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)
def get_value_str(self, value):
if value is Gappa_Unknown:
return "?"
elif isinstance(value, sollya.SollyaObject) and value.is_range():
return "[%s, %s]" % (sollya.inf(value), sollya.sup(value))
else:
return str(value)
def generate_test_case(self,
input_signals,
io_map,
index,
test_range=Interval(-1.0, 1.0)):
""" generic test case generation: generate a random input
with index @p index
Args:
index (int): integer index of the test case
Returns:
dict: mapping (input tag -> numeric value)
"""
# extracting test interval boundaries
low_input = sollya.inf(test_range)
high_input = sollya.sup(test_range)
input_values = {}
for input_tag in input_signals:
input_signal = io_map[input_tag]
# FIXME: correct value generation depending on signal precision
input_precision = input_signal.get_precision().get_base_format()
if isinstance(input_precision, ML_FP_Format):
input_value = generate_random_fp_value(input_precision,
low_input, high_input)
elif isinstance(input_precision, ML_Fixed_Format):
# TODO: does not depend on low and high range bounds
input_value = generate_random_fixed_value(input_precision)
else:
input_value = random.randrange(
2**input_precision.get_bit_size())
# registering input value
input_values[input_tag] = input_value
return input_values
def generate_fptaylor(x):
x_low = sollya.inf(x)
x_high = sollya.sup(x)
query = "\n".join([
"Variables", " real x in [{},{}];".format(x_low, x_high),
"Definitions", " r rnd64= x;",
" retval rnd64= {};".format(poly_expr), "Expressions",
" retval;"
])
rnd_rel_err = None
rnd_abs_err = None
try:
res = fptaylor.Result(query, {
**config, "--rel-error": "true",
"--abs-error": "true"
})
rnd_rel_err = float(
res.result["relative_errors"]["final_total"]["value"])
rnd_abs_err = float(
res.result["absolute_errors"]["final_total"]["value"])
except AssertionError:
pass
except KeyError:
try:
rnd_abs_err = float(
res.result["absolute_errors"]["final_total"]["value"])
except KeyError:
pass
if rnd_abs_err is None:
try:
res = fptaylor.Result(query, {
**config, "--rel-error": "false",
"--abs-error": "true"
})
rnd_abs_err = float(
res.result["absolute_errors"]["final_total"]["value"])
except AssertionError:
pass
err_int = sollya.supnorm(self.poly_object.get_sollya_object(),
sollya.exp(sollya.x), x, sollya.relative,
2**-100)
algo_rel_err = sollya.sup(err_int)
err_int = sollya.supnorm(self.poly_object.get_sollya_object(),
sollya.exp(sollya.x), x, sollya.absolute,
2**-100)
algo_abs_err = sollya.sup(err_int)
if rnd_rel_err is None or str(algo_rel_err) == "error":
rel_err = float("inf")
else:
rel_err = rnd_rel_err + algo_rel_err
abs_err = rnd_abs_err + algo_abs_err
return rel_err, abs_err
def get_integer_format(backend, optree):
""" return integer format to use for optree """
int_range = optree.get_interval()
if int_range == None:
return backend.default_integer_format
elif inf(int_range) < 0:
# signed
if sup(int_range) > 2**31 - 1 or inf(int_range) < -2**31:
return ML_Int64
else:
return ML_Int32
else:
# unsigned
if sup(int_range) >= 2**32 - 1:
return ML_UInt64
else:
return ML_UInt32
def inf(obj):
""" generic getter for interval inferior bound """
if isinstance(obj, SollyaObject) and obj.is_range():
return sollya.inf(obj)
elif isinstance(obj, (MetaInterval, MetaIntervalList)):
return obj.inf
else:
raise NotImplementedError
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
def is_simplifiable_to_cst(node):
""" node can be simplified to a constant """
node_interval = node.get_interval()
if node_interval is None or isinstance(node, Constant):
return False
elif isinstance(node_interval, SollyaObject) and node_interval.is_range():
return sollya.inf(node_interval) == sollya.sup(node_interval)
elif isinstance(node_interval, (MetaInterval, MetaIntervalList)):
return not node_interval.is_empty and (node_interval.inf == node_interval.sup)
else:
return False
def split_domain(starting_domain, slivers):
in_domains = [starting_domain]
# abs
out_domains = list()
for I in in_domains:
if sollya.inf(I) < 0 and sollya.sup(I) > 0:
out_domains.append(sollya.Interval(sollya.inf(I), 0))
out_domains.append(sollya.Interval(0, sollya.sup(I)))
else:
out_domains.append(I)
in_domains = out_domains
# k
out_domains = list()
while len(in_domains) > 0:
I = in_domains.pop()
#print("in: [{}, {}]".format(float(sollya.inf(I)), float(sollya.sup(I))))
unround_mult = I * n_invpi
mult_low = sollya.floor(sollya.inf(unround_mult))
mult_high = sollya.floor(sollya.sup(unround_mult))
if mult_low == mult_high or (mult_low == -1
and mult_high == 0):
#print(" accepted")
out_domains.append(I)
continue
if sollya.sup(I) <= 0:
divider_low = (mult_low + 1) * n_pi
divider_high = divider_low - divider_low * 2**-53
else:
divider_high = (mult_low + 1) * n_pi
divider_low = divider_high - divider_high * 2**-53
lower_part = sollya.Interval(sollya.inf(I), divider_low)
upper_part = sollya.Interval(divider_high, sollya.sup(I))
#print(" -> [{}, {}]".format(float(sollya.inf(lower_part)), float(sollya.sup(lower_part))))
#print(" -> [{}, {}]".format(float(sollya.inf(upper_part)), float(sollya.sup(upper_part))))
in_domains.append(lower_part)
in_domains.append(upper_part)
in_domains = out_domains
# subdivide each section into 2**subd sections
for _ in range(slivers):
out_domains = list()
for I in in_domains:
mid = sollya.mid(I)
out_domains.append(sollya.Interval(sollya.inf(I), mid))
out_domains.append(sollya.Interval(mid, sollya.sup(I)))
in_domains = out_domains
in_domains = set(in_domains)
in_domains = sorted(in_domains, key=lambda x: float(sollya.inf(x)))
in_domains = [
d for d in in_domains if sollya.inf(d) != sollya.sup(d)
]
return in_domains
def addsub_signed_predicate(lhs, lhs_prec, rhs, rhs_prec, op=operator.__sub__, default=True):
""" determine whether subtraction output on a signed or
unsigned format """
left_range = evaluate_range(lhs)
right_range = evaluate_range(rhs)
result_range = safe(op)(left_range, right_range)
if result_range is None:
return default
elif sollya.inf(result_range) < 0:
return True
else:
return False
def simplify(self, node):
def get_node_input(index):
# look for input into simpifield list
# and return directly node input if simplified input is None
return node.get_input(index)
result = None
if node in self.memoization_map:
return self.memoization_map[node]
else:
if not is_leaf_node(node):
for index, op in enumerate(node.inputs):
new_op = self.simplify(op)
# replacing modified inputs
if not new_op is None:
node.set_input(index, new_op)
if is_simplifiable_to_cst(node):
new_node = Constant(
sollya.inf(node.get_interval()),
precision=node.get_precision()
)
forward_attributes(node, new_node)
result = new_node
elif isinstance(node, Multiplication) and is_simplifiable_multiplication(node, get_node_input(0), get_node_input(1)):
result = simplify_multiplication(node)
elif isinstance(node, Min):
simplified_min = is_simplifiable_min(node, get_node_input(0), get_node_input(1))
if simplified_min:
result = simplified_min
elif isinstance(node, Max):
simplified_max = is_simplifiable_max(node, get_node_input(0), get_node_input(1))
if simplified_max:
result = simplified_max
elif isinstance(node, Comparison):
cmp_value = is_simplifiable_cmp(node, get_node_input(0), get_node_input(1))
if cmp_value is BooleanValue.AlwaysTrue:
result = generate_uniform_cst(True, node.get_precision())
elif cmp_value is BooleanValue.AlwaysFalse:
result = generate_uniform_cst(False, node.get_precision())
elif isinstance(node, Test):
test_value = is_simplifiable_test(node, node.inputs)
if test_value is BooleanValue.AlwaysTrue:
result = generate_uniform_cst(True, node.get_precision())
elif test_value is BooleanValue.AlwaysFalse:
result = generate_uniform_cst(False, node.get_precision())
elif isinstance(node, ConditionBlock):
result = simplify_condition_block(node)
elif isinstance(node, LogicOperation):
result = simplify_logical_op(node)
if not result is None:
Log.report(LOG_VERBOSE_NUMERICAL_SIMPLIFICATION, "{} has been simplified to {}", node, result)
self.memoization_map[node] = result
return result
def get_value_str(self, value):
if value is Gappa_Unknown:
return "?"
