def check_dTF(self, tf, margin=0, prec=165):
"""
Check if a transfer function satisfy the Gabarit
This is done using Sollya and gabarit.sol
Parameters:
- tf: (dTF) transfer function we want to check
- margin: margin we can tolerate in the check (not in dB)
- prec: (int) precision in bits given to Sollya.checkModulusFilterInSpecification
Returns a tuple (isOk, res)
- isOk: True if the transfer function is in the gabarit
- res: sollya object embedded the result
"""
Gabarit.readyToRunWithSollya()
# get num,den as sollya objects
num, den = tf.to_Sollya()
# build the constraints to verify
constraints = [b.sollyaConstraint(margin) for b in self._bands]
# run sollya check
# print("-> calling checkModulusFilterInSpecification")
res = sollya.parse("checkModulusFilterInSpecification")(num, den, constraints, prec)
sollya.parse("presentResults")(res)
return dict(res)["okay"], res
def parse_gappa_interval(interval_value):
# search for middle ","
end_index = len(interval_value)
tmp_str = re.sub("[ \[\]]", lambda _: "", interval_value)
while "{" in tmp_str:
start = tmp_str.index("{")
end = tmp_str.index("}")
tmp_str = tmp_str[:start] + tmp_str[end + 1:]
v0, v1 = tmp_str.split(",")
return sollya.Interval(sollya.parse(v0), sollya.parse(v1))
def parse_with_error(s):
""" parse string s as a SollyaObject,
raise an error if the value conversion fails """
v = sollya.parse(s)
if v == sollya.error:
Log.report(Log.Error, "not able to parse value {} => {}", s, v)
return v
class FunctionTemplate(ScalarUnaryFunction):
function_name = "func_template"
def __init__(self, args=DefaultArgTemplate):
# initializing base class
super().__init__(args)
@staticmethod
def get_default_args(**kw):
""" Return a structure containing the arguments for FunctionTemplate,
builtin from a default argument mapping overloaded with @p kw """
default_args_exp = {
"output_file": "func_template.c",
"function_name": "func_template",
"precision": ML_Binary32,
"accuracy": ML_Faithful,
"target": GenericProcessor.get_target_instance()
}
default_args_exp.update(kw)
return DefaultArgTemplate(**default_args_exp)
def generate_scalar_scheme(self, vx):
scheme = Statement(Return(vx), )
return scheme
def numeric_emulate(self, input_value):
""" Numeric emaluation of exponential """
return input_value
standard_test_cases = [
(sollya.parse("0x1.1p0"), ),
]
def standard_test_cases(self):
generic_list = [
# test-case #1
(sollya.parse("0x1.bbe2f2p-1"), sollya.parse("0x1.2d34ep+9")),
# test-case #2
(sollya.parse("0x0p+0"), sollya.parse("0x1.a45a2ep-56"), FP_PlusZero(self.precision)),
# test-case #0
(sollya.parse("0x1.5d20b8p-115"), sollya.parse("0x1.c20048p+0")),
# special cases
(sollya.parse("0x0p+0"), 1),
(sollya.parse("0x0p+0"), 0),
]
fp64_list = [
# subnormal output
(sollya.parse("0x1.21998d0c5039bp-976"), sollya.parse("0x1.bc68e3d0ffd24p+3")),
]
return generic_list + (fp64_list if self.precision.get_bit_size() >= 64 else [])
def numeric_emulate(self, x):
""" numeric emulation """
# extracting mantissa from x
# abs_x = abs(x)
# mantissa = abs_x / S2**sollya.floor(sollya.log2(abs_x))
# index = sollya.floor((mantissa - 1.0) * 2**8)
# result = sollya.round(1/sollya.sqrt(1.0 + index * S2**-8), 9, sollya.RN)
if x == 0:
return sollya.parse("infty")
result = sollya.round(1.0 / x, 9, sollya.RN)
return result
def parse(s, precision=None):
""" parse a numerical value from a string """
obj = sollya.parse(s)
if obj == SOLLYA_INFTY:
return FP_PlusInfty(precision)
elif obj == -SOLLYA_INFTY:
return FP_MinusInfty(precision)
elif obj != obj:
# by default Sollya's NaNs are assumed to be quiet NaNs
return FP_QNaN(precision)
else:
return NumericValue(obj)
def standard_test_cases(self):
return [
(sollya.parse("0xbf50bc3a"),),
(sollya.parse("0x1.0p-126"),),
(sollya.parse("0x1.0p-127"),),
(sollya.parse("-0x1.fffffep126"),),
(sollya.parse("-infty"),),
(sollya.parse("infty"),),
(FP_QNaN(self.precision),),
# issue in generic newlib implementation
(sollya.parse("0x1.62e302p+6"),),
]
def WCPGmp(self, delta=2**-53):
"""
This functions computes the WCPG of the state-space system
with absolute error bounded by delta.
The result is given as a list W of sollya objects, which represents a
p x q WCPG matrix.
Parameters
----------
delta - bound of the absolute
Returns
-------
W - a list of sollya objects representing elemnts of the WCPG matrix
"""
import sollya
# load gabarit.sol
# sollya.suppressmessage(57, 174, 130, 457)
sollya.execute("fipogen/LTI/wcpg.sol")
wcpg = sollya.parse("wcpg")
# construct the inputs for the wcpg function in sollyaObject format
A, _, _ = mpf_matrix_to_sollya(self._A)
B, _, _ = mpf_matrix_to_sollya(self._B)
C, _, _ = mpf_matrix_to_sollya(self._C)
D, _, _ = mpf_matrix_to_sollya(self._D)
# W = sollya.parse("wcpg")(A, B, C, D, self._n, self._p, self._q, eps)
W = wcpg(A, B, C, D, self._n, self._p, self._q, delta)
return W
class FP_Divider(ML_Entity("fp_div")):
def __init__(
self,
arg_template=DefaultEntityArgTemplate,
):
# initializing base class
ML_EntityBasis.__init__(self, arg_template=arg_template)
self.disable_sub_testing = arg_template.disable_sub_testing
self.disable_sv_testing = arg_template.disable_sv_testing
self.pipelined = arg_template.pipelined
## default argument template generation
@staticmethod
def get_default_args(**kw):
default_dict = {
"precision": ML_Binary32,
"target": VHDLBackend(),
"output_file": "my_fp_div.vhd",
"entity_name": "my_fp_div",
"language": VHDL_Code,
"pipelined": False,
}
default_dict.update(kw)
return DefaultEntityArgTemplate(**default_dict)
def generate_scheme(self):
def get_virtual_cst(prec, value, language):
return prec.get_support_format().get_cst(
prec.get_base_format().get_integer_coding(value, language))
## convert @p value from an input floating-point precision
# @p in_precision to an output support format @p out_precision
io_precision = VirtualFormat(base_format=self.precision,
support_format=ML_StdLogicVectorFormat(
self.precision.get_bit_size()),
get_cst=get_virtual_cst)
# declaring main input variable
vx = self.implementation.add_input_signal("x", io_precision)
# rounding mode input
rnd_mode = self.implementation.add_input_signal(
"rnd_mode", rnd_mode_format)
if self.pipelined:
self.implementation.add_input_signal("reset", ML_StdLogic)
vx_precision = self.precision
p = vx_precision.get_mantissa_size()
exp_size = vx_precision.get_exponent_size()
exp_vx_precision = ML_StdLogicVectorFormat(
vx_precision.get_exponent_size())
mant_vx_precision = ML_StdLogicVectorFormat(p)
# fixed-point precision for operand's exponent
exp_fixed_precision = fixed_point(exp_size, 0, signed=False)
# mantissa extraction
mant_vx = TypeCast(MantissaExtraction(vx,
precision=mant_vx_precision,
tag="extracted_mantissa"),
precision=fixed_point(1, p - 1, signed=False),
debug=debug_fixed,
tag="mant_vx")
# exponent extraction
exp_vx = TypeCast(RawExponentExtraction(vx,
precision=exp_vx_precision,
tag="exp_vx"),
precision=exp_fixed_precision)
approx_index_size = 8
approx_precision = fixed_point(
2,
approx_index_size,
)
# selecting table index from input mantissa MSBs
tab_index = SubSignalSelection(mant_vx,
p - 2 - approx_index_size + 1,
p - 2,
tag="tab_index")
# declaring reciprocal approximation table
inv_approx_table = ML_NewTable(dimensions=[2**approx_index_size],
storage_precision=approx_precision,
tag="inv_approx_table")
for i in range(2**approx_index_size):
num_input = 1 + i * S2**-approx_index_size
table_value = io_precision.get_base_format().round_sollya_object(
1 / num_input)
inv_approx_table[i] = table_value
# extracting initial reciprocal approximation
inv_approx_value = TableLoad(inv_approx_table,
tab_index,
precision=approx_precision,
tag="inv_approx_value",
debug=debug_fixed)
#inv_approx_value = TypeCast(inv_approx_value, precision = approx_precision)
pre_it0_input = zext(
SubSignalSelection(mant_vx,
p - 1 - approx_index_size,
p - 1,
tag="it0_input"), 1)
it0_input = TypeCast(pre_it0_input,
precision=approx_precision,
tag="it0_input",
debug=debug_fixed)
it1_precision = RTL_FixedPointFormat(
2,
2 * approx_index_size,
support_format=ML_StdLogicVectorFormat(2 + 2 * approx_index_size))
it1_input = mant_vx
final_approx = generate_NR_iteration(
mant_vx,
inv_approx_value,
(2, approx_index_size * 2), # mult precision
(-3, 2 * approx_index_size), # error precision
(2, approx_index_size * 3), # new-approx mult
(2, approx_index_size * 2), # new approx precision
self.implementation,
pipelined=0, #1 if self.pipelined else 0,
tag_suffix="_first")
# Inserting post-input pipeline stage
if self.pipelined: self.implementation.start_new_stage()
final_approx = generate_NR_iteration(
mant_vx,
final_approx,
# mult precision
(2, approx_index_size * 3),
# error precision
(-6, approx_index_size * 3),
# approx mult precision
(2, approx_index_size * 3),
# new approx precision
(2, approx_index_size * 3),
self.implementation,
pipelined=1 if self.pipelined else 0,
tag_suffix="_second")
# Inserting post-input pipeline stage
if self.pipelined: self.implementation.start_new_stage()
final_approx = generate_NR_iteration(
mant_vx,
final_approx,
# mult-precision
(2, 2 * p - 1),
# error precision
(-(3 * approx_index_size) / 2, approx_index_size * 2 + p - 1),
# mult approx mult precision
(2, approx_index_size * 2 + p - 1),
# approx precision
(2, p),
self.implementation,
pipelined=2 if self.pipelined else 0,
tag_suffix="_third")
# Inserting post-input pipeline stage
if self.pipelined: self.implementation.start_new_stage()
final_approx = generate_NR_iteration(
mant_vx,
final_approx, (2, 2 * p), (-(4 * p) / 5, 2 * p), (2, 2 * p),
(2, 2 * p),
self.implementation,
pipelined=2 if self.pipelined else 0,
tag_suffix="_last")
# Inserting post-input pipeline stage
if self.pipelined: self.implementation.start_new_stage()
final_approx.set_attributes(tag="final_approx", debug=debug_hex)
last_approx_norm = final_approx
offset_bit = BitSelection(last_approx_norm,
FixedPointPosition(
last_approx_norm,
0,
align=FixedPointPosition.FromPointToLSB),
tag="offset_bit",
debug=debug_std)
# extracting bit to determine if result should be left-shifted and
# exponent incremented
not_decrement = offset_bit
final_approx_reduced = SubSignalSelection(
final_approx,
FixedPointPosition(final_approx,
-(p - 1),
align=FixedPointPosition.FromPointToLSB),
FixedPointPosition(final_approx,
0,
align=FixedPointPosition.FromPointToLSB),
precision=fixed_point(p, 0, signed=False))
final_approx_reduced_shifted = SubSignalSelection(
final_approx,
FixedPointPosition(final_approx,
-p,
align=FixedPointPosition.FromPointToLSB),
FixedPointPosition(final_approx,
-1,
align=FixedPointPosition.FromPointToLSB),
precision=fixed_point(p, 0, signed=False))
# unrounded mantissa field excluding leading digit
unrounded_mant_field = Select(
equal_to(not_decrement, 1),
final_approx_reduced,
final_approx_reduced_shifted,
precision=fixed_point(p, 0, signed=False),
tag="unrounded_mant_field",
debug=debug_hex,
)
def get_bit(optree, bit_index):
bit_sel = BitSelection(
optree,
FixedPointPosition(optree,
-bit_index,
align=FixedPointPosition.FromPointToLSB))
return bit_sel
mant_lsb = Select(
equal_to(not_decrement, 1),
get_bit(final_approx, p - 1),
get_bit(final_approx, p),
precision=ML_StdLogic,
tag="mant_lsb",
debug=debug_std,
)
round_bit = Select(
equal_to(not_decrement, 1),
get_bit(final_approx, p),
get_bit(final_approx, p + 1),
precision=ML_StdLogic,
tag="round_bit",
debug=debug_std,
)
sticky_bit_input = Select(
equal_to(not_decrement, 1),
SubSignalSelection(final_approx,
0,
FixedPointPosition(
final_approx,
-(p + 1),
align=FixedPointPosition.FromPointToLSB),
precision=None,
tag="sticky_bit_input"),
SubSignalSelection(final_approx,
0,
FixedPointPosition(
final_approx,
-(p + 2),
align=FixedPointPosition.FromPointToLSB),
precision=None,
tag="sticky_bit_input"),
)
sticky_bit = Select(Equal(sticky_bit_input, Constant(0,
precision=None)),
Constant(0, precision=ML_StdLogic),
Constant(1, precision=ML_StdLogic),
precision=ML_StdLogic,
tag="sticky_bit",
debug=debug_std)
# TODO: manage leading digit (in case of subnormal result)
pre_result = unrounded_mant_field
# real_exp = exp_vx - bias
# - real_exp = bias - exp_vx
# encoded negated exp = bias - exp_vx + bias = 2 * bias - exp_vx
fp_io_precision = io_precision.get_base_format()
neg_exp = -2 * fp_io_precision.get_bias() - exp_vx
neg_exp.set_attributes(tag="neg_exp", debug=debug_fixed)
res_exp = Subtraction(neg_exp,
Select(equal_to(not_decrement, 1),
Constant(0,
precision=exp_fixed_precision),
Constant(1,
precision=exp_fixed_precision),
precision=None,
tag="exp_offset",
debug=debug_fixed),
tag="res_exp",
debug=debug_fixed)
res_exp_field = SubSignalSelection(
res_exp,
FixedPointPosition(res_exp,
0,
align=FixedPointPosition.FromPointToLSB,
tag="res_exp_field LSB"),
FixedPointPosition(res_exp,
exp_size - 1,
align=FixedPointPosition.FromPointToLSB,
tag="res_exp_field MSB"),
precision=None,
tag="res_exp_field",
# debug=debug_fixed
)
result_sign = CopySign(vx, precision=ML_StdLogic)
exp_mant_precision = ML_StdLogicVectorFormat(
io_precision.get_bit_size() - 1)
rnd_mode_is_rne = Equal(rnd_mode, rnd_rne, precision=ML_Bool)
rnd_mode_is_ru = Equal(rnd_mode, rnd_ru, precision=ML_Bool)
rnd_mode_is_rd = Equal(rnd_mode, rnd_rd, precision=ML_Bool)
rnd_mode_is_rz = Equal(rnd_mode, rnd_rz, precision=ML_Bool)
round_incr = Conversion(
logical_or_reduce([
logical_and_reduce([
rnd_mode_is_rne,
equal_to(round_bit, 1),
equal_to(sticky_bit, 1)
]),
logical_and_reduce([
rnd_mode_is_rne,
equal_to(round_bit, 1),
equal_to(sticky_bit, 0),
equal_to(mant_lsb, 1)
]),
logical_and_reduce([
rnd_mode_is_ru,
equal_to(result_sign, 0),
LogicalOr(equal_to(round_bit, 1),
equal_to(sticky_bit, 1),
precision=ML_Bool)
]),
logical_and_reduce([
rnd_mode_is_rd,
equal_to(result_sign, 1),
LogicalOr(equal_to(round_bit, 1),
equal_to(sticky_bit, 1),
precision=ML_Bool)
]),
]),
precision=fixed_point(1, 0, signed=False),
tag="round_incr",
#debug=debug_fixed
)
# Precision for result without sign
unsigned_result_prec = fixed_point((p - 1) + exp_size, 0)
unrounded_mant_field_nomsb = Conversion(
unrounded_mant_field,
precision=fixed_point(p - 1, 0, signed=False),
tag="unrounded_mant_field_nomsb",
debug=debug_hex)
pre_rounded_unsigned_result = Concatenation(
res_exp_field,
unrounded_mant_field_nomsb,
precision=unsigned_result_prec,
tag="pre_rounded_unsigned_result")
unsigned_result_rounded = Addition(pre_rounded_unsigned_result,
round_incr,
precision=unsigned_result_prec,
tag="unsigned_result")
vr_out = TypeCast(Concatenation(
result_sign,
TypeCast(unsigned_result_rounded,
precision=ML_StdLogicVectorFormat(p - 1 + exp_size)),
precision=ML_StdLogicVectorFormat(io_precision.get_bit_size())),
precision=io_precision,
debug=debug_hex,
tag="vr_out")
self.implementation.add_output_signal("vr_out", vr_out)
return [self.implementation]
def init_test_generator(self):
""" Initialize test case generator """
weight_map = {
FPRandomGen.Category.SpecialValues:
0.0 if self.disable_sv_testing else 0.1,
FPRandomGen.Category.Subnormal:
0.0 if self.disable_sub_testing else 0.2,
FPRandomGen.Category.Normal:
0.7,
}
self.input_generator = FPRandomGen(self.precision,
weight_map=weight_map)
def generate_test_case(self,
input_signals,
io_map,
