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"""Fortran/C symbolic expressions
References:
- J3/21-007: Draft Fortran 202x. https://j3-fortran.org/doc/year/21/21-007.pdf
"""
# To analyze Fortran expressions to solve dimensions specifications,
# for instances, we implement a minimal symbolic engine for parsing
# expressions into a tree of expression instances. As a first
# instance, we care only about arithmetic expressions involving
# integers and operations like addition (+), subtraction (-),
# multiplication (*), division (Fortran / is Python //, Fortran // is
# concatenate), and exponentiation (**). In addition, .pyf files may
# contain C expressions that support here is implemented as well.
#
# TODO: support logical constants (Op.BOOLEAN)
# TODO: support logical operators (.AND., ...)
# TODO: support defined operators (.MYOP., ...)
#
__all__ = ['Expr']
import re
import warnings
from enum import Enum
from math import gcd
class Language(Enum):
"""
Used as Expr.tostring language argument.
"""
Python = 0
Fortran = 1
C = 2
class Op(Enum):
"""
Used as Expr op attribute.
"""
INTEGER = 10
REAL = 12
COMPLEX = 15
STRING = 20
ARRAY = 30
SYMBOL = 40
TERNARY = 100
APPLY = 200
INDEXING = 210
CONCAT = 220
RELATIONAL = 300
TERMS = 1000
FACTORS = 2000
REF = 3000
DEREF = 3001
class RelOp(Enum):
"""
Used in Op.RELATIONAL expression to specify the function part.
"""
EQ = 1
NE = 2
LT = 3
LE = 4
GT = 5
GE = 6
@classmethod
def fromstring(cls, s, language=Language.C):
if language is Language.Fortran:
return {'.eq.': RelOp.EQ, '.ne.': RelOp.NE,
'.lt.': RelOp.LT, '.le.': RelOp.LE,
'.gt.': RelOp.GT, '.ge.': RelOp.GE}[s.lower()]
return {'==': RelOp.EQ, '!=': RelOp.NE, '<': RelOp.LT,
'<=': RelOp.LE, '>': RelOp.GT, '>=': RelOp.GE}[s]
def tostring(self, language=Language.C):
if language is Language.Fortran:
return {RelOp.EQ: '.eq.', RelOp.NE: '.ne.',
RelOp.LT: '.lt.', RelOp.LE: '.le.',
RelOp.GT: '.gt.', RelOp.GE: '.ge.'}[self]
return {RelOp.EQ: '==', RelOp.NE: '!=',
RelOp.LT: '<', RelOp.LE: '<=',
RelOp.GT: '>', RelOp.GE: '>='}[self]
class ArithOp(Enum):
"""
Used in Op.APPLY expression to specify the function part.
"""
POS = 1
NEG = 2
ADD = 3
SUB = 4
MUL = 5
DIV = 6
POW = 7
class OpError(Exception):
pass
class Precedence(Enum):
"""
Used as Expr.tostring precedence argument.
"""
ATOM = 0
POWER = 1
UNARY = 2
PRODUCT = 3
SUM = 4
LT = 6
EQ = 7
LAND = 11
LOR = 12
TERNARY = 13
ASSIGN = 14
TUPLE = 15
NONE = 100
integer_types = (int,)
number_types = (int, float)
def _pairs_add(d, k, v):
# Internal utility method for updating terms and factors data.
c = d.get(k)
if c is None:
d[k] = v
else:
c = c + v
if c:
d[k] = c
else:
del d[k]
class ExprWarning(UserWarning):
pass
def ewarn(message):
warnings.warn(message, ExprWarning, stacklevel=2)
class Expr:
"""Represents a Fortran expression as a op-data pair.
Expr instances are hashable and sortable.
"""
@staticmethod
def parse(s, language=Language.C):
"""Parse a Fortran expression to a Expr.
"""
return fromstring(s, language=language)
def __init__(self, op, data):
assert isinstance(op, Op)
# sanity checks
if op is Op.INTEGER:
# data is a 2-tuple of numeric object and a kind value
# (default is 4)
assert isinstance(data, tuple) and len(data) == 2
assert isinstance(data[0], int)
assert isinstance(data[1], (int, str)), data
elif op is Op.REAL:
# data is a 2-tuple of numeric object and a kind value
# (default is 4)
assert isinstance(data, tuple) and len(data) == 2
assert isinstance(data[0], float)
assert isinstance(data[1], (int, str)), data
elif op is Op.COMPLEX:
# data is a 2-tuple of constant expressions
assert isinstance(data, tuple) and len(data) == 2
elif op is Op.STRING:
# data is a 2-tuple of quoted string and a kind value
# (default is 1)
assert isinstance(data, tuple) and len(data) == 2
assert (isinstance(data[0], str)
and data[0][::len(data[0])-1] in ('""', "''", '@@'))
assert isinstance(data[1], (int, str)), data
elif op is Op.SYMBOL:
# data is any hashable object
assert hash(data) is not None
elif op in (Op.ARRAY, Op.CONCAT):
# data is a tuple of expressions
assert isinstance(data, tuple)
assert all(isinstance(item, Expr) for item in data), data
elif op in (Op.TERMS, Op.FACTORS):
# data is {<term|base>:<coeff|exponent>} where dict values
# are nonzero Python integers
assert isinstance(data, dict)
elif op is Op.APPLY:
# data is (<function>, <operands>, <kwoperands>) where
# operands are Expr instances
assert isinstance(data, tuple) and len(data) == 3
# function is any hashable object
assert hash(data[0]) is not None
assert isinstance(data[1], tuple)
assert isinstance(data[2], dict)
elif op is Op.INDEXING:
# data is (<object>, <indices>)
assert isinstance(data, tuple) and len(data) == 2
# function is any hashable object
assert hash(data[0]) is not None
elif op is Op.TERNARY:
# data is (<cond>, <expr1>, <expr2>)
assert isinstance(data, tuple) and len(data) == 3
elif op in (Op.REF, Op.DEREF):
# data is Expr instance
assert isinstance(data, Expr)
elif op is Op.RELATIONAL:
# data is (<relop>, <left>, <right>)
assert isinstance(data, tuple) and len(data) == 3
else:
raise NotImplementedError(
f'unknown op or missing sanity check: {op}')
self.op = op
self.data = data
def __eq__(self, other):
