def test_var():
expr1.convert_to_expr(src, "f")
ls = expr1.return_expr()
for iter in expr1.return_expr():
assert isinstance(iter, Declaration)
assert ls[0] == Declaration(
Variable(Symbol("a"), type=IntBaseType(String("integer")), value=Integer(0))
)
assert ls[1] == Declaration(
Variable(Symbol("b"), type=IntBaseType(String("integer")), value=Integer(0))
)
assert ls[2] == Declaration(
Variable(Symbol("c"), type=IntBaseType(String("integer")), value=Integer(0))
)
assert ls[3] == Declaration(
Variable(Symbol("d"), type=IntBaseType(String("integer")), value=Integer(0))
)
assert ls[4] == Declaration(
Variable(Symbol("p"), type=FloatBaseType(String("real")), value=Float(0.0))
)
assert ls[5] == Declaration(
Variable(Symbol("q"), type=FloatBaseType(String("real")), value=Float(0.0))
)
assert ls[6] == Declaration(
Variable(Symbol("r"), type=FloatBaseType(String("real")), value=Float(0.0))
)
assert ls[7] == Declaration(
Variable(Symbol("s"), type=FloatBaseType(String("real")), value=Float(0.0))
)
def test_c_parse():
src1 = """\
int a, b = 4;
float c, d = 2.4;
"""
expr1.convert_to_expr(src1, "c")
ls = expr1.return_expr()
assert ls[0] == Declaration(
Variable(Symbol("a"),
type=IntBaseType(String("integer")),
value=Integer(0)))
assert ls[1] == Declaration(
Variable(Symbol("b"),
type=IntBaseType(String("integer")),
value=Integer(4)))
assert ls[2] == Declaration(
Variable(
Symbol("c"),
type=FloatBaseType(String("real")),
value=Float("0.0", precision=53),
))
assert ls[3] == Declaration(
Variable(
Symbol("d"),
type=FloatBaseType(String("real")),
value=Float("2.3999999999999999", precision=53),
))
def _print_NumberSymbol(self, expr):
if self._settings.get("inline", False):
return self._print(Float(expr.evalf(self._settings["precision"])))
else:
# A Number symbol that is not implemented here or with _printmethod
# is registered and evaluated
self._number_symbols.add((expr,
Float(expr.evalf(self._settings["precision"]))))
return str(expr)
def test_sympy_parser():
x = Symbol('x')
inputs = {
'2*x': 2 * x,
'3.00': Float(3),
'22/7': Rational(22, 7),
'2+3j': 2 + 3*I,
'exp(x)': exp(x),
'x!': factorial(x),
'x!!': factorial2(x),
'(x + 1)! - 1': factorial(x + 1) - 1,
'3.[3]': Rational(10, 3),
'.0[3]': Rational(1, 30),
'3.2[3]': Rational(97, 30),
'1.3[12]': Rational(433, 330),
'1 + 3.[3]': Rational(13, 3),
'1 + .0[3]': Rational(31, 30),
'1 + 3.2[3]': Rational(127, 30),
'.[0011]': Rational(1, 909),
'0.1[00102] + 1': Rational(366697, 333330),
'1.[0191]': Rational(10190, 9999),
'10!': 3628800,
'-(2)': -Integer(2),
'[-1, -2, 3]': [Integer(-1), Integer(-2), Integer(3)],
'Symbol("x").free_symbols': x.free_symbols,
"S('S(3).n(n=3)')": 3.00,
'factorint(12, visual=True)': Mul(
Pow(2, 2, evaluate=False),
Pow(3, 1, evaluate=False),
evaluate=False),
'Limit(sin(x), x, 0, dir="-")': Limit(sin(x), x, 0, dir='-'),
}
for text, result in inputs.items():
assert parse_expr(text) == result
def visit_Variable(self, node):
"""Visitor Function for Variable Declaration
Visits each variable declaration present in the ASR and creates a
Symbol declaration for each variable
Notes
=====
The functions currently only support declaration of integer and
real variables. Other data types are still under development.
