def dirty_multi_node_expand(node, precision, mem_map=None, fma=True):
""" Dirty expand node into Hi and Lo part, storing
already processed temporary values in mem_map """
mem_map = mem_map or {}
if node in mem_map:
return mem_map[node]
elif isinstance(node, Constant):
value = node.get_value()
value_hi = sollya.round(value, precision.sollya_object, sollya.RN)
value_lo = sollya.round(value - value_hi, precision.sollya_object,
sollya.RN)
ch = Constant(value_hi, tag=node.get_tag() + "hi", precision=precision)
cl = Constant(value_lo, tag=node.get_tag() +
"lo", precision=precision) if value_lo != 0 else None
if cl is None:
Log.report(Log.Info, "simplified constant")
result = ch, cl
mem_map[node] = result
return result
else:
# Case of Addition or Multiplication nodes:
# 1. retrieve inputs
# 2. dirty convert inputs recursively
# 3. forward to the right metamacro
assert isinstance(node, Addition) or isinstance(node, Multiplication)
lhs = node.get_input(0)
rhs = node.get_input(1)
op1h, op1l = dirty_multi_node_expand(lhs, precision, mem_map, fma)
op2h, op2l = dirty_multi_node_expand(rhs, precision, mem_map, fma)
if isinstance(node, Addition):
result = Add222(op1h, op1l, op2h, op2l) \
if op1l is not None and op2l is not None \
else Add212(op1h, op2h, op2l) \
if op1l is None and op2l is not None \
else Add212(op2h, op1h, op1l) \
if op2l is None and op1l is not None \
else Add211(op1h, op2h)
mem_map[node] = result
return result
elif isinstance(node, Multiplication):
result = Mul222(op1h, op1l, op2h, op2l, fma=fma) \
if op1l is not None and op2l is not None \
else Mul212(op1h, op2h, op2l, fma=fma) \
if op1l is None and op2l is not None \
else Mul212(op2h, op1h, op1l, fma=fma) \
if op2l is None and op1l is not None \
else Mul211(op1h, op2h, fma=fma)
mem_map[node] = result
return result
def compute_log(_vx, exp_corr_factor=None):
_vx_mant = MantissaExtraction(_vx,
tag="_vx_mant",
precision=self.precision,
debug=debug_multi)
_vx_exp = ExponentExtraction(_vx, tag="_vx_exp", debug=debug_multi)
table_index = inv_approx_table.index_function(_vx_mant)
table_index.set_attributes(tag="table_index", debug=debug_multi)
tho_cond = _vx_mant > Constant(sollya.sqrt(2),
precision=self.precision)
tho = Select(tho_cond,
Constant(1.0, precision=self.precision),
Constant(0.0, precision=self.precision),
precision=self.precision,
tag="tho",
debug=debug_multi)
rcp = ReciprocalSeed(_vx_mant, precision=self.precision, tag="rcp")
r = Multiplication(rcp,
_vx_mant,
precision=self.precision,
tag="r")
int_format = self.precision.get_integer_format()
# argument reduction
# TODO: detect if single operand inverse seed is supported by the targeted architecture
pre_arg_red_index = TypeCast(BitLogicAnd(
TypeCast(ReciprocalSeed(_vx_mant,
precision=self.precision,
tag="seed",
debug=debug_multi,
silent=True),
precision=int_format),
Constant(-2, precision=int_format),
precision=int_format),
precision=self.precision,
tag="pre_arg_red_index",
debug=debug_multi)
arg_red_index = Select(Equal(table_index, 0),
1.0,
pre_arg_red_index,
tag="arg_red_index",
debug=debug_multi)
_red_vx = arg_red_index * _vx_mant - 1.0
inv_err = S2**-6
red_interval = Interval(1 - inv_err, 1 + inv_err)
_red_vx.set_attributes(tag="_red_vx",
debug=debug_multi,
interval=red_interval)
# return in case of standard (non-special) input
_log_inv_lo = Select(tho_cond,
TableLoad(log_table_tho, table_index, 1),
TableLoad(log_table, table_index, 1),
tag="log_inv_lo",
debug=debug_multi)
_log_inv_hi = Select(tho_cond,
