def test_PythonCodePrinter():
prntr = PythonCodePrinter()
assert not prntr.module_imports
assert prntr.doprint(x**y) == 'x**y'
assert prntr.doprint(Mod(x, 2)) == 'x % 2'
assert prntr.doprint(-Mod(x, y)) == '-(x % y)'
assert prntr.doprint(Mod(-x, y)) == '(-x) % y'
assert prntr.doprint(And(x, y)) == 'x and y'
assert prntr.doprint(Or(x, y)) == 'x or y'
assert not prntr.module_imports
assert prntr.doprint(pi) == 'math.pi'
assert prntr.module_imports == {'math': {'pi'}}
assert prntr.doprint(x**Rational(1, 2)) == 'math.sqrt(x)'
assert prntr.doprint(sqrt(x)) == 'math.sqrt(x)'
assert prntr.module_imports == {'math': {'pi', 'sqrt'}}
assert prntr.doprint(acos(x)) == 'math.acos(x)'
assert prntr.doprint(Assignment(x, 2)) == 'x = 2'
assert prntr.doprint(Piecewise((1, Eq(x, 0)),
(2, x>6))) == '((1) if (x == 0) else (2) if (x > 6) else None)'
assert prntr.doprint(Piecewise((2, Le(x, 0)),
(3, Gt(x, 0)), evaluate=False)) == '((2) if (x <= 0) else'\
' (3) if (x > 0) else None)'
assert prntr.doprint(sign(x)) == '(0.0 if x == 0 else math.copysign(1, x))'
assert prntr.doprint(p[0, 1]) == 'p[0, 1]'
assert prntr.doprint(KroneckerDelta(x,y)) == '(1 if x == y else 0)'
assert prntr.doprint((2,3)) == "(2, 3)"
assert prntr.doprint([2,3]) == "[2, 3]"
def test_ccode_exceptions():
assert ccode(gamma(x), standard='C99') == "tgamma(x)"
assert 'not supported in c' in ccode(gamma(x), standard='C89').lower()
assert ccode(ceiling(x)) == "ceil(x)"
assert ccode(Abs(x)) == "fabs(x)"
assert ccode(gamma(x)) == "tgamma(x)"
r, s = symbols('r,s', real=True)
assert ccode(Mod(ceiling(r), ceiling(s))) == "((ceil(r)) % (ceil(s)))"
assert ccode(Mod(r, s)) == "fmod(r, s)"
def test_C99CodePrinter__precision():
n = symbols('n', integer=True)
f32_printer = C99CodePrinter(dict(type_aliases={real: float32}))
f64_printer = C99CodePrinter(dict(type_aliases={real: float64}))
f80_printer = C99CodePrinter(dict(type_aliases={real: float80}))
assert f32_printer.doprint(sin(x+2.1)) == 'sinf(x + 2.1F)'
assert f64_printer.doprint(sin(x+2.1)) == 'sin(x + 2.1000000000000001)'
assert f80_printer.doprint(sin(x+Float('2.0'))) == 'sinl(x + 2.0L)'
for printer, suffix in zip([f32_printer, f64_printer, f80_printer], ['f', '', 'l']):
def check(expr, ref):
assert printer.doprint(expr) == ref.format(s=suffix, S=suffix.upper())
check(Abs(n), 'abs(n)')
check(Abs(x + 2.0), 'fabs{s}(x + 2.0{S})')
check(sin(x + 4.0)**cos(x - 2.0), 'pow{s}(sin{s}(x + 4.0{S}), cos{s}(x - 2.0{S}))')
check(exp(x*8.0), 'exp{s}(8.0{S}*x)')
check(exp2(x), 'exp2{s}(x)')
check(expm1(x*4.0), 'expm1{s}(4.0{S}*x)')
check(Mod(n, 2), '((n) % (2))')
check(Mod(2*n + 3, 3*n + 5), '((2*n + 3) % (3*n + 5))')
check(Mod(x + 2.0, 3.0), 'fmod{s}(1.0{S}*x + 2.0{S}, 3.0{S})')
