diff --git a/pre_commit_hooks/check_executables_have_shebangs.py b/pre_commit_hooks/check_executables_have_shebangs.py
index c34c7b7..1c50ea0 100644
--- a/pre_commit_hooks/check_executables_have_shebangs.py
+++ b/pre_commit_hooks/check_executables_have_shebangs.py
@@ -2,26 +2,60 @@
 import argparse
 import shlex
 import sys
+from typing import List
 from typing import Optional
 from typing import Sequence
+from typing import Set
 
+from pre_commit_hooks.util import cmd_output
 
-def check_has_shebang(path: str) -> int:
+EXECUTABLE_VALUES = frozenset(('1', '3', '5', '7'))
+
+
+def check_executables(paths: List[str]) -> int:
+    if sys.platform == 'win32':  # pragma: win32 cover
+        return _check_git_filemode(paths)
+    else:  # pragma: win32 no cover
+        retv = 0
+        for path in paths:
+            if not _check_has_shebang(path):
+                _message(path)
+                retv = 1
+
+        return retv
+
+
+def _check_git_filemode(paths: Sequence[str]) -> int:
+    outs = cmd_output('git', 'ls-files', '--stage', '--', *paths)
+    seen: Set[str] = set()
+    for out in outs.splitlines():
+        metadata, path = out.split('\t')
+        tagmode = metadata.split(' ', 1)[0]
+
+        is_executable = any(b in EXECUTABLE_VALUES for b in tagmode[-3:])
+        has_shebang = _check_has_shebang(path)
+        if is_executable and not has_shebang:
+            _message(path)
+            seen.add(path)
+
+    return int(bool(seen))
+
+
+def _check_has_shebang(path: str) -> int:
     with open(path, 'rb') as f:
         first_bytes = f.read(2)
 
-    if first_bytes != b'#!':
-        quoted = shlex.quote(path)
-        print(
-            f'{path}: marked executable but has no (or invalid) shebang!\n'
-            f"  If it isn't supposed to be executable, try: "
-            f'`chmod -x {quoted}`\n'
-            f'  If it is supposed to be executable, double-check its shebang.',
-            file=sys.stderr,
-        )
-        return 1
-    else:
-        return 0
+    return first_bytes == b'#!'
+
+
+def _message(path: str) -> None:
+    print(
+        f'{path}: marked executable but has no (or invalid) shebang!\n'
+        f"  If it isn't supposed to be executable, try: "
+        f'`chmod -x {shlex.quote(path)}`\n'
+        f'  If it is supposed to be executable, double-check its shebang.',
+        file=sys.stderr,
+    )
 
 
 def main(argv: Optional[Sequence[str]] = None) -> int:
@@ -29,12 +63,7 @@ def main(argv: Optional[Sequence[str]] = None) -> int:
     parser.add_argument('filenames', nargs='*')
     args = parser.parse_args(argv)
 
-    retv = 0
-
-    for filename in args.filenames:
-        retv |= check_has_shebang(filename)
-
-    return retv
+    return check_executables(args.filenames)
 
 
 if __name__ == '__main__':
diff --git a/pre_commit_hooks/requirements_txt_fixer.py b/pre_commit_hooks/requirements_txt_fixer.py
index 6190692..78103a1 100644
--- a/pre_commit_hooks/requirements_txt_fixer.py
+++ b/pre_commit_hooks/requirements_txt_fixer.py
@@ -1,4 +1,5 @@
 import argparse
+import re
 from typing import IO
 from typing import List
 from typing import Optional
@@ -10,6 +11,9 @@ FAIL = 1
 
 
 class Requirement:
+    UNTIL_COMPARISON = re.compile(b'={2,3}|!=|~=|>=?|<=?')
+    UNTIL_SEP = re.compile(rb'[^;\s]+')
+
     def __init__(self) -> None:
         self.value: Optional[bytes] = None
         self.comments: List[bytes] = []
@@ -17,11 +21,20 @@ class Requirement:
     @property
     def name(self) -> bytes:
         assert self.value is not None, self.value
+        name = self.value.lower()
         for egg in (b'#egg=', b'&egg='):
             if egg in self.value:
-                return self.value.lower().partition(egg)[-1]
+                return name.partition(egg)[-1]
+
+        m = self.UNTIL_SEP.match(name)
+        assert m is not None
+
+        name = m.group()
+        m = self.UNTIL_COMPARISON.search(name)
+        if not m:
+            return name
 
-        return self.value.lower().partition(b'==')[0]
+        return name[:m.start()]
 
     def __lt__(self, requirement: 'Requirement') -> int:
         # \n means top of file comment, so always return True,

diff --git a/tests/check_executables_have_shebangs_test.py b/tests/check_executables_have_shebangs_test.py
index 15f0c79..3b77612 100644
--- a/tests/check_executables_have_shebangs_test.py
+++ b/tests/check_executables_have_shebangs_test.py
@@ -1,8 +1,19 @@
+import os
+import sys
+
 import pytest
 
