
precision=self.precision),
precision=self.precision)),
Return(vx),
), ),
),
ConditionBlock(
# rootn(±0, n) is ±∞ for odd n < 0.
LogicalAnd(LogicalAnd(n_is_odd, n < 0),
Equal(vx, 0),
tag="n_is_odd_and_neg"),
Return(
Select(Test(vx, specifier=Test.IsPositiveZero),
Constant(FP_PlusInfty(self.precision),
precision=self.precision),
Constant(FP_MinusInfty(self.precision),
precision=self.precision),
precision=self.precision)),
),
ConditionBlock(
# rootn( ±0, n) is +∞ for even n< 0.
LogicalAnd(LogicalAnd(n_is_even, n < 0), Equal(vx, 0)),
Return(FP_PlusInfty(self.precision))),
ConditionBlock(
# rootn(±0, n) is +0 for even n > 0.
LogicalAnd(n_is_even, Equal(vx, 0)),
Return(vx)),
ConditionBlock(
Equal(n, 1), Return(unmodified_vx),
Return(result_sign * exp2_r * exp2_e_n_int *
exp2_e_n_frac))))
return result
def piecewise_approximation(function,
variable,
precision,
bound_low=-1.0,
bound_high=1.0,
num_intervals=16,
max_degree=2,
error_threshold=S2**-24,
odd=False,
even=False):
""" Generate a piecewise approximation
:param function: function to be approximated
:type function: SollyaObject
:param variable: input variable
:type variable: Variable
:param precision: variable's format
:type precision: ML_Format
:param bound_low: lower bound for the approximation interval
:param bound_high: upper bound for the approximation interval
:param num_intervals: number of sub-interval / sub-division of the main interval
:param max_degree: maximum degree for an approximation on any sub-interval
:param error_threshold: error bound for an approximation on any sub-interval
:return: pair (scheme, error) where scheme is a graph node for an
approximation scheme of function evaluated at variable, and error
is the maximum approximation error encountered
:rtype tuple(ML_Operation, SollyaObject): """
degree_generator = piecewise_approximation_degree_generator(
function,
bound_low,
bound_high,
num_intervals=num_intervals,
error_threshold=error_threshold,
)
degree_list = list(degree_generator)
# if max_degree is None then we determine it locally
if max_degree is None:
max_degree = max(degree_list)
# table to store coefficients of the approximation on each segment
coeff_table = ML_NewTable(
dimensions=[num_intervals, max_degree + 1],
storage_precision=precision,
tag="coeff_table",
const=True # by default all approximation coeff table are const
)
error_function = lambda p, f, ai, mod, t: sollya.dirtyinfnorm(p - f, ai)
max_approx_error = 0.0
interval_size = (bound_high - bound_low) / num_intervals
for i in range(num_intervals):
subint_low = bound_low + i * interval_size
subint_high = bound_low + (i + 1) * interval_size
local_function = function(sollya.x + subint_low)
local_interval = Interval(-interval_size, interval_size)
local_degree = degree_list[i]
if local_degree > max_degree:
Log.report(
Log.Warning,
"local_degree {} exceeds max_degree bound ({}) in piecewise_approximation",
local_degree, max_degree)
# as max_degree defines the size of the table we can use
# it as the degree for each sub-interval polynomial
# as there is nothing to gain (yet) by using a smaller polynomial
degree = max_degree # min(max_degree, local_degree)
if function(subint_low) == 0.0:
# if the lower bound is a zero to the function, we
# need to force value=0 for the constant coefficient
# and extend the approximation interval
local_poly_degree_list = list(
range(1 if even else 0, degree + 1, 2 if odd or even else 1))
poly_object, approx_error = Polynomial.build_from_approximation_with_error(
function(sollya.x) / sollya.x,
local_poly_degree_list,
[precision] * len(local_poly_degree_list),
Interval(-subint_high * 0.95, subint_high),
sollya.absolute,
error_function=error_function)
# multiply by sollya.x
poly_object = poly_object.sub_poly(offset=-1)
else:
try:
poly_object, approx_error = Polynomial.build_from_approximation_with_error(
local_function,
degree, [precision] * (degree + 1),