TableLoad(log_table_tho, table_index, 0),
TableLoad(log_table, table_index, 0),
tag="log_inv_hi",
debug=debug_multi)
Log.report(Log.Info, "building mathematical polynomial")
approx_interval = Interval(-inv_err, inv_err)
poly_degree = sup(
guessdegree(
log(1 + sollya.x) / sollya.x, approx_interval, S2**
-(self.precision.get_field_size() + 1))) + 1
global_poly_object = Polynomial.build_from_approximation(
log(1 + x) / x, poly_degree,
[self.precision] * (poly_degree + 1), approx_interval,
sollya.absolute)
poly_object = global_poly_object.sub_poly(start_index=1)
Log.report(Log.Info, "generating polynomial evaluation scheme")
_poly = PolynomialSchemeEvaluator.generate_horner_scheme(
poly_object, _red_vx, unified_precision=self.precision)
_poly.set_attributes(tag="poly", debug=debug_multi)
Log.report(Log.Info, poly_object.get_sollya_object())
corr_exp = Conversion(_vx_exp if exp_corr_factor == None else
_vx_exp + exp_corr_factor,
precision=self.precision) + tho
corr_exp.set_attributes(tag="corr_exp", debug=debug_multi)
# _poly approximates log10(1+r)/r
# _poly * red_vx approximates log10(x)
m0h, m0l = Mul211(_red_vx, _poly)
m0h, m0l = Add212(_red_vx, m0h, m0l)
m0h.set_attributes(tag="m0h", debug=debug_multi)
m0l.set_attributes(tag="m0l")
l0_h = corr_exp * log2_hi
l0_l = corr_exp * log2_lo
l0_h.set_attributes(tag="l0_h")
l0_l.set_attributes(tag="l0_l")
rh, rl = Add222(l0_h, l0_l, m0h, m0l)
rh.set_attributes(tag="rh0", debug=debug_multi)
rl.set_attributes(tag="rl0", debug=debug_multi)
rh, rl = Add222(-_log_inv_hi, -_log_inv_lo, rh, rl)
rh.set_attributes(tag="rh", debug=debug_multi)
rl.set_attributes(tag="rl", debug=debug_multi)
if sollya.log(self.basis) != 1.0:
lbh = self.precision.round_sollya_object(
1 / sollya.log(self.basis))
lbl = self.precision.round_sollya_object(
1 / sollya.log(self.basis) - lbh)
rh, rl = Mul222(rh, rl, lbh, lbl)
return rh
else:
return rh
def generate_scheme(self):
"""Produce an abstract scheme for the logarithm.
This abstract scheme will be used by the code generation backend.
"""
if self.precision not in [ML_Binary32, ML_Binary64]:
Log.report(Log.Error, "The demanded precision is not supported")
vx = self.implementation.add_input_variable("x", self.precision)
def default_bool_convert(optree, precision=None, **kw):
return bool_convert(optree, precision, -1, 0, **kw) \
if isinstance(self.processor, VectorBackend) \
else bool_convert(optree, precision, 1, 0, **kw)
precision = self.precision.sollya_object
int_prec = self.precision.get_integer_format()
Log.report(Log.Info, "int_prec is %s" % int_prec)
uint_prec = self.precision.get_unsigned_integer_format()
Log.report(Log.Info, "MDL constants")
cgpe_scheme_idx = int(self.cgpe_index)
table_index_size = int(self.tbl_index_size)
#
table_nb_elements = 2**(table_index_size)
table_dimensions = [2*table_nb_elements] # two values are stored for each element
field_size = Constant(self.precision.get_field_size(),
precision = int_prec,
tag = 'field_size')
if self.log_radix == EXP_1:
log2_hi = Constant(
round(log(2), precision, sollya.RN),
precision = self.precision,
tag = 'log2_hi')
log2_lo = Constant(
round(log(2) - round(log(2), precision, sollya.RN),
precision, sollya.RN),
precision = self.precision,
tag = 'log2_lo')
elif self.log_radix == 10:
log2_hi = Constant(
round(log10(2), precision, sollya.RN),
precision = self.precision,
tag = 'log2_hi')
log2_lo = Constant(
round(log10(2) - round(log10(2), precision, sollya.RN),
precision, sollya.RN),
precision = self.precision,
tag = 'log2_lo')