elif isinstance(value, MetaInterval):
return self.get_value_str(value.interval)
elif isinstance(value, MetaIntervalList):
# MetaIntervalList should have been catched early and
# should have generated a disjonction of cases
raise NotImplementedError
elif isinstance(value, sollya.SollyaObject) and value.is_range():
return "[%s, %s]" % (sollya.inf(value), sollya.sup(value))
else:
return str(value)
def findMaxIssue(res): """ Find the issue with the maximum error Parameters: - res: (sollya object) result from the checkModulusFilterInSpecification function Returns the maximum value (0 if not available) """ maxError = 0 for b in dict(res)["results"]: # for every band okay = dict(b)["okay"] if not okay: for i in dict(b)["issue"]: # for every issues H = dict(i)["H"] betaInf = dict(dict(i)["specification"])["betaInf"] betaSup = dict(dict(i)["specification"])["betaSup"] if sollya.inf(H) > betaSup: maxError = sollya.max(maxError, sollya.sup(H) - betaSup) else: maxError = sollya.max(maxError, betaSup - sollya.inf(H)) return maxError
def generate_json(errors, domain):
errors = [err for err in errors if err[0] in domain]
errors.sort(key=lambda err: err[2])
epsilon = errors[0][2]
delta = max(err[1] for err in errors)
d = {
"cname": self.function_name,
"delta": float(delta),
"domain": [float(sollya.inf(domain)),
float(sollya.sup(domain)),],
"epsilon": float(epsilon),
"operation": "log"
}
return d
def split_domain(starting_domain, slivers):
in_domains = [starting_domain]
out_domains = list()
while len(in_domains) > 0:
I = in_domains.pop()
unround_e = sollya.log2(I)
e_low = sollya.floor(sollya.inf(unround_e))
e_high = sollya.floor(sollya.sup(unround_e))
#print("in: [{}, {}] ({}, {})".format(float(sollya.inf(I)), float(sollya.sup(I)), int(e_low), int(e_high)))
if e_low == e_high:
#print(" accepted")
out_domains.append(I)
continue
e_range = sollya.Interval(e_low, e_low+1)
I_range = 2**e_range
for _ in range(100):
mid = sollya.mid(I_range)
e = sollya.floor(sollya.log2(mid))
if e == e_low:
I_range = sollya.Interval(mid, sollya.sup(I_range))
else:
I_range = sollya.Interval(sollya.inf(I_range), mid)
divider_high = sollya.sup(I_range)
divider_low = sollya.inf(I_range)
lower_part = sollya.Interval(sollya.inf(I), divider_low)
upper_part = sollya.Interval(divider_high, sollya.sup(I))
#print(" -> [{}, {}]".format(float(sollya.inf(lower_part)), float(sollya.sup(lower_part))))
#print(" -> [{}, {}]".format(float(sollya.inf(upper_part)), float(sollya.sup(upper_part))))
in_domains.append(upper_part)
in_domains.append(lower_part)
in_domains = out_domains
# subdivide each section into 2**subd sections
for _ in range(slivers):
out_domains = list()
for I in in_domains:
mid = sollya.mid(I)
out_domains.append(sollya.Interval(sollya.inf(I), mid))
out_domains.append(sollya.Interval(mid, sollya.sup(I)))
in_domains = out_domains
in_domains = set(in_domains)
in_domains = sorted(in_domains, key=lambda x:float(sollya.inf(x)))
in_domains = [d for d in in_domains if sollya.inf(d) != sollya.sup(d)]
return in_domains
def solve_format_shift(optree):
""" Legalize shift node """
assert isinstance(optree, BitLogicRightShift) or isinstance(
optree, BitLogicLeftShift)
shift_input = optree.get_input(0)
shift_input_precision = shift_input.get_precision()
shift_amount = optree.get_input(1)
shift_amount_prec = shift_amount.get_precision()
if is_fixed_point(shift_amount_prec):
sa_range = evaluate_range(shift_amount)
if sollya.inf(sa_range) < 0:
Log.report(
Log.Error, "shift amount of {} may be negative {}\n".format(
optree, sa_range))
if is_fixed_point(shift_input_precision):
return shift_input_precision
else:
return optree.get_precision()
def get_precision_rng(precision, value_range=None):
if value_range is None:
# default full-range value generation
base_format = precision.get_base_format()
if isinstance(base_format, ML_FP_MultiElementFormat):
return MPFPRandomGen(precision)
elif isinstance(base_format, ML_FP_Format):
return FPRandomGen(precision, include_snan=False)
elif isinstance(base_format, ML_Fixed_Format):
return FixedPointRandomGen(precision)
else:
Log.report(Log.Error,
"unsupported format {}/{} in get_precision_rng",
precision, base_format)
else:
low_bound = sollya.inf(value_range)
high_bound = sollya.sup(value_range)
return get_precision_rng_with_defined_range(precision, low_bound,
high_bound)
def generate_scheme(self):
## convert @p value from an input floating-point precision
# @p in_precision to an output support format @p out_precision
io_precision = self.precision
# 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)
# size of most significant table index (for linear slope tabulation)
alpha = self.alpha # 6
# size of medium significant table index (for initial value table index LSB)
beta = self.beta # 5
# size of least significant table index (for linear offset tabulation)
gamma = self.gamma # 5
guard_bits = self.guard_bits # 3
vx.set_interval(self.interval)
range_hi = sollya.sup(self.interval)
range_lo = sollya.inf(self.interval)
f_hi = self.function(range_hi)
f_lo = self.function(range_lo)
# fixed by format used for reduced_x
range_size = range_hi - range_lo
range_size_log2 = int(sollya.log2(range_size))
assert 2**range_size_log2 == range_size
print("range_size_log2={}".format(range_size_log2))
reduced_x = Conversion(BitLogicRightShift(vx - range_lo,
range_size_log2),
precision=fixed_point(0,
alpha + beta + gamma,
signed=False),
tag="reduced_x",
debug=debug_fixed)
alpha_index = get_fixed_slice(reduced_x,
0,
alpha - 1,
align_hi=FixedPointPosition.FromMSBToLSB,
align_lo=FixedPointPosition.FromMSBToLSB,
tag="alpha_index",
debug=debug_std)
gamma_index = get_fixed_slice(reduced_x,
gamma - 1,
0,
align_hi=FixedPointPosition.FromLSBToLSB,
align_lo=FixedPointPosition.FromLSBToLSB,
tag="gamma_index",
debug=debug_std)
beta_index = get_fixed_slice(reduced_x,
alpha,
gamma,
align_hi=FixedPointPosition.FromMSBToLSB,
align_lo=FixedPointPosition.FromLSBToLSB,
tag="beta_index",
debug=debug_std)
# Assuming monotonic function
f_absmax = max(abs(f_hi), abs(f_lo))
f_absmin = min(abs(f_hi), abs(f_lo))
f_msb = int(sollya.ceil(sollya.log2(f_absmax))) + 1
f_lsb = int(sollya.floor(sollya.log2(f_absmin)))
storage_lsb = f_lsb - io_precision.get_bit_size() - guard_bits
f_int_size = f_msb
f_frac_size = -storage_lsb
storage_format = fixed_point(f_int_size, f_frac_size, signed=False)
Log.report(Log.Info, "storage_format is {}".format(storage_format))
# table of initial value index
tiv_index = Concatenation(alpha_index,
beta_index,
tag="tiv_index",
debug=debug_std)
# table of offset value index
to_index = Concatenation(alpha_index,
gamma_index,
tag="to_index",
debug=debug_std)
tiv_index_size = alpha + beta
to_index_size = alpha + gamma
Log.report(Log.Info, "initial table structures")
table_iv = ML_NewTable(dimensions=[2**tiv_index_size],
storage_precision=storage_format,
tag="tiv")
table_offset = ML_NewTable(dimensions=[2**to_index_size],
storage_precision=storage_format,
tag="to")
slope_table = [None] * (2**alpha)
slope_delta = 1.0 / sollya.SollyaObject(2**alpha)
delta_u = range_size * slope_delta * 2**-15
Log.report(Log.Info, "computing slope value")
for i in range(2**alpha):
# slope is computed at the middle of range_size interval
slope_x = range_lo + (i + 0.5) * range_size * slope_delta
# TODO: gross approximation of derivatives
f_xpu = self.function(slope_x + delta_u / 2)
f_xmu = self.function(slope_x - delta_u / 2)
slope = (f_xpu - f_xmu) / delta_u
slope_table[i] = slope
range_rcp_steps = 1.0 / sollya.SollyaObject(2**tiv_index_size)
Log.report(Log.Info, "computing value for initial-value table")
for i in range(2**tiv_index_size):
slope_index = i / 2**beta
iv_x = range_lo + i * range_rcp_steps * range_size
offset_x = 0.5 * range_rcp_steps * range_size
# initial value is computed so that the piecewise linear
# approximation intersects the function at iv_x + offset_x
iv_y = self.function(
iv_x + offset_x) - offset_x * slope_table[int(slope_index)]
initial_value = storage_format.round_sollya_object(iv_y)
table_iv[i] = initial_value
# determining table of initial value interval
tiv_min = table_iv[0]
tiv_max = table_iv[0]
for i in range(1, 2**tiv_index_size):
tiv_min = min(tiv_min, table_iv[i])
tiv_max = max(tiv_max, table_iv[i])
table_iv.set_interval(Interval(tiv_min, tiv_max))
offset_step = range_size / S2**(alpha + beta + gamma)
for i in range(2**alpha):
Log.report(Log.Info,
"computing offset value for sub-table {}".format(i))
for j in range(2**gamma):
to_i = i * 2**gamma + j
offset = slope_table[i] * j * offset_step
table_offset[to_i] = offset
# determining table of offset interval
to_min = table_offset[0]
to_max = table_offset[0]
for i in range(1, 2**(alpha + gamma)):
to_min = min(to_min, table_offset[i])
to_max = max(to_max, table_offset[i])
offset_interval = Interval(to_min, to_max)
table_offset.set_interval(offset_interval)
initial_value = TableLoad(table_iv,
tiv_index,
precision=storage_format,
tag="initial_value",
debug=debug_fixed)
offset_precision = get_fixed_type_from_interval(offset_interval, 16)
print("offset_precision is {} ({} bits)".format(
offset_precision, offset_precision.get_bit_size()))
table_offset.get_precision().storage_precision = offset_precision
# rounding table value
for i in range(1, 2**(alpha + gamma)):
table_offset[i] = offset_precision.round_sollya_object(
table_offset[i])
offset_value = TableLoad(table_offset,
to_index,
precision=offset_precision,
tag="offset_value",
debug=debug_fixed)
Log.report(
Log.Verbose,
"initial_value's interval: {}, offset_value's interval: {}".format(
evaluate_range(initial_value), evaluate_range(offset_value)))
final_add = initial_value + offset_value
round_bit = final_add # + FixedPointPosition(final_add, io_precision.get_bit_size(), align=FixedPointPosition.FromMSBToLSB)
vr_out = Conversion(initial_value + offset_value,
precision=io_precision,
tag="vr_out",
debug=debug_fixed)
self.implementation.add_output_signal("vr_out", vr_out)
# Approximation error evaluation
approx_error = 0.0
for i in range(2**alpha):
for j in range(2**beta):
tiv_i = (i * 2**beta + j)
# = range_lo + tiv_i * range_rcp_steps * range_size
iv = table_iv[tiv_i]
for k in range(2**gamma):
to_i = i * 2**gamma + k
offset = table_offset[to_i]
approx_value = offset + iv
table_x = range_lo + range_size * (
(i * 2**beta + j) * 2**gamma + k) / S2**(alpha + beta +
gamma)
local_error = abs(1 / (table_x) - approx_value)
approx_error = max(approx_error, local_error)
error_log2 = float(sollya.log2(approx_error))
print("approx_error is {}, error_log2 is {}".format(
float(approx_error), error_log2))
# table size
table_iv_size = 2**(alpha + beta)
table_offset_size = 2**(alpha + gamma)
print("tables' size are {} entries".format(table_iv_size +
table_offset_size))
return [self.implementation]
def random_log_sample(interval):
lo = sollya.inf(interval)
hi = sollya.sup(interval)
def generate_expr(
self,
code_object,
optree,
folded=False,
result_var=None,
initial=False,
language=None,
## force to store result in a variable, wrapping CodeExpression
# in CodeVariable
force_variable_storing=False):
""" code generation function """
language = self.language if language is None else language
# search if <optree> has already been processed
if self.has_memoization(optree):
result = self.get_memoization(optree)
if isinstance(result, CodeExpression) and force_variable_storing:
# forcing storing and translation CodeExpression to CodeVariable
# if force_variable_storing is set
result_precision = result.precision
prefix_tag = optree.get_tag(
default="var_result"
) if force_variable_storing else "tmp_result"
final_var = result_var if result_var else code_object.get_free_var_name(
result_precision, prefix=prefix_tag, declare=True)
code_object << self.generate_code_assignation(
code_object, final_var, result.get())
result = CodeVariable(final_var, result_precision)
return result
result = None
# implementation generation
if isinstance(optree, CodeVariable):
result = optree
elif isinstance(optree, Variable):
if optree.get_var_type() is Variable.Local:
final_var = code_object.get_free_var_name(
