Naive ways to compute a fractional part f of a float number x rely on the computation of either _, f = divmod(x, 1.0) or f = x % 1.0. This works well for many numbers, but not for all. For instance: x = -math.ulp(0.49999999999999994) (k, f) = divmod(x, 1.0) # k = -1.0 and f = 1.0 The computation is correct and divmod does its job as advertised, under the constraints of inexact computations inherent to the finite representation of numbers. But f fails to be the fractional part of x because mathematicians do not allow a genuine fractional part to take the value 1.0. Thus, the vanilla flavor of either divmod or % is not the right tool when one desires to compute a fractional part. Hand-Made Solution 1 f = (x % 1.0) % 1.0 k = round(x - f) Hand-Made Solution 2 (Patch) (k, f) = divmod(x, 1.0) if 1.0 == f: f -= math.ulp(1.0) Hand-Made Solution 3 (One attempt to be accurate) Remark: math.ulp(1.0) / 2.0 != math.ulp(0.49999999999999994) (k, f) = (0.0, 0.0) if x <= -math.ulp(1.0): (k, f) = divmod(x, 1.0) elif x < -math.ulp(1.0) / 2.0: (k, f) = (-1.0, 1.0 - math.ulp(1.0)) elif x < 0.0: (k, f) = (0.0, 0.0) else: (k, f) = divmod(x, 1.0) Does a native Python function exist that returns a genuine fractional part in the spirit of the hand-made approaches above? Continue reading...
