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1511 lines
52 KiB
1511 lines
52 KiB
3 years ago
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"""Fortran/C symbolic expressions
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References:
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- J3/21-007: Draft Fortran 202x. https://j3-fortran.org/doc/year/21/21-007.pdf
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"""
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# To analyze Fortran expressions to solve dimensions specifications,
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# for instances, we implement a minimal symbolic engine for parsing
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# expressions into a tree of expression instances. As a first
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# instance, we care only about arithmetic expressions involving
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# integers and operations like addition (+), subtraction (-),
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# multiplication (*), division (Fortran / is Python //, Fortran // is
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# concatenate), and exponentiation (**). In addition, .pyf files may
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# contain C expressions that support here is implemented as well.
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#
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# TODO: support logical constants (Op.BOOLEAN)
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# TODO: support logical operators (.AND., ...)
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# TODO: support defined operators (.MYOP., ...)
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#
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__all__ = ['Expr']
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import re
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import warnings
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from enum import Enum
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from math import gcd
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class Language(Enum):
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"""
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Used as Expr.tostring language argument.
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"""
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Python = 0
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Fortran = 1
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C = 2
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class Op(Enum):
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"""
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Used as Expr op attribute.
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"""
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INTEGER = 10
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REAL = 12
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COMPLEX = 15
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STRING = 20
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ARRAY = 30
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SYMBOL = 40
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TERNARY = 100
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APPLY = 200
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INDEXING = 210
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CONCAT = 220
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RELATIONAL = 300
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TERMS = 1000
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FACTORS = 2000
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REF = 3000
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DEREF = 3001
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class RelOp(Enum):
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"""
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Used in Op.RELATIONAL expression to specify the function part.
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"""
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EQ = 1
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NE = 2
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LT = 3
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LE = 4
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GT = 5
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GE = 6
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@classmethod
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def fromstring(cls, s, language=Language.C):
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if language is Language.Fortran:
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return {'.eq.': RelOp.EQ, '.ne.': RelOp.NE,
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'.lt.': RelOp.LT, '.le.': RelOp.LE,
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'.gt.': RelOp.GT, '.ge.': RelOp.GE}[s.lower()]
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return {'==': RelOp.EQ, '!=': RelOp.NE, '<': RelOp.LT,
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'<=': RelOp.LE, '>': RelOp.GT, '>=': RelOp.GE}[s]
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def tostring(self, language=Language.C):
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if language is Language.Fortran:
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return {RelOp.EQ: '.eq.', RelOp.NE: '.ne.',
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RelOp.LT: '.lt.', RelOp.LE: '.le.',
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RelOp.GT: '.gt.', RelOp.GE: '.ge.'}[self]
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return {RelOp.EQ: '==', RelOp.NE: '!=',
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RelOp.LT: '<', RelOp.LE: '<=',
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RelOp.GT: '>', RelOp.GE: '>='}[self]
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class ArithOp(Enum):
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"""
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Used in Op.APPLY expression to specify the function part.
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"""
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POS = 1
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NEG = 2
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ADD = 3
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SUB = 4
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MUL = 5
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DIV = 6
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POW = 7
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class OpError(Exception):
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pass
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class Precedence(Enum):
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"""
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Used as Expr.tostring precedence argument.
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"""
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ATOM = 0
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POWER = 1
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UNARY = 2
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PRODUCT = 3
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SUM = 4
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LT = 6
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EQ = 7
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LAND = 11
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LOR = 12
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TERNARY = 13
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ASSIGN = 14
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TUPLE = 15
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NONE = 100
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integer_types = (int,)
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number_types = (int, float)
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def _pairs_add(d, k, v):
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# Internal utility method for updating terms and factors data.
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c = d.get(k)
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if c is None:
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d[k] = v
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else:
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c = c + v
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if c:
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d[k] = c
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else:
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del d[k]
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class ExprWarning(UserWarning):
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pass
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def ewarn(message):
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warnings.warn(message, ExprWarning, stacklevel=2)
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class Expr:
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"""Represents a Fortran expression as a op-data pair.