optree.get_precision(),
prefix=optree.get_tag(),
declare=True,
var_ctor=Variable)
result = CodeVariable(final_var, optree.get_precision())
else:
result = CodeVariable(optree.get_tag(), optree.get_precision())
elif isinstance(optree, Signal):
if optree.get_var_type() is Variable.Local:
final_var = code_object.declare_signal(optree,
optree.get_precision(),
prefix=optree.get_tag())
result = CodeVariable(final_var, optree.get_precision())
else:
result = CodeVariable(optree.get_tag(), optree.get_precision())
elif isinstance(optree, Constant):
precision = optree.get_precision() # .get_base_format()
if force_variable_storing or self.declare_cst or optree.get_precision(
).is_cst_decl_required():
cst_prefix = "cst" if optree.get_tag(
) is None else optree.get_tag()
cst_varname = code_object.declare_cst(optree,
prefix=cst_prefix)
result = CodeVariable(cst_varname, precision)
else:
if precision is ML_Integer:
result = CodeExpression("%d" % optree.get_value(),
precision)
else:
try:
result = CodeExpression(
precision.get_cst(optree.get_value(),
language=language), precision)
except:
result = CodeExpression(
precision.get_cst(optree.get_value(),
language=language), precision)
Log.report(
Log.Error,
"Error during get_cst call for Constant: {} ",
optree) # Exception print
elif isinstance(optree, Assert):
cond = optree.get_input(0)
error_msg = optree.get_error_msg()
severity = optree.get_severity()
cond_code = self.generate_expr(code_object,
cond,
folded=False,
language=language)
code_object << " assert {cond} report {error_msg} severity {severity};\n".format(
cond=cond_code.get(),
error_msg=error_msg,
severity=severity.descriptor)
return None
elif isinstance(optree, Wait):
time_ns = optree.get_time_ns()
code_object << "wait for {time_ns} ns;\n".format(time_ns=time_ns)
return None
elif isinstance(optree, SwitchBlock):
switch_value = optree.inputs[0]
# generating pre_statement
self.generate_expr(code_object,
optree.get_pre_statement(),
folded=folded,
language=language)
switch_value_code = self.generate_expr(code_object,
switch_value,
folded=folded,
language=language)
case_map = optree.get_case_map()
code_object << "\nswitch(%s) {\n" % switch_value_code.get()
for case in case_map:
case_value = case
case_statement = case_map[case]
if isinstance(case_value, tuple):
for sub_case in case:
code_object << "case %s:\n" % sub_case
else:
code_object << "case %s:\n" % case
code_object.open_level()
self.generate_expr(code_object,
case_statement,
folded=folded,
language=language)
code_object.close_level()
code_object << "}\n"
return None
elif isinstance(optree, ReferenceAssign):
output_var = optree.inputs[0]
result_value = optree.inputs[1]
output_var_code = self.generate_expr(code_object,
output_var,
folded=False,
language=language)
def get_assign_symbol(node):
if isinstance(node, Signal):
assign_sign = "<="
elif isinstance(node, Variable):
assign_sign = ":="
else:
Log.report(Log.Error,
"unsupported node for assign symbol:\n {}",
node)
return assign_sign
if isinstance(output_var, Signal) or isinstance(
output_var, Variable):
assign_sign = get_assign_symbol(output_var)
elif isinstance(output_var, VectorElementSelection) or isinstance(
output_var, SubSignalSelection):
select_input = output_var.get_input(0)
assign_sign = get_assign_symbol(select_input)
else:
Log.report(Log.Error,
"unsupported node for assign symbol:\n {}", node)
if isinstance(result_value, Constant):
# generate assignation
result_value_code = self.generate_expr(code_object,
result_value,
folded=folded,
language=language)
code_object << self.generate_assignation(
output_var_code.get(),
result_value_code.get(),
assign_sign=assign_sign)
else:
#result_value_code = self.generate_expr(code_object, result_value, folded = True, force_variable_storing = True, language = language)
result_value_code = self.generate_expr(code_object,
result_value,
folded=True,
language=language)
code_object << self.generate_assignation(
output_var_code.get(),
result_value_code.get(),
assign_sign=assign_sign)
if optree.get_debug() and not self.disable_debug:
self.generate_debug_msg(result_value,
result_value_code,
code_object,
debug_object=optree.get_debug())
#code_object << self.generate_assignation(output_var_code.get(), result_value_code.get())
#code_object << output_var.get_precision().generate_c_assignation(output_var_code, result_value_code)
return None
elif isinstance(optree, RangeLoop):
iterator = optree.get_input(0)
loop_body = optree.get_input(1)
loop_range = optree.get_loop_range()
specifier = optree.get_specifier()
range_pattern = "{lower} to {upper}" if specifier is RangeLoop.Increasing else "{upper} dowto {lower}"
range_code = range_pattern.format(lower=sollya.inf(loop_range),
upper=sollya.sup(loop_range))
iterator_code = self.generate_expr(code_object,
iterator,
folded=folded,
language=language)
code_object << "\n for {iterator} in {loop_range} loop\n".format(
iterator=iterator_code.get(), loop_range=range_code)
code_object.inc_level()
body_code = self.generate_expr(code_object,
loop_body,
folded=folded,
language=language)
assert body_code is None
code_object.dec_level()
code_object << "end loop;\n"
return None
elif isinstance(optree, Loop):
init_statement = optree.inputs[0]
exit_condition = optree.inputs[1]
loop_body = optree.inputs[2]
self.generate_expr(code_object,
init_statement,
folded=folded,
language=language)
code_object << "\nfor (;%s;)" % self.generate_expr(
code_object, exit_condition, folded=False,
language=language).get()
code_object.open_level()
self.generate_expr(code_object,
loop_body,
folded=folded,
language=language)
code_object.close_level()
return None
elif isinstance(optree, Process):
# generating pre_statement for process
pre_statement = optree.get_pre_statement()
self.generate_expr(code_object,
optree.get_pre_statement(),
folded=folded,
language=language)
sensibility_list = [
self.generate_expr(code_object,
op,
folded=True,
language=language).get()
for op in optree.get_sensibility_list()
]
sensibility_list = "({})".format(", ".join(
sensibility_list)) if len(sensibility_list) != 0 else ""
code_object << "process{}\n".format(sensibility_list)
self.open_memoization_level()
code_object.open_level(
extra_shared_tables=[MultiSymbolTable.SignalSymbol],
var_ctor=Variable)
for process_stat in optree.inputs:
self.generate_expr(code_object,
process_stat,
folded=folded,
initial=False,
language=language)
code_object.close_level()
self.close_memoization_level()
code_object << "end process;\n\n"
return None
elif isinstance(optree, PlaceHolder):
first_input = optree.get_input(0)
first_input_code = self.generate_expr(code_object,
first_input,
folded=folded,
language=language)
for op in optree.get_inputs()[1:]:
_ = self.generate_expr(code_object,
op,
folded=folded,
language=language)
result = first_input_code
elif isinstance(optree, ComponentInstance):
component_object = optree.get_component_object()
component_name = component_object.get_name()
code_object.declare_component(component_name, component_object)
io_map = optree.get_io_map()
component_tag = optree.get_tag()
if component_tag is None:
component_tag = "{component_name}_i{instance_id}".format(
component_name=component_name,
instance_id=optree.get_instance_id())
# component tag uniquifying
component_tag = code_object.get_free_name(component_object,
prefix=component_tag)
mapped_io = {}
for io_tag in io_map:
mapped_io[io_tag] = self.generate_expr(code_object,
io_map[io_tag],
folded=True,
language=language)
code_object << "\n{component_tag} : {component_name}\n".format(
component_name=component_name, component_tag=component_tag)
code_object << " port map (\n"
code_object << " " + ", \n ".join(
"{} => {}".format(io_tag, mapped_io[io_tag].get())
for io_tag in mapped_io)
code_object << "\n);\n"
return None
elif isinstance(optree, ConditionBlock):
condition = optree.inputs[0]
if_branch = optree.inputs[1]
else_branch = optree.inputs[2] if len(optree.inputs) > 2 else None
# generating pre_statement
self.generate_expr(code_object,
optree.get_pre_statement(),
folded=folded,
language=language)
cond_code = self.generate_expr(code_object,
condition,
folded=False,
language=language)
try:
cond_likely = condition.get_likely()
except AttributeError:
Log.report(
Log.Error,
"The following condition has no (usable) likely attribute: {}",
condition)
code_object << "if %s then\n " % cond_code.get()
code_object.inc_level()
if_branch_code = self.generate_expr(code_object,
if_branch,
folded=False,
language=language)
code_object.dec_level()
if else_branch:
code_object << " else\n "
code_object.inc_level()
else_branch_code = self.generate_expr(code_object,
else_branch,
folded=True,
language=language)
code_object.dec_level()
else:
# code_object << "\n"
pass
code_object << "end if;\n"
return None
elif isinstance(optree, Select):
# we go through all of select operands to
# flatten the select tree
def flatten_select(op, cond=None):
""" Process recursively a Select operation to build a list
of tuple (result, condition) """
if not isinstance(op, Select): return [(op, cond)]
lcond = op.inputs[0] if cond is None else LogicalAnd(
op.inputs[0], cond, precision=cond.get_precision())
return flatten_select(op.inputs[1], lcond) + flatten_select(
op.inputs[2], cond)
def legalize_select_input(select_input):
if select_input.get_precision().get_bit_size(
) != optree.get_precision().get_bit_size():
return Conversion(select_input,
precision=optree.get_precision())
else:
return select_input
prefix = optree.get_tag(default="setmp")
result_varname = result_var if result_var != None else code_object.get_free_var_name(
optree.get_precision(), prefix=prefix)
result = CodeVariable(result_varname, optree.get_precision())
select_opcond_list = flatten_select(optree)
if not select_opcond_list[-1][1] is None:
Log.report(
Log.Error,
"last condition in flatten select differs from None")
gen_list = []
for op, cond in select_opcond_list:
op = legalize_select_input(op)
op_code = self.generate_expr(code_object,
op,
folded=folded,
language=language)
if not cond is None:
cond_code = self.generate_expr(code_object,
cond,
folded=True,
force_variable_storing=True,
language=language)
gen_list.append((op_code, cond_code))
else:
gen_list.append((op_code, None))
code_object << "{result} <= \n".format(result=result.get())
code_object.inc_level()
for op_code, cond_code in gen_list:
if not cond_code is None:
code_object << "{op_code} when {cond_code} else\n".format(
op_code=op_code.get(), cond_code=cond_code.get())
else:
code_object << "{op_code};\n".format(op_code=op_code.get())
code_object.dec_level()
elif isinstance(optree, TableLoad):
table = optree.get_input(0)
index = optree.get_input(1)
index_code = self.generate_expr(code_object,
index,
folded=folded,
language=language)
prefix = optree.get_tag(default="table_value")
result_varname = result_var if result_var != None else code_object.get_free_var_name(
optree.get_precision(), prefix=prefix)
result = CodeVariable(result_varname, optree.get_precision())
code_object << "with {index} select {result} <=\n".format(
index=index_code.get(), result=result.get())
table_dimensions = table.get_precision().get_dimensions()
assert len(table_dimensions) == 1
table_size = table_dimensions[0]
default_value = 0
# linearizing table selection
for tabid, value in enumerate(table.get_data()):
code_object << "\t{} when {},\n".format(
table.get_precision().get_storage_precision().get_cst(
value),
index.get_precision().get_cst(tabid))
code_object << "\t{} when others;\n".format(table.get_precision(
).get_storage_precision().get_cst(default_value))
# result is set
elif isinstance(optree, Return):
return_result = optree.inputs[0]
return_code = self.generate_expr(code_object,
return_result,
folded=folded,
language=language)
code_object << "return %s;\n" % return_code.get()
return None #return_code
elif isinstance(optree, ExceptionOperation):
if optree.get_specifier() in [
ExceptionOperation.RaiseException,
ExceptionOperation.ClearException,
ExceptionOperation.RaiseReturn
]:
result_code = self.processor.generate_expr(
self,
code_object,
optree,
