2 ms·
In floating point a = b * (a / b) is not always a true statement. >>> import random >>> random.random() 0.4667867537470992 >>> n = 0 >>> for i in ran
by eesmith 2y ago
In floating point a = b * (a / b) is not always a true statement.
>>> import random
>>> random.random()
0.4667867537470992
>>> n = 0
>>> for i in range(1_000_000):
... a = random.random()
... b = random.random()
... if (a == b * (a / b)):
... n += 1
...
>>> n
886304
For example:
>>> a, b = 0.7959754927336106, 0.7345016612407793
>>> a == b * (a / b)
False
>>> a
0.7959754927336106
>>> b * (a / b)
0.7959754927336105
This is off by one ulp ("unit in the last place").
And of course the division of two finite floating point numbers may be infinite:
>>> a, b = 2, 1.5e-323
>>> a
2
>>> b
1.5e-323
>>> b * (a / b)
inf
>>> a/b
inf
As a minor technical point, x/0 can be -INF if sgn(x) < 0, and NaN if x is a NaN.