def check_false(element):
if element.get_precision() is ML_Bool:
return LogicalNot(element, precision=ML_Bool)
else:
return Equal(
element, Constant(0,
precision=element.get_precision()))
def get_output_check_statement(output_signal, output_tag, output_value):
""" Generate output value check statement """
test_pass_cond = Comparison(
output_signal,
output_value,
specifier=Comparison.Equal,
precision=ML_Bool
)
check_statement = ConditionBlock(
LogicalNot(
test_pass_cond,
precision = ML_Bool
),
Report(
Concatenation(
" result for {}: ".format(output_tag),
Conversion(
output_signal if output_signal.get_precision() is ML_StdLogic else
TypeCast(
output_signal,
precision=ML_StdLogicVectorFormat(
output_signal.get_precision().get_bit_size()
)
),
precision = ML_String
),
precision = ML_String
)
)
)
return test_pass_cond, check_statement
def simplify_logical_or_not(node, leaf_transform):
""" Simplify a tree of LogicalOr nodes, whose
leaf are LogicalNot nodes """
# the leaf_function transforms a leaf by extracting
# its single input (decapsulating LogicalNot) and
# calling leaf_transform on this input
def leaf_function(op):
return leaf_transform(op.get_input(0))
result = simplify_logical_tree(
node,
op_predicate=(lambda op: isinstance(op, LogicalOr)),
leaf_predicate=(lambda op: isinstance(op, LogicalNot)),
result_ctor=lambda op, op_list: LogicalNot(
logical_reduce(list(map(leaf_transform, op_list)),
LogicalAnd,
precision=node.get_precision()),
precision=node.get_precision()))
forward_attributes(node, result)
return result
def generate_scheme(self):
""" main scheme generation """
input_precision = self.precision
output_precision = self.precision
# declaring main input variable
x_interval = Interval(-10.3, 10.7)
var_x = self.implementation.add_input_variable("x",
input_precision,
interval=x_interval)
y_interval = Interval(-17.9, 17.2)
var_y = self.implementation.add_input_variable("y",
input_precision,
interval=y_interval)
z_interval = Interval(-70.3, -57.7)
var_z = self.implementation.add_input_variable("z",
input_precision,
interval=z_interval)
min_yz = Min(var_z, var_y)
cst0 = Constant(42.5, tag="cst0", precision=self.precision)
cst1 = Constant(2.5, tag="cst1", precision=self.precision)
cst2 = Constant(12.5, tag="cst2", precision=self.precision)
new_cst = cst0 + cst1 * cst2
result = min_yz + new_cst
scheme = ConditionBlock(
LogicalAnd(
LogicalOr(cst0 > cst1, LogicalNot(cst1 > cst0)),
var_x > var_y,
), Return(result), Return(cst2))
return scheme
def generate_scalar_scheme(self, vx):
Log.set_dump_stdout(True)
Log.report(Log.Info, "\033[33;1m generating implementation scheme \033[0m")
if self.debug_flag:
Log.report(Log.Info, "\033[31;1m debug has been enabled \033[0;m")
# 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, tag="k")
ik = NearestInteger(unround_k, precision = self.precision.get_integer_format(), debug = debug_multi, tag="ik")
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 gappa_utils.is_gappa_installed():
eval_error = self.gappa_engine.get_eval_error_v2(
self.opt_engine, opt_r, cg_eval_error_copy_map,
gappa_filename=gappa_utils.generate_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
MAX_NUM_ITERATION = 20
for _ in range(MAX_NUM_ITERATION):
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 gappa_utils.is_gappa_installed():
sub_poly_eval_error = -1.0
gappa_sub_poly_filename = gappa_utils.generate_gappa_filename("{}_gappa_sub_poly.g".format(self.function_name))
sub_poly_eval_error = self.gappa_engine.get_eval_error_v2(self.opt_engine, opt_sub_poly, sub_poly_error_copy_map, gappa_filename =gappa_sub_poly_filename)
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],
},
]
gappa_poly_filename = gappa_utils.generate_gappa_filename("gappa_poly.g")
poly_eval_error_dico = self.gappa_engine.get_eval_error_v3(self.opt_engine, opt_poly, poly_error_copy_map, gappa_filename=gappa_poly_filename, 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 = int(self.precision.get_emax() - self.precision.get_field_size() / 2)
cst_overflow_exp_offset = Constant(overflow_exp_offset, precision=self.precision.get_integer_format())
diff_k = Subtraction(
ik,
cst_overflow_exp_offset,
precision=self.precision.get_integer_format(),
debug=debug_multi,
tag="diff_k",
)
late_overflow_result = (ExponentInsertion(diff_k, precision = self.precision) * poly) * ExponentInsertion(cst_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, tag="late_underflow_test")
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)
std_cond = LogicalNot(LogicalOr(late_overflow_test, late_underflow_test), likely=True)
result_scheme = ConditionBlock(
std_cond,
Return(std_result, precision=self.precision),
ConditionBlock(
late_overflow_test,
late_overflow_return,
late_underflow_return,
)
)
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_scalar_scheme(self, vx, vy):
# fixing inputs' node tag
vx.set_attributes(tag="x")
vy.set_attributes(tag="y")
int_precision = self.precision.get_integer_format()