index,
test_range=None):
""" specific test case generation for K1C TCA BLAU """
rnd_mode = random.randrange(4)
input_values = {
"rnd_mode": rnd_mode,
"x": self.input_generator.get_new_value()
}
return input_values
def numeric_emulate(self, io_map):
vx = io_map["x"]
rnd_mode_i = io_map["rnd_mode"]
def div_numeric_emulate(vx):
sollya_format = self.precision.get_sollya_object()
return sollya.round(1.0 / vx, sollya_format, rnd_mode)
rnd_mode = {
0: sollya.RN,
1: sollya.RU,
2: sollya.RD,
3: sollya.RZ
}[rnd_mode_i]
value_mapping = {
is_plus_infty:
lambda _: 0.0,
is_nan:
lambda _: FP_QNaN(self.precision),
is_minus_infty:
lambda _: FP_QNaN(self.precision),
is_plus_zero:
lambda _: FP_PlusInfty(self.precision),
is_minus_zero:
lambda _: FP_MinusInfty(self.precision),
is_sv_omega:
lambda op: lambda _: div_numeric_emulate(op.get_value()),
lambda op: not (FP_SpecialValue.is_special_value(op)):
div_numeric_emulate,
}
result = {}
for predicate in value_mapping:
if predicate(vx):
result["vr_out"] = value_mapping[predicate](vx)
return result
Log.report(Log.Error,
"no predicate fits {} in numeric_emulate\n".format(vx))
#standard_test_cases = [({"x": 1.0, "y": (S2**-11 + S2**-17)}, None)]
standard_test_cases = [
({
"x": 2.0,
"rnd_mode": 0
}, None),
({
"x": sollya.parse("0x1.24f608p0"),
"rnd_mode": 0
}, None),
({
"x": 1.5,
"rnd_mode": 0
}, None),
]
class ML_Exp2(ScalarUnaryFunction):
function_name = "ml_exp2"
def __init__(self, args=DefaultArgTemplate):
# initializing base class
super().__init__(args)
@staticmethod
def get_default_args(**kw):
""" Return a structure containing the arguments for ML_Exponential,
builtin from a default argument mapping overloaded with @p kw """
default_args_exp2 = {
"output_file": "ml_exp2.c",
"function_name": "ml_exp2",
"precision": ML_Binary32,
"accuracy": ML_Faithful,
"target": GenericProcessor.get_target_instance()
}
default_args_exp2.update(kw)
return DefaultArgTemplate(**default_args_exp2)
def generate_scalar_scheme(self, vx, inline_select=False):
Log.set_dump_stdout(True)
Log.report(Log.Info,
"\033[33;1m generating implementation scheme \033[0m")
if self.debug_flag:
Log.report(Log.Info, "\033[31;1m debug has been enabled \033[0;m")
# local overloading of RaiseReturn operation
def ExpRaiseReturn(*args, **kwords):
kwords["arg_value"] = vx
kwords["function_name"] = self.function_name
return RaiseReturn(*args, **kwords)
# r_interval = Interval(0, 1.0)
index_size = 3
r_interval = Interval(-2**(-index_size), 2**-index_size)
local_ulp = sup(ulp(2**r_interval, self.precision))
Log.report(Log.Info, "ulp: ", local_ulp)
error_goal = S2**-1 * local_ulp
Log.report(Log.Info, "error goal: ", error_goal)
sollya_precision = {
ML_Binary32: sollya.binary32,
ML_Binary64: sollya.binary64
}[self.precision]
int_precision = {
ML_Binary32: ML_Int32,
ML_Binary64: ML_Int64
}[self.precision]
# Argument Reduction
# r = x - floor(x), r >= 0
vx_floor = Floor(vx,
precision=self.precision,
tag='vx_floor',
debug=debug_multi)
vx_int = Conversion(vx_floor,
precision=int_precision,
tag="vx_int",
debug=debug_multi)
vx_intf = vx_floor # Conversion(vx_int, precision = self.precision)
vx_r = vx - vx_intf
r_hi = NearestInteger(vx_r * 2**index_size,
precision=self.precision,
tag="r_hi",
debug=debug_multi)
# clamping r_hi_int within table-size to make sure
# it does not exceeds hi_part_table when used to index it
r_hi_int = Max(
Min(
Conversion(r_hi,
precision=int_precision,
tag="r_hi_int",
debug=debug_multi), 2**index_size + 1), 0)
r_lo = vx_r - r_hi * 2**-index_size
r_lo.set_attributes(tag="r_lo", debug=debug_multi)
vx_r.set_attributes(tag="vx_r", debug=debug_multi)
degree = sup(guessdegree(2**(sollya.x), r_interval, error_goal)) + 2
precision_list = [1] + [self.precision] * degree
exp_X = ExponentInsertion(vx_int,
tag="exp_X",
debug=debug_multi,
precision=self.precision)
#Polynomial Approx
polynomial_scheme_builder = PolynomialSchemeEvaluator.generate_horner_scheme
poly_object, poly_error = Polynomial.build_from_approximation_with_error(
2**(sollya.x) - 1, degree, precision_list, r_interval,
sollya.absolute)
Log.report(Log.Info, "Poly : %s" % poly_object)
Log.report(Log.Info, "poly_error : ", poly_error)
poly = polynomial_scheme_builder(poly_object.sub_poly(start_index=1),
r_lo,
unified_precision=self.precision)
poly.set_attributes(tag="poly", debug=debug_multi)
hi_part_table = ML_NewTable(dimensions=[2**index_size + 1],
storage_precision=self.precision,
tag=self.uniquify_name("exp2_table"),
const=True)
for i in range(2**index_size + 1):
input_value = i * 2**-index_size
tab_value = self.precision.round_sollya_object(
sollya.SollyaObject(2)**(input_value))
hi_part_table[i] = tab_value
hi_part_value = TableLoad(hi_part_table,
r_hi_int,
precision=self.precision,
tag="hi_part_value",
debug=debug_multi)
#Handling special cases
oflow_bound = Constant(self.precision.get_emax() + 1,
precision=self.precision)
subnormal_bound = self.precision.get_emin_subnormal()
uflow_bound = self.precision.get_emin_normal()
Log.report(Log.Info, "oflow : ", oflow_bound)
#print "uflow : ", uflow_bound
#print "sub : ", subnormal_bound
test_overflow = Comparison(vx,
oflow_bound,
specifier=Comparison.GreaterOrEqual)
test_overflow.set_attributes(tag="oflow_test",
debug=debug_multi,
likely=False,
precision=ML_Bool)
test_underflow = Comparison(vx, uflow_bound, specifier=Comparison.Less)
test_underflow.set_attributes(tag="uflow_test",
debug=debug_multi,
likely=False,
precision=ML_Bool)
test_subnormal = Comparison(vx,
subnormal_bound,
specifier=Comparison.Greater)
test_subnormal.set_attributes(tag="sub_test",
debug=debug_multi,
likely=False,
precision=ML_Bool)
subnormal_offset = -(uflow_bound - vx_int)
subnormal_offset.set_attributes(tag="offset", debug=debug_multi)
exp_offset = ExponentInsertion(subnormal_offset,
precision=self.precision,
debug=debug_multi,
tag="exp_offset")
exp_min = ExponentInsertion(uflow_bound,
precision=self.precision,
debug=debug_multi,
tag="exp_min")
subnormal_result = hi_part_value * exp_offset * exp_min * poly + hi_part_value * exp_offset * exp_min
test_std = LogicalOr(test_overflow,
test_underflow,
precision=ML_Bool,
tag="std_test",
likely=False,
debug=debug_multi)
#Reconstruction
result = hi_part_value * exp_X * poly + hi_part_value * exp_X
result.set_attributes(tag="result", debug=debug_multi)
C0 = Constant(0, precision=self.precision)
if inline_select:
scheme = Select(
test_std,
Select(test_overflow, FP_PlusInfty(self.precision),
Select(
test_subnormal,
subnormal_result,
C0,
)),
result,
)
return scheme
else:
return_inf = Return(FP_PlusInfty(self.precision))
return_C0 = Return(C0)
return_sub = Return(subnormal_result)
return_std = Return(result)
non_std_statement = Statement(
ConditionBlock(
test_overflow, return_inf,
ConditionBlock(test_subnormal, return_sub, return_C0)))
scheme = Statement(
ConditionBlock(test_std, non_std_statement, return_std))
return scheme
def generate_emulate(self, result_ternary, result, mpfr_x, mpfr_rnd):
""" generate the emulation code for ML_Log2 functions
mpfr_x is a mpfr_t variable which should have the right precision
mpfr_rnd is the rounding mode
"""
emulate_func_name = "mpfr_exp"
emulate_func_op = FunctionOperator(emulate_func_name,
arg_map={
0: FO_Arg(0),
1: FO_Arg(1),
2: FO_Arg(2)
},
require_header=["mpfr.h"])
emulate_func = FunctionObject(emulate_func_name,
[ML_Mpfr_t, ML_Mpfr_t, ML_Int32],
ML_Int32, emulate_func_op)
mpfr_call = Statement(
ReferenceAssign(result_ternary,
emulate_func(result, mpfr_x, mpfr_rnd)))
return mpfr_call
def numeric_emulate(self, input_value):
return sollya.SollyaObject(2)**(input_value)
standard_test_cases = [[sollya.parse(x)] for x in [
"0x1.ffead1bac7ad2p+9", "-0x1.ee9cb4p+1", "-0x1.db0928p+3",
"0x1.c3a07c4c711cfp-1", "0x1.e79d45fd647f3p-1", "-infty"
]]
class ML_Erf(ScalarUnaryFunction):
""" Meta implementation of the error-function """
function_name = "ml_erf"
def __init__(self, args):
super().__init__(args)
@staticmethod
def get_default_args(**kw):
""" Return a structure containing the arguments for ML_Erf,
builtin from a default argument mapping overloaded with @p kw """
default_args_erf = {
"output_file":
"my_erf.c",
"function_name":
"my_erf",
"precision":
ML_Binary32,
"accuracy":
ML_Faithful,
"target":
GenericProcessor.get_target_instance(),
"passes": [("start:instantiate_abstract_prec"),
("start:instantiate_prec"),
("start:basic_legalization"),
("start:expand_multi_precision")],
}
default_args_erf.update(kw)
return DefaultArgTemplate(**default_args_erf)
def generate_scalar_scheme(self, vx):
abs_vx = Abs(vx, precision=self.precision)
FCT_LIMIT = 1.0
one_limit = search_bound_threshold(sollya.erf, FCT_LIMIT, 1.0, 10.0,
self.precision)
one_limit_exp = int(sollya.floor(sollya.log2(one_limit)))
Log.report(Log.Debug, "erf(x) = 1.0 limit is {}, with exp={}",
one_limit, one_limit_exp)
upper_approx_bound = 10
# empiral numbers
eps_exp = {ML_Binary32: -3, ML_Binary64: -5}[self.precision]
eps = S2**eps_exp
Log.report(Log.Info, "building mathematical polynomial")
approx_interval = Interval(0, eps)
# fonction to approximate is erf(x) / x
# it is an even function erf(x) / x = erf(-x) / (-x)
approx_fct = sollya.erf(sollya.x) - (sollya.x)
poly_degree = int(
sup(
guessdegree(approx_fct, approx_interval, S2**
-(self.precision.get_field_size() + 5)))) + 1
poly_degree_list = list(range(1, poly_degree, 2))
Log.report(Log.Debug, "poly_degree is {} and list {}", poly_degree,
poly_degree_list)
global_poly_object = Polynomial.build_from_approximation(
approx_fct, poly_degree_list,
[self.precision] * len(poly_degree_list), approx_interval,
sollya.relative)
Log.report(
Log.Debug, "inform is {}",
dirtyinfnorm(approx_fct - global_poly_object.get_sollya_object(),
approx_interval))
poly_object = global_poly_object.sub_poly(start_index=1, offset=1)
ext_precision = {
ML_Binary32: ML_SingleSingle,
ML_Binary64: ML_DoubleDouble,
}[self.precision]
pre_poly = PolynomialSchemeEvaluator.generate_horner_scheme(
poly_object, abs_vx, unified_precision=self.precision)
result = FMA(pre_poly, abs_vx, abs_vx)
result.set_attributes(tag="result", debug=debug_multi)
eps_target = S2**-(self.precision.get_field_size() + 5)
def offset_div_function(fct):
return lambda offset: fct(sollya.x + offset)
# empiral numbers
field_size = {ML_Binary32: 6, ML_Binary64: 8}[self.precision]
near_indexing = SubFPIndexing(eps_exp, 0, 6, self.precision)
near_approx = generic_poly_split(offset_div_function(sollya.erf),
near_indexing, eps_target,
self.precision, abs_vx)
near_approx.set_attributes(tag="near_approx", debug=debug_multi)
def offset_function(fct):
return lambda offset: fct(sollya.x + offset)
medium_indexing = SubFPIndexing(1, one_limit_exp, 7, self.precision)
medium_approx = generic_poly_split(offset_function(sollya.erf),
medium_indexing, eps_target,
self.precision, abs_vx)
medium_approx.set_attributes(tag="medium_approx", debug=debug_multi)
# approximation for positive values
scheme = ConditionBlock(
abs_vx < eps, Return(result),
ConditionBlock(
abs_vx < near_indexing.get_max_bound(), Return(near_approx),
ConditionBlock(abs_vx < medium_indexing.get_max_bound(),
Return(medium_approx),
Return(Constant(1.0,
precision=self.precision)))))
return scheme
def numeric_emulate(self, input_value):
return sollya.erf(input_value)
standard_test_cases = [
(sollya.parse("0x1.4c0d4e9f58p-8"), ),
(1.0, None),
(4.0, None),
(0.5, None),
(1.5, None),
(1024.0, None),
(sollya.parse("0x1.13b2c6p-2"), None),
(sollya.parse("0x1.2cb10ap-5"), None),
(0.0, None),
(sollya.parse("0x1.07e08ep+1"), None),
]
import sys
#sys.path.append("/home/lauter/pythonsollya-install/lib/python2.7/site-packages")
import sollya
sollya.execute("wcpg.sol")
wcpg = sollya.parse("wcpg")
def function(self,
fct_expr="exp(x)",
io_format="binary32",
vector_size=1,
target="generic",
registered_pass_list="",
sub_vector_size="default",
debug=False,
language="c",
range_nan="false",
range_lo="-infty",
range_hi="+infty",
bench="false",
eval_error="false"):
total_time = None
input_url = ("{localhost}/function?fct_expr={fct_expr}&io_format={io_format}&" +\
"vector_size={vector_size}&target={target}&" +\
"registered_pass_list={registered_pass_list}&" + \
"debug={debug}&language={language}&eval_error={eval_error}").format(
localhost=self.mwa.LOCALHOST,
fct_expr=fct_expr, io_format=io_format,
vector_size=vector_size, target=target,
registered_pass_list=registered_pass_list,
sub_vector_size=sub_vector_size, debug=debug,
language=language,
eval_error=eval_error)
# generate git commentary (indicating which version of metalibm was
# used to generate code)
ml_code_configuration.GLOBAL_GET_GIT_COMMENT = custom_get_common_git_comment(
self.mwa.LOCALHOST, lambda: input_url)
registered_pass_list = [
tag for tag in registered_pass_list.split(",") if tag != ""
]
error = None
source_code = ""
build_cmd = ""
report_issue_url = ""
# function results
max_error = None
# checking inputs
class KnownError(Exception):
""" known error exception which can are raised
when a manageable error is detected """
pass
try:
no_error = False
if not ml_function_expr.check_fct_expr(fct_expr):
source_code = "invalid function expression \"{}\"".format(
fct_expr)
elif not all((pass_tag in self.mwa.ALLOWED_PASS_LIST)
for pass_tag in registered_pass_list):
source_code = "unknown pass in {}".format([
pass_tag for pass_tag in registered_pass_list
if not pass_tag in self.mwa.ALLOWED_PASS_LIST
])
print(source_code)
# no allowed target list for now
elif not io_format in self.mwa.format_list:
source_code = ("forbidden format {}".format(io_format))
print(source_code)
elif not int(vector_size) in self.mwa.vector_size_list:
source_code = ("forbidden vector_size {}".format(vector_size))
print(source_code)
elif sub_vector_size != "default" and not int(
sub_vector_size) in self.mwa.sub_vector_size_list:
source_code = (
"forbidden sub_vector_size {}".format(sub_vector_size))
print(source_code)
elif not language in self.mwa.LANGUAGE_MAP:
source_code = ("forbidden language {}".format(language))
print(source_code)
elif not range_nan.lower() in ["true", "false"]:
source_code = ("invalid range NaN flag {}".format(range_nan))
print(source_code)
elif not bench.lower() in ["true", "false"]:
source_code = ("invalid bench flag {}".format(bench))
print(source_code)
elif not eval_error.lower() in ["true", "false"]:
source_code = ("invalid eval_error flag {}".format(bench))
print(source_code)
else:
no_error = True
if not no_error:
raise KnownError(source_code)
except KnownError as e:
# stat counter
self.stats.num_known_errors += 1
error = e
self.log_msg(e, tag="error")
except:
# stat counter
self.stats.num_unknwon_errors += 1
e = sys.exc_info()
error = "Exception:\n {}".format("".join(
traceback.format_exception(*e))).replace('\n', '<br/>')
source_code = ""
self.log_msg(error, tag="error")
else:
# clearing logs
ml_log_report.Log.log_stream.log_output = ""
try:
start_time = time.perf_counter()
fct_ctor = ml_function_expr.FunctionExpression
arity = ml_function_expr.count_expr_arity(fct_expr)
fct_extra_args = {}
language_object = self.mwa.LANGUAGE_MAP[language]
precision = precision_parser(io_format)
vector_size = int(vector_size)
sub_vector_size = None if sub_vector_size == "default" else int(