check(Mod(x, 2.0*x + 3.0), 'fmod{s}(1.0{S}*x, 2.0{S}*x + 3.0{S})')
check(log(x/2), 'log{s}((1.0{S}/2.0{S})*x)')
check(log10(3*x/2), 'log10{s}((3.0{S}/2.0{S})*x)')
check(log2(x*8.0), 'log2{s}(8.0{S}*x)')
check(log1p(x), 'log1p{s}(x)')
check(2**x, 'pow{s}(2, x)')
check(2.0**x, 'pow{s}(2.0{S}, x)')
check(x**3, 'pow{s}(x, 3)')
check(x**4.0, 'pow{s}(x, 4.0{S})')
check(sqrt(3+x), 'sqrt{s}(x + 3)')
check(Cbrt(x-2.0), 'cbrt{s}(x - 2.0{S})')
check(hypot(x, y), 'hypot{s}(x, y)')
check(sin(3.*x + 2.), 'sin{s}(3.0{S}*x + 2.0{S})')
check(cos(3.*x - 1.), 'cos{s}(3.0{S}*x - 1.0{S})')
check(tan(4.*y + 2.), 'tan{s}(4.0{S}*y + 2.0{S})')
check(asin(3.*x + 2.), 'asin{s}(3.0{S}*x + 2.0{S})')
check(acos(3.*x + 2.), 'acos{s}(3.0{S}*x + 2.0{S})')
check(atan(3.*x + 2.), 'atan{s}(3.0{S}*x + 2.0{S})')
check(atan2(3.*x, 2.*y), 'atan2{s}(3.0{S}*x, 2.0{S}*y)')
check(sinh(3.*x + 2.), 'sinh{s}(3.0{S}*x + 2.0{S})')
check(cosh(3.*x - 1.), 'cosh{s}(3.0{S}*x - 1.0{S})')
check(tanh(4.0*y + 2.), 'tanh{s}(4.0{S}*y + 2.0{S})')
check(asinh(3.*x + 2.), 'asinh{s}(3.0{S}*x + 2.0{S})')
check(acosh(3.*x + 2.), 'acosh{s}(3.0{S}*x + 2.0{S})')
check(atanh(3.*x + 2.), 'atanh{s}(3.0{S}*x + 2.0{S})')
check(erf(42.*x), 'erf{s}(42.0{S}*x)')
check(erfc(42.*x), 'erfc{s}(42.0{S}*x)')
check(gamma(x), 'tgamma{s}(x)')
check(loggamma(x), 'lgamma{s}(x)')
check(ceiling(x + 2.), "ceil{s}(x + 2.0{S})")
check(floor(x + 2.), "floor{s}(x + 2.0{S})")
check(fma(x, y, -z), 'fma{s}(x, y, -z)')
check(Max(x, 8.0, x**4.0), 'fmax{s}(8.0{S}, fmax{s}(x, pow{s}(x, 4.0{S})))')
check(Min(x, 2.0), 'fmin{s}(2.0{S}, x)')
def test_ccode_exceptions():
assert ccode(gamma(x), standard='C99') == "tgamma(x)"
gamma_c89 = ccode(gamma(x), standard='C89')
assert 'not supported in c' in gamma_c89.lower()
gamma_c89 = ccode(gamma(x), standard='C89', allow_unknown_functions=False)
assert 'not supported in c' in gamma_c89.lower()
gamma_c89 = ccode(gamma(x), standard='C89', allow_unknown_functions=True)
assert not 'not supported in c' in gamma_c89.lower()
assert ccode(ceiling(x)) == "ceil(x)"
assert ccode(Abs(x)) == "fabs(x)"
assert ccode(gamma(x)) == "tgamma(x)"
r, s = symbols('r,s', real=True)
assert ccode(Mod(ceiling(r), ceiling(s))) == "((ceil(r)) % (ceil(s)))"
assert ccode(Mod(r, s)) == "fmod(r, s)"
def perform_operation(self, lhs, rhs, op):
"""Performs operation supported by the SymPy core
Returns
=======
combined_variable: list
contains variable content and type of variable
"""
lhs_value = self.get_expr_for_operand(lhs)
rhs_value = self.get_expr_for_operand(rhs)
if op == '+':
return [Add(lhs_value, rhs_value), 'expr']
if op == '-':
return [Add(lhs_value, -rhs_value), 'expr']
if op == '*':
return [Mul(lhs_value, rhs_value), 'expr']
if op == '/':
return [Mul(lhs_value, Pow(rhs_value, Integer(-1))), 'expr']