# assuming x = m.2^e (m in [1, 2[)
# n, positive or null integers
#
# pow(x, n) = x^(y)
# = exp(y * log(x))
# = 2^(y * log2(x))
# = 2^(y * (log2(m) + e))
#
e = ExponentExtraction(vx, tag="e", precision=int_precision)
m = MantissaExtraction(vx, tag="m", precision=self.precision)
# approximation log2(m)
# retrieving processor inverse approximation table
dummy_var = Variable("dummy", precision = self.precision)
dummy_div_seed = ReciprocalSeed(dummy_var, precision = self.precision)
inv_approx_table = self.processor.get_recursive_implementation(
dummy_div_seed, language=None,
table_getter= lambda self: self.approx_table_map)
log_f = sollya.log(sollya.x) # /sollya.log(self.basis)
ml_log_args = ML_GenericLog.get_default_args(precision=self.precision, basis=2)
ml_log = ML_GenericLog(ml_log_args)
log_table, log_table_tho, table_index_range = ml_log.generate_log_table(log_f, inv_approx_table)
log_approx = ml_log.generate_reduced_log_split(Abs(m, precision=self.precision), log_f, inv_approx_table, log_table)
log_approx = Select(Equal(vx, 0), FP_MinusInfty(self.precision), log_approx)
log_approx.set_attributes(tag="log_approx", debug=debug_multi)
r = Multiplication(log_approx, vy, tag="r", debug=debug_multi)
# 2^(y * (log2(m) + e)) = 2^(y * log2(m)) * 2^(y * e)
#
# log_approx = log2(Abs(m))
# r = y * log_approx ~ y * log2(m)
#
# NOTES: manage cases where e is negative and
# (y * log2(m)) AND (y * e) could cancel out
# if e positive, whichever the sign of y (y * log2(m)) and (y * e) CANNOT
# be of opposite signs
# log2(m) in [0, 1[ so cancellation can occur only if e == -1
# we split 2^x in 2^x = 2^t0 * 2^t1
# if e < 0: t0 = y * (log2(m) + e), t1=0
# else: t0 = y * log2(m), t1 = y * e
t_cond = e < 0
# e_y ~ e * y
e_f = Conversion(e, precision=self.precision)
#t0 = Select(t_cond, (e_f + log_approx) * vy, Multiplication(e_f, vy), tag="t0")
#NearestInteger(t0, precision=self.precision, tag="t0_int")
EY = NearestInteger(e_f * vy, tag="EY", precision=self.precision)
LY = NearestInteger(log_approx * vy, tag="LY", precision=self.precision)
t0_int = Select(t_cond, EY + LY, EY, tag="t0_int")
t0_frac = Select(t_cond, FMA(e_f, vy, -EY) + FMA(log_approx, vy, -LY) ,EY - t0_int, tag="t0_frac")
#t0_frac.set_attributes(tag="t0_frac")
ml_exp2_args = ML_Exp2.get_default_args(precision=self.precision)
ml_exp2 = ML_Exp2(ml_exp2_args)
exp2_t0_frac = ml_exp2.generate_scalar_scheme(t0_frac, inline_select=True)
exp2_t0_frac.set_attributes(tag="exp2_t0_frac", debug=debug_multi)
exp2_t0_int = ExponentInsertion(Conversion(t0_int, precision=int_precision), precision=self.precision, tag="exp2_t0_int")
t1 = Select(t_cond, Constant(0, precision=self.precision), r)
exp2_t1 = ml_exp2.generate_scalar_scheme(t1, inline_select=True)
exp2_t1.set_attributes(tag="exp2_t1", debug=debug_multi)
result_sign = Constant(1.0, precision=self.precision) # Select(n_is_odd, CopySign(vx, Constant(1.0, precision=self.precision)), 1)
y_int = NearestInteger(vy, precision=self.precision)
y_is_integer = Equal(y_int, vy)
y_is_even = LogicalOr(
# if y is a number (exc. inf) greater than 2**mantissa_size * 2,
# then it is an integer multiple of 2 => even
Abs(vy) >= 2**(self.precision.get_mantissa_size()+1),
LogicalAnd(
y_is_integer and Abs(vy) < 2**(self.precision.get_mantissa_size()+1),
# we want to limit the modulo computation to an integer input
Equal(Modulo(Conversion(y_int, precision=int_precision), 2), 0)
)
)
y_is_odd = LogicalAnd(
LogicalAnd(
Abs(vy) < 2**(self.precision.get_mantissa_size()+1),
y_is_integer
),
Equal(Modulo(Conversion(y_int, precision=int_precision), 2), 1)
)
# special cases management
special_case_results = Statement(
# x is sNaN OR y is sNaN
ConditionBlock(
LogicalOr(Test(vx, specifier=Test.IsSignalingNaN), Test(vy, specifier=Test.IsSignalingNaN)),
Return(FP_QNaN(self.precision))
),
# pow(x, ±0) is 1 if x is not a signaling NaN
ConditionBlock(
Test(vy, specifier=Test.IsZero),
Return(Constant(1.0, precision=self.precision))
),
# pow(±0, y) is ±∞ and signals the divideByZero exception for y an odd integer <0
ConditionBlock(
LogicalAnd(Test(vx, specifier=Test.IsZero), LogicalAnd(y_is_odd, vy < 0)),
Return(Select(Test(vx, specifier=Test.IsPositiveZero), FP_PlusInfty(self.precision), FP_MinusInfty(self.precision))),
),
# pow(±0, −∞) is +∞ with no exception
ConditionBlock(
LogicalAnd(Test(vx, specifier=Test.IsZero), Test(vy, specifier=Test.IsNegativeInfty)),
Return(FP_MinusInfty(self.precision)),
),
# pow(±0, +∞) is +0 with no exception
ConditionBlock(
LogicalAnd(Test(vx, specifier=Test.IsZero), Test(vy, specifier=Test.IsPositiveInfty)),
Return(FP_PlusInfty(self.precision)),
),
# pow(±0, y) is ±0 for finite y>0 an odd integer
ConditionBlock(
LogicalAnd(Test(vx, specifier=Test.IsZero), LogicalAnd(y_is_odd, vy > 0)),
Return(vx),
),
# pow(−1, ±∞) is 1 with no exception
ConditionBlock(
LogicalAnd(Equal(vx, -1), Test(vy, specifier=Test.IsInfty)),
Return(Constant(1.0, precision=self.precision)),
),
# pow(+1, y) is 1 for any y (even a quiet NaN)
ConditionBlock(
vx == 1,
Return(Constant(1.0, precision=self.precision)),