sub_vector_size)
range_nan = range_nan.lower() in ["true"]
eval_error = eval_error.lower() in ["true"]
bench = bench.lower() in ["true"]
if range_nan:
input_interval = None
else:
input_interval = sollya.Interval(sollya.parse(range_lo),
sollya.parse(range_hi))
debug = bool(debug)
target_class = target_parser(target)
target_inst = target_class()
passes = [
"beforecodegen:{}".format(pass_tag)
for pass_tag in registered_pass_list
if pass_tag in self.mwa.ALLOWED_PASS_LIST
]
args = fct_ctor.get_default_args(
function_expr_str=[fct_expr],
precision=precision,
input_precisions=(precision, ) * arity,
input_intervals=(input_interval, ) * arity,
vector_size=vector_size,
sub_vector_size=sub_vector_size,
passes=passes,
language=language_object,
debug=debug,
bench_test_number=100 if bench else None,
compute_max_error=eval_error,
execute_trigger=eval_error,
bench_test_range=input_interval,
target=target_inst,
**fct_extra_args)
# function instance object
fct_instance = fct_ctor(args=args)
# principal scheme
function_only_group = fct_instance.generate_function_list()
function_only_group = fct_instance.transform_function_group(
function_only_group)
function_only_code_obj = fct_instance.get_new_main_code_object(
)
function_only_code_obj = fct_instance.generate_code(
function_only_code_obj,
function_only_group,
language=fct_instance.language)
# actual source code
source_code = function_only_code_obj.get(
fct_instance.main_code_generator)
with open("source_code.dump.c", "w") as output_stream:
output_stream.write(source_code)
if eval_error:
fct_instance.main_code_generator.clear_memoization_map()
main_pre_statement, main_statement, function_group = fct_instance.instrument_function_group(
function_only_group, enable_subexpr_sharing=True)
EMBEDDING_BINARY = True
fct_instance.main_code_object = fct_instance.get_new_main_code_object(
)
bench_source_code_obj = fct_instance.generate_output(
EMBEDDING_BINARY, main_pre_statement, main_statement,
function_group)
execute_result = fct_instance.build_and_execute_source_code(
function_group, bench_source_code_obj)
max_error = execute_result["max_error"]
# constructing build command
build_cmd = SourceFile.get_build_command("<source_path>",
target_inst,
bin_name="ml_bench",
shared_object=False,
link=True,
expand_env_var=False)
total_time = time.perf_counter() - start_time
except:
self.stats.num_gen_errors += 1
e = sys.exc_info()
error = "Output: \n{}\nException:\n {}".format(
ml_log_report.Log.log_stream.log_output,
"".join(traceback.format_exception(*e))).replace(
'\n', '<br/>')
source_code = ""
self.log_msg(error, tag="error")
report_issue_url = gen_report_issue_url(
MetalibmWebApp.REPORT_ISSUE_BASE_URL,
precision=io_format,
fct_expr=fct_expr,
target=target,
vector_size=vector_size,
debug=debug,
language=language,
sub_vector_size=sub_vector_size,
registered_pass_list=registered_pass_list,
)
else:
self.stats.num_generated_function += 1
self.log_msg(input_url, tag="info")
return dict(code=source_code,
build_cmd=build_cmd,
precision=io_format,
fct_expr=fct_expr,
target=target,
vector_size=vector_size,
debug=debug,
language=language,
sub_vector_size=sub_vector_size,
registered_pass_list=registered_pass_list,
report_issue_url=report_issue_url,
error=error,
range_lo=range_lo,
range_hi=range_hi,
range_nan=range_nan,
total_time=total_time,
max_error=max_error,
eval_error=eval_error,
**self.mwa.option_dict)
class ML_HyperbolicSine(ScalarUnaryFunction):
function_name = "ml_sinh"
""" Implementation of hyperbolic sine function """
def __init__(self, args=DefaultArgTemplate):
# initializing base class
super().__init__(args)
@staticmethod
def get_default_args(**kw):
""" Return a structure containing the arguments for ML_HyperbolicSine,
builtin from a default argument mapping overloaded with @p kw """
default_args_sinh = {
"output_file": "my_sinh.c",
"function_name": "my_sinh",
"precision": ML_Binary32,
"accuracy": ML_Faithful,
"target": GenericProcessor.get_target_instance()
}
default_args_sinh.update(kw)
return DefaultArgTemplate(**default_args_sinh)
def generate_scalar_scheme(self, vx):
Log.set_dump_stdout(True)
Log.report(Log.Info, "\033[33;1m generating implementation scheme \033[0m")
if self.debug_flag:
Log.report(Log.Info, "\033[31;1m debug has been enabled \033[0;m")
index_size = 5
comp_lo = (vx < 0)
comp_lo.set_attributes(tag = "comp_lo", precision = ML_Bool)
sign = Select(comp_lo, -1, 1, precision = self.precision)
# as sinh is an odd function, we can simplify the input to its absolute
# value once the sign has been extracted
vx = Abs(vx)
int_precision = self.precision.get_integer_format()
# argument reduction
arg_reg_value = log(2)/2**index_size
inv_log2_value = round(1/arg_reg_value, self.precision.get_sollya_object(), sollya.RN)
inv_log2_cst = Constant(inv_log2_value, precision = self.precision, tag = "inv_log2")
# for r_hi to be accurate we ensure k * log2_hi_value_cst is exact
# by limiting the number of non-zero bits in log2_hi_value_cst
# cosh(x) ~ exp(abs(x))/2 for a big enough x
# cosh(x) > 2^1023 <=> exp(x) > 2^1024 <=> x > log(2^1024)
# k = inv_log2_value * x
# -1 for guard
max_k_approx = inv_log2_value * log(sollya.SollyaObject(2)**1024)
max_k_bitsize = int(ceil(log2(max_k_approx)))
Log.report(Log.Info, "max_k_bitsize: %d" % max_k_bitsize)
log2_hi_value_precision = self.precision.get_precision() - max_k_bitsize - 1
log2_hi_value = round(arg_reg_value, log2_hi_value_precision, sollya.RN)
log2_lo_value = round(arg_reg_value - log2_hi_value, self.precision.get_sollya_object(), sollya.RN)
log2_hi_value_cst = Constant(log2_hi_value, tag = "log2_hi_value", precision = self.precision)
log2_lo_value_cst = Constant(log2_lo_value, tag = "log2_lo_value", precision = self.precision)
k = Trunc(Multiplication(inv_log2_cst, vx), precision = self.precision)
k_log2 = Multiplication(k, log2_hi_value_cst, precision = self.precision, exact = True, tag = "k_log2", unbreakable = True)
r_hi = vx - k_log2
r_hi.set_attributes(tag = "r_hi", debug = debug_multi, unbreakable = True)
r_lo = -k * log2_lo_value_cst
# reduced argument
r = r_hi + r_lo
r.set_attributes(tag = "r", debug = debug_multi)
if is_gappa_installed():
r_eval_error = self.get_eval_error(r_hi, variable_copy_map =
{
vx: Variable("vx", interval = Interval(0, 715), precision = self.precision),
k: Variable("k", interval = Interval(0, 1024), precision = self.precision)
})
Log.report(Log.Verbose, "r_eval_error: ", r_eval_error)
approx_interval = Interval(-arg_reg_value, arg_reg_value)
error_goal_approx = 2**-(self.precision.get_precision())
poly_degree = sup(guessdegree(exp(sollya.x), approx_interval, error_goal_approx)) + 3
precision_list = [1] + [self.precision] * (poly_degree)
k_integer = Conversion(k, precision = int_precision, tag = "k_integer", debug = debug_multi)
k_hi = BitLogicRightShift(k_integer, Constant(index_size, precision=int_precision), tag = "k_int_hi", precision = int_precision, debug = debug_multi)
k_lo = Modulo(k_integer, 2**index_size, tag = "k_int_lo", precision = int_precision, debug = debug_multi)
pow_exp = ExponentInsertion(Conversion(k_hi, precision = int_precision), precision = self.precision, tag = "pow_exp", debug = debug_multi)
exp_table = ML_NewTable(dimensions = [2 * 2**index_size, 4], storage_precision = self.precision, tag = self.uniquify_name("exp2_table"))
for i in range(2 * 2**index_size):
input_value = i - 2**index_size if i >= 2**index_size else i
reduced_hi_prec = int(self.precision.get_mantissa_size() - 8)
# using SollyaObject wrapper to force evaluation by sollya
# with higher precision
exp_value = sollya.SollyaObject(2)**((input_value)* 2**-index_size)
mexp_value = sollya.SollyaObject(2)**((-input_value)* 2**-index_size)
pos_value_hi = round(exp_value, reduced_hi_prec, sollya.RN)
pos_value_lo = round(exp_value - pos_value_hi, self.precision.get_sollya_object(), sollya.RN)
neg_value_hi = round(mexp_value, reduced_hi_prec, sollya.RN)
neg_value_lo = round(mexp_value - neg_value_hi, self.precision.get_sollya_object(), sollya.RN)
exp_table[i][0] = neg_value_hi
exp_table[i][1] = neg_value_lo
exp_table[i][2] = pos_value_hi
exp_table[i][3] = pos_value_lo
# log2_value = log(2) / 2^index_size
# sinh(x) = 1/2 * (exp(x) - exp(-x))
# exp(x) = exp(x - k * log2_value + k * log2_value)
#
# r = x - k * log2_value
# exp(x) = exp(r) * 2 ^ (k / 2^index_size)
#
# k / 2^index_size = h + l * 2^-index_size, with k, h, l integers
# exp(x) = exp(r) * 2^h * 2^(l *2^-index_size)
#
# sinh(x) = exp(r) * 2^(h-1) * 2^(l *2^-index_size) - exp(-r) * 2^(-h-1) * 2^(-l *2^-index_size)
# S=2^(h-1), T = 2^(-h-1)
# exp(r) = 1 + poly_pos(r)
# exp(-r) = 1 + poly_neg(r)
# 2^(l / 2^index_size) = pos_value_hi + pos_value_lo
# 2^(-l / 2^index_size) = neg_value_hi + neg_value_lo
#
error_function = lambda p, f, ai, mod, t: dirtyinfnorm(f - p, ai)
poly_object, poly_approx_error = Polynomial.build_from_approximation_with_error(exp(sollya.x), poly_degree, precision_list, approx_interval, sollya.absolute, error_function = error_function)
Log.report(Log.Verbose, "poly_approx_error: {}, {}".format(poly_approx_error, float(log2(poly_approx_error))))
polynomial_scheme_builder = PolynomialSchemeEvaluator.generate_horner_scheme
poly_pos = polynomial_scheme_builder(poly_object.sub_poly(start_index = 1), r, unified_precision = self.precision)
poly_pos.set_attributes(tag = "poly_pos", debug = debug_multi)
poly_neg = polynomial_scheme_builder(poly_object.sub_poly(start_index = 1), -r, unified_precision = self.precision)
poly_neg.set_attributes(tag = "poly_neg", debug = debug_multi)
table_index = Addition(k_lo, Constant(2**index_size, precision = int_precision), precision = int_precision, tag = "table_index", debug = debug_multi)
neg_value_load_hi = TableLoad(exp_table, table_index, 0, tag = "neg_value_load_hi", debug = debug_multi)
neg_value_load_lo = TableLoad(exp_table, table_index, 1, tag = "neg_value_load_lo", debug = debug_multi)
pos_value_load_hi = TableLoad(exp_table, table_index, 2, tag = "pos_value_load_hi", debug = debug_multi)
pos_value_load_lo = TableLoad(exp_table, table_index, 3, tag = "pos_value_load_lo", debug = debug_multi)
k_plus = Max(
Subtraction(k_hi, Constant(1, precision = int_precision), precision=int_precision, tag="k_plus", debug=debug_multi),
Constant(self.precision.get_emin_normal(), precision = int_precision))
k_neg = Max(
Subtraction(-k_hi, Constant(1, precision=int_precision), precision=int_precision, tag="k_neg", debug=debug_multi),
Constant(self.precision.get_emin_normal(), precision = int_precision))
# 2^(h-1)
pow_exp_pos = ExponentInsertion(k_plus, precision = self.precision, tag="pow_exp_pos", debug=debug_multi)
# 2^(-h-1)
pow_exp_neg = ExponentInsertion(k_neg, precision = self.precision, tag="pow_exp_neg", debug=debug_multi)
hi_terms = (pos_value_load_hi * pow_exp_pos - neg_value_load_hi * pow_exp_neg)
hi_terms.set_attributes(tag = "hi_terms", debug=debug_multi)
pos_exp = (pos_value_load_hi * poly_pos + (pos_value_load_lo + pos_value_load_lo * poly_pos)) * pow_exp_pos
pos_exp.set_attributes(tag = "pos_exp", debug = debug_multi)
neg_exp = (neg_value_load_hi * poly_neg + (neg_value_load_lo + neg_value_load_lo * poly_neg)) * pow_exp_neg
neg_exp.set_attributes(tag = "neg_exp", debug = debug_multi)
result = Addition(
Subtraction(
pos_exp,
neg_exp,
precision=self.precision,
),
hi_terms,
precision=self.precision,
tag="result",
debug=debug_multi
)
# ov_value
ov_value = round(asinh(self.precision.get_max_value()), self.precision.get_sollya_object(), sollya.RD)
ov_flag = Comparison(Abs(vx), Constant(ov_value, precision = self.precision), specifier = Comparison.Greater)
# main scheme
scheme = Statement(
Return(
Select(
ov_flag,
sign*FP_PlusInfty(self.precision),
sign*result
)))
return scheme
def numeric_emulate(self, input_value):
return sinh(input_value)
standard_test_cases =[[sollya.parse(x)] for x in [
"0x1.8d3694p-5", "0x1.efc2cp-6", "0x1.f55ddap-5"]
]
# created: Dec 23rd, 2013 # last-modified: Oct 6th, 2015 # # author(s): Nicolas Brunie ([email protected]) ############################################################################### import sollya from ..utility.log_report import Log from ..code_generation.code_constant import * import re S2 = sollya.SollyaObject(2) # numerical floating-point constants ml_nan = sollya.parse("nan") ml_infty = sollya.parse("infty") ## class for floating-point exception class ML_FloatingPointException: pass ## class for type of floating-point exceptions class ML_FloatingPointException_Type(object): ## dummy placeholder to generate C constant for FP exception (should raise error) def get_cst(self, value, language = C_Code): return "NONE" def is_cst_decl_required(self): return False ## ML object for floating-point exception type ML_FPE_Type = ML_FloatingPointException_Type()
def numeric_emulate(self, x, y):
if x != 0 and y == 0:
# multiplication to correct the sign
return x * sollya.parse("infty")
return x / y
class ML_Division(ML_FunctionBasis):
function_name = "ml_div"
arity = 2
def __init__(self, args=DefaultArgTemplate):
# initializing base class
ML_FunctionBasis.__init__(self, args=args)
self.num_iter = args.num_iter
@staticmethod
def get_default_args(**args):
""" Generate a default argument structure set specifically for
the Hyperbolic Cosine """
default_div_args = {
"precision":
ML_Binary32,
"accuracy":
ML_CorrectlyRounded,
"target":
GenericProcessor.get_target_instance(),
"output_file":
"my_div.c",
"function_name":
"my_div",
"input_intervals": [DefaultArgTemplate.input_intervals[0]] * 2,
"auto_test_range":
DefaultArgTemplate.auto_test_range * 2,
"bench_test_range":
DefaultArgTemplate.bench_test_range * 2,
"language":
C_Code,
"num_iter":
3,
"passes": [
"typing:basic_legalization",
"beforecodegen:expand_multi_precision"
],
"vector_size":
1,
}
default_div_args.update(args)
return DefaultArgTemplate(**default_div_args)
def generate_scheme(self):
# 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])
# maximum exponent magnitude (to avoid overflow/ underflow during
# intermediary computations
int_prec = self.precision.get_integer_format()
max_exp_mag = Constant(self.precision.get_emax() - 1,
precision=int_prec)
exact_ex = ExponentExtraction(vx,
tag="exact_ex",
precision=int_prec,
debug=debug_multi)
exact_ey = ExponentExtraction(vy,
tag="exact_ey",
precision=int_prec,
debug=debug_multi)
ex = Max(Min(exact_ex, max_exp_mag, precision=int_prec),
-max_exp_mag,
tag="ex",
precision=int_prec)
ey = Max(Min(exact_ey, max_exp_mag, precision=int_prec),
-max_exp_mag,
tag="ey",
precision=int_prec)
Attributes.set_default_rounding_mode(ML_RoundToNearest)
Attributes.set_default_silent(True)
# computing the inverse square root
init_approx = None
scaling_factor_x = ExponentInsertion(-ex,
tag="sfx_ei",
precision=self.precision,
debug=debug_multi)
scaling_factor_y = ExponentInsertion(-ey,
tag="sfy_ei",
precision=self.precision,
debug=debug_multi)
def test_interval_out_of_bound_risk(x_range, y_range):
""" Try to determine from x and y's interval if there is a risk
of underflow or overflow """
div_range = abs(x_range / y_range)
underflow_risk = sollya.inf(div_range) < S2**(
self.precision.get_emin_normal() + 2)
overflow_risk = sollya.sup(div_range) > S2**(