return (isinstance(other, Expr)
and self.op is other.op
and self.data == other.data)
def __hash__(self):
if self.op in (Op.TERMS, Op.FACTORS):
data = tuple(sorted(self.data.items()))
elif self.op is Op.APPLY:
data = self.data[:2] + tuple(sorted(self.data[2].items()))
else:
data = self.data
return hash((self.op, data))
def __lt__(self, other):
if isinstance(other, Expr):
if self.op is not other.op:
return self.op.value < other.op.value
if self.op in (Op.TERMS, Op.FACTORS):
return (tuple(sorted(self.data.items()))
< tuple(sorted(other.data.items())))
if self.op is Op.APPLY:
if self.data[:2] != other.data[:2]:
return self.data[:2] < other.data[:2]
return tuple(sorted(self.data[2].items())) < tuple(
sorted(other.data[2].items()))
return self.data < other.data
return NotImplemented
def __le__(self, other): return self == other or self < other
def __gt__(self, other): return not (self <= other)
def __ge__(self, other): return not (self < other)
def __repr__(self):
return f'{type(self).__name__}({self.op}, {self.data!r})'
def __str__(self):
return self.tostring()
def tostring(self, parent_precedence=Precedence.NONE,
language=Language.Fortran):
"""Return a string representation of Expr.
"""
if self.op in (Op.INTEGER, Op.REAL):
precedence = (Precedence.SUM if self.data[0] < 0
else Precedence.ATOM)
r = str(self.data[0]) + (f'_{self.data[1]}'
if self.data[1] != 4 else '')
elif self.op is Op.COMPLEX:
r = ', '.join(item.tostring(Precedence.TUPLE, language=language)
for item in self.data)
r = '(' + r + ')'
precedence = Precedence.ATOM
elif self.op is Op.SYMBOL:
precedence = Precedence.ATOM
r = str(self.data)
elif self.op is Op.STRING:
r = self.data[0]
if self.data[1] != 1:
r = self.data[1] + '_' + r
precedence = Precedence.ATOM
elif self.op is Op.ARRAY:
r = ', '.join(item.tostring(Precedence.TUPLE, language=language)
for item in self.data)
r = '[' + r + ']'
precedence = Precedence.ATOM
elif self.op is Op.TERMS:
terms = []
for term, coeff in sorted(self.data.items()):
if coeff < 0:
op = ' - '
coeff = -coeff
else:
op = ' + '
if coeff == 1:
term = term.tostring(Precedence.SUM, language=language)
else:
if term == as_number(1):
term = str(coeff)
else:
term = f'{coeff} * ' + term.tostring(
Precedence.PRODUCT, language=language)
if terms:
terms.append(op)
elif op == ' - ':
terms.append('-')
terms.append(term)
r = ''.join(terms) or '0'
precedence = Precedence.SUM if terms else Precedence.ATOM
elif self.op is Op.FACTORS:
factors = []
tail = []
for base, exp in sorted(self.data.items()):
op = ' * '
if exp == 1:
factor = base.tostring(Precedence.PRODUCT,
language=language)
elif language is Language.C:
if exp in range(2, 10):
factor = base.tostring(Precedence.PRODUCT,
language=language)
factor = ' * '.join([factor] * exp)
elif exp in range(-10, 0):
factor = base.tostring(Precedence.PRODUCT,
language=language)
tail += [factor] * -exp
continue
else:
factor = base.tostring(Precedence.TUPLE,
language=language)
factor = f'pow({factor}, {exp})'
else:
factor = base.tostring(Precedence.POWER,
language=language) + f' ** {exp}'
if factors:
factors.append(op)
factors.append(factor)
if tail:
if not factors:
factors += ['1']
factors += ['/', '(', ' * '.join(tail), ')']
r = ''.join(factors) or '1'
precedence = Precedence.PRODUCT if factors else Precedence.ATOM
elif self.op is Op.APPLY:
name, args, kwargs = self.data
if name is ArithOp.DIV and language is Language.C:
numer, denom = [arg.tostring(Precedence.PRODUCT,
language=language)
for arg in args]
r = f'{numer} / {denom}'
precedence = Precedence.PRODUCT
else:
args = [arg.tostring(Precedence.TUPLE, language=language)
for arg in args]
args += [k + '=' + v.tostring(Precedence.NONE)
for k, v in kwargs.items()]
r = f'{name}({", ".join(args)})'
precedence = Precedence.ATOM
elif self.op is Op.INDEXING:
name = self.data[0]
args = [arg.tostring(Precedence.TUPLE, language=language)
for arg in self.data[1:]]
r = f'{name}[{", ".join(args)}]'
precedence = Precedence.ATOM
elif self.op is Op.CONCAT:
args = [arg.tostring(Precedence.PRODUCT, language=language)
for arg in self.data]
r = " // ".join(args)
precedence = Precedence.PRODUCT
elif self.op is Op.TERNARY:
cond, expr1, expr2 = [a.tostring(Precedence.TUPLE,
language=language)
for a in self.data]
if language is Language.C:
r = f'({cond}?{expr1}:{expr2})'
elif language is Language.Python:
r = f'({expr1} if {cond} else {expr2})'
elif language is Language.Fortran:
r = f'merge({expr1}, {expr2}, {cond})'
else:
raise NotImplementedError(
f'tostring for {self.op} and {language}')
precedence = Precedence.ATOM
elif self.op is Op.REF:
r = '&' + self.data.tostring(Precedence.UNARY, language=language)
precedence = Precedence.UNARY
elif self.op is Op.DEREF:
r = '*' + self.data.tostring(Precedence.UNARY, language=language)
precedence = Precedence.UNARY
elif self.op is Op.RELATIONAL:
rop, left, right = self.data
precedence = (Precedence.EQ if rop in (RelOp.EQ, RelOp.NE)
else Precedence.LT)
left = left.tostring(precedence, language=language)
right = right.tostring(precedence, language=language)
rop = rop.tostring(language=language)
r = f'{left} {rop} {right}'
else:
raise NotImplementedError(f'tostring for op {self.op}')
if parent_precedence.value < precedence.value:
