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stringlengths 2
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⌀ | name
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| docstring
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10,224 | pygments.lexer | add_filter |
Add a new stream filter to this lexer.
| def add_filter(self, filter_, **options):
"""
Add a new stream filter to this lexer.
"""
if not isinstance(filter_, Filter):
filter_ = get_filter_by_name(filter_, **options)
self.filters.append(filter_)
| (self, filter_, **options) |
10,225 | pygments.util | text_analyse |
A static method which is called for lexer guessing.
It should analyse the text and return a float in the range
from ``0.0`` to ``1.0``. If it returns ``0.0``, the lexer
will not be selected as the most probable one, if it returns
``1.0``, it will be selected immediately. This is used by
`guess_lexer`.
The `LexerMeta` metaclass automatically wraps this function so
that it works like a static method (no ``self`` or ``cls``
parameter) and the return value is automatically converted to
`float`. If the return value is an object that is boolean `False`
it's the same as if the return values was ``0.0``.
| def make_analysator(f):
"""Return a static text analyser function that returns float values."""
def text_analyse(text):
try:
rv = f(text)
except Exception:
return 0.0
if not rv:
return 0.0
try:
return min(1.0, max(0.0, float(rv)))
except (ValueError, TypeError):
return 0.0
text_analyse.__doc__ = f.__doc__
return staticmethod(text_analyse)
| (text) |
10,226 | pygments.lexer | get_tokens |
This method is the basic interface of a lexer. It is called by
the `highlight()` function. It must process the text and return an
iterable of ``(tokentype, value)`` pairs from `text`.
Normally, you don't need to override this method. The default
implementation processes the options recognized by all lexers
(`stripnl`, `stripall` and so on), and then yields all tokens
from `get_tokens_unprocessed()`, with the ``index`` dropped.
If `unfiltered` is set to `True`, the filtering mechanism is
bypassed even if filters are defined.
| def get_tokens(self, text, unfiltered=False):
"""
This method is the basic interface of a lexer. It is called by
the `highlight()` function. It must process the text and return an
iterable of ``(tokentype, value)`` pairs from `text`.
Normally, you don't need to override this method. The default
implementation processes the options recognized by all lexers
(`stripnl`, `stripall` and so on), and then yields all tokens
from `get_tokens_unprocessed()`, with the ``index`` dropped.
If `unfiltered` is set to `True`, the filtering mechanism is
bypassed even if filters are defined.
"""
text = self._preprocess_lexer_input(text)
def streamer():
for _, t, v in self.get_tokens_unprocessed(text):
yield t, v
stream = streamer()
if not unfiltered:
stream = apply_filters(stream, self.filters, self)
return stream
| (self, text, unfiltered=False) |
10,227 | pygments.lexer | get_tokens_unprocessed |
Split ``text`` into (tokentype, text) pairs.
``stack`` is the initial stack (default: ``['root']``)
| def get_tokens_unprocessed(self, text, stack=('root',)):
"""
Split ``text`` into (tokentype, text) pairs.
``stack`` is the initial stack (default: ``['root']``)
"""
pos = 0
tokendefs = self._tokens
statestack = list(stack)
statetokens = tokendefs[statestack[-1]]
while 1:
for rexmatch, action, new_state in statetokens:
m = rexmatch(text, pos)
if m:
if action is not None:
if type(action) is _TokenType:
yield pos, action, m.group()
else:
yield from action(self, m)
pos = m.end()
if new_state is not None:
# state transition
if isinstance(new_state, tuple):
for state in new_state:
if state == '#pop':
if len(statestack) > 1:
statestack.pop()
elif state == '#push':
statestack.append(statestack[-1])
else:
statestack.append(state)
elif isinstance(new_state, int):
# pop, but keep at least one state on the stack
# (random code leading to unexpected pops should
# not allow exceptions)
if abs(new_state) >= len(statestack):
del statestack[1:]
else:
del statestack[new_state:]
elif new_state == '#push':
statestack.append(statestack[-1])
else:
assert False, f"wrong state def: {new_state!r}"
statetokens = tokendefs[statestack[-1]]
break
else:
# We are here only if all state tokens have been considered
# and there was not a match on any of them.
try:
if text[pos] == '\n':
# at EOL, reset state to "root"
statestack = ['root']
statetokens = tokendefs['root']
yield pos, Whitespace, '\n'
pos += 1
continue
yield pos, Error, text[pos]
pos += 1
except IndexError:
break
| (self, text, stack=('root',)) |
10,229 | itertools | chain | chain(*iterables) --> chain object
Return a chain object whose .__next__() method returns elements from the
first iterable until it is exhausted, then elements from the next
iterable, until all of the iterables are exhausted. | from itertools import chain
| null |
10,230 | wsdiff | cli | null | def cli():
parser = argparse.ArgumentParser(description="Given two source files or directories this application creates an html page that highlights the differences between the two.")
parser.add_argument('-b', '--open', action='store_true', help='Open output file in a browser')
parser.add_argument('-s', '--syntax-css', help='Path to custom Pygments CSS file for code syntax highlighting')
parser.add_argument('-l', '--lexer', help='Manually select pygments lexer (default: guess from filename, use -L to list available lexers.)')
parser.add_argument('-L', '--list-lexers', action='store_true', help='List available lexers for -l/--lexer')
parser.add_argument('-t', '--pagetitle', help='Override page title of output HTML file')
parser.add_argument('-o', '--output', default=sys.stdout, type=argparse.FileType('w'), help='Name of output file (default: stdout)')
parser.add_argument('--header', action='store_true', help='Only output HTML header with stylesheets and stuff, and no diff')
parser.add_argument('--content', action='store_true', help='Only output HTML content, without header')
parser.add_argument('--nofilename', action='store_true', help='Do not output file name headers')
parser.add_argument('old', nargs='?', help='source file or directory to compare ("before" file)')
parser.add_argument('new', nargs='?', help='source file or directory to compare ("after" file)')
args = parser.parse_args()
if args.list_lexers:
for longname, aliases, filename_patterns, _mimetypes in get_all_lexers():
print(f'{longname:<20} alias {"/".join(aliases)} for {", ".join(filename_patterns)}')
sys.exit(0)
if args.pagetitle or (args.old and args.new):
pagetitle = args.pagetitle or f'diff: {args.old} / {args.new}'
else:
pagetitle = 'diff'
if args.syntax_css:
syntax_css = Path(args.syntax_css).read_text()
else:
syntax_css = PYGMENTS_CSS
if args.header:
print(string.Template(HTML_TEMPLATE).substitute(
title=pagetitle,
pygments_css=syntax_css,
main_css=MAIN_CSS,
diff_style_toggle=DIFF_STYLE_TOGGLE,
diff_style_script=DIFF_STYLE_SCRIPT,
body='$body'), file=args.output)
sys.exit(0)
if not (args.old and args.new):
print('Error: The command line arguments "old" and "new" are required.', file=sys.stderr)
parser.print_usage()
sys.exit(2)
if args.open and args.output == sys.stdout:
print('Error: --open requires --output to be given.', file=sys.stderr)
parser.print_usage()
sys.exit(2)
old, new = Path(args.old), Path(args.new)
if not old.exists():
print(f'Error: Path "{old}" does not exist.', file=sys.stderr)
sys.exit(1)
if not new.exists():
print(f'Error: Path "{new}" does not exist.', file=sys.stderr)
sys.exit(1)
if old.is_file() != new.is_file():
print(f'Error: You must give either two files, or two paths to compare, not a mix of both.', file=sys.stderr)
sys.exit(1)
if old.is_file():
found_files = {str(new): (old, new)}
else:
found_files = defaultdict(lambda: [None, None])
for fn in old.glob('**/*'):
found_files[str(fn.relative_to(old))][0] = fn
for fn in new.glob('**/*'):
found_files[str(fn.relative_to(new))][1] = fn
diff_blocks = []
for suffix, (old, new) in sorted(found_files.items()):
old_text = '' if old is None else old.read_text()
new_text = '' if new is None else new.read_text()
if args.lexer:
lexer = get_lexer_by_name(lexer)
else:
try:
lexer = guess_lexer_for_filename(new, new_text)
except:
lexer = get_lexer_by_name('text')
diff_blocks.append(html_diff_block(old_text, new_text, suffix, lexer, hide_filename=args.nofilename))
body = '\n'.join(diff_blocks)
if args.content:
print(body, file=args.output)
else:
print(string.Template(HTML_TEMPLATE).substitute(
title=pagetitle,
pygments_css=syntax_css,
main_css=MAIN_CSS,
diff_style_toggle=DIFF_STYLE_TOGGLE,
diff_style_script=DIFF_STYLE_SCRIPT,
body=body), file=args.output)
if args.open:
webbrowser.open('file://' + str(Path(args.output.name).absolute()))
| () |
10,231 | collections | defaultdict | defaultdict(default_factory=None, /, [...]) --> dict with default factory
The default factory is called without arguments to produce
a new value when a key is not present, in __getitem__ only.
A defaultdict compares equal to a dict with the same items.
All remaining arguments are treated the same as if they were
passed to the dict constructor, including keyword arguments.
| from collections import defaultdict
| null |
10,233 | pygments.lexers | get_all_lexers | Return a generator of tuples in the form ``(name, aliases,
filenames, mimetypes)`` of all know lexers.
If *plugins* is true (the default), plugin lexers supplied by entrypoints
are also returned. Otherwise, only builtin ones are considered.
| def get_all_lexers(plugins=True):
"""Return a generator of tuples in the form ``(name, aliases,
filenames, mimetypes)`` of all know lexers.
If *plugins* is true (the default), plugin lexers supplied by entrypoints
are also returned. Otherwise, only builtin ones are considered.
"""
for item in LEXERS.values():
yield item[1:]
if plugins:
for lexer in find_plugin_lexers():
yield lexer.name, lexer.aliases, lexer.filenames, lexer.mimetypes
| (plugins=True) |
10,234 | pygments.lexers | get_lexer_by_name |
Return an instance of a `Lexer` subclass that has `alias` in its
aliases list. The lexer is given the `options` at its
instantiation.
Will raise :exc:`pygments.util.ClassNotFound` if no lexer with that alias is
found.
| def get_lexer_by_name(_alias, **options):
"""
Return an instance of a `Lexer` subclass that has `alias` in its
aliases list. The lexer is given the `options` at its
instantiation.
Will raise :exc:`pygments.util.ClassNotFound` if no lexer with that alias is
found.
"""
if not _alias:
raise ClassNotFound(f'no lexer for alias {_alias!r} found')
# lookup builtin lexers
for module_name, name, aliases, _, _ in LEXERS.values():
if _alias.lower() in aliases:
if name not in _lexer_cache:
_load_lexers(module_name)
return _lexer_cache[name](**options)
# continue with lexers from setuptools entrypoints
for cls in find_plugin_lexers():
if _alias.lower() in cls.aliases:
return cls(**options)
raise ClassNotFound(f'no lexer for alias {_alias!r} found')
| (_alias, **options) |
10,235 | itertools | groupby | make an iterator that returns consecutive keys and groups from the iterable
iterable
Elements to divide into groups according to the key function.
key
A function for computing the group category for each element.
If the key function is not specified or is None, the element itself
is used for grouping. | from itertools import groupby
| (iterable, key=None) |
10,236 | pygments.lexers | guess_lexer_for_filename |
As :func:`guess_lexer()`, but only lexers which have a pattern in `filenames`
or `alias_filenames` that matches `filename` are taken into consideration.
:exc:`pygments.util.ClassNotFound` is raised if no lexer thinks it can
handle the content.
| def guess_lexer_for_filename(_fn, _text, **options):
"""
As :func:`guess_lexer()`, but only lexers which have a pattern in `filenames`
or `alias_filenames` that matches `filename` are taken into consideration.
:exc:`pygments.util.ClassNotFound` is raised if no lexer thinks it can
handle the content.
"""
fn = basename(_fn)
primary = {}
matching_lexers = set()
for lexer in _iter_lexerclasses():
for filename in lexer.filenames:
if _fn_matches(fn, filename):
matching_lexers.add(lexer)
primary[lexer] = True
for filename in lexer.alias_filenames:
if _fn_matches(fn, filename):
matching_lexers.add(lexer)
primary[lexer] = False
if not matching_lexers:
raise ClassNotFound(f'no lexer for filename {fn!r} found')
if len(matching_lexers) == 1:
return matching_lexers.pop()(**options)
result = []
for lexer in matching_lexers:
rv = lexer.analyse_text(_text)
if rv == 1.0:
return lexer(**options)
result.append((rv, lexer))
def type_sort(t):
# sort by:
# - analyse score
# - is primary filename pattern?
# - priority
# - last resort: class name
return (t[0], primary[t[1]], t[1].priority, t[1].__name__)
result.sort(key=type_sort)
return result[-1][1](**options)
| (_fn, _text, **options) |
10,238 | wsdiff | html_diff_block | null | def html_diff_block(old, new, filename, lexer, hide_filename=True):
code = html_diff_content(old, new, lexer)
filename = f'<div class="wsd-file-title"><div class="wsd-filename">‭{filename}</div></div>'
if hide_filename:
filename = ''
return textwrap.dedent(f'''<div class="wsd-file-container">
{filename}
<div class="wsd-diff">
{code}
</div>
</div>''')
| (old, new, filename, lexer, hide_filename=True) |
10,239 | wsdiff | html_diff_content | null | def html_diff_content(old, new, lexer):
diff = list(difflib._mdiff(old.splitlines(), new.splitlines()))
fmt_l = RecordFormatter('left', diff)
pygments.highlight(old, lexer, fmt_l)
fmt_r = RecordFormatter('right', diff)
pygments.highlight(new, lexer, fmt_r)
return '\n'.join(chain.from_iterable(zip(fmt_l.lines, fmt_r.lines)))
| (old, new, lexer) |
10,241 | wsdiff | iter_token_lines | null | def iter_token_lines(tokensource):
lineno = 1
for ttype, value in tokensource:
left, newline, right = value.partition('\n')
while newline:
yield lineno, ttype, left
lineno += 1
left, newline, right = right.partition('\n')
if left != '':
yield lineno, ttype, left
| (tokensource) |
10,242 | functools | lru_cache | Least-recently-used cache decorator.
If *maxsize* is set to None, the LRU features are disabled and the cache
can grow without bound.
If *typed* is True, arguments of different types will be cached separately.
For example, f(3.0) and f(3) will be treated as distinct calls with
distinct results.
Arguments to the cached function must be hashable.
View the cache statistics named tuple (hits, misses, maxsize, currsize)
with f.cache_info(). Clear the cache and statistics with f.cache_clear().
Access the underlying function with f.__wrapped__.
See: https://en.wikipedia.org/wiki/Cache_replacement_policies#Least_recently_used_(LRU)
| def lru_cache(maxsize=128, typed=False):
"""Least-recently-used cache decorator.
If *maxsize* is set to None, the LRU features are disabled and the cache
can grow without bound.
If *typed* is True, arguments of different types will be cached separately.
For example, f(3.0) and f(3) will be treated as distinct calls with
distinct results.
Arguments to the cached function must be hashable.
View the cache statistics named tuple (hits, misses, maxsize, currsize)
with f.cache_info(). Clear the cache and statistics with f.cache_clear().
Access the underlying function with f.__wrapped__.
See: https://en.wikipedia.org/wiki/Cache_replacement_policies#Least_recently_used_(LRU)
"""
# Users should only access the lru_cache through its public API:
# cache_info, cache_clear, and f.__wrapped__
# The internals of the lru_cache are encapsulated for thread safety and
# to allow the implementation to change (including a possible C version).
if isinstance(maxsize, int):
# Negative maxsize is treated as 0
if maxsize < 0:
maxsize = 0
elif callable(maxsize) and isinstance(typed, bool):
# The user_function was passed in directly via the maxsize argument
user_function, maxsize = maxsize, 128
wrapper = _lru_cache_wrapper(user_function, maxsize, typed, _CacheInfo)
wrapper.cache_parameters = lambda : {'maxsize': maxsize, 'typed': typed}
return update_wrapper(wrapper, user_function)
elif maxsize is not None:
raise TypeError(
'Expected first argument to be an integer, a callable, or None')
def decorating_function(user_function):
wrapper = _lru_cache_wrapper(user_function, maxsize, typed, _CacheInfo)
wrapper.cache_parameters = lambda : {'maxsize': maxsize, 'typed': typed}
return update_wrapper(wrapper, user_function)
return decorating_function
| (maxsize=128, typed=False) |
10,251 | collections | Counter | Dict subclass for counting hashable items. Sometimes called a bag
or multiset. Elements are stored as dictionary keys and their counts
are stored as dictionary values.