local_interval,
sollya.absolute,
error_function=error_function)
except SollyaError as err:
# try to see if function is constant on the interval (possible
# failure cause for fpminmax)
cst_value = precision.round_sollya_object(
function(subint_low), sollya.RN)
accuracy = error_threshold
diff_with_cst_range = sollya.supnorm(cst_value, local_function,
local_interval,
sollya.absolute, accuracy)
diff_with_cst = sup(abs(diff_with_cst_range))
if diff_with_cst < error_threshold:
Log.report(Log.Info, "constant polynomial detected")
poly_object = Polynomial([function(subint_low)] +
[0] * degree)
approx_error = diff_with_cst
else:
Log.report(
Log.error,
"degree: {} for index {}, diff_with_cst={} (vs error_threshold={}) ",
degree,
i,
diff_with_cst,
error_threshold,
error=err)
for ci in range(max_degree + 1):
if ci in poly_object.coeff_map:
coeff_table[i][ci] = poly_object.coeff_map[ci]
else:
coeff_table[i][ci] = 0.0
if approx_error > error_threshold:
Log.report(
Log.Warning,
"piecewise_approximation on index {} exceeds error threshold: {} > {}",
i, approx_error, error_threshold)
max_approx_error = max(max_approx_error, abs(approx_error))
# computing offset
diff = Subtraction(variable,
Constant(bound_low, precision=precision),
tag="diff",
debug=debug_multi,
precision=precision)
int_prec = precision.get_integer_format()
# delta = bound_high - bound_low
delta_ratio = Constant(num_intervals / (bound_high - bound_low),
precision=precision)
# computing table index
# index = nearestint(diff / delta * <num_intervals>)
index = Max(0,
Min(
NearestInteger(
Multiplication(diff, delta_ratio, precision=precision),
precision=int_prec,
), num_intervals - 1),
tag="index",
debug=debug_multi,
precision=int_prec)
poly_var = Subtraction(diff,
Multiplication(
Conversion(index, precision=precision),
Constant(interval_size, precision=precision)),
precision=precision,
tag="poly_var",
debug=debug_multi)
# generating indexed polynomial
coeffs = [(ci, TableLoad(coeff_table, index, ci))
for ci in range(max_degree + 1)][::-1]
poly_scheme = PolynomialSchemeEvaluator.generate_horner_scheme2(
coeffs, poly_var, precision, {}, precision)
return poly_scheme, max_approx_error
def check_processor_support(self,
optree,
memoization_map=None,
debug=False,
language=C_Code):
""" check if all precision-instantiated operation are supported by the processor """
memoization_map = memoization_map if not memoization_map is None else {}
if debug:
print("checking processor support: ",
self.processor.__class__) # Debug print
if optree in memoization_map:
return True
if not isinstance(optree, ML_LeafNode):
for inp in optree.inputs:
self.check_processor_support(inp,
memoization_map,
debug=debug,
language=language)
if isinstance(optree, ConditionBlock):
self.check_processor_support(optree.get_pre_statement(),
memoization_map,
debug=debug,
language=language)
pass
elif isinstance(optree, Statement):
pass
elif isinstance(optree, Loop):
pass
elif isinstance(optree, Return):
pass
elif isinstance(optree, ReferenceAssign):
pass
elif isinstance(optree, PlaceHolder):
pass
elif isinstance(optree, SwitchBlock):
#self.check_processor_support(optree.get_pre_statement(), memoization_map)
for op in optree.get_extra_inputs():
# TODO: assert case is integer constant
self.check_processor_support(op,
memoization_map,
debug=debug,
language=language)
elif not self.processor.is_supported_operation(
optree, debug=debug, language=language):
# trying operand format escalation
init_optree = optree
old_list = optree.inputs
while False: #optree.__class__ in type_escalation:
match_found = False
for result_type_cond in type_escalation[optree.__class__]:
if result_type_cond(optree.get_precision()):
for op_index in range(len(optree.inputs)):
op = optree.inputs[op_index]
for op_type_cond in type_escalation[
optree.__class__][result_type_cond]:
if op_type_cond(op.get_precision()):
new_type = type_escalation[
optree.