),
# pow(x, +∞) is +0 for −1<x<1
ConditionBlock(
LogicalAnd(Abs(vx) < 1, Test(vy, specifier=Test.IsPositiveInfty)),
Return(FP_PlusZero(self.precision))
),
# pow(x, +∞) is +∞ for x<−1 or for 1<x (including ±∞)
ConditionBlock(
LogicalAnd(Abs(vx) > 1, Test(vy, specifier=Test.IsPositiveInfty)),
Return(FP_PlusInfty(self.precision))
),
# pow(x, −∞) is +∞ for −1<x<1
ConditionBlock(
LogicalAnd(Abs(vx) < 1, Test(vy, specifier=Test.IsNegativeInfty)),
Return(FP_PlusInfty(self.precision))
),
# pow(x, −∞) is +0 for x<−1 or for 1<x (including ±∞)
ConditionBlock(
LogicalAnd(Abs(vx) > 1, Test(vy, specifier=Test.IsNegativeInfty)),
Return(FP_PlusZero(self.precision))
),
# pow(+∞, y) is +0 for a number y < 0
ConditionBlock(
LogicalAnd(Test(vx, specifier=Test.IsPositiveInfty), vy < 0),
Return(FP_PlusZero(self.precision))
),
# pow(+∞, y) is +∞ for a number y > 0
ConditionBlock(
LogicalAnd(Test(vx, specifier=Test.IsPositiveInfty), vy > 0),
Return(FP_PlusInfty(self.precision))
),
# pow(−∞, y) is −0 for finite y < 0 an odd integer
# TODO: check y is finite
ConditionBlock(
LogicalAnd(Test(vx, specifier=Test.IsNegativeInfty), LogicalAnd(y_is_odd, vy < 0)),
Return(FP_MinusZero(self.precision)),
),
# pow(−∞, y) is −∞ for finite y > 0 an odd integer
# TODO: check y is finite
ConditionBlock(
LogicalAnd(Test(vx, specifier=Test.IsNegativeInfty), LogicalAnd(y_is_odd, vy > 0)),
Return(FP_MinusInfty(self.precision)),
),
# pow(−∞, y) is +0 for finite y < 0 and not an odd integer
# TODO: check y is finite
ConditionBlock(
LogicalAnd(Test(vx, specifier=Test.IsNegativeInfty), LogicalAnd(LogicalNot(y_is_odd), vy < 0)),
Return(FP_PlusZero(self.precision)),
),
# pow(−∞, y) is +∞ for finite y > 0 and not an odd integer
# TODO: check y is finite
ConditionBlock(
LogicalAnd(Test(vx, specifier=Test.IsNegativeInfty), LogicalAnd(LogicalNot(y_is_odd), vy > 0)),
Return(FP_PlusInfty(self.precision)),
),
# pow(±0, y) is +∞ and signals the divideByZero exception for finite y<0 and not an odd integer
# TODO: signal divideByZero exception
ConditionBlock(
LogicalAnd(Test(vx, specifier=Test.IsZero), LogicalAnd(LogicalNot(y_is_odd), vy < 0)),
Return(FP_PlusInfty(self.precision)),
),
# pow(±0, y) is +0 for finite y>0 and not an odd integer
ConditionBlock(
LogicalAnd(Test(vx, specifier=Test.IsZero), LogicalAnd(LogicalNot(y_is_odd), vy > 0)),
Return(FP_PlusZero(self.precision)),
),
)
# manage n=1 separately to avoid catastrophic propagation of errors
# between log2 and exp2 to eventually compute the identity function
# test-case #3
result = Statement(
special_case_results,
# fallback default cases
Return(result_sign * exp2_t1 * exp2_t0_int * exp2_t0_frac))
return result
def generic_atan2_generate(self, _vx, vy=None):
""" if vy is None, compute atan(_vx), else compute atan2(vy / vx) """
if vy is None:
# approximation
# if abs_vx <= 1.0 then atan(abx_vx) is directly approximated
# if abs_vx > 1.0 then atan(abs_vx) = pi/2 - atan(1 / abs_vx)
#
# for vx >= 0, atan(vx) = atan(abs_vx)
#
# for vx < 0, atan(vx) = -atan(abs_vx) for vx < 0
# = -pi/2 + atan(1 / abs_vx)
vx = _vx
sign_cond = vx < 0
abs_vx = Select(vx < 0, -vx, vx, tag="abs_vx", debug=debug_multi)
bound_cond = abs_vx > 1
inv_abs_vx = 1 / abs_vx
# condition to select subtraction
cond = LogicalOr(LogicalAnd(vx < 0, LogicalNot(bound_cond)),
vx > 1,
tag="cond",
debug=debug_multi)
# reduced argument
red_vx = Select(bound_cond,
inv_abs_vx,
abs_vx,
tag="red_vx",
debug=debug_multi)
offset = None
else:
# bound_cond is True iff Abs(vy / _vx) > 1.0
bound_cond = Abs(vy) > Abs(_vx)
bound_cond.set_attributes(tag="bound_cond", debug=debug_multi)
# vx and vy are of opposite signs
#sign_cond = (_vx * vy) < 0
# using cast to int(signed) and bitwise xor
# to determine if _vx and vy are of opposite sign rapidly
fast_sign_cond = BitLogicXor(
TypeCast(_vx, precision=self.precision.get_integer_format()),
TypeCast(vy, precision=self.precision.get_integer_format()),
precision=self.precision.get_integer_format()) < 0
# sign_cond = (_vx * vy) < 0
sign_cond = fast_sign_cond
sign_cond.set_attributes(tag="sign_cond", debug=debug_multi)
# condition to select subtraction
# TODO: could be accelerated if LogicalXor existed
slow_cond = LogicalOr(
LogicalAnd(sign_cond,
LogicalNot(bound_cond)), # 1 < (vy / _vx) < 0
LogicalAnd(bound_cond,
LogicalNot(sign_cond)), # (vy / _vx) > 1
tag="cond",
debug=debug_multi)
cond = slow_cond
numerator = Select(bound_cond,
_vx,
vy,
tag="numerator",
debug=debug_multi)
denominator = Select(bound_cond,
vy,
_vx,
tag="denominator",
debug=debug_multi)
# reduced argument
red_vx = Abs(numerator) / Abs(denominator)
red_vx.set_attributes(tag="red_vx", debug=debug_multi)
offset = Select(
_vx > 0,
Constant(0, precision=self.precision),
# vx < 0
Select(
sign_cond,
# vy > 0
Constant(sollya.pi, precision=self.precision),
Constant(-sollya.pi, precision=self.precision),
precision=self.precision),
precision=self.precision,
tag="offset")
approx_fct = sollya.atan(sollya.x)
if self.method == "piecewise":
sign_vx = Select(cond,
-1,
1,