Raises
======
NotImplementedError() when called for unsupported data types
"""
if isinstance(node.type, asr.Integer):
var_type = IntBaseType(String('integer'))
value = Integer(0)
elif isinstance(node.type, asr.Real):
var_type = FloatBaseType(String('real'))
value = Float(0.0)
else:
raise NotImplementedError("Data type not supported")
if not (node.intent == 'in'):
new_node = Variable(node.name).as_Declaration(type=var_type,
value=value)
self._py_ast.append(new_node)
def test_c_parse():
src1 = """\
int a, b = 4;
float c, d = 2.4;
"""
expr1.convert_to_expr(src1, 'c')
ls = expr1.return_expr()
assert ls[0] == Declaration(
Variable(Symbol('a'), type=IntBaseType(String('intc'))))
assert ls[1] == Declaration(
Variable(Symbol('b'),
type=IntBaseType(String('intc')),
value=Integer(4)))
assert ls[2] == Declaration(
Variable(Symbol('c'),
type=FloatType(String('float32'),
nbits=Integer(32),
nmant=Integer(23),
nexp=Integer(8))))
assert ls[3] == Declaration(
Variable(Symbol('d'),
type=FloatType(String('float32'),
nbits=Integer(32),
nmant=Integer(23),
nexp=Integer(8)),
value=Float('2.3999999999999999', precision=53)))
def test_sym_expr():
src1 = (src + """\
d = a + b -c
""")
expr3 = SymPyExpression(src, 'f')
expr4 = SymPyExpression(src1, 'f')
ls1 = expr3.return_expr()
ls2 = expr4.return_expr()
for i in range(0, 7):
assert isinstance(ls1[i], Declaration)
assert isinstance(ls2[i], Declaration)
assert isinstance(ls2[8], Assignment)
assert ls1[0] == Declaration(
Variable(Symbol('a'),
type=IntBaseType(String('integer')),
value=Integer(0)))
assert ls1[1] == Declaration(
Variable(Symbol('b'),
type=IntBaseType(String('integer')),
value=Integer(0)))
assert ls1[2] == Declaration(
Variable(Symbol('c'),
type=IntBaseType(String('integer')),
value=Integer(0)))
assert ls1[3] == Declaration(
Variable(Symbol('d'),
type=IntBaseType(String('integer')),
value=Integer(0)))
assert ls1[4] == Declaration(
Variable(Symbol('p'),
type=FloatBaseType(String('real')),
value=Float(0.0)))
assert ls1[5] == Declaration(
Variable(Symbol('q'),
type=FloatBaseType(String('real')),
value=Float(0.0)))
assert ls1[6] == Declaration(
Variable(Symbol('r'),
type=FloatBaseType(String('real')),
value=Float(0.0)))
assert ls1[7] == Declaration(
Variable(Symbol('s'),
type=FloatBaseType(String('real')),
value=Float(0.0)))
assert ls2[8] == Assignment(Variable(Symbol('d')),
Symbol('a') + Symbol('b') - Symbol('c'))
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_fortran_parse():
expr = SymPyExpression(src, "f")
ls = expr.return_expr()
assert ls[0] == Declaration(
Variable(Symbol("a"),
type=IntBaseType(String("integer")),
value=Integer(0)))
assert ls[1] == Declaration(
Variable(Symbol("b"),
type=IntBaseType(String("integer")),
value=Integer(0)))
assert ls[2] == Declaration(
Variable(Symbol("c"),
type=IntBaseType(String("integer")),
value=Integer(0)))
assert ls[3] == Declaration(
Variable(Symbol("d"),
type=IntBaseType(String("integer")),
value=Integer(0)))
assert ls[4] == Declaration(
