没有 Decimal.quantize 的快速和精确的最近步浮点天花板/地板

Question

The following function is supposed to ceil the given number to the nearest step:

def ceil_step(x, step):
    return math.ceil(x / step) * step

This works well... until it does not:

print(ceil_step(1000.365, 0.01)) # 1000.37
print(ceil_step(1000.369, 0.01)) # 1000.37
print(ceil_step(1000.370, 0.01)) # 1000.37
print(ceil_step(1000.371, 0.01)) # 1000.38

print(ceil_step(10000.365, 0.01)) # 10000.37
print(ceil_step(10000.369, 0.01)) # 10000.37
print(ceil_step(10000.370, 0.01)) # 10000.380000000001
print(ceil_step(10000.371, 0.01)) # 10000.380000000001

A working implementation would be:

def ceil_step(x, step):
    return Decimal(str(x)).quantize(Decimal(str(step)), rounding=ROUND_CEILING)

Unfortunately, I cannot use it because I am writing Numba-accelerated Python code. Therefore, my question: Is there a way to implement the ceil_step (and analogously floor_step ) function such that it only uses basic floating point operations or Numba-supported function calls and produces reliable results?

Answer 1

For now, I have settled with the following function:

def round_step(x, step, method=-1):
    eps = np.finfo(np.float64).eps
    digits = math.ceil(-np.log10(step))
    return round(math.ceil(x * (1 - eps) / step) * step, digits)

The multiplication with (1 - eps) makes sure (hopefully!) that math.ceil does not overshoot. The round is necessary to get rid of stuff like ...0000000001 .