>>> c = Counter('abcdeabcdabcaba') # count elements from a string
>>> c.most_common(3) # three most common elements
[('a', 5), ('b', 4), ('c', 3)]
>>> sorted(c) # list all unique elements
['a', 'b', 'c', 'd', 'e']
>>> ''.join(sorted(c.elements())) # list elements with repetitions
'aaaaabbbbcccdde'
>>> sum(c.values()) # total of all counts
15
>>> c['a'] # count of letter 'a'
5
>>> for elem in 'shazam': # update counts from an iterable
... c[elem] += 1 # by adding 1 to each element's count
>>> c['a'] # now there are seven 'a'
7
>>> del c['b'] # remove all 'b'
>>> c['b'] # now there are zero 'b'
0
>>> d = Counter('simsalabim') # make another counter
>>> c.update(d) # add in the second counter
>>> c['a'] # now there are nine 'a'
9
>>> c.clear() # empty the counter
>>> c
Counter()
Note: If a count is set to zero or reduced to zero, it will remain
in the counter until the entry is deleted or the counter is cleared:
>>> c = Counter('aaabbc')
>>> c['b'] -= 2 # reduce the count of 'b' by two
>>> c.most_common() # 'b' is still in, but its count is zero
[('a', 3), ('c', 1), ('b', 0)]
| class Counter(dict):
'''Dict subclass for counting hashable items. Sometimes called a bag
or multiset. Elements are stored as dictionary keys and their counts
are stored as dictionary values.
>>> c = Counter('abcdeabcdabcaba') # count elements from a string
>>> c.most_common(3) # three most common elements
[('a', 5), ('b', 4), ('c', 3)]
>>> sorted(c) # list all unique elements
['a', 'b', 'c', 'd', 'e']
>>> ''.join(sorted(c.elements())) # list elements with repetitions
'aaaaabbbbcccdde'
>>> sum(c.values()) # total of all counts
15
>>> c['a'] # count of letter 'a'
5
>>> for elem in 'shazam': # update counts from an iterable
... c[elem] += 1 # by adding 1 to each element's count
>>> c['a'] # now there are seven 'a'
7
>>> del c['b'] # remove all 'b'
>>> c['b'] # now there are zero 'b'
0
>>> d = Counter('simsalabim') # make another counter
>>> c.update(d) # add in the second counter
>>> c['a'] # now there are nine 'a'
9
>>> c.clear() # empty the counter
>>> c
Counter()
Note: If a count is set to zero or reduced to zero, it will remain
in the counter until the entry is deleted or the counter is cleared:
>>> c = Counter('aaabbc')
>>> c['b'] -= 2 # reduce the count of 'b' by two
>>> c.most_common() # 'b' is still in, but its count is zero
[('a', 3), ('c', 1), ('b', 0)]
'''
# References:
# http://en.wikipedia.org/wiki/Multiset
# http://www.gnu.org/software/smalltalk/manual-base/html_node/Bag.html
# http://www.demo2s.com/Tutorial/Cpp/0380__set-multiset/Catalog0380__set-multiset.htm
# http://code.activestate.com/recipes/259174/
# Knuth, TAOCP Vol. II section 4.6.3
def __init__(self, iterable=None, /, **kwds):
'''Create a new, empty Counter object. And if given, count elements
from an input iterable. Or, initialize the count from another mapping
of elements to their counts.
>>> c = Counter() # a new, empty counter
>>> c = Counter('gallahad') # a new counter from an iterable
>>> c = Counter({'a': 4, 'b': 2}) # a new counter from a mapping
>>> c = Counter(a=4, b=2) # a new counter from keyword args
'''
super().__init__()
self.update(iterable, **kwds)
def __missing__(self, key):
'The count of elements not in the Counter is zero.'
# Needed so that self[missing_item] does not raise KeyError
return 0
def total(self):
'Sum of the counts'
return sum(self.values())
def most_common(self, n=None):
'''List the n most common elements and their counts from the most
common to the least. If n is None, then list all element counts.
>>> Counter('abracadabra').most_common(3)
[('a', 5), ('b', 2), ('r', 2)]
'''
# Emulate Bag.sortedByCount from Smalltalk
if n is None:
return sorted(self.items(), key=_itemgetter(1), reverse=True)
# Lazy import to speedup Python startup time
import heapq
return heapq.nlargest(n, self.items(), key=_itemgetter(1))
def elements(self):
'''Iterator over elements repeating each as many times as its count.
>>> c = Counter('ABCABC')
>>> sorted(c.elements())
['A', 'A', 'B', 'B', 'C', 'C']
# Knuth's example for prime factors of 1836: 2**2 * 3**3 * 17**1
>>> prime_factors = Counter({2: 2, 3: 3, 17: 1})
>>> product = 1
>>> for factor in prime_factors.elements(): # loop over factors
... product *= factor # and multiply them
>>> product
1836
Note, if an element's count has been set to zero or is a negative
number, elements() will ignore it.
'''
# Emulate Bag.do from Smalltalk and Multiset.begin from C++.
return _chain.from_iterable(_starmap(_repeat, self.items()))
# Override dict methods where necessary
@classmethod
def fromkeys(cls, iterable, v=None):
# There is no equivalent method for counters because the semantics
# would be ambiguous in cases such as Counter.fromkeys('aaabbc', v=2).
# Initializing counters to zero values isn't necessary because zero
# is already the default value for counter lookups. Initializing
# to one is easily accomplished with Counter(set(iterable)). For
# more exotic cases, create a dictionary first using a dictionary
# comprehension or dict.fromkeys().
raise NotImplementedError(
'Counter.fromkeys() is undefined. Use Counter(iterable) instead.')
def update(self, iterable=None, /, **kwds):
'''Like dict.update() but add counts instead of replacing them.
Source can be an iterable, a dictionary, or another Counter instance.
>>> c = Counter('which')
>>> c.update('witch') # add elements from another iterable
>>> d = Counter('watch')
>>> c.update(d) # add elements from another counter
>>> c['h'] # four 'h' in which, witch, and watch
4
'''
# The regular dict.update() operation makes no sense here because the
# replace behavior results in the some of original untouched counts
# being mixed-in with all of the other counts for a mismash that
# doesn't have a straight-forward interpretation in most counting
# contexts. Instead, we implement straight-addition. Both the inputs
# and outputs are allowed to contain zero and negative counts.
if iterable is not None:
if isinstance(iterable, _collections_abc.Mapping):
if self:
self_get = self.get
for elem, count in iterable.items():
self[elem] = count + self_get(elem, 0)
else:
# fast path when counter is empty
super().update(iterable)
else:
_count_elements(self, iterable)
if kwds:
self.update(kwds)
def subtract(self, iterable=None, /, **kwds):
'''Like dict.update() but subtracts counts instead of replacing them.
Counts can be reduced below zero. Both the inputs and outputs are
allowed to contain zero and negative counts.
Source can be an iterable, a dictionary, or another Counter instance.
>>> c = Counter('which')
>>> c.subtract('witch') # subtract elements from another iterable
>>> c.subtract(Counter('watch')) # subtract elements from another counter
>>> c['h'] # 2 in which, minus 1 in witch, minus 1 in watch
0
>>> c['w'] # 1 in which, minus 1 in witch, minus 1 in watch
-1
'''
if iterable is not None:
self_get = self.get
if isinstance(iterable, _collections_abc.Mapping):
for elem, count in iterable.items():
self[elem] = self_get(elem, 0) - count
else:
for elem in iterable:
self[elem] = self_get(elem, 0) - 1
if kwds:
self.subtract(kwds)
def copy(self):
'Return a shallow copy.'
return self.__class__(self)
def __reduce__(self):
return self.__class__, (dict(self),)
def __delitem__(self, elem):
'Like dict.__delitem__() but does not raise KeyError for missing values.'
if elem in self:
super().__delitem__(elem)
def __eq__(self, other):
'True if all counts agree. Missing counts are treated as zero.'
if not isinstance(other, Counter):
return NotImplemented
return all(self[e] == other[e] for c in (self, other) for e in c)
def __ne__(self, other):
'True if any counts disagree. Missing counts are treated as zero.'
if not isinstance(other, Counter):
return NotImplemented
return not self == other
def __le__(self, other):
'True if all counts in self are a subset of those in other.'
if not isinstance(other, Counter):
return NotImplemented
return all(self[e] <= other[e] for c in (self, other) for e in c)
def __lt__(self, other):
'True if all counts in self are a proper subset of those in other.'
if not isinstance(other, Counter):
return NotImplemented
return self <= other and self != other
def __ge__(self, other):
'True if all counts in self are a superset of those in other.'
if not isinstance(other, Counter):
return NotImplemented
return all(self[e] >= other[e] for c in (self, other) for e in c)
def __gt__(self, other):
'True if all counts in self are a proper superset of those in other.'
if not isinstance(other, Counter):
return NotImplemented
return self >= other and self != other
def __repr__(self):
if not self:
return f'{self.__class__.__name__}()'
try:
# dict() preserves the ordering returned by most_common()
d = dict(self.most_common())
except TypeError:
# handle case where values are not orderable
d = dict(self)
return f'{self.__class__.__name__}({d!r})'
# Multiset-style mathematical operations discussed in:
# Knuth TAOCP Volume II section 4.6.3 exercise 19
# and at http://en.wikipedia.org/wiki/Multiset
#
# Outputs guaranteed to only include positive counts.
#
# To strip negative and zero counts, add-in an empty counter:
# c += Counter()
#
# Results are ordered according to when an element is first
# encountered in the left operand and then by the order
# encountered in the right operand.
#
# When the multiplicities are all zero or one, multiset operations
# are guaranteed to be equivalent to the corresponding operations
# for regular sets.
# Given counter multisets such as:
# cp = Counter(a=1, b=0, c=1)
# cq = Counter(c=1, d=0, e=1)
# The corresponding regular sets would be:
# sp = {'a', 'c'}
# sq = {'c', 'e'}
# All of the following relations would hold:
# set(cp + cq) == sp | sq
# set(cp - cq) == sp - sq
# set(cp | cq) == sp | sq
# set(cp & cq) == sp & sq
# (cp == cq) == (sp == sq)
# (cp != cq) == (sp != sq)
# (cp <= cq) == (sp <= sq)
# (cp < cq) == (sp < sq)
# (cp >= cq) == (sp >= sq)
# (cp > cq) == (sp > sq)
def __add__(self, other):
'''Add counts from two counters.
>>> Counter('abbb') + Counter('bcc')
Counter({'b': 4, 'c': 2, 'a': 1})
'''
if not isinstance(other, Counter):
return NotImplemented
result = Counter()
for elem, count in self.items():
newcount = count + other[elem]
if newcount > 0:
result[elem] = newcount
for elem, count in other.items():
if elem not in self and count > 0:
result[elem] = count
return result
def __sub__(self, other):
''' Subtract count, but keep only results with positive counts.
>>> Counter('abbbc') - Counter('bccd')
Counter({'b': 2, 'a': 1})
'''
if not isinstance(other, Counter):
return NotImplemented
result = Counter()
for elem, count in self.items():
newcount = count - other[elem]
if newcount > 0:
result[elem] = newcount
for elem, count in other.items():
if elem not in self and count < 0:
result[elem] = 0 - count
return result
def __or__(self, other):
'''Union is the maximum of value in either of the input counters.
>>> Counter('abbb') | Counter('bcc')
Counter({'b': 3, 'c': 2, 'a': 1})
'''
if not isinstance(other, Counter):
return NotImplemented
result = Counter()
for elem, count in self.items():
other_count = other[elem]
newcount = other_count if count < other_count else count
if newcount > 0:
result[elem] = newcount
for elem, count in other.items():
if elem not in self and count > 0:
result[elem] = count
return result
def __and__(self, other):
''' Intersection is the minimum of corresponding counts.
>>> Counter('abbb') & Counter('bcc')
Counter({'b': 1})
'''
if not isinstance(other, Counter):
return NotImplemented
result = Counter()
for elem, count in self.items():
other_count = other[elem]
newcount = count if count < other_count else other_count
if newcount > 0:
result[elem] = newcount
return result
def __pos__(self):
'Adds an empty counter, effectively stripping negative and zero counts'
result = Counter()
for elem, count in self.items():
if count > 0:
result[elem] = count
return result
def __neg__(self):
'''Subtracts from an empty counter. Strips positive and zero counts,
and flips the sign on negative counts.
'''
result = Counter()
for elem, count in self.items():
if count < 0:
result[elem] = 0 - count
return result
def _keep_positive(self):
'''Internal method to strip elements with a negative or zero count'''
nonpositive = [elem for elem, count in self.items() if not count > 0]
for elem in nonpositive:
del self[elem]
return self
def __iadd__(self, other):
'''Inplace add from another counter, keeping only positive counts.
>>> c = Counter('abbb')
>>> c += Counter('bcc')
>>> c
Counter({'b': 4, 'c': 2, 'a': 1})
'''
for elem, count in other.items():
self[elem] += count
return self._keep_positive()
def __isub__(self, other):
'''Inplace subtract counter, but keep only results with positive counts.
>>> c = Counter('abbbc')
>>> c -= Counter('bccd')
>>> c
Counter({'b': 2, 'a': 1})
'''
for elem, count in other.items():
self[elem] -= count
return self._keep_positive()
def __ior__(self, other):
'''Inplace union is the maximum of value from either counter.
>>> c = Counter('abbb')
>>> c |= Counter('bcc')
>>> c
Counter({'b': 3, 'c': 2, 'a': 1})
'''
for elem, other_count in other.items():
count = self[elem]
if other_count > count:
self[elem] = other_count
return self._keep_positive()
def __iand__(self, other):
'''Inplace intersection is the minimum of corresponding counts.
>>> c = Counter('abbb')
>>> c &= Counter('bcc')
>>> c
Counter({'b': 1})
'''
for elem, count in self.items():
other_count = other[elem]
if other_count < count:
self[elem] = other_count
return self._keep_positive()
| (iterable=None, /, **kwds) |
10,252 | collections | __add__ | Add counts from two counters.
>>> Counter('abbb') + Counter('bcc')
Counter({'b': 4, 'c': 2, 'a': 1})
| def __add__(self, other):
'''Add counts from two counters.
>>> Counter('abbb') + Counter('bcc')
Counter({'b': 4, 'c': 2, 'a': 1})
'''
if not isinstance(other, Counter):
return NotImplemented
result = Counter()
for elem, count in self.items():
newcount = count + other[elem]
if newcount > 0:
result[elem] = newcount
for elem, count in other.items():
if elem not in self and count > 0:
result[elem] = count
return result
| (self, other) |
10,253 | collections | __and__ | Intersection is the minimum of corresponding counts.
>>> Counter('abbb') & Counter('bcc')
Counter({'b': 1})
| def __and__(self, other):
''' Intersection is the minimum of corresponding counts.
>>> Counter('abbb') & Counter('bcc')
Counter({'b': 1})
'''
if not isinstance(other, Counter):
return NotImplemented
result = Counter()
for elem, count in self.items():
other_count = other[elem]
newcount = count if count < other_count else other_count
if newcount > 0:
result[elem] = newcount
return result
| (self, other) |
10,254 | collections | __delitem__ | Like dict.__delitem__() but does not raise KeyError for missing values. | def __delitem__(self, elem):
'Like dict.__delitem__() but does not raise KeyError for missing values.'
if elem in self:
super().__delitem__(elem)
| (self, elem) |
10,255 | collections | __eq__ | True if all counts agree. Missing counts are treated as zero. | def __eq__(self, other):
'True if all counts agree. Missing counts are treated as zero.'
if not isinstance(other, Counter):
return NotImplemented
return all(self[e] == other[e] for c in (self, other) for e in c)
| (self, other) |
10,256 | collections | __ge__ | True if all counts in self are a superset of those in other. | def __ge__(self, other):
'True if all counts in self are a superset of those in other.'
if not isinstance(other, Counter):
return NotImplemented
return all(self[e] >= other[e] for c in (self, other) for e in c)
| (self, other) |
10,257 | collections | __gt__ | True if all counts in self are a proper superset of those in other. | def __gt__(self, other):
'True if all counts in self are a proper superset of those in other.'
if not isinstance(other, Counter):
return NotImplemented
return self >= other and self != other
| (self, other) |
10,258 | collections | __iadd__ | Inplace add from another counter, keeping only positive counts.
>>> c = Counter('abbb')
>>> c += Counter('bcc')
>>> c
Counter({'b': 4, 'c': 2, 'a': 1})
| def __iadd__(self, other):
'''Inplace add from another counter, keeping only positive counts.
>>> c = Counter('abbb')
>>> c += Counter('bcc')
>>> c
Counter({'b': 4, 'c': 2, 'a': 1})
'''
for elem, count in other.items():
self[elem] += count
return self._keep_positive()
| (self, other) |
10,259 | collections | __iand__ | Inplace intersection is the minimum of corresponding counts.
>>> c = Counter('abbb')
>>> c &= Counter('bcc')
>>> c
Counter({'b': 1})
| def __iand__(self, other):
'''Inplace intersection is the minimum of corresponding counts.
>>> c = Counter('abbb')
>>> c &= Counter('bcc')
>>> c
Counter({'b': 1})
'''
for elem, count in self.items():
other_count = other[elem]
if other_count < count:
self[elem] = other_count
return self._keep_positive()
| (self, other) |
10,260 | collections | __init__ | Create a new, empty Counter object. And if given, count elements
from an input iterable. Or, initialize the count from another mapping
of elements to their counts.