optree.inputs,
folded=False,
result_var=result_var,
language=language)
code_object << "%s;\n" % result_code.get()
if optree.get_specifier() == ExceptionOperation.RaiseReturn:
if self.libm_compliant:
# libm compliant exception management
code_object.add_header(
"support_lib/ml_libm_compatibility.h")
return_value = self.generate_expr(
code_object,
optree.get_return_value(),
folded=folded,
language=language)
arg_value = self.generate_expr(code_object,
optree.get_arg_value(),
folded=folded,
language=language)
function_name = optree.function_name
exception_list = [
op.get_value() for op in optree.inputs
]
if ML_FPE_Inexact in exception_list:
exception_list.remove(ML_FPE_Inexact)
if len(exception_list) > 1:
raise NotImplementedError
if ML_FPE_Overflow in exception_list:
code_object << "return ml_raise_libm_overflowf(%s, %s, \"%s\");\n" % (
return_value.get(), arg_value.get(),
function_name)
elif ML_FPE_Underflow in exception_list:
code_object << "return ml_raise_libm_underflowf(%s, %s, \"%s\");\n" % (
return_value.get(), arg_value.get(),
function_name)
elif ML_FPE_Invalid in exception_list:
code_object << "return %s;\n" % return_value.get()
else:
return_precision = optree.get_return_value(
).get_precision()
self.generate_expr(code_object,
Return(optree.get_return_value(),
precision=return_precision),
folded=folded,
language=language)
return None
else:
result = self.processor.generate_expr(self,
code_object,
optree,
optree.inputs,
folded=folded,
result_var=result_var,
language=language)
elif isinstance(optree, NoResultOperation):
result_code = self.processor.generate_expr(self,
code_object,
optree,
optree.inputs,
folded=False,
result_var=result_var,
language=language)
code_object << "%s;\n" % result_code.get()
return None
elif isinstance(optree, Statement):
for op in optree.inputs:
if not self.has_memoization(op):
self.generate_expr(code_object,
op,
folded=folded,
initial=True,
language=language)
return None
else:
# building ordered list of required node by depth
working_list = [op for op in optree.get_inputs()]
processing_list = [op for op in working_list]
resolved = {}
while working_list != []:
op = working_list.pop(0)
# node has already been processed: SKIP
if op in resolved:
continue
if isinstance(op, ML_Table):
# ML_Table instances are skipped (should be generated directly by TableLoad)
continue
elif isinstance(op, ML_LeafNode):
processing_list.append(op)
else:
memo = self.get_memoization(op)
if not memo is None:
# node has already been generated: STOP HERE
resolved[op] = memo
else:
# enqueue node to be processed
processing_list.append(op)
# enqueue node inputs
working_list += [op for op in op.get_inputs()]
resolved[op] = memo
# processing list in reverse order (starting with deeper node to avoid too much recursion)
for op in processing_list[::-1]:
_ = self.generate_expr(code_object,
op,
folded=folded,
initial=initial,
language=language)
# processing main node
generate_pre_process = self.generate_clear_exception if optree.get_clearprevious(
) else None
result = self.processor.generate_expr(
self,
code_object,
optree,
optree.inputs,
generate_pre_process=generate_pre_process,
folded=folded,
result_var=result_var,
language=language)
# registering result into memoization table
self.add_memoization(optree, result)
# debug management
if optree.get_debug() and not self.disable_debug:
self.generate_debug_msg(optree, result, code_object)
if (initial or force_variable_storing
or result_too_long(result)) and not isinstance(
result, CodeVariable) and not result is None:
# result could have been modified from initial optree
result_precision = result.precision
prefix_tag = optree.get_tag(
default="var_result"
) if force_variable_storing else "tmp_result"
final_var = result_var if result_var else code_object.get_free_var_name(
result_precision, prefix=prefix_tag, declare=True)
code_object << self.generate_code_assignation(
code_object, final_var, result.get())
return CodeVariable(final_var, result_precision)
return result
def generate_reduction_fptaylor(x):
# get sign and abs_x, must be the same at endpoints
if sollya.sup(x) <= 0:
sign_x_expr = "-1.0"
abs_x_expr = "-x"
abs_x = -x
elif sollya.inf(x) >= 0:
sign_x_expr = "1.0"
abs_x_expr = "x"
abs_x = x
else:
assert False, "Interval must not straddle 0"
# get k, must be the same at endpoints
unround_k = abs_x * n_invpi
k_low = sollya.floor(sollya.inf(unround_k))
k_high = sollya.floor(sollya.sup(unround_k))
if k_low != k_high:
assert False, "Interval must not straddle multples of pi"
k = int(k_low)
part = k % 2
r_expr = "abs_x - whole"
r = abs_x - k * n_pi
z_expr = "r"
z = r
if part == 1:
flipped_poly_expr = "-poly"
else:
flipped_poly_expr = "poly"
x_low = sollya.inf(x)
x_high = sollya.sup(x)
query = "\n".join([
"Variables", " real x in [{},{}];".format(x_low, x_high),
"Definitions", " abs_x rnd64= {};".format(abs_x_expr),
" whole rnd64= {} * {};".format(k, n_pi),
" r rnd64= abs_x - whole;", " z rnd64= {};".format(z_expr),
" poly rnd64= {};".format(poly_expr),
" flipped_poly rnd64= {};".format(flipped_poly_expr),
" retval rnd64= flipped_poly*{};".format(sign_x_expr),
"Expressions", " retval;"
])
rnd_rel_err = None
rnd_abs_err = None
try:
res = fptaylor.Result(query, {
**config, "--rel-error": "true",
"--abs-error": "true"
})
rnd_rel_err = float(
res.result["relative_errors"]["final_total"]["value"])
rnd_abs_err = float(
res.result["absolute_errors"]["final_total"]["value"])
except AssertionError:
pass
except KeyError:
try:
rnd_abs_err = float(
res.result["absolute_errors"]["final_total"]["value"])
except KeyError:
pass
if rnd_abs_err is None:
try:
res = fptaylor.Result(query, {
**config, "--rel-error": "false",
"--abs-error": "true"
})
rnd_abs_err = float(
res.result["absolute_errors"]["final_total"]["value"])
except AssertionError:
pass
err_int = sollya.supnorm(self.poly_object.get_sollya_object(),
sollya.sin(sollya.x), z, sollya.relative,
2**-100)
algo_rel_err = sollya.sup(err_int)
err_int = sollya.supnorm(self.poly_object.get_sollya_object(),
sollya.sin(sollya.x), z, sollya.absolute,
2**-100)
algo_abs_err = sollya.sup(err_int)
if rnd_rel_err is None or str(algo_rel_err) == "error":
rel_err = float("inf")
else:
rel_err = rnd_rel_err + algo_rel_err
abs_err = rnd_abs_err + algo_abs_err
return rel_err, abs_err
def determine_error(self):
sollya.settings.display = sollya.hexadecimal
n_pi = self.precision.round_sollya_object(sollya.pi, sollya.RN)
n_invpi = self.precision.round_sollya_object(1 / sollya.pi, sollya.RN)
poly_expr = str(sollya.horner(self.poly_object.get_sollya_object()))
poly_expr = poly_expr.replace("_x_", "z")
poly_expr = poly_expr.replace("z^0x1p1", "z*z")
config = fptaylor.CHECK_CONFIG.copy()
del config["--abs-error"]
config["--opt"] = "bb-eval"
config["--rel-error-threshold"] = "0.0"
config["--intermediate-opt"] = "false"
config["--uncertainty"] = "false"
def generate_fptaylor(x):
x_low = sollya.inf(x)
x_high = sollya.sup(x)
query = "\n".join([
"Variables", " real z in [{},{}];".format(x_low, x_high),
"Definitions", " retval rnd64= {};".format(poly_expr),
"Expressions", " retval;"
])
rnd_rel_err = None
rnd_abs_err = None
try:
res = fptaylor.Result(query, {
**config, "--rel-error": "true",
"--abs-error": "true"
})
rnd_rel_err = float(
res.result["relative_errors"]["final_total"]["value"])
rnd_abs_err = float(
res.result["absolute_errors"]["final_total"]["value"])
except AssertionError:
pass
except KeyError:
try:
rnd_abs_err = float(
res.result["absolute_errors"]["final_total"]["value"])
except KeyError:
pass
if rnd_abs_err is None:
try:
res = fptaylor.Result(query, {
**config, "--rel-error": "false",
"--abs-error": "true"
})
rnd_abs_err = float(
res.result["absolute_errors"]["final_total"]["value"])
except AssertionError:
pass
err_int = sollya.supnorm(self.poly_object.get_sollya_object(),
sollya.sin(sollya.x), x, sollya.relative,
2**-100)
algo_rel_err = sollya.sup(err_int)
err_int = sollya.supnorm(self.poly_object.get_sollya_object(),
sollya.sin(sollya.x), x, sollya.absolute,
2**-100)
algo_abs_err = sollya.sup(err_int)
if rnd_rel_err is None or str(algo_rel_err) == "error":
rel_err = float("inf")
else:
rel_err = rnd_rel_err + algo_rel_err
abs_err = rnd_abs_err + algo_abs_err
return rel_err, abs_err
def generate_reduction_fptaylor(x):
# get sign and abs_x, must be the same at endpoints
if sollya.sup(x) <= 0:
sign_x_expr = "-1.0"
abs_x_expr = "-x"
abs_x = -x
elif sollya.inf(x) >= 0:
sign_x_expr = "1.0"
abs_x_expr = "x"
abs_x = x
else:
assert False, "Interval must not straddle 0"
# get k, must be the same at endpoints
unround_k = abs_x * n_invpi
k_low = sollya.floor(sollya.inf(unround_k))
k_high = sollya.floor(sollya.sup(unround_k))
if k_low != k_high:
assert False, "Interval must not straddle multples of pi"
k = int(k_low)
part = k % 2
r_expr = "abs_x - whole"
r = abs_x - k * n_pi
z_expr = "r"
z = r
if part == 1:
flipped_poly_expr = "-poly"
else:
flipped_poly_expr = "poly"
x_low = sollya.inf(x)
x_high = sollya.sup(x)
query = "\n".join([
"Variables", " real x in [{},{}];".format(x_low, x_high),
"Definitions", " abs_x rnd64= {};".format(abs_x_expr),
" whole rnd64= {} * {};".format(k, n_pi),
" r rnd64= abs_x - whole;", " z rnd64= {};".format(z_expr),
" poly rnd64= {};".format(poly_expr),
" flipped_poly rnd64= {};".format(flipped_poly_expr),
" retval rnd64= flipped_poly*{};".format(sign_x_expr),
"Expressions", " retval;"
])
rnd_rel_err = None
rnd_abs_err = None
try:
res = fptaylor.Result(query, {
**config, "--rel-error": "true",
"--abs-error": "true"
})
rnd_rel_err = float(
res.result["relative_errors"]["final_total"]["value"])
rnd_abs_err = float(
res.result["absolute_errors"]["final_total"]["value"])
except AssertionError:
pass
except KeyError:
try:
rnd_abs_err = float(
res.result["absolute_errors"]["final_total"]["value"])
except KeyError:
pass
if rnd_abs_err is None:
try:
res = fptaylor.Result(query, {
**config, "--rel-error": "false",
"--abs-error": "true"
})
rnd_abs_err = float(
res.result["absolute_errors"]["final_total"]["value"])
except AssertionError:
pass
err_int = sollya.supnorm(self.poly_object.get_sollya_object(),
sollya.sin(sollya.x), z, sollya.relative,
2**-100)
algo_rel_err = sollya.sup(err_int)
err_int = sollya.supnorm(self.poly_object.get_sollya_object(),
sollya.sin(sollya.x), z, sollya.absolute,
2**-100)
algo_abs_err = sollya.sup(err_int)
if rnd_rel_err is None or str(algo_rel_err) == "error":
rel_err = float("inf")
else:
rel_err = rnd_rel_err + algo_rel_err
abs_err = rnd_abs_err + algo_abs_err
return rel_err, abs_err
def split_domain(starting_domain, slivers):
in_domains = [starting_domain]
# abs
out_domains = list()
for I in in_domains:
if sollya.inf(I) < 0 and sollya.sup(I) > 0:
out_domains.append(sollya.Interval(sollya.inf(I), 0))
out_domains.append(sollya.Interval(0, sollya.sup(I)))
else:
out_domains.append(I)
in_domains = out_domains
# k
out_domains = list()
while len(in_domains) > 0:
I = in_domains.pop()
#print("in: [{}, {}]".format(float(sollya.inf(I)), float(sollya.sup(I))))
unround_mult = I * n_invpi
mult_low = sollya.floor(sollya.inf(unround_mult))
mult_high = sollya.floor(sollya.sup(unround_mult))
if mult_low == mult_high or (mult_low == -1
and mult_high == 0):
#print(" accepted")
out_domains.append(I)
continue
if sollya.sup(I) <= 0:
divider_low = (mult_low + 1) * n_pi
divider_high = divider_low - divider_low * 2**-53
else:
divider_high = (mult_low + 1) * n_pi
divider_low = divider_high - divider_high * 2**-53
lower_part = sollya.Interval(sollya.inf(I), divider_low)
upper_part = sollya.Interval(divider_high, sollya.sup(I))
#print(" -> [{}, {}]".format(float(sollya.inf(lower_part)), float(sollya.sup(lower_part))))
#print(" -> [{}, {}]".format(float(sollya.inf(upper_part)), float(sollya.sup(upper_part))))
in_domains.append(lower_part)
in_domains.append(upper_part)
in_domains = out_domains
# subdivide each section into 2**subd sections
for _ in range(slivers):
out_domains = list()
for I in in_domains:
mid = sollya.mid(I)
out_domains.append(sollya.Interval(sollya.inf(I), mid))
out_domains.append(sollya.Interval(mid, sollya.sup(I)))