__class__][result_type_cond][
op_type_cond](optree)
if op.get_precision() != new_type:
# conversion insertion
input_list = list(optree.inputs)
input_list[op_index] = Conversion(
op, precision=new_type)
optree.inputs = tuple(input_list)
match_found = True
break
break
if not match_found:
break
# checking final processor support
if not self.processor.is_supported_operation(optree):
# look for possible simplification
if self.has_support_simplification(optree):
simplified_tree = self.get_support_simplification(
optree)
Log.report(
Log.Verbose, "simplifying %s" %
optree.get_str(depth=2, display_precision=True))
Log.report(
Log.Verbose, "into %s" % simplified_tree.get_str(
depth=2, display_precision=True))
optree.change_to(simplified_tree)
if self.processor.is_supported_operation(optree):
memoization_map[optree] = True
return True
print(optree) # Error print
print("pre escalation: ", old_list) # Error print
print(self.processor.get_operation_keys(
optree)) # Error print
print(
optree.get_str(display_precision=True,
display_id=True,
memoization_map={})) # Error print
Log.report(Log.Error, "unsupported operation\n")
# memoization
memoization_map[optree] = True
return True
def recursive_support_check(optree):
if optree in memoization_map:
return True
elif not isinstance(optree, ML_LeafNode):
# memoization
memoization_map[optree] = True
for inp in optree.inputs:
recursive_support_check(inp)
if isinstance(optree, ConditionBlock):
pass
elif isinstance(optree, Statement):
pass
elif isinstance(optree, ConditionalBranch):
pass
elif isinstance(optree, UnconditionalBranch):
pass
elif isinstance(optree, BasicBlock):
pass
elif isinstance(optree, PhiNode):
pass
elif isinstance(optree, Loop):
pass
elif isinstance(optree, Return):
pass
elif isinstance(optree, ReferenceAssign):
pass
elif isinstance(optree, PlaceHolder):
pass
elif isinstance(optree, SwitchBlock):
for op in optree.get_extra_inputs():
# TODO: assert case is integer constant
recursive_support_check(op)
elif not processor.is_supported_operation(
optree, debug=debug, language=language):
# trying operand format escalation
init_optree = optree
old_list = optree.inputs
while False: #optree.__class__ in type_escalation:
match_found = False
for result_type_cond in type_escalation[
optree.__class__]:
if result_type_cond(optree.get_precision()):
for op_index in range(len(optree.inputs)):
op = optree.inputs[op_index]
for op_type_cond in type_escalation[
optree.
__class__][result_type_cond]:
if op_type_cond(op.get_precision()):
new_type = type_escalation[
optree.
__class__][result_type_cond][
op_type_cond](optree)
if op.get_precision() != new_type:
# conversion insertion
input_list = list(
optree.inputs)
input_list[
op_index] = Conversion(
op, precision=new_type)
optree.inputs = tuple(
input_list)
match_found = True
break
break
if not match_found:
break
# checking final processor support
if not processor.is_supported_operation(optree,
language=language):
# look for possible simplification
if has_support_simplification(optree):
simplified_tree = get_support_simplification(
optree, processor)
Log.report(
Log.Verbose, "simplifying %s" % optree.get_str(
depth=2, display_precision=True))
Log.report(
Log.Verbose,
"into %s" % simplified_tree.get_str(
depth=2, display_precision=True))
optree.change_to(simplified_tree)
if processor.is_supported_operation(
optree, language=language):
memoization_map[optree] = True
return True
print("pre escalation node is: ",
old_list) # Error print
print("languages is {}".format(language))
print("Operation' keys are: {}".format(
processor.get_operation_keys(
optree))) # Error print
print("Operation tree is: \n",
optree.get_str(
display_precision=True,
depth=1,
display_id=True,
memoization_map=None)) # Error print
Log.report(
Log.Error,
"unsupported operation in PassCheckProcessorSupport's check_processor_support {}:\n{}",
processor, optree)
else:
# memoization
memoization_map[optree] = True
return True
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
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 insert_conversion_when_required(op_input, final_precision):