# If parent precedence is higher than operand precedence,
# operand will be enclosed in parenthesis.
return '(' + r + ')'
return r
def __pos__(self):
return self
def __neg__(self):
return self * -1
def __add__(self, other):
other = as_expr(other)
if isinstance(other, Expr):
if self.op is other.op:
if self.op in (Op.INTEGER, Op.REAL):
return as_number(
self.data[0] + other.data[0],
max(self.data[1], other.data[1]))
if self.op is Op.COMPLEX:
r1, i1 = self.data
r2, i2 = other.data
return as_complex(r1 + r2, i1 + i2)
if self.op is Op.TERMS:
r = Expr(self.op, dict(self.data))
for k, v in other.data.items():
_pairs_add(r.data, k, v)
return normalize(r)
if self.op is Op.COMPLEX and other.op in (Op.INTEGER, Op.REAL):
return self + as_complex(other)
elif self.op in (Op.INTEGER, Op.REAL) and other.op is Op.COMPLEX:
return as_complex(self) + other
elif self.op is Op.REAL and other.op is Op.INTEGER:
return self + as_real(other, kind=self.data[1])
elif self.op is Op.INTEGER and other.op is Op.REAL:
return as_real(self, kind=other.data[1]) + other
return as_terms(self) + as_terms(other)
return NotImplemented
def __radd__(self, other):
if isinstance(other, number_types):
return as_number(other) + self
return NotImplemented
def __sub__(self, other):
return self + (-other)
def __rsub__(self, other):
if isinstance(other, number_types):
return as_number(other) - self
return NotImplemented
def __mul__(self, other):
other = as_expr(other)
if isinstance(other, Expr):
if self.op is other.op:
if self.op in (Op.INTEGER, Op.REAL):
return as_number(self.data[0] * other.data[0],
max(self.data[1], other.data[1]))
elif self.op is Op.COMPLEX:
r1, i1 = self.data
r2, i2 = other.data
return as_complex(r1 * r2 - i1 * i2, r1 * i2 + r2 * i1)
if self.op is Op.FACTORS:
r = Expr(self.op, dict(self.data))
for k, v in other.data.items():
_pairs_add(r.data, k, v)
return normalize(r)
elif self.op is Op.TERMS:
r = Expr(self.op, {})
for t1, c1 in self.data.items():
for t2, c2 in other.data.items():
_pairs_add(r.data, t1 * t2, c1 * c2)
return normalize(r)
if self.op is Op.COMPLEX and other.op in (Op.INTEGER, Op.REAL):
return self * as_complex(other)
elif other.op is Op.COMPLEX and self.op in (Op.INTEGER, Op.REAL):
return as_complex(self) * other
elif self.op is Op.REAL and other.op is Op.INTEGER:
return self * as_real(other, kind=self.data[1])
elif self.op is Op.INTEGER and other.op is Op.REAL:
return as_real(self, kind=other.data[1]) * other
if self.op is Op.TERMS:
return self * as_terms(other)
elif other.op is Op.TERMS:
return as_terms(self) * other
return as_factors(self) * as_factors(other)
return NotImplemented
def __rmul__(self, other):
if isinstance(other, number_types):
return as_number(other) * self
return NotImplemented
def __pow__(self, other):
other = as_expr(other)
if isinstance(other, Expr):
if other.op is Op.INTEGER:
exponent = other.data[0]
# TODO: other kind not used
if exponent == 0:
return as_number(1)
if exponent == 1:
return self
if exponent > 0:
if self.op is Op.FACTORS:
r = Expr(self.op, {})
for k, v in self.data.items():
r.data[k] = v * exponent
return normalize(r)
return self * (self ** (exponent - 1))
elif exponent != -1:
return (self ** (-exponent)) ** -1
return Expr(Op.FACTORS, {self: exponent})
return as_apply(ArithOp.POW, self, other)
return NotImplemented
def __truediv__(self, other):
other = as_expr(other)
if isinstance(other, Expr):
# Fortran / is different from Python /:
# - `/` is a truncate operation for integer operands
return normalize(as_apply(ArithOp.DIV, self, other))
return NotImplemented
def __rtruediv__(self, other):
other = as_expr(other)
if isinstance(other, Expr):
return other / self
return NotImplemented
def __floordiv__(self, other):
other = as_expr(other)
if isinstance(other, Expr):
# Fortran // is different from Python //:
# - `//` is a concatenate operation for string operands
return normalize(Expr(Op.CONCAT, (self, other)))
return NotImplemented
def __rfloordiv__(self, other):
other = as_expr(other)
if isinstance(other, Expr):
return other // self
return NotImplemented
def __call__(self, *args, **kwargs):
# In Fortran, parenthesis () are use for both function call as
# well as indexing operations.
#
# TODO: implement a method for deciding when __call__ should
# return an INDEXING expression.
return as_apply(self, *map(as_expr, args),
**dict((k, as_expr(v)) for k, v in kwargs.items()))
def __getitem__(self, index):
# Provided to support C indexing operations that .pyf files
# may contain.
index = as_expr(index)
if not isinstance(index, tuple):
index = index,
if len(index) > 1:
ewarn(f'C-index should be a single expression but got `{index}`')
return Expr(Op.INDEXING, (self,) + index)
def substitute(self, symbols_map):
"""Recursively substitute symbols with values in symbols map.
