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 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 generate_reduction_fptaylor(x):
# get k, must be the same at endpoints
unround_k = x * n_invlog2
k_low = sollya.floor(sollya.inf(unround_k))
k_high = sollya.floor(sollya.sup(unround_k))
if not (k_low == k_high or (k_low == -1 and sollya.sup(x) == 0)):
assert False, "Interval must not straddle multples of log(2)"
k = int(k_low)
r = x - k * n_log2
twok = 2**k
x_low = sollya.inf(x)
x_high = sollya.sup(x)
query = "\n".join([
"Variables", " real x in [{},{}];".format(x_low, x_high),
"Definitions", " whole rnd64= {} * {};".format(k, n_log2),
" r rnd64= x - whole;", " poly rnd64= {};".format(poly_expr),
" retval rnd64= poly*{};".format(twok), "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), r, 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), r, 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):
unround_e = sollya.log2(I)
e_low = sollya.floor(sollya.inf(unround_e))
e_high = sollya.floor(sollya.sup(unround_e))
if e_low != e_high:
assert False, "Interval must not stradle a binade"
e = int(e_low) + 1
z = x / (2**e) * 0.5
query = "\n".join(
["Variables",
" real z in [{},{}];".format(sollya.inf(z), sollya.sup(z)),
"Definitions",
" poly rnd64= {};".format(poly_expr),
" retval rnd64= {}*{} + poly;".format(e, n_log2),
"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.log(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.log(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