在MATLAB中将双精度转换为单精度而不会损失精度

Question

I don't think this is possible, hence I decided to ask here to see as googling around hasn't returned any results that hint that I can do so.

Especially after reading this:

Can doubles be used to represent a 64 bit number without loss of precision

Though my numbers can be held in 32bit as the example below shows.

But is there any way in MATLAB to convert a double precision value to single without loosing information?

eg in MATLAB

> a = 103364148
a =
   103364148
> single(a)
ans =
   103364144

Or maybe there is another way in another language, eg Python?

I'm working with GPUMat where I can only use GPUSingle, so I'm trying to find a way to work with stuff that is double to MATLAB in single to the GPU.

Thanks,

Answer 1

A single can hold integer numbers up to 2^24 (16,777,216) without loss of precision - some bits are required for the sign and the exponent .

In other words, no, there is no way that you can make a number larger than 2^24 fit into a single without error (note that it can hold some larger numbers, as long as they can be written as the product of a number smaller 2^24 and some power of 2).

However, are you sure you need that kind of precision for your calculations? As long as all your integers are less than 2^24, you should be fine.

Answer 2

When you're doing these kinds of experiments, you should turn on

format long

so you can see more decimal values. For example,

>> pi     
ans =
    3.1416
>> format long
>> ans
ans =
   3.141592653589793

Answer 3

如果您唯一关心的是整数，则可以使用int32代替