self.precision.get_emax() - 2)
return underflow_risk or overflow_risk
out_of_bound_risk = (self.input_intervals[0] is None
or self.input_intervals[1] is None
) or test_interval_out_of_bound_risk(
self.input_intervals[0],
self.input_intervals[1])
Log.report(Log.Debug,
"out_of_bound_risk: {}".format(out_of_bound_risk))
# scaled version of vx and vy, to avoid overflow and underflow
if out_of_bound_risk:
scaled_vx = vx * scaling_factor_x
scaled_vy = vy * scaling_factor_y
scaled_interval = MetaIntervalList(
[MetaInterval(Interval(-2, -1)),
MetaInterval(Interval(1, 2))])
scaled_vx.set_attributes(tag="scaled_vx",
debug=debug_multi,
interval=scaled_interval)
scaled_vy.set_attributes(tag="scaled_vy",
debug=debug_multi,
interval=scaled_interval)
seed_interval = 1 / scaled_interval
print("seed_interval=1/{}={}".format(scaled_interval,
seed_interval))
else:
scaled_vx = vx
scaled_vy = vy
seed_interval = 1 / scaled_vy.get_interval()
# We need a first approximation to 1 / scaled_vy
dummy_seed = ReciprocalSeed(EmptyOperand(precision=self.precision),
precision=self.precision)
if self.processor.is_supported_operation(dummy_seed, self.language):
init_approx = ReciprocalSeed(scaled_vy,
precision=self.precision,
tag="init_approx",
debug=debug_multi)
else:
# generate tabulated version of seed
raise NotImplementedError
current_approx_std = init_approx
# correctly-rounded inverse computation
num_iteration = self.num_iter
Attributes.unset_default_rounding_mode()
Attributes.unset_default_silent()
# check if inputs are zeros
x_zero = Test(vx,
specifier=Test.IsZero,
likely=False,
precision=ML_Bool)
y_zero = Test(vy,
specifier=Test.IsZero,
likely=False,
precision=ML_Bool)
comp_sign = Test(vx,
vy,
specifier=Test.CompSign,
tag="comp_sign",
debug=debug_multi)
# check if divisor is NaN
y_nan = Test(vy, specifier=Test.IsNaN, likely=False, precision=ML_Bool)
# check if inputs are signaling NaNs
x_snan = Test(vx,
specifier=Test.IsSignalingNaN,
likely=False,
precision=ML_Bool)
y_snan = Test(vy,
specifier=Test.IsSignalingNaN,
likely=False,
precision=ML_Bool)
# check if inputs are infinities
x_inf = Test(vx,
specifier=Test.IsInfty,
likely=False,
tag="x_inf",
precision=ML_Bool)
y_inf = Test(vy,
specifier=Test.IsInfty,
likely=False,
tag="y_inf",
debug=debug_multi,
precision=ML_Bool)
scheme = None
gappa_vx, gappa_vy = None, None
# initial reciprocal approximation of 1.0 / scaled_vy
inv_iteration_list, recp_approx = compute_reduced_reciprocal(
init_approx, scaled_vy, self.num_iter)
recp_approx.set_attributes(tag="recp_approx", debug=debug_multi)
# approximation of scaled_vx / scaled_vy
yerr_last, reduced_div_approx, div_iteration_list = compute_reduced_division(
scaled_vx, scaled_vy, recp_approx)
eval_error_range, div_eval_error_range = self.solve_eval_error(
init_approx, recp_approx, reduced_div_approx, scaled_vx, scaled_vy,
inv_iteration_list, div_iteration_list, S2**-7, seed_interval)
eval_error = sup(abs(eval_error_range))
recp_interval = 1 / scaled_vy.get_interval() + eval_error_range
recp_approx.set_interval(recp_interval)
div_interval = scaled_vx.get_interval() / scaled_vy.get_interval(
) + div_eval_error_range
reduced_div_approx.set_interval(div_interval)
reduced_div_approx.set_tag("reduced_div_approx")
if out_of_bound_risk:
unscaled_result = scaling_div_result(reduced_div_approx, ex,
scaling_factor_y,
self.precision)
subnormal_result = subnormalize_result(recp_approx,
reduced_div_approx, ex, ey,
yerr_last, self.precision)
else:
unscaled_result = reduced_div_approx
subnormal_result = reduced_div_approx
x_inf_or_nan = Test(vx, specifier=Test.IsInfOrNaN, likely=False)
y_inf_or_nan = Test(vy,
specifier=Test.IsInfOrNaN,
likely=False,
tag="y_inf_or_nan",
debug=debug_multi)
# generate IEEE exception raising only of libm-compliant
# mode is enabled
enable_raise = self.libm_compliant
# managing special cases
# x inf and y inf
pre_scheme = ConditionBlock(
x_inf_or_nan,
ConditionBlock(
x_inf,
ConditionBlock(
y_inf_or_nan,
Statement(
# signaling NaNs raise invalid operation flags
ConditionBlock(y_snan, Raise(ML_FPE_Invalid))
if enable_raise else Statement(),
Return(FP_QNaN(self.precision)),
),
ConditionBlock(comp_sign,
Return(FP_MinusInfty(self.precision)),
Return(FP_PlusInfty(self.precision)))),
Statement(
ConditionBlock(x_snan, Raise(ML_FPE_Invalid))
if enable_raise else Statement(),
Return(FP_QNaN(self.precision)))),
ConditionBlock(
x_zero,
ConditionBlock(
LogicalOr(y_zero, y_nan, precision=ML_Bool),
Statement(
ConditionBlock(y_snan, Raise(ML_FPE_Invalid))
if enable_raise else Statement(),
Return(FP_QNaN(self.precision))), Return(vx)),
ConditionBlock(
y_inf_or_nan,
ConditionBlock(
y_inf,
Return(
Select(comp_sign, FP_MinusZero(self.precision),
FP_PlusZero(self.precision))),
Statement(
ConditionBlock(y_snan, Raise(ML_FPE_Invalid))
if enable_raise else Statement(),
Return(FP_QNaN(self.precision)))),
ConditionBlock(
y_zero,
Statement(
Raise(ML_FPE_DivideByZero)
if enable_raise else Statement(),
ConditionBlock(
comp_sign,
Return(FP_MinusInfty(self.precision)),
Return(FP_PlusInfty(self.precision)))),
# managing numerical value result cases
Statement(
recp_approx,
reduced_div_approx,
ConditionBlock(
Test(unscaled_result,
specifier=Test.IsSubnormal,
likely=False),
# result is subnormal
Statement(
# inexact flag should have been raised when computing yerr_last
# ConditionBlock(
# Comparison(
# yerr_last, 0,
# specifier=Comparison.NotEqual, likely=True),
# Statement(Raise(ML_FPE_Inexact, ML_FPE_Underflow))
#),
Return(subnormal_result), ),
# result is normal
Statement(
# inexact flag should have been raised when computing yerr_last
#ConditionBlock(
# Comparison(
# yerr_last, 0,
# specifier=Comparison.NotEqual, likely=True),
# Raise(ML_FPE_Inexact)
#),
Return(unscaled_result))),
)))))
# managing rounding mode save and restore
# to ensure intermediary computations are performed in round-to-nearest
# clearing exception before final computation
#rnd_mode = GetRndMode()
#scheme = Statement(
# rnd_mode,
# SetRndMode(ML_RoundToNearest),
# yerr_last,
# SetRndMode(rnd_mode),
# unscaled_result,
# ClearException(),
# pre_scheme
#)
scheme = pre_scheme
return scheme
def numeric_emulate(self, x, y):
if x != 0 and y == 0:
# multiplication to correct the sign
return x * sollya.parse("infty")
return x / y
def solve_eval_error(self, gappa_init_approx, gappa_current_approx,
div_approx, gappa_vx, gappa_vy, inv_iteration_list,
div_iteration_list, seed_accuracy, seed_interval):
""" compute the evaluation error of reciprocal approximation of
(1 / gappa_vy)
:param seed_accuracy: absolute error for seed value
:type seed_accuracy: SollyaObject
"""
seed_var = Variable("seed",
precision=self.precision,
interval=seed_interval)
cg_eval_error_copy_map = {
gappa_init_approx.get_handle().get_node():
seed_var,
gappa_vy.get_handle().get_node():
Variable("y", precision=self.precision, interval=Interval(1, 2)),
gappa_vx.get_handle().get_node():
Variable("x", precision=self.precision, interval=Interval(1, 2)),
}
yerr_last = div_iteration_list[-1].yerr
# copying cg_eval_error_copy_map to allow mutation during
# optimise_scheme while keeping a clean copy for later use
optimisation_copy_map = cg_eval_error_copy_map.copy()
gappa_current_approx = self.optimise_scheme(gappa_current_approx,
copy=optimisation_copy_map)
div_approx = self.optimise_scheme(div_approx,
copy=optimisation_copy_map)
yerr_last = self.optimise_scheme(yerr_last, copy=optimisation_copy_map)
yerr_last.get_handle().set_node(yerr_last)
G1 = Constant(1, precision=ML_Exact)
exact_recp = G1 / gappa_vy
exact_recp.set_precision(ML_Exact)
exact_recp.set_tag("exact_recp")
recp_approx_error_goal = gappa_current_approx - exact_recp
recp_approx_error_goal.set_attributes(precision=ML_Exact,
tag="recp_approx_error_goal")
gappacg = GappaCodeGenerator(self.processor,
declare_cst=False,
disable_debug=True)
gappa_code = GappaCodeObject()
exact_div = gappa_vx * exact_recp
exact_div.set_attributes(precision=ML_Exact, tag="exact_div")
div_approx_error_goal = div_approx - exact_div
div_approx_error_goal.set_attributes(precision=ML_Exact,
tag="div_approx_error_goal")
bound_list = [op for op in cg_eval_error_copy_map]
gappacg.add_goal(gappa_code, yerr_last)
gappa_code = gappacg.get_interval_code(
[recp_approx_error_goal, div_approx_error_goal],
bound_list,
cg_eval_error_copy_map,
gappa_code=gappa_code,
register_bound_hypothesis=False)
for node in bound_list:
gappacg.add_hypothesis(gappa_code, cg_eval_error_copy_map[node],
cg_eval_error_copy_map[node].get_interval())
new_exact_recp_node = exact_recp.get_handle().get_node()
new_exact_div_node = exact_div.get_handle().get_node()
# adding specific hints for Newton-Raphson reciprocal iteration
for nr in inv_iteration_list:
nr.get_hint_rules(gappacg, gappa_code, new_exact_recp_node)
for div_iter in div_iteration_list:
div_iter.get_hint_rules(gappacg, gappa_code, new_exact_recp_node,
new_exact_div_node)
seed_wrt_exact = seed_var - new_exact_recp_node
seed_wrt_exact.set_attributes(precision=ML_Exact, tag="seed_wrt_exact")
gappacg.add_hypothesis(gappa_code, seed_wrt_exact,
Interval(-seed_accuracy, seed_accuracy))
try:
gappa_results = execute_gappa_script_extract(
gappa_code.get(gappacg))
recp_eval_error = gappa_results["recp_approx_error_goal"]
div_eval_error = gappa_results["div_approx_error_goal"]
print("eval error(s): recp={}, div={}".format(
recp_eval_error, div_eval_error))
except:
print("error during gappa run")
raise
recp_eval_error = None
div_eval_error = None
return recp_eval_error, div_eval_error
standard_test_cases = [
(1.0, sollya.parse("0x1.fffffffffffffp+1023"),
sollya.parse("0x1p-1024")),
(sollya.parse("-0x1.34a246p-2"), sollya.parse("-0x1.26e2e2p-1")),
(sollya.parse("0x1.p0"), sollya.parse("0x1.e0ef5ep-49")),
(sollya.parse("0x1.7fddbp0"), sollya.parse("0x1.e0ef5ep-49")),
(sollya.parse("0x1.7fddbp-126"), sollya.parse("0x1.e0ef5ep-49")),
(1.0, sollya.parse("-0x1.fffffffffffffp+1023"),
sollya.parse("-0x1p-1024")),
]
class MetaAtan(ScalarUnaryFunction):
""" Meta implementation of arctangent function """
function_name = "ml_atan"
default_args_atan = {
"output_file": "my_atan.c",
"function_name": "my_atan",
"precision": ML_Binary32,
"accuracy": ML_Faithful,
"num_sub_intervals": 8,
"method": "piecewise",
"target": GenericProcessor.get_target_instance()
}
def __init__(self, args):
super().__init__(args)
self.method = args.method
self.num_sub_intervals = args.num_sub_intervals
@classmethod
def get_default_args(cls, **kw):
""" Return a structure containing the arguments for MetaAtan,
builtin from a default argument mapping overloaded with @p kw
"""
arg_dict = cls.default_args_atan.copy()
arg_dict.update(kw)
return DefaultArgTemplate(**arg_dict)
def generate_scalar_scheme(self, vx):
""" Evaluation scheme generation """
return self.generic_atan2_generate(vx)
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 numeric_emulate(self, input_value):
return sollya.atan(input_value)
standard_test_cases = [[sollya.parse(x)]
for x in ["0x1.107a78p+0", "0x1.9e75a6p+0"]]
class MetaAtan2(ScalarBinaryFunction, MetaAtan):
""" Meta-function for 2-argument arc tangent (atan2) """
arity = 2
function_name = "ml_atan2"
def __init__(self, args):
ScalarBinaryFunction.__init__(self, args)
self.method = args.method
@classmethod
def get_default_args(cls, **kw):
""" Return a structure containing the arguments for MetaAtan,
builtin from a default argument mapping overloaded with @p kw
"""
arg_dict = cls.default_args_atan.copy()
arg_dict.update({
"output_file": "my_atan2.c",
"function_name": "my_atan2",
"input_intervals": [Interval(-5, 5)] * 2,
})
arg_dict.update(kw)
return DefaultArgTemplate(**arg_dict)
def generate_scalar_scheme(self, vy, vx):
# as in standard library atan2(y, x), take y as first
# parameter and x as second, we inverse vy and vx in method
# argument list
# extract of atan2 specification from man page
# If y is +0 (-0) and x is less than 0, +pi (-pi) is returned.
# If y is +0 (-0) and x is greater than 0, +0 (-0) is returned.
# If y is less than 0 and x is +0 or -0, -pi/2 is returned.
# If y is greater than 0 and x is +0 or -0, pi/2 is returned.
# If either x or y is NaN, a NaN is returned.
# If y is +0 (-0) and x is -0, +pi (-pi) is returned.
# If y is +0 (-0) and x is +0, +0 (-0) is returned.
# If y is a finite value greater (less) than 0, and x is negative infinity, +pi (-pi) is
# returned.
# If y is a finite value greater (less) than 0, and x is positive infinity, +0 (-0) is returned.
# If y is positive infinity (negative infinity), and x is finite, pi/2 (-pi/2) is returned.
# If y is positive infinity (negative infinity) and x is negative infinity, +3*pi/4 (-3*pi/4) is
# returned.
# If y is positive infinity (negative infinity) and x is positive infinity, +pi/4 (-pi/4) is
# returned.
vy.set_attributes(tag="y")
vx.set_attributes(tag="x")
return self.generic_atan2_generate(vx, vy)
def numeric_emulate(self, vy, vx):
if vx > 0:
return sollya.atan(vy / vx)
elif vy < 0:
# vy / vx > 0
return -sollya.pi + sollya.atan(vy / vx)
else:
# vy > 0, vy / vx < 0
return sollya.pi + sollya.atan(vy / vx)
standard_test_cases = [
(sollya.parse("0x1.08495cp+2"), sollya.parse("-0x1.88569ep+1")),
(sollya.parse("0x1.08495cp+2"), sollya.parse("-0x1.88569ep+1")),
(sollya.parse("0x1.08495cp+2"), sollya.parse("-0x1.88569ep+1")),
(sollya.parse("0x1.08495cp+2"), sollya.parse("-0x1.88569ep+1")),
]
class ML_HyperbolicTangent(ScalarUnaryFunction):
""" Implementation of hyperbolic tangent function """
function_name = "ml_tanh"
def __init__(self, args=DefaultArgTemplate):
# initializing base class
super().__init__(args)
@staticmethod
def get_default_args(**kw):
""" Return a structure containing the arguments for ML_HyperbolicTangent,
builtin from a default argument mapping overloaded with @p kw """
default_args_tanh = {
"output_file": "my_tanh.c",
"function_name": "my_tanh",
"precision": ML_Binary32,
"accuracy": ML_Faithful,
"target": GenericProcessor.get_target_instance()
}
default_args_tanh.update(kw)
return DefaultArgTemplate(**default_args_tanh)
def generate_approx_poly_near_zero(self, function, high_bound, error_bound,
variable):
""" Generate polynomial approximation scheme """
error_function = lambda p, f, ai, mod, t: sollya.dirtyinfnorm(
p - f, ai)
# Some issues encountered when 0 is one of the interval bound
# so we use a symetric interval around it
approx_interval = Interval(2**-100, high_bound)
local_function = function / sollya.x
degree = sollya.sup(
sollya.guessdegree(local_function, approx_interval, error_bound))
degree_list = range(0, int(degree) + 4, 2)
poly_object, approx_error = Polynomial.build_from_approximation_with_error(
function / sollya.x,
degree_list, [1] + [self.precision] * (len(degree_list) - 1),
approx_interval,
sollya.absolute,
error_function=error_function)
Log.report(
Log.Info, "approximation poly: {}\n with error {}".format(
poly_object, approx_error))
poly_scheme = Multiplication(
variable,
PolynomialSchemeEvaluator.generate_horner_scheme(
poly_object, variable, self.precision))
return poly_scheme, approx_error
def generate_scalar_scheme(self, vx):
""" Generating implementation script for hyperic tangent
meta-function """