in_domains = out_domains
in_domains = set(in_domains)
in_domains = sorted(in_domains, key=lambda x: float(sollya.inf(x)))
in_domains = [
d for d in in_domains if sollya.inf(d) != sollya.sup(d)
]
return in_domains
if self.skip_reduction:
starting_domain = sollya.Interval(-n_pi - 2**-7, n_pi + 2**-7)
else:
reduction_k = 20
starting_domain = sollya.Interval(-reduction_k * n_pi,
reduction_k * n_pi)
# analyse each piece
in_domains = split_domain(starting_domain, self.slivers)
errors = list()
for I in in_domains:
if self.skip_reduction:
rel_err, abs_err = generate_fptaylor(I)
else:
rel_err, abs_err = generate_reduction_fptaylor(I)
print("{}\t{}\t{}\t{}".format(float(sollya.inf(I)),
float(sollya.sup(I)), float(abs_err),
float(rel_err)))
errors.append((I, abs_err, rel_err))
def generate_json(errors, domain):
errors = [err for err in errors if err[0] in domain]
errors.sort(key=lambda err: err[2])
epsilon = errors[0][2]
delta = max(err[1] for err in errors)
d = {
"cname": self.function_name,
"delta": float(delta),
"domain": [
float(sollya.inf(domain)),
float(sollya.sup(domain)),
],
"epsilon": float(epsilon),
"operation": "sin"
}
return d
if self.skip_reduction:
d = generate_json(errors,
sollya.Interval(-n_pi - 2**-7, n_pi + 2**-7))
json_str = json.dumps(d, sort_keys=True, indent=4)
json_str = "spec: " + json_str.replace("\n", "\nspec: ")
print(json_str)
else:
specs = list()
for k in range(1, reduction_k):
d = generate_json(errors, sollya.Interval(-k * n_pi, k * n_pi))
specs.append(d)
for i in range(len(specs)):
d = specs[i]
if i == len(specs) - 1:
json_str = json.dumps(d, sort_keys=True, indent=4)
json_str = "spec: " + json_str.replace("\n", "\nspec: ")
print(json_str)
break
nd = specs[i + 1]
if d["epsilon"] == nd["epsilon"] and d["delta"] == nd["delta"]:
continue
json_str = json.dumps(d, sort_keys=True, indent=4)
json_str = "spec: " + json_str.replace("\n", "\nspec: ")
print(json_str)
def __init__(self,
precision = ML_Binary32,
abs_accuracy = S2**-24,
libm_compliant = True,
debug_flag = False,
fuse_fma = True,
fast_path_extract = True,
target = GenericProcessor(),
output_file = "expf.c",
function_name = "expf"):
# declaring target and instantiating optimization engine
processor = target
self.precision = precision
opt_eng = OptimizationEngine(processor)
gappacg = GappaCodeGenerator(processor, declare_cst = True, disable_debug = True)
# declaring CodeFunction and retrieving input variable
self.function_name = function_name
exp_implementation = CodeFunction(self.function_name, output_format = self.precision)
vx = exp_implementation.add_input_variable("x", self.precision)
Log.report(Log.Info, "\033[33;1m generating implementation scheme \033[0m")
# 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)))
# return in case of infinity input
infty_return = Statement(ConditionBlock(test_positive, Return(FP_PlusInfty(self.precision)), Return(FP_PlusZero(self.precision))))
# return in case of specific value input (NaN or inf)
specific_return = ConditionBlock(test_nan, ConditionBlock(test_signaling_nan, return_snan, Return(FP_QNaN(self.precision))), infty_return)
# return in case of standard (non-special) input
# exclusion of early overflow and underflow cases
precision_emax = self.precision.get_emax()
precision_max_value = S2 * S2**precision_emax
exp_overflow_bound = ceil(log(precision_max_value))
early_overflow_test = Comparison(vx, exp_overflow_bound, likely = False, specifier = Comparison.Greater)
early_overflow_return = Statement(ClearException(), ExpRaiseReturn(ML_FPE_Inexact, ML_FPE_Overflow, return_value = FP_PlusInfty(self.precision)))
precision_emin = self.precision.get_emin_subnormal()
precision_min_value = S2 ** precision_emin
exp_underflow_bound = floor(log(precision_min_value))
early_underflow_test = Comparison(vx, exp_underflow_bound, likely = False, specifier = Comparison.Less)
early_underflow_return = Statement(ClearException(), ExpRaiseReturn(ML_FPE_Inexact, ML_FPE_Underflow, return_value = FP_PlusZero(self.precision)))
sollya_prec_map = {ML_Binary32: sollya.binary32, ML_Binary64: sollya.binary64}
# constant computation
invlog2 = round(1/log(2), sollya_prec_map[self.precision], RN)
interval_vx = Interval(exp_underflow_bound, exp_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() - (ceil(log2(sup(abs(interval_k)))) + 2)
Log.report(Log.Info, "log2_hi_precision: "), log2_hi_precision
invlog2_cst = Constant(invlog2, precision = self.precision)
log2_hi = round(log(2), log2_hi_precision, sollya.RN)
log2_lo = round(log(2) - log2_hi, sollya_prec_map[self.precision], sollya.RN)
# argument reduction
unround_k = vx * invlog2
unround_k.set_attributes(tag = "unround_k", debug = ML_Debug(display_format = "%f"))
k = NearestInteger(unround_k, precision = self.precision, debug = ML_Debug(display_format = "%f"))
ik = NearestInteger(unround_k, precision = ML_Int32, debug = ML_Debug(display_format = "%d"), tag = "ik")
ik.set_tag("ik")
k.set_tag("k")
exact_pre_mul = (k * log2_hi)
exact_pre_mul.set_attributes(exact= True)
exact_hi_part = vx - exact_pre_mul
exact_hi_part.set_attributes(exact = True)
r = exact_hi_part - k * log2_lo
r.set_tag("r")
r.set_attributes(debug = ML_Debug(display_format = "%f"))
opt_r = opt_eng.optimization_process(r, self.precision, copy = True, fuse_fma = fuse_fma)
tag_map = {}
opt_eng.register_nodes_by_tag(opt_r, tag_map)
cg_eval_error_copy_map = {
vx: Variable("x", precision = self.precision, interval = interval_vx),
tag_map["k"]: Variable("k", interval = interval_k, precision = self.precision)
}
#try:
if 1:
#eval_error = gappacg.get_eval_error(opt_r, cg_eval_error_copy_map, gappa_filename = "red_arg.g")
eval_error = gappacg.get_eval_error_v2(opt_eng, opt_r, cg_eval_error_copy_map, gappa_filename = "red_arg.g")
Log.report(Log.Info, "eval error: %s" % eval_error)
#except:
# Log.report(Log.Info, "gappa error evaluation failed")
print r.get_str(depth = None, display_precision = True, display_attribute = True)
print opt_r.get_str(depth = None, display_precision = True, display_attribute = True)
approx_interval = Interval(-log(2)/2, log(2)/2)
local_ulp = sup(ulp(exp(approx_interval), self.precision))
print "ulp: ", local_ulp
error_goal = local_ulp #S2**-(self.precision.get_field_size()+1)
error_goal_approx = S2**-1 * error_goal
Log.report(Log.Info, "\033[33;1m building mathematical polynomial \033[0m\n")
poly_degree = sup(guessdegree(exp(x), approx_interval, error_goal_approx)) #- 1
init_poly_degree = poly_degree
return
while 1:
Log.report(Log.Info, "attempting poly degree: %d" % poly_degree)
poly_object, poly_approx_error = Polynomial.build_from_approximation_with_error(exp(x), poly_degree, [self.precision]*(poly_degree+1), approx_interval, absolute)
Log.report(Log.Info, "poly approx error: %s" % poly_approx_error)
Log.report(Log.Info, "\033[33;1m generating polynomial evaluation scheme \033[0m")
poly = PolynomialSchemeEvaluator.generate_horner_scheme(poly_object, r, unified_precision = self.precision)
poly.set_tag("poly")
# optimizing poly before evaluation error computation
opt_poly = opt_eng.optimization_process(poly, self.precision)
#print "poly: ", poly.get_str(depth = None, display_precision = True)
#print "opt_poly: ", opt_poly.get_str(depth = None, display_precision = True)
# evaluating error of the polynomial approximation
r_gappa_var = Variable("r", precision = self.precision, interval = approx_interval)
poly_error_copy_map = {
r.get_handle().get_node(): r_gappa_var
}
gappacg = GappaCodeGenerator(target, declare_cst = False, disable_debug = True)
poly_eval_error = gappacg.get_eval_error_v2(opt_eng, poly.get_handle().get_node(), poly_error_copy_map, gappa_filename = "gappa_poly.g")
Log.report(Log.Info, "poly evaluation error: %s" % poly_eval_error)
global_poly_error = poly_eval_error + poly_approx_error
global_rel_poly_error = global_poly_error / exp(approx_interval)
print "global_poly_error: ", global_poly_error, global_rel_poly_error
flag = local_ulp > sup(abs(global_rel_poly_error))
print "test: ", flag
if flag: break
else:
if poly_degree > init_poly_degree + 5:
Log.report(Log.Error, "poly degree search did not converge")
poly_degree += 1
late_overflow_test = Comparison(ik, self.precision.get_emax(), specifier = Comparison.Greater, likely = False, debug = True, tag = "late_overflow_test")
overflow_exp_offset = (self.precision.get_emax() - self.precision.get_field_size() / 2)
diff_k = ik - overflow_exp_offset
diff_k.set_attributes(debug = ML_Debug(display_format = "%d"), tag = "diff_k")
late_overflow_result = (ExponentInsertion(diff_k) * poly) * ExponentInsertion(overflow_exp_offset)
late_overflow_result.set_attributes(silent = False, tag = "late_overflow_result", debug = debugf)
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()
late_underflow_result = (ExponentInsertion(ik + underflow_exp_offset) * poly) * ExponentInsertion(-underflow_exp_offset)
late_underflow_result.set_attributes(debug = ML_Debug(display_format = "%e"), tag = "late_underflow_result", silent = False)
test_subnormal = Test(late_underflow_result, specifier = Test.IsSubnormal)
late_underflow_return = Statement(ConditionBlock(test_subnormal, ExpRaiseReturn(ML_FPE_Underflow, return_value = late_underflow_result)), Return(late_underflow_result))
std_result = poly * ExponentInsertion(ik, tag = "exp_ik", debug = debug_lftolx)
std_result.set_attributes(tag = "std_result", debug = debug_lftolx)
result_scheme = ConditionBlock(late_overflow_test, late_overflow_return, ConditionBlock(late_underflow_test, late_underflow_return, Return(std_result)))
std_return = ConditionBlock(early_overflow_test, early_overflow_return, ConditionBlock(early_underflow_test, early_underflow_return, result_scheme))
# main scheme
Log.report(Log.Info, "\033[33;1m MDL scheme \033[0m")
scheme = ConditionBlock(test_nan_or_inf, Statement(ClearException(), specific_return), std_return)
#print scheme.get_str(depth = None, display_precision = True)
# fusing FMA
if fuse_fma:
Log.report(Log.Info, "\033[33;1m MDL fusing FMA \033[0m")
scheme = opt_eng.fuse_multiply_add(scheme, silence = True)
Log.report(Log.Info, "\033[33;1m MDL abstract scheme \033[0m")
opt_eng.instantiate_abstract_precision(scheme, None)
Log.report(Log.Info, "\033[33;1m MDL instantiated scheme \033[0m")
opt_eng.instantiate_precision(scheme, default_precision = self.precision)
Log.report(Log.Info, "\033[33;1m subexpression sharing \033[0m")
opt_eng.subexpression_sharing(scheme)
Log.report(Log.Info, "\033[33;1m silencing operation \033[0m")
opt_eng.silence_fp_operations(scheme)
# registering scheme as function implementation
exp_implementation.set_scheme(scheme)
# check processor support
Log.report(Log.Info, "\033[33;1m checking processor support \033[0m")
opt_eng.check_processor_support(scheme)
# factorizing fast path
if fast_path_extract:
Log.report(Log.Info, "\033[33;1m factorizing fast path\033[0m")
opt_eng.factorize_fast_path(scheme)
Log.report(Log.Info, "\033[33;1m generating source code \033[0m")
cg = CCodeGenerator(processor, declare_cst = False, disable_debug = not debug_flag, libm_compliant = libm_compliant)
self.result = exp_implementation.get_definition(cg, C_Code, static_cst = True)
#self.result.add_header("support_lib/ml_types.h")
self.result.add_header("support_lib/ml_special_values.h")
self.result.add_header_comment("polynomial degree for exp(x): %d" % poly_degree)
self.result.add_header_comment("sollya polynomial for exp(x): %s" % poly_object.get_sollya_object())
if debug_flag:
self.result.add_header("stdio.h")
self.result.add_header("inttypes.h")
output_stream = open(output_file, "w")#"%s.c" % exp_implementation.get_name(), "w")
output_stream.write(self.result.get(cg))
output_stream.close()
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 generic_poly_split(offset_fct, indexing, target_eps, coeff_precision, vx):
""" generate the meta approximation for @p offset_fct over several
intervals defined by @p indexing object
For each sub-interval, a polynomial approximation with
maximal_error @p target_eps is tabulated, and evaluated using format
@p coeff_precision.
