Differences in rounded result when calling pow()

Question

OK, I know that there was many question about pow function and casting it\'s result to int, but I couldn\'t find answer to this a bit specific question.

OK, this is

Answer 1

This is caused by a combination of two problems:

• The implementation of pow you are using is not high quality. Floating-point arithmetic is necessarily approximate in many cases, but good implementations take care to ensure that simple cases such as pow(5, 2) return exact results. The pow you are using is returning a result that is less than 25 by an amount greater than 0 but less than or equal to 2^–49. For example, it might be returning 25–2^-50.
• The C implementation you are using sometimes uses a 64-bit floating-point format and sometimes uses an 80-bit floating-point format. As long as the number is kept in the 80-bit format, it retains the complete value that pow returned. If you convert this value to an integer, it produces 24, because the value is less than 25 and conversion to integer truncates; it does not round. When the number is converted to the 64-bit format, it is rounded. Converting between floating-point formats rounds, so the result is rounded to the nearest representable value, 25. After that, conversion to integer produces 25.

The compiler may switch formats whenever it is “convenient” in some sense. For example, there are a limited number of registers with the 80-bit format. When they are full, the compiler may convert some values to the 64-bit format and store them in memory. The compiler may also rearrange expressions or perform parts of them at compile-time instead of run-time, and these can affect the arithmetic performed and the format used.

It is troublesome when a C implementation mixes floating-point formats, because users generally cannot predict or control when the conversions between formats occur. This leads to results that are not easily reproducible and interferes with deriving or controlling numerical properties of software. C implementations can be designed to use a single format throughout and avoid some of these problems, but your C implementation is apparently not so designed.