Variable(
Symbol("p"),
type=FloatBaseType(String("real")),
value=Float("0.0", precision=53),
))
assert ls[5] == Declaration(
Variable(
Symbol("q"),
type=FloatBaseType(String("real")),
value=Float("0.0", precision=53),
))
assert ls[6] == Declaration(
Variable(
Symbol("r"),
type=FloatBaseType(String("real")),
value=Float("0.0", precision=53),
))
assert ls[7] == Declaration(
Variable(
Symbol("s"),
type=FloatBaseType(String("real")),
value=Float("0.0", precision=53),
))
def test_sym_expr():
src1 = (
src
+ """\
d = a + b -c
"""
)
expr3 = SymPyExpression(src, "f")
expr4 = SymPyExpression(src1, "f")
ls1 = expr3.return_expr()
ls2 = expr4.return_expr()
for i in range(0, 7):
assert isinstance(ls1[i], Declaration)
assert isinstance(ls2[i], Declaration)
assert isinstance(ls2[8], Assignment)
assert ls1[0] == Declaration(
Variable(Symbol("a"), type=IntBaseType(String("integer")), value=Integer(0))
)
assert ls1[1] == Declaration(
Variable(Symbol("b"), type=IntBaseType(String("integer")), value=Integer(0))
)
assert ls1[2] == Declaration(
Variable(Symbol("c"), type=IntBaseType(String("integer")), value=Integer(0))
)
assert ls1[3] == Declaration(
Variable(Symbol("d"), type=IntBaseType(String("integer")), value=Integer(0))
)
assert ls1[4] == Declaration(
Variable(Symbol("p"), type=FloatBaseType(String("real")), value=Float(0.0))
)
assert ls1[5] == Declaration(
Variable(Symbol("q"), type=FloatBaseType(String("real")), value=Float(0.0))
)
assert ls1[6] == Declaration(
Variable(Symbol("r"), type=FloatBaseType(String("real")), value=Float(0.0))
)
assert ls1[7] == Declaration(
Variable(Symbol("s"), type=FloatBaseType(String("real")), value=Float(0.0))
)
assert ls2[8] == Assignment(
Variable(Symbol("d")), Symbol("a") + Symbol("b") - Symbol("c")
)
def _eval_eq_direct(e, subs=None):
'''do the actual interval evaluation'''
rv = None
if not isinstance(e, Expr):
raise RuntimeError("Expected sympy Expr: " + repr(e))
if isinstance(e, Symbol):
if subs == None:
raise RuntimeError("Symbol '" + str(e) +
"' found but no substitutions were provided")
val = subs.get(str(e))
if val == None:
raise RuntimeError("No substitution was provided for symbol '" +
str(e) + "'")
rv = val
elif isinstance(e, Number):
rv = interval(Float(e))
elif isinstance(e, Mul):
rv = interval(1)
for child in e.args:
rv *= _eval_eq_direct(child, subs)
elif isinstance(e, Add):
rv = interval(0)
for child in e.args:
rv += _eval_eq_direct(child, subs)
elif isinstance(e, Pow):
term = _eval_eq_direct(e.args[0], subs)
exponent = _eval_eq_direct(e.args[1], subs)
rv = term**exponent
else:
# interval function evaluation (like sin)
func_map = [(sin, iv.sin), (cos, iv.cos), (tan, iv.tan)]
for entry in func_map:
t = entry[0] # type
f = entry[1] # function to call
if isinstance(e, t):
inner_arg = _eval_eq_direct(e.args[0], subs)
rv = f(inner_arg)
break
if rv == None:
raise RuntimeError("Type '" + str(type(e)) + "' is not yet implemented for interval evaluation. " + \
"Subexpression was '" + str(e) + "'.")