The input variable is @p vx """
# computing degree for a different polynomial approximation on each
# sub-interval
poly_degree_list = [
int(sup(guessdegree(offset_fct(offset), sub_interval, target_eps)))
for offset, sub_interval in indexing.get_offseted_sub_list()
]
poly_max_degree = max(poly_degree_list)
# tabulating polynomial coefficients on split_num sub-interval of interval
poly_table = ML_NewTable(
dimensions=[indexing.split_num, poly_max_degree + 1],
storage_precision=coeff_precision,
const=True)
offset_table = ML_NewTable(dimensions=[indexing.split_num],
storage_precision=coeff_precision,
const=True)
max_error = 0.0
for sub_index in range(indexing.split_num):
poly_degree = poly_degree_list[sub_index]
offset, approx_interval = indexing.get_offseted_sub_interval(sub_index)
offset_table[sub_index] = offset
if poly_degree == 0:
# managing constant approximation separately since it seems
# to break sollya
local_approx = coeff_precision.round_sollya_object(
offset_fct(offset)(inf(approx_interval)))
poly_table[sub_index][0] = local_approx
for monomial_index in range(1, poly_max_degree + 1):
poly_table[sub_index][monomial_index] = 0
approx_error = sollya.infnorm(
offset_fct(offset) - local_approx, approx_interval)
else:
poly_object, approx_error = Polynomial.build_from_approximation_with_error(
offset_fct(offset), poly_degree,
[coeff_precision] * (poly_degree + 1), approx_interval,
sollya.relative)
for monomial_index in range(poly_max_degree + 1):
if monomial_index <= poly_degree:
poly_table[sub_index][
monomial_index] = poly_object.coeff_map[monomial_index]
else:
poly_table[sub_index][monomial_index] = 0
max_error = max(approx_error, max_error)
Log.report(Log.Debug, "max approx error is {}", max_error)
# indexing function: derive index from input @p vx value
poly_index = indexing.get_index_node(vx)
poly_index.set_attributes(tag="poly_index", debug=debug_multi)
ext_precision = get_extended_fp_precision(coeff_precision)
# building polynomial evaluation scheme
offset = TableLoad(offset_table,
poly_index,
precision=coeff_precision,
tag="offset",
debug=debug_multi)
poly = TableLoad(poly_table,
poly_index,
poly_max_degree,
precision=coeff_precision,
tag="poly_init",
debug=debug_multi)
red_vx = Subtraction(vx,
offset,
precision=vx.precision,
tag="red_vx",
debug=debug_multi)
for monomial_index in range(poly_max_degree, -1, -1):
coeff = TableLoad(poly_table,
poly_index,
monomial_index,
precision=coeff_precision,
tag="poly_%d" % monomial_index,
debug=debug_multi)
#fma_precision = coeff_precision if monomial_index > 1 else ext_precision
fma_precision = coeff_precision
poly = FMA(red_vx, poly, coeff, precision=fma_precision)
#return Conversion(poly, precision=coeff_precision)
#return poly.hi
return poly
def generate_test_tables(self,
test_num,
test_ranges=[Interval(-1.0, 1.0)]):
""" Generate inputs and output table to be shared between auto test
and max_error tests """
random_sizes = self.generate_random_sizes()
output_tensor_descriptor_list = self.generate_output_tensor_descriptors(
random_sizes)
input_tensor_descriptor_list = self.generate_innput_tensor_descriptors(
random_sizes)
index_range = self.test_index_range
# number of arrays expected as inputs for tested_function
NUM_INPUT_ARRAY = len(input_tensor_descriptor_list)
# position of the input array in tested_function operands (generally
# equals to 1 as to 0-th input is often the destination array)
INPUT_INDEX_OFFSET = 1
# concatenating standard test array at the beginning of randomly
# generated array
INPUT_ARRAY_SIZE = [
td.get_bounding_size() for td in input_tensor_descriptor_list
]
# TODO/FIXME: implement proper input range depending on input index
# assuming a single input array
input_precisions = [
td.scalar_format for td in input_tensor_descriptor_list
]
rng_map = [
get_precision_rng(precision, inf(test_range), sup(test_range))
for precision, test_range in zip(input_precisions, test_ranges)
]
# generated table of inputs
input_tables = [
generate_1d_table(
INPUT_ARRAY_SIZE[table_id],
input_precisions[table_id],
self.uniquify_name("input_table_arg%d" % table_id),
value_gen=(
lambda _: input_precisions[table_id].round_sollya_object(
rng_map[table_id].get_new_value(), sollya.RN)))
for table_id in range(NUM_INPUT_ARRAY)
]
OUTPUT_ARRAY_SIZE = [
td.get_bounding_size() for td in output_tensor_descriptor_list
]
OUTPUT_PRECISION = [
td.scalar_format for td in output_tensor_descriptor_list
]
NUM_OUTPUT_ARRAY = len(output_tensor_descriptor_list)
# generate output_array
output_tables = [
generate_1d_table(
OUTPUT_ARRAY_SIZE[table_id],
OUTPUT_PRECISION[table_id],
self.uniquify_name("output_array_%d" % table_id),
const=False,
#value_gen=(lambda _: FP_QNaN(self.precision))
value_gen=(lambda _: 0))
for table_id in range(NUM_OUTPUT_ARRAY)
]
tensor_descriptors = (input_tensor_descriptor_list,
output_tensor_descriptor_list)
return tensor_descriptors, input_tables, output_tables
def generate_bench_wrapper(self,
test_num=1,
loop_num=100000,
test_ranges=[Interval(-1.0, 1.0)],
debug=False):
# interval where the array lenght is chosen from (randomly)
index_range = self.test_index_range
auto_test = CodeFunction("bench_wrapper", output_format=ML_Binary64)
tested_function = self.implementation.get_function_object()
function_name = self.implementation.get_name()
failure_report_op = FunctionOperator("report_failure")
failure_report_function = FunctionObject("report_failure", [], ML_Void,
failure_report_op)
printf_success_op = FunctionOperator(
"printf",
arg_map={0: "\"test successful %s\\n\"" % function_name},
void_function=True)
printf_success_function = FunctionObject("printf", [], ML_Void,
printf_success_op)
output_precision = FormatAttributeWrapper(self.precision, ["volatile"])
test_total = test_num
# number of arrays expected as inputs for tested_function
NUM_INPUT_ARRAY = 1
# position of the input array in tested_function operands (generally
# equals to 1 as to 0-th input is often the destination array)
INPUT_INDEX_OFFSET = 1
# concatenating standard test array at the beginning of randomly
# generated array
TABLE_SIZE_VALUES = [
len(std_table) for std_table in self.standard_test_cases
] + [
random.randrange(index_range[0], index_range[1] + 1)
for i in range(test_num)
]
OFFSET_VALUES = [sum(TABLE_SIZE_VALUES[:i]) for i in range(test_total)]
table_size_offset_array = generate_2d_table(
test_total,
2,
ML_UInt32,
self.uniquify_name("table_size_array"),
value_gen=(lambda row_id:
(TABLE_SIZE_VALUES[row_id], OFFSET_VALUES[row_id])))
INPUT_ARRAY_SIZE = sum(TABLE_SIZE_VALUES)
# TODO/FIXME: implement proper input range depending on input index
# assuming a single input array
input_precisions = [self.get_input_precision(1).get_data_precision()]
rng_map = [
get_precision_rng(precision, inf(test_range), sup(test_range))
for precision, test_range in zip(input_precisions, test_ranges)
]
# generated table of inputs
input_tables = [
generate_1d_table(
INPUT_ARRAY_SIZE,
self.get_input_precision(INPUT_INDEX_OFFSET +
table_id).get_data_precision(),
self.uniquify_name("input_table_arg%d" % table_id),
value_gen=(
lambda _: input_precisions[table_id].round_sollya_object(
rng_map[table_id].get_new_value(), sollya.RN)))
for table_id in range(NUM_INPUT_ARRAY)
]
# generate output_array
output_array = generate_1d_table(
INPUT_ARRAY_SIZE,
output_precision,
self.uniquify_name("output_array"),
#value_gen=(lambda _: FP_QNaN(self.precision))
value_gen=(lambda _: None),
const=False,
empty=True)
# accumulate element number
acc_num = Variable("acc_num",
precision=ML_Int64,
var_type=Variable.Local)
def empty_post_statement_gen(input_tables, output_array,
table_size_offset_array, array_offset,
array_len, test_id):
return Statement()
test_loop = self.get_array_test_wrapper(test_total, tested_function,
table_size_offset_array,
input_tables, output_array,
acc_num,
empty_post_statement_gen)
timer = Variable("timer", precision=ML_Int64, var_type=Variable.Local)
printf_timing_op = FunctionOperator(
"printf",
arg_map={
0:
"\"%s %%\"PRIi64\" elts computed in %%\"PRIi64\" nanoseconds => %%.3f CPE \\n\""
% function_name,
1:
FO_Arg(0),
2:
FO_Arg(1),
3:
FO_Arg(2)
},
void_function=True)
printf_timing_function = FunctionObject(
"printf", [ML_Int64, ML_Int64, ML_Binary64], ML_Void,
printf_timing_op)
vj = Variable("j", precision=ML_Int32, var_type=Variable.Local)
loop_num_cst = Constant(loop_num, precision=ML_Int32, tag="loop_num")
loop_increment = 1
# bench measure of clock per element
cpe_measure = Division(
Conversion(timer, precision=ML_Binary64),
Conversion(acc_num, precision=ML_Binary64),
precision=ML_Binary64,
tag="cpe_measure",
)
# common test scheme between scalar and vector functions
test_scheme = Statement(
self.processor.get_init_timestamp(),
ReferenceAssign(timer, self.processor.get_current_timestamp()),
ReferenceAssign(acc_num, 0),
Loop(
ReferenceAssign(vj, Constant(0, precision=ML_Int32)),
vj < loop_num_cst,
Statement(test_loop, ReferenceAssign(vj,
vj + loop_increment))),
ReferenceAssign(
timer,
Subtraction(self.processor.get_current_timestamp(),
timer,
precision=ML_Int64)),
printf_timing_function(
Conversion(acc_num, precision=ML_Int64),
timer,
cpe_measure,
),
Return(cpe_measure),
# Return(Constant(0, precision = ML_Int32))
)
auto_test.set_scheme(test_scheme)
return FunctionGroup([auto_test])
def generate_bench(self, processor, test_num=1000, unroll_factor=10):
""" generate performance bench for self.op_class """
initial_inputs = [
Constant(random.uniform(inf(self.init_interval),
sup(self.init_interval)),
precision=precision)
for i, precision in enumerate(self.input_precisions)
]
var_inputs = [
Variable("var_%d" % i,
precision=FormatAttributeWrapper(precision, ["volatile"]),
var_type=Variable.Local)
for i, precision in enumerate(self.input_precisions)
]
printf_timing_op = FunctionOperator(
"printf",
arg_map={
0: "\"%s[%s] %%lld elts computed "\
"in %%lld cycles =>\\n %%.3f CPE \\n\"" %
(
self.bench_name,
self.output_precision.get_display_format()
),
1: FO_Arg(0),
2: FO_Arg(1),
3: FO_Arg(2),
4: FO_Arg(3)
