Are all the system's floating points operations the same?

Question

We're making this web app in PHP and when working in the reports we have Excel files to compare our results to make sure our coding is doing the right operations.

Now we're running into some differences due floating point arithmetics. We're doing the same divisions and multiplications and running into slightly different numbers, that add up to a notable difference.

My question is if Excel is delegating it's floating point arithmetic to the CPU and PHP is also relying in the CPU for it's operations. Or does each application implements its own set of math algorithms?

Answer 1

Most of the systems out there implement IEEE 754, which is not terribly great but is good enough for most purposes. If you want better precision then look at something like GMP.

Answer 2

Microsoft Excel uses the native Double type on a particular machine to perform its calculations. I am unsure exactly what PHP is using.

However, it should be noted that even copying a floating point number on x86 based machines may change it's value. Floating points are stored internally in registers that are 80 bits wide. They are stored in memory in blocks 64 bits wide. Therefore, assuming both Excel and PHP are running on x86 based machines, you can get different values even with similar calculations. Particularly at the extremes of the ranges supported by floating point types.

Lastly, there's an obvious difference between the double that Excel is using, and (if your PHP code is using one) a float in PHP code. Ensure you aren't mismatching these as floats have much less precision.

EDIT: Forgot about this too -- there will be differences in output if either PHP or Excel (more likely Excel) is/are employing SSE extensions, as their floating point operations operate on 64 bit, not 80 bit, doubles.

Answer 3

Be very careful when dealing with PHP float calculations. PHP is a flexible scripting language, but its flexibility and loose typing can cause hazards when casting between types or reading in data.

I highly suggest you read the pages on floats in the PHP manual. There is a module called BC Math that is provided for arbitrary precision calculations, and depending on what you are doing, you may want to take advantage of it.

Answer 4

For longer but not arbitrary precision, try qd.