# tanh(x) = sinh(x) / cosh(x)
# = (e^x - e^-x) / (e^x + e^-x)
# = (e^(2x) - 1) / (e^(2x) + 1)
# when x -> +inf, tanh(x) -> 1
# when x -> -inf, tanh(x) -> -1
# ~0 e^x ~ 1 + x - x^2 / 2 + x^3 / 6 + ...
# e^(-x) ~ 1 - x - x^2 / 2- x^3/6 + ...
# when x -> 0, tanh(x) ~ (2 (x + x^3/6 + ...)) / (2 - x^2 + ...) ~ x
# We can divide the input interval into 3 parts
# positive, around 0, and finally negative
# Possible argument reduction
# x = m.2^E = k * log(2) + r
# (k != 0) => tanh(x) = (2k * e^(2r) - 1) / (2k * e^(2r) + 1)
# = (1 - 1 * e^(-2r) / 2k) / (1 + e^(-2r) / 2k)
#
# tanh(x) = (e^(2x) - 1) / (e^(2x) + 1)
# = (e^(2x) + 1 - 1- 1) / (e^(2x) + 1)
# = 1 - 2 / (e^(2x) + 1)
# tanh is odd so we reduce the computation to the absolute value of
# vx
abs_vx = Abs(vx, precision=self.precision)
# if p is the expected output precision
# x > (p+2) * log(2) / 2 => tanh(x) = 1 - eps
# where eps < 1/2 * 2^-p
p = self.precision.get_mantissa_size()
high_bound = (p + 2) * sollya.log(2) / 2
near_zero_bound = 0.125
interval_num = 1024
Log.report(Log.Verbose,
"high_bound={}, near_zero_bound={}, interval_num={}",
float(high_bound), near_zero_bound, interval_num)
interval_size = (high_bound - near_zero_bound) / (1024)
new_interval_size = S2**int(sollya.log2(interval_size))
interval_num *= 2
high_bound = new_interval_size * interval_num + near_zero_bound
Log.report(Log.Verbose,
"high_bound={}, near_zero_bound={}, interval_num={}",
float(high_bound), near_zero_bound, interval_num)
ERROR_THRESHOLD = S2**-p
Log.report(Log.Info, "ERROR_THRESHOLD={}", ERROR_THRESHOLD)
# Near 0 approximation
near_zero_scheme, near_zero_error = self.generate_approx_poly_near_zero(
sollya.tanh(sollya.x), near_zero_bound, S2**-p, abs_vx)
# approximation parameters
poly_degree = 7
approx_interval = Interval(near_zero_bound, high_bound)
sollya.settings.points = 117
approx_scheme, approx_error = piecewise_approximation(
sollya.tanh,
abs_vx,
self.precision,
bound_low=near_zero_bound,
bound_high=high_bound,
num_intervals=interval_num,
max_degree=poly_degree,
error_threshold=ERROR_THRESHOLD)
Log.report(Log.Warning, "approx_error={}".format(approx_error))
comp_near_zero_bound = abs_vx < near_zero_bound
comp_near_zero_bound.set_attributes(tag="comp_near_zero_bound",
debug=debug_multi)
comp_high_bound = abs_vx < high_bound
comp_high_bound.set_attributes(tag="comp_high_bound",
debug=debug_multi)
complete_scheme = Select(
comp_near_zero_bound, near_zero_scheme,
Select(comp_high_bound, approx_scheme,
Constant(1.0, precision=self.precision)))
scheme = Return(Select(vx < 0, Negation(complete_scheme),
complete_scheme),
precision=self.precision)
return scheme
def numeric_emulate(self, input_value):
return tanh(input_value)
standard_test_cases = [[sollya.parse(x)] for x in [
"-0x1.572306p+0", "0x1.af0bf2p+1", "-0x1.af0bf2p+1", "-0x1.51b618p-13",
"0x1.ffb99ep-1", "0x1.f68b2cp-4"
]]
############################################################################### # created: Apr 23th, 2014 # last-modified: Mar 7th, 2018 # # author(s): Nicolas Brunie ([email protected]) ############################################################################### """ command-line argument templates """ import sys import os import argparse import traceback from sollya import Interval import sollya ml_infty = sollya.parse("infty") from .arg_utils import extract_option_value, test_flag_option from .log_report import Log from ..core.ml_formats import * from ..core.precisions import * from ..code_generation.generic_processor import GenericProcessor from ..core.target import TargetRegister from ..targets import * from ..code_generation.code_constant import * from ..core.passes import Pass from ..core.ml_hdl_format import (fixed_point, ML_StdLogicVectorFormat, RTL_FixedPointFormat, HdlVirtualFormat)
class ML_ExponentialM1_Red(ML_FunctionBasis):
function_name = "ml_expm1"
def __init__(self, args):
# initializing base class
ML_FunctionBasis.__init__(self, args)
@staticmethod
def get_default_args(**kw):
""" Return a structure containing the arguments for ML_ExponentialM1_Red,
builtin from a default argument mapping overloaded with @p kw """
default_args_expm1 = {
"output_file": "my_expm1.c",
"function_name": "my_expm1",
"precision": ML_Binary32,
"accuracy": ML_Faithful,
"target": GenericProcessor()
}
default_args_expm1.update(kw)
return DefaultArgTemplate(**default_args_expm1)
def generate_scheme(self):
# declaring target and instantiating optimization engine
vx = self.implementation.add_input_variable("x", self.precision)
Log.set_dump_stdout(True)
Log.report(Log.Info, "\033[33;1m generating implementation scheme \033[0m")
if self.debug_flag:
Log.report(Log.Info, "\033[31;1m debug has been enabled \033[0;m")
# local overloading of RaiseReturn operation
def ExpRaiseReturn(*args, **kwords):
kwords["arg_value"] = vx
kwords["function_name"] = self.function_name
return RaiseReturn(*args, **kwords)
C_m1 = Constant(-1, precision = self.precision)
test_NaN_or_inf = Test(vx, specifier = Test.IsInfOrNaN, likely = False, debug = debug_multi, tag = "NaN_or_inf", precision = ML_Bool)
test_NaN = Test(vx, specifier = Test.IsNaN, likely = False, debug = debug_multi, tag = "is_NaN", precision = ML_Bool)
test_inf = Comparison(vx, 0, specifier = Comparison.Greater, debug = debug_multi, tag = "sign", precision = ML_Bool, likely = False);
# Infnty input
infty_return = Statement(ConditionBlock(test_inf, Return(FP_PlusInfty(self.precision)), Return(C_m1)))
# non-std input (inf/nan)
specific_return = ConditionBlock(test_NaN, Return(FP_QNaN(self.precision)), infty_return)
# Over/Underflow Tests
precision_emax = self.precision.get_emax()
precision_max_value = S2**(precision_emax + 1)
expm1_overflow_bound = ceil(log(precision_max_value + 1))
overflow_test = Comparison(vx, expm1_overflow_bound, likely = False, specifier = Comparison.Greater, precision = ML_Bool)
overflow_return = Statement(Return(FP_PlusInfty(self.precision)))
precision_emin = self.precision.get_emin_subnormal()
precision_min_value = S2** precision_emin
expm1_underflow_bound = floor(log(precision_min_value) + 1)
underflow_test = Comparison(vx, expm1_underflow_bound, likely = False, specifier = Comparison.Less, precision = ML_Bool)
underflow_return = Statement(Return(C_m1))
sollya_precision = {ML_Binary32: sollya.binary32, ML_Binary64: sollya.binary64}[self.precision]
int_precision = {ML_Binary32: ML_Int32, ML_Binary64: ML_Int64}[self.precision]
# Constants
log_2 = round(log(2), sollya_precision, sollya.RN)
invlog2 = round(1/log(2), sollya_precision, sollya.RN)
log_2_cst = Constant(log_2, precision = self.precision)
interval_vx = Interval(expm1_underflow_bound, expm1_overflow_bound)
interval_fk = interval_vx * invlog2
interval_k = Interval(floor(inf(interval_fk)), ceil(sup(interval_fk)))
log2_hi_precision = self.precision.get_field_size() - 6
log2_hi = round(log(2), log2_hi_precision, sollya.RN)
log2_lo = round(log(2) - log2_hi, sollya_precision, sollya.RN)
# Reduction
unround_k = vx * invlog2
ik = NearestInteger(unround_k, precision = int_precision, debug = debug_multi, tag = "ik")
k = Conversion(ik, precision = self.precision, tag = "k")
red_coeff1 = Multiplication(k, log2_hi, precision = self.precision)
red_coeff2 = Multiplication(Negation(k, precision = self.precision), log2_lo, precision = self.precision)
pre_sub_mul = Subtraction(vx, red_coeff1, precision = self.precision)
s = Addition(pre_sub_mul, red_coeff2, precision = self.precision)
z = Subtraction(s, pre_sub_mul, precision = self.precision)
t = Subtraction(red_coeff2, z, precision = self.precision)
r = Addition(s, t, precision = self.precision)
r.set_attributes(tag = "r", debug = debug_multi)
r_interval = Interval(-log_2/S2, log_2/S2)
local_ulp = sup(ulp(exp(r_interval), self.precision))
print("ulp: ", local_ulp)
error_goal = S2**-1*local_ulp
print("error goal: ", error_goal)
# Polynomial Approx
error_function = lambda p, f, ai, mod, t: dirtyinfnorm(f - p, ai)
Log.report(Log.Info, "\033[33;1m Building polynomial \033[0m\n")
poly_degree = sup(guessdegree(expm1(sollya.x), r_interval, error_goal) + 1)
polynomial_scheme_builder = PolynomialSchemeEvaluator.generate_horner_scheme
poly_degree_list = range(0, poly_degree)
precision_list = [self.precision] *(len(poly_degree_list) + 1)
poly_object, poly_error = Polynomial.build_from_approximation_with_error(expm1(sollya.x), poly_degree, precision_list, r_interval, sollya.absolute, error_function = error_function)
sub_poly = poly_object.sub_poly(start_index = 2)
Log.report(Log.Info, "Poly : %s" % sub_poly)
Log.report(Log.Info, "poly error : {} / {:d}".format(poly_error, int(sollya.log2(poly_error))))
pre_sub_poly = polynomial_scheme_builder(sub_poly, r, unified_precision = self.precision)
poly = r + pre_sub_poly
poly.set_attributes(tag = "poly", debug = debug_multi)
exp_k = ExponentInsertion(ik, tag = "exp_k", debug = debug_multi, precision = self.precision)
exp_mk = ExponentInsertion(-ik, tag = "exp_mk", debug = debug_multi, precision = self.precision)
diff = 1 - exp_mk
diff.set_attributes(tag = "diff", debug = debug_multi)
# Late Tests
late_overflow_test = Comparison(ik, self.precision.get_emax(), specifier = Comparison.Greater, likely = False, debug = debug_multi, tag = "late_overflow_test")
overflow_exp_offset = (self.precision.get_emax() - self.precision.get_field_size() / 2)
diff_k = ik - overflow_exp_offset
exp_diff_k = ExponentInsertion(diff_k, precision = self.precision, tag = "exp_diff_k", debug = debug_multi)
exp_oflow_offset = ExponentInsertion(overflow_exp_offset, precision = self.precision, tag = "exp_offset", debug = debug_multi)
late_overflow_result = (exp_diff_k * (1 + poly)) * exp_oflow_offset - 1.0
late_overflow_return = ConditionBlock(
Test(late_overflow_result, specifier = Test.IsInfty, likely = False),
ExpRaiseReturn(ML_FPE_Overflow, return_value = FP_PlusInfty(self.precision)),
Return(late_overflow_result)
)
late_underflow_test = Comparison(k, self.precision.get_emin_normal(), specifier = Comparison.LessOrEqual, likely = False)
underflow_exp_offset = 2 * self.precision.get_field_size()
corrected_coeff = ik + underflow_exp_offset
exp_corrected = ExponentInsertion(corrected_coeff, precision = self.precision)
exp_uflow_offset = ExponentInsertion(-underflow_exp_offset, precision = self.precision)
late_underflow_result = ( exp_corrected * (1 + poly)) * exp_uflow_offset - 1.0
test_subnormal = Test(late_underflow_result, specifier = Test.IsSubnormal, likely = False)
late_underflow_return = Statement(
ConditionBlock(
test_subnormal,
ExpRaiseReturn(ML_FPE_Underflow, return_value = late_underflow_result)),
Return(late_underflow_result)
)
# Reconstruction
std_result = exp_k * ( poly + diff )
std_result.set_attributes(tag = "result", debug = debug_multi)
result_scheme = ConditionBlock(
late_overflow_test,
late_overflow_return,
ConditionBlock(
late_underflow_test,
late_underflow_return,
Return(std_result)
)
)
std_return = ConditionBlock(
overflow_test,
overflow_return,
ConditionBlock(
underflow_test,
underflow_return,
result_scheme)
)
scheme = ConditionBlock(
test_NaN_or_inf,
Statement(specific_return),
std_return
)
return scheme
def numeric_emulate(self, input_value):
return expm1(input_value)
standard_test_cases = [[sollya.parse(x)] for x in ["0x1.9b3216p-2", "0x1.8c108p-2"]]
def standard_test_cases(self):
general_list = [
# ERROR: rootn: inf ulp error at {inf, -2}: *0x0p+0 vs. inf (0x7f800000) at index: 1226
(FP_PlusInfty(self.precision), -2, FP_PlusZero(self.precision)),
# ERROR: rootn: inf ulp error at {inf, -2147483648}: *0x0.0000000000000p+0 vs. inf
(FP_PlusInfty(self.precision), -2147483648,
FP_PlusZero(self.precision)),
#
(FP_PlusZero(self.precision), -1, FP_PlusInfty(self.precision)),
(FP_MinusInfty(self.precision), 1, FP_MinusInfty(self.precision)),
(FP_MinusInfty(self.precision), -1, FP_MinusZero(self.precision)),
# ERROR coucou7: rootn: -inf ulp error at {inf 7f800000, 479638026}: *inf vs. 0x1.000018p+0 (0x3f80000c) at index: 2367
(FP_PlusInfty(self.precision), 479638026,
FP_PlusInfty(self.precision)),
(FP_MinusInfty(self.precision), 479638026),
#(FP_MinusInfty(self.precision), -479638026),
#(FP_PlusInfty(self.precision), -479638026),
# rootn( ±0, n) is ±∞ for odd n< 0.
(FP_PlusZero(self.precision), -1337, FP_PlusInfty(self.precision)),
(FP_MinusZero(self.precision), -1337,
FP_MinusInfty(self.precision)),
# rootn( ±0, n) is +∞ for even n< 0.
(FP_PlusZero(self.precision), -1330, FP_PlusInfty(self.precision)),
# rootn( ±0, n) is +0 for even n> 0.
(FP_PlusZero(self.precision), random.randrange(0, 2**31, 2),
FP_PlusZero(self.precision)),
(FP_MinusZero(self.precision), random.randrange(0, 2**31, 2),
FP_PlusZero(self.precision)),
# rootn( ±0, n) is ±0 for odd n> 0.
(FP_PlusZero(self.precision), random.randrange(1, 2**31, 2),
FP_PlusZero(self.precision)),
(FP_MinusZero(self.precision), random.randrange(1, 2**31, 2),
FP_MinusZero(self.precision)),
# rootn( x, n) returns a NaN for x< 0 and n is even.
(-random.random(), 2 * random.randrange(1, 2**30),
FP_QNaN(self.precision)),
# rootn( x, 0 ) returns a NaN
(random.random(), 0, FP_QNaN(self.precision)),
# vx=nan
(sollya.parse("-nan"), -1811577079, sollya.parse("nan")),
(sollya.parse("-nan"), 832501219, sollya.parse("nan")),
(sollya.parse("-nan"), -857435762, sollya.parse("nan")),
(sollya.parse("-nan"), -1503049611, sollya.parse("nan")),
(sollya.parse("-nan"), 2105620996, sollya.parse("nan")),
#ERROR: rootn: inf ulp error at {-nan, 832501219}: *-nan vs. -0x1.00000df2bed98p+1
#ERROR: rootn: inf ulp error at {-nan, -857435762}: *-nan vs. 0x1.0000000000000p+1
#ERROR: rootn: inf ulp error at {-nan, -1503049611}: *-nan vs. -0x1.0000000000000p+1
#ERROR: rootn: inf ulp error at {-nan, 2105620996}: *-nan vs. 0x1.00000583c4b7ap+1
(sollya.parse("-0x1.cd150ap-105"), 105297051),
(sollya.parse("0x1.ec3bf8p+71"), -1650769017),
# test-case #12
(0.1, 17),
# test-case #11, fails in OpenCL CTS
(sollya.parse("0x0.000000001d600p-1022"), 14),
# test-case #10, fails test with dar(2**-23)
(sollya.parse("-0x1.20aadp-114"), 17),
# test-case #9
(sollya.parse("0x1.a44d8ep+121"), 7),
# test-case #8
(sollya.parse("-0x1.3ef124p+103"), 3),
# test-case #7
(sollya.parse("-0x1.01047ep-2"), 39),
# test-case #6
(sollya.parse("-0x1.0105bp+67"), 23),
# test-case #5
(sollya.parse("0x1.c1f72p+51"), 6),
# special cases
(sollya.parse("0x0p+0"), 1),
(sollya.parse("0x0p+0"), 0),
# test-case #3, catastrophic error for n=1
(sollya.parse("0x1.fc61a2p-121"), 1.0),
# test-case #4 , k=14 < 0 not supported by bigfloat
# (sollya.parse("0x1.ad067ap-66"), -14),
]
# NOTE: expected value assumed 32-bit precision output
fp_32_only = [
#
(sollya.parse("0x1.80bb0ep+70"), 377778829,
sollya.parse("0x1.000002p+0")),
]
# NOTE: the following test-case are only valid if meta-function supports 64-bit integer
# 2nd_input
fp_64_only = [
(sollya.parse("0x1.fffffffffffffp+1023"), -1,
sollya.parse("0x0.4000000000000p-1022")),
(sollya.parse("-0x1.fffffffffffffp1023"), -1,
sollya.parse("-0x0.4000000000000p-1022")),
#(sollya.parse("-0x1.fffffffffffffp+1023"), 1),
#(sollya.parse("0x1.fffffffffffffp+1023"), -1),
# ERROR coucou8: rootn: inf ulp error at {-inf, 1854324695}: *-inf vs. -0x1.0000066bfdd60p+0
(FP_MinusInfty(self.precision), 1854324695,
FP_MinusInfty(self.precision)),