>>> c = Counter() # a new, empty counter
>>> c = Counter('gallahad') # a new counter from an iterable
>>> c = Counter({'a': 4, 'b': 2}) # a new counter from a mapping
>>> c = Counter(a=4, b=2) # a new counter from keyword args
| def __init__(self, iterable=None, /, **kwds):
'''Create a new, empty Counter object. And if given, count elements
from an input iterable. Or, initialize the count from another mapping
of elements to their counts.
>>> c = Counter() # a new, empty counter
>>> c = Counter('gallahad') # a new counter from an iterable
>>> c = Counter({'a': 4, 'b': 2}) # a new counter from a mapping
>>> c = Counter(a=4, b=2) # a new counter from keyword args
'''
super().__init__()
self.update(iterable, **kwds)
| (self, iterable=None, /, **kwds) |
10,261 | collections | __ior__ | Inplace union is the maximum of value from either counter.
>>> c = Counter('abbb')
>>> c |= Counter('bcc')
>>> c
Counter({'b': 3, 'c': 2, 'a': 1})
| def __ior__(self, other):
'''Inplace union is the maximum of value from either counter.
>>> c = Counter('abbb')
>>> c |= Counter('bcc')
>>> c
Counter({'b': 3, 'c': 2, 'a': 1})
'''
for elem, other_count in other.items():
count = self[elem]
if other_count > count:
self[elem] = other_count
return self._keep_positive()
| (self, other) |
10,262 | collections | __isub__ | Inplace subtract counter, but keep only results with positive counts.
>>> c = Counter('abbbc')
>>> c -= Counter('bccd')
>>> c
Counter({'b': 2, 'a': 1})
| def __isub__(self, other):
'''Inplace subtract counter, but keep only results with positive counts.
>>> c = Counter('abbbc')
>>> c -= Counter('bccd')
>>> c
Counter({'b': 2, 'a': 1})
'''
for elem, count in other.items():
self[elem] -= count
return self._keep_positive()
| (self, other) |
10,263 | collections | __le__ | True if all counts in self are a subset of those in other. | def __le__(self, other):
'True if all counts in self are a subset of those in other.'
if not isinstance(other, Counter):
return NotImplemented
return all(self[e] <= other[e] for c in (self, other) for e in c)
| (self, other) |
10,264 | collections | __lt__ | True if all counts in self are a proper subset of those in other. | def __lt__(self, other):
'True if all counts in self are a proper subset of those in other.'
if not isinstance(other, Counter):
return NotImplemented
return self <= other and self != other
| (self, other) |
10,265 | collections | __missing__ | The count of elements not in the Counter is zero. | def __missing__(self, key):
'The count of elements not in the Counter is zero.'
# Needed so that self[missing_item] does not raise KeyError
return 0
| (self, key) |
10,266 | collections | __ne__ | True if any counts disagree. Missing counts are treated as zero. | def __ne__(self, other):
'True if any counts disagree. Missing counts are treated as zero.'
if not isinstance(other, Counter):
return NotImplemented
return not self == other
| (self, other) |
10,267 | collections | __neg__ | Subtracts from an empty counter. Strips positive and zero counts,
and flips the sign on negative counts.
| def __neg__(self):
'''Subtracts from an empty counter. Strips positive and zero counts,
and flips the sign on negative counts.
'''
result = Counter()
for elem, count in self.items():
if count < 0:
result[elem] = 0 - count
return result
| (self) |
10,268 | collections | __or__ | Union is the maximum of value in either of the input counters.
>>> Counter('abbb') | Counter('bcc')
Counter({'b': 3, 'c': 2, 'a': 1})
| def __or__(self, other):
'''Union is the maximum of value in either of the input counters.
>>> Counter('abbb') | Counter('bcc')
Counter({'b': 3, 'c': 2, 'a': 1})
'''
if not isinstance(other, Counter):
return NotImplemented
result = Counter()
for elem, count in self.items():
other_count = other[elem]
newcount = other_count if count < other_count else count
if newcount > 0:
result[elem] = newcount
for elem, count in other.items():
if elem not in self and count > 0:
result[elem] = count
return result
| (self, other) |
10,269 | collections | __pos__ | Adds an empty counter, effectively stripping negative and zero counts | def __pos__(self):
'Adds an empty counter, effectively stripping negative and zero counts'
result = Counter()
for elem, count in self.items():
if count > 0:
result[elem] = count
return result
| (self) |
10,270 | collections | __reduce__ | null | def __reduce__(self):
return self.__class__, (dict(self),)
| (self) |
10,271 | collections | __repr__ | null | def __repr__(self):
if not self:
return f'{self.__class__.__name__}()'
try:
# dict() preserves the ordering returned by most_common()
d = dict(self.most_common())
except TypeError:
# handle case where values are not orderable
d = dict(self)
return f'{self.__class__.__name__}({d!r})'
| (self) |
10,272 | collections | __sub__ | Subtract count, but keep only results with positive counts.
>>> Counter('abbbc') - Counter('bccd')
Counter({'b': 2, 'a': 1})
| def __sub__(self, other):
''' Subtract count, but keep only results with positive counts.
>>> Counter('abbbc') - Counter('bccd')
Counter({'b': 2, 'a': 1})
'''
if not isinstance(other, Counter):
return NotImplemented
result = Counter()
for elem, count in self.items():
newcount = count - other[elem]
if newcount > 0:
result[elem] = newcount
for elem, count in other.items():
if elem not in self and count < 0:
result[elem] = 0 - count
return result
| (self, other) |
10,273 | collections | _keep_positive | Internal method to strip elements with a negative or zero count | def _keep_positive(self):
'''Internal method to strip elements with a negative or zero count'''
nonpositive = [elem for elem, count in self.items() if not count > 0]
for elem in nonpositive:
del self[elem]
return self
| (self) |
10,274 | collections | copy | Return a shallow copy. | def copy(self):
'Return a shallow copy.'
return self.__class__(self)
| (self) |
10,275 | collections | elements | Iterator over elements repeating each as many times as its count.
>>> c = Counter('ABCABC')
>>> sorted(c.elements())
['A', 'A', 'B', 'B', 'C', 'C']
# Knuth's example for prime factors of 1836: 2**2 * 3**3 * 17**1
>>> prime_factors = Counter({2: 2, 3: 3, 17: 1})
>>> product = 1
>>> for factor in prime_factors.elements(): # loop over factors
... product *= factor # and multiply them
>>> product
1836
Note, if an element's count has been set to zero or is a negative
number, elements() will ignore it.
| def elements(self):
'''Iterator over elements repeating each as many times as its count.
>>> c = Counter('ABCABC')
>>> sorted(c.elements())
['A', 'A', 'B', 'B', 'C', 'C']
# Knuth's example for prime factors of 1836: 2**2 * 3**3 * 17**1
>>> prime_factors = Counter({2: 2, 3: 3, 17: 1})
>>> product = 1
>>> for factor in prime_factors.elements(): # loop over factors
... product *= factor # and multiply them
>>> product
1836
Note, if an element's count has been set to zero or is a negative
number, elements() will ignore it.
'''
# Emulate Bag.do from Smalltalk and Multiset.begin from C++.
return _chain.from_iterable(_starmap(_repeat, self.items()))
| (self) |
10,276 | collections | most_common | List the n most common elements and their counts from the most
common to the least. If n is None, then list all element counts.
>>> Counter('abracadabra').most_common(3)
[('a', 5), ('b', 2), ('r', 2)]
| def most_common(self, n=None):
'''List the n most common elements and their counts from the most
common to the least. If n is None, then list all element counts.
>>> Counter('abracadabra').most_common(3)
[('a', 5), ('b', 2), ('r', 2)]
'''
# Emulate Bag.sortedByCount from Smalltalk
if n is None:
return sorted(self.items(), key=_itemgetter(1), reverse=True)
# Lazy import to speedup Python startup time
import heapq
return heapq.nlargest(n, self.items(), key=_itemgetter(1))
| (self, n=None) |
10,277 | collections | subtract | Like dict.update() but subtracts counts instead of replacing them.
Counts can be reduced below zero. Both the inputs and outputs are
allowed to contain zero and negative counts.
Source can be an iterable, a dictionary, or another Counter instance.
>>> c = Counter('which')
>>> c.subtract('witch') # subtract elements from another iterable
>>> c.subtract(Counter('watch')) # subtract elements from another counter
>>> c['h'] # 2 in which, minus 1 in witch, minus 1 in watch
0
>>> c['w'] # 1 in which, minus 1 in witch, minus 1 in watch
-1
| def subtract(self, iterable=None, /, **kwds):
'''Like dict.update() but subtracts counts instead of replacing them.
Counts can be reduced below zero. Both the inputs and outputs are
allowed to contain zero and negative counts.
Source can be an iterable, a dictionary, or another Counter instance.
>>> c = Counter('which')
>>> c.subtract('witch') # subtract elements from another iterable
>>> c.subtract(Counter('watch')) # subtract elements from another counter
>>> c['h'] # 2 in which, minus 1 in witch, minus 1 in watch
0
>>> c['w'] # 1 in which, minus 1 in witch, minus 1 in watch
-1
'''
if iterable is not None:
self_get = self.get
if isinstance(iterable, _collections_abc.Mapping):
for elem, count in iterable.items():
self[elem] = self_get(elem, 0) - count
else:
for elem in iterable:
self[elem] = self_get(elem, 0) - 1
if kwds:
self.subtract(kwds)
| (self, iterable=None, /, **kwds) |
10,278 | collections | total | Sum of the counts | def total(self):
'Sum of the counts'
return sum(self.values())
| (self) |
10,279 | collections | update | Like dict.update() but add counts instead of replacing them.
Source can be an iterable, a dictionary, or another Counter instance.
>>> c = Counter('which')
>>> c.update('witch') # add elements from another iterable
>>> d = Counter('watch')
>>> c.update(d) # add elements from another counter
>>> c['h'] # four 'h' in which, witch, and watch
4
| def update(self, iterable=None, /, **kwds):
'''Like dict.update() but add counts instead of replacing them.
Source can be an iterable, a dictionary, or another Counter instance.
>>> c = Counter('which')
>>> c.update('witch') # add elements from another iterable
>>> d = Counter('watch')
>>> c.update(d) # add elements from another counter
>>> c['h'] # four 'h' in which, witch, and watch
4
'''
# The regular dict.update() operation makes no sense here because the
# replace behavior results in the some of original untouched counts
# being mixed-in with all of the other counts for a mismash that
# doesn't have a straight-forward interpretation in most counting
# contexts. Instead, we implement straight-addition. Both the inputs
# and outputs are allowed to contain zero and negative counts.
if iterable is not None:
if isinstance(iterable, _collections_abc.Mapping):
if self:
self_get = self.get
for elem, count in iterable.items():
self[elem] = count + self_get(elem, 0)
else:
# fast path when counter is empty
super().update(iterable)
else:
_count_elements(self, iterable)
if kwds:
self.update(kwds)
| (self, iterable=None, /, **kwds) |
10,280 | fractions | Fraction | This class implements rational numbers.
In the two-argument form of the constructor, Fraction(8, 6) will
produce a rational number equivalent to 4/3. Both arguments must
be Rational. The numerator defaults to 0 and the denominator
defaults to 1 so that Fraction(3) == 3 and Fraction() == 0.
Fractions can also be constructed from:
- numeric strings similar to those accepted by the
float constructor (for example, '-2.3' or '1e10')
- strings of the form '123/456'
- float and Decimal instances
- other Rational instances (including integers)
| class Fraction(numbers.Rational):
"""This class implements rational numbers.
In the two-argument form of the constructor, Fraction(8, 6) will
produce a rational number equivalent to 4/3. Both arguments must
be Rational. The numerator defaults to 0 and the denominator
defaults to 1 so that Fraction(3) == 3 and Fraction() == 0.
Fractions can also be constructed from:
- numeric strings similar to those accepted by the
float constructor (for example, '-2.3' or '1e10')
- strings of the form '123/456'
- float and Decimal instances
- other Rational instances (including integers)
"""
__slots__ = ('_numerator', '_denominator')
# We're immutable, so use __new__ not __init__
def __new__(cls, numerator=0, denominator=None, *, _normalize=True):
"""Constructs a Rational.
Takes a string like '3/2' or '1.5', another Rational instance, a
numerator/denominator pair, or a float.
Examples
--------
>>> Fraction(10, -8)
Fraction(-5, 4)
>>> Fraction(Fraction(1, 7), 5)
Fraction(1, 35)
>>> Fraction(Fraction(1, 7), Fraction(2, 3))
Fraction(3, 14)
>>> Fraction('314')
Fraction(314, 1)
>>> Fraction('-35/4')
Fraction(-35, 4)
>>> Fraction('3.1415') # conversion from numeric string
Fraction(6283, 2000)
>>> Fraction('-47e-2') # string may include a decimal exponent
Fraction(-47, 100)
>>> Fraction(1.47) # direct construction from float (exact conversion)
Fraction(6620291452234629, 4503599627370496)
>>> Fraction(2.25)
Fraction(9, 4)
>>> Fraction(Decimal('1.47'))
Fraction(147, 100)
"""
self = super(Fraction, cls).__new__(cls)
if denominator is None:
if type(numerator) is int:
self._numerator = numerator
self._denominator = 1
return self
elif isinstance(numerator, numbers.Rational):
self._numerator = numerator.numerator
self._denominator = numerator.denominator
return self
elif isinstance(numerator, (float, Decimal)):
# Exact conversion
self._numerator, self._denominator = numerator.as_integer_ratio()
return self
elif isinstance(numerator, str):
# Handle construction from strings.
m = _RATIONAL_FORMAT.match(numerator)
if m is None:
raise ValueError('Invalid literal for Fraction: %r' %
numerator)
numerator = int(m.group('num') or '0')
denom = m.group('denom')
if denom:
denominator = int(denom)
else:
denominator = 1
decimal = m.group('decimal')
if decimal:
scale = 10**len(decimal)
numerator = numerator * scale + int(decimal)
denominator *= scale
exp = m.group('exp')
if exp:
exp = int(exp)
if exp >= 0:
numerator *= 10**exp
else:
denominator *= 10**-exp
if m.group('sign') == '-':
numerator = -numerator
else:
raise TypeError("argument should be a string "
"or a Rational instance")
elif type(numerator) is int is type(denominator):
pass # *very* normal case
elif (isinstance(numerator, numbers.Rational) and
isinstance(denominator, numbers.Rational)):
numerator, denominator = (
numerator.numerator * denominator.denominator,
denominator.numerator * numerator.denominator
)
else:
raise TypeError("both arguments should be "
"Rational instances")
if denominator == 0:
raise ZeroDivisionError('Fraction(%s, 0)' % numerator)
if _normalize:
g = math.gcd(numerator, denominator)
if denominator < 0:
g = -g
numerator //= g
denominator //= g
self._numerator = numerator
self._denominator = denominator
return self
@classmethod
def from_float(cls, f):
"""Converts a finite float to a rational number, exactly.
Beware that Fraction.from_float(0.3) != Fraction(3, 10).
"""
if isinstance(f, numbers.Integral):
return cls(f)
elif not isinstance(f, float):
raise TypeError("%s.from_float() only takes floats, not %r (%s)" %
(cls.__name__, f, type(f).__name__))
return cls(*f.as_integer_ratio())
@classmethod
def from_decimal(cls, dec):
"""Converts a finite Decimal instance to a rational number, exactly."""
from decimal import Decimal
if isinstance(dec, numbers.Integral):
dec = Decimal(int(dec))
elif not isinstance(dec, Decimal):
raise TypeError(
"%s.from_decimal() only takes Decimals, not %r (%s)" %
(cls.__name__, dec, type(dec).__name__))
return cls(*dec.as_integer_ratio())
def as_integer_ratio(self):
"""Return the integer ratio as a tuple.
Return a tuple of two integers, whose ratio is equal to the
Fraction and with a positive denominator.
"""
return (self._numerator, self._denominator)
def limit_denominator(self, max_denominator=1000000):
"""Closest Fraction to self with denominator at most max_denominator.
>>> Fraction('3.141592653589793').limit_denominator(10)
Fraction(22, 7)
>>> Fraction('3.141592653589793').limit_denominator(100)
Fraction(311, 99)
>>> Fraction(4321, 8765).limit_denominator(10000)
Fraction(4321, 8765)
"""
# Algorithm notes: For any real number x, define a *best upper
# approximation* to x to be a rational number p/q such that:
#
# (1) p/q >= x, and
# (2) if p/q > r/s >= x then s > q, for any rational r/s.
#
# Define *best lower approximation* similarly. Then it can be
# proved that a rational number is a best upper or lower
# approximation to x if, and only if, it is a convergent or
# semiconvergent of the (unique shortest) continued fraction
# associated to x.
#
# To find a best rational approximation with denominator <= M,
# we find the best upper and lower approximations with
# denominator <= M and take whichever of these is closer to x.
# In the event of a tie, the bound with smaller denominator is
# chosen. If both denominators are equal (which can happen
# only when max_denominator == 1 and self is midway between
# two integers) the lower bound---i.e., the floor of self, is
# taken.
if max_denominator < 1:
raise ValueError("max_denominator should be at least 1")
if self._denominator <= max_denominator:
return Fraction(self)
p0, q0, p1, q1 = 0, 1, 1, 0
n, d = self._numerator, self._denominator
while True:
a = n//d
q2 = q0+a*q1
if q2 > max_denominator:
break
p0, q0, p1, q1 = p1, q1, p0+a*p1, q2
n, d = d, n-a*d
k = (max_denominator-q0)//q1
bound1 = Fraction(p0+k*p1, q0+k*q1)
bound2 = Fraction(p1, q1)
if abs(bound2 - self) <= abs(bound1-self):
return bound2
else:
return bound1
@property
def numerator(a):
return a._numerator
@property
def denominator(a):
return a._denominator
def __repr__(self):
"""repr(self)"""
return '%s(%s, %s)' % (self.__class__.__name__,
self._numerator, self._denominator)
def __str__(self):
"""str(self)"""
if self._denominator == 1:
return str(self._numerator)
else:
return '%s/%s' % (self._numerator, self._denominator)
def _operator_fallbacks(monomorphic_operator, fallback_operator):
"""Generates forward and reverse operators given a purely-rational
operator and a function from the operator module.