+from pre_commit_hooks import check_executables_have_shebangs
 from pre_commit_hooks.check_executables_have_shebangs import main
+from pre_commit_hooks.util import cmd_output
+
+skip_win32 = pytest.mark.skipif(
+    sys.platform == 'win32',
+    reason="non-git checks aren't relevant on windows",
+)
 
 
+@skip_win32  # pragma: win32 no cover
 @pytest.mark.parametrize(
     'content', (
         b'#!/bin/bash\nhello world\n',
@@ -17,6 +28,7 @@ def test_has_shebang(content, tmpdir):
     assert main((path.strpath,)) == 0
 
 
+@skip_win32  # pragma: win32 no cover
 @pytest.mark.parametrize(
     'content', (
         b'',
@@ -24,7 +36,6 @@ def test_has_shebang(content, tmpdir):
         b'\n#!python\n',
         b'python\n',
         '☃'.encode(),
-
     ),
 )
 def test_bad_shebang(content, tmpdir, capsys):
@@ -33,3 +44,67 @@ def test_bad_shebang(content, tmpdir, capsys):
     assert main((path.strpath,)) == 1
     _, stderr = capsys.readouterr()
     assert stderr.startswith(f'{path}: marked executable but')
+
+
+def test_check_git_filemode_passing(tmpdir):
+    with tmpdir.as_cwd():
+        cmd_output('git', 'init', '.')
+
+        f = tmpdir.join('f')
+        f.write('#!/usr/bin/env bash')
+        f_path = str(f)
+        cmd_output('chmod', '+x', f_path)
+        cmd_output('git', 'add', f_path)
+        cmd_output('git', 'update-index', '--chmod=+x', f_path)
+
+        g = tmpdir.join('g').ensure()
+        g_path = str(g)
+        cmd_output('git', 'add', g_path)
+
+        # this is potentially a problem, but not something the script intends
+        # to check for -- we're only making sure that things that are
+        # executable have shebangs
+        h = tmpdir.join('h')
+        h.write('#!/usr/bin/env bash')
+        h_path = str(h)
+        cmd_output('git', 'add', h_path)
+
+        files = (f_path, g_path, h_path)
+        assert check_executables_have_shebangs._check_git_filemode(files) == 0
+
+
+def test_check_git_filemode_failing(tmpdir):
+    with tmpdir.as_cwd():
+        cmd_output('git', 'init', '.')
+
+        f = tmpdir.join('f').ensure()
+        f_path = str(f)
+        cmd_output('chmod', '+x', f_path)
+        cmd_output('git', 'add', f_path)
+        cmd_output('git', 'update-index', '--chmod=+x', f_path)
+
+        files = (f_path,)
+        assert check_executables_have_shebangs._check_git_filemode(files) == 1
+
+
+@pytest.mark.parametrize(
+    ('content', 'mode', 'expected'),
+    (
+        pytest.param('#!python', '+x', 0, id='shebang with executable'),
+        pytest.param('#!python', '-x', 0, id='shebang without executable'),
+        pytest.param('', '+x', 1, id='no shebang with executable'),
+        pytest.param('', '-x', 0, id='no shebang without executable'),
+    ),
+)
+def test_git_executable_shebang(temp_git_dir, content, mode, expected):
+    with temp_git_dir.as_cwd():
+        path = temp_git_dir.join('path')
+        path.write(content)
+        cmd_output('git', 'add', str(path))
+        cmd_output('chmod', mode, str(path))
+        cmd_output('git', 'update-index', f'--chmod={mode}', str(path))
+
+        # simulate how identify choses that something is executable
+        filenames = [path for path in [str(path)] if os.access(path, os.X_OK)]
+
+        assert main(filenames) == expected
diff --git a/tests/requirements_txt_fixer_test.py b/tests/requirements_txt_fixer_test.py
index 17a9a41..fae5a72 100644
--- a/tests/requirements_txt_fixer_test.py
+++ b/tests/requirements_txt_fixer_test.py
@@ -33,9 +33,28 @@ from pre_commit_hooks.requirements_txt_fixer import Requirement
         (b'\nfoo\nbar\n', FAIL, b'bar\n\nfoo\n'),
         (b'\nbar\nfoo\n', PASS, b'\nbar\nfoo\n'),
         (
-            b'pyramid==1\npyramid-foo==2\n',
-            PASS,
-            b'pyramid==1\npyramid-foo==2\n',
+            b'pyramid-foo==1\npyramid>=2\n',
+            FAIL,
+            b'pyramid>=2\npyramid-foo==1\n',
+        ),
+        (
+            b'a==1\n'
+            b'c>=1\n'
+            b'bbbb!=1\n'
+            b'c-a>=1;python_version>="3.6"\n'
+            b'e>=2\n'
+            b'd>2\n'
+            b'g<2\n'
+            b'f<=2\n',
+            FAIL,
+            b'a==1\n'
+            b'bbbb!=1\n'
+            b'c>=1\n'
+            b'c-a>=1;python_version>="3.6"\n'
+            b'd>2\n'
+            b'e>=2\n'
+            b'f<=2\n'
+            b'g<2\n',
         ),
         (b'ocflib\nDjango\nPyMySQL\n', FAIL, b'Django\nocflib\nPyMySQL\n'),
         (

requirements-txt-fixer does not parse all requirements
While working on #330 I noticed that the requirements-txt-fixer hook only parses a small subset of requirement specifiers. Take this example:

    pyramid-foo==1
    pyramid>=2

`pyramid` should sort before `pyramid-foo`, but the hook interprets the `>=2` as part of the name.