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Expr instances are hashable and sortable.
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"""
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@staticmethod
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def parse(s, language=Language.C):
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"""Parse a Fortran expression to a Expr.
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"""
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return fromstring(s, language=language)
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def __init__(self, op, data):
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assert isinstance(op, Op)
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# sanity checks
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if op is Op.INTEGER:
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# data is a 2-tuple of numeric object and a kind value
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# (default is 4)
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assert isinstance(data, tuple) and len(data) == 2
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assert isinstance(data[0], int)
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assert isinstance(data[1], (int, str)), data
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elif op is Op.REAL:
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# data is a 2-tuple of numeric object and a kind value
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# (default is 4)
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assert isinstance(data, tuple) and len(data) == 2
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assert isinstance(data[0], float)
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assert isinstance(data[1], (int, str)), data
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elif op is Op.COMPLEX:
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# data is a 2-tuple of constant expressions
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assert isinstance(data, tuple) and len(data) == 2
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elif op is Op.STRING:
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# data is a 2-tuple of quoted string and a kind value
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# (default is 1)
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assert isinstance(data, tuple) and len(data) == 2
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assert (isinstance(data[0], str)
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and data[0][::len(data[0])-1] in ('""', "''", '@@'))
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assert isinstance(data[1], (int, str)), data
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elif op is Op.SYMBOL:
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# data is any hashable object
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assert hash(data) is not None
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elif op in (Op.ARRAY, Op.CONCAT):
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# data is a tuple of expressions
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assert isinstance(data, tuple)
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assert all(isinstance(item, Expr) for item in data), data
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elif op in (Op.TERMS, Op.FACTORS):
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# data is {<term|base>:<coeff|exponent>} where dict values
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# are nonzero Python integers
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assert isinstance(data, dict)
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elif op is Op.APPLY:
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# data is (<function>, <operands>, <kwoperands>) where
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# operands are Expr instances
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assert isinstance(data, tuple) and len(data) == 3
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# function is any hashable object
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assert hash(data[0]) is not None
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assert isinstance(data[1], tuple)
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assert isinstance(data[2], dict)
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elif op is Op.INDEXING:
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# data is (<object>, <indices>)
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assert isinstance(data, tuple) and len(data) == 2
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# function is any hashable object
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assert hash(data[0]) is not None
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elif op is Op.TERNARY:
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# data is (<cond>, <expr1>, <expr2>)
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assert isinstance(data, tuple) and len(data) == 3
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elif op in (Op.REF, Op.DEREF):
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# data is Expr instance
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assert isinstance(data, Expr)
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elif op is Op.RELATIONAL:
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# data is (<relop>, <left>, <right>)
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assert isinstance(data, tuple) and len(data) == 3
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else:
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raise NotImplementedError(
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f'unknown op or missing sanity check: {op}')
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self.op = op
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self.data = data
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def __eq__(self, other):
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return (isinstance(other, Expr)
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and self.op is other.op
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and self.data == other.data)
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def __hash__(self):
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if self.op in (Op.TERMS, Op.FACTORS):
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data = tuple(sorted(self.data.items()))
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elif self.op is Op.APPLY:
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data = self.data[:2] + tuple(sorted(self.data[2].items()))
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else:
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data = self.data
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return hash((self.op, data))
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def __lt__(self, other):
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if isinstance(other, Expr):
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if self.op is not other.op:
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return self.op.value < other.op.value
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if self.op in (Op.TERMS, Op.FACTORS):
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return (tuple(sorted(self.data.items()))
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< tuple(sorted(other.data.items())))
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if self.op is Op.APPLY:
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if self.data[:2] != other.data[:2]:
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return self.data[:2] < other.data[:2]
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return tuple(sorted(self.data[2].items())) < tuple(
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sorted(other.data[2].items()))
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return self.data < other.data
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return NotImplemented
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def __le__(self, other): return self == other or self < other
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def __gt__(self, other): return not (self <= other)
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def __ge__(self, other): return not (self < other)
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def __repr__(self):
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return f'{type(self).__name__}({self.op}, {self.data!r})'
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def __str__(self):
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return self.tostring()
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def tostring(self, parent_precedence=Precedence.NONE,
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language=Language.Fortran):
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"""Return a string representation of Expr.