}, void_function=True
)
printf_timing_function = FunctionObject(
"printf", [self.output_precision, ML_Int64, ML_Int64, ML_Binary64],
ML_Void, printf_timing_op)
timer = Variable("timer", precision=ML_Int64, var_type=Variable.Local)
void_function_op = FunctionOperator("(void)",
arity=1,
void_function=True)
void_function = FunctionObject("(void)", [self.output_precision],
ML_Void, void_function_op)
# initialization of operation inputs
init_assign = metaop.Statement()
for var_input, init_value in zip(var_inputs, initial_inputs):
init_assign.push(ReferenceAssign(var_input, init_value))
# test loop
loop_i = Variable("i", precision=ML_Int64, var_type=Variable.Local)
test_num_cst = Constant(test_num / unroll_factor,
precision=ML_Int64,
tag="test_num")
# Goal build a chain of dependant operation to measure
# elementary operation latency
local_inputs = tuple(var_inputs)
local_result = self.op_class(*local_inputs,
precision=self.output_precision,
unbreakable=True)
for i in range(unroll_factor - 1):
local_inputs = tuple([local_result] + var_inputs[1:])
local_result = self.op_class(*local_inputs,
precision=self.output_precision,
unbreakable=True)
# renormalisation
local_result = self.renorm_function(local_result)
# variable assignation to build dependency chain
var_assign = Statement()
var_assign.push(ReferenceAssign(var_inputs[0], local_result))
final_value = var_inputs[0]
# loop increment value
loop_increment = 1
test_loop = Loop(
ReferenceAssign(loop_i, Constant(0, precision=ML_Int32)),
loop_i < test_num_cst,
Statement(var_assign,
ReferenceAssign(loop_i, loop_i + loop_increment)),
)
# bench scheme
test_scheme = Statement(
ReferenceAssign(timer, processor.get_current_timestamp()),
init_assign,
test_loop,
ReferenceAssign(
timer,
Subtraction(processor.get_current_timestamp(),
timer,
precision=ML_Int64)),
# prevent intermediary variable simplification
void_function(final_value),
printf_timing_function(
final_value, Constant(test_num, precision=ML_Int64), timer,
Division(Conversion(timer, precision=ML_Binary64),
Constant(test_num, precision=ML_Binary64),
precision=ML_Binary64))
# ,Return(Constant(0, precision = ML_Int32))
)
return test_scheme
def generate_scheme(self):
# declaring target and instantiating optimization engine
vx = self.implementation.add_input_variable("x", self.precision)
Log.set_dump_stdout(True)
Log.report(Log.Info,
"\033[33;1m generating implementation scheme \033[0m")
if self.debug_flag:
Log.report(Log.Info, "\033[31;1m debug has been enabled \033[0;m")
# local overloading of RaiseReturn operation
def ExpRaiseReturn(*args, **kwords):
kwords["arg_value"] = vx
kwords["function_name"] = self.function_name
if self.libm_compliant:
return RaiseReturn(*args, precision=self.precision, **kwords)
else:
return Return(kwords["return_value"], precision=self.precision)
test_nan_or_inf = Test(vx,
specifier=Test.IsInfOrNaN,
likely=False,
debug=debug_multi,
tag="nan_or_inf")
test_nan = Test(vx,
specifier=Test.IsNaN,
debug=debug_multi,
tag="is_nan_test")
test_positive = Comparison(vx,
0,
specifier=Comparison.GreaterOrEqual,
debug=debug_multi,
tag="inf_sign")
test_signaling_nan = Test(vx,
specifier=Test.IsSignalingNaN,
debug=debug_multi,
tag="is_signaling_nan")
return_snan = Statement(
ExpRaiseReturn(ML_FPE_Invalid,
return_value=FP_QNaN(self.precision)))
# return in case of infinity input
infty_return = Statement(
ConditionBlock(
test_positive,
Return(FP_PlusInfty(self.precision), precision=self.precision),
Return(FP_PlusZero(self.precision), precision=self.precision)))
# return in case of specific value input (NaN or inf)
specific_return = ConditionBlock(
test_nan,
ConditionBlock(
test_signaling_nan, return_snan,
Return(FP_QNaN(self.precision), precision=self.precision)),
infty_return)
# return in case of standard (non-special) input
# exclusion of early overflow and underflow cases
precision_emax = self.precision.get_emax()
precision_max_value = S2 * S2**precision_emax
exp_overflow_bound = sollya.ceil(log(precision_max_value))
early_overflow_test = Comparison(vx,
exp_overflow_bound,
likely=False,
specifier=Comparison.Greater)
early_overflow_return = Statement(
ClearException() if self.libm_compliant else Statement(),
ExpRaiseReturn(ML_FPE_Inexact,
ML_FPE_Overflow,
return_value=FP_PlusInfty(self.precision)))
precision_emin = self.precision.get_emin_subnormal()
precision_min_value = S2**precision_emin
exp_underflow_bound = floor(log(precision_min_value))
early_underflow_test = Comparison(vx,
exp_underflow_bound,
likely=False,
specifier=Comparison.Less)
early_underflow_return = Statement(
ClearException() if self.libm_compliant else Statement(),
ExpRaiseReturn(ML_FPE_Inexact,
ML_FPE_Underflow,
return_value=FP_PlusZero(self.precision)))
# constant computation
invlog2 = self.precision.round_sollya_object(1 / log(2), sollya.RN)
interval_vx = Interval(exp_underflow_bound, exp_overflow_bound)
interval_fk = interval_vx * invlog2
interval_k = Interval(floor(inf(interval_fk)),
sollya.ceil(sup(interval_fk)))
log2_hi_precision = self.precision.get_field_size() - (
sollya.ceil(log2(sup(abs(interval_k)))) + 2)
Log.report(Log.Info, "log2_hi_precision: %d" % log2_hi_precision)
invlog2_cst = Constant(invlog2, precision=self.precision)
log2_hi = round(log(2), log2_hi_precision, sollya.RN)
log2_lo = self.precision.round_sollya_object(
log(2) - log2_hi, sollya.RN)
# argument reduction
unround_k = vx * invlog2
unround_k.set_attributes(tag="unround_k", debug=debug_multi)
k = NearestInteger(unround_k,
precision=self.precision,
debug=debug_multi)
ik = NearestInteger(unround_k,
precision=self.precision.get_integer_format(),
debug=debug_multi,
tag="ik")
ik.set_tag("ik")
k.set_tag("k")
exact_pre_mul = (k * log2_hi)
exact_pre_mul.set_attributes(exact=True)
exact_hi_part = vx - exact_pre_mul
exact_hi_part.set_attributes(exact=True,
tag="exact_hi",
debug=debug_multi,
prevent_optimization=True)
exact_lo_part = -k * log2_lo
exact_lo_part.set_attributes(tag="exact_lo",
debug=debug_multi,
prevent_optimization=True)
r = exact_hi_part + exact_lo_part
r.set_tag("r")
r.set_attributes(debug=debug_multi)
approx_interval = Interval(-log(2) / 2, log(2) / 2)
approx_interval_half = approx_interval / 2
approx_interval_split = [
Interval(-log(2) / 2, inf(approx_interval_half)),
approx_interval_half,
Interval(sup(approx_interval_half),
log(2) / 2)
]
# TODO: should be computed automatically
exact_hi_interval = approx_interval
exact_lo_interval = -interval_k * log2_lo
opt_r = self.optimise_scheme(r, copy={})
tag_map = {}
self.opt_engine.register_nodes_by_tag(opt_r, tag_map)
cg_eval_error_copy_map = {
vx:
Variable("x", precision=self.precision, interval=interval_vx),
tag_map["k"]:
Variable("k", interval=interval_k, precision=self.precision)
}
#try:
if is_gappa_installed():
eval_error = self.gappa_engine.get_eval_error_v2(
self.opt_engine,
opt_r,
cg_eval_error_copy_map,
gappa_filename="red_arg.g")
else:
eval_error = 0.0
Log.report(Log.Warning,
"gappa is not installed in this environnement")
Log.report(Log.Info, "eval error: %s" % eval_error)
local_ulp = sup(ulp(sollya.exp(approx_interval), self.precision))
# FIXME refactor error_goal from accuracy
Log.report(Log.Info, "accuracy: %s" % self.accuracy)
if isinstance(self.accuracy, ML_Faithful):
error_goal = local_ulp
elif isinstance(self.accuracy, ML_CorrectlyRounded):
error_goal = S2**-1 * local_ulp
elif isinstance(self.accuracy, ML_DegradedAccuracyAbsolute):
error_goal = self.accuracy.goal
elif isinstance(self.accuracy, ML_DegradedAccuracyRelative):
error_goal = self.accuracy.goal
else:
Log.report(Log.Error, "unknown accuracy: %s" % self.accuracy)
# error_goal = local_ulp #S2**-(self.precision.get_field_size()+1)
error_goal_approx = S2**-1 * error_goal
Log.report(Log.Info,
"\033[33;1m building mathematical polynomial \033[0m\n")
poly_degree = max(
sup(
guessdegree(
expm1(sollya.x) / sollya.x, approx_interval,
error_goal_approx)) - 1, 2)
init_poly_degree = poly_degree
error_function = lambda p, f, ai, mod, t: dirtyinfnorm(f - p, ai)
polynomial_scheme_builder = PolynomialSchemeEvaluator.generate_estrin_scheme
#polynomial_scheme_builder = PolynomialSchemeEvaluator.generate_horner_scheme
while 1:
Log.report(Log.Info, "attempting poly degree: %d" % poly_degree)
precision_list = [1] + [self.precision] * (poly_degree)
poly_object, poly_approx_error = Polynomial.build_from_approximation_with_error(
expm1(sollya.x),
poly_degree,
precision_list,
approx_interval,
sollya.absolute,
error_function=error_function)
Log.report(Log.Info, "polynomial: %s " % poly_object)
sub_poly = poly_object.sub_poly(start_index=2)
Log.report(Log.Info, "polynomial: %s " % sub_poly)
Log.report(Log.Info, "poly approx error: %s" % poly_approx_error)
Log.report(
Log.Info,
"\033[33;1m generating polynomial evaluation scheme \033[0m")
pre_poly = polynomial_scheme_builder(
poly_object, r, unified_precision=self.precision)
pre_poly.set_attributes(tag="pre_poly", debug=debug_multi)
pre_sub_poly = polynomial_scheme_builder(
sub_poly, r, unified_precision=self.precision)
pre_sub_poly.set_attributes(tag="pre_sub_poly", debug=debug_multi)
poly = 1 + (exact_hi_part + (exact_lo_part + pre_sub_poly))
poly.set_tag("poly")
# optimizing poly before evaluation error computation
#opt_poly = self.opt_engine.optimization_process(poly, self.precision, fuse_fma = fuse_fma)
#opt_sub_poly = self.opt_engine.optimization_process(pre_sub_poly, self.precision, fuse_fma = fuse_fma)
opt_poly = self.optimise_scheme(poly)
opt_sub_poly = self.optimise_scheme(pre_sub_poly)
# evaluating error of the polynomial approximation
r_gappa_var = Variable("r",
precision=self.precision,
interval=approx_interval)
exact_hi_gappa_var = Variable("exact_hi",
precision=self.precision,
interval=exact_hi_interval)
exact_lo_gappa_var = Variable("exact_lo",
precision=self.precision,
interval=exact_lo_interval)
vx_gappa_var = Variable("x",
precision=self.precision,
interval=interval_vx)
k_gappa_var = Variable("k",
interval=interval_k,
precision=self.precision)
#print "exact_hi interval: ", exact_hi_interval