Use this like:
__op__, __rop__ = _operator_fallbacks(just_rational_op, operator.op)
In general, we want to implement the arithmetic operations so
that mixed-mode operations either call an implementation whose
author knew about the types of both arguments, or convert both
to the nearest built in type and do the operation there. In
Fraction, that means that we define __add__ and __radd__ as:
def __add__(self, other):
# Both types have numerators/denominator attributes,
# so do the operation directly
if isinstance(other, (int, Fraction)):
return Fraction(self.numerator * other.denominator +
other.numerator * self.denominator,
self.denominator * other.denominator)
# float and complex don't have those operations, but we
# know about those types, so special case them.
elif isinstance(other, float):
return float(self) + other
elif isinstance(other, complex):
return complex(self) + other
# Let the other type take over.
return NotImplemented
def __radd__(self, other):
# radd handles more types than add because there's
# nothing left to fall back to.
if isinstance(other, numbers.Rational):
return Fraction(self.numerator * other.denominator +
other.numerator * self.denominator,
self.denominator * other.denominator)
elif isinstance(other, Real):
return float(other) + float(self)
elif isinstance(other, Complex):
return complex(other) + complex(self)
return NotImplemented
There are 5 different cases for a mixed-type addition on
Fraction. I'll refer to all of the above code that doesn't
refer to Fraction, float, or complex as "boilerplate". 'r'
will be an instance of Fraction, which is a subtype of
Rational (r : Fraction <: Rational), and b : B <:
Complex. The first three involve 'r + b':
1. If B <: Fraction, int, float, or complex, we handle
that specially, and all is well.
2. If Fraction falls back to the boilerplate code, and it
were to return a value from __add__, we'd miss the
possibility that B defines a more intelligent __radd__,
so the boilerplate should return NotImplemented from
__add__. In particular, we don't handle Rational
here, even though we could get an exact answer, in case
the other type wants to do something special.
3. If B <: Fraction, Python tries B.__radd__ before
Fraction.__add__. This is ok, because it was
implemented with knowledge of Fraction, so it can
handle those instances before delegating to Real or
Complex.
The next two situations describe 'b + r'. We assume that b
didn't know about Fraction in its implementation, and that it
uses similar boilerplate code:
4. If B <: Rational, then __radd_ converts both to the
builtin rational type (hey look, that's us) and
proceeds.
5. Otherwise, __radd__ tries to find the nearest common
base ABC, and fall back to its builtin type. Since this
class doesn't subclass a concrete type, there's no
implementation to fall back to, so we need to try as
hard as possible to return an actual value, or the user
will get a TypeError.
"""
def forward(a, b):
if isinstance(b, (int, Fraction)):
return monomorphic_operator(a, b)
elif isinstance(b, float):
return fallback_operator(float(a), b)
elif isinstance(b, complex):
return fallback_operator(complex(a), b)
else:
return NotImplemented
forward.__name__ = '__' + fallback_operator.__name__ + '__'
forward.__doc__ = monomorphic_operator.__doc__
def reverse(b, a):
if isinstance(a, numbers.Rational):
# Includes ints.
return monomorphic_operator(a, b)
elif isinstance(a, numbers.Real):
return fallback_operator(float(a), float(b))
elif isinstance(a, numbers.Complex):
return fallback_operator(complex(a), complex(b))
else:
return NotImplemented
reverse.__name__ = '__r' + fallback_operator.__name__ + '__'
reverse.__doc__ = monomorphic_operator.__doc__
return forward, reverse
# Rational arithmetic algorithms: Knuth, TAOCP, Volume 2, 4.5.1.
#
# Assume input fractions a and b are normalized.
#
# 1) Consider addition/subtraction.
#
# Let g = gcd(da, db). Then
#
# na nb na*db ± nb*da
# a ± b == -- ± -- == ------------- ==
# da db da*db
#
# na*(db//g) ± nb*(da//g) t
# == ----------------------- == -
# (da*db)//g d
#
# Now, if g > 1, we're working with smaller integers.
#
# Note, that t, (da//g) and (db//g) are pairwise coprime.
#
# Indeed, (da//g) and (db//g) share no common factors (they were
# removed) and da is coprime with na (since input fractions are
# normalized), hence (da//g) and na are coprime. By symmetry,
# (db//g) and nb are coprime too. Then,
#
# gcd(t, da//g) == gcd(na*(db//g), da//g) == 1
# gcd(t, db//g) == gcd(nb*(da//g), db//g) == 1
#
# Above allows us optimize reduction of the result to lowest
# terms. Indeed,
#
# g2 = gcd(t, d) == gcd(t, (da//g)*(db//g)*g) == gcd(t, g)
#
# t//g2 t//g2
# a ± b == ----------------------- == ----------------
# (da//g)*(db//g)*(g//g2) (da//g)*(db//g2)
#
# is a normalized fraction. This is useful because the unnormalized
# denominator d could be much larger than g.
#
# We should special-case g == 1 (and g2 == 1), since 60.8% of
# randomly-chosen integers are coprime:
# https://en.wikipedia.org/wiki/Coprime_integers#Probability_of_coprimality
# Note, that g2 == 1 always for fractions, obtained from floats: here
# g is a power of 2 and the unnormalized numerator t is an odd integer.
#
# 2) Consider multiplication
#
# Let g1 = gcd(na, db) and g2 = gcd(nb, da), then
#
# na*nb na*nb (na//g1)*(nb//g2)
# a*b == ----- == ----- == -----------------
# da*db db*da (db//g1)*(da//g2)
#
# Note, that after divisions we're multiplying smaller integers.
#
# Also, the resulting fraction is normalized, because each of
# two factors in the numerator is coprime to each of the two factors
# in the denominator.
#
# Indeed, pick (na//g1). It's coprime with (da//g2), because input
# fractions are normalized. It's also coprime with (db//g1), because
# common factors are removed by g1 == gcd(na, db).
#
# As for addition/subtraction, we should special-case g1 == 1
# and g2 == 1 for same reason. That happens also for multiplying
# rationals, obtained from floats.
def _add(a, b):
"""a + b"""
na, da = a.numerator, a.denominator
nb, db = b.numerator, b.denominator
g = math.gcd(da, db)
if g == 1:
return Fraction(na * db + da * nb, da * db, _normalize=False)
s = da // g
t = na * (db // g) + nb * s
g2 = math.gcd(t, g)
if g2 == 1:
return Fraction(t, s * db, _normalize=False)
return Fraction(t // g2, s * (db // g2), _normalize=False)
__add__, __radd__ = _operator_fallbacks(_add, operator.add)
def _sub(a, b):
"""a - b"""
na, da = a.numerator, a.denominator
nb, db = b.numerator, b.denominator
g = math.gcd(da, db)
if g == 1:
return Fraction(na * db - da * nb, da * db, _normalize=False)
s = da // g
t = na * (db // g) - nb * s
g2 = math.gcd(t, g)
if g2 == 1:
return Fraction(t, s * db, _normalize=False)
return Fraction(t // g2, s * (db // g2), _normalize=False)
__sub__, __rsub__ = _operator_fallbacks(_sub, operator.sub)
def _mul(a, b):
"""a * b"""
na, da = a.numerator, a.denominator
nb, db = b.numerator, b.denominator
g1 = math.gcd(na, db)
if g1 > 1:
na //= g1
db //= g1
g2 = math.gcd(nb, da)
if g2 > 1:
nb //= g2
da //= g2
return Fraction(na * nb, db * da, _normalize=False)
__mul__, __rmul__ = _operator_fallbacks(_mul, operator.mul)
def _div(a, b):
"""a / b"""
# Same as _mul(), with inversed b.
na, da = a.numerator, a.denominator
nb, db = b.numerator, b.denominator
g1 = math.gcd(na, nb)
if g1 > 1:
na //= g1
nb //= g1
g2 = math.gcd(db, da)
if g2 > 1:
da //= g2
db //= g2
n, d = na * db, nb * da
if d < 0:
n, d = -n, -d
return Fraction(n, d, _normalize=False)
__truediv__, __rtruediv__ = _operator_fallbacks(_div, operator.truediv)
def _floordiv(a, b):
"""a // b"""
return (a.numerator * b.denominator) // (a.denominator * b.numerator)
__floordiv__, __rfloordiv__ = _operator_fallbacks(_floordiv, operator.floordiv)
def _divmod(a, b):
"""(a // b, a % b)"""
da, db = a.denominator, b.denominator
div, n_mod = divmod(a.numerator * db, da * b.numerator)
return div, Fraction(n_mod, da * db)
__divmod__, __rdivmod__ = _operator_fallbacks(_divmod, divmod)
def _mod(a, b):
"""a % b"""
da, db = a.denominator, b.denominator
return Fraction((a.numerator * db) % (b.numerator * da), da * db)
__mod__, __rmod__ = _operator_fallbacks(_mod, operator.mod)
def __pow__(a, b):
"""a ** b
If b is not an integer, the result will be a float or complex
since roots are generally irrational. If b is an integer, the
result will be rational.
"""
if isinstance(b, numbers.Rational):
if b.denominator == 1:
power = b.numerator
if power >= 0:
return Fraction(a._numerator ** power,
a._denominator ** power,
_normalize=False)
elif a._numerator >= 0:
return Fraction(a._denominator ** -power,
a._numerator ** -power,
_normalize=False)
else:
return Fraction((-a._denominator) ** -power,
(-a._numerator) ** -power,
_normalize=False)
else:
# A fractional power will generally produce an
# irrational number.
return float(a) ** float(b)
else:
return float(a) ** b
def __rpow__(b, a):
"""a ** b"""
if b._denominator == 1 and b._numerator >= 0:
# If a is an int, keep it that way if possible.
return a ** b._numerator
if isinstance(a, numbers.Rational):
return Fraction(a.numerator, a.denominator) ** b
if b._denominator == 1:
return a ** b._numerator
return a ** float(b)
def __pos__(a):
"""+a: Coerces a subclass instance to Fraction"""
return Fraction(a._numerator, a._denominator, _normalize=False)
def __neg__(a):
"""-a"""
return Fraction(-a._numerator, a._denominator, _normalize=False)
def __abs__(a):
"""abs(a)"""
return Fraction(abs(a._numerator), a._denominator, _normalize=False)
def __trunc__(a):
"""trunc(a)"""
if a._numerator < 0:
return -(-a._numerator // a._denominator)
else:
return a._numerator // a._denominator
def __floor__(a):
"""math.floor(a)"""
return a.numerator // a.denominator
def __ceil__(a):
"""math.ceil(a)"""
# The negations cleverly convince floordiv to return the ceiling.
return -(-a.numerator // a.denominator)
def __round__(self, ndigits=None):
"""round(self, ndigits)
Rounds half toward even.
"""
if ndigits is None:
floor, remainder = divmod(self.numerator, self.denominator)
if remainder * 2 < self.denominator:
return floor
elif remainder * 2 > self.denominator:
return floor + 1
# Deal with the half case:
elif floor % 2 == 0:
return floor
else:
return floor + 1
shift = 10**abs(ndigits)
# See _operator_fallbacks.forward to check that the results of
# these operations will always be Fraction and therefore have
# round().
if ndigits > 0:
return Fraction(round(self * shift), shift)
else:
return Fraction(round(self / shift) * shift)
def __hash__(self):
"""hash(self)"""
# To make sure that the hash of a Fraction agrees with the hash
# of a numerically equal integer, float or Decimal instance, we
# follow the rules for numeric hashes outlined in the
# documentation. (See library docs, 'Built-in Types').
try:
dinv = pow(self._denominator, -1, _PyHASH_MODULUS)
except ValueError:
# ValueError means there is no modular inverse.
hash_ = _PyHASH_INF
else:
# The general algorithm now specifies that the absolute value of
# the hash is
# (|N| * dinv) % P
# where N is self._numerator and P is _PyHASH_MODULUS. That's
# optimized here in two ways: first, for a non-negative int i,
# hash(i) == i % P, but the int hash implementation doesn't need
# to divide, and is faster than doing % P explicitly. So we do
# hash(|N| * dinv)
# instead. Second, N is unbounded, so its product with dinv may
# be arbitrarily expensive to compute. The final answer is the
# same if we use the bounded |N| % P instead, which can again
# be done with an int hash() call. If 0 <= i < P, hash(i) == i,
# so this nested hash() call wastes a bit of time making a
# redundant copy when |N| < P, but can save an arbitrarily large
# amount of computation for large |N|.
hash_ = hash(hash(abs(self._numerator)) * dinv)
result = hash_ if self._numerator >= 0 else -hash_
return -2 if result == -1 else result
def __eq__(a, b):
"""a == b"""
if type(b) is int:
return a._numerator == b and a._denominator == 1
if isinstance(b, numbers.Rational):
return (a._numerator == b.numerator and
a._denominator == b.denominator)
if isinstance(b, numbers.Complex) and b.imag == 0:
b = b.real
if isinstance(b, float):
if math.isnan(b) or math.isinf(b):
# comparisons with an infinity or nan should behave in
# the same way for any finite a, so treat a as zero.
return 0.0 == b
else:
return a == a.from_float(b)
else:
# Since a doesn't know how to compare with b, let's give b
# a chance to compare itself with a.
return NotImplemented
def _richcmp(self, other, op):
"""Helper for comparison operators, for internal use only.
Implement comparison between a Rational instance `self`, and
either another Rational instance or a float `other`. If
`other` is not a Rational instance or a float, return
NotImplemented. `op` should be one of the six standard
comparison operators.
"""
# convert other to a Rational instance where reasonable.
if isinstance(other, numbers.Rational):
return op(self._numerator * other.denominator,
self._denominator * other.numerator)
if isinstance(other, float):
if math.isnan(other) or math.isinf(other):
return op(0.0, other)
else:
return op(self, self.from_float(other))
else:
return NotImplemented
def __lt__(a, b):
"""a < b"""
return a._richcmp(b, operator.lt)
def __gt__(a, b):
"""a > b"""
return a._richcmp(b, operator.gt)
def __le__(a, b):
"""a <= b"""
return a._richcmp(b, operator.le)
def __ge__(a, b):
"""a >= b"""
return a._richcmp(b, operator.ge)
def __bool__(a):
"""a != 0"""
# bpo-39274: Use bool() because (a._numerator != 0) can return an
# object which is not a bool.
return bool(a._numerator)
# support for pickling, copy, and deepcopy
def __reduce__(self):
return (self.__class__, (str(self),))
def __copy__(self):
if type(self) == Fraction:
return self # I'm immutable; therefore I am my own clone
return self.__class__(self._numerator, self._denominator)
def __deepcopy__(self, memo):
if type(self) == Fraction:
return self # My components are also immutable
return self.__class__(self._numerator, self._denominator)
| (numerator=0, denominator=None, *, _normalize=True) |
10,281 | fractions | __abs__ | abs(a) | def __abs__(a):
"""abs(a)"""
return Fraction(abs(a._numerator), a._denominator, _normalize=False)
| (a) |
10,282 | fractions | __add__ | a + b | def _operator_fallbacks(monomorphic_operator, fallback_operator):
"""Generates forward and reverse operators given a purely-rational
operator and a function from the operator module.
Use this like:
__op__, __rop__ = _operator_fallbacks(just_rational_op, operator.op)
In general, we want to implement the arithmetic operations so
that mixed-mode operations either call an implementation whose
author knew about the types of both arguments, or convert both
to the nearest built in type and do the operation there. In
Fraction, that means that we define __add__ and __radd__ as:
def __add__(self, other):
# Both types have numerators/denominator attributes,
# so do the operation directly
if isinstance(other, (int, Fraction)):
return Fraction(self.numerator * other.denominator +
other.numerator * self.denominator,
self.denominator * other.denominator)
# float and complex don't have those operations, but we
# know about those types, so special case them.
elif isinstance(other, float):
return float(self) + other
elif isinstance(other, complex):
return complex(self) + other
# Let the other type take over.
return NotImplemented
def __radd__(self, other):
# radd handles more types than add because there's
# nothing left to fall back to.
if isinstance(other, numbers.Rational):
return Fraction(self.numerator * other.denominator +
other.numerator * self.denominator,
self.denominator * other.denominator)
elif isinstance(other, Real):
return float(other) + float(self)
elif isinstance(other, Complex):
return complex(other) + complex(self)
return NotImplemented
There are 5 different cases for a mixed-type addition on
Fraction. I'll refer to all of the above code that doesn't
refer to Fraction, float, or complex as "boilerplate". 'r'
will be an instance of Fraction, which is a subtype of
Rational (r : Fraction <: Rational), and b : B <:
Complex. The first three involve 'r + b':
1. If B <: Fraction, int, float, or complex, we handle
that specially, and all is well.