Symbols map is a dictionary of symbol-expression pairs.
"""
if self.op is Op.SYMBOL:
value = symbols_map.get(self)
if value is None:
return self
m = re.match(r'\A(@__f2py_PARENTHESIS_(\w+)_\d+@)\Z', self.data)
if m:
# complement to fromstring method
items, paren = m.groups()
if paren in ['ROUNDDIV', 'SQUARE']:
return as_array(value)
assert paren == 'ROUND', (paren, value)
return value
if self.op in (Op.INTEGER, Op.REAL, Op.STRING):
return self
if self.op in (Op.ARRAY, Op.COMPLEX):
return Expr(self.op, tuple(item.substitute(symbols_map)
for item in self.data))
if self.op is Op.CONCAT:
return normalize(Expr(self.op, tuple(item.substitute(symbols_map)
for item in self.data)))
if self.op is Op.TERMS:
r = None
for term, coeff in self.data.items():
if r is None:
r = term.substitute(symbols_map) * coeff
else:
r += term.substitute(symbols_map) * coeff
if r is None:
ewarn('substitute: empty TERMS expression interpreted as'
' int-literal 0')
return as_number(0)
return r
if self.op is Op.FACTORS:
r = None
for base, exponent in self.data.items():
if r is None:
r = base.substitute(symbols_map) ** exponent
else:
r *= base.substitute(symbols_map) ** exponent
if r is None:
ewarn('substitute: empty FACTORS expression interpreted'
' as int-literal 1')
return as_number(1)
return r
if self.op is Op.APPLY:
target, args, kwargs = self.data
if isinstance(target, Expr):
target = target.substitute(symbols_map)
args = tuple(a.substitute(symbols_map) for a in args)
kwargs = dict((k, v.substitute(symbols_map))
for k, v in kwargs.items())
return normalize(Expr(self.op, (target, args, kwargs)))
if self.op is Op.INDEXING:
func = self.data[0]
if isinstance(func, Expr):
func = func.substitute(symbols_map)
args = tuple(a.substitute(symbols_map) for a in self.data[1:])
return normalize(Expr(self.op, (func,) + args))
if self.op is Op.TERNARY:
operands = tuple(a.substitute(symbols_map) for a in self.data)
return normalize(Expr(self.op, operands))
if self.op in (Op.REF, Op.DEREF):
return normalize(Expr(self.op, self.data.substitute(symbols_map)))
if self.op is Op.RELATIONAL:
rop, left, right = self.data
left = left.substitute(symbols_map)
right = right.substitute(symbols_map)
return normalize(Expr(self.op, (rop, left, right)))
raise NotImplementedError(f'substitute method for {self.op}: {self!r}')
def traverse(self, visit, *args, **kwargs):
"""Traverse expression tree with visit function.
The visit function is applied to an expression with given args
and kwargs.
Traverse call returns an expression returned by visit when not
None, otherwise return a new normalized expression with
traverse-visit sub-expressions.
"""
result = visit(self, *args, **kwargs)
if result is not None:
return result
if self.op in (Op.INTEGER, Op.REAL, Op.STRING, Op.SYMBOL):
return self
elif self.op in (Op.COMPLEX, Op.ARRAY, Op.CONCAT, Op.TERNARY):
return normalize(Expr(self.op, tuple(
item.traverse(visit, *args, **kwargs)
for item in self.data)))
elif self.op in (Op.TERMS, Op.FACTORS):
data = {}
for k, v in self.data.items():
k = k.traverse(visit, *args, **kwargs)
v = (v.traverse(visit, *args, **kwargs)
if isinstance(v, Expr) else v)
if k in data:
v = data[k] + v
data[k] = v
return normalize(Expr(self.op, data))
elif self.op is Op.APPLY:
obj = self.data[0]
func = (obj.traverse(visit, *args, **kwargs)
if isinstance(obj, Expr) else obj)
operands = tuple(operand.traverse(visit, *args, **kwargs)
for operand in self.data[1])
kwoperands = dict((k, v.traverse(visit, *args, **kwargs))
for k, v in self.data[2].items())
return normalize(Expr(self.op, (func, operands, kwoperands)))
elif self.op is Op.INDEXING:
obj = self.data[0]
obj = (obj.traverse(visit, *args, **kwargs)
if isinstance(obj, Expr) else obj)
indices = tuple(index.traverse(visit, *args, **kwargs)
for index in self.data[1:])
return normalize(Expr(self.op, (obj,) + indices))
elif self.op in (Op.REF, Op.DEREF):
return normalize(Expr(self.op,
self.data.traverse(visit, *args, **kwargs)))
elif self.op is Op.RELATIONAL:
rop, left, right = self.data
left = left.traverse(visit, *args, **kwargs)
right = right.traverse(visit, *args, **kwargs)
return normalize(Expr(self.op, (rop, left, right)))
raise NotImplementedError(f'traverse method for {self.op}')
def contains(self, other):
"""Check if self contains other.
"""
found = []
def visit(expr, found=found):
if found:
return expr
elif expr == other:
found.append(1)
return expr
self.traverse(visit)
return len(found) != 0
def symbols(self):
"""Return a set of symbols contained in self.
"""
found = set()
def visit(expr, found=found):
if expr.op is Op.SYMBOL:
found.add(expr)
self.traverse(visit)
return found
def polynomial_atoms(self):
"""Return a set of expressions used as atoms in polynomial self.