return rv
def test_zero():
x = Symbol('x')
y = Symbol('y')
assert 0**x != 0
assert 0**(2 * x) == 0**x
assert 0**(1.0 * x) == 0**x
assert 0**(2.0 * x) == 0**x
assert (0**(2 - x)).as_base_exp() == (0, 2 - x)
assert 0**(x - 2) != S.Infinity**(2 - x)
assert 0**(2 * x * y) == 0**(x * y)
assert 0**(-2 * x * y) == S.ComplexInfinity**(x * y)
assert Float(0)**2 is not S.Zero
assert Float(0)**2 == 0.0
assert Float(0)**-2 is zoo
assert Float(0)**oo is S.Zero
#Test issue 19572
assert 0**-oo is zoo
assert power(0, -oo) is zoo
assert Float(0)**-oo is zoo
def test_var():
expr1.convert_to_expr(src, 'f')
ls = expr1.return_expr()
for iter in expr1.return_expr():
assert isinstance(iter, Declaration)
assert ls[0] == Declaration(
Variable(Symbol('a'),
type=IntBaseType(String('integer')),
value=Integer(0)))
assert ls[1] == Declaration(
Variable(Symbol('b'),
type=IntBaseType(String('integer')),
value=Integer(0)))
assert ls[2] == Declaration(
Variable(Symbol('c'),
type=IntBaseType(String('integer')),
value=Integer(0)))
assert ls[3] == Declaration(
Variable(Symbol('d'),
type=IntBaseType(String('integer')),
value=Integer(0)))
assert ls[4] == Declaration(
Variable(Symbol('p'),
type=FloatBaseType(String('real')),
value=Float(0.0)))
assert ls[5] == Declaration(
Variable(Symbol('q'),
type=FloatBaseType(String('real')),
value=Float(0.0)))
assert ls[6] == Declaration(
Variable(Symbol('r'),
type=FloatBaseType(String('real')),
value=Float(0.0)))
assert ls[7] == Declaration(
Variable(Symbol('s'),
type=FloatBaseType(String('real')),
value=Float(0.0)))
def test_fortran_parse():
expr = SymPyExpression(src, 'f')
ls = expr.return_expr()
assert ls[0] == Declaration(
Variable(Symbol('a'),
type=IntBaseType(String('integer')),
value=Integer(0)))
assert ls[1] == Declaration(
Variable(Symbol('b'),
type=IntBaseType(String('integer')),
value=Integer(0)))
assert ls[2] == Declaration(
Variable(Symbol('c'),
type=IntBaseType(String('integer')),
value=Integer(0)))
assert ls[3] == Declaration(
Variable(Symbol('d'),
type=IntBaseType(String('integer')),
value=Integer(0)))
assert ls[4] == Declaration(
Variable(Symbol('p'),
type=FloatBaseType(String('real')),
value=Float('0.0', precision=53)))
assert ls[5] == Declaration(
Variable(Symbol('q'),
type=FloatBaseType(String('real')),
value=Float('0.0', precision=53)))
assert ls[6] == Declaration(
Variable(Symbol('r'),
type=FloatBaseType(String('real')),
value=Float('0.0', precision=53)))
assert ls[7] == Declaration(
Variable(Symbol('s'),
type=FloatBaseType(String('real')),
value=Float('0.0', precision=53)))
def test_issue_2993():
x = Symbol("x")
assert str((2.3 * x - 4)**0.3) == "1.5157165665104*(0.575*x - 1)**0.3"
assert str((2.3 * x + 4)**0.3) == "1.5157165665104*(0.575*x + 1)**0.3"
assert str((-2.3 * x + 4)**0.3) == "1.5157165665104*(1 - 0.575*x)**0.3"
assert str((-2.3 * x - 4)**0.3) == "1.5157165665104*(-0.575*x - 1)**0.3"
assert str(
(2.3 * x - 2)**0.3) == "1.28386201800527*(x - 0.869565217391304)**0.3"
assert (str((-2.3 * x -
2)**0.3) == "1.28386201800527*(-x - 0.869565217391304)**0.3")
assert str(
(-2.3 * x + 2)**0.3) == "1.28386201800527*(0.869565217391304 - x)**0.3"
assert str(