# ... if log_radix == '2' then log2(2) == 1
# subnormal_mask aims at trapping positive subnormals except zero.
# That's why we will subtract 1 to the integer bitstring of the input, and
# then compare for Less (strict) the resulting integer bitstring to this
# mask, e.g. 0x7fffff for binary32.
if self.no_subnormal == False:
subnormal_mask = Constant((1 << self.precision.get_field_size()) - 1,
precision = int_prec, tag = 'subnormal_mask')
fp_one = Constant(1.0, precision = self.precision, tag = 'fp_one')
fp_one_as_uint = TypeCast(fp_one, precision = uint_prec,
tag = 'fp_one_as_uint')
int_zero = Constant(0, precision = int_prec, tag = 'int_zero')
int_one = Constant(1, precision = int_prec, tag = 'int_one')
table_mantissa_half_ulp = Constant(
1 << (self.precision.field_size - table_index_size - 1),
precision = int_prec
)
table_s_exp_index_mask = Constant(
~((table_mantissa_half_ulp.get_value() << 1) - 1),
precision = uint_prec
)
Log.report(Log.Info, "MDL table")
# The table holds approximations of -log(2^tau * r_i) so we first compute
# the index value for which tau changes from 1 to 0.
cut = sqrt(2.)
tau_index_limit = floor(table_nb_elements * (2./cut - 1))
sollya_logtbl = [
(-log1p(float(i) / table_nb_elements)
+ (0 if i <= tau_index_limit else log(2.))) / log(self.log_radix)
for i in range(table_nb_elements)
]
# ...
init_logtbl_hi = [
round(sollya_logtbl[i],
self.precision.get_mantissa_size(),
sollya.RN)
for i in range(table_nb_elements)
]
init_logtbl_lo = [
round(sollya_logtbl[i] - init_logtbl_hi[i],
self.precision.get_mantissa_size(),
sollya.RN)
for i in range(table_nb_elements)
]
init_logtbl = [tmp[i] for i in range(len(init_logtbl_hi)) for tmp in [init_logtbl_hi, init_logtbl_lo]]
log1p_table = ML_NewTable(dimensions = table_dimensions,
storage_precision = self.precision,
init_data = init_logtbl,
tag = 'ml_log1p_table')
# ...
if self.no_rcp:
sollya_rcptbl = [
(1/((1+float(i)/table_nb_elements)+2**(-1-int(self.tbl_index_size))))
for i in range(table_nb_elements)
]
init_rcptbl = [
round(sollya_rcptbl[i],
int(self.tbl_index_size)+1, # self.precision.get_mantissa_size(),
sollya.RN)
for i in range(table_nb_elements)
]
rcp_table = ML_NewTable(dimensions = [table_nb_elements],
storage_precision = self.precision,
init_data = init_rcptbl,
tag = 'ml_rcp_table')