precision=self.precision,
tag="sign_vx",
debug=debug_multi)
cst_sign = Select(sign_cond,
-1,
1,
precision=self.precision,
tag="cst_sign",
debug=debug_multi)
cst = cst_sign * Select(
bound_cond, sollya.pi / 2, 0, precision=self.precision)
cst.set_attributes(tag="cst", debug=debug_multi)
bound_low = 0.0
bound_high = 1.0
num_intervals = self.num_sub_intervals
error_threshold = S2**-(self.precision.get_mantissa_size() + 8)
approx, eval_error = piecewise_approximation(
approx_fct,
red_vx,
self.precision,
bound_low=bound_low,
bound_high=bound_high,
max_degree=None,
num_intervals=num_intervals,
error_threshold=error_threshold,
odd=True)
result = cst + sign_vx * approx
result.set_attributes(tag="result",
precision=self.precision,
debug=debug_multi)
elif self.method == "single":
approx_interval = Interval(0, 1.0)
# determining the degree of the polynomial approximation
poly_degree_range = sollya.guessdegree(
approx_fct / sollya.x, approx_interval,
S2**-(self.precision.get_field_size() + 2))
poly_degree = int(sollya.sup(poly_degree_range)) + 4
Log.report(Log.Info, "poly_degree={}".format(poly_degree))
# arctan is an odd function, so only odd coefficient must be non-zero
poly_degree_list = list(range(1, poly_degree + 1, 2))
poly_object, poly_error = Polynomial.build_from_approximation_with_error(
approx_fct, poly_degree_list,
[1] + [self.precision.get_sollya_object()] *
(len(poly_degree_list) - 1), approx_interval)
odd_predicate = lambda index, _: ((index - 1) % 4 != 0)
even_predicate = lambda index, _: (index != 1 and
(index - 1) % 4 == 0)
poly_odd_object = poly_object.sub_poly_cond(odd_predicate,
offset=1)
poly_even_object = poly_object.sub_poly_cond(even_predicate,
offset=1)
sollya.settings.display = sollya.hexadecimal
Log.report(Log.Info, "poly_error: {}".format(poly_error))
Log.report(Log.Info, "poly_odd: {}".format(poly_odd_object))
Log.report(Log.Info, "poly_even: {}".format(poly_even_object))
poly_odd = PolynomialSchemeEvaluator.generate_horner_scheme(
poly_odd_object, abs_vx)
poly_odd.set_attributes(tag="poly_odd", debug=debug_multi)
poly_even = PolynomialSchemeEvaluator.generate_horner_scheme(
poly_even_object, abs_vx)
poly_even.set_attributes(tag="poly_even", debug=debug_multi)
exact_sum = poly_odd + poly_even
exact_sum.set_attributes(tag="exact_sum", debug=debug_multi)
# poly_even should be (1 + poly_even)
result = vx + vx * exact_sum
result.set_attributes(tag="result",
precision=self.precision,
debug=debug_multi)
else:
raise NotImplementedError
if not offset is None:
result = result + offset
std_scheme = Statement(Return(result))
scheme = std_scheme
return scheme
def generate_scalar_scheme(self, vx, n):
# fixing inputs' node tag
vx.set_attributes(tag="x")
n.set_attributes(tag="n")
int_precision = self.precision.get_integer_format()
# assuming x = m.2^e (m in [1, 2[)
# n, positive or null integers
#
# rootn(x, n) = x^(1/n)
# = exp(1/n * log(x))
# = 2^(1/n * log2(x))
# = 2^(1/n * (log2(m) + e))
#
# approximation log2(m)
# retrieving processor inverse approximation table
dummy_var = Variable("dummy", precision=self.precision)
dummy_div_seed = ReciprocalSeed(dummy_var, precision=self.precision)
inv_approx_table = self.processor.get_recursive_implementation(
dummy_div_seed,
language=None,
table_getter=lambda self: self.approx_table_map)
log_f = sollya.log(sollya.x) # /sollya.log(self.basis)
use_reciprocal = False
# non-scaled vx used to compute vx^1
unmodified_vx = vx
is_subnormal = Test(vx, specifier=Test.IsSubnormal, tag="is_subnormal")
exp_correction_factor = self.precision.get_mantissa_size()
mantissa_factor = Constant(2**exp_correction_factor,
tag="mantissa_factor")
vx = Select(is_subnormal, vx * mantissa_factor, vx, tag="corrected_vx")
m = MantissaExtraction(vx, tag="m", precision=self.precision)
e = ExponentExtraction(vx, tag="e", precision=int_precision)
e = Select(is_subnormal,
e - exp_correction_factor,
e,
tag="corrected_e")
ml_log_args = ML_GenericLog.get_default_args(precision=self.precision,
basis=2)
ml_log = ML_GenericLog(ml_log_args)
log_table, log_table_tho, table_index_range = ml_log.generate_log_table(
log_f, inv_approx_table)
log_approx = ml_log.generate_reduced_log_split(
Abs(m, precision=self.precision), log_f, inv_approx_table,
log_table)
# floating-point version of n
n_f = Conversion(n, precision=self.precision, tag="n_f")
inv_n = Division(Constant(1, precision=self.precision), n_f)
log_approx = Select(Equal(vx, 0), FP_MinusInfty(self.precision),
log_approx)
log_approx.set_attributes(tag="log_approx", debug=debug_multi)
if use_reciprocal:
r = Multiplication(log_approx, inv_n, tag="r", debug=debug_multi)
else:
r = Division(log_approx, n_f, tag="r", debug=debug_multi)
# e_n ~ e / n
e_f = Conversion(e, precision=self.precision, tag="e_f")
if use_reciprocal:
e_n = Multiplication(e_f, inv_n, tag="e_n")
else:
e_n = Division(e_f, n_f, tag="e_n")
error_e_n = FMA(e_n, -n_f, e_f, tag="error_e_n")
e_n_int = NearestInteger(e_n, precision=self.precision, tag="e_n_int")
pre_e_n_frac = e_n - e_n_int