sub_poly_error_copy_map = {
#r.get_handle().get_node(): r_gappa_var,
#vx.get_handle().get_node(): vx_gappa_var,
exact_hi_part.get_handle().get_node():
exact_hi_gappa_var,
exact_lo_part.get_handle().get_node():
exact_lo_gappa_var,
#k.get_handle().get_node(): k_gappa_var,
}
poly_error_copy_map = {
exact_hi_part.get_handle().get_node(): exact_hi_gappa_var,
exact_lo_part.get_handle().get_node(): exact_lo_gappa_var,
}
if is_gappa_installed():
sub_poly_eval_error = -1.0
sub_poly_eval_error = self.gappa_engine.get_eval_error_v2(
self.opt_engine,
opt_sub_poly,
sub_poly_error_copy_map,
gappa_filename="%s_gappa_sub_poly.g" % self.function_name)
dichotomy_map = [
{
exact_hi_part.get_handle().get_node():
approx_interval_split[0],
},
{
exact_hi_part.get_handle().get_node():
approx_interval_split[1],
},
{
exact_hi_part.get_handle().get_node():
approx_interval_split[2],
},
]
poly_eval_error_dico = self.gappa_engine.get_eval_error_v3(
self.opt_engine,
opt_poly,
poly_error_copy_map,
gappa_filename="gappa_poly.g",
dichotomy=dichotomy_map)
poly_eval_error = max(
[sup(abs(err)) for err in poly_eval_error_dico])
else:
poly_eval_error = 0.0
sub_poly_eval_error = 0.0
Log.report(Log.Warning,
"gappa is not installed in this environnement")
Log.report(Log.Info, "stopping autonomous degree research")
# incrementing polynomial degree to counteract initial decrementation effect
poly_degree += 1
break
Log.report(Log.Info, "poly evaluation error: %s" % poly_eval_error)
Log.report(Log.Info,
"sub poly evaluation error: %s" % sub_poly_eval_error)
global_poly_error = None
global_rel_poly_error = None
for case_index in range(3):
poly_error = poly_approx_error + poly_eval_error_dico[
case_index]
rel_poly_error = sup(
abs(poly_error /
sollya.exp(approx_interval_split[case_index])))
if global_rel_poly_error == None or rel_poly_error > global_rel_poly_error:
global_rel_poly_error = rel_poly_error
global_poly_error = poly_error
flag = error_goal > global_rel_poly_error
if flag:
break
else:
poly_degree += 1
late_overflow_test = Comparison(ik,
self.precision.get_emax(),
specifier=Comparison.Greater,
likely=False,
debug=debug_multi,
tag="late_overflow_test")
overflow_exp_offset = (self.precision.get_emax() -
self.precision.get_field_size() / 2)
diff_k = Subtraction(
ik,
Constant(overflow_exp_offset,
precision=self.precision.get_integer_format()),
precision=self.precision.get_integer_format(),
debug=debug_multi,
tag="diff_k",
)
late_overflow_result = (ExponentInsertion(
diff_k, precision=self.precision) * poly) * ExponentInsertion(
overflow_exp_offset, precision=self.precision)
late_overflow_result.set_attributes(silent=False,
tag="late_overflow_result",
debug=debug_multi,
precision=self.precision)
late_overflow_return = ConditionBlock(
Test(late_overflow_result, specifier=Test.IsInfty, likely=False),
ExpRaiseReturn(ML_FPE_Overflow,
return_value=FP_PlusInfty(self.precision)),
Return(late_overflow_result, precision=self.precision))
late_underflow_test = Comparison(k,
self.precision.get_emin_normal(),
specifier=Comparison.LessOrEqual,
likely=False)
underflow_exp_offset = 2 * self.precision.get_field_size()
corrected_exp = Addition(
ik,
Constant(underflow_exp_offset,
precision=self.precision.get_integer_format()),
precision=self.precision.get_integer_format(),
tag="corrected_exp")
late_underflow_result = (
ExponentInsertion(corrected_exp, precision=self.precision) *
poly) * ExponentInsertion(-underflow_exp_offset,
precision=self.precision)
late_underflow_result.set_attributes(debug=debug_multi,
tag="late_underflow_result",
silent=False)
test_subnormal = Test(late_underflow_result,
specifier=Test.IsSubnormal)
late_underflow_return = Statement(
ConditionBlock(
test_subnormal,
ExpRaiseReturn(ML_FPE_Underflow,
return_value=late_underflow_result)),
Return(late_underflow_result, precision=self.precision))
twok = ExponentInsertion(ik,
tag="exp_ik",
debug=debug_multi,
precision=self.precision)
#std_result = twok * ((1 + exact_hi_part * pre_poly) + exact_lo_part * pre_poly)
std_result = twok * poly
std_result.set_attributes(tag="std_result", debug=debug_multi)
result_scheme = ConditionBlock(
late_overflow_test, late_overflow_return,
ConditionBlock(late_underflow_test, late_underflow_return,
Return(std_result, precision=self.precision)))
std_return = ConditionBlock(
early_overflow_test, early_overflow_return,
ConditionBlock(early_underflow_test, early_underflow_return,
result_scheme))
# main scheme
Log.report(Log.Info, "\033[33;1m MDL scheme \033[0m")
scheme = ConditionBlock(
test_nan_or_inf,
Statement(ClearException() if self.libm_compliant else Statement(),
specific_return), std_return)
return scheme
def generate_argument_reduction(self, memory_limit):
best_arg_reduc = None
best_arg_reduc = self.eval_argument_reduction(6,10,12,13)
best_arg_reduc['sizeof_tables'] = best_arg_reduc['sizeof_table1'] + best_arg_reduc['sizeof_table2']
best_arg_reduc['degree_poly1'] = 4
best_arg_reduc['degree_poly2'] = 8
return best_arg_reduc
# iterate through all possible parameters, and return the best argument reduction
# the order of importance of the caracteristics of a good argument reduction is:
# 1- the argument reduction is valid
# 2- the degree of the polynomials obtains are minimals
# 3- the memory used is minimal
# An arument reduction is valid iff:
# - the memory used is less than memory_limit
# - y-1 and z-1 fit into a uint64_t
# - the second argument reduction should usefull (ie: it should add at least 1 bit to the argument reduction)
# From thoses validity constraint we deduce some bound on the parameters to reduce the space of value searched:
# (note that thoses bound are implied by, but not equivalents to the constraints)
# size1 <= log2(memory_limit/17) (memory_limit on the first table)
# prec1 < 13 + size1 (y-1 fits into a uint64_t)
# size2 <= log2((memory_limit - sizeof_table1)/17/midinterval) (memory_limit on both tables)
# size2 >= 1 - log2(midinterval) (second arg red should be usefull)
# prec2 < 12 - prec1 - log2((y-y1)/y1), for all possible y (z-1 fits into a uint64_t)
# note: it is hard to deduce a tight bound on prec2 from the last inequality
# a good approximation is size2 ~= max[for y]( - log2((y-y1)/y1)), but using it may eliminate valid arg reduc
#self.eval_argument_reduction(12, 20, 22, 14)
min_size1 = 1
max_size1 = floor(log(memory_limit/17)/log(2)).getConstantAsInt()
for size1 in xrange(max_size1, min_size1-1, -1):
min_prec1 = size1
max_prec1 = 12 + size1
for prec1 in xrange(min_prec1,max_prec1+1):
# we need sizeof_table1 and mid_interval for the bound on size2 and prec2
first_arg_reduc = self.eval_argument_reduction(size1, prec1, prec1, prec1)
mid_interval = first_arg_reduc['mid_interval']
sizeof_table1 = first_arg_reduc['sizeof_table1']
if not(0 <= inf(mid_interval) and sup(mid_interval) < S2**(64 - 52 - prec1)):
continue
if not(first_arg_reduc['sizeof_table1'] < memory_limit):
continue
min_size2 = 1 - ceil(log(sup(mid_interval))/log(2)).getConstantAsInt()
max_size2 = floor(log((memory_limit - sizeof_table1)/(17 * sup(mid_interval)))/log(2)).getConstantAsInt()
# during execution of the prec2 loop, it can reduces the interval of valid values for prec2
# so min_prec2 and max_prec2 are setted here and not before the the prec2 loop
# (because they are modified inside the body of the loop, for the next iteration of size2)
min_prec2 = 0
max_prec2 = 12 + max_size2 - prec1
for size2 in xrange(max_size2,min_size2-1,-1):
max_prec2 = min(max_prec2, 12 + size2 - prec1)
for prec2 in xrange(max_prec2,min_prec2-1,-1):
#print '=====\t\033[1m{}\033[0m({}/{}),\t\033[1m{}\033[0m({}/{}),\t\033[1m{}\033[0m({}/{}),\t\033[1m{}\033[0m({}/{})\t====='.format(size1,min_size1,max_size1,prec1,min_prec1,max_prec1,size2,min_size2,max_size2,prec2,min_prec2,max_prec2)
#print resource.getrusage(resource.RUSAGE_SELF).ru_maxrss #memory used by the programm
arg_reduc = self.eval_argument_reduction(size1, prec1, size2, prec2)
mid_interval = arg_reduc['mid_interval']
out_interval = arg_reduc['out_interval']
sizeof_tables = arg_reduc['sizeof_table1'] + arg_reduc['sizeof_table2']
if not(0 <= inf(out_interval) and sup(out_interval) < S2**(64-52-prec1-prec2)):
max_prec2 = prec2 - 1
continue
if memory_limit < sizeof_tables:
continue
#assert(prec2 < 12 + size2 - prec1) # test the approximation size2 ~= max[for y]( - log2((y-y1)/y1))
# guess the degree of the two polynomials (relative error <= 2^-52 and absolute error <= 2^-120)
# note: we exclude zero from out_interval to not perturb sollya (log(1+x)/x is not well defined on 0)
sollya_out_interval = Interval(S2**(-52-prec1-prec2), sup(out_interval))
guess_degree_poly1 = guessdegree(log(1+sollya.x)/sollya.x, sollya_out_interval, S2**-52)
guess_degree_poly2 = guessdegree(log(1+sollya.x), sollya_out_interval, S2**-120)
# TODO: detect when guessdegree return multiple possible degree, and find the right one
if False and inf(guess_degree_poly1) <> sup(guess_degree_poly1):
print "improvable guess_degree_poly1:", guess_degree_poly1
if False and inf(guess_degree_poly2) <> sup(guess_degree_poly2):
print "improvable guess_degree_poly2:", guess_degree_poly2
degree_poly1 = sup(guess_degree_poly1).getConstantAsInt() + 1
degree_poly2 = sup(guess_degree_poly2).getConstantAsInt()
if ((best_arg_reduc is not None)
and (best_arg_reduc['degree_poly1'] < degree_poly1 or best_arg_reduc['degree_poly2'] < degree_poly2)):
min_prec2 = prec2 + 1
break
if ((best_arg_reduc is None)
or (best_arg_reduc['degree_poly1'] > degree_poly1)
or (best_arg_reduc['degree_poly1'] == degree_poly1 and best_arg_reduc['degree_poly2'] > degree_poly2)
or (best_arg_reduc['degree_poly1'] == degree_poly1 and best_arg_reduc['degree_poly2'] == degree_poly2 and best_arg_reduc['sizeof_tables'] > sizeof_tables)):
arg_reduc['degree_poly1'] = degree_poly1
arg_reduc['degree_poly2'] = degree_poly2
arg_reduc['sizeof_tables'] = sizeof_tables
best_arg_reduc = arg_reduc
#print "\n --new best-- \n", arg_reduc, "\n"
#print "\nBest arg reduc: \n", best_arg_reduc, "\n"
return best_arg_reduc