# ...
Log.report(Log.Info, 'MDL unified subnormal handling')
vx_as_int = TypeCast(vx, precision = int_prec, tag = 'vx_as_int')
if self.no_subnormal == False:
vx_as_uint = TypeCast(vx, precision = uint_prec, tag = 'vx_as_uint')
# Avoid the 0.0 case by subtracting 1 from vx_as_int
tmp = Comparison(vx_as_int - 1, subnormal_mask,
specifier = Comparison.Less)
is_subnormal = default_bool_convert(
tmp, # Will catch negative values as well as NaNs with sign bit set
precision = int_prec)
is_subnormal.set_attributes(tag = "is_subnormal")
if not(isinstance(self.processor, VectorBackend)):
is_subnormal = Subtraction(Constant(0, precision = int_prec),
is_subnormal,
precision = int_prec)
#################################################
# Vectorizable integer based subnormal handling #
#################################################
# 1. lzcnt
# custom lzcount-like for subnormal numbers using FPU (see draft article)
Zi = BitLogicOr(vx_as_uint, fp_one_as_uint, precision = uint_prec, tag="Zi")
Zf = Subtraction(
TypeCast(Zi, precision = self.precision),
fp_one,
precision = self.precision,
tag="Zf")
# Zf exponent is -(nlz(x) - exponent_size).
# 2. compute shift value
# Vectorial comparison on x86+sse/avx is going to look like
# '|0x00|0xff|0x00|0x00|' and that's why we use Negate.
# But for scalar code generation, comparison will rather be either 0 or 1
# in C. Thus mask below won't be correct for a scalar implementation.
# FIXME: Can we know the backend that will be called and choose in
# consequence? Should we make something arch-agnostic instead?
#
n_value = BitLogicAnd(
Addition(
DirtyExponentExtraction(Zf, self.precision),
Constant(
self.precision.get_bias(),
precision = int_prec),
precision = int_prec),
is_subnormal,
precision = int_prec,
tag = "n_value")
alpha = Negation(n_value, tag="alpha")
#
# 3. shift left
# renormalized_mantissa = BitLogicLeftShift(vx_as_int, value)
normal_vx_as_int = BitLogicLeftShift(vx_as_int, alpha)
# 4. set exponent to the right value
# Compute the exponent to add : (p-1)-(value) + 1 = p-1-value
# The final "+ 1" comes from the fact that once renormalized, the
# floating-point datum has a biased exponent of 1
#tmp0 = Subtraction(
# field_size,
# value,
# precision = int_prec,
# tag="tmp0")
# Set the value to 0 if the number is not subnormal
#tmp1 = BitLogicAnd(tmp0, is_subnormal)
#renormalized_exponent = BitLogicLeftShift(
# tmp1,
# field_size
# )
else: # no_subnormal == True
normal_vx_as_int = vx_as_int
#normal_vx_as_int = renormalized_mantissa + renormalized_exponent
normal_vx = TypeCast(normal_vx_as_int, precision = self.precision,
tag = 'normal_vx')
# alpha = BitLogicAnd(field_size, is_subnormal, tag = 'alpha')
# XXX Extract the mantissa, see if this is supported in the x86 vector
# backend or if it still uses the support_lib.
vx_mantissa = MantissaExtraction(normal_vx, precision = self.precision)
Log.report(Log.Info, "MDL scheme")
if self.force_division == True:
rcp_m = Division(fp_one, vx_mantissa, precision = self.precision)
elif self.no_rcp == False:
rcp_m = ReciprocalSeed(vx_mantissa, precision = self.precision)
if not self.processor.is_supported_operation(rcp_m):
if self.precision == ML_Binary64:
# Try using a binary32 FastReciprocal
binary32_m = Conversion(vx_mantissa, precision = ML_Binary32)
rcp_m = ReciprocalSeed(binary32_m, precision = ML_Binary32)
rcp_m = Conversion(rcp_m, precision = ML_Binary64)
if not self.processor.is_supported_operation(rcp_m):