if op == '%':
return [Mod(lhs_value, rhs_value), 'expr']
if op in ['<', '<=', '>', '>=', '==', '!=']:
return [Rel(lhs_value, rhs_value, op), 'expr']
if op == '&&':
return [And(as_Boolean(lhs_value), as_Boolean(rhs_value)), 'expr']
if op == '||':
return [Or(as_Boolean(lhs_value), as_Boolean(rhs_value)), 'expr']
if op == '=':
return [Assignment(Variable(lhs_value), rhs_value), 'expr']
if op in ['+=', '-=', '*=', '/=', '%=']:
return [aug_assign(Variable(lhs_value), op[0], rhs_value), 'expr']
def test_PythonCodePrinter():
prntr = PythonCodePrinter()
assert not prntr.module_imports
assert prntr.doprint(x**y) == "x**y"
assert prntr.doprint(Mod(x, 2)) == "x % 2"
assert prntr.doprint(And(x, y)) == "x and y"
assert prntr.doprint(Or(x, y)) == "x or y"
assert not prntr.module_imports
assert prntr.doprint(pi) == "math.pi"
assert prntr.module_imports == {"math": {"pi"}}
assert prntr.doprint(x**Rational(1, 2)) == "math.sqrt(x)"
assert prntr.doprint(sqrt(x)) == "math.sqrt(x)"
assert prntr.module_imports == {"math": {"pi", "sqrt"}}
assert prntr.doprint(acos(x)) == "math.acos(x)"
assert prntr.doprint(Assignment(x, 2)) == "x = 2"
assert (prntr.doprint(Piecewise(
(1, Eq(x, 0)),
(2, x > 6))) == "((1) if (x == 0) else (2) if (x > 6) else None)")
assert (prntr.doprint(
Piecewise((2, Le(x, 0)), (3, Gt(x, 0)),
evaluate=False)) == "((2) if (x <= 0) else"
" (3) if (x > 0) else None)")
assert prntr.doprint(sign(x)) == "(0.0 if x == 0 else math.copysign(1, x))"
assert prntr.doprint(p[0, 1]) == "p[0, 1]"
def test_Functions():
assert rust_code(sin(x) ** cos(x)) == "x.sin().powf(x.cos())"
assert rust_code(abs(x)) == "x.abs()"
assert rust_code(ceiling(x)) == "x.ceil()"
assert rust_code(floor(x)) == "x.floor()"
# Automatic rewrite
assert rust_code(Mod(x, 3)) == 'x - 3*((1_f64/3.0)*x).floor()'
def compute(l):
# first check that no two differ by an integer
for i, b in enumerate(l):
if not b.is_Rational:
return oo
for j in range(i + 1, len(l)):
if not Mod((b - l[j]).simplify(), 1):
return oo
return reduce(ilcm, (x.q for x in l), 1)
def test_Mod():
assert jscode(Mod(x, y)) == '((x % y) + y) % y'
assert jscode(Mod(x, x + y)) == '((x % (x + y)) + (x + y)) % (x + y)'
p1, p2 = symbols('p1 p2', positive=True)
assert jscode(Mod(p1, p2)) == 'p1 % p2'
assert jscode(Mod(p1, p2 + 3)) == 'p1 % (p2 + 3)'
assert jscode(Mod(-3, -7, evaluate=False)) == '(-3) % (-7)'
assert jscode(-Mod(p1, p2)) == '-(p1 % p2)'
assert jscode(x * Mod(p1, p2)) == 'x*(p1 % p2)'
def test_PythonCodePrinter():
prntr = PythonCodePrinter()
assert not prntr.module_imports
assert prntr.doprint(x**y) == 'x**y'
assert prntr.doprint(Mod(x, 2)) == 'x % 2'
assert prntr.doprint(And(x, y)) == 'x and y'
assert prntr.doprint(Or(x, y)) == 'x or y'