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"""
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if self.op in (Op.INTEGER, Op.REAL):
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precedence = (Precedence.SUM if self.data[0] < 0
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else Precedence.ATOM)
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r = str(self.data[0]) + (f'_{self.data[1]}'
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if self.data[1] != 4 else '')
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elif self.op is Op.COMPLEX:
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r = ', '.join(item.tostring(Precedence.TUPLE, language=language)
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for item in self.data)
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r = '(' + r + ')'
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precedence = Precedence.ATOM
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elif self.op is Op.SYMBOL:
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precedence = Precedence.ATOM
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r = str(self.data)
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elif self.op is Op.STRING:
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r = self.data[0]
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if self.data[1] != 1:
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r = self.data[1] + '_' + r
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precedence = Precedence.ATOM
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elif self.op is Op.ARRAY:
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r = ', '.join(item.tostring(Precedence.TUPLE, language=language)
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for item in self.data)
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r = '[' + r + ']'
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precedence = Precedence.ATOM
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elif self.op is Op.TERMS:
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terms = []
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for term, coeff in sorted(self.data.items()):
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if coeff < 0:
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op = ' - '
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coeff = -coeff
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else:
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op = ' + '
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if coeff == 1:
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term = term.tostring(Precedence.SUM, language=language)
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else:
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if term == as_number(1):
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term = str(coeff)
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else:
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term = f'{coeff} * ' + term.tostring(
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Precedence.PRODUCT, language=language)
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if terms:
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terms.append(op)
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elif op == ' - ':
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terms.append('-')
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terms.append(term)
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r = ''.join(terms) or '0'
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precedence = Precedence.SUM if terms else Precedence.ATOM
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elif self.op is Op.FACTORS:
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factors = []
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tail = []
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for base, exp in sorted(self.data.items()):
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op = ' * '
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if exp == 1:
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factor = base.tostring(Precedence.PRODUCT,
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language=language)
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elif language is Language.C:
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if exp in range(2, 10):
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factor = base.tostring(Precedence.PRODUCT,
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language=language)
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factor = ' * '.join([factor] * exp)
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elif exp in range(-10, 0):
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factor = base.tostring(Precedence.PRODUCT,
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language=language)
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tail += [factor] * -exp
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continue
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else:
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factor = base.tostring(Precedence.TUPLE,
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language=language)
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factor = f'pow({factor}, {exp})'
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else:
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factor = base.tostring(Precedence.POWER,
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language=language) + f' ** {exp}'
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if factors:
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factors.append(op)
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factors.append(factor)
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if tail:
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if not factors:
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factors += ['1']
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factors += ['/', '(', ' * '.join(tail), ')']
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r = ''.join(factors) or '1'
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precedence = Precedence.PRODUCT if factors else Precedence.ATOM
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elif self.op is Op.APPLY:
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name, args, kwargs = self.data
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if name is ArithOp.DIV and language is Language.C:
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numer, denom = [arg.tostring(Precedence.PRODUCT,
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language=language)
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for arg in args]
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r = f'{numer} / {denom}'
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precedence = Precedence.PRODUCT
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else:
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||
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args = [arg.tostring(Precedence.TUPLE, language=language)
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||
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for arg in args]
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args += [k + '=' + v.tostring(Precedence.NONE)
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||
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for k, v in kwargs.items()]
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r = f'{name}({", ".join(args)})'
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precedence = Precedence.ATOM
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elif self.op is Op.INDEXING:
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name = self.data[0]
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args = [arg.tostring(Precedence.TUPLE, language=language)
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||
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for arg in self.data[1:]]
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r = f'{name}[{", ".join(args)}]'
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precedence = Precedence.ATOM
|
||
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elif self.op is Op.CONCAT:
|
||
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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: deterimine 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: deterimine 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)
|