(2.3 * x + 2)**0.3) == "1.28386201800527*(x + 0.869565217391304)**0.3"
assert str((2.3 * x - 4)**Rational(1,
3)) == "2**(2/3)*(0.575*x - 1)**(1/3)"
eq = 2.3 * x + 4
assert eq**2 == 16 * (0.575 * x + 1)**2
assert (1 / eq).args == (eq, -1) # don't change trivial power
# issue 17735
q = 0.5 * exp(x) - 0.5 * exp(-x) + 0.1
assert int((q**2).subs(x, 1)) == 1
# issue 17756
y = Symbol("y")
assert (len(
sqrt(x / (x + y)**2 + Float("0.008", 30)).subs(
y, pi.n(25)).atoms(Float)) == 2)
# issue 17756
a, b, c, d, e, f, g = symbols("a:g")
expr = (sqrt(1 + a * (c**4 + g * d - 2 * g * e - f * (-g + d))**2 /
(c**3 * b**2 * (d - 3 * e + 2 * f)**2)) / 2)
r = [
(a, N("0.0170992456333788667034850458615", 30)),
(b, N("0.0966594956075474769169134801223", 30)),
(c, N("0.390911862903463913632151616184", 30)),
(d, N("0.152812084558656566271750185933", 30)),
(e, N("0.137562344465103337106561623432", 30)),
(f, N("0.174259178881496659302933610355", 30)),
(g, N("0.220745448491223779615401870086", 30)),
]
tru = expr.n(30, subs=dict(r))
seq = expr.subs(r)
# although `tru` is the right way to evaluate
# expr with numerical values, `seq` will have
# significant loss of precision if extraction of
# the largest coefficient of a power's base's terms
# is done improperly
assert seq == tru
def test_sympy_parser():
x = Symbol('x')
inputs = {
'2*x': 2 * x,
'3.00': Float(3),
'22/7': Rational(22, 7),
'2+3j': 2 + 3*I,
'exp(x)': exp(x),
'x!': factorial(x),
'3.[3]': Rational(10, 3),
'10!': 3628800,
'(_kern)': Symbol('_kern'),
'-(2)': -Integer(2),
'[-1, -2, 3]': [Integer(-1), Integer(-2), Integer(3)]
}
for text, result in inputs.items():
assert parse_expr(text) == result
def confidence(s, p):
"""Return a symmetric (p*100)% confidence interval. For example,
p=0.95 gives a 95% confidence interval. Currently this function
only handles numerical values except in the trivial case p=1.
For example, one standard deviation:
>>> from sympy.statistics import Normal
>>> N = Normal(0, 1)
>>> N.confidence(0.68)
(-0.994457883209753, 0.994457883209753)
>>> N.probability(*_).evalf()
0.680000000000000
Two standard deviations:
>>> N = Normal(0, 1)
>>> N.confidence(0.95)
(-1.95996398454005, 1.95996398454005)
>>> N.probability(*_).evalf()
0.950000000000000
"""
if p == 1:
return (-oo, oo)
if p > 1:
raise ValueError("p cannot be greater than 1")
# In terms of n*sigma, we have n = sqrt(2)*ierf(p). The inverse
# error function is not yet implemented in SymPy but can easily be
# computed numerically
from sympy.mpmath import mpf, erfinv
# calculate y = ierf(p) by solving erf(y) - p = 0
y = erfinv(mpf(p))
t = Float(str(mpf(float(s.sigma)) * mpf(2)**0.5 * y))
mu = s.mu.evalf()
return (mu - t, mu + t)
def visit_rlpsum(self, rlpsum):
"""
Visitor Method, which is called in case the current node of the syntax tree is an instance of a rlpsum
:param rlpsum: The current node, which is an instance of a rlpsum
:type rlpsum: RLPSum
:return:
"""
answers = self.logkb.ask(rlpsum.query_symbols, rlpsum.query)
result = Float(0.0)
for answer in answers:
expression_eval_subs = rlpsum.expression
for index, symbol in enumerate(rlpsum.query_symbols):
subanswer = answer[index]
expression_eval_subs = expression_eval_subs.subs(