assert not prntr.module_imports
assert prntr.doprint(pi) == 'math.pi'
assert prntr.module_imports == {'math': {'pi'}}
assert prntr.doprint(acos(x)) == 'math.acos(x)'
def test_ccode_functions2():
assert ccode(ceiling(x)) == "ceil(x)"
assert ccode(Abs(x)) == "fabs(x)"
assert ccode(gamma(x)) == "tgamma(x)"
r, s = symbols('r,s', real=True)
assert ccode(Mod(ceiling(r), ceiling(s))) == '((ceil(r) % ceil(s)) + '\
'ceil(s)) % ceil(s)'
assert ccode(Mod(r, s)) == "fmod(r, s)"
p1, p2 = symbols('p1 p2', integer=True, positive=True)
assert ccode(Mod(p1, p2)) == 'p1 % p2'
assert ccode(Mod(p1, p2 + 3)) == 'p1 % (p2 + 3)'
assert ccode(Mod(-3, -7, evaluate=False)) == '(-3) % (-7)'
assert ccode(-Mod(3, 7, evaluate=False)) == '-(3 % 7)'
assert ccode(r * Mod(p1, p2)) == 'r*(p1 % p2)'
assert ccode(Mod(p1, p2)**s) == 'pow(p1 % p2, s)'
n = symbols('n', integer=True, negative=True)
assert ccode(Mod(-n, p2)) == '(-n) % p2'
def test_PythonCodePrinter():
prntr = PythonCodePrinter()
assert not prntr.module_imports
assert prntr.doprint(x**y) == 'x**y'
assert prntr.doprint(Mod(x, 2)) == 'x % 2'
assert prntr.doprint(And(x, y)) == 'x and y'
assert prntr.doprint(Or(x, y)) == 'x or y'
assert not prntr.module_imports
assert prntr.doprint(pi) == 'math.pi'
assert prntr.module_imports == {'math': {'pi'}}
assert prntr.doprint(acos(x)) == 'math.acos(x)'
assert prntr.doprint(Assignment(x, 2)) == 'x = 2'
assert prntr.doprint(Piecewise((1, Eq(x, 0)),
(2, x>6))) == '((1) if (x == 0) else (2) if (x > 6) else None)'
assert prntr.doprint(Piecewise((2, Le(x, 0)),
(3, Gt(x, 0)), evaluate=False)) == '((2) if (x <= 0) else'\
' (3) if (x > 0) else None)'
def test_PythonCodePrinter():
prntr = PythonCodePrinter()
assert prntr.doprint(x**y) == 'x**y'
assert prntr.doprint(Mod(x, 2)) == 'x % 2'
assert prntr.doprint(And(x, y)) == 'x and y'
assert prntr.doprint(Or(x, y)) == 'x or y'
assert prntr.doprint(Piecewise((x, x > 1), (y, True))) == ('if x > 1:\n'
' return x\n'
'else:\n'
' return y')
pw = Piecewise((x, x > 1), (y, x > 0))
assert prntr.doprint(pw) == (
'if x > 1:\n'
' return x\n'
'elif x > 0:\n'
' return y\n'
'else:\n'
' raise NotImplementedError("Unhandled condition in: %s")' % pw)
def is_nilpotent_number(n):
"""
Check whether `n` is a nilpotent number. A number `n` is said to be
nilpotent if and only if every finite group of order `n` is nilpotent.
For more information see [1]_.
Examples
========
>>> from sympy.combinatorics.group_numbers import is_nilpotent_number
>>> from sympy import randprime
>>> is_nilpotent_number(21)
False
>>> is_nilpotent_number(randprime(1, 30)**12)
True
References
==========
.. [1] Pakianathan, J., Shankar, K., *Nilpotent Numbers*,
The American Mathematical Monthly, 107(7), 631-634.