pre_e_n_frac.set_attributes(tag="pre_e_n_frac")
e_n_frac = pre_e_n_frac + error_e_n * inv_n
e_n_frac.set_attributes(tag="e_n_frac")
ml_exp2_args = ML_Exp2.get_default_args(precision=self.precision)
ml_exp2 = ML_Exp2(ml_exp2_args)
exp2_r = ml_exp2.generate_scalar_scheme(r, inline_select=True)
exp2_r.set_attributes(tag="exp2_r", debug=debug_multi)
exp2_e_n_frac = ml_exp2.generate_scalar_scheme(e_n_frac,
inline_select=True)
exp2_e_n_frac.set_attributes(tag="exp2_e_n_frac", debug=debug_multi)
exp2_e_n_int = ExponentInsertion(Conversion(e_n_int,
precision=int_precision),
precision=self.precision,
tag="exp2_e_n_int")
n_is_even = Equal(Modulo(n, 2), 0, tag="n_is_even", debug=debug_multi)
n_is_odd = LogicalNot(n_is_even, tag="n_is_odd")
result_sign = Select(
n_is_odd, CopySign(vx, Constant(1.0, precision=self.precision)), 1)
# managing n == -1
if self.expand_div:
ml_division_args = ML_Division.get_default_args(
precision=self.precision, input_formats=[self.precision] * 2)
ml_division = ML_Division(ml_division_args)
self.division_implementation = ml_division.implementation
self.division_implementation.set_scheme(
ml_division.generate_scheme())
ml_division_fct = self.division_implementation.get_function_object(
)
else:
ml_division_fct = Division
# manage n=1 separately to avoid catastrophic propagation of errors
# between log2 and exp2 to eventually compute the identity function
# test-case #3
result = ConditionBlock(
LogicalOr(LogicalOr(Test(vx, specifier=Test.IsNaN), Equal(n, 0)),
LogicalAnd(n_is_even, vx < 0)),
Return(FP_QNaN(self.precision)),
Statement(
ConditionBlock(
Equal(n, -1, tag="n_is_mone"),
#Return(Division(Constant(1, precision=self.precision), unmodified_vx, tag="div_res", precision=self.precision)),
Return(
ml_division_fct(Constant(1, precision=self.precision),
unmodified_vx,
tag="div_res",
precision=self.precision)),
),
ConditionBlock(
# rootn( ±inf, n) is +∞ for even n< 0.
Test(vx, specifier=Test.IsInfty),
Statement(
ConditionBlock(
n < 0,
#LogicalAnd(n_is_odd, n < 0),
Return(
Select(Test(vx,
specifier=Test.IsPositiveInfty),
Constant(FP_PlusZero(self.precision),
precision=self.precision),
Constant(FP_MinusZero(self.precision),
precision=self.precision),
precision=self.precision)),
Return(vx),
), ),
),
ConditionBlock(
# rootn(±0, n) is ±∞ for odd n < 0.
LogicalAnd(LogicalAnd(n_is_odd, n < 0),
Equal(vx, 0),
tag="n_is_odd_and_neg"),
Return(
Select(Test(vx, specifier=Test.IsPositiveZero),
Constant(FP_PlusInfty(self.precision),
precision=self.precision),
Constant(FP_MinusInfty(self.precision),
precision=self.precision),
precision=self.precision)),
),
ConditionBlock(
# rootn( ±0, n) is +∞ for even n< 0.
LogicalAnd(LogicalAnd(n_is_even, n < 0), Equal(vx, 0)),
Return(FP_PlusInfty(self.precision))),
ConditionBlock(
# rootn(±0, n) is +0 for even n > 0.
LogicalAnd(n_is_even, Equal(vx, 0)),
Return(vx)),
ConditionBlock(
Equal(n, 1), Return(unmodified_vx),
Return(result_sign * exp2_r * exp2_e_n_int *
exp2_e_n_frac))))
return result
def generate_auto_test(self,
test_num=10,
test_range=Interval(-1.0, 1.0),
debug=False,
time_step=10):
""" time_step: duration of a stage (in ns) """
# instanciating tested component
# map of input_tag -> input_signal and output_tag -> output_signal
io_map = {}
# map of input_tag -> input_signal, excludind commodity signals
# (e.g. clock and reset)
input_signals = {}
# map of output_tag -> output_signal
output_signals = {}
# excluding clock and reset signals from argument list
# reduced_arg_list = [input_port for input_port in self.implementation.get_arg_list() if not input_port.get_tag() in ["clk", "reset"]]
reduced_arg_list = self.implementation.get_arg_list()
for input_port in reduced_arg_list:
input_tag = input_port.get_tag()
input_signal = Signal(input_tag + "_i",
precision=input_port.get_precision(),
var_type=Signal.Local)
io_map[input_tag] = input_signal
if not input_tag in ["clk", "reset"]:
input_signals[input_tag] = input_signal
for output_port in self.implementation.get_output_port():
output_tag = output_port.get_tag()
output_signal = Signal(output_tag + "_o",
precision=output_port.get_precision(),
var_type=Signal.Local)
io_map[output_tag] = output_signal
output_signals[output_tag] = output_signal
# building list of test cases
tc_list = []
self_component = self.implementation.get_component_object()
self_instance = self_component(io_map=io_map, tag="tested_entity")
test_statement = Statement()
# initializing random test case generator
self.init_test_generator()
# Appending standard test cases if required
if self.auto_test_std:
tc_list += self.standard_test_cases
for i in range(test_num):
input_values = self.generate_test_case(input_signals, io_map, i,
test_range)
tc_list.append((input_values, None))
def compute_results(tc):
""" update test case with output values if required """
input_values, output_values = tc
if output_values is None:
return input_values, self.numeric_emulate(input_values)
else:
return tc
# filling output values
tc_list = [compute_results(tc) for tc in tc_list]