"""
found = set()
def visit(expr, found=found):
if expr.op is Op.FACTORS:
for b in expr.data:
b.traverse(visit)
return expr
if expr.op in (Op.TERMS, Op.COMPLEX):
return
if expr.op is Op.APPLY and isinstance(expr.data[0], ArithOp):
if expr.data[0] is ArithOp.POW:
expr.data[1][0].traverse(visit)
return expr
return
if expr.op in (Op.INTEGER, Op.REAL):
return expr
found.add(expr)
if expr.op in (Op.INDEXING, Op.APPLY):
return expr
self.traverse(visit)
return found
def linear_solve(self, symbol):
"""Return a, b such that a * symbol + b == self.
If self is not linear with respect to symbol, raise RuntimeError.
"""
b = self.substitute({symbol: as_number(0)})
ax = self - b
a = ax.substitute({symbol: as_number(1)})
zero, _ = as_numer_denom(a * symbol - ax)
if zero != as_number(0):
raise RuntimeError(f'not a {symbol}-linear equation:'
f' {a} * {symbol} + {b} == {self}')
return a, b
def normalize(obj):
"""Normalize Expr and apply basic evaluation methods.
"""
if not isinstance(obj, Expr):
return obj
if obj.op is Op.TERMS:
d = {}
for t, c in obj.data.items():
if c == 0:
continue
if t.op is Op.COMPLEX and c != 1:
t = t * c
c = 1
if t.op is Op.TERMS:
for t1, c1 in t.data.items():
_pairs_add(d, t1, c1 * c)
else:
_pairs_add(d, t, c)
if len(d) == 0:
# TODO: determine correct kind
return as_number(0)
elif len(d) == 1:
(t, c), = d.items()
if c == 1:
return t
return Expr(Op.TERMS, d)
if obj.op is Op.FACTORS:
coeff = 1
d = {}
for b, e in obj.data.items():
if e == 0:
continue
if b.op is Op.TERMS and isinstance(e, integer_types) and e > 1:
# expand integer powers of sums
b = b * (b ** (e - 1))
e = 1
if b.op in (Op.INTEGER, Op.REAL):
if e == 1:
coeff *= b.data[0]
elif e > 0:
coeff *= b.data[0] ** e
else:
_pairs_add(d, b, e)
elif b.op is Op.FACTORS:
if e > 0 and isinstance(e, integer_types):
for b1, e1 in b.data.items():
_pairs_add(d, b1, e1 * e)
else:
_pairs_add(d, b, e)
else:
_pairs_add(d, b, e)
if len(d) == 0 or coeff == 0:
# TODO: determine correct kind
assert isinstance(coeff, number_types)
return as_number(coeff)
elif len(d) == 1:
(b, e), = d.items()
if e == 1:
t = b
else:
t = Expr(Op.FACTORS, d)
if coeff == 1:
return t
return Expr(Op.TERMS, {t: coeff})
elif coeff == 1:
return Expr(Op.FACTORS, d)
else:
return Expr(Op.TERMS, {Expr(Op.FACTORS, d): coeff})
if obj.op is Op.APPLY and obj.data[0] is ArithOp.DIV:
dividend, divisor = obj.data[1]
t1, c1 = as_term_coeff(dividend)
t2, c2 = as_term_coeff(divisor)
if isinstance(c1, integer_types) and isinstance(c2, integer_types):
g = gcd(c1, c2)
c1, c2 = c1//g, c2//g
else:
c1, c2 = c1/c2, 1
if t1.op is Op.APPLY and t1.data[0] is ArithOp.DIV:
numer = t1.data[1][0] * c1
denom = t1.data[1][1] * t2 * c2
return as_apply(ArithOp.DIV, numer, denom)
if t2.op is Op.APPLY and t2.data[0] is ArithOp.DIV:
numer = t2.data[1][1] * t1 * c1
denom = t2.data[1][0] * c2
return as_apply(ArithOp.DIV, numer, denom)
d = dict(as_factors(t1).data)
for b, e in as_factors(t2).data.items():
_pairs_add(d, b, -e)
numer, denom = {}, {}
for b, e in d.items():
if e > 0:
numer[b] = e
else:
denom[b] = -e
numer = normalize(Expr(Op.FACTORS, numer)) * c1
denom = normalize(Expr(Op.FACTORS, denom)) * c2
if denom.op in (Op.INTEGER, Op.REAL) and denom.data[0] == 1:
# TODO: denom kind not used
return numer
return as_apply(ArithOp.DIV, numer, denom)
if obj.op is Op.CONCAT:
lst = [obj.data[0]]
for s in obj.data[1:]:
last = lst[-1]
if (
last.op is Op.STRING
and s.op is Op.STRING
and last.data[0][0] in '"\''
and s.data[0][0] == last.data[0][-1]
):
new_last = as_string(last.data[0][:-1] + s.data[0][1:],
max(last.data[1], s.data[1]))
lst[-1] = new_last
else:
lst.append(s)
if len(lst) == 1:
return lst[0]
return Expr(Op.CONCAT, tuple(lst))
if obj.op is Op.TERNARY:
cond, expr1, expr2 = map(normalize, obj.data)
if cond.op is Op.INTEGER:
return expr1 if cond.data[0] else expr2
return Expr(Op.TERNARY, (cond, expr1, expr2))
return obj
def as_expr(obj):
"""Convert non-Expr objects to Expr objects.
"""
if isinstance(obj, complex):
return as_complex(obj.real, obj.imag)
if isinstance(obj, number_types):
return as_number(obj)
if isinstance(obj, str):
# STRING expression holds string with boundary quotes, hence
# applying repr:
return as_string(repr(obj))
if isinstance(obj, tuple):
return tuple(map(as_expr, obj))
return obj
def as_symbol(obj):
"""Return object as SYMBOL expression (variable or unparsed expression).
"""
return Expr(Op.SYMBOL, obj)
def as_number(obj, kind=4):
"""Return object as INTEGER or REAL constant.