"""
if n <= 0 or int(n) != n:
raise ValueError("n must be a positive integer, not %i" % n)
n = Integer(n)
prime_factors = list(factorint(n).items())
is_nilpotent = True
for p_j, a_j in prime_factors:
for p_i, a_i in prime_factors:
if any([Mod(Pow(p_i, k), p_j) == 1 for k in range(1, a_i + 1)]):
is_nilpotent = False
break
if not is_nilpotent:
break
return is_nilpotent
def test_Function_change_name():
assert mcode(abs(x)) == "abs(x)"
assert mcode(ceiling(x)) == "ceil(x)"
assert mcode(arg(x)) == "angle(x)"
assert mcode(im(x)) == "imag(x)"
assert mcode(re(x)) == "real(x)"
assert mcode(conjugate(x)) == "conj(x)"
assert mcode(chebyshevt(y, x)) == "chebyshevT(y, x)"
assert mcode(chebyshevu(y, x)) == "chebyshevU(y, x)"
assert mcode(laguerre(x, y)) == "laguerreL(x, y)"
assert mcode(Chi(x)) == "coshint(x)"
assert mcode(Shi(x)) == "sinhint(x)"
assert mcode(Ci(x)) == "cosint(x)"
assert mcode(Si(x)) == "sinint(x)"
assert mcode(li(x)) == "logint(x)"
assert mcode(loggamma(x)) == "gammaln(x)"
assert mcode(polygamma(x, y)) == "psi(x, y)"
assert mcode(RisingFactorial(x, y)) == "pochhammer(x, y)"
assert mcode(DiracDelta(x)) == "dirac(x)"
assert mcode(DiracDelta(x, 3)) == "dirac(3, x)"
assert mcode(Heaviside(x)) == "heaviside(x, 1/2)"
assert mcode(Heaviside(x, y)) == "heaviside(x, y)"
assert mcode(binomial(x, y)) == "bincoeff(x, y)"
assert mcode(Mod(x, y)) == "mod(x, y)"
def _eval_rewrite_as_gamma(self, n, **kwargs):
from sympy import gamma, Piecewise, sqrt
return 2**(n / 2) * gamma(n / 2 + 1) * Piecewise(
(1, Eq(Mod(n, 2), 0)), (sqrt(2 / pi), Eq(Mod(n, 2), 1)))
def _simplification_technique_1(rels):
"""
All relators are checked to see if they are of the form `gen^n`. If any
such relators are found then all other relators are processed for strings
in the `gen` known order.
Examples
========
>>> from sympy.combinatorics.free_group import free_group
>>> from sympy.combinatorics.fp_groups import _simplification_technique_1
>>> F, x, y = free_group("x, y")
>>> w1 = [x**2*y**4, x**3]
>>> _simplification_technique_1(w1)
[[(x, 3)], [(x, -1), (y, 4)]]
>>> w2 = [x**2*y**-4*x**5, x**3, x**2*y**8, y**5]
>>> _simplification_technique_1(w2)
[[(x, 3)], [(y, 5)], [(x, -1), (y, -2)], [(x, -1), (y, 1), (x, -1)]]
>>> w3 = [x**6*y**4, x**4]
>>> _simplification_technique_1(w3)
[[(x, 4)], [(x, 2), (y, 4)]]
"""
rels = list(set(rels))
rels.sort()
l_rels = len(rels)
# all syllables with single syllable
one_syllable_rels = set()
# since "nw" has a max size = l_rels, only identity element
# removal can possibly happen
nw = [None]*l_rels
for i in range(l_rels):
w = rels[i].identity_cyclic_reduction()
if w.number_syllables() == 1:
# replace one syllable relator with the corresponding inverse
# element, for ex. x**-4 -> x**4 in relator list
if w.array_form[0][1] < 0:
rels[i] = w**-1
one_syllable_rels.add(rels[i])
# since modifies the array rep., so should be
# added a list
nw[i] = list(rels[i].array_form)
# bound the exponent of relators, making use of the single
# syllable relators
for i in range(l_rels):
k = nw[i]
rels_i = rels[i]
for gen in one_syllable_rels:
n = gen.array_form[0][1]
gen_arr0 = gen.array_form[0][0]
j = len(k) - 1
while j >= 0:
if gen_arr0 == k[j][0] and gen is not rels_i:
t = Mod(k[j][1], n)
# multiple of one syllable relator
if t == 0:
del k[j]
zero_mul_simp(k, j - 1)
j = len(k)
# power should be bounded by (-n/2, n/2]
elif t <= n/2:
k[j] = k[j][0], Mod(k[j][1], n)
elif t > n/2:
k[j] = k[j][0], Mod(k[j][1], n) - n
j -= 1
return nw
def _diff_wrt_parameter(self, idx):