2. If Fraction falls back to the boilerplate code, and it
were to return a value from __add__, we'd miss the
possibility that B defines a more intelligent __radd__,
so the boilerplate should return NotImplemented from
__add__. In particular, we don't handle Rational
here, even though we could get an exact answer, in case
the other type wants to do something special.
3. If B <: Fraction, Python tries B.__radd__ before
Fraction.__add__. This is ok, because it was
implemented with knowledge of Fraction, so it can
handle those instances before delegating to Real or
Complex.
The next two situations describe 'b + r'. We assume that b
didn't know about Fraction in its implementation, and that it
uses similar boilerplate code:
4. If B <: Rational, then __radd_ converts both to the
builtin rational type (hey look, that's us) and
proceeds.
5. Otherwise, __radd__ tries to find the nearest common
base ABC, and fall back to its builtin type. Since this
class doesn't subclass a concrete type, there's no
implementation to fall back to, so we need to try as
hard as possible to return an actual value, or the user
will get a TypeError.
"""
def forward(a, b):
if isinstance(b, (int, Fraction)):
return monomorphic_operator(a, b)
elif isinstance(b, float):
return fallback_operator(float(a), b)
elif isinstance(b, complex):
return fallback_operator(complex(a), b)
else:
return NotImplemented
forward.__name__ = '__' + fallback_operator.__name__ + '__'
forward.__doc__ = monomorphic_operator.__doc__
def reverse(b, a):
if isinstance(a, numbers.Rational):
# Includes ints.
return monomorphic_operator(a, b)
elif isinstance(a, numbers.Real):
return fallback_operator(float(a), float(b))
elif isinstance(a, numbers.Complex):
return fallback_operator(complex(a), complex(b))
else:
return NotImplemented
reverse.__name__ = '__r' + fallback_operator.__name__ + '__'
reverse.__doc__ = monomorphic_operator.__doc__
return forward, reverse
| (a, b) |
10,283 | fractions | __bool__ | a != 0 | def __bool__(a):
"""a != 0"""
# bpo-39274: Use bool() because (a._numerator != 0) can return an
# object which is not a bool.
return bool(a._numerator)
| (a) |
10,284 | fractions | __ceil__ | math.ceil(a) | def __ceil__(a):
"""math.ceil(a)"""
# The negations cleverly convince floordiv to return the ceiling.
return -(-a.numerator // a.denominator)
| (a) |
10,285 | numbers | __complex__ | complex(self) == complex(float(self), 0) | def __complex__(self):
"""complex(self) == complex(float(self), 0)"""
return complex(float(self))
| (self) |
10,286 | fractions | __copy__ | null | def __copy__(self):
if type(self) == Fraction:
return self # I'm immutable; therefore I am my own clone
return self.__class__(self._numerator, self._denominator)
| (self) |
10,287 | fractions | __deepcopy__ | null | def __deepcopy__(self, memo):
if type(self) == Fraction:
return self # My components are also immutable
return self.__class__(self._numerator, self._denominator)
| (self, memo) |
10,288 | fractions | __divmod__ | (a // b, a % b) | def _operator_fallbacks(monomorphic_operator, fallback_operator):
"""Generates forward and reverse operators given a purely-rational
operator and a function from the operator module.
Use this like:
__op__, __rop__ = _operator_fallbacks(just_rational_op, operator.op)
In general, we want to implement the arithmetic operations so
that mixed-mode operations either call an implementation whose
author knew about the types of both arguments, or convert both
to the nearest built in type and do the operation there. In
Fraction, that means that we define __add__ and __radd__ as:
def __add__(self, other):
# Both types have numerators/denominator attributes,
# so do the operation directly
if isinstance(other, (int, Fraction)):
return Fraction(self.numerator * other.denominator +
other.numerator * self.denominator,
self.denominator * other.denominator)
# float and complex don't have those operations, but we
# know about those types, so special case them.
elif isinstance(other, float):
return float(self) + other
elif isinstance(other, complex):
return complex(self) + other
# Let the other type take over.
return NotImplemented
def __radd__(self, other):
# radd handles more types than add because there's
# nothing left to fall back to.
if isinstance(other, numbers.Rational):
return Fraction(self.numerator * other.denominator +
other.numerator * self.denominator,
self.denominator * other.denominator)
elif isinstance(other, Real):
return float(other) + float(self)
elif isinstance(other, Complex):
return complex(other) + complex(self)
return NotImplemented
There are 5 different cases for a mixed-type addition on
Fraction. I'll refer to all of the above code that doesn't
refer to Fraction, float, or complex as "boilerplate". 'r'
will be an instance of Fraction, which is a subtype of
Rational (r : Fraction <: Rational), and b : B <:
Complex. The first three involve 'r + b':
1. If B <: Fraction, int, float, or complex, we handle
that specially, and all is well.
2. If Fraction falls back to the boilerplate code, and it
were to return a value from __add__, we'd miss the
possibility that B defines a more intelligent __radd__,
so the boilerplate should return NotImplemented from
__add__. In particular, we don't handle Rational
here, even though we could get an exact answer, in case
the other type wants to do something special.
3. If B <: Fraction, Python tries B.__radd__ before
Fraction.__add__. This is ok, because it was
implemented with knowledge of Fraction, so it can
handle those instances before delegating to Real or
Complex.
The next two situations describe 'b + r'. We assume that b
didn't know about Fraction in its implementation, and that it
uses similar boilerplate code:
4. If B <: Rational, then __radd_ converts both to the
builtin rational type (hey look, that's us) and
proceeds.
5. Otherwise, __radd__ tries to find the nearest common
base ABC, and fall back to its builtin type. Since this
class doesn't subclass a concrete type, there's no
implementation to fall back to, so we need to try as
hard as possible to return an actual value, or the user
will get a TypeError.
"""
def forward(a, b):
if isinstance(b, (int, Fraction)):
return monomorphic_operator(a, b)
elif isinstance(b, float):
return fallback_operator(float(a), b)
elif isinstance(b, complex):
return fallback_operator(complex(a), b)
else:
return NotImplemented
forward.__name__ = '__' + fallback_operator.__name__ + '__'
forward.__doc__ = monomorphic_operator.__doc__
def reverse(b, a):
if isinstance(a, numbers.Rational):
# Includes ints.
return monomorphic_operator(a, b)
elif isinstance(a, numbers.Real):
return fallback_operator(float(a), float(b))
elif isinstance(a, numbers.Complex):
return fallback_operator(complex(a), complex(b))
else:
return NotImplemented
reverse.__name__ = '__r' + fallback_operator.__name__ + '__'
reverse.__doc__ = monomorphic_operator.__doc__
return forward, reverse
| (a, b) |
10,289 | fractions | __eq__ | a == b | def __eq__(a, b):
"""a == b"""
if type(b) is int:
return a._numerator == b and a._denominator == 1
if isinstance(b, numbers.Rational):
return (a._numerator == b.numerator and
a._denominator == b.denominator)
if isinstance(b, numbers.Complex) and b.imag == 0:
b = b.real
if isinstance(b, float):
if math.isnan(b) or math.isinf(b):
# comparisons with an infinity or nan should behave in
# the same way for any finite a, so treat a as zero.
return 0.0 == b
else:
return a == a.from_float(b)
else:
# Since a doesn't know how to compare with b, let's give b
# a chance to compare itself with a.
return NotImplemented
| (a, b) |
10,290 | numbers | __float__ | float(self) = self.numerator / self.denominator
It's important that this conversion use the integer's "true"
division rather than casting one side to float before dividing
so that ratios of huge integers convert without overflowing.
| def __float__(self):
"""float(self) = self.numerator / self.denominator
It's important that this conversion use the integer's "true"
division rather than casting one side to float before dividing
so that ratios of huge integers convert without overflowing.
"""
return int(self.numerator) / int(self.denominator)
| (self) |
10,291 | fractions | __floor__ | math.floor(a) | def __floor__(a):
"""math.floor(a)"""
return a.numerator // a.denominator
| (a) |
10,292 | fractions | __floordiv__ | a // b | def _operator_fallbacks(monomorphic_operator, fallback_operator):
"""Generates forward and reverse operators given a purely-rational
operator and a function from the operator module.
Use this like:
__op__, __rop__ = _operator_fallbacks(just_rational_op, operator.op)
In general, we want to implement the arithmetic operations so
that mixed-mode operations either call an implementation whose
author knew about the types of both arguments, or convert both
to the nearest built in type and do the operation there. In
Fraction, that means that we define __add__ and __radd__ as:
def __add__(self, other):
# Both types have numerators/denominator attributes,
# so do the operation directly
if isinstance(other, (int, Fraction)):
return Fraction(self.numerator * other.denominator +
other.numerator * self.denominator,
self.denominator * other.denominator)
# float and complex don't have those operations, but we
# know about those types, so special case them.
elif isinstance(other, float):
return float(self) + other
elif isinstance(other, complex):
return complex(self) + other
# Let the other type take over.
return NotImplemented
def __radd__(self, other):
# radd handles more types than add because there's
# nothing left to fall back to.
if isinstance(other, numbers.Rational):
return Fraction(self.numerator * other.denominator +
other.numerator * self.denominator,
self.denominator * other.denominator)
elif isinstance(other, Real):
return float(other) + float(self)
elif isinstance(other, Complex):
return complex(other) + complex(self)
return NotImplemented
There are 5 different cases for a mixed-type addition on
Fraction. I'll refer to all of the above code that doesn't
refer to Fraction, float, or complex as "boilerplate". 'r'
will be an instance of Fraction, which is a subtype of
Rational (r : Fraction <: Rational), and b : B <:
Complex. The first three involve 'r + b':
1. If B <: Fraction, int, float, or complex, we handle
that specially, and all is well.
2. If Fraction falls back to the boilerplate code, and it
were to return a value from __add__, we'd miss the
possibility that B defines a more intelligent __radd__,
so the boilerplate should return NotImplemented from
__add__. In particular, we don't handle Rational
here, even though we could get an exact answer, in case
the other type wants to do something special.
3. If B <: Fraction, Python tries B.__radd__ before
Fraction.__add__. This is ok, because it was
implemented with knowledge of Fraction, so it can
handle those instances before delegating to Real or
Complex.
The next two situations describe 'b + r'. We assume that b
didn't know about Fraction in its implementation, and that it
uses similar boilerplate code:
4. If B <: Rational, then __radd_ converts both to the
builtin rational type (hey look, that's us) and
proceeds.
5. Otherwise, __radd__ tries to find the nearest common
base ABC, and fall back to its builtin type. Since this
class doesn't subclass a concrete type, there's no
implementation to fall back to, so we need to try as
hard as possible to return an actual value, or the user
will get a TypeError.
"""
def forward(a, b):
if isinstance(b, (int, Fraction)):
return monomorphic_operator(a, b)
elif isinstance(b, float):
return fallback_operator(float(a), b)
elif isinstance(b, complex):
return fallback_operator(complex(a), b)
else:
return NotImplemented
forward.__name__ = '__' + fallback_operator.__name__ + '__'
forward.__doc__ = monomorphic_operator.__doc__
def reverse(b, a):
if isinstance(a, numbers.Rational):
# Includes ints.
return monomorphic_operator(a, b)
elif isinstance(a, numbers.Real):
return fallback_operator(float(a), float(b))
elif isinstance(a, numbers.Complex):
return fallback_operator(complex(a), complex(b))
else:
return NotImplemented
reverse.__name__ = '__r' + fallback_operator.__name__ + '__'
reverse.__doc__ = monomorphic_operator.__doc__
return forward, reverse
| (a, b) |
10,293 | fractions | __ge__ | a >= b | def __ge__(a, b):
"""a >= b"""
return a._richcmp(b, operator.ge)
| (a, b) |
10,294 | fractions | __gt__ | a > b | def __gt__(a, b):
"""a > b"""
return a._richcmp(b, operator.gt)
| (a, b) |
10,295 | fractions | __hash__ | hash(self) | def __hash__(self):
"""hash(self)"""
# To make sure that the hash of a Fraction agrees with the hash
# of a numerically equal integer, float or Decimal instance, we
# follow the rules for numeric hashes outlined in the
# documentation. (See library docs, 'Built-in Types').
try:
dinv = pow(self._denominator, -1, _PyHASH_MODULUS)
except ValueError:
# ValueError means there is no modular inverse.
hash_ = _PyHASH_INF
else:
# The general algorithm now specifies that the absolute value of
# the hash is
# (|N| * dinv) % P
# where N is self._numerator and P is _PyHASH_MODULUS. That's
# optimized here in two ways: first, for a non-negative int i,
# hash(i) == i % P, but the int hash implementation doesn't need
# to divide, and is faster than doing % P explicitly. So we do
# hash(|N| * dinv)
# instead. Second, N is unbounded, so its product with dinv may
# be arbitrarily expensive to compute. The final answer is the
# same if we use the bounded |N| % P instead, which can again
# be done with an int hash() call. If 0 <= i < P, hash(i) == i,
# so this nested hash() call wastes a bit of time making a
# redundant copy when |N| < P, but can save an arbitrarily large
# amount of computation for large |N|.
hash_ = hash(hash(abs(self._numerator)) * dinv)
result = hash_ if self._numerator >= 0 else -hash_
return -2 if result == -1 else result
| (self) |
10,296 | fractions | __le__ | a <= b | def __le__(a, b):
"""a <= b"""
return a._richcmp(b, operator.le)
| (a, b) |
10,297 | fractions | __lt__ | a < b | def __lt__(a, b):
"""a < b"""
return a._richcmp(b, operator.lt)
| (a, b) |
10,298 | fractions | __mod__ | a % b | def _operator_fallbacks(monomorphic_operator, fallback_operator):
"""Generates forward and reverse operators given a purely-rational
operator and a function from the operator module.
Use this like:
__op__, __rop__ = _operator_fallbacks(just_rational_op, operator.op)
In general, we want to implement the arithmetic operations so
that mixed-mode operations either call an implementation whose
author knew about the types of both arguments, or convert both
to the nearest built in type and do the operation there. In
Fraction, that means that we define __add__ and __radd__ as:
def __add__(self, other):
# Both types have numerators/denominator attributes,
# so do the operation directly
if isinstance(other, (int, Fraction)):
return Fraction(self.numerator * other.denominator +
other.numerator * self.denominator,
self.denominator * other.denominator)
# float and complex don't have those operations, but we
# know about those types, so special case them.
elif isinstance(other, float):
return float(self) + other
elif isinstance(other, complex):
return complex(self) + other
# Let the other type take over.
return NotImplemented
def __radd__(self, other):
# radd handles more types than add because there's
# nothing left to fall back to.
if isinstance(other, numbers.Rational):
return Fraction(self.numerator * other.denominator +
other.numerator * self.denominator,
self.denominator * other.denominator)
elif isinstance(other, Real):
return float(other) + float(self)
elif isinstance(other, Complex):
return complex(other) + complex(self)
return NotImplemented
There are 5 different cases for a mixed-type addition on
Fraction. I'll refer to all of the above code that doesn't
refer to Fraction, float, or complex as "boilerplate". 'r'
will be an instance of Fraction, which is a subtype of
Rational (r : Fraction <: Rational), and b : B <:
Complex. The first three involve 'r + b':
1. If B <: Fraction, int, float, or complex, we handle
that specially, and all is well.
2. If Fraction falls back to the boilerplate code, and it
were to return a value from __add__, we'd miss the
possibility that B defines a more intelligent __radd__,
so the boilerplate should return NotImplemented from
__add__. In particular, we don't handle Rational
here, even though we could get an exact answer, in case
the other type wants to do something special.
3. If B <: Fraction, Python tries B.__radd__ before
Fraction.__add__. This is ok, because it was
implemented with knowledge of Fraction, so it can
handle those instances before delegating to Real or
Complex.
The next two situations describe 'b + r'. We assume that b
didn't know about Fraction in its implementation, and that it
uses similar boilerplate code:
4. If B <: Rational, then __radd_ converts both to the
builtin rational type (hey look, that's us) and
proceeds.
5. Otherwise, __radd__ tries to find the nearest common
base ABC, and fall back to its builtin type. Since this
class doesn't subclass a concrete type, there's no
implementation to fall back to, so we need to try as
hard as possible to return an actual value, or the user
will get a TypeError.