if op_input.get_precision() != final_precision:
return Conversion(op_input, precision=final_precision)
else:
return op_input
def generate_scalar_scheme(self, vx, vy):
# fixing inputs' node tag
vx.set_attributes(tag="x")
vy.set_attributes(tag="y")
int_precision = self.precision.get_integer_format()
# assuming x = m.2^e (m in [1, 2[)
# n, positive or null integers
#
# pow(x, n) = x^(y)
# = exp(y * log(x))
# = 2^(y * log2(x))
# = 2^(y * (log2(m) + e))
#
e = ExponentExtraction(vx, tag="e", precision=int_precision)
m = MantissaExtraction(vx, tag="m", precision=self.precision)
# approximation log2(m)
# retrieving processor inverse approximation table
dummy_var = Variable("dummy", precision = self.precision)
dummy_div_seed = ReciprocalSeed(dummy_var, precision = self.precision)
inv_approx_table = self.processor.get_recursive_implementation(
dummy_div_seed, language=None,
table_getter= lambda self: self.approx_table_map)
log_f = sollya.log(sollya.x) # /sollya.log(self.basis)
ml_log_args = ML_GenericLog.get_default_args(precision=self.precision, basis=2)
ml_log = ML_GenericLog(ml_log_args)
log_table, log_table_tho, table_index_range = ml_log.generate_log_table(log_f, inv_approx_table)
log_approx = ml_log.generate_reduced_log_split(Abs(m, precision=self.precision), log_f, inv_approx_table, log_table)
log_approx = Select(Equal(vx, 0), FP_MinusInfty(self.precision), log_approx)
log_approx.set_attributes(tag="log_approx", debug=debug_multi)
r = Multiplication(log_approx, vy, tag="r", debug=debug_multi)
# 2^(y * (log2(m) + e)) = 2^(y * log2(m)) * 2^(y * e)
#
# log_approx = log2(Abs(m))
# r = y * log_approx ~ y * log2(m)
#
# NOTES: manage cases where e is negative and
# (y * log2(m)) AND (y * e) could cancel out
# if e positive, whichever the sign of y (y * log2(m)) and (y * e) CANNOT
# be of opposite signs
# log2(m) in [0, 1[ so cancellation can occur only if e == -1
# we split 2^x in 2^x = 2^t0 * 2^t1
# if e < 0: t0 = y * (log2(m) + e), t1=0
# else: t0 = y * log2(m), t1 = y * e
t_cond = e < 0
# e_y ~ e * y
e_f = Conversion(e, precision=self.precision)
#t0 = Select(t_cond, (e_f + log_approx) * vy, Multiplication(e_f, vy), tag="t0")
#NearestInteger(t0, precision=self.precision, tag="t0_int")
EY = NearestInteger(e_f * vy, tag="EY", precision=self.precision)
LY = NearestInteger(log_approx * vy, tag="LY", precision=self.precision)
t0_int = Select(t_cond, EY + LY, EY, tag="t0_int")
t0_frac = Select(t_cond, FMA(e_f, vy, -EY) + FMA(log_approx, vy, -LY) ,EY - t0_int, tag="t0_frac")
#t0_frac.set_attributes(tag="t0_frac")
ml_exp2_args = ML_Exp2.get_default_args(precision=self.precision)
ml_exp2 = ML_Exp2(ml_exp2_args)
exp2_t0_frac = ml_exp2.generate_scalar_scheme(t0_frac, inline_select=True)
exp2_t0_frac.set_attributes(tag="exp2_t0_frac", debug=debug_multi)
exp2_t0_int = ExponentInsertion(Conversion(t0_int, precision=int_precision), precision=self.precision, tag="exp2_t0_int")
t1 = Select(t_cond, Constant(0, precision=self.precision), r)
exp2_t1 = ml_exp2.generate_scalar_scheme(t1, inline_select=True)
exp2_t1.set_attributes(tag="exp2_t1", debug=debug_multi)
result_sign = Constant(1.0, precision=self.precision) # Select(n_is_odd, CopySign(vx, Constant(1.0, precision=self.precision)), 1)
y_int = NearestInteger(vy, precision=self.precision)
y_is_integer = Equal(y_int, vy)
y_is_even = LogicalOr(
# if y is a number (exc. inf) greater than 2**mantissa_size * 2,
# then it is an integer multiple of 2 => even
Abs(vy) >= 2**(self.precision.get_mantissa_size()+1),
LogicalAnd(
y_is_integer and Abs(vy) < 2**(self.precision.get_mantissa_size()+1),
# we want to limit the modulo computation to an integer input
Equal(Modulo(Conversion(y_int, precision=int_precision), 2), 0)
)
)
y_is_odd = LogicalAnd(
LogicalAnd(
Abs(vy) < 2**(self.precision.get_mantissa_size()+1),
y_is_integer
),
Equal(Modulo(Conversion(y_int, precision=int_precision), 2), 1)
)
# special cases management
special_case_results = Statement(
# x is sNaN OR y is sNaN
ConditionBlock(
