GENERAL: Pow Function Precision Problems

Information in this article applies to:

• C166 All Versions
• C251 All Versions
• Cx51 All Versions

QUESTION

I'm using the pow function in my program and I have serious problems with it. For example, the following code generates incorrect results:

unsigned long v;v = 40 * pow(10,1);  // gives correct result: 400v = 40 * pow(10,3);  // wrong result: 39999     (expected: 40000)v = 40 * pow(10,5);  // wrong result: 4000004   (expected: 40000000)v = 40 * pow(10,7);  // wrong result: 399999872 (expected: 4000000000)

Is this a problem with my code or a problem with the pow function?

ANSWER

There is no problem with the pow function.

The problem is that the pow function accepts and returns floating-point numbers (which have a maximum precision of 7 decimal digits). The exp and log functions are used by pow for its calculations. Therefore, there is an additional loss of precision which yields the results you get.

Another effect is that float to long conversions are rounded-down. This is an ANSI requirement.

RESOLUTION

If you use the C166 or C251 compiler you can solve this issue by using the double arithmetic library.

If you use the C51 compiler or do not wish to use the double-precision arithmetic, you may rewrite your code as shown below to add +0.5 before the long conversion. This will give the results you expect.

  v = (40 * pow(10,1)) + 0.5;  v = (40 * pow(10,3)) + 0.5;  v = (40 * pow(10,5)) + 0.5;  v = (40 * pow(10,7)) + 0.5;

If the arguments to the pow function are integers, you may consider using a series of multiplications instead.

SEE ALSO

• GENERAL: Precision of printf %f Format String
• C166: Double Precision Floats Truncated to Single Precision

Last Reviewed: Thursday, February 25, 2021