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Diffstat (limited to '.venv/lib/python3.12/site-packages/numpy/f2py/symbolic.py')
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diff --git a/.venv/lib/python3.12/site-packages/numpy/f2py/symbolic.py b/.venv/lib/python3.12/site-packages/numpy/f2py/symbolic.py new file mode 100644 index 00000000..67120d79 --- /dev/null +++ b/.venv/lib/python3.12/site-packages/numpy/f2py/symbolic.py @@ -0,0 +1,1517 @@ +"""Fortran/C symbolic expressions + +References: +- J3/21-007: Draft Fortran 202x. https://j3-fortran.org/doc/year/21/21-007.pdf + +Copyright 1999 -- 2011 Pearu Peterson all rights reserved. +Copyright 2011 -- present NumPy Developers. +Permission to use, modify, and distribute this software is given under the +terms of the NumPy License. + +NO WARRANTY IS EXPRESSED OR IMPLIED. USE AT YOUR OWN RISK. +""" + +# 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) |