# FIXME An approximation table could be used instead but for vector
# implementations another GATHER would be required.
# However this may well be better than a division...
rcp_m = Division(fp_one, vx_mantissa, precision = self.precision)
else: # ... use a look-up table
rcp_shift = BitLogicLeftShift(normal_vx_as_int, self.precision.get_exponent_size() + 1)
rcp_idx = BitLogicRightShift(rcp_shift, self.precision.get_exponent_size() + 1 + self.precision.get_field_size() - int(self.tbl_index_size))
rcp_m = TableLoad(rcp_table, rcp_idx, tag = 'rcp_idx',
debug = debug_multi)
#
rcp_m.set_attributes(tag = 'rcp_m')
# exponent is normally either 0 or -1, since m is in [1, 2). Possible
# optimization?
# exponent = ExponentExtraction(rcp_m, precision = self.precision,
# tag = 'exponent')
ri_round = TypeCast(
Addition(
TypeCast(rcp_m, precision = int_prec),
table_mantissa_half_ulp,
precision = int_prec
),
precision = uint_prec
)
ri_fast_rndn = BitLogicAnd(
ri_round,
table_s_exp_index_mask,
tag = 'ri_fast_rndn',
precision = uint_prec
)
# u = m * ri - 1
ul = None
if self.no_rcp == True: # ... u does not fit on a single word
tmp_u, tmp_ul = Mul211(vx_mantissa,
TypeCast(ri_fast_rndn, precision = self.precision),
fma = (self.no_fma == False))
fp_minus_one = Constant(-1.0, precision = self.precision, tag = 'fp_minus_one')
u, ul = Add212(fp_minus_one, tmp_u, tmp_ul)
u.set_attributes(tag='uh')
ul.set_attributes(tag='ul')
elif self.no_fma == False:
u = FusedMultiplyAdd(
vx_mantissa,
TypeCast(ri_fast_rndn, precision = self.precision),
fp_one,
specifier = FusedMultiplyAdd.Subtract,
tag = 'u')
else: # disable FMA
# tmph + tmpl = m * ri, where tmph ~ 1
tmph, tmpl = Mul211(vx_mantissa,
TypeCast(ri_fast_rndn, precision = self.precision),
fma = False)
# u_tmp = tmph - 1 ... exact due to Sterbenz
u_tmp = Subtraction(tmph, fp_one, precision = self.precision)
# u = u_tmp - tmpl ... exact since the result u is representable as a single word
u = Addition(u_tmp, tmpl, precision = self.precision, tag = 'u')
unneeded_bits = Constant(
self.precision.field_size - table_index_size,
precision=uint_prec,
tag="unneeded_bits"
)
assert self.precision.field_size - table_index_size >= 0
ri_bits = BitLogicRightShift(
ri_fast_rndn,
unneeded_bits,
precision = uint_prec,
tag = "ri_bits"
)
# Retrieve mantissa's MSBs + first bit of exponent, for tau computation in case
# exponent is 0 (i.e. biased 127, i.e. first bit of exponent is set.).
# In this particular case, i = 0 but tau is 1
# table_index does not need to be as long as uint_prec might be,
# try and keep it the size of size_t.
size_t_prec = ML_UInt32
signed_size_t_prec = ML_Int32
table_index_mask = Constant(
(1 << (table_index_size + 1)) - 1,
precision = size_t_prec
)
table_index = BitLogicAnd(
Conversion(ri_bits, precision = size_t_prec),
table_index_mask,
tag = 'table_index',
precision = size_t_prec
)
# Compute tau using the tau_index_limit value.
tmp = default_bool_convert(
Comparison(
TypeCast(table_index, precision = signed_size_t_prec),
Constant(tau_index_limit, precision = signed_size_t_prec),
specifier = Comparison.Greater
if isinstance(self.processor, VectorBackend)
else Comparison.LessOrEqual
),
precision = signed_size_t_prec,
tag="tmp"
)