for input_values, output_values in tc_list:
input_msg = ""
# Adding input setting
for input_tag in input_values:
input_signal = io_map[input_tag]
# FIXME: correct value generation depending on signal precision
input_value = input_values[input_tag]
test_statement.add(
ReferenceAssign(
input_signal,
Constant(input_value,
precision=input_signal.get_precision())))
value_msg = input_signal.get_precision().get_cst(
input_value, language=VHDL_Code).replace('"', "'")
value_msg += " / " + hex(input_signal.get_precision(
).get_base_format().get_integer_coding(input_value))
input_msg += " {}={} ".format(input_tag, value_msg)
test_statement.add(Wait(time_step * self.stage_num))
# Adding output value comparison
for output_tag in output_signals:
output_signal = output_signals[output_tag]
output_value = Constant(
output_values[output_tag],
precision=output_signal.get_precision())
output_precision = output_signal.get_precision()
expected_dec = output_precision.get_cst(
output_values[output_tag],
language=VHDL_Code).replace('"', "'")
expected_hex = " / " + hex(
output_precision.get_base_format().get_integer_coding(
output_values[output_tag]))
value_msg = "{} / {}".format(expected_dec, expected_hex)
test_pass_cond = Comparison(output_signal,
output_value,
specifier=Comparison.Equal,
precision=ML_Bool)
test_statement.add(
ConditionBlock(
LogicalNot(test_pass_cond, precision=ML_Bool),
Report(
Concatenation(
" result for {}: ".format(output_tag),
Conversion(TypeCast(
output_signal,
precision=ML_StdLogicVectorFormat(
output_signal.get_precision(
).get_bit_size())),
precision=ML_String),
precision=ML_String))))
test_statement.add(
Assert(
test_pass_cond,
"\"unexpected value for inputs {input_msg}, output {output_tag}, expecting {value_msg}, got: \""
.format(input_msg=input_msg,
output_tag=output_tag,
value_msg=value_msg),
severity=Assert.Failure))
testbench = CodeEntity("testbench")
test_process = Process(
test_statement,
# end of test
Assert(Constant(0, precision=ML_Bool),
" \"end of test, no error encountered \"",
severity=Assert.Failure))
testbench_scheme = Statement(self_instance, test_process)
if self.pipelined:
half_time_step = time_step / 2
assert (half_time_step * 2) == time_step
# adding clock process for pipelined bench
clk_process = Process(
Statement(
ReferenceAssign(io_map["clk"],
Constant(1, precision=ML_StdLogic)),
Wait(half_time_step),
ReferenceAssign(io_map["clk"],
Constant(0, precision=ML_StdLogic)),
Wait(half_time_step),
))
testbench_scheme.push(clk_process)
testbench.add_process(testbench_scheme)
return [testbench]
def generate_scheme(self):
# declaring target and instantiating optimization engine
vx = self.implementation.add_input_variable("x", self.precision)
vx.set_attributes(precision=self.precision,
tag="vx",
debug=debug_multi)
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")
C0 = Constant(0, precision=self.precision)
C0_plus = Constant(FP_PlusZero(self.precision))
C0_minus = Constant(FP_MinusZero(self.precision))
def local_test(specifier, tag):
""" Local wrapper to generate Test operations """
return Test(vx,
specifier=specifier,
likely=False,
debug=debug_multi,
tag="is_%s" % tag,
precision=ML_Bool)
test_NaN = local_test(Test.IsNaN, "is_NaN")
test_inf = local_test(Test.IsInfty, "is_Inf")
test_NaN_or_Inf = local_test(Test.IsInfOrNaN, "is_Inf_Or_Nan")
test_negative = Comparison(vx,
C0,
specifier=Comparison.Less,
debug=debug_multi,
tag="is_Negative",
precision=ML_Bool,
likely=False)
test_NaN_or_Neg = LogicalOr(test_NaN, test_negative, precision=ML_Bool)
test_std = LogicalNot(LogicalOr(test_NaN_or_Inf,
test_negative,
precision=ML_Bool,
likely=False),
precision=ML_Bool,
likely=True)
test_zero = Comparison(vx,
C0,
specifier=Comparison.Equal,
likely=False,
debug=debug_multi,
tag="Is_Zero",
precision=ML_Bool)
return_NaN_or_neg = Statement(Return(FP_QNaN(self.precision)))
return_inf = Statement(Return(FP_PlusInfty(self.precision)))
return_PosZero = Return(C0_plus)
return_NegZero = Return(C0_minus)
NR_init = ReciprocalSquareRootSeed(vx,
precision=self.precision,
tag="sqrt_seed",
debug=debug_multi)
result = compute_sqrt(vx,
NR_init,
int(self.num_iter),
precision=self.precision)
return_non_std = ConditionBlock(
test_NaN_or_Neg, return_NaN_or_neg,
ConditionBlock(
test_inf, return_inf,
ConditionBlock(test_zero, return_PosZero, return_NegZero)))
return_std = Return(result)
scheme = ConditionBlock(test_std, return_std, return_non_std)
return scheme
def booth_radix4_multiply(lhs, rhs, pos_bit_heap, neg_bit_heap):
""" Compute the multiplication @p lhs x @p rhs using radix 4 Booth
recoding and drop the generated partial product in @p
pos_bit_heap and @p neg_bit_heap based on their sign """
# booth recoded partial product for n-th digit
# is based on digit from n-1 to n+1
# (n+1) | (n) | (n-1) | PP |
# ------|-----|-------|------|
# 0 | 0 | 0 | +0 |
# 0 | 0 | 1 | +X |
# 0 | 1 | 0 | +X |
# 0 | 1 | 1 | +2x |
# 1 | 0 | 0 | -2X |
# 1 | 0 | 1 | -X |
# 1 | 1 | 0 | -X |
# 1 | 1 | 1 | +0 |
# ------|-----|-------|------|
assert lhs.get_precision().get_bit_size() >= 2