"""
if isinstance(obj, int):
return Expr(Op.INTEGER, (obj, kind))
if isinstance(obj, float):
return Expr(Op.REAL, (obj, kind))
if isinstance(obj, Expr):
if obj.op in (Op.INTEGER, Op.REAL):
return obj
raise OpError(f'cannot convert {obj} to INTEGER or REAL constant')
def as_integer(obj, kind=4):
"""Return object as INTEGER constant.
"""
if isinstance(obj, int):
return Expr(Op.INTEGER, (obj, kind))
if isinstance(obj, Expr):
if obj.op is Op.INTEGER:
return obj
raise OpError(f'cannot convert {obj} to INTEGER constant')
def as_real(obj, kind=4):
"""Return object as REAL constant.
"""
if isinstance(obj, int):
return Expr(Op.REAL, (float(obj), kind))
if isinstance(obj, float):
return Expr(Op.REAL, (obj, kind))
if isinstance(obj, Expr):
if obj.op is Op.REAL:
return obj
elif obj.op is Op.INTEGER:
return Expr(Op.REAL, (float(obj.data[0]), kind))
raise OpError(f'cannot convert {obj} to REAL constant')
def as_string(obj, kind=1):
"""Return object as STRING expression (string literal constant).
"""
return Expr(Op.STRING, (obj, kind))
def as_array(obj):
"""Return object as ARRAY expression (array constant).
"""
if isinstance(obj, Expr):
obj = obj,
return Expr(Op.ARRAY, obj)
def as_complex(real, imag=0):
"""Return object as COMPLEX expression (complex literal constant).
"""
return Expr(Op.COMPLEX, (as_expr(real), as_expr(imag)))
def as_apply(func, *args, **kwargs):
"""Return object as APPLY expression (function call, constructor, etc.)
"""
return Expr(Op.APPLY,
(func, tuple(map(as_expr, args)),
dict((k, as_expr(v)) for k, v in kwargs.items())))
def as_ternary(cond, expr1, expr2):
"""Return object as TERNARY expression (cond?expr1:expr2).
"""
return Expr(Op.TERNARY, (cond, expr1, expr2))
def as_ref(expr):
"""Return object as referencing expression.
"""
return Expr(Op.REF, expr)
def as_deref(expr):
"""Return object as dereferencing expression.
"""
return Expr(Op.DEREF, expr)
def as_eq(left, right):
return Expr(Op.RELATIONAL, (RelOp.EQ, left, right))
def as_ne(left, right):
return Expr(Op.RELATIONAL, (RelOp.NE, left, right))
def as_lt(left, right):
return Expr(Op.RELATIONAL, (RelOp.LT, left, right))
def as_le(left, right):
return Expr(Op.RELATIONAL, (RelOp.LE, left, right))
def as_gt(left, right):
return Expr(Op.RELATIONAL, (RelOp.GT, left, right))
def as_ge(left, right):
return Expr(Op.RELATIONAL, (RelOp.GE, left, right))
def as_terms(obj):
"""Return expression as TERMS expression.
"""
if isinstance(obj, Expr):
obj = normalize(obj)
if obj.op is Op.TERMS:
return obj
if obj.op is Op.INTEGER:
return Expr(Op.TERMS, {as_integer(1, obj.data[1]): obj.data[0]})
if obj.op is Op.REAL:
return Expr(Op.TERMS, {as_real(1, obj.data[1]): obj.data[0]})
return Expr(Op.TERMS, {obj: 1})
raise OpError(f'cannot convert {type(obj)} to terms Expr')
def as_factors(obj):
"""Return expression as FACTORS expression.
"""
if isinstance(obj, Expr):
obj = normalize(obj)
if obj.op is Op.FACTORS:
return obj
if obj.op is Op.TERMS:
if len(obj.data) == 1:
(term, coeff), = obj.data.items()
if coeff == 1:
return Expr(Op.FACTORS, {term: 1})
return Expr(Op.FACTORS, {term: 1, Expr.number(coeff): 1})
if ((obj.op is Op.APPLY
and obj.data[0] is ArithOp.DIV
and not obj.data[2])):
return Expr(Op.FACTORS, {obj.data[1][0]: 1, obj.data[1][1]: -1})
return Expr(Op.FACTORS, {obj: 1})
raise OpError(f'cannot convert {type(obj)} to terms Expr')
def as_term_coeff(obj):
"""Return expression as term-coefficient pair.
"""
if isinstance(obj, Expr):
obj = normalize(obj)
if obj.op is Op.INTEGER:
return as_integer(1, obj.data[1]), obj.data[0]
if obj.op is Op.REAL:
return as_real(1, obj.data[1]), obj.data[0]
if obj.op is Op.TERMS:
if len(obj.data) == 1:
(term, coeff), = obj.data.items()
return term, coeff
# TODO: find common divisor of coefficients
if obj.op is Op.APPLY and obj.data[0] is ArithOp.DIV:
t, c = as_term_coeff(obj.data[1][0])
return as_apply(ArithOp.DIV, t, obj.data[1][1]), c
return obj, 1
raise OpError(f'cannot convert {type(obj)} to term and coeff')
def as_numer_denom(obj):
"""Return expression as numer-denom pair.