# Differentiation wrt a parameter can only be done in very special
# cases. In particular, if we want to differentiate with respect to
# `a`, all other gamma factors have to reduce to rational functions.
#
# Let MT denote mellin transform. Suppose T(-s) is the gamma factor
# appearing in the definition of G. Then
#
# MT(log(z)G(z)) = d/ds T(s) = d/da T(s) + ...
#
# Thus d/da G(z) = log(z)G(z) - ...
# The ... can be evaluated as a G function under the above conditions,
# the formula being most easily derived by using
#
# d Gamma(s + n) Gamma(s + n) / 1 1 1 \
# -- ------------ = ------------ | - + ---- + ... + --------- |
# ds Gamma(s) Gamma(s) \ s s + 1 s + n - 1 /
#
# which follows from the difference equation of the digamma function.
# (There is a similar equation for -n instead of +n).
# We first figure out how to pair the parameters.
an = list(self.an)
ap = list(self.aother)
bm = list(self.bm)
bq = list(self.bother)
if idx < len(an):
an.pop(idx)
else:
idx -= len(an)
if idx < len(ap):
ap.pop(idx)
else:
idx -= len(ap)
if idx < len(bm):
bm.pop(idx)
else:
bq.pop(idx - len(bm))
pairs1 = []
pairs2 = []
for l1, l2, pairs in [(an, bq, pairs1), (ap, bm, pairs2)]:
while l1:
x = l1.pop()
found = None
for i, y in enumerate(l2):
if not Mod((x - y).simplify(), 1):
found = i
break
if found is None:
raise NotImplementedError('Derivative not expressible '
'as G-function?')
y = l2[i]
l2.pop(i)
pairs.append((x, y))
# Now build the result.
res = log(self.argument) * self
for a, b in pairs1:
sign = 1
n = a - b
base = b
if n < 0:
sign = -1
n = b - a
base = a
for k in range(n):
res -= sign * meijerg(self.an + (base + k + 1, ), self.aother,
self.bm, self.bother +
(base + k + 0, ), self.argument)
for a, b in pairs2:
sign = 1
n = b - a
base = a
if n < 0:
sign = -1
n = a - b
base = b
for k in range(n):
res -= sign * meijerg(
self.an, self.aother + (base + k + 1, ), self.bm +
(base + k + 0, ), self.bother, self.argument)
return res
def _eval_rewrite_as_gamma(self, n, piecewise=True, **kwargs):
from sympy.functions.elementary.miscellaneous import sqrt
from sympy.functions.elementary.piecewise import Piecewise
from sympy.functions.special.gamma_functions import gamma
return 2**(n / 2) * gamma(n / 2 + 1) * Piecewise(
(1, Eq(Mod(n, 2), 0)), (sqrt(2 / pi), Eq(Mod(n, 2), 1)))
def test_C99CodePrinter__precision():
n = symbols("n", integer=True)
f32_printer = C99CodePrinter(dict(type_aliases={real: float32}))
f64_printer = C99CodePrinter(dict(type_aliases={real: float64}))