"""
def forward(a, b):
if isinstance(b, (int, Fraction)):
return monomorphic_operator(a, b)
elif isinstance(b, float):
return fallback_operator(float(a), b)
elif isinstance(b, complex):
return fallback_operator(complex(a), b)
else:
return NotImplemented
forward.__name__ = '__' + fallback_operator.__name__ + '__'
forward.__doc__ = monomorphic_operator.__doc__
def reverse(b, a):
if isinstance(a, numbers.Rational):
# Includes ints.
return monomorphic_operator(a, b)
elif isinstance(a, numbers.Real):
return fallback_operator(float(a), float(b))
elif isinstance(a, numbers.Complex):
return fallback_operator(complex(a), complex(b))
else:
return NotImplemented
reverse.__name__ = '__r' + fallback_operator.__name__ + '__'
reverse.__doc__ = monomorphic_operator.__doc__
return forward, reverse
| (a, b) |
10,299 | fractions | __mul__ | a * b | def _operator_fallbacks(monomorphic_operator, fallback_operator):
"""Generates forward and reverse operators given a purely-rational
operator and a function from the operator module.
Use this like:
__op__, __rop__ = _operator_fallbacks(just_rational_op, operator.op)
In general, we want to implement the arithmetic operations so
that mixed-mode operations either call an implementation whose
author knew about the types of both arguments, or convert both
to the nearest built in type and do the operation there. In
Fraction, that means that we define __add__ and __radd__ as:
def __add__(self, other):
# Both types have numerators/denominator attributes,
# so do the operation directly
if isinstance(other, (int, Fraction)):
return Fraction(self.numerator * other.denominator +
other.numerator * self.denominator,
self.denominator * other.denominator)
# float and complex don't have those operations, but we
# know about those types, so special case them.
elif isinstance(other, float):
return float(self) + other
elif isinstance(other, complex):
return complex(self) + other
# Let the other type take over.
return NotImplemented
def __radd__(self, other):
# radd handles more types than add because there's
# nothing left to fall back to.
if isinstance(other, numbers.Rational):
return Fraction(self.numerator * other.denominator +
other.numerator * self.denominator,
self.denominator * other.denominator)
elif isinstance(other, Real):
return float(other) + float(self)
elif isinstance(other, Complex):
return complex(other) + complex(self)
return NotImplemented
There are 5 different cases for a mixed-type addition on
Fraction. I'll refer to all of the above code that doesn't
refer to Fraction, float, or complex as "boilerplate". 'r'
will be an instance of Fraction, which is a subtype of
Rational (r : Fraction <: Rational), and b : B <:
Complex. The first three involve 'r + b':
1. If B <: Fraction, int, float, or complex, we handle
that specially, and all is well.
2. If Fraction falls back to the boilerplate code, and it
were to return a value from __add__, we'd miss the
possibility that B defines a more intelligent __radd__,
so the boilerplate should return NotImplemented from
__add__. In particular, we don't handle Rational
here, even though we could get an exact answer, in case
the other type wants to do something special.
3. If B <: Fraction, Python tries B.__radd__ before
Fraction.__add__. This is ok, because it was
implemented with knowledge of Fraction, so it can
handle those instances before delegating to Real or
Complex.
The next two situations describe 'b + r'. We assume that b
didn't know about Fraction in its implementation, and that it
uses similar boilerplate code:
4. If B <: Rational, then __radd_ converts both to the
builtin rational type (hey look, that's us) and
proceeds.
5. Otherwise, __radd__ tries to find the nearest common
base ABC, and fall back to its builtin type. Since this
class doesn't subclass a concrete type, there's no
implementation to fall back to, so we need to try as
hard as possible to return an actual value, or the user
will get a TypeError.
"""
def forward(a, b):
if isinstance(b, (int, Fraction)):
return monomorphic_operator(a, b)
elif isinstance(b, float):
return fallback_operator(float(a), b)
elif isinstance(b, complex):
return fallback_operator(complex(a), b)
else:
return NotImplemented
forward.__name__ = '__' + fallback_operator.__name__ + '__'
forward.__doc__ = monomorphic_operator.__doc__
def reverse(b, a):
if isinstance(a, numbers.Rational):
# Includes ints.
return monomorphic_operator(a, b)
elif isinstance(a, numbers.Real):
return fallback_operator(float(a), float(b))
elif isinstance(a, numbers.Complex):
return fallback_operator(complex(a), complex(b))
else:
return NotImplemented
reverse.__name__ = '__r' + fallback_operator.__name__ + '__'
reverse.__doc__ = monomorphic_operator.__doc__
return forward, reverse
| (a, b) |
10,300 | fractions | __neg__ | -a | def __neg__(a):
"""-a"""
return Fraction(-a._numerator, a._denominator, _normalize=False)
| (a) |
10,301 | fractions | __new__ | Constructs a Rational.
Takes a string like '3/2' or '1.5', another Rational instance, a
numerator/denominator pair, or a float.
Examples
--------
>>> Fraction(10, -8)
Fraction(-5, 4)
>>> Fraction(Fraction(1, 7), 5)
Fraction(1, 35)
>>> Fraction(Fraction(1, 7), Fraction(2, 3))
Fraction(3, 14)
>>> Fraction('314')
Fraction(314, 1)
>>> Fraction('-35/4')
Fraction(-35, 4)
>>> Fraction('3.1415') # conversion from numeric string
Fraction(6283, 2000)
>>> Fraction('-47e-2') # string may include a decimal exponent
Fraction(-47, 100)
>>> Fraction(1.47) # direct construction from float (exact conversion)
Fraction(6620291452234629, 4503599627370496)
>>> Fraction(2.25)
Fraction(9, 4)
>>> Fraction(Decimal('1.47'))
Fraction(147, 100)
| def __new__(cls, numerator=0, denominator=None, *, _normalize=True):
"""Constructs a Rational.
Takes a string like '3/2' or '1.5', another Rational instance, a
numerator/denominator pair, or a float.
Examples
--------
>>> Fraction(10, -8)
Fraction(-5, 4)
>>> Fraction(Fraction(1, 7), 5)
Fraction(1, 35)
>>> Fraction(Fraction(1, 7), Fraction(2, 3))
Fraction(3, 14)
>>> Fraction('314')
Fraction(314, 1)
>>> Fraction('-35/4')
Fraction(-35, 4)
>>> Fraction('3.1415') # conversion from numeric string
Fraction(6283, 2000)
>>> Fraction('-47e-2') # string may include a decimal exponent
Fraction(-47, 100)
>>> Fraction(1.47) # direct construction from float (exact conversion)
Fraction(6620291452234629, 4503599627370496)
>>> Fraction(2.25)
Fraction(9, 4)
>>> Fraction(Decimal('1.47'))
Fraction(147, 100)
"""
self = super(Fraction, cls).__new__(cls)
if denominator is None:
if type(numerator) is int:
self._numerator = numerator
self._denominator = 1
return self
elif isinstance(numerator, numbers.Rational):
self._numerator = numerator.numerator
self._denominator = numerator.denominator
return self
elif isinstance(numerator, (float, Decimal)):
# Exact conversion
self._numerator, self._denominator = numerator.as_integer_ratio()
return self
elif isinstance(numerator, str):
# Handle construction from strings.
m = _RATIONAL_FORMAT.match(numerator)
if m is None:
raise ValueError('Invalid literal for Fraction: %r' %
numerator)
numerator = int(m.group('num') or '0')
denom = m.group('denom')
if denom:
denominator = int(denom)
else:
denominator = 1
decimal = m.group('decimal')
if decimal:
scale = 10**len(decimal)
numerator = numerator * scale + int(decimal)
denominator *= scale
exp = m.group('exp')
if exp:
exp = int(exp)
if exp >= 0:
numerator *= 10**exp
else:
denominator *= 10**-exp
if m.group('sign') == '-':
numerator = -numerator
else:
raise TypeError("argument should be a string "
"or a Rational instance")
elif type(numerator) is int is type(denominator):
pass # *very* normal case
elif (isinstance(numerator, numbers.Rational) and
isinstance(denominator, numbers.Rational)):
numerator, denominator = (
numerator.numerator * denominator.denominator,
denominator.numerator * numerator.denominator
)
else:
raise TypeError("both arguments should be "
"Rational instances")
if denominator == 0:
raise ZeroDivisionError('Fraction(%s, 0)' % numerator)
if _normalize:
g = math.gcd(numerator, denominator)
if denominator < 0:
g = -g
numerator //= g
denominator //= g
self._numerator = numerator
self._denominator = denominator
return self
| (cls, numerator=0, denominator=None, *, _normalize=True) |
10,302 | fractions | __pos__ | +a: Coerces a subclass instance to Fraction | def __pos__(a):
"""+a: Coerces a subclass instance to Fraction"""
return Fraction(a._numerator, a._denominator, _normalize=False)
| (a) |
10,303 | fractions | __pow__ | a ** b
If b is not an integer, the result will be a float or complex
since roots are generally irrational. If b is an integer, the
result will be rational.
| def __pow__(a, b):
"""a ** b
If b is not an integer, the result will be a float or complex
since roots are generally irrational. If b is an integer, the
result will be rational.
"""
if isinstance(b, numbers.Rational):
if b.denominator == 1:
power = b.numerator
if power >= 0:
return Fraction(a._numerator ** power,
a._denominator ** power,
_normalize=False)
elif a._numerator >= 0:
return Fraction(a._denominator ** -power,
a._numerator ** -power,
_normalize=False)
else:
return Fraction((-a._denominator) ** -power,
(-a._numerator) ** -power,
_normalize=False)
else:
# A fractional power will generally produce an
# irrational number.
return float(a) ** float(b)
else:
return float(a) ** b
| (a, b) |
10,306 | fractions | __reduce__ | null | def __reduce__(self):
return (self.__class__, (str(self),))
| (self) |
10,307 | fractions | __repr__ | repr(self) | def __repr__(self):
"""repr(self)"""
return '%s(%s, %s)' % (self.__class__.__name__,
self._numerator, self._denominator)
| (self) |
10,311 | fractions | __round__ | round(self, ndigits)
Rounds half toward even.
| def __round__(self, ndigits=None):
"""round(self, ndigits)
Rounds half toward even.
"""
if ndigits is None:
floor, remainder = divmod(self.numerator, self.denominator)
if remainder * 2 < self.denominator:
return floor
elif remainder * 2 > self.denominator:
return floor + 1
# Deal with the half case:
elif floor % 2 == 0:
return floor
else:
return floor + 1
shift = 10**abs(ndigits)
# See _operator_fallbacks.forward to check that the results of
# these operations will always be Fraction and therefore have
# round().
if ndigits > 0:
return Fraction(round(self * shift), shift)
else:
return Fraction(round(self / shift) * shift)
| (self, ndigits=None) |
10,312 | fractions | __rpow__ | a ** b | def __rpow__(b, a):
"""a ** b"""
if b._denominator == 1 and b._numerator >= 0:
# If a is an int, keep it that way if possible.
return a ** b._numerator
if isinstance(a, numbers.Rational):
return Fraction(a.numerator, a.denominator) ** b
if b._denominator == 1:
return a ** b._numerator
return a ** float(b)
| (b, a) |
10,313 | fractions | __rsub__ | a - b | def _operator_fallbacks(monomorphic_operator, fallback_operator):
"""Generates forward and reverse operators given a purely-rational
operator and a function from the operator module.
Use this like:
__op__, __rop__ = _operator_fallbacks(just_rational_op, operator.op)
In general, we want to implement the arithmetic operations so
that mixed-mode operations either call an implementation whose
author knew about the types of both arguments, or convert both
to the nearest built in type and do the operation there. In
Fraction, that means that we define __add__ and __radd__ as:
def __add__(self, other):
# Both types have numerators/denominator attributes,
# so do the operation directly
if isinstance(other, (int, Fraction)):
return Fraction(self.numerator * other.denominator +
other.numerator * self.denominator,
self.denominator * other.denominator)
# float and complex don't have those operations, but we
# know about those types, so special case them.
elif isinstance(other, float):
return float(self) + other
elif isinstance(other, complex):
return complex(self) + other
# Let the other type take over.
return NotImplemented
def __radd__(self, other):
# radd handles more types than add because there's
# nothing left to fall back to.
if isinstance(other, numbers.Rational):
return Fraction(self.numerator * other.denominator +
other.numerator * self.denominator,
self.denominator * other.denominator)
elif isinstance(other, Real):
return float(other) + float(self)
elif isinstance(other, Complex):
return complex(other) + complex(self)
return NotImplemented
There are 5 different cases for a mixed-type addition on
Fraction. I'll refer to all of the above code that doesn't
refer to Fraction, float, or complex as "boilerplate". 'r'
will be an instance of Fraction, which is a subtype of
Rational (r : Fraction <: Rational), and b : B <:
Complex. The first three involve 'r + b':
1. If B <: Fraction, int, float, or complex, we handle
that specially, and all is well.
2. If Fraction falls back to the boilerplate code, and it
were to return a value from __add__, we'd miss the
possibility that B defines a more intelligent __radd__,
so the boilerplate should return NotImplemented from
__add__. In particular, we don't handle Rational
here, even though we could get an exact answer, in case
the other type wants to do something special.
3. If B <: Fraction, Python tries B.__radd__ before
Fraction.__add__. This is ok, because it was
implemented with knowledge of Fraction, so it can
handle those instances before delegating to Real or
Complex.
The next two situations describe 'b + r'. We assume that b
didn't know about Fraction in its implementation, and that it
uses similar boilerplate code:
4. If B <: Rational, then __radd_ converts both to the
builtin rational type (hey look, that's us) and
proceeds.
5. Otherwise, __radd__ tries to find the nearest common
base ABC, and fall back to its builtin type. Since this
class doesn't subclass a concrete type, there's no
implementation to fall back to, so we need to try as
hard as possible to return an actual value, or the user
will get a TypeError.
"""
def forward(a, b):
if isinstance(b, (int, Fraction)):
return monomorphic_operator(a, b)
elif isinstance(b, float):
return fallback_operator(float(a), b)
elif isinstance(b, complex):
return fallback_operator(complex(a), b)
else:
return NotImplemented
forward.__name__ = '__' + fallback_operator.__name__ + '__'
forward.__doc__ = monomorphic_operator.__doc__
def reverse(b, a):
if isinstance(a, numbers.Rational):
# Includes ints.
return monomorphic_operator(a, b)
elif isinstance(a, numbers.Real):
return fallback_operator(float(a), float(b))
elif isinstance(a, numbers.Complex):
return fallback_operator(complex(a), complex(b))
else:
return NotImplemented
reverse.__name__ = '__r' + fallback_operator.__name__ + '__'
reverse.__doc__ = monomorphic_operator.__doc__
return forward, reverse
| (b, a) |
10,314 | fractions | __rtruediv__ | a / b | def _operator_fallbacks(monomorphic_operator, fallback_operator):
"""Generates forward and reverse operators given a purely-rational
operator and a function from the operator module.
Use this like:
__op__, __rop__ = _operator_fallbacks(just_rational_op, operator.op)
In general, we want to implement the arithmetic operations so
that mixed-mode operations either call an implementation whose
author knew about the types of both arguments, or convert both
to the nearest built in type and do the operation there. In
Fraction, that means that we define __add__ and __radd__ as:
def __add__(self, other):
# Both types have numerators/denominator attributes,
# so do the operation directly
if isinstance(other, (int, Fraction)):
return Fraction(self.numerator * other.denominator +
other.numerator * self.denominator,
self.denominator * other.denominator)
# float and complex don't have those operations, but we
# know about those types, so special case them.
elif isinstance(other, float):
return float(self) + other
elif isinstance(other, complex):
return complex(self) + other
# Let the other type take over.
return NotImplemented
def __radd__(self, other):
# radd handles more types than add because there's
# nothing left to fall back to.
if isinstance(other, numbers.Rational):
return Fraction(self.numerator * other.denominator +
other.numerator * self.denominator,
self.denominator * other.denominator)
elif isinstance(other, Real):
return float(other) + float(self)
elif isinstance(other, Complex):
return complex(other) + complex(self)
return NotImplemented
There are 5 different cases for a mixed-type addition on
Fraction. I'll refer to all of the above code that doesn't
refer to Fraction, float, or complex as "boilerplate". 'r'
will be an instance of Fraction, which is a subtype of
Rational (r : Fraction <: Rational), and b : B <:
Complex. The first three involve 'r + b':
1. If B <: Fraction, int, float, or complex, we handle
that specially, and all is well.
2. If Fraction falls back to the boilerplate code, and it
were to return a value from __add__, we'd miss the
possibility that B defines a more intelligent __radd__,
so the boilerplate should return NotImplemented from
__add__. In particular, we don't handle Rational
here, even though we could get an exact answer, in case
the other type wants to do something special.
3. If B <: Fraction, Python tries B.__radd__ before
Fraction.__add__. This is ok, because it was
implemented with knowledge of Fraction, so it can
handle those instances before delegating to Real or
Complex.
The next two situations describe 'b + r'. We assume that b
didn't know about Fraction in its implementation, and that it
uses similar boilerplate code:
4. If B <: Rational, then __radd_ converts both to the
builtin rational type (hey look, that's us) and
proceeds.
5. Otherwise, __radd__ tries to find the nearest common
base ABC, and fall back to its builtin type. Since this
class doesn't subclass a concrete type, there's no
implementation to fall back to, so we need to try as
hard as possible to return an actual value, or the user
will get a TypeError.