"""
if isinstance(obj, Expr):
obj = normalize(obj)
if obj.op in (Op.INTEGER, Op.REAL, Op.COMPLEX, Op.SYMBOL,
Op.INDEXING, Op.TERNARY):
return obj, as_number(1)
elif obj.op is Op.APPLY:
if obj.data[0] is ArithOp.DIV and not obj.data[2]:
numers, denoms = map(as_numer_denom, obj.data[1])
return numers[0] * denoms[1], numers[1] * denoms[0]
return obj, as_number(1)
elif obj.op is Op.TERMS:
numers, denoms = [], []
for term, coeff in obj.data.items():
n, d = as_numer_denom(term)
n = n * coeff
numers.append(n)
denoms.append(d)
numer, denom = as_number(0), as_number(1)
for i in range(len(numers)):
n = numers[i]
for j in range(len(numers)):
if i != j:
n *= denoms[j]
numer += n
denom *= denoms[i]
if denom.op in (Op.INTEGER, Op.REAL) and denom.data[0] < 0:
numer, denom = -numer, -denom
return numer, denom
elif obj.op is Op.FACTORS:
numer, denom = as_number(1), as_number(1)
for b, e in obj.data.items():
bnumer, bdenom = as_numer_denom(b)
if e > 0:
numer *= bnumer ** e
denom *= bdenom ** e
elif e < 0:
numer *= bdenom ** (-e)
denom *= bnumer ** (-e)
return numer, denom
raise OpError(f'cannot convert {type(obj)} to numer and denom')
def _counter():
# Used internally to generate unique dummy symbols
counter = 0
while True:
counter += 1
yield counter
COUNTER = _counter()
def eliminate_quotes(s):
"""Replace quoted substrings of input string.
Return a new string and a mapping of replacements.
"""
d = {}
def repl(m):
kind, value = m.groups()[:2]
if kind:
# remove trailing underscore
kind = kind[:-1]
p = {"'": "SINGLE", '"': "DOUBLE"}[value[0]]
k = f'{kind}@__f2py_QUOTES_{p}_{COUNTER.__next__()}@'
d[k] = value
return k
new_s = re.sub(r'({kind}_|)({single_quoted}|{double_quoted})'.format(
kind=r'\w[\w\d_]*',
single_quoted=r"('([^'\\]|(\\.))*')",
double_quoted=r'("([^"\\]|(\\.))*")'),
repl, s)
assert '"' not in new_s
assert "'" not in new_s
return new_s, d
def insert_quotes(s, d):
"""Inverse of eliminate_quotes.
"""
for k, v in d.items():
kind = k[:k.find('@')]
if kind:
kind += '_'
s = s.replace(k, kind + v)
return s
def replace_parenthesis(s):
"""Replace substrings of input that are enclosed in parenthesis.
Return a new string and a mapping of replacements.
"""
# Find a parenthesis pair that appears first.
# Fortran deliminator are `(`, `)`, `[`, `]`, `(/', '/)`, `/`.
# We don't handle `/` deliminator because it is not a part of an
# expression.
left, right = None, None
mn_i = len(s)
for left_, right_ in (('(/', '/)'),
'()',
'{}', # to support C literal structs
'[]'):
i = s.find(left_)
if i == -1:
continue
if i < mn_i:
mn_i = i
left, right = left_, right_
if left is None:
return s, {}
i = mn_i
j = s.find(right, i)
while s.count(left, i + 1, j) != s.count(right, i + 1, j):
j = s.find(right, j + 1)
if j == -1:
raise ValueError(f'Mismatch of {left+right} parenthesis in {s!r}')
p = {'(': 'ROUND', '[': 'SQUARE', '{': 'CURLY', '(/': 'ROUNDDIV'}[left]
k = f'@__f2py_PARENTHESIS_{p}_{COUNTER.__next__()}@'
v = s[i+len(left):j]
r, d = replace_parenthesis(s[j+len(right):])
d[k] = v
return s[:i] + k + r, d
def _get_parenthesis_kind(s):
assert s.startswith('@__f2py_PARENTHESIS_'), s
return s.split('_')[4]
def unreplace_parenthesis(s, d):
"""Inverse of replace_parenthesis.
"""
for k, v in d.items():
p = _get_parenthesis_kind(k)
left = dict(ROUND='(', SQUARE='[', CURLY='{', ROUNDDIV='(/')[p]
right = dict(ROUND=')', SQUARE=']', CURLY='}', ROUNDDIV='/)')[p]
s = s.replace(k, left + v + right)
return s
def fromstring(s, language=Language.C):
"""Create an expression from a string.
This is a "lazy" parser, that is, only arithmetic operations are
resolved, non-arithmetic operations are treated as symbols.
"""
r = _FromStringWorker(language=language).parse(s)
if isinstance(r, Expr):
return r
raise ValueError(f'failed to parse `{s}` to Expr instance: got `{r}`')
class _Pair:
# Internal class to represent a pair of expressions
def __init__(self, left, right):
self.left = left
self.right = right
def substitute(self, symbols_map):
left, right = self.left, self.right
if isinstance(left, Expr):
left = left.substitute(symbols_map)
if isinstance(right, Expr):
right = right.substitute(symbols_map)
return _Pair(left, right)
def __repr__(self):
return f'{type(self).__name__}({self.left}, {self.right})'
class _FromStringWorker:
def __init__(self, language=Language.C):
self.original = None
self.quotes_map = None
self.language = language
def finalize_string(self, s):
return insert_quotes(s, self.quotes_map)
def parse(self, inp):
self.original = inp
unquoted, self.quotes_map = eliminate_quotes(inp)
return self.process(unquoted)
def process(self, s, context='expr'):
"""Parse string within the given context.
The context may define the result in case of ambiguous
expressions. For instance, consider expressions `f(x, y)` and
`(x, y) + (a, b)` where `f` is a function and pair `(x, y)`
denotes complex number. Specifying context as "args" or
"expr", the subexpression `(x, y)` will be parse to an
argument list or to a complex number, respectively.
