如何高精度地减去浮点数

Question

Basically I have a number say 5.112 I want to subtract it in each iteration by 0.001 like 5.111, 5.110, 5.109, 5.108 etc.

Currently, I am thinking of using the split method to separate the number form decimal point and then subtract the 1st index by 1 and join.

I am just wondering If there is any other better way of doing this.

Answer 1

Floats are imprecise (see Frank's answer and Is floating point math broken? ).

Use decimal instead.

from decimal import Decimal as D

x = D('5.112')
mille = D('.001')
for i in range(5):
    x -= mille
    print(x)

Output:

5.111
5.110
5.109
5.108
5.107

Answer 2

If you were to do

x = 5.112
while True:
    x -= .001
    print(x)

You would quickly see the problems with floating point numbers and accumulating roundoff errors. The easiest method to avoid this is to instead calculate 5.112 - i * .001 , where i is the number of subtractions you've performed so far.

Answer 3

You can use numpy and list comprehension, like so:

import numpy
start = 5.112
[start-val for val in numpy.arange(0, 0.1, 0.001)]

You just need to know how many times you want to perform this operation.