# A true tmp will typically be -1 for VectorBackends, but 1 for standard C.
tau = Conversion(
Addition(tmp, Constant(1, precision=signed_size_t_prec), precision = signed_size_t_prec, tag="pre_add")
if isinstance(self.processor, VectorBackend)
else tmp,
precision=int_prec,
tag="pre_tau"
)
tau.set_attributes(tag = 'tau')
# Update table_index: keep only table_index_size bits
table_index_hi = BitLogicAnd(
table_index,
Constant((1 << table_index_size) - 1, precision = size_t_prec),
precision = size_t_prec
)
# table_index_hi = table_index_hi << 1
table_index_hi = BitLogicLeftShift(
table_index_hi,
Constant(1, precision = size_t_prec),
precision = size_t_prec,
tag = "table_index_hi"
)
# table_index_lo = table_index_hi + 1
table_index_lo = Addition(
table_index_hi,
Constant(1, precision = size_t_prec),
precision = size_t_prec,
tag = "table_index_lo"
)
tbl_hi = TableLoad(log1p_table, table_index_hi, tag = 'tbl_hi',
debug = debug_multi)
tbl_lo = TableLoad(log1p_table, table_index_lo, tag = 'tbl_lo',
debug = debug_multi)
# Compute exponent e + tau - alpha, but first subtract the bias.
if self.no_subnormal == False:
tmp_eptau = Addition(
Addition(
BitLogicRightShift(
normal_vx_as_int,
field_size,
tag = 'exponent',
interval = self.precision.get_exponent_interval(),
precision = int_prec),
Constant(
self.precision.get_bias(),
precision = int_prec)),
tau,
tag = 'tmp_eptau',
precision = int_prec)
exponent = Subtraction(tmp_eptau, alpha, precision = int_prec)
else:
exponent = Addition(
Addition(
BitLogicRightShift(
normal_vx_as_int,
field_size,
tag = 'exponent',
interval = self.precision.get_exponent_interval(),
precision = int_prec),
Constant(
self.precision.get_bias(),
precision = int_prec)),
tau,
tag = 'tmp_eptau',
precision = int_prec)
#
fp_exponent = Conversion(exponent, precision = self.precision,
tag = 'fp_exponent')
Log.report(Log.Info, 'MDL polynomial approximation')
if self.log_radix == EXP_1:
sollya_function = log(1 + sollya.x)
elif self.log_radix == 2:
sollya_function = log2(1 + sollya.x)
elif self.log_radix == 10:
sollya_function = log10(1 + sollya.x)
# ...
if self.force_division == True: # rcp accuracy is 2^(-p)
boundrcp = 2**(-self.precision.get_precision())
else:
boundrcp = 1.5 * 2**(-12) # ... see Intel intrinsics guide
if self.precision in [ML_Binary64]:
if not self.processor.is_supported_operation(rcp_m):
boundrcp = (1+boundrcp)*(1+2**(-24)) - 1
else:
boundrcp = 2**(-14) # ... see Intel intrinsics guide
arg_red_mag = boundrcp + 2**(-table_index_size-1) + boundrcp * 2**(-table_index_size-1)
if self.no_rcp == False:
approx_interval = Interval(-arg_red_mag, arg_red_mag)
else:
approx_interval = Interval(-2**(-int(self.tbl_index_size)+1),2**(-int(self.tbl_index_size)+1))
max_eps = 2**-(2*(self.precision.get_field_size()))
Log.report(Log.Info, "max acceptable error for polynomial = {}".format(float.hex(max_eps)))
poly_degree = sup(
guessdegree(
sollya_function,
approx_interval,
max_eps,
)
)
Log.report(Log.Info, "poly degree is ", poly_degree)
if self.log_radix == EXP_1:
poly_object = Polynomial.build_from_approximation(
sollya_function,
range(2, int(poly_degree) + 1), # Force 1st 2 coeffs to 0 and 1, resp.
