Improve several stubs. (math, _random, time, etc.)

Some of these are derived from mypy/stubs/.

2.7/math.pyi

@@ -1,90 +1,48 @@
-"""Stub file for the 'math' module."""
-# This is an autogenerated file. It serves as a starting point
-# for a more precise manual annotation of this module.
-# Feel free to edit the source below, but remove this header when you do.
+# Stubs for math
+# See: http://docs.python.org/2/library/math.html
 
-from typing import Any, List, Tuple, Dict, GenericType
+from typing import Tuple, Iterable, Optional
 
-def acos(*args, **kwargs) -> float: ...
+e = ...  # type: float
+pi = ...  # type: float
 
-def acosh(*args, **kwargs) -> float: ...
-
-def asin(*args, **kwargs) -> float: ...
-
-def asinh(*args, **kwargs) -> float: ...
-
-def atan(*args, **kwargs) -> float: ...
-
-def atan2(*args, **kwargs) -> float: ...
-
-def atanh(*args, **kwargs) -> float: ...
-
-def ceil(*args, **kwargs) -> float: ...
-
-def copysign(*args, **kwargs) -> float: ...
-
-def cos(*args, **kwargs) -> float: ...
-
-def cosh(*args, **kwargs) -> float: ...
-
-def degrees(*args, **kwargs) -> float: ...
-
-def erf(*args, **kwargs) -> float: ...
-
-def erfc(*args, **kwargs) -> float: ...
-
-def exp(*args, **kwargs) -> float: ...
-
-def expm1(*args, **kwargs) -> float: ...
-
-def fabs(*args, **kwargs) -> float: ...
-
-def factorial(*args, **kwargs) -> int:
-    raise ValueError()
-
-def floor(*args, **kwargs) -> float: ...
-
-def fmod(*args, **kwargs) -> float: ...
-
-def frexp(*args, **kwargs) -> tuple: ...
-
-def fsum(*args, **kwargs) -> float:
-    raise OverflowError()
-    raise ValueError()
-
-def gamma(*args, **kwargs) -> float: ...
-
-def hypot(*args, **kwargs) -> float: ...
-
-def isinf(*args, **kwargs) -> bool: ...
-
-def isnan(*args, **kwargs) -> bool: ...
-
-def ldexp(a: float, b) -> float:
-    raise TypeError()
-
-def lgamma(*args, **kwargs) -> float: ...
-
-def log(*args, **kwargs) -> float: ...
-
-def log10(*args, **kwargs) -> float: ...
-
-def log1p(*args, **kwargs) -> float: ...
-
-def modf(*args, **kwargs) -> tuple: ...
-
-def pow(*args, **kwargs) -> float: ...
-
-def radians(*args, **kwargs) -> float: ...
-
-def sin(*args, **kwargs) -> float: ...
-
-def sinh(*args, **kwargs) -> float: ...
-
-def sqrt(*args, **kwargs) -> float: ...
-
-def tan(*args, **kwargs) -> float: ...
-
-def tanh(*args, **kwargs) -> float: ...
-
-def trunc(*args, **kwargs) -> Any: ...
+def acos(x: float) -> float: ...
+def acosh(x: float) -> float: ...
+def asin(x: float) -> float: ...
+def asinh(x: float) -> float: ...
+def atan(x: float) -> float: ...
+def atan2(y: float, x: float) -> float: ...
+def atanh(x: float) -> float: ...
+def ceil(x: float) -> int: ...
+def copysign(x: float, y: float) -> float: ...
+def cos(x: float) -> float: ...
+def cosh(x: float) -> float: ...
+def degrees(x: float) -> float: ...
+def erf(x: float) -> float: ...
+def erfc(x: float) -> float: ...
+def exp(x: float) -> float: ...
+def expm1(x: float) -> float: ...
+def fabs(x: float) -> float: ...
+def factorial(x: int) -> int: ...
+def floor(x: float) -> float: ...
+def fmod(x: float, y: float) -> float: ...
+def frexp(x: float) -> Tuple[float, int]: ...
+def fsum(iterable: Iterable) -> float: ...
+def gamma(x: float) -> float: ...
+def hypot(x: float, y: float) -> float: ...
+def isinf(x: float) -> bool: ...
+def isnan(x: float) -> bool: ...
+def ldexp(x: float, i: int) -> float: ...
+def lgamma(x: float) -> float: ...
+def log(x: float, base: Optional[float]) -> float: ...
+def log10(x: float) -> float: ...
+def log1p(x: float) -> float: ...
+def modf(x: float) -> Tuple[float, float]: ...
+def pow(x: float, y: float) -> float: ...
+def radians(x: float) -> float: ...
+def sin(x: float) -> float: ...
+def sinh(x: float) -> float: ...
+def sqrt(x: float) -> float: ...
+def tan(x: float) -> float: ...
+def tanh(x: float) -> float: ...
+def trunc(x: float) -> int: ...