Steven D'Aprano wrote:
On Tue, 09 Jun 2009 18:28:23 -0700, John Yeung wrote:
The docs are now... sort of correct. For some values of a and b,
uniform() can never return b. Notably, I believe uniform(0, 1) is
equivalent to random(), and will never return 1. However, uniform(1, 2)
CAN return 2, if this is any indication:
a=0.0
b=1.0
a+(b-a)*z < b
True
a=1.0
b=2.0
a+(b-a)*z < b
False
But you haven't shown what value z has, so there's no way of interpreting
that example.
I'd say that uniform(1, 2) should NOT return 2, at least for systems
which round correctly. Given a random z such that:
0 <= z < 1
and two floats a, b such that:
a < b
(b is strictly the larger of the two) then:
0 <= z < 1
Multiply all sides by (b-a):
0 <= (b-a)*z < (b-a)
Add a to all sides:
a <= a + (b-a)*z < b
Hence uniform(a, b) should always return a result less than b, and
greater or equal to a.
However, there is one proviso: floats are not reals. The above holds true
for real numbers, but floats are subject to weird rounding effects. That
means that there may be weird edge cases where Bad Things happen and
things cancel catastrophically or round incorrectly.
A realistic edge case is that a + (b-a) doesn't always give b:
a = -1e90
b = 1.0
a < b
True
a + (b-a) == b
False
a + (b-a)
0.0
However, even in this case, it merely narrows the range of possible
results, it doesn't widen it.
Did you try to find the edge case for z ? For the following, I'm using
Python 2.6.2, running on XP, on a Pentium Core Duo.
I figure the highest theoretical value that random.random() should
return is a number just under 1.0 The easiest way to generate that
value is using the fromhex() method of float.
>>> z = float.fromhex("0x1.fffffffffffffp-1")
>>> z
0.99999999999999989
>>> z<1.0
True
>>> z2 = 1.0 + z
>>> z2
2.0
>>> z2 < 2.0
False
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