"""
if isinstance(s, (list, tuple)):
return type(s)(self.process(s_, context) for s_ in s)
assert isinstance(s, str), (type(s), s)
# replace subexpressions in parenthesis with f2py @-names
r, raw_symbols_map = replace_parenthesis(s)
r = r.strip()
def restore(r):
# restores subexpressions marked with f2py @-names
if isinstance(r, (list, tuple)):
return type(r)(map(restore, r))
return unreplace_parenthesis(r, raw_symbols_map)
# comma-separated tuple
if ',' in r:
operands = restore(r.split(','))
if context == 'args':
return tuple(self.process(operands))
if context == 'expr':
if len(operands) == 2:
# complex number literal
return as_complex(*self.process(operands))
raise NotImplementedError(
f'parsing comma-separated list (context={context}): {r}')
# ternary operation
m = re.match(r'\A([^?]+)[?]([^:]+)[:](.+)\Z', r)
if m:
assert context == 'expr', context
oper, expr1, expr2 = restore(m.groups())
oper = self.process(oper)
expr1 = self.process(expr1)
expr2 = self.process(expr2)
return as_ternary(oper, expr1, expr2)
# relational expression
if self.language is Language.Fortran:
m = re.match(
r'\A(.+)\s*[.](eq|ne|lt|le|gt|ge)[.]\s*(.+)\Z', r, re.I)
else:
m = re.match(
r'\A(.+)\s*([=][=]|[!][=]|[<][=]|[<]|[>][=]|[>])\s*(.+)\Z', r)
if m:
left, rop, right = m.groups()
if self.language is Language.Fortran:
rop = '.' + rop + '.'
left, right = self.process(restore((left, right)))
rop = RelOp.fromstring(rop, language=self.language)
return Expr(Op.RELATIONAL, (rop, left, right))
# keyword argument
m = re.match(r'\A(\w[\w\d_]*)\s*[=](.*)\Z', r)
if m:
keyname, value = m.groups()
value = restore(value)
return _Pair(keyname, self.process(value))
# addition/subtraction operations
operands = re.split(r'((?<!\d[edED])[+-])', r)
if len(operands) > 1:
result = self.process(restore(operands[0] or '0'))
for op, operand in zip(operands[1::2], operands[2::2]):
operand = self.process(restore(operand))
op = op.strip()
if op == '+':
result += operand
else:
assert op == '-'
result -= operand
return result
# string concatenate operation
if self.language is Language.Fortran and '//' in r:
operands = restore(r.split('//'))
return Expr(Op.CONCAT,
tuple(self.process(operands)))
# multiplication/division operations
operands = re.split(r'(?<=[@\w\d_])\s*([*]|/)',
(r if self.language is Language.C
else r.replace('**', '@__f2py_DOUBLE_STAR@')))
if len(operands) > 1:
operands = restore(operands)
if self.language is not Language.C:
operands = [operand.replace('@__f2py_DOUBLE_STAR@', '**')
for operand in operands]
# Expression is an arithmetic product
result = self.process(operands[0])
for op, operand in zip(operands[1::2], operands[2::2]):
operand = self.process(operand)
op = op.strip()
if op == '*':
result *= operand
else:
assert op == '/'
result /= operand
return result
# referencing/dereferencing
if r.startswith('*') or r.startswith('&'):
op = {'*': Op.DEREF, '&': Op.REF}[r[0]]
operand = self.process(restore(r[1:]))
return Expr(op, operand)
# exponentiation operations
if self.language is not Language.C and '**' in r:
operands = list(reversed(restore(r.split('**'))))
result = self.process(operands[0])
for operand in operands[1:]:
operand = self.process(operand)
result = operand ** result
return result
# int-literal-constant
m = re.match(r'\A({digit_string})({kind}|)\Z'.format(
digit_string=r'\d+',
kind=r'_(\d+|\w[\w\d_]*)'), r)
if m:
value, _, kind = m.groups()
if kind and kind.isdigit():
kind = int(kind)
return as_integer(int(value), kind or 4)
# real-literal-constant
m = re.match(r'\A({significant}({exponent}|)|\d+{exponent})({kind}|)\Z'
.format(
significant=r'[.]\d+|\d+[.]\d*',
exponent=r'[edED][+-]?\d+',
kind=r'_(\d+|\w[\w\d_]*)'), r)
if m:
value, _, _, kind = m.groups()
if kind and kind.isdigit():
kind = int(kind)
value = value.lower()
if 'd' in value:
return as_real(float(value.replace('d', 'e')), kind or 8)
return as_real(float(value), kind or 4)
# string-literal-constant with kind parameter specification
if r in self.quotes_map:
kind = r[:r.find('@')]
return as_string(self.quotes_map[r], kind or 1)
# array constructor or literal complex constant or
# parenthesized expression
if r in raw_symbols_map:
paren = _get_parenthesis_kind(r)
items = self.process(restore(raw_symbols_map[r]),
'expr' if paren == 'ROUND' else 'args')
if paren == 'ROUND':
if isinstance(items, Expr):
return items
if paren in ['ROUNDDIV', 'SQUARE']:
# Expression is a array constructor
if isinstance(items, Expr):
items = (items,)
return as_array(items)
# function call/indexing
m = re.match(r'\A(.+)\s*(@__f2py_PARENTHESIS_(ROUND|SQUARE)_\d+@)\Z',
r)
if m:
target, args, paren = m.groups()
target = self.process(restore(target))
args = self.process(restore(args)[1:-1], 'args')
if not isinstance(args, tuple):
args = args,
if paren == 'ROUND':
kwargs = dict((a.left, a.right) for a in args
if isinstance(a, _Pair))
args = tuple(a for a in args if not isinstance(a, _Pair))
# Warning: this could also be Fortran indexing operation..
return as_apply(target, *args, **kwargs)
else:
# Expression is a C/Python indexing operation
# (e.g. used in .pyf files)
assert paren == 'SQUARE'
return target[args]
# Fortran standard conforming identifier
m = re.match(r'\A\w[\w\d_]*\Z', r)
if m:
return as_symbol(r)
# fall-back to symbol
r = self.finalize_string(restore(r))
ewarn(
f'fromstring: treating {r!r} as symbol (original={self.original})')
return as_symbol(r)
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