symbol, subanswer)
# expression_eval_subs = expression_eval_subs.subs(symbol, answer[index])
result += expression_eval_subs
return result
def test_sympy_parser():
x = Symbol('x')
inputs = {
'2*x': 2 * x,
'3.00': Float(3),
'22/7': Rational(22, 7),
'2+3j': 2 + 3*I,
'exp(x)': exp(x),
'x!': factorial(x),
'3.[3]': Rational(10, 3),
'10!': 3628800,
'-(2)': -Integer(2),
'[-1, -2, 3]': [Integer(-1), Integer(-2), Integer(3)],
'Symbol("x").free_symbols': x.free_symbols,
"S('S(3).n(n=3)')": 3.00,
'factorint(12, visual=True)': Mul(
Pow(2, 2, evaluate=False),
Pow(3, 1, evaluate=False),
evaluate=False),
'Limit(sin(x), x, 0, dir="-")': Limit(sin(x), x, 0, dir='-'),
}
for text, result in inputs.items():
assert parse_expr(text) == result
def _random(s):
return Float(random.uniform(float(s.a), float(s.b)))
def _print_Pow(self, expr):
if expr.base.is_integer and not expr.exp.is_integer:
expr = type(expr)(Float(expr.base), expr.exp)
return self._print(expr)
return self._print_Function(expr)
def test_sympy_parser():
x = Symbol("x")
inputs = {
"2*x":
2 * x,
"3.00":
Float(3),
"22/7":
Rational(22, 7),
"2+3j":
2 + 3 * I,
"exp(x)":
exp(x),
"x!":
factorial(x),
"x!!":
factorial2(x),
"(x + 1)! - 1":
factorial(x + 1) - 1,
"3.[3]":
Rational(10, 3),
".0[3]":
Rational(1, 30),
"3.2[3]":
Rational(97, 30),
"1.3[12]":
Rational(433, 330),
"1 + 3.[3]":
Rational(13, 3),
"1 + .0[3]":
Rational(31, 30),
"1 + 3.2[3]":
Rational(127, 30),
".[0011]":
Rational(1, 909),
"0.1[00102] + 1":
Rational(366697, 333330),
"1.[0191]":
Rational(10190, 9999),
"10!":
3628800,
"-(2)":
-Integer(2),
"[-1, -2, 3]": [Integer(-1), Integer(-2),
Integer(3)],
'Symbol("x").free_symbols':
x.free_symbols,
"S('S(3).n(n=3)')":
3.00,
"factorint(12, visual=True)":
Mul(Pow(2, 2, evaluate=False),
Pow(3, 1, evaluate=False),
evaluate=False),
'Limit(sin(x), x, 0, dir="-")':
Limit(sin(x), x, 0, dir="-"),
}
for text, result in inputs.items():
assert parse_expr(text) == result
raises(TypeError, lambda: parse_expr("x", standard_transformations))
raises(TypeError, lambda: parse_expr("x", transformations=lambda x, y: 1))
raises(TypeError,
lambda: parse_expr("x", transformations=(lambda x, y: 1,
)))
raises(TypeError, lambda: parse_expr("x", transformations=((), )))
raises(TypeError, lambda: parse_expr("x", {}, [], []))
raises(TypeError, lambda: parse_expr("x", [], [], {}))
raises(TypeError, lambda: parse_expr("x", [], [], {}))
def test_ccode_sqrt():
assert ccode(sqrt(x)) == "sqrt(x)"
assert ccode(x**0.5) == "sqrt(x)"
assert ccode(sqrt(Float(10))) == "3.16227766016838"
def visit_number(self, node, children):
return Float(node.value)
def _print_NumberSymbol(self, expr):
# A Number symbol that is not implemented here or with _printmethod
# is registered and evaluated
self._number_symbols.add(
(expr, Float(expr.evalf(self._settings['precision']))))
return str(expr)
def test_negative_real():
def feq(a, b):
return abs(a - b) < 1E-10
assert feq(S.One / Float(-0.5), -Integer(2))
def test_C99CodePrinter__precision_f80():
f80_printer = C99CodePrinter(dict(type_aliases={real: float80}))
assert f80_printer.doprint(sin(x + Float('2.1'))) == 'sinl(x + 2.1L)'
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)")