According to [PEP 508](https://www.python.org/dev/peps/pep-0508/) there are a couple of things that can be specified after the name (extras, versions, markers) so maybe an approach would be to use a regular expression to extract only the package name?
tests/check_executables_have_shebangs_test.py::test_check_git_filemode_passing tests/check_executables_have_shebangs_test.py::test_check_git_filemode_failing tests/requirements_txt_fixer_test.py::test_integration[pyramid-foo==1\npyramid>=2\n-1-pyramid>=2\npyramid-foo==1\n] tests/requirements_txt_fixer_test.py::test_integration[a==1\nc>=1\nbbbb!=1\nc-a>=1;python_version>="3.6"\ne>=2\nd>2\ng<2\nf<=2\n-1-a==1\nbbbb!=1\nc>=1\nc-a>=1;python_version>="3.6"\nd>2\ne>=2\nf<=2\ng<2\n]
tests/check_executables_have_shebangs_test.py::test_has_shebang[#!/bin/bash\nhello tests/check_executables_have_shebangs_test.py::test_has_shebang[#!/usr/bin/env tests/check_executables_have_shebangs_test.py::test_has_shebang[#!python] tests/check_executables_have_shebangs_test.py::test_has_shebang[#!\xe2\x98\x83] tests/check_executables_have_shebangs_test.py::test_bad_shebang[] tests/check_executables_have_shebangs_test.py::test_bad_shebang[ tests/check_executables_have_shebangs_test.py::test_bad_shebang[\n#!python\n] tests/check_executables_have_shebangs_test.py::test_bad_shebang[python\n] tests/check_executables_have_shebangs_test.py::test_bad_shebang[\xe2\x98\x83] tests/check_executables_have_shebangs_test.py::test_git_executable_shebang[shebang tests/check_executables_have_shebangs_test.py::test_git_executable_shebang[no tests/requirements_txt_fixer_test.py::test_integration[-0-] tests/requirements_txt_fixer_test.py::test_integration[\n-0-\n] tests/requirements_txt_fixer_test.py::test_integration[# tests/requirements_txt_fixer_test.py::test_integration[foo\n# tests/requirements_txt_fixer_test.py::test_integration[foo\nbar\n-1-bar\nfoo\n] tests/requirements_txt_fixer_test.py::test_integration[bar\nfoo\n-0-bar\nfoo\n] tests/requirements_txt_fixer_test.py::test_integration[a\nc\nb\n-1-a\nb\nc\n] tests/requirements_txt_fixer_test.py::test_integration[a\nc\nb-1-a\nb\nc\n] tests/requirements_txt_fixer_test.py::test_integration[a\nb\nc-1-a\nb\nc\n] tests/requirements_txt_fixer_test.py::test_integration[#comment1\nfoo\n#comment2\nbar\n-1-#comment2\nbar\n#comment1\nfoo\n] tests/requirements_txt_fixer_test.py::test_integration[#comment1\nbar\n#comment2\nfoo\n-0-#comment1\nbar\n#comment2\nfoo\n] tests/requirements_txt_fixer_test.py::test_integration[#comment\n\nfoo\nbar\n-1-#comment\n\nbar\nfoo\n] tests/requirements_txt_fixer_test.py::test_integration[#comment\n\nbar\nfoo\n-0-#comment\n\nbar\nfoo\n] tests/requirements_txt_fixer_test.py::test_integration[\nfoo\nbar\n-1-bar\n\nfoo\n] tests/requirements_txt_fixer_test.py::test_integration[\nbar\nfoo\n-0-\nbar\nfoo\n] tests/requirements_txt_fixer_test.py::test_integration[ocflib\nDjango\nPyMySQL\n-1-Django\nocflib\nPyMySQL\n] tests/requirements_txt_fixer_test.py::test_integration[-e tests/requirements_txt_fixer_test.py::test_integration[bar\npkg-resources==0.0.0\nfoo\n-1-bar\nfoo\n] tests/requirements_txt_fixer_test.py::test_integration[foo\npkg-resources==0.0.0\nbar\n-1-bar\nfoo\n] tests/requirements_txt_fixer_test.py::test_integration[git+ssh://git_url@tag#egg=ocflib\nDjango\nijk\n-1-Django\nijk\ngit+ssh://git_url@tag#egg=ocflib\n] tests/requirements_txt_fixer_test.py::test_integration[b==1.0.0\nc=2.0.0 tests/requirements_txt_fixer_test.py::test_integration[a=2.0.0 tests/requirements_txt_fixer_test.py::test_requirement_object