# lhs is the recoded operand
# RECODING DIGITS
# first recoded digit is padded right by 0
first_digit = Concatenation(SubSignalSelection(
lhs, 0, 1, precision=ML_StdLogicVectorFormat(2)),
Constant(0, precision=ML_StdLogic),
precision=ML_StdLogicVectorFormat(3),
debug=debug_std,
tag="booth_digit_0")
digit_list = [(first_digit, 0)]
for digit_index in range(2, lhs.get_precision().get_bit_size(), 2):
if digit_index + 1 < lhs.get_precision().get_bit_size():
# digits exist completely in lhs
digit = SubSignalSelection(lhs,
digit_index - 1,
digit_index + 1,
tag="booth_digit_%d" % digit_index,
debug=debug_std)
else:
# MSB padding required
sign_ext = Constant(0, precision=ML_StdLogic) if not (
lhs.get_precision().get_signed()) else BitSelection(
lhs,
lhs.get_precision().get_bit_size() - 1)
digit = Concatenation(sign_ext,
SubSignalSelection(lhs, digit_index - 1,
digit_index),
precision=ML_StdLogicVectorFormat(3),
debug=debug_std,
tag="booth_digit_%d" % digit_index)
digit_list.append((digit, digit_index))
# if lhs size is a mutiple of two and it is unsigned
# than an extra digit must be generated to ensure a positive result
if lhs.get_precision().get_bit_size() % 2 == 0 and not (
lhs.get_precision().get_signed()):
digit_index = lhs.get_precision().get_bit_size() - 1
digit = Concatenation(Constant(0,
precision=ML_StdLogicVectorFormat(2)),
BitSelection(lhs, digit_index),
precision=ML_StdLogicVectorFormat(3),
debug=debug_std,
tag="booth_digit_%d" % (digit_index + 1))
digit_list.append((digit, digit_index + 1))
def DCV(value):
""" Digit Constante Value """
return Constant(value, precision=ML_StdLogicVectorFormat(3))
# PARTIAL PRODUCT GENERATION
# Radix-4 booth recoding requires the following Partial Products
# -2.rhs, -rhs, 0, rhs and 2.rhs
# Negative PP are obtained by 1's complement of the value correctly shifted
# adding a positive one to the LSB (inserted separately) and assuming
# MSB digit has a negative weight
for digit, index in digit_list:
pp_zero = LogicalOr(Equal(digit, DCV(0), precision=ML_Bool),
Equal(digit, DCV(7), precision=ML_Bool),
precision=ML_Bool)
pp_shifted = LogicalOr(Equal(digit, DCV(3), precision=ML_Bool),
Equal(digit, DCV(4), precision=ML_Bool),
precision=ML_Bool)
# excluding zero case
pp_neg_bit = BitSelection(digit, 2)
pp_neg = equal_to(pp_neg_bit, 1)
pp_neg_lsb_carryin = Select(LogicalAnd(pp_neg, LogicalNot(pp_zero)),
Constant(1, precision=ML_StdLogic),
Constant(0, precision=ML_StdLogic),
tag="pp_%d_neg_lsb_carryin" % index,
debug=debug_std)
# LSB digit
lsb_pp_digit = Select(pp_shifted,
Constant(0, precision=ML_StdLogic),
BitSelection(rhs, 0),
precision=ML_StdLogic)
lsb_local_pp = Select(pp_zero,
Constant(0, precision=ML_StdLogic),
Select(pp_neg,
BitLogicNegate(lsb_pp_digit),
lsb_pp_digit,
precision=ML_StdLogic),
debug=debug_std,
tag="lsb_local_pp_%d" % index,
precision=ML_StdLogic)
pos_bit_heap.insert_bit(index, lsb_local_pp)
pos_bit_heap.insert_bit(index, pp_neg_lsb_carryin)
# other digits
rhs_size = rhs.get_precision().get_bit_size()
for k in range(1, rhs_size):
pp_digit = Select(pp_shifted,
BitSelection(rhs, k - 1),
BitSelection(rhs, k),
precision=ML_StdLogic)
local_pp = Select(pp_zero,
Constant(0, precision=ML_StdLogic),
Select(pp_neg,
BitLogicNegate(pp_digit),
pp_digit,
precision=ML_StdLogic),
debug=debug_std,
tag="local_pp_%d_%d" % (index, k),
precision=ML_StdLogic)
pos_bit_heap.insert_bit(index + k, local_pp)
# MSB digit
msb_pp_digit = pp_digit = Select(
pp_shifted,
BitSelection(rhs, rhs_size - 1),
# TODO: fix for signed rhs
Constant(0, precision=ML_StdLogic)
if not (rhs.get_precision().get_signed()) else BitSelection(
rhs, rhs_size - 1),
precision=ML_StdLogic)
msb_pp = Select(pp_zero,
Constant(0, precision=ML_StdLogic),
Select(pp_neg,
BitLogicNegate(msb_pp_digit),
msb_pp_digit,
precision=ML_StdLogic),
debug=debug_std,
tag="msb_pp_%d" % (index),
precision=ML_StdLogic)
if rhs.get_precision().get_signed():
neg_bit_heap.insert_bit(index + rhs_size, msb_pp)
else:
pos_bit_heap.insert_bit(index + rhs_size, msb_pp)
# MSB negative digit,
# 'rhs_size + index) is the position of the MSB digit of rhs shifted by 1
# we add +1 to get to the sign position
neg_bit_heap.insert_bit(index + rhs_size + 1, pp_neg_lsb_carryin)
def LogicalXor(a, b):
return LogicalOr(LogicalAnd(a, LogicalNot(b)), LogicalAnd(LogicalNot(a), b))
def generate_datafile_testbench(self, tc_list, io_map, input_signals, output_signals, time_step, test_fname="test.input"):
""" Generate testbench with input and output data externalized in
a data file """
# textio function to read hexadecimal text
def FCT_HexaRead_gen(input_format):
legalized_input_format = input_format
FCT_HexaRead = FunctionObject("hread", [HDL_LINE, legalized_input_format], ML_Void, FunctionOperator("hread", void_function=True, arity=2))
return FCT_HexaRead
# textio function to read binary text
FCT_Read = FunctionObject("read", [HDL_LINE, ML_StdLogic], ML_Void, FunctionOperator("read", void_function=True, arity=2))
input_line = Variable("input_line", precision=HDL_LINE, var_type=Variable.Local)