# ERROR: rootn: -60.962402 ulp error at {0x0.000000001d600p-1022, 14}: *0x1.67d4ff97d1fd9p-76 vs. 0x1.67d4ff97d1f9cp-76
(sollya.parse("0x0.000000001d600p-1022"), 14,
sollya.parse("0x1.67d4ff97d1fd9p-76")),
# ERROR: rootn: -430452000.000000 ulp error at {0x1.ffffffff38c00p-306, 384017876}: *0x1.ffffed870ff01p-1 vs. 0x1.ffffebec8d1d2p-1
(sollya.parse("0x1.ffffffff38c00p-306"), 384017876,
sollya.parse("0x1.ffffed870ff01p-1")), # vs. 0x1.ffffebec8d1d2p-1
# ERROR: rootn: 92996584.000000 ulp error at {0x1.ffffffffdae80p-858, -888750231}: *0x1.00000b36b1173p+0 vs. 0x1.00000b8f6155ep+0
(sollya.parse("0x1.ffffffffdae80p-858"), -888750231,
sollya.parse("0x1.00000b36b1173p+0")),
# ERROR: rootn: 379474.906250 ulp error at {0x0.0000000000022p-1022, -1538297900}: *0x1.00000814a68ffp+0 vs. 0x1.0000081503352p+0
(sollya.parse("0x0.00000006abfffp-1022"), -1221802473,
sollya.parse("0x1.00000a01818a4p+0")),
(sollya.parse("0x1.ffffffffd0a00p-260"), 1108043946,
sollya.parse("0x1.fffffa9042997p-1")),
(sollya.parse("0x1.3fffffffff1c0p-927"), -1997086266,
sollya.parse("0x1.0000056564c5ep+0")),
(sollya.parse("0x1.ffffffff38c00p-306"), 384017876,
sollya.parse("0x1.ffffed870ff01p-1")),
(sollya.parse("0x0.15c000000002ap-1022"), 740015941,
sollya.parse("0x1.ffffdfc47b57ep-1")),
(sollya.parse("0x0.00000000227ffp-1022"), -1859058847,
sollya.parse("0x1.0000069c7a01bp+0")),
(sollya.parse("0x0.0568000000012p-1022"), -447352599,
sollya.parse("0x1.00001ab640c38p+0")),
(sollya.parse("0x0.000000000000dp-1022"), 132283432,
sollya.parse("0x1.ffff43d1db82ap-1")),
(sollya.parse("-0x1.c80000000026ap+1023"), 275148531,
sollya.parse("-0x1.00002b45a7314p+0")),
(sollya.parse("0x0.022200000000ep-1022"), -1969769414,
sollya.parse("0x1.000006130e858p+0")),
(sollya.parse("0x0.0000000000011p-1022"), 851990770,
sollya.parse("0x1.ffffe2cafaff6p-1")),
(sollya.parse("0x1.8fffffffff348p-1010"), 526938360,
sollya.parse("0x1.ffffd372e2b81p-1")),
(sollya.parse("0x0.0000000000317p-1022"), -1315106194,
sollya.parse("0x1.0000096973ac9p+0")),
(sollya.parse("0x1.1ffffffff2d20p-971"), 378658008,
sollya.parse("0x1.ffffc45e803b2p-1")),
#
(sollya.parse("0x0.0568000000012p-1022"), -447352599,
sollya.parse("0x1.00001ab640c38p+0")),
#
(sollya.parse("0x1.ffffffffd0a00p-260"), 1108043946,
sollya.parse("0x1.fffffa9042997p-1")),
(FP_MinusZero(self.precision), -21015979,
FP_MinusInfty(self.precision)),
(FP_MinusZero(self.precision), -85403731,
FP_MinusInfty(self.precision)),
(FP_MinusZero(self.precision), -180488973,
FP_MinusInfty(self.precision)),
(FP_MinusZero(self.precision), -1365227287,
FP_MinusInfty(self.precision)),
(FP_MinusZero(self.precision), -1802885579,
FP_MinusInfty(self.precision)),
(FP_MinusZero(self.precision), -1681209663,
FP_MinusInfty(self.precision)),
(FP_MinusZero(self.precision), -1152797721,
FP_MinusInfty(self.precision)),
(FP_MinusZero(self.precision), -1614890585,
FP_MinusInfty(self.precision)),
(FP_MinusZero(self.precision), -812655517,
FP_MinusInfty(self.precision)),
(FP_MinusZero(self.precision), -628647891,
FP_MinusInfty(self.precision)),
(sollya.parse("0x1.ffffffffdae80p-858"), -888750231,
sollya.parse("0x1.00000b36b1173p+0")),
(sollya.parse("0x0.0568000000012p-1022"), -447352599,
sollya.parse("0x1.00001ab640c38p+0")),
(sollya.parse("0x0.00000006abfffp-1022"), -1221802473,
sollya.parse("0x1.00000a01818a4p+0")),
(sollya.parse("0x0.0000000000022p-1022"), -1538297900,
sollya.parse("0x1.00000814a68ffp+0")),
#ERROR: rootn: inf ulp error at {-0x0.0000000000000p+0, -1889147085}: *-inf vs. inf
#ERROR: rootn: inf ulp error at {-0x0.0000000000000p+0, -373548013}: *-inf vs. inf
(FP_MinusZero(self.precision), -1889147085,
FP_MinusInfty(self.precision)),
(FP_MinusZero(self.precision), -373548013,
FP_MinusInfty(self.precision)),
#ERROR: rootn: inf ulp error at {-0x0.0000000000000p+0, -1889147085}: *-inf vs. inf
#ERROR: rootn: inf ulp error at {-0x0.0000000000000p+0, -373548013}: *-inf vs. inf
# [email protected]: PE 0: error[84]: ml_rootn(-0x1.b1a6765727e72p-902, -7.734955e+08/-773495525), result is -0x1.00000d8cb5b3cp+0 vs expected [nan;nan]
(sollya.parse("-0x1.b1a6765727e72p-902"), -773495525),
# ERROR: rootn: -40564819207303340847894502572032.000000 ulp error at {-0x0.fffffffffffffp-1022, 1}: *-0x0.fffffffffffffp-1022 vs. -0x1.ffffffffffffep-970
(sollya.parse("-0x0.fffffffffffffp-1022 "), 1,
sollya.parse("-0x0.fffffffffffffp-1022 ")),
# ERROR: rootn: 1125899906842624.000000 ulp error at {-0x1.fffffffffffffp+1023, -1}: *-0x0.4000000000000p-1022 vs. -0x0.0000000000000p+0
(sollya.parse("-0x1.fffffffffffffp+1023"), -1,
sollya.parse("-0x0.4000000000000p-1022")),
(sollya.parse("0x1.fffffffffffffp+1023"), -1,
sollya.parse("0x0.4000000000000p-1022")),
]
return (fp_64_only if self.precision.get_bit_size() >= 64 else []) \
+ (fp_32_only if self.precision.get_bit_size() == 32 else []) \
+ general_list
class ML_Gamma(ScalarUnaryFunction):
""" Meta implementation of the error-function """
function_name = "gamma"
def __init__(self, args):
super().__init__(args)
@staticmethod
def get_default_args(**kw):
""" Return a structure containing the arguments for ML_Gamma,
builtin from a default argument mapping overloaded with @p kw """
default_args_erf = {
"output_file":
"gamma.c",
"function_name":
"gamma",
"precision":
ML_Binary32,
"accuracy":
ML_Faithful,
"target":
GenericProcessor.get_target_instance(),
"passes": [("start:instantiate_abstract_prec"),
("start:instantiate_prec"),
("start:basic_legalization"),
("start:expand_multi_precision")],
}
default_args_erf.update(kw)
return DefaultArgTemplate(**default_args_erf)
def generate_scalar_scheme(self, vx):
# approximation the gamma function
abs_vx = Abs(vx, precision=self.precision)
FCT_LIMIT = 1.0
omega_value = self.precision.get_omega()
def sollya_wrap_bigfloat_fct(bfct):
""" wrap bigfloat's function <bfct> such that is can be used
on SollyaObject inputs and returns SollyaObject results """
def fct(x):
return sollya.SollyaObject(bfct(SollyaObject(x).bigfloat()))
return fct
sollya_gamma = sollya_wrap_bigfloat_fct(bigfloat.gamma)
sollya_digamma = sollya_wrap_bigfloat_fct(bigfloat.digamma)
# first derivative of gamma is digamma * gamma
bigfloat_gamma_d0 = lambda x: bigfloat.gamma(x) * bigfloat.digamma(x)
sollya_gamma_d0 = sollya_wrap_bigfloat_fct(bigfloat_gamma_d0)
# approximating trigamma with straightforward derivatives formulae of digamma
U = 2**-64
bigfloat_trigamma = lambda x: (
(bigfloat.digamma(x * (1 + U)) - bigfloat.digamma(x)) / (x * U))
sollya_trigamma = sollya_wrap_bigfloat_fct(bigfloat_trigamma)
bigfloat_gamma_d1 = lambda x: (bigfloat_trigamma(x) * bigfloat.gamma(
x) + bigfloat_gamma_d0(x) * bigfloat.digamma(x))
sollya_gamma_d1 = sollya_wrap_bigfloat_fct(bigfloat_gamma_d1)
def sollya_gamma_fct(x, diff_order, prec):
""" wrapper to use bigfloat implementation of exponential
rather than sollya's implementation directly.
This wrapper implements sollya's function API.
:param x: numerical input value (may be an Interval)
:param diff_order: differential order
:param prec: numerical precision expected (min)
"""
fct = None
if diff_order == 0:
fct = sollya_gamma
elif diff_order == 1:
fct = sollya_gamma_d0
elif diff_order == 2:
fct = sollya_gamma_d1
else:
raise NotImplementedError
with bigfloat.precision(prec):
if x.is_range():
lo = sollya.inf(x)
hi = sollya.sup(x)
return sollya.Interval(fct(lo), fct(hi))
else:
return fct(x)
# search the lower x such that gamma(x) >= omega
omega_upper_limit = search_bound_threshold(sollya_gamma, omega_value,
2, 1000.0, self.precision)
Log.report(Log.Debug, "gamma(x) = {} limit is {}", omega_value,
omega_upper_limit)
# evaluate gamma(<min-normal-value>)
lower_x_bound = self.precision.get_min_normal_value()
value_min = sollya_gamma(lower_x_bound)
Log.report(Log.Debug, "gamma({}) = {}(log2={})", lower_x_bound,
value_min, int(sollya.log2(value_min)))
# evaluate gamma(<min-subnormal-value>)
lower_x_bound = self.precision.get_min_subnormal_value()
value_min = sollya_gamma(lower_x_bound)
Log.report(Log.Debug, "gamma({}) = {}(log2={})", lower_x_bound,
value_min, int(sollya.log2(value_min)))
# Gamma is defined such that gamma(x+1) = x * gamma(x)
#
# we approximate gamma over [1, 2]
# y in [1, 2]
# gamma(y) = (y-1) * gamma(y-1)
# gamma(y-1) = gamma(y) / (y-1)
Log.report(Log.Info, "building mathematical polynomial")
approx_interval = Interval(1, 2)
approx_fct = sollya.function(sollya_gamma_fct)
poly_degree = int(
sup(
guessdegree(approx_fct, approx_interval, S2**
-(self.precision.get_field_size() + 5)))) + 1
Log.report(Log.Debug, "approximation's poly degree over [1, 2] is {}",
poly_degree)
sys.exit(1)
poly_degree_list = list(range(1, poly_degree, 2))
Log.report(Log.Debug, "poly_degree is {} and list {}", poly_degree,
poly_degree_list)
global_poly_object = Polynomial.build_from_approximation(
approx_fct, poly_degree_list,
[self.precision] * len(poly_degree_list), approx_interval,
sollya.relative)
Log.report(
Log.Debug, "inform is {}",
dirtyinfnorm(approx_fct - global_poly_object.get_sollya_object(),
approx_interval))
poly_object = global_poly_object.sub_poly(start_index=1, offset=1)
ext_precision = {
ML_Binary32: ML_SingleSingle,
ML_Binary64: ML_DoubleDouble,
}[self.precision]
pre_poly = PolynomialSchemeEvaluator.generate_horner_scheme(
poly_object, abs_vx, unified_precision=self.precision)
result = FMA(pre_poly, abs_vx, abs_vx)
result.set_attributes(tag="result", debug=debug_multi)
eps_target = S2**-(self.precision.get_field_size() + 5)
def offset_div_function(fct):
return lambda offset: fct(sollya.x + offset)
# empiral numbers
field_size = {ML_Binary32: 6, ML_Binary64: 8}[self.precision]
near_indexing = SubFPIndexing(eps_exp, 0, 6, self.precision)
near_approx = generic_poly_split(offset_div_function(sollya.erf),
near_indexing, eps_target,
self.precision, abs_vx)
near_approx.set_attributes(tag="near_approx", debug=debug_multi)
def offset_function(fct):
return lambda offset: fct(sollya.x + offset)
medium_indexing = SubFPIndexing(1, one_limit_exp, 7, self.precision)
medium_approx = generic_poly_split(offset_function(sollya.erf),
medium_indexing, eps_target,
self.precision, abs_vx)
medium_approx.set_attributes(tag="medium_approx", debug=debug_multi)
# approximation for positive values
scheme = ConditionBlock(
abs_vx < eps, Return(result),
ConditionBlock(
abs_vx < near_indexing.get_max_bound(), Return(near_approx),
ConditionBlock(abs_vx < medium_indexing.get_max_bound(),
Return(medium_approx),
Return(Constant(1.0,
precision=self.precision)))))
return scheme
def numeric_emulate(self, input_value):
return bigfloat.gamma(sollya.SollyaObject(input_value).bigfloat())
standard_test_cases = [
(1.0, None),
(sollya.parse("0x1.13b2c6p-2"), None),
]
class ML_Log1p(ML_FunctionBasis):
function_name = "ml_log1p"
def __init__(self, args):
ML_FunctionBasis.__init__(self, args)
@staticmethod
def get_default_args(**kw):
""" Return a structure containing the arguments for ML_Log1p,
builtin from a default argument mapping overloaded with @p kw """
default_args_log1p = {
"output_file": "my_log1p.c",
"function_name": "my_log1pf",
"precision": ML_Binary32,
"accuracy": ML_Faithful,
"target": GenericProcessor.get_target_instance(),
"passes": [("start:instantiate_abstract_prec"), ("start:instantiate_prec"), ("start:basic_legalization"), ("start:expand_multi_precision")],
}
default_args_log1p.update(kw)
return DefaultArgTemplate(**default_args_log1p)
def generate_scheme(self):
vx = self.implementation.add_input_variable("x", self.precision)
sollya_precision = self.get_input_precision().sollya_object
# local overloading of RaiseReturn operation
def ExpRaiseReturn(*args, **kwords):
kwords["arg_value"] = vx
kwords["function_name"] = self.function_name
return RaiseReturn(*args, **kwords)
# 2-limb approximation of log(2)
# hi part precision is reduced to provide exact operation
# when multiplied by an exponent value
log2_hi_value = round(log(2), self.precision.get_field_size() - (self.precision.get_exponent_size() + 1), sollya.RN)
log2_lo_value = round(log(2) - log2_hi_value, self.precision.sollya_object, sollya.RN)
log2_hi = Constant(log2_hi_value, precision=self.precision)
log2_lo = Constant(log2_lo_value, precision=self.precision)
int_precision = self.precision.get_integer_format()
# retrieving processor inverse approximation table
dummy_var = Variable("dummy", precision = self.precision)
dummy_rcp_seed = ReciprocalSeed(dummy_var, precision = self.precision)
inv_approx_table = self.processor.get_recursive_implementation(dummy_rcp_seed, language = None, table_getter = lambda self: self.approx_table_map)
# table creation
table_index_size = inv_approx_table.index_size
log_table = ML_NewTable(dimensions = [2**table_index_size, 2], storage_precision = self.precision)
# storing accurate logarithm approximation of value returned
# by the fast reciprocal operation
for i in range(0, 2**table_index_size):
inv_value = inv_approx_table[i]
value_high = round(log(inv_value), self.precision.get_field_size() - (self.precision.get_exponent_size() + 1), sollya.RN)
value_low = round(log(inv_value) - value_high, sollya_precision, sollya.RN)
log_table[i][0] = value_high
log_table[i][1] = value_low
neg_input = Comparison(vx, -1, likely=False, precision=ML_Bool, specifier=Comparison.Less, debug=debug_multi, tag="neg_input")
vx_nan_or_inf = Test(vx, specifier=Test.IsInfOrNaN, likely=False, precision=ML_Bool, debug=debug_multi, tag="nan_or_inf")
vx_snan = Test(vx, specifier=Test.IsSignalingNaN, likely=False, debug=debug_multi, tag="snan")
vx_inf = Test(vx, specifier=Test.IsInfty, likely=False, debug=debug_multi, tag="inf")
vx_subnormal = Test(vx, specifier=Test.IsSubnormal, likely=False, debug=debug_multi, tag="vx_subnormal")
# for x = m.2^e, such that e >= 0
#
# log(1+x) = log(1 + m.2^e)
# = log(2^e . 2^-e + m.2^e)
# = log(2^e . (2^-e + m))
# = log(2^e) + log(2^-e + m)
# = e . log(2) + log (2^-e + m)
#
# t = (2^-e + m)
# t = m_t . 2^e_t
# r ~ 1 / m_t => r.m_t ~ 1 ~ 0
#
# t' = t . 2^-e_t
# = 2^-e-e_t + m . 2^-e_t
#
# if e >= 0, then 2^-e <= 1, then 1 <= m + 2^-e <= 3
# r = m_r . 2^e_r
#
# log(1+x) = e.log(2) + log(r . 2^e_t . 2^-e_t . (2^-e + m) / r)
# = e.log(2) + log(r . 2^(-e-e_t) + r.m.2^-e_t) + e_t . log(2)- log(r)
# = (e+e_t).log(2) + log(r . t') - log(r)
# = (e+e_t).log(2) + log(r . t') - log(r)
# = (e+e_t).log(2) + P_log1p(r . t' - 1) - log(r)
#
#
# argument reduction
m = MantissaExtraction(vx, tag="vx", precision=self.precision, debug=debug_multi)
e = ExponentExtraction(vx, tag="e", precision=int_precision, debug=debug_multi)
# 2^-e
TwoMinusE = ExponentInsertion(-e, tag="Two_minus_e", precision=self.precision, debug=debug_multi)
t = Addition(TwoMinusE, m, precision=self.precision, tag="t", debug=debug_multi)
m_t = MantissaExtraction(t, tag="m_t", precision=self.precision, debug=debug_multi)
e_t = ExponentExtraction(t, tag="e_t", precision=int_precision, debug=debug_multi)
# 2^(-e-e_t)
TwoMinusEEt = ExponentInsertion(-e-e_t, tag="Two_minus_e_et", precision=self.precision)
TwoMinusEt = ExponentInsertion(-e_t, tag="Two_minus_et", precision=self.precision, debug=debug_multi)
rcp_mt = ReciprocalSeed(m_t, tag="rcp_mt", precision=self.precision, debug=debug_multi)
INDEX_SIZE = table_index_size
table_index = generic_mantissa_msb_index_fct(INDEX_SIZE, m_t)