LogicalOr(Test(vx, specifier=Test.IsSignalingNaN), Test(vy, specifier=Test.IsSignalingNaN)),
Return(FP_QNaN(self.precision))
),
# pow(x, ±0) is 1 if x is not a signaling NaN
ConditionBlock(
Test(vy, specifier=Test.IsZero),
Return(Constant(1.0, precision=self.precision))
),
# pow(±0, y) is ±∞ and signals the divideByZero exception for y an odd integer <0
ConditionBlock(
LogicalAnd(Test(vx, specifier=Test.IsZero), LogicalAnd(y_is_odd, vy < 0)),
Return(Select(Test(vx, specifier=Test.IsPositiveZero), FP_PlusInfty(self.precision), FP_MinusInfty(self.precision))),
),
# pow(±0, −∞) is +∞ with no exception
ConditionBlock(
LogicalAnd(Test(vx, specifier=Test.IsZero), Test(vy, specifier=Test.IsNegativeInfty)),
Return(FP_MinusInfty(self.precision)),
),
# pow(±0, +∞) is +0 with no exception
ConditionBlock(
LogicalAnd(Test(vx, specifier=Test.IsZero), Test(vy, specifier=Test.IsPositiveInfty)),
Return(FP_PlusInfty(self.precision)),
),
# pow(±0, y) is ±0 for finite y>0 an odd integer
ConditionBlock(
LogicalAnd(Test(vx, specifier=Test.IsZero), LogicalAnd(y_is_odd, vy > 0)),
Return(vx),
),
# pow(−1, ±∞) is 1 with no exception
ConditionBlock(
LogicalAnd(Equal(vx, -1), Test(vy, specifier=Test.IsInfty)),
Return(Constant(1.0, precision=self.precision)),
),
# pow(+1, y) is 1 for any y (even a quiet NaN)
ConditionBlock(
vx == 1,
Return(Constant(1.0, precision=self.precision)),
),
# pow(x, +∞) is +0 for −1<x<1
ConditionBlock(
LogicalAnd(Abs(vx) < 1, Test(vy, specifier=Test.IsPositiveInfty)),
Return(FP_PlusZero(self.precision))
),
# pow(x, +∞) is +∞ for x<−1 or for 1<x (including ±∞)
ConditionBlock(
LogicalAnd(Abs(vx) > 1, Test(vy, specifier=Test.IsPositiveInfty)),
Return(FP_PlusInfty(self.precision))
),
# pow(x, −∞) is +∞ for −1<x<1
ConditionBlock(
LogicalAnd(Abs(vx) < 1, Test(vy, specifier=Test.IsNegativeInfty)),
Return(FP_PlusInfty(self.precision))
),
# pow(x, −∞) is +0 for x<−1 or for 1<x (including ±∞)
ConditionBlock(
LogicalAnd(Abs(vx) > 1, Test(vy, specifier=Test.IsNegativeInfty)),
Return(FP_PlusZero(self.precision))
),
# pow(+∞, y) is +0 for a number y < 0
ConditionBlock(
LogicalAnd(Test(vx, specifier=Test.IsPositiveInfty), vy < 0),
Return(FP_PlusZero(self.precision))
),
# pow(+∞, y) is +∞ for a number y > 0
ConditionBlock(
LogicalAnd(Test(vx, specifier=Test.IsPositiveInfty), vy > 0),
Return(FP_PlusInfty(self.precision))
),
# pow(−∞, y) is −0 for finite y < 0 an odd integer
# TODO: check y is finite
ConditionBlock(
LogicalAnd(Test(vx, specifier=Test.IsNegativeInfty), LogicalAnd(y_is_odd, vy < 0)),
Return(FP_MinusZero(self.precision)),
),
# pow(−∞, y) is −∞ for finite y > 0 an odd integer
# TODO: check y is finite
ConditionBlock(
LogicalAnd(Test(vx, specifier=Test.IsNegativeInfty), LogicalAnd(y_is_odd, vy > 0)),
Return(FP_MinusInfty(self.precision)),
),
# pow(−∞, y) is +0 for finite y < 0 and not an odd integer
# TODO: check y is finite
ConditionBlock(
LogicalAnd(Test(vx, specifier=Test.IsNegativeInfty), LogicalAnd(LogicalNot(y_is_odd), vy < 0)),
Return(FP_PlusZero(self.precision)),
),
# pow(−∞, y) is +∞ for finite y > 0 and not an odd integer
# TODO: check y is finite
ConditionBlock(
LogicalAnd(Test(vx, specifier=Test.IsNegativeInfty), LogicalAnd(LogicalNot(y_is_odd), vy > 0)),
Return(FP_PlusInfty(self.precision)),
),
# pow(±0, y) is +∞ and signals the divideByZero exception for finite y<0 and not an odd integer
# TODO: signal divideByZero exception
ConditionBlock(
LogicalAnd(Test(vx, specifier=Test.IsZero), LogicalAnd(LogicalNot(y_is_odd), vy < 0)),
Return(FP_PlusInfty(self.precision)),
),
# pow(±0, y) is +0 for finite y>0 and not an odd integer
ConditionBlock(
LogicalAnd(Test(vx, specifier=Test.IsZero), LogicalAnd(LogicalNot(y_is_odd), vy > 0)),
Return(FP_PlusZero(self.precision)),
),
)
# manage n=1 separately to avoid catastrophic propagation of errors
# between log2 and exp2 to eventually compute the identity function
# test-case #3
result = Statement(
special_case_results,
# fallback default cases
Return(result_sign * exp2_t1 * exp2_t0_int * exp2_t0_frac))
return result
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