"""
def forward(a, b):
if isinstance(b, (int, Fraction)):
return monomorphic_operator(a, b)
elif isinstance(b, float):
return fallback_operator(float(a), b)
elif isinstance(b, complex):
return fallback_operator(complex(a), b)
else:
return NotImplemented
forward.__name__ = '__' + fallback_operator.__name__ + '__'
forward.__doc__ = monomorphic_operator.__doc__
def reverse(b, a):
if isinstance(a, numbers.Rational):
# Includes ints.
return monomorphic_operator(a, b)
elif isinstance(a, numbers.Real):
return fallback_operator(float(a), float(b))
elif isinstance(a, numbers.Complex):
return fallback_operator(complex(a), complex(b))
else:
return NotImplemented
reverse.__name__ = '__r' + fallback_operator.__name__ + '__'
reverse.__doc__ = monomorphic_operator.__doc__
return forward, reverse
| (b, a) |
10,315 | fractions | __str__ | str(self) | def __str__(self):
"""str(self)"""
if self._denominator == 1:
return str(self._numerator)
else:
return '%s/%s' % (self._numerator, self._denominator)
| (self) |
10,318 | fractions | __trunc__ | trunc(a) | def __trunc__(a):
"""trunc(a)"""
if a._numerator < 0:
return -(-a._numerator // a._denominator)
else:
return a._numerator // a._denominator
| (a) |
10,319 | fractions | _add | a + b | def _add(a, b):
"""a + b"""
na, da = a.numerator, a.denominator
nb, db = b.numerator, b.denominator
g = math.gcd(da, db)
if g == 1:
return Fraction(na * db + da * nb, da * db, _normalize=False)
s = da // g
t = na * (db // g) + nb * s
g2 = math.gcd(t, g)
if g2 == 1:
return Fraction(t, s * db, _normalize=False)
return Fraction(t // g2, s * (db // g2), _normalize=False)
| (a, b) |
10,320 | fractions | _div | a / b | def _div(a, b):
"""a / b"""
# Same as _mul(), with inversed b.
na, da = a.numerator, a.denominator
nb, db = b.numerator, b.denominator
g1 = math.gcd(na, nb)
if g1 > 1:
na //= g1
nb //= g1
g2 = math.gcd(db, da)
if g2 > 1:
da //= g2
db //= g2
n, d = na * db, nb * da
if d < 0:
n, d = -n, -d
return Fraction(n, d, _normalize=False)
| (a, b) |
10,321 | fractions | _divmod | (a // b, a % b) | def _divmod(a, b):
"""(a // b, a % b)"""
da, db = a.denominator, b.denominator
div, n_mod = divmod(a.numerator * db, da * b.numerator)
return div, Fraction(n_mod, da * db)
| (a, b) |
10,322 | fractions | _floordiv | a // b | def _floordiv(a, b):
"""a // b"""
return (a.numerator * b.denominator) // (a.denominator * b.numerator)
| (a, b) |
10,323 | fractions | _mod | a % b | def _mod(a, b):
"""a % b"""
da, db = a.denominator, b.denominator
return Fraction((a.numerator * db) % (b.numerator * da), da * db)
| (a, b) |
10,324 | fractions | _mul | a * b | def _mul(a, b):
"""a * b"""
na, da = a.numerator, a.denominator
nb, db = b.numerator, b.denominator
g1 = math.gcd(na, db)
if g1 > 1:
na //= g1
db //= g1
g2 = math.gcd(nb, da)
if g2 > 1:
nb //= g2
da //= g2
return Fraction(na * nb, db * da, _normalize=False)
| (a, b) |
10,325 | fractions | _operator_fallbacks | Generates forward and reverse operators given a purely-rational
operator and a function from the operator module.
Use this like:
__op__, __rop__ = _operator_fallbacks(just_rational_op, operator.op)
In general, we want to implement the arithmetic operations so
that mixed-mode operations either call an implementation whose
author knew about the types of both arguments, or convert both
to the nearest built in type and do the operation there. In
Fraction, that means that we define __add__ and __radd__ as:
def __add__(self, other):
# Both types have numerators/denominator attributes,
# so do the operation directly
if isinstance(other, (int, Fraction)):
return Fraction(self.numerator * other.denominator +
other.numerator * self.denominator,
self.denominator * other.denominator)
# float and complex don't have those operations, but we
# know about those types, so special case them.
elif isinstance(other, float):
return float(self) + other
elif isinstance(other, complex):
return complex(self) + other
# Let the other type take over.
return NotImplemented
def __radd__(self, other):
# radd handles more types than add because there's
# nothing left to fall back to.
if isinstance(other, numbers.Rational):
return Fraction(self.numerator * other.denominator +
other.numerator * self.denominator,
self.denominator * other.denominator)
elif isinstance(other, Real):
return float(other) + float(self)
elif isinstance(other, Complex):
return complex(other) + complex(self)
return NotImplemented
There are 5 different cases for a mixed-type addition on
Fraction. I'll refer to all of the above code that doesn't
refer to Fraction, float, or complex as "boilerplate". 'r'
will be an instance of Fraction, which is a subtype of
Rational (r : Fraction <: Rational), and b : B <:
Complex. The first three involve 'r + b':
1. If B <: Fraction, int, float, or complex, we handle
that specially, and all is well.
2. If Fraction falls back to the boilerplate code, and it
were to return a value from __add__, we'd miss the
possibility that B defines a more intelligent __radd__,
so the boilerplate should return NotImplemented from
__add__. In particular, we don't handle Rational
here, even though we could get an exact answer, in case
the other type wants to do something special.
3. If B <: Fraction, Python tries B.__radd__ before
Fraction.__add__. This is ok, because it was
implemented with knowledge of Fraction, so it can
handle those instances before delegating to Real or
Complex.
The next two situations describe 'b + r'. We assume that b
didn't know about Fraction in its implementation, and that it
uses similar boilerplate code:
4. If B <: Rational, then __radd_ converts both to the
builtin rational type (hey look, that's us) and
proceeds.
5. Otherwise, __radd__ tries to find the nearest common
base ABC, and fall back to its builtin type. Since this
class doesn't subclass a concrete type, there's no
implementation to fall back to, so we need to try as
hard as possible to return an actual value, or the user
will get a TypeError.
| def _operator_fallbacks(monomorphic_operator, fallback_operator):
"""Generates forward and reverse operators given a purely-rational
operator and a function from the operator module.
Use this like:
__op__, __rop__ = _operator_fallbacks(just_rational_op, operator.op)
In general, we want to implement the arithmetic operations so
that mixed-mode operations either call an implementation whose
author knew about the types of both arguments, or convert both
to the nearest built in type and do the operation there. In
Fraction, that means that we define __add__ and __radd__ as:
def __add__(self, other):
# Both types have numerators/denominator attributes,
# so do the operation directly
if isinstance(other, (int, Fraction)):
return Fraction(self.numerator * other.denominator +
other.numerator * self.denominator,
self.denominator * other.denominator)
# float and complex don't have those operations, but we
# know about those types, so special case them.
elif isinstance(other, float):
return float(self) + other
elif isinstance(other, complex):
return complex(self) + other
# Let the other type take over.
return NotImplemented
def __radd__(self, other):
# radd handles more types than add because there's
# nothing left to fall back to.
if isinstance(other, numbers.Rational):
return Fraction(self.numerator * other.denominator +
other.numerator * self.denominator,
self.denominator * other.denominator)
elif isinstance(other, Real):
return float(other) + float(self)
elif isinstance(other, Complex):
return complex(other) + complex(self)
return NotImplemented
There are 5 different cases for a mixed-type addition on
Fraction. I'll refer to all of the above code that doesn't
refer to Fraction, float, or complex as "boilerplate". 'r'
will be an instance of Fraction, which is a subtype of
Rational (r : Fraction <: Rational), and b : B <:
Complex. The first three involve 'r + b':
1. If B <: Fraction, int, float, or complex, we handle
that specially, and all is well.
2. If Fraction falls back to the boilerplate code, and it
were to return a value from __add__, we'd miss the
possibility that B defines a more intelligent __radd__,
so the boilerplate should return NotImplemented from
__add__. In particular, we don't handle Rational
here, even though we could get an exact answer, in case
the other type wants to do something special.
3. If B <: Fraction, Python tries B.__radd__ before
Fraction.__add__. This is ok, because it was
implemented with knowledge of Fraction, so it can
handle those instances before delegating to Real or
Complex.
The next two situations describe 'b + r'. We assume that b
didn't know about Fraction in its implementation, and that it
uses similar boilerplate code:
4. If B <: Rational, then __radd_ converts both to the
builtin rational type (hey look, that's us) and
proceeds.
5. Otherwise, __radd__ tries to find the nearest common
base ABC, and fall back to its builtin type. Since this
class doesn't subclass a concrete type, there's no
implementation to fall back to, so we need to try as
hard as possible to return an actual value, or the user
will get a TypeError.
"""
def forward(a, b):
if isinstance(b, (int, Fraction)):
return monomorphic_operator(a, b)
elif isinstance(b, float):
return fallback_operator(float(a), b)
elif isinstance(b, complex):
return fallback_operator(complex(a), b)
else:
return NotImplemented
forward.__name__ = '__' + fallback_operator.__name__ + '__'
forward.__doc__ = monomorphic_operator.__doc__
def reverse(b, a):
if isinstance(a, numbers.Rational):
# Includes ints.
return monomorphic_operator(a, b)
elif isinstance(a, numbers.Real):
return fallback_operator(float(a), float(b))
elif isinstance(a, numbers.Complex):
return fallback_operator(complex(a), complex(b))
else:
return NotImplemented
reverse.__name__ = '__r' + fallback_operator.__name__ + '__'
reverse.__doc__ = monomorphic_operator.__doc__
return forward, reverse
| (monomorphic_operator, fallback_operator) |
10,326 | fractions | _richcmp | Helper for comparison operators, for internal use only.
Implement comparison between a Rational instance `self`, and
either another Rational instance or a float `other`. If
`other` is not a Rational instance or a float, return
NotImplemented. `op` should be one of the six standard
comparison operators.
| def _richcmp(self, other, op):
"""Helper for comparison operators, for internal use only.
Implement comparison between a Rational instance `self`, and
either another Rational instance or a float `other`. If
`other` is not a Rational instance or a float, return
NotImplemented. `op` should be one of the six standard
comparison operators.
"""
# convert other to a Rational instance where reasonable.
if isinstance(other, numbers.Rational):
return op(self._numerator * other.denominator,
self._denominator * other.numerator)
if isinstance(other, float):
if math.isnan(other) or math.isinf(other):
return op(0.0, other)
else:
return op(self, self.from_float(other))
else:
return NotImplemented
| (self, other, op) |
10,327 | fractions | _sub | a - b | def _sub(a, b):
"""a - b"""
na, da = a.numerator, a.denominator
nb, db = b.numerator, b.denominator
g = math.gcd(da, db)
if g == 1:
return Fraction(na * db - da * nb, da * db, _normalize=False)
s = da // g
t = na * (db // g) - nb * s
g2 = math.gcd(t, g)
if g2 == 1:
return Fraction(t, s * db, _normalize=False)
return Fraction(t // g2, s * (db // g2), _normalize=False)
| (a, b) |
10,328 | fractions | as_integer_ratio | Return the integer ratio as a tuple.
Return a tuple of two integers, whose ratio is equal to the
Fraction and with a positive denominator.
| def as_integer_ratio(self):
"""Return the integer ratio as a tuple.
Return a tuple of two integers, whose ratio is equal to the
Fraction and with a positive denominator.
"""
return (self._numerator, self._denominator)
| (self) |
10,329 | numbers | conjugate | Conjugate is a no-op for Reals. | def conjugate(self):
"""Conjugate is a no-op for Reals."""
return +self
| (self) |
10,330 | fractions | limit_denominator | Closest Fraction to self with denominator at most max_denominator.
>>> Fraction('3.141592653589793').limit_denominator(10)
Fraction(22, 7)
>>> Fraction('3.141592653589793').limit_denominator(100)
Fraction(311, 99)
>>> Fraction(4321, 8765).limit_denominator(10000)
Fraction(4321, 8765)
| def limit_denominator(self, max_denominator=1000000):
"""Closest Fraction to self with denominator at most max_denominator.
>>> Fraction('3.141592653589793').limit_denominator(10)
Fraction(22, 7)
>>> Fraction('3.141592653589793').limit_denominator(100)
Fraction(311, 99)
>>> Fraction(4321, 8765).limit_denominator(10000)
Fraction(4321, 8765)
"""
# Algorithm notes: For any real number x, define a *best upper
# approximation* to x to be a rational number p/q such that:
#
# (1) p/q >= x, and
# (2) if p/q > r/s >= x then s > q, for any rational r/s.
#
# Define *best lower approximation* similarly. Then it can be
# proved that a rational number is a best upper or lower
# approximation to x if, and only if, it is a convergent or
# semiconvergent of the (unique shortest) continued fraction
# associated to x.
#
# To find a best rational approximation with denominator <= M,
# we find the best upper and lower approximations with
# denominator <= M and take whichever of these is closer to x.
# In the event of a tie, the bound with smaller denominator is
# chosen. If both denominators are equal (which can happen
# only when max_denominator == 1 and self is midway between
# two integers) the lower bound---i.e., the floor of self, is
# taken.
if max_denominator < 1:
raise ValueError("max_denominator should be at least 1")
if self._denominator <= max_denominator:
return Fraction(self)
p0, q0, p1, q1 = 0, 1, 1, 0
n, d = self._numerator, self._denominator
while True:
a = n//d
q2 = q0+a*q1
if q2 > max_denominator:
break
p0, q0, p1, q1 = p1, q1, p0+a*p1, q2
n, d = d, n-a*d
k = (max_denominator-q0)//q1
bound1 = Fraction(p0+k*p1, q0+k*q1)
bound2 = Fraction(p1, q1)
if abs(bound2 - self) <= abs(bound1-self):
return bound2
else:
return bound1
| (self, max_denominator=1000000) |
10,333 | itertools | count | Return a count object whose .__next__() method returns consecutive values.
Equivalent to:
def count(firstval=0, step=1):
x = firstval
while 1:
yield x
x += step | from itertools import count
| (start=0, step=1) |
10,334 | torch_pitch_shift.main | get_fast_shifts |
Search for pitch-shift targets that can be computed quickly for a given sample rate.
Parameters
----------
sample_rate: int
The sample rate of an audio clip.
condition: Callable [optional]
A function to validate fast shift ratios.
Default is `lambda x: x >= 0.5 and x <= 2 and x != 1` (between -1 and +1 octaves).
Returns
-------
output: List[Fraction]
A list of fast pitch-shift target ratios
| def get_fast_shifts(
sample_rate: int,
condition: Optional[Callable] = lambda x: x >= 0.5 and x <= 2 and x != 1,
) -> List[Fraction]:
"""
Search for pitch-shift targets that can be computed quickly for a given sample rate.
Parameters
----------
sample_rate: int
The sample rate of an audio clip.
condition: Callable [optional]
A function to validate fast shift ratios.
Default is `lambda x: x >= 0.5 and x <= 2 and x != 1` (between -1 and +1 octaves).
Returns
-------
output: List[Fraction]
A list of fast pitch-shift target ratios
"""
fast_shifts = set()
factors = primes.factors(sample_rate)
products = []
for i in range(1, len(factors) + 1):
products.extend(
[
reduce(lambda x, y: x * y, x)
for x in _combinations_without_repetition(i, iterable=factors)
]
)
for i in products:
for j in products:
f = Fraction(i, j)
if condition(f):
fast_shifts.add(f)
return list(fast_shifts)
| (sample_rate: int, condition: Optional[Callable] = <function <lambda> at 0x7f1812901ea0>) -> List[fractions.Fraction] |
10,335 | itertools | islice | islice(iterable, stop) --> islice object
islice(iterable, start, stop[, step]) --> islice object
Return an iterator whose next() method returns selected values from an
iterable. If start is specified, will skip all preceding elements;
otherwise, start defaults to zero. Step defaults to one. If
specified as another value, step determines how many values are
skipped between successive calls. Works like a slice() on a list
but returns an iterator. | from itertools import islice
| null |
10,337 | torch.nn.functional | pad |
pad(input, pad, mode="constant", value=None) -> Tensor
Pads tensor.
Padding size:
The padding size by which to pad some dimensions of :attr:`input`
are described starting from the last dimension and moving forward.
:math:`\left\lfloor\frac{\text{len(pad)}}{2}\right\rfloor` dimensions
of ``input`` will be padded.
For example, to pad only the last dimension of the input tensor, then
:attr:`pad` has the form
:math:`(\text{padding\_left}, \text{padding\_right})`;
to pad the last 2 dimensions of the input tensor, then use
:math:`(\text{padding\_left}, \text{padding\_right},`
:math:`\text{padding\_top}, \text{padding\_bottom})`;
to pad the last 3 dimensions, use
:math:`(\text{padding\_left}, \text{padding\_right},`
:math:`\text{padding\_top}, \text{padding\_bottom}`
:math:`\text{padding\_front}, \text{padding\_back})`.