# Emulate double-self.precision coefficient formats
[self.precision.get_mantissa_size()*2 + 1]*(poly_degree - 1),
approx_interval,
sollya.absolute,
0 + sollya._x_) # Force the first 2 coefficients to 0 and 1, resp.
else: # ... == '2' or '10'
poly_object = Polynomial.build_from_approximation(
sollya_function,
range(1, int(poly_degree) + 1), # Force 1st coeff to 0
# Emulate double-self.precision coefficient formats
[self.precision.get_mantissa_size()*2 + 1]*(poly_degree),
approx_interval,
sollya.absolute,
0) # Force the first coefficients to 0
Log.report(Log.Info, str(poly_object))
constant_precision = ML_SingleSingle if self.precision == ML_Binary32 \
else ML_DoubleDouble if self.precision == ML_Binary64 \
else None
if is_cgpe_available():
log1pu_poly = PolynomialSchemeEvaluator.generate_cgpe_scheme(
poly_object,
u,
unified_precision = self.precision,
constant_precision = constant_precision, scheme_id = cgpe_scheme_idx
)
else:
Log.report(Log.Warning,
"CGPE not available, falling back to std poly evaluator")
log1pu_poly = PolynomialSchemeEvaluator.generate_horner_scheme(
poly_object,
u,
unified_precision = self.precision,
constant_precision = constant_precision
)
# XXX Dirty implementation of double-(self.precision) poly
def dirty_poly_node_conversion(node, variable_h, variable_l, use_fma):
return dirty_multi_node_expand(
node, self.precision, mem_map={variable_h: (variable_h, variable_l)}, fma=use_fma)
log1pu_poly_hi, log1pu_poly_lo = dirty_poly_node_conversion(log1pu_poly, u, ul,
use_fma=(self.no_fma == False))
log1pu_poly_hi.set_attributes(tag = 'log1pu_poly_hi')
log1pu_poly_lo.set_attributes(tag = 'log1pu_poly_lo')
# Compute log(2) * (e + tau - alpha)
if self.log_radix != 2: # 'e' or '10'
log2e_hi, log2e_lo = Mul212(fp_exponent, log2_hi, log2_lo,
fma = (self.no_fma == False))
# Add log1p(u)
if self.log_radix != 2: # 'e' or '10'
tmp_res_hi, tmp_res_lo = Add222(log2e_hi, log2e_lo,
log1pu_poly_hi, log1pu_poly_lo)
else:
tmp_res_hi, tmp_res_lo = Add212(fp_exponent,
log1pu_poly_hi, log1pu_poly_lo)
# Add -log(2^(tau)/m) approximation retrieved by two table lookups
logx_hi = Add122(tmp_res_hi, tmp_res_lo, tbl_hi, tbl_lo)[0]
logx_hi.set_attributes(tag = 'logx_hi')
scheme = Return(logx_hi, precision = self.precision)
return scheme
def generate_reduced_log_split(self,
_vx_mant,
log_f,
inv_approx_table,
log_table,
log_table_tho=None,
corr_exp=None,
tho_cond=None):
""" Generate a logarithm approximation (log_f(_vx_mant) + corr_exp) for a reduced argument
_vx_mant which is assumed to be within [1, 2[ (i.e. an extracted mantissa)
Addiing exponent correction (optionnal) """
log2_hi_value = round(
log_f(2),
self.precision.get_field_size() -
(self.precision.get_exponent_size() + 1), RN)
log2_lo_value = round(
log_f(2) - log2_hi_value, self.precision.sollya_object, RN)
log2_hi = Constant(log2_hi_value, precision=self.precision)
log2_lo = Constant(log2_lo_value, precision=self.precision)
table_index = inv_approx_table.index_function(_vx_mant)
table_index.set_attributes(tag="table_index", debug=debug_multi)
rcp = ReciprocalSeed(_vx_mant, precision=self.precision, tag="rcp")
r = Multiplication(rcp, _vx_mant, precision=self.precision, tag="r")
int_format = self.precision.get_integer_format()