table_index.set_attributes(tag="table_index", debug=debug_multi)
log_inv_lo = TableLoad(log_table, table_index, 1, tag="log_inv_lo", debug=debug_multi)
log_inv_hi = TableLoad(log_table, table_index, 0, tag="log_inv_hi", debug=debug_multi)
inv_err = S2**-6 # TODO: link to target DivisionSeed precision
Log.report(Log.Info, "building mathematical polynomial")
approx_interval = Interval(-inv_err, inv_err)
approx_fct = sollya.log1p(sollya.x) / (sollya.x)
poly_degree = sup(guessdegree(approx_fct, approx_interval, S2**-(self.precision.get_field_size()+1))) + 1
Log.report(Log.Debug, "poly_degree is {}", poly_degree)
global_poly_object = Polynomial.build_from_approximation(approx_fct, poly_degree, [self.precision]*(poly_degree+1), approx_interval, sollya.absolute)
poly_object = global_poly_object # .sub_poly(start_index=1)
EXT_PRECISION_MAP = {
ML_Binary32: ML_SingleSingle,
ML_Binary64: ML_DoubleDouble,
ML_SingleSingle: ML_TripleSingle,
ML_DoubleDouble: ML_TripleDouble
}
if not self.precision in EXT_PRECISION_MAP:
Log.report(Log.Error, "no extended precision available for {}", self.precision)
ext_precision = EXT_PRECISION_MAP[self.precision]
# pre_rtp = r . 2^(-e-e_t) + m .2^-e_t
pre_rtp = Addition(
rcp_mt * TwoMinusEEt,
Multiplication(
rcp_mt,
Multiplication(
m,
TwoMinusEt,
precision=self.precision,
tag="pre_mult",
debug=debug_multi,
),
precision=ext_precision,
tag="pre_mult2",
debug=debug_multi,
),
precision=ext_precision,
tag="pre_rtp",
debug=debug_multi
)
pre_red_vx = Addition(
pre_rtp,
-1,
precision=ext_precision,
)
red_vx = Conversion(pre_red_vx, precision=self.precision, tag="red_vx", debug=debug_multi)
Log.report(Log.Info, "generating polynomial evaluation scheme")
poly = PolynomialSchemeEvaluator.generate_horner_scheme(
poly_object, red_vx, unified_precision=self.precision)
poly.set_attributes(tag="poly", debug=debug_multi)
Log.report(Log.Debug, "{}", global_poly_object.get_sollya_object())
fp_e = Conversion(e + e_t, precision=self.precision, tag="fp_e", debug=debug_multi)
ext_poly = Multiplication(red_vx, poly, precision=ext_precision)
pre_result = Addition(
Addition(
fp_e * log2_hi,
fp_e * log2_lo,
precision=ext_precision
),
Addition(
Addition(
-log_inv_hi,
-log_inv_lo,
precision=ext_precision
),
ext_poly,
precision=ext_precision
),
precision=ext_precision
)
result = Conversion(pre_result, precision=self.precision, tag="result", debug=debug_multi)
# main scheme
Log.report(Log.Info, "MDL scheme")
pre_scheme = ConditionBlock(neg_input,
Statement(
ClearException(),
Raise(ML_FPE_Invalid),
Return(FP_QNaN(self.precision))
),
ConditionBlock(vx_nan_or_inf,
ConditionBlock(vx_inf,
Statement(
ClearException(),
Return(FP_PlusInfty(self.precision)),
),
Statement(
ClearException(),
ConditionBlock(vx_snan,
Raise(ML_FPE_Invalid)
),
Return(FP_QNaN(self.precision))
)
),
Return(result)
)
)
scheme = pre_scheme
return scheme
def numeric_emulate(self, input_value):
return log1p(input_value)
standard_test_cases = [
(1.0, None),
(1.0, None),
(1.0, None),
(1.0, None),
]
_ = [
(4.0, None),
(1.0, None),
(0.5, None),
(1.5, None),
(1024.0, None),
(sollya.parse("0x1.13b2c6p-2"), None),
(sollya.parse("0x1.2cb10ap-5"), None),
(0.0, None),
(sollya.parse("0x1.ce4492p-21"), None),
]
class ML_Log2(ML_Function("ml_log2")):
def __init__(self, args=DefaultArgTemplate):
# initializing base class
ML_FunctionBasis.__init__(self, args)
@staticmethod
def get_default_args(**kw):
""" Return a structure containing the arguments for ML_Log2,
builtin from a default argument mapping overloaded with @p kw """
default_args_log2 = {
"output_file": "my_log2f.c",
"function_name": "my_log2f",
"precision": ML_Binary32,
"accuracy": ML_Faithful,
"target": GenericProcessor()
}
default_args_log2.update(kw)
return DefaultArgTemplate(**default_args_log2)
def generate_emulate(self, result, mpfr_x, mpfr_rnd):
""" generate the emulation code for ML_Log2 functions
mpfr_x is a mpfr_t variable which should have the right precision
mpfr_rnd is the rounding mode
Deprecated: the new test bench uses numeric_emulate method
"""
emulate_func_name = "mpfr_log2"
emulate_func_op = FunctionOperator(emulate_func_name,
arg_map={
0: FO_Result(0),
1: FO_Arg(0),
2: FO_Arg(1)
},
require_header=["mpfr.h"])
emulate_func = FunctionObject(emulate_func_name, [ML_Mpfr_t, ML_Int32],
ML_Mpfr_t, emulate_func_op)
mpfr_call = Statement(
ReferenceAssign(result, emulate_func(mpfr_x, mpfr_rnd)))
return mpfr_call
def generate_scheme(self):
vx = self.implementation.add_input_variable("x",
self.get_input_precision())
sollya_precision = self.get_input_precision().get_sollya_object()
# local overloading of RaiseReturn operation
def ExpRaiseReturn(*args, **kwords):
kwords["arg_value"] = vx
kwords["function_name"] = self.function_name
return RaiseReturn(*args, **kwords)
# testing special value inputs
test_nan_or_inf = Test(vx,
specifier=Test.IsInfOrNaN,
likely=False,
debug=True,
tag="nan_or_inf")
test_nan = Test(vx,
specifier=Test.IsNaN,
debug=True,
tag="is_nan_test")
test_positive = Comparison(vx,
0,
specifier=Comparison.GreaterOrEqual,
debug=True,
tag="inf_sign")
test_signaling_nan = Test(vx,
specifier=Test.IsSignalingNaN,
debug=True,
tag="is_signaling_nan")
# if input is a signaling NaN, raise an invalid exception and returns
# a quiet NaN
return_snan = Statement(
ExpRaiseReturn(ML_FPE_Invalid,
return_value=FP_QNaN(self.precision)))
vx_exp = ExponentExtraction(vx, tag="vx_exp", debug=debugd)
int_precision = self.precision.get_integer_format()
# log2(vx)
# r = vx_mant
# e = vx_exp
# vx reduced to r in [1, 2[
# log2(vx) = log2(r * 2^e)
# = log2(r) + e
#
## log2(r) is approximated by
# log2(r) = log2(inv_seed(r) * r / inv_seed(r)
# = log2(inv_seed(r) * r) - log2(inv_seed(r))
# inv_seed(r) in ]1/2, 1] => log2(inv_seed(r)) in ]-1, 0]
#
# inv_seed(r) * r ~ 1
# we can easily tabulate -log2(inv_seed(r))
#
# retrieving processor inverse approximation table
dummy_var = Variable("dummy", precision=self.precision)
dummy_div_seed = DivisionSeed(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)
# table creation
table_index_size = 7
log_table = ML_NewTable(dimensions=[2**table_index_size, 2],
storage_precision=self.precision,
tag=self.uniquify_name("inv_table"))
# value for index 0 is set to 0.0
log_table[0][0] = 0.0
log_table[0][1] = 0.0
for i in range(1, 2**table_index_size):
#inv_value = (1.0 + (self.processor.inv_approx_table[i] / S2**9) + S2**-52) * S2**-1
#inv_value = (1.0 + (inv_approx_table[i][0] / S2**9) ) * S2**-1
#print inv_approx_table[i][0], inv_value
inv_value = inv_approx_table[i][0]
value_high_bitsize = self.precision.get_field_size() - (
self.precision.get_exponent_size() + 1)
value_high = round(log2(inv_value), value_high_bitsize, sollya.RN)
value_low = round(
log2(inv_value) - value_high, sollya_precision, sollya.RN)
log_table[i][0] = value_high
log_table[i][1] = value_low
def compute_log(_vx, exp_corr_factor=None):
_vx_mant = MantissaExtraction(_vx,
tag="_vx_mant",
precision=self.precision,
debug=debug_lftolx)
_vx_exp = ExponentExtraction(_vx, tag="_vx_exp", debug=debugd)
# The main table is indexed by the 7 most significant bits
# of the mantissa
table_index = inv_approx_table.index_function(_vx_mant)
table_index.set_attributes(tag="table_index", debug=debuglld)
# argument reduction
# Using AND -2 to exclude LSB set to 1 for Newton-Raphson convergence
# TODO: detect if single operand inverse seed is supported by the targeted architecture
pre_arg_red_index = TypeCast(BitLogicAnd(
TypeCast(DivisionSeed(_vx_mant,
precision=self.precision,
tag="seed",
debug=debug_lftolx,
silent=True),
precision=ML_UInt64),
Constant(-2, precision=ML_UInt64),
precision=ML_UInt64),
precision=self.precision,
tag="pre_arg_red_index",
debug=debug_lftolx)
arg_red_index = Select(Equal(table_index, 0),
1.0,
pre_arg_red_index,
tag="arg_red_index",
debug=debug_lftolx)
_red_vx = FMA(arg_red_index, _vx_mant, -1.0)
_red_vx.set_attributes(tag="_red_vx", debug=debug_lftolx)
inv_err = S2**-inv_approx_table.index_size
red_interval = Interval(1 - inv_err, 1 + inv_err)
# return in case of standard (non-special) input
_log_inv_lo = TableLoad(log_table,
table_index,
1,
tag="log_inv_lo",
debug=debug_lftolx)
_log_inv_hi = TableLoad(log_table,
table_index,
0,
tag="log_inv_hi",
debug=debug_lftolx)
Log.report(Log.Verbose, "building mathematical polynomial")
approx_interval = Interval(-inv_err, inv_err)
poly_degree = sup(
guessdegree(
log2(1 + sollya.x) / sollya.x, approx_interval, S2**
-(self.precision.get_field_size() * 1.1))) + 1
sollya.settings.display = sollya.hexadecimal
global_poly_object, approx_error = Polynomial.build_from_approximation_with_error(
log2(1 + sollya.x) / sollya.x,
poly_degree, [self.precision] * (poly_degree + 1),
approx_interval,
sollya.absolute,
error_function=lambda p, f, ai, mod, t: sollya.dirtyinfnorm(
p - f, ai))
Log.report(
Log.Info, "poly_degree={}, approx_error={}".format(
poly_degree, approx_error))
poly_object = global_poly_object.sub_poly(start_index=1, offset=1)
#poly_object = global_poly_object.sub_poly(start_index=0,offset=0)
Attributes.set_default_silent(True)
Attributes.set_default_rounding_mode(ML_RoundToNearest)
Log.report(Log.Verbose, "generating polynomial evaluation scheme")
pre_poly = PolynomialSchemeEvaluator.generate_horner_scheme(
poly_object, _red_vx, unified_precision=self.precision)
_poly = FMA(pre_poly, _red_vx,
global_poly_object.get_cst_coeff(0, self.precision))
_poly.set_attributes(tag="poly", debug=debug_lftolx)
Log.report(
Log.Verbose, "sollya global_poly_object: {}".format(
global_poly_object.get_sollya_object()))
Log.report(
Log.Verbose, "sollya poly_object: {}".format(
poly_object.get_sollya_object()))
corr_exp = _vx_exp if exp_corr_factor == None else _vx_exp + exp_corr_factor
Attributes.unset_default_rounding_mode()
Attributes.unset_default_silent()
pre_result = -_log_inv_hi + (_red_vx * _poly + (-_log_inv_lo))
pre_result.set_attributes(tag="pre_result", debug=debug_lftolx)
exact_log2_hi_exp = Conversion(corr_exp, precision=self.precision)
exact_log2_hi_exp.set_attributes(tag="exact_log2_hi_hex",
debug=debug_lftolx)
_result = exact_log2_hi_exp + pre_result
return _result, _poly, _log_inv_lo, _log_inv_hi, _red_vx
result, poly, log_inv_lo, log_inv_hi, red_vx = compute_log(vx)
result.set_attributes(tag="result", debug=debug_lftolx)
# specific input value predicate
neg_input = Comparison(vx,
0,
likely=False,
specifier=Comparison.Less,
debug=debugd,
tag="neg_input")
vx_nan_or_inf = Test(vx,
specifier=Test.IsInfOrNaN,
likely=False,
debug=debugd,
tag="nan_or_inf")
vx_snan = Test(vx,
specifier=Test.IsSignalingNaN,
likely=False,
debug=debugd,
tag="vx_snan")
vx_inf = Test(vx,
specifier=Test.IsInfty,
likely=False,
debug=debugd,
tag="vx_inf")
vx_subnormal = Test(vx,
specifier=Test.IsSubnormal,
likely=False,
debug=debugd,
tag="vx_subnormal")
vx_zero = Test(vx,
specifier=Test.IsZero,
likely=False,
debug=debugd,
tag="vx_zero")
exp_mone = Equal(vx_exp,
-1,
tag="exp_minus_one",
debug=debugd,
likely=False)
vx_one = Equal(vx, 1.0, tag="vx_one", likely=False, debug=debugd)
# Specific specific for the case exp == -1
# log2(x) = log2(m) - 1
#
# as m in [1, 2[, log2(m) in [0, 1[
# if r is close to 2, a catastrophic cancellation can occur
#
# r = seed(m)
# log2(x) = log2(seed(m) * m / seed(m)) - 1
# = log2(seed(m) * m) - log2(seed(m)) - 1
#
# for m really close to 2 => seed(m) = 0.5
# => log2(x) = log2(0.5 * m)
# =
result_exp_m1 = (-log_inv_hi - 1.0) + FMA(poly, red_vx, -log_inv_lo)
result_exp_m1.set_attributes(tag="result_exp_m1", debug=debug_lftolx)
m100 = -100
S2100 = Constant(S2**100, precision=self.precision)
result_subnormal, _, _, _, _ = compute_log(vx * S2100,
exp_corr_factor=m100)
result_subnormal.set_attributes(tag="result_subnormal",
debug=debug_lftolx)
one_err = S2**-7
approx_interval_one = Interval(-one_err, one_err)
red_vx_one = vx - 1.0
poly_degree_one = sup(
guessdegree(
log(1 + x) / x, approx_interval_one, S2**
-(self.precision.get_field_size() + 1))) + 1
poly_object_one = Polynomial.build_from_approximation(
log(1 + sollya.x) / sollya.x, poly_degree_one,
[self.precision] * (poly_degree_one + 1), approx_interval_one,
absolute).sub_poly(start_index=1)
poly_one = PolynomialSchemeEvaluator.generate_horner_scheme(
poly_object_one, red_vx_one, unified_precision=self.precision)
poly_one.set_attributes(tag="poly_one", debug=debug_lftolx)
result_one = red_vx_one + red_vx_one * poly_one
cond_one = (vx < (1 + one_err)) & (vx > (1 - one_err))
cond_one.set_attributes(tag="cond_one", debug=debugd, likely=False)
# main scheme
pre_scheme = ConditionBlock(
neg_input,
Statement(ClearException(), Raise(ML_FPE_Invalid),
Return(FP_QNaN(self.precision))),
ConditionBlock(
vx_nan_or_inf,
ConditionBlock(
vx_inf,
Statement(
ClearException(),
Return(FP_PlusInfty(self.precision)),
),
Statement(ClearException(),
ConditionBlock(vx_snan, Raise(ML_FPE_Invalid)),
Return(FP_QNaN(self.precision)))),
ConditionBlock(
vx_subnormal,
ConditionBlock(
vx_zero,
Statement(
ClearException(),
Raise(ML_FPE_DivideByZero),
Return(FP_MinusInfty(self.precision)),
),
Statement(ClearException(), result_subnormal,
Return(result_subnormal))),
ConditionBlock(
vx_one,
Statement(
ClearException(),
Return(FP_PlusZero(self.precision)),
),
ConditionBlock(exp_mone, Return(result_exp_m1),
Return(result))))))
scheme = Statement(result, pre_scheme)
return scheme
standard_test_cases = [(sollya.parse("0x1.ffd6906acffc7p-1"), )]
def numeric_emulate(self, input_value):
""" Numeric emulation to generate expected value
corresponding to input_value input """
return log2(input_value)
class ML_Log(ML_Function("ml_log")):
def __init__(self, args):
# initializing base class
ML_FunctionBasis.__init__(self, args)
@staticmethod
def get_default_args(**kw):
""" Return a structure containing the arguments for ML_Log,
builtin from a default argument mapping overloaded with @p kw """
default_args_log = {
"output_file": "my_logf.c",
"function_name": "my_log",
"precision": ML_Binary32,
"accuracy": ML_Faithful,
"target": GenericProcessor()
}
default_args_log.update(kw)
return DefaultArgTemplate(**default_args_log)
def generate_emulate(self, result_ternary, result, mpfr_x, mpfr_rnd):
""" generate the emulation code for ML_Log2 functions
mpfr_x is a mpfr_t variable which should have the right precision
mpfr_rnd is the rounding mode
"""
emulate_func_name = "mpfr_log"
emulate_func_op = FunctionOperator(emulate_func_name,
arg_map={
0: FO_Arg(0),
1: FO_Arg(1),
2: FO_Arg(2)
},
require_header=["mpfr.h"])
emulate_func = FunctionObject(emulate_func_name,
[ML_Mpfr_t, ML_Mpfr_t, ML_Int32],
ML_Int32, emulate_func_op)
mpfr_call = Statement(
ReferenceAssign(result_ternary,
emulate_func(result, mpfr_x, mpfr_rnd)))
return mpfr_call
def generate_scheme(self):
vx = self.implementation.add_input_variable("x", self.precision)
sollya_precision = self.precision.sollya_object
# constant computation
invlog2 = round(1 / log(2), sollya_precision, sollya.RN)
invlog2_cst = Constant(invlog2, precision=self.precision)
#v_log2_hi = round(log(2), 16, sollya.RN)
#v_log2_lo = round(log(2) - v_log2_hi, sollya_precision, sollya.RN)
#log2_hi = Constant(v_log2_hi, precision = self.precision, tag = "log2_hi")
#log2_lo = Constant(v_log2_lo, precision = self.precision, tag = "log2_lo")