Padding mode:
See :class:`torch.nn.CircularPad2d`, :class:`torch.nn.ConstantPad2d`,
:class:`torch.nn.ReflectionPad2d`, and :class:`torch.nn.ReplicationPad2d`
for concrete examples on how each of the padding modes works. Constant
padding is implemented for arbitrary dimensions. Circular, replicate and
reflection padding are implemented for padding the last 3 dimensions of a
4D or 5D input tensor, the last 2 dimensions of a 3D or 4D input tensor,
or the last dimension of a 2D or 3D input tensor.
Note:
When using the CUDA backend, this operation may induce nondeterministic
behaviour in its backward pass that is not easily switched off.
Please see the notes on :doc:`/notes/randomness` for background.
Args:
input (Tensor): N-dimensional tensor
pad (tuple): m-elements tuple, where
:math:`\frac{m}{2} \leq` input dimensions and :math:`m` is even.
mode: ``'constant'``, ``'reflect'``, ``'replicate'`` or ``'circular'``.
Default: ``'constant'``
value: fill value for ``'constant'`` padding. Default: ``0``
Examples::
>>> t4d = torch.empty(3, 3, 4, 2)
>>> p1d = (1, 1) # pad last dim by 1 on each side
>>> out = F.pad(t4d, p1d, "constant", 0) # effectively zero padding
>>> print(out.size())
torch.Size([3, 3, 4, 4])
>>> p2d = (1, 1, 2, 2) # pad last dim by (1, 1) and 2nd to last by (2, 2)
>>> out = F.pad(t4d, p2d, "constant", 0)
>>> print(out.size())
torch.Size([3, 3, 8, 4])
>>> t4d = torch.empty(3, 3, 4, 2)
>>> p3d = (0, 1, 2, 1, 3, 3) # pad by (0, 1), (2, 1), and (3, 3)
>>> out = F.pad(t4d, p3d, "constant", 0)
>>> print(out.size())
torch.Size([3, 9, 7, 3])
| def pad(input: Tensor, pad: List[int], mode: str = "constant", value: Optional[float] = None) -> Tensor:
r"""
pad(input, pad, mode="constant", value=None) -> Tensor
Pads tensor.
Padding size:
The padding size by which to pad some dimensions of :attr:`input`
are described starting from the last dimension and moving forward.
:math:`\left\lfloor\frac{\text{len(pad)}}{2}\right\rfloor` dimensions
of ``input`` will be padded.
For example, to pad only the last dimension of the input tensor, then
:attr:`pad` has the form
:math:`(\text{padding\_left}, \text{padding\_right})`;
to pad the last 2 dimensions of the input tensor, then use
:math:`(\text{padding\_left}, \text{padding\_right},`
:math:`\text{padding\_top}, \text{padding\_bottom})`;
to pad the last 3 dimensions, use
:math:`(\text{padding\_left}, \text{padding\_right},`
:math:`\text{padding\_top}, \text{padding\_bottom}`
:math:`\text{padding\_front}, \text{padding\_back})`.
Padding mode:
See :class:`torch.nn.CircularPad2d`, :class:`torch.nn.ConstantPad2d`,
:class:`torch.nn.ReflectionPad2d`, and :class:`torch.nn.ReplicationPad2d`
for concrete examples on how each of the padding modes works. Constant
padding is implemented for arbitrary dimensions. Circular, replicate and
reflection padding are implemented for padding the last 3 dimensions of a
4D or 5D input tensor, the last 2 dimensions of a 3D or 4D input tensor,
or the last dimension of a 2D or 3D input tensor.
Note:
When using the CUDA backend, this operation may induce nondeterministic
behaviour in its backward pass that is not easily switched off.
Please see the notes on :doc:`/notes/randomness` for background.
Args:
input (Tensor): N-dimensional tensor
pad (tuple): m-elements tuple, where
:math:`\frac{m}{2} \leq` input dimensions and :math:`m` is even.
mode: ``'constant'``, ``'reflect'``, ``'replicate'`` or ``'circular'``.
Default: ``'constant'``
value: fill value for ``'constant'`` padding. Default: ``0``
Examples::
>>> t4d = torch.empty(3, 3, 4, 2)
>>> p1d = (1, 1) # pad last dim by 1 on each side
>>> out = F.pad(t4d, p1d, "constant", 0) # effectively zero padding
>>> print(out.size())
torch.Size([3, 3, 4, 4])
>>> p2d = (1, 1, 2, 2) # pad last dim by (1, 1) and 2nd to last by (2, 2)
>>> out = F.pad(t4d, p2d, "constant", 0)
>>> print(out.size())
torch.Size([3, 3, 8, 4])
>>> t4d = torch.empty(3, 3, 4, 2)
>>> p3d = (0, 1, 2, 1, 3, 3) # pad by (0, 1), (2, 1), and (3, 3)
>>> out = F.pad(t4d, p3d, "constant", 0)
>>> print(out.size())
torch.Size([3, 9, 7, 3])
"""
if has_torch_function_unary(input):
return handle_torch_function(
torch.nn.functional.pad, (input,), input, pad, mode=mode, value=value)
if not torch.jit.is_scripting():
if torch.are_deterministic_algorithms_enabled() and input.is_cuda:
if mode == 'replicate':
# Use slow decomp whose backward will be in terms of index_put.
# importlib is required because the import cannot be top level
# (cycle) and cannot be nested (TS doesn't support)
return importlib.import_module('torch._decomp.decompositions')._replication_pad(
input, pad
)
return torch._C._nn.pad(input, pad, mode, value)
| (input: torch.Tensor, pad: List[int], mode: str = 'constant', value: Optional[float] = None) -> torch.Tensor |
10,338 | torch_pitch_shift.main | pitch_shift |
Shift the pitch of a batch of waveforms by a given amount.
Parameters
----------
input: torch.Tensor [shape=(batch_size, channels, samples)]
Input audio clips of shape (batch_size, channels, samples)
shift: float OR Fraction
`float`: Amount to pitch-shift in # of bins. (1 bin == 1 semitone if `bins_per_octave` == 12)
`Fraction`: A `fractions.Fraction` object indicating the shift ratio. Usually an element in `get_fast_shifts()`.
sample_rate: int
The sample rate of the input audio clips.
bins_per_octave: int [optional]
Number of bins per octave. Default is 12.
n_fft: int [optional]
Size of FFT. Default is `sample_rate // 64`.
hop_length: int [optional]
Size of hop length. Default is `n_fft // 32`.
Returns
-------
output: torch.Tensor [shape=(batch_size, channels, samples)]
The pitch-shifted batch of audio clips
| def pitch_shift(
input: torch.Tensor,
shift: Union[float, Fraction],
sample_rate: int,
bins_per_octave: Optional[int] = 12,
n_fft: Optional[int] = 0,
hop_length: Optional[int] = 0,
) -> torch.Tensor:
"""
Shift the pitch of a batch of waveforms by a given amount.
Parameters
----------
input: torch.Tensor [shape=(batch_size, channels, samples)]
Input audio clips of shape (batch_size, channels, samples)
shift: float OR Fraction
`float`: Amount to pitch-shift in # of bins. (1 bin == 1 semitone if `bins_per_octave` == 12)
`Fraction`: A `fractions.Fraction` object indicating the shift ratio. Usually an element in `get_fast_shifts()`.
sample_rate: int
The sample rate of the input audio clips.
bins_per_octave: int [optional]
Number of bins per octave. Default is 12.
n_fft: int [optional]
Size of FFT. Default is `sample_rate // 64`.
hop_length: int [optional]
Size of hop length. Default is `n_fft // 32`.
Returns
-------
output: torch.Tensor [shape=(batch_size, channels, samples)]
The pitch-shifted batch of audio clips
"""
if not n_fft:
n_fft = sample_rate // 64
if not hop_length:
hop_length = n_fft // 32
batch_size, channels, samples = input.shape
if not isinstance(shift, Fraction):
shift = 2.0 ** (float(shift) / bins_per_octave)
resampler = T.Resample(sample_rate, int(sample_rate / shift)).to(input.device)
output = input
output = output.reshape(batch_size * channels, samples)
v011 = version.parse(torchaudio.__version__) >= version.parse("0.11.0")
output = torch.stft(output, n_fft, hop_length, return_complex=v011)[None, ...]
stretcher = T.TimeStretch(
fixed_rate=float(1 / shift), n_freq=output.shape[2], hop_length=hop_length
).to(input.device)
output = stretcher(output)
output = torch.istft(output[0], n_fft, hop_length)
output = resampler(output)
del resampler, stretcher
if output.shape[1] >= input.shape[2]:
output = output[:, : (input.shape[2])]
else:
output = pad(output, pad=(0, input.shape[2] - output.shape[1], 0, 0))
output = output.reshape(batch_size, channels, samples)
return output
| (input: torch.Tensor, shift: Union[float, fractions.Fraction], sample_rate: int, bins_per_octave: Optional[int] = 12, n_fft: Optional[int] = 0, hop_length: Optional[int] = 0) -> torch.Tensor |
10,340 | torch_pitch_shift.main | ratio_to_semitones |
Convert rational shifts to semitones.
Parameters
----------
ratio: Fraction
The ratio for a desired shift.
Returns
-------
output: float
The magnitude of a pitch shift in semitones
| def ratio_to_semitones(ratio: Fraction) -> float:
"""
Convert rational shifts to semitones.
Parameters
----------
ratio: Fraction
The ratio for a desired shift.
Returns
-------
output: float
The magnitude of a pitch shift in semitones
"""
return float(12.0 * log2(ratio))
| (ratio: fractions.Fraction) -> float |
10,341 | itertools | repeat | repeat(object [,times]) -> create an iterator which returns the object
for the specified number of times. If not specified, returns the object
endlessly. | from itertools import repeat
| null |
10,342 | torch_pitch_shift.main | semitones_to_ratio |
Convert semitonal shifts into ratios.
Parameters
----------
semitones: float
The number of semitones for a desired shift.
Returns
-------
output: Fraction
A Fraction indicating a pitch shift ratio
| def semitones_to_ratio(semitones: float) -> Fraction:
"""
Convert semitonal shifts into ratios.
Parameters
----------
semitones: float
The number of semitones for a desired shift.
Returns
-------
output: Fraction
A Fraction indicating a pitch shift ratio
"""
return Fraction(2.0 ** (semitones / 12.0))
| (semitones: float) -> fractions.Fraction |
10,347 | tracking_numbers.types | TrackingNumber | TrackingNumber(number: str, courier: tracking_numbers.types.Courier, product: tracking_numbers.types.Product, serial_number: Optional[List[int]], tracking_url: Optional[str], validation_errors: List[Tuple[str, str]]) | class TrackingNumber:
number: str
courier: Courier
product: Product
serial_number: Optional[SerialNumber]
tracking_url: Optional[str]
validation_errors: List[ValidationError]
@property
def valid(self) -> bool:
return not self.validation_errors
| (number: str, courier: tracking_numbers.types.Courier, product: tracking_numbers.types.Product, serial_number: Optional[List[int]], tracking_url: Optional[str], validation_errors: List[Tuple[str, str]]) -> None |
10,348 | tracking_numbers.types | __eq__ | null | from dataclasses import dataclass
from typing import Any
from typing import Dict
from typing import List
from typing import Optional
from typing import Tuple
Spec = Dict[str, Any]
SerialNumber = List[int]
ValidationError = Tuple[str, str]
@dataclass
class Product:
name: str
| (self, other) |
10,351 | tracking_numbers.definition | TrackingNumberDefinition | null | class TrackingNumberDefinition:
courier: Courier
product: Product
number_regex: Pattern
tracking_url_template: Optional[str]
serial_number_parser: SerialNumberParser
checksum_validator: Optional[ChecksumValidator]
additional_validations: List[AdditionalValidation]
def __init__(
self,
courier: Courier,
product: Product,
number_regex: Pattern,
tracking_url_template: Optional[str],
serial_number_parser: SerialNumberParser,
checksum_validator: Optional[ChecksumValidator],
additional_validations: List[AdditionalValidation],
):
self.courier = courier
self.product = product
self.number_regex = number_regex
self.tracking_url_template = tracking_url_template
self.serial_number_parser = serial_number_parser
self.checksum_validator = checksum_validator
self.additional_validations = additional_validations
def __repr__(self):
return repr_with_args(
self,
courier=self.courier,
product=self.product,
number_regex=self.number_regex,
tracking_url_template=self.tracking_url_template,
serial_number_parser=self.serial_number_parser,
checksum_validator=self.checksum_validator,
additional_validations=self.additional_validations,
)
@classmethod
def from_spec(cls, courier: Courier, tn_spec: Spec) -> "TrackingNumberDefinition":
product = Product(name=tn_spec["name"])
tracking_url_template = tn_spec.get("tracking_url")
number_regex = parse_regex(tn_spec["regex"])
validation_spec = tn_spec["validation"]
serial_number_parser = (
UPSSerialNumberParser()
if courier.code == "ups"
else DefaultSerialNumberParser.from_spec(validation_spec)
)
additional_spec = tn_spec.get("additional")
additional_validations: List[AdditionalValidation] = []
if isinstance(additional_spec, list):
# Handles None and 1 that is a dict (seems like old format / mistake)
for spec in additional_spec:
additional_validations.append(AdditionalValidation.from_spec(spec))
return TrackingNumberDefinition(
courier=courier,
product=product,
number_regex=number_regex,
tracking_url_template=tracking_url_template,
serial_number_parser=serial_number_parser,
checksum_validator=ChecksumValidator.from_spec(validation_spec),
additional_validations=additional_validations,
)
def test(self, tracking_number: str) -> Optional[TrackingNumber]:
match = self.number_regex.fullmatch(tracking_number)
if not match:
return None
match_data = match.groupdict() if match else {}
serial_number = self._get_serial_number(match_data)
validation_errors = self._get_validation_errors(serial_number, match_data)
return TrackingNumber(
number=tracking_number,
courier=self.courier,
product=self.product,
serial_number=serial_number,
tracking_url=self.tracking_url(tracking_number),
validation_errors=validation_errors,
)
def _get_serial_number(self, match_data: MatchData) -> Optional[SerialNumber]:
raw_serial_number = match_data.get("SerialNumber")
if raw_serial_number:
return self.serial_number_parser.parse(
_remove_whitespace(raw_serial_number),
)
return None
def _get_validation_errors(
self,
serial_number: Optional[SerialNumber],
match_data: MatchData,
) -> List[ValidationError]:
errors: List[ValidationError] = []
checksum_error = self._get_checksum_errors(serial_number, match_data)
if checksum_error:
errors.append(checksum_error)
for validation in self.additional_validations:
additional_error = self._get_additional_error(validation, match_data)
if additional_error:
errors.append(additional_error)
return errors
def _get_checksum_errors(
self,
serial_number: Optional[SerialNumber],
match_data: MatchData,
) -> Optional[ValidationError]:
if not self.checksum_validator:
return None
if not serial_number:
return "checksum", "SerialNumber not found"
check_digit = match_data.get("CheckDigit")
if not check_digit:
return "checksum", "CheckDigit not found"
passes_checksum = self.checksum_validator.passes(
serial_number=serial_number,
check_digit=int(check_digit),
)
if not passes_checksum:
return "checksum", "Checksum validation failed"
return None
@staticmethod
def _get_additional_error(
validation: AdditionalValidation,
match_data: MatchData,
) -> Optional[ValidationError]:
group_key = validation.regex_group_name
raw_value = match_data.get(group_key)
if not raw_value:
return validation.name, f"{group_key} not found"
value = _remove_whitespace(raw_value)
matches_any_value = any(
value_matcher.matches(value) for value_matcher in validation.value_matchers
)
if not matches_any_value:
return validation.name, f"Match not found for {group_key}: {value}"
return None
def tracking_url(self, tracking_number: str) -> Optional[str]:
if not self.tracking_url_template:
return None
return self.tracking_url_template % tracking_number
| (courier: tracking_numbers.types.Courier, product: tracking_numbers.types.Product, number_regex: Pattern, tracking_url_template: Optional[str], serial_number_parser: tracking_numbers.serial_number.SerialNumberParser, checksum_validator: Optional[tracking_numbers.checksum_validator.ChecksumValidator], additional_validations: List[tracking_numbers.definition.AdditionalValidation]) |
10,352 | tracking_numbers.definition | __init__ | null | def __init__(
self,
courier: Courier,
product: Product,
number_regex: Pattern,
tracking_url_template: Optional[str],
serial_number_parser: SerialNumberParser,
checksum_validator: Optional[ChecksumValidator],
additional_validations: List[AdditionalValidation],
):
self.courier = courier
self.product = product
self.number_regex = number_regex
self.tracking_url_template = tracking_url_template
self.serial_number_parser = serial_number_parser
self.checksum_validator = checksum_validator
self.additional_validations = additional_validations
| (self, courier: tracking_numbers.types.Courier, product: tracking_numbers.types.Product, number_regex: Pattern, tracking_url_template: Optional[str], serial_number_parser: tracking_numbers.serial_number.SerialNumberParser, checksum_validator: Optional[tracking_numbers.checksum_validator.ChecksumValidator], additional_validations: List[tracking_numbers.definition.AdditionalValidation]) |
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