# argument reduction
# TODO: detect if single operand inverse seed is supported by the targeted architecture
pre_arg_red_index = TypeCast(BitLogicAnd(
TypeCast(ReciprocalSeed(_vx_mant,
precision=self.precision,
tag="seed",
debug=debug_multi,
silent=True),
precision=int_format),
Constant(-2, precision=int_format),
precision=int_format),
precision=self.precision,
tag="pre_arg_red_index",
debug=debug_multi)
C0 = Constant(0, precision=table_index.get_precision())
index_comp_0 = Equal(table_index,
C0,
tag="index_comp_0",
debug=debug_multi)
arg_red_index = Select(index_comp_0,
1.0,
pre_arg_red_index,
tag="arg_red_index",
debug=debug_multi)
#_red_vx = arg_red_index * _vx_mant - 1.0
_red_vx = FMA(arg_red_index, _vx_mant, -1.0)
inv_err = S2**-6
red_interval = Interval(1 - inv_err, 1 + inv_err)
_red_vx.set_attributes(tag="_red_vx",
debug=debug_multi,
interval=red_interval)
# return in case of standard (non-special) input
if not tho_cond is None:
assert not log_table_tho is None
_log_inv_lo = Select(tho_cond,
TableLoad(log_table_tho, table_index, 1),
TableLoad(log_table, table_index, 1),
tag="log_inv_lo",
debug=debug_multi)
_log_inv_hi = Select(tho_cond,
TableLoad(log_table_tho, table_index, 0),
TableLoad(log_table, table_index, 0),
tag="log_inv_hi",
debug=debug_multi)
else:
assert log_table_tho is None
_log_inv_lo = TableLoad(log_table, table_index, 1)
_log_inv_hi = TableLoad(log_table, table_index, 0)
Log.report(Log.Info, "building mathematical polynomial")
approx_interval = Interval(-inv_err, inv_err)
poly_degree = sup(
guessdegree(
log(1 + sollya.x) / sollya.x, approx_interval, S2**
-(self.precision.get_field_size() + 1))) + 1
global_poly_object = Polynomial.build_from_approximation(
log(1 + x) / x, poly_degree, [self.precision] * (poly_degree + 1),
approx_interval, sollya.absolute)
poly_object = global_poly_object.sub_poly(start_index=1)
Log.report(Log.Info, "generating polynomial evaluation scheme")
_poly = PolynomialSchemeEvaluator.generate_horner_scheme(
poly_object, _red_vx, unified_precision=self.precision)
_poly.set_attributes(tag="poly", debug=debug_multi)
Log.report(Log.Info, "{}", poly_object.get_sollya_object())
# _poly approximates log10(1+r)/r
# _poly * red_vx approximates log10(x)
m0h, m0l = Mul211(_red_vx, _poly)
m0h, m0l = Add212(_red_vx, m0h, m0l)
m0h.set_attributes(tag="m0h", debug=debug_multi)
m0l.set_attributes(tag="m0l")
if not corr_exp is None:
l0_h = corr_exp * log2_hi
l0_l = corr_exp * log2_lo
l0_h.set_attributes(tag="l0_h")
l0_l.set_attributes(tag="l0_l")
rh, rl = Add222(l0_h, l0_l, m0h, m0l)
else:
# bypass exponent addition if no exponent correction is disabled
rh, rl = m0h, m0l
rh.set_attributes(tag="rh0", debug=debug_multi)
rl.set_attributes(tag="rl0", debug=debug_multi)
rh, rl = Add222(-_log_inv_hi, -_log_inv_lo, rh, rl)
rh.set_attributes(tag="rh", debug=debug_multi)
rl.set_attributes(tag="rl", debug=debug_multi)
# FIXME: log<self.basis>(vx) is computed as log(vx) / log(self.basis)
# which could be optimized for some value of self.basis (e.g. 2)
if sollya.log(self.basis) != 1.0:
lbh = self.precision.round_sollya_object(1 /
sollya.log(self.basis))
lbl = self.precision.round_sollya_object(1 /
sollya.log(self.basis) -
lbh)
rh, rl = Mul222(rh, rl, lbh, lbl)
return rh
else:
return rh