# local overloading of RaiseReturn operation
def ExpRaiseReturn(*args, **kwords):
kwords["arg_value"] = vx
kwords["function_name"] = self.function_name
return RaiseReturn(*args, **kwords)
test_nan_or_inf = Test(vx,
specifier=Test.IsInfOrNaN,
likely=False,
debug=True,
tag="nan_or_inf")
test_nan = Test(vx,
specifier=Test.IsNaN,
debug=True,
tag="is_nan_test")
test_positive = Comparison(vx,
0,
specifier=Comparison.GreaterOrEqual,
debug=True,
tag="inf_sign")
test_signaling_nan = Test(vx,
specifier=Test.IsSignalingNaN,
debug=True,
tag="is_signaling_nan")
return_snan = Statement(
ExpRaiseReturn(ML_FPE_Invalid,
return_value=FP_QNaN(self.precision)))
v_log2_hi = round(
log(2),
self.precision.get_field_size() -
(self.precision.get_exponent_size() + 1), sollya.RN)
v_log2_lo = round(
log(2) - v_log2_hi, self.precision.sollya_object, sollya.RN)
log2_hi = Constant(v_log2_hi, precision=self.precision, tag="log2_hi")
log2_lo = Constant(v_log2_lo, precision=self.precision, tag="log2_lo")
vx_exp = ExponentExtraction(vx, tag="vx_exp", debug=debug_multi)
int_precision = self.precision.get_integer_format()
# table creation
table_index_size = 7
log_table = ML_NewTable(dimensions=[2**table_index_size, 2],
storage_precision=self.precision,
tag=self.uniquify_name("inv_table"))
log_table[0][0] = 0.0
log_table[0][1] = 0.0
# 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)
integer_precision = {
ML_Binary32: ML_UInt32,
ML_Binary64: ML_UInt64
}[self.precision]
for i in range(1, 2**table_index_size):
#inv_value = (1.0 + (self.processor.inv_approx_table[i] / S2**9) + S2**-52) * S2**-1
inv_value = inv_approx_table[
i] # (1.0 + (inv_approx_table[i][0] / S2**9) ) * S2**-1
value_high = round(
log(inv_value),
self.precision.get_field_size() -
(self.precision.get_exponent_size() + 1), sollya.RN)
value_low = round(
log(inv_value) - value_high, sollya_precision, sollya.RN)
log_table[i][0] = value_high
log_table[i][1] = value_low
def compute_log(_vx, exp_corr_factor=None):
_vx_mant = MantissaExtraction(_vx,
tag="_vx_mant",
debug=debug_multi,
precision=self.precision)
_vx_exp = ExponentExtraction(_vx, tag="_vx_exp", debug=debug_multi)
table_index = BitLogicAnd(BitLogicRightShift(
TypeCast(_vx_mant, precision=int_precision, debug=debug_multi),
self.precision.get_field_size() - 7,
debug=debug_multi),
0x7f,
tag="table_index",
debug=debug_multi)
# argument reduction
# TODO: detect if single operand inverse seed is supported by the targeted architecture
pre_arg_red_index = TypeCast(BitLogicAnd(
TypeCast(ReciprocalSeed(_vx_mant,
precision=self.precision,
tag="seed",
debug=debug_multi,
silent=True),
precision=integer_precision),
Constant(-2, precision=integer_precision),
precision=integer_precision),
precision=self.precision,
tag="pre_arg_red_index",
debug=debug_multi)
arg_red_index = Select(Equal(table_index, 0), 1.0,
pre_arg_red_index)
#_red_vx = arg_red_index * _vx_mant - 1.0
_red_vx = FusedMultiplyAdd(arg_red_index,
_vx_mant,
1.0,
specifier=FusedMultiplyAdd.Subtract)
_red_vx.set_attributes(tag="_red_vx", debug=debug_multi)
inv_err = S2**-7
red_interval = Interval(1 - inv_err, 1 + inv_err)
# return in case of standard (non-special) input
_log_inv_lo = TableLoad(log_table,
table_index,
1,
tag="log_inv_lo",
debug=debug_multi)
_log_inv_hi = TableLoad(log_table,
table_index,
0,
tag="log_inv_hi",
debug=debug_multi)
Log.report(Log.Verbose, "building mathematical polynomial")
approx_interval = Interval(-inv_err, inv_err)
poly_degree = sup(
guessdegree(
log(1 + sollya.x) / sollya.x, approx_interval, S2**
-(self.precision.get_field_size() + 1))) + 1
global_poly_object = Polynomial.build_from_approximation(
log(1 + sollya.x) / sollya.x, poly_degree,
[1] + [self.precision] * (poly_degree), approx_interval,
sollya.absolute)
poly_object = global_poly_object.sub_poly(start_index=1)
Log.report(Log.Verbose, "generating polynomial evaluation scheme")
#_poly = PolynomialSchemeEvaluator.generate_horner_scheme(poly_object, _red_vx, unified_precision = self.precision)
_poly = PolynomialSchemeEvaluator.generate_estrin_scheme(
poly_object, _red_vx, unified_precision=self.precision)
_poly.set_attributes(tag="poly", debug=debug_multi)
corr_exp = Conversion(
_vx_exp if exp_corr_factor == None else _vx_exp +
exp_corr_factor,
precision=self.precision)
split_red_vx = Split(_red_vx,
precision=ML_DoubleDouble,
tag="split_red_vx",
debug=debug_multi)
red_vx_hi = split_red_vx.hi
red_vx_lo = split_red_vx.lo
# result = _red_vx * poly - log_inv_hi - log_inv_lo + _vx_exp * log2_hi + _vx_exp * log2_lo
pre_result = -_log_inv_hi + (_red_vx +
(_red_vx * _poly +
(corr_exp * log2_lo - _log_inv_lo)))
pre_result.set_attributes(tag="pre_result", debug=debug_multi)
exact_log2_hi_exp = corr_exp * log2_hi
exact_log2_hi_exp.set_attributes(tag="exact_log2_hi_exp",
debug=debug_multi)
cancel_part = (corr_exp * log2_hi - _log_inv_hi)
cancel_part.set_attributes(tag="cancel_part", debug=debug_multi)
sub_part = red_vx_hi + cancel_part
sub_part.set_attributes(tag="sub_part", debug=debug_multi)
#result_one_low_part = (red_vx_hi * _poly + (red_vx_lo + (red_vx_lo * _poly + (corr_exp * log2_lo - _log_inv_lo))))
result_one_low_part = ((red_vx_lo +
(red_vx_lo * _poly +
(corr_exp * log2_lo - _log_inv_lo))))
result_one_low_part.set_attributes(tag="result_one_low_part",
debug=debug_multi)
_result_one = (
(sub_part) + red_vx_hi * _poly) + result_one_low_part
return exact_log2_hi_exp + pre_result, _poly, _log_inv_lo, _log_inv_hi, _red_vx, _result_one
result, poly, log_inv_lo, log_inv_hi, red_vx, new_result_one = compute_log(
vx)
result.set_attributes(tag="result", debug=debug_multi)
new_result_one.set_attributes(tag="new_result_one", debug=debug_multi)
neg_input = Comparison(vx,
0,
likely=False,
specifier=Comparison.Less,
debug=debug_multi,
tag="neg_input")
vx_nan_or_inf = Test(vx,
specifier=Test.IsInfOrNaN,
likely=False,
debug=debug_multi,
tag="nan_or_inf")
vx_snan = Test(vx,
specifier=Test.IsSignalingNaN,
likely=False,
debug=debug_multi,
tag="snan")
vx_inf = Test(vx,
specifier=Test.IsInfty,
likely=False,
debug=debug_multi,
tag="inf")
vx_subnormal = Test(vx,
specifier=Test.IsSubnormal,
likely=False,
debug=debug_multi,
tag="vx_subnormal")
vx_zero = Test(vx,
specifier=Test.IsZero,
likely=False,
debug=debug_multi,
tag="vx_zero")
exp_mone = Equal(vx_exp,
-1,
tag="exp_minus_one",
debug=debug_multi,
likely=False)
vx_one = Equal(vx, 1.0, tag="vx_one", likely=False, debug=debug_multi)
# exp=-1 case
Log.report(Log.Verbose, "managing exp=-1 case")
result2 = (-log_inv_hi - log2_hi) + (
(red_vx + poly * red_vx) - log2_lo - log_inv_lo)
result2.set_attributes(tag="result2", debug=debug_multi)
m100 = -100
S2100 = Constant(S2**100, precision=self.precision)
result_subnormal, _, _, _, _, _ = compute_log(vx * S2100,
exp_corr_factor=m100)
Log.report(Log.Verbose, "managing close to 1.0 cases")
one_err = S2**-7
approx_interval_one = Interval(-one_err, one_err)
red_vx_one = vx - 1.0
poly_degree_one = sup(
guessdegree(
log(1 + sollya.x) / sollya.x, approx_interval_one, S2**
-(self.precision.get_field_size() + 1))) + 1
poly_object_one = Polynomial.build_from_approximation(
log(1 + sollya.x) / sollya.x, poly_degree_one,
[self.precision] * (poly_degree_one + 1), approx_interval_one,
sollya.absolute).sub_poly(start_index=1)
poly_one = PolynomialSchemeEvaluator.generate_horner_scheme(
poly_object_one, red_vx_one, unified_precision=self.precision)
poly_one.set_attributes(tag="poly_one", debug=debug_multi)
result_one = red_vx_one + red_vx_one * poly_one
cond_one = (vx < (1 + one_err)) & (vx > (1 - one_err))
cond_one.set_attributes(tag="cond_one",
debug=debug_multi,
likely=False)
# main scheme
pre_scheme = ConditionBlock(
neg_input,
Statement(ClearException(), Raise(ML_FPE_Invalid),
Return(FP_QNaN(self.precision))),
ConditionBlock(
vx_nan_or_inf,
ConditionBlock(
vx_inf,
Statement(
ClearException(),
Return(FP_PlusInfty(self.precision)),
),
Statement(ClearException(),
ConditionBlock(vx_snan, Raise(ML_FPE_Invalid)),
Return(FP_QNaN(self.precision)))),
ConditionBlock(
vx_subnormal,
ConditionBlock(
vx_zero,
Statement(
ClearException(),
Raise(ML_FPE_DivideByZero),
Return(FP_MinusInfty(self.precision)),
), Return(result_subnormal)),
ConditionBlock(
vx_one,
Statement(
ClearException(),
Return(FP_PlusZero(self.precision)),
),
ConditionBlock(exp_mone, Return(result2),
Return(result))
#ConditionBlock(cond_one,
#Return(new_result_one),
#ConditionBlock(exp_mone,
#Return(result2),
#Return(result)
#)
#)
))))
scheme = pre_scheme
return scheme
standard_test_cases = [(sollya.parse("0x1.fe9a5p-1"), ),
(sollya.parse("0x1.fe9a5p-1"), )]
def numeric_emulate(self, input_value):
return log(input_value)
# float step = 0x1.p-11;
# unsigned index_size = 11;
# for (int i = 0; i < (1<<index_size); ++i) {
# float input = 1.0f + i * step;
# float approx = 0.0f;
# _mm_store_ss(&approx, _mm_rcp_ss (_mm_set_ss(input)));
# printf("\"%a\", ", approx);
# if (i % 5 == 4) printf("\n");
# }
# return 0;
# }
x86_rcp_table = ML_ApproxTable(
dimensions = [2**11],
index_size=11,
storage_precision = ML_Binary32,
init_data = [sollya.parse(v) for v in [
"0x1.ffep-1", "0x1.ffap-1", "0x1.ff6p-1", "0x1.ff2p-1", "0x1.feep-1",
"0x1.feap-1", "0x1.fe6p-1", "0x1.fe2p-1", "0x1.fdep-1", "0x1.fdap-1",
"0x1.fd6p-1", "0x1.fd2p-1", "0x1.fcep-1", "0x1.fcap-1", "0x1.fc6p-1",
"0x1.fc2p-1", "0x1.fbfp-1", "0x1.fbbp-1", "0x1.fb7p-1", "0x1.fb3p-1",
"0x1.fafp-1", "0x1.fabp-1", "0x1.fa7p-1", "0x1.fa3p-1", "0x1.f9fp-1",
"0x1.f9bp-1", "0x1.f97p-1", "0x1.f93p-1", "0x1.f9p-1", "0x1.f8cp-1",
"0x1.f88p-1", "0x1.f84p-1", "0x1.f8p-1", "0x1.f7cp-1", "0x1.f78p-1",
"0x1.f74p-1", "0x1.f71p-1", "0x1.f6dp-1", "0x1.f69p-1", "0x1.f65p-1",
"0x1.f61p-1", "0x1.f5dp-1", "0x1.f59p-1", "0x1.f56p-1", "0x1.f52p-1",
"0x1.f4ep-1", "0x1.f4ap-1", "0x1.f46p-1", "0x1.f42p-1", "0x1.f3fp-1",
"0x1.f3bp-1", "0x1.f37p-1", "0x1.f33p-1", "0x1.f2fp-1", "0x1.f2cp-1",
"0x1.f28p-1", "0x1.f24p-1", "0x1.f2p-1", "0x1.f1cp-1", "0x1.f19p-1",
"0x1.f15p-1", "0x1.f11p-1", "0x1.f0dp-1", "0x1.f0ap-1", "0x1.f06p-1",
"0x1.f02p-1", "0x1.efep-1", "0x1.efbp-1", "0x1.ef7p-1", "0x1.ef3p-1",
"0x1.eefp-1", "0x1.eecp-1", "0x1.ee8p-1", "0x1.ee4p-1", "0x1.eep-1",
class ML_Exp2(ML_FunctionBasis):
function_name = "ml_exp2"
def __init__(self, args=DefaultArgTemplate):
# initializing base class
ML_FunctionBasis.__init__(self, args)
@staticmethod
def get_default_args(**kw):
""" Return a structure containing the arguments for ML_Exponential,
builtin from a default argument mapping overloaded with @p kw """
default_args_exp2 = {
"output_file": "ml_exp2.c",
"function_name": "ml_exp2",
"precision": ML_Binary32,
"accuracy": ML_Faithful,
"target": GenericProcessor()
}
default_args_exp2.update(kw)
return DefaultArgTemplate(**default_args_exp2)
def generate_scheme(self):
# declaring target and instantiating optimization engine
vx = self.implementation.add_input_variable("x", self.precision)
Log.set_dump_stdout(True)
Log.report(Log.Info,
"\033[33;1m generating implementation scheme \033[0m")
if self.debug_flag:
Log.report(Log.Info, "\033[31;1m debug has been enabled \033[0;m")
# local overloading of RaiseReturn operation
def ExpRaiseReturn(*args, **kwords):
kwords["arg_value"] = vx
kwords["function_name"] = self.function_name
return RaiseReturn(*args, **kwords)
r_interval = Interval(-0.5, 0.5)
local_ulp = sup(ulp(2**r_interval, self.precision))
Log.report(Log.Info, "ulp: ", local_ulp)
error_goal = S2**-1 * local_ulp
Log.report(Log.Info, "error goal: ", error_goal)
sollya_precision = {
ML_Binary32: sollya.binary32,
ML_Binary64: sollya.binary64
}[self.precision]
int_precision = {
ML_Binary32: ML_Int32,
ML_Binary64: ML_Int64
}[self.precision]
#Argument Reduction
vx_int = NearestInteger(vx,
precision=int_precision,
tag='vx_int',
debug=debug_multi)
vx_intf = Conversion(vx_int, precision=self.precision)
vx_r = vx - vx_intf
vx_r.set_attributes(tag="vx_r", debug=debug_multi)
degree = sup(guessdegree(2**(sollya.x), r_interval, error_goal)) + 2
precision_list = [1] + [self.precision] * degree
exp_X = ExponentInsertion(vx_int,
tag="exp_X",
debug=debug_multi,
precision=self.precision)
#Polynomial Approx
polynomial_scheme_builder = PolynomialSchemeEvaluator.generate_horner_scheme
poly_object, poly_error = Polynomial.build_from_approximation_with_error(
2**(sollya.x) - 1, degree, precision_list, r_interval,
sollya.absolute)
Log.report(Log.Info, "Poly : %s" % poly_object)
Log.report(Log.Info, "poly_error : ", poly_error)
poly = polynomial_scheme_builder(poly_object.sub_poly(start_index=1),
vx_r,
unified_precision=self.precision)
poly.set_attributes(tag="poly", debug=debug_multi)
#Handling special cases
oflow_bound = Constant(self.precision.get_emax() + 1,
precision=self.precision)
subnormal_bound = self.precision.get_emin_subnormal()
uflow_bound = self.precision.get_emin_normal()
Log.report(Log.Info, "oflow : ", oflow_bound)
#print "uflow : ", uflow_bound
#print "sub : ", subnormal_bound
test_overflow = Comparison(vx,
oflow_bound,
specifier=Comparison.GreaterOrEqual)
test_overflow.set_attributes(tag="oflow_test",
debug=debug_multi,
likely=False,
precision=ML_Bool)
test_underflow = Comparison(vx, uflow_bound, specifier=Comparison.Less)
test_underflow.set_attributes(tag="uflow_test",
debug=debug_multi,
likely=False,
precision=ML_Bool)
test_subnormal = Comparison(vx,
subnormal_bound,
specifier=Comparison.Greater)
test_subnormal.set_attributes(tag="sub_test",
debug=debug_multi,
likely=False,
precision=ML_Bool)
subnormal_offset = -(uflow_bound - vx_int)
subnormal_offset.set_attributes(tag="offset", debug=debug_multi)
exp_offset = ExponentInsertion(subnormal_offset,
precision=self.precision,
debug=debug_multi,
tag="exp_offset")
exp_min = ExponentInsertion(uflow_bound,
precision=self.precision,
debug=debug_multi,
tag="exp_min")
subnormal_result = exp_offset * exp_min * poly + exp_offset * exp_min
test_std = LogicalOr(test_overflow,
test_underflow,
precision=ML_Bool,
tag="std_test",
likely=False)
#Reconstruction
result = exp_X * poly + exp_X
result.set_attributes(tag="result", debug=debug_multi)
C0 = Constant(0, precision=self.precision)
return_inf = Return(FP_PlusInfty(self.precision))
return_C0 = Return(C0)
return_sub = Return(subnormal_result)
return_std = Return(result)
non_std_statement = Statement(
ConditionBlock(
test_overflow, return_inf,
ConditionBlock(test_subnormal, return_sub, return_C0)))
scheme = Statement(
ConditionBlock(test_std, non_std_statement, return_std))
return scheme
def generate_emulate(self, result_ternary, result, mpfr_x, mpfr_rnd):
""" generate the emulation code for ML_Log2 functions
mpfr_x is a mpfr_t variable which should have the right precision
mpfr_rnd is the rounding mode
"""
emulate_func_name = "mpfr_exp"
emulate_func_op = FunctionOperator(emulate_func_name,
arg_map={
0: FO_Arg(0),
1: FO_Arg(1),
2: FO_Arg(2)
},
require_header=["mpfr.h"])
emulate_func = FunctionObject(emulate_func_name,
[ML_Mpfr_t, ML_Mpfr_t, ML_Int32],
ML_Int32, emulate_func_op)
mpfr_call = Statement(
ReferenceAssign(result_ternary,
emulate_func(result, mpfr_x, mpfr_rnd)))
return mpfr_call
def numeric_emulate(self, input_value):
return sollya.SollyaObject(2)**(input_value)
standard_test_cases = [[
sollya.parse(x)
] for x in ["0x1.ffead1bac7ad2p+9", "-0x1.ee9cb4p+1", "-0x1.db0928p+3"]]