# building ordered list of input and output signal names
input_signal_list = [sname for sname in input_signals.keys()]
input_statement = Statement()
for input_name in input_signal_list:
input_format = input_signals[input_name].precision
input_var = Variable(
"v_" + input_name,
precision=input_format,
var_type=Variable.Local)
if input_format is ML_StdLogic:
input_statement.add(FCT_Read(input_line, input_var))
else:
input_statement.add(FCT_HexaRead_gen(input_format)(input_line, input_var))
input_statement.add(ReferenceAssign(input_signals[input_name], input_var))
output_signal_list = [sname for sname in output_signals.keys()]
output_statement = Statement()
for output_name in output_signal_list:
output_format = output_signals[output_name].precision
output_var = Variable(
"v_" + output_name,
precision=output_format,
var_type=Variable.Local)
if output_format is ML_StdLogic:
output_statement.add(FCT_Read(input_line, output_var))
else:
output_statement.add(FCT_HexaRead_gen(output_format)(input_line, output_var))
output_signal = output_signals[output_name]
#value_msg = get_output_value_msg(output_signal, output_value)
test_pass_cond, check_statement = get_output_check_statement(output_signal, output_name, output_var)
input_msg = multi_Concatenation(*tuple(sum([[" %s=" % input_tag, signal_str_conversion(input_signals[input_tag], input_signals[input_tag].precision)] for input_tag in input_signal_list], [])))
output_statement.add(check_statement)
assert_statement = Assert(
test_pass_cond,
multi_Concatenation(
"unexpected value for inputs ",
input_msg,
" expecting :",
signal_str_conversion(output_var, output_format),
" got :",
signal_str_conversion(output_signal, output_format),
precision = ML_String
),
severity=Assert.Failure
)
output_statement.add(assert_statement)
self_component = self.implementation.get_component_object()
self_instance = self_component(io_map = io_map, tag = "tested_entity")
test_statement = Statement()
DATA_FILE_NAME = test_fname
with open(DATA_FILE_NAME, "w") as data_file:
# dumping column tags
data_file.write("# " + " ".join(input_signal_list + output_signal_list) + "\n")
def get_raw_cst_string(cst_format, cst_value):
size = int((cst_format.get_bit_size() + 3) / 4)
return ("{:x}").format(cst_format.get_base_format().get_integer_coding(cst_value)).zfill(size)
for input_values, output_values in tc_list:
# TODO; generate test data file
cst_list = []
for input_name in input_signal_list:
input_value = input_values[input_name]
input_format = input_signals[input_name].get_precision()
cst_list.append(get_raw_cst_string(input_format, input_value))
for output_name in output_signal_list:
output_value = output_values[output_name]
output_format = output_signals[output_name].get_precision()
cst_list.append(get_raw_cst_string(output_format, output_value))
# dumping line into file
data_file.write(" ".join(cst_list) + "\n")
input_stream = Variable("data_file", precision=HDL_FILE, var_type=Variable.Local)
file_status = Variable("file_status", precision=HDL_OPEN_FILE_STATUS, var_type=Variable.Local)
FCT_EndFile = FunctionObject("endfile", [HDL_FILE], ML_Bool, FunctionOperator("endfile", arity=1))
FCT_OpenFile = FunctionObject(
"FILE_OPEN", [HDL_OPEN_FILE_STATUS, HDL_FILE, ML_String], ML_Void,
FunctionOperator(
"FILE_OPEN",
arg_map={0: FO_Arg(0), 1: FO_Arg(1), 2: FO_Arg(2), 3: "READ_MODE"},
void_function=True))
FCT_ReadLine = FunctionObject(
"readline", [HDL_FILE, HDL_LINE], ML_Void,
FunctionOperator("readline", void_function=True, arity=2))
reset_statement = self.get_reset_statement(io_map, time_step)
OPEN_OK = Constant("OPEN_OK", precision=HDL_OPEN_FILE_STATUS)
testbench = CodeEntity("testbench")
test_process = Process(
reset_statement,
FCT_OpenFile(file_status, input_stream, DATA_FILE_NAME),
ConditionBlock(
Comparison(file_status, OPEN_OK, specifier=Comparison.NotEqual),
Assert(
Constant(0, precision=ML_Bool),
" \"failed to open file {}\"".format(DATA_FILE_NAME),
severity=Assert.Failure
)
),
# consume legend line
FCT_ReadLine(input_stream, input_line),
WhileLoop(
LogicalNot(FCT_EndFile(input_stream)),
Statement(
FCT_ReadLine(input_stream, input_line),
input_statement,
Wait(time_step * (self.stage_num + 2)),
output_statement,
),
),
# end of test
Assert(
Constant(0, precision = ML_Bool),
" \"end of test, no error encountered \"",
severity = Assert.Warning
),
# infinite end loop
WhileLoop(
Constant(1, precision=ML_Bool),
Statement(
Wait(time_step * (self.stage_num + 2)),
)
)
)
testbench_scheme = Statement(
self_instance,
test_process
)
if self.pipelined:
half_time_step = time_step / 2
assert (half_time_step * 2) == time_step
# adding clock process for pipelined bench
clk_process = Process(
Statement(
ReferenceAssign(
io_map["clk"],
Constant(1, precision = ML_StdLogic)
),
Wait(half_time_step),
ReferenceAssign(
io_map["clk"],
Constant(0, precision = ML_StdLogic)
),
Wait(half_time_step),
)
)
testbench_scheme.push(clk_process)
testbench.add_process(testbench_scheme)
return [testbench]
