--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/env/lib/python3.7/site-packages/boltons/mathutils.py	Sat May 02 07:14:21 2020 -0400
@@ -0,0 +1,229 @@
+"""This module provides useful math functions on top of Python's
+built-in :mod:`math` module.
+"""
+from __future__ import division
+
+from math import ceil as _ceil, floor as _floor
+import bisect
+import binascii
+
+
+def clamp(x, lower=float('-inf'), upper=float('inf')):
+    """Limit a value to a given range.
+
+    Args:
+        x (int or float): Number to be clamped.
+        lower (int or float): Minimum value for x.
+        upper (int or float): Maximum value for x.
+
+    The returned value is guaranteed to be between *lower* and
+    *upper*. Integers, floats, and other comparable types can be
+    mixed.
+
+    >>> clamp(1.0, 0, 5)
+    1.0
+    >>> clamp(-1.0, 0, 5)
+    0
+    >>> clamp(101.0, 0, 5)
+    5
+    >>> clamp(123, upper=5)
+    5
+
+    Similar to `numpy's clip`_ function.
+
+    .. _numpy's clip: http://docs.scipy.org/doc/numpy/reference/generated/numpy.clip.html
+
+    """
+    if upper < lower:
+        raise ValueError('expected upper bound (%r) >= lower bound (%r)'
+                         % (upper, lower))
+    return min(max(x, lower), upper)
+
+
+def ceil(x, options=None):
+    """Return the ceiling of *x*. If *options* is set, return the smallest
+    integer or float from *options* that is greater than or equal to
+    *x*.
+
+    Args:
+        x (int or float): Number to be tested.
+        options (iterable): Optional iterable of arbitrary numbers
+          (ints or floats).
+
+    >>> VALID_CABLE_CSA = [1.5, 2.5, 4, 6, 10, 25, 35, 50]
+    >>> ceil(3.5, options=VALID_CABLE_CSA)
+    4
+    >>> ceil(4, options=VALID_CABLE_CSA)
+    4
+    """
+    if options is None:
+        return _ceil(x)
+    options = sorted(options)
+    i = bisect.bisect_left(options, x)
+    if i == len(options):
+        raise ValueError("no ceil options greater than or equal to: %r" % x)
+    return options[i]
+
+
+def floor(x, options=None):
+    """Return the floor of *x*. If *options* is set, return the largest
+    integer or float from *options* that is less than or equal to
+    *x*.
+
+    Args:
+        x (int or float): Number to be tested.
+        options (iterable): Optional iterable of arbitrary numbers
+          (ints or floats).
+
+    >>> VALID_CABLE_CSA = [1.5, 2.5, 4, 6, 10, 25, 35, 50]
+    >>> floor(3.5, options=VALID_CABLE_CSA)
+    2.5
+    >>> floor(2.5, options=VALID_CABLE_CSA)
+    2.5
+
+    """
+    if options is None:
+        return _floor(x)
+    options = sorted(options)
+
+    i = bisect.bisect_right(options, x)
+    if not i:
+        raise ValueError("no floor options less than or equal to: %r" % x)
+    return options[i - 1]
+
+
+try:
+    _int_types = (int, long)
+    bytes = str
+except NameError:
+    # py3 has no long
+    _int_types = (int,)
+    unicode = str
+
+
+class Bits(object):
+    '''
+    An immutable bit-string or bit-array object.
+    Provides list-like access to bits as bools,
+    as well as bitwise masking and shifting operators.
+    Bits also make it easy to convert between many
+    different useful representations:
+
+    * bytes -- good for serializing raw binary data
+    * int -- good for incrementing (e.g. to try all possible values)
+    * list of bools -- good for iterating over or treating as flags
+    * hex/bin string -- good for human readability
+
+    '''
+    __slots__ = ('val', 'len')
+
+    def __init__(self, val=0, len_=None):
+        if type(val) not in _int_types:
+            if type(val) is list:
+                val = ''.join(['1' if e else '0' for e in val])
+            if type(val) is bytes:
+                val = val.decode('ascii')
+            if type(val) is unicode:
+                if len_ is None:
+                    len_ = len(val)
+                    if val.startswith('0x'):
+                        len_ = (len_ - 2) * 4
+                if val.startswith('0x'):
+                    val = int(val, 16)
+                else:
+                    if val:
+                        val = int(val, 2)
+                    else:
+                        val = 0
+            if type(val) not in _int_types:
+                raise TypeError('initialized with bad type: {0}'.format(type(val).__name__))
+        if val < 0:
+            raise ValueError('Bits cannot represent negative values')
+        if len_ is None:
+            len_ = len('{0:b}'.format(val))
+        if val > 2 ** len_:
+            raise ValueError('value {0} cannot be represented with {1} bits'.format(val, len_))
+        self.val = val  # data is stored internally as integer
+        self.len = len_
+
+    def __getitem__(self, k):
+        if type(k) is slice:
+            return Bits(self.as_bin()[k])
+        if type(k) is int:
+            if k >= self.len:
+                raise IndexError(k)
+            return bool((1 << (self.len - k - 1)) & self.val)
+        raise TypeError(type(k))
+
+    def __len__(self):
+        return self.len
+
+    def __eq__(self, other):
+        if type(self) is not type(other):
+            return NotImplemented
+        return self.val == other.val and self.len == other.len
+
+    def __or__(self, other):
+        if type(self) is not type(other):
+            return NotImplemented
+        return Bits(self.val | other.val, max(self.len, other.len))
+
+    def __and__(self, other):
+        if type(self) is not type(other):
+            return NotImplemented
+        return Bits(self.val & other.val, max(self.len, other.len))
+
+    def __lshift__(self, other):
+        return Bits(self.val << other, self.len + other)
+
+    def __rshift__(self, other):
+        return Bits(self.val >> other, self.len - other)
+
+    def __hash__(self):
+        return hash(self.val)
+
+    def as_list(self):
+        return [c == '1' for c in '{0:b}'.format(self.val)]
+
+    def as_bin(self):
+        return '{{0:0{0}b}}'.format(self.len).format(self.val)
+
+    def as_hex(self):
+        # make template to pad out to number of bytes necessary to represent bits
+        tmpl = '%0{0}X'.format(2 * (self.len // 8 + ((self.len % 8) != 0)))
+        ret = tmpl % self.val
+        return ret
+
+    def as_int(self):
+        return self.val
+
+    def as_bytes(self):
+        return binascii.unhexlify(self.as_hex())
+
+    @classmethod
+    def from_list(cls, list_):
+        return cls(list_)
+
+    @classmethod
+    def from_bin(cls, bin):
+        return cls(bin)
+
+    @classmethod
+    def from_hex(cls, hex):
+        if isinstance(hex, bytes):
+            hex = hex.decode('ascii')
+        if not hex.startswith('0x'):
+            hex = '0x' + hex
+        return cls(hex)
+
+    @classmethod
+    def from_int(cls, int_, len_=None):
+        return cls(int_, len_)
+
+    @classmethod
+    def from_bytes(cls, bytes_):
+        return cls.from_hex(binascii.hexlify(bytes_))
+
+    def __repr__(self):
+        cn = self.__class__.__name__
+        return "{0}('{1}')".format(cn, self.as_bin())