f80_printer = C99CodePrinter(dict(type_aliases={real: float80}))
assert f32_printer.doprint(sin(x + 2.1)) == "sinf(x + 2.1F)"
assert f64_printer.doprint(sin(x + 2.1)) == "sin(x + 2.1000000000000001)"
assert f80_printer.doprint(sin(x + Float("2.0"))) == "sinl(x + 2.0L)"
for printer, suffix in zip([f32_printer, f64_printer, f80_printer], ["f", "", "l"]):
def check(expr, ref):
assert printer.doprint(expr) == ref.format(s=suffix, S=suffix.upper())
check(Abs(n), "abs(n)")
check(Abs(x + 2.0), "fabs{s}(x + 2.0{S})")
check(
sin(x + 4.0) ** cos(x - 2.0),
"pow{s}(sin{s}(x + 4.0{S}), cos{s}(x - 2.0{S}))",
)
check(exp(x * 8.0), "exp{s}(8.0{S}*x)")
check(exp2(x), "exp2{s}(x)")
check(expm1(x * 4.0), "expm1{s}(4.0{S}*x)")
check(Mod(n, 2), "((n) % (2))")
check(Mod(2 * n + 3, 3 * n + 5), "((2*n + 3) % (3*n + 5))")
check(Mod(x + 2.0, 3.0), "fmod{s}(1.0{S}*x + 2.0{S}, 3.0{S})")
check(Mod(x, 2.0 * x + 3.0), "fmod{s}(1.0{S}*x, 2.0{S}*x + 3.0{S})")
check(log(x / 2), "log{s}((1.0{S}/2.0{S})*x)")
check(log10(3 * x / 2), "log10{s}((3.0{S}/2.0{S})*x)")
check(log2(x * 8.0), "log2{s}(8.0{S}*x)")
check(log1p(x), "log1p{s}(x)")
check(2 ** x, "pow{s}(2, x)")
check(2.0 ** x, "pow{s}(2.0{S}, x)")
check(x ** 3, "pow{s}(x, 3)")
check(x ** 4.0, "pow{s}(x, 4.0{S})")
check(sqrt(3 + x), "sqrt{s}(x + 3)")
check(Cbrt(x - 2.0), "cbrt{s}(x - 2.0{S})")
check(hypot(x, y), "hypot{s}(x, y)")
check(sin(3.0 * x + 2.0), "sin{s}(3.0{S}*x + 2.0{S})")
check(cos(3.0 * x - 1.0), "cos{s}(3.0{S}*x - 1.0{S})")
check(tan(4.0 * y + 2.0), "tan{s}(4.0{S}*y + 2.0{S})")
check(asin(3.0 * x + 2.0), "asin{s}(3.0{S}*x + 2.0{S})")
check(acos(3.0 * x + 2.0), "acos{s}(3.0{S}*x + 2.0{S})")
check(atan(3.0 * x + 2.0), "atan{s}(3.0{S}*x + 2.0{S})")
check(atan2(3.0 * x, 2.0 * y), "atan2{s}(3.0{S}*x, 2.0{S}*y)")
check(sinh(3.0 * x + 2.0), "sinh{s}(3.0{S}*x + 2.0{S})")
check(cosh(3.0 * x - 1.0), "cosh{s}(3.0{S}*x - 1.0{S})")
check(tanh(4.0 * y + 2.0), "tanh{s}(4.0{S}*y + 2.0{S})")
check(asinh(3.0 * x + 2.0), "asinh{s}(3.0{S}*x + 2.0{S})")
check(acosh(3.0 * x + 2.0), "acosh{s}(3.0{S}*x + 2.0{S})")
check(atanh(3.0 * x + 2.0), "atanh{s}(3.0{S}*x + 2.0{S})")
check(erf(42.0 * x), "erf{s}(42.0{S}*x)")
check(erfc(42.0 * x), "erfc{s}(42.0{S}*x)")
check(gamma(x), "tgamma{s}(x)")
check(loggamma(x), "lgamma{s}(x)")
check(ceiling(x + 2.0), "ceil{s}(x + 2.0{S})")
check(floor(x + 2.0), "floor{s}(x + 2.0{S})")
check(fma(x, y, -z), "fma{s}(x, y, -z)")
check(Max(x, 8.0, x ** 4.0), "fmax{s}(8.0{S}, fmax{s}(x, pow{s}(x, 4.0{S})))")
check(Min(x, 2.0), "fmin